Properties

Label 105.3.t.b.11.3
Level 105
Weight 3
Character 105.11
Analytic conductor 2.861
Analytic rank 0
Dimension 36
CM no
Inner twists 4

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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 11.3
Character \(\chi\) \(=\) 105.11
Dual form 105.3.t.b.86.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.60397 + 1.50340i) q^{2} +(2.88780 - 0.812762i) q^{3} +(2.52044 - 4.36553i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-6.29785 + 6.45794i) q^{6} +(-0.494553 - 6.98251i) q^{7} +3.12973i q^{8} +(7.67884 - 4.69420i) q^{9} +O(q^{10})\) \(q+(-2.60397 + 1.50340i) q^{2} +(2.88780 - 0.812762i) 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} +(7.67884 - 4.69420i) q^{9} +(-3.36171 + 5.82265i) q^{10} +(-16.3666 - 9.44928i) q^{11} +(3.73040 - 14.6553i) 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} +(-12.9382 + 23.7679i) q^{18} +(-1.28629 - 2.22791i) q^{19} -11.2718i q^{20} +(-7.10329 - 19.7622i) q^{21} +56.8243 q^{22} +(0.196138 - 0.113240i) q^{23} +(2.54372 + 9.03804i) 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} +(-4.97553 + 19.5470i) q^{30} +(-26.5324 + 45.9555i) q^{31} +(-38.8423 - 22.4256i) q^{32} +(-54.9436 - 13.9855i) 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} +(49.9119 - 14.0475i) q^{39} +(3.49914 + 6.06069i) q^{40} +4.80764i q^{41} +(48.2073 + 40.7810i) q^{42} -1.49099 q^{43} +(-82.5022 + 47.6327i) q^{44} +(9.62173 - 17.6755i) 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} +(73.1444 + 18.6184i) q^{51} +(43.5625 - 75.4525i) q^{52} +(28.3732 + 16.3813i) q^{53} +(-18.0453 + 79.1528i) 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} +(-9.16125 - 32.5506i) q^{60} +(-3.00507 - 5.20494i) q^{61} -159.556i q^{62} +(-36.5749 - 51.2960i) q^{63} +91.8467 q^{64} +(33.4697 - 19.3238i) q^{65} +(164.097 - 46.1846i) 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} +(14.6916 + 24.0327i) q^{72} +(6.02722 - 10.4395i) q^{73} +(28.2260 + 16.2963i) q^{74} +(3.70015 - 14.5365i) 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} +(36.9290 - 72.0919i) q^{81} +(-7.22782 - 12.5190i) q^{82} -34.0479i q^{83} +(-104.176 - 18.7997i) q^{84} +56.2571 q^{85} +(3.88250 - 2.24156i) q^{86} +(-9.55956 - 33.9658i) 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} +(-39.2696 + 154.275i) q^{93} +(-0.199364 + 0.345309i) q^{94} +(-4.98177 - 2.87622i) q^{95} +(-130.396 - 33.1912i) 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 −0.980744 0.195296i \(-0.937433\pi\)
−0.321241 + 0.946998i \(0.604100\pi\)
\(3\) 2.88780 0.812762i 0.962602 0.270921i
\(4\) 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
\(9\) 7.67884 4.69420i 0.853204 0.521578i
\(10\) −3.36171 + 5.82265i −0.336171 + 0.582265i
\(11\) −16.3666 9.44928i −1.48788 0.859025i −0.487971 0.872860i \(-0.662263\pi\)
−0.999904 + 0.0138346i \(0.995596\pi\)
\(12\) 3.73040 14.6553i 0.310867 1.22128i
\(13\) 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 0.977152 0.212540i \(-0.0681736\pi\)
0.304511 + 0.952509i \(0.401507\pi\)
\(18\) −12.9382 + 23.7679i −0.718788 + 1.32044i
\(19\) −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
\(21\) −7.10329 19.7622i −0.338252 0.941056i
\(22\) 56.8243 2.58292
\(23\) 0.196138 0.113240i 0.00852774 0.00492349i −0.495730 0.868477i \(-0.665099\pi\)
0.504258 + 0.863553i \(0.331766\pi\)
\(24\) 2.54372 + 9.03804i 0.105988 + 0.376585i
\(25\) 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 \(-0.934999\pi\)
0.979222 0.202790i \(-0.0650009\pi\)
\(30\) −4.97553 + 19.5470i −0.165851 + 0.651565i
\(31\) −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
\(33\) −54.9436 13.9855i −1.66496 0.423803i
\(34\) −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
\(39\) 49.9119 14.0475i 1.27979 0.360193i
\(40\) 3.49914 + 6.06069i 0.0874785 + 0.151517i
