Properties

Label 105.3.k.d.62.7
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 62.7
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.d.83.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.67168 + 1.67168i) q^{2} +(-2.55943 + 1.56503i) q^{3} -1.58906i q^{4} +(0.529219 + 4.97191i) q^{5} +(1.66231 - 6.89480i) q^{6} +(-1.73590 + 6.78135i) q^{7} +(-4.03033 - 4.03033i) q^{8} +(4.10134 - 8.01118i) q^{9} +O(q^{10})\) \(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} +(-1.73590 + 6.78135i) 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} +(-6.17013 - 20.0731i) 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} +(10.7760 + 2.75844i) 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} +(-34.6349 - 5.04191i) 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} +(43.8704 + 23.2414i) 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} +(47.2071 + 41.7192i) 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} +(66.3272 - 49.4702i) 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} +(29.9586 + 7.66883i) 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} +(-31.8974 + 9.80471i) 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} +(111.195 - 32.4807i) 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
\(7\) −1.73590 + 6.78135i −0.247985 + 0.968764i
\(8\) −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 0.641946 0.766750i \(-0.278127\pi\)
−0.766750 + 0.641946i \(0.778127\pi\)
\(14\) −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 0.166839 0.985984i \(-0.446644\pi\)
−0.985984 + 0.166839i \(0.946644\pi\)
\(18\) 6.53602 + 20.2483i 0.363112 + 1.12491i
\(19\) 0.694013 0.0365270 0.0182635 0.999833i \(-0.494186\pi\)
0.0182635 + 0.999833i \(0.494186\pi\)
\(20\) 7.90067 0.840961i 0.395034 0.0420481i
\(21\) −6.17013 20.0731i −0.293816 0.955862i
\(22\) 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
\(28\) 10.7760 + 2.75844i 0.384856 + 0.0985158i
\(29\) −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 \(0.184002\pi\)
−0.837524 + 0.546401i \(0.815998\pi\)
\(32\) −17.0301 + 17.0301i −0.532190 + 0.532190i
\(33\) 6.91399 + 11.3070i 0.209515 + 0.342637i
\(34\) 46.5580 1.36935
\(35\) −34.6349 5.04191i −0.989570 0.144054i
\(36\) −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 \(-0.370244\pi\)
0.396446 + 0.918058i \(0.370244\pi\)
\(42\) 43.8704 + 23.2414i 1.04453 + 0.553366i
\(43\) −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 0.478522 0.878076i \(-0.341173\pi\)
−0.878076 + 0.478522i \(0.841173\pi\)
\(48\) −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 \(-0.937270\pi\)
0.980644 0.195798i \(-0.0627296\pi\)
\(60\) −18.9051 + 14.5172i −0.315084 + 0.241953i
\(61\) 12.9880i 0.212919i −0.994317 0.106459i \(-0.966049\pi\)
0.994317 0.106459i \(-0.0339514\pi\)
\(62\) −56.6314 56.6314i −0.913410 0.913410i
\(63\) 47.2071 + 41.7192i 0.749319 + 0.662209i
\(64\) 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
\(70\) 66.3272 49.4702i 0.947531 0.706718i
\(71\) 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 \(-0.874460\pi\)
−0.384251 0.923229i \(-0.625540\pi\)
\(74\) −6.77295 −0.0915263
\(75\) 54.3161 51.7181i 0.724215 0.689574i
\(76\) 1.10283i 0.0145109i
\(77\) 29.9586 + 7.66883i 0.389072 + 0.0995952i
\(78\) −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 −0.672403 0.740185i \(-0.734738\pi\)
0.740185 + 0.672403i \(0.234738\pi\)
\(84\) −31.8974 + 9.80471i −0.379731 + 0.116723i
\(85\) 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 \(0.350275\pi\)
−0.453220 + 0.891399i \(0.649725\pi\)
