Properties

Label 177.3.b.a.119.22
Level $177$
Weight $3$
Character 177.119
Analytic conductor $4.823$
Analytic rank $0$
Dimension $38$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(38\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.22
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.17

$q$-expansion

\(f(q)\) \(=\) \(q+0.472796i q^{2} +(-1.33002 + 2.68906i) q^{3} +3.77646 q^{4} +7.63899i q^{5} +(-1.27138 - 0.628829i) q^{6} -9.20830 q^{7} +3.67668i q^{8} +(-5.46208 - 7.15302i) q^{9} +O(q^{10})\) \(q+0.472796i q^{2} +(-1.33002 + 2.68906i) q^{3} +3.77646 q^{4} +7.63899i q^{5} +(-1.27138 - 0.628829i) q^{6} -9.20830 q^{7} +3.67668i q^{8} +(-5.46208 - 7.15302i) q^{9} -3.61168 q^{10} -2.06521i q^{11} +(-5.02278 + 10.1551i) q^{12} +15.4082 q^{13} -4.35364i q^{14} +(-20.5417 - 10.1600i) q^{15} +13.3675 q^{16} -15.6666i q^{17} +(3.38192 - 2.58245i) q^{18} -31.9933 q^{19} +28.8484i q^{20} +(12.2472 - 24.7617i) q^{21} +0.976424 q^{22} +41.9436i q^{23} +(-9.88681 - 4.89007i) q^{24} -33.3541 q^{25} +7.28491i q^{26} +(26.4996 - 5.17418i) q^{27} -34.7748 q^{28} +41.7036i q^{29} +(4.80362 - 9.71202i) q^{30} -6.91310 q^{31} +21.0268i q^{32} +(5.55348 + 2.74678i) q^{33} +7.40712 q^{34} -70.3421i q^{35} +(-20.6274 - 27.0131i) q^{36} +63.0547 q^{37} -15.1263i q^{38} +(-20.4932 + 41.4335i) q^{39} -28.0861 q^{40} -28.7568i q^{41} +(11.7072 + 5.79044i) q^{42} +59.9306 q^{43} -7.79920i q^{44} +(54.6418 - 41.7248i) q^{45} -19.8308 q^{46} +37.1422i q^{47} +(-17.7791 + 35.9461i) q^{48} +35.7927 q^{49} -15.7697i q^{50} +(42.1285 + 20.8370i) q^{51} +58.1884 q^{52} -0.0188512i q^{53} +(2.44633 + 12.5289i) q^{54} +15.7761 q^{55} -33.8560i q^{56} +(42.5519 - 86.0320i) q^{57} -19.7173 q^{58} -7.68115i q^{59} +(-77.5750 - 38.3690i) q^{60} -21.9824 q^{61} -3.26849i q^{62} +(50.2965 + 65.8671i) q^{63} +43.5288 q^{64} +117.703i q^{65} +(-1.29867 + 2.62566i) q^{66} +25.9477 q^{67} -59.1645i q^{68} +(-112.789 - 55.7860i) q^{69} +33.2574 q^{70} +40.5584i q^{71} +(26.2994 - 20.0823i) q^{72} -42.2494 q^{73} +29.8120i q^{74} +(44.3618 - 89.6913i) q^{75} -120.822 q^{76} +19.0171i q^{77} +(-19.5896 - 9.68910i) q^{78} +32.2588 q^{79} +102.114i q^{80} +(-21.3314 + 78.1407i) q^{81} +13.5961 q^{82} -19.0053i q^{83} +(46.2513 - 93.5115i) q^{84} +119.677 q^{85} +28.3349i q^{86} +(-112.144 - 55.4667i) q^{87} +7.59312 q^{88} -77.7511i q^{89} +(19.7273 + 25.8344i) q^{90} -141.883 q^{91} +158.399i q^{92} +(9.19458 - 18.5897i) q^{93} -17.5607 q^{94} -244.397i q^{95} +(-56.5424 - 27.9662i) q^{96} +123.092 q^{97} +16.9226i q^{98} +(-14.7725 + 11.2804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + O(q^{10}) \) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + 36q^{10} - 4q^{13} - 17q^{15} + 100q^{16} - 2q^{18} - 28q^{19} - 11q^{21} + 84q^{22} - 6q^{24} - 166q^{25} + 3q^{27} + 12q^{28} + 102q^{30} - 40q^{31} - 46q^{33} - 148q^{34} - 96q^{36} + 112q^{37} + 62q^{39} - 56q^{40} + 14q^{42} + 164q^{43} + 55q^{45} - 4q^{46} - 124q^{48} + 242q^{49} + 52q^{51} + 8q^{52} + 18q^{54} - 228q^{55} - 147q^{57} - 80q^{58} + 128q^{60} + 12q^{61} + 86q^{63} + 48q^{64} - 24q^{66} + 124q^{67} - 240q^{69} + 148q^{70} + 166q^{72} - 192q^{73} - 78q^{75} - 304q^{76} + 244q^{78} + 64q^{79} - 156q^{81} - 180q^{82} + 300q^{84} - 52q^{85} - 83q^{87} - 96q^{88} - 376q^{90} - 332q^{91} + 454q^{93} + 768q^{94} - 722q^{96} + 416q^{97} + 494q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.472796i 0.236398i 0.992990 + 0.118199i \(0.0377121\pi\)
−0.992990 + 0.118199i \(0.962288\pi\)
\(3\) −1.33002 + 2.68906i −0.443341 + 0.896353i
\(4\) 3.77646 0.944116
\(5\) 7.63899i 1.52780i 0.645336 + 0.763899i \(0.276717\pi\)
−0.645336 + 0.763899i \(0.723283\pi\)
\(6\) −1.27138 0.628829i −0.211896 0.104805i
\(7\) −9.20830 −1.31547 −0.657735 0.753249i \(-0.728486\pi\)
−0.657735 + 0.753249i \(0.728486\pi\)
\(8\) 3.67668i 0.459585i
\(9\) −5.46208 7.15302i −0.606898 0.794780i
\(10\) −3.61168 −0.361168
\(11\) 2.06521i 0.187747i −0.995584 0.0938733i \(-0.970075\pi\)
0.995584 0.0938733i \(-0.0299249\pi\)
\(12\) −5.02278 + 10.1551i −0.418565 + 0.846261i
\(13\) 15.4082 1.18524 0.592621 0.805481i \(-0.298093\pi\)
0.592621 + 0.805481i \(0.298093\pi\)
\(14\) 4.35364i 0.310975i
\(15\) −20.5417 10.1600i −1.36945 0.677335i
\(16\) 13.3675 0.835471
\(17\) 15.6666i 0.921567i −0.887513 0.460783i \(-0.847569\pi\)
0.887513 0.460783i \(-0.152431\pi\)
\(18\) 3.38192 2.58245i 0.187884 0.143469i
\(19\) −31.9933 −1.68386 −0.841930 0.539586i \(-0.818581\pi\)
−0.841930 + 0.539586i \(0.818581\pi\)
\(20\) 28.8484i 1.44242i
\(21\) 12.2472 24.7617i 0.583202 1.17913i
\(22\) 0.976424 0.0443829
\(23\) 41.9436i 1.82364i 0.410595 + 0.911818i \(0.365321\pi\)
−0.410595 + 0.911818i \(0.634679\pi\)
\(24\) −9.88681 4.89007i −0.411950 0.203753i
\(25\) −33.3541 −1.33417
\(26\) 7.28491i 0.280189i
\(27\) 26.4996 5.17418i 0.981466 0.191636i
\(28\) −34.7748 −1.24196
\(29\) 41.7036i 1.43806i 0.694981 + 0.719028i \(0.255413\pi\)
−0.694981 + 0.719028i \(0.744587\pi\)
