Properties

Label 105.3.t.b.11.16
Level 105
Weight 3
Character 105.11
Analytic conductor 2.861
Analytic rank 0
Dimension 36
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.16
Character \(\chi\) \(=\) 105.11
Dual form 105.3.t.b.86.16

$q$-expansion

\(f(q)\) \(=\) \(q+(2.60397 - 1.50340i) q^{2} +(-0.740030 - 2.90729i) q^{3} +(2.52044 - 4.36553i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-6.29785 - 6.45794i) q^{6} +(-0.494553 - 6.98251i) q^{7} -3.12973i q^{8} +(-7.90471 + 4.30297i) q^{9} +O(q^{10})\) \(q+(2.60397 - 1.50340i) q^{2} +(-0.740030 - 2.90729i) q^{3} +(2.52044 - 4.36553i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-6.29785 - 6.45794i) q^{6} +(-0.494553 - 6.98251i) q^{7} -3.12973i q^{8} +(-7.90471 + 4.30297i) q^{9} +(-3.36171 + 5.82265i) q^{10} +(16.3666 + 9.44928i) q^{11} +(-14.5571 - 4.09704i) q^{12} +17.2837 q^{13} +(-11.7853 - 17.4387i) q^{14} +(4.68351 + 4.80257i) q^{15} +(5.37652 + 9.31241i) q^{16} +(-21.7883 - 12.5795i) q^{17} +(-14.1145 + 23.0888i) q^{18} +(-1.28629 - 2.22791i) q^{19} +11.2718i q^{20} +(-19.9342 + 6.60507i) q^{21} +56.8243 q^{22} +(-0.196138 + 0.113240i) q^{23} +(-9.09904 + 2.31609i) q^{24} +(2.50000 - 4.33013i) q^{25} +(45.0062 - 25.9844i) q^{26} +(18.3597 + 19.7970i) q^{27} +(-31.7288 - 15.4400i) q^{28} +11.7618i q^{29} +(19.4159 + 5.46454i) q^{30} +(-26.5324 + 45.9555i) q^{31} +(38.8423 + 22.4256i) q^{32} +(15.3600 - 54.5753i) q^{33} -75.6480 q^{34} +(8.76438 + 12.9686i) q^{35} +(-1.13862 + 45.3536i) q^{36} +(-5.41981 - 9.38738i) q^{37} +(-6.69890 - 3.86761i) q^{38} +(-12.7904 - 50.2488i) q^{39} +(3.49914 + 6.06069i) q^{40} -4.80764i q^{41} +(-41.9780 + 47.1686i) q^{42} -1.49099 q^{43} +(82.5022 - 47.6327i) q^{44} +(10.4965 - 17.1704i) q^{45} +(-0.340492 + 0.589749i) q^{46} +(-0.114843 + 0.0663044i) q^{47} +(23.0951 - 22.5226i) q^{48} +(-48.5108 + 6.90644i) q^{49} -15.0340i q^{50} +(-20.4482 + 72.6541i) q^{51} +(43.5625 - 75.4525i) q^{52} +(-28.3732 - 16.3813i) q^{53} +(77.5710 + 23.9487i) q^{54} -42.2585 q^{55} +(-21.8533 + 1.54782i) q^{56} +(-5.52531 + 5.38834i) q^{57} +(17.6828 + 30.6274i) q^{58} +(-35.6419 - 20.5778i) q^{59} +(32.7703 - 8.34143i) q^{60} +(-3.00507 - 5.20494i) q^{61} +159.556i q^{62} +(33.9548 + 53.0667i) q^{63} +91.8467 q^{64} +(-33.4697 + 19.3238i) q^{65} +(-42.0517 - 165.205i) q^{66} +(-48.0577 + 83.2384i) q^{67} +(-109.832 + 63.4116i) q^{68} +(0.474371 + 0.486430i) q^{69} +(42.3193 + 20.5936i) q^{70} -81.2784i q^{71} +(13.4671 + 24.7396i) q^{72} +(6.02722 - 10.4395i) q^{73} +(-28.2260 - 16.2963i) q^{74} +(-14.4390 - 4.06381i) q^{75} -12.9680 q^{76} +(57.8855 - 118.953i) q^{77} +(-108.850 - 111.617i) q^{78} +(-43.6564 - 75.6150i) q^{79} +(-20.8232 - 12.0223i) q^{80} +(43.9689 - 68.0274i) q^{81} +(-7.22782 - 12.5190i) q^{82} +34.0479i q^{83} +(-21.4084 + 103.671i) q^{84} +56.2571 q^{85} +(-3.88250 + 2.24156i) q^{86} +(34.1951 - 8.70410i) q^{87} +(29.5737 - 51.2231i) q^{88} +(14.2548 - 8.23003i) q^{89} +(1.51867 - 60.4917i) q^{90} +(-8.54770 - 120.684i) q^{91} +1.14166i q^{92} +(153.241 + 43.1291i) q^{93} +(-0.199364 + 0.345309i) q^{94} +(4.98177 + 2.87622i) q^{95} +(36.4534 - 129.522i) q^{96} +48.3801 q^{97} +(-115.938 + 90.9155i) q^{98} +(-170.033 - 4.26874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + O(q^{10}) \) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + 20q^{10} - 42q^{12} - 100q^{13} + 20q^{15} - 12q^{16} - 14q^{18} + 50q^{19} - 12q^{21} + 256q^{22} - 140q^{24} + 90q^{25} + 4q^{27} - 48q^{28} + 60q^{30} - 82q^{31} - 76q^{33} - 64q^{34} + 296q^{36} - 26q^{37} - 130q^{39} - 60q^{40} - 98q^{42} - 204q^{43} + 40q^{45} + 28q^{46} + 532q^{48} - 382q^{49} + 208q^{51} + 200q^{52} - 44q^{54} - 160q^{55} + 252q^{57} + 264q^{58} - 130q^{60} - 324q^{61} - 258q^{63} - 24q^{64} - 164q^{66} - 142q^{67} - 112q^{69} + 200q^{70} - 322q^{72} + 386q^{73} - 20q^{75} - 424q^{76} - 440q^{78} + 334q^{79} + 186q^{81} - 68q^{82} + 80q^{84} - 200q^{85} + 342q^{87} + 180q^{88} + 100q^{90} + 46q^{91} - 2q^{93} + 324q^{94} + 732q^{96} + 1616q^{97} + 384q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.60397 1.50340i 1.30199 0.751701i 0.321241 0.946998i \(-0.395900\pi\)
0.980744 + 0.195296i \(0.0625668\pi\)
\(3\) −0.740030 2.90729i −0.246677 0.969098i
\(4\) 2.52044 4.36553i 0.630110 1.09138i
\(5\) −1.93649 + 1.11803i −0.387298 + 0.223607i
\(6\) −6.29785 6.45794i −1.04964 1.07632i
\(7\) −0.494553 6.98251i −0.0706504 0.997501i
\(8\) 3.12973i 0.391216i
\(9\) −7.90471 + 4.30297i −0.878301 + 0.478108i
\(10\) −3.36171 + 5.82265i −0.336171 + 0.582265i
\(11\) 16.3666 + 9.44928i 1.48788 + 0.859025i 0.999904 0.0138346i \(-0.00440384\pi\)
0.487971 + 0.872860i \(0.337737\pi\)
\(12\) −14.5571 4.09704i −1.21309 0.341420i
\(13\) 17.2837 1.32951 0.664757 0.747059i \(-0.268535\pi\)
0.664757 + 0.747059i \(0.268535\pi\)
\(14\) −11.7853 17.4387i −0.841809 1.24562i
\(15\) 4.68351 + 4.80257i 0.312234 + 0.320171i
\(16\) 5.37652 + 9.31241i 0.336033 + 0.582026i
\(17\) −21.7883 12.5795i −1.28166 0.739969i −0.304511 0.952509i \(-0.598493\pi\)
−0.977152 + 0.212540i \(0.931826\pi\)
\(18\) −14.1145 + 23.0888i −0.784141 + 1.28271i
\(19\) −1.28629 2.22791i −0.0676993 0.117259i 0.830189 0.557482i \(-0.188233\pi\)
−0.897888 + 0.440224i \(0.854899\pi\)
\(20\) 11.2718i 0.563588i
\(21\) −19.9342 + 6.60507i −0.949248 + 0.314527i
\(22\) 56.8243 2.58292
\(23\) −0.196138 + 0.113240i −0.00852774 + 0.00492349i −0.504258 0.863553i \(-0.668234\pi\)
0.495730 + 0.868477i \(0.334901\pi\)
\(24\) −9.09904 + 2.31609i −0.379126 + 0.0965038i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) 45.0062 25.9844i 1.73101 0.999398i
\(27\) 18.3597 + 19.7970i 0.679989 + 0.733222i
\(28\) −31.7288 15.4400i −1.13317 0.551429i
\(29\) 11.7618i 0.405580i 0.979222 + 0.202790i \(0.0650009\pi\)
−0.979222 + 0.202790i \(0.934999\pi\)
\(30\) 19.4159 + 5.46454i 0.647198 + 0.182151i
\(31\) −26.5324 + 45.9555i −0.855885 + 1.48244i 0.0199372 + 0.999801i \(0.493653\pi\)
