Properties

Label 108.3.k.a.29.1
Level 108
Weight 3
Character 108.29
Analytic conductor 2.943
Analytic rank 0
Dimension 36
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 29.1
Character \(\chi\) \(=\) 108.29
Dual form 108.3.k.a.41.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.78257 + 1.12129i) q^{3} +(-2.69546 - 3.21232i) q^{5} +(11.1367 - 4.05342i) q^{7} +(6.48544 - 6.24012i) q^{9} +O(q^{10})\) \(q+(-2.78257 + 1.12129i) q^{3} +(-2.69546 - 3.21232i) q^{5} +(11.1367 - 4.05342i) q^{7} +(6.48544 - 6.24012i) q^{9} +(7.66419 - 9.13382i) q^{11} +(-0.429892 - 2.43804i) q^{13} +(11.1022 + 5.91614i) q^{15} +(-11.9968 + 6.92637i) q^{17} +(1.88960 - 3.27289i) q^{19} +(-26.4436 + 23.7663i) q^{21} +(9.18883 - 25.2461i) q^{23} +(1.28769 - 7.30285i) q^{25} +(-11.0493 + 24.6356i) q^{27} +(-40.6205 - 7.16249i) q^{29} +(32.7920 + 11.9353i) q^{31} +(-11.0845 + 34.0093i) q^{33} +(-43.0393 - 24.8488i) q^{35} +(33.5308 + 58.0771i) q^{37} +(3.92995 + 6.30200i) q^{39} +(5.01099 - 0.883573i) q^{41} +(-35.5382 - 29.8201i) q^{43} +(-37.5265 - 4.01333i) q^{45} +(31.9088 + 87.6686i) q^{47} +(70.0593 - 58.7867i) q^{49} +(25.6156 - 32.7250i) q^{51} -51.4760i q^{53} -49.9992 q^{55} +(-1.58812 + 11.2258i) q^{57} +(9.45130 + 11.2636i) q^{59} +(-48.1278 + 17.5171i) q^{61} +(46.9324 - 95.7824i) q^{63} +(-6.67301 + 7.95258i) q^{65} +(2.35762 + 13.3707i) q^{67} +(2.73949 + 80.5524i) q^{69} +(-27.9939 + 16.1623i) q^{71} +(-20.3025 + 35.1650i) q^{73} +(4.60549 + 21.7646i) q^{75} +(48.3304 - 132.787i) q^{77} +(12.9014 - 73.1676i) q^{79} +(3.12181 - 80.9398i) q^{81} +(150.972 + 26.6204i) q^{83} +(54.5866 + 19.8679i) q^{85} +(121.061 - 25.6170i) q^{87} +(-18.0718 - 10.4337i) q^{89} +(-14.6700 - 25.4091i) q^{91} +(-104.629 + 3.55830i) q^{93} +(-15.6069 + 2.75192i) q^{95} +(-36.5526 - 30.6713i) q^{97} +(-7.29054 - 107.062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 9q^{5} + 6q^{9} + O(q^{10}) \) \( 36q - 9q^{5} + 6q^{9} + 36q^{11} + 45q^{15} + 42q^{21} - 18q^{23} - 9q^{25} - 18q^{29} + 45q^{31} - 153q^{33} - 243q^{35} - 123q^{39} - 198q^{41} + 90q^{43} - 333q^{45} - 243q^{47} + 72q^{49} - 99q^{51} + 243q^{57} + 252q^{59} - 144q^{61} + 381q^{63} + 747q^{65} + 108q^{67} + 585q^{69} + 324q^{71} - 63q^{73} + 597q^{75} + 495q^{77} + 36q^{79} - 54q^{81} - 27q^{83} - 180q^{85} - 441q^{87} - 567q^{89} + 99q^{91} - 699q^{93} - 1044q^{95} - 216q^{97} - 945q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.78257 + 1.12129i −0.927525 + 0.373762i
\(4\) 0 0
\(5\) −2.69546 3.21232i −0.539091 0.642464i 0.425892 0.904774i \(-0.359960\pi\)
−0.964984 + 0.262310i \(0.915516\pi\)
\(6\) 0 0
\(7\) 11.1367 4.05342i 1.59095 0.579060i 0.613406 0.789768i \(-0.289799\pi\)
0.977549 + 0.210708i \(0.0675769\pi\)
\(8\) 0 0
