Properties

Label 177.3.b.a.119.10
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 119.10
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.29

$q$-expansion

\(f(q)\) \(=\) \(q-2.12813i q^{2} +(-2.98150 + 0.332673i) q^{3} -0.528939 q^{4} +5.15735i q^{5} +(0.707972 + 6.34502i) q^{6} +2.69104 q^{7} -7.38687i q^{8} +(8.77866 - 1.98373i) q^{9} +O(q^{10})\) \(q-2.12813i q^{2} +(-2.98150 + 0.332673i) q^{3} -0.528939 q^{4} +5.15735i q^{5} +(0.707972 + 6.34502i) q^{6} +2.69104 q^{7} -7.38687i q^{8} +(8.77866 - 1.98373i) q^{9} +10.9755 q^{10} -15.4011i q^{11} +(1.57703 - 0.175964i) q^{12} +18.6528 q^{13} -5.72689i q^{14} +(-1.71571 - 15.3766i) q^{15} -17.8360 q^{16} +4.88346i q^{17} +(-4.22163 - 18.6821i) q^{18} +3.41065 q^{19} -2.72792i q^{20} +(-8.02334 + 0.895238i) q^{21} -32.7756 q^{22} -15.9679i q^{23} +(2.45741 + 22.0239i) q^{24} -1.59821 q^{25} -39.6955i q^{26} +(-25.5136 + 8.83491i) q^{27} -1.42340 q^{28} -24.8107i q^{29} +(-32.7234 + 3.65126i) q^{30} +28.0319 q^{31} +8.40981i q^{32} +(5.12354 + 45.9184i) q^{33} +10.3926 q^{34} +13.8786i q^{35} +(-4.64338 + 1.04927i) q^{36} +60.2239 q^{37} -7.25831i q^{38} +(-55.6131 + 6.20527i) q^{39} +38.0966 q^{40} +37.6168i q^{41} +(1.90518 + 17.0747i) q^{42} -15.8209 q^{43} +8.14626i q^{44} +(10.2308 + 45.2746i) q^{45} -33.9818 q^{46} -13.1463i q^{47} +(53.1779 - 5.93355i) q^{48} -41.7583 q^{49} +3.40120i q^{50} +(-1.62460 - 14.5600i) q^{51} -9.86617 q^{52} +35.0364i q^{53} +(18.8018 + 54.2963i) q^{54} +79.4290 q^{55} -19.8784i q^{56} +(-10.1688 + 1.13463i) q^{57} -52.8004 q^{58} +7.68115i q^{59} +(0.907507 + 8.13330i) q^{60} -83.7144 q^{61} -59.6555i q^{62} +(23.6238 - 5.33830i) q^{63} -53.4467 q^{64} +96.1987i q^{65} +(97.7204 - 10.9036i) q^{66} +72.8285 q^{67} -2.58305i q^{68} +(5.31210 + 47.6083i) q^{69} +29.5356 q^{70} +27.7175i q^{71} +(-14.6535 - 64.8468i) q^{72} +54.4224 q^{73} -128.164i q^{74} +(4.76507 - 0.531683i) q^{75} -1.80403 q^{76} -41.4451i q^{77} +(13.2056 + 118.352i) q^{78} -123.594 q^{79} -91.9863i q^{80} +(73.1296 - 34.8290i) q^{81} +80.0535 q^{82} +143.471i q^{83} +(4.24386 - 0.473527i) q^{84} -25.1857 q^{85} +33.6690i q^{86} +(8.25385 + 73.9730i) q^{87} -113.766 q^{88} -21.8428i q^{89} +(96.3502 - 21.7724i) q^{90} +50.1954 q^{91} +8.44606i q^{92} +(-83.5770 + 9.32545i) q^{93} -27.9771 q^{94} +17.5899i q^{95} +(-2.79772 - 25.0738i) q^{96} -98.9417 q^{97} +88.8671i q^{98} +(-30.5517 - 135.201i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.12813i 1.06407i −0.846724 0.532033i \(-0.821428\pi\)
0.846724 0.532033i \(-0.178572\pi\)
\(3\) −2.98150 + 0.332673i −0.993833 + 0.110891i
\(4\) −0.528939 −0.132235
\(5\) 5.15735i 1.03147i 0.856748 + 0.515735i \(0.172481\pi\)
−0.856748 + 0.515735i \(0.827519\pi\)
\(6\) 0.707972 + 6.34502i 0.117995 + 1.05750i
\(7\) 2.69104 0.384435 0.192217 0.981352i \(-0.438432\pi\)
0.192217 + 0.981352i \(0.438432\pi\)
\(8\) 7.38687i 0.923359i
\(9\) 8.77866 1.98373i 0.975406 0.220414i
\(10\) 10.9755 1.09755
\(11\) 15.4011i 1.40010i −0.714092 0.700051i \(-0.753160\pi\)
0.714092 0.700051i \(-0.246840\pi\)
\(12\) 1.57703 0.175964i 0.131419 0.0146637i
\(13\) 18.6528 1.43483 0.717414 0.696648i \(-0.245326\pi\)
0.717414 + 0.696648i \(0.245326\pi\)
\(14\) 5.72689i 0.409064i
\(15\) −1.71571 15.3766i −0.114381 1.02511i
\(16\) −17.8360 −1.11475
\(17\) 4.88346i 0.287262i 0.989631 + 0.143631i \(0.0458779\pi\)
−0.989631 + 0.143631i \(0.954122\pi\)
\(18\) −4.22163 18.6821i −0.234535 1.03790i
\(19\) 3.41065 0.179508 0.0897540 0.995964i \(-0.471392\pi\)
0.0897540 + 0.995964i \(0.471392\pi\)
\(20\) 2.72792i 0.136396i
\(21\) −8.02334 + 0.895238i −0.382064 + 0.0426304i
\(22\) −32.7756 −1.48980
\(23\) 15.9679i 0.694257i −0.937818 0.347129i \(-0.887157\pi\)
0.937818 0.347129i \(-0.112843\pi\)
\(24\) 2.45741 + 22.0239i 0.102392 + 0.917664i
\(25\) −1.59821 −0.0639285
\(26\) 39.6955i 1.52675i
\(27\) −25.5136 + 8.83491i −0.944949 + 0.327219i
\(28\) −1.42340 −0.0508357
\(29\) 24.8107i 0.855541i −0.903887 0.427770i \(-0.859299\pi\)
0.903887 0.427770i \(-0.140701\pi\)
\(30\) −32.7234 + 3.65126i −1.09078 + 0.121709i
\(31\) 28.0319 0.904254 0.452127 0.891954i \(-0.350665\pi\)
0.452127 + 0.891954i \(0.350665\pi\)
\(32\) 8.40981i 0.262807i
\(33\) 5.12354 + 45.9184i 0.155259 + 1.39147i
\(34\) 10.3926 0.305666
\(35\) 13.8786i 0.396533i
\(36\) −4.64338 + 1.04927i −0.128983 + 0.0291465i
\(37\) 60.2239 1.62767 0.813837 0.581093i \(-0.197375\pi\)
0.813837 + 0.581093i \(0.197375\pi\)
\(38\) 7.25831i 0.191008i
\(39\) −55.6131 + 6.20527i −1.42598 + 0.159110i
\(40\) 38.0966 0.952416
\(41\) 37.6168i 0.917483i 0.888570 + 0.458742i \(0.151700\pi\)
−0.888570 + 0.458742i \(0.848300\pi\)
\(42\) 1.90518 + 17.0747i 0.0453615 + 0.406541i
\(43\) −15.8209 −0.367928 −0.183964 0.982933i \(-0.558893\pi\)
−0.183964 + 0.982933i \(0.558893\pi\)
\(44\) 8.14626i 0.185142i
\(45\) 10.2308 + 45.2746i 0.227351 + 1.00610i