−0.875822 + 0.482635i \(0.839680\pi\)
\(32\) 38.8423 + 22.4256i 1.21382 + 0.700800i
\(33\) 15.3600 54.5753i 0.465455 1.65380i
\(34\) −75.6480 −2.22494
\(35\) 8.76438 + 12.9686i 0.250411 + 0.370533i
\(36\) −1.13862 + 45.3536i −0.0316283 + 1.25982i
\(37\) −5.41981 9.38738i −0.146481 0.253713i 0.783443 0.621463i \(-0.213461\pi\)
−0.929925 + 0.367750i \(0.880128\pi\)
\(38\) −6.69890 3.86761i −0.176287 0.101779i
\(39\) −12.7904 50.2488i −0.327960 1.28843i
\(40\) 3.49914 + 6.06069i 0.0874785 + 0.151517i
\(41\) 4.80764i 0.117260i −0.998280 0.0586298i \(-0.981327\pi\)
0.998280 0.0586298i \(-0.0186731\pi\)
\(42\) −41.9780 + 47.1686i −0.999477 + 1.12306i
\(43\) −1.49099 −0.0346742 −0.0173371 0.999850i \(-0.505519\pi\)
−0.0173371 + 0.999850i \(0.505519\pi\)
\(44\) 82.5022 47.6327i 1.87505 1.08256i
\(45\) 10.4965 17.1704i 0.233257 0.381564i
\(46\) −0.340492 + 0.589749i −0.00740200 + 0.0128206i
\(47\) −0.114843 + 0.0663044i −0.00244346 + 0.00141073i −0.501221 0.865319i \(-0.667116\pi\)
0.498778 + 0.866730i \(0.333782\pi\)
\(48\) 23.0951 22.5226i 0.481148 0.469221i
\(49\) −48.5108 + 6.90644i −0.990017 + 0.140948i
\(50\) 15.0340i 0.300681i
\(51\) −20.4482 + 72.6541i −0.400946 + 1.42459i
\(52\) 43.5625 75.4525i 0.837741 1.45101i
\(53\) −28.3732 16.3813i −0.535344 0.309081i 0.207846 0.978162i \(-0.433355\pi\)
−0.743190 + 0.669081i \(0.766688\pi\)
\(54\) 77.5710 + 23.9487i 1.43650 + 0.443495i
\(55\) −42.2585 −0.768336
\(56\) −21.8533 + 1.54782i −0.390238 + 0.0276396i
\(57\) −5.52531 + 5.38834i −0.0969352 + 0.0945322i
\(58\) 17.6828 + 30.6274i 0.304875 + 0.528059i
\(59\) −35.6419 20.5778i −0.604100 0.348777i 0.166553 0.986032i \(-0.446736\pi\)
−0.770653 + 0.637255i \(0.780070\pi\)
\(60\) 32.7703 8.34143i 0.546172 0.139024i
\(61\) −3.00507 5.20494i −0.0492635 0.0853269i 0.840342 0.542056i \(-0.182354\pi\)
−0.889606 + 0.456729i \(0.849021\pi\)
\(62\) 159.556i 2.57348i
\(63\) 33.9548 + 53.0667i 0.538965 + 0.842328i
\(64\) 91.8467 1.43511
\(65\) −33.4697 + 19.3238i −0.514919 + 0.297289i
\(66\) −42.0517 165.205i −0.637146 2.50310i
\(67\) −48.0577 + 83.2384i −0.717279 + 1.24236i 0.244794 + 0.969575i \(0.421280\pi\)
−0.962074 + 0.272789i \(0.912054\pi\)
\(68\) −109.832 + 63.4116i −1.61518 + 0.932523i
\(69\) 0.474371 + 0.486430i 0.00687494 + 0.00704971i
\(70\) 42.3193 + 20.5936i 0.604561 + 0.294194i
\(71\) 81.2784i 1.14477i −0.819986 0.572383i \(-0.806019\pi\)
0.819986 0.572383i \(-0.193981\pi\)
\(72\) 13.4671 + 24.7396i 0.187043 + 0.343605i
\(73\) 6.02722 10.4395i 0.0825647 0.143006i −0.821786 0.569796i \(-0.807022\pi\)
0.904351 + 0.426790i \(0.140356\pi\)
\(74\) −28.2260 16.2963i −0.381433 0.220220i
\(75\) −14.4390 4.06381i −0.192520 0.0541841i
\(76\) −12.9680 −0.170632
\(77\) 57.8855 118.953i 0.751760 1.54485i
\(78\) −108.850 111.617i −1.39551 1.43099i
\(79\) −43.6564 75.6150i −0.552612 0.957152i −0.998085 0.0618570i \(-0.980298\pi\)
0.445473 0.895295i \(-0.353036\pi\)
\(80\) −20.8232 12.0223i −0.260290 0.150278i
\(81\) 43.9689 68.0274i 0.542826 0.839845i
\(82\) −7.22782 12.5190i −0.0881441 0.152670i
\(83\) 34.0479i 0.410216i 0.978739 + 0.205108i \(0.0657545\pi\)
−0.978739 + 0.205108i \(0.934245\pi\)
\(84\) −21.4084 + 103.671i −0.254861 + 1.23418i
\(85\) 56.2571 0.661848
\(86\) −3.88250 + 2.24156i −0.0451454 + 0.0260647i
\(87\) 34.1951 8.70410i 0.393047 0.100047i
\(88\) 29.5737 51.2231i 0.336064 0.582080i
\(89\) 14.2548 8.23003i 0.160167 0.0924722i −0.417774 0.908551i \(-0.637190\pi\)
0.577941 + 0.816079i \(0.303856\pi\)
\(90\) 1.51867 60.4917i 0.0168741 0.672130i
\(91\) −8.54770 120.684i −0.0939308 1.32619i
\(92\) 1.14166i 0.0124094i
\(93\) 153.241 + 43.1291i 1.64775 + 0.463754i
\(94\) −0.199364 + 0.345309i −0.00212090 + 0.00367350i
\(95\) 4.98177 + 2.87622i 0.0524396 + 0.0302760i
\(96\) 36.4534 129.522i 0.379723 1.34918i
\(97\) 48.3801 0.498763 0.249382 0.968405i \(-0.419773\pi\)
0.249382 + 0.968405i \(0.419773\pi\)
\(98\) −115.938 + 90.9155i −1.18304 + 0.927709i
\(99\) −170.033 4.26874i −1.71751 0.0431186i
\(100\) −12.6022 21.8277i −0.126022 0.218277i
\(101\) −2.00405 1.15704i −0.0198421 0.0114558i 0.490046 0.871696i \(-0.336980\pi\)
−0.509888 + 0.860241i \(0.670313\pi\)
\(102\) 55.9818 + 219.931i 0.548841 + 2.15619i
\(103\) 51.9063 + 89.9043i 0.503944 + 0.872857i 0.999990 + 0.00456054i \(0.00145167\pi\)
−0.496045 + 0.868297i \(0.665215\pi\)
\(104\) 54.0932i 0.520127i
\(105\) 31.2177 35.0778i 0.297312 0.334074i
\(106\) −98.5107 −0.929346
\(107\) 72.0244 41.5833i 0.673126 0.388629i −0.124134 0.992265i \(-0.539615\pi\)
0.797260 + 0.603636i \(0.206282\pi\)
\(108\) 132.699 30.2527i 1.22869 0.280118i
\(109\) 13.0273 22.5640i 0.119517 0.207009i −0.800059 0.599921i \(-0.795199\pi\)
0.919576 + 0.392911i \(0.128532\pi\)
\(110\) −110.040 + 63.5315i −1.00036 + 0.577559i
\(111\) −23.2811 + 22.7039i −0.209739 + 0.204540i
\(112\) 62.3650 42.1471i 0.556830 0.376313i
\(113\) 78.0189i 0.690433i −0.938523 0.345216i \(-0.887806\pi\)
0.938523 0.345216i \(-0.112194\pi\)
\(114\) −6.28690 + 22.3378i −0.0551483 + 0.195946i
\(115\) 0.253213 0.438578i 0.00220185 0.00381372i
\(116\) 51.3466 + 29.6450i 0.442643 + 0.255560i
\(117\) −136.623 + 74.3712i −1.16771 + 0.635651i
\(118\) −123.747 −1.04870
\(119\) −77.0608 + 158.358i −0.647570 + 1.33074i
\(120\) 15.0307 14.6581i 0.125256 0.122151i
\(121\) 118.078 + 204.517i 0.975849 + 1.69022i
\(122\) −15.6502 9.03567i −0.128281 0.0740629i
\(123\) −13.9772 + 3.55780i −0.113636 + 0.0289252i
\(124\) 133.747 + 231.656i 1.07860 + 1.86820i
\(125\) 11.1803i 0.0894427i
\(126\) 168.198 + 87.1363i 1.33490 + 0.691558i
\(127\) 44.9179 0.353684 0.176842 0.984239i \(-0.443412\pi\)
0.176842 + 0.984239i \(0.443412\pi\)
\(128\) 83.7970 48.3802i 0.654664 0.377970i
\(129\) 1.10338 + 4.33475i 0.00855332 + 0.0336027i
\(130\) −58.1028 + 100.637i −0.446944 + 0.774131i
\(131\) −27.3345 + 15.7816i −0.208661 + 0.120470i −0.600689 0.799483i \(-0.705107\pi\)
