Properties

Label 105.3.k.d.62.8
Level 105
Weight 3
Character 105.62
Analytic conductor 2.861
Analytic rank 0
Dimension 32
CM no
Inner twists 8

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
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 62.8
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.d.83.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.67168 + 1.67168i) q^{2} +(2.55943 - 1.56503i) q^{3} -1.58906i q^{4} +(-0.529219 - 4.97191i) q^{5} +(-1.66231 + 6.89480i) q^{6} +(6.78135 - 1.73590i) q^{7} +(-4.03033 - 4.03033i) q^{8} +(4.10134 - 8.01118i) q^{9} +O(q^{10})\) \(q+(-1.67168 + 1.67168i) q^{2} +(2.55943 - 1.56503i) q^{3} -1.58906i q^{4} +(-0.529219 - 4.97191i) q^{5} +(-1.66231 + 6.89480i) q^{6} +(6.78135 - 1.73590i) q^{7} +(-4.03033 - 4.03033i) q^{8} +(4.10134 - 8.01118i) q^{9} +(9.19616 + 7.42678i) q^{10} -4.41779i q^{11} +(-2.48693 - 4.06708i) q^{12} +(1.62244 + 1.62244i) q^{13} +(-8.43440 + 14.2381i) q^{14} +(-9.13571 - 11.8970i) q^{15} +19.8311 q^{16} +(13.9255 + 13.9255i) q^{17} +(6.53602 + 20.2483i) q^{18} -0.694013 q^{19} +(-7.90067 + 0.840961i) q^{20} +(14.6396 - 15.0559i) q^{21} +(7.38515 + 7.38515i) q^{22} +(23.1818 + 23.1818i) q^{23} +(-16.6229 - 4.00774i) q^{24} +(-24.4399 + 5.26247i) q^{25} -5.42443 q^{26} +(-2.04067 - 26.9228i) q^{27} +(-2.75844 - 10.7760i) q^{28} -49.1234 q^{29} +(35.1601 + 4.61602i) q^{30} -33.8768i q^{31} +(-17.0301 + 17.0301i) q^{32} +(-6.91399 - 11.3070i) q^{33} -46.5580 q^{34} +(-12.2195 - 32.7976i) q^{35} +(-12.7302 - 6.51728i) q^{36} +(2.02579 + 2.02579i) q^{37} +(1.16017 - 1.16017i) q^{38} +(6.69171 + 1.61335i) q^{39} +(-17.9055 + 22.1714i) q^{40} -32.5085 q^{41} +(0.695926 + 49.6416i) q^{42} +(-30.4591 + 30.4591i) q^{43} -7.02014 q^{44} +(-42.0014 - 16.1518i) q^{45} -77.5053 q^{46} +(18.7790 + 18.7790i) q^{47} +(50.7563 - 31.0364i) q^{48} +(42.9733 - 23.5434i) q^{49} +(32.0585 - 49.6529i) q^{50} +(57.4350 + 13.8474i) q^{51} +(2.57816 - 2.57816i) q^{52} +(33.8448 + 33.8448i) q^{53} +(48.4178 + 41.5950i) q^{54} +(-21.9649 + 2.33798i) q^{55} +(-34.3273 - 20.3348i) q^{56} +(-1.77628 + 1.08615i) q^{57} +(82.1189 - 82.1189i) q^{58} +23.1041i q^{59} +(-18.9051 + 14.5172i) q^{60} +12.9880i q^{61} +(56.6314 + 56.6314i) q^{62} +(13.9060 - 61.4461i) q^{63} +22.3867i q^{64} +(7.20802 - 8.92528i) q^{65} +(30.4598 + 7.34376i) q^{66} +(-56.3395 - 56.3395i) q^{67} +(22.1284 - 22.1284i) q^{68} +(95.6125 + 23.0519i) q^{69} +(75.2545 + 34.4000i) q^{70} +92.7547i q^{71} +(-48.8175 + 15.7579i) q^{72} +(95.4460 + 95.4460i) q^{73} -6.77295 q^{74} +(-54.3161 + 51.7181i) q^{75} +1.10283i q^{76} +(-7.66883 - 29.9586i) q^{77} +(-13.8834 + 8.48941i) q^{78} +100.280i q^{79} +(-10.4950 - 98.5987i) q^{80} +(-47.3580 - 65.7132i) q^{81} +(54.3440 - 54.3440i) q^{82} +(-5.62594 + 5.62594i) q^{83} +(-23.9248 - 23.2633i) q^{84} +(61.8666 - 76.6059i) q^{85} -101.836i q^{86} +(-125.728 + 76.8798i) q^{87} +(-17.8052 + 17.8052i) q^{88} -158.669i q^{89} +(97.2139 - 43.2123i) q^{90} +(13.8188 + 8.18596i) q^{91} +(36.8373 - 36.8373i) q^{92} +(-53.0184 - 86.7053i) q^{93} -62.7852 q^{94} +(0.367285 + 3.45057i) q^{95} +(-16.9346 + 70.2399i) q^{96} +(-37.1038 + 37.1038i) q^{97} +(-32.4807 + 111.195i) q^{98} +(-35.3917 - 18.1189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q - 48q^{15} - 24q^{16} - 92q^{18} - 60q^{21} + 112q^{22} - 72q^{25} + 88q^{28} - 108q^{30} + 416q^{36} + 72q^{37} + 300q^{42} - 328q^{43} + 32q^{46} + 148q^{51} - 748q^{57} - 392q^{58} + 544q^{60} - 220q^{63} - 648q^{67} - 8q^{70} - 8q^{72} + 500q^{78} - 948q^{81} + 672q^{85} + 1288q^{88} + 808q^{91} + 292q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.67168 + 1.67168i −0.835842 + 0.835842i −0.988309 0.152466i \(-0.951278\pi\)
0.152466 + 0.988309i \(0.451278\pi\)
\(3\) 2.55943 1.56503i 0.853143 0.521678i
\(4\) 1.58906i 0.397265i
\(5\) −0.529219 4.97191i −0.105844 0.994383i
\(6\) −1.66231 + 6.89480i −0.277052 + 1.14913i
\(7\) 6.78135 1.73590i 0.968764 0.247985i
\(8\) −4.03033 4.03033i −0.503791 0.503791i
\(9\) 4.10134 8.01118i 0.455705 0.890131i
\(10\) 9.19616 + 7.42678i 0.919616 + 0.742678i
\(11\) 4.41779i 0.401617i −0.979630 0.200809i \(-0.935643\pi\)
0.979630 0.200809i \(-0.0643570\pi\)
\(12\) −2.48693 4.06708i −0.207244 0.338924i
\(13\) 1.62244 + 1.62244i 0.124803 + 0.124803i 0.766750 0.641946i \(-0.221873\pi\)
−0.641946 + 0.766750i \(0.721873\pi\)
\(14\) −8.43440 + 14.2381i −0.602457 + 1.01701i
\(15\) −9.13571 11.8970i −0.609047 0.793134i
\(16\) 19.8311 1.23945
\(17\) 13.9255 + 13.9255i 0.819145 + 0.819145i 0.985984 0.166839i \(-0.0533560\pi\)
−0.166839 + 0.985984i \(0.553356\pi\)
\(18\) 6.53602 + 20.2483i 0.363112 + 1.12491i
\(19\) −0.694013 −0.0365270 −0.0182635 0.999833i \(-0.505814\pi\)
−0.0182635 + 0.999833i \(0.505814\pi\)
\(20\) −7.90067 + 0.840961i −0.395034 + 0.0420481i
\(21\) 14.6396 15.0559i 0.697125 0.716949i
\(22\) 7.38515 + 7.38515i 0.335689 + 0.335689i
\(23\) 23.1818 + 23.1818i 1.00790 + 1.00790i 0.999969 + 0.00793606i \(0.00252615\pi\)
0.00793606 + 0.999969i \(0.497474\pi\)
\(24\) −16.6229 4.00774i −0.692623 0.166989i
\(25\) −24.4399 + 5.26247i −0.977594 + 0.210499i
\(26\) −5.42443 −0.208632
\(27\) −2.04067 26.9228i −0.0755805 0.997140i
\(28\) −2.75844 10.7760i −0.0985158 0.384856i
\(29\) −49.1234 −1.69391 −0.846956 0.531663i \(-0.821567\pi\)
−0.846956 + 0.531663i \(0.821567\pi\)
\(30\) 35.1601 + 4.61602i 1.17200 + 0.153867i
\(31\) 33.8768i 1.09280i −0.837524 0.546401i \(-0.815998\pi\)
0.837524 0.546401i \(-0.184002\pi\)
\(32\) −17.0301 + 17.0301i −0.532190 + 0.532190i
\(33\) −6.91399 11.3070i −0.209515 0.342637i
\(34\) −46.5580 −1.36935
\(35\) −12.2195 32.7976i −0.349130 0.937074i
\(36\) −12.7302 6.51728i −0.353618 0.181036i
\(37\) 2.02579 + 2.02579i 0.0547510 + 0.0547510i 0.733952 0.679201i \(-0.237674\pi\)
