Properties

Label 177.3.b.a.119.3
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 119.3
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.36

$q$-expansion

\(f(q)\) \(=\) \(q-3.55815i q^{2} +(-1.69290 - 2.47671i) q^{3} -8.66046 q^{4} +6.82324i q^{5} +(-8.81252 + 6.02359i) q^{6} +0.148532 q^{7} +16.5826i q^{8} +(-3.26820 + 8.38564i) q^{9} +O(q^{10})\) \(q-3.55815i q^{2} +(-1.69290 - 2.47671i) q^{3} -8.66046 q^{4} +6.82324i q^{5} +(-8.81252 + 6.02359i) q^{6} +0.148532 q^{7} +16.5826i q^{8} +(-3.26820 + 8.38564i) q^{9} +24.2782 q^{10} -1.80659i q^{11} +(14.6613 + 21.4495i) q^{12} -17.1364 q^{13} -0.528501i q^{14} +(16.8992 - 11.5511i) q^{15} +24.3617 q^{16} +18.3201i q^{17} +(29.8374 + 11.6287i) q^{18} -19.6285 q^{19} -59.0924i q^{20} +(-0.251450 - 0.367871i) q^{21} -6.42813 q^{22} -40.3036i q^{23} +(41.0704 - 28.0727i) q^{24} -21.5567 q^{25} +60.9738i q^{26} +(26.3015 - 6.10165i) q^{27} -1.28636 q^{28} +33.8473i q^{29} +(-41.1004 - 60.1300i) q^{30} -46.0774 q^{31} -20.3523i q^{32} +(-4.47440 + 3.05837i) q^{33} +65.1857 q^{34} +1.01347i q^{35} +(28.3041 - 72.6235i) q^{36} +40.6329 q^{37} +69.8412i q^{38} +(29.0101 + 42.4418i) q^{39} -113.147 q^{40} -21.3927i q^{41} +(-1.30894 + 0.894697i) q^{42} +4.07233 q^{43} +15.6459i q^{44} +(-57.2172 - 22.2997i) q^{45} -143.406 q^{46} +45.7277i q^{47} +(-41.2419 - 60.3370i) q^{48} -48.9779 q^{49} +76.7019i q^{50} +(45.3736 - 31.0140i) q^{51} +148.409 q^{52} +29.4395i q^{53} +(-21.7106 - 93.5849i) q^{54} +12.3268 q^{55} +2.46306i q^{56} +(33.2290 + 48.6141i) q^{57} +120.434 q^{58} -7.68115i q^{59} +(-146.355 + 100.037i) q^{60} -28.5354 q^{61} +163.950i q^{62} +(-0.485432 + 1.24554i) q^{63} +25.0305 q^{64} -116.926i q^{65} +(10.8822 + 15.9206i) q^{66} -6.55405 q^{67} -158.660i q^{68} +(-99.8203 + 68.2298i) q^{69} +3.60609 q^{70} +11.4894i q^{71} +(-139.056 - 54.1953i) q^{72} -113.523 q^{73} -144.578i q^{74} +(36.4932 + 53.3896i) q^{75} +169.992 q^{76} -0.268337i q^{77} +(151.014 - 103.222i) q^{78} -32.0057 q^{79} +166.226i q^{80} +(-59.6378 - 54.8118i) q^{81} -76.1184 q^{82} -145.911i q^{83} +(2.17767 + 3.18594i) q^{84} -125.002 q^{85} -14.4900i q^{86} +(83.8300 - 57.3000i) q^{87} +29.9580 q^{88} -148.358i q^{89} +(-79.3458 + 203.588i) q^{90} -2.54530 q^{91} +349.048i q^{92} +(78.0043 + 114.120i) q^{93} +162.706 q^{94} -133.930i q^{95} +(-50.4066 + 34.4543i) q^{96} -133.709 q^{97} +174.271i q^{98} +(15.1494 + 5.90429i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.55815i 1.77908i −0.456860 0.889539i \(-0.651026\pi\)
0.456860 0.889539i \(-0.348974\pi\)
\(3\) −1.69290 2.47671i −0.564299 0.825570i
\(4\) −8.66046 −2.16512
\(5\) 6.82324i 1.36465i 0.731049 + 0.682324i \(0.239031\pi\)
−0.731049 + 0.682324i \(0.760969\pi\)
\(6\) −8.81252 + 6.02359i −1.46875 + 1.00393i
\(7\) 0.148532 0.0212189 0.0106094 0.999944i \(-0.496623\pi\)
0.0106094 + 0.999944i \(0.496623\pi\)
\(8\) 16.5826i 2.07283i
\(9\) −3.26820 + 8.38564i −0.363133 + 0.931737i
\(10\) 24.2782 2.42782
\(11\) 1.80659i 0.164235i −0.996623 0.0821177i \(-0.973832\pi\)
0.996623 0.0821177i \(-0.0261684\pi\)
\(12\) 14.6613 + 21.4495i 1.22177 + 1.78745i
\(13\) −17.1364 −1.31818 −0.659091 0.752064i \(-0.729059\pi\)
−0.659091 + 0.752064i \(0.729059\pi\)
\(14\) 0.528501i 0.0377500i
\(15\) 16.8992 11.5511i 1.12661 0.770070i
\(16\) 24.3617 1.52261
\(17\) 18.3201i 1.07765i 0.842417 + 0.538826i \(0.181132\pi\)
−0.842417 + 0.538826i \(0.818868\pi\)
\(18\) 29.8374 + 11.6287i 1.65763 + 0.646041i
\(19\) −19.6285 −1.03308 −0.516539 0.856264i \(-0.672780\pi\)
−0.516539 + 0.856264i \(0.672780\pi\)
\(20\) 59.0924i 2.95462i
\(21\) −0.251450 0.367871i −0.0119738 0.0175177i
\(22\) −6.42813 −0.292188
\(23\) 40.3036i 1.75233i −0.482012 0.876165i \(-0.660094\pi\)
0.482012 0.876165i \(-0.339906\pi\)
\(24\) 41.0704 28.0727i 1.71127 1.16970i
\(25\) −21.5567 −0.862267
\(26\) 60.9738i 2.34515i
\(27\) 26.3015 6.10165i 0.974130 0.225987i
\(28\) −1.28636 −0.0459413
\(29\) 33.8473i 1.16715i 0.812060 + 0.583574i \(0.198346\pi\)
−0.812060 + 0.583574i \(0.801654\pi\)
\(30\) −41.1004 60.1300i −1.37001 2.00433i
\(31\) −46.0774 −1.48637 −0.743184 0.669087i \(-0.766685\pi\)
−0.743184 + 0.669087i \(0.766685\pi\)
\(32\) 20.3523i 0.636008i
\(33\) −4.47440 + 3.05837i −0.135588 + 0.0926779i
\(34\) 65.1857 1.91723
\(35\) 1.01347i 0.0289563i
\(36\) 28.3041 72.6235i 0.786224 2.01732i
\(37\) 40.6329 1.09819 0.549093 0.835761i \(-0.314973\pi\)
0.549093 + 0.835761i \(0.314973\pi\)
\(38\) 69.8412i 1.83793i
\(39\) 29.0101 + 42.4418i 0.743849 + 1.08825i
\(40\) −113.147 −2.82868
\(41\) 21.3927i 0.521772i −0.965370 0.260886i \(-0.915985\pi\)
0.965370 0.260886i \(-0.0840147\pi\)
\(42\) −1.30894 + 0.894697i −0.0311653 + 0.0213023i
\(43\) 4.07233 0.0947053 0.0473527 0.998878i \(-0.484922\pi\)
0.0473527 + 0.998878i \(0.484922\pi\)
\(44\) 15.6459i 0.355589i
