Properties

Label 403.2.c.b.311.5
Level 403
Weight 2
Character 403.311
Analytic conductor 3.218
Analytic rank 0
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(32\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 311.5
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.28

$q$-expansion

\(f(q)\) \(=\) \(q-2.21678i q^{2} -2.59178 q^{3} -2.91410 q^{4} +1.00571i q^{5} +5.74540i q^{6} +1.82096i q^{7} +2.02635i q^{8} +3.71732 q^{9} +O(q^{10})\) \(q-2.21678i q^{2} -2.59178 q^{3} -2.91410 q^{4} +1.00571i q^{5} +5.74540i q^{6} +1.82096i q^{7} +2.02635i q^{8} +3.71732 q^{9} +2.22943 q^{10} +2.73558i q^{11} +7.55270 q^{12} +(2.90778 - 2.13186i) q^{13} +4.03666 q^{14} -2.60657i q^{15} -1.33623 q^{16} +2.66819 q^{17} -8.24047i q^{18} +2.04700i q^{19} -2.93073i q^{20} -4.71953i q^{21} +6.06418 q^{22} +1.36011 q^{23} -5.25186i q^{24} +3.98855 q^{25} +(-4.72587 - 6.44589i) q^{26} -1.85914 q^{27} -5.30645i q^{28} -3.75197 q^{29} -5.77819 q^{30} -1.00000i q^{31} +7.01482i q^{32} -7.09003i q^{33} -5.91478i q^{34} -1.83135 q^{35} -10.8326 q^{36} +5.04610i q^{37} +4.53774 q^{38} +(-7.53631 + 5.52532i) q^{39} -2.03792 q^{40} -3.02730i q^{41} -10.4621 q^{42} +9.12211 q^{43} -7.97176i q^{44} +3.73854i q^{45} -3.01506i q^{46} +7.62683i q^{47} +3.46321 q^{48} +3.68411 q^{49} -8.84173i q^{50} -6.91536 q^{51} +(-8.47354 + 6.21246i) q^{52} +5.26937 q^{53} +4.12130i q^{54} -2.75120 q^{55} -3.68990 q^{56} -5.30537i q^{57} +8.31728i q^{58} +2.66100i q^{59} +7.59581i q^{60} +7.14518 q^{61} -2.21678 q^{62} +6.76909i q^{63} +12.8778 q^{64} +(2.14403 + 2.92437i) q^{65} -15.7170 q^{66} +9.48459i q^{67} -7.77536 q^{68} -3.52511 q^{69} +4.05970i q^{70} +4.99950i q^{71} +7.53260i q^{72} +4.50699i q^{73} +11.1861 q^{74} -10.3374 q^{75} -5.96516i q^{76} -4.98139 q^{77} +(12.2484 + 16.7063i) q^{78} -0.813843 q^{79} -1.34386i q^{80} -6.33348 q^{81} -6.71086 q^{82} -1.18611i q^{83} +13.7532i q^{84} +2.68342i q^{85} -20.2217i q^{86} +9.72428 q^{87} -5.54325 q^{88} -16.2385i q^{89} +8.28751 q^{90} +(3.88204 + 5.29494i) q^{91} -3.96350 q^{92} +2.59178i q^{93} +16.9070 q^{94} -2.05868 q^{95} -18.1809i q^{96} -3.69072i q^{97} -8.16684i q^{98} +10.1690i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.21678i 1.56750i −0.621078 0.783749i \(-0.713305\pi\)
0.621078 0.783749i \(-0.286695\pi\)
\(3\) −2.59178 −1.49636 −0.748182 0.663493i \(-0.769073\pi\)
−0.748182 + 0.663493i \(0.769073\pi\)
\(4\) −2.91410 −1.45705
\(5\) 1.00571i 0.449766i 0.974386 + 0.224883i \(0.0722001\pi\)
−0.974386 + 0.224883i \(0.927800\pi\)
\(6\) 5.74540i 2.34555i
\(7\) 1.82096i 0.688258i 0.938922 + 0.344129i \(0.111826\pi\)
−0.938922 + 0.344129i \(0.888174\pi\)
\(8\) 2.02635i 0.716423i
\(9\) 3.71732 1.23911
\(10\) 2.22943 0.705008
\(11\) 2.73558i 0.824810i 0.911001 + 0.412405i \(0.135311\pi\)
−0.911001 + 0.412405i \(0.864689\pi\)
\(12\) 7.55270 2.18028
\(13\) 2.90778 2.13186i 0.806472 0.591273i
\(14\) 4.03666 1.07884
\(15\) 2.60657i 0.673015i
\(16\) −1.33623 −0.334057
\(17\) 2.66819 0.647131 0.323565 0.946206i \(-0.395118\pi\)
0.323565 + 0.946206i \(0.395118\pi\)
\(18\) 8.24047i 1.94230i
\(19\) 2.04700i 0.469614i 0.972042 + 0.234807i \(0.0754458\pi\)
−0.972042 + 0.234807i \(0.924554\pi\)
\(20\) 2.93073i 0.655332i
\(21\) 4.71953i 1.02988i
\(22\) 6.06418 1.29289
\(23\) 1.36011 0.283603 0.141802 0.989895i \(-0.454711\pi\)
0.141802 + 0.989895i \(0.454711\pi\)
\(24\) 5.25186i 1.07203i
\(25\) 3.98855 0.797710
\(26\) −4.72587 6.44589i −0.926818 1.26414i
\(27\) −1.85914 −0.357792
\(28\) 5.30645i 1.00283i
\(29\) −3.75197 −0.696724 −0.348362 0.937360i \(-0.613262\pi\)
−0.348362 + 0.937360i \(0.613262\pi\)
\(30\) −5.77819 −1.05495
\(31\) 1.00000i 0.179605i
\(32\) 7.01482i 1.24006i
\(33\) 7.09003i 1.23422i
\(34\) 5.91478i 1.01438i
\(35\) −1.83135 −0.309555
\(36\) −10.8326 −1.80544
\(37\) 5.04610i 0.829573i 0.909919 + 0.414787i \(0.136144\pi\)
−0.909919 + 0.414787i \(0.863856\pi\)
\(38\) 4.53774 0.736118
\(39\) −7.53631 + 5.52532i −1.20678 + 0.884759i
\(40\) −2.03792 −0.322223
\(41\) 3.02730i 0.472785i −0.971658 0.236393i \(-0.924035\pi\)
0.971658 0.236393i \(-0.0759652\pi\)
\(42\) −10.4621 −1.61434
\(43\) 9.12211 1.39111 0.695554 0.718474i \(-0.255159\pi\)
0.695554 + 0.718474i \(0.255159\pi\)
\(44\) 7.97176i 1.20179i
\(45\) 3.73854i 0.557309i