−0.679201 + 0.733952i \(0.737674\pi\)
\(38\) 1.16017 1.16017i 0.0305308 0.0305308i
\(39\) 6.69171 + 1.61335i 0.171582 + 0.0413679i
\(40\) −17.9055 + 22.1714i −0.447638 + 0.554285i
\(41\) −32.5085 −0.792891 −0.396446 0.918058i \(-0.629756\pi\)
−0.396446 + 0.918058i \(0.629756\pi\)
\(42\) 0.695926 + 49.6416i 0.0165697 + 1.18194i
\(43\) −30.4591 + 30.4591i −0.708351 + 0.708351i −0.966188 0.257838i \(-0.916990\pi\)
0.257838 + 0.966188i \(0.416990\pi\)
\(44\) −7.02014 −0.159549
\(45\) −42.0014 16.1518i −0.933365 0.358930i
\(46\) −77.5053 −1.68490
\(47\) 18.7790 + 18.7790i 0.399554 + 0.399554i 0.878076 0.478522i \(-0.158827\pi\)
−0.478522 + 0.878076i \(0.658827\pi\)
\(48\) 50.7563 31.0364i 1.05742 0.646591i
\(49\) 42.9733 23.5434i 0.877007 0.480478i
\(50\) 32.0585 49.6529i 0.641171 0.993058i
\(51\) 57.4350 + 13.8474i 1.12618 + 0.271518i
\(52\) 2.57816 2.57816i 0.0495800 0.0495800i
\(53\) 33.8448 + 33.8448i 0.638581 + 0.638581i 0.950205 0.311624i \(-0.100873\pi\)
−0.311624 + 0.950205i \(0.600873\pi\)
\(54\) 48.4178 + 41.5950i 0.896625 + 0.770278i
\(55\) −21.9649 + 2.33798i −0.399361 + 0.0425087i
\(56\) −34.3273 20.3348i −0.612988 0.363122i
\(57\) −1.77628 + 1.08615i −0.0311627 + 0.0190553i
\(58\) 82.1189 82.1189i 1.41584 1.41584i
\(59\) 23.1041i 0.391596i 0.980644 + 0.195798i \(0.0627296\pi\)
−0.980644 + 0.195798i \(0.937270\pi\)
\(60\) −18.9051 + 14.5172i −0.315084 + 0.241953i
\(61\) 12.9880i 0.212919i 0.994317 + 0.106459i \(0.0339514\pi\)
−0.994317 + 0.106459i \(0.966049\pi\)
\(62\) 56.6314 + 56.6314i 0.913410 + 0.913410i
\(63\) 13.9060 61.4461i 0.220731 0.975335i
\(64\) 22.3867i 0.349792i
\(65\) 7.20802 8.92528i 0.110893 0.137312i
\(66\) 30.4598 + 7.34376i 0.461512 + 0.111269i
\(67\) −56.3395 56.3395i −0.840888 0.840888i 0.148086 0.988974i \(-0.452689\pi\)
−0.988974 + 0.148086i \(0.952689\pi\)
\(68\) 22.1284 22.1284i 0.325418 0.325418i
\(69\) 95.6125 + 23.0519i 1.38569 + 0.334085i
\(70\) 75.2545 + 34.4000i 1.07506 + 0.491429i
\(71\) 92.7547i 1.30640i 0.757184 + 0.653202i \(0.226575\pi\)
−0.757184 + 0.653202i \(0.773425\pi\)
\(72\) −48.8175 + 15.7579i −0.678020 + 0.218860i
\(73\) 95.4460 + 95.4460i 1.30748 + 1.30748i 0.923229 + 0.384251i \(0.125540\pi\)
0.384251 + 0.923229i \(0.374460\pi\)
\(74\) −6.77295 −0.0915263
\(75\) −54.3161 + 51.7181i −0.724215 + 0.689574i
\(76\) 1.10283i 0.0145109i
\(77\) −7.66883 29.9586i −0.0995952 0.389072i
\(78\) −13.8834 + 8.48941i −0.177993 + 0.108839i
\(79\) 100.280i 1.26937i 0.772770 + 0.634687i \(0.218871\pi\)
−0.772770 + 0.634687i \(0.781129\pi\)
\(80\) −10.4950 98.5987i −0.131188 1.23248i
\(81\) −47.3580 65.7132i −0.584667 0.811274i
\(82\) 54.3440 54.3440i 0.662732 0.662732i
\(83\) −5.62594 + 5.62594i −0.0677824 + 0.0677824i −0.740185 0.672403i \(-0.765262\pi\)
0.672403 + 0.740185i \(0.265262\pi\)
\(84\) −23.9248 23.2633i −0.284819 0.276944i
\(85\) 61.8666 76.6059i 0.727842 0.901245i
\(86\) 101.836i 1.18414i
\(87\) −125.728 + 76.8798i −1.44515 + 0.883676i
\(88\) −17.8052 + 17.8052i −0.202331 + 0.202331i
\(89\) 158.669i 1.78280i −0.453220 0.891399i \(-0.649725\pi\)
0.453220 0.891399i \(-0.350275\pi\)
\(90\) 97.2139 43.2123i 1.08015 0.480137i
\(91\) 13.8188 + 8.18596i 0.151854 + 0.0899556i
\(92\) 36.8373 36.8373i 0.400405 0.400405i
\(93\) −53.0184 86.7053i −0.570090 0.932315i
\(94\) −62.7852 −0.667928
\(95\) 0.367285 + 3.45057i 0.00386616 + 0.0363218i
\(96\) −16.9346 + 70.2399i −0.176402 + 0.731665i
\(97\) −37.1038 + 37.1038i −0.382514 + 0.382514i −0.872007 0.489493i \(-0.837182\pi\)
0.489493 + 0.872007i \(0.337182\pi\)
\(98\) −32.4807 + 111.195i −0.331435 + 1.13464i
\(99\) −35.3917 18.1189i −0.357492 0.183019i
\(100\) 8.36238 + 38.8364i 0.0836238 + 0.388364i
\(101\) 17.6626 0.174877 0.0874384 0.996170i \(-0.472132\pi\)
0.0874384 + 0.996170i \(0.472132\pi\)
\(102\) −119.162 + 72.8648i −1.16825 + 0.714361i
\(103\) −96.5666 96.5666i −0.937540 0.937540i 0.0606213 0.998161i \(-0.480692\pi\)
−0.998161 + 0.0606213i \(0.980692\pi\)
\(104\) 13.0780i 0.125750i
\(105\) −82.6044 64.8191i −0.786708 0.617325i
\(106\) −113.156 −1.06751
\(107\) −7.22790 + 7.22790i −0.0675504 + 0.0675504i −0.740075 0.672524i \(-0.765210\pi\)
0.672524 + 0.740075i \(0.265210\pi\)
\(108\) −42.7819 + 3.24275i −0.396129 + 0.0300255i
\(109\) 125.106i 1.14776i 0.818940 + 0.573880i \(0.194562\pi\)
−0.818940 + 0.573880i \(0.805438\pi\)
\(110\) 32.8100 40.6267i 0.298273 0.369334i
\(111\) 8.35527 + 2.01443i 0.0752727 + 0.0181480i
\(112\) 134.482 34.4248i 1.20073 0.307364i
\(113\) 71.6887 + 71.6887i 0.634414 + 0.634414i 0.949172 0.314758i \(-0.101923\pi\)
−0.314758 + 0.949172i \(0.601923\pi\)
\(114\) 1.15367 4.78508i 0.0101199 0.0419744i
\(115\) 102.990 127.526i 0.895562 1.10892i
\(116\) 78.0601i 0.672932i
\(117\) 19.6519 6.34349i 0.167965 0.0542179i
\(118\) −38.6228 38.6228i −0.327312 0.327312i
\(119\) 118.607 + 70.2603i 0.996694 + 0.590422i
\(120\) −11.1290 + 84.7688i −0.0927413 + 0.706407i
\(121\) 101.483 0.838703
\(122\) −21.7119 21.7119i −0.177966 0.177966i
\(123\) −83.2032 + 50.8769i −0.676449 + 0.413634i
\(124\) −53.8323 −0.434132
\(125\) 39.0986 + 118.728i 0.312789 + 0.949823i
\(126\) 79.4720 + 125.965i 0.630730 + 0.999722i
\(127\) 4.25412 + 4.25412i 0.0334970 + 0.0334970i 0.723657 0.690160i \(-0.242460\pi\)
−0.690160 + 0.723657i \(0.742460\pi\)
\(128\) −105.544 105.544i −0.824561 0.824561i
\(129\) −30.2883 + 125.627i −0.234793 + 0.973855i
\(130\) 2.87071 + 26.9698i 0.0220824 + 0.207460i
\(131\) 115.412 0.881007 0.440504 0.897751i \(-0.354800\pi\)
0.440504 + 0.897751i \(0.354800\pi\)
\(132\) −17.9675 + 10.9867i −0.136118 + 0.0832329i
\(133\) −4.70634 + 1.20473i −0.0353860 + 0.00905815i
\(134\) 188.364 1.40570
\(135\) −132.778 + 24.3941i −0.983539 + 0.180697i
\(136\) 112.249i 0.825357i
