Properties

Label 731.2.e.a.307.16
Level 731
Weight 2
Character 731.307
Analytic conductor 5.837
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 307.16
Character \(\chi\) = 731.307
Dual form 731.2.e.a.681.16

$q$-expansion

\(f(q)\) \(=\) \(q+0.220069 q^{2} +(1.00430 - 1.73949i) q^{3} -1.95157 q^{4} +(-1.15229 + 1.99582i) q^{5} +(0.221015 - 0.382808i) q^{6} +(-1.47386 - 2.55280i) q^{7} -0.869618 q^{8} +(-0.517225 - 0.895859i) q^{9} +O(q^{10})\) \(q+0.220069 q^{2} +(1.00430 - 1.73949i) q^{3} -1.95157 q^{4} +(-1.15229 + 1.99582i) q^{5} +(0.221015 - 0.382808i) q^{6} +(-1.47386 - 2.55280i) q^{7} -0.869618 q^{8} +(-0.517225 - 0.895859i) q^{9} +(-0.253582 + 0.439217i) q^{10} -1.64230 q^{11} +(-1.95996 + 3.39474i) q^{12} +(0.208462 + 0.361068i) q^{13} +(-0.324350 - 0.561791i) q^{14} +(2.31447 + 4.00879i) q^{15} +3.71176 q^{16} +(0.500000 + 0.866025i) q^{17} +(-0.113825 - 0.197151i) q^{18} +(-3.05184 + 5.28595i) q^{19} +(2.24877 - 3.89498i) q^{20} -5.92076 q^{21} -0.361419 q^{22} +(-4.31162 + 7.46794i) q^{23} +(-0.873354 + 1.51269i) q^{24} +(-0.155524 - 0.269375i) q^{25} +(0.0458761 + 0.0794597i) q^{26} +3.94799 q^{27} +(2.87634 + 4.98196i) q^{28} +(-2.51609 - 4.35800i) q^{29} +(0.509344 + 0.882209i) q^{30} +(-4.45225 + 7.71152i) q^{31} +2.55608 q^{32} +(-1.64935 + 2.85676i) q^{33} +(0.110034 + 0.190585i) q^{34} +6.79322 q^{35} +(1.00940 + 1.74833i) q^{36} +(-0.989017 + 1.71303i) q^{37} +(-0.671616 + 1.16327i) q^{38} +0.837433 q^{39} +(1.00205 - 1.73560i) q^{40} -10.7766 q^{41} -1.30298 q^{42} +(-0.694915 - 6.52051i) q^{43} +3.20506 q^{44} +2.38396 q^{45} +(-0.948854 + 1.64346i) q^{46} -9.44409 q^{47} +(3.72771 - 6.45659i) q^{48} +(-0.844515 + 1.46274i) q^{49} +(-0.0342260 - 0.0592812i) q^{50} +2.00859 q^{51} +(-0.406829 - 0.704648i) q^{52} +(6.15840 - 10.6667i) q^{53} +0.868831 q^{54} +(1.89239 - 3.27772i) q^{55} +(1.28169 + 2.21996i) q^{56} +(6.12991 + 10.6173i) q^{57} +(-0.553714 - 0.959060i) q^{58} -0.141509 q^{59} +(-4.51686 - 7.82343i) q^{60} +(3.34872 + 5.80015i) q^{61} +(-0.979802 + 1.69707i) q^{62} +(-1.52463 + 2.64074i) q^{63} -6.86101 q^{64} -0.960833 q^{65} +(-0.362972 + 0.628685i) q^{66} +(-2.65555 + 4.59954i) q^{67} +(-0.975785 - 1.69011i) q^{68} +(8.66029 + 15.0001i) q^{69} +1.49498 q^{70} +(-5.73972 - 9.94149i) q^{71} +(0.449788 + 0.779055i) q^{72} +(7.34581 + 12.7233i) q^{73} +(-0.217652 + 0.376984i) q^{74} -0.624769 q^{75} +(5.95588 - 10.3159i) q^{76} +(2.42051 + 4.19245i) q^{77} +0.184293 q^{78} +(0.649518 + 1.12500i) q^{79} +(-4.27701 + 7.40800i) q^{80} +(5.51663 - 9.55509i) q^{81} -2.37160 q^{82} +(8.30770 - 14.3894i) q^{83} +11.5548 q^{84} -2.30457 q^{85} +(-0.152929 - 1.43496i) q^{86} -10.1076 q^{87} +1.42817 q^{88} +(1.61108 - 2.79048i) q^{89} +0.524636 q^{90} +(0.614488 - 1.06432i) q^{91} +(8.41443 - 14.5742i) q^{92} +(8.94276 + 15.4893i) q^{93} -2.07835 q^{94} +(-7.03319 - 12.1818i) q^{95} +(2.56706 - 4.44628i) q^{96} -2.99182 q^{97} +(-0.185852 + 0.321904i) q^{98} +(0.849436 + 1.47127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + O(q^{10}) \) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + 4q^{10} + 16q^{11} + 12q^{12} + 2q^{13} - 11q^{14} + 7q^{15} + 30q^{16} + 29q^{17} + 8q^{18} + 8q^{19} - 33q^{20} - 26q^{21} - 22q^{22} - 5q^{23} + 12q^{24} - 36q^{25} - 12q^{27} + 15q^{28} + 2q^{29} + 11q^{30} + 3q^{31} - 40q^{32} + 17q^{33} - 3q^{34} + 38q^{35} - 7q^{36} + 2q^{37} + q^{38} - 54q^{39} + 5q^{40} + 14q^{41} - 112q^{42} + 31q^{43} - 24q^{44} - 46q^{45} - 13q^{46} - 28q^{47} - 28q^{49} - 13q^{50} + 6q^{51} + 85q^{52} - 10q^{53} + 34q^{54} + 36q^{55} - 54q^{56} - 23q^{57} + 3q^{58} + 12q^{59} + 2q^{60} - q^{61} - q^{62} - 14q^{63} + 28q^{64} + 80q^{65} - 74q^{66} + 11q^{67} + 27q^{68} - 11q^{69} + 2q^{70} + 16q^{71} + 21q^{72} + 14q^{73} + 21q^{74} - 54q^{75} + 44q^{76} + 25q^{77} + 88q^{78} - 4q^{79} - 112q^{80} + 11q^{81} - 176q^{82} - 3q^{83} + 100q^{84} - 2q^{85} + 44q^{86} + 8q^{87} - 106q^{88} + 82q^{89} + 54q^{90} - 15q^{91} + 42q^{92} + 88q^{94} + 29q^{95} + 20q^{96} + 20q^{97} + 44q^{98} - 54q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.220069 0.155612 0.0778061 0.996969i \(-0.475208\pi\)
0.0778061 + 0.996969i \(0.475208\pi\)
\(3\) 1.00430 1.73949i 0.579831 1.00430i −0.415667 0.909517i \(-0.636452\pi\)
0.995498 0.0947801i \(-0.0302148\pi\)
\(4\) −1.95157 −0.975785
\(5\) −1.15229 + 1.99582i −0.515318 + 0.892557i 0.484524 + 0.874778i \(0.338993\pi\)
−0.999842 + 0.0177787i \(0.994341\pi\)
\(6\) 0.221015 0.382808i 0.0902288 0.156281i
\(7\) −1.47386 2.55280i −0.557066 0.964867i −0.997740 0.0671992i \(-0.978594\pi\)
0.440674 0.897667i \(-0.354740\pi\)
\(8\) −0.869618 −0.307456
\(9\) −0.517225 0.895859i −0.172408 0.298620i
\(10\) −0.253582 + 0.439217i −0.0801897 + 0.138893i
\(11\) −1.64230 −0.495171 −0.247586 0.968866i \(-0.579637\pi\)
−0.247586 + 0.968866i \(0.579637\pi\)
\(12\) −1.95996 + 3.39474i −0.565790 + 0.979978i
\(13\) 0.208462 + 0.361068i 0.0578171 + 0.100142i 0.893485 0.449093i \(-0.148253\pi\)
−0.835668 + 0.549235i \(0.814919\pi\)
\(14\) −0.324350 0.561791i −0.0866863 0.150145i
\(15\) 2.31447 + 4.00879i 0.597595 + 1.03506i
\(16\) 3.71176 0.927941
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) −0.113825 0.197151i −0.0268288 0.0464689i
\(19\) −3.05184 + 5.28595i −0.700141 + 1.21268i 0.268276 + 0.963342i \(0.413546\pi\)
−0.968417 + 0.249337i \(0.919787\pi\)
\(20\) 2.24877 3.89498i 0.502839 0.870943i
\(21\) −5.92076 −1.29202
\(22\) −0.361419 −0.0770547
\(23\) −4.31162 + 7.46794i −0.899035 + 1.55717i −0.0703047 + 0.997526i \(0.522397\pi\)
−0.828730 + 0.559648i \(0.810936\pi\)
\(24\) −0.873354 + 1.51269i −0.178273 + 0.308777i
\(25\) −0.155524 0.269375i −0.0311048 0.0538751i