\(90\) −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 −0.489493 0.872007i \(-0.662818\pi\)
0.872007 + 0.489493i \(0.162818\pi\)
\(98\) 111.195 32.4807i 1.13464 0.331435i
\(99\) −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 \(-0.527868\pi\)
−0.0874384 + 0.996170i \(0.527868\pi\)
\(102\) −119.162 + 72.8648i −1.16825 + 0.714361i
\(103\) 96.5666 + 96.5666i 0.937540 + 0.937540i 0.998161 0.0606213i \(-0.0193082\pi\)
−0.0606213 + 0.998161i \(0.519308\pi\)
\(104\) 13.0780i 0.125750i
\(105\) 96.5364 41.3004i 0.919394 0.393338i
\(106\) −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
\(112\) −34.4248 + 134.482i −0.307364 + 1.20073i
\(113\) 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
\(126\) −148.657 + 9.17401i −1.17982 + 0.0728096i
\(127\) 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 \(-0.645200\pi\)
−0.440504 + 0.897751i \(0.645200\pi\)
\(132\) 17.9675 10.9867i 0.136118 0.0832329i
\(133\) −1.20473 + 4.70634i −0.00905815 + 0.0353860i
\(134\) 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 \(-0.193124\pi\)
0.821524 + 0.570174i \(0.193124\pi\)
\(140\) −8.01189 + 55.0370i −0.0572278 + 0.393121i
\(141\) 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
\(147\) 146.833 6.99698i 0.998867 0.0475985i
\(148\) 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 −0.664997 0.746846i \(-0.731567\pi\)
0.746846 + 0.664997i \(0.231567\pi\)
\(158\) −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 0.885697 0.464263i \(-0.153681\pi\)
−0.464263 + 0.885697i \(0.653681\pi\)
\(168\) −56.0336 + 105.769i −0.333533 + 0.629577i
\(169\) 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 −0.889790 0.456371i \(-0.849149\pi\)
0.456371 + 0.889790i \(0.349149\pi\)
\(174\) −81.6586 + 338.696i −0.469302 + 1.94653i
\(175\) 6.73844 174.870i 0.0385054 0.999258i
\(176\) 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 \(0.0513808\pi\)
−0.987000 + 0.160717i \(0.948619\pi\)
\(182\) −9.41625 + 36.7849i −0.0517376 + 0.202115i
\(183\) 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
\(189\) −186.115 32.8966i −0.984736 0.174056i
\(190\) −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 \(-0.298004\pi\)
0.592848 + 0.805314i \(0.298004\pi\)
\(200\) 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
\(203\) 85.2732 333.123i 0.420065 1.64100i
\(204\) 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
\(210\) −92.3371 + 230.420i −0.439700 + 1.09724i
\(211\) −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
\(217\) −229.731 58.8067i −1.05867 0.270999i
\(218\) −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 0.489880 0.871790i \(-0.337041\pi\)
−0.871790 + 0.489880i \(0.837041\pi\)
\(224\) −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 0.932865 0.360226i \(-0.117300\pi\)
−0.360226 + 0.932865i \(0.617300\pi\)
\(228\) 1.72596 + 2.82261i 0.00757001 + 0.0123799i
\(229\) −109.923 −0.480011 −0.240006 0.970771i \(-0.577149\pi\)
−0.240006 + 0.970771i \(0.577149\pi\)
\(230\) −41.0173 385.350i −0.178336 1.67543i
\(231\) −88.6788 + 27.2584i −0.383891 + 0.118002i
\(232\) 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
\(238\) −80.8198 + 315.726i −0.339579 + 1.32658i
\(239\) −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 \(0.179481\pi\)
−0.845201 + 0.534449i \(0.820519\pi\)
\(242\) −169.648 + 169.648i −0.701024 + 0.701024i
\(243\) 224.053 + 94.0713i 0.922027 + 0.387125i
\(244\) −20.6388 −0.0845852
\(245\) 94.3136 226.119i 0.384953 0.922936i
\(246\) 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 \(-0.375369\pi\)