\(46\) −33.9818 −0.738735
\(47\) 13.1463i 0.279709i −0.990172 0.139854i \(-0.955337\pi\)
0.990172 0.139854i \(-0.0446634\pi\)
\(48\) 53.1779 5.93355i 1.10787 0.123616i
\(49\) −41.7583 −0.852210
\(50\) 3.40120i 0.0680241i
\(51\) −1.62460 14.5600i −0.0318548 0.285490i
\(52\) −9.86617 −0.189734
\(53\) 35.0364i 0.661065i 0.943795 + 0.330532i \(0.107228\pi\)
−0.943795 + 0.330532i \(0.892772\pi\)
\(54\) 18.8018 + 54.2963i 0.348182 + 1.00549i
\(55\) 79.4290 1.44416
\(56\) 19.8784i 0.354971i
\(57\) −10.1688 + 1.13463i −0.178401 + 0.0199058i
\(58\) −52.8004 −0.910351
\(59\) 7.68115i 0.130189i
\(60\) 0.907507 + 8.13330i 0.0151251 + 0.135555i
\(61\) −83.7144 −1.37237 −0.686183 0.727429i \(-0.740715\pi\)
−0.686183 + 0.727429i \(0.740715\pi\)
\(62\) 59.6555i 0.962185i
\(63\) 23.6238 5.33830i 0.374980 0.0847350i
\(64\) −53.4467 −0.835105
\(65\) 96.1987i 1.47998i
\(66\) 97.7204 10.9036i 1.48061 0.165206i
\(67\) 72.8285 1.08699 0.543497 0.839411i \(-0.317100\pi\)
0.543497 + 0.839411i \(0.317100\pi\)
\(68\) 2.58305i 0.0379861i
\(69\) 5.31210 + 47.6083i 0.0769869 + 0.689975i
\(70\) 29.5356 0.421937
\(71\) 27.7175i 0.390387i 0.980765 + 0.195193i \(0.0625334\pi\)
−0.980765 + 0.195193i \(0.937467\pi\)
\(72\) −14.6535 64.8468i −0.203522 0.900650i
\(73\) 54.4224 0.745513 0.372756 0.927929i \(-0.378413\pi\)
0.372756 + 0.927929i \(0.378413\pi\)
\(74\) 128.164i 1.73195i
\(75\) 4.76507 0.531683i 0.0635342 0.00708910i
\(76\) −1.80403 −0.0237372
\(77\) 41.4451i 0.538248i
\(78\) 13.2056 + 118.352i 0.169303 + 1.51733i
\(79\) −123.594 −1.56448 −0.782242 0.622975i \(-0.785924\pi\)
−0.782242 + 0.622975i \(0.785924\pi\)
\(80\) 91.9863i 1.14983i
\(81\) 73.1296 34.8290i 0.902835 0.429987i
\(82\) 80.0535 0.976262
\(83\) 143.471i 1.72857i 0.503003 + 0.864285i \(0.332228\pi\)
−0.503003 + 0.864285i \(0.667772\pi\)
\(84\) 4.24386 0.473527i 0.0505222 0.00563722i
\(85\) −25.1857 −0.296302
\(86\) 33.6690i 0.391500i
\(87\) 8.25385 + 73.9730i 0.0948718 + 0.850264i
\(88\) −113.766 −1.29280
\(89\) 21.8428i 0.245425i −0.992442 0.122713i \(-0.960841\pi\)
0.992442 0.122713i \(-0.0391593\pi\)
\(90\) 96.3502 21.7724i 1.07056 0.241916i
\(91\) 50.1954 0.551598
\(92\) 8.44606i 0.0918050i
\(93\) −83.5770 + 9.32545i −0.898677 + 0.100274i
\(94\) −27.9771 −0.297628
\(95\) 17.5899i 0.185157i
\(96\) −2.79772 25.0738i −0.0291429 0.261186i
\(97\) −98.9417 −1.02002 −0.510009 0.860169i \(-0.670358\pi\)
−0.510009 + 0.860169i \(0.670358\pi\)
\(98\) 88.8671i 0.906807i
\(99\) −30.5517 135.201i −0.308603 1.36567i
\(100\) 0.845357 0.00845357
\(101\) 11.1986i 0.110877i 0.998462 + 0.0554386i \(0.0176557\pi\)
−0.998462 + 0.0554386i \(0.982344\pi\)
\(102\) −30.9856 + 3.45735i −0.303780 + 0.0338956i
\(103\) −103.065 −1.00064 −0.500318 0.865842i \(-0.666783\pi\)
−0.500318 + 0.865842i \(0.666783\pi\)
\(104\) 137.785i 1.32486i
\(105\) −4.61705 41.3791i −0.0439719 0.394087i
\(106\) 74.5621 0.703416
\(107\) 159.235i 1.48818i −0.668081 0.744089i \(-0.732884\pi\)
0.668081 0.744089i \(-0.267116\pi\)
\(108\) 13.4952 4.67313i 0.124955 0.0432697i
\(109\) −106.870 −0.980461 −0.490230 0.871593i \(-0.663087\pi\)
−0.490230 + 0.871593i \(0.663087\pi\)
\(110\) 169.035i 1.53668i
\(111\) −179.558 + 20.0349i −1.61764 + 0.180495i
\(112\) −47.9974 −0.428548
\(113\) 163.994i 1.45127i 0.688079 + 0.725636i \(0.258454\pi\)
−0.688079 + 0.725636i \(0.741546\pi\)
\(114\) 2.41465 + 21.6406i 0.0211811 + 0.189830i
\(115\) 82.3520 0.716105
\(116\) 13.1233i 0.113132i
\(117\) 163.746 37.0020i 1.39954 0.316256i
\(118\) 16.3465 0.138529
\(119\) 13.1416i 0.110434i
\(120\) −113.585 + 12.6737i −0.946542 + 0.105614i
\(121\) −116.195 −0.960288
\(122\) 178.155i 1.46029i
\(123\) −12.5141 112.154i −0.101741 0.911825i
\(124\) −14.8272 −0.119574
\(125\) 120.691i 0.965529i
\(126\) −11.3606 50.2744i −0.0901635 0.399003i
\(127\) 150.567 1.18556 0.592782 0.805363i \(-0.298029\pi\)
0.592782 + 0.805363i \(0.298029\pi\)
\(128\) 147.381i 1.15141i
\(129\) 47.1700 5.26319i 0.365659 0.0407999i
\(130\) 204.723 1.57480
\(131\) 245.946i 1.87745i −0.344669 0.938724i \(-0.612009\pi\)
0.344669 0.938724i \(-0.387991\pi\)
\(132\) −2.71004 24.2881i −0.0205306 0.184001i
\(133\) 9.17821 0.0690091
\(134\) 154.989i 1.15663i
\(135\) −45.5647 131.583i −0.337516 0.974685i
\(136\) 36.0735 0.265246
\(137\) 196.040i 1.43095i 0.698640 + 0.715474i \(0.253789\pi\)
−0.698640 + 0.715474i \(0.746211\pi\)
\(138\) 101.317 11.3048i 0.734179 0.0819191i
\(139\) 81.6219 0.587208 0.293604 0.955927i \(-0.405145\pi\)
0.293604 + 0.955927i \(0.405145\pi\)
\(140\) 7.34096i 0.0524354i
\(141\) 4.37343 + 39.1957i 0.0310172 + 0.277984i
\(142\) 58.9864 0.415397
\(143\) 287.273i 2.00891i
\(144\) −156.576 + 35.3818i −1.08733 + 0.245707i
\(145\) 127.957 0.882464
\(146\) 115.818i 0.793274i
\(147\) 124.502 13.8919i 0.846954 0.0945025i
\(148\) −31.8548 −0.215235
\(149\) 244.737i 1.64253i −0.570545 0.821266i \(-0.693268\pi\)