\(137\) 134.388 134.388i 0.980935 0.980935i −0.0188868 0.999822i \(-0.506012\pi\)
0.999822 + 0.0188868i \(0.00601221\pi\)
\(138\) −198.369 + 121.298i −1.43746 + 0.878974i
\(139\) −228.384 −1.64305 −0.821524 0.570174i \(-0.806876\pi\)
−0.821524 + 0.570174i \(0.806876\pi\)
\(140\) −52.1174 + 19.4176i −0.372267 + 0.138697i
\(141\) 77.4534 + 18.6738i 0.549315 + 0.132438i
\(142\) −155.057 155.057i −1.09195 1.09195i
\(143\) 7.16762 7.16762i 0.0501232 0.0501232i
\(144\) 81.3342 158.871i 0.564821 1.10327i
\(145\) 25.9971 + 244.237i 0.179290 + 1.68440i
\(146\) −319.111 −2.18569
\(147\) 73.1409 127.512i 0.497557 0.867431i
\(148\) 3.21909 3.21909i 0.0217506 0.0217506i
\(149\) −67.7175 −0.454480 −0.227240 0.973839i \(-0.572970\pi\)
−0.227240 + 0.973839i \(0.572970\pi\)
\(150\) 4.34307 177.256i 0.0289538 1.18171i
\(151\) 108.833 0.720749 0.360375 0.932808i \(-0.382649\pi\)
0.360375 + 0.932808i \(0.382649\pi\)
\(152\) 2.79710 + 2.79710i 0.0184020 + 0.0184020i
\(153\) 168.673 54.4463i 1.10243 0.355858i
\(154\) 62.9012 + 37.2614i 0.408449 + 0.241957i
\(155\) −168.433 + 17.9283i −1.08666 + 0.115666i
\(156\) 2.56371 10.6335i 0.0164340 0.0681636i
\(157\) −12.8504 + 12.8504i −0.0818495 + 0.0818495i −0.746846 0.664997i \(-0.768433\pi\)
0.664997 + 0.746846i \(0.268433\pi\)
\(158\) −167.637 167.637i −1.06100 1.06100i
\(159\) 139.592 + 33.6551i 0.877935 + 0.211667i
\(160\) 93.6847 + 75.6594i 0.585529 + 0.472871i
\(161\) 197.445 + 116.963i 1.22637 + 0.726476i
\(162\) 189.019 + 30.6841i 1.16679 + 0.189408i
\(163\) −140.352 + 140.352i −0.861054 + 0.861054i −0.991461 0.130407i \(-0.958372\pi\)
0.130407 + 0.991461i \(0.458372\pi\)
\(164\) 51.6580i 0.314988i
\(165\) −52.5585 + 40.3597i −0.318536 + 0.244604i
\(166\) 18.8096i 0.113311i
\(167\) −70.3795 70.3795i −0.421434 0.421434i 0.464263 0.885697i \(-0.346319\pi\)
−0.885697 + 0.464263i \(0.846319\pi\)
\(168\) −119.683 + 1.67784i −0.712399 + 0.00998712i
\(169\) 163.735i 0.968848i
\(170\) 24.6394 + 231.482i 0.144938 + 1.36166i
\(171\) −2.84638 + 5.55986i −0.0166455 + 0.0325138i
\(172\) 48.4013 + 48.4013i 0.281403 + 0.281403i
\(173\) 74.9815 74.9815i 0.433419 0.433419i −0.456371 0.889790i \(-0.650851\pi\)
0.889790 + 0.456371i \(0.150851\pi\)
\(174\) 81.6586 338.696i 0.469302 1.94653i
\(175\) −156.600 + 78.1117i −0.894857 + 0.446352i
\(176\) 87.6098i 0.497783i
\(177\) 36.1587 + 59.1334i 0.204287 + 0.334087i
\(178\) 265.245 + 265.245i 1.49014 + 1.49014i
\(179\) −110.262 −0.615991 −0.307996 0.951388i \(-0.599658\pi\)
−0.307996 + 0.951388i \(0.599658\pi\)
\(180\) −25.6663 + 66.7428i −0.142590 + 0.370793i
\(181\) 58.1797i 0.321435i −0.987000 0.160717i \(-0.948619\pi\)
0.987000 0.160717i \(-0.0513808\pi\)
\(182\) −36.7849 + 9.41625i −0.202115 + 0.0517376i
\(183\) 20.3267 + 33.2420i 0.111075 + 0.181650i
\(184\) 186.861i 1.01555i
\(185\) 8.99995 11.1441i 0.0486484 0.0602385i
\(186\) 233.574 + 56.3140i 1.25577 + 0.302763i
\(187\) 61.5198 61.5198i 0.328983 0.328983i
\(188\) 29.8410 29.8410i 0.158729 0.158729i
\(189\) −60.5737 179.030i −0.320496 0.947250i
\(190\) −6.38225 5.15428i −0.0335908 0.0271278i
\(191\) 12.6214i 0.0660807i −0.999454 0.0330403i \(-0.989481\pi\)
0.999454 0.0330403i \(-0.0105190\pi\)
\(192\) 35.0359 + 57.2971i 0.182479 + 0.298423i
\(193\) 211.567 211.567i 1.09620 1.09620i 0.101353 0.994851i \(-0.467683\pi\)
0.994851 0.101353i \(-0.0323171\pi\)
\(194\) 124.052i 0.639442i
\(195\) 4.48005 34.1244i 0.0229746 0.174997i
\(196\) −37.4119 68.2872i −0.190877 0.348404i
\(197\) −102.520 + 102.520i −0.520407 + 0.520407i −0.917694 0.397288i \(-0.869952\pi\)
0.397288 + 0.917694i \(0.369952\pi\)
\(198\) 89.4528 28.8748i 0.451782 0.145832i
\(199\) −235.953 −1.18570 −0.592848 0.805314i \(-0.701996\pi\)
−0.592848 + 0.805314i \(0.701996\pi\)
\(200\) 119.710 + 77.2912i 0.598551 + 0.386456i
\(201\) −232.370 56.0237i −1.15607 0.278725i
\(202\) −29.5262 + 29.5262i −0.146169 + 0.146169i
\(203\) −333.123 + 85.2732i −1.64100 + 0.420065i
\(204\) 22.0044 91.2677i 0.107865 0.447391i
\(205\) 17.2041 + 161.630i 0.0839227 + 0.788437i
\(206\) 322.858 1.56727
\(207\) 280.790 90.6371i 1.35647 0.437860i
\(208\) 32.1749 + 32.1749i 0.154687 + 0.154687i
\(209\) 3.06600i 0.0146699i
\(210\) 246.446 29.7314i 1.17355 0.141578i
\(211\) −89.6482 −0.424873 −0.212437 0.977175i \(-0.568140\pi\)
−0.212437 + 0.977175i \(0.568140\pi\)
\(212\) 53.7814 53.7814i 0.253686 0.253686i
\(213\) 145.164 + 237.399i 0.681522 + 1.11455i
\(214\) 24.1655i 0.112923i
\(215\) 167.559 + 135.320i 0.779346 + 0.629397i
\(216\) −100.283 + 116.732i −0.464274 + 0.540427i
\(217\) −58.8067 229.731i −0.270999 1.05867i
\(218\) −209.137 209.137i −0.959346 0.959346i
\(219\) 393.663 + 94.9110i 1.79755 + 0.433384i
\(220\) 3.71519 + 34.9035i 0.0168872 + 0.158652i
\(221\) 45.1866i 0.204464i
\(222\) −17.3349 + 10.5999i −0.0780850 + 0.0477473i
\(223\) 85.1659 + 85.1659i 0.381910 + 0.381910i 0.871790 0.489880i \(-0.162959\pi\)
−0.489880 + 0.871790i \(0.662959\pi\)
\(224\) −85.9244 + 145.049i −0.383591 + 0.647541i
\(225\) −58.0776 + 217.375i −0.258123 + 0.966112i
\(226\) −239.682 −1.06054
\(227\) −129.989 129.989i −0.572639 0.572639i 0.360226 0.932865i \(-0.382700\pi\)
−0.932865 + 0.360226i \(0.882700\pi\)
\(228\) 1.72596 + 2.82261i 0.00757001 + 0.0123799i
\(229\) 109.923 0.480011 0.240006 0.970771i \(-0.422851\pi\)
0.240006 + 0.970771i \(0.422851\pi\)
\(230\) 41.0173 + 385.350i 0.178336 + 1.67543i
\(231\) −66.5140 64.6748i −0.287939 0.279978i
\(232\) 197.984 + 197.984i 0.853378 + 0.853378i
\(233\) 218.319 + 218.319i 0.936990 + 0.936990i 0.998129 0.0611395i \(-0.0194735\pi\)
−0.0611395 + 0.998129i \(0.519473\pi\)
\(234\) −22.2474 + 43.4561i −0.0950745 + 0.185710i
\(235\) 83.4295 103.306i 0.355019 0.439600i
\(236\) 36.7139 0.155567
\(237\) 156.942 + 256.661i 0.662204 + 1.08296i
\(238\) −315.726 + 80.8198i −1.32658 + 0.339579i