\(26\) 0.0458761 + 0.0794597i 0.00899704 + 0.0155833i
\(27\) 3.94799 0.759792
\(28\) 2.87634 + 4.98196i 0.543577 + 0.941502i
\(29\) −2.51609 4.35800i −0.467226 0.809260i 0.532072 0.846699i \(-0.321413\pi\)
−0.999299 + 0.0374389i \(0.988080\pi\)
\(30\) 0.509344 + 0.882209i 0.0929930 + 0.161069i
\(31\) −4.45225 + 7.71152i −0.799648 + 1.38503i 0.120198 + 0.992750i \(0.461647\pi\)
−0.919846 + 0.392280i \(0.871686\pi\)
\(32\) 2.55608 0.451855
\(33\) −1.64935 + 2.85676i −0.287116 + 0.497299i
\(34\) 0.110034 + 0.190585i 0.0188708 + 0.0326851i
\(35\) 6.79322 1.14826
\(36\) 1.00940 + 1.74833i 0.168233 + 0.291389i
\(37\) −0.989017 + 1.71303i −0.162593 + 0.281620i −0.935798 0.352537i \(-0.885319\pi\)
0.773205 + 0.634157i \(0.218653\pi\)
\(38\) −0.671616 + 1.16327i −0.108950 + 0.188708i
\(39\) 0.837433 0.134097
\(40\) 1.00205 1.73560i 0.158438 0.274422i
\(41\) −10.7766 −1.68302 −0.841512 0.540238i \(-0.818334\pi\)
−0.841512 + 0.540238i \(0.818334\pi\)
\(42\) −1.30298 −0.201054
\(43\) −0.694915 6.52051i −0.105974 0.994369i
\(44\) 3.20506 0.483180
\(45\) 2.38396 0.355380
\(46\) −0.948854 + 1.64346i −0.139901 + 0.242315i
\(47\) −9.44409 −1.37756 −0.688781 0.724969i \(-0.741854\pi\)
−0.688781 + 0.724969i \(0.741854\pi\)
\(48\) 3.72771 6.45659i 0.538049 0.931928i
\(49\) −0.844515 + 1.46274i −0.120645 + 0.208963i
\(50\) −0.0342260 0.0592812i −0.00484029 0.00838362i
\(51\) 2.00859 0.281259
\(52\) −0.406829 0.704648i −0.0564170 0.0977172i
\(53\) 6.15840 10.6667i 0.845921 1.46518i −0.0388975 0.999243i \(-0.512385\pi\)
0.884819 0.465935i \(-0.154282\pi\)
\(54\) 0.868831 0.118233
\(55\) 1.89239 3.27772i 0.255170 0.441968i
\(56\) 1.28169 + 2.21996i 0.171273 + 0.296654i
\(57\) 6.12991 + 10.6173i 0.811927 + 1.40630i
\(58\) −0.553714 0.959060i −0.0727061 0.125931i
\(59\) −0.141509 −0.0184229 −0.00921144 0.999958i \(-0.502932\pi\)
−0.00921144 + 0.999958i \(0.502932\pi\)
\(60\) −4.51686 7.82343i −0.583124 1.01000i
\(61\) 3.34872 + 5.80015i 0.428759 + 0.742633i 0.996763 0.0803928i \(-0.0256175\pi\)
−0.568004 + 0.823026i \(0.692284\pi\)
\(62\) −0.979802 + 1.69707i −0.124435 + 0.215528i
\(63\) −1.52463 + 2.64074i −0.192086 + 0.332702i
\(64\) −6.86101 −0.857627
\(65\) −0.960833 −0.119177
\(66\) −0.362972 + 0.628685i −0.0446787 + 0.0773858i
\(67\) −2.65555 + 4.59954i −0.324427 + 0.561923i −0.981396 0.191994i \(-0.938505\pi\)
0.656970 + 0.753917i \(0.271838\pi\)
\(68\) −0.975785 1.69011i −0.118331 0.204956i
\(69\) 8.66029 + 15.0001i 1.04258 + 1.80580i
\(70\) 1.49498 0.178684
\(71\) −5.73972 9.94149i −0.681180 1.17984i −0.974621 0.223861i \(-0.928134\pi\)
0.293442 0.955977i \(-0.405199\pi\)
\(72\) 0.449788 + 0.779055i 0.0530080 + 0.0918125i
\(73\) 7.34581 + 12.7233i 0.859762 + 1.48915i 0.872156 + 0.489229i \(0.162722\pi\)
−0.0123933 + 0.999923i \(0.503945\pi\)
\(74\) −0.217652 + 0.376984i −0.0253015 + 0.0438235i
\(75\) −0.624769 −0.0721421
\(76\) 5.95588 10.3159i 0.683187 1.18331i
\(77\) 2.42051 + 4.19245i 0.275843 + 0.477774i
\(78\) 0.184293 0.0208671
\(79\) 0.649518 + 1.12500i 0.0730765 + 0.126572i 0.900248 0.435377i \(-0.143385\pi\)
−0.827172 + 0.561949i \(0.810052\pi\)
\(80\) −4.27701 + 7.40800i −0.478184 + 0.828240i
\(81\) 5.51663 9.55509i 0.612959 1.06168i
\(82\) −2.37160 −0.261899
\(83\) 8.30770 14.3894i 0.911888 1.57944i 0.100494 0.994938i \(-0.467958\pi\)
0.811394 0.584499i \(-0.198709\pi\)
\(84\) 11.5548 1.26073
\(85\) −2.30457 −0.249966
\(86\) −0.152929 1.43496i −0.0164908 0.154736i
\(87\) −10.1076 −1.08365
\(88\) 1.42817 0.152243
\(89\) 1.61108 2.79048i 0.170775 0.295790i −0.767916 0.640550i \(-0.778706\pi\)
0.938691 + 0.344760i \(0.112040\pi\)
\(90\) 0.524636 0.0553015
\(91\) 0.614488 1.06432i 0.0644159 0.111572i
\(92\) 8.41443 14.5742i 0.877265 1.51947i
\(93\) 8.94276 + 15.4893i 0.927321 + 1.60617i
\(94\) −2.07835 −0.214366
\(95\) −7.03319 12.1818i −0.721590 1.24983i
\(96\) 2.56706 4.44628i 0.262000 0.453797i
\(97\) −2.99182 −0.303773 −0.151887 0.988398i \(-0.548535\pi\)
−0.151887 + 0.988398i \(0.548535\pi\)
\(98\) −0.185852 + 0.321904i −0.0187738 + 0.0325173i
\(99\) 0.849436 + 1.47127i 0.0853716 + 0.147868i
\(100\) 0.303516 + 0.525705i 0.0303516 + 0.0525705i
\(101\) 5.62081 + 9.73553i 0.559291 + 0.968721i 0.997556 + 0.0698750i \(0.0222600\pi\)
−0.438264 + 0.898846i \(0.644407\pi\)
\(102\) 0.442029 0.0437674
\(103\) −0.547585 0.948445i −0.0539552 0.0934531i 0.837786 0.545998i \(-0.183849\pi\)
−0.891742 + 0.452545i \(0.850516\pi\)
\(104\) −0.181283 0.313991i −0.0177762 0.0307893i
\(105\) 6.82241 11.8168i 0.665799 1.15320i
\(106\) 1.35527 2.34740i 0.131636 0.228000i
\(107\) −11.5557 −1.11713 −0.558565 0.829461i \(-0.688648\pi\)
−0.558565 + 0.829461i \(0.688648\pi\)
\(108\) −7.70478 −0.741393
\(109\) 2.73925 4.74452i 0.262372 0.454442i −0.704499 0.709704i \(-0.748828\pi\)
0.966872 + 0.255262i \(0.0821618\pi\)
\(110\) 0.416457 0.721325i 0.0397076 0.0687757i
\(111\) 1.98653 + 3.44078i 0.188553 + 0.326584i
\(112\) −5.47061 9.47538i −0.516924 0.895339i
\(113\) 12.5300 1.17872 0.589360 0.807870i \(-0.299380\pi\)
0.589360 + 0.807870i \(0.299380\pi\)
\(114\) 1.34900 + 2.33654i 0.126346 + 0.218837i
\(115\) −9.93643 17.2104i −0.926577 1.60488i
\(116\) 4.91033 + 8.50494i 0.455912 + 0.789664i
\(117\) 0.215644 0.373506i 0.0199363 0.0345306i
\(118\) −0.0311417 −0.00286682
\(119\) 1.47386 2.55280i 0.135108 0.234015i
\(120\) −2.01271 3.48611i −0.183734 0.318237i
\(121\) −8.30286 −0.754806
\(122\) 0.736949 + 1.27643i 0.0667202 + 0.115563i
\(123\) −10.8229 + 18.7459i −0.975870 + 1.69026i
\(124\) 8.68887 15.0496i 0.780284 1.35149i
\(125\) −10.8060 −0.966520
\(126\) −0.335524 + 0.581145i −0.0298909 + 0.0517725i
\(127\) −12.1778 −1.08061 −0.540304 0.841470i \(-0.681691\pi\)
−0.540304 + 0.841470i \(0.681691\pi\)