0.381612 + 0.924323i \(0.375369\pi\)
\(252\) 66.2943 75.0149i 0.263073 0.297678i
\(253\) 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 0.983154 0.182779i \(-0.0585094\pi\)
−0.182779 + 0.983154i \(0.558509\pi\)
\(258\) 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 \(-0.936278\pi\)
0.980029 0.198854i \(-0.0637220\pi\)
\(270\) 181.183 262.742i 0.671049 0.973118i
\(271\) 187.036i 0.690171i −0.938571 0.345085i \(-0.887850\pi\)
0.938571 0.345085i \(-0.112150\pi\)
\(272\) −276.158 276.158i −1.01529 1.01529i
\(273\) −22.5568 + 42.5782i −0.0826256 + 0.155964i
\(274\) 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
\(280\) 119.270 + 159.911i 0.425963 + 0.571110i
\(281\) 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 0.969317 0.245813i \(-0.0790551\pi\)
−0.245813 + 0.969317i \(0.579055\pi\)
\(284\) 147.393 0.518989
\(285\) −6.34030 8.25667i −0.0222467 0.0289708i
\(286\) 23.9640i 0.0837902i
\(287\) −56.4314 + 220.452i −0.196625 + 0.768124i
\(288\) 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 −0.923517 0.383558i \(-0.874699\pi\)
0.383558 + 0.923517i \(0.374699\pi\)
\(294\) −233.762 + 257.156i −0.795110 + 0.874680i
\(295\) 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 \(0.605992\pi\)
−0.945071 + 0.326865i \(0.894008\pi\)
\(308\) 12.1862 47.6060i 0.0395657 0.154565i
\(309\) −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 \(-0.668540\pi\)
−0.505087 + 0.863068i \(0.668540\pi\)
\(312\) −20.4675 33.4721i −0.0656009 0.107282i
\(313\) 138.521 + 138.521i 0.442558 + 0.442558i 0.892871 0.450313i \(-0.148688\pi\)
−0.450313 + 0.892871i \(0.648688\pi\)
\(314\) 42.9635i 0.136827i
\(315\) −182.441 + 256.788i −0.579179 + 0.815200i
\(316\) 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
\(322\) 134.541 525.591i 0.417830 1.63227i
\(323\) −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
\(336\) −122.361 398.072i −0.364169 1.18474i
\(337\) −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
\(343\) 234.253 250.548i 0.682955 0.730461i
\(344\) 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 \(-0.653434\pi\)
−0.463576 + 0.886057i \(0.653434\pi\)
\(350\) 281.063 + 303.592i 0.803038 + 0.867407i
\(351\) 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 −0.858449 0.512899i \(-0.828572\pi\)
0.512899 + 0.858449i \(0.328572\pi\)
\(354\) −159.298 38.4063i −0.449995 0.108492i
\(355\) −461.168 + 49.0876i −1.29907 + 0.138275i
\(356\) 252.135 0.708243
\(357\) −193.605 + 365.449i −0.542312 + 1.02367i
\(358\) 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 −0.631576 0.775314i \(-0.717591\pi\)
0.775314 + 0.631576i \(0.217591\pi\)
\(368\) 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
\(378\) 366.118 256.133i 0.968567 0.677600i
\(379\) 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 −0.461955 0.886903i \(-0.652852\pi\)
0.886903 + 0.461955i \(0.152852\pi\)
\(384\) 435.311 + 104.952i 1.13362 + 0.273313i
\(385\) −22.2741 + 153.010i −0.0578548 + 0.397428i
\(386\) 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
\(392\) 78.3089 + 268.085i 0.199768 + 0.683889i
\(393\) 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 \(-0.440980\pi\)
0.982859 0.184357i \(-0.0590203\pi\)
\(398\) −394.440 + 394.440i −0.991055 + 0.991055i
\(399\) −4.28215 13.9310i −0.0107322 0.0349148i
\(400\) −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 \(-0.546501\pi\)
−0.145570 + 0.989348i \(0.546501\pi\)
\(410\) −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
\(413\) 156.677 + 40.1064i 0.379364 + 0.0971099i
\(414\) −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 \(0.338412\pi\)