\(239\) −20.1742 −0.0844109 −0.0422054 0.999109i \(-0.513438\pi\)
−0.0422054 + 0.999109i \(0.513438\pi\)
\(240\) −181.171 235.931i −0.754881 0.983046i
\(241\) 257.604i 1.06890i −0.845201 0.534449i \(-0.820519\pi\)
0.845201 0.534449i \(-0.179481\pi\)
\(242\) −169.648 + 169.648i −0.701024 + 0.701024i
\(243\) −224.053 94.0713i −0.922027 0.387125i
\(244\) 20.6388 0.0845852
\(245\) −139.798 201.200i −0.570605 0.821225i
\(246\) 54.0394 224.140i 0.219672 0.911137i
\(247\) −1.12600 1.12600i −0.00455869 0.00455869i
\(248\) −136.535 + 136.535i −0.550544 + 0.550544i
\(249\) −5.59441 + 23.2040i −0.0224675 + 0.0931887i
\(250\) −263.836 133.115i −1.05534 0.532460i
\(251\) −191.569 −0.763223 −0.381612 0.924323i \(-0.624631\pi\)
−0.381612 + 0.924323i \(0.624631\pi\)
\(252\) −97.6415 22.0975i −0.387466 0.0876887i
\(253\) 102.412 102.412i 0.404792 0.404792i
\(254\) −14.2231 −0.0559964
\(255\) 38.4524 292.890i 0.150794 1.14859i
\(256\) 263.325 1.02861
\(257\) −205.696 205.696i −0.800374 0.800374i 0.182779 0.983154i \(-0.441491\pi\)
−0.983154 + 0.182779i \(0.941491\pi\)
\(258\) −159.377 260.642i −0.617739 1.01024i
\(259\) 17.2541 + 10.2210i 0.0666182 + 0.0394633i
\(260\) −14.1828 11.4540i −0.0545493 0.0440538i
\(261\) −201.472 + 393.537i −0.771923 + 1.50780i
\(262\) −192.932 + 192.932i −0.736383 + 0.736383i
\(263\) 4.82449 + 4.82449i 0.0183441 + 0.0183441i 0.716219 0.697875i \(-0.245871\pi\)
−0.697875 + 0.716219i \(0.745871\pi\)
\(264\) −17.7054 + 73.4367i −0.0670657 + 0.278169i
\(265\) 150.362 186.185i 0.567404 0.702584i
\(266\) 5.85358 9.88145i 0.0220059 0.0371483i
\(267\) −248.322 406.102i −0.930046 1.52098i
\(268\) −89.5269 + 89.5269i −0.334056 + 0.334056i
\(269\) 106.984i 0.397708i 0.980029 + 0.198854i \(0.0637220\pi\)
−0.980029 + 0.198854i \(0.936278\pi\)
\(270\) 181.183 262.742i 0.671049 0.973118i
\(271\) 187.036i 0.690171i 0.938571 + 0.345085i \(0.112150\pi\)
−0.938571 + 0.345085i \(0.887850\pi\)
\(272\) 276.158 + 276.158i 1.01529 + 1.01529i
\(273\) 48.1794 0.675427i 0.176481 0.00247409i
\(274\) 449.309i 1.63981i
\(275\) 23.2485 + 107.970i 0.0845399 + 0.392619i
\(276\) 36.6308 151.934i 0.132720 0.550485i
\(277\) 95.7717 + 95.7717i 0.345746 + 0.345746i 0.858522 0.512776i \(-0.171383\pi\)
−0.512776 + 0.858522i \(0.671383\pi\)
\(278\) 381.786 381.786i 1.37333 1.37333i
\(279\) −271.393 138.941i −0.972736 0.497995i
\(280\) −82.9364 + 181.434i −0.296201 + 0.647979i
\(281\) 140.834i 0.501189i −0.968092 0.250594i \(-0.919374\pi\)
0.968092 0.250594i \(-0.0806261\pi\)
\(282\) −160.694 + 98.2610i −0.569838 + 0.348443i
\(283\) −204.752 204.752i −0.723504 0.723504i 0.245813 0.969317i \(-0.420945\pi\)
−0.969317 + 0.245813i \(0.920945\pi\)
\(284\) 147.393 0.518989
\(285\) 6.34030 + 8.25667i 0.0222467 + 0.0289708i
\(286\) 23.9640i 0.0837902i
\(287\) −220.452 + 56.4314i −0.768124 + 0.196625i
\(288\) 66.5848 + 206.277i 0.231197 + 0.716240i
\(289\) 98.8373i 0.341998i
\(290\) −451.747 364.829i −1.55775 1.25803i
\(291\) −36.8958 + 153.033i −0.126790 + 0.525888i
\(292\) 151.669 151.669i 0.519416 0.519416i
\(293\) 158.208 158.208i 0.539959 0.539959i −0.383558 0.923517i \(-0.625301\pi\)
0.923517 + 0.383558i \(0.125301\pi\)
\(294\) 90.8920 + 335.429i 0.309157 + 1.14092i
\(295\) 114.872 12.2272i 0.389396 0.0414480i
\(296\) 16.3292i 0.0551661i
\(297\) −118.939 + 9.01527i −0.400469 + 0.0303544i
\(298\) 113.202 113.202i 0.379873 0.379873i
\(299\) 75.2224i 0.251580i
\(300\) 82.1832 + 86.3116i 0.273944 + 0.287705i
\(301\) −153.680 + 259.427i −0.510564 + 0.861885i
\(302\) −181.935 + 181.935i −0.602433 + 0.602433i
\(303\) 45.2060 27.6425i 0.149195 0.0912293i
\(304\) −13.7631 −0.0452732
\(305\) 64.5754 6.87352i 0.211723 0.0225361i
\(306\) −190.950 + 372.984i −0.624020 + 1.21890i
\(307\) 390.484 390.484i 1.27194 1.27194i 0.326865 0.945071i \(-0.394008\pi\)
0.945071 0.326865i \(-0.105992\pi\)
\(308\) −47.6060 + 12.1862i −0.154565 + 0.0395657i
\(309\) −398.285 96.0253i −1.28895 0.310761i
\(310\) 251.596 311.537i 0.811600 1.00496i
\(311\) 314.164 1.01017 0.505087 0.863068i \(-0.331460\pi\)
0.505087 + 0.863068i \(0.331460\pi\)
\(312\) −20.4675 33.4721i −0.0656009 0.107282i
\(313\) −138.521 138.521i −0.442558 0.442558i 0.450313 0.892871i \(-0.351312\pi\)
−0.892871 + 0.450313i \(0.851312\pi\)
\(314\) 42.9635i 0.136827i
\(315\) −312.864 36.6212i −0.993219 0.116258i
\(316\) 159.352 0.504278
\(317\) 171.788 171.788i 0.541917 0.541917i −0.382174 0.924090i \(-0.624824\pi\)
0.924090 + 0.382174i \(0.124824\pi\)
\(318\) −289.614 + 177.092i −0.910736 + 0.556895i
\(319\) 217.017i 0.680304i
\(320\) 111.305 11.8475i 0.347827 0.0370234i
\(321\) −7.18738 + 29.8112i −0.0223906 + 0.0928697i
\(322\) −525.591 + 134.541i −1.63227 + 0.417830i
\(323\) −9.66445 9.66445i −0.0299209 0.0299209i
\(324\) −104.422 + 75.2547i −0.322291 + 0.232268i
\(325\) −48.1904 31.1142i −0.148278 0.0957361i
\(326\) 469.248i 1.43941i
\(327\) 195.795 + 320.199i 0.598761 + 0.979203i
\(328\) 131.020 + 131.020i 0.399452 + 0.399452i
\(329\) 159.946 + 94.7486i 0.486157 + 0.287990i
\(330\) 20.3926 155.330i 0.0617958 0.470697i
\(331\) −97.1798 −0.293595 −0.146797 0.989167i \(-0.546897\pi\)
−0.146797 + 0.989167i \(0.546897\pi\)
\(332\) 8.93996 + 8.93996i 0.0269276 + 0.0269276i
\(333\) 24.5374 7.92049i 0.0736858 0.0237853i
\(334\) 235.305 0.704505
\(335\) −250.299 + 309.931i −0.747162 + 0.925168i
\(336\) 290.320 298.576i 0.864049 0.888620i
\(337\) −142.405 142.405i −0.422566 0.422566i 0.463520 0.886086i \(-0.346586\pi\)
−0.886086 + 0.463520i \(0.846586\pi\)
\(338\) 273.714 + 273.714i 0.809804 + 0.809804i
\(339\) 295.677 + 71.2869i 0.872205 + 0.210286i
\(340\) −121.731 98.3097i −0.358033 0.289146i
\(341\) −149.661 −0.438888
\(342\) −4.53608 14.0526i −0.0132634 0.0410894i
\(343\) 250.548 234.253i 0.730461 0.682955i
\(344\) 245.520 0.713722
