Properties

Label 105.3.k.d.62.9
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 62.9
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.d.83.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.67168 - 1.67168i) q^{2} +(-1.56503 + 2.55943i) q^{3} -1.58906i q^{4} +(0.529219 + 4.97191i) q^{5} +(1.66231 + 6.89480i) q^{6} +(6.78135 - 1.73590i) q^{7} +(4.03033 + 4.03033i) q^{8} +(-4.10134 - 8.01118i) q^{9} +O(q^{10})\) \(q+(1.67168 - 1.67168i) q^{2} +(-1.56503 + 2.55943i) q^{3} -1.58906i q^{4} +(0.529219 + 4.97191i) q^{5} +(1.66231 + 6.89480i) q^{6} +(6.78135 - 1.73590i) q^{7} +(4.03033 + 4.03033i) q^{8} +(-4.10134 - 8.01118i) q^{9} +(9.19616 + 7.42678i) q^{10} +4.41779i q^{11} +(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} +(-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} +(26.9228 + 2.04067i) q^{27} +(-2.75844 - 10.7760i) 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} +(12.2195 + 32.7976i) q^{35} +(-12.7302 + 6.51728i) q^{36} +(2.02579 + 2.02579i) q^{37} +(-1.16017 + 1.16017i) q^{38} +(-6.69171 + 1.61335i) q^{39} +(-17.9055 + 22.1714i) q^{40} +32.5085 q^{41} +(23.2414 + 43.8704i) 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} +(-41.7192 - 47.2071i) q^{63} +22.3867i q^{64} +(-7.20802 + 8.92528i) q^{65} +(-30.4598 + 7.34376i) q^{66} +(-56.3395 - 56.3395i) q^{67} +(-22.1284 + 22.1284i) q^{68} +(95.6125 - 23.0519i) q^{69} +(75.2545 + 34.4000i) q^{70} -92.7547i q^{71} +(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} +(7.66883 + 29.9586i) 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} +(31.8974 + 9.80471i) 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} +(32.4807 - 111.195i) q^{98} +(35.3917 - 18.1189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q - 48q^{15} - 24q^{16} - 92q^{18} - 60q^{21} + 112q^{22} - 72q^{25} + 88q^{28} - 108q^{30} + 416q^{36} + 72q^{37} + 300q^{42} - 328q^{43} + 32q^{46} + 148q^{51} - 748q^{57} - 392q^{58} + 544q^{60} - 220q^{63} - 648q^{67} - 8q^{70} - 8q^{72} + 500q^{78} - 948q^{81} + 672q^{85} + 1288q^{88} + 808q^{91} + 292q^{93} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.67168 1.67168i 0.835842 0.835842i −0.152466 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
\(7\) 6.78135 1.73590i 0.968764 0.247985i
\(8\) 4.03033 + 4.03033i 0.503791 + 0.503791i
\(9\) −4.10134 8.01118i −0.455705 0.890131i
\(10\) 9.19616 + 7.42678i 0.919616 + 0.742678i
\(11\) 4.41779i 0.401617i 0.979630 + 0.200809i \(0.0643570\pi\)
−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 0.766750 0.641946i \(-0.221873\pi\)
−0.641946 + 0.766750i \(0.721873\pi\)
\(14\) 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 0.166839 0.985984i \(-0.446644\pi\)
−0.985984 + 0.166839i \(0.946644\pi\)
\(18\) −20.2483 6.53602i −1.12491 0.363112i
\(19\) −0.694013 −0.0365270 −0.0182635 0.999833i \(-0.505814\pi\)
−0.0182635 + 0.999833i \(0.505814\pi\)
\(20\) 7.90067 0.840961i 0.395034 0.0420481i
\(21\) −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 \(-0.997474\pi\)
−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
\(28\) −2.75844 10.7760i −0.0985158 0.384856i
\(29\) 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 \(-0.815998\pi\)
0.837524 0.546401i \(-0.184002\pi\)
\(32\) 17.0301 17.0301i 0.532190 0.532190i
\(33\) −11.3070 6.91399i −0.342637 0.209515i
\(34\) −46.5580 −1.36935