\(30\) 4.80362 9.71202i 0.160121 0.323734i
\(31\) −6.91310 −0.223003 −0.111502 0.993764i \(-0.535566\pi\)
−0.111502 + 0.993764i \(0.535566\pi\)
\(32\) 21.0268i 0.657088i
\(33\) 5.55348 + 2.74678i 0.168287 + 0.0832357i
\(34\) 7.40712 0.217856
\(35\) 70.3421i 2.00977i
\(36\) −20.6274 27.0131i −0.572982 0.750364i
\(37\) 63.0547 1.70418 0.852091 0.523394i \(-0.175334\pi\)
0.852091 + 0.523394i \(0.175334\pi\)
\(38\) 15.1263i 0.398061i
\(39\) −20.4932 + 41.4335i −0.525467 + 1.06240i
\(40\) −28.0861 −0.702153
\(41\) 28.7568i 0.701384i −0.936491 0.350692i \(-0.885946\pi\)
0.936491 0.350692i \(-0.114054\pi\)
\(42\) 11.7072 + 5.79044i 0.278743 + 0.137868i
\(43\) 59.9306 1.39373 0.696867 0.717200i \(-0.254577\pi\)
0.696867 + 0.717200i \(0.254577\pi\)
\(44\) 7.79920i 0.177255i
\(45\) 54.6418 41.7248i 1.21426 0.927217i
\(46\) −19.8308 −0.431104
\(47\) 37.1422i 0.790259i 0.918625 + 0.395129i \(0.129300\pi\)
−0.918625 + 0.395129i \(0.870700\pi\)
\(48\) −17.7791 + 35.9461i −0.370398 + 0.748877i
\(49\) 35.7927 0.730464
\(50\) 15.7697i 0.315394i
\(51\) 42.1285 + 20.8370i 0.826049 + 0.408568i
\(52\) 58.1884 1.11901
\(53\) 0.0188512i 0.000355682i −1.00000 0.000177841i \(-0.999943\pi\)
1.00000 0.000177841i \(-5.66086e-5\pi\)
\(54\) 2.44633 + 12.5289i 0.0453024 + 0.232016i
\(55\) 15.7761 0.286839
\(56\) 33.8560i 0.604571i
\(57\) 42.5519 86.0320i 0.746524 1.50933i
\(58\) −19.7173 −0.339953
\(59\) 7.68115i 0.130189i
\(60\) −77.5750 38.3690i −1.29292 0.639483i
\(61\) −21.9824 −0.360367 −0.180184 0.983633i \(-0.557669\pi\)
−0.180184 + 0.983633i \(0.557669\pi\)
\(62\) 3.26849i 0.0527175i
\(63\) 50.2965 + 65.8671i 0.798356 + 1.04551i
\(64\) 43.5288 0.680137
\(65\) 117.703i 1.81081i
\(66\) −1.29867 + 2.62566i −0.0196768 + 0.0397827i
\(67\) 25.9477 0.387279 0.193639 0.981073i \(-0.437971\pi\)
0.193639 + 0.981073i \(0.437971\pi\)
\(68\) 59.1645i 0.870066i
\(69\) −112.789 55.7860i −1.63462 0.808492i
\(70\) 33.2574 0.475106
\(71\) 40.5584i 0.571245i 0.958342 + 0.285623i \(0.0922004\pi\)
−0.958342 + 0.285623i \(0.907800\pi\)
\(72\) 26.2994 20.0823i 0.365269 0.278921i
\(73\) −42.2494 −0.578759 −0.289379 0.957215i \(-0.593449\pi\)
−0.289379 + 0.957215i \(0.593449\pi\)
\(74\) 29.8120i 0.402865i
\(75\) 44.3618 89.6913i 0.591490 1.19588i
\(76\) −120.822 −1.58976
\(77\) 19.0171i 0.246975i
\(78\) −19.5896 9.68910i −0.251148 0.124219i
\(79\) 32.2588 0.408340 0.204170 0.978935i \(-0.434551\pi\)
0.204170 + 0.978935i \(0.434551\pi\)
\(80\) 102.114i 1.27643i
\(81\) −21.3314 + 78.1407i −0.263350 + 0.964700i
\(82\) 13.5961 0.165806
\(83\) 19.0053i 0.228980i −0.993424 0.114490i \(-0.963477\pi\)
0.993424 0.114490i \(-0.0365233\pi\)
\(84\) 46.2513 93.5115i 0.550610 1.11323i
\(85\) 119.677 1.40797
\(86\) 28.3349i 0.329476i
\(87\) −112.144 55.4667i −1.28901 0.637549i
\(88\) 7.59312 0.0862855
\(89\) 77.7511i 0.873608i −0.899557 0.436804i \(-0.856110\pi\)
0.899557 0.436804i \(-0.143890\pi\)
\(90\) 19.7273 + 25.8344i 0.219192 + 0.287049i
\(91\) −141.883 −1.55915
\(92\) 158.399i 1.72172i
\(93\) 9.19458 18.5897i 0.0988665 0.199890i
\(94\) −17.5607 −0.186816
\(95\) 244.397i 2.57260i
\(96\) −56.5424 27.9662i −0.588983 0.291314i
\(97\) 123.092 1.26899 0.634496 0.772926i \(-0.281208\pi\)
0.634496 + 0.772926i \(0.281208\pi\)
\(98\) 16.9226i 0.172680i
\(99\) −14.7725 + 11.2804i −0.149217 + 0.113943i
\(100\) −125.961 −1.25961
\(101\) 73.9979i 0.732653i −0.930486 0.366326i \(-0.880615\pi\)
0.930486 0.366326i \(-0.119385\pi\)
\(102\) −9.85163 + 19.9182i −0.0965846 + 0.195276i
\(103\) 93.7664 0.910353 0.455176 0.890401i \(-0.349576\pi\)
0.455176 + 0.890401i \(0.349576\pi\)
\(104\) 56.6509i 0.544720i
\(105\) 189.154 + 93.5565i 1.80147 + 0.891015i
\(106\) 0.00891275 8.40825e−5
\(107\) 51.8016i 0.484127i −0.970260 0.242063i \(-0.922176\pi\)
0.970260 0.242063i \(-0.0778242\pi\)
\(108\) 100.075 19.5401i 0.926618 0.180927i
\(109\) 29.7585 0.273014 0.136507 0.990639i \(-0.456412\pi\)
0.136507 + 0.990639i \(0.456412\pi\)
\(110\) 7.45889i 0.0678081i
\(111\) −83.8642 + 169.558i −0.755533 + 1.52755i
\(112\) −123.092 −1.09904
\(113\) 114.745i 1.01544i 0.861523 + 0.507719i \(0.169511\pi\)
−0.861523 + 0.507719i \(0.830489\pi\)
\(114\) 40.6756 + 20.1183i 0.356803 + 0.176477i
\(115\) −320.407 −2.78615
\(116\) 157.492i 1.35769i
\(117\) −84.1606 110.215i −0.719321 0.942007i
\(118\) 3.63161 0.0307764
\(119\) 144.263i 1.21229i
\(120\) 37.3552 75.5252i 0.311293 0.629377i
\(121\) 116.735 0.964751
\(122\) 10.3932i 0.0851900i
\(123\) 77.3286 + 38.2471i 0.628688 + 0.310952i
\(124\) −26.1071 −0.210541
\(125\) 63.8172i 0.510537i
\(126\) −31.1417 + 23.7800i −0.247156 + 0.188730i
\(127\) −70.5037 −0.555147 −0.277574 0.960704i \(-0.589530\pi\)
−0.277574 + 0.960704i \(0.589530\pi\)
\(128\) 104.688i 0.817871i
\(129\) −79.7090 + 161.157i −0.617900 + 1.24928i
\(130\) −55.6494 −0.428072
\(131\) 169.629i 1.29488i −0.762116 0.647441i \(-0.775839\pi\)
0.762116 0.647441i \(-0.224161\pi\)
\(132\) 20.9725 + 10.3731i 0.158883 + 0.0785842i