\(345\) 64.0119 487.576i 0.185542 1.41326i
\(346\) 250.691i 0.724540i
\(347\) 42.5261 42.5261i 0.122554 0.122554i −0.643170 0.765723i \(-0.722381\pi\)
0.765723 + 0.643170i \(0.222381\pi\)
\(348\) 122.167 + 199.789i 0.351054 + 0.574107i
\(349\) 323.576 0.927152 0.463576 0.886057i \(-0.346566\pi\)
0.463576 + 0.886057i \(0.346566\pi\)
\(350\) 131.208 392.364i 0.374879 1.12104i
\(351\) 40.3698 46.9916i 0.115014 0.133879i
\(352\) 75.2353 + 75.2353i 0.213737 + 0.213737i
\(353\) 121.979 121.979i 0.345550 0.345550i −0.512899 0.858449i \(-0.671428\pi\)
0.858449 + 0.512899i \(0.171428\pi\)
\(354\) −159.298 38.4063i −0.449995 0.108492i
\(355\) 461.168 49.0876i 1.29907 0.138275i
\(356\) −252.135 −0.708243
\(357\) 413.525 5.79721i 1.15833 0.0162387i
\(358\) 184.324 184.324i 0.514872 0.514872i
\(359\) −456.029 −1.27028 −0.635138 0.772399i \(-0.719057\pi\)
−0.635138 + 0.772399i \(0.719057\pi\)
\(360\) 104.182 + 234.377i 0.289395 + 0.651047i
\(361\) −360.518 −0.998666
\(362\) 97.2581 + 97.2581i 0.268669 + 0.268669i
\(363\) 259.739 158.824i 0.715534 0.437533i
\(364\) 13.0080 21.9588i 0.0357362 0.0603264i
\(365\) 424.037 525.061i 1.16175 1.43852i
\(366\) −89.5499 21.5902i −0.244672 0.0589896i
\(367\) −52.7521 + 52.7521i −0.143739 + 0.143739i −0.775314 0.631576i \(-0.782409\pi\)
0.631576 + 0.775314i \(0.282409\pi\)
\(368\) 459.721 + 459.721i 1.24924 + 1.24924i
\(369\) −133.329 + 260.432i −0.361324 + 0.705777i
\(370\) 3.58438 + 33.6745i 0.00968750 + 0.0910122i
\(371\) 288.264 + 170.762i 0.776993 + 0.460276i
\(372\) −137.780 + 84.2494i −0.370376 + 0.226477i
\(373\) −269.362 + 269.362i −0.722150 + 0.722150i −0.969043 0.246893i \(-0.920591\pi\)
0.246893 + 0.969043i \(0.420591\pi\)
\(374\) 205.683i 0.549956i
\(375\) 285.883 + 242.685i 0.762355 + 0.647159i
\(376\) 151.371i 0.402583i
\(377\) −79.7000 79.7000i −0.211406 0.211406i
\(378\) 400.542 + 198.022i 1.05964 + 0.523868i
\(379\) 253.497i 0.668856i −0.942421 0.334428i \(-0.891457\pi\)
0.942421 0.334428i \(-0.108543\pi\)
\(380\) 5.48317 0.583638i 0.0144294 0.00153589i
\(381\) 17.5459 + 4.23027i 0.0460523 + 0.0111031i
\(382\) 21.0990 + 21.0990i 0.0552330 + 0.0552330i
\(383\) −162.755 + 162.755i −0.424948 + 0.424948i −0.886903 0.461955i \(-0.847148\pi\)
0.461955 + 0.886903i \(0.347148\pi\)
\(384\) −435.311 104.952i −1.13362 0.273313i
\(385\) −144.893 + 53.9834i −0.376345 + 0.140217i
\(386\) 707.348i 1.83251i
\(387\) 119.090 + 368.936i 0.307726 + 0.953324i
\(388\) 58.9602 + 58.9602i 0.151959 + 0.151959i
\(389\) −309.463 −0.795534 −0.397767 0.917486i \(-0.630215\pi\)
−0.397767 + 0.917486i \(0.630215\pi\)
\(390\) 49.5560 + 64.5345i 0.127067 + 0.165473i
\(391\) 645.635i 1.65124i
\(392\) −268.085 78.3089i −0.683889 0.199768i
\(393\) 295.389 180.624i 0.751625 0.459602i
\(394\) 342.763i 0.869956i
\(395\) 498.586 53.0704i 1.26224 0.134355i
\(396\) −28.7920 + 56.2396i −0.0727070 + 0.142019i
\(397\) −463.385 + 463.385i −1.16722 + 1.16722i −0.184357 + 0.982859i \(0.559020\pi\)
−0.982859 + 0.184357i \(0.940980\pi\)
\(398\) 394.440 394.440i 0.991055 0.991055i
\(399\) −10.1601 + 10.4490i −0.0254639 + 0.0261880i
\(400\) −484.670 + 104.361i −1.21167 + 0.260902i
\(401\) 516.485i 1.28799i −0.765028 0.643997i \(-0.777275\pi\)
0.765028 0.643997i \(-0.222725\pi\)
\(402\) 482.104 294.796i 1.19926 0.733323i
\(403\) 54.9633 54.9633i 0.136385 0.136385i
\(404\) 28.0669i 0.0694724i
\(405\) −301.657 + 270.237i −0.744833 + 0.667251i
\(406\) 414.327 699.427i 1.02051 1.72273i
\(407\) 8.94950 8.94950i 0.0219889 0.0219889i
\(408\) −175.673 287.292i −0.430570 0.704147i
\(409\) 119.076 0.291139 0.145570 0.989348i \(-0.453499\pi\)
0.145570 + 0.989348i \(0.453499\pi\)
\(410\) −298.954 241.434i −0.729155 0.588863i
\(411\) 133.635 554.278i 0.325145 1.34861i
\(412\) −153.450 + 153.450i −0.372452 + 0.372452i
\(413\) 40.1064 + 156.677i 0.0971099 + 0.379364i
\(414\) −317.876 + 620.909i −0.767816 + 1.49978i
\(415\) 30.9491 + 24.9943i 0.0745760 + 0.0602273i
\(416\) −55.2607 −0.132838
\(417\) −584.532 + 357.428i −1.40175 + 0.857142i
\(418\) −5.12539 5.12539i −0.0122617 0.0122617i
\(419\) 732.322i 1.74778i −0.486120 0.873892i \(-0.661588\pi\)
0.486120 0.873892i \(-0.338412\pi\)
\(420\) −103.001 + 131.263i −0.245242 + 0.312532i
\(421\) 307.320 0.729976 0.364988 0.931012i \(-0.381073\pi\)
0.364988 + 0.931012i \(0.381073\pi\)
\(422\) 149.864 149.864i 0.355127 0.355127i
\(423\) 227.461 73.4229i 0.537734 0.173577i
\(424\) 272.812i 0.643424i
\(425\) −413.619 267.054i −0.973220 0.628363i
\(426\) −639.525 154.187i −1.50123 0.361942i
\(427\) 22.5459 + 88.0764i 0.0528007 + 0.206268i
\(428\) 11.4856 + 11.4856i 0.0268354 + 0.0268354i
\(429\) 7.12744 29.5626i 0.0166141 0.0689104i
\(430\) −506.320 + 53.8936i −1.17749 + 0.125334i
\(431\) 205.822i 0.477546i −0.971075 0.238773i \(-0.923255\pi\)
0.971075 0.238773i \(-0.0767452\pi\)
\(432\) −40.4689 533.909i −0.0936779 1.23590i
\(433\) −291.861 291.861i −0.674043 0.674043i 0.284603 0.958646i \(-0.408138\pi\)
−0.958646 + 0.284603i \(0.908138\pi\)
\(434\) 482.343 + 285.731i 1.11139 + 0.658366i
\(435\) 448.777 + 584.422i 1.03167 + 1.34350i
\(436\) 198.801 0.455965
\(437\) −16.0885 16.0885i −0.0368157 0.0368157i
\(438\) −816.742 + 499.420i −1.86471 + 1.14023i
\(439\) −116.671 −0.265765 −0.132882 0.991132i \(-0.542423\pi\)
−0.132882 + 0.991132i \(0.542423\pi\)
\(440\) 97.9486 + 79.1029i 0.222610 + 0.179779i
\(441\) −12.3623 440.827i −0.0280325 0.999607i
\(442\) −75.5377 75.5377i −0.170900 0.170900i
\(443\) −282.021 282.021i −0.636617 0.636617i 0.313102 0.949719i \(-0.398632\pi\)
−0.949719 + 0.313102i \(0.898632\pi\)
\(444\) 3.20105 13.2770i 0.00720957 0.0299032i
\(445\) −788.888 + 83.9707i −1.77278 + 0.188698i
\(446\) −284.741 −0.638433
\(447\) −173.318 + 105.980i −0.387736 + 0.237092i
\(448\) 38.8610 + 151.812i 0.0867433 + 0.338866i