\(35\) 12.2195 + 32.7976i 0.349130 + 0.937074i
\(36\) −12.7302 + 6.51728i −0.353618 + 0.181036i
\(37\) 2.02579 + 2.02579i 0.0547510 + 0.0547510i 0.733952 0.679201i \(-0.237674\pi\)
−0.679201 + 0.733952i \(0.737674\pi\)
\(38\) −1.16017 + 1.16017i −0.0305308 + 0.0305308i
\(39\) −6.69171 + 1.61335i −0.171582 + 0.0413679i
\(40\) −17.9055 + 22.1714i −0.447638 + 0.554285i
\(41\) 32.5085 0.792891 0.396446 0.918058i \(-0.370244\pi\)
0.396446 + 0.918058i \(0.370244\pi\)
\(42\) 23.2414 + 43.8704i 0.553366 + 1.04453i
\(43\) −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 0.478522 0.878076i \(-0.341173\pi\)
−0.878076 + 0.478522i \(0.841173\pi\)
\(48\) −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 \(-0.937270\pi\)
0.980644 0.195798i \(-0.0627296\pi\)
\(60\) −10.2124 + 21.5373i −0.170207 + 0.358955i
\(61\) 12.9880i 0.212919i 0.994317 + 0.106459i \(0.0339514\pi\)
−0.994317 + 0.106459i \(0.966049\pi\)
\(62\) −56.6314 56.6314i −0.913410 0.913410i
\(63\) −41.7192 47.2071i −0.662209 0.749319i
\(64\) 22.3867i 0.349792i
\(65\) −7.20802 + 8.92528i −0.110893 + 0.137312i
\(66\) −30.4598 + 7.34376i −0.461512 + 0.111269i
\(67\) −56.3395 56.3395i −0.840888 0.840888i 0.148086 0.988974i \(-0.452689\pi\)
−0.988974 + 0.148086i \(0.952689\pi\)
\(68\) −22.1284 + 22.1284i −0.325418 + 0.325418i
\(69\) 95.6125 23.0519i 1.38569 0.334085i
\(70\) 75.2545 + 34.4000i 1.07506 + 0.491429i
\(71\) 92.7547i 1.30640i −0.757184 0.653202i \(-0.773425\pi\)
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 \(0.125540\pi\)
0.384251 + 0.923229i \(0.374460\pi\)
\(74\) 6.77295 0.0915263
\(75\) 24.7803 70.7880i 0.330404 0.943840i
\(76\) 1.10283i 0.0145109i
\(77\) 7.66883 + 29.9586i 0.0995952 + 0.389072i
\(78\) −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 −0.672403 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
\(87\) −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 \(0.350275\pi\)
−0.453220 + 0.891399i \(0.649725\pi\)
\(90\) 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 −0.872007 0.489493i \(-0.837182\pi\)
0.489493 + 0.872007i \(0.337182\pi\)
\(98\) 32.4807 111.195i 0.331435 1.13464i
\(99\) 35.3917 18.1189i 0.357492 0.183019i
\(100\) 8.36238 + 38.8364i 0.0836238 + 0.388364i
\(101\) −17.6626 −0.174877 −0.0874384 0.996170i \(-0.527868\pi\)
−0.0874384 + 0.996170i \(0.527868\pi\)
\(102\) 72.8648 119.162i 0.714361 1.16825i
\(103\) −96.5666 96.5666i −0.937540 0.937540i 0.0606213 0.998161i \(-0.480692\pi\)
−0.998161 + 0.0606213i \(0.980692\pi\)
\(104\) 13.0780i 0.125750i
\(105\) −103.067 20.0543i −0.981591 0.190993i
\(106\) −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
\(112\) 134.482 34.4248i 1.20073 0.307364i
\(113\) −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
\(126\) −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 \(0.645200\pi\)
\(132\) −10.9867 + 17.9675i −0.0832329 + 0.136118i
\(133\) −4.70634 + 1.20473i −0.0353860 + 0.00905815i
\(134\) −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 \(-0.806876\pi\)
−0.821524 + 0.570174i \(0.806876\pi\)
\(140\) 52.1174 19.4176i 0.372267 0.138697i
\(141\) 77.4534 18.6738i 0.549315 0.132438i
\(142\) −155.057 155.057i −1.09195 1.09195i
\(143\) −7.16762 + 7.16762i −0.0501232 + 0.0501232i
\(144\) −81.3342 158.871i −0.564821 1.10327i
\(145\) 25.9971 + 244.237i 0.179290 + 1.68440i
\(146\) 319.111 2.18569
\(147\) −6.99698 + 146.833i −0.0475985 + 0.998867i