\(133\) 294.604 2.21507
\(134\) 12.2680i 0.0915519i
\(135\) 39.5255 + 202.430i 0.292782 + 1.49948i
\(136\) 57.6012 0.423538
\(137\) 92.5010i 0.675189i −0.941292 0.337595i \(-0.890387\pi\)
0.941292 0.337595i \(-0.109613\pi\)
\(138\) 26.3754 53.3261i 0.191126 0.386421i
\(139\) −132.666 −0.954432 −0.477216 0.878786i \(-0.658354\pi\)
−0.477216 + 0.878786i \(0.658354\pi\)
\(140\) 265.644i 1.89746i
\(141\) −99.8775 49.3999i −0.708351 0.350354i
\(142\) −19.1758 −0.135041
\(143\) 31.8211i 0.222525i
\(144\) −73.0146 95.6183i −0.507046 0.664016i
\(145\) −318.573 −2.19706
\(146\) 19.9753i 0.136817i
\(147\) −47.6051 + 96.2488i −0.323844 + 0.654753i
\(148\) 238.124 1.60895
\(149\) 38.9276i 0.261259i 0.991431 + 0.130630i \(0.0416999\pi\)
−0.991431 + 0.130630i \(0.958300\pi\)
\(150\) 42.4056 + 20.9740i 0.282704 + 0.139827i
\(151\) −187.145 −1.23937 −0.619685 0.784851i \(-0.712740\pi\)
−0.619685 + 0.784851i \(0.712740\pi\)
\(152\) 117.629i 0.773877i
\(153\) −112.064 + 85.5724i −0.732443 + 0.559297i
\(154\) −8.99120 −0.0583844
\(155\) 52.8091i 0.340704i
\(156\) −77.3918 + 156.472i −0.496101 + 1.00303i
\(157\) −88.9609 −0.566630 −0.283315 0.959027i \(-0.591434\pi\)
−0.283315 + 0.959027i \(0.591434\pi\)
\(158\) 15.2518i 0.0965306i
\(159\) 0.0506919 + 0.0250725i 0.000318817 + 0.000157688i
\(160\) −160.624 −1.00390
\(161\) 386.229i 2.39894i
\(162\) −36.9446 10.0854i −0.228053 0.0622554i
\(163\) −192.945 −1.18371 −0.591857 0.806043i \(-0.701605\pi\)
−0.591857 + 0.806043i \(0.701605\pi\)
\(164\) 108.599i 0.662188i
\(165\) −20.9826 + 42.4230i −0.127167 + 0.257109i
\(166\) 8.98563 0.0541303
\(167\) 131.823i 0.789358i 0.918819 + 0.394679i \(0.129144\pi\)
−0.918819 + 0.394679i \(0.870856\pi\)
\(168\) 91.0407 + 45.0292i 0.541909 + 0.268031i
\(169\) 68.4113 0.404801
\(170\) 56.5829i 0.332840i
\(171\) 174.750 + 228.849i 1.02193 + 1.33830i
\(172\) 226.326 1.31585
\(173\) 117.008i 0.676348i −0.941084 0.338174i \(-0.890191\pi\)
0.941084 0.338174i \(-0.109809\pi\)
\(174\) 26.2244 53.0210i 0.150715 0.304718i
\(175\) 307.135 1.75506
\(176\) 27.6068i 0.156857i
\(177\) 20.6551 + 10.2161i 0.116695 + 0.0577181i
\(178\) 36.7604 0.206519
\(179\) 15.2966i 0.0854561i 0.999087 + 0.0427280i \(0.0136049\pi\)
−0.999087 + 0.0427280i \(0.986395\pi\)
\(180\) 206.353 157.572i 1.14640 0.875401i
\(181\) 339.189 1.87397 0.936986 0.349366i \(-0.113603\pi\)
0.936986 + 0.349366i \(0.113603\pi\)
\(182\) 67.0816i 0.368580i
\(183\) 29.2371 59.1120i 0.159765 0.323016i
\(184\) −154.213 −0.838116
\(185\) 481.674i 2.60364i
\(186\) 8.78915 + 4.34716i 0.0472535 + 0.0233718i
\(187\) −32.3549 −0.173021
\(188\) 140.266i 0.746096i
\(189\) −244.016 + 47.6454i −1.29109 + 0.252092i
\(190\) 115.550 0.608157
\(191\) 210.673i 1.10300i −0.834175 0.551500i \(-0.814056\pi\)
0.834175 0.551500i \(-0.185944\pi\)
\(192\) −57.8942 + 117.051i −0.301532 + 0.609643i
\(193\) 127.355 0.659871 0.329936 0.944003i \(-0.392973\pi\)
0.329936 + 0.944003i \(0.392973\pi\)
\(194\) 58.1975i 0.299987i
\(195\) −316.510 156.547i −1.62313 0.802807i
\(196\) 135.170 0.689643
\(197\) 153.834i 0.780882i 0.920628 + 0.390441i \(0.127677\pi\)
−0.920628 + 0.390441i \(0.872323\pi\)
\(198\) −5.33331 6.98438i −0.0269359 0.0352746i
\(199\) 139.680 0.701910 0.350955 0.936392i \(-0.385857\pi\)
0.350955 + 0.936392i \(0.385857\pi\)
\(200\) 122.632i 0.613162i
\(201\) −34.5110 + 69.7749i −0.171697 + 0.347139i
\(202\) 34.9859 0.173198
\(203\) 384.019i 1.89172i
\(204\) 159.097 + 78.6901i 0.779886 + 0.385736i
\(205\) 219.673 1.07157
\(206\) 44.3323i 0.215206i
\(207\) 300.024 229.099i 1.44939 1.10676i
\(208\) 205.969 0.990236
\(209\) 66.0731i 0.316139i
\(210\) −44.2331 + 89.4312i −0.210634 + 0.425863i
\(211\) 350.086 1.65918 0.829588 0.558375i \(-0.188575\pi\)
0.829588 + 0.558375i \(0.188575\pi\)
\(212\) 0.0711907i 0.000335805i
\(213\) −109.064 53.9436i −0.512037 0.253256i
\(214\) 24.4916 0.114447
\(215\) 457.809i 2.12934i
\(216\) 19.0238 + 97.4305i 0.0880732 + 0.451067i
\(217\) 63.6579 0.293354
\(218\) 14.0697i 0.0645399i
\(219\) 56.1926 113.611i 0.256587 0.518772i
\(220\) 59.5780 0.270809
\(221\) 241.394i 1.09228i
\(222\) −80.1662 39.6506i −0.361109 0.178606i
\(223\) −190.680 −0.855069 −0.427534 0.903999i \(-0.640618\pi\)
−0.427534 + 0.903999i \(0.640618\pi\)
\(224\) 193.621i 0.864381i
\(225\) 182.183 + 238.583i 0.809702 + 1.06037i
\(226\) −54.2507 −0.240047
\(227\) 255.387i 1.12505i −0.826779 0.562526i \(-0.809829\pi\)
0.826779 0.562526i \(-0.190171\pi\)
\(228\) 160.696 324.897i 0.704805 1.42499i
\(229\) −57.9236 −0.252942 −0.126471 0.991970i \(-0.540365\pi\)
−0.126471 + 0.991970i \(0.540365\pi\)
\(230\) 151.487i 0.658639i
\(231\) −51.1381 25.2932i −0.221377 0.109494i
\(232\) −153.331 −0.660909
\(233\) 53.0200i 0.227553i −0.993506 0.113777i \(-0.963705\pi\)
0.993506 0.113777i \(-0.0362949\pi\)
\(234\) 52.1091 39.7908i 0.222688 0.170046i
\(235\) −283.729 −1.20736
\(236\) 29.0076i 0.122913i
\(237\) −42.9050 + 86.7459i −0.181034 + 0.366016i
\(238\) −68.2069 −0.286584
