Properties

Label 105.3.k.d.62.10
Level 105
Weight 3
Character 105.62
Analytic conductor 2.861
Analytic rank 0
Dimension 32
CM no
Inner twists 8

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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 62.10
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.d.83.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.67168 - 1.67168i) q^{2} +(1.56503 - 2.55943i) q^{3} -1.58906i q^{4} +(-0.529219 - 4.97191i) q^{5} +(-1.66231 - 6.89480i) q^{6} +(-1.73590 + 6.78135i) q^{7} +(4.03033 + 4.03033i) q^{8} +(-4.10134 - 8.01118i) q^{9} +O(q^{10})\) \(q+(1.67168 - 1.67168i) q^{2} +(1.56503 - 2.55943i) 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} +(-4.06708 - 2.48693i) q^{12} +(-1.62244 - 1.62244i) q^{13} +(8.43440 + 14.2381i) q^{14} +(-13.5535 - 6.42671i) q^{15} +19.8311 q^{16} +(13.9255 + 13.9255i) q^{17} +(-20.2483 - 6.53602i) 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} +(-26.9228 - 2.04067i) q^{27} +(10.7760 + 2.75844i) q^{28} +49.1234 q^{29} +(-33.4006 + 11.9137i) q^{30} +33.8768i q^{31} +(17.0301 - 17.0301i) q^{32} +(11.3070 + 6.91399i) 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} +(49.6416 + 0.695926i) q^{42} +(-30.4591 + 30.4591i) q^{43} +7.02014 q^{44} +(-37.6604 + 24.6312i) q^{45} -77.5053 q^{46} +(18.7790 + 18.7790i) q^{47} +(31.0364 - 50.7563i) 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} +(1.08615 - 1.77628i) q^{57} +(82.1189 - 82.1189i) q^{58} +23.1041i q^{59} +(-10.2124 + 21.5373i) q^{60} -12.9880i q^{61} +(56.6314 + 56.6314i) q^{62} +(61.4461 - 13.9060i) 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} +(15.7579 - 48.8175i) q^{72} +(-95.4460 - 95.4460i) q^{73} +6.77295 q^{74} +(-24.7803 + 70.7880i) q^{75} -1.10283i q^{76} +(-29.9586 - 7.66883i) q^{77} +(-8.48941 + 13.8834i) 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} +(76.8798 - 125.728i) q^{87} +(-17.8052 + 17.8052i) q^{88} -158.669i q^{89} +(-21.7807 + 104.132i) q^{90} +(13.8188 - 8.18596i) q^{91} +(-36.8373 + 36.8373i) q^{92} +(86.7053 + 53.0184i) 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 −0.152466 0.988309i \(-0.548722\pi\)
0.988309 + 0.152466i \(0.0487215\pi\)
\(3\) 1.56503 2.55943i 0.521678 0.853143i
\(4\) 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 \(0.0643570\pi\)
−0.979630 + 0.200809i \(0.935643\pi\)
\(12\) −4.06708 2.48693i −0.338924 0.207244i
\(13\) −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
\(15\) −13.5535 6.42671i −0.903567 0.428447i
\(16\) 19.8311 1.23945
\(17\) 13.9255 + 13.9255i 0.819145 + 0.819145i 0.985984 0.166839i \(-0.0533560\pi\)
−0.166839 + 0.985984i \(0.553356\pi\)
\(18\) −20.2483 6.53602i −1.12491 0.363112i
\(19\) 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
\(21\) 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 \(-0.997474\pi\)
−0.00793606 0.999969i \(-0.502526\pi\)
\(24\) 16.6229 4.00774i 0.692623 0.166989i
\(25\) −24.4399 + 5.26247i −0.977594 + 0.210499i
\(26\) −5.42443 −0.208632
\(27\) −26.9228 2.04067i −0.997140 0.0755805i
\(28\) 10.7760 + 2.75844i 0.384856 + 0.0985158i
\(29\) 49.1234 1.69391 0.846956 0.531663i \(-0.178433\pi\)
0.846956 + 0.531663i \(0.178433\pi\)
