Properties

Label 690.2.i.e.47.6
Level $690$
Weight $2$
Character 690.47
Analytic conductor $5.510$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.6
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.e.323.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.31856 + 1.12312i) q^{3} -1.00000i q^{4} +(-1.11299 - 1.93940i) q^{5} +(-1.72653 + 0.138191i) q^{6} +(1.56700 + 1.56700i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.477181 + 2.96181i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.31856 + 1.12312i) q^{3} -1.00000i q^{4} +(-1.11299 - 1.93940i) q^{5} +(-1.72653 + 0.138191i) q^{6} +(1.56700 + 1.56700i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.477181 + 2.96181i) q^{9} +(2.15836 + 0.584357i) q^{10} -5.67280i q^{11} +(1.12312 - 1.31856i) q^{12} +(1.86804 - 1.86804i) q^{13} -2.21607 q^{14} +(0.710643 - 3.80723i) q^{15} -1.00000 q^{16} +(4.87994 - 4.87994i) q^{17} +(-2.43173 - 1.75690i) q^{18} +3.95832i q^{19} +(-1.93940 + 1.11299i) q^{20} +(0.306241 + 3.82612i) q^{21} +(4.01127 + 4.01127i) q^{22} +(0.707107 + 0.707107i) q^{23} +(0.138191 + 1.72653i) q^{24} +(-2.52251 + 4.31705i) q^{25} +2.64181i q^{26} +(-2.69729 + 4.44124i) q^{27} +(1.56700 - 1.56700i) q^{28} -0.714554 q^{29} +(2.18962 + 3.19462i) q^{30} +6.39562 q^{31} +(0.707107 - 0.707107i) q^{32} +(6.37126 - 7.47990i) q^{33} +6.90128i q^{34} +(1.29498 - 4.78309i) q^{35} +(2.96181 - 0.477181i) q^{36} +(-2.92359 - 2.92359i) q^{37} +(-2.79896 - 2.79896i) q^{38} +(4.56117 - 0.365074i) q^{39} +(0.584357 - 2.15836i) q^{40} +4.88651i q^{41} +(-2.92202 - 2.48893i) q^{42} +(8.81584 - 8.81584i) q^{43} -5.67280 q^{44} +(5.21302 - 4.22190i) q^{45} -1.00000 q^{46} +(-4.01373 + 4.01373i) q^{47} +(-1.31856 - 1.12312i) q^{48} -2.08902i q^{49} +(-1.26894 - 4.83630i) q^{50} +(11.9153 - 0.953694i) q^{51} +(-1.86804 - 1.86804i) q^{52} +(5.27160 + 5.27160i) q^{53} +(-1.23316 - 5.04770i) q^{54} +(-11.0018 + 6.31377i) q^{55} +2.21607i q^{56} +(-4.44569 + 5.21927i) q^{57} +(0.505266 - 0.505266i) q^{58} +7.32082 q^{59} +(-3.80723 - 0.710643i) q^{60} -4.73865 q^{61} +(-4.52238 + 4.52238i) q^{62} +(-3.89341 + 5.38890i) q^{63} +1.00000i q^{64} +(-5.70199 - 1.54376i) q^{65} +(0.783929 + 9.79425i) q^{66} +(6.02909 + 6.02909i) q^{67} +(-4.87994 - 4.87994i) q^{68} +(0.138191 + 1.72653i) q^{69} +(2.46647 + 4.29784i) q^{70} +4.27468i q^{71} +(-1.75690 + 2.43173i) q^{72} +(-5.13585 + 5.13585i) q^{73} +4.13458 q^{74} +(-8.17466 + 2.85919i) q^{75} +3.95832 q^{76} +(8.88928 - 8.88928i) q^{77} +(-2.96708 + 3.48338i) q^{78} +7.27349i q^{79} +(1.11299 + 1.93940i) q^{80} +(-8.54460 + 2.82664i) q^{81} +(-3.45528 - 3.45528i) q^{82} +(-10.9094 - 10.9094i) q^{83} +(3.82612 - 0.306241i) q^{84} +(-14.8955 - 4.03281i) q^{85} +12.4675i q^{86} +(-0.942179 - 0.802533i) q^{87} +(4.01127 - 4.01127i) q^{88} -8.06770 q^{89} +(-0.700822 + 6.67150i) q^{90} +5.85445 q^{91} +(0.707107 - 0.707107i) q^{92} +(8.43298 + 7.18308i) q^{93} -5.67627i q^{94} +(7.67675 - 4.40558i) q^{95} +(1.72653 - 0.138191i) q^{96} +(-0.309834 - 0.309834i) q^{97} +(1.47716 + 1.47716i) q^{98} +(16.8017 - 2.70695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{3} - 4q^{6} - 8q^{7} + O(q^{10}) \) \( 32q + 4q^{3} - 4q^{6} - 8q^{7} - 8q^{10} - 4q^{12} - 4q^{15} - 32q^{16} + 8q^{18} - 32q^{21} - 8q^{22} + 4q^{27} - 8q^{28} + 20q^{30} - 24q^{31} + 20q^{36} - 32q^{37} - 16q^{40} + 8q^{42} + 144q^{43} + 36q^{45} - 32q^{46} - 4q^{48} + 12q^{51} - 64q^{55} + 52q^{57} + 16q^{58} + 4q^{60} - 24q^{61} - 116q^{63} + 12q^{66} - 16q^{67} - 80q^{70} - 8q^{72} + 40q^{73} + 44q^{75} + 24q^{76} - 36q^{78} - 108q^{81} - 32q^{82} - 80q^{85} + 68q^{87} - 8q^{88} + 16q^{90} + 120q^{91} + 12q^{93} + 4q^{96} - 8q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 1.31856 + 1.12312i 0.761269 + 0.648436i
\(4\) 1.00000i 0.500000i
\(5\) −1.11299 1.93940i −0.497744 0.867324i
\(6\) −1.72653 + 0.138191i −0.704853 + 0.0564162i
\(7\) 1.56700 + 1.56700i 0.592271 + 0.592271i 0.938244 0.345974i \(-0.112451\pi\)
−0.345974 + 0.938244i \(0.612451\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 0.477181 + 2.96181i 0.159060 + 0.987269i
\(10\) 2.15836 + 0.584357i 0.682534 + 0.184790i
\(11\) 5.67280i 1.71041i −0.518287 0.855207i \(-0.673430\pi\)
0.518287 0.855207i \(-0.326570\pi\)
\(12\) 1.12312 1.31856i 0.324218 0.380634i
\(13\) 1.86804 1.86804i 0.518102 0.518102i −0.398895 0.916997i \(-0.630606\pi\)
0.916997 + 0.398895i \(0.130606\pi\)
\(14\) −2.21607 −0.592271
\(15\) 0.710643 3.80723i 0.183487 0.983022i
\(16\) −1.00000 −0.250000
\(17\) 4.87994 4.87994i 1.18356 1.18356i 0.204744 0.978816i \(-0.434364\pi\)
0.978816 0.204744i \(-0.0656362\pi\)
\(18\) −2.43173 1.75690i −0.573165 0.414104i
\(19\) 3.95832i 0.908102i 0.890976 + 0.454051i \(0.150022\pi\)
−0.890976 + 0.454051i \(0.849978\pi\)
\(20\) −1.93940 + 1.11299i −0.433662 + 0.248872i
\(21\) 0.306241 + 3.82612i 0.0668273 + 0.834927i
\(22\) 4.01127 + 4.01127i 0.855207 + 0.855207i
\(23\) 0.707107 + 0.707107i 0.147442 + 0.147442i
\(24\) 0.138191 + 1.72653i 0.0282081 + 0.352426i
\(25\) −2.52251 + 4.31705i −0.504501 + 0.863411i
\(26\) 2.64181i 0.518102i
\(27\) −2.69729 + 4.44124i −0.519093 + 0.854718i
\(28\) 1.56700 1.56700i 0.296135 0.296135i
\(29\) −0.714554 −0.132689 −0.0663447 0.997797i \(-0.521134\pi\)
−0.0663447 + 0.997797i \(0.521134\pi\)
\(30\) 2.18962 + 3.19462i 0.399767 + 0.583255i
\(31\) 6.39562 1.14869 0.574343 0.818615i \(-0.305257\pi\)
0.574343 + 0.818615i \(0.305257\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 6.37126 7.47990i 1.10909 1.30208i
\(34\) 6.90128i 1.18356i
\(35\) 1.29498 4.78309i 0.218891 0.808490i
\(36\) 2.96181 0.477181i 0.493634 0.0795302i
\(37\) −2.92359 2.92359i −0.480635 0.480635i 0.424699 0.905334i \(-0.360380\pi\)
−0.905334 + 0.424699i \(0.860380\pi\)
\(38\) −2.79896 2.79896i −0.454051 0.454051i