0.392028 + 0.919953i \(0.371774\pi\)
\(132\) −199.536 204.609i −1.51164 1.55007i
\(133\) −14.9203 + 10.0833i −0.112183 + 0.0758145i
\(134\) 289.000i 2.15672i
\(135\) −57.6871 17.8099i −0.427312 0.131925i
\(136\) −39.3703 + 68.1914i −0.289487 + 0.501407i
\(137\) −105.015 60.6306i −0.766535 0.442559i 0.0651022 0.997879i \(-0.479263\pi\)
−0.831637 + 0.555319i \(0.812596\pi\)
\(138\) 1.96655 + 0.553478i 0.0142503 + 0.00401071i
\(139\) 269.674 1.94010 0.970049 0.242910i \(-0.0781021\pi\)
0.970049 + 0.242910i \(0.0781021\pi\)
\(140\) 78.7051 5.57448i 0.562179 0.0398177i
\(141\) 0.277753 + 0.284814i 0.00196988 + 0.00201996i
\(142\) −122.194 211.647i −0.860523 1.49047i
\(143\) 282.876 + 163.318i 1.97815 + 1.14209i
\(144\) −82.5708 50.4769i −0.573409 0.350534i
\(145\) −13.1501 22.7767i −0.0906905 0.157080i
\(146\) 36.2454i 0.248256i
\(147\) 55.9785 + 135.924i 0.380806 + 0.924655i
\(148\) −54.6412 −0.369197
\(149\) 82.9520 47.8924i 0.556725 0.321425i −0.195105 0.980782i \(-0.562505\pi\)
0.751830 + 0.659357i \(0.229171\pi\)
\(150\) −43.7083 + 11.1256i −0.291389 + 0.0741709i
\(151\) −115.680 + 200.364i −0.766095 + 1.32691i 0.173571 + 0.984821i \(0.444469\pi\)
−0.939666 + 0.342093i \(0.888864\pi\)
\(152\) −6.97276 + 4.02573i −0.0458734 + 0.0264850i
\(153\) 226.359 + 5.68282i 1.47947 + 0.0371426i
\(154\) −28.1026 396.776i −0.182484 2.57647i
\(155\) 118.657i 0.765527i
\(156\) −251.600 70.8119i −1.61282 0.453923i
\(157\) −45.7767 + 79.2876i −0.291571 + 0.505017i −0.974182 0.225766i \(-0.927511\pi\)
0.682610 + 0.730783i \(0.260845\pi\)
\(158\) −227.360 131.266i −1.43899 0.830799i
\(159\) −26.6282 + 94.6119i −0.167473 + 0.595043i
\(160\) −100.290 −0.626815
\(161\) 0.887703 + 1.31353i 0.00551368 + 0.00815859i
\(162\) 12.2212 243.244i 0.0754393 1.50151i
\(163\) −96.9595 167.939i −0.594844 1.03030i −0.993569 0.113229i \(-0.963881\pi\)
0.398725 0.917070i \(-0.369453\pi\)
\(164\) −20.9879 12.1174i −0.127975 0.0738864i
\(165\) 31.2725 + 122.858i 0.189530 + 0.744592i
\(166\) 51.1877 + 88.6598i 0.308360 + 0.534095i
\(167\) 117.515i 0.703681i 0.936060 + 0.351840i \(0.114444\pi\)
−0.936060 + 0.351840i \(0.885556\pi\)
\(168\) 20.6721 + 62.3887i 0.123048 + 0.371361i
\(169\) 129.726 0.767610
\(170\) 146.492 84.5771i 0.861716 0.497512i
\(171\) 19.7544 + 12.0762i 0.115523 + 0.0706209i
\(172\) −3.75796 + 6.50897i −0.0218486 + 0.0378429i
\(173\) 77.1460 44.5403i 0.445931 0.257458i −0.260179 0.965560i \(-0.583782\pi\)
0.706110 + 0.708102i \(0.250448\pi\)
\(174\) 75.9572 74.0742i 0.436535 0.425714i
\(175\) −31.4715 15.3148i −0.179837 0.0875131i
\(176\) 203.217i 1.15464i
\(177\) −33.4498 + 118.850i −0.188982 + 0.671467i
\(178\) 24.7461 42.8615i 0.139023 0.240795i
\(179\) −190.279 109.858i −1.06301 0.613731i −0.136749 0.990606i \(-0.543666\pi\)
−0.926264 + 0.376874i \(0.876999\pi\)
\(180\) −48.5020 89.1000i −0.269455 0.495000i
\(181\) −154.815 −0.855330 −0.427665 0.903937i \(-0.640664\pi\)
−0.427665 + 0.903937i \(0.640664\pi\)
\(182\) −203.694 301.406i −1.11920 1.65608i
\(183\) −12.9084 + 12.5884i −0.0705379 + 0.0687893i
\(184\) 0.354411 + 0.613859i 0.00192615 + 0.00333619i
\(185\) 20.9908 + 12.1191i 0.113464 + 0.0655084i
\(186\) 463.875 118.076i 2.49395 0.634817i
\(187\) −237.734 411.767i −1.27130 2.20196i
\(188\) 0.668465i 0.00355566i
\(189\) 129.153 137.987i 0.683348 0.730093i
\(190\) 17.2965 0.0910342
\(191\) 110.734 63.9324i 0.579760 0.334724i −0.181278 0.983432i \(-0.558023\pi\)
0.761038 + 0.648707i \(0.224690\pi\)
\(192\) −67.9693 267.025i −0.354007 1.39076i
\(193\) 173.100 299.819i 0.896894 1.55347i 0.0654500 0.997856i \(-0.479152\pi\)
0.831443 0.555609i \(-0.187515\pi\)
\(194\) 125.980 72.7347i 0.649383 0.374921i
\(195\) 80.9484 + 83.0062i 0.415120 + 0.425673i
\(196\) −92.1184 + 229.183i −0.469992 + 1.16930i
\(197\) 233.189i 1.18370i −0.806048 0.591851i \(-0.798397\pi\)
0.806048 0.591851i \(-0.201603\pi\)
\(198\) −449.180 + 244.513i −2.26858 + 1.23491i
\(199\) −164.523 + 284.961i −0.826747 + 1.43197i 0.0738305 + 0.997271i \(0.476478\pi\)
−0.900577 + 0.434696i \(0.856856\pi\)
\(200\) −13.5521 7.82432i −0.0677606 0.0391216i
\(201\) 277.563 + 78.1190i 1.38091 + 0.388652i
\(202\) −6.95797 −0.0344454
\(203\) 82.1270 5.81684i 0.404567 0.0286544i
\(204\) 265.635 + 272.388i 1.30213 + 1.33523i
\(205\) 5.37511 + 9.30996i 0.0262200 + 0.0454144i
\(206\) 270.325 + 156.072i 1.31226 + 0.757631i
\(207\) 1.06315 1.73911i 0.00513597 0.00840149i
\(208\) 92.9261 + 160.953i 0.446760 + 0.773812i
\(209\) 48.6179i 0.232622i
\(210\) 28.5540 138.274i 0.135972 0.658450i
\(211\) 38.0500 0.180332 0.0901659 0.995927i \(-0.471260\pi\)
0.0901659 + 0.995927i \(0.471260\pi\)
\(212\) −143.026 + 82.5761i −0.674651 + 0.389510i
\(213\) −236.300 + 60.1485i −1.10939 + 0.282387i
\(214\) 125.033 216.563i 0.584266 1.01198i
\(215\) 2.88729 1.66698i 0.0134293 0.00775340i
\(216\) 61.9592 57.4609i 0.286848 0.266023i
\(217\) 334.006 + 162.535i 1.53920 + 0.749011i
\(218\) 78.3414i 0.359364i
\(219\) −34.8109 9.79740i −0.158954 0.0447370i
\(220\) −106.510 + 184.481i −0.484136 + 0.838548i
\(221\) −376.582 217.420i −1.70399 0.983799i
\(222\) −26.4900 + 94.1211i −0.119325 + 0.423969i
\(223\) −22.8272 −0.102364 −0.0511820 0.998689i \(-0.516299\pi\)
−0.0511820 + 0.998689i \(0.516299\pi\)
\(224\) 137.377 282.307i 0.613292 1.26030i
\(225\) −1.12938 + 44.9858i −0.00501948 + 0.199937i
\(226\) −117.294 203.159i −0.518999 0.898933i
\(227\) −185.074 106.852i −0.815303 0.470715i 0.0334912 0.999439i \(-0.489337\pi\)
−0.848794 + 0.528724i \(0.822671\pi\)
\(228\) 9.59673 + 37.7019i 0.0420909 + 0.165359i
\(229\) −110.289 191.026i −0.481612 0.834176i 0.518166 0.855280i \(-0.326615\pi\)
−0.999777 + 0.0211043i \(0.993282\pi\)
\(230\) 1.52273i 0.00662055i
\(231\) −388.669 80.2612i −1.68255 0.347451i
\(232\) 36.8113 0.158669
\(233\) −214.785 + 124.006i −0.921824 + 0.532215i −0.884217 0.467077i \(-0.845307\pi\)
−0.0376076 + 0.999293i \(0.511974\pi\)