\(9\) 6.48544 6.24012i 0.720604 0.693347i
\(10\) 0 0
\(11\) 7.66419 9.13382i 0.696744 0.830347i −0.295410 0.955371i \(-0.595456\pi\)
0.992154 + 0.125023i \(0.0399006\pi\)
\(12\) 0 0
\(13\) −0.429892 2.43804i −0.0330686 0.187542i 0.963799 0.266630i \(-0.0859102\pi\)
−0.996868 + 0.0790884i \(0.974799\pi\)
\(14\) 0 0
\(15\) 11.1022 + 5.91614i 0.740149 + 0.394410i
\(16\) 0 0
\(17\) −11.9968 + 6.92637i −0.705695 + 0.407433i −0.809465 0.587168i \(-0.800243\pi\)
0.103770 + 0.994601i \(0.466910\pi\)
\(18\) 0 0
\(19\) 1.88960 3.27289i 0.0994528 0.172257i −0.812005 0.583650i \(-0.801624\pi\)
0.911458 + 0.411392i \(0.134957\pi\)
\(20\) 0 0
\(21\) −26.4436 + 23.7663i −1.25922 + 1.13173i
\(22\) 0 0
\(23\) 9.18883 25.2461i 0.399514 1.09766i −0.563008 0.826452i \(-0.690356\pi\)
0.962522 0.271204i \(-0.0874219\pi\)
\(24\) 0 0
\(25\) 1.28769 7.30285i 0.0515076 0.292114i
\(26\) 0 0
\(27\) −11.0493 + 24.6356i −0.409232 + 0.912431i
\(28\) 0 0
\(29\) −40.6205 7.16249i −1.40071 0.246982i −0.578273 0.815843i \(-0.696273\pi\)
−0.822434 + 0.568861i \(0.807384\pi\)
\(30\) 0 0
\(31\) 32.7920 + 11.9353i 1.05781 + 0.385010i 0.811604 0.584208i \(-0.198595\pi\)
0.246203 + 0.969218i \(0.420817\pi\)
\(32\) 0 0
\(33\) −11.0845 + 34.0093i −0.335895 + 1.03058i
\(34\) 0 0
\(35\) −43.0393 24.8488i −1.22970 0.709965i
\(36\) 0 0
\(37\) 33.5308 + 58.0771i 0.906238 + 1.56965i 0.819246 + 0.573442i \(0.194392\pi\)
0.0869922 + 0.996209i \(0.472274\pi\)
\(38\) 0 0
\(39\) 3.92995 + 6.30200i 0.100768 + 0.161590i
\(40\) 0 0
\(41\) 5.01099 0.883573i 0.122219 0.0215506i −0.112204 0.993685i \(-0.535791\pi\)
0.234423 + 0.972135i \(0.424680\pi\)
\(42\) 0 0
\(43\) −35.5382 29.8201i −0.826470 0.693490i 0.128008 0.991773i \(-0.459142\pi\)
−0.954478 + 0.298283i \(0.903586\pi\)
\(44\) 0 0
\(45\) −37.5265 4.01333i −0.833922 0.0891851i
\(46\) 0 0
\(47\) 31.9088 + 87.6686i 0.678910 + 1.86529i 0.454331 + 0.890833i \(0.349878\pi\)
0.224579 + 0.974456i \(0.427899\pi\)
\(48\) 0 0
\(49\) 70.0593 58.7867i 1.42978 1.19973i
\(50\) 0 0
\(51\) 25.6156 32.7250i 0.502267 0.641667i
\(52\) 0 0
\(53\) 51.4760i 0.971245i −0.874169 0.485622i \(-0.838593\pi\)
0.874169 0.485622i \(-0.161407\pi\)
\(54\) 0 0
\(55\) −49.9992 −0.909077
\(56\) 0 0
\(57\) −1.58812 + 11.2258i −0.0278617 + 0.196945i
\(58\) 0 0
\(59\) 9.45130 + 11.2636i 0.160192 + 0.190909i 0.840170 0.542323i \(-0.182455\pi\)
−0.679978 + 0.733232i \(0.738011\pi\)
\(60\) 0 0
\(61\) −48.1278 + 17.5171i −0.788980 + 0.287165i −0.704912 0.709295i \(-0.749013\pi\)
−0.0840678 + 0.996460i \(0.526791\pi\)
\(62\) 0 0
\(63\) 46.9324 95.7824i 0.744959 1.52036i
\(64\) 0 0
\(65\) −6.67301 + 7.95258i −0.102662 + 0.122347i
\(66\) 0 0
\(67\) 2.35762 + 13.3707i 0.0351884 + 0.199563i 0.997334 0.0729728i \(-0.0232486\pi\)