\(30\) −33.4006 + 11.9137i −1.11335 + 0.397125i
\(31\) 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
\(33\) 11.3070 + 6.91399i 0.342637 + 0.209515i
\(34\) 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 \(-0.629756\pi\)
−0.396446 + 0.918058i \(0.629756\pi\)
\(42\) 49.6416 + 0.695926i 1.18194 + 0.0165697i
\(43\) −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
\(45\) −37.6604 + 24.6312i −0.836897 + 0.547360i
\(46\) −77.5053 −1.68490
\(47\) 18.7790 + 18.7790i 0.399554 + 0.399554i 0.878076 0.478522i \(-0.158827\pi\)
−0.478522 + 0.878076i \(0.658827\pi\)
\(48\) 31.0364 50.7563i 0.646591 1.05742i
\(49\) −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 0.311624 0.950205i \(-0.399127\pi\)
−0.950205 + 0.311624i \(0.899127\pi\)
\(54\) −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
\(57\) 1.08615 1.77628i 0.0190553 0.0311627i
\(58\) 82.1189 82.1189i 1.41584 1.41584i
\(59\) 23.1041i 0.391596i 0.980644 + 0.195798i \(0.0627296\pi\)
−0.980644 + 0.195798i \(0.937270\pi\)
\(60\) −10.2124 + 21.5373i −0.170207 + 0.358955i
\(61\) 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
\(63\) 61.4461 13.9060i 0.975335 0.220731i
\(64\) 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 \(-0.773425\pi\)
0.757184 0.653202i \(-0.226575\pi\)
\(72\) 15.7579 48.8175i 0.218860 0.678020i
\(73\) −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
\(75\) −24.7803 + 70.7880i −0.330404 + 0.943840i
\(76\) 1.10283i 0.0145109i
\(77\) −29.9586 7.66883i −0.389072 0.0995952i
\(78\) −8.48941 + 13.8834i −0.108839 + 0.177993i
\(79\) 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
\(87\) 76.8798 125.728i 0.883676 1.44515i
\(88\) −17.8052 + 17.8052i −0.202331 + 0.202331i
\(89\) 158.669i 1.78280i −0.453220 0.891399i \(-0.649725\pi\)
0.453220 0.891399i \(-0.350275\pi\)
\(90\) −21.7807 + 104.132i −0.242008 + 1.15702i
\(91\) 13.8188 8.18596i 0.151854 0.0899556i
\(92\) −36.8373 + 36.8373i −0.400405 + 0.400405i
\(93\) 86.7053 + 53.0184i 0.932315 + 0.570090i
\(94\) 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 \(-0.472132\pi\)
0.0874384 + 0.996170i \(0.472132\pi\)
\(102\) 72.8648 119.162i 0.714361 1.16825i
\(103\) 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
\(105\) 67.1092 80.7549i 0.639136 0.769094i
\(106\) −113.156 −1.06751
\(107\) 7.22790 7.22790i 0.0675504 0.0675504i −0.672524 0.740075i \(-0.734790\pi\)
0.740075 + 0.672524i \(0.234790\pi\)
\(108\) −3.24275 + 42.7819i −0.0300255 + 0.396129i
\(109\) 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 0.314758 0.949172i \(-0.398077\pi\)
−0.949172 + 0.314758i \(0.898077\pi\)
\(114\) −1.15367 4.78508i −0.0101199 0.0419744i
\(115\) −102.990 + 127.526i −0.895562 + 1.10892i
\(116\) 78.0601i 0.672932i
\(117\) −6.34349 + 19.6519i −0.0542179 + 0.167965i
\(118\) 38.6228 + 38.6228i 0.327312 + 0.327312i
\(119\) −118.607 + 70.2603i −0.996694 + 0.590422i
\(120\) −28.7233 80.5269i −0.239361 0.671057i
\(121\) 101.483 0.838703
\(122\) −21.7119 21.7119i −0.177966 0.177966i
\(123\) −50.8769 + 83.2032i −0.413634 + 0.676449i
\(124\) 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 \(0.354800\pi\)
\(132\) 10.9867 17.9675i 0.0832329 0.136118i
\(133\) −1.20473 + 4.70634i −0.00905815 + 0.0353860i