\(39\) 4.56117 0.365074i 0.730371 0.0584587i
\(40\) 0.584357 2.15836i 0.0923949 0.341267i
\(41\) 4.88651i 0.763144i 0.924339 + 0.381572i \(0.124617\pi\)
−0.924339 + 0.381572i \(0.875383\pi\)
\(42\) −2.92202 2.48893i −0.450877 0.384050i
\(43\) 8.81584 8.81584i 1.34440 1.34440i 0.452782 0.891621i \(-0.350431\pi\)
0.891621 0.452782i \(-0.149569\pi\)
\(44\) −5.67280 −0.855207
\(45\) 5.21302 4.22190i 0.777110 0.629364i
\(46\) −1.00000 −0.147442
\(47\) −4.01373 + 4.01373i −0.585462 + 0.585462i −0.936399 0.350937i \(-0.885863\pi\)
0.350937 + 0.936399i \(0.385863\pi\)
\(48\) −1.31856 1.12312i −0.190317 0.162109i
\(49\) 2.08902i 0.298431i
\(50\) −1.26894 4.83630i −0.179455 0.683956i
\(51\) 11.9153 0.953694i 1.66847 0.133544i
\(52\) −1.86804 1.86804i −0.259051 0.259051i
\(53\) 5.27160 + 5.27160i 0.724111 + 0.724111i 0.969440 0.245329i \(-0.0788961\pi\)
−0.245329 + 0.969440i \(0.578896\pi\)
\(54\) −1.23316 5.04770i −0.167812 0.686905i
\(55\) −11.0018 + 6.31377i −1.48348 + 0.851348i
\(56\) 2.21607i 0.296135i
\(57\) −4.44569 + 5.21927i −0.588846 + 0.691310i
\(58\) 0.505266 0.505266i 0.0663447 0.0663447i
\(59\) 7.32082 0.953089 0.476545 0.879150i \(-0.341889\pi\)
0.476545 + 0.879150i \(0.341889\pi\)
\(60\) −3.80723 0.710643i −0.491511 0.0917436i
\(61\) −4.73865 −0.606722 −0.303361 0.952876i \(-0.598109\pi\)
−0.303361 + 0.952876i \(0.598109\pi\)
\(62\) −4.52238 + 4.52238i −0.574343 + 0.574343i
\(63\) −3.89341 + 5.38890i −0.490524 + 0.678937i
\(64\) 1.00000i 0.125000i
\(65\) −5.70199 1.54376i −0.707244 0.191480i
\(66\) 0.783929 + 9.79425i 0.0964950 + 1.20559i
\(67\) 6.02909 + 6.02909i 0.736571 + 0.736571i 0.971913 0.235342i \(-0.0756210\pi\)
−0.235342 + 0.971913i \(0.575621\pi\)
\(68\) −4.87994 4.87994i −0.591780 0.591780i
\(69\) 0.138191 + 1.72653i 0.0166362 + 0.207850i
\(70\) 2.46647 + 4.29784i 0.294799 + 0.513691i
\(71\) 4.27468i 0.507311i 0.967295 + 0.253656i \(0.0816330\pi\)
−0.967295 + 0.253656i \(0.918367\pi\)
\(72\) −1.75690 + 2.43173i −0.207052 + 0.286582i
\(73\) −5.13585 + 5.13585i −0.601106 + 0.601106i −0.940606 0.339500i \(-0.889742\pi\)
0.339500 + 0.940606i \(0.389742\pi\)
\(74\) 4.13458 0.480635
\(75\) −8.17466 + 2.85919i −0.943928 + 0.330151i
\(76\) 3.95832 0.454051
\(77\) 8.88928 8.88928i 1.01303 1.01303i
\(78\) −2.96708 + 3.48338i −0.335956 + 0.394415i
\(79\) 7.27349i 0.818332i 0.912460 + 0.409166i \(0.134180\pi\)
−0.912460 + 0.409166i \(0.865820\pi\)
\(80\) 1.11299 + 1.93940i 0.124436 + 0.216831i
\(81\) −8.54460 + 2.82664i −0.949400 + 0.314071i
\(82\) −3.45528 3.45528i −0.381572 0.381572i
\(83\) −10.9094 10.9094i −1.19746 1.19746i −0.974924 0.222537i \(-0.928566\pi\)
−0.222537 0.974924i \(-0.571434\pi\)
\(84\) 3.82612 0.306241i 0.417464 0.0334137i
\(85\) −14.8955 4.03281i −1.61564 0.437420i
\(86\) 12.4675i 1.34440i
\(87\) −0.942179 0.802533i −0.101012 0.0860406i
\(88\) 4.01127 4.01127i 0.427603 0.427603i
\(89\) −8.06770 −0.855175 −0.427587 0.903974i \(-0.640636\pi\)
−0.427587 + 0.903974i \(0.640636\pi\)
\(90\) −0.700822 + 6.67150i −0.0738731 + 0.703237i
\(91\) 5.85445 0.613713
\(92\) 0.707107 0.707107i 0.0737210 0.0737210i
\(93\) 8.43298 + 7.18308i 0.874459 + 0.744850i
\(94\) 5.67627i 0.585462i
\(95\) 7.67675 4.40558i 0.787618 0.452002i
\(96\) 1.72653 0.138191i 0.176213 0.0141040i
\(97\) −0.309834 0.309834i −0.0314589 0.0314589i 0.691202 0.722661i \(-0.257081\pi\)
−0.722661 + 0.691202i \(0.757081\pi\)
\(98\) 1.47716 + 1.47716i 0.149215 + 0.149215i
\(99\) 16.8017 2.70695i 1.68864 0.272059i
\(100\) 4.31705 + 2.52251i 0.431705 + 0.252251i
\(101\) 3.88898i 0.386968i 0.981103 + 0.193484i \(0.0619787\pi\)
−0.981103 + 0.193484i \(0.938021\pi\)
\(102\) −7.75100 + 9.09972i −0.767463 + 0.901007i
\(103\) 7.73444 7.73444i 0.762097 0.762097i −0.214604 0.976701i \(-0.568846\pi\)
0.976701 + 0.214604i \(0.0688462\pi\)
\(104\) 2.64181 0.259051
\(105\) 7.07951 4.85235i 0.690889 0.473541i
\(106\) −7.45518 −0.724111
\(107\) −6.15366 + 6.15366i −0.594897 + 0.594897i −0.938950 0.344053i \(-0.888200\pi\)
0.344053 + 0.938950i \(0.388200\pi\)
\(108\) 4.44124 + 2.69729i 0.427359 + 0.259547i
\(109\) 8.34777i 0.799571i 0.916609 + 0.399786i \(0.130915\pi\)
−0.916609 + 0.399786i \(0.869085\pi\)
\(110\) 3.31494 12.2440i 0.316067 1.16742i
\(111\) −0.571361 7.13847i −0.0542312 0.677554i
\(112\) −1.56700 1.56700i −0.148068 0.148068i
\(113\) −9.04524 9.04524i −0.850904 0.850904i 0.139340 0.990245i \(-0.455502\pi\)
−0.990245 + 0.139340i \(0.955502\pi\)
\(114\) −0.547004 6.83416i −0.0512316 0.640078i
\(115\) 0.584357 2.15836i 0.0544915 0.201268i
\(116\) 0.714554i 0.0663447i
\(117\) 6.42418 + 4.64139i 0.593915 + 0.429096i
\(118\) −5.17660 + 5.17660i −0.476545 + 0.476545i
\(119\) 15.2937 1.40198
\(120\) 3.19462 2.18962i 0.291627 0.199884i
\(121\) −21.1806 −1.92551
\(122\) 3.35073 3.35073i 0.303361 0.303361i
\(123\) −5.48816 + 6.44314i −0.494851 + 0.580958i
\(124\) 6.39562i 0.574343i
\(125\) 11.1800 + 0.0872994i 0.999970 + 0.00780829i
\(126\) −1.05747 6.56358i −0.0942068 0.584730i
\(127\) −6.47403 6.47403i −0.574477 0.574477i 0.358899 0.933376i \(-0.383152\pi\)
−0.933376 + 0.358899i \(0.883152\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 21.5255 1.72289i 1.89521 0.151692i
\(130\) 5.12352 2.94031i 0.449362 0.257882i
\(131\) 20.4667i 1.78819i −0.447879 0.894094i \(-0.647821\pi\)
0.447879 0.894094i \(-0.352179\pi\)
\(132\) −7.47990 6.37126i −0.651042 0.554547i
\(133\) −6.20270 + 6.20270i −0.537842 + 0.537842i
\(134\) −8.52642 −0.736571
\(135\) 11.6154 + 0.288049i 0.999693 + 0.0247914i
\(136\) 6.90128 0.591780
\(137\) −4.59633 + 4.59633i −0.392691 + 0.392691i −0.875646 0.482954i \(-0.839564\pi\)
0.482954 + 0.875646i \(0.339564\pi\)
\(138\) −1.31856 1.12312i −0.112243 0.0956067i
\(139\) 3.93595i 0.333843i −0.985970 0.166921i \(-0.946617\pi\)