\(45\) −57.2172 22.2997i −1.27149 0.495549i
\(46\) −143.406 −3.11753
\(47\) 45.7277i 0.972930i 0.873700 + 0.486465i \(0.161714\pi\)
−0.873700 + 0.486465i \(0.838286\pi\)
\(48\) −41.2419 60.3370i −0.859207 1.25702i
\(49\) −48.9779 −0.999550
\(50\) 76.7019i 1.53404i
\(51\) 45.3736 31.0140i 0.889678 0.608118i
\(52\) 148.409 2.85401
\(53\) 29.4395i 0.555462i 0.960659 + 0.277731i \(0.0895823\pi\)
−0.960659 + 0.277731i \(0.910418\pi\)
\(54\) −21.7106 93.5849i −0.402048 1.73305i
\(55\) 12.3268 0.224124
\(56\) 2.46306i 0.0439831i
\(57\) 33.2290 + 48.6141i 0.582965 + 0.852879i
\(58\) 120.434 2.07645
\(59\) 7.68115i 0.130189i
\(60\) −146.355 + 100.037i −2.43925 + 1.66729i
\(61\) −28.5354 −0.467793 −0.233897 0.972261i \(-0.575148\pi\)
−0.233897 + 0.972261i \(0.575148\pi\)
\(62\) 163.950i 2.64436i
\(63\) −0.485432 + 1.24554i −0.00770528 + 0.0197704i
\(64\) 25.0305 0.391101
\(65\) 116.926i 1.79885i
\(66\) 10.8822 + 15.9206i 0.164881 + 0.241221i
\(67\) −6.55405 −0.0978217 −0.0489108 0.998803i \(-0.515575\pi\)
−0.0489108 + 0.998803i \(0.515575\pi\)
\(68\) 158.660i 2.33324i
\(69\) −99.8203 + 68.2298i −1.44667 + 0.988838i
\(70\) 3.60609 0.0515155
\(71\) 11.4894i 0.161823i 0.996721 + 0.0809115i \(0.0257831\pi\)
−0.996721 + 0.0809115i \(0.974217\pi\)
\(72\) −139.056 54.1953i −1.93133 0.752712i
\(73\) −113.523 −1.55510 −0.777552 0.628818i \(-0.783539\pi\)
−0.777552 + 0.628818i \(0.783539\pi\)
\(74\) 144.578i 1.95376i
\(75\) 36.4932 + 53.3896i 0.486576 + 0.711862i
\(76\) 169.992 2.23673
\(77\) 0.268337i 0.00348489i
\(78\) 151.014 103.222i 1.93608 1.32336i
\(79\) −32.0057 −0.405135 −0.202568 0.979268i \(-0.564929\pi\)
−0.202568 + 0.979268i \(0.564929\pi\)
\(80\) 166.226i 2.07783i
\(81\) −59.6378 54.8118i −0.736269 0.676689i
\(82\) −76.1184 −0.928273
\(83\) 145.911i 1.75797i −0.476854 0.878983i \(-0.658223\pi\)
0.476854 0.878983i \(-0.341777\pi\)
\(84\) 2.17767 + 3.18594i 0.0259247 + 0.0379278i
\(85\) −125.002 −1.47062
\(86\) 14.4900i 0.168488i
\(87\) 83.8300 57.3000i 0.963563 0.658621i
\(88\) 29.9580 0.340432
\(89\) 148.358i 1.66695i −0.552560 0.833473i \(-0.686349\pi\)
0.552560 0.833473i \(-0.313651\pi\)
\(90\) −79.3458 + 203.588i −0.881620 + 2.26209i
\(91\) −2.54530 −0.0279703
\(92\) 349.048i 3.79399i
\(93\) 78.0043 + 114.120i 0.838756 + 1.22710i
\(94\) 162.706 1.73092
\(95\) 133.930i 1.40979i
\(96\) −50.4066 + 34.4543i −0.525069 + 0.358899i
\(97\) −133.709 −1.37844 −0.689222 0.724550i \(-0.742048\pi\)
−0.689222 + 0.724550i \(0.742048\pi\)
\(98\) 174.271i 1.77828i
\(99\) 15.1494 + 5.90429i 0.153024 + 0.0596393i
\(100\) 186.691 1.86691
\(101\) 98.8253i 0.978468i −0.872152 0.489234i \(-0.837276\pi\)
0.872152 0.489234i \(-0.162724\pi\)
\(102\) −110.353 161.446i −1.08189 1.58281i
\(103\) 9.65442 0.0937322 0.0468661 0.998901i \(-0.485077\pi\)
0.0468661 + 0.998901i \(0.485077\pi\)
\(104\) 284.166i 2.73236i
\(105\) 2.51008 1.71570i 0.0239055 0.0163400i
\(106\) 104.750 0.988209
\(107\) 179.075i 1.67360i 0.547510 + 0.836799i \(0.315576\pi\)
−0.547510 + 0.836799i \(0.684424\pi\)
\(108\) −227.783 + 52.8431i −2.10910 + 0.489288i
\(109\) 173.922 1.59561 0.797805 0.602915i \(-0.205994\pi\)
0.797805 + 0.602915i \(0.205994\pi\)
\(110\) 43.8607i 0.398733i
\(111\) −68.7873 100.636i −0.619705 0.906629i
\(112\) 3.61850 0.0323081
\(113\) 119.474i 1.05729i 0.848843 + 0.528646i \(0.177300\pi\)
−0.848843 + 0.528646i \(0.822700\pi\)
\(114\) 172.976 118.234i 1.51734 1.03714i
\(115\) 275.001 2.39131
\(116\) 293.133i 2.52701i
\(117\) 56.0050 143.699i 0.478675 1.22820i
\(118\) −27.3307 −0.231616
\(119\) 2.72112i 0.0228666i
\(120\) 191.547 + 280.233i 1.59622 + 2.33528i
\(121\) 117.736 0.973027
\(122\) 101.533i 0.832241i
\(123\) −52.9835 + 36.2156i −0.430760 + 0.294436i
\(124\) 399.051 3.21816
\(125\) 23.4947i 0.187958i
\(126\) 4.43181 + 1.72724i 0.0351731 + 0.0137083i
\(127\) 4.26470 0.0335803 0.0167902 0.999859i \(-0.494655\pi\)
0.0167902 + 0.999859i \(0.494655\pi\)
\(128\) 170.471i 1.33181i
\(129\) −6.89404 10.0860i −0.0534421 0.0781859i
\(130\) −416.039 −3.20030
\(131\) 177.455i 1.35462i 0.735697 + 0.677311i \(0.236855\pi\)
−0.735697 + 0.677311i \(0.763145\pi\)
\(132\) 38.7504 26.4869i 0.293563 0.200658i
\(133\) −2.91546 −0.0219208
\(134\) 23.3203i 0.174032i
\(135\) 41.6330 + 179.462i 0.308393 + 1.32935i
\(136\) −303.795 −2.23379
\(137\) 75.8430i 0.553599i 0.960928 + 0.276799i \(0.0892737\pi\)
−0.960928 + 0.276799i \(0.910726\pi\)
\(138\) 242.772 + 355.176i 1.75922 + 2.57374i
\(139\) −75.6188 −0.544020 −0.272010 0.962294i \(-0.587688\pi\)
−0.272010 + 0.962294i \(0.587688\pi\)
\(140\) 8.77713i 0.0626938i
\(141\) 113.254 77.4123i 0.803222 0.549024i
\(142\) 40.8812 0.287896
\(143\) 30.9584i 0.216492i
\(144\) −79.6189 + 204.289i −0.552909 + 1.41867i
\(145\) −230.948 −1.59275
\(146\) 403.931i 2.76665i
\(147\) 82.9146 + 121.304i 0.564045 + 0.825199i
\(148\) −351.899 −2.37770