\(41\) 4.80764i 0.117260i 0.998280 + 0.0586298i \(0.0186731\pi\)
−0.998280 + 0.0586298i \(0.981327\pi\)
\(42\) 48.2073 + 40.7810i 1.14779 + 0.970976i
\(43\) −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
\(45\) 9.62173 17.6755i 0.213816 0.392788i
\(46\) −0.340492 + 0.589749i −0.00740200 + 0.0128206i
\(47\) 0.114843 0.0663044i 0.00244346 0.00141073i −0.498778 0.866730i \(-0.666218\pi\)
0.501221 + 0.865319i \(0.332884\pi\)
\(48\) 23.0951 + 22.5226i 0.481148 + 0.469221i
\(49\) −48.5108 + 6.90644i −0.990017 + 0.140948i
\(50\) 15.0340i 0.300681i
\(51\) 73.1444 + 18.6184i 1.43420 + 0.365066i
\(52\) 43.5625 75.4525i 0.837741 1.45101i
\(53\) 28.3732 + 16.3813i 0.535344 + 0.309081i 0.743190 0.669081i \(-0.233312\pi\)
−0.207846 + 0.978162i \(0.566645\pi\)
\(54\) −18.0453 + 79.1528i −0.334172 + 1.46579i
\(55\) −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 0.770653 0.637255i \(-0.219930\pi\)
−0.166553 + 0.986032i \(0.553264\pi\)
\(60\) −9.16125 32.5506i −0.152688 0.542510i
\(61\) −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
\(63\) −36.5749 51.2960i −0.580553 0.814222i
\(64\) 91.8467 1.43511
\(65\) 33.4697 19.3238i 0.514919 0.297289i
\(66\) 164.097 46.1846i 2.48632 0.699767i
\(67\) −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 \(0.193981\pi\)
−0.819986 + 0.572383i \(0.806019\pi\)
\(72\) 14.6916 + 24.0327i 0.204049 + 0.333787i
\(73\) 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
\(75\) 3.70015 14.5365i 0.0493353 0.193820i
\(76\) −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
\(81\) 36.9290 72.0919i 0.455914 0.890024i
\(82\) −7.22782 12.5190i −0.0881441 0.152670i
\(83\) 34.0479i 0.410216i −0.978739 0.205108i \(-0.934245\pi\)
0.978739 0.205108i \(-0.0657545\pi\)
\(84\) −104.176 18.7997i −1.24019 0.223806i
\(85\) 56.2571 0.661848
\(86\) 3.88250 2.24156i 0.0451454 0.0260647i
\(87\) −9.55956 33.9658i −0.109880 0.390412i
\(88\) 29.5737 51.2231i 0.336064 0.582080i
\(89\) −14.2548 + 8.23003i −0.160167 + 0.0924722i −0.577941 0.816079i \(-0.696144\pi\)
0.417774 + 0.908551i \(0.362810\pi\)
\(90\) 1.51867 + 60.4917i 0.0168741 + 0.672130i
\(91\) −8.54770 120.684i −0.0939308 1.32619i
\(92\) 1.14166i 0.0124094i
\(93\) −39.2696 + 154.275i −0.422253 + 1.65887i
\(94\) −0.199364 + 0.345309i −0.00212090 + 0.00367350i
\(95\) −4.98177 2.87622i −0.0524396 0.0302760i
\(96\) −130.396 33.1912i −1.35829 0.345742i
\(97\) 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 0.509888 0.860241i \(-0.329687\pi\)
−0.490046 + 0.871696i \(0.663020\pi\)
\(102\) −218.457 + 61.4839i −2.14173 + 0.602783i
\(103\) 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
\(105\) −35.8502 30.3276i −0.341431 0.288834i
\(106\) −98.5107 −0.929346
\(107\) −72.0244 + 41.5833i −0.673126 + 0.388629i −0.797260 0.603636i \(-0.793718\pi\)
0.124134 + 0.992265i \(0.460385\pi\)
\(108\) −40.1498 130.047i −0.371758 1.20414i
\(109\) 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 \(0.112194\pi\)
−0.938523 + 0.345216i \(0.887806\pi\)
\(114\) 22.4886 + 5.72430i 0.197268 + 0.0502131i
\(115\) 0.253213 0.438578i 0.00220185 0.00381372i
\(116\) −51.3466 29.6450i −0.442643 0.255560i
\(117\) 132.719 81.1331i 1.13435 0.693445i
\(118\) −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
\(123\) 3.90747 + 13.8835i 0.0317680 + 0.112874i
\(124\) 133.747 + 231.656i 1.07860 + 1.86820i
\(125\) 11.1803i 0.0894427i
\(126\) 172.358 + 78.5865i 1.36792 + 0.623702i
\(127\) 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
\(129\) −4.30570 + 1.21182i −0.0333775 + 0.00939397i
\(130\) −58.1028 + 100.637i −0.446944 + 0.774131i
\(131\) 27.3345 15.7816i 0.208661 0.120470i −0.392028 0.919953i \(-0.628226\pi\)
0.600689 + 0.799483i \(0.294893\pi\)
\(132\) −199.536 + 204.609i −1.51164 + 1.55007i
\(133\) −14.9203 + 10.0833i −0.112183 + 0.0758145i