\(46\) 3.01506i 0.444547i
\(47\) 7.62683i 1.11249i 0.831019 + 0.556244i \(0.187758\pi\)
−0.831019 + 0.556244i \(0.812242\pi\)
\(48\) 3.46321 0.499871
\(49\) 3.68411 0.526301
\(50\) 8.84173i 1.25041i
\(51\) −6.91536 −0.968343
\(52\) −8.47354 + 6.21246i −1.17507 + 0.861513i
\(53\) 5.26937 0.723804 0.361902 0.932216i \(-0.382127\pi\)
0.361902 + 0.932216i \(0.382127\pi\)
\(54\) 4.12130i 0.560838i
\(55\) −2.75120 −0.370972
\(56\) −3.68990 −0.493084
\(57\) 5.30537i 0.702713i
\(58\) 8.31728i 1.09211i
\(59\) 2.66100i 0.346433i 0.984884 + 0.173216i \(0.0554160\pi\)
−0.984884 + 0.173216i \(0.944584\pi\)
\(60\) 7.59581i 0.980615i
\(61\) 7.14518 0.914847 0.457424 0.889249i \(-0.348772\pi\)
0.457424 + 0.889249i \(0.348772\pi\)
\(62\) −2.21678 −0.281531
\(63\) 6.76909i 0.852825i
\(64\) 12.8778 1.60973
\(65\) 2.14403 + 2.92437i 0.265935 + 0.362724i
\(66\) −15.7170 −1.93463
\(67\) 9.48459i 1.15873i 0.815069 + 0.579364i \(0.196699\pi\)
−0.815069 + 0.579364i \(0.803301\pi\)
\(68\) −7.77536 −0.942901
\(69\) −3.52511 −0.424374
\(70\) 4.05970i 0.485227i
\(71\) 4.99950i 0.593331i 0.954981 + 0.296665i \(0.0958746\pi\)
−0.954981 + 0.296665i \(0.904125\pi\)
\(72\) 7.53260i 0.887725i
\(73\) 4.50699i 0.527503i 0.964591 + 0.263751i \(0.0849598\pi\)
−0.964591 + 0.263751i \(0.915040\pi\)
\(74\) 11.1861 1.30035
\(75\) −10.3374 −1.19367
\(76\) 5.96516i 0.684250i
\(77\) −4.98139 −0.567682
\(78\) 12.2484 + 16.7063i 1.38686 + 1.89162i
\(79\) −0.813843 −0.0915645 −0.0457822 0.998951i \(-0.514578\pi\)
−0.0457822 + 0.998951i \(0.514578\pi\)
\(80\) 1.34386i 0.150248i
\(81\) −6.33348 −0.703720
\(82\) −6.71086 −0.741090
\(83\) 1.18611i 0.130193i −0.997879 0.0650963i \(-0.979265\pi\)
0.997879 0.0650963i \(-0.0207355\pi\)
\(84\) 13.7532i 1.50059i
\(85\) 2.68342i 0.291058i
\(86\) 20.2217i 2.18056i
\(87\) 9.72428 1.04255
\(88\) −5.54325 −0.590913
\(89\) 16.2385i 1.72128i −0.509212 0.860641i \(-0.670063\pi\)
0.509212 0.860641i \(-0.329937\pi\)
\(90\) 8.28751 0.873580
\(91\) 3.88204 + 5.29494i 0.406948 + 0.555061i
\(92\) −3.96350 −0.413223
\(93\) 2.59178i 0.268755i
\(94\) 16.9070 1.74382
\(95\) −2.05868 −0.211216
\(96\) 18.1809i 1.85558i
\(97\) 3.69072i 0.374736i −0.982290 0.187368i \(-0.940004\pi\)
0.982290 0.187368i \(-0.0599957\pi\)
\(98\) 8.16684i 0.824976i
\(99\) 10.1690i 1.02203i
\(100\) −11.6230 −1.16230
\(101\) −9.39142 −0.934481 −0.467241 0.884130i \(-0.654752\pi\)
−0.467241 + 0.884130i \(0.654752\pi\)
\(102\) 15.3298i 1.51788i
\(103\) 7.79135 0.767705 0.383852 0.923394i \(-0.374597\pi\)
0.383852 + 0.923394i \(0.374597\pi\)
\(104\) 4.31990 + 5.89217i 0.423601 + 0.577775i
\(105\) 4.74647 0.463208
\(106\) 11.6810i 1.13456i
\(107\) −18.3141 −1.77049 −0.885245 0.465125i \(-0.846009\pi\)
−0.885245 + 0.465125i \(0.846009\pi\)
\(108\) 5.41772 0.521320
\(109\) 19.3010i 1.84870i 0.381542 + 0.924352i \(0.375393\pi\)
−0.381542 + 0.924352i \(0.624607\pi\)
\(110\) 6.09879i 0.581497i
\(111\) 13.0784i 1.24134i
\(112\) 2.43322i 0.229918i
\(113\) 1.71217 0.161067 0.0805335 0.996752i \(-0.474338\pi\)
0.0805335 + 0.996752i \(0.474338\pi\)
\(114\) −11.7608 −1.10150
\(115\) 1.36788i 0.127555i
\(116\) 10.9336 1.01516
\(117\) 10.8091 7.92482i 0.999305 0.732650i
\(118\) 5.89884 0.543032
\(119\) 4.85866i 0.445393i
\(120\) 5.28183 0.482163
\(121\) 3.51658 0.319689
\(122\) 15.8393i 1.43402i
\(123\) 7.84610i 0.707459i
\(124\) 2.91410i 0.261694i
\(125\) 9.03986i 0.808550i
\(126\) 15.0056 1.33680
\(127\) 16.9909 1.50770 0.753849 0.657048i \(-0.228195\pi\)
0.753849 + 0.657048i \(0.228195\pi\)
\(128\) 14.5176i 1.28319i
\(129\) −23.6425 −2.08161
\(130\) 6.48268 4.75284i 0.568569 0.416852i
\(131\) −12.4908 −1.09133 −0.545663 0.838005i \(-0.683722\pi\)
−0.545663 + 0.838005i \(0.683722\pi\)
\(132\) 20.6610i 1.79831i
\(133\) −3.72750 −0.323215
\(134\) 21.0252 1.81630
\(135\) 1.86975i 0.160923i
\(136\) 5.40669i 0.463619i
\(137\) 3.57641i 0.305553i 0.988261 + 0.152777i \(0.0488215\pi\)
−0.988261 + 0.152777i \(0.951179\pi\)
\(138\) 7.81438i 0.665205i
\(139\) −17.1808 −1.45725 −0.728627 0.684911i \(-0.759841\pi\)
−0.728627 + 0.684911i \(0.759841\pi\)
\(140\) 5.33675 0.451037
\(141\) 19.7671i 1.66469i
\(142\) 11.0828 0.930045
\(143\) 5.83189 + 7.95446i 0.487687 + 0.665186i
\(144\) −4.96719 −0.413933
\(145\) 3.77339i 0.313363i