0.570545 0.821266i \(-0.306732\pi\)
\(150\) −1.13149 10.1407i −0.00754327 0.0676046i
\(151\) −140.296 −0.929114 −0.464557 0.885543i \(-0.653786\pi\)
−0.464557 + 0.885543i \(0.653786\pi\)
\(152\) 25.1940i 0.165750i
\(153\) 9.68745 + 42.8702i 0.0633167 + 0.280197i
\(154\) −88.2006 −0.572731
\(155\) 144.570i 0.932710i
\(156\) 29.4160 3.28221i 0.188564 0.0210398i
\(157\) 101.021 0.643443 0.321721 0.946834i \(-0.395739\pi\)
0.321721 + 0.946834i \(0.395739\pi\)
\(158\) 263.025i 1.66471i
\(159\) −11.6557 104.461i −0.0733062 0.656988i
\(160\) −43.3723 −0.271077
\(161\) 42.9704i 0.266897i
\(162\) −74.1206 155.629i −0.457534 0.960675i
\(163\) 36.6971 0.225135 0.112568 0.993644i \(-0.464092\pi\)
0.112568 + 0.993644i \(0.464092\pi\)
\(164\) 19.8970i 0.121323i
\(165\) −236.817 + 26.4239i −1.43526 + 0.160145i
\(166\) 305.326 1.83931
\(167\) 91.5908i 0.548448i 0.961666 + 0.274224i \(0.0884210\pi\)
−0.961666 + 0.274224i \(0.911579\pi\)
\(168\) 6.61301 + 59.2674i 0.0393631 + 0.352782i
\(169\) 178.925 1.05873
\(170\) 53.5984i 0.315285i
\(171\) 29.9409 6.76581i 0.175093 0.0395661i
\(172\) 8.36830 0.0486529
\(173\) 32.3306i 0.186882i 0.995625 + 0.0934411i \(0.0297867\pi\)
−0.995625 + 0.0934411i \(0.970213\pi\)
\(174\) 157.424 17.5653i 0.904736 0.100950i
\(175\) −4.30086 −0.0245763
\(176\) 274.694i 1.56076i
\(177\) −2.55531 22.9013i −0.0144368 0.129386i
\(178\) −46.4844 −0.261148
\(179\) 265.603i 1.48382i 0.670502 + 0.741908i \(0.266079\pi\)
−0.670502 + 0.741908i \(0.733921\pi\)
\(180\) −5.41146 23.9475i −0.0300637 0.133042i
\(181\) −208.834 −1.15378 −0.576888 0.816823i \(-0.695733\pi\)
−0.576888 + 0.816823i \(0.695733\pi\)
\(182\) 106.822i 0.586936i
\(183\) 249.594 27.8495i 1.36390 0.152183i
\(184\) −117.953 −0.641048
\(185\) 310.596i 1.67890i
\(186\) 19.8458 + 177.863i 0.106698 + 0.956251i
\(187\) 75.2108 0.402197
\(188\) 6.95360i 0.0369872i
\(189\) −68.6583 + 23.7751i −0.363271 + 0.125794i
\(190\) 37.4336 0.197019
\(191\) 35.2665i 0.184641i −0.995729 0.0923207i \(-0.970572\pi\)
0.995729 0.0923207i \(-0.0294285\pi\)
\(192\) 159.351 17.7803i 0.829955 0.0926057i
\(193\) 24.8793 0.128908 0.0644541 0.997921i \(-0.479469\pi\)
0.0644541 + 0.997921i \(0.479469\pi\)
\(194\) 210.561i 1.08536i
\(195\) −32.0027 286.816i −0.164117 1.47085i
\(196\) 22.0876 0.112692
\(197\) 26.9086i 0.136592i 0.997665 + 0.0682959i \(0.0217562\pi\)
−0.997665 + 0.0682959i \(0.978244\pi\)
\(198\) −287.726 + 65.0179i −1.45316 + 0.328373i
\(199\) −142.574 −0.716453 −0.358226 0.933635i \(-0.616618\pi\)
−0.358226 + 0.933635i \(0.616618\pi\)
\(200\) 11.8058i 0.0590289i
\(201\) −217.138 + 24.2281i −1.08029 + 0.120538i
\(202\) 23.8321 0.117981
\(203\) 66.7666i 0.328900i
\(204\) 0.859312 + 7.70136i 0.00421232 + 0.0377518i
\(205\) −194.003 −0.946356
\(206\) 219.337i 1.06474i
\(207\) −31.6760 140.177i −0.153024 0.677183i
\(208\) −332.690 −1.59947
\(209\) 52.5279i 0.251330i
\(210\) −88.0602 + 9.82569i −0.419334 + 0.0467890i
\(211\) 279.331 1.32384 0.661921 0.749574i \(-0.269742\pi\)
0.661921 + 0.749574i \(0.269742\pi\)
\(212\) 18.5322i 0.0874158i
\(213\) −9.22085 82.6395i −0.0432904 0.387979i
\(214\) −338.873 −1.58352
\(215\) 81.5939i 0.379506i
\(216\) 65.2623 + 188.466i 0.302140 + 0.872527i
\(217\) 75.4350 0.347627
\(218\) 227.434i 1.04327i
\(219\) −162.260 + 18.1049i −0.740915 + 0.0826707i
\(220\) −42.0131 −0.190969
\(221\) 91.0899i 0.412172i
\(222\) 42.6369 + 382.122i 0.192058 + 1.72127i
\(223\) −189.218 −0.848512 −0.424256 0.905542i \(-0.639464\pi\)
−0.424256 + 0.905542i \(0.639464\pi\)
\(224\) 22.6312i 0.101032i
\(225\) −14.0302 + 3.17042i −0.0623563 + 0.0140908i
\(226\) 349.000 1.54425
\(227\) 388.040i 1.70943i −0.519101 0.854713i \(-0.673733\pi\)
0.519101 0.854713i \(-0.326267\pi\)
\(228\) 5.37870 0.600152i 0.0235908 0.00263224i
\(229\) 377.427 1.64815 0.824076 0.566479i \(-0.191695\pi\)
0.824076 + 0.566479i \(0.191695\pi\)
\(230\) 175.256i 0.761982i
\(231\) 13.7877 + 123.569i 0.0596869 + 0.534929i
\(232\) −183.273 −0.789971
\(233\) 369.450i 1.58562i 0.609468 + 0.792811i \(0.291383\pi\)
−0.609468 + 0.792811i \(0.708617\pi\)
\(234\) −78.7451 348.473i −0.336518 1.48920i
\(235\) 67.8001 0.288511
\(236\) 4.06286i 0.0172155i
\(237\) 368.496 41.1165i 1.55484 0.173487i
\(238\) 27.9670 0.117509
\(239\) 456.633i 1.91060i 0.295640 + 0.955299i \(0.404467\pi\)
−0.295640 + 0.955299i \(0.595533\pi\)
\(240\) 30.6014 + 274.257i 0.127506 + 1.14274i
\(241\) −221.449 −0.918876 −0.459438 0.888210i \(-0.651949\pi\)
−0.459438 + 0.888210i \(0.651949\pi\)
\(242\) 247.278i 1.02181i
\(243\) −206.449 + 128.171i −0.849585 + 0.527452i
\(244\) 44.2798 0.181475
\(245\) 215.362i 0.879028i
\(246\) −238.679 + 26.6317i −0.970241 + 0.108259i
\(247\) 63.6180 0.257563
\(248\) 207.068i 0.834951i
\(249\) −47.7290 427.759i −0.191683 1.71791i
\(250\) 256.846 1.02739
\(251\) 245.569i 0.978362i −0.872182 0.489181i \(-0.837296\pi\)