\(134\) 289.000i 2.15672i
\(135\) 13.4197 58.8635i 0.0994053 0.436026i
\(136\) −39.3703 + 68.1914i −0.289487 + 0.501407i
\(137\) 105.015 + 60.6306i 0.766535 + 0.442559i 0.831637 0.555319i \(-0.187404\pi\)
−0.0651022 + 0.997879i \(0.520737\pi\)
\(138\) −0.503948 + 1.97982i −0.00365180 + 0.0143465i
\(139\) 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
\(144\) 84.9997 + 46.2700i 0.590276 + 0.321319i
\(145\) −13.1501 22.7767i −0.0906905 0.157080i
\(146\) 36.2454i 0.248256i
\(147\) −134.477 + 59.3722i −0.914806 + 0.403893i
\(148\) −54.6412 −0.369197
\(149\) −82.9520 + 47.8924i −0.556725 + 0.321425i −0.751830 0.659357i \(-0.770829\pi\)
0.195105 + 0.980782i \(0.437495\pi\)
\(150\) 12.2191 + 43.4153i 0.0814606 + 0.289436i
\(151\) −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
\(156\) 64.4751 253.298i 0.413302 1.62371i
\(157\) −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
\(159\) 95.2504 + 24.2453i 0.599059 + 0.152486i
\(160\) −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
\(165\) −122.034 + 34.3461i −0.739601 + 0.208158i
\(166\) 51.1877 + 88.6598i 0.308360 + 0.534095i
\(167\) 117.515i 0.703681i −0.936060 0.351840i \(-0.885556\pi\)
0.936060 0.351840i \(-0.114444\pi\)
\(168\) 61.8502 22.2314i 0.368156 0.132330i
\(169\) 129.726 0.767610
\(170\) −146.492 + 84.5771i −0.861716 + 0.497512i
\(171\) −20.3355 11.0697i −0.118921 0.0647351i
\(172\) −3.75796 + 6.50897i −0.0218486 + 0.0378429i
\(173\) −77.1460 + 44.5403i −0.445931 + 0.257458i −0.706110 0.708102i \(-0.749552\pi\)
0.260179 + 0.965560i \(0.416218\pi\)
\(174\) 75.9572 + 74.0742i 0.436535 + 0.425714i
\(175\) −31.4715 15.3148i −0.179837 0.0875131i
\(176\) 203.217i 1.15464i
\(177\) 119.652 + 30.4564i 0.675998 + 0.172070i
\(178\) 24.7461 42.8615i 0.139023 0.240795i
\(179\) 190.279 + 109.858i 1.06301 + 0.613731i 0.926264 0.376874i \(-0.123001\pi\)
0.136749 + 0.990606i \(0.456334\pi\)
\(180\) −52.9118 86.5539i −0.293955 0.480855i
\(181\) −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
\(186\) −129.681 460.766i −0.697209 2.47724i
\(187\) −237.734 411.767i −1.27130 2.20196i
\(188\) 0.668465i 0.00355566i
\(189\) −147.313 118.406i −0.779431 0.626488i
\(190\) 17.2965 0.0910342
\(191\) −110.734 + 63.9324i −0.579760 + 0.334724i −0.761038 0.648707i \(-0.775310\pi\)
0.181278 + 0.983432i \(0.441977\pi\)
\(192\) 265.235 74.6496i 1.38143 0.388800i
\(193\) 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 \(0.201603\pi\)
−0.806048 + 0.591851i \(0.798397\pi\)
\(198\) 436.344 266.744i 2.20376 1.34719i
\(199\) −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
\(201\) −71.1283 + 279.436i −0.353872 + 1.39023i
\(202\) −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
\(207\) 0.974539 1.79027i 0.00470792 0.00864862i
\(208\) 92.9261 + 160.953i 0.446760 + 0.773812i
\(209\) 48.6179i 0.232622i
\(210\) 138.947 + 25.0747i 0.661655 + 0.119403i
\(211\) 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
\(213\) 66.0600 + 234.716i 0.310141 + 1.10195i
\(214\) 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
\(219\) 8.92065 35.0458i 0.0407336 0.160027i
\(220\) −106.510 + 184.481i −0.484136 + 0.838548i
\(221\) 376.582 + 217.420i 1.70399 + 0.983799i
\(222\) 94.7563 + 24.1195i 0.426830 + 0.108646i
\(223\) −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 0.848794 0.528724i \(-0.177329\pi\)
−0.0334912 + 0.999439i \(0.510663\pi\)
\(228\) −37.4492 + 10.5399i −0.164251 + 0.0462278i
\(229\) −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
\(231\) −70.4813 + 390.561i −0.305114 + 1.69074i
\(232\) 36.8113 0.158669
\(233\) 214.785 124.006i 0.921824 0.532215i 0.0376076 0.999293i \(-0.488026\pi\)
0.884217 + 0.467077i \(0.154693\pi\)
\(234\) −223.620 + 410.798i −0.955640 + 1.75555i
\(235\) 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 \(-0.629362\pi\)