\(239\) 313.540i 1.31188i −0.754813 0.655940i \(-0.772272\pi\)
0.754813 0.655940i \(-0.227728\pi\)
\(240\) −274.592 135.815i −1.14413 0.565894i
\(241\) −189.180 −0.784980 −0.392490 0.919756i \(-0.628386\pi\)
−0.392490 + 0.919756i \(0.628386\pi\)
\(242\) 55.1918i 0.228065i
\(243\) −181.754 161.290i −0.747958 0.663746i
\(244\) −83.0157 −0.340228
\(245\) 273.420i 1.11600i
\(246\) −18.0831 + 36.5606i −0.0735085 + 0.148621i
\(247\) −492.959 −1.99578
\(248\) 25.4173i 0.102489i
\(249\) 51.1064 + 25.2775i 0.205247 + 0.101516i
\(250\) 30.1725 0.120690
\(251\) 0.0945816i 0.000376819i 1.00000 0.000188410i \(5.99726e-5\pi\)
−1.00000 0.000188410i \(0.999940\pi\)
\(252\) 189.943 + 248.745i 0.753741 + 0.987083i
\(253\) 86.6225 0.342381
\(254\) 33.3338i 0.131236i
\(255\) −159.173 + 321.819i −0.624209 + 1.26204i
\(256\) 124.619 0.486794
\(257\) 1.58343i 0.00616119i 0.999995 + 0.00308059i \(0.000980585\pi\)
−0.999995 + 0.00308059i \(0.999019\pi\)
\(258\) −76.1943 37.6861i −0.295327 0.146070i
\(259\) −580.627 −2.24180
\(260\) 444.500i 1.70962i
\(261\) 298.307 227.789i 1.14294 0.872753i
\(262\) 80.2001 0.306107
\(263\) 335.725i 1.27652i 0.769820 + 0.638261i \(0.220346\pi\)
−0.769820 + 0.638261i \(0.779654\pi\)
\(264\) −10.0990 + 20.4184i −0.0382539 + 0.0773423i
\(265\) 0.144004 0.000543411
\(266\) 139.288i 0.523638i
\(267\) 209.077 + 103.411i 0.783061 + 0.387306i
\(268\) 97.9905 0.365636
\(269\) 211.343i 0.785663i −0.919610 0.392831i \(-0.871496\pi\)
0.919610 0.392831i \(-0.128504\pi\)
\(270\) −95.7080 + 18.6875i −0.354474 + 0.0692130i
\(271\) 71.0257 0.262087 0.131044 0.991377i \(-0.458167\pi\)
0.131044 + 0.991377i \(0.458167\pi\)
\(272\) 209.424i 0.769942i
\(273\) 188.707 381.532i 0.691236 1.39755i
\(274\) 43.7341 0.159613
\(275\) 68.8834i 0.250485i
\(276\) −425.943 210.674i −1.54327 0.763311i
\(277\) −7.50451 −0.0270921 −0.0135460 0.999908i \(-0.504312\pi\)
−0.0135460 + 0.999908i \(0.504312\pi\)
\(278\) 62.7239i 0.225626i
\(279\) 37.7599 + 49.4495i 0.135340 + 0.177239i
\(280\) 258.625 0.923661
\(281\) 354.561i 1.26178i −0.775871 0.630891i \(-0.782690\pi\)
0.775871 0.630891i \(-0.217310\pi\)
\(282\) 23.3561 47.2217i 0.0828229 0.167453i
\(283\) −7.69162 −0.0271789 −0.0135894 0.999908i \(-0.504326\pi\)
−0.0135894 + 0.999908i \(0.504326\pi\)
\(284\) 153.167i 0.539322i
\(285\) 657.198 + 325.053i 2.30596 + 1.14054i
\(286\) 15.0449 0.0526045
\(287\) 264.801i 0.922651i
\(288\) 150.405 114.850i 0.522241 0.398786i
\(289\) 43.5566 0.150715
\(290\) 150.620i 0.519380i
\(291\) −163.716 + 331.002i −0.562596 + 1.13747i
\(292\) −159.553 −0.546415
\(293\) 234.206i 0.799339i −0.916659 0.399670i \(-0.869125\pi\)
0.916659 0.399670i \(-0.130875\pi\)
\(294\) −45.5060 22.5075i −0.154782 0.0765561i
\(295\) 58.6762 0.198902
\(296\) 231.832i 0.783216i
\(297\) −10.6858 54.7273i −0.0359791 0.184267i
\(298\) −18.4048 −0.0617611
\(299\) 646.274i 2.16145i
\(300\) 167.531 338.716i 0.558435 1.12905i
\(301\) −551.859 −1.83342
\(302\) 88.4813i 0.292984i
\(303\) 198.985 + 98.4189i 0.656716 + 0.324815i
\(304\) −427.672 −1.40682
\(305\) 167.923i 0.550568i
\(306\) −40.4583 52.9832i −0.132217 0.173148i
\(307\) 323.794 1.05470 0.527351 0.849647i \(-0.323185\pi\)
0.527351 + 0.849647i \(0.323185\pi\)
\(308\) 71.8174i 0.233173i
\(309\) −124.711 + 252.143i −0.403597 + 0.815998i
\(310\) 24.9679 0.0805417
\(311\) 288.450i 0.927493i −0.885968 0.463746i \(-0.846505\pi\)
0.885968 0.463746i \(-0.153495\pi\)
\(312\) −152.338 75.3469i −0.488261 0.241496i
\(313\) 86.2308 0.275498 0.137749 0.990467i \(-0.456013\pi\)
0.137749 + 0.990467i \(0.456013\pi\)
\(314\) 42.0603i 0.133950i
\(315\) −503.158 + 384.214i −1.59733 + 1.21973i
\(316\) 121.824 0.385520
\(317\) 382.059i 1.20523i 0.798031 + 0.602617i \(0.205875\pi\)
−0.798031 + 0.602617i \(0.794125\pi\)
\(318\) −0.0118542 + 0.0239669i −3.72772e−5 + 7.53676e-5i
\(319\) 86.1268 0.269990
\(320\) 332.516i 1.03911i
\(321\) 139.297 + 68.8972i 0.433949 + 0.214633i
\(322\) 182.608 0.567104
\(323\) 501.228i 1.55179i
\(324\) −80.5571 + 295.096i −0.248633 + 0.910789i
\(325\) −513.926 −1.58131
\(326\) 91.2237i 0.279827i
\(327\) −39.5795 + 80.0225i −0.121038 + 0.244717i
\(328\) 105.729 0.322346
\(329\) 342.016i 1.03956i
\(330\) −20.0574 9.92049i −0.0607800 0.0300621i
\(331\) 71.0716 0.214718 0.107359 0.994220i \(-0.465761\pi\)
0.107359 + 0.994220i \(0.465761\pi\)
\(332\) 71.7729i 0.216183i
\(333\) −344.410 451.032i −1.03426 1.35445i
\(334\) −62.3252 −0.186603
\(335\) 198.214i 0.591684i
\(336\) 163.715 331.002i 0.487248 0.985126i
\(337\) −374.174 −1.11031 −0.555155 0.831747i \(-0.687341\pi\)
−0.555155 + 0.831747i \(0.687341\pi\)
\(338\) 32.3446i 0.0956940i
\(339\) −308.555 152.613i −0.910191 0.450185i
\(340\) 451.957 1.32928
\(341\) 14.2770i 0.0418681i
\(342\) −108.199 + 82.6212i −0.316371 + 0.241582i
\(343\) 121.617 0.354567
\(344\) 220.346i 0.640540i
\(345\) 426.148 861.593i 1.23521 2.49737i
\(346\) 55.3209 0.159887
\(347\) 363.525i 1.04762i 0.851834 + 0.523812i \(0.175491\pi\)