0.985970 0.166921i \(-0.0533826\pi\)
\(140\) −4.78309 1.29498i −0.404245 0.109446i
\(141\) −9.80025 + 0.784409i −0.825330 + 0.0660591i
\(142\) −3.02266 3.02266i −0.253656 0.253656i
\(143\) −10.5970 10.5970i −0.886168 0.886168i
\(144\) −0.477181 2.96181i −0.0397651 0.246817i
\(145\) 0.795291 + 1.38580i 0.0660453 + 0.115085i
\(146\) 7.26319i 0.601106i
\(147\) 2.34622 2.75448i 0.193513 0.227186i
\(148\) −2.92359 + 2.92359i −0.240318 + 0.240318i
\(149\) 8.75534 0.717265 0.358633 0.933479i \(-0.383243\pi\)
0.358633 + 0.933479i \(0.383243\pi\)
\(150\) 3.75860 7.80211i 0.306889 0.637039i
\(151\) −2.00457 −0.163130 −0.0815650 0.996668i \(-0.525992\pi\)
−0.0815650 + 0.996668i \(0.525992\pi\)
\(152\) −2.79896 + 2.79896i −0.227025 + 0.227025i
\(153\) 16.7821 + 12.1248i 1.35675 + 0.980234i
\(154\) 12.5713i 1.01303i
\(155\) −7.11826 12.4036i −0.571752 0.996283i
\(156\) −0.365074 4.56117i −0.0292293 0.365186i
\(157\) −11.6798 11.6798i −0.932150 0.932150i 0.0656901 0.997840i \(-0.479075\pi\)
−0.997840 + 0.0656901i \(0.979075\pi\)
\(158\) −5.14314 5.14314i −0.409166 0.409166i
\(159\) 1.03024 + 12.8716i 0.0817031 + 1.02078i
\(160\) −2.15836 0.584357i −0.170634 0.0461975i
\(161\) 2.21607i 0.174651i
\(162\) 4.04321 8.04068i 0.317664 0.631735i
\(163\) 7.42502 7.42502i 0.581572 0.581572i −0.353763 0.935335i \(-0.615098\pi\)
0.935335 + 0.353763i \(0.115098\pi\)
\(164\) 4.88651 0.381572
\(165\) −21.5976 4.03133i −1.68137 0.313839i
\(166\) 15.4282 1.19746
\(167\) −16.1431 + 16.1431i −1.24919 + 1.24919i −0.293107 + 0.956080i \(0.594689\pi\)
−0.956080 + 0.293107i \(0.905311\pi\)
\(168\) −2.48893 + 2.92202i −0.192025 + 0.225439i
\(169\) 6.02083i 0.463141i
\(170\) 13.3843 7.68105i 1.02653 0.589110i
\(171\) −11.7238 + 1.88884i −0.896541 + 0.144443i
\(172\) −8.81584 8.81584i −0.672202 0.672202i
\(173\) −5.17329 5.17329i −0.393318 0.393318i 0.482550 0.875868i \(-0.339711\pi\)
−0.875868 + 0.482550i \(0.839711\pi\)
\(174\) 1.23370 0.0987448i 0.0935264 0.00748583i
\(175\) −10.7176 + 2.81206i −0.810174 + 0.212572i
\(176\) 5.67280i 0.427603i
\(177\) 9.65291 + 8.22219i 0.725557 + 0.618018i
\(178\) 5.70473 5.70473i 0.427587 0.427587i
\(179\) −5.95726 −0.445266 −0.222633 0.974902i \(-0.571465\pi\)
−0.222633 + 0.974902i \(0.571465\pi\)
\(180\) −4.22190 5.21302i −0.314682 0.388555i
\(181\) −1.45319 −0.108015 −0.0540074 0.998541i \(-0.517199\pi\)
−0.0540074 + 0.998541i \(0.517199\pi\)
\(182\) −4.13972 + 4.13972i −0.306857 + 0.306857i
\(183\) −6.24818 5.32209i −0.461878 0.393421i
\(184\) 1.00000i 0.0737210i
\(185\) −2.41607 + 8.92392i −0.177633 + 0.656100i
\(186\) −11.0422 + 0.883816i −0.809655 + 0.0648045i
\(187\) −27.6829 27.6829i −2.02438 2.02438i
\(188\) 4.01373 + 4.01373i 0.292731 + 0.292731i
\(189\) −11.1861 + 2.73278i −0.813668 + 0.198780i
\(190\) −2.31307 + 8.54350i −0.167808 + 0.619810i
\(191\) 18.2037i 1.31717i 0.752506 + 0.658586i \(0.228845\pi\)
−0.752506 + 0.658586i \(0.771155\pi\)
\(192\) −1.12312 + 1.31856i −0.0810546 + 0.0951586i
\(193\) 16.1230 16.1230i 1.16056 1.16056i 0.176208 0.984353i \(-0.443617\pi\)
0.984353 0.176208i \(-0.0563830\pi\)
\(194\) 0.438172 0.0314589
\(195\) −5.78455 8.43958i −0.414241 0.604371i
\(196\) −2.08902 −0.149215
\(197\) −18.1766 + 18.1766i −1.29503 + 1.29503i −0.363393 + 0.931636i \(0.618382\pi\)
−0.931636 + 0.363393i \(0.881618\pi\)
\(198\) −9.96651 + 13.7947i −0.708289 + 0.980348i
\(199\) 0.617379i 0.0437648i −0.999761 0.0218824i \(-0.993034\pi\)
0.999761 0.0218824i \(-0.00696594\pi\)
\(200\) −4.83630 + 1.26894i −0.341978 + 0.0897274i
\(201\) 1.17827 + 14.7211i 0.0831090 + 1.03835i
\(202\) −2.74992 2.74992i −0.193484 0.193484i
\(203\) −1.11971 1.11971i −0.0785880 0.0785880i
\(204\) −0.953694 11.9153i −0.0667719 0.834235i
\(205\) 9.47687 5.43863i 0.661893 0.379851i
\(206\) 10.9381i 0.762097i
\(207\) −1.75690 + 2.43173i −0.122113 + 0.169017i
\(208\) −1.86804 + 1.86804i −0.129525 + 0.129525i
\(209\) 22.4548 1.55323
\(210\) −1.57484 + 8.43710i −0.108674 + 0.582215i
\(211\) −9.86494 −0.679130 −0.339565 0.940583i \(-0.610280\pi\)
−0.339565 + 0.940583i \(0.610280\pi\)
\(212\) 5.27160 5.27160i 0.362055 0.362055i
\(213\) −4.80100 + 5.63641i −0.328959 + 0.386200i
\(214\) 8.70259i 0.594897i
\(215\) −26.9093 7.28546i −1.83520 0.496864i
\(216\) −5.04770 + 1.23316i −0.343453 + 0.0839060i
\(217\) 10.0219 + 10.0219i 0.680334 + 0.680334i
\(218\) −5.90276 5.90276i −0.399786 0.399786i
\(219\) −12.5401 + 1.00371i −0.847383 + 0.0678242i
\(220\) 6.31377 + 11.0018i 0.425674 + 0.741741i
\(221\) 18.2319i 1.22641i
\(222\) 5.45168 + 4.64365i 0.365892 + 0.311661i
\(223\) −3.88670 + 3.88670i −0.260273 + 0.260273i −0.825165 0.564892i \(-0.808918\pi\)
0.564892 + 0.825165i \(0.308918\pi\)
\(224\) 2.21607 0.148068
\(225\) −13.9900 5.41116i −0.932665 0.360744i
\(226\) 12.7919 0.850904
\(227\) 17.3335 17.3335i 1.15046 1.15046i 0.164003 0.986460i \(-0.447559\pi\)
0.986460 0.164003i \(-0.0524406\pi\)
\(228\) 5.21927 + 4.44569i 0.345655 + 0.294423i
\(229\) 7.33027i 0.484398i 0.970227 + 0.242199i \(0.0778687\pi\)
−0.970227 + 0.242199i \(0.922131\pi\)
\(230\) 1.11299 + 1.93940i 0.0733884 + 0.127880i
\(231\) 21.7048 1.73724i 1.42807 0.114302i
\(232\) −0.505266 0.505266i −0.0331723 0.0331723i
\(233\) 5.63455 + 5.63455i 0.369131 + 0.369131i 0.867160 0.498029i \(-0.165943\pi\)
−0.498029 + 0.867160i \(0.665943\pi\)
\(234\) −7.82454 + 1.26062i −0.511506 + 0.0824095i
\(235\) 12.2514 + 3.31697i 0.799196 + 0.216375i
\(236\) 7.32082i 0.476545i
\(237\) −8.16904 + 9.59051i −0.530636 + 0.622971i
\(238\) −10.8143 + 10.8143i −0.700988 + 0.700988i
\(239\) −2.57538 −0.166588 −0.0832938 0.996525i \(-0.526544\pi\)
−0.0832938 + 0.996525i \(0.526544\pi\)
\(240\) −0.710643 + 3.80723i −0.0458718 + 0.245756i
\(241\) 19.0373 1.22630 0.613150 0.789966i \(-0.289902\pi\)
0.613150 + 0.789966i \(0.289902\pi\)