0.395307 0.918549i \(-0.370638\pi\)
\(240\) 69.9045 + 17.7937i 0.291269 + 0.0741403i
\(241\) 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
\(243\) 48.0502 238.202i 0.197737 0.980255i
\(244\) −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
\(249\) −27.6729 98.3237i −0.111136 0.394874i
\(250\) 16.8086 + 29.1133i 0.0672342 + 0.116453i
\(251\) 279.901i 1.11515i −0.830128 0.557573i \(-0.811733\pi\)
0.830128 0.557573i \(-0.188267\pi\)
\(252\) −316.119 + 30.3802i −1.25444 + 0.120556i
\(253\) −4.28016 −0.0169176
\(254\) −116.965 + 67.5297i −0.460492 + 0.265865i
\(255\) 162.459 45.7236i 0.637096 0.179308i
\(256\) −38.2236 + 66.2052i −0.149311 + 0.258614i
\(257\) −138.330 + 79.8651i −0.538251 + 0.310759i −0.744370 0.667768i \(-0.767250\pi\)
0.206119 + 0.978527i \(0.433917\pi\)
\(258\) 9.39005 9.62875i 0.0363955 0.0373207i
\(259\) −62.8671 + 42.4864i −0.242730 + 0.164040i
\(260\) 194.818i 0.749298i
\(261\) −55.2123 90.3171i −0.211541 0.346042i
\(262\) −47.4522 + 82.1896i −0.181115 + 0.313701i
\(263\) −300.143 173.287i −1.14123 0.658888i −0.194493 0.980904i \(-0.562306\pi\)
−0.946734 + 0.322016i \(0.895639\pi\)
\(264\) 43.7708 171.959i 0.165798 0.651358i
\(265\) 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 0.0956633 0.995414i \(-0.469503\pi\)
−0.814222 + 0.580554i \(0.802836\pi\)
\(270\) 53.5510 + 173.454i 0.198337 + 0.642422i
\(271\) −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
\(273\) −122.771 341.563i −0.449711 1.25115i
\(274\) −364.609 −1.33069
\(275\) −81.8331 + 47.2464i −0.297575 + 0.171805i
\(276\) −0.927900 3.29690i −0.00336196 0.0119453i
\(277\) −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 \(0.206663\pi\)
−0.796537 + 0.604589i \(0.793337\pi\)
\(282\) −0.295071 + 1.15922i −0.00104635 + 0.00411071i
\(283\) 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
\(285\) −16.7241 4.25698i −0.0586809 0.0149368i
\(286\) 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
\(291\) 139.712 39.3215i 0.480111 0.135125i
\(292\) −30.3825 52.6241i −0.104050 0.180219i
\(293\) 130.253i 0.444548i 0.974984 + 0.222274i \(0.0713480\pi\)
−0.974984 + 0.222274i \(0.928652\pi\)
\(294\) 260.913 356.776i 0.887458 1.21352i
\(295\) 92.0269 0.311956
\(296\) 29.3799 16.9625i 0.0992565 0.0573058i
\(297\) −487.554 + 150.524i −1.64160 + 0.506815i
\(298\) 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
\(303\) 6.72770 + 1.71248i 0.0222036 + 0.00565176i
\(304\) 13.8315 23.9569i 0.0454983 0.0788054i
\(305\) −11.6386 6.71955i −0.0381593 0.0220313i
\(306\) −580.889 + 355.107i −1.89833 + 1.16048i
\(307\) 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 0.226581 0.973992i \(-0.427245\pi\)
−0.730212 + 0.683221i \(0.760579\pi\)
\(312\) 43.9649 + 156.211i 0.140913 + 0.500675i
\(313\) −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
\(315\) −128.178 58.4423i −0.406913 0.185531i
\(316\) −440.133 −1.39283
\(317\) 408.341 235.756i 1.28814 0.743709i 0.309820 0.950795i \(-0.399731\pi\)
0.978323 + 0.207086i \(0.0663980\pi\)
\(318\) −284.480 + 80.0658i −0.894590 + 0.251779i
\(319\) −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
\(324\) −221.642 342.918i −0.684081 1.05839i
\(325\) 43.2092 74.8406i 0.132951 0.230279i
\(326\) 504.959 + 291.538i 1.54895 + 0.894289i
\(327\) 19.2812 75.7486i 0.0589641 0.231647i
\(328\) −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
\(333\) −85.6840 46.6425i −0.257309 0.140068i
\(334\) 176.672 + 306.005i 0.528958 + 0.916182i
\(335\) 214.921i 0.641554i
\(336\) 145.842 172.400i 0.434055 0.513097i
\(337\) −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
\(339\) 63.4108 + 225.303i 0.187053 + 0.664612i
\(340\) 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
\(345\) 0.374771 1.47233i 0.00108629 0.00426762i
\(346\) 133.924 231.963i 0.387064 0.670414i