\(149\) 186.834i 1.25392i −0.779051 0.626960i \(-0.784299\pi\)
0.779051 0.626960i \(-0.215701\pi\)
\(150\) 189.969 129.849i 1.26646 0.865657i
\(151\) −59.5580 −0.394424 −0.197212 0.980361i \(-0.563189\pi\)
−0.197212 + 0.980361i \(0.563189\pi\)
\(152\) 325.492i 2.14140i
\(153\) −153.626 59.8736i −1.00409 0.391331i
\(154\) −0.954784 −0.00619989
\(155\) 314.397i 2.02837i
\(156\) −251.241 367.566i −1.61052 2.35619i
\(157\) 163.179 1.03936 0.519679 0.854362i \(-0.326052\pi\)
0.519679 + 0.854362i \(0.326052\pi\)
\(158\) 113.881i 0.720767i
\(159\) 72.9131 49.8380i 0.458573 0.313447i
\(160\) 138.868 0.867927
\(161\) 5.98638i 0.0371825i
\(162\) −195.029 + 212.200i −1.20388 + 1.30988i
\(163\) 121.738 0.746856 0.373428 0.927659i \(-0.378182\pi\)
0.373428 + 0.927659i \(0.378182\pi\)
\(164\) 185.270i 1.12970i
\(165\) −20.8680 30.5299i −0.126473 0.185030i
\(166\) −519.174 −3.12756
\(167\) 53.8804i 0.322637i 0.986902 + 0.161319i \(0.0515747\pi\)
−0.986902 + 0.161319i \(0.948425\pi\)
\(168\) 6.10028 4.16970i 0.0363112 0.0248196i
\(169\) 124.655 0.737601
\(170\) 444.778i 2.61634i
\(171\) 64.1497 164.597i 0.375145 0.962558i
\(172\) −35.2682 −0.205048
\(173\) 116.857i 0.675472i −0.941241 0.337736i \(-0.890339\pi\)
0.941241 0.337736i \(-0.109661\pi\)
\(174\) −203.882 298.280i −1.17174 1.71425i
\(175\) −3.20186 −0.0182963
\(176\) 44.0117i 0.250066i
\(177\) −19.0240 + 13.0034i −0.107480 + 0.0734655i
\(178\) −527.881 −2.96563
\(179\) 200.408i 1.11960i 0.828628 + 0.559800i \(0.189122\pi\)
−0.828628 + 0.559800i \(0.810878\pi\)
\(180\) 495.528 + 193.126i 2.75293 + 1.07292i
\(181\) −188.879 −1.04353 −0.521765 0.853089i \(-0.674726\pi\)
−0.521765 + 0.853089i \(0.674726\pi\)
\(182\) 9.05657i 0.0497614i
\(183\) 48.3075 + 70.6739i 0.263975 + 0.386196i
\(184\) 668.340 3.63228
\(185\) 277.248i 1.49864i
\(186\) 406.058 277.551i 2.18311 1.49221i
\(187\) 33.0969 0.176989
\(188\) 396.023i 2.10651i
\(189\) 3.90662 0.906291i 0.0206700 0.00479519i
\(190\) −476.543 −2.50812
\(191\) 334.562i 1.75163i −0.482646 0.875816i \(-0.660324\pi\)
0.482646 0.875816i \(-0.339676\pi\)
\(192\) −42.3740 61.9933i −0.220698 0.322882i
\(193\) 258.231 1.33798 0.668991 0.743270i \(-0.266726\pi\)
0.668991 + 0.743270i \(0.266726\pi\)
\(194\) 475.757i 2.45236i
\(195\) −289.591 + 197.943i −1.48508 + 1.01509i
\(196\) 424.171 2.16414
\(197\) 88.8263i 0.450895i 0.974255 + 0.225447i \(0.0723844\pi\)
−0.974255 + 0.225447i \(0.927616\pi\)
\(198\) 21.0084 53.9039i 0.106103 0.272242i
\(199\) −49.8385 −0.250445 −0.125222 0.992129i \(-0.539964\pi\)
−0.125222 + 0.992129i \(0.539964\pi\)
\(200\) 357.466i 1.78733i
\(201\) 11.0953 + 16.2325i 0.0552007 + 0.0807587i
\(202\) −351.636 −1.74077
\(203\) 5.02742i 0.0247656i
\(204\) −392.956 + 268.596i −1.92625 + 1.31665i
\(205\) 145.967 0.712036
\(206\) 34.3519i 0.166757i
\(207\) 337.971 + 131.720i 1.63271 + 0.636328i
\(208\) −417.471 −2.00707
\(209\) 35.4606i 0.169668i
\(210\) −6.10474 8.93124i −0.0290702 0.0425297i
\(211\) −162.127 −0.768375 −0.384187 0.923255i \(-0.625518\pi\)
−0.384187 + 0.923255i \(0.625518\pi\)
\(212\) 254.959i 1.20264i
\(213\) 28.4560 19.4504i 0.133596 0.0913166i
\(214\) 637.176 2.97746
\(215\) 27.7865i 0.129240i
\(216\) 101.181 + 436.149i 0.468432 + 2.01921i
\(217\) −6.84398 −0.0315391
\(218\) 618.840i 2.83871i
\(219\) 192.182 + 281.163i 0.877544 + 1.28385i
\(220\) −106.756 −0.485254
\(221\) 313.939i 1.42054i
\(222\) −358.078 + 244.756i −1.61296 + 1.10250i
\(223\) −132.740 −0.595248 −0.297624 0.954683i \(-0.596194\pi\)
−0.297624 + 0.954683i \(0.596194\pi\)
\(224\) 3.02297i 0.0134954i
\(225\) 70.4514 180.766i 0.313117 0.803406i
\(226\) 425.107 1.88100
\(227\) 104.312i 0.459525i 0.973247 + 0.229762i \(0.0737949\pi\)
−0.973247 + 0.229762i \(0.926205\pi\)
\(228\) −287.779 421.020i −1.26219 1.84658i
\(229\) 62.2509 0.271838 0.135919 0.990720i \(-0.456601\pi\)
0.135919 + 0.990720i \(0.456601\pi\)
\(230\) 978.496i 4.25433i
\(231\) −0.664593 + 0.454267i −0.00287703 + 0.00196652i
\(232\) −561.277 −2.41930
\(233\) 18.0515i 0.0774742i −0.999249 0.0387371i \(-0.987667\pi\)
0.999249 0.0387371i \(-0.0123335\pi\)
\(234\) −511.304 199.274i −2.18506 0.851599i
\(235\) −312.011 −1.32771
\(236\) 66.5223i 0.281874i
\(237\) 54.1824 + 79.2689i 0.228618 + 0.334468i
\(238\) 9.68217 0.0406814
\(239\) 17.4492i 0.0730091i 0.999333 + 0.0365045i \(0.0116223\pi\)
−0.999333 + 0.0365045i \(0.988378\pi\)
\(240\) 411.694 281.404i 1.71539 1.17252i
\(241\) −211.523 −0.877689 −0.438845 0.898563i \(-0.644612\pi\)
−0.438845 + 0.898563i \(0.644612\pi\)
\(242\) 418.924i 1.73109i
\(243\) −34.7923 + 240.496i −0.143178 + 0.989697i
\(244\) 247.130 1.01283
\(245\) 334.188i 1.36403i
\(246\) 128.861 + 188.523i 0.523824 + 0.766355i
\(247\) 336.361 1.36178
\(248\) 764.085i 3.08099i
\(249\) −361.380 + 247.013i −1.45132 + 0.992018i
\(250\) 83.5978 0.334391