\(146\) 9.99098 0.826859
\(147\) −9.54839 −0.787538
\(148\) 14.7048i 1.20873i
\(149\) 9.50590i 0.778754i −0.921078 0.389377i \(-0.872690\pi\)
0.921078 0.389377i \(-0.127310\pi\)
\(150\) 22.9158i 1.87107i
\(151\) 0.701427i 0.0570814i −0.999593 0.0285407i \(-0.990914\pi\)
0.999593 0.0285407i \(-0.00908601\pi\)
\(152\) −4.14794 −0.336442
\(153\) 9.91851 0.801864
\(154\) 11.0426i 0.889840i
\(155\) 1.00571 0.0807804
\(156\) 21.9616 16.1013i 1.75833 1.28914i
\(157\) −19.7650 −1.57742 −0.788710 0.614765i \(-0.789251\pi\)
−0.788710 + 0.614765i \(0.789251\pi\)
\(158\) 1.80411i 0.143527i
\(159\) −13.6571 −1.08307
\(160\) −7.05487 −0.557736
\(161\) 2.47671i 0.195192i
\(162\) 14.0399i 1.10308i
\(163\) 12.0409i 0.943115i 0.881835 + 0.471557i \(0.156308\pi\)
−0.881835 + 0.471557i \(0.843692\pi\)
\(164\) 8.82186i 0.688872i
\(165\) 7.13050 0.555109
\(166\) −2.62934 −0.204077
\(167\) 20.4561i 1.58294i −0.611205 0.791472i \(-0.709315\pi\)
0.611205 0.791472i \(-0.290685\pi\)
\(168\) 9.56342 0.737834
\(169\) 3.91031 12.3980i 0.300793 0.953689i
\(170\) 5.94854 0.456232
\(171\) 7.60935i 0.581902i
\(172\) −26.5827 −2.02691
\(173\) 6.97691 0.530445 0.265222 0.964187i \(-0.414555\pi\)
0.265222 + 0.964187i \(0.414555\pi\)
\(174\) 21.5566i 1.63420i
\(175\) 7.26299i 0.549030i
\(176\) 3.65537i 0.275534i
\(177\) 6.89672i 0.518389i
\(178\) −35.9972 −2.69811
\(179\) 8.92044 0.666745 0.333372 0.942795i \(-0.391813\pi\)
0.333372 + 0.942795i \(0.391813\pi\)
\(180\) 10.8945i 0.812026i
\(181\) −10.7089 −0.795988 −0.397994 0.917388i \(-0.630293\pi\)
−0.397994 + 0.917388i \(0.630293\pi\)
\(182\) 11.7377 8.60561i 0.870056 0.637890i
\(183\) −18.5187 −1.36894
\(184\) 2.75606i 0.203180i
\(185\) −5.07490 −0.373114
\(186\) 5.74540 0.421273
\(187\) 7.29905i 0.533760i
\(188\) 22.2253i 1.62095i
\(189\) 3.38542i 0.246253i
\(190\) 4.56364i 0.331081i
\(191\) −18.3129 −1.32507 −0.662537 0.749029i \(-0.730520\pi\)
−0.662537 + 0.749029i \(0.730520\pi\)
\(192\) −33.3765 −2.40874
\(193\) 5.31567i 0.382630i −0.981529 0.191315i \(-0.938725\pi\)
0.981529 0.191315i \(-0.0612753\pi\)
\(194\) −8.18151 −0.587398
\(195\) −5.55686 7.57933i −0.397935 0.542767i
\(196\) −10.7358 −0.766846
\(197\) 6.99284i 0.498219i 0.968475 + 0.249109i \(0.0801379\pi\)
−0.968475 + 0.249109i \(0.919862\pi\)
\(198\) 22.5425 1.60203
\(199\) −4.55657 −0.323007 −0.161503 0.986872i \(-0.551634\pi\)
−0.161503 + 0.986872i \(0.551634\pi\)
\(200\) 8.08220i 0.571498i
\(201\) 24.5820i 1.73388i
\(202\) 20.8187i 1.46480i
\(203\) 6.83219i 0.479526i
\(204\) 20.1520 1.41092
\(205\) 3.04458 0.212643
\(206\) 17.2717i 1.20338i
\(207\) 5.05597 0.351415
\(208\) −3.88545 + 2.84866i −0.269408 + 0.197519i
\(209\) −5.59974 −0.387342
\(210\) 10.5219i 0.726077i
\(211\) 17.7764 1.22378 0.611889 0.790944i \(-0.290410\pi\)
0.611889 + 0.790944i \(0.290410\pi\)
\(212\) −15.3555 −1.05462
\(213\) 12.9576i 0.887839i
\(214\) 40.5983i 2.77524i
\(215\) 9.17418i 0.625674i
\(216\) 3.76727i 0.256330i
\(217\) 1.82096 0.123615
\(218\) 42.7861 2.89784
\(219\) 11.6811i 0.789336i
\(220\) 8.01726 0.540524
\(221\) 7.75849 5.68821i 0.521893 0.382631i
\(222\) −28.9918 −1.94580
\(223\) 28.1562i 1.88548i −0.333532 0.942739i \(-0.608240\pi\)
0.333532 0.942739i \(-0.391760\pi\)
\(224\) −12.7737 −0.853479
\(225\) 14.8267 0.988448
\(226\) 3.79549i 0.252472i
\(227\) 10.2989i 0.683561i −0.939780 0.341781i \(-0.888970\pi\)
0.939780 0.341781i \(-0.111030\pi\)
\(228\) 15.4604i 1.02389i
\(229\) 11.7672i 0.777601i −0.921322 0.388800i \(-0.872890\pi\)
0.921322 0.388800i \(-0.127110\pi\)
\(230\) 3.03228 0.199942
\(231\) 12.9107 0.849459
\(232\) 7.60281i 0.499149i
\(233\) 15.0623 0.986765 0.493382 0.869813i \(-0.335760\pi\)
0.493382 + 0.869813i \(0.335760\pi\)
\(234\) −17.5676 23.9614i −1.14843 1.56641i
\(235\) −7.67036 −0.500359
\(236\) 7.75441i 0.504769i
\(237\) 2.10930 0.137014
\(238\) 10.7706 0.698152
\(239\) 4.17457i 0.270030i 0.990844 + 0.135015i \(0.0431083\pi\)
−0.990844 + 0.135015i \(0.956892\pi\)
\(240\) 3.48298i 0.224825i
\(241\) 17.7274i 1.14192i 0.820978 + 0.570960i \(0.193429\pi\)
−0.820978 + 0.570960i \(0.806571\pi\)
\(242\) 7.79548i 0.501112i
\(243\) 21.9924 1.41081
\(244\) −20.8218 −1.33298
\(245\) 3.70514i 0.236713i
\(246\) 17.3931 1.10894
\(247\) 4.36392 + 5.95221i 0.277670 + 0.378730i