\(134\) −188.364 −1.40570
\(135\) 4.10200 + 134.938i 0.0303852 + 0.999538i
\(136\) 112.249i 0.825357i
\(137\) −134.388 + 134.388i −0.980935 + 0.980935i −0.999822 0.0188868i \(-0.993988\pi\)
0.0188868 + 0.999822i \(0.493988\pi\)
\(138\) −121.298 + 198.369i −0.878974 + 1.43746i
\(139\) 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
\(147\) −127.512 + 73.1409i −0.867431 + 0.497557i
\(148\) 3.21909 3.21909i 0.0217506 0.0217506i
\(149\) 67.7175 0.454480 0.227240 0.973839i \(-0.427030\pi\)
0.227240 + 0.973839i \(0.427030\pi\)
\(150\) 76.9104 + 159.760i 0.512736 + 1.06507i
\(151\) 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
\(153\) 54.4463 168.673i 0.355858 1.10243i
\(154\) −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
\(162\) 30.6841 + 189.019i 0.189408 + 1.16679i
\(163\) −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
\(165\) 28.3919 59.8765i 0.172072 0.362888i
\(166\) 18.8096i 0.113311i
\(167\) −70.3795 70.3795i −0.421434 0.421434i 0.464263 0.885697i \(-0.346319\pi\)
−0.885697 + 0.464263i \(0.846319\pi\)
\(168\) −1.67784 + 119.683i −0.00998712 + 0.712399i
\(169\) 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
\(175\) 6.73844 174.870i 0.0385054 0.999258i
\(176\) 87.6098i 0.497783i
\(177\) 59.1334 + 36.1587i 0.334087 + 0.204287i
\(178\) −265.245 265.245i −1.49014 1.49014i
\(179\) 110.262 0.615991 0.307996 0.951388i \(-0.400342\pi\)
0.307996 + 0.951388i \(0.400342\pi\)
\(180\) 39.1404 + 59.8446i 0.217447 + 0.332470i
\(181\) 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
\(183\) −33.2420 20.3267i −0.181650 0.111075i
\(184\) 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 \(0.0105190\pi\)
−0.999454 + 0.0330403i \(0.989481\pi\)
\(192\) 57.2971 + 35.0359i 0.298423 + 0.182479i
\(193\) 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
\(195\) 11.5628 + 32.4168i 0.0592965 + 0.166240i
\(196\) −37.4119 + 68.2872i −0.190877 + 0.348404i
\(197\) 102.520 102.520i 0.520407 0.520407i −0.397288 0.917694i \(-0.630048\pi\)
0.917694 + 0.397288i \(0.130048\pi\)
\(198\) 28.8748 89.4528i 0.145832 0.451782i
\(199\) 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
\(207\) −90.6371 + 280.790i −0.437860 + 1.35647i
\(208\) −32.1749 32.1749i −0.154687 0.154687i
\(209\) 3.06600i 0.0146699i
\(210\) −22.8112 247.182i −0.108625 1.17706i
\(211\) −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
\(213\) −237.399 145.164i −1.11455 0.681522i
\(214\) 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
\(222\) 10.5999 17.3349i 0.0477473 0.0780850i
\(223\) −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
\(225\) 142.395 + 174.209i 0.632866 + 0.774262i
\(226\) −239.682 −1.06054
\(227\) −129.989 129.989i −0.572639 0.572639i 0.360226 0.932865i \(-0.382700\pi\)
−0.932865 + 0.360226i \(0.882700\pi\)
\(228\) −2.82261 1.72596i −0.0123799 0.00757001i
\(229\) −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
\(231\) −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 0.0611395 0.998129i \(-0.480527\pi\)
−0.998129 + 0.0611395i \(0.980527\pi\)
\(234\) 22.2474 + 43.4561i 0.0950745 + 0.185710i
\(235\) 83.4295 103.306i 0.355019 0.439600i
\(236\) 36.7139 0.155567
\(237\) 256.661 + 156.942i 1.08296 + 0.662204i