\(251\) 127.331i 0.507295i 0.967297 + 0.253647i \(0.0816303\pi\)
−0.967297 + 0.253647i \(0.918370\pi\)
\(252\) 4.20407 10.7869i 0.0166828 0.0428053i
\(253\) −72.8120 −0.287795
\(254\) 15.1745i 0.0597419i
\(255\) 211.616 + 309.595i 0.829868 + 1.21410i
\(256\) −506.441 −1.97829
\(257\) 136.584i 0.531457i 0.964048 + 0.265729i \(0.0856125\pi\)
−0.964048 + 0.265729i \(0.914388\pi\)
\(258\) −35.8875 + 24.5300i −0.139099 + 0.0950777i
\(259\) 6.03529 0.0233023
\(260\) 1012.63i 3.89473i
\(261\) −283.831 110.620i −1.08748 0.423830i
\(262\) 631.414 2.40998
\(263\) 232.681i 0.884718i 0.896838 + 0.442359i \(0.145858\pi\)
−0.896838 + 0.442359i \(0.854142\pi\)
\(264\) −50.7159 74.1974i −0.192106 0.281051i
\(265\) −200.873 −0.758010
\(266\) 10.3737i 0.0389987i
\(267\) −367.440 + 251.155i −1.37618 + 0.940656i
\(268\) 56.7611 0.211795
\(269\) 139.297i 0.517832i −0.965900 0.258916i \(-0.916635\pi\)
0.965900 0.258916i \(-0.0833652\pi\)
\(270\) 638.552 148.137i 2.36501 0.548655i
\(271\) 340.939 1.25808 0.629038 0.777375i \(-0.283449\pi\)
0.629038 + 0.777375i \(0.283449\pi\)
\(272\) 446.309i 1.64084i
\(273\) 4.30893 + 6.30397i 0.0157836 + 0.0230915i
\(274\) 269.861 0.984895
\(275\) 38.9441i 0.141615i
\(276\) 864.490 590.902i 3.13221 2.14095i
\(277\) −181.171 −0.654047 −0.327024 0.945016i \(-0.606046\pi\)
−0.327024 + 0.945016i \(0.606046\pi\)
\(278\) 269.063i 0.967853i
\(279\) 150.590 386.388i 0.539749 1.38490i
\(280\) −16.8060 −0.0600215
\(281\) 382.735i 1.36205i 0.732262 + 0.681023i \(0.238465\pi\)
−0.732262 + 0.681023i \(0.761535\pi\)
\(282\) −275.445 402.976i −0.976755 1.42899i
\(283\) −35.7887 −0.126462 −0.0632309 0.997999i \(-0.520140\pi\)
−0.0632309 + 0.997999i \(0.520140\pi\)
\(284\) 99.5038i 0.350365i
\(285\) −331.706 + 226.730i −1.16388 + 0.795543i
\(286\) 110.155 0.385156
\(287\) 3.17750i 0.0110714i
\(288\) 170.667 + 66.5151i 0.592592 + 0.230955i
\(289\) −46.6255 −0.161334
\(290\) 821.750i 2.83362i
\(291\) 226.356 + 331.159i 0.777855 + 1.13800i
\(292\) 983.158 3.36698
\(293\) 243.685i 0.831688i 0.909436 + 0.415844i \(0.136514\pi\)
−0.909436 + 0.415844i \(0.863486\pi\)
\(294\) 431.619 295.023i 1.46809 1.00348i
\(295\) 52.4103 0.177662
\(296\) 673.800i 2.27635i
\(297\) −11.0232 47.5161i −0.0371151 0.159987i
\(298\) −664.785 −2.23082
\(299\) 690.656i 2.30989i
\(300\) −316.048 462.379i −1.05349 1.54126i
\(301\) 0.604872 0.00200954
\(302\) 211.917i 0.701711i
\(303\) −244.762 + 167.301i −0.807794 + 0.552149i
\(304\) −478.184 −1.57297
\(305\) 194.704i 0.638374i
\(306\) −213.040 + 546.623i −0.696208 + 1.78635i
\(307\) 153.107 0.498718 0.249359 0.968411i \(-0.419780\pi\)
0.249359 + 0.968411i \(0.419780\pi\)
\(308\) 2.32392i 0.00754520i
\(309\) −16.3439 23.9112i −0.0528930 0.0773825i
\(310\) −1118.67 −3.60863
\(311\) 173.317i 0.557290i −0.960394 0.278645i \(-0.910115\pi\)
0.960394 0.278645i \(-0.0898853\pi\)
\(312\) −703.797 + 481.064i −2.25576 + 1.54187i
\(313\) 440.611 1.40770 0.703851 0.710347i \(-0.251462\pi\)
0.703851 + 0.710347i \(0.251462\pi\)
\(314\) 580.617i 1.84910i
\(315\) −8.49860 3.31222i −0.0269797 0.0105150i
\(316\) 277.184 0.877165
\(317\) 122.299i 0.385800i 0.981218 + 0.192900i \(0.0617894\pi\)
−0.981218 + 0.192900i \(0.938211\pi\)
\(318\) −177.331 259.436i −0.557646 0.815836i
\(319\) 61.1482 0.191687
\(320\) 170.789i 0.533716i
\(321\) 443.517 303.156i 1.38167 0.944410i
\(322\) −21.3005 −0.0661505
\(323\) 359.596i 1.11330i
\(324\) 516.491 + 474.695i 1.59411 + 1.46511i
\(325\) 369.403 1.13662
\(326\) 433.161i 1.32872i
\(327\) −294.431 430.753i −0.900402 1.31729i
\(328\) 354.747 1.08155
\(329\) 6.79204i 0.0206445i
\(330\) −108.630 + 74.2516i −0.329182 + 0.225005i
\(331\) 198.661 0.600183 0.300092 0.953910i \(-0.402983\pi\)
0.300092 + 0.953910i \(0.402983\pi\)
\(332\) 1263.66i 3.80620i
\(333\) −132.796 + 340.732i −0.398787 + 1.02322i
\(334\) 191.715 0.573996
\(335\) 44.7199i 0.133492i
\(336\) −6.12575 8.96198i −0.0182314 0.0266726i
\(337\) −31.0112 −0.0920215 −0.0460108 0.998941i \(-0.514651\pi\)
−0.0460108 + 0.998941i \(0.514651\pi\)
\(338\) 443.540i 1.31225i
\(339\) 295.902 202.257i 0.872868 0.596629i
\(340\) 1082.58 3.18405
\(341\) 83.2430i 0.244114i
\(342\) −585.663 228.255i −1.71246 0.667411i
\(343\) −14.5529 −0.0424282
\(344\) 67.5300i 0.196308i
\(345\) −465.549 681.098i −1.34942 1.97420i
\(346\) −415.794 −1.20172
\(347\) 384.717i 1.10869i −0.832286 0.554347i \(-0.812968\pi\)
0.832286 0.554347i \(-0.187032\pi\)
\(348\) −726.006 + 496.245i −2.08622 + 1.42599i
\(349\) 122.340 0.350545 0.175273 0.984520i \(-0.443919\pi\)
0.175273 + 0.984520i \(0.443919\pi\)
\(350\) 11.3927i 0.0325506i
\(351\) −450.712 + 104.560i −1.28408 + 0.297892i
\(352\) −36.7682 −0.104455
\(353\) 659.650i 1.86870i 0.356360 + 0.934349i \(0.384018\pi\)
−0.356360 + 0.934349i \(0.615982\pi\)
\(354\) 46.2681 + 67.6902i 0.130701 + 0.191215i