\(148\) 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 −0.746846 0.664997i \(-0.768433\pi\)
0.664997 + 0.746846i \(0.268433\pi\)
\(158\) 167.637 + 167.637i 1.06100 + 1.06100i
\(159\) 139.592 33.6551i 0.877935 0.211667i
\(160\) 93.6847 + 75.6594i 0.585529 + 0.472871i
\(161\) −197.445 116.963i −1.22637 0.726476i
\(162\) 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 0.885697 0.464263i \(-0.153681\pi\)
−0.464263 + 0.885697i \(0.653681\pi\)
\(168\) −105.769 + 56.0336i −0.629577 + 0.333533i
\(169\) 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
\(175\) −156.600 + 78.1117i −0.894857 + 0.446352i
\(176\) 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 \(-0.948619\pi\)
0.987000 0.160717i \(-0.0513808\pi\)
\(182\) 36.7849 9.41625i 0.202115 0.0517376i
\(183\) −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
\(189\) 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 \(0.0105190\pi\)
−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 \(-0.701996\pi\)
−0.592848 + 0.805314i \(0.701996\pi\)
\(200\) −119.710 77.2912i −0.598551 0.386456i
\(201\) 232.370 56.0237i 1.15607 0.278725i
\(202\) −29.5262 + 29.5262i −0.146169 + 0.146169i
\(203\) 333.123 85.2732i 1.64100 0.420065i
\(204\) −22.0044 91.2677i −0.107865 0.447391i
\(205\) 17.2041 + 161.630i 0.0839227 + 0.788437i
\(206\) −322.858 −1.56727
\(207\) −90.6371 + 280.790i −0.437860 + 1.35647i
\(208\) 32.1749 + 32.1749i 0.154687 + 0.154687i
\(209\) 3.06600i 0.0146699i
\(210\) −205.820 + 138.771i −0.980096 + 0.660815i
\(211\) −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
\(217\) −58.8067 229.731i −0.270999 1.05867i
\(218\) 209.137 + 209.137i 0.959346 + 0.959346i
\(219\) −393.663 + 94.9110i −1.79755 + 0.433384i
\(220\) 3.71519 + 34.9035i 0.0168872 + 0.158652i
\(221\) 45.1866i 0.204464i
\(222\) −10.5999 + 17.3349i −0.0477473 + 0.0780850i
\(223\) 85.1659 + 85.1659i 0.381910 + 0.381910i 0.871790 0.489880i \(-0.162959\pi\)
−0.489880 + 0.871790i \(0.662959\pi\)
\(224\) 85.9244 145.049i 0.383591 0.647541i
\(225\) 142.395 + 174.209i 0.632866 + 0.774262i
\(226\) −239.682 −1.06054
\(227\) 129.989 + 129.989i 0.572639 + 0.572639i 0.932865 0.360226i \(-0.117300\pi\)
−0.360226 + 0.932865i \(0.617300\pi\)
\(228\) −2.82261 1.72596i −0.0123799 0.00757001i
\(229\) 109.923 0.480011 0.240006 0.970771i \(-0.422851\pi\)
0.240006 + 0.970771i \(0.422851\pi\)
\(230\) −41.0173 385.350i −0.178336 1.67543i
\(231\) −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 0.0611395 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
\(238\) −315.726 + 80.8198i −1.32658 + 0.339579i
\(239\) 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 \(-0.820519\pi\)
0.845201 0.534449i \(-0.179481\pi\)
\(242\) 169.648 169.648i 0.701024 0.701024i
\(243\) −94.0713 224.053i −0.387125 0.922027i
\(244\) 20.6388 0.0845852
\(245\) 139.798 + 201.200i 0.570605 + 0.821225i
\(246\) 54.0394 + 224.140i 0.219672 + 0.911137i
\(247\) −1.12600 1.12600i −0.00455869 0.00455869i
\(248\) 136.535 136.535i 0.550544 0.550544i
\(249\) 5.59441 + 23.2040i 0.0224675 + 0.0931887i
\(250\) −263.836 133.115i −1.05534 0.532460i
\(251\) 191.569 0.763223 0.381612 0.924323i \(-0.375369\pi\)
0.381612 + 0.924323i \(0.375369\pi\)
\(252\) −75.0149 + 66.2943i −0.297678 + 0.263073i
\(253\) 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 0.983154 0.182779i \(-0.0585094\pi\)