−0.486120 + 0.873892i \(0.661588\pi\)
\(420\) −65.6289 153.402i −0.156259 0.365243i
\(421\) 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
\(427\) 88.0764 + 22.5459i 0.206268 + 0.0528007i
\(428\) 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 0.958646 0.284603i \(-0.0918617\pi\)
−0.284603 + 0.958646i \(0.591862\pi\)
\(434\) 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 \(-0.457577\pi\)
0.132882 + 0.991132i \(0.457577\pi\)
\(440\) −97.9486 79.1029i −0.222610 0.179779i
\(441\) −364.859 + 247.707i −0.827345 + 0.561695i
\(442\) −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
\(448\) −151.812 38.8610i −0.338866 0.0867433i
\(449\) 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
\(455\) 48.0130 + 64.3735i 0.105523 + 0.141480i
\(456\) 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 \(-0.173233\pi\)
0.855528 + 0.517757i \(0.173233\pi\)
\(462\) 102.676 193.810i 0.222242 0.419503i
\(463\) −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 0.310194 0.950673i \(-0.399606\pi\)
−0.950673 + 0.310194i \(0.899606\pi\)
\(468\) 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 \(-0.797666\pi\)
0.804685 0.593702i \(-0.202334\pi\)
\(480\) 358.189 + 47.0251i 0.746226 + 0.0979690i
\(481\) 6.57345i 0.0136662i
\(482\) −430.633 430.633i −0.893430 0.893430i
\(483\) 322.296 608.366i 0.667279 1.25956i
\(484\) 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
\(490\) 220.338 + 535.663i 0.449669 + 1.09319i
\(491\) 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
\(497\) −629.002 161.012i −1.26560 0.323969i
\(498\) −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 −0.372111 0.928188i \(-0.621366\pi\)
0.928188 + 0.372111i \(0.121366\pi\)
\(504\) −22.1180 358.402i −0.0438849 0.711116i
\(505\) −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 \(0.161218\pi\)
−0.874457 + 0.485104i \(0.838782\pi\)
\(510\) −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
\(518\) 11.7571 45.9297i 0.0226972 0.0886674i
\(519\) 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 \(-0.504967\pi\)
−0.0156039 + 0.999878i \(0.504967\pi\)
\(522\) −321.072 994.667i −0.615080 1.90549i
\(523\) −629.367 629.367i −1.20338 1.20338i −0.973132 0.230246i \(-0.926047\pi\)
−0.230246 0.973132i \(-0.573953\pi\)
\(524\) 183.397i 0.349993i
\(525\) 256.431 + 458.114i 0.488440 + 0.872597i
\(526\) −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
\(532\) 7.47866 + 1.91439i 0.0140576 + 0.00359849i
\(533\) −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
\(546\) −33.4695 108.885i −0.0612994 0.199423i
\(547\) −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
\(553\) −680.037 174.077i −1.22972 0.314786i
\(554\) −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
\(560\) −686.850 99.9867i −1.22652 0.178548i
\(561\) 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 \(-0.416540\pi\)
0.965823 0.259204i \(-0.0834602\pi\)
\(564\) 29.6737 123.078i 0.0526130 0.218223i
\(565\) −318.491 + 394.369i −0.563701 + 0.697999i
\(566\) −684.560 −1.20947
\(567\) 527.832 207.080i 0.930921 0.365220i
\(568\) 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 −0.822607 0.568610i \(-0.807481\pi\)
0.568610 + 0.822607i \(0.307481\pi\)
\(578\) −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 0.776346 0.630307i \(-0.217071\pi\)
−0.630307 + 0.776346i \(0.717071\pi\)
\(588\) −11.1186 233.327i −0.0189092 0.396815i
\(589\) 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 \(-0.492276\pi\)
0.999706 0.0242632i \(-0.00772398\pi\)