\(248\) 2.02635 0.128673
\(249\) 3.07414i 0.194816i
\(250\) 20.0393 1.26740
\(251\) 1.71621 0.108326 0.0541632 0.998532i \(-0.482751\pi\)
0.0541632 + 0.998532i \(0.482751\pi\)
\(252\) 19.7258i 1.24261i
\(253\) 3.72070i 0.233918i
\(254\) 37.6650i 2.36331i
\(255\) 6.95483i 0.435528i
\(256\) −6.42669 −0.401668
\(257\) 17.8955 1.11629 0.558147 0.829742i \(-0.311513\pi\)
0.558147 + 0.829742i \(0.311513\pi\)
\(258\) 52.4101i 3.26291i
\(259\) −9.18874 −0.570961
\(260\) −6.24792 8.52191i −0.387480 0.528507i
\(261\) −13.9473 −0.863315
\(262\) 27.6893i 1.71065i
\(263\) −0.133456 −0.00822927 −0.00411463 0.999992i \(-0.501310\pi\)
−0.00411463 + 0.999992i \(0.501310\pi\)
\(264\) 14.3669 0.884221
\(265\) 5.29945i 0.325543i
\(266\) 8.26304i 0.506639i
\(267\) 42.0867i 2.57567i
\(268\) 27.6390i 1.68832i
\(269\) 24.3960 1.48745 0.743725 0.668485i \(-0.233057\pi\)
0.743725 + 0.668485i \(0.233057\pi\)
\(270\) −4.14482 −0.252246
\(271\) 3.25829i 0.197927i 0.995091 + 0.0989635i \(0.0315527\pi\)
−0.995091 + 0.0989635i \(0.968447\pi\)
\(272\) −3.56531 −0.216179
\(273\) −10.0614 13.7233i −0.608943 0.830573i
\(274\) 7.92809 0.478954
\(275\) 10.9110i 0.657959i
\(276\) 10.2725 0.618333
\(277\) 10.6944 0.642563 0.321282 0.946984i \(-0.395886\pi\)
0.321282 + 0.946984i \(0.395886\pi\)
\(278\) 38.0859i 2.28424i
\(279\) 3.71732i 0.222550i
\(280\) 3.71097i 0.221773i
\(281\) 0.279634i 0.0166816i 0.999965 + 0.00834078i \(0.00265498\pi\)
−0.999965 + 0.00834078i \(0.997345\pi\)
\(282\) −43.8191 −2.60939
\(283\) 8.05685 0.478930 0.239465 0.970905i \(-0.423028\pi\)
0.239465 + 0.970905i \(0.423028\pi\)
\(284\) 14.5690i 0.864512i
\(285\) 5.33565 0.316057
\(286\) 17.6333 12.9280i 1.04268 0.764449i
\(287\) 5.51260 0.325398
\(288\) 26.0764i 1.53656i
\(289\) −9.88077 −0.581222
\(290\) −8.36476 −0.491196
\(291\) 9.56554i 0.560742i
\(292\) 13.1338i 0.768597i
\(293\) 23.0395i 1.34598i −0.739650 0.672992i \(-0.765009\pi\)
0.739650 0.672992i \(-0.234991\pi\)
\(294\) 21.1667i 1.23446i
\(295\) −2.67619 −0.155814
\(296\) −10.2252 −0.594326
\(297\) 5.08583i 0.295110i
\(298\) −21.0725 −1.22070
\(299\) 3.95490 2.89957i 0.228718 0.167687i
\(300\) 30.1243 1.73923
\(301\) 16.6110i 0.957441i
\(302\) −1.55491 −0.0894749
\(303\) 24.3405 1.39832
\(304\) 2.73526i 0.156878i
\(305\) 7.18597i 0.411468i
\(306\) 21.9871i 1.25692i
\(307\) 31.6411i 1.80585i 0.429796 + 0.902926i \(0.358585\pi\)
−0.429796 + 0.902926i \(0.641415\pi\)
\(308\) 14.5162 0.827140
\(309\) −20.1935 −1.14877
\(310\) 2.22943i 0.126623i
\(311\) −30.7261 −1.74232 −0.871158 0.491003i \(-0.836630\pi\)
−0.871158 + 0.491003i \(0.836630\pi\)
\(312\) −11.1962 15.2712i −0.633862 0.864562i
\(313\) 33.4766 1.89221 0.946105 0.323860i \(-0.104981\pi\)
0.946105 + 0.323860i \(0.104981\pi\)
\(314\) 43.8146i 2.47260i
\(315\) −6.80773 −0.383572
\(316\) 2.37162 0.133414
\(317\) 6.42234i 0.360714i 0.983601 + 0.180357i \(0.0577254\pi\)
−0.983601 + 0.180357i \(0.942275\pi\)
\(318\) 30.2746i 1.69772i
\(319\) 10.2638i 0.574664i
\(320\) 12.9513i 0.724002i
\(321\) 47.4661 2.64930
\(322\) 5.49031 0.305963
\(323\) 5.46178i 0.303901i
\(324\) 18.4564 1.02536
\(325\) 11.5978 8.50305i 0.643331 0.471664i
\(326\) 26.6920 1.47833
\(327\) 50.0240i 2.76633i
\(328\) 6.13438 0.338714
\(329\) −13.8881 −0.765678
\(330\) 15.8067i 0.870132i
\(331\) 33.3045i 1.83058i −0.402792 0.915291i \(-0.631960\pi\)
0.402792 0.915291i \(-0.368040\pi\)
\(332\) 3.45644i 0.189697i
\(333\) 18.7580i 1.02793i
\(334\) −45.3467 −2.48126
\(335\) −9.53874 −0.521157
\(336\) 6.30637i 0.344040i
\(337\) −0.475146 −0.0258829 −0.0129414 0.999916i \(-0.504120\pi\)
−0.0129414 + 0.999916i \(0.504120\pi\)
\(338\) −27.4835 8.66829i −1.49491 0.471493i
\(339\) −4.43755 −0.241015
\(340\) 7.81975i 0.424085i
\(341\) 2.73558 0.148140
\(342\) 16.8682 0.912130
\(343\) 19.4553i 1.05049i
\(344\) 18.4846i 0.996622i
\(345\) 3.54523i 0.190869i
\(346\) 15.4663i 0.831471i
\(347\) 12.3110 0.660887 0.330443 0.943826i \(-0.392802\pi\)
0.330443 + 0.943826i \(0.392802\pi\)
\(348\) −28.3375 −1.51905
\(349\) 34.9537i 1.87103i −0.353289 0.935514i \(-0.614937\pi\)
0.353289 0.935514i \(-0.385063\pi\)
\(350\) 16.1004 0.860604
\(351\) −5.40596 + 3.96343i −0.288549 + 0.211552i
\(352\) −19.1896 −1.02281
\(353\) 10.5811i 0.563177i 0.959535 + 0.281589i \(0.0908614\pi\)