−0.182779 + 0.983154i \(0.558509\pi\)
\(258\) −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 \(-0.936278\pi\)
0.980029 0.198854i \(-0.0637220\pi\)
\(270\) 232.430 + 218.716i 0.860854 + 0.810059i
\(271\) 187.036i 0.690171i 0.938571 + 0.345085i \(0.112150\pi\)
−0.938571 + 0.345085i \(0.887850\pi\)
\(272\) −276.158 276.158i −1.01529 1.01529i
\(273\) −42.5782 + 22.5568i −0.155964 + 0.0826256i
\(274\) 449.309i 1.63981i
\(275\) −23.2485 107.970i −0.0845399 0.392619i
\(276\) −36.6308 151.934i −0.132720 0.550485i
\(277\) 95.7717 + 95.7717i 0.345746 + 0.345746i 0.858522 0.512776i \(-0.171383\pi\)
−0.512776 + 0.858522i \(0.671383\pi\)
\(278\) −381.786 + 381.786i −1.37333 + 1.37333i
\(279\) −271.393 + 138.941i −0.972736 + 0.497995i
\(280\) −82.9364 + 181.434i −0.296201 + 0.647979i
\(281\) 140.834i 0.501189i 0.968092 + 0.250594i \(0.0806261\pi\)
−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 0.245813 0.969317i \(-0.420945\pi\)
−0.969317 + 0.245813i \(0.920945\pi\)
\(284\) −147.393 −0.518989
\(285\) 9.40630 + 4.46022i 0.0330046 + 0.0156499i
\(286\) 23.9640i 0.0837902i
\(287\) 220.452 56.4314i 0.768124 0.196625i
\(288\) −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 −0.923517 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
\(297\) −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 \(-0.394008\pi\)
0.945071 0.326865i \(-0.105992\pi\)
\(308\) 47.6060 12.1862i 0.154565 0.0395657i
\(309\) 398.285 96.0253i 1.28895 0.310761i
\(310\) 251.596 311.537i 0.811600 1.00496i
\(311\) −314.164 −1.01017 −0.505087 0.863068i \(-0.668540\pi\)
−0.505087 + 0.863068i \(0.668540\pi\)
\(312\) −33.4721 20.4675i −0.107282 0.0656009i
\(313\) −138.521 138.521i −0.442558 0.442558i 0.450313 0.892871i \(-0.351312\pi\)
−0.892871 + 0.450313i \(0.851312\pi\)
\(314\) 42.9635i 0.136827i
\(315\) 212.631 232.407i 0.675019 0.737800i
\(316\) 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
\(322\) −525.591 + 134.541i −1.63227 + 0.417830i
\(323\) 9.66445 + 9.66445i 0.0299209 + 0.0299209i
\(324\) 104.422 + 75.2547i 0.322291 + 0.232268i
\(325\) −48.1904 31.1142i −0.148278 0.0957361i
\(326\) 469.248i 1.43941i
\(327\) −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
\(336\) −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
\(342\) 14.0526 + 4.53608i 0.0410894 + 0.0132634i
\(343\) 250.548 234.253i 0.730461 0.682955i
\(344\) −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 \(-0.346566\pi\)
0.463576 + 0.886057i \(0.346566\pi\)
\(350\) −131.208 + 392.364i −0.374879 + 1.12104i
\(351\) 40.3698 + 46.9916i 0.115014 + 0.133879i
\(352\) 75.2353 + 75.2353i 0.213737 + 0.213737i
\(353\) −121.979 + 121.979i −0.345550 + 0.345550i −0.858449 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
\(357\) 365.449 193.605i 1.02367 0.542312i
\(358\) 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 −0.775314 0.631576i \(-0.782409\pi\)
0.631576 + 0.775314i \(0.282409\pi\)
\(368\) −459.721 459.721i −1.24924 1.24924i
\(369\) −133.329 260.432i −0.361324 0.705777i
\(370\) 3.58438 + 33.6745i 0.00968750 + 0.0910122i
\(371\) −288.264 170.762i −0.776993 0.460276i
\(372\) 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
\(378\) 256.133 366.118i 0.677600 0.968567i
\(379\) 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
\(385\) −144.893 + 53.9834i −0.376345 + 0.140217i