\(128\) −6.62205 −0.585312
\(129\) −12.0403 5.33973i −1.06009 0.470137i
\(130\) −0.211450 −0.0185453
\(131\) 1.56016 0.136312 0.0681561 0.997675i \(-0.478288\pi\)
0.0681561 + 0.997675i \(0.478288\pi\)
\(132\) 3.21883 5.57517i 0.280163 0.485257i
\(133\) 17.9919 1.56010
\(134\) −0.584403 + 1.01222i −0.0504847 + 0.0874421i
\(135\) −4.54922 + 7.87947i −0.391534 + 0.678157i
\(136\) −0.434809 0.753111i −0.0372846 0.0645787i
\(137\) −9.83288 −0.840080 −0.420040 0.907506i \(-0.637984\pi\)
−0.420040 + 0.907506i \(0.637984\pi\)
\(138\) 1.90586 + 3.30105i 0.162238 + 0.281004i
\(139\) −3.76437 + 6.52007i −0.319289 + 0.553025i −0.980340 0.197316i \(-0.936778\pi\)
0.661051 + 0.750341i \(0.270111\pi\)
\(140\) −13.2574 −1.12046
\(141\) −9.48467 + 16.4279i −0.798753 + 1.38348i
\(142\) −1.26313 2.18781i −0.106000 0.183597i
\(143\) −0.342357 0.592980i −0.0286293 0.0495875i
\(144\) −1.91982 3.32522i −0.159985 0.277102i
\(145\) 11.5970 0.963080
\(146\) 1.61658 + 2.80001i 0.133790 + 0.231730i
\(147\) 1.69629 + 2.93806i 0.139908 + 0.242327i
\(148\) 1.93013 3.34309i 0.158656 0.274800i
\(149\) −9.63327 + 16.6853i −0.789188 + 1.36691i 0.137277 + 0.990533i \(0.456165\pi\)
−0.926465 + 0.376381i \(0.877168\pi\)
\(150\) −0.137492 −0.0112262
\(151\) −1.93280 −0.157289 −0.0786447 0.996903i \(-0.525059\pi\)
−0.0786447 + 0.996903i \(0.525059\pi\)
\(152\) 2.65394 4.59675i 0.215263 0.372846i
\(153\) 0.517225 0.895859i 0.0418151 0.0724259i
\(154\) 0.532680 + 0.922628i 0.0429245 + 0.0743475i
\(155\) −10.2605 17.7718i −0.824145 1.42746i
\(156\) −1.63431 −0.130849
\(157\) −10.4277 18.0612i −0.832217 1.44144i −0.896276 0.443496i \(-0.853738\pi\)
0.0640590 0.997946i \(-0.479595\pi\)
\(158\) 0.142939 + 0.247577i 0.0113716 + 0.0196962i
\(159\) −12.3697 21.4250i −0.980983 1.69911i
\(160\) −2.94533 + 5.10147i −0.232849 + 0.403306i
\(161\) 25.4189 2.00329
\(162\) 1.21404 2.10278i 0.0953839 0.165210i
\(163\) 12.3348 + 21.3645i 0.966134 + 1.67339i 0.706536 + 0.707677i \(0.250257\pi\)
0.259598 + 0.965717i \(0.416410\pi\)
\(164\) 21.0313 1.64227
\(165\) −3.80105 6.58362i −0.295912 0.512534i
\(166\) 1.82827 3.16665i 0.141901 0.245780i
\(167\) −1.15299 + 1.99704i −0.0892213 + 0.154536i −0.907182 0.420738i \(-0.861771\pi\)
0.817961 + 0.575274i \(0.195104\pi\)
\(168\) 5.14880 0.397239
\(169\) 6.41309 11.1078i 0.493314 0.854446i
\(170\) −0.507165 −0.0388977
\(171\) 6.31395 0.482840
\(172\) 1.35618 + 12.7252i 0.103407 + 0.970290i
\(173\) −7.88055 −0.599147 −0.299574 0.954073i \(-0.596844\pi\)
−0.299574 + 0.954073i \(0.596844\pi\)
\(174\) −2.22437 −0.168629
\(175\) −0.458441 + 0.794042i −0.0346549 + 0.0600240i
\(176\) −6.09582 −0.459490
\(177\) −0.142117 + 0.246154i −0.0106822 + 0.0185020i
\(178\) 0.354550 0.614098i 0.0265746 0.0460286i
\(179\) −10.1491 17.5788i −0.758582 1.31390i −0.943574 0.331162i \(-0.892559\pi\)
0.184992 0.982740i \(-0.440774\pi\)
\(180\) −4.65247 −0.346774
\(181\) −4.75480 8.23556i −0.353422 0.612144i 0.633425 0.773804i \(-0.281649\pi\)
−0.986847 + 0.161660i \(0.948315\pi\)
\(182\) 0.135230 0.234225i 0.0100239 0.0173619i
\(183\) 13.4524 0.994432
\(184\) 3.74946 6.49426i 0.276414 0.478763i
\(185\) −2.27926 3.94779i −0.167574 0.290247i
\(186\) 1.96802 + 3.40872i 0.144303 + 0.249939i
\(187\) −0.821148 1.42227i −0.0600483 0.104007i
\(188\) 18.4308 1.34420
\(189\) −5.81878 10.0784i −0.423254 0.733098i
\(190\) −1.54779 2.68084i −0.112288 0.194489i
\(191\) 1.67133 2.89483i 0.120933 0.209463i −0.799203 0.601062i \(-0.794745\pi\)
0.920136 + 0.391599i \(0.128078\pi\)
\(192\) −6.89049 + 11.9347i −0.497279 + 0.861312i
\(193\) 18.4289 1.32654 0.663270 0.748380i \(-0.269168\pi\)
0.663270 + 0.748380i \(0.269168\pi\)
\(194\) −0.658406 −0.0472708
\(195\) −0.964962 + 1.67136i −0.0691023 + 0.119689i
\(196\) 1.64813 2.85465i 0.117724 0.203903i
\(197\) 10.1812 + 17.6343i 0.725378 + 1.25639i 0.958818 + 0.284020i \(0.0916683\pi\)
−0.233441 + 0.972371i \(0.574998\pi\)
\(198\) 0.186935 + 0.323780i 0.0132849 + 0.0230101i
\(199\) −10.6168 −0.752605 −0.376302 0.926497i \(-0.622805\pi\)
−0.376302 + 0.926497i \(0.622805\pi\)
\(200\) 0.135246 + 0.234254i 0.00956337 + 0.0165642i
\(201\) 5.33391 + 9.23861i 0.376225 + 0.651641i
\(202\) 1.23697 + 2.14249i 0.0870326 + 0.150745i
\(203\) −7.41672 + 12.8461i −0.520552 + 0.901622i
\(204\) −3.91991 −0.274449
\(205\) 12.4177 21.5082i 0.867292 1.50219i
\(206\) −0.120506 0.208723i −0.00839609 0.0145424i
\(207\) 8.92030 0.620004
\(208\) 0.773763 + 1.34020i 0.0536508 + 0.0929260i
\(209\) 5.01203 8.68109i 0.346690 0.600484i
\(210\) 1.50140 2.60050i 0.103607 0.179452i
\(211\) −4.25702 −0.293065 −0.146533 0.989206i \(-0.546811\pi\)
−0.146533 + 0.989206i \(0.546811\pi\)
\(212\) −12.0185 + 20.8167i −0.825437 + 1.42970i
\(213\) −23.0575 −1.57988
\(214\) −2.54305 −0.173839
\(215\) 13.8145 + 6.12657i 0.942141 + 0.417829i
\(216\) −3.43324 −0.233603
\(217\) 26.2479 1.78183
\(218\) 0.602823 1.04412i 0.0408284 0.0707168i
\(219\) 29.5095 1.99407
\(220\) −3.69314 + 6.39671i −0.248991 + 0.431266i
\(221\) −0.208462 + 0.361068i −0.0140227 + 0.0242880i
\(222\) 0.437174 + 0.757208i 0.0293412 + 0.0508205i
\(223\) 14.4824 0.969812 0.484906 0.874566i \(-0.338854\pi\)
0.484906 + 0.874566i \(0.338854\pi\)
\(224\) −3.76730 6.52515i −0.251713 0.435980i
\(225\) −0.160882 + 0.278655i −0.0107254 + 0.0185770i
\(226\) 2.75746 0.183423
\(227\) −12.3928 + 21.4649i −0.822537 + 1.42468i 0.0812505 + 0.996694i \(0.474109\pi\)
−0.903787 + 0.427982i \(0.859225\pi\)
\(228\) −11.9630 20.7204i −0.792266 1.37224i
\(229\) 14.0392 + 24.3166i 0.927738 + 1.60689i 0.787098 + 0.616828i \(0.211583\pi\)
0.140640 + 0.990061i \(0.455084\pi\)
\(230\) −2.18670 3.78748i −0.144187 0.249739i
\(231\) 9.72365 0.639769