−0.959535 + 0.281589i \(0.909139\pi\)
\(354\) −15.2885 −0.812574
\(355\) −5.02803 −0.266860
\(356\) 47.3207i 2.50799i
\(357\) 12.5926i 0.666470i
\(358\) 19.7746i 1.04512i
\(359\) 16.8943i 0.891646i 0.895121 + 0.445823i \(0.147089\pi\)
−0.895121 + 0.445823i \(0.852911\pi\)
\(360\) −7.57560 −0.399269
\(361\) 14.8098 0.779463
\(362\) 23.7393i 1.24771i
\(363\) −9.11421 −0.478372
\(364\) −11.3126 15.4300i −0.592943 0.808751i
\(365\) −4.53271 −0.237253
\(366\) 41.0519i 2.14582i
\(367\) −10.0627 −0.525270 −0.262635 0.964895i \(-0.584592\pi\)
−0.262635 + 0.964895i \(0.584592\pi\)
\(368\) −1.81742 −0.0947396
\(369\) 11.2535i 0.585832i
\(370\) 11.2499i 0.584856i
\(371\) 9.59531i 0.498164i
\(372\) 7.55270i 0.391589i
\(373\) −21.3532 −1.10563 −0.552814 0.833305i \(-0.686446\pi\)
−0.552814 + 0.833305i \(0.686446\pi\)
\(374\) 16.1804 0.836667
\(375\) 23.4293i 1.20989i
\(376\) −15.4546 −0.797012
\(377\) −10.9099 + 7.99869i −0.561888 + 0.411954i
\(378\) −7.50472 −0.386001
\(379\) 14.8171i 0.761101i −0.924760 0.380551i \(-0.875735\pi\)
0.924760 0.380551i \(-0.124265\pi\)
\(380\) 5.99921 0.307753
\(381\) −44.0366 −2.25607
\(382\) 40.5956i 2.07705i
\(383\) 36.9845i 1.88982i −0.327333 0.944909i \(-0.606150\pi\)
0.327333 0.944909i \(-0.393850\pi\)
\(384\) 37.6265i 1.92012i
\(385\) 5.00982i 0.255324i
\(386\) −11.7837 −0.599772
\(387\) 33.9098 1.72373
\(388\) 10.7551i 0.546009i
\(389\) −4.01436 −0.203536 −0.101768 0.994808i \(-0.532450\pi\)
−0.101768 + 0.994808i \(0.532450\pi\)
\(390\) −16.8017 + 12.3183i −0.850786 + 0.623762i
\(391\) 3.62904 0.183528
\(392\) 7.46529i 0.377054i
\(393\) 32.3734 1.63302
\(394\) 15.5016 0.780957
\(395\) 0.818488i 0.0411826i
\(396\) 29.6336i 1.48914i
\(397\) 19.4208i 0.974702i 0.873206 + 0.487351i \(0.162037\pi\)
−0.873206 + 0.487351i \(0.837963\pi\)
\(398\) 10.1009i 0.506312i
\(399\) 9.66086 0.483648
\(400\) −5.32962 −0.266481
\(401\) 3.27194i 0.163393i −0.996657 0.0816965i \(-0.973966\pi\)
0.996657 0.0816965i \(-0.0260338\pi\)
\(402\) −54.4928 −2.71785
\(403\) −2.13186 2.90778i −0.106196 0.144847i
\(404\) 27.3675 1.36159
\(405\) 6.36964i 0.316510i
\(406\) −15.1454 −0.751655
\(407\) −13.8040 −0.684240
\(408\) 14.0129i 0.693744i
\(409\) 13.7956i 0.682149i 0.940036 + 0.341075i \(0.110791\pi\)
−0.940036 + 0.341075i \(0.889209\pi\)
\(410\) 6.74916i 0.333317i
\(411\) 9.26926i 0.457219i
\(412\) −22.7048 −1.11858
\(413\) −4.84557 −0.238435
\(414\) 11.2080i 0.550841i
\(415\) 1.19288 0.0585562
\(416\) 14.9546 + 20.3975i 0.733212 + 1.00007i
\(417\) 44.5287 2.18058
\(418\) 12.4134i 0.607157i
\(419\) −28.8551 −1.40967 −0.704833 0.709374i \(-0.748978\pi\)
−0.704833 + 0.709374i \(0.748978\pi\)
\(420\) −13.8317 −0.674916
\(421\) 14.0841i 0.686417i 0.939259 + 0.343209i \(0.111514\pi\)
−0.939259 + 0.343209i \(0.888486\pi\)
\(422\) 39.4063i 1.91827i
\(423\) 28.3514i 1.37849i
\(424\) 10.6776i 0.518550i
\(425\) 10.6422 0.516223
\(426\) −28.7241 −1.39169
\(427\) 13.0111i 0.629651i
\(428\) 53.3691 2.57969
\(429\) −15.1150 20.6162i −0.729758 0.995360i
\(430\) 20.3371 0.980742
\(431\) 21.1516i 1.01884i 0.860519 + 0.509419i \(0.170139\pi\)
−0.860519 + 0.509419i \(0.829861\pi\)
\(432\) 2.48424 0.119523
\(433\) −32.6610 −1.56959 −0.784795 0.619756i \(-0.787232\pi\)
−0.784795 + 0.619756i \(0.787232\pi\)
\(434\) 4.03666i 0.193766i
\(435\) 9.77979i 0.468905i
\(436\) 56.2451i 2.69365i
\(437\) 2.78415i 0.133184i
\(438\) −25.8944 −1.23728
\(439\) 28.3889 1.35493 0.677463 0.735557i \(-0.263079\pi\)
0.677463 + 0.735557i \(0.263079\pi\)
\(440\) 5.57490i 0.265773i
\(441\) 13.6950 0.652143
\(442\) −12.6095 17.1988i −0.599773 0.818065i
\(443\) 34.5066 1.63946 0.819729 0.572751i \(-0.194124\pi\)
0.819729 + 0.572751i \(0.194124\pi\)
\(444\) 38.1117i 1.80870i
\(445\) 16.3312 0.774175
\(446\) −62.4160 −2.95548
\(447\) 24.6372i 1.16530i
\(448\) 23.4500i 1.10791i
\(449\) 8.05040i 0.379922i −0.981792 0.189961i \(-0.939164\pi\)
0.981792 0.189961i \(-0.0608362\pi\)
\(450\) 32.8675i 1.54939i
\(451\) 8.28144 0.389958
\(452\) −4.98942 −0.234682
\(453\) 1.81795i 0.0854145i
\(454\) −22.8303 −1.07148
\(455\) −5.32517 + 3.90420i −0.249648 + 0.183032i
\(456\) 10.7505 0.503440
\(457\) 1.80609i 0.0844853i −0.999107 0.0422427i \(-0.986550\pi\)
0.999107 0.0422427i \(-0.0134503\pi\)
\(458\) −26.0853 −1.21889