\(347\) −69.2183 39.9632i −0.199476 0.115168i 0.396935 0.917847i \(-0.370074\pi\)
−0.596411 + 0.802679i \(0.703407\pi\)
\(348\) −172.373 43.8763i −0.495325 0.126081i
\(349\) −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 0.607856 0.794047i \(-0.292030\pi\)
−0.383737 + 0.923442i \(0.625363\pi\)
\(354\) −357.358 + 100.577i −1.00948 + 0.284116i
\(355\) 90.8721 + 157.395i 0.255978 + 0.443366i
\(356\) 82.9732i 0.233071i
\(357\) 93.8291 519.939i 0.262827 1.45641i
\(358\) −660.643 −1.84537
\(359\) 7.94558 4.58738i 0.0221325 0.0127782i −0.488893 0.872344i \(-0.662599\pi\)
0.511025 + 0.859566i \(0.329266\pi\)
\(360\) 55.3194 + 30.1134i 0.153665 + 0.0836483i
\(361\) 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
\(366\) 52.5387 + 13.3733i 0.143548 + 0.0365392i
\(367\) 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
\(369\) 22.5680 + 36.9171i 0.0611599 + 0.100046i
\(370\) 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
\(375\) −9.08696 32.2866i −0.0242319 0.0860977i
\(376\) 0.207515 + 0.359426i 0.000551900 + 0.000955920i
\(377\) 203.288i 0.539225i
\(378\) 561.610 + 86.8561i 1.48574 + 0.229778i
\(379\) 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
\(381\) 129.714 36.5076i 0.340457 0.0958204i
\(382\) 192.232 332.956i 0.503226 0.871612i
\(383\) 331.493 191.387i 0.865516 0.499706i −0.000339247 1.00000i \(-0.500108\pi\)
0.865856 + 0.500294i \(0.166775\pi\)
\(384\) −202.668 + 207.820i −0.527781 + 0.541197i
\(385\) 20.8990 + 295.070i 0.0542832 + 0.766416i
\(386\) 1040.96i 2.69678i
\(387\) −11.4491 + 6.99901i −0.0295842 + 0.0180853i
\(388\) 121.939 211.205i 0.314276 0.544342i
\(389\) −587.895 339.421i −1.51130 0.872548i −0.999913 0.0131966i \(-0.995799\pi\)
−0.511385 0.859352i \(-0.670867\pi\)
\(390\) −85.9956 + 337.844i −0.220501 + 0.866266i
\(391\) 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
\(396\) −409.924 + 753.045i −1.03516 + 1.90163i
\(397\) 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
\(399\) −34.8915 + 41.2453i −0.0874475 + 0.103372i
\(400\) 53.7652 0.134413
\(401\) −468.635 + 270.567i −1.16867 + 0.674730i −0.953365 0.301818i \(-0.902406\pi\)
−0.215300 + 0.976548i \(0.569073\pi\)
\(402\) −234.889 834.577i −0.584300 2.07606i
\(403\) −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
\(408\) −58.2704 + 228.922i −0.142820 + 0.561083i
\(409\) 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
\(411\) 352.542 + 89.7369i 0.857766 + 0.218338i
\(412\) 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
\(417\) 778.765 219.180i 1.86754 0.525613i
\(418\) −73.0923 126.600i −0.174862 0.302870i
\(419\) 459.984i 1.09781i 0.835883 + 0.548907i \(0.184956\pi\)
−0.835883 + 0.548907i \(0.815044\pi\)
\(420\) −222.754 + 80.0665i −0.530367 + 0.190635i
\(421\) −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
\(423\) 0.570611 1.04823i 0.00134896 0.00247809i
\(424\) −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
\(429\) −949.629 241.721i −2.21359 0.563452i
\(430\) 5.01229 8.68153i 0.0116565 0.0201896i
\(431\) −523.781 302.405i −1.21527 0.701635i −0.251366 0.967892i \(-0.580880\pi\)
−0.963902 + 0.266257i \(0.914213\pi\)
\(432\) 283.069 + 64.5342i 0.655252 + 0.149385i
\(433\) −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
\(438\) 29.4589 + 104.670i 0.0672577 + 0.238972i
\(439\) 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
\(441\) −340.087 + 280.753i −0.771171 + 0.636628i
\(442\) −1307.48 −2.95809
\(443\) 599.024 345.846i 1.35220 0.780692i 0.363641 0.931539i \(-0.381534\pi\)
0.988557 + 0.150847i \(0.0482002\pi\)
\(444\) −157.793 + 44.4103i −0.355390 + 0.100023i
\(445\) −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 \(0.0848264\pi\)
−0.964701 + 0.263347i \(0.915174\pi\)
\(450\) 70.5727 + 115.444i 0.156828 + 0.256542i
\(451\) 45.4287 78.6849i 0.100729 0.174468i