\(234\) −243.951 + 399.059i −1.04253 + 1.70538i
\(235\) 0.148261 0.256796i 0.000630898 0.00109275i
\(236\) −179.666 + 103.730i −0.761298 + 0.439536i
\(237\) −187.528 + 182.879i −0.791258 + 0.771642i
\(238\) 37.4119 + 528.213i 0.157193 + 2.21938i
\(239\) 439.067i 1.83710i 0.395307 + 0.918549i \(0.370638\pi\)
−0.395307 + 0.918549i \(0.629362\pi\)
\(240\) −19.5425 + 69.4359i −0.0814270 + 0.289316i
\(241\) 32.2173 55.8020i 0.133682 0.231543i −0.791411 0.611284i \(-0.790653\pi\)
0.925093 + 0.379740i \(0.123987\pi\)
\(242\) 614.942 + 355.037i 2.54108 + 1.46709i
\(243\) −230.314 77.4883i −0.947794 0.318882i
\(244\) −30.2964 −0.124166
\(245\) 86.2192 67.6110i 0.351915 0.275963i
\(246\) −31.0475 + 30.2778i −0.126209 + 0.123080i
\(247\) −22.2318 38.5066i −0.0900072 0.155897i
\(248\) 143.828 + 83.0392i 0.579952 + 0.334836i
\(249\) 98.9873 25.1965i 0.397539 0.101191i
\(250\) 16.8086 + 29.1133i 0.0672342 + 0.116453i
\(251\) 279.901i 1.11515i 0.830128 + 0.557573i \(0.188267\pi\)
−0.830128 + 0.557573i \(0.811733\pi\)
\(252\) 317.245 14.4794i 1.25891 0.0574578i
\(253\) −4.28016 −0.0169176
\(254\) 116.965 67.5297i 0.460492 0.265865i
\(255\) −41.6319 163.556i −0.163262 0.641396i
\(256\) −38.2236 + 66.2052i −0.149311 + 0.258614i
\(257\) 138.330 79.8651i 0.538251 0.310759i −0.206119 0.978527i \(-0.566083\pi\)
0.744370 + 0.667768i \(0.232750\pi\)
\(258\) 9.39005 + 9.62875i 0.0363955 + 0.0373207i
\(259\) −62.8671 + 42.4864i −0.242730 + 0.164040i
\(260\) 194.818i 0.749298i
\(261\) −50.6107 92.9738i −0.193911 0.356221i
\(262\) −47.4522 + 82.1896i −0.181115 + 0.313701i
\(263\) 300.143 + 173.287i 1.14123 + 0.658888i 0.946734 0.322016i \(-0.104361\pi\)
0.194493 + 0.980904i \(0.437694\pi\)
\(264\) −170.806 48.0727i −0.646992 0.182094i
\(265\) 73.2593 0.276450
\(266\) −23.6927 + 48.6879i −0.0890702 + 0.183037i
\(267\) −34.4761 35.3525i −0.129124 0.132406i
\(268\) 242.253 + 419.595i 0.903930 + 1.56565i
\(269\) 193.292 + 111.597i 0.718559 + 0.414860i 0.814222 0.580554i \(-0.197164\pi\)
−0.0956633 + 0.995414i \(0.530497\pi\)
\(270\) −176.991 + 40.3505i −0.655523 + 0.149446i
\(271\) −190.698 330.299i −0.703684 1.21882i −0.967164 0.254152i \(-0.918204\pi\)
0.263480 0.964665i \(-0.415130\pi\)
\(272\) 270.535i 0.994614i
\(273\) −344.537 + 114.160i −1.26204 + 0.418169i
\(274\) −364.609 −1.33069
\(275\) 81.8331 47.2464i 0.297575 0.171805i
\(276\) 3.31915 0.844864i 0.0120259 0.00306110i
\(277\) −81.5686 + 141.281i −0.294471 + 0.510039i −0.974862 0.222810i \(-0.928477\pi\)
0.680390 + 0.732850i \(0.261810\pi\)
\(278\) 702.222 405.428i 2.52598 1.45837i
\(279\) 11.9861 477.433i 0.0429610 1.71123i
\(280\) 40.5883 27.4301i 0.144958 0.0979647i
\(281\) 339.779i 1.20918i −0.796537 0.604589i \(-0.793337\pi\)
0.796537 0.604589i \(-0.206663\pi\)
\(282\) 1.15145 + 0.324072i 0.00408316 + 0.00114919i
\(283\) 230.515 399.264i 0.814542 1.41083i −0.0951141 0.995466i \(-0.530322\pi\)
0.909656 0.415362i \(-0.136345\pi\)
\(284\) −354.824 204.857i −1.24938 0.721329i
\(285\) 4.67537 16.6119i 0.0164048 0.0582875i
\(286\) 982.134 3.43403
\(287\) −33.5694 + 2.37763i −0.116966 + 0.00828443i
\(288\) −403.534 10.1308i −1.40116 0.0351766i
\(289\) 171.986 + 297.888i 0.595107 + 1.03076i
\(290\) −68.4850 39.5398i −0.236155 0.136344i
\(291\) −35.8027 140.655i −0.123033 0.483351i
\(292\) −30.3825 52.6241i −0.104050 0.180219i
\(293\) 130.253i 0.444548i −0.974984 0.222274i \(-0.928652\pi\)
0.974984 0.222274i \(-0.0713480\pi\)
\(294\) 350.115 + 269.785i 1.19087 + 0.917634i
\(295\) 92.0269 0.311956
\(296\) −29.3799 + 16.9625i −0.0992565 + 0.0573058i
\(297\) 113.419 + 497.496i 0.381883 + 1.67507i
\(298\) 144.003 249.421i 0.483232 0.836982i
\(299\) −3.38999 + 1.95721i −0.0113378 + 0.00654586i
\(300\) −54.1334 + 52.7914i −0.180445 + 0.175971i
\(301\) 0.737375 + 10.4109i 0.00244975 + 0.0345876i
\(302\) 695.656i 2.30350i
\(303\) −1.88079 + 6.68260i −0.00620724 + 0.0220548i
\(304\) 13.8315 23.9569i 0.0454983 0.0788054i
\(305\) 11.6386 + 6.71955i 0.0381593 + 0.0220313i
\(306\) 597.976 325.511i 1.95417 1.06376i
\(307\) 54.0187 0.175957 0.0879783 0.996122i \(-0.471959\pi\)
0.0879783 + 0.996122i \(0.471959\pi\)
\(308\) −373.397 552.516i −1.21233 1.79388i
\(309\) 222.966 217.439i 0.721573 0.703685i
\(310\) −178.389 308.978i −0.575447 0.996704i
\(311\) 156.629 + 90.4299i 0.503631 + 0.290772i 0.730212 0.683221i \(-0.239421\pi\)
−0.226581 + 0.973992i \(0.572755\pi\)
\(312\) −157.265 + 40.0306i −0.504054 + 0.128303i
\(313\) −190.732 330.358i −0.609369 1.05546i −0.991345 0.131285i \(-0.958090\pi\)
0.381976 0.924172i \(-0.375244\pi\)
\(314\) 275.283i 0.876699i
\(315\) −125.084 64.8005i −0.397091 0.205716i
\(316\) −440.133 −1.39283
\(317\) −408.341 + 235.756i −1.28814 + 0.743709i −0.978323 0.207086i \(-0.933602\pi\)
−0.309820 + 0.950795i \(0.600269\pi\)
\(318\) 72.9008 + 286.399i 0.229248 + 0.900627i
\(319\) −111.141 + 192.501i −0.348403 + 0.603453i
\(320\) −177.860 + 102.688i −0.555814 + 0.320899i
\(321\) −174.195 178.623i −0.542664 0.556459i
\(322\) 4.28632 + 2.08582i 0.0133116 + 0.00647772i
\(323\) 64.7232i 0.200381i
\(324\) −186.155 363.407i −0.574552 1.12163i
\(325\) 43.2092 74.8406i 0.132951 0.230279i
\(326\) −504.959 291.538i −1.54895 0.894289i
\(327\) −75.2409 21.1763i −0.230094 0.0647592i
\(328\) −15.0466 −0.0458738
\(329\) 0.519766 + 0.769098i 0.00157984 + 0.00233768i
\(330\) 266.137 + 272.903i 0.806477 + 0.826978i
\(331\) 82.0009 + 142.030i 0.247737 + 0.429093i 0.962898 0.269867i \(-0.0869798\pi\)
−0.715161 + 0.698960i \(0.753646\pi\)
\(332\) 148.637 + 85.8158i 0.447703 + 0.258481i
\(333\) 83.2356 + 50.8833i 0.249957 + 0.152803i
\(334\) 176.672 + 306.005i 0.528958 + 0.916182i
\(335\) 214.921i 0.641554i
\(336\) −168.686 150.123i −0.502041 0.446795i
\(337\) −8.24664 −0.0244707 −0.0122354 0.999925i \(-0.503895\pi\)
−0.0122354 + 0.999925i \(0.503895\pi\)
\(338\) 337.803 195.031i 0.999417 0.577013i
\(339\) −226.824 + 57.7363i −0.669097 + 0.170314i