\(355\) −78.3952 −0.220832
\(356\) 1284.85i 3.60913i
\(357\) 6.73944 4.60658i 0.0188780 0.0129036i
\(358\) 713.084 1.99186
\(359\) 107.767i 0.300186i −0.988672 0.150093i \(-0.952043\pi\)
0.988672 0.150093i \(-0.0479573\pi\)
\(360\) 369.788 948.813i 1.02719 2.63559i
\(361\) 24.2775 0.0672507
\(362\) 672.061i 1.85652i
\(363\) −199.315 291.599i −0.549078 0.803302i
\(364\) 22.0435 0.0605590
\(365\) 774.593i 2.12217i
\(366\) 251.469 171.886i 0.687073 0.469633i
\(367\) −606.039 −1.65133 −0.825666 0.564159i \(-0.809201\pi\)
−0.825666 + 0.564159i \(0.809201\pi\)
\(368\) 981.865i 2.66811i
\(369\) 179.391 + 69.9154i 0.486155 + 0.189473i
\(370\) 986.491 2.66619
\(371\) 4.37271i 0.0117863i
\(372\) −675.553 988.335i −1.81600 2.65681i
\(373\) −42.6708 −0.114399 −0.0571995 0.998363i \(-0.518217\pi\)
−0.0571995 + 0.998363i \(0.518217\pi\)
\(374\) 117.764i 0.314877i
\(375\) 58.1896 39.7742i 0.155172 0.106064i
\(376\) −758.286 −2.01672
\(377\) 580.019i 1.53851i
\(378\) −3.22472 13.9004i −0.00853102 0.0367735i
\(379\) −548.047 −1.44604 −0.723018 0.690830i \(-0.757245\pi\)
−0.723018 + 0.690830i \(0.757245\pi\)
\(380\) 1159.90i 3.05236i
\(381\) −7.21970 10.5624i −0.0189493 0.0277229i
\(382\) −1190.42 −3.11629
\(383\) 435.197i 1.13628i −0.822931 0.568142i \(-0.807663\pi\)
0.822931 0.568142i \(-0.192337\pi\)
\(384\) −422.208 + 288.590i −1.09950 + 0.751538i
\(385\) 1.83093 0.00475566
\(386\) 918.824i 2.38037i
\(387\) −13.3092 + 34.1491i −0.0343906 + 0.0882405i
\(388\) 1157.98 2.98449
\(389\) 227.077i 0.583746i 0.956457 + 0.291873i \(0.0942784\pi\)
−0.956457 + 0.291873i \(0.905722\pi\)
\(390\) 704.312 + 1030.41i 1.80593 + 2.64207i
\(391\) 738.365 1.88840
\(392\) 812.183i 2.07190i
\(393\) 439.506 300.414i 1.11834 0.764412i
\(394\) 316.058 0.802177
\(395\) 218.383i 0.552868i
\(396\) −131.201 51.1339i −0.331315 0.129126i
\(397\) 740.164 1.86439 0.932197 0.361952i \(-0.117890\pi\)
0.932197 + 0.361952i \(0.117890\pi\)
\(398\) 177.333i 0.445560i
\(399\) 4.93558 + 7.22076i 0.0123699 + 0.0180971i
\(400\) −525.158 −1.31289
\(401\) 306.471i 0.764268i 0.924107 + 0.382134i \(0.124811\pi\)
−0.924107 + 0.382134i \(0.875189\pi\)
\(402\) 57.7577 39.4789i 0.143676 0.0982063i
\(403\) 789.599 1.95930
\(404\) 855.873i 2.11850i
\(405\) 373.994 406.923i 0.923443 1.00475i
\(406\) 17.8883 0.0440599
\(407\) 73.4069i 0.180361i
\(408\) 514.294 + 752.413i 1.26053 + 1.84415i
\(409\) −572.519 −1.39980 −0.699901 0.714240i \(-0.746772\pi\)
−0.699901 + 0.714240i \(0.746772\pi\)
\(410\) 519.374i 1.26677i
\(411\) 187.841 128.394i 0.457035 0.312395i
\(412\) −83.6117 −0.202941
\(413\) 1.14090i 0.00276246i
\(414\) 468.680 1202.55i 1.13208 2.90472i
\(415\) 995.587 2.39901
\(416\) 348.763i 0.838374i
\(417\) 128.015 + 187.286i 0.306990 + 0.449127i
\(418\) 126.174 0.301853
\(419\) 50.8652i 0.121397i 0.998156 + 0.0606984i \(0.0193328\pi\)
−0.998156 + 0.0606984i \(0.980667\pi\)
\(420\) −21.7384 + 14.8588i −0.0517581 + 0.0353781i
\(421\) −320.698 −0.761753 −0.380876 0.924626i \(-0.624378\pi\)
−0.380876 + 0.924626i \(0.624378\pi\)
\(422\) 576.873i 1.36700i
\(423\) −383.456 149.447i −0.906515 0.353303i
\(424\) −488.184 −1.15138
\(425\) 394.920i 0.929223i
\(426\) −69.2076 101.251i −0.162459 0.237678i
\(427\) −4.23843 −0.00992606
\(428\) 1550.87i 3.62353i
\(429\) 76.6749 52.4093i 0.178729 0.122166i
\(430\) 98.8686 0.229927
\(431\) 137.310i 0.318584i −0.987232 0.159292i \(-0.949079\pi\)
0.987232 0.159292i \(-0.0509211\pi\)
\(432\) 640.751 148.647i 1.48322 0.344090i
\(433\) −721.580 −1.66647 −0.833233 0.552921i \(-0.813513\pi\)
−0.833233 + 0.552921i \(0.813513\pi\)
\(434\) 24.3519i 0.0561104i
\(435\) 390.972 + 571.993i 0.898786 + 1.31493i
\(436\) −1506.24 −3.45468
\(437\) 791.098i 1.81029i
\(438\) 1000.42 683.814i 2.28407 1.56122i
\(439\) −288.042 −0.656132 −0.328066 0.944655i \(-0.606397\pi\)
−0.328066 + 0.944655i \(0.606397\pi\)
\(440\) 204.411i 0.464570i
\(441\) 160.069 410.711i 0.362969 0.931318i
\(442\) −1117.05 −2.52725
\(443\) 656.684i 1.48236i −0.671308 0.741178i \(-0.734267\pi\)
0.671308 0.741178i \(-0.265733\pi\)
\(444\) 595.730 + 871.553i 1.34173 + 1.96296i
\(445\) 1012.28 2.27480
\(446\) 472.311i 1.05899i
\(447\) −462.734 + 316.291i −1.03520 + 0.707586i
\(448\) 3.71783 0.00829873
\(449\) 265.029i 0.590266i −0.955456 0.295133i \(-0.904636\pi\)
0.955456 0.295133i \(-0.0953640\pi\)
\(450\) −643.195 250.677i −1.42932 0.557060i
\(451\) −38.6478 −0.0856935
\(452\) 1034.70i 2.28916i
\(453\) 100.826 + 147.508i 0.222573 + 0.325625i
\(454\) 371.159 0.817530
\(455\) 17.3672i 0.0381697i
\(456\) −806.150 + 551.025i −1.76787 + 1.20839i
\(457\) −751.980 −1.64547 −0.822736 0.568424i \(-0.807553\pi\)
−0.822736 + 0.568424i \(0.807553\pi\)
\(458\) 221.498i 0.483621i
\(459\) 111.783 + 481.846i 0.243535 + 1.04977i
\(460\) −2381.64 −5.17747
\(461\) 342.840i 0.743689i 0.928295 + 0.371844i \(0.121274\pi\)