\(232\) 2.18804 + 3.78979i 0.143652 + 0.248812i
\(233\) 5.30708 + 9.19214i 0.347679 + 0.602197i 0.985837 0.167708i \(-0.0536367\pi\)
−0.638158 + 0.769905i \(0.720303\pi\)
\(234\) 0.0474565 0.0821971i 0.00310233 0.00537339i
\(235\) 10.8823 18.8487i 0.709882 1.22955i
\(236\) 0.276164 0.0179768
\(237\) 2.60924 0.169488
\(238\) 0.324350 0.561791i 0.0210245 0.0364155i
\(239\) 6.03257 10.4487i 0.390214 0.675871i −0.602263 0.798298i \(-0.705734\pi\)
0.992478 + 0.122427i \(0.0390676\pi\)
\(240\) 8.59078 + 14.8797i 0.554532 + 0.960478i
\(241\) 10.5287 + 18.2362i 0.678211 + 1.17470i 0.975519 + 0.219915i \(0.0705779\pi\)
−0.297308 + 0.954782i \(0.596089\pi\)
\(242\) −1.82720 −0.117457
\(243\) −5.15868 8.93510i −0.330930 0.573187i
\(244\) −6.53526 11.3194i −0.418377 0.724650i
\(245\) −1.94625 3.37100i −0.124341 0.215365i
\(246\) −2.38179 + 4.12538i −0.151857 + 0.263025i
\(247\) −2.54478 −0.161920
\(248\) 3.87175 6.70608i 0.245857 0.425836i
\(249\) −16.6868 28.9024i −1.05748 1.83161i
\(250\) −2.37807 −0.150402
\(251\) −1.82652 3.16362i −0.115289 0.199686i 0.802606 0.596509i \(-0.203446\pi\)
−0.917895 + 0.396823i \(0.870113\pi\)
\(252\) 2.97542 5.15359i 0.187434 0.324645i
\(253\) 7.08096 12.2646i 0.445176 0.771068i
\(254\) −2.67996 −0.168156
\(255\) −2.31447 + 4.00879i −0.144938 + 0.251040i
\(256\) 12.2647 0.766545
\(257\) −0.808273 −0.0504187 −0.0252093 0.999682i \(-0.508025\pi\)
−0.0252093 + 0.999682i \(0.508025\pi\)
\(258\) −2.64969 1.17511i −0.164963 0.0731591i
\(259\) 5.83068 0.362301
\(260\) 1.87513 0.116291
\(261\) −2.60277 + 4.50813i −0.161107 + 0.279046i
\(262\) 0.343344 0.0212118
\(263\) −1.16776 + 2.02262i −0.0720072 + 0.124720i −0.899781 0.436342i \(-0.856274\pi\)
0.827774 + 0.561062i \(0.189607\pi\)
\(264\) 1.43431 2.48429i 0.0882755 0.152898i
\(265\) 14.1925 + 24.5821i 0.871837 + 1.51007i
\(266\) 3.95947 0.242770
\(267\) −3.23601 5.60494i −0.198041 0.343017i
\(268\) 5.18248 8.97632i 0.316571 0.548316i
\(269\) −13.0837 −0.797726 −0.398863 0.917011i \(-0.630595\pi\)
−0.398863 + 0.917011i \(0.630595\pi\)
\(270\) −1.00114 + 1.73403i −0.0609275 + 0.105530i
\(271\) −12.7245 22.0395i −0.772958 1.33880i −0.935935 0.352172i \(-0.885443\pi\)
0.162978 0.986630i \(-0.447890\pi\)
\(272\) 1.85588 + 3.21448i 0.112529 + 0.194907i
\(273\) −1.23426 2.13780i −0.0747006 0.129385i
\(274\) −2.16391 −0.130727
\(275\) 0.255417 + 0.442394i 0.0154022 + 0.0266774i
\(276\) −16.9012 29.2737i −1.01733 1.76207i
\(277\) 3.40012 5.88917i 0.204293 0.353846i −0.745614 0.666378i \(-0.767844\pi\)
0.949907 + 0.312532i \(0.101177\pi\)
\(278\) −0.828420 + 1.43487i −0.0496853 + 0.0860575i
\(279\) 9.21125 0.551463
\(280\) −5.90751 −0.353041
\(281\) −0.188053 + 0.325717i −0.0112183 + 0.0194306i −0.871580 0.490253i \(-0.836904\pi\)
0.860362 + 0.509684i \(0.170238\pi\)
\(282\) −2.08728 + 3.61528i −0.124296 + 0.215287i
\(283\) 15.0711 + 26.1039i 0.895883 + 1.55171i 0.832708 + 0.553712i \(0.186789\pi\)
0.0631750 + 0.998002i \(0.479877\pi\)
\(284\) 11.2015 + 19.4015i 0.664685 + 1.15127i
\(285\) −28.2536 −1.67360
\(286\) −0.0753422 0.130496i −0.00445508 0.00771642i
\(287\) 15.8832 + 27.5105i 0.937556 + 1.62389i
\(288\) −1.32207 2.28989i −0.0779036 0.134933i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 2.55214 0.149867
\(291\) −3.00467 + 5.20425i −0.176137 + 0.305078i
\(292\) −14.3359 24.8304i −0.838943 1.45309i
\(293\) −22.7806 −1.33086 −0.665429 0.746461i \(-0.731751\pi\)
−0.665429 + 0.746461i \(0.731751\pi\)
\(294\) 0.373300 + 0.646575i 0.0217713 + 0.0377090i
\(295\) 0.163058 0.282426i 0.00949363 0.0164435i
\(296\) 0.860066 1.48968i 0.0499903 0.0865858i
\(297\) −6.48378 −0.376227
\(298\) −2.11998 + 3.67192i −0.122807 + 0.212708i
\(299\) −3.59524 −0.207918
\(300\) 1.21928 0.0703952
\(301\) −15.6213 + 11.3843i −0.900399 + 0.656179i
\(302\) −0.425350 −0.0244761
\(303\) 22.5798 1.29718
\(304\) −11.3277 + 19.6202i −0.649689 + 1.12529i
\(305\) −15.4347 −0.883789
\(306\) 0.113825 0.197151i 0.00650695 0.0112704i
\(307\) 10.7818 18.6747i 0.615352 1.06582i −0.374971 0.927036i \(-0.622347\pi\)
0.990323 0.138784i \(-0.0443193\pi\)
\(308\) −4.72380 8.18186i −0.269163 0.466205i
\(309\) −2.19975 −0.125140
\(310\) −2.25802 3.91101i −0.128247 0.222130i
\(311\) 6.27978 10.8769i 0.356094 0.616772i −0.631211 0.775611i \(-0.717442\pi\)
0.987304 + 0.158839i \(0.0507751\pi\)
\(312\) −0.728246 −0.0412288
\(313\) 13.8469 23.9835i 0.782671 1.35563i −0.147710 0.989031i \(-0.547190\pi\)
0.930381 0.366595i \(-0.119476\pi\)
\(314\) −2.29480 3.97471i −0.129503 0.224306i
\(315\) −3.51362 6.08577i −0.197970 0.342894i
\(316\) −1.26758 2.19551i −0.0713069 0.123507i
\(317\) 1.44487 0.0811523 0.0405761 0.999176i \(-0.487081\pi\)
0.0405761 + 0.999176i \(0.487081\pi\)
\(318\) −2.72219 4.71497i −0.152653 0.264403i
\(319\) 4.13217 + 7.15713i 0.231357 + 0.400722i
\(320\) 7.90585 13.6933i 0.441950 0.765480i
\(321\) −11.6053 + 20.1010i −0.647746 + 1.12193i
\(322\) 5.59390 0.311736
\(323\) −6.10369 −0.339618
\(324\) −10.7661 + 18.6474i −0.598116 + 1.03597i
\(325\) 0.0648418 0.112309i 0.00359678 0.00622980i
\(326\) 2.71450 + 4.70165i 0.150342 + 0.260400i
\(327\) −5.50204 9.52981i −0.304263 0.527000i
\(328\) 9.37154 0.517457
\(329\) 13.9193 + 24.1088i 0.767393 + 1.32916i
\(330\) −0.836494 1.44885i −0.0460475 0.0797565i
\(331\) −2.38518 4.13126i −0.131102 0.227074i 0.793000 0.609222i \(-0.208518\pi\)
−0.924101 + 0.382147i \(0.875185\pi\)
\(332\) −16.2131 + 28.0818i −0.889807 + 1.54119i
\(333\) 2.04618 0.112130
\(334\) −0.253738 + 0.439487i −0.0138839 + 0.0240477i
\(335\) −6.11989 10.6000i −0.334366 0.579138i
\(336\) −21.9765 −1.19892
\(337\) 6.97749 + 12.0854i 0.380088 + 0.658332i 0.991075 0.133309i \(-0.0425603\pi\)