\(386\) 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
\(392\) 268.085 + 78.3089i 0.683889 + 0.199768i
\(393\) 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 \(0.559020\pi\)
−0.982859 + 0.184357i \(0.940980\pi\)
\(398\) −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 \(0.222725\pi\)
−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 \(-0.453499\pi\)
0.145570 + 0.989348i \(0.453499\pi\)
\(410\) 298.954 + 241.434i 0.729155 + 0.588863i
\(411\) −133.635 554.278i −0.325145 1.34861i
\(412\) −153.450 + 153.450i −0.372452 + 0.372452i
\(413\) −40.1064 156.677i −0.0971099 0.379364i
\(414\) 317.876 + 620.909i 0.767816 + 1.49978i
\(415\) 30.9491 + 24.9943i 0.0745760 + 0.0602273i
\(416\) 55.2607 0.132838
\(417\) 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 \(0.338412\pi\)
−0.486120 + 0.873892i \(0.661588\pi\)
\(420\) −31.8675 + 163.780i −0.0758749 + 0.389952i
\(421\) 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
\(427\) 22.5459 + 88.0764i 0.0528007 + 0.206268i
\(428\) −11.4856 11.4856i −0.0268354 0.0268354i
\(429\) −7.12744 29.5626i −0.0166141 0.0689104i
\(430\) −506.320 + 53.8936i −1.17749 + 0.125334i
\(431\) 205.822i 0.477546i 0.971075 + 0.238773i \(0.0767452\pi\)
−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 0.284603 0.958646i \(-0.408138\pi\)
−0.958646 + 0.284603i \(0.908138\pi\)
\(434\) −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 \(-0.542423\pi\)
−0.132882 + 0.991132i \(0.542423\pi\)
\(440\) −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 0.949719 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
\(448\) 38.8610 + 151.812i 0.0867433 + 0.338866i
\(449\) −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
\(455\) −33.3867 + 73.0378i −0.0733775 + 0.160523i
\(456\) 11.5365 2.78142i 0.0252994 0.00609961i
\(457\) 461.473 + 461.473i 1.00979 + 1.00979i 0.999952 + 0.00983627i \(0.00313103\pi\)
0.00983627 + 0.999952i \(0.496869\pi\)
\(458\) 183.756 183.756i 0.401214 0.401214i
\(459\) −346.495 403.330i −0.754891 0.878714i
\(460\) −202.647 163.657i −0.440537 0.355776i
\(461\) 788.797 1.71106 0.855528 0.517757i \(-0.173233\pi\)
0.855528 + 0.517757i \(0.173233\pi\)
\(462\) −193.810 + 102.676i −0.419503 + 0.222242i
\(463\) −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 0.310194 0.950673i \(-0.399606\pi\)
−0.950673 + 0.310194i \(0.899606\pi\)
\(468\) −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 \(-0.797666\pi\)
0.804685 0.593702i \(-0.202334\pi\)
\(480\) −340.264 + 121.370i −0.708884 + 0.252854i
\(481\) 6.57345i 0.0136662i
\(482\) −430.633 430.633i −0.893430 0.893430i
\(483\) 608.366 322.296i 1.25956 0.667279i
\(484\) 161.263i 0.333188i
\(485\) −204.113 164.841i −0.420852 0.339878i
\(486\) −531.803 217.288i −1.09424 0.447094i
\(487\) 382.818 + 382.818i 0.786073 + 0.786073i 0.980848 0.194775i \(-0.0623976\pi\)
−0.194775 + 0.980848i \(0.562398\pi\)
\(488\) −52.3461 + 52.3461i −0.107267 + 0.107267i
\(489\) −139.565 578.875i −0.285409 1.18379i
\(490\) 570.042 + 102.644i 1.16335 + 0.209479i
\(491\) 1.38553i 0.00282185i 0.999999 + 0.00141093i \(0.000449112\pi\)
−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
\(497\) −161.012 629.002i −0.323969 1.26560i
\(498\) 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 −0.372111 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