0.872182 0.489181i \(-0.162704\pi\)
\(252\) −12.4955 + 2.82364i −0.0495854 + 0.0112049i
\(253\) −245.924 −0.972031
\(254\) 320.426i 1.26152i
\(255\) 75.0910 8.37860i 0.294475 0.0328573i
\(256\) 99.8588 0.390073
\(257\) 47.6112i 0.185258i 0.995701 + 0.0926288i \(0.0295270\pi\)
−0.995701 + 0.0926288i \(0.970473\pi\)
\(258\) −11.2008 100.384i −0.0434138 0.389085i
\(259\) 162.065 0.625735
\(260\) 50.8833i 0.195705i
\(261\) −49.2177 217.804i −0.188573 0.834500i
\(262\) −523.405 −1.99773
\(263\) 24.3897i 0.0927366i 0.998924 + 0.0463683i \(0.0147648\pi\)
−0.998924 + 0.0463683i \(0.985235\pi\)
\(264\) 339.194 37.8470i 1.28482 0.143360i
\(265\) −180.695 −0.681868
\(266\) 19.5324i 0.0734302i
\(267\) 7.26653 + 65.1244i 0.0272155 + 0.243911i
\(268\) −38.5219 −0.143738
\(269\) 77.7143i 0.288901i 0.989512 + 0.144450i \(0.0461414\pi\)
−0.989512 + 0.144450i \(0.953859\pi\)
\(270\) −280.025 + 96.9676i −1.03713 + 0.359139i
\(271\) 400.159 1.47660 0.738302 0.674471i \(-0.235628\pi\)
0.738302 + 0.674471i \(0.235628\pi\)
\(272\) 87.1012i 0.320225i
\(273\) −149.657 + 16.6987i −0.548196 + 0.0611672i
\(274\) 417.198 1.52262
\(275\) 24.6143i 0.0895065i
\(276\) −2.80978 25.1819i −0.0101804 0.0912388i
\(277\) 397.402 1.43466 0.717332 0.696731i \(-0.245363\pi\)
0.717332 + 0.696731i \(0.245363\pi\)
\(278\) 173.702i 0.624827i
\(279\) 246.082 55.6076i 0.882015 0.199311i
\(280\) 102.520 0.366142
\(281\) 83.6606i 0.297725i 0.988858 + 0.148862i \(0.0475611\pi\)
−0.988858 + 0.148862i \(0.952439\pi\)
\(282\) 83.4136 9.30722i 0.295793 0.0330043i
\(283\) −105.287 −0.372039 −0.186020 0.982546i \(-0.559559\pi\)
−0.186020 + 0.982546i \(0.559559\pi\)
\(284\) 14.6609i 0.0516227i
\(285\) −5.85169 52.4443i −0.0205323 0.184015i
\(286\) −611.355 −2.13761
\(287\) 101.229i 0.352713i
\(288\) 16.6828 + 73.8269i 0.0579264 + 0.256343i
\(289\) 265.152 0.917480
\(290\) 272.310i 0.938999i
\(291\) 294.994 32.9152i 1.01373 0.113111i
\(292\) −28.7862 −0.0985828
\(293\) 53.8078i 0.183644i 0.995775 + 0.0918221i \(0.0292691\pi\)
−0.995775 + 0.0918221i \(0.970731\pi\)
\(294\) −29.5637 264.957i −0.100557 0.901214i
\(295\) −39.6143 −0.134286
\(296\) 444.866i 1.50293i
\(297\) 136.068 + 392.938i 0.458140 + 1.32303i
\(298\) −520.833 −1.74776
\(299\) 297.846i 0.996139i
\(300\) −2.52043 + 0.281228i −0.00840144 + 0.000937426i
\(301\) −42.5748 −0.141444
\(302\) 298.569i 0.988638i
\(303\) −3.72547 33.3886i −0.0122953 0.110193i
\(304\) −60.8323 −0.200106
\(305\) 431.744i 1.41555i
\(306\) 91.2334 20.6162i 0.298148 0.0673731i
\(307\) 203.837 0.663963 0.331982 0.943286i \(-0.392283\pi\)
0.331982 + 0.943286i \(0.392283\pi\)
\(308\) 21.9220i 0.0711752i
\(309\) 307.289 34.2871i 0.994464 0.110962i
\(310\) 307.664 0.992464
\(311\) 503.727i 1.61970i 0.586636 + 0.809851i \(0.300452\pi\)
−0.586636 + 0.809851i \(0.699548\pi\)
\(312\) 45.8375 + 410.807i 0.146915 + 1.31669i
\(313\) 212.727 0.679638 0.339819 0.940491i \(-0.389634\pi\)
0.339819 + 0.940491i \(0.389634\pi\)
\(314\) 214.985i 0.684665i
\(315\) 27.5315 + 121.836i 0.0874015 + 0.386780i
\(316\) 65.3739 0.206879
\(317\) 460.556i 1.45286i −0.687242 0.726428i \(-0.741179\pi\)
0.687242 0.726428i \(-0.258821\pi\)
\(318\) −222.307 + 24.8048i −0.699078 + 0.0780026i
\(319\) −382.112 −1.19784
\(320\) 275.643i 0.861385i
\(321\) 52.9732 + 474.759i 0.165026 + 1.47900i
\(322\) −91.4465 −0.283995
\(323\) 16.6558i 0.0515658i
\(324\) −38.6811 + 18.4224i −0.119386 + 0.0568593i
\(325\) −29.8111 −0.0917263
\(326\) 78.0961i 0.239559i
\(327\) 318.633 35.5529i 0.974414 0.108724i
\(328\) 277.871 0.847166
\(329\) 35.3773i 0.107530i
\(330\) 56.2335 + 503.978i 0.170404 + 1.52721i
\(331\) −414.786 −1.25313 −0.626565 0.779369i \(-0.715540\pi\)
−0.626565 + 0.779369i \(0.715540\pi\)
\(332\) 75.8876i 0.228577i
\(333\) 528.685 119.468i 1.58764 0.358763i
\(334\) 194.917 0.583585
\(335\) 375.602i 1.12120i
\(336\) 143.104 15.9675i 0.425905 0.0475222i
\(337\) −343.388 −1.01896 −0.509478 0.860484i \(-0.670161\pi\)
−0.509478 + 0.860484i \(0.670161\pi\)
\(338\) 380.776i 1.12656i
\(339\) −54.5563 488.947i −0.160933 1.44232i
\(340\) 13.3217 0.0391814
\(341\) 431.723i 1.26605i
\(342\) −14.3985 63.7182i −0.0421009 0.186311i
\(343\) −244.235 −0.712054
\(344\) 116.867i 0.339730i
\(345\) −245.532 + 27.3963i −0.711688 + 0.0794096i
\(346\) 68.8038 0.198855
\(347\) 6.99097i 0.0201469i 0.999949 + 0.0100734i \(0.00320653\pi\)
−0.999949 + 0.0100734i \(0.996793\pi\)
\(348\) −4.36579 39.1272i −0.0125454 0.112435i
\(349\) −445.031 −1.27516 −0.637580 0.770384i \(-0.720065\pi\)
−0.637580 + 0.770384i \(0.720065\pi\)
\(350\) 9.15279i 0.0261508i
\(351\) −475.899 + 164.795i −1.35584 + 0.469502i
\(352\) 129.521 0.367956
\(353\) 247.520i 0.701190i 0.936527 + 0.350595i \(0.114021\pi\)
−0.936527 + 0.350595i \(0.885979\pi\)
\(354\) −48.7370 + 5.43804i −0.137675 + 0.0153617i
\(355\) −142.948 −0.402672