−0.928295 + 0.371844i \(0.878726\pi\)
\(462\) 1.61635 + 2.36472i 0.00349860 + 0.00511845i
\(463\) −610.900 −1.31944 −0.659719 0.751512i \(-0.729325\pi\)
−0.659719 + 0.751512i \(0.729325\pi\)
\(464\) 824.579i 1.77711i
\(465\) −778.671 + 532.242i −1.67456 + 1.14461i
\(466\) −64.2300 −0.137833
\(467\) 70.7483i 0.151495i −0.997127 0.0757477i \(-0.975866\pi\)
0.997127 0.0757477i \(-0.0241344\pi\)
\(468\) −485.029 + 1244.50i −1.03639 + 2.65919i
\(469\) −0.973488 −0.00207567
\(470\) 1110.18i 2.36209i
\(471\) −276.246 404.148i −0.586509 0.858063i
\(472\) 127.374 0.269859
\(473\) 7.35703i 0.0155540i
\(474\) 282.051 192.789i 0.595044 0.406728i
\(475\) 423.125 0.890789
\(476\) 23.5662i 0.0495088i
\(477\) −246.869 96.2140i −0.517544 0.201706i
\(478\) 62.0868 0.129889
\(479\) 86.5788i 0.180749i 0.995908 + 0.0903746i \(0.0288064\pi\)
−0.995908 + 0.0903746i \(0.971194\pi\)
\(480\) −235.090 343.937i −0.489771 0.716535i
\(481\) −696.299 −1.44761
\(482\) 752.632i 1.56148i
\(483\) −14.8265 + 10.1343i −0.0306968 + 0.0209820i
\(484\) −1019.65 −2.10671
\(485\) 912.330i 1.88109i
\(486\) 855.723 + 123.796i 1.76075 + 0.254725i
\(487\) 167.140 0.343203 0.171601 0.985166i \(-0.445106\pi\)
0.171601 + 0.985166i \(0.445106\pi\)
\(488\) 473.192i 0.969656i
\(489\) −206.089 301.509i −0.421450 0.616583i
\(490\) −1189.09 −2.42672
\(491\) 732.046i 1.49093i 0.666546 + 0.745464i \(0.267772\pi\)
−0.666546 + 0.745464i \(0.732228\pi\)
\(492\) 458.861 313.644i 0.932645 0.637487i
\(493\) −620.085 −1.25778
\(494\) 1196.82i 2.42272i
\(495\) −40.2864 + 103.368i −0.0813867 + 0.208824i
\(496\) −1122.53 −2.26316
\(497\) 1.70655i 0.00343370i
\(498\) 878.909 + 1285.84i 1.76488 + 2.58202i
\(499\) 756.899 1.51683 0.758416 0.651771i \(-0.225974\pi\)
0.758416 + 0.651771i \(0.225974\pi\)
\(500\) 203.475i 0.406950i
\(501\) 133.446 91.2140i 0.266360 0.182064i
\(502\) 453.063 0.902516
\(503\) 424.962i 0.844856i 0.906397 + 0.422428i \(0.138822\pi\)
−0.906397 + 0.422428i \(0.861178\pi\)
\(504\) −20.6543 8.04975i −0.0409807 0.0159717i
\(505\) 674.309 1.33527
\(506\) 259.076i 0.512009i
\(507\) −211.028 308.734i −0.416228 0.608942i
\(508\) −36.9343 −0.0727052
\(509\) 163.430i 0.321081i −0.987029 0.160540i \(-0.948676\pi\)
0.987029 0.160540i \(-0.0513237\pi\)
\(510\) 1101.59 752.963i 2.15997 1.47640i
\(511\) −16.8618 −0.0329976
\(512\) 1120.11i 2.18772i
\(513\) −516.259 + 119.766i −1.00635 + 0.233462i
\(514\) 485.989 0.945503
\(515\) 65.8744i 0.127912i
\(516\) 59.7055 + 87.3493i 0.115708 + 0.169282i
\(517\) 82.6112 0.159790
\(518\) 21.4745i 0.0414565i
\(519\) −289.420 + 197.826i −0.557650 + 0.381168i
\(520\) 1938.93 3.72872
\(521\) 643.967i 1.23602i −0.786169 0.618011i \(-0.787939\pi\)
0.786169 0.618011i \(-0.212061\pi\)
\(522\) −393.602 + 1009.92i −0.754026 + 1.93470i
\(523\) 371.188 0.709729 0.354864 0.934918i \(-0.384527\pi\)
0.354864 + 0.934918i \(0.384527\pi\)
\(524\) 1536.85i 2.93291i
\(525\) 5.42042 + 7.93008i 0.0103246 + 0.0151049i
\(526\) 827.914 1.57398
\(527\) 844.142i 1.60179i
\(528\) −109.004 + 74.5072i −0.206447 + 0.141112i
\(529\) −1095.38 −2.07066
\(530\) 714.736i 1.34856i
\(531\) 64.4113 + 25.1035i 0.121302 + 0.0472759i
\(532\) 25.2493 0.0474610
\(533\) 366.592i 0.687790i
\(534\) 893.649 + 1307.41i 1.67350 + 2.44833i
\(535\) −1221.87 −2.28387
\(536\) 108.683i 0.202768i
\(537\) 496.354 339.271i 0.924309 0.631790i
\(538\) −495.639 −0.921262
\(539\) 88.4831i 0.164162i
\(540\) −360.561 1554.22i −0.667706 2.87819i
\(541\) 175.446 0.324300 0.162150 0.986766i \(-0.448157\pi\)
0.162150 + 0.986766i \(0.448157\pi\)
\(542\) 1213.11i 2.23821i
\(543\) 319.753 + 467.799i 0.588864 + 0.861508i
\(544\) 372.855 0.685395
\(545\) 1186.71i 2.17745i
\(546\) 22.4305 15.3318i 0.0410815 0.0280803i
\(547\) 209.300 0.382632 0.191316 0.981528i \(-0.438724\pi\)
0.191316 + 0.981528i \(0.438724\pi\)
\(548\) 656.835i 1.19860i
\(549\) 93.2593 239.288i 0.169871 0.435861i
\(550\) 138.569 0.251944
\(551\) 664.371i 1.20576i
\(552\) −1131.43 1655.28i −2.04969 2.99870i
\(553\) −4.75388 −0.00859652
\(554\) 644.635i 1.16360i
\(555\) 686.663 469.352i 1.23723 0.845680i
\(556\) 654.893 1.17787
\(557\) 46.3436i 0.0832022i 0.999134 + 0.0416011i \(0.0132459\pi\)
−0.999134 + 0.0416011i \(0.986754\pi\)
\(558\) −1374.83 535.822i −2.46385 0.960255i
\(559\) −69.7849 −0.124839
\(560\) 24.6899i 0.0440892i
\(561\) −56.0296 81.9714i −0.0998746 0.146117i
\(562\) 1361.83 2.42318
\(563\) 866.791i 1.53959i 0.638290 + 0.769796i \(0.279642\pi\)
−0.638290 + 0.769796i \(0.720358\pi\)
\(564\) −980.835 + 670.426i −1.73907 + 1.18870i
\(565\) −815.200 −1.44283
\(566\) 127.342i 0.224985i
\(567\) −8.85813 8.14132i −0.0156228 0.0143586i
\(568\) −190.525 −0.335431
\(569\) 116.360i 0.204500i 0.994759 + 0.102250i \(0.0326041\pi\)
−0.994759 + 0.102250i \(0.967396\pi\)
\(570\) 806.739 + 1180.26i 1.41533 + 2.07063i