\(507\) 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 \(0.161218\pi\)
−0.874457 + 0.485104i \(0.838782\pi\)
\(510\) 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
\(518\) 45.9297 11.7571i 0.0886674 0.0226972i
\(519\) −74.5612 309.258i −0.143663 0.595873i
\(520\) −65.0226 + 6.92112i −0.125043 + 0.0133098i
\(521\) −16.2593 −0.0312079 −0.0156039 0.999878i \(-0.504967\pi\)
−0.0156039 + 0.999878i \(0.504967\pi\)
\(522\) −994.667 321.072i −1.90549 0.615080i
\(523\) 629.367 + 629.367i 1.20338 + 1.20338i 0.973132 + 0.230246i \(0.0739530\pi\)
0.230246 + 0.973132i \(0.426047\pi\)
\(524\) 183.397i 0.349993i
\(525\) 45.1631 523.054i 0.0860249 0.996293i
\(526\) −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
\(532\) 1.91439 + 7.47866i 0.00359849 + 0.0140576i
\(533\) 52.7433 + 52.7433i 0.0989555 + 0.0989555i
\(534\) −1093.99 + 263.758i −2.04867 + 0.493928i
\(535\) 39.7616 + 32.1113i 0.0743208 + 0.0600212i
\(536\) 454.134i 0.847265i
\(537\) −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
\(546\) −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
\(552\) 478.257 + 292.443i 0.866407 + 0.529788i
\(553\) 174.077 + 680.037i 0.314786 + 1.22972i
\(554\) 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
\(560\) 242.327 + 650.413i 0.432728 + 1.16145i
\(561\) 61.1750 + 253.736i 0.109046 + 0.452292i
\(562\) 235.430 + 235.430i 0.418915 + 0.418915i
\(563\) 689.690 689.690i 1.22503 1.22503i 0.259204 0.965823i \(-0.416540\pi\)
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
\(567\) −207.080 + 527.832i −0.365220 + 0.930921i
\(568\) 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 −0.568610 0.822607i \(-0.692519\pi\)
0.822607 + 0.568610i \(0.192519\pi\)
\(578\) 165.225 + 165.225i 0.285856 + 0.285856i
\(579\) 210.381 + 872.601i 0.363353 + 1.50708i
\(580\) 388.108 41.3109i 0.669152 0.0712257i
\(581\) 28.3854 47.9175i 0.0488561 0.0824742i
\(582\) −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 0.776346 0.630307i \(-0.217071\pi\)
−0.630307 + 0.776346i \(0.717071\pi\)
\(588\) 233.327 + 11.1186i 0.396815 + 0.0189092i
\(589\) 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
\(595\) 286.559 626.885i 0.481612 1.05359i
\(596\) 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 \(0.189767\pi\)
−0.827492 + 0.561478i \(0.810233\pi\)
\(602\) 176.777 + 690.585i 0.293649 + 1.14715i
\(603\) −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 −0.965827 0.259189i \(-0.916545\pi\)
0.259189 + 0.965827i \(0.416545\pi\)
\(608\) −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
\(612\) 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 \(-0.218406\pi\)
0.773695 + 0.633558i \(0.218406\pi\)
\(620\) −28.4891 267.650i −0.0459502 0.431693i
\(621\) −576.812 671.425i −0.928844 1.08120i
\(622\) −525.184 + 525.184i −0.844347 + 0.844347i
\(623\) 275.433 + 1075.99i 0.442107 + 1.72711i
\(624\) −132.704 + 31.9945i −0.212667 + 0.0512733i
\(625\) 569.613 257.228i 0.911381 0.411564i
\(626\) −463.126 −0.739817
\(627\) 7.84721 + 4.79840i 0.0125155 + 0.00765295i
\(628\) 20.4200 + 20.4200i 0.0325159 + 0.0325159i
\(629\) 56.4200i 0.0896980i
\(630\) −33.0596 743.963i −0.0524756 1.18089i
\(631\) −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
\(637\) 107.920 + 31.5239i 0.169419 + 0.0494881i
\(638\) 362.784 + 362.784i 0.568627 + 0.568627i
\(639\) −743.074 + 380.419i −1.16287 + 0.595334i