\(452\) 340.594 + 196.642i 0.753526 + 0.435049i
\(453\) −171.214 + 672.633i −0.377955 + 1.48484i
\(454\) −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
\(459\) 649.062 200.387i 1.41408 0.436573i
\(460\) −1.27642 2.21082i −0.00277482 0.00480613i
\(461\) 391.999i 0.850322i −0.905118 0.425161i \(-0.860217\pi\)
0.905118 0.425161i \(-0.139783\pi\)
\(462\) −403.639 1122.97i −0.873678 2.43067i
\(463\) 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
\(465\) 96.4396 + 342.657i 0.207397 + 0.736897i
\(466\) −372.863 + 645.817i −0.800134 + 1.38587i
\(467\) −714.814 + 412.698i −1.53065 + 0.883722i −0.531319 + 0.847172i \(0.678303\pi\)
−0.999332 + 0.0365500i \(0.988363\pi\)
\(468\) −19.6795 783.878i −0.0420503 1.67495i
\(469\) 604.980 + 294.398i 1.28994 + 0.627713i
\(470\) 0.891585i 0.00189699i
\(471\) −67.7523 + 266.173i −0.143848 + 0.565123i
\(472\) −64.4030 + 111.549i −0.136447 + 0.236333i
\(473\) 24.4025 + 14.0888i 0.0515910 + 0.0297861i
\(474\) 763.259 + 194.282i 1.61025 + 0.409877i
\(475\) −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 0.0463272 0.998926i \(-0.485248\pi\)
−0.841932 + 0.539584i \(0.818582\pi\)
\(480\) −289.619 + 81.5122i −0.603373 + 0.169817i
\(481\) −93.6743 162.249i −0.194749 0.337315i
\(482\) 193.742i 0.401955i
\(483\) −3.63110 3.07173i −0.00751781 0.00635970i
\(484\) 1190.43 2.45957
\(485\) 93.6876 54.0905i 0.193170 0.111527i
\(486\) 232.992 + 692.510i 0.479408 + 1.42492i
\(487\) 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 \(0.202815\pi\)
−0.803788 + 0.594916i \(0.797185\pi\)
\(492\) 70.4575 + 17.9344i 0.143206 + 0.0364521i
\(493\) 147.957 256.270i 0.300117 0.519817i
\(494\) 115.782 + 66.8467i 0.234376 + 0.135317i
\(495\) −324.496 + 198.370i −0.655547 + 0.400747i
\(496\) −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
\(501\) −95.5115 339.360i −0.190642 0.677364i
\(502\) 420.805 + 728.855i 0.838256 + 1.45190i
\(503\) 357.039i 0.709820i 0.934900 + 0.354910i \(0.115488\pi\)
−0.934900 + 0.354910i \(0.884512\pi\)
\(504\) 160.542 114.469i 0.318537 0.227122i
\(505\) 5.17443 0.0102464
\(506\) 11.1454 6.43480i 0.0220265 0.0127170i
\(507\) 374.624 105.436i 0.738903 0.207961i
\(508\) 113.213 196.090i 0.222860 0.386005i
\(509\) 389.039 224.612i 0.764321 0.441281i −0.0665240 0.997785i \(-0.521191\pi\)
0.830845 + 0.556504i \(0.187858\pi\)
\(510\) −354.299 + 363.305i −0.694703 + 0.712363i
\(511\) −75.8744 36.9223i −0.148482 0.0722549i
\(512\) 616.903i 1.20489i
\(513\) −67.7218 15.4392i −0.132011 0.0300960i
\(514\) 240.139 415.933i 0.467196 0.809208i
\(515\) 201.032 + 116.066i 0.390354 + 0.225371i
\(516\) −5.56200 + 21.8510i −0.0107791 + 0.0423469i
\(517\) −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 0.0585900 0.998282i \(-0.481340\pi\)
−0.835243 + 0.549881i \(0.814673\pi\)
\(522\) 279.554 + 152.177i 0.535544 + 0.291526i
\(523\) −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
\(525\) −103.331 18.6473i −0.196821 0.0355186i
\(526\) 1042.08 1.98115
\(527\) −1156.19 + 667.528i −2.19391 + 1.26666i
\(528\) −165.167 586.851i −0.312816 1.11146i
\(529\) −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
\(534\) 36.6257 143.888i 0.0685874 0.269454i
\(535\) −92.9831 + 161.052i −0.173800 + 0.301031i
\(536\) −260.514 150.408i −0.486033 0.280611i
\(537\) 638.778 + 162.596i 1.18953 + 0.302786i
\(538\) 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
\(543\) −447.075 + 125.828i −0.823342 + 0.231727i
\(544\) −564.204 977.231i −1.03714 1.79638i
\(545\) 58.2601i 0.106899i
\(546\) 833.199 + 704.846i 1.52601 + 1.29093i
\(547\) 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
\(549\) −47.5085 25.8615i −0.0865364 0.0471065i
\(550\) 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
\(555\) −70.4673 17.9369i −0.126968 0.0323188i
\(556\) 679.696 1177.27i 1.22248 2.11739i