\(449\) 407.834 0.908317 0.454158 0.890921i \(-0.349940\pi\)
0.454158 + 0.890921i \(0.349940\pi\)
\(450\) −266.295 460.470i −0.591767 1.02327i
\(451\) 143.616i 0.318439i
\(452\) 113.918 113.918i 0.252030 0.252030i
\(453\) 278.550 170.327i 0.614902 0.375999i
\(454\) 434.602 0.957272
\(455\) 33.3867 73.0378i 0.0733775 0.160523i
\(456\) 11.5365 + 2.78142i 0.0252994 + 0.00609961i
\(457\) 461.473 + 461.473i 1.00979 + 1.00979i 0.999952 + 0.00983627i \(0.00313103\pi\)
0.00983627 + 0.999952i \(0.496869\pi\)
\(458\) −183.756 + 183.756i −0.401214 + 0.401214i
\(459\) 346.495 403.330i 0.754891 0.878714i
\(460\) −202.647 163.657i −0.440537 0.355776i
\(461\) −788.797 −1.71106 −0.855528 0.517757i \(-0.826767\pi\)
−0.855528 + 0.517757i \(0.826767\pi\)
\(462\) 219.306 3.07446i 0.474689 0.00665467i
\(463\) −548.664 + 548.664i −1.18502 + 1.18502i −0.206592 + 0.978427i \(0.566237\pi\)
−0.978427 + 0.206592i \(0.933763\pi\)
\(464\) −974.173 −2.09951
\(465\) −403.033 + 309.489i −0.866738 + 0.665568i
\(466\) −729.920 −1.56635
\(467\) 299.104 + 299.104i 0.640480 + 0.640480i 0.950673 0.310194i \(-0.100394\pi\)
−0.310194 + 0.950673i \(0.600394\pi\)
\(468\) −10.0802 31.2280i −0.0215389 0.0667266i
\(469\) −479.857 284.258i −1.02315 0.606094i
\(470\) 33.2272 + 312.163i 0.0706961 + 0.664176i
\(471\) −12.7783 + 53.0009i −0.0271302 + 0.112528i
\(472\) 93.1173 93.1173i 0.197283 0.197283i
\(473\) 134.562 + 134.562i 0.284486 + 0.284486i
\(474\) −691.414 166.698i −1.45868 0.351683i
\(475\) 16.9616 3.65222i 0.0357086 0.00768888i
\(476\) 111.648 188.473i 0.234554 0.395952i
\(477\) 409.946 132.328i 0.859426 0.277417i
\(478\) 33.7249 33.7249i 0.0705542 0.0705542i
\(479\) 568.767i 1.18740i 0.804685 + 0.593702i \(0.202334\pi\)
−0.804685 + 0.593702i \(0.797666\pi\)
\(480\) 358.189 + 47.0251i 0.746226 + 0.0979690i
\(481\) 6.57345i 0.0136662i
\(482\) 430.633 + 430.633i 0.893430 + 0.893430i
\(483\) 688.397 9.65064i 1.42525 0.0199806i
\(484\) 161.263i 0.333188i
\(485\) 204.113 + 164.841i 0.420852 + 0.339878i
\(486\) 531.803 217.288i 1.09424 0.447094i
\(487\) 382.818 + 382.818i 0.786073 + 0.786073i 0.980848 0.194775i \(-0.0623976\pi\)
−0.194775 + 0.980848i \(0.562398\pi\)
\(488\) 52.3461 52.3461i 0.107267 0.107267i
\(489\) −139.565 + 578.875i −0.285409 + 1.18379i
\(490\) 570.042 + 102.644i 1.16335 + 0.209479i
\(491\) 1.38553i 0.00282185i −0.999999 0.00141093i \(-0.999551\pi\)
0.999999 0.00141093i \(-0.000449112\pi\)
\(492\) 80.8465 + 132.215i 0.164322 + 0.268730i
\(493\) −684.067 684.067i −1.38756 1.38756i
\(494\) 3.76462 0.00762070
\(495\) −71.3555 + 185.553i −0.144152 + 0.374855i
\(496\) 671.816i 1.35447i
\(497\) 161.012 + 629.002i 0.323969 + 1.26560i
\(498\) −29.4377 48.1418i −0.0591118 0.0966703i
\(499\) 356.741i 0.714913i −0.933930 0.357456i \(-0.883644\pi\)
0.933930 0.357456i \(-0.116356\pi\)
\(500\) 188.666 62.1300i 0.377331 0.124260i
\(501\) −290.277 69.9849i −0.579396 0.139691i
\(502\) 320.243 320.243i 0.637934 0.637934i
\(503\) −279.707 + 279.707i −0.556078 + 0.556078i −0.928188 0.372111i \(-0.878634\pi\)
0.372111 + 0.928188i \(0.378634\pi\)
\(504\) −303.694 + 191.602i −0.602568 + 0.380163i
\(505\) −9.34737 87.8167i −0.0185096 0.173894i
\(506\) 342.402i 0.676685i
\(507\) −256.251 419.069i −0.505427 0.826566i
\(508\) 6.76005 6.76005i 0.0133072 0.0133072i
\(509\) 493.836i 0.970208i −0.874457 0.485104i \(-0.838782\pi\)
0.874457 0.485104i \(-0.161218\pi\)
\(510\) 425.340 + 553.901i 0.834000 + 1.08608i
\(511\) 812.937 + 481.568i 1.59087 + 0.942403i
\(512\) −18.0214 + 18.0214i −0.0351981 + 0.0351981i
\(513\) 1.41625 + 18.6847i 0.00276073 + 0.0364225i
\(514\) 687.719 1.33797
\(515\) −429.016 + 531.226i −0.833040 + 1.03151i
\(516\) 199.629 + 48.1300i 0.386879 + 0.0932752i
\(517\) 82.9618 82.9618i 0.160468 0.160468i
\(518\) −45.9297 + 11.7571i −0.0886674 + 0.0226972i
\(519\) 74.5612 309.258i 0.143663 0.595873i
\(520\) −65.0226 + 6.92112i −0.125043 + 0.0133098i
\(521\) 16.2593 0.0312079 0.0156039 0.999878i \(-0.495033\pi\)
0.0156039 + 0.999878i \(0.495033\pi\)
\(522\) −321.072 994.667i −0.615080 1.90549i
\(523\) 629.367 + 629.367i 1.20338 + 1.20338i 0.973132 + 0.230246i \(0.0739530\pi\)
0.230246 + 0.973132i \(0.426047\pi\)
\(524\) 183.397i 0.349993i
\(525\) −278.559 + 445.005i −0.530589 + 0.847629i
\(526\) −16.1301 −0.0306655
\(527\) 471.751 471.751i 0.895163 0.895163i
\(528\) −137.112 224.231i −0.259682 0.424680i
\(529\) 545.792i 1.03174i
\(530\) 59.8842 + 562.600i 0.112989 + 1.06151i
\(531\) 185.091 + 94.7580i 0.348571 + 0.178452i
\(532\) 1.91439 + 7.47866i 0.00359849 + 0.0140576i
\(533\) −52.7433 52.7433i −0.0989555 0.0989555i
\(534\) 1093.99 + 263.758i 2.04867 + 0.493928i
\(535\) 39.7616 + 32.1113i 0.0743208 + 0.0600212i
\(536\) 454.134i 0.847265i
\(537\) −282.209 + 172.564i −0.525528 + 0.321349i
\(538\) −178.843 178.843i −0.332421 0.332421i
\(539\) −104.010 189.847i −0.192968 0.352221i
\(540\) 38.7637 + 210.992i 0.0717846 + 0.390726i
\(541\) 577.099 1.06673 0.533364 0.845886i \(-0.320928\pi\)
0.533364 + 0.845886i \(0.320928\pi\)
\(542\) −312.666 312.666i −0.576874 0.576874i
\(543\) −91.0532 148.907i −0.167685 0.274230i
\(544\) −474.303 −0.871881
\(545\) 622.015 66.2084i 1.14131 0.121483i
\(546\) −79.4117 + 81.6699i −0.145443 + 0.149579i
\(547\) −289.511 289.511i −0.529270 0.529270i 0.391084 0.920355i \(-0.372100\pi\)
−0.920355 + 0.391084i \(0.872100\pi\)
\(548\) −213.551 213.551i −0.389691 0.389691i
\(549\) 104.050 + 53.2684i 0.189526 + 0.0970280i
\(550\) −219.356 141.628i −0.398829 0.257505i
\(551\) 34.0923 0.0618735
\(552\) −292.443 478.257i −0.529788 0.866407i
\(553\) 174.077 + 680.037i 0.314786 + 1.22972i
\(554\) −320.200 −0.577979
\(555\) 5.59380 42.6078i 0.0100789 0.0767708i
\(556\) 362.915i 0.652726i