\(242\) 14.9770 14.9770i 0.962756 0.962756i
\(243\) −14.4412 5.86957i −0.926403 0.376533i
\(244\) 4.73865i 0.303361i
\(245\) −4.05143 + 2.32505i −0.258836 + 0.148542i
\(246\) −0.675271 8.43670i −0.0430537 0.537904i
\(247\) 7.39432 + 7.39432i 0.470489 + 0.470489i
\(248\) 4.52238 + 4.52238i 0.287172 + 0.287172i
\(249\) −2.13204 26.6373i −0.135112 1.68807i
\(250\) −7.96718 + 7.84372i −0.503889 + 0.496081i
\(251\) 4.04938i 0.255595i 0.991800 + 0.127797i \(0.0407907\pi\)
−0.991800 + 0.127797i \(0.959209\pi\)
\(252\) 5.38890 + 3.89341i 0.339469 + 0.245262i
\(253\) 4.01127 4.01127i 0.252187 0.252187i
\(254\) 9.15566 0.574477
\(255\) −15.1112 22.0469i −0.946297 1.38063i
\(256\) 1.00000 0.0625000
\(257\) 4.10051 4.10051i 0.255783 0.255783i −0.567554 0.823336i \(-0.692110\pi\)
0.823336 + 0.567554i \(0.192110\pi\)
\(258\) −14.0025 + 16.4391i −0.871760 + 1.02345i
\(259\) 9.16253i 0.569332i
\(260\) −1.54376 + 5.70199i −0.0957400 + 0.353622i
\(261\) −0.340972 2.11637i −0.0211056 0.131000i
\(262\) 14.4722 + 14.4722i 0.894094 + 0.894094i
\(263\) −13.1034 13.1034i −0.807991 0.807991i 0.176338 0.984330i \(-0.443575\pi\)
−0.984330 + 0.176338i \(0.943575\pi\)
\(264\) 9.79425 0.783929i 0.602795 0.0482475i
\(265\) 4.35648 16.0910i 0.267617 0.988460i
\(266\) 8.77194i 0.537842i
\(267\) −10.6377 9.06104i −0.651018 0.554526i
\(268\) 6.02909 6.02909i 0.368285 0.368285i
\(269\) −8.38175 −0.511044 −0.255522 0.966803i \(-0.582247\pi\)
−0.255522 + 0.966803i \(0.582247\pi\)
\(270\) −8.41699 + 8.00963i −0.512242 + 0.487451i
\(271\) −5.96566 −0.362388 −0.181194 0.983447i \(-0.557996\pi\)
−0.181194 + 0.983447i \(0.557996\pi\)
\(272\) −4.87994 + 4.87994i −0.295890 + 0.295890i
\(273\) 7.71942 + 6.57528i 0.467201 + 0.397954i
\(274\) 6.50020i 0.392691i
\(275\) 24.4898 + 14.3097i 1.47679 + 0.862906i
\(276\) 1.72653 0.138191i 0.103925 0.00831811i
\(277\) 0.912280 + 0.912280i 0.0548136 + 0.0548136i 0.733982 0.679169i \(-0.237660\pi\)
−0.679169 + 0.733982i \(0.737660\pi\)
\(278\) 2.78313 + 2.78313i 0.166921 + 0.166921i
\(279\) 3.05187 + 18.9426i 0.182711 + 1.13406i
\(280\) 4.29784 2.46647i 0.256845 0.147400i
\(281\) 28.8512i 1.72112i 0.509353 + 0.860558i \(0.329885\pi\)
−0.509353 + 0.860558i \(0.670115\pi\)
\(282\) 6.37516 7.48448i 0.379635 0.445694i
\(283\) −17.7013 + 17.7013i −1.05223 + 1.05223i −0.0536753 + 0.998558i \(0.517094\pi\)
−0.998558 + 0.0536753i \(0.982906\pi\)
\(284\) 4.27468 0.253656
\(285\) 15.0702 + 2.81296i 0.892684 + 0.166625i
\(286\) 14.9865 0.886168
\(287\) −7.65716 + 7.65716i −0.451988 + 0.451988i
\(288\) 2.43173 + 1.75690i 0.143291 + 0.103526i
\(289\) 30.6277i 1.80163i
\(290\) −1.54227 0.417554i −0.0905650 0.0245196i
\(291\) −0.0605514 0.756517i −0.00354958 0.0443478i
\(292\) 5.13585 + 5.13585i 0.300553 + 0.300553i
\(293\) 23.0340 + 23.0340i 1.34566 + 1.34566i 0.890313 + 0.455348i \(0.150485\pi\)
0.455348 + 0.890313i \(0.349515\pi\)
\(294\) 0.288683 + 3.60675i 0.0168363 + 0.210350i
\(295\) −8.14799 14.1980i −0.474395 0.826637i
\(296\) 4.13458i 0.240318i
\(297\) 25.1943 + 15.3012i 1.46192 + 0.887864i
\(298\) −6.19096 + 6.19096i −0.358633 + 0.358633i
\(299\) 2.64181 0.152780
\(300\) 2.85919 + 8.17466i 0.165075 + 0.471964i
\(301\) 27.6289 1.59250
\(302\) 1.41745 1.41745i 0.0815650 0.0815650i
\(303\) −4.36781 + 5.12784i −0.250924 + 0.294587i
\(304\) 3.95832i 0.227025i
\(305\) 5.27407 + 9.19011i 0.301992 + 0.526224i
\(306\) −20.4403 + 3.29316i −1.16849 + 0.188257i
\(307\) 8.12472 + 8.12472i 0.463702 + 0.463702i 0.899867 0.436164i \(-0.143663\pi\)
−0.436164 + 0.899867i \(0.643663\pi\)
\(308\) −8.88928 8.88928i −0.506514 0.506514i
\(309\) 18.8850 1.51155i 1.07433 0.0859892i
\(310\) 13.8041 + 3.73732i 0.784018 + 0.212266i
\(311\) 12.7900i 0.725256i 0.931934 + 0.362628i \(0.118120\pi\)
−0.931934 + 0.362628i \(0.881880\pi\)
\(312\) 3.48338 + 2.96708i 0.197207 + 0.167978i
\(313\) −3.96504 + 3.96504i −0.224117 + 0.224117i −0.810230 0.586112i \(-0.800658\pi\)
0.586112 + 0.810230i \(0.300658\pi\)
\(314\) 16.5177 0.932150
\(315\) 14.7845 + 1.55307i 0.833014 + 0.0875058i
\(316\) 7.27349 0.409166
\(317\) 0.469818 0.469818i 0.0263876 0.0263876i −0.693790 0.720177i \(-0.744060\pi\)
0.720177 + 0.693790i \(0.244060\pi\)
\(318\) −9.83007 8.37309i −0.551243 0.469540i
\(319\) 4.05352i 0.226954i
\(320\) 1.93940 1.11299i 0.108415 0.0622180i
\(321\) −15.0253 + 1.20262i −0.838630 + 0.0671237i
\(322\) −1.56700 1.56700i −0.0873256 0.0873256i
\(323\) 19.3164 + 19.3164i 1.07479 + 1.07479i
\(324\) 2.82664 + 8.54460i 0.157035 + 0.474700i
\(325\) 3.35229 + 12.7766i 0.185952 + 0.708718i
\(326\) 10.5006i 0.581572i
\(327\) −9.37559 + 11.0070i −0.518471 + 0.608689i
\(328\) −3.45528 + 3.45528i −0.190786 + 0.190786i
\(329\) −12.5790 −0.693505
\(330\) 18.1224 12.4213i 0.997606 0.683767i
\(331\) −21.1336 −1.16161 −0.580805 0.814043i \(-0.697262\pi\)
−0.580805 + 0.814043i \(0.697262\pi\)
\(332\) −10.9094 + 10.9094i −0.598731 + 0.598731i
\(333\) 7.26402 10.0542i 0.398066 0.550966i
\(334\) 22.8297i 1.24919i
\(335\) 4.98247 18.4031i 0.272222 1.00547i
\(336\) −0.306241 3.82612i −0.0167068 0.208732i
\(337\) 10.8685 + 10.8685i 0.592045 + 0.592045i 0.938183 0.346138i \(-0.112507\pi\)
−0.346138 + 0.938183i \(0.612507\pi\)
\(338\) −4.25737 4.25737i −0.231570 0.231570i
\(339\) −1.76772 22.0856i −0.0960095 1.19952i
\(340\) −4.03281 + 14.8955i −0.218710 + 0.807820i
\(341\) 36.2810i 1.96473i
\(342\) 6.95436 9.62558i 0.376049 0.520492i
\(343\) 14.2425 14.2425i 0.769023 0.769023i
\(344\) 12.4675 0.672202
\(345\) 3.19462 2.18962i 0.171992 0.117885i
\(346\) 7.31614 0.393318
\(347\) 14.4344 14.4344i 0.774878 0.774878i −0.204077 0.978955i \(-0.565419\pi\)
0.978955 + 0.204077i \(0.0654191\pi\)
\(348\) −0.802533 + 0.942179i −0.0430203 + 0.0505061i
\(349\) 35.9155i 1.92251i 0.275655 + 0.961257i \(0.411105\pi\)