\(356\) 11.5535i 0.0324537i
\(357\) −4.37186 39.1816i −0.0122461 0.109752i
\(358\) 565.238 1.57888
\(359\) 336.875i 0.938370i −0.883100 0.469185i \(-0.844548\pi\)
0.883100 0.469185i \(-0.155452\pi\)
\(360\) 334.437 75.5734i 0.928993 0.209926i
\(361\) −349.367 −0.967777
\(362\) 444.425i 1.22769i
\(363\) 346.435 38.6549i 0.954365 0.106487i
\(364\) −26.5503 −0.0729404
\(365\) 280.675i 0.768973i
\(366\) −59.2674 531.169i −0.161933 1.45128i
\(367\) −407.857 −1.11133 −0.555663 0.831407i \(-0.687536\pi\)
−0.555663 + 0.831407i \(0.687536\pi\)
\(368\) 284.803i 0.773922i
\(369\) 74.6216 + 330.225i 0.202227 + 0.894919i
\(370\) 660.988 1.78645
\(371\) 94.2846i 0.254136i
\(372\) 44.2071 4.93260i 0.118836 0.0132597i
\(373\) −86.5149 −0.231943 −0.115972 0.993253i \(-0.536998\pi\)
−0.115972 + 0.993253i \(0.536998\pi\)
\(374\) 160.058i 0.427963i
\(375\) −40.1507 359.840i −0.107069 0.959574i
\(376\) −97.1101 −0.258272
\(377\) 462.787i 1.22755i
\(378\) 50.5966 + 146.114i 0.133853 + 0.386544i
\(379\) −444.400 −1.17256 −0.586279 0.810109i \(-0.699408\pi\)
−0.586279 + 0.810109i \(0.699408\pi\)
\(380\) 9.30399i 0.0244842i
\(381\) −448.914 + 50.0895i −1.17825 + 0.131469i
\(382\) −75.0517 −0.196470
\(383\) 11.2111i 0.0292719i 0.999893 + 0.0146359i \(0.00465893\pi\)
−0.999893 + 0.0146359i \(0.995341\pi\)
\(384\) −49.0297 439.416i −0.127681 1.14431i
\(385\) 213.747 0.555186
\(386\) 52.9463i 0.137167i
\(387\) −138.886 + 31.3844i −0.358879 + 0.0810966i
\(388\) 52.3341 0.134882
\(389\) 343.975i 0.884255i −0.896952 0.442127i \(-0.854224\pi\)
0.896952 0.442127i \(-0.145776\pi\)
\(390\) −610.382 + 68.1060i −1.56508 + 0.174631i
\(391\) 77.9786 0.199434
\(392\) 308.463i 0.786895i
\(393\) 81.8196 + 733.287i 0.208192 + 1.86587i
\(394\) 57.2649 0.145343
\(395\) 637.418i 1.61372i
\(396\) 16.1600 + 71.5133i 0.0408080 + 0.180589i
\(397\) 1.87556 0.00472433 0.00236216 0.999997i \(-0.499248\pi\)
0.00236216 + 0.999997i \(0.499248\pi\)
\(398\) 303.416i 0.762353i
\(399\) −27.3648 + 3.05335i −0.0685835 + 0.00765250i
\(400\) 28.5057 0.0712642
\(401\) 366.293i 0.913450i −0.889608 0.456725i \(-0.849022\pi\)
0.889608 0.456725i \(-0.150978\pi\)
\(402\) 51.5606 + 462.098i 0.128260 + 1.14950i
\(403\) 522.872 1.29745
\(404\) 5.92338i 0.0146618i
\(405\) 179.625 + 377.155i 0.443518 + 0.931246i
\(406\) −142.088 −0.349971
\(407\) 927.517i 2.27891i
\(408\) −107.553 + 12.0007i −0.263610 + 0.0294134i
\(409\) −246.497 −0.602682 −0.301341 0.953516i \(-0.597434\pi\)
−0.301341 + 0.953516i \(0.597434\pi\)
\(410\) 412.864i 1.00698i
\(411\) −65.2172 584.492i −0.158679 1.42212i
\(412\) 54.5154 0.132319
\(413\) 20.6703i 0.0500492i
\(414\) −298.315 + 67.4107i −0.720567 + 0.162828i
\(415\) −739.931 −1.78297
\(416\) 156.866i 0.377082i
\(417\) −243.355 + 27.1534i −0.583586 + 0.0651161i
\(418\) −111.786 −0.267431
\(419\) 560.527i 1.33777i 0.743364 + 0.668887i \(0.233229\pi\)
−0.743364 + 0.668887i \(0.766771\pi\)
\(420\) 2.44214 + 21.8871i 0.00581462 + 0.0521120i
\(421\) 657.045 1.56068 0.780339 0.625357i \(-0.215047\pi\)
0.780339 + 0.625357i \(0.215047\pi\)
\(422\) 594.452i 1.40865i
\(423\) −26.0787 115.407i −0.0616518 0.272830i
\(424\) 258.810 0.610400
\(425\) 7.80480i 0.0183642i
\(426\) −175.868 + 19.6232i −0.412835 + 0.0460638i
\(427\) −225.279 −0.527586
\(428\) 84.2256i 0.196789i
\(429\) 95.5682 + 856.505i 0.222770 + 1.99652i
\(430\) −173.642 −0.403820
\(431\) 805.638i 1.86923i 0.355662 + 0.934615i \(0.384255\pi\)
−0.355662 + 0.934615i \(0.615745\pi\)
\(432\) 455.060 157.579i 1.05338 0.364767i
\(433\) 17.6191 0.0406907 0.0203454 0.999793i \(-0.493523\pi\)
0.0203454 + 0.999793i \(0.493523\pi\)
\(434\) 160.536i 0.369898i
\(435\) −381.504 + 42.5679i −0.877021 + 0.0978574i
\(436\) 56.5279 0.129651
\(437\) 54.4610i 0.124625i
\(438\) 38.5296 + 345.311i 0.0879670 + 0.788382i
\(439\) −159.746 −0.363887 −0.181943 0.983309i \(-0.558239\pi\)
−0.181943 + 0.983309i \(0.558239\pi\)
\(440\) 586.731i 1.33348i
\(441\) −366.582 + 82.8371i −0.831251 + 0.187839i
\(442\) 193.851 0.438577
\(443\) 421.604i 0.951702i 0.879526 + 0.475851i \(0.157860\pi\)
−0.879526 + 0.475851i \(0.842140\pi\)
\(444\) 94.9750 10.5972i 0.213908 0.0238677i
\(445\) 112.651 0.253148
\(446\) 402.681i 0.902872i
\(447\) 81.4175 + 729.684i 0.182142 + 1.63240i
\(448\) −143.828 −0.321044
\(449\) 148.008i 0.329638i 0.986324 + 0.164819i \(0.0527040\pi\)
−0.986324 + 0.164819i \(0.947296\pi\)
\(450\) 6.74707 + 29.8580i 0.0149935 + 0.0663511i
\(451\) 579.342 1.28457
\(452\) 86.7428i 0.191909i
\(453\) 418.293 46.6728i 0.923384 0.103030i
\(454\) −825.799 −1.81894
\(455\) 258.875i 0.568956i
\(456\) 8.38138 + 75.1160i 0.0183802 + 0.164728i
\(457\) −47.4974 −0.103933 −0.0519665 0.998649i \(-0.516549\pi\)
−0.0519665 + 0.998649i \(0.516549\pi\)
\(458\) 803.213i 1.75374i
\(459\) −43.1449 124.595i −0.0939976 0.271448i
\(460\) −43.5592 −0.0946940
\(461\) 510.179i 1.10668i 0.832956 + 0.553340i \(0.186647\pi\)