\(557\) 741.277 + 427.976i 1.33084 + 0.768360i 0.985428 0.170093i \(-0.0544067\pi\)
0.345410 + 0.938452i \(0.387740\pi\)
\(558\) −748.986 1225.20i −1.34227 2.19570i
\(559\) −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 0.600710 0.799467i \(-0.294885\pi\)
−0.392004 + 0.919963i \(0.628218\pi\)
\(564\) −0.543303 1.93040i −0.000963303 0.00342269i
\(565\) 87.2278 + 151.083i 0.154385 + 0.267403i
\(566\) 1386.23i 2.44917i
\(567\) −521.646 222.204i −0.920010 0.391894i
\(568\) −254.379 −0.447851
\(569\) −110.739 + 63.9351i −0.194620 + 0.112364i −0.594144 0.804359i \(-0.702509\pi\)
0.399523 + 0.916723i \(0.369176\pi\)
\(570\) 49.9489 14.0579i 0.0876297 0.0246630i
\(571\) 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
\(576\) 705.276 431.147i 1.22444 0.748519i
\(577\) −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
\(579\) 256.199 1006.51i 0.442485 1.73836i
\(580\) −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
\(585\) 166.299 305.497i 0.284272 0.522218i
\(586\) −195.822 339.174i −0.334168 0.578795i
\(587\) 45.3083i 0.0771863i −0.999255 0.0385931i \(-0.987712\pi\)
0.999255 0.0385931i \(-0.0122876\pi\)
\(588\) −79.7489 + 736.706i −0.135627 + 1.25290i
\(589\) 136.513 0.231771
\(590\) −239.635 + 138.354i −0.406162 + 0.234498i
\(591\) 189.527 + 673.405i 0.320689 + 1.13943i
\(592\) 58.2794 100.943i 0.0984449 0.170512i
\(593\) −749.171 + 432.534i −1.26336 + 0.729399i −0.973722 0.227738i \(-0.926867\pi\)
−0.289634 + 0.957137i \(0.593534\pi\)
\(594\) 1043.28 1124.95i 1.75636 1.89386i
\(595\) −27.8221 392.816i −0.0467598 0.660194i
\(596\) 482.840i 0.810134i
\(597\) −243.503 + 956.631i −0.407878 + 1.60240i
\(598\) −5.88496 + 10.1930i −0.00984106 + 0.0170452i
\(599\) −584.928 337.708i −0.976507 0.563787i −0.0752933 0.997161i \(-0.523989\pi\)
−0.901214 + 0.433375i \(0.857323\pi\)
\(600\) 45.4952 + 11.5805i 0.0758253 + 0.0193008i
\(601\) −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
\(606\) −20.0933 + 5.65518i −0.0331572 + 0.00933198i
\(607\) 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
\(609\) −232.439 + 83.5476i −0.381673 + 0.137188i
\(610\) 40.4087 0.0662439
\(611\) 1.98490 1.14598i 0.00324861 0.00187559i
\(612\) 545.716 1002.50i 0.891693 1.63807i
\(613\) 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 \(-0.749953\pi\)
0.707002 0.707211i \(-0.250047\pi\)
\(618\) −907.495 230.996i −1.46844 0.373780i
\(619\) 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
\(621\) 1.35922 5.96201i 0.00218876 0.00960065i
\(622\) 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
\(627\) 39.5148 + 140.399i 0.0630220 + 0.223922i
\(628\) 230.755 + 399.679i 0.367444 + 0.636432i
\(629\) 272.713i 0.433566i
\(630\) 421.633 40.5204i 0.669259 0.0643182i
\(631\) 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
\(633\) 109.881 30.9256i 0.173588 0.0488556i
\(634\) −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
\(639\) 381.537 + 624.124i 0.597085 + 0.976719i
\(640\) −108.181 + 187.376i −0.169033 + 0.292775i
\(641\) −142.301 82.1573i −0.221998 0.128171i 0.384877 0.922968i \(-0.374244\pi\)
−0.606875 + 0.794797i \(0.707577\pi\)
\(642\) 185.056 727.015i 0.288250 1.13242i
\(643\) 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 −0.248707 0.968579i \(-0.580006\pi\)
−0.963167 + 0.268903i \(0.913339\pi\)
\(648\) 225.628 + 115.578i 0.348191 + 0.178361i
\(649\) −388.892 673.580i −0.599217 1.03787i
\(650\) 259.844i 0.399759i
\(651\) 1096.65 + 197.903i 1.68456 + 0.303998i
\(652\) −977.523 −1.49927
\(653\) 469.305 270.953i 0.718690 0.414936i −0.0955804 0.995422i \(-0.530471\pi\)
0.814270 + 0.580486i \(0.197137\pi\)
\(654\) 63.6729 + 226.235i 0.0973592 + 0.345925i
\(655\) 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 \(-0.810356\pi\)
0.827709 0.561158i \(-0.189644\pi\)
\(660\) −157.641 + 619.311i −0.238850 + 0.938350i