\(557\) −12.4652 + 12.4652i −0.0223792 + 0.0223792i −0.718208 0.695829i \(-0.755037\pi\)
0.695829 + 0.718208i \(0.255037\pi\)
\(558\) 685.949 221.420i 1.22930 0.396809i
\(559\) −98.8363 −0.176809
\(560\) −242.327 650.413i −0.432728 1.16145i
\(561\) 61.1750 253.736i 0.109046 0.452292i
\(562\) 235.430 + 235.430i 0.418915 + 0.418915i
\(563\) −689.690 + 689.690i −1.22503 + 1.22503i −0.259204 + 0.965823i \(0.583460\pi\)
−0.965823 + 0.259204i \(0.916540\pi\)
\(564\) 29.6737 123.078i 0.0526130 0.218223i
\(565\) 318.491 394.369i 0.563701 0.697999i
\(566\) 684.560 1.20947
\(567\) −435.222 363.415i −0.767588 0.640944i
\(568\) 373.832 373.832i 0.658155 0.658155i
\(569\) −44.3368 −0.0779205 −0.0389602 0.999241i \(-0.512405\pi\)
−0.0389602 + 0.999241i \(0.512405\pi\)
\(570\) −24.4015 3.20358i −0.0428097 0.00562031i
\(571\) 89.1696 0.156164 0.0780819 0.996947i \(-0.475120\pi\)
0.0780819 + 0.996947i \(0.475120\pi\)
\(572\) −11.3898 11.3898i −0.0199122 0.0199122i
\(573\) −19.7529 32.3036i −0.0344728 0.0563762i
\(574\) 274.190 462.861i 0.477683 0.806378i
\(575\) −688.553 444.566i −1.19748 0.773159i
\(576\) 179.344 + 91.8155i 0.311361 + 0.159402i
\(577\) 146.556 146.556i 0.253997 0.253997i −0.568610 0.822607i \(-0.692519\pi\)
0.822607 + 0.568610i \(0.192519\pi\)
\(578\) −165.225 165.225i −0.285856 0.285856i
\(579\) 210.381 872.601i 0.363353 1.50708i
\(580\) 388.108 41.3109i 0.669152 0.0712257i
\(581\) −28.3854 + 47.9175i −0.0488561 + 0.0824742i
\(582\) −194.145 317.502i −0.333583 0.545535i
\(583\) 149.519 149.519i 0.256465 0.256465i
\(584\) 769.358i 1.31739i
\(585\) −41.9395 94.3504i −0.0716914 0.161283i
\(586\) 528.948i 0.902642i
\(587\) −85.7254 85.7254i −0.146040 0.146040i 0.630307 0.776346i \(-0.282929\pi\)
−0.776346 + 0.630307i \(0.782929\pi\)
\(588\) −202.625 116.225i −0.344600 0.197662i
\(589\) 23.5110i 0.0399167i
\(590\) −171.589 + 212.469i −0.290830 + 0.360118i
\(591\) −101.945 + 422.840i −0.172496 + 0.715465i
\(592\) 40.1736 + 40.1736i 0.0678608 + 0.0678608i
\(593\) −607.214 + 607.214i −1.02397 + 1.02397i −0.0242632 + 0.999706i \(0.507724\pi\)
−0.999706 + 0.0242632i \(0.992276\pi\)
\(594\) 183.758 213.900i 0.309357 0.360100i
\(595\) 286.559 626.885i 0.481612 1.05359i
\(596\) 107.607i 0.180549i
\(597\) −603.906 + 369.275i −1.01157 + 0.618551i
\(598\) −125.748 125.748i −0.210281 0.210281i
\(599\) 214.278 0.357726 0.178863 0.983874i \(-0.442758\pi\)
0.178863 + 0.983874i \(0.442758\pi\)
\(600\) 427.353 + 10.4709i 0.712255 + 0.0174515i
\(601\) 674.896i 1.12296i 0.827492 + 0.561478i \(0.189767\pi\)
−0.827492 + 0.561478i \(0.810233\pi\)
\(602\) −176.777 690.585i −0.293649 1.14715i
\(603\) −682.414 + 220.278i −1.13170 + 0.365304i
\(604\) 172.942i 0.286328i
\(605\) −53.7068 504.565i −0.0887716 0.833992i
\(606\) −29.3607 + 121.780i −0.0484500 + 0.200957i
\(607\) −428.929 + 428.929i −0.706638 + 0.706638i −0.965827 0.259189i \(-0.916545\pi\)
0.259189 + 0.965827i \(0.416545\pi\)
\(608\) 11.8191 11.8191i 0.0194393 0.0194393i
\(609\) −719.149 + 739.599i −1.18087 + 1.21445i
\(610\) −96.4594 + 119.440i −0.158130 + 0.195803i
\(611\) 60.9358i 0.0997313i
\(612\) −86.5185 268.031i −0.141370 0.437959i
\(613\) −134.802 + 134.802i −0.219905 + 0.219905i −0.808458 0.588553i \(-0.799698\pi\)
0.588553 + 0.808458i \(0.299698\pi\)
\(614\) 1305.53i 2.12628i
\(615\) 296.989 + 386.754i 0.482908 + 0.628869i
\(616\) −89.8351 + 151.651i −0.145836 + 0.246187i
\(617\) −525.987 + 525.987i −0.852491 + 0.852491i −0.990439 0.137948i \(-0.955949\pi\)
0.137948 + 0.990439i \(0.455949\pi\)
\(618\) 826.331 505.283i 1.33711 0.817610i
\(619\) 957.834 1.54739 0.773695 0.633558i \(-0.218406\pi\)
0.773695 + 0.633558i \(0.218406\pi\)
\(620\) 28.4891 + 267.650i 0.0459502 + 0.431693i
\(621\) 576.812 671.425i 0.928844 1.08120i
\(622\) −525.184 + 525.184i −0.844347 + 0.844347i
\(623\) −275.433 1075.99i −0.442107 1.72711i
\(624\) 132.704 + 31.9945i 0.212667 + 0.0512733i
\(625\) 569.613 257.228i 0.911381 0.411564i
\(626\) 463.126 0.739817
\(627\) 4.79840 + 7.84721i 0.00765295 + 0.0125155i
\(628\) 20.4200 + 20.4200i 0.0325159 + 0.0325159i
\(629\) 56.4200i 0.0896980i
\(630\) 584.229 461.791i 0.927348 0.733001i
\(631\) −482.882 −0.765265 −0.382633 0.923901i \(-0.624983\pi\)
−0.382633 + 0.923901i \(0.624983\pi\)
\(632\) 404.164 404.164i 0.639499 0.639499i
\(633\) −229.448 + 140.302i −0.362477 + 0.221647i
\(634\) 574.349i 0.905914i
\(635\) 18.8997 23.4025i 0.0297634 0.0368543i
\(636\) 53.4800 221.819i 0.0840880 0.348773i
\(637\) 107.920 + 31.5239i 0.169419 + 0.0494881i
\(638\) −362.784 362.784i −0.568627 0.568627i
\(639\) 743.074 + 380.419i 1.16287 + 0.595334i
\(640\) −468.899 + 580.610i −0.732654 + 0.907204i
\(641\) 618.098i 0.964272i 0.876096 + 0.482136i \(0.160139\pi\)
−0.876096 + 0.482136i \(0.839861\pi\)
\(642\) −37.8199 61.8499i −0.0589094 0.0963395i
\(643\) −235.650 235.650i −0.366485 0.366485i 0.499709 0.866193i \(-0.333440\pi\)
−0.866193 + 0.499709i \(0.833440\pi\)
\(644\) 185.861 313.752i 0.288604 0.487193i
\(645\) 640.637 + 84.1067i 0.993236 + 0.130398i
\(646\) 32.3118 0.0500183
\(647\) 129.060 + 129.060i 0.199474 + 0.199474i 0.799775 0.600300i \(-0.204952\pi\)
−0.600300 + 0.799775i \(0.704952\pi\)
\(648\) −73.9775 + 455.714i −0.114163 + 0.703263i
\(649\) 102.069 0.157272
\(650\) 132.572 28.5459i 0.203957 0.0439167i
\(651\) −510.048 495.945i −0.783483 0.761820i
\(652\) 223.027 + 223.027i 0.342066 + 0.342066i
\(653\) 607.844 + 607.844i 0.930849 + 0.930849i 0.997759 0.0669099i \(-0.0213140\pi\)
−0.0669099 + 0.997759i \(0.521314\pi\)
\(654\) −862.579 207.965i −1.31893 0.317990i
\(655\) −61.0782 573.818i −0.0932492 0.876059i
\(656\) −644.681 −0.982745
\(657\) 1156.09 373.178i 1.75965 0.568004i
\(658\) −425.768 + 108.989i −0.647064 + 0.165636i
\(659\) 795.993 1.20788 0.603940 0.797030i \(-0.293597\pi\)
0.603940 + 0.797030i \(0.293597\pi\)