\(340\) 141.793 245.592i 0.417037 0.722330i
\(341\) −868.493 + 501.424i −2.54690 + 1.47045i
\(342\) 69.5951 + 1.74721i 0.203495 + 0.00510880i
\(343\) 72.2154 + 335.312i 0.210541 + 0.977585i
\(344\) 4.66640i 0.0135651i
\(345\) −1.46246 0.411604i −0.00423902 0.00119306i
\(346\) 133.924 231.963i 0.387064 0.670414i
\(347\) 69.2183 + 39.9632i 0.199476 + 0.115168i 0.596411 0.802679i \(-0.296593\pi\)
−0.396935 + 0.917847i \(0.629926\pi\)
\(348\) 48.1886 171.218i 0.138473 0.492005i
\(349\) −590.802 −1.69284 −0.846421 0.532514i \(-0.821248\pi\)
−0.846421 + 0.532514i \(0.821248\pi\)
\(350\) −104.975 + 7.43512i −0.299929 + 0.0212432i
\(351\) 317.324 + 342.165i 0.904056 + 0.974830i
\(352\) 423.812 + 734.063i 1.20401 + 2.08541i
\(353\) −79.1141 45.6765i −0.224119 0.129395i 0.383737 0.923442i \(-0.374637\pi\)
−0.607856 + 0.794047i \(0.707970\pi\)
\(354\) 91.5766 + 359.769i 0.258691 + 1.01630i
\(355\) 90.8721 + 157.395i 0.255978 + 0.443366i
\(356\) 82.9732i 0.233071i
\(357\) 517.421 + 106.849i 1.44936 + 0.299296i
\(358\) −660.643 −1.84537
\(359\) −7.94558 + 4.58738i −0.0221325 + 0.0127782i −0.511025 0.859566i \(-0.670734\pi\)
0.488893 + 0.872344i \(0.337401\pi\)
\(360\) −53.7387 32.8513i −0.149274 0.0912537i
\(361\) 177.191 306.904i 0.490834 0.850149i
\(362\) −403.133 + 232.749i −1.11363 + 0.642953i
\(363\) 507.209 494.635i 1.39727 1.36263i
\(364\) −548.392 266.860i −1.50657 0.733133i
\(365\) 26.9546i 0.0738481i
\(366\) −14.6877 + 52.1865i −0.0401303 + 0.142586i
\(367\) 5.39389 9.34249i 0.0146972 0.0254564i −0.858583 0.512674i \(-0.828655\pi\)
0.873280 + 0.487218i \(0.161988\pi\)
\(368\) −2.10908 1.21768i −0.00573120 0.00330891i
\(369\) 20.6871 + 38.0030i 0.0560627 + 0.102989i
\(370\) 72.8793 0.196971
\(371\) −100.350 + 206.218i −0.270486 + 0.555843i
\(372\) 574.516 560.274i 1.54440 1.50611i
\(373\) −172.725 299.168i −0.463069 0.802060i 0.536043 0.844191i \(-0.319919\pi\)
−0.999112 + 0.0421312i \(0.986585\pi\)
\(374\) −1238.10 714.819i −3.31044 1.91128i
\(375\) 32.5045 8.27378i 0.0866787 0.0220634i
\(376\) 0.207515 + 0.359426i 0.000551900 + 0.000955920i
\(377\) 203.288i 0.539225i
\(378\) 128.859 553.484i 0.340898 1.46424i
\(379\) 494.429 1.30456 0.652281 0.757977i \(-0.273812\pi\)
0.652281 + 0.757977i \(0.273812\pi\)
\(380\) 25.1125 14.4987i 0.0660855 0.0381545i
\(381\) −33.2406 130.590i −0.0872456 0.342755i
\(382\) 192.232 332.956i 0.503226 0.871612i
\(383\) −331.493 + 191.387i −0.865516 + 0.499706i −0.865856 0.500294i \(-0.833225\pi\)
0.000339247 1.00000i \(0.499892\pi\)
\(384\) −202.668 207.820i −0.527781 0.541197i
\(385\) 20.8990 + 295.070i 0.0542832 + 0.766416i
\(386\) 1040.96i 2.69678i
\(387\) 11.7859 6.41569i 0.0304544 0.0165780i
\(388\) 121.939 211.205i 0.314276 0.544342i
\(389\) 587.895 + 339.421i 1.51130 + 0.872548i 0.999913 + 0.0131966i \(0.00420074\pi\)
0.511385 + 0.859352i \(0.329133\pi\)
\(390\) 335.579 + 94.4475i 0.860459 + 0.242173i
\(391\) 5.69801 0.0145729
\(392\) 21.6153 + 151.826i 0.0551410 + 0.387310i
\(393\) 66.1101 + 67.7907i 0.168219 + 0.172495i
\(394\) −350.577 607.218i −0.889790 1.54116i
\(395\) 169.080 + 97.6186i 0.428052 + 0.247136i
\(396\) −447.194 + 731.527i −1.12928 + 1.84729i
\(397\) 85.6381 + 148.330i 0.215713 + 0.373626i 0.953493 0.301415i \(-0.0974590\pi\)
−0.737780 + 0.675041i \(0.764126\pi\)
\(398\) 989.375i 2.48587i
\(399\) 40.3567 + 35.9157i 0.101144 + 0.0900143i
\(400\) 53.7652 0.134413
\(401\) 468.635 270.567i 1.16867 0.674730i 0.215300 0.976548i \(-0.430927\pi\)
0.953365 + 0.301818i \(0.0975936\pi\)
\(402\) 840.209 213.869i 2.09007 0.532012i
\(403\) −458.578 + 794.281i −1.13791 + 1.97092i
\(404\) −10.1022 + 5.83249i −0.0250054 + 0.0144369i
\(405\) −9.08850 + 180.893i −0.0224407 + 0.446650i
\(406\) 205.111 138.617i 0.505200 0.341421i
\(407\) 204.853i 0.503324i
\(408\) 227.387 + 63.9974i 0.557322 + 0.156856i
\(409\) 88.3409 153.011i 0.215992 0.374110i −0.737587 0.675253i \(-0.764035\pi\)
0.953579 + 0.301143i \(0.0973680\pi\)
\(410\) 27.9932 + 16.1619i 0.0682762 + 0.0394193i
\(411\) −98.5565 + 350.179i −0.239797 + 0.852016i
\(412\) 523.307 1.27016
\(413\) −126.058 + 259.046i −0.305226 + 0.627231i
\(414\) 0.153818 6.12692i 0.000371542 0.0147993i
\(415\) −38.0667 65.9335i −0.0917271 0.158876i
\(416\) 671.338 + 387.597i 1.61379 + 0.931724i
\(417\) −199.566 784.020i −0.478577 1.88014i
\(418\) −73.0923 126.600i −0.174862 0.302870i
\(419\) 459.984i 1.09781i −0.835883 0.548907i \(-0.815044\pi\)
0.835883 0.548907i \(-0.184956\pi\)
\(420\) −74.4508 224.694i −0.177264 0.534985i
\(421\) −467.559 −1.11059 −0.555296 0.831653i \(-0.687395\pi\)
−0.555296 + 0.831653i \(0.687395\pi\)
\(422\) 99.0811 57.2045i 0.234789 0.135556i
\(423\) 0.622492 1.01828i 0.00147161 0.00240728i
\(424\) −51.2689 + 88.8004i −0.120917 + 0.209435i
\(425\) −108.941 + 62.8973i −0.256333 + 0.147994i
\(426\) −524.892 + 511.879i −1.23214 + 1.20159i
\(427\) −34.8574 + 23.5571i −0.0816332 + 0.0551688i
\(428\) 419.233i 0.979517i
\(429\) 265.478 943.263i 0.618830 2.19875i
\(430\) 5.01229 8.68153i 0.0116565 0.0201896i
\(431\) 523.781 + 302.405i 1.21527 + 0.701635i 0.963902 0.266257i \(-0.0857869\pi\)
0.251366 + 0.967892i \(0.419120\pi\)
\(432\) −85.6463 + 277.412i −0.198255 + 0.642158i
\(433\) −548.815 −1.26747 −0.633736 0.773549i \(-0.718479\pi\)
−0.633736 + 0.773549i \(0.718479\pi\)
\(434\) 1114.10 78.9087i 2.56705 0.181817i
\(435\) −56.4870 + 55.0867i −0.129855 + 0.126636i
\(436\) −65.6693 113.743i −0.150618 0.260877i
\(437\) 0.504580 + 0.291319i 0.00115464 + 0.000666634i
\(438\) −105.376 + 26.8227i −0.240584 + 0.0612389i
\(439\) 341.530 + 591.547i 0.777972 + 1.34749i 0.933109 + 0.359594i \(0.117085\pi\)
−0.155137 + 0.987893i \(0.549582\pi\)
\(440\) 132.257i 0.300585i
\(441\) 353.746 263.334i 0.802145 0.597129i
\(442\) −1307.48 −2.95809
\(443\) −599.024 + 345.846i −1.35220 + 0.780692i −0.988557 0.150847i \(-0.951800\pi\)
−0.363641 + 0.931539i \(0.618466\pi\)