−0.832956 + 0.553340i \(0.813353\pi\)
\(462\) 262.970 29.3420i 0.569199 0.0635108i
\(463\) 470.002 1.01512 0.507562 0.861615i \(-0.330547\pi\)
0.507562 + 0.861615i \(0.330547\pi\)
\(464\) 442.523i 0.953713i
\(465\) −48.0946 431.035i −0.103429 0.926958i
\(466\) 786.238 1.68721
\(467\) 534.667i 1.14490i 0.819941 + 0.572449i \(0.194006\pi\)
−0.819941 + 0.572449i \(0.805994\pi\)
\(468\) −86.6118 + 19.5718i −0.185068 + 0.0418201i
\(469\) 195.985 0.417878
\(470\) 144.287i 0.306994i
\(471\) −301.192 + 33.6068i −0.639474 + 0.0713521i
\(472\) 56.7396 0.120211
\(473\) 243.660i 0.515137i
\(474\) −87.5013 784.207i −0.184602 1.65445i
\(475\) −5.45095 −0.0114757
\(476\) 6.95111i 0.0146032i
\(477\) 69.5028 + 307.573i 0.145708 + 0.644807i
\(478\) 971.775 2.03300
\(479\) 399.048i 0.833085i −0.909116 0.416542i \(-0.863242\pi\)
0.909116 0.416542i \(-0.136758\pi\)
\(480\) 129.314 14.4288i 0.269405 0.0300600i
\(481\) 1123.34 2.33543
\(482\) 471.273i 0.977744i
\(483\) 14.2951 + 128.116i 0.0295965 + 0.265251i
\(484\) 61.4600 0.126983
\(485\) 510.276i 1.05212i
\(486\) 272.764 + 439.351i 0.561243 + 0.904014i
\(487\) −461.325 −0.947279 −0.473639 0.880719i \(-0.657060\pi\)
−0.473639 + 0.880719i \(0.657060\pi\)
\(488\) 618.387i 1.26719i
\(489\) −109.412 + 12.2081i −0.223747 + 0.0249655i
\(490\) −458.318 −0.935343
\(491\) 660.058i 1.34431i 0.740409 + 0.672156i \(0.234632\pi\)
−0.740409 + 0.672156i \(0.765368\pi\)
\(492\) 6.61920 + 59.3229i 0.0134537 + 0.120575i
\(493\) 121.162 0.245764
\(494\) 135.387i 0.274064i
\(495\) 697.280 157.566i 1.40865 0.318314i
\(496\) −499.976 −1.00802
\(497\) 74.5889i 0.150078i
\(498\) −910.327 + 101.574i −1.82797 + 0.203963i
\(499\) 131.114 0.262754 0.131377 0.991332i \(-0.458060\pi\)
0.131377 + 0.991332i \(0.458060\pi\)
\(500\) 63.8383i 0.127677i
\(501\) −30.4698 273.078i −0.0608180 0.545066i
\(502\) −522.603 −1.04104
\(503\) 7.20522i 0.0143245i 0.999974 + 0.00716225i \(0.00227983\pi\)
−0.999974 + 0.00716225i \(0.997720\pi\)
\(504\) −39.4333 174.506i −0.0782408 0.346241i
\(505\) −57.7551 −0.114366
\(506\) 523.358i 1.03430i
\(507\) −533.465 + 59.5236i −1.05220 + 0.117404i
\(508\) −79.6407 −0.156773
\(509\) 155.141i 0.304796i 0.988319 + 0.152398i \(0.0486995\pi\)
−0.988319 + 0.152398i \(0.951300\pi\)
\(510\) −17.8308 159.803i −0.0349623 0.313340i
\(511\) 146.453 0.286601
\(512\) 377.011i 0.736350i
\(513\) −87.0180 + 30.1328i −0.169626 + 0.0587384i
\(514\) 101.323 0.197126
\(515\) 531.544i 1.03212i
\(516\) −24.9501 + 2.78391i −0.0483529 + 0.00539517i
\(517\) −202.468 −0.391621
\(518\) 344.896i 0.665822i
\(519\) −10.7555 96.3936i −0.0207236 0.185730i
\(520\) 710.607 1.36655
\(521\) 453.960i 0.871323i 0.900110 + 0.435662i \(0.143486\pi\)
−0.900110 + 0.435662i \(0.856514\pi\)
\(522\) −463.516 + 104.742i −0.887962 + 0.200654i
\(523\) 198.044 0.378670 0.189335 0.981913i \(-0.439367\pi\)
0.189335 + 0.981913i \(0.439367\pi\)
\(524\) 130.090i 0.248264i
\(525\) 12.8230 1.43078i 0.0244248 0.00272530i
\(526\) 51.9045 0.0986778
\(527\) 136.892i 0.259758i
\(528\) −91.3834 819.000i −0.173075 1.55114i
\(529\) 274.026 0.518007
\(530\) 384.543i 0.725552i
\(531\) 15.2373 + 67.4301i 0.0286955 + 0.126987i
\(532\) −4.85472 −0.00912541
\(533\) 701.657i 1.31643i
\(534\) 138.593 15.4641i 0.259538 0.0289590i
\(535\) 821.230 1.53501
\(536\) 537.975i 1.00368i
\(537\) −88.3590 791.895i −0.164542 1.47466i
\(538\) 165.386 0.307409
\(539\) 643.125i 1.19318i
\(540\) 24.1009 + 69.5992i 0.0446314 + 0.128887i
\(541\) −283.459 −0.523954 −0.261977 0.965074i \(-0.584374\pi\)
−0.261977 + 0.965074i \(0.584374\pi\)
\(542\) 851.592i 1.57120i
\(543\) 622.637 69.4733i 1.14666 0.127944i
\(544\) −41.0690 −0.0754944
\(545\) 551.167i 1.01131i
\(546\) 35.5369 + 318.490i 0.0650859 + 0.583316i
\(547\) 35.6589 0.0651899 0.0325949 0.999469i \(-0.489623\pi\)
0.0325949 + 0.999469i \(0.489623\pi\)
\(548\) 103.693i 0.189221i
\(549\) −734.900 + 166.067i −1.33862 + 0.302489i
\(550\) 52.3824 0.0952407
\(551\) 84.6206i 0.153576i
\(552\) 351.676 39.2398i 0.637095 0.0710865i
\(553\) −332.598 −0.601442
\(554\) 845.723i 1.52658i
\(555\) −103.327 926.040i −0.186175 1.66854i
\(556\) −43.1730 −0.0776493
\(557\) 105.727i 0.189816i 0.995486 + 0.0949078i \(0.0302556\pi\)
−0.995486 + 0.0949078i \(0.969744\pi\)
\(558\) −118.340 523.695i −0.212079 0.938522i
\(559\) −295.104 −0.527913
\(560\) 247.539i 0.442034i
\(561\) −224.241 + 25.0206i −0.399716 + 0.0446000i
\(562\) 178.041 0.316799
\(563\) 521.415i 0.926137i −0.886323 0.463068i \(-0.846748\pi\)
0.886323 0.463068i \(-0.153252\pi\)
\(564\) −2.31328 20.7321i −0.00410155 0.0367591i
\(565\) −845.773 −1.49694
\(566\) 224.065i 0.395874i
\(567\) 196.795 93.7262i 0.347081 0.165302i
\(568\) 204.745 0.360467
\(569\) 646.759i 1.13666i −0.822801 0.568330i \(-0.807590\pi\)
0.822801 0.568330i \(-0.192410\pi\)
\(570\) −111.608 + 12.4532i −0.195804 + 0.0218477i