\(459\) −4.96053 −0.231538
\(460\) 3.98613i 0.185854i
\(461\) 31.7743i 1.47988i 0.672675 + 0.739938i \(0.265145\pi\)
−0.672675 + 0.739938i \(0.734855\pi\)
\(462\) 28.6200i 1.33152i
\(463\) 38.5673i 1.79237i −0.443677 0.896187i \(-0.646326\pi\)
0.443677 0.896187i \(-0.353674\pi\)
\(464\) 5.01349 0.232745
\(465\) −2.60657 −0.120877
\(466\) 33.3898i 1.54675i
\(467\) −32.7853 −1.51712 −0.758561 0.651602i \(-0.774097\pi\)
−0.758561 + 0.651602i \(0.774097\pi\)
\(468\) −31.4989 + 23.0937i −1.45604 + 1.06751i
\(469\) −17.2711 −0.797504
\(470\) 17.0035i 0.784312i
\(471\) 51.2266 2.36040
\(472\) −5.39212 −0.248192
\(473\) 24.9543i 1.14740i
\(474\) 4.67585i 0.214769i
\(475\) 8.16456i 0.374616i
\(476\) 14.1586i 0.648959i
\(477\) 19.5880 0.896871
\(478\) 9.25409 0.423272
\(479\) 31.2073i 1.42590i −0.701217 0.712948i \(-0.747359\pi\)
0.701217 0.712948i \(-0.252641\pi\)
\(480\) 18.2847 0.834577
\(481\) 10.7576 + 14.6729i 0.490504 + 0.669028i
\(482\) 39.2976 1.78996
\(483\) 6.41908i 0.292078i
\(484\) −10.2477 −0.465803
\(485\) 3.71179 0.168544
\(486\) 48.7523i 2.21145i
\(487\) 0.361759i 0.0163929i 0.999966 + 0.00819643i \(0.00260903\pi\)
−0.999966 + 0.00819643i \(0.997391\pi\)
\(488\) 14.4787i 0.655418i
\(489\) 31.2073i 1.41124i
\(490\) 8.21346 0.371046
\(491\) −40.0199 −1.80607 −0.903036 0.429565i \(-0.858667\pi\)
−0.903036 + 0.429565i \(0.858667\pi\)
\(492\) 22.8643i 1.03080i
\(493\) −10.0110 −0.450871
\(494\) 13.1947 9.67384i 0.593659 0.435247i
\(495\) −10.2271 −0.459674
\(496\) 1.33623i 0.0599984i
\(497\) −9.10388 −0.408365
\(498\) 6.81468 0.305373
\(499\) 25.3343i 1.13412i −0.823677 0.567060i \(-0.808081\pi\)
0.823677 0.567060i \(-0.191919\pi\)
\(500\) 26.3430i 1.17810i
\(501\) 53.0178i 2.36866i
\(502\) 3.80446i 0.169801i
\(503\) −26.7858 −1.19432 −0.597159 0.802123i \(-0.703704\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(504\) −13.7166 −0.610984
\(505\) 9.44503i 0.420298i
\(506\) 8.24796 0.366667
\(507\) −10.1347 + 32.1328i −0.450097 + 1.42707i
\(508\) −49.5131 −2.19679
\(509\) 37.9869i 1.68374i 0.539680 + 0.841870i \(0.318545\pi\)
−0.539680 + 0.841870i \(0.681455\pi\)
\(510\) −15.4173 −0.682690
\(511\) −8.20704 −0.363058
\(512\) 14.7887i 0.653576i
\(513\) 3.80566i 0.168024i
\(514\) 39.6704i 1.74979i
\(515\) 7.83583i 0.345288i
\(516\) 68.8965 3.03300
\(517\) −20.8638 −0.917590
\(518\) 20.3694i 0.894979i
\(519\) −18.0826 −0.793739
\(520\) −5.92581 + 4.34456i −0.259864 + 0.190522i
\(521\) −8.49756 −0.372285 −0.186143 0.982523i \(-0.559599\pi\)
−0.186143 + 0.982523i \(0.559599\pi\)
\(522\) 30.9180i 1.35324i
\(523\) 16.0250 0.700722 0.350361 0.936615i \(-0.386059\pi\)
0.350361 + 0.936615i \(0.386059\pi\)
\(524\) 36.3994 1.59012
\(525\) 18.8241i 0.821550i
\(526\) 0.295843i 0.0128994i
\(527\) 2.66819i 0.116228i
\(528\) 9.47390i 0.412299i
\(529\) −21.1501 −0.919569
\(530\) 11.7477 0.510288
\(531\) 9.89179i 0.429267i
\(532\) 10.8623 0.470941
\(533\) −6.45380 8.80272i −0.279545 0.381288i
\(534\) 93.2969 4.03735
\(535\) 18.4186i 0.796307i
\(536\) −19.2191 −0.830139
\(537\) −23.1198 −0.997694
\(538\) 54.0805i 2.33158i
\(539\) 10.0782i 0.434098i
\(540\) 5.44864i 0.234472i
\(541\) 26.8172i 1.15296i 0.817111 + 0.576481i \(0.195575\pi\)
−0.817111 + 0.576481i \(0.804425\pi\)
\(542\) 7.22290 0.310250
\(543\) 27.7552 1.19109
\(544\) 18.7169i 0.802479i
\(545\) −19.4112 −0.831485
\(546\) −30.4215 + 22.3038i −1.30192 + 0.954516i
\(547\) 0.552928 0.0236415 0.0118207 0.999930i \(-0.496237\pi\)
0.0118207 + 0.999930i \(0.496237\pi\)
\(548\) 10.4220i 0.445206i
\(549\) 26.5609 1.13359
\(550\) 24.1873 1.03135
\(551\) 7.68028i 0.327191i
\(552\) 7.14311i 0.304031i
\(553\) 1.48197i 0.0630200i
\(554\) 23.7071i 1.00722i
\(555\) 13.1530 0.558315
\(556\) 50.0664 2.12329
\(557\) 15.0526i 0.637797i 0.947789 + 0.318899i \(0.103313\pi\)
−0.947789 + 0.318899i \(0.896687\pi\)
\(558\) −8.24047 −0.348847
\(559\) 26.5250 19.4471i 1.12189 0.822524i
\(560\) 2.44711 0.103409
\(561\) 18.9175i 0.798699i
\(562\) 0.619886 0.0261483
\(563\) −1.95269 −0.0822963 −0.0411481 0.999153i \(-0.513102\pi\)
−0.0411481 + 0.999153i \(0.513102\pi\)
\(564\) 57.6031i 2.42553i
\(565\) 1.72194i 0.0724425i
\(566\) 17.8602i 0.750721i
\(567\) 11.5330i 0.484341i
\(568\) −10.1307 −0.425076
\(569\) −10.6879 −0.448062 −0.224031 0.974582i \(-0.571922\pi\)