\(444\) 40.4361 + 158.858i 0.0910723 + 0.357788i
\(445\) −18.4029 + 31.8748i −0.0413548 + 0.0716287i
\(446\) −59.4413 + 34.3185i −0.133276 + 0.0769472i
\(447\) −200.624 205.724i −0.448824 0.460233i
\(448\) −45.4231 641.321i −0.101391 1.43152i
\(449\) 236.486i 0.526694i −0.964701 0.263347i \(-0.915174\pi\)
0.964701 0.263347i \(-0.0848264\pi\)
\(450\) 64.6909 + 118.840i 0.143758 + 0.264088i
\(451\) 45.4287 78.6849i 0.100729 0.174468i
\(452\) −340.594 196.642i −0.753526 0.435049i
\(453\) 668.124 + 188.041i 1.47489 + 0.415102i
\(454\) −642.569 −1.41535
\(455\) 151.481 + 224.146i 0.332925 + 0.492629i
\(456\) 16.8640 + 17.2927i 0.0369825 + 0.0379226i
\(457\) −179.329 310.607i −0.392405 0.679665i 0.600362 0.799729i \(-0.295023\pi\)
−0.992766 + 0.120064i \(0.961690\pi\)
\(458\) −574.379 331.618i −1.25410 0.724056i
\(459\) −150.991 662.298i −0.328956 1.44291i
\(460\) −1.27642 2.21082i −0.00277482 0.00480613i
\(461\) 391.999i 0.850322i 0.905118 + 0.425161i \(0.139783\pi\)
−0.905118 + 0.425161i \(0.860217\pi\)
\(462\) −1132.75 + 375.329i −2.45183 + 0.812400i
\(463\) 205.210 0.443219 0.221609 0.975136i \(-0.428869\pi\)
0.221609 + 0.975136i \(0.428869\pi\)
\(464\) −109.531 + 63.2377i −0.236058 + 0.136288i
\(465\) −344.970 + 87.8094i −0.741870 + 0.188837i
\(466\) −372.863 + 645.817i −0.800134 + 1.38587i
\(467\) 714.814 412.698i 1.53065 0.883722i 0.531319 0.847172i \(-0.321697\pi\)
0.999332 0.0365500i \(-0.0116368\pi\)
\(468\) −19.6795 + 783.878i −0.0420503 + 1.67495i
\(469\) 604.980 + 294.398i 1.28994 + 0.627713i
\(470\) 0.891585i 0.00189699i
\(471\) 264.388 + 74.4112i 0.561334 + 0.157986i
\(472\) −64.4030 + 111.549i −0.136447 + 0.236333i
\(473\) −24.4025 14.0888i −0.0515910 0.0297861i
\(474\) −213.376 + 758.142i −0.450161 + 1.59946i
\(475\) −12.8629 −0.0270797
\(476\) 497.090 + 735.543i 1.04431 + 1.54526i
\(477\) 294.770 + 7.40030i 0.617967 + 0.0155143i
\(478\) 660.094 + 1143.32i 1.38095 + 2.39187i
\(479\) 381.095 + 220.025i 0.795605 + 0.459343i 0.841932 0.539584i \(-0.181418\pi\)
−0.0463272 + 0.998926i \(0.514752\pi\)
\(480\) 74.2179 + 291.574i 0.154621 + 0.607445i
\(481\) −93.6743 162.249i −0.194749 0.337315i
\(482\) 193.742i 0.401955i
\(483\) 3.16190 3.55286i 0.00654637 0.00735583i
\(484\) 1190.43 2.45957
\(485\) −93.6876 + 54.0905i −0.193170 + 0.111527i
\(486\) −716.227 + 144.478i −1.47372 + 0.297279i
\(487\) 74.0085 128.187i 0.151968 0.263217i −0.779983 0.625801i \(-0.784772\pi\)
0.931951 + 0.362584i \(0.118106\pi\)
\(488\) −16.2900 + 9.40506i −0.0333812 + 0.0192727i
\(489\) −416.494 + 406.169i −0.851727 + 0.830612i
\(490\) 122.866 305.679i 0.250746 0.623835i
\(491\) 584.207i 1.18983i −0.803788 0.594916i \(-0.797185\pi\)
0.803788 0.594916i \(-0.202815\pi\)
\(492\) −19.6971 + 69.9852i −0.0400347 + 0.142246i
\(493\) 147.957 256.270i 0.300117 0.519817i
\(494\) −115.782 66.8467i −0.234376 0.135317i
\(495\) 334.041 181.837i 0.674830 0.367347i
\(496\) −570.609 −1.15042
\(497\) −567.527 + 40.1965i −1.14191 + 0.0808782i
\(498\) 219.880 214.429i 0.441525 0.430580i
\(499\) 188.889 + 327.165i 0.378535 + 0.655642i 0.990849 0.134972i \(-0.0430946\pi\)
−0.612314 + 0.790615i \(0.709761\pi\)
\(500\) 48.8081 + 28.1794i 0.0976162 + 0.0563588i
\(501\) 341.650 86.9644i 0.681936 0.173582i
\(502\) 420.805 + 728.855i 0.838256 + 1.45190i
\(503\) 357.039i 0.709820i −0.934900 0.354910i \(-0.884512\pi\)
0.934900 0.354910i \(-0.115488\pi\)
\(504\) 166.084 106.269i 0.329532 0.210852i
\(505\) 5.17443 0.0102464
\(506\) −11.1454 + 6.43480i −0.0220265 + 0.0127170i
\(507\) −96.0012 377.152i −0.189351 0.743889i
\(508\) 113.213 196.090i 0.222860 0.386005i
\(509\) −389.039 + 224.612i −0.764321 + 0.441281i −0.830845 0.556504i \(-0.812142\pi\)
0.0665240 + 0.997785i \(0.478809\pi\)
\(510\) −354.299 363.305i −0.694703 0.712363i
\(511\) −75.8744 36.9223i −0.148482 0.0722549i
\(512\) 616.903i 1.20489i
\(513\) 20.4901 66.3685i 0.0399418 0.129373i
\(514\) 240.139 415.933i 0.467196 0.809208i
\(515\) −201.032 116.066i −0.390354 0.225371i
\(516\) 21.7045 + 6.10865i 0.0420630 + 0.0118385i
\(517\) −2.50611 −0.00484742
\(518\) −99.8298 + 205.148i −0.192722 + 0.396038i
\(519\) −186.582 191.325i −0.359503 0.368642i
\(520\) 60.4781 + 104.751i 0.116304 + 0.201444i
\(521\) 404.636 + 233.617i 0.776653 + 0.448401i 0.835243 0.549881i \(-0.185327\pi\)
−0.0585900 + 0.998282i \(0.518660\pi\)
\(522\) −271.566 166.013i −0.520241 0.318032i
\(523\) −101.842 176.396i −0.194727 0.337276i 0.752084 0.659067i \(-0.229049\pi\)
−0.946811 + 0.321791i \(0.895715\pi\)
\(524\) 159.106i 0.303638i
\(525\) −21.2347 + 102.830i −0.0404471 + 0.195867i
\(526\) 1042.08 1.98115
\(527\) 1156.19 667.528i 2.19391 1.26666i
\(528\) 590.811 150.387i 1.11896 0.284823i
\(529\) −264.474 + 458.083i −0.499952 + 0.865941i
\(530\) 190.765 110.138i 0.359934 0.207808i
\(531\) 370.285 + 9.29612i 0.697334 + 0.0175068i
\(532\) 6.41338 + 90.5494i 0.0120552 + 0.170206i
\(533\) 83.0938i 0.155898i
\(534\) −142.924 40.2254i −0.267647 0.0753284i
\(535\) −92.9831 + 161.052i −0.173800 + 0.301031i
\(536\) 260.514 + 150.408i 0.486033 + 0.280611i
\(537\) −178.577 + 634.496i −0.332545 + 1.18156i
\(538\) 671.103 1.24740
\(539\) −859.220 345.357i −1.59410 0.640737i
\(540\) −223.147 + 206.946i −0.413235 + 0.383234i
\(541\) 394.603 + 683.473i 0.729396 + 1.26335i 0.957139 + 0.289629i \(0.0935320\pi\)
−0.227743 + 0.973721i \(0.573135\pi\)
\(542\) −993.146 573.393i −1.83237 1.05792i
\(543\) 114.567 + 450.092i 0.210990 + 0.828898i
\(544\) −564.204 977.231i −1.03714 1.79638i
\(545\) 58.2601i 0.106899i
\(546\) −725.535 + 815.247i −1.32882 + 1.49313i
\(547\) 156.388 0.285902 0.142951 0.989730i \(-0.454341\pi\)
0.142951 + 0.989730i \(0.454341\pi\)
\(548\) −529.370 + 305.632i −0.966003 + 0.557722i
\(549\) 46.1509 + 28.2128i 0.0840636 + 0.0513895i
\(550\) 142.061 246.056i 0.258292 0.447375i
\(551\) 26.2043 15.1291i 0.0475578 0.0274575i
\(552\) 1.52239 1.48465i 0.00275796 0.00268959i