\(571\) −1073.49 −1.88002 −0.940010 0.341146i \(-0.889185\pi\)
−0.940010 + 0.341146i \(0.889185\pi\)
\(572\) 151.950i 0.265647i
\(573\) 11.7322 + 105.147i 0.0204751 + 0.183503i
\(574\) 215.427 0.375309
\(575\) 25.5201i 0.0443828i
\(576\) −469.191 + 106.024i −0.814567 + 0.184069i
\(577\) −495.612 −0.858947 −0.429473 0.903079i \(-0.641301\pi\)
−0.429473 + 0.903079i \(0.641301\pi\)
\(578\) 564.278i 0.976259i
\(579\) −74.1775 + 8.27667i −0.128113 + 0.0142948i
\(580\) −67.6816 −0.116692
\(581\) 386.087i 0.664522i
\(582\) −70.0479 627.786i −0.120357 1.07867i
\(583\) 539.601 0.925559
\(584\) 402.011i 0.688376i
\(585\) 190.832 + 844.495i 0.326209 + 1.44358i
\(586\) 114.510 0.195410
\(587\) 219.909i 0.374632i −0.982300 0.187316i \(-0.940021\pi\)
0.982300 0.187316i \(-0.0599788\pi\)
\(588\) −65.8541 + 7.34795i −0.111997 + 0.0124965i
\(589\) 95.6070 0.162321
\(590\) 84.3044i 0.142889i
\(591\) −8.95176 80.2278i −0.0151468 0.135749i
\(592\) −1074.15 −1.81445
\(593\) 344.715i 0.581307i 0.956828 + 0.290654i \(0.0938728\pi\)
−0.956828 + 0.290654i \(0.906127\pi\)
\(594\) 836.224 289.570i 1.40779 0.487491i
\(595\) −67.7758 −0.113909
\(596\) 129.451i 0.217200i
\(597\) 425.084 47.4306i 0.712034 0.0794482i
\(598\) −633.854 −1.05996
\(599\) 72.2992i 0.120700i −0.998177 0.0603499i \(-0.980778\pi\)
0.998177 0.0603499i \(-0.0192216\pi\)
\(600\) −3.92747 35.1989i −0.00654578 0.0586649i
\(601\) 1109.43 1.84597 0.922985 0.384836i \(-0.125742\pi\)
0.922985 + 0.384836i \(0.125742\pi\)
\(602\) 90.6047i 0.150506i
\(603\) 639.337 144.472i 1.06026 0.239589i
\(604\) 74.2082 0.122861
\(605\) 599.257i 0.990507i
\(606\) −71.0553 + 7.92830i −0.117253 + 0.0130830i
\(607\) −311.142 −0.512589 −0.256295 0.966599i \(-0.582502\pi\)
−0.256295 + 0.966599i \(0.582502\pi\)
\(608\) 28.6829i 0.0471759i
\(609\) 22.2115 + 199.065i 0.0364720 + 0.326871i
\(610\) −918.808 −1.50624
\(611\) 245.215i 0.401334i
\(612\) −5.12408 22.6757i −0.00837267 0.0370518i
\(613\) −93.5672 −0.152638 −0.0763191 0.997083i \(-0.524317\pi\)
−0.0763191 + 0.997083i \(0.524317\pi\)
\(614\) 433.791i 0.706500i
\(615\) 578.419 64.5396i 0.940519 0.104942i
\(616\) −306.150 −0.496996
\(617\) 837.167i 1.35683i −0.734677 0.678417i \(-0.762666\pi\)
0.734677 0.678417i \(-0.237334\pi\)
\(618\) −72.9675 653.952i −0.118070 1.05817i
\(619\) 416.723 0.673219 0.336609 0.941644i \(-0.390720\pi\)
0.336609 + 0.941644i \(0.390720\pi\)
\(620\) 76.4688i 0.123337i
\(621\) 141.075 + 407.399i 0.227174 + 0.656037i
\(622\) 1072.00 1.72347
\(623\) 58.7800i 0.0943500i
\(624\) 991.915 110.677i 1.58961 0.177367i
\(625\) −662.401 −1.05984
\(626\) 452.710i 0.723179i
\(627\) 17.4746 + 156.612i 0.0278702 + 0.249780i
\(628\) −53.4337 −0.0850855
\(629\) 294.101i 0.467569i
\(630\) 259.283 58.5906i 0.411560 0.0930009i
\(631\) 609.967 0.966668 0.483334 0.875436i \(-0.339426\pi\)
0.483334 + 0.875436i \(0.339426\pi\)
\(632\) 912.975i 1.44458i
\(633\) −832.823 + 92.9258i −1.31568 + 0.146802i
\(634\) −980.122 −1.54593
\(635\) 776.525i 1.22287i
\(636\) 6.16515 + 55.2536i 0.00969363 + 0.0868767i
\(637\) −778.907 −1.22277
\(638\) 813.185i 1.27458i
\(639\) 54.9839 + 243.322i 0.0860468 + 0.380786i
\(640\) −760.094 −1.18765
\(641\) 1232.43i 1.92266i 0.275394 + 0.961331i \(0.411192\pi\)
−0.275394 + 0.961331i \(0.588808\pi\)
\(642\) 1010.35 112.734i 1.57375 0.175598i
\(643\) −919.351 −1.42978 −0.714892 0.699235i \(-0.753524\pi\)
−0.714892 + 0.699235i \(0.753524\pi\)
\(644\) 22.7287i 0.0352930i
\(645\) 27.1441 + 243.272i 0.0420839 + 0.377166i
\(646\) 35.4456 0.0548694
\(647\) 270.021i 0.417343i 0.977986 + 0.208671i \(0.0669139\pi\)
−0.977986 + 0.208671i \(0.933086\pi\)
\(648\) −257.277 540.199i −0.397032 0.833641i
\(649\) 118.298 0.182278
\(650\) 63.4418i 0.0976028i
\(651\) −224.909 + 25.0952i −0.345483 + 0.0385487i
\(652\) −19.4105 −0.0297707
\(653\) 430.290i 0.658943i −0.944166 0.329472i \(-0.893129\pi\)
0.944166 0.329472i \(-0.106871\pi\)
\(654\) −75.6611 678.093i −0.115690 1.03684i
\(655\) 1268.43 1.93653
\(656\) 670.933i 1.02276i
\(657\) 477.756 107.959i 0.727178 0.164322i
\(658\) −75.2875 −0.114419
\(659\) 1083.87i 1.64473i −0.568964 0.822363i \(-0.692656\pi\)
0.568964 0.822363i \(-0.307344\pi\)
\(660\) 125.262 13.9766i 0.189791 0.0211767i
\(661\) −114.088 −0.172599 −0.0862996 0.996269i \(-0.527504\pi\)
−0.0862996 + 0.996269i \(0.527504\pi\)
\(662\) 882.719i 1.33341i
\(663\) −30.3032 271.584i −0.0457061 0.409629i
\(664\) 1059.80 1.59609
\(665\) 47.3352i 0.0711808i
\(666\) −254.243 1125.11i −0.381747 1.68936i
\(667\) −396.175 −0.593965
\(668\) 48.4460i 0.0725239i
\(669\) 564.153 62.9478i 0.843279 0.0940924i
\(670\) 799.330 1.19303
\(671\) 1289.30i 1.92145i
\(672\) −7.52879 67.4748i −0.0112036 0.100409i
\(673\) 340.904 0.506544 0.253272 0.967395i \(-0.418493\pi\)
0.253272 + 0.967395i \(0.418493\pi\)
\(674\) 730.775i 1.08424i
\(675\) 40.7762 14.1201i 0.0604091 0.0209186i