\(594\) −183.758 + 213.900i −0.309357 + 0.360100i
\(595\) 412.097 + 552.519i 0.692600 + 0.928603i
\(596\) 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 \(-0.810233\pi\)
0.827492 0.561478i \(-0.189767\pi\)
\(602\) 690.585 + 176.777i 1.14715 + 0.293649i
\(603\) −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 −0.259189 0.965827i \(-0.583455\pi\)
0.965827 + 0.259189i \(0.0834552\pi\)
\(608\) −11.8191 + 11.8191i −0.0194393 + 0.0194393i
\(609\) 303.098 + 986.060i 0.497698 + 1.61915i
\(610\) −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 \(-0.781594\pi\)
−0.773695 + 0.633558i \(0.781594\pi\)
\(620\) 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
\(623\) −1075.99 275.433i −1.72711 0.442107i
\(624\) 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
\(630\) −124.284 734.253i −0.197277 1.16548i
\(631\) −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
\(637\) 31.5239 + 107.920i 0.0494881 + 0.169419i
\(638\) −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 0.866193 0.499709i \(-0.166560\pi\)
−0.499709 + 0.866193i \(0.666560\pi\)
\(644\) 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 0.600300 0.799775i \(-0.295048\pi\)
−0.799775 + 0.600300i \(0.795048\pi\)
\(648\) −73.9775 + 455.714i −0.114163 + 0.703263i
\(649\) −102.069 −0.157272
\(650\) −132.572 + 28.5459i −0.203957 + 0.0439167i
\(651\) 680.013 209.025i 1.04457 0.321082i
\(652\) 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
\(658\) −108.989 + 425.768i −0.165636 + 0.647064i
\(659\) 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 \(-0.913927\pi\)
0.963662 0.267124i \(-0.0860734\pi\)
\(662\) 162.454 162.454i 0.245399 0.245399i
\(663\) −70.7185 115.652i −0.106664 0.174437i
\(664\) −45.3488 −0.0682964
\(665\) −24.0371 3.49915i −0.0361460 0.00526188i
\(666\) −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
\(672\) 446.924 + 236.769i 0.665066 + 0.352334i
\(673\) 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 \(-0.927661\pi\)
−0.225309 0.974287i \(-0.572339\pi\)
\(678\) 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 \(0.395571\pi\)
−0.322219 + 0.946665i \(0.604429\pi\)
\(692\) 119.150 + 119.150i 0.172182 + 0.172182i
\(693\) 184.307 208.551i 0.265955 0.300939i
\(694\) 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
\(700\) −277.879 10.7078i −0.396970 0.0152968i
\(701\) 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
\(707\) 30.6604 119.776i 0.0433669 0.169414i
\(708\) 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
\(714\) −287.269 934.563i −0.402337 1.30891i
\(715\) −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 \(0.146783\pi\)
−0.895549 + 0.444963i \(0.853217\pi\)
\(720\) 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 −0.660848 0.750520i \(-0.729803\pi\)
0.750520 + 0.660848i \(0.229803\pi\)
\(728\) −88.6863 22.7020i −0.121822 0.0311841i
\(729\) −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 0.991583 0.129473i \(-0.0413285\pi\)
−0.129473 + 0.991583i \(0.541329\pi\)
\(734\) 176.370i 0.240286i
\(735\) 112.495 + 726.340i 0.153055 + 0.988218i
\(736\) −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
\(742\) 196.427 767.348i 0.264726 1.03416i
\(743\) 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
\(756\) −52.2747 + 295.748i −0.0691464 + 0.391201i
\(757\) 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 \(-0.483515\pi\)
0.0517644 + 0.998659i \(0.483515\pi\)
\(762\) 36.4029 22.2596i 0.0477729 0.0292121i
\(763\) −848.386 217.171i −1.11191 0.284627i
\(764\) −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 +