\(553\) −506.392 + 342.227i −0.915718 + 0.618855i
\(554\) 490.522i 0.885418i
\(555\) 19.6998 69.9949i 0.0354952 0.126117i
\(556\) 679.696 1177.27i 1.22248 2.11739i
\(557\) −741.277 427.976i −1.33084 0.768360i −0.345410 0.938452i \(-0.612260\pi\)
−0.985428 + 0.170093i \(0.945593\pi\)
\(558\) −686.563 1261.24i −1.23040 2.26029i
\(559\) −25.7699 −0.0460999
\(560\) −73.6474 + 151.344i −0.131513 + 0.270257i
\(561\) −1021.20 + 995.882i −1.82032 + 1.77519i
\(562\) −510.825 884.775i −0.908941 1.57433i
\(563\) −117.501 67.8393i −0.208705 0.120496i 0.392004 0.919963i \(-0.371782\pi\)
−0.600710 + 0.799467i \(0.705115\pi\)
\(564\) 1.94342 0.494684i 0.00344579 0.000877099i
\(565\) 87.2278 + 151.083i 0.154385 + 0.267403i
\(566\) 1386.23i 2.44917i
\(567\) −496.747 273.370i −0.876097 0.482135i
\(568\) −254.379 −0.447851
\(569\) 110.739 63.9351i 0.194620 0.112364i −0.399523 0.916723i \(-0.630824\pi\)
0.594144 + 0.804359i \(0.297491\pi\)
\(570\) −12.7999 50.2860i −0.0224560 0.0882210i
\(571\) 439.755 761.678i 0.770148 1.33394i −0.167333 0.985900i \(-0.553515\pi\)
0.937481 0.348036i \(-0.113151\pi\)
\(572\) 1425.94 823.269i 2.49291 1.43928i
\(573\) −267.817 274.625i −0.467394 0.479275i
\(574\) −83.8391 + 56.6596i −0.146061 + 0.0987101i
\(575\) 1.13240i 0.00196940i
\(576\) −726.022 + 395.214i −1.26045 + 0.686135i
\(577\) −352.510 + 610.566i −0.610937 + 1.05817i 0.380146 + 0.924926i \(0.375874\pi\)
−0.991083 + 0.133247i \(0.957460\pi\)
\(578\) 895.693 + 517.128i 1.54964 + 0.894686i
\(579\) −999.761 281.379i −1.72670 0.485974i
\(580\) −132.576 −0.228580
\(581\) 237.740 16.8385i 0.409191 0.0289819i
\(582\) −304.690 312.436i −0.523523 0.536831i
\(583\) −309.583 536.213i −0.531016 0.919748i
\(584\) −32.6726 18.8636i −0.0559463 0.0323006i
\(585\) 181.419 296.768i 0.310118 0.507296i
\(586\) −195.822 339.174i −0.334168 0.578795i
\(587\) 45.3083i 0.0771863i 0.999255 + 0.0385931i \(0.0122876\pi\)
−0.999255 + 0.0385931i \(0.987712\pi\)
\(588\) 734.472 + 98.2132i 1.24910 + 0.167029i
\(589\) 136.513 0.231771
\(590\) 239.635 138.354i 0.406162 0.234498i
\(591\) −677.949 + 172.567i −1.14712 + 0.291991i
\(592\) 58.2794 100.943i 0.0984449 0.170512i
\(593\) 749.171 432.534i 1.26336 0.729399i 0.289634 0.957137i \(-0.406466\pi\)
0.973722 + 0.227738i \(0.0731330\pi\)
\(594\) 1043.28 + 1124.95i 1.75636 + 1.89386i
\(595\) −27.8221 392.816i −0.0467598 0.660194i
\(596\) 482.840i 0.810134i
\(597\) 950.218 + 267.435i 1.59166 + 0.447966i
\(598\) −5.88496 + 10.1930i −0.00984106 + 0.0170452i
\(599\) 584.928 + 337.708i 0.976507 + 0.563787i 0.901214 0.433375i \(-0.142677\pi\)
0.0752933 + 0.997161i \(0.476011\pi\)
\(600\) −12.7186 + 45.1902i −0.0211977 + 0.0753170i
\(601\) −246.707 −0.410495 −0.205247 0.978710i \(-0.565800\pi\)
−0.205247 + 0.978710i \(0.565800\pi\)
\(602\) 17.5718 + 26.0010i 0.0291891 + 0.0431911i
\(603\) 21.7102 864.766i 0.0360037 1.43411i
\(604\) 583.131 + 1010.01i 0.965448 + 1.67220i
\(605\) −457.313 264.030i −0.755889 0.436413i
\(606\) 5.14911 + 20.2289i 0.00849688 + 0.0333810i
\(607\) 39.7254 + 68.8064i 0.0654454 + 0.113355i 0.896891 0.442251i \(-0.145820\pi\)
−0.831446 + 0.555605i \(0.812487\pi\)
\(608\) 115.383i 0.189775i
\(609\) −77.6877 234.463i −0.127566 0.384996i
\(610\) 40.4087 0.0662439
\(611\) −1.98490 + 1.14598i −0.00324861 + 0.00187559i
\(612\) 595.333 973.854i 0.972767 1.59127i
\(613\) 57.6568 99.8645i 0.0940567 0.162911i −0.815158 0.579239i \(-0.803350\pi\)
0.909215 + 0.416328i \(0.136683\pi\)
\(614\) 140.663 81.2118i 0.229093 0.132267i
\(615\) 23.0890 22.5167i 0.0375431 0.0366124i
\(616\) −372.291 181.166i −0.604369 0.294100i
\(617\) 872.699i 1.41442i 0.707002 + 0.707211i \(0.250047\pi\)
−0.707002 + 0.707211i \(0.749953\pi\)
\(618\) 253.699 901.411i 0.410516 1.45859i
\(619\) 269.292 466.428i 0.435044 0.753518i −0.562255 0.826964i \(-0.690066\pi\)
0.997299 + 0.0734455i \(0.0233995\pi\)
\(620\) −517.999 299.067i −0.835482 0.482366i
\(621\) −5.84286 1.80388i −0.00940879 0.00290481i
\(622\) 543.811 0.874293
\(623\) −64.5160 95.4642i −0.103557 0.153233i
\(624\) 399.169 389.273i 0.639694 0.623836i
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) −993.323 573.495i −1.58678 0.916127i
\(627\) −141.347 + 35.9787i −0.225433 + 0.0573823i
\(628\) 230.755 + 399.679i 0.367444 + 0.636432i
\(629\) 272.713i 0.433566i
\(630\) −423.135 + 19.3123i −0.671643 + 0.0306544i
\(631\) 253.785 0.402196 0.201098 0.979571i \(-0.435549\pi\)
0.201098 + 0.979571i \(0.435549\pi\)
\(632\) −236.654 + 136.633i −0.374453 + 0.216191i
\(633\) −28.1581 110.623i −0.0444836 0.174759i
\(634\) −708.872 + 1227.80i −1.11809 + 1.93660i
\(635\) −86.9831 + 50.2197i −0.136981 + 0.0790862i
\(636\) 345.916 + 354.710i 0.543894 + 0.557720i
\(637\) −838.446 + 119.369i −1.31624 + 0.187392i
\(638\) 668.357i 1.04758i
\(639\) 349.738 + 642.483i 0.547322 + 1.00545i
\(640\) −108.181 + 187.376i −0.169033 + 0.292775i
\(641\) 142.301 + 82.1573i 0.221998 + 0.128171i 0.606875 0.794797i \(-0.292423\pi\)
−0.384877 + 0.922968i \(0.625756\pi\)
\(642\) −722.142 203.244i −1.12483 0.316580i
\(643\) 1008.97 1.56917 0.784583 0.620024i \(-0.212877\pi\)
0.784583 + 0.620024i \(0.212877\pi\)
\(644\) 7.97167 0.564612i 0.0123784 0.000876727i
\(645\) −6.98309 7.16060i −0.0108265 0.0111017i
\(646\) 97.3050 + 168.537i 0.150627 + 0.260894i
\(647\) 784.083 + 452.690i 1.21187 + 0.699676i 0.963167 0.268903i \(-0.0866610\pi\)
0.248707 + 0.968579i \(0.419994\pi\)
\(648\) −212.907 137.611i −0.328561 0.212362i
\(649\) −388.892 673.580i −0.599217 1.03787i
\(650\) 259.844i 0.399759i
\(651\) 225.364 1091.34i 0.346181 1.67640i
\(652\) −977.523 −1.49927
\(653\) −469.305 + 270.953i −0.718690 + 0.414936i −0.814270 0.580486i \(-0.802863\pi\)
0.0955804 + 0.995422i \(0.469529\pi\)
\(654\) −227.761 + 57.9750i −0.348259 + 0.0886467i
\(655\) 35.2887 61.1219i 0.0538759 0.0933158i
\(656\) 44.7707 25.8484i 0.0682480 0.0394030i
\(657\) −2.72282 + 108.456i −0.00414432 + 0.165077i