\(676\) −94.6406 −0.140001
\(677\) 905.939i 1.33817i −0.743187 0.669084i \(-0.766687\pi\)
0.743187 0.669084i \(-0.233313\pi\)
\(678\) −1040.54 + 116.103i −1.53472 + 0.171243i
\(679\) −266.256 −0.392130
\(680\) 186.043i 0.273593i
\(681\) 129.090 + 1156.94i 0.189560 + 1.69888i
\(682\) −918.762 −1.34716
\(683\) 172.470i 0.252518i 0.991997 + 0.126259i \(0.0402970\pi\)
−0.991997 + 0.126259i \(0.959703\pi\)
\(684\) −15.8369 + 3.57870i −0.0231534 + 0.00523202i
\(685\) −1011.05 −1.47598
\(686\) 519.763i 0.757672i
\(687\) −1125.30 + 125.560i −1.63799 + 0.182765i
\(688\) 282.181 0.410147
\(689\) 653.526i 0.948514i
\(690\) 58.3029 + 522.525i 0.0844970 + 0.757283i
\(691\) −762.162 −1.10298 −0.551492 0.834180i \(-0.685941\pi\)
−0.551492 + 0.834180i \(0.685941\pi\)
\(692\) 17.1009i 0.0247123i
\(693\) −82.2159 363.832i −0.118638 0.525011i
\(694\) 14.8777 0.0214376
\(695\) 420.952i 0.605687i
\(696\) 546.429 60.9701i 0.785099 0.0876007i
\(697\) −183.700 −0.263558
\(698\) 947.084i 1.35685i
\(699\) −122.906 1101.51i −0.175831 1.57584i
\(700\) 2.27489 0.00324985
\(701\) 1223.58i 1.74548i −0.488188 0.872739i \(-0.662342\pi\)
0.488188 0.872739i \(-0.337658\pi\)
\(702\) 350.706 + 1012.78i 0.499581 + 1.44270i
\(703\) 205.403 0.292180
\(704\) 823.140i 1.16923i
\(705\) −202.146 + 22.5553i −0.286732 + 0.0319933i
\(706\) 526.755 0.746112
\(707\) 30.1359i 0.0426251i
\(708\) 1.35160 + 12.1134i 0.00190905 + 0.0171093i
\(709\) 110.240 0.155487 0.0777435 0.996973i \(-0.475228\pi\)
0.0777435 + 0.996973i \(0.475228\pi\)
\(710\) 304.213i 0.428469i
\(711\) −1084.99 + 245.177i −1.52601 + 0.344835i
\(712\) −161.350 −0.226615
\(713\) 447.611i 0.627785i
\(714\) −83.3836 + 9.30388i −0.116784 + 0.0130306i
\(715\) 1481.57 2.07212
\(716\) 140.488i 0.196212i
\(717\) −151.910 1361.45i −0.211868 1.89882i
\(718\) −716.914 −0.998487
\(719\) 663.517i 0.922834i −0.887183 0.461417i \(-0.847341\pi\)
0.887183 0.461417i \(-0.152659\pi\)
\(720\) −182.476 807.516i −0.253439 1.12155i
\(721\) −277.354 −0.384679
\(722\) 743.500i 1.02978i
\(723\) 660.250 73.6702i 0.913209 0.101895i
\(724\) 110.460 0.152569
\(725\) 39.6527i 0.0546934i
\(726\) −82.2627 737.258i −0.113309 1.01551i
\(727\) 684.753 0.941889 0.470944 0.882163i \(-0.343913\pi\)
0.470944 + 0.882163i \(0.343913\pi\)
\(728\) 370.787i 0.509322i
\(729\) 572.889 450.821i 0.785856 0.618410i
\(730\) 597.314 0.818238
\(731\) 77.2607i 0.105692i
\(732\) −132.020 + 14.7307i −0.180355 + 0.0201239i
\(733\) 981.794 1.33942 0.669709 0.742624i \(-0.266419\pi\)
0.669709 + 0.742624i \(0.266419\pi\)
\(734\) 867.973i 1.18252i
\(735\) 71.6451 + 642.101i 0.0974764 + 0.873607i
\(736\) 134.287 0.182455
\(737\) 1121.64i 1.52190i
\(738\) 702.762 158.804i 0.952252 0.215182i
\(739\) 820.477 1.11025 0.555126 0.831766i \(-0.312670\pi\)
0.555126 + 0.831766i \(0.312670\pi\)
\(740\) 164.286i 0.222008i
\(741\) −189.677 + 21.1640i −0.255974 + 0.0285614i
\(742\) 200.650 0.270418
\(743\) 252.899i 0.340376i 0.985412 + 0.170188i \(0.0544374\pi\)
−0.985412 + 0.170188i \(0.945563\pi\)
\(744\) 68.8859 + 617.372i 0.0925886 + 0.829801i
\(745\) 1262.19 1.69422
\(746\) 184.115i 0.246803i
\(747\) 284.608 + 1259.48i 0.381001 + 1.68606i
\(748\) −39.7819 −0.0531844
\(749\) 428.508i 0.572107i
\(750\) −765.787 + 85.4459i −1.02105 + 0.113928i
\(751\) 565.853 0.753466 0.376733 0.926322i \(-0.377047\pi\)
0.376733 + 0.926322i \(0.377047\pi\)
\(752\) 234.477i 0.311805i
\(753\) 81.6942 + 732.163i 0.108492 + 0.972328i
\(754\) −984.872 −1.30620
\(755\) 723.556i 0.958352i
\(756\) 36.3160 12.5756i 0.0480371 0.0166344i
\(757\) 366.712 0.484428 0.242214 0.970223i \(-0.422126\pi\)
0.242214 + 0.970223i \(0.422126\pi\)
\(758\) 945.740i 1.24768i
\(759\) 733.222 81.8123i 0.966036 0.107790i
\(760\) 129.934 0.170966
\(761\) 246.039i 0.323310i −0.986847 0.161655i \(-0.948317\pi\)
0.986847 0.161655i \(-0.0516832\pi\)
\(762\) 106.597 + 955.348i 0.139891 + 1.25374i
\(763\) −287.592 −0.376923
\(764\) 18.6538i 0.0244160i
\(765\) −221.096 + 49.9615i −0.289015 + 0.0653092i
\(766\) 23.8587 0.0311472
\(767\) 143.275i 0.186799i
\(768\) −297.729 + 33.2204i −0.387668 + 0.0432557i
\(769\) 1153.63 1.50017 0.750083 0.661344i \(-0.230014\pi\)
0.750083 + 0.661344i \(0.230014\pi\)
\(770\) 454.881i 0.590755i
\(771\) −15.8390 141.953i −0.0205434 0.184115i
\(772\) −13.1596 −0.0170461
\(773\) 841.471i 1.08858i 0.838898 + 0.544289i \(0.183200\pi\)
−0.838898 + 0.544289i \(0.816800\pi\)
\(774\) 66.7901 + 295.568i 0.0862921 + 0.381871i
\(775\) −44.8009 −0.0578076
\(776\) 730.869i 0.941842i
\(777\) −483.197 + 53.9148i −0.621875 + 0.0693884i
\(778\) −732.024 −0.940905
\(779\) 128.298i 0.164696i
\(780\) 16.9275 + 151.708i 0.0217019 + 0.194498i
\(781\) 426.880 0.546581
\(782\) 165.949i 0.212211i
\(783\) 219.200 + 633.010i 0.279949 + 0.808442i
\(784\) 744.800 0.950000
\(785\) 520.998i 0.663691i
\(786\) 1560.53 174.123i