−0.851834 + 0.523812i \(0.824509\pi\)
\(348\) −423.506 209.468i −1.21697 0.601920i
\(349\) −277.377 −0.794776 −0.397388 0.917651i \(-0.630083\pi\)
−0.397388 + 0.917651i \(0.630083\pi\)
\(350\) 145.212i 0.414892i
\(351\) 408.310 79.7246i 1.16328 0.227136i
\(352\) 43.4249 0.123366
\(353\) 453.778i 1.28549i 0.766080 + 0.642745i \(0.222205\pi\)
−0.766080 + 0.642745i \(0.777795\pi\)
\(354\) −4.83013 + 9.76562i −0.0136444 + 0.0275865i
\(355\) −309.825 −0.872747
\(356\) 293.624i 0.824787i
\(357\) −387.932 191.873i −1.08664 0.537459i
\(358\) −7.23218 −0.0202016
\(359\) 288.922i 0.804798i −0.915464 0.402399i \(-0.868177\pi\)
0.915464 0.402399i \(-0.131823\pi\)
\(360\) 153.409 + 200.900i 0.426135 + 0.558057i
\(361\) 662.574 1.83539
\(362\) 160.367i 0.443003i
\(363\) −155.260 + 313.907i −0.427714 + 0.864758i
\(364\) −535.816 −1.47202
\(365\) 322.742i 0.884226i
\(366\) 27.9479 + 13.8232i 0.0763604 + 0.0377682i
\(367\) 89.6102 0.244169 0.122085 0.992520i \(-0.461042\pi\)
0.122085 + 0.992520i \(0.461042\pi\)
\(368\) 560.683i 1.52360i
\(369\) −205.698 + 157.072i −0.557446 + 0.425669i
\(370\) −227.734 −0.615496
\(371\) 0.173587i 0.000467890i
\(372\) 34.7230 70.2035i 0.0933414 0.188719i
\(373\) 106.852 0.286466 0.143233 0.989689i \(-0.454250\pi\)
0.143233 + 0.989689i \(0.454250\pi\)
\(374\) 15.2973i 0.0409018i
\(375\) 171.608 + 84.8783i 0.457622 + 0.226342i
\(376\) −136.560 −0.363191
\(377\) 642.576i 1.70445i
\(378\) −22.5265 115.370i −0.0595940 0.305211i
\(379\) 72.5836 0.191513 0.0957567 0.995405i \(-0.469473\pi\)
0.0957567 + 0.995405i \(0.469473\pi\)
\(380\) 922.956i 2.42883i
\(381\) 93.7715 189.589i 0.246119 0.497608i
\(382\) 99.6053 0.260747
\(383\) 560.752i 1.46411i −0.681248 0.732053i \(-0.738563\pi\)
0.681248 0.732053i \(-0.261437\pi\)
\(384\) −281.511 139.237i −0.733102 0.362596i
\(385\) −145.271 −0.377328
\(386\) 60.2130i 0.155992i
\(387\) −327.346 428.685i −0.845855 1.10771i
\(388\) 464.854 1.19808
\(389\) 258.485i 0.664487i −0.943194 0.332244i \(-0.892194\pi\)
0.943194 0.332244i \(-0.107806\pi\)
\(390\) 74.0149 149.644i 0.189782 0.383704i
\(391\) 657.115 1.68060
\(392\) 131.598i 0.335710i
\(393\) 456.144 + 225.611i 1.16067 + 0.574074i
\(394\) −72.7319 −0.184599
\(395\) 246.425i 0.623860i
\(396\) −55.7878 + 42.5999i −0.140878 + 0.107575i
\(397\) −181.745 −0.457796 −0.228898 0.973450i \(-0.573512\pi\)
−0.228898 + 0.973450i \(0.573512\pi\)
\(398\) 66.0402i 0.165930i
\(399\) −391.830 + 792.208i −0.982031 + 1.98548i
\(400\) −445.863 −1.11466
\(401\) 401.247i 1.00061i −0.865848 0.500307i \(-0.833220\pi\)
0.865848 0.500307i \(-0.166780\pi\)
\(402\) −32.9893 16.3167i −0.0820628 0.0405887i
\(403\) −106.518 −0.264313
\(404\) 279.451i 0.691709i
\(405\) −596.916 162.950i −1.47387 0.402346i
\(406\) 181.563 0.447199
\(407\) 130.221i 0.319954i
\(408\) −76.6109 + 154.893i −0.187772 + 0.379640i
\(409\) 399.897 0.977744 0.488872 0.872356i \(-0.337409\pi\)
0.488872 + 0.872356i \(0.337409\pi\)
\(410\) 103.860i 0.253318i
\(411\) 248.741 + 123.028i 0.605208 + 0.299339i
\(412\) 354.105 0.859479
\(413\) 70.7303i 0.171260i
\(414\) 108.317 + 141.850i 0.261636 + 0.342633i
\(415\) 145.181 0.349834
\(416\) 323.985i 0.778809i
\(417\) 176.449 356.747i 0.423138 0.855508i
\(418\) −31.2391 −0.0747346
\(419\) 355.555i 0.848579i 0.905527 + 0.424290i \(0.139476\pi\)
−0.905527 + 0.424290i \(0.860524\pi\)
\(420\) 714.333 + 353.313i 1.70079 + 0.841221i
\(421\) −123.497 −0.293343 −0.146671 0.989185i \(-0.546856\pi\)
−0.146671 + 0.989185i \(0.546856\pi\)
\(422\) 165.519i 0.392226i
\(423\) 265.679 202.874i 0.628082 0.479606i
\(424\) 0.0693097 0.000163466
\(425\) 522.547i 1.22952i
\(426\) 25.5043 51.5650i 0.0598693 0.121045i
\(427\) 202.420 0.474053
\(428\) 195.627i 0.457072i
\(429\) 85.5689 + 42.3228i 0.199461 + 0.0986546i
\(430\) −216.450 −0.503373
\(431\) 275.384i 0.638942i 0.947596 + 0.319471i \(0.103505\pi\)
−0.947596 + 0.319471i \(0.896495\pi\)
\(432\) 354.234 69.1661i 0.819987 0.160107i
\(433\) 172.056 0.397357 0.198679 0.980065i \(-0.436335\pi\)
0.198679 + 0.980065i \(0.436335\pi\)
\(434\) 30.0972i 0.0693483i
\(435\) 423.710 856.663i 0.974046 1.96934i
\(436\) 112.382 0.257757
\(437\) 1341.92i 3.07075i
\(438\) 53.7148 + 26.5676i 0.122637 + 0.0606567i
\(439\) −69.7491 −0.158882 −0.0794409 0.996840i \(-0.525313\pi\)
−0.0794409 + 0.996840i \(0.525313\pi\)
\(440\) 58.0038i 0.131827i
\(441\) −195.503 256.026i −0.443317 0.580558i
\(442\) 114.130 0.258213
\(443\) 524.445i 1.18385i −0.805994 0.591924i \(-0.798369\pi\)
0.805994 0.591924i \(-0.201631\pi\)
\(444\) −316.710 + 640.329i −0.713311 + 1.44218i
\(445\) 593.940 1.33470
\(446\) 90.1529i 0.202136i
\(447\) −104.679 51.7746i −0.234180 0.115827i
\(448\) −400.826 −0.894700
\(449\) 36.1045i 0.0804109i 0.999191 + 0.0402055i \(0.0128012\pi\)
−0.999191 + 0.0402055i \(0.987199\pi\)
\(450\) −112.801 + 86.1353i −0.250669 + 0.191412i
\(451\) −59.3888 −0.131683
\(452\) 433.329i 0.958692i
\(453\) 248.907 503.243i 0.549463 1.11091i
\(454\) 120.746 0.265960