−0.610986 + 0.791641i \(0.709227\pi\)
\(338\) 1.41132 2.44448i 0.0767658 0.132962i
\(339\) 12.5838 21.7958i 0.683459 1.18379i
\(340\) 4.49753 0.243913
\(341\) 7.31192 12.6646i 0.395962 0.685827i
\(342\) 1.38951 0.0751358
\(343\) −15.6552 −0.845303
\(344\) 0.604310 + 5.67035i 0.0325822 + 0.305725i
\(345\) −39.9165 −2.14903
\(346\) −1.73426 −0.0932347
\(347\) −11.7649 + 20.3774i −0.631574 + 1.09392i 0.355656 + 0.934617i \(0.384258\pi\)
−0.987230 + 0.159302i \(0.949076\pi\)
\(348\) 19.7257 1.05741
\(349\) −16.9809 + 29.4118i −0.908967 + 1.57438i −0.0934640 + 0.995623i \(0.529794\pi\)
−0.815502 + 0.578754i \(0.803539\pi\)
\(350\) −0.100889 + 0.174744i −0.00539272 + 0.00934046i
\(351\) 0.823008 + 1.42549i 0.0439289 + 0.0760871i
\(352\) −4.19784 −0.223746
\(353\) 4.82942 + 8.36480i 0.257044 + 0.445213i 0.965449 0.260593i \(-0.0839181\pi\)
−0.708405 + 0.705807i \(0.750585\pi\)
\(354\) −0.0312755 + 0.0541707i −0.00166227 + 0.00287914i
\(355\) 26.4552 1.40410
\(356\) −3.14414 + 5.44582i −0.166639 + 0.288628i
\(357\) −2.96038 5.12753i −0.156680 0.271378i
\(358\) −2.23351 3.86855i −0.118045 0.204459i
\(359\) 10.4061 + 18.0239i 0.549214 + 0.951266i 0.998329 + 0.0577921i \(0.0184060\pi\)
−0.449115 + 0.893474i \(0.648261\pi\)
\(360\) −2.07314 −0.109264
\(361\) −9.12749 15.8093i −0.480394 0.832067i
\(362\) −1.04638 1.81239i −0.0549967 0.0952571i
\(363\) −8.33854 + 14.4428i −0.437660 + 0.758049i
\(364\) −1.19922 + 2.07710i −0.0628560 + 0.108870i
\(365\) −33.8579 −1.77220
\(366\) 2.96046 0.154746
\(367\) −5.70727 + 9.88529i −0.297917 + 0.516008i −0.975659 0.219292i \(-0.929625\pi\)
0.677742 + 0.735300i \(0.262959\pi\)
\(368\) −16.0037 + 27.7192i −0.834251 + 1.44497i
\(369\) 5.57393 + 9.65433i 0.290167 + 0.502584i
\(370\) −0.501594 0.868786i −0.0260766 0.0451661i
\(371\) −36.3064 −1.88494
\(372\) −17.4524 30.2285i −0.904866 1.56727i
\(373\) 13.5678 + 23.5001i 0.702513 + 1.21679i 0.967582 + 0.252558i \(0.0812720\pi\)
−0.265069 + 0.964229i \(0.585395\pi\)
\(374\) −0.180709 0.312998i −0.00934425 0.0161847i
\(375\) −10.8525 + 18.7970i −0.560418 + 0.970673i
\(376\) 8.21275 0.423540
\(377\) 1.04902 1.81696i 0.0540273 0.0935781i
\(378\) −1.28053 2.21795i −0.0658635 0.114079i
\(379\) −13.3847 −0.687527 −0.343764 0.939056i \(-0.611702\pi\)
−0.343764 + 0.939056i \(0.611702\pi\)
\(380\) 13.7258 + 23.7737i 0.704117 + 1.21957i
\(381\) −12.2302 + 21.1832i −0.626570 + 1.08525i
\(382\) 0.367808 0.637062i 0.0188187 0.0325950i
\(383\) −3.67464 −0.187765 −0.0938826 0.995583i \(-0.529928\pi\)
−0.0938826 + 0.995583i \(0.529928\pi\)
\(384\) −6.65051 + 11.5190i −0.339382 + 0.587827i
\(385\) −11.1565 −0.568587
\(386\) 4.05562 0.206426
\(387\) −5.48204 + 3.99512i −0.278668 + 0.203083i
\(388\) 5.83874 0.296417
\(389\) 8.54804 0.433403 0.216701 0.976238i \(-0.430470\pi\)
0.216701 + 0.976238i \(0.430470\pi\)
\(390\) −0.212358 + 0.367815i −0.0107532 + 0.0186250i
\(391\) −8.62324 −0.436096
\(392\) 0.734406 1.27203i 0.0370931 0.0642471i
\(393\) 1.56687 2.71390i 0.0790380 0.136898i
\(394\) 2.24056 + 3.88076i 0.112878 + 0.195510i
\(395\) −2.99372 −0.150630
\(396\) −1.65773 2.87128i −0.0833043 0.144287i
\(397\) 6.92612 11.9964i 0.347612 0.602082i −0.638213 0.769860i \(-0.720326\pi\)
0.985825 + 0.167778i \(0.0536593\pi\)
\(398\) −2.33643 −0.117114
\(399\) 18.0692 31.2968i 0.904594 1.56680i
\(400\) −0.577268 0.999858i −0.0288634 0.0499929i
\(401\) −15.8727 27.4923i −0.792645 1.37290i −0.924324 0.381609i \(-0.875370\pi\)
0.131678 0.991292i \(-0.457963\pi\)
\(402\) 1.17383 + 2.03313i 0.0585452 + 0.101403i
\(403\) −3.71251 −0.184933
\(404\) −10.9694 18.9996i −0.545748 0.945263i
\(405\) 12.7135 + 22.0204i 0.631737 + 1.09420i
\(406\) −1.63219 + 2.82704i −0.0810042 + 0.140303i
\(407\) 1.62426 2.81330i 0.0805115 0.139450i
\(408\) −1.74671 −0.0864750
\(409\) 24.4235 1.20767 0.603833 0.797111i \(-0.293639\pi\)
0.603833 + 0.797111i \(0.293639\pi\)
\(410\) 2.73276 4.73328i 0.134961 0.233760i
\(411\) −9.87513 + 17.1042i −0.487104 + 0.843690i
\(412\) 1.06865 + 1.85096i 0.0526486 + 0.0911901i
\(413\) 0.208564 + 0.361243i 0.0102628 + 0.0177756i
\(414\) 1.96308 0.0964802
\(415\) 19.1457 + 33.1613i 0.939825 + 1.62782i
\(416\) 0.532847 + 0.922917i 0.0261250 + 0.0452497i
\(417\) 7.56108 + 13.0962i 0.370268 + 0.641323i
\(418\) 1.10299 1.91044i 0.0539491 0.0934426i
\(419\) 19.8652 0.970480 0.485240 0.874381i \(-0.338732\pi\)
0.485240 + 0.874381i \(0.338732\pi\)
\(420\) −13.3144 + 23.0612i −0.649677 + 1.12527i
\(421\) 13.3761 + 23.1680i 0.651910 + 1.12914i 0.982659 + 0.185422i \(0.0593652\pi\)
−0.330749 + 0.943719i \(0.607301\pi\)
\(422\) −0.936837 −0.0456045
\(423\) 4.88472 + 8.46058i 0.237503 + 0.411367i
\(424\) −5.35545 + 9.27592i −0.260084 + 0.450478i
\(425\) 0.155524 0.269375i 0.00754402 0.0130666i
\(426\) −5.07425 −0.245848
\(427\) 9.87107 17.0972i 0.477695 0.827391i
\(428\) 22.5517 1.09008
\(429\) −1.37531 −0.0664007
\(430\) 3.04014 + 1.34827i 0.146609 + 0.0650192i
\(431\) 16.9822 0.818004 0.409002 0.912533i \(-0.365877\pi\)
0.409002 + 0.912533i \(0.365877\pi\)
\(432\) 14.6540 0.705042
\(433\) 3.59178 6.22114i 0.172610 0.298969i −0.766722 0.641980i \(-0.778113\pi\)
0.939331 + 0.343011i \(0.111447\pi\)
\(434\) 5.77636 0.277274
\(435\) 11.6469 20.1729i 0.558424 0.967219i
\(436\) −5.34583 + 9.25926i −0.256019 + 0.443438i
\(437\) −26.3168 45.5820i −1.25890 2.18048i
\(438\) 6.49413 0.310301
\(439\) −11.6415 20.1637i −0.555621 0.962363i −0.997855 0.0654636i \(-0.979147\pi\)
0.442234 0.896900i \(-0.354186\pi\)
\(440\) −1.64566 + 2.85037i −0.0784538 + 0.135886i
\(441\) 1.74722 0.0832008
\(442\) −0.0458761 + 0.0794597i −0.00218210 + 0.00377951i
\(443\) −5.47968 9.49109i −0.260348 0.450935i 0.705987 0.708225i \(-0.250504\pi\)