\(238\) −80.8198 + 315.726i −0.339579 + 1.32658i
\(239\) 20.1742 0.0844109 0.0422054 0.999109i \(-0.486562\pi\)
0.0422054 + 0.999109i \(0.486562\pi\)
\(240\) −268.781 127.449i −1.11992 0.531037i
\(241\) 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
\(243\) 94.0713 + 224.053i 0.387125 + 0.922027i
\(244\) −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 \(-0.624631\pi\)
−0.381612 + 0.924323i \(0.624631\pi\)
\(252\) −22.0975 97.6415i −0.0876887 0.387466i
\(253\) 102.412 102.412i 0.404792 0.404792i
\(254\) 14.2231 0.0559964
\(255\) −99.2439 278.234i −0.389192 1.09111i
\(256\) 263.325 1.02861
\(257\) −205.696 205.696i −0.800374 0.800374i 0.182779 0.983154i \(-0.441491\pi\)
−0.983154 + 0.182779i \(0.941491\pi\)
\(258\) 260.642 + 159.377i 1.01024 + 0.617739i
\(259\) −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 0.697875 0.716219i \(-0.254129\pi\)
−0.716219 + 0.697875i \(0.754129\pi\)
\(264\) 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
\(267\) −406.102 248.322i −1.52098 0.930046i
\(268\) −89.5269 + 89.5269i −0.334056 + 0.334056i
\(269\) 106.984i 0.397708i 0.980029 + 0.198854i \(0.0637220\pi\)
−0.980029 + 0.198854i \(0.936278\pi\)
\(270\) 232.430 + 218.716i 0.860854 + 0.810059i
\(271\) 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
\(273\) 0.675427 48.1794i 0.00247409 0.176481i
\(274\) 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 \(0.0806261\pi\)
−0.968092 + 0.250594i \(0.919374\pi\)
\(282\) 98.2610 160.694i 0.348443 0.569838i
\(283\) 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
\(285\) −9.40630 4.46022i −0.0330046 0.0156499i
\(286\) 23.9640i 0.0837902i
\(287\) 56.4314 220.452i 0.196625 0.768124i
\(288\) −206.277 66.5848i −0.716240 0.231197i
\(289\) 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
\(297\) 9.01527 118.939i 0.0303544 0.400469i
\(298\) 113.202 113.202i 0.379873 0.379873i
\(299\) 75.2224i 0.251580i
\(300\) 112.486 + 39.3774i 0.374955 + 0.131258i
\(301\) −153.680 259.427i −0.510564 0.861885i
\(302\) 181.935 181.935i 0.602433 0.602433i
\(303\) 27.6425 45.2060i 0.0912293 0.149195i
\(304\) 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 \(-0.331460\pi\)
0.505087 + 0.863068i \(0.331460\pi\)
\(312\) −33.4721 20.4675i −0.107282 0.0656009i
\(313\) 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
\(315\) −101.658 298.145i −0.322724 0.946493i
\(316\) 159.352 0.504278
\(317\) −171.788 + 171.788i −0.541917 + 0.541917i −0.924090 0.382174i \(-0.875176\pi\)
0.382174 + 0.924090i \(0.375176\pi\)
\(318\) −177.092 + 289.614i −0.556895 + 0.910736i
\(319\) 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
\(327\) 320.199 + 195.795i 0.979203 + 0.598761i
\(328\) −131.020 131.020i −0.399452 0.399452i
\(329\) −159.946 + 94.7486i −0.486157 + 0.287990i
\(330\) −52.6324 147.557i −0.159492 0.447142i
\(331\) −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
\(333\) 7.92049 24.5374i 0.0237853 0.0736858i
\(334\) −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
\(342\) −14.0526 4.53608i −0.0410894 0.0132634i
\(343\) 234.253 250.548i 0.682955 0.730461i
\(344\) −245.520 −0.713722
\(345\) 165.212 + 463.177i 0.478875 + 1.34254i
\(346\) 250.691i 0.724540i