\(455\) 1083.84i 2.38207i
\(456\) 316.312 + 156.450i 0.693667 + 0.343091i
\(457\) −163.409 −0.357569 −0.178784 0.983888i \(-0.557216\pi\)
−0.178784 + 0.983888i \(0.557216\pi\)
\(458\) 27.3861i 0.0597949i
\(459\) −81.0620 415.159i −0.176606 0.904486i
\(460\) −1210.01 −2.63045
\(461\) 297.609i 0.645572i 0.946472 + 0.322786i \(0.104619\pi\)
−0.946472 + 0.322786i \(0.895381\pi\)
\(462\) 11.9585 24.1779i 0.0258842 0.0523330i
\(463\) −442.567 −0.955868 −0.477934 0.878396i \(-0.658614\pi\)
−0.477934 + 0.878396i \(0.658614\pi\)
\(464\) 557.475i 1.20145i
\(465\) 142.007 + 70.2373i 0.305391 + 0.151048i
\(466\) 25.0676 0.0537932
\(467\) 244.305i 0.523136i 0.965185 + 0.261568i \(0.0842396\pi\)
−0.965185 + 0.261568i \(0.915760\pi\)
\(468\) −317.829 416.222i −0.679123 0.889364i
\(469\) −238.934 −0.509454
\(470\) 134.146i 0.285416i
\(471\) 118.320 239.221i 0.251210 0.507901i
\(472\) 28.2411 0.0598329
\(473\) 123.769i 0.261669i
\(474\) −41.0131 20.2853i −0.0865255 0.0427959i
\(475\) 1067.11 2.24655
\(476\) 544.804i 1.14455i
\(477\) −0.134843 + 0.102967i −0.000282689 + 0.000215863i
\(478\) 148.240 0.310126
\(479\) 639.138i 1.33432i 0.744915 + 0.667159i \(0.232490\pi\)
−0.744915 + 0.667159i \(0.767510\pi\)
\(480\) 213.633 431.927i 0.445069 0.899847i
\(481\) 971.557 2.01987
\(482\) 89.4436i 0.185568i
\(483\) 1038.59 + 513.694i 2.15030 + 1.06355i
\(484\) 440.845 0.910837
\(485\) 940.301i 1.93876i
\(486\) 76.2573 85.9325i 0.156908 0.176816i
\(487\) −485.955 −0.997855 −0.498927 0.866644i \(-0.666273\pi\)
−0.498927 + 0.866644i \(0.666273\pi\)
\(488\) 80.8222i 0.165619i
\(489\) 256.622 518.841i 0.524789 1.06103i
\(490\) −129.272 −0.263820
\(491\) 377.155i 0.768137i 0.923305 + 0.384068i \(0.125477\pi\)
−0.923305 + 0.384068i \(0.874523\pi\)
\(492\) 292.029 + 144.439i 0.593555 + 0.293575i
\(493\) 653.355 1.32526
\(494\) 233.069i 0.471799i
\(495\) −86.1705 112.847i −0.174082 0.227974i
\(496\) −92.4112 −0.186313
\(497\) 373.474i 0.751457i
\(498\) −11.9511 + 24.1629i −0.0239982 + 0.0485199i
\(499\) −622.890 −1.24828 −0.624138 0.781314i \(-0.714550\pi\)
−0.624138 + 0.781314i \(0.714550\pi\)
\(500\) 241.003i 0.482007i
\(501\) −354.479 175.327i −0.707543 0.349955i
\(502\) −0.0447178 −8.90793e−5
\(503\) 941.653i 1.87207i −0.351903 0.936036i \(-0.614465\pi\)
0.351903 0.936036i \(-0.385535\pi\)
\(504\) −242.172 + 184.924i −0.480500 + 0.366913i
\(505\) 565.269 1.11935
\(506\) 40.9548i 0.0809383i
\(507\) −90.9886 + 183.962i −0.179465 + 0.362844i
\(508\) −266.255 −0.524123
\(509\) 646.240i 1.26963i 0.772666 + 0.634813i \(0.218923\pi\)
−0.772666 + 0.634813i \(0.781077\pi\)
\(510\) −152.155 75.2565i −0.298343 0.147562i
\(511\) 389.045 0.761340
\(512\) 477.670i 0.932948i
\(513\) −847.810 + 165.539i −1.65265 + 0.322689i
\(514\) −0.748637 −0.00145649
\(515\) 716.280i 1.39084i
\(516\) −301.018 + 608.603i −0.583369 + 1.17946i
\(517\) 76.7065 0.148368
\(518\) 274.518i 0.529957i
\(519\) 314.642 + 155.623i 0.606246 + 0.299852i
\(520\) −432.755 −0.832222
\(521\) 941.837i 1.80775i 0.427799 + 0.903874i \(0.359289\pi\)
−0.427799 + 0.903874i \(0.640711\pi\)
\(522\) 107.697 + 141.038i 0.206317 + 0.270188i
\(523\) −384.235 −0.734674 −0.367337 0.930088i \(-0.619730\pi\)
−0.367337 + 0.930088i \(0.619730\pi\)
\(524\) 640.600i 1.22252i
\(525\) −408.496 + 825.904i −0.778088 + 1.57315i
\(526\) −158.729 −0.301767
\(527\) 108.305i 0.205512i
\(528\) 74.2364 + 36.7177i 0.140599 + 0.0695411i
\(529\) −1230.27 −2.32565
\(530\) 0.0680844i 0.000128461i
\(531\) −54.9434 + 41.9550i −0.103472 + 0.0790114i
\(532\) 1112.56 2.09128
\(533\) 443.089i 0.831311i
\(534\) −48.8922 + 98.8509i −0.0915583 + 0.185114i
\(535\) 395.712 0.739648
\(536\) 95.4013i 0.177988i
\(537\) −41.1336 20.3449i −0.0765988 0.0378862i
\(538\) 99.9222 0.185729
\(539\) 73.9196i 0.137142i
\(540\) 149.267 + 764.470i 0.276420 + 1.41568i
\(541\) −498.752 −0.921908 −0.460954 0.887424i \(-0.652493\pi\)
−0.460954 + 0.887424i \(0.652493\pi\)
\(542\) 33.5807i 0.0619569i
\(543\) −451.129 + 912.099i −0.830808 + 1.67974i
\(544\) 329.420 0.605551
\(545\) 227.325i 0.417110i
\(546\) 180.386 + 89.2201i 0.330378 + 0.163407i
\(547\) 38.8715 0.0710631 0.0355315 0.999369i \(-0.488688\pi\)
0.0355315 + 0.999369i \(0.488688\pi\)
\(548\) 349.327i 0.637457i
\(549\) 120.070 + 157.240i 0.218706 + 0.286413i
\(550\) −32.5678 −0.0592141
\(551\) 1334.24i 2.42149i
\(552\) 205.107 414.689i 0.371571 0.751248i
\(553\) −297.049 −0.537159
\(554\) 3.54810i 0.00640451i
\(555\) −1295.25 640.638i −2.33379 1.15430i
\(556\) −501.008 −0.901094
\(557\) 621.587i 1.11596i −0.829856 0.557978i \(-0.811577\pi\)
0.829856 0.557978i \(-0.188423\pi\)
\(558\) −23.3795 + 17.8527i −0.0418988 + 0.0319941i
\(559\) 923.420 1.65191
\(560\) 940.300i 1.67911i
\(561\) 43.0328 87.0043i 0.0767073 0.155088i
\(562\) 167.635 0.298283
\(563\) 572.900i 1.01758i −0.860889 0.508792i \(-0.830092\pi\)
0.860889 0.508792i \(-0.169908\pi\)
\(564\) −377.184 186.557i −0.668766 0.330775i
\(565\) −876.532 −1.55138