−0.275655 + 0.961257i \(0.588895\pi\)
\(350\) 5.59006 9.56691i 0.298801 0.511373i
\(351\) 3.25778 + 13.3351i 0.173888 + 0.711774i
\(352\) −4.01127 4.01127i −0.213802 0.213802i
\(353\) −4.89196 4.89196i −0.260373 0.260373i 0.564833 0.825206i \(-0.308941\pi\)
−0.825206 + 0.564833i \(0.808941\pi\)
\(354\) −12.6396 + 1.01167i −0.671787 + 0.0537697i
\(355\) 8.29030 4.75768i 0.440003 0.252511i
\(356\) 8.06770i 0.427587i
\(357\) 20.1657 + 17.1768i 1.06728 + 0.909092i
\(358\) 4.21242 4.21242i 0.222633 0.222633i
\(359\) −32.9343 −1.73821 −0.869103 0.494630i \(-0.835303\pi\)
−0.869103 + 0.494630i \(0.835303\pi\)
\(360\) 6.67150 + 0.700822i 0.351619 + 0.0369365i
\(361\) 3.33167 0.175351
\(362\) 1.02756 1.02756i 0.0540074 0.0540074i
\(363\) −27.9279 23.7885i −1.46583 1.24857i
\(364\) 5.85445i 0.306857i
\(365\) 15.6766 + 4.24430i 0.820551 + 0.222157i
\(366\) 8.18142 0.654838i 0.427649 0.0342289i
\(367\) −16.9661 16.9661i −0.885624 0.885624i 0.108475 0.994099i \(-0.465403\pi\)
−0.994099 + 0.108475i \(0.965403\pi\)
\(368\) −0.707107 0.707107i −0.0368605 0.0368605i
\(369\) −14.4729 + 2.33175i −0.753429 + 0.121386i
\(370\) −4.60174 8.01858i −0.239233 0.416866i
\(371\) 16.5212i 0.857739i
\(372\) 7.18308 8.43298i 0.372425 0.437230i
\(373\) −7.20832 + 7.20832i −0.373233 + 0.373233i −0.868653 0.495420i \(-0.835014\pi\)
0.495420 + 0.868653i \(0.335014\pi\)
\(374\) 39.1496 2.02438
\(375\) 14.6434 + 12.6716i 0.756182 + 0.654361i
\(376\) −5.67627 −0.292731
\(377\) −1.33482 + 1.33482i −0.0687466 + 0.0687466i
\(378\) 5.97739 9.84212i 0.307444 0.506224i
\(379\) 0.269443i 0.0138404i 0.999976 + 0.00692018i \(0.00220278\pi\)
−0.999976 + 0.00692018i \(0.997797\pi\)
\(380\) −4.40558 7.67675i −0.226001 0.393809i
\(381\) −1.26523 15.8075i −0.0648197 0.809844i
\(382\) −12.8719 12.8719i −0.658586 0.658586i
\(383\) 14.7895 + 14.7895i 0.755707 + 0.755707i 0.975538 0.219831i \(-0.0705506\pi\)
−0.219831 + 0.975538i \(0.570551\pi\)
\(384\) −0.138191 1.72653i −0.00705202 0.0881066i
\(385\) −27.1335 7.34615i −1.38285 0.374394i
\(386\) 22.8014i 1.16056i
\(387\) 30.3176 + 21.9041i 1.54113 + 1.11345i
\(388\) −0.309834 + 0.309834i −0.0157295 + 0.0157295i
\(389\) −34.0408 −1.72594 −0.862970 0.505256i \(-0.831398\pi\)
−0.862970 + 0.505256i \(0.831398\pi\)
\(390\) 10.0580 + 1.87739i 0.509306 + 0.0950651i
\(391\) 6.90128 0.349013
\(392\) 1.47716 1.47716i 0.0746077 0.0746077i
\(393\) 22.9867 26.9866i 1.15953 1.36129i
\(394\) 25.7056i 1.29503i
\(395\) 14.1062 8.09533i 0.709759 0.407320i
\(396\) −2.70695 16.8017i −0.136029 0.844319i
\(397\) 15.3440 + 15.3440i 0.770093 + 0.770093i 0.978122 0.208030i \(-0.0667051\pi\)
−0.208030 + 0.978122i \(0.566705\pi\)
\(398\) 0.436553 + 0.436553i 0.0218824 + 0.0218824i
\(399\) −15.1450 + 1.21220i −0.758199 + 0.0606860i
\(400\) 2.52251 4.31705i 0.126125 0.215853i
\(401\) 11.5244i 0.575503i 0.957705 + 0.287752i \(0.0929078\pi\)
−0.957705 + 0.287752i \(0.907092\pi\)
\(402\) −11.2426 9.57624i −0.560728 0.477619i
\(403\) 11.9473 11.9473i 0.595137 0.595137i
\(404\) 3.88898 0.193484
\(405\) 14.9920 + 13.4253i 0.744959 + 0.667110i
\(406\) 1.58350 0.0785880
\(407\) −16.5849 + 16.5849i −0.822084 + 0.822084i
\(408\) 9.09972 + 7.75100i 0.450504 + 0.383732i
\(409\) 14.4328i 0.713658i 0.934170 + 0.356829i \(0.116142\pi\)
−0.934170 + 0.356829i \(0.883858\pi\)
\(410\) −2.85546 + 10.5469i −0.141021 + 0.520872i
\(411\) −11.2228 + 0.898268i −0.553579 + 0.0443083i
\(412\) −7.73444 7.73444i −0.381048 0.381048i
\(413\) 11.4717 + 11.4717i 0.564487 + 0.564487i
\(414\) −0.477181 2.96181i −0.0234522 0.145565i
\(415\) −9.01558 + 33.2997i −0.442557 + 1.63462i
\(416\) 2.64181i 0.129525i
\(417\) 4.42056 5.18977i 0.216476 0.254144i
\(418\) −15.8779 + 15.8779i −0.776615 + 0.776615i
\(419\) −1.59881 −0.0781072 −0.0390536 0.999237i \(-0.512434\pi\)
−0.0390536 + 0.999237i \(0.512434\pi\)
\(420\) −4.85235 7.07951i −0.236771 0.345445i
\(421\) −3.21224 −0.156555 −0.0782774 0.996932i \(-0.524942\pi\)
−0.0782774 + 0.996932i \(0.524942\pi\)
\(422\) 6.97557 6.97557i 0.339565 0.339565i
\(423\) −13.8032 9.97261i −0.671133 0.484885i
\(424\) 7.45518i 0.362055i
\(425\) 8.75729 + 33.3767i 0.424791 + 1.61901i
\(426\) −0.590722 7.38036i −0.0286206 0.357580i
\(427\) −7.42547 7.42547i −0.359344 0.359344i
\(428\) 6.15366 + 6.15366i 0.297449 + 0.297449i
\(429\) −2.07099 25.8746i −0.0999885 1.24924i
\(430\) 24.1794 13.8762i 1.16603 0.669169i
\(431\) 16.9446i 0.816195i 0.912938 + 0.408097i \(0.133808\pi\)
−0.912938 + 0.408097i \(0.866192\pi\)
\(432\) 2.69729 4.44124i 0.129773 0.213679i
\(433\) −23.5807 + 23.5807i −1.13321 + 1.13321i −0.143576 + 0.989639i \(0.545860\pi\)
−0.989639 + 0.143576i \(0.954140\pi\)
\(434\) −14.1732 −0.680334
\(435\) −0.507793 + 2.72047i −0.0243468 + 0.130437i
\(436\) 8.34777 0.399786
\(437\) −2.79896 + 2.79896i −0.133892 + 0.133892i
\(438\) 8.15747 9.57693i 0.389779 0.457603i
\(439\) 18.7018i 0.892590i 0.894886 + 0.446295i \(0.147257\pi\)
−0.894886 + 0.446295i \(0.852743\pi\)
\(440\) −12.2440 3.31494i −0.583708 0.158033i
\(441\) 6.18726 0.996839i 0.294631 0.0474685i
\(442\) 12.8919 + 12.8919i 0.613205 + 0.613205i
\(443\) 14.4583 + 14.4583i 0.686934 + 0.686934i 0.961553 0.274619i \(-0.0885517\pi\)
−0.274619 + 0.961553i \(0.588552\pi\)
\(444\) −7.13847 + 0.571361i −0.338777 + 0.0271156i
\(445\) 8.97927 + 15.6465i 0.425658 + 0.741713i
\(446\) 5.49662i 0.260273i
\(447\) 11.5444 + 9.83333i 0.546031 + 0.465101i
\(448\) −1.56700 + 1.56700i −0.0740338 + 0.0740338i
\(449\) −21.0282 −0.992382 −0.496191 0.868213i \(-0.665268\pi\)
−0.496191 + 0.868213i \(0.665268\pi\)
\(450\) 13.7187 6.06614i 0.646704 0.285960i
\(451\) 27.7202 1.30529
\(452\) −9.04524 + 9.04524i −0.425452 + 0.425452i
\(453\) −2.64314 2.25139i −0.124186 0.105779i
\(454\) 24.5132i 1.15046i
\(455\) −6.51595 11.3541i −0.305472 0.532288i