\(347\) −42.5261 + 42.5261i −0.122554 + 0.122554i −0.765723 0.643170i \(-0.777619\pi\)
0.643170 + 0.765723i \(0.277619\pi\)
\(348\) −199.789 122.167i −0.574107 0.351054i
\(349\) −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 −0.512899 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
\(357\) −5.79721 + 413.525i −0.0162387 + 1.15833i
\(358\) 184.324 184.324i 0.514872 0.514872i
\(359\) 456.029 1.27028 0.635138 0.772399i \(-0.280943\pi\)
0.635138 + 0.772399i \(0.280943\pi\)
\(360\) −251.056 52.5120i −0.697377 0.145867i
\(361\) −360.518 −0.998666
\(362\) 97.2581 + 97.2581i 0.268669 + 0.268669i
\(363\) 158.824 259.739i 0.437533 0.715534i
\(364\) −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
\(372\) 84.2494 137.780i 0.226477 0.370376i
\(373\) −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
\(375\) 365.066 + 85.7431i 0.973509 + 0.228648i
\(376\) 151.371i 0.402583i
\(377\) −79.7000 79.7000i −0.211406 0.211406i
\(378\) −198.022 400.542i −0.523868 1.05964i
\(379\) 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
\(385\) −22.2741 + 153.010i −0.0578548 + 0.397428i
\(386\) 707.348i 1.83251i
\(387\) 368.936 + 119.090i 0.953324 + 0.307726i
\(388\) −58.9602 58.9602i −0.151959 0.151959i
\(389\) 309.463 0.795534 0.397767 0.917486i \(-0.369785\pi\)
0.397767 + 0.917486i \(0.369785\pi\)
\(390\) 73.5200 + 34.8613i 0.188513 + 0.0893878i
\(391\) 645.635i 1.65124i
\(392\) −78.3089 268.085i −0.199768 0.683889i
\(393\) 180.624 295.389i 0.459602 0.751625i
\(394\) 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
\(399\) 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 \(0.222725\pi\)
−0.765028 + 0.643997i \(0.777275\pi\)
\(402\) −294.796 + 482.104i −0.733323 + 1.19926i
\(403\) 54.9633 54.9633i 0.136385 0.136385i
\(404\) 28.0669i 0.0694724i
\(405\) 351.783 + 200.683i 0.868600 + 0.495514i
\(406\) 414.327 + 699.427i 1.02051 + 1.72273i
\(407\) −8.94950 + 8.94950i −0.0219889 + 0.0219889i
\(408\) 287.292 + 175.673i 0.704147 + 0.430570i
\(409\) −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
\(417\) 357.428 584.532i 0.857142 1.40175i
\(418\) 5.12539 + 5.12539i 0.0122617 + 0.0122617i
\(419\) 732.322i 1.74778i −0.486120 0.873892i \(-0.661588\pi\)
0.486120 0.873892i \(-0.338412\pi\)
\(420\) −128.324 106.641i −0.305534 0.253906i
\(421\) 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
\(423\) 73.4229 227.461i 0.173577 0.537734i
\(424\) 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 \(0.0767452\pi\)
−0.971075 + 0.238773i \(0.923255\pi\)
\(432\) −533.909 40.4689i −1.23590 0.0936779i
\(433\) 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
\(435\) −665.795 315.702i −1.53056 0.725752i
\(436\) 198.801 0.455965
\(437\) −16.0885 16.0885i −0.0368157 0.0368157i
\(438\) −499.420 + 816.742i −1.14023 + 1.86471i
\(439\) 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
\(441\) −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 0.949719 0.313102i \(-0.101368\pi\)
−0.313102 + 0.949719i \(0.601368\pi\)
\(444\) −3.20105 13.2770i −0.00720957 0.0299032i
\(445\) −788.888 + 83.9707i −1.77278 + 0.188698i
\(446\) −284.741 −0.638433
\(447\) 105.980 173.318i 0.237092 0.387736i
\(448\) −151.812 38.8610i −0.338866 0.0867433i