\(566\) 3.63656i 0.00642503i
\(567\) 196.425 719.543i 0.346429 1.26904i
\(568\) −149.120 −0.262536
\(569\) 880.655i 1.54772i 0.633354 + 0.773862i \(0.281678\pi\)
−0.633354 + 0.773862i \(0.718322\pi\)
\(570\) −153.684 + 310.720i −0.269621 + 0.545123i
\(571\) 961.034 1.68307 0.841535 0.540202i \(-0.181652\pi\)
0.841535 + 0.540202i \(0.181652\pi\)
\(572\) 120.171i 0.210090i
\(573\) 566.512 + 280.200i 0.988677 + 0.489005i
\(574\) −125.197 −0.218113
\(575\) 1398.99i 2.43303i
\(576\) −237.758 311.362i −0.412774 0.540559i
\(577\) −188.373 −0.326469 −0.163234 0.986587i \(-0.552193\pi\)
−0.163234 + 0.986587i \(0.552193\pi\)
\(578\) 20.5934i 0.0356287i
\(579\) −169.385 + 342.466i −0.292548 + 0.591478i
\(580\) −1203.08 −2.07428
\(581\) 175.006i 0.301216i
\(582\) −156.497 77.4040i −0.268894 0.132997i
\(583\) −0.0389317 −6.67781e−5
\(584\) 155.337i 0.265989i
\(585\) 841.930 642.902i 1.43920 1.09898i
\(586\) 110.732 0.188962
\(587\) 523.610i 0.892010i 0.895030 + 0.446005i \(0.147154\pi\)
−0.895030 + 0.446005i \(0.852846\pi\)
\(588\) −179.779 + 363.480i −0.305747 + 0.618163i
\(589\) 221.173 0.375506
\(590\) 27.7418i 0.0470201i
\(591\) −413.668 204.602i −0.699946 0.346197i
\(592\) 842.886 1.42379
\(593\) 238.602i 0.402364i −0.979554 0.201182i \(-0.935522\pi\)
0.979554 0.201182i \(-0.0644783\pi\)
\(594\) 25.8748 5.05220i 0.0435603 0.00850538i
\(595\) −1102.02 −1.85214
\(596\) 147.009i 0.246659i
\(597\) −185.778 + 375.608i −0.311185 + 0.629159i
\(598\) −305.556 −0.510963
\(599\) 275.680i 0.460234i −0.973163 0.230117i \(-0.926089\pi\)
0.973163 0.230117i \(-0.0739110\pi\)
\(600\) 329.766 + 163.104i 0.549610 + 0.271840i
\(601\) −116.291 −0.193495 −0.0967477 0.995309i \(-0.530844\pi\)
−0.0967477 + 0.995309i \(0.530844\pi\)
\(602\) 260.916i 0.433416i
\(603\) −141.728 185.604i −0.235039 0.307802i
\(604\) −706.746 −1.17011
\(605\) 891.737i 1.47394i
\(606\) −46.5321 + 94.0792i −0.0767856 + 0.155246i
\(607\) 174.518 0.287508 0.143754 0.989613i \(-0.454083\pi\)
0.143754 + 0.989613i \(0.454083\pi\)
\(608\) 672.719i 1.10645i
\(609\) 1032.65 + 510.754i 1.69565 + 0.838677i
\(610\) 79.3934 0.130153
\(611\) 572.292i 0.936649i
\(612\) −423.205 + 323.161i −0.691511 + 0.528041i
\(613\) 320.145 0.522259 0.261130 0.965304i \(-0.415905\pi\)
0.261130 + 0.965304i \(0.415905\pi\)
\(614\) 153.088i 0.249329i
\(615\) −292.169 + 590.713i −0.475072 + 0.960508i
\(616\) −69.9197 −0.113506
\(617\) 881.663i 1.42895i −0.699661 0.714475i \(-0.746665\pi\)
0.699661 0.714475i \(-0.253335\pi\)
\(618\) −119.212 58.9630i −0.192900 0.0954094i
\(619\) 510.282 0.824366 0.412183 0.911101i \(-0.364766\pi\)
0.412183 + 0.911101i \(0.364766\pi\)
\(620\) 199.432i 0.321664i
\(621\) 217.024 + 1111.49i 0.349475 + 1.78984i
\(622\) 136.378 0.219257
\(623\) 715.955i 1.14921i
\(624\) −273.944 + 553.863i −0.439012 + 0.887601i
\(625\) −346.355 −0.554168
\(626\) 40.7696i 0.0651271i
\(627\) −177.674 87.8787i −0.283372 0.140157i
\(628\) −335.958 −0.534964
\(629\) 987.855i 1.57052i
\(630\) −181.655 237.891i −0.288341 0.377605i
\(631\) 167.330 0.265182 0.132591 0.991171i \(-0.457670\pi\)
0.132591 + 0.991171i \(0.457670\pi\)
\(632\) 118.605i 0.187667i
\(633\) −465.623 + 941.403i −0.735581 + 1.48721i
\(634\) −180.636 −0.284915
\(635\) 538.577i 0.848153i
\(636\) 0.191436 + 0.0946853i 0.000301000 + 0.000148876i
\(637\) 551.500 0.865777
\(638\) 40.7204i 0.0638251i
\(639\) 290.115 221.533i 0.454014 0.346688i
\(640\) −799.707 −1.24954
\(641\) 486.167i 0.758452i 0.925304 + 0.379226i \(0.123810\pi\)
−0.925304 + 0.379226i \(0.876190\pi\)
\(642\) −32.5743 + 65.8593i −0.0507388 + 0.102585i
\(643\) 657.600 1.02271 0.511353 0.859371i \(-0.329144\pi\)
0.511353 + 0.859371i \(0.329144\pi\)
\(644\) 1458.58i 2.26488i
\(645\) −1231.08 608.896i −1.90864 0.944026i
\(646\) −236.978 −0.366840
\(647\) 1134.78i 1.75392i 0.480568 + 0.876958i \(0.340431\pi\)
−0.480568 + 0.876958i \(0.659569\pi\)
\(648\) −287.298 78.4285i −0.443362 0.121032i
\(649\) −15.8632 −0.0244425
\(650\) 242.982i 0.373818i
\(651\) −84.6664 + 171.180i −0.130056 + 0.262949i
\(652\) −728.651 −1.11756
\(653\) 572.427i 0.876611i 0.898826 + 0.438306i \(0.144421\pi\)
−0.898826 + 0.438306i \(0.855579\pi\)
\(654\) −37.8343 18.7130i −0.0578506 0.0286132i
\(655\) 1295.80 1.97832
\(656\) 384.407i 0.585986i
\(657\) 230.769 + 302.211i 0.351247 + 0.459986i
\(658\) 161.704 0.245750
\(659\) 321.495i 0.487853i −0.969794 0.243926i \(-0.921565\pi\)
0.969794 0.243926i \(-0.0784355\pi\)
\(660\) −79.2401 + 160.209i −0.120061 + 0.242741i
\(661\) −649.633 −0.982803 −0.491402 0.870933i \(-0.663515\pi\)
−0.491402 + 0.870933i \(0.663515\pi\)
\(662\) 33.6023i 0.0507588i
\(663\) 649.123 + 321.059i 0.979069 + 0.484252i
\(664\) 69.8764 0.105236
\(665\) 2250.48i 3.38418i
\(666\) 213.246 162.836i 0.320189 0.244498i
\(667\) −1749.20 −2.62249
\(668\) 497.824i 0.745246i
\(669\) 253.609 512.751i 0.379087 0.766444i
\(670\) −93.7148 −0.139873
\(671\) 45.3983i 0.0676577i
\(672\) 520.659 + 257.521i 0.774790 + 0.383215i