−0.966334 + 0.257290i \(0.917170\pi\)
\(444\) −3.87686 6.71491i −0.183987 0.318676i
\(445\) 3.71286 + 6.43086i 0.176006 + 0.304852i
\(446\) 3.18712 0.150915
\(447\) 19.3493 + 33.5140i 0.915191 + 1.58516i
\(448\) 10.1122 + 17.5148i 0.477755 + 0.827495i
\(449\) 4.62872 8.01717i 0.218443 0.378354i −0.735889 0.677102i \(-0.763236\pi\)
0.954332 + 0.298748i \(0.0965690\pi\)
\(450\) −0.0354051 + 0.0613234i −0.00166901 + 0.00289081i
\(451\) 17.6984 0.833385
\(452\) −24.4531 −1.15018
\(453\) −1.94111 + 3.36210i −0.0912012 + 0.157965i
\(454\) −2.72726 + 4.72376i −0.127997 + 0.221697i
\(455\) 1.41613 + 2.45281i 0.0663893 + 0.114990i
\(456\) −5.33068 9.23301i −0.249632 0.432375i
\(457\) −2.50708 −0.117276 −0.0586381 0.998279i \(-0.518676\pi\)
−0.0586381 + 0.998279i \(0.518676\pi\)
\(458\) 3.08960 + 5.35134i 0.144367 + 0.250052i
\(459\) 1.97400 + 3.41906i 0.0921383 + 0.159588i
\(460\) 19.3916 + 33.5873i 0.904140 + 1.56602i
\(461\) 4.50785 7.80782i 0.209951 0.363646i −0.741748 0.670679i \(-0.766003\pi\)
0.951699 + 0.307033i \(0.0993361\pi\)
\(462\) 2.13987 0.0995559
\(463\) 1.81301 3.14022i 0.0842576 0.145938i −0.820817 0.571191i \(-0.806481\pi\)
0.905075 + 0.425253i \(0.139815\pi\)
\(464\) −9.33914 16.1759i −0.433558 0.750945i
\(465\) −41.2185 −1.91146
\(466\) 1.16792 + 2.02290i 0.0541031 + 0.0937092i
\(467\) −4.29907 + 7.44620i −0.198937 + 0.344569i −0.948184 0.317722i \(-0.897082\pi\)
0.749247 + 0.662291i \(0.230416\pi\)
\(468\) −0.420844 + 0.728923i −0.0194535 + 0.0336945i
\(469\) 15.6556 0.722908
\(470\) 2.39485 4.14801i 0.110466 0.191333i
\(471\) −41.8898 −1.93018
\(472\) 0.123059 0.00566423
\(473\) 1.14126 + 10.7086i 0.0524750 + 0.492383i
\(474\) 0.574212 0.0263744
\(475\) 1.89854 0.0871110
\(476\) −2.87634 + 4.98196i −0.131837 + 0.228348i
\(477\) −12.7411 −0.583375
\(478\) 1.32758 2.29944i 0.0607221 0.105174i
\(479\) −10.1942 + 17.6569i −0.465785 + 0.806764i −0.999237 0.0390668i \(-0.987561\pi\)
0.533451 + 0.845831i \(0.320895\pi\)
\(480\) 5.91598 + 10.2468i 0.270026 + 0.467699i
\(481\) −0.824691 −0.0376027
\(482\) 2.31703 + 4.01322i 0.105538 + 0.182797i
\(483\) 25.5281 44.2159i 1.16157 2.01189i
\(484\) 16.2036 0.736528
\(485\) 3.44743 5.97112i 0.156540 0.271135i
\(486\) −1.13527 1.96634i −0.0514967 0.0891949i
\(487\) −3.71859 6.44079i −0.168506 0.291860i 0.769389 0.638780i \(-0.220561\pi\)
−0.937895 + 0.346920i \(0.887227\pi\)
\(488\) −2.91210 5.04391i −0.131825 0.228327i
\(489\) 49.5511 2.24078
\(490\) −0.428308 0.741852i −0.0193490 0.0335134i
\(491\) −1.03175 1.78704i −0.0465622 0.0806480i 0.841805 0.539782i \(-0.181493\pi\)
−0.888367 + 0.459134i \(0.848160\pi\)
\(492\) 21.1217 36.5838i 0.952239 1.64933i
\(493\) 2.51609 4.35800i 0.113319 0.196274i
\(494\) −0.560027 −0.0251968
\(495\) −3.91517 −0.175974
\(496\) −16.5257 + 28.6233i −0.742026 + 1.28523i
\(497\) −16.9191 + 29.3047i −0.758924 + 1.31449i
\(498\) −3.67224 6.36051i −0.164557 0.285021i
\(499\) −5.92150 10.2563i −0.265083 0.459137i 0.702503 0.711681i \(-0.252066\pi\)
−0.967585 + 0.252544i \(0.918733\pi\)
\(500\) 21.0887 0.943116
\(501\) 2.31589 + 4.01125i 0.103467 + 0.179209i
\(502\) −0.401960 0.696216i −0.0179404 0.0310736i
\(503\) −6.85454 11.8724i −0.305629 0.529364i 0.671772 0.740758i \(-0.265533\pi\)
−0.977401 + 0.211393i \(0.932200\pi\)
\(504\) 1.32585 2.29643i 0.0590579 0.102291i
\(505\) −25.9071 −1.15285
\(506\) 1.55830 2.69905i 0.0692748 0.119988i
\(507\) −12.8813 22.3110i −0.572078 0.990868i
\(508\) 23.7659 1.05444
\(509\) −7.96559 13.7968i −0.353068 0.611533i 0.633717 0.773565i \(-0.281528\pi\)
−0.986785 + 0.162032i \(0.948195\pi\)
\(510\) −0.509344 + 0.882209i −0.0225541 + 0.0390649i
\(511\) 21.6534 37.5047i 0.957889 1.65911i
\(512\) 15.9432 0.704596
\(513\) −12.0487 + 20.8689i −0.531961 + 0.921384i
\(514\) −0.177876 −0.00784576
\(515\) 2.52390 0.111216
\(516\) 23.4975 + 10.4209i 1.03442 + 0.458753i
\(517\) 15.5100 0.682129
\(518\) 1.28315 0.0563784
\(519\) −7.91442 + 13.7082i −0.347404 + 0.601722i
\(520\) 0.835557 0.0366416
\(521\) 6.64470 11.5090i 0.291109 0.504216i −0.682963 0.730453i \(-0.739309\pi\)
0.974072 + 0.226237i \(0.0726423\pi\)
\(522\) −0.572789 + 0.992099i −0.0250703 + 0.0434230i
\(523\) 10.0942 + 17.4837i 0.441388 + 0.764507i 0.997793 0.0664044i \(-0.0211528\pi\)
−0.556404 + 0.830912i \(0.687819\pi\)
\(524\) −3.04477 −0.133011
\(525\) 0.920821 + 1.59491i 0.0401879 + 0.0696075i
\(526\) −0.256988 + 0.445116i −0.0112052 + 0.0194080i
\(527\) −8.90450 −0.387886
\(528\) −6.12201 + 10.6036i −0.266426 + 0.461464i
\(529\) −25.6801 44.4793i −1.11653 1.93388i
\(530\) 3.12332 + 5.40975i 0.135668 + 0.234985i
\(531\) 0.0731918 + 0.126772i 0.00317625 + 0.00550143i
\(532\) −35.1125 −1.52232
\(533\) −2.24652 3.89109i −0.0973076 0.168542i
\(534\) −0.712146 1.23347i −0.0308176 0.0533776i
\(535\) 13.3154 23.0630i 0.575677 0.997101i
\(536\) 2.30931 3.99984i 0.0997470 0.172767i
\(537\) −40.7710 −1.75940
\(538\) −2.87931 −0.124136
\(539\) 1.38695 2.40226i 0.0597400 0.103473i
\(540\) 8.87811 15.3773i 0.382053 0.661735i
\(541\) 12.0721 + 20.9095i 0.519020 + 0.898970i 0.999756 + 0.0221039i \(0.00703647\pi\)
−0.480735 + 0.876866i \(0.659630\pi\)
\(542\) −2.80026 4.85020i −0.120282 0.208334i
\(543\) −19.1009 −0.819699
\(544\) 1.27804 + 2.21363i 0.0547955 + 0.0949086i
\(545\) 6.31279 + 10.9341i 0.270410 + 0.468364i
\(546\) −0.271622 0.470462i −0.0116243 0.0201339i
\(547\) −3.21134 + 5.56220i −0.137307 + 0.237822i −0.926476 0.376353i \(-0.877178\pi\)
0.789169 + 0.614176i \(0.210511\pi\)
\(548\) 19.1896 0.819737
\(549\) 3.46408 5.99996i 0.147843 0.256072i
\(550\) 0.0562093 + 0.0973573i 0.00239677 + 0.00415133i
\(551\) 30.7149 1.30850
\(552\) −7.53114 13.0443i −0.320547 0.555203i