\(456\) −6.83416 + 0.547004i −0.320039 + 0.0256158i
\(457\) −15.3590 15.3590i −0.718465 0.718465i 0.249826 0.968291i \(-0.419627\pi\)
−0.968291 + 0.249826i \(0.919627\pi\)
\(458\) −5.18329 5.18329i −0.242199 0.242199i
\(459\) 8.51039 + 34.8356i 0.397231 + 1.62599i
\(460\) −2.15836 0.584357i −0.100634 0.0272458i
\(461\) 33.5271i 1.56151i 0.624837 + 0.780756i \(0.285166\pi\)
−0.624837 + 0.780756i \(0.714834\pi\)
\(462\) −14.1192 + 16.5760i −0.656884 + 0.771186i
\(463\) 22.9496 22.9496i 1.06656 1.06656i 0.0689368 0.997621i \(-0.478039\pi\)
0.997621 0.0689368i \(-0.0219607\pi\)
\(464\) 0.714554 0.0331723
\(465\) 4.54500 24.3496i 0.210769 1.12918i
\(466\) −7.96845 −0.369131
\(467\) 17.4583 17.4583i 0.807875 0.807875i −0.176437 0.984312i \(-0.556457\pi\)
0.984312 + 0.176437i \(0.0564571\pi\)
\(468\) 4.64139 6.42418i 0.214548 0.296958i
\(469\) 18.8952i 0.872499i
\(470\) −11.0085 + 6.31763i −0.507786 + 0.291411i
\(471\) −2.28260 28.5184i −0.105177 1.31406i
\(472\) 5.17660 + 5.17660i 0.238272 + 0.238272i
\(473\) −50.0105 50.0105i −2.29949 2.29949i
\(474\) −1.00513 12.5579i −0.0461672 0.576803i
\(475\) −17.0883 9.98490i −0.784065 0.458139i
\(476\) 15.2937i 0.700988i
\(477\) −13.0980 + 18.1290i −0.599715 + 0.830069i
\(478\) 1.82107 1.82107i 0.0832938 0.0832938i
\(479\) 16.3083 0.745147 0.372573 0.928003i \(-0.378475\pi\)
0.372573 + 0.928003i \(0.378475\pi\)
\(480\) −2.18962 3.19462i −0.0999419 0.145814i
\(481\) −10.9228 −0.498036
\(482\) −13.4614 + 13.4614i −0.613150 + 0.613150i
\(483\) −2.48893 + 2.92202i −0.113250 + 0.132956i
\(484\) 21.1806i 0.962756i
\(485\) −0.256049 + 0.945734i −0.0116266 + 0.0429436i
\(486\) 14.3619 6.06106i 0.651468 0.274935i
\(487\) −12.6082 12.6082i −0.571334 0.571334i 0.361167 0.932501i \(-0.382378\pi\)
−0.932501 + 0.361167i \(0.882378\pi\)
\(488\) −3.35073 3.35073i −0.151680 0.151680i
\(489\) 18.1295 1.45108i 0.819846 0.0656202i
\(490\) 1.22073 4.50885i 0.0551470 0.203689i
\(491\) 29.1446i 1.31528i −0.753334 0.657638i \(-0.771556\pi\)
0.753334 0.657638i \(-0.228444\pi\)
\(492\) 6.44314 + 5.48816i 0.290479 + 0.247425i
\(493\) −3.48698 + 3.48698i −0.157046 + 0.157046i
\(494\) −10.4571 −0.470489
\(495\) −23.9500 29.5724i −1.07647 1.32918i
\(496\) −6.39562 −0.287172
\(497\) −6.69843 + 6.69843i −0.300466 + 0.300466i
\(498\) 20.3430 + 17.3278i 0.911590 + 0.776478i
\(499\) 2.64641i 0.118469i 0.998244 + 0.0592347i \(0.0188660\pi\)
−0.998244 + 0.0592347i \(0.981134\pi\)
\(500\) 0.0872994 11.1800i 0.00390415 0.499985i
\(501\) −39.4162 + 3.15486i −1.76099 + 0.140949i
\(502\) −2.86334 2.86334i −0.127797 0.127797i
\(503\) −3.51592 3.51592i −0.156767 0.156767i 0.624365 0.781133i \(-0.285358\pi\)
−0.781133 + 0.624365i \(0.785358\pi\)
\(504\) −6.56358 + 1.05747i −0.292365 + 0.0471034i
\(505\) 7.54227 4.32839i 0.335626 0.192611i
\(506\) 5.67280i 0.252187i
\(507\) −6.76214 + 7.93880i −0.300317 + 0.352575i
\(508\) −6.47403 + 6.47403i −0.287239 + 0.287239i
\(509\) 0.570411 0.0252830 0.0126415 0.999920i \(-0.495976\pi\)
0.0126415 + 0.999920i \(0.495976\pi\)
\(510\) 26.2747 + 4.90435i 1.16347 + 0.217168i
\(511\) −16.0958 −0.712035
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −17.5799 10.6767i −0.776171 0.471390i
\(514\) 5.79900i 0.255783i
\(515\) −23.6085 6.39178i −1.04031 0.281655i
\(516\) −1.72289 21.5255i −0.0758461 0.947606i
\(517\) 22.7691 + 22.7691i 1.00138 + 1.00138i
\(518\) 6.47889 + 6.47889i 0.284666 + 0.284666i
\(519\) −1.01102 12.6315i −0.0443790 0.554463i
\(520\) −2.94031 5.12352i −0.128941 0.224681i
\(521\) 22.9010i 1.00331i 0.865067 + 0.501656i \(0.167276\pi\)
−0.865067 + 0.501656i \(0.832724\pi\)
\(522\) 1.73760 + 1.25540i 0.0760528 + 0.0549472i
\(523\) 23.8359 23.8359i 1.04227 1.04227i 0.0432069 0.999066i \(-0.486243\pi\)
0.999066 0.0432069i \(-0.0137575\pi\)
\(524\) −20.4667 −0.894094
\(525\) −17.2901 8.32935i −0.754600 0.363522i
\(526\) 18.5310 0.807991
\(527\) 31.2102 31.2102i 1.35954 1.35954i
\(528\) −6.37126 + 7.47990i −0.277274 + 0.325521i
\(529\) 1.00000i 0.0434783i
\(530\) 8.29753 + 14.4585i 0.360422 + 0.628038i
\(531\) 3.49336 + 21.6828i 0.151599 + 0.940955i
\(532\) 6.20270 + 6.20270i 0.268921 + 0.268921i
\(533\) 9.12821 + 9.12821i 0.395387 + 0.395387i
\(534\) 13.9291 1.11488i 0.602772 0.0482457i
\(535\) 18.7833 + 5.08542i 0.812075 + 0.219862i
\(536\) 8.52642i 0.368285i
\(537\) −7.85498 6.69074i −0.338967 0.288727i
\(538\) 5.92679 5.92679i 0.255522 0.255522i
\(539\) −11.8506 −0.510440
\(540\) 0.288049 11.6154i 0.0123957 0.499846i
\(541\) −19.8837 −0.854868 −0.427434 0.904047i \(-0.640582\pi\)
−0.427434 + 0.904047i \(0.640582\pi\)
\(542\) 4.21836 4.21836i 0.181194 0.181194i
\(543\) −1.91611 1.63211i −0.0822283 0.0700407i
\(544\) 6.90128i 0.295890i
\(545\) 16.1896 9.29098i 0.693487 0.397982i
\(546\) −10.1079 + 0.809032i −0.432577 + 0.0346234i
\(547\) 1.43836 + 1.43836i 0.0614997 + 0.0614997i 0.737188 0.675688i \(-0.236153\pi\)
−0.675688 + 0.737188i \(0.736153\pi\)
\(548\) 4.59633 + 4.59633i 0.196346 + 0.196346i
\(549\) −2.26119 14.0350i −0.0965054 0.598998i
\(550\) −27.4354 + 7.19842i −1.16985 + 0.306942i
\(551\) 2.82844i 0.120495i
\(552\) −1.12312 + 1.31856i −0.0478034 + 0.0561215i
\(553\) −11.3976 + 11.3976i −0.484674 + 0.484674i
\(554\) −1.29016 −0.0548136
\(555\) −13.2084 + 9.05314i −0.560665 + 0.384284i
\(556\) −3.93595 −0.166921
\(557\) 4.53628 4.53628i 0.192208 0.192208i −0.604441 0.796650i \(-0.706604\pi\)
0.796650 + 0.604441i \(0.206604\pi\)
\(558\) −15.5524 11.2364i −0.658387 0.475676i
\(559\) 32.9367i 1.39308i
\(560\) −1.29498 + 4.78309i −0.0547228 + 0.202122i
\(561\) −5.41011 67.5929i −0.228415 2.85377i
\(562\) −20.4008 20.4008i −0.860558 0.860558i
\(563\) 1.12010 + 1.12010i 0.0472067 + 0.0472067i 0.730316 0.683109i \(-0.239373\pi\)
−0.683109 + 0.730316i \(0.739373\pi\)
\(564\) 0.784409 + 9.80025i 0.0330296 + 0.412665i