\(640\) −468.899 + 580.610i −0.732654 + 0.907204i
\(641\) 618.098i 0.964272i −0.876096 0.482136i \(-0.839861\pi\)
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 0.499709 0.866193i \(-0.333440\pi\)
−0.866193 + 0.499709i \(0.833440\pi\)
\(644\) −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 0.600300 0.799775i \(-0.295048\pi\)
−0.799775 + 0.600300i \(0.795048\pi\)
\(648\) −455.714 + 73.9775i −0.703263 + 0.114163i
\(649\) 102.069 0.157272
\(650\) −132.572 + 28.5459i −0.203957 + 0.0439167i
\(651\) 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 0.0669099 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
\(658\) −425.768 + 108.989i −0.647064 + 0.165636i
\(659\) −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 \(0.0860734\pi\)
−0.963662 + 0.267124i \(0.913927\pi\)
\(662\) −162.454 + 162.454i −0.245399 + 0.245399i
\(663\) 115.652 + 70.7185i 0.174437 + 0.106664i
\(664\) 45.3488 0.0682964
\(665\) −8.48052 22.7620i −0.0127527 0.0342285i
\(666\) −27.7782 54.2593i −0.0417090 0.0814704i
\(667\) −1138.77 1138.77i −1.70730 1.70730i
\(668\) 111.837 111.837i 0.167421 0.167421i
\(669\) −351.263 + 84.6885i −0.525058 + 0.126590i
\(670\) −99.6858 936.529i −0.148785 1.39780i
\(671\) −57.3785 −0.0855119
\(672\) 236.769 + 446.924i 0.352334 + 0.665066i
\(673\) 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 \(-0.927661\pi\)
−0.225309 0.974287i \(-0.572339\pi\)
\(678\) 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 \(-0.604429\pi\)
0.322219 0.946665i \(-0.395571\pi\)
\(692\) 119.150 + 119.150i 0.172182 + 0.172182i
\(693\) 208.551 184.307i 0.300939 0.265955i
\(694\) 142.180i 0.204871i
\(695\) −120.865 1135.50i −0.173907 1.63382i
\(696\) −816.576 + 196.874i −1.17324 + 0.282865i
\(697\) −452.697 452.697i −0.649493 0.649493i
\(698\) 540.917 540.917i 0.774953 0.774953i
\(699\) 900.447 217.095i 1.28819 0.310579i
\(700\) 124.124 + 248.847i 0.177320 + 0.355496i
\(701\) 793.166i 1.13148i 0.824584 + 0.565739i \(0.191409\pi\)
−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
\(707\) −119.776 + 30.6604i −0.169414 + 0.0433669i
\(708\) 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
\(714\) 287.269 934.563i 0.402337 1.30891i
\(715\) −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 \(0.146783\pi\)
−0.895549 + 0.444963i \(0.853217\pi\)
\(720\) 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 −0.750520 0.660848i \(-0.770197\pi\)
0.660848 + 0.750520i \(0.270197\pi\)
\(728\) 22.7020 + 88.6863i 0.0311841 + 0.121822i
\(729\) 720.671 + 109.881i 0.988575 + 0.150729i
\(730\) 168.880 + 1586.59i 0.231342 + 2.17342i
\(731\) 848.314 1.16048
\(732\) −32.3004 + 52.8235i −0.0441262 + 0.0721632i
\(733\) −631.927 631.927i −0.862110 0.862110i 0.129473 0.991583i \(-0.458671\pi\)
−0.991583 + 0.129473i \(0.958671\pi\)
\(734\) 176.370i 0.240286i
\(735\) −733.746 + 42.9187i −0.998294 + 0.0583928i
\(736\) −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
\(742\) −767.348 + 196.427i −1.03416 + 0.264726i
\(743\) −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
\(756\) −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 \(0.483515\pi\)
\(762\) −22.2596 + 36.4029i −0.0292121 + 0.0477729i
\(763\) 217.171 + 848.386i 0.284627 + 1.11191i
\(764\) 20.0562 0.0262515
\(765\) −867.439 181.438i −1.13391 0.237173i
\(766\) 544.150i 0.710379i
\(767\) 37.4852 37.4852i 0.0488725