\(571\) 487.416 0.853618 0.426809 0.904342i \(-0.359638\pi\)
0.426809 + 0.904342i \(0.359638\pi\)
\(572\) 268.114i 0.468730i
\(573\) −828.612 + 566.378i −1.44609 + 0.988444i
\(574\) −11.3060 −0.0196969
\(575\) 868.811i 1.51098i
\(576\) −81.8045 + 209.897i −0.142022 + 0.364404i
\(577\) 672.310 1.16518 0.582591 0.812766i \(-0.302039\pi\)
0.582591 + 0.812766i \(0.302039\pi\)
\(578\) 165.901i 0.287026i
\(579\) −437.158 639.563i −0.755023 1.10460i
\(580\) 2000.12 3.44848
\(581\) 21.6725i 0.0373021i
\(582\) 1178.31 805.409i 2.02459 1.38386i
\(583\) 53.1851 0.0912265
\(584\) 1882.50i 3.22347i
\(585\) 980.495 + 382.136i 1.67606 + 0.653223i
\(586\) 867.067 1.47964
\(587\) 320.616i 0.546194i 0.961986 + 0.273097i \(0.0880480\pi\)
−0.961986 + 0.273097i \(0.911952\pi\)
\(588\) −718.079 1050.55i −1.22122 1.78665i
\(589\) 904.429 1.53553
\(590\) 186.484i 0.316075i
\(591\) 219.997 150.374i 0.372245 0.254440i
\(592\) 989.887 1.67211
\(593\) 779.831i 1.31506i 0.753428 + 0.657530i \(0.228399\pi\)
−0.753428 + 0.657530i \(0.771601\pi\)
\(594\) −169.069 + 39.2222i −0.284629 + 0.0660306i
\(595\) −18.5669 −0.0312049
\(596\) 1618.07i 2.71488i
\(597\) 84.3714 + 123.436i 0.141326 + 0.206760i
\(598\) 2457.46 4.10947
\(599\) 315.093i 0.526032i −0.964791 0.263016i \(-0.915283\pi\)
0.964791 0.263016i \(-0.0847172\pi\)
\(600\) −885.341 + 605.154i −1.47557 + 1.00859i
\(601\) −474.472 −0.789470 −0.394735 0.918795i \(-0.629164\pi\)
−0.394735 + 0.918795i \(0.629164\pi\)
\(602\) 2.15223i 0.00357513i
\(603\) 21.4199 54.9599i 0.0355223 0.0911441i
\(604\) 515.800 0.853973
\(605\) 803.343i 1.32784i
\(606\) 595.283 + 870.900i 0.982315 + 1.43713i
\(607\) 368.145 0.606500 0.303250 0.952911i \(-0.401928\pi\)
0.303250 + 0.952911i \(0.401928\pi\)
\(608\) 399.484i 0.657046i
\(609\) 12.4515 8.51090i 0.0204457 0.0139752i
\(610\) −692.787 −1.13572
\(611\) 783.606i 1.28250i
\(612\) 1330.47 + 518.533i 2.17397 + 0.847276i
\(613\) 25.3403 0.0413382 0.0206691 0.999786i \(-0.493420\pi\)
0.0206691 + 0.999786i \(0.493420\pi\)
\(614\) 544.777i 0.887259i
\(615\) −247.108 361.519i −0.401801 0.587836i
\(616\) 4.44973 0.00722359
\(617\) 410.846i 0.665876i −0.942949 0.332938i \(-0.891960\pi\)
0.942949 0.332938i \(-0.108040\pi\)
\(618\) −85.0797 + 58.1543i −0.137669 + 0.0941007i
\(619\) −652.761 −1.05454 −0.527271 0.849697i \(-0.676785\pi\)
−0.527271 + 0.849697i \(0.676785\pi\)
\(620\) 2722.83i 4.39165i
\(621\) −245.918 1060.05i −0.396004 1.70700i
\(622\) −616.689 −0.991462
\(623\) 22.0360i 0.0353707i
\(624\) 706.736 + 1033.96i 1.13259 + 1.65698i
\(625\) −699.227 −1.11876
\(626\) 1567.76i 2.50441i
\(627\) 87.8257 60.0312i 0.140073 0.0957436i
\(628\) −1413.21 −2.25033
\(629\) 744.398i 1.18346i
\(630\) −11.7854 + 30.2393i −0.0187070 + 0.0479990i
\(631\) −869.264 −1.37760 −0.688799 0.724952i \(-0.741862\pi\)
−0.688799 + 0.724952i \(0.741862\pi\)
\(632\) 530.739i 0.839777i
\(633\) 274.465 + 401.542i 0.433593 + 0.634347i
\(634\) 435.158 0.686369
\(635\) 29.0991i 0.0458253i
\(636\) −631.461 + 431.620i −0.992863 + 0.678648i
\(637\) 839.303 1.31759
\(638\) 217.575i 0.341026i
\(639\) −96.3462 37.5497i −0.150777 0.0587632i
\(640\) 1163.17 1.81745
\(641\) 252.973i 0.394653i 0.980338 + 0.197327i \(0.0632259\pi\)
−0.980338 + 0.197327i \(0.936774\pi\)
\(642\) −1078.67 1578.10i −1.68018 2.45810i
\(643\) −1098.13 −1.70782 −0.853910 0.520421i \(-0.825775\pi\)
−0.853910 + 0.520421i \(0.825775\pi\)
\(644\) 51.8448i 0.0805044i
\(645\) 68.8191 47.0397i 0.106696 0.0729298i
\(646\) −1279.50 −1.98064
\(647\) 634.640i 0.980896i −0.871470 0.490448i \(-0.836833\pi\)
0.871470 0.490448i \(-0.163167\pi\)
\(648\) 908.924 988.952i 1.40266 1.52616i
\(649\) −13.8767 −0.0213816
\(650\) 1314.39i 2.02214i
\(651\) 11.5862 + 16.9506i 0.0177975 + 0.0260377i
\(652\) −1054.30 −1.61703
\(653\) 743.777i 1.13901i −0.821986 0.569507i \(-0.807134\pi\)
0.821986 0.569507i \(-0.192866\pi\)
\(654\) −1532.69 + 1047.63i −2.34356 + 1.60188i
\(655\) −1210.82 −1.84858
\(656\) 521.162i 0.794455i
\(657\) 371.014 951.960i 0.564710 1.44895i
\(658\) 24.1671 0.0367281
\(659\) 9.11578i 0.0138327i −0.999976 0.00691637i \(-0.997798\pi\)
0.999976 0.00691637i \(-0.00220157\pi\)
\(660\) 180.727 + 264.403i 0.273828 + 0.400611i
\(661\) −350.843 −0.530776 −0.265388 0.964142i \(-0.585500\pi\)
−0.265388 + 0.964142i \(0.585500\pi\)
\(662\) 706.865i 1.06777i
\(663\) −777.537 + 531.467i −1.17276 + 0.801610i
\(664\) 2419.59 3.64396
\(665\) 19.8929i 0.0299142i
\(666\) 1212.38 + 472.509i 1.82039 + 0.709473i
\(667\) 1364.17 2.04523
\(668\) 466.629i 0.698547i
\(669\) 224.716 + 328.759i 0.335898 + 0.491419i
\(670\) −159.120 −0.237493
\(671\) 51.5518i 0.0768283i
\(672\) −7.48701 + 5.11757i −0.0111414 + 0.00761543i
\(673\) −1036.60 −1.54027 −0.770134 0.637882i \(-0.779811\pi\)
−0.770134 + 0.637882i \(0.779811\pi\)
\(674\) 110.343i 0.163713i