\(661\) −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
\(663\) 1264.21 + 321.794i 1.90680 + 0.485361i
\(664\) 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
\(669\) −65.9204 + 18.5531i −0.0985358 + 0.0277325i
\(670\) −323.112 559.647i −0.482257 0.835294i
\(671\) 113.583i 0.169274i
\(672\) −167.271 + 926.904i −0.248914 + 1.37932i
\(673\) 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
\(675\) −39.8242 128.992i −0.0589988 0.191100i
\(676\) 326.967 566.323i 0.483679 0.837756i
\(677\) −898.560 + 518.784i −1.32727 + 0.766298i −0.984876 0.173259i \(-0.944570\pi\)
−0.342391 + 0.939557i \(0.611237\pi\)
\(678\) −503.842 491.351i −0.743129 0.724707i
\(679\) −23.9265 337.814i −0.0352378 0.497517i
\(680\) 176.069i 0.258925i
\(681\) 621.302 + 158.148i 0.912338 + 0.232229i
\(682\) −1507.69 + 2611.39i −2.21068 + 3.82902i
\(683\) −151.000 87.1801i −0.221084 0.127643i 0.385368 0.922763i \(-0.374074\pi\)
−0.606452 + 0.795120i \(0.707408\pi\)
\(684\) −99.5794 + 60.8745i −0.145584 + 0.0889978i
\(685\) 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
\(690\) 1.23761 + 4.39734i 0.00179364 + 0.00637295i
\(691\) 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
\(693\) 113.897 + 1185.15i 0.164354 + 1.71017i
\(694\) 240.323 0.346287
\(695\) 522.221 301.504i 0.751397 0.433819i
\(696\) 106.304 29.9188i 0.152735 0.0429868i
\(697\) −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 \(0.0416702\pi\)
−0.991443 + 0.130537i \(0.958330\pi\)
\(702\) −311.889 + 1368.05i −0.444287 + 1.94879i
\(703\) −13.9428 + 24.1497i −0.0198334 + 0.0343524i
\(704\) −1503.22 867.885i −2.13526 1.23279i
\(705\) 0.219435 0.862077i 0.000311256 0.00122280i
\(706\) −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
\(711\) −690.182 375.704i −0.970720 0.528416i
\(712\) −25.7577 44.6137i −0.0361766 0.0626597i
\(713\) 12.0182i 0.0168558i
\(714\) 537.350 + 1494.97i 0.752591 + 2.09379i
\(715\) −730.382 −1.02151
\(716\) 959.176 553.781i 1.33963 0.773437i
\(717\) −356.857 1267.94i −0.497708 1.76839i
\(718\) −13.7934 + 23.8908i −0.0192108 + 0.0332741i
\(719\) 213.235 123.111i 0.296572 0.171226i −0.344330 0.938849i \(-0.611894\pi\)
0.640902 + 0.767623i \(0.278561\pi\)
\(720\) 216.333 5.43110i 0.300462 0.00754320i
\(721\) 602.087 406.898i 0.835072 0.564353i
\(722\) 1065.56i 1.47584i
\(723\) 47.6835 187.330i 0.0659523 0.259101i
\(724\) −390.201 + 675.848i −0.538952 + 0.933492i
\(725\) −50.9302 29.4046i −0.0702485 0.0405580i
\(726\) −2064.39 525.475i −2.84351 0.723795i
\(727\) −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
\(732\) −87.4902 + 24.6238i −0.119522 + 0.0336391i
\(733\) 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
\(735\) −194.033 + 265.323i −0.263990 + 0.360984i
\(736\) −10.1579 −0.0138015
\(737\) 1573.09 908.221i 2.13444 1.23232i
\(738\) −114.268 62.2021i −0.154834 0.0842848i
\(739\) −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 \(0.0506736\pi\)
−0.987355 + 0.158524i \(0.949326\pi\)
\(744\) −482.839 122.903i −0.648977 0.165192i
\(745\) −107.091 + 185.486i −0.143746 + 0.248975i
\(746\) 899.541 + 519.350i 1.20582 + 0.696180i
\(747\) −159.828 261.448i −0.213959 0.349998i
\(748\) −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
\(753\) −227.493 808.301i −0.302116 1.07344i
\(754\) 305.623 + 529.355i 0.405336 + 0.702063i
\(755\) 517.338i 0.685216i
\(756\) −888.198 + 344.662i −1.17487 + 0.455902i
\(757\) 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
\(759\) −12.3603 + 3.47875i −0.0162849 + 0.00458334i
\(760\) 9.00180 15.5916i 0.0118445 0.0205152i
\(761\) −811.403 + 468.464i −1.06623 + 0.615590i −0.927150 0.374691i \(-0.877749\pi\)
−0.139083 + 0.990281i \(0.544415\pi\)
\(762\) −282.886 + 290.077i −0.371242 + 0.380679i
\(763\) −163.996 79.8044i −0.214936 0.104593i
\(764\) 644.551i 0.843653i
\(765\) 431.989 264.082i