\(553\) 1.91459 3.31618i 0.0814169 0.141018i
\(554\) 0.748260 1.29602i 0.0317905 0.0550628i
\(555\) −9.15621 −0.388660
\(556\) 7.34642 12.7244i 0.311558 0.539634i
\(557\) 29.5285 1.25116 0.625582 0.780158i \(-0.284862\pi\)
0.625582 + 0.780158i \(0.284862\pi\)
\(558\) 2.02711 0.0858144
\(559\) 2.20948 1.61019i 0.0934511 0.0681039i
\(560\) 25.2148 1.06552
\(561\) −3.29871 −0.139272
\(562\) −0.0413846 + 0.0716802i −0.00174570 + 0.00302365i
\(563\) 25.7525 1.08534 0.542669 0.839946i \(-0.317414\pi\)
0.542669 + 0.839946i \(0.317414\pi\)
\(564\) 18.5100 32.0603i 0.779411 1.34998i
\(565\) −14.4381 + 25.0075i −0.607415 + 1.05207i
\(566\) 3.31668 + 5.74465i 0.139410 + 0.241466i
\(567\) −32.5229 −1.36583
\(568\) 4.99136 + 8.64530i 0.209433 + 0.362749i
\(569\) 3.60245 6.23962i 0.151022 0.261578i −0.780581 0.625054i \(-0.785077\pi\)
0.931604 + 0.363476i \(0.118410\pi\)
\(570\) −6.21775 −0.260433
\(571\) −2.63208 + 4.55890i −0.110149 + 0.190784i −0.915830 0.401566i \(-0.868466\pi\)
0.805681 + 0.592349i \(0.201800\pi\)
\(572\) 0.668134 + 1.15724i 0.0279361 + 0.0483867i
\(573\) −3.35703 5.81454i −0.140242 0.242906i
\(574\) 3.49540 + 6.05421i 0.145895 + 0.252698i
\(575\) 2.68224 0.111857
\(576\) 3.54869 + 6.14650i 0.147862 + 0.256104i
\(577\) 1.55886 + 2.70002i 0.0648962 + 0.112403i 0.896648 0.442744i \(-0.145995\pi\)
−0.831752 + 0.555148i \(0.812662\pi\)
\(578\) −0.110034 + 0.190585i −0.00457683 + 0.00792730i
\(579\) 18.5081 32.0569i 0.769169 1.33224i
\(580\) −22.6324 −0.939759
\(581\) −48.9775 −2.03193
\(582\) −0.661235 + 1.14529i −0.0274091 + 0.0474739i
\(583\) −10.1139 + 17.5178i −0.418876 + 0.725514i
\(584\) −6.38805 11.0644i −0.264339 0.457849i
\(585\) 0.496967 + 0.860771i 0.0205470 + 0.0355885i
\(586\) −5.01331 −0.207098
\(587\) −4.71158 8.16070i −0.194468 0.336828i 0.752258 0.658868i \(-0.228965\pi\)
−0.946726 + 0.322040i \(0.895631\pi\)
\(588\) −3.31043 5.73382i −0.136520 0.236459i
\(589\) −27.1751 47.0687i −1.11973 1.93943i
\(590\) 0.0358841 0.0621531i 0.00147733 0.00255880i
\(591\) 40.8996 1.68239
\(592\) −3.67100 + 6.35835i −0.150877 + 0.261327i
\(593\) 10.9182 + 18.9109i 0.448358 + 0.776579i 0.998279 0.0586377i \(-0.0186757\pi\)
−0.549921 + 0.835216i \(0.685342\pi\)
\(594\) −1.42688 −0.0585455
\(595\) 3.39661 + 5.88310i 0.139247 + 0.241184i
\(596\) 18.8000 32.5625i 0.770078 1.33381i
\(597\) −10.6624 + 18.4678i −0.436384 + 0.755838i
\(598\) −0.791201 −0.0323546
\(599\) 6.14432 10.6423i 0.251050 0.434831i −0.712765 0.701403i \(-0.752558\pi\)
0.963815 + 0.266571i \(0.0858908\pi\)
\(600\) 0.543310 0.0221805
\(601\) −0.142548 −0.00581465 −0.00290733 0.999996i \(-0.500925\pi\)
−0.00290733 + 0.999996i \(0.500925\pi\)
\(602\) −3.43777 + 2.50533i −0.140113 + 0.102110i
\(603\) 5.49406 0.223735
\(604\) 3.77200 0.153481
\(605\) 9.56727 16.5710i 0.388965 0.673707i
\(606\) 4.96912 0.201857
\(607\) −0.621706 + 1.07683i −0.0252343 + 0.0437071i −0.878367 0.477987i \(-0.841367\pi\)
0.853132 + 0.521694i \(0.174700\pi\)
\(608\) −7.80075 + 13.5113i −0.316362 + 0.547956i
\(609\) 14.8972 + 25.8027i 0.603664 + 1.04558i
\(610\) −3.39670 −0.137528
\(611\) −1.96874 3.40995i −0.0796466 0.137952i
\(612\) −1.00940 + 1.74833i −0.0408026 + 0.0706721i
\(613\) −40.3607 −1.63015 −0.815077 0.579352i \(-0.803306\pi\)
−0.815077 + 0.579352i \(0.803306\pi\)
\(614\) 2.37275 4.10972i 0.0957562 0.165855i
\(615\) −24.9422 43.2011i −1.00577 1.74204i
\(616\) −2.10492 3.64583i −0.0848097 0.146895i
\(617\) 4.08078 + 7.06812i 0.164286 + 0.284552i 0.936402 0.350931i \(-0.114135\pi\)
−0.772115 + 0.635482i \(0.780801\pi\)
\(618\) −0.484097 −0.0194732
\(619\) 13.1827 + 22.8330i 0.529856 + 0.917738i 0.999393 + 0.0348250i \(0.0110874\pi\)
−0.469537 + 0.882913i \(0.655579\pi\)
\(620\) 20.0241 + 34.6828i 0.804188 + 1.39290i
\(621\) −17.0222 + 29.4834i −0.683079 + 1.18313i
\(622\) 1.38198 2.39367i 0.0554125 0.0959773i
\(623\) −9.49804 −0.380531
\(624\) 3.10835 0.124434
\(625\) 13.2292 22.9137i 0.529170 0.916549i
\(626\) 3.04726 5.27801i 0.121793 0.210952i
\(627\) −10.0671 17.4368i −0.402043 0.696358i
\(628\) 20.3503 + 35.2477i 0.812065 + 1.40654i
\(629\) −1.97803 −0.0788693
\(630\) −0.773239 1.33929i −0.0308066 0.0533586i
\(631\) −6.64008 11.5010i −0.264337 0.457846i 0.703052 0.711138i \(-0.251820\pi\)
−0.967390 + 0.253292i \(0.918487\pi\)
\(632\) −0.564832 0.978318i −0.0224678 0.0389154i
\(633\) −4.27531 + 7.40505i −0.169928 + 0.294325i
\(634\) 0.317972 0.0126283
\(635\) 14.0323 24.3047i 0.556856 0.964503i
\(636\) 24.1404 + 41.8124i 0.957228 + 1.65797i
\(637\) −0.704199 −0.0279014
\(638\) 0.909362 + 1.57506i 0.0360020 + 0.0623573i
\(639\) −5.93745 + 10.2840i −0.234882 + 0.406827i
\(640\) 7.63050 13.2164i 0.301622 0.522424i
\(641\) −14.9672 −0.591170 −0.295585 0.955316i \(-0.595515\pi\)
−0.295585 + 0.955316i \(0.595515\pi\)
\(642\) −2.55397 + 4.42361i −0.100797 + 0.174586i
\(643\) 1.57563 0.0621369 0.0310684 0.999517i \(-0.490109\pi\)
0.0310684 + 0.999517i \(0.490109\pi\)
\(644\) −49.6067 −1.95478
\(645\) 24.5310 17.8773i 0.965906 0.703919i
\(646\) −1.34323 −0.0528487
\(647\) 9.25001 0.363655 0.181828 0.983330i \(-0.441799\pi\)
0.181828 + 0.983330i \(0.441799\pi\)
\(648\) −4.79736 + 8.30927i −0.188458 + 0.326419i
\(649\) 0.232399 0.00912247
\(650\) 0.0142697 0.0247158i 0.000559703 0.000969433i
\(651\) 26.3607 45.6581i 1.03316 1.78948i
\(652\) −24.0722 41.6942i −0.942739 1.63287i
\(653\) −1.44783 −0.0566579 −0.0283290 0.999599i \(-0.509019\pi\)
−0.0283290 + 0.999599i \(0.509019\pi\)
\(654\) −1.21083 2.09721i −0.0473471 0.0820076i
\(655\) −1.79775 + 3.11380i −0.0702441 + 0.121666i
\(656\) −40.0002 −1.56175
\(657\) 7.59887 13.1616i 0.296460 0.513484i
\(658\) 3.06319 + 5.30561i 0.119416 + 0.206834i