\(658\) 2.50972 + 1.22129i 0.00381416 + 0.00185606i
\(659\) 739.606i 1.12232i 0.827709 + 0.561158i \(0.189644\pi\)
−0.827709 + 0.561158i \(0.810356\pi\)
\(660\) 615.160 + 173.134i 0.932060 + 0.262325i
\(661\) −84.2027 + 145.843i −0.127387 + 0.220640i −0.922663 0.385606i \(-0.873992\pi\)
0.795277 + 0.606247i \(0.207326\pi\)
\(662\) 427.056 + 246.561i 0.645100 + 0.372449i
\(663\) −353.421 + 1255.73i −0.533063 + 1.89401i
\(664\) 106.561 0.160483
\(665\) 17.6195 36.2077i 0.0264955 0.0544476i
\(666\) 293.241 + 7.36191i 0.440302 + 0.0110539i
\(667\) −1.33191 2.30694i −0.00199687 0.00345868i
\(668\) 513.014 + 296.189i 0.767985 + 0.443397i
\(669\) 16.8928 + 66.3653i 0.0252508 + 0.0992008i
\(670\) −323.112 559.647i −0.482257 0.835294i
\(671\) 113.583i 0.169274i
\(672\) −922.414 190.481i −1.37264 0.283453i
\(673\) 593.902 0.882469 0.441235 0.897392i \(-0.354541\pi\)
0.441235 + 0.897392i \(0.354541\pi\)
\(674\) −21.4740 + 12.3980i −0.0318605 + 0.0183947i
\(675\) 131.623 30.0074i 0.194997 0.0444554i
\(676\) 326.967 566.323i 0.483679 0.837756i
\(677\) 898.560 518.784i 1.32727 0.766298i 0.342391 0.939557i \(-0.388763\pi\)
0.984876 + 0.173259i \(0.0554298\pi\)
\(678\) −503.842 + 491.351i −0.743129 + 0.724707i
\(679\) −23.9265 337.814i −0.0352378 0.497517i
\(680\) 176.069i 0.258925i
\(681\) −173.691 + 617.138i −0.255053 + 0.906223i
\(682\) −1507.69 + 2611.39i −2.21068 + 3.82902i
\(683\) 151.000 + 87.1801i 0.221084 + 0.127643i 0.606452 0.795120i \(-0.292592\pi\)
−0.385368 + 0.922763i \(0.625926\pi\)
\(684\) 102.509 55.8010i 0.149866 0.0815805i
\(685\) 271.148 0.395837
\(686\) 692.155 + 764.573i 1.00897 + 1.11454i
\(687\) −473.752 + 462.008i −0.689596 + 0.672501i
\(688\) −8.01635 13.8847i −0.0116517 0.0201813i
\(689\) −490.394 283.129i −0.711747 0.410928i
\(690\) −4.42701 + 1.12686i −0.00641596 + 0.00163313i
\(691\) 23.0452 + 39.9155i 0.0333505 + 0.0577648i 0.882219 0.470839i \(-0.156049\pi\)
−0.848868 + 0.528604i \(0.822716\pi\)
\(692\) 449.045i 0.648908i
\(693\) 54.2839 + 1189.37i 0.0783318 + 1.71626i
\(694\) 240.323 0.346287
\(695\) −522.221 + 301.504i −0.751397 + 0.433819i
\(696\) −27.2414 107.021i −0.0391400 0.153766i
\(697\) −60.4776 + 104.750i −0.0867684 + 0.150287i
\(698\) −1538.43 + 888.214i −2.20406 + 1.27251i
\(699\) 519.470 + 532.675i 0.743161 + 0.762053i
\(700\) −146.179 + 98.7899i −0.208828 + 0.141128i
\(701\) 183.013i 0.261074i −0.991443 0.130537i \(-0.958330\pi\)
0.991443 0.130537i \(-0.0416702\pi\)
\(702\) 1340.71 + 413.923i 1.90985 + 0.589633i
\(703\) −13.9428 + 24.1497i −0.0198334 + 0.0343524i
\(704\) 1503.22 + 867.885i 2.13526 + 1.23279i
\(705\) −0.856298 0.241002i −0.00121461 0.000341847i
\(706\) −274.681 −0.389066
\(707\) −7.08792 + 14.5655i −0.0100253 + 0.0206018i
\(708\) 434.533 + 445.579i 0.613748 + 0.629350i
\(709\) −405.233 701.884i −0.571556 0.989963i −0.996407 0.0847000i \(-0.973007\pi\)
0.424851 0.905263i \(-0.360327\pi\)
\(710\) 473.256 + 273.235i 0.666558 + 0.384838i
\(711\) 670.460 + 409.863i 0.942982 + 0.576460i
\(712\) −25.7577 44.6137i −0.0361766 0.0626597i
\(713\) 12.0182i 0.0168558i
\(714\) 1507.98 499.661i 2.11202 0.699805i
\(715\) −730.382 −1.02151
\(716\) −959.176 + 553.781i −1.33963 + 0.773437i
\(717\) 1276.50 324.922i 1.78033 0.453169i
\(718\) −13.7934 + 23.8908i −0.0192108 + 0.0332741i
\(719\) −213.235 + 123.111i −0.296572 + 0.171226i −0.640902 0.767623i \(-0.721439\pi\)
0.344330 + 0.938849i \(0.388106\pi\)
\(720\) 216.333 + 5.43110i 0.300462 + 0.00754320i
\(721\) 602.087 406.898i 0.835072 0.564353i
\(722\) 1065.56i 1.47584i
\(723\) −186.074 52.3700i −0.257364 0.0724343i
\(724\) −390.201 + 675.848i −0.538952 + 0.933492i
\(725\) 50.9302 + 29.4046i 0.0702485 + 0.0405580i
\(726\) 577.121 2050.55i 0.794932 2.82445i
\(727\) −323.366 −0.444796 −0.222398 0.974956i \(-0.571388\pi\)
−0.222398 + 0.974956i \(0.571388\pi\)
\(728\) −377.706 + 26.7520i −0.518828 + 0.0367472i
\(729\) −54.8420 + 726.934i −0.0752290 + 0.997166i
\(730\) 40.5236 + 70.1889i 0.0555117 + 0.0961491i
\(731\) 32.4862 + 18.7559i 0.0444407 + 0.0256579i
\(732\) 22.4203 + 88.0806i 0.0306288 + 0.120329i
\(733\) 324.949 + 562.827i 0.443313 + 0.767841i 0.997933 0.0642630i \(-0.0204696\pi\)
−0.554620 + 0.832104i \(0.687136\pi\)
\(734\) 32.4367i 0.0441917i
\(735\) −260.370 200.630i −0.354245 0.272966i
\(736\) −10.1579 −0.0138015
\(737\) −1573.09 + 908.221i −2.13444 + 1.23232i
\(738\) 111.002 + 67.8576i 0.150410 + 0.0919480i
\(739\) −275.779 + 477.663i −0.373178 + 0.646364i −0.990053 0.140698i \(-0.955065\pi\)
0.616874 + 0.787062i \(0.288399\pi\)
\(740\) 105.812 61.0907i 0.142989 0.0825550i
\(741\) −95.4977 + 93.1303i −0.128877 + 0.125682i
\(742\) 48.7187 + 687.852i 0.0656587 + 0.927024i
\(743\) 235.567i 0.317049i −0.987355 0.158524i \(-0.949326\pi\)
0.987355 0.158524i \(-0.0506736\pi\)
\(744\) 134.982 479.602i 0.181428 0.644627i
\(745\) −107.091 + 185.486i −0.143746 + 0.248975i
\(746\) −899.541 519.350i −1.20582 0.696180i
\(747\) −146.507 269.139i −0.196127 0.360293i
\(748\) −2396.78 −3.20424
\(749\) −325.976 482.346i −0.435215 0.643987i
\(750\) 72.2020 70.4121i 0.0962693 0.0938828i
\(751\) −457.312 792.087i −0.608937 1.05471i −0.991416 0.130746i \(-0.958263\pi\)
0.382479 0.923964i \(-0.375071\pi\)
\(752\) −1.23491 0.712974i −0.00164216 0.000948103i
\(753\) 813.756 207.135i 1.08068 0.275080i
\(754\) 305.623 + 529.355i 0.405336 + 0.702063i
\(755\) 517.338i 0.685216i
\(756\) −276.867 911.610i −0.366226 1.20583i
\(757\) 669.981 0.885048 0.442524 0.896757i \(-0.354083\pi\)
0.442524 + 0.896757i \(0.354083\pi\)
\(758\) 1287.48 743.326i 1.69852 0.980641i
\(759\) 3.16745 + 12.4437i 0.00417318 + 0.0163948i
\(760\) 9.00180 15.5916i 0.0118445 0.0205152i
\(761\) 811.403 468.464i 1.06623 0.615590i 0.139083 0.990281i \(-0.455585\pi\)
0.927150 + 0.374691i \(0.122251\pi\)
\(762\) −282.886 290.077i −0.371242 0.380679i
\(763\) −163.996 79.8044i −0.214936 0.104593i
\(764\) 644.551i 0.843653i
\(765\) −444.696 +