\(675\) −566.973 + 131.531i −0.839960 + 0.194861i
\(676\) −1079.57 −1.59699
\(677\) 446.603i 0.659680i 0.944037 + 0.329840i \(0.106995\pi\)
−0.944037 + 0.329840i \(0.893005\pi\)
\(678\) −719.662 1052.87i −1.06145 1.55290i
\(679\) −19.8601 −0.0292491
\(680\) 2072.87i 3.04834i
\(681\) 258.351 176.590i 0.379370 0.259309i
\(682\) 296.191 0.434298
\(683\) 751.761i 1.10067i 0.834942 + 0.550337i \(0.185501\pi\)
−0.834942 + 0.550337i \(0.814499\pi\)
\(684\) −555.566 + 1425.49i −0.812231 + 2.08405i
\(685\) −517.495 −0.755468
\(686\) 51.7814i 0.0754831i
\(687\) −105.384 154.178i −0.153398 0.224422i
\(688\) 99.2090 0.144199
\(689\) 504.485i 0.732199i
\(690\) −2423.45 + 1656.49i −3.51225 + 2.40072i
\(691\) 296.414 0.428964 0.214482 0.976728i \(-0.431194\pi\)
0.214482 + 0.976728i \(0.431194\pi\)
\(692\) 1012.03i 1.46247i
\(693\) 2.25018 + 0.876977i 0.00324701 + 0.00126548i
\(694\) −1368.88 −1.97245
\(695\) 515.965i 0.742396i
\(696\) 950.185 + 1390.12i 1.36521 + 1.99730i
\(697\) 391.915 0.562289
\(698\) 435.305i 0.623647i
\(699\) −44.7083 + 30.5593i −0.0639604 + 0.0437186i
\(700\) 27.7296 0.0396137
\(701\) 317.412i 0.452799i 0.974035 + 0.226400i \(0.0726955\pi\)
−0.974035 + 0.226400i \(0.927304\pi\)
\(702\) 372.041 + 1603.70i 0.529972 + 2.28448i
\(703\) −797.562 −1.13451
\(704\) 45.2198i 0.0642327i
\(705\) 528.203 + 772.762i 0.749224 + 1.09612i
\(706\) 2347.14 3.32456
\(707\) 14.6787i 0.0207620i
\(708\) 164.756 112.615i 0.232707 0.159061i
\(709\) −981.184 −1.38390 −0.691950 0.721946i \(-0.743248\pi\)
−0.691950 + 0.721946i \(0.743248\pi\)
\(710\) 278.942i 0.392876i
\(711\) 104.601 268.388i 0.147118 0.377480i
\(712\) 2460.17 3.45530
\(713\) 1857.08i 2.60461i
\(714\) −16.3909 23.9800i −0.0229565 0.0335854i
\(715\) −211.237 −0.295436
\(716\) 1735.63i 2.42406i
\(717\) 43.2165 29.5397i 0.0602741 0.0411990i
\(718\) −383.450 −0.534054
\(719\) 73.9197i 0.102809i −0.998678 0.0514045i \(-0.983630\pi\)
0.998678 0.0514045i \(-0.0163698\pi\)
\(720\) −1393.91 543.259i −1.93599 0.754527i
\(721\) 1.43399 0.00198889
\(722\) 86.3831i 0.119644i
\(723\) 358.087 + 523.882i 0.495279 + 0.724594i
\(724\) 1635.78 2.25936
\(725\) 729.635i 1.00639i
\(726\) −1037.55 + 709.195i −1.42914 + 0.976852i
\(727\) 1232.61 1.69547 0.847735 0.530420i \(-0.177966\pi\)
0.847735 + 0.530420i \(0.177966\pi\)
\(728\) 42.2078i 0.0579777i
\(729\) 654.540 320.965i 0.897860 0.440281i
\(730\) −2756.12 −3.77551
\(731\) 74.6054i 0.102059i
\(732\) −418.365 612.069i −0.571537 0.836160i
\(733\) 325.363 0.443878 0.221939 0.975061i \(-0.428761\pi\)
0.221939 + 0.975061i \(0.428761\pi\)
\(734\) 2156.38i 2.93785i
\(735\) −827.688 + 565.747i −1.12611 + 0.769724i
\(736\) −820.269 −1.11450
\(737\) 11.8405i 0.0160658i
\(738\) 248.770 638.301i 0.337086 0.864907i
\(739\) 411.718 0.557129 0.278564 0.960418i \(-0.410141\pi\)
0.278564 + 0.960418i \(0.410141\pi\)
\(740\) 2401.10i 3.24472i
\(741\) −569.424 833.068i −0.768454 1.12425i
\(742\) 15.5588 0.0209687
\(743\) 31.6240i 0.0425626i −0.999774 0.0212813i \(-0.993225\pi\)
0.999774 0.0212813i \(-0.00677456\pi\)
\(744\) −1892.42 + 1293.52i −2.54357 + 1.73860i
\(745\) 1274.81 1.71116
\(746\) 151.829i 0.203525i
\(747\) 1223.56 + 476.866i 1.63796 + 0.638375i
\(748\) −286.634 −0.383201
\(749\) 26.5984i 0.0355119i
\(750\) −141.523 207.048i −0.188697 0.276064i
\(751\) −827.119 −1.10136 −0.550678 0.834718i \(-0.685631\pi\)
−0.550678 + 0.834718i \(0.685631\pi\)
\(752\) 1114.01i 1.48139i
\(753\) 315.362 215.558i 0.418807 0.286266i
\(754\) −2063.80 −2.73713
\(755\) 406.379i 0.538250i
\(756\) −33.8332 + 7.84890i −0.0447528 + 0.0103821i
\(757\) 422.114 0.557615 0.278807 0.960347i \(-0.410061\pi\)
0.278807 + 0.960347i \(0.410061\pi\)
\(758\) 1950.04i 2.57261i
\(759\) 123.263 + 180.334i 0.162402 + 0.237595i
\(760\) 2220.91 2.92225
\(761\) 37.4749i 0.0492443i 0.999697 + 0.0246222i \(0.00783827\pi\)
−0.999697 + 0.0246222i \(0.992162\pi\)
\(762\) −37.5827 + 25.6888i −0.0493212 + 0.0337123i
\(763\) 25.8330 0.0338571
\(764\) 2897.46i 3.79248i
\(765\) 408.532 1048.22i 0.534029 1.37023i
\(766\) −1548.50 −2.02154
\(767\) 131.627i 0.171613i
\(768\) 857.353 + 1254.31i 1.11635 + 1.63321i
\(769\) 162.942 0.211888 0.105944 0.994372i \(-0.466214\pi\)
0.105944 + 0.994372i \(0.466214\pi\)
\(770\) 6.51472i 0.00846068i
\(771\) 338.280 231.224i 0.438755 0.299901i
\(772\) −2236.40 −2.89689
\(773\) 817.034i 1.05697i 0.848944 + 0.528483i \(0.177239\pi\)
−0.848944 + 0.528483i \(0.822761\pi\)
\(774\) 121.508 + 47.3561i 0.156987 + 0.0611836i
\(775\) 993.275 1.28164
\(776\) 2217.25i 2.85728i
\(777\) −10.2171 14.9477i −0.0131495 0.0192377i
\(778\) 807.975 1.03853
\(779\) 419.906i 0.539032i
\(780\) 2507.99 1714.28i 3.21537 2.19779i
\(781\) 20.7567 0.0265771
\(782\) 2627.22i 3.35961i
\(783\) 206.524 + 890.235i 0.263760 + 1.13695i
\(784\) −1193.19 −1.52192
\(785\) 1113.41i 1.41836i
\(786\) −1068.92 1563.83i