\(659\) 8.11526 + 14.0560i 0.316125 + 0.547545i 0.979676 0.200586i \(-0.0642846\pi\)
−0.663551 + 0.748131i \(0.730951\pi\)
\(660\) 7.41802 + 12.8484i 0.288746 + 0.500123i
\(661\) 43.8423 1.70527 0.852634 0.522508i \(-0.175004\pi\)
0.852634 + 0.522508i \(0.175004\pi\)
\(662\) −0.524905 0.909161i −0.0204010 0.0353356i
\(663\) 0.418716 + 0.725238i 0.0162616 + 0.0281659i
\(664\) −7.22452 + 12.5132i −0.280366 + 0.485608i
\(665\) −20.7318 + 35.9086i −0.803946 + 1.39248i
\(666\) 0.450300 0.0174488
\(667\) 43.3937 1.68021
\(668\) 2.25015 3.89737i 0.0870607 0.150794i
\(669\) 14.5446 25.1920i 0.562327 0.973979i
\(670\) −1.34680 2.33272i −0.0520314 0.0901210i
\(671\) −5.49959 9.52557i −0.212309 0.367730i
\(672\) −15.1339 −0.583805
\(673\) 7.90166 + 13.6861i 0.304586 + 0.527559i 0.977169 0.212463i \(-0.0681484\pi\)
−0.672583 + 0.740022i \(0.734815\pi\)
\(674\) 1.53553 + 2.65961i 0.0591464 + 0.102445i
\(675\) −0.614008 1.06349i −0.0236332 0.0409338i
\(676\) −12.5156 + 21.6776i −0.481369 + 0.833755i
\(677\) −35.8935 −1.37950 −0.689750 0.724048i \(-0.742279\pi\)
−0.689750 + 0.724048i \(0.742279\pi\)
\(678\) 2.76931 4.79658i 0.106355 0.184211i
\(679\) 4.40952 + 7.63750i 0.169222 + 0.293101i
\(680\) 2.00410 0.0768536
\(681\) 24.8920 + 43.1143i 0.953865 + 1.65214i
\(682\) 1.60913 2.78709i 0.0616166 0.106723i
\(683\) −22.1662 + 38.3930i −0.848166 + 1.46907i 0.0346775 + 0.999399i \(0.488960\pi\)
−0.882843 + 0.469668i \(0.844374\pi\)
\(684\) −12.3221 −0.471148
\(685\) 11.3303 19.6246i 0.432908 0.749819i
\(686\) −3.44523 −0.131539
\(687\) 56.3982 2.15172
\(688\) −2.57936 24.2026i −0.0983372 0.922716i
\(689\) 5.13518 0.195635
\(690\) −8.78439 −0.334416
\(691\) 19.2588 33.3572i 0.732638 1.26897i −0.223114 0.974792i \(-0.571622\pi\)
0.955752 0.294174i \(-0.0950444\pi\)
\(692\) 15.3794 0.584639
\(693\) 2.50390 4.33688i 0.0951152 0.164744i
\(694\) −2.58909 + 4.48444i −0.0982807 + 0.170227i
\(695\) −8.67525 15.0260i −0.329071 0.569968i
\(696\) 8.78976 0.333175
\(697\) −5.38831 9.33282i −0.204097 0.353506i
\(698\) −3.73697 + 6.47262i −0.141446 + 0.244992i
\(699\) 21.3196 0.806380
\(700\) 0.894679 1.54963i 0.0338157 0.0585705i
\(701\) 5.34283 + 9.25405i 0.201796 + 0.349520i 0.949107 0.314954i \(-0.101989\pi\)
−0.747311 + 0.664474i \(0.768656\pi\)
\(702\) 0.181119 + 0.313707i 0.00683588 + 0.0118401i
\(703\) −6.03665 10.4558i −0.227676 0.394347i
\(704\) 11.2678 0.424672
\(705\) −21.8581 37.8593i −0.823224 1.42587i
\(706\) 1.06281 + 1.84083i 0.0399992 + 0.0692806i
\(707\) 16.5685 28.6976i 0.623124 1.07928i
\(708\) 0.277351 0.480386i 0.0104235 0.0180540i
\(709\) −26.6054 −0.999186 −0.499593 0.866260i \(-0.666517\pi\)
−0.499593 + 0.866260i \(0.666517\pi\)
\(710\) 5.82197 0.218494
\(711\) 0.671893 1.16375i 0.0251980 0.0436442i
\(712\) −1.40103 + 2.42665i −0.0525057 + 0.0909426i
\(713\) −38.3928 66.4983i −1.43782 2.49038i
\(714\) −0.651488 1.12841i −0.0243813 0.0422297i
\(715\) 1.57797 0.0590128
\(716\) 19.8067 + 34.3063i 0.740212 + 1.28209i
\(717\) −12.1170 20.9872i −0.452517 0.783782i
\(718\) 2.29006 + 3.96650i 0.0854644 + 0.148029i
\(719\) −23.2094 + 40.1999i −0.865566 + 1.49920i 0.000918687 1.00000i \(0.499708\pi\)
−0.866484 + 0.499204i \(0.833626\pi\)
\(720\) 8.84870 0.329772
\(721\) −1.61413 + 2.79575i −0.0601132 + 0.104119i
\(722\) −2.00868 3.47913i −0.0747552 0.129480i
\(723\) 42.2956 1.57299
\(724\) 9.27932 + 16.0723i 0.344863 + 0.597321i
\(725\) −0.782625 + 1.35555i −0.0290660 + 0.0503437i
\(726\) −1.83505 + 3.17841i −0.0681052 + 0.117962i
\(727\) −6.30831 −0.233962 −0.116981 0.993134i \(-0.537322\pi\)
−0.116981 + 0.993134i \(0.537322\pi\)
\(728\) −0.534370 + 0.925556i −0.0198051 + 0.0343034i
\(729\) 12.3764 0.458385
\(730\) −7.45107 −0.275776
\(731\) 5.29947 3.86207i 0.196008 0.142844i
\(732\) −26.2534 −0.970352
\(733\) 10.1907 0.376401 0.188200 0.982131i \(-0.439735\pi\)
0.188200 + 0.982131i \(0.439735\pi\)
\(734\) −1.25599 + 2.17544i −0.0463596 + 0.0802971i
\(735\) −7.81844 −0.288387
\(736\) −11.0208 + 19.0887i −0.406234 + 0.703617i
\(737\) 4.36119 7.55381i 0.160647 0.278248i
\(738\) 1.22665 + 2.12462i 0.0451536 + 0.0782083i
\(739\) 11.4077 0.419637 0.209819 0.977740i \(-0.432713\pi\)
0.209819 + 0.977740i \(0.432713\pi\)
\(740\) 4.44813 + 7.70439i 0.163517 + 0.283219i
\(741\) −2.55571 + 4.42663i −0.0938865 + 0.162616i
\(742\) −7.98992 −0.293319
\(743\) 13.3183 23.0680i 0.488602 0.846283i −0.511312 0.859395i \(-0.670840\pi\)
0.999914 + 0.0131118i \(0.00417374\pi\)
\(744\) −7.77678 13.4698i −0.285111 0.493826i
\(745\) −22.2005 38.4525i −0.813365 1.40879i
\(746\) 2.98585 + 5.17164i 0.109320 + 0.189347i
\(747\) −17.1878 −0.628868
\(748\) 1.60253 + 2.77566i 0.0585942 + 0.101488i
\(749\) 17.0314 + 29.4993i 0.622315 + 1.07788i
\(750\) −2.38829 + 4.13664i −0.0872080 + 0.151049i
\(751\) −12.7080 + 22.0109i −0.463722 + 0.803190i −0.999143 0.0413955i \(-0.986820\pi\)
0.535421 + 0.844585i \(0.320153\pi\)
\(752\) −35.0542 −1.27830
\(753\) −7.33747 −0.267392
\(754\) 0.230857 0.399856i 0.00840731 0.0145619i
\(755\) 2.22714 3.85752i 0.0810540 0.140390i
\(756\) 11.3558 + 19.6687i 0.413005 + 0.715346i
\(757\) 17.1555 + 29.7142i 0.623527 + 1.07998i 0.988824 + 0.149090i \(0.0476343\pi\)
−0.365297 + 0.930891i \(0.619032\pi\)
\(758\) −2.94556 −0.106988
\(759\) −14.2228 24.6346i −0.516254 0.894178i
\(760\) 6.11619 + 10.5935i 0.221857 + 0.384268i
\(761\) −9.75023 16.8879i −0.353446 0.612186i 0.633405 0.773820i \(-0.281657\pi\)
−0.986851 + 0.161635i \(0.948323\pi\)
\(762\) −2.69148 + 4.66178i −0.0975019 + 0.168878i
\(763\) −16.1491 −0.584635
\(764\) −3.26172 + 5.64947i −0.118005 + 0.204390i
\(765\) 1.19198 + 2.06457i 0.0430962 + 0.0746447i
\(766\) −0.808674 −0.0292186
\(767\) −0.0294993 0.0510942i −0.00106516 0.00184491i