\(565\) −7.47503 + 27.6095i −0.314477 + 1.16154i
\(566\) 25.0334i 1.05223i
\(567\) −17.8187 8.96005i −0.748317 0.376287i
\(568\) −3.02266 + 3.02266i −0.126828 + 0.126828i
\(569\) 22.6299 0.948693 0.474347 0.880338i \(-0.342684\pi\)
0.474347 + 0.880338i \(0.342684\pi\)
\(570\) −12.6453 + 8.66721i −0.529655 + 0.363030i
\(571\) 46.0793 1.92836 0.964178 0.265254i \(-0.0854559\pi\)
0.964178 + 0.265254i \(0.0854559\pi\)
\(572\) −10.5970 + 10.5970i −0.443084 + 0.443084i
\(573\) −20.4450 + 24.0026i −0.854102 + 1.00272i
\(574\) 10.8289i 0.451988i
\(575\) −4.83630 + 1.26894i −0.201688 + 0.0529183i
\(576\) −2.96181 + 0.477181i −0.123409 + 0.0198825i
\(577\) −11.0358 11.0358i −0.459427 0.459427i 0.439041 0.898467i \(-0.355318\pi\)
−0.898467 + 0.439041i \(0.855318\pi\)
\(578\) 21.6570 + 21.6570i 0.900813 + 0.900813i
\(579\) 39.3673 3.15095i 1.63605 0.130949i
\(580\) 1.38580 0.795291i 0.0575423 0.0330227i
\(581\) 34.1901i 1.41844i
\(582\) 0.577755 + 0.492122i 0.0239487 + 0.0203991i
\(583\) 29.9048 29.9048i 1.23853 1.23853i
\(584\) −7.26319 −0.300553
\(585\) 1.85144 17.6248i 0.0765476 0.728697i
\(586\) −32.5750 −1.34566
\(587\) 16.2913 16.2913i 0.672415 0.672415i −0.285857 0.958272i \(-0.592278\pi\)
0.958272 + 0.285857i \(0.0922783\pi\)
\(588\) −2.75448 2.34622i −0.113593 0.0967567i
\(589\) 25.3159i 1.04312i
\(590\) 15.8010 + 4.27797i 0.650516 + 0.176121i
\(591\) −44.3814 + 3.55228i −1.82561 + 0.146121i
\(592\) 2.92359 + 2.92359i 0.120159 + 0.120159i
\(593\) 23.5367 + 23.5367i 0.966535 + 0.966535i 0.999458 0.0329233i \(-0.0104817\pi\)
−0.0329233 + 0.999458i \(0.510482\pi\)
\(594\) −28.6346 + 6.99548i −1.17489 + 0.287028i
\(595\) −17.0218 29.6606i −0.697825 1.21597i
\(596\) 8.75534i 0.358633i
\(597\) 0.693393 0.814049i 0.0283787 0.0333168i
\(598\) −1.86804 + 1.86804i −0.0763900 + 0.0763900i
\(599\) −3.05690 −0.124901 −0.0624507 0.998048i \(-0.519892\pi\)
−0.0624507 + 0.998048i \(0.519892\pi\)
\(600\) −7.80211 3.75860i −0.318520 0.153444i
\(601\) −0.352393 −0.0143744 −0.00718721 0.999974i \(-0.502288\pi\)
−0.00718721 + 0.999974i \(0.502288\pi\)
\(602\) −19.5366 + 19.5366i −0.796251 + 0.796251i
\(603\) −14.9800 + 20.7340i −0.610034 + 0.844353i
\(604\) 2.00457i 0.0815650i
\(605\) 23.5738 + 41.0776i 0.958413 + 1.67004i
\(606\) −0.537421 6.71444i −0.0218312 0.272755i
\(607\) −4.89133 4.89133i −0.198533 0.198533i 0.600838 0.799371i \(-0.294834\pi\)
−0.799371 + 0.600838i \(0.794834\pi\)
\(608\) 2.79896 + 2.79896i 0.113513 + 0.113513i
\(609\) −0.218826 2.73397i −0.00886727 0.110786i
\(610\) −10.2277 2.76906i −0.414108 0.112116i
\(611\) 14.9956i 0.606659i
\(612\) 12.1248 16.7821i 0.490117 0.678375i
\(613\) 12.5329 12.5329i 0.506199 0.506199i −0.407158 0.913358i \(-0.633480\pi\)
0.913358 + 0.407158i \(0.133480\pi\)
\(614\) −11.4901 −0.463702
\(615\) 18.6041 + 3.47256i 0.750188 + 0.140027i
\(616\) 12.5713 0.506514
\(617\) 32.9202 32.9202i 1.32532 1.32532i 0.415916 0.909403i \(-0.363461\pi\)
0.909403 0.415916i \(-0.136539\pi\)
\(618\) −12.2849 + 14.4226i −0.494171 + 0.580160i
\(619\) 35.6199i 1.43168i 0.698262 + 0.715842i \(0.253957\pi\)
−0.698262 + 0.715842i \(0.746043\pi\)
\(620\) −12.4036 + 7.11826i −0.498142 + 0.285876i
\(621\) −5.04770 + 1.23316i −0.202557 + 0.0494851i
\(622\) −9.04391 9.04391i −0.362628 0.362628i
\(623\) −12.6421 12.6421i −0.506495 0.506495i
\(624\) −4.56117 + 0.365074i −0.182593 + 0.0146147i
\(625\) −12.2739 21.7796i −0.490957 0.871184i
\(626\) 5.60742i 0.224117i
\(627\) 29.6079 + 25.2195i 1.18243 + 1.00717i
\(628\) −11.6798 + 11.6798i −0.466075 + 0.466075i
\(629\) −28.5339 −1.13772
\(630\) −11.5524 + 9.35605i −0.460260 + 0.372754i
\(631\) 2.84251 0.113159 0.0565793 0.998398i \(-0.481981\pi\)
0.0565793 + 0.998398i \(0.481981\pi\)
\(632\) −5.14314 + 5.14314i −0.204583 + 0.204583i
\(633\) −13.0075 11.0796i −0.517001 0.440373i
\(634\) 0.664424i 0.0263876i
\(635\) −5.35017 + 19.7612i −0.212315 + 0.784201i
\(636\) 12.8716 1.03024i 0.510391 0.0408516i
\(637\) −3.90237 3.90237i −0.154618 0.154618i
\(638\) −2.86627 2.86627i −0.113477 0.113477i
\(639\) −12.6608 + 2.03980i −0.500853 + 0.0806931i
\(640\) −0.584357 + 2.15836i −0.0230987 + 0.0853168i
\(641\) 2.31899i 0.0915947i 0.998951 + 0.0457973i \(0.0145828\pi\)
−0.998951 + 0.0457973i \(0.985417\pi\)
\(642\) 9.77410 11.4749i 0.385753 0.452877i
\(643\) −3.83141 + 3.83141i −0.151096 + 0.151096i −0.778607 0.627511i \(-0.784074\pi\)
0.627511 + 0.778607i \(0.284074\pi\)
\(644\) 2.21607 0.0873256
\(645\) −27.2990 39.8288i −1.07490 1.56826i
\(646\) −27.3175 −1.07479
\(647\) −8.83653 + 8.83653i −0.347400 + 0.347400i −0.859140 0.511740i \(-0.829001\pi\)
0.511740 + 0.859140i \(0.329001\pi\)
\(648\) −8.04068 4.04321i −0.315868 0.158832i
\(649\) 41.5295i 1.63018i
\(650\) −11.4048 6.66399i −0.447335 0.261383i
\(651\) 1.95860 + 24.4704i 0.0767637 + 0.959070i
\(652\) −7.42502 7.42502i −0.290786 0.290786i
\(653\) −1.60062 1.60062i −0.0626369 0.0626369i 0.675094 0.737731i \(-0.264103\pi\)
−0.737731 + 0.675094i \(0.764103\pi\)
\(654\) −1.15359 14.4127i −0.0451088 0.563580i
\(655\) −39.6931 + 22.7793i −1.55094 + 0.890060i
\(656\) 4.88651i 0.190786i
\(657\) −17.6621 12.7607i −0.689066 0.497841i
\(658\) 8.89472 8.89472i 0.346752 0.346752i
\(659\) 24.4088 0.950831 0.475415 0.879761i \(-0.342298\pi\)
0.475415 + 0.879761i \(0.342298\pi\)
\(660\) −4.03133 + 21.5976i −0.156919 + 0.840687i
\(661\) −32.4790 −1.26329 −0.631643 0.775259i \(-0.717619\pi\)
−0.631643 + 0.775259i \(0.717619\pi\)
\(662\) 14.9437 14.9437i 0.580805 0.580805i
\(663\) 20.4767 24.0398i 0.795248 0.933627i
\(664\) 15.4282i 0.598731i
\(665\) 18.9330 + 5.12594i 0.734191 + 0.198776i
\(666\) 1.97294 + 12.2458i 0.0764500 + 0.474516i
\(667\) −0.505266 0.505266i −0.0195640 0.0195640i
\(668\) 16.1431 + 16.1431i 0.624593 + 0.624593i
\(669\) −9.49008 + 0.759583i −0.366908 + 0.0293672i