\(673\) 1232.00 1.83061 0.915303 0.402766i \(-0.131951\pi\)
0.915303 + 0.402766i \(0.131951\pi\)
\(674\) 176.908i 0.262475i
\(675\) −883.871 + 172.580i −1.30944 + 0.255675i
\(676\) 258.353 0.382179
\(677\) 216.524i 0.319829i 0.987131 + 0.159915i \(0.0511219\pi\)
−0.987131 + 0.159915i \(0.948878\pi\)
\(678\) 72.1547 145.883i 0.106423 0.215167i
\(679\) −1133.47 −1.66932
\(680\) 440.015i 0.647080i
\(681\) 686.751 + 339.670i 1.00844 + 0.498782i
\(682\) −6.75012 −0.00989753
\(683\) 1.94504i 0.00284779i −0.999999 0.00142390i \(-0.999547\pi\)
0.999999 0.00142390i \(-0.000453240\pi\)
\(684\) 659.938 + 864.240i 0.964822 + 1.26351i
\(685\) 706.614 1.03155
\(686\) 57.4998i 0.0838189i
\(687\) 77.0398 155.760i 0.112139 0.226725i
\(688\) 801.125 1.16443
\(689\) 0.290462i 0.000421570i
\(690\) 407.358 + 201.481i 0.590373 + 0.292002i
\(691\) 632.425 0.915232 0.457616 0.889150i \(-0.348704\pi\)
0.457616 + 0.889150i \(0.348704\pi\)
\(692\) 441.877i 0.638551i
\(693\) 136.030 103.873i 0.196291 0.149889i
\(694\) −171.873 −0.247656
\(695\) 1013.43i 1.45818i
\(696\) 203.933 412.316i 0.293008 0.592408i
\(697\) −450.522 −0.646372
\(698\) 131.143i 0.187883i
\(699\) 142.574 + 70.5177i 0.203968 + 0.100884i
\(700\) 1159.88 1.65698
\(701\) 324.722i 0.463226i 0.972808 + 0.231613i \(0.0744004\pi\)
−0.972808 + 0.231613i \(0.925600\pi\)
\(702\) 37.6935 + 193.047i 0.0536944 + 0.274996i
\(703\) −2017.33 −2.86960
\(704\) 89.8961i 0.127693i
\(705\) 377.365 762.963i 0.535270 1.08222i
\(706\) −214.544 −0.303887
\(707\) 681.395i 0.963784i
\(708\) 78.0031 + 38.5807i 0.110174 + 0.0544925i
\(709\) −705.852 −0.995560 −0.497780 0.867303i \(-0.665851\pi\)
−0.497780 + 0.867303i \(0.665851\pi\)
\(710\) 146.484i 0.206316i
\(711\) −176.200 230.748i −0.247820 0.324540i
\(712\) 285.866 0.401497
\(713\) 289.961i 0.406677i
\(714\) 90.7167 183.412i 0.127054 0.256880i
\(715\) 243.081 0.339974
\(716\) 57.7672i 0.0806804i
\(717\) 843.126 + 417.015i 1.17591 + 0.581610i
\(718\) 136.601 0.190252
\(719\) 221.233i 0.307695i 0.988095 + 0.153848i \(0.0491665\pi\)
−0.988095 + 0.153848i \(0.950834\pi\)
\(720\) 730.427 557.757i 1.01448 0.774663i
\(721\) −863.428 −1.19754
\(722\) 313.262i 0.433881i
\(723\) 251.614 508.717i 0.348014 0.703620i
\(724\) 1280.94 1.76925
\(725\) 1390.99i 1.91860i
\(726\) −148.414 73.4063i −0.204427 0.101111i
\(727\) 800.622 1.10127 0.550634 0.834747i \(-0.314386\pi\)
0.550634 + 0.834747i \(0.314386\pi\)
\(728\) 521.658i 0.716563i
\(729\) 675.456 274.227i 0.926551 0.376169i
\(730\) 152.591 0.209029
\(731\) 938.911i 1.28442i
\(732\) 110.413 223.234i 0.150837 0.304965i
\(733\) 632.139 0.862400 0.431200 0.902256i \(-0.358090\pi\)
0.431200 + 0.902256i \(0.358090\pi\)
\(734\) 42.3673i 0.0577211i
\(735\) −735.243 363.655i −1.00033 0.494769i
\(736\) −881.942 −1.19829
\(737\) 53.5875i 0.0727103i
\(738\) −74.2628 97.2530i −0.100627 0.131779i
\(739\) −431.988 −0.584558 −0.292279 0.956333i \(-0.594414\pi\)
−0.292279 + 0.956333i \(0.594414\pi\)
\(740\) 1819.03i 2.45814i
\(741\) 655.646 1325.59i 0.884812 1.78893i
\(742\) −0.0820712 −0.000110608
\(743\) 1135.31i 1.52801i −0.645213 0.764003i \(-0.723231\pi\)
0.645213 0.764003i \(-0.276769\pi\)
\(744\) 68.3485 + 33.8055i 0.0918663 + 0.0454375i
\(745\) −297.368 −0.399151
\(746\) 50.5192i 0.0677200i
\(747\) −135.945 + 103.809i −0.181988 + 0.138967i
\(748\) −122.187 −0.163352
\(749\) 477.004i 0.636855i
\(750\) −40.1301 + 81.1356i −0.0535068 + 0.108181i
\(751\) 95.9451 0.127756 0.0638782 0.997958i \(-0.479653\pi\)
0.0638782 + 0.997958i \(0.479653\pi\)
\(752\) 496.499i 0.660239i
\(753\) −0.254336 0.125796i −0.000337763 0.000167059i
\(754\) −303.807 −0.402927
\(755\) 1429.60i 1.89351i
\(756\) −921.518 + 179.931i −1.21894 + 0.238004i
\(757\) 708.368 0.935757 0.467879 0.883793i \(-0.345018\pi\)
0.467879 + 0.883793i \(0.345018\pi\)
\(758\) 34.3172i 0.0452734i
\(759\) −115.210 + 232.933i −0.151792 + 0.306895i
\(760\) 898.569 1.18233
\(761\) 872.545i 1.14658i 0.819353 + 0.573289i \(0.194333\pi\)
−0.819353 + 0.573289i \(0.805667\pi\)
\(762\) 89.6367 + 44.3348i 0.117633 + 0.0581821i
\(763\) −274.025 −0.359142
\(764\) 795.599i 1.04136i
\(765\) −653.687 856.053i −0.854492 1.11902i
\(766\) 265.121 0.346111
\(767\) 118.352i 0.154305i
\(768\) −165.746 + 335.108i −0.215816 + 0.436339i
\(769\) −945.954 −1.23011 −0.615055 0.788484i \(-0.710866\pi\)
−0.615055 + 0.788484i \(0.710866\pi\)
\(770\) 68.6837i 0.0891996i
\(771\) −4.25793 2.10599i −0.00552260 0.00273151i
\(772\) 480.952 0.622995
\(773\) 1230.18i 1.59144i 0.605665 + 0.795720i \(0.292907\pi\)
−0.605665 + 0.795720i \(0.707093\pi\)
\(774\) 202.680 154.768i 0.261861 0.199958i
\(775\) 230.581 0.297523
\(776\) 452.571i 0.583210i
\(777\) 772.246 1561.34i 0.993882 2.00945i
\(778\) 122.211 0.157083
\(779\) 920.025i 1.18103i
\(780\) −1195.29 591.195i −1.53242 0.757943i
\(781\) 83.7618 0.107249
\(782\) 310.681i 0.397291i
\(783\) 215.782 + 1105.13i 0.275584 + 1.41140i
\(784\) 478.461 0.610281
\(785\) 679.571i 0.865696i
\(786\)