\(449\) −407.834 −0.908317 −0.454158 0.890921i \(-0.650060\pi\)
−0.454158 + 0.890921i \(0.650060\pi\)
\(450\) 529.261 + 53.1832i 1.17614 + 0.118185i
\(451\) 143.616i 0.318439i
\(452\) −113.918 + 113.918i −0.252030 + 0.252030i
\(453\) 170.327 278.550i 0.375999 0.614902i
\(454\) −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 \(-0.826767\pi\)
−0.855528 + 0.517757i \(0.826767\pi\)
\(462\) −3.07446 + 219.306i −0.00665467 + 0.474689i
\(463\) −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
\(465\) 217.717 459.150i 0.468208 0.987419i
\(466\) −729.920 −1.56635
\(467\) 299.104 + 299.104i 0.640480 + 0.640480i 0.950673 0.310194i \(-0.100394\pi\)
−0.310194 + 0.950673i \(0.600394\pi\)
\(468\) 31.2280 + 10.0802i 0.0667266 + 0.0215389i
\(469\) 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
\(477\) −132.328 + 409.946i −0.277417 + 0.859426i
\(478\) 33.7249 33.7249i 0.0705542 0.0705542i
\(479\) 568.767i 1.18740i 0.804685 + 0.593702i \(0.202334\pi\)
−0.804685 + 0.593702i \(0.797666\pi\)
\(480\) −340.264 + 121.370i −0.708884 + 0.252854i
\(481\) 6.57345i 0.0136662i
\(482\) 430.633 + 430.633i 0.893430 + 0.893430i
\(483\) 9.65064 688.397i 0.0199806 1.42525i
\(484\) 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 \(0.000449112\pi\)
−0.999999 + 0.00141093i \(0.999551\pi\)
\(492\) 132.215 + 80.8465i 0.268730 + 0.164322i
\(493\) 684.067 + 684.067i 1.38756 + 1.38756i
\(494\) −3.76462 −0.00762070
\(495\) −108.815 166.376i −0.219829 0.336113i
\(496\) 671.816i 1.35447i
\(497\) 629.002 + 161.012i 1.26560 + 0.323969i
\(498\) 48.1418 + 29.4377i 0.0966703 + 0.0591118i
\(499\) 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
\(507\) −419.069 256.251i −0.826566 0.505427i
\(508\) 6.76005 6.76005i 0.0133072 0.0133072i
\(509\) 493.836i 0.970208i −0.874457 0.485104i \(-0.838782\pi\)
0.874457 0.485104i \(-0.161218\pi\)
\(510\) −631.024 299.215i −1.23730 0.586696i
\(511\) 812.937 481.568i 1.59087 0.942403i
\(512\) 18.0214 18.0214i 0.0351981 0.0351981i
\(513\) −18.6847 1.41625i −0.0364225 0.00276073i
\(514\) −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 \(-0.495033\pi\)
0.0156039 + 0.999878i \(0.495033\pi\)
\(522\) −994.667 321.072i −1.90549 0.615080i
\(523\) −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
\(525\) −437.022 290.924i −0.832423 0.554141i
\(526\) −16.1301 −0.0306655
\(527\) −471.751 + 471.751i −0.895163 + 0.895163i
\(528\) 224.231 + 137.112i 0.424680 + 0.259682i
\(529\) 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
\(537\) 172.564 282.209i 0.321349 0.525528i
\(538\) 178.843 + 178.843i 0.332421 + 0.332421i
\(539\) 104.010 189.847i 0.192968 0.352221i
\(540\) 214.424 6.51832i 0.397082 0.0120710i
\(541\) 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
\(543\) 148.907 + 91.0532i 0.274230 + 0.167685i
\(544\) 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
\(552\) −478.257 292.443i −0.866407 0.529788i
\(553\) −680.037 174.077i −1.22972 0.314786i
\(554\) 320.200 0.577979
\(555\) −14.4373 40.4756i −0.0260132 0.0729290i
\(556\) 362.915i 0.652726i
\(557\) 12.4652 12.4652i 0.0223792 0.0223792i −0.695829 0.718208i \(-0.744963\pi\)
0.718208 + 0.695829i \(0.244963\pi\)