\(660\) 64.1339 + 83.5186i 0.0971726 + 0.126543i
\(661\) 353.138i 0.534248i 0.963662 + 0.267124i \(0.0860734\pi\)
−0.963662 + 0.267124i \(0.913927\pi\)
\(662\) 162.454 162.454i 0.245399 0.245399i
\(663\) 70.7185 + 115.652i 0.106664 + 0.174437i
\(664\) 45.3488 0.0682964
\(665\) 8.48052 + 22.7620i 0.0127527 + 0.0342285i
\(666\) −27.7782 + 54.2593i −0.0417090 + 0.0814704i
\(667\) −1138.77 1138.77i −1.70730 1.70730i
\(668\) −111.837 + 111.837i −0.167421 + 0.167421i
\(669\) 351.263 + 84.6885i 0.525058 + 0.126590i
\(670\) −99.6858 936.529i −0.148785 1.39780i
\(671\) 57.3785 0.0855119
\(672\) 7.08966 + 505.718i 0.0105501 + 0.752556i
\(673\) 45.1352 45.1352i 0.0670657 0.0670657i −0.672778 0.739844i \(-0.734899\pi\)
0.739844 + 0.672778i \(0.234899\pi\)
\(674\) 476.112 0.706398
\(675\) 191.554 + 647.250i 0.283784 + 0.958888i
\(676\) −260.185 −0.384890
\(677\) 812.127 + 812.127i 1.19960 + 1.19960i 0.974287 + 0.225309i \(0.0723392\pi\)
0.225309 + 0.974287i \(0.427661\pi\)
\(678\) −613.449 + 375.110i −0.904791 + 0.553260i
\(679\) −187.206 + 316.022i −0.275708 + 0.465423i
\(680\) −558.090 + 59.4041i −0.820720 + 0.0873589i
\(681\) −536.135 129.260i −0.787276 0.189810i
\(682\) 250.186 250.186i 0.366841 0.366841i
\(683\) −654.128 654.128i −0.957728 0.957728i 0.0414145 0.999142i \(-0.486814\pi\)
−0.999142 + 0.0414145i \(0.986814\pi\)
\(684\) 8.83495 + 4.52307i 0.0129166 + 0.00661268i
\(685\) −739.287 597.045i −1.07925 0.871599i
\(686\) −27.2396 + 810.435i −0.0397078 + 1.18139i
\(687\) 281.339 172.033i 0.409518 0.250411i
\(688\) −604.038 + 604.038i −0.877962 + 0.877962i
\(689\) 109.823i 0.159394i
\(690\) 708.066 + 922.082i 1.02618 + 1.33635i
\(691\) 1308.29i 1.89333i −0.322219 0.946665i \(-0.604429\pi\)
0.322219 0.946665i \(-0.395571\pi\)
\(692\) −119.150 119.150i −0.172182 0.172182i
\(693\) −271.456 61.4340i −0.391711 0.0886493i
\(694\) 142.180i 0.204871i
\(695\) 120.865 + 1135.50i 0.173907 + 1.63382i
\(696\) 816.576 + 196.874i 1.17324 + 0.282865i
\(697\) −452.697 452.697i −0.649493 0.649493i
\(698\) −540.917 + 540.917i −0.774953 + 0.774953i
\(699\) 900.447 + 217.095i 1.28819 + 0.310579i
\(700\) 124.124 + 248.847i 0.177320 + 0.355496i
\(701\) 793.166i 1.13148i −0.824584 0.565739i \(-0.808591\pi\)
0.824584 0.565739i \(-0.191409\pi\)
\(702\) 11.0695 + 146.041i 0.0157685 + 0.208035i
\(703\) −1.40592 1.40592i −0.00199989 0.00199989i
\(704\) 98.8997 0.140483
\(705\) 51.8545 394.974i 0.0735525 0.560247i
\(706\) 407.822i 0.577651i
\(707\) 119.776 30.6604i 0.169414 0.0433669i
\(708\) 93.9665 57.4584i 0.132721 0.0811560i
\(709\) 283.272i 0.399538i −0.979843 0.199769i \(-0.935981\pi\)
0.979843 0.199769i \(-0.0640192\pi\)
\(710\) −688.869 + 852.987i −0.970238 + 1.20139i
\(711\) 803.365 + 411.285i 1.12991 + 0.578459i
\(712\) −639.489 + 639.489i −0.898158 + 0.898158i
\(713\) 785.326 785.326i 1.10144 1.10144i
\(714\) −681.592 + 700.974i −0.954610 + 0.981756i
\(715\) −39.4300 31.8435i −0.0551469 0.0445364i
\(716\) 175.214i 0.244712i
\(717\) −51.6344 + 31.5733i −0.0720145 + 0.0440353i
\(718\) 762.337 762.337i 1.06175 1.06175i
\(719\) 639.857i 0.889927i −0.895549 0.444963i \(-0.853217\pi\)
0.895549 0.444963i \(-0.146783\pi\)
\(720\) −832.935 320.309i −1.15685 0.444874i
\(721\) −822.481 487.222i −1.14075 0.675758i
\(722\) 602.673 602.673i 0.834727 0.834727i
\(723\) −403.159 659.320i −0.557620 0.911922i
\(724\) −92.4510 −0.127695
\(725\) 1200.57 258.510i 1.65596 0.356566i
\(726\) −168.697 + 699.706i −0.232365 + 0.963782i
\(727\) −65.1910 + 65.1910i −0.0896713 + 0.0896713i −0.750520 0.660848i \(-0.770197\pi\)
0.660848 + 0.750520i \(0.270197\pi\)
\(728\) −22.7020 88.6863i −0.0311841 0.121822i
\(729\) −720.671 + 109.881i −0.988575 + 0.150729i
\(730\) 168.880 + 1586.59i 0.231342 + 2.17342i
\(731\) −848.314 −1.16048
\(732\) 52.8235 32.3004i 0.0721632 0.0441262i
\(733\) −631.927 631.927i −0.862110 0.862110i 0.129473 0.991583i \(-0.458671\pi\)
−0.991583 + 0.129473i \(0.958671\pi\)
\(734\) 176.370i 0.240286i
\(735\) −672.688 296.168i −0.915222 0.402950i
\(736\) −789.576 −1.07279
\(737\) −248.896 + 248.896i −0.337715 + 0.337715i
\(738\) −212.476 658.243i −0.287908 0.891928i
\(739\) 235.665i 0.318898i −0.987206 0.159449i \(-0.949028\pi\)
0.987206 0.159449i \(-0.0509717\pi\)
\(740\) −17.7087 14.3015i −0.0239306 0.0193263i
\(741\) −4.64413 1.11969i −0.00626738 0.00151105i
\(742\) −767.348 + 196.427i −1.03416 + 0.264726i
\(743\) 122.316 + 122.316i 0.164625 + 0.164625i 0.784612 0.619987i \(-0.212862\pi\)
−0.619987 + 0.784612i \(0.712862\pi\)
\(744\) −135.770 + 563.133i −0.182486 + 0.756899i
\(745\) 35.8374 + 336.685i 0.0481039 + 0.451927i
\(746\) 900.577i 1.20721i
\(747\) 21.9965 + 68.1443i 0.0294465 + 0.0912240i
\(748\) −97.7587 97.7587i −0.130693 0.130693i
\(749\) −36.4680 + 61.5618i −0.0486889 + 0.0821919i
\(750\) −883.599 + 72.2138i −1.17813 + 0.0962851i
\(751\) 314.517 0.418797 0.209399 0.977830i \(-0.432849\pi\)
0.209399 + 0.977830i \(0.432849\pi\)
\(752\) 372.409 + 372.409i 0.495225 + 0.495225i
\(753\) −490.307 + 299.812i −0.651138 + 0.398157i
\(754\) 266.467 0.353404
\(755\) −57.5966 541.109i −0.0762869 0.716700i
\(756\) −284.490 + 96.2552i −0.376309 + 0.127322i
\(757\) 782.579 + 782.579i 1.03379 + 1.03379i 0.999409 + 0.0343817i \(0.0109462\pi\)
0.0343817 + 0.999409i \(0.489054\pi\)
\(758\) 423.766 + 423.766i 0.559058 + 0.559058i
\(759\) 101.838 422.396i 0.134174 0.556516i
\(760\) 12.4267 15.3872i 0.0163509 0.0202463i
\(761\) −78.7855 −0.103529 −0.0517644 0.998659i \(-0.516485\pi\)
−0.0517644 + 0.998659i \(0.516485\pi\)
\(762\) −36.4029 + 22.2596i −0.0477729 + 0.0292121i
\(763\) 217.171 + 848.386i 0.284627 + 1.11191i
\(764\) −20.0562 −0.0262515
\(765\) −359.967 809.811i −0.470545 1.05858i
\(766\) 544.150i 0.710379i
\(767\) −37.4852 + 37.4852i −0.0488725 +