\(670\) 9.48982 + 16.5361i 0.366624 + 0.638845i
\(671\) 26.8814i 1.03774i
\(672\) 2.92202 + 2.48893i 0.112719 + 0.0960125i
\(673\) 0.870095 0.870095i 0.0335397 0.0335397i −0.690138 0.723678i \(-0.742450\pi\)
0.723678 + 0.690138i \(0.242450\pi\)
\(674\) −15.3704 −0.592045
\(675\) −12.3692 22.8474i −0.476089 0.879397i
\(676\) 6.02083 0.231570
\(677\) 6.92072 6.92072i 0.265985 0.265985i −0.561495 0.827480i \(-0.689774\pi\)
0.827480 + 0.561495i \(0.189774\pi\)
\(678\) 16.8668 + 14.3669i 0.647767 + 0.551757i
\(679\) 0.971022i 0.0372644i
\(680\) −7.68105 13.3843i −0.294555 0.513265i
\(681\) 42.3228 3.38750i 1.62181 0.129809i
\(682\) 25.6546 + 25.6546i 0.982364 + 0.982364i
\(683\) −5.87527 5.87527i −0.224811 0.224811i 0.585710 0.810521i \(-0.300816\pi\)
−0.810521 + 0.585710i \(0.800816\pi\)
\(684\) 1.88884 + 11.7238i 0.0722215 + 0.448270i
\(685\) 14.0298 + 3.79843i 0.536050 + 0.145131i
\(686\) 20.1419i 0.769023i
\(687\) −8.23281 + 9.66538i −0.314101 + 0.368757i
\(688\) −8.81584 + 8.81584i −0.336101 + 0.336101i
\(689\) 19.6952 0.750326
\(690\) −0.710643 + 3.80723i −0.0270537 + 0.144939i
\(691\) −9.37992 −0.356829 −0.178414 0.983955i \(-0.557097\pi\)
−0.178414 + 0.983955i \(0.557097\pi\)
\(692\) −5.17329 + 5.17329i −0.196659 + 0.196659i
\(693\) 30.5701 + 22.0865i 1.16126 + 0.838998i
\(694\) 20.4133i 0.774878i
\(695\) −7.63336 + 4.38067i −0.289550 + 0.166168i
\(696\) −0.0987448 1.23370i −0.00374291 0.0467632i
\(697\) 23.8459 + 23.8459i 0.903227 + 0.903227i
\(698\) −25.3961 25.3961i −0.961257 0.961257i
\(699\) 1.10117 + 13.7578i 0.0416500 + 0.520366i
\(700\) 2.81206 + 10.7176i 0.106286 + 0.405087i
\(701\) 3.17498i 0.119918i 0.998201 + 0.0599588i \(0.0190969\pi\)
−0.998201 + 0.0599588i \(0.980903\pi\)
\(702\) −11.7329 7.12573i −0.442831 0.268943i
\(703\) 11.5725 11.5725i 0.436466 0.436466i
\(704\) 5.67280 0.213802
\(705\) 12.4289 + 18.1335i 0.468098 + 0.682947i
\(706\) 6.91828 0.260373
\(707\) −6.09403 + 6.09403i −0.229190 + 0.229190i
\(708\) 8.22219 9.65291i 0.309009 0.362778i
\(709\) 11.9551i 0.448982i −0.974476 0.224491i \(-0.927928\pi\)
0.974476 0.224491i \(-0.0720719\pi\)
\(710\) −2.49794 + 9.22631i −0.0937460 + 0.346257i
\(711\) −21.5427 + 3.47077i −0.807914 + 0.130164i
\(712\) −5.70473 5.70473i −0.213794 0.213794i
\(713\) 4.52238 + 4.52238i 0.169365 + 0.169365i
\(714\) −26.4051 + 2.11346i −0.988186 + 0.0790941i
\(715\) −8.75744 + 32.3462i −0.327510 + 1.20968i
\(716\) 5.95726i 0.222633i
\(717\) −3.39578 2.89247i −0.126818 0.108021i
\(718\) 23.2881 23.2881i 0.869103 0.869103i
\(719\) −19.3497 −0.721622 −0.360811 0.932639i \(-0.617500\pi\)
−0.360811 + 0.932639i \(0.617500\pi\)
\(720\) −5.21302 + 4.22190i −0.194278 + 0.157341i
\(721\) 24.2397 0.902735
\(722\) −2.35585 + 2.35585i −0.0876755 + 0.0876755i
\(723\) 25.1018 + 21.3813i 0.933544 + 0.795178i
\(724\) 1.45319i 0.0540074i
\(725\) 1.80247 3.08477i 0.0669419 0.114565i
\(726\) 36.5690 2.92697i 1.35720 0.108630i
\(727\) 19.9504 + 19.9504i 0.739918 + 0.739918i 0.972562 0.232644i \(-0.0747376\pi\)
−0.232644 + 0.972562i \(0.574738\pi\)
\(728\) 4.13972 + 4.13972i 0.153428 + 0.153428i
\(729\) −12.4493 23.9586i −0.461084 0.887356i
\(730\) −14.0862 + 8.08386i −0.521354 + 0.299197i
\(731\) 86.0416i 3.18236i
\(732\) −5.32209 + 6.24818i −0.196710 + 0.230939i
\(733\) 3.98501 3.98501i 0.147190 0.147190i −0.629672 0.776861i \(-0.716811\pi\)
0.776861 + 0.629672i \(0.216811\pi\)
\(734\) 23.9937 0.885624
\(735\) −7.95336 1.48454i −0.293364 0.0547582i
\(736\) 1.00000 0.0368605
\(737\) 34.2018 34.2018i 1.25984 1.25984i
\(738\) 8.58508 11.8827i 0.316021 0.437407i
\(739\) 24.8589i 0.914450i −0.889351 0.457225i \(-0.848843\pi\)
0.889351 0.457225i \(-0.151157\pi\)
\(740\) 8.92392 + 2.41607i 0.328050 + 0.0888165i
\(741\) 1.44508 + 18.0546i 0.0530864 + 0.663251i
\(742\) −11.6823 11.6823i −0.428870 0.428870i
\(743\) 36.6681 + 36.6681i 1.34522 + 1.34522i 0.890773 + 0.454449i \(0.150164\pi\)
0.454449 + 0.890773i \(0.349836\pi\)
\(744\) 0.883816 + 11.0422i 0.0324023 + 0.404827i
\(745\) −9.74460 16.9801i −0.357015 0.622101i
\(746\) 10.1941i 0.373233i
\(747\) 27.1058 37.5173i 0.991748 1.37268i
\(748\) −27.6829 + 27.6829i −1.01219 + 1.01219i
\(749\) −19.2856 −0.704680
\(750\) −19.3147 + 1.39425i −0.705272 + 0.0509108i
\(751\) −15.8379 −0.577935 −0.288967 0.957339i \(-0.593312\pi\)
−0.288967 + 0.957339i \(0.593312\pi\)
\(752\) 4.01373 4.01373i 0.146366 0.146366i
\(753\) −4.54796 + 5.33934i −0.165737 + 0.194576i
\(754\) 1.88772i 0.0687466i
\(755\) 2.23107 + 3.88766i 0.0811970 + 0.141486i
\(756\) 2.73278 + 11.1861i 0.0993902 + 0.406834i
\(757\) −31.2042 31.2042i −1.13413 1.13413i −0.989483 0.144652i \(-0.953794\pi\)
−0.144652 0.989483i \(-0.546206\pi\)
\(758\) −0.190525 0.190525i −0.00692018 0.00692018i
\(759\) 9.79425 0.783929i 0.355509 0.0284548i
\(760\) 8.54350 + 2.31307i 0.309905 + 0.0839040i
\(761\) 3.09150i 0.112067i −0.998429 0.0560334i \(-0.982155\pi\)
0.998429 0.0560334i \(-0.0178453\pi\)
\(762\) 12.0723 + 10.2830i 0.437332 + 0.372512i
\(763\) −13.0810 + 13.0810i −0.473563 + 0.473563i
\(764\) 18.2037 0.658586
\(765\) 4.83657 46.0419i 0.174866 1.66465i
\(766\) −20.9155 −0.755707
\(767\) 13.6756 13.6756i 0.493797 0.493797i
\(768\) 1.31856 + 1.12312i 0.0475793 + 0.0405273i
\(769\) 10.4531i 0.376947i 0.982078 + 0.188473i \(0.0603539\pi\)
−0.982078 + 0.188473i \(0.939646\pi\)
\(770\) 24.3808 13.9918i 0.878623 0.504229i
\(771\) 10.0121 0.801368i 0.360578 0.0288606i
\(772\) −16.1230 16.1230i −0.580280 0.580280i
\(773\) 16.2711 + 16.2711i 0.585231 + 0.585231i 0.936336 0.351105i \(-0.114194\pi\)
−0.351105 + 0.936336i \(0.614194\pi\)
\(774\) −36.9263 + 5.94925i −1.32729 + 0.213841i
\(775\) −16.1330 + 27.6102i −0.579514 + 0.991789i
\(776\) 0.438172i 0.0157295i
\(777\) 10.2907 12.0813i 0.369176 0.433415i
\(778\)