\(558\) 221.420 685.949i 0.396809 1.22930i
\(559\) 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 \(0.583460\pi\)
−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
\(567\) −363.415 435.222i −0.640944 0.767588i
\(568\) 373.832 373.832i 0.658155 0.658155i
\(569\) 44.3368 0.0779205 0.0389602 0.999241i \(-0.487595\pi\)
0.0389602 + 0.999241i \(0.487595\pi\)
\(570\) −23.1805 + 8.26829i −0.0406675 + 0.0145058i
\(571\) 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
\(573\) 32.3036 + 19.7529i 0.0563762 + 0.0344728i
\(574\) −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
\(582\) −317.502 194.145i −0.545535 0.333583i
\(583\) 149.519 149.519i 0.256465 0.256465i
\(584\) 769.358i 1.31739i
\(585\) 101.065 + 21.1391i 0.172760 + 0.0361353i
\(586\) 528.948i 0.902642i
\(587\) −85.7254 85.7254i −0.146040 0.146040i 0.630307 0.776346i \(-0.282929\pi\)
−0.776346 + 0.630307i \(0.782929\pi\)
\(588\) 116.225 + 202.625i 0.197662 + 0.344600i
\(589\) 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
\(595\) 412.097 + 552.519i 0.692600 + 0.928603i
\(596\) 107.607i 0.180549i
\(597\) 369.275 603.906i 0.618551 1.01157i
\(598\) 125.748 + 125.748i 0.210281 + 0.210281i
\(599\) −214.278 −0.357726 −0.178863 0.983874i \(-0.557242\pi\)
−0.178863 + 0.983874i \(0.557242\pi\)
\(600\) −385.172 + 185.426i −0.641953 + 0.309044i
\(601\) 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
\(603\) −220.278 + 682.414i −0.365304 + 1.13170i
\(604\) 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
\(609\) 719.149 + 739.599i 1.18087 + 1.21445i
\(610\) −96.4594 + 119.440i −0.158130 + 0.195803i
\(611\) 60.9358i 0.0997313i
\(612\) −268.031 86.5185i −0.437959 0.141370i
\(613\) −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
\(615\) 440.604 + 208.923i 0.716430 + 0.339712i
\(616\) −89.8351 151.651i −0.145836 0.246187i
\(617\) 525.987 525.987i 0.852491 0.852491i −0.137948 0.990439i \(-0.544051\pi\)
0.990439 + 0.137948i \(0.0440507\pi\)
\(618\) 505.283 826.331i 0.817610 1.33711i
\(619\) −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
\(627\) 7.84721 + 4.79840i 0.0125155 + 0.00765295i
\(628\) −20.4200 20.4200i −0.0325159 0.0325159i
\(629\) 56.4200i 0.0896980i
\(630\) −668.345 328.465i −1.06087 0.521372i
\(631\) −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
\(633\) −140.302 + 229.448i −0.221647 + 0.362477i
\(634\) 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 \(-0.839861\pi\)
0.876096 0.482136i \(-0.160139\pi\)
\(642\) −61.8499 37.8199i −0.0963395 0.0589094i
\(643\) 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
\(645\) 608.579 217.075i 0.943533 0.336551i
\(646\) 32.3118 0.0500183
\(647\) 129.060 + 129.060i 0.199474 + 0.199474i 0.799775 0.600300i \(-0.204952\pi\)
−0.600300 + 0.799775i \(0.704952\pi\)
\(648\) −455.714 + 73.9775i −0.703263 + 0.114163i
\(649\) −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 0.0669099 0.997759i \(-0.478686\pi\)
−0.997759 + 0.0669099i \(0.978686\pi\)
\(654\) 862.579 207.965i 1.31893 0.317990i
\(655\) −61.0782 573.818i −0.0932492 0.876059i
\(656\) −644.681 −0.982745
\(657\) −373.178 + 1156.09i −0.568004 + 1.75965i
\(658\) −108.989 + 425.768i −0.165636 + 0.647064i
\(659\) −795.993 −1.20788 −0.603940 0.797030i \(-0.706403\pi\)