−0.224031 + 0.974582i \(0.571922\pi\)
\(570\) 11.8280i 0.495418i
\(571\) −11.1927 −0.468401 −0.234201 0.972188i \(-0.575247\pi\)
−0.234201 + 0.972188i \(0.575247\pi\)
\(572\) −16.9947 23.1801i −0.710584 0.969208i
\(573\) 47.4630 1.98279
\(574\) 12.2202i 0.510061i
\(575\) 5.42488 0.226233
\(576\) 47.8711 1.99463
\(577\) 38.1339i 1.58753i −0.608222 0.793767i \(-0.708117\pi\)
0.608222 0.793767i \(-0.291883\pi\)
\(578\) 21.9035i 0.911064i
\(579\) 13.7770i 0.572554i
\(580\) 10.9960i 0.456585i
\(581\) 2.15986 0.0896061
\(582\) 21.2047 0.878962
\(583\) 14.4148i 0.597000i
\(584\) −9.13273 −0.377915
\(585\) 7.97006 + 10.8708i 0.329521 + 0.449454i
\(586\) −51.0735 −2.10983
\(587\) 5.26098i 0.217144i 0.994089 + 0.108572i \(0.0346278\pi\)
−0.994089 + 0.108572i \(0.965372\pi\)
\(588\) 27.8250 1.14748
\(589\) 2.04700 0.0843451
\(590\) 5.93251i 0.244238i
\(591\) 18.1239i 0.745517i
\(592\) 6.74274i 0.277125i
\(593\) 25.9148i 1.06419i −0.846684 0.532096i \(-0.821405\pi\)
0.846684 0.532096i \(-0.178595\pi\)
\(594\) −11.2742 −0.462584
\(595\) −4.88640 −0.200323
\(596\) 27.7011i 1.13468i
\(597\) 11.8096 0.483336
\(598\) −6.42771 8.76713i −0.262848 0.358515i
\(599\) 41.6832 1.70313 0.851564 0.524250i \(-0.175654\pi\)
0.851564 + 0.524250i \(0.175654\pi\)
\(600\) 20.9473i 0.855170i
\(601\) 21.5712 0.879908 0.439954 0.898020i \(-0.354995\pi\)
0.439954 + 0.898020i \(0.354995\pi\)
\(602\) 36.8228 1.50079
\(603\) 35.2573i 1.43579i
\(604\) 2.04403i 0.0831703i
\(605\) 3.53666i 0.143786i
\(606\) 53.9574i 2.19187i
\(607\) 34.8299 1.41370 0.706851 0.707362i \(-0.250115\pi\)
0.706851 + 0.707362i \(0.250115\pi\)
\(608\) −14.3593 −0.582348
\(609\) 17.7075i 0.717545i
\(610\) 15.9297 0.644974
\(611\) 16.2594 + 22.1771i 0.657783 + 0.897190i
\(612\) −28.9035 −1.16836
\(613\) 19.2039i 0.775639i −0.921735 0.387819i \(-0.873228\pi\)
0.921735 0.387819i \(-0.126772\pi\)
\(614\) 70.1412 2.83067
\(615\) −7.89089 −0.318191
\(616\) 10.0940i 0.406700i
\(617\) 13.1172i 0.528079i 0.964512 + 0.264040i \(0.0850550\pi\)
−0.964512 + 0.264040i \(0.914945\pi\)
\(618\) 44.7644i 1.80069i
\(619\) 7.80176i 0.313579i 0.987632 + 0.156790i \(0.0501145\pi\)
−0.987632 + 0.156790i \(0.949886\pi\)
\(620\) −2.93073 −0.117701
\(621\) −2.52864 −0.101471
\(622\) 68.1128i 2.73108i
\(623\) 29.5697 1.18469
\(624\) 10.0702 7.38309i 0.403132 0.295560i
\(625\) 10.8513 0.434052
\(626\) 74.2102i 2.96603i
\(627\) 14.5133 0.579605
\(628\) 57.5972 2.29838
\(629\) 13.4639i 0.536842i
\(630\) 15.0912i 0.601249i
\(631\) 4.02885i 0.160386i 0.996779 + 0.0801930i \(0.0255537\pi\)
−0.996779 + 0.0801930i \(0.974446\pi\)
\(632\) 1.64913i 0.0655989i
\(633\) −46.0725 −1.83122
\(634\) 14.2369 0.565419
\(635\) 17.0879i 0.678112i
\(636\) 39.7980 1.57809
\(637\) 10.7126 7.85401i 0.424447 0.311187i
\(638\) −22.7526 −0.900785
\(639\) 18.5847i 0.735201i
\(640\) 14.6005 0.577136
\(641\) −2.73730 −0.108117 −0.0540584 0.998538i \(-0.517216\pi\)
−0.0540584 + 0.998538i \(0.517216\pi\)
\(642\) 105.222i 4.15277i
\(643\) 7.54898i 0.297703i −0.988860 0.148851i \(-0.952442\pi\)
0.988860 0.148851i \(-0.0475576\pi\)
\(644\) 7.21737i 0.284404i
\(645\) 23.7774i 0.936236i
\(646\) 12.1075 0.476365
\(647\) −9.51543 −0.374090 −0.187045 0.982351i \(-0.559891\pi\)
−0.187045 + 0.982351i \(0.559891\pi\)
\(648\) 12.8339i 0.504162i
\(649\) −7.27939 −0.285741
\(650\) −18.8494 25.7098i −0.739332 1.00842i
\(651\) −4.71953 −0.184973
\(652\) 35.0883i 1.37416i
\(653\) −15.6207 −0.611286 −0.305643 0.952146i \(-0.598871\pi\)
−0.305643 + 0.952146i \(0.598871\pi\)
\(654\) −110.892 −4.33622
\(655\) 12.5621i 0.490842i
\(656\) 4.04517i 0.157937i
\(657\) 16.7539i 0.653632i
\(658\) 30.7869i 1.20020i
\(659\) 5.25385 0.204661 0.102330 0.994750i \(-0.467370\pi\)
0.102330 + 0.994750i \(0.467370\pi\)
\(660\) −20.7790 −0.808821
\(661\) 27.8552i 1.08344i −0.840558 0.541721i \(-0.817773\pi\)
0.840558 0.541721i \(-0.182227\pi\)
\(662\) −73.8287 −2.86943
\(663\) −20.1083 + 14.7426i −0.780942 + 0.572555i
\(664\) 2.40348 0.0932730
\(665\) 3.74878i 0.145371i
\(666\) 41.5822 1.61128
\(667\) −5.10310 −0.197593
\(668\) 59.6112i 2.30643i
\(669\) 72.9746i 2.82136i
\(670\) 21.1452i 0.816912i
\(671\) 19.5463i 0.754575i
\(672\) 33.1066 1.27712
\(673\) −36.1550 −1.39367 −0.696837 0.717229i \(-0.745410\pi\)