−0.603940 + 0.797030i \(0.706403\pi\)
\(660\) −95.1474 45.1164i −0.144163 0.0683582i
\(661\) 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
\(663\) −115.652 70.7185i −0.174437 0.106664i
\(664\) −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
\(672\) 505.718 + 7.08966i 0.752556 + 0.0105501i
\(673\) 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
\(675\) 668.728 91.8064i 0.990708 0.136009i
\(676\) −260.185 −0.384890
\(677\) 812.127 + 812.127i 1.19960 + 1.19960i 0.974287 + 0.225309i \(0.0723392\pi\)
0.225309 + 0.974287i \(0.427661\pi\)
\(678\) −375.110 + 613.449i −0.553260 + 0.904791i
\(679\) 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 0.999142 0.0414145i \(-0.0131864\pi\)
−0.0414145 + 0.999142i \(0.513186\pi\)
\(684\) −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
\(687\) −172.033 + 281.339i −0.250411 + 0.409518i
\(688\) −604.038 + 604.038i −0.877962 + 0.877962i
\(689\) 109.823i 0.159394i
\(690\) 1050.47 + 498.104i 1.52242 + 0.721891i
\(691\) 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
\(693\) 61.4340 + 271.456i 0.0886493 + 0.391711i
\(694\) 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 \(0.191409\pi\)
−0.824584 + 0.565739i \(0.808591\pi\)
\(702\) 146.041 + 11.0695i 0.208035 + 0.0157685i
\(703\) 1.40592 + 1.40592i 0.00199989 + 0.00199989i
\(704\) −98.8997 −0.140483
\(705\) −133.834 375.209i −0.189836 0.532211i
\(706\) 407.822i 0.577651i
\(707\) −30.6604 + 119.776i −0.0433669 + 0.169414i
\(708\) 57.4584 93.9665i 0.0811560 0.132721i
\(709\) 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
\(717\) 31.5733 51.6344i 0.0440353 0.0720145i
\(718\) 762.337 762.337i 1.06175 1.06175i
\(719\) 639.857i 0.889927i −0.895549 0.444963i \(-0.853217\pi\)
0.895549 0.444963i \(-0.146783\pi\)
\(720\) −746.848 + 488.464i −1.03729 + 0.678423i
\(721\) −822.481 + 487.222i −1.14075 + 0.675758i
\(722\) −602.673 + 602.673i −0.834727 + 0.834727i
\(723\) 659.320 + 403.159i 0.911922 + 0.557620i
\(724\) 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
\(732\) −32.3004 + 52.8235i −0.0441262 + 0.0721632i
\(733\) 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
\(735\) 431.132 + 595.273i 0.586574 + 0.809895i
\(736\) −789.576 −1.07279
\(737\) 248.896 248.896i 0.337715 0.337715i
\(738\) 658.243 + 212.476i 0.891928 + 0.287908i
\(739\) 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 0.619987 0.784612i \(-0.287138\pi\)
−0.784612 + 0.619987i \(0.787138\pi\)
\(744\) 135.770 + 563.133i 0.182486 + 0.756899i
\(745\) −35.8374 336.685i −0.0481039 0.451927i
\(746\) 900.577i 1.20721i
\(747\) 68.1443 + 21.9965i 0.0912240 + 0.0294465i
\(748\) 97.7587 + 97.7587i 0.130693 + 0.130693i
\(749\) 36.4680 + 61.5618i 0.0486889 + 0.0821919i
\(750\) 753.611 466.940i 1.00481 0.622586i
\(751\) 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
\(753\) −299.812 + 490.307i −0.398157 + 0.651138i
\(754\) −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 \(0.516485\pi\)
\(762\) 22.2596 36.4029i 0.0292121 0.0477729i
\(763\) −848.386 217.171i −1.11191 0.284627i
\(764\) 20.0562 0.0262515
\(765\) −867.439 181.438i −1.13391 0.237173i
\(766\) 544.150i 0.710379i
\(767\) 37.4852 37.4852i