−0.696837 + 0.717229i \(0.745410\pi\)
\(674\) 1.05329i 0.0405713i
\(675\) −7.41527 −0.285414
\(676\) −11.3950 + 36.1289i −0.438271 + 1.38957i
\(677\) −27.9179 −1.07297 −0.536487 0.843909i \(-0.680249\pi\)
−0.536487 + 0.843909i \(0.680249\pi\)
\(678\) 9.83707i 0.377790i
\(679\) 6.72066 0.257915
\(680\) −5.43755 −0.208520
\(681\) 26.6924i 1.02286i
\(682\) 6.06418i 0.232209i
\(683\) 37.1396i 1.42111i −0.703642 0.710554i \(-0.748444\pi\)
0.703642 0.710554i \(-0.251556\pi\)
\(684\) 22.1744i 0.847859i
\(685\) −3.59682 −0.137428
\(686\) 43.1281 1.64664
\(687\) 30.4981i 1.16357i
\(688\) −12.1892 −0.464710
\(689\) 15.3222 11.2336i 0.583728 0.427965i
\(690\) −7.85899 −0.299187
\(691\) 40.0257i 1.52265i −0.648371 0.761324i \(-0.724549\pi\)
0.648371 0.761324i \(-0.275451\pi\)
\(692\) −20.3314 −0.772884
\(693\) −18.5174 −0.703419
\(694\) 27.2906i 1.03594i
\(695\) 17.2788i 0.655424i
\(696\) 19.7048i 0.746909i
\(697\) 8.07742i 0.305954i
\(698\) −77.4845 −2.93283
\(699\) −39.0382 −1.47656
\(700\) 21.1651i 0.799964i
\(701\) −30.3361 −1.14578 −0.572890 0.819632i \(-0.694178\pi\)
−0.572890 + 0.819632i \(0.694178\pi\)
\(702\) 8.78604 + 11.9838i 0.331608 + 0.452300i
\(703\) −10.3294 −0.389579
\(704\) 35.2284i 1.32772i
\(705\) 19.8799 0.748720
\(706\) 23.4560 0.882779
\(707\) 17.1014i 0.643164i
\(708\) 20.0977i 0.755319i
\(709\) 4.72511i 0.177455i −0.996056 0.0887276i \(-0.971720\pi\)
0.996056 0.0887276i \(-0.0282801\pi\)
\(710\) 11.1460i 0.418303i
\(711\) −3.02532 −0.113458
\(712\) 32.9050 1.23317
\(713\) 1.36011i 0.0509366i
\(714\) −27.9149 −1.04469
\(715\) −7.99987 + 5.86518i −0.299178 + 0.219345i
\(716\) −25.9950 −0.971480
\(717\) 10.8196i 0.404064i
\(718\) 37.4509 1.39765
\(719\) −0.620833 −0.0231532 −0.0115766 0.999933i \(-0.503685\pi\)
−0.0115766 + 0.999933i \(0.503685\pi\)
\(720\) 4.99555i 0.186173i
\(721\) 14.1877i 0.528379i
\(722\) 32.8300i 1.22181i
\(723\) 45.9454i 1.70873i
\(724\) 31.2068 1.15979
\(725\) −14.9649 −0.555783
\(726\) 20.2042i 0.749847i
\(727\) 5.87302 0.217818 0.108909 0.994052i \(-0.465264\pi\)
0.108909 + 0.994052i \(0.465264\pi\)
\(728\) −10.7294 + 7.86637i −0.397658 + 0.291547i
\(729\) −37.9990 −1.40737
\(730\) 10.0480i 0.371894i
\(731\) 24.3395 0.900229
\(732\) 53.9654 1.99462
\(733\) 37.4352i 1.38270i 0.722520 + 0.691350i \(0.242984\pi\)
−0.722520 + 0.691350i \(0.757016\pi\)
\(734\) 22.3068i 0.823360i
\(735\) 9.60290i 0.354208i
\(736\) 9.54095i 0.351684i
\(737\) −25.9459 −0.955730
\(738\) −24.9464 −0.918290
\(739\) 2.78103i 0.102302i 0.998691 + 0.0511509i \(0.0162890\pi\)
−0.998691 + 0.0511509i \(0.983711\pi\)
\(740\) 14.7888 0.543646
\(741\) −11.3103 15.4268i −0.415495 0.566719i
\(742\) 21.2707 0.780871
\(743\) 18.4482i 0.676799i −0.941003 0.338399i \(-0.890115\pi\)
0.941003 0.338399i \(-0.109885\pi\)
\(744\) −5.25186 −0.192542
\(745\) 9.56017 0.350257
\(746\) 47.3353i 1.73307i
\(747\) 4.40916i 0.161323i
\(748\) 21.2702i 0.777714i
\(749\) 33.3492i 1.21855i
\(750\) −51.9376 −1.89649
\(751\) 34.9474 1.27525 0.637624 0.770348i \(-0.279917\pi\)
0.637624 + 0.770348i \(0.279917\pi\)
\(752\) 10.1912i 0.371634i
\(753\) −4.44805 −0.162096
\(754\) 17.7313 + 24.1848i 0.645736 + 0.880758i
\(755\) 0.705431 0.0256733
\(756\) 9.86544i 0.358803i
\(757\) 40.5867 1.47515 0.737574 0.675266i \(-0.235971\pi\)
0.737574 + 0.675266i \(0.235971\pi\)
\(758\) −32.8461 −1.19302
\(759\) 9.64324i 0.350027i
\(760\) 4.17162i 0.151320i
\(761\) 35.5111i 1.28728i −0.765330 0.643638i \(-0.777424\pi\)
0.765330 0.643638i \(-0.222576\pi\)
\(762\) 97.6194i 3.53638i
\(763\) −35.1464 −1.27238
\(764\) 53.3655 1.93070
\(765\) 9.97513i 0.360652i
\(766\) −81.9863 −2.96229
\(767\) 5.67289 + 7.73759i 0.204836 + 0.279388i
\(768\) 16.6566 0.601042
\(769\) 5.42518i 0.195637i 0.995204 + 0.0978186i \(0.0311865\pi\)
−0.995204 + 0.0978186i \(0.968814\pi\)
\(770\) −11.1057 −0.400220
\(771\) −46.3813 −1.67038
\(772\) 15.4904i 0.557511i
\(773\) 16.2454i 0.584305i −0.956372 0.292152i \(-0.905629\pi\)
0.956372 0.292152i \(-0.0943715\pi\)
\(774\) 75.1705i 2.70195i
\(775\) 3.98855i 0.143273i
\(776\) 7.47870 0.268470
\(777\) 23.8152 0.854365
\(778\) 8.89893i 0.319042i
\(779\) 6.19689 0.222027
\(780\) 16.1932 + 22.0869i 0.579811 + 0.790839i
\(781\) −13.6765 −0.489385
\(782\) 8.04476i 0.287680i
\(783\) 6.97544 0.249282