−0.962146 + 0.272536i \(0.912138\pi\)
\(68\) 0 0
\(69\) 2.73949 + 80.5524i 0.0397027 + 1.16743i
\(70\) 0 0
\(71\) −27.9939 + 16.1623i −0.394281 + 0.227638i −0.684013 0.729470i \(-0.739767\pi\)
0.289733 + 0.957108i \(0.406434\pi\)
\(72\) 0 0
\(73\) −20.3025 + 35.1650i −0.278117 + 0.481713i −0.970917 0.239417i \(-0.923044\pi\)
0.692800 + 0.721130i \(0.256377\pi\)
\(74\) 0 0
\(75\) 4.60549 + 21.7646i 0.0614065 + 0.290195i
\(76\) 0 0
\(77\) 48.3304 132.787i 0.627667 1.72450i
\(78\) 0 0
\(79\) 12.9014 73.1676i 0.163309 0.926172i −0.787481 0.616338i \(-0.788615\pi\)
0.950791 0.309834i \(-0.100273\pi\)
\(80\) 0 0
\(81\) 3.12181 80.9398i 0.0385408 0.999257i
\(82\) 0 0
\(83\) 150.972 + 26.6204i 1.81894 + 0.320728i 0.976080 0.217411i \(-0.0697611\pi\)
0.842857 + 0.538138i \(0.180872\pi\)
\(84\) 0 0
\(85\) 54.5866 + 19.8679i 0.642196 + 0.233740i
\(86\) 0 0
\(87\) 121.061 25.6170i 1.39150 0.294449i
\(88\) 0 0
\(89\) −18.0718 10.4337i −0.203054 0.117233i 0.395025 0.918670i \(-0.370736\pi\)
−0.598079 + 0.801437i \(0.704069\pi\)
\(90\) 0 0
\(91\) −14.6700 25.4091i −0.161209 0.279221i
\(92\) 0 0
\(93\) −104.629 + 3.55830i −1.12504 + 0.0382613i
\(94\) 0 0
\(95\) −15.6069 + 2.75192i −0.164283 + 0.0289676i
\(96\) 0 0
\(97\) −36.5526 30.6713i −0.376831 0.316199i 0.434626 0.900611i \(-0.356881\pi\)
−0.811457 + 0.584412i \(0.801325\pi\)
\(98\) 0 0
\(99\) −7.29054 107.062i −0.0736418 1.08144i
\(100\) 0 0
\(101\) 16.2462 + 44.6361i 0.160854 + 0.441942i 0.993769 0.111458i \(-0.0355522\pi\)
−0.832915 + 0.553400i \(0.813330\pi\)
\(102\) 0 0
\(103\) −80.7592 + 67.7650i −0.784070 + 0.657912i −0.944270 0.329172i \(-0.893230\pi\)
0.160200 + 0.987085i \(0.448786\pi\)
\(104\) 0 0
\(105\) 147.623 + 20.8842i 1.40593 + 0.198897i
\(106\) 0 0
\(107\) 189.677i 1.77268i 0.463031 + 0.886342i \(0.346762\pi\)
−0.463031 + 0.886342i \(0.653238\pi\)
\(108\) 0 0
\(109\) −86.7332 −0.795718 −0.397859 0.917447i \(-0.630247\pi\)
−0.397859 + 0.917447i \(0.630247\pi\)
\(110\) 0 0
\(111\) −158.423 124.006i −1.42723 1.11717i
\(112\) 0 0
\(113\) 99.7785 + 118.911i 0.882996 + 1.05231i 0.998259 + 0.0589785i \(0.0187844\pi\)
−0.115263 + 0.993335i \(0.536771\pi\)
\(114\) 0 0
\(115\) −105.867 + 38.5323i −0.920579 + 0.335063i
\(116\) 0 0
\(117\) −18.0017 13.1292i −0.153861 0.112215i
\(118\) 0 0
\(119\) −105.529 + 125.765i −0.886801 + 1.05685i
\(120\) 0 0
\(121\) −3.67551 20.8449i −0.0303761 0.172271i
\(122\) 0 0
\(123\) −12.9527 + 8.07736i −0.105307 + 0.0656696i
\(124\) 0 0
\(125\) −117.719 + 67.9654i −0.941756 + 0.543723i
\(126\) 0 0
\(127\) −100.294 + 173.715i −0.789720 + 1.36784i 0.136418 + 0.990651i \(0.456441\pi\)
−0.926138 + 0.377184i \(0.876892\pi\)
\(128\) 0 0
\(129\) 132.324 + 43.1281i 1.02577 + 0.334327i
\(130\) 0 0
\(131\) 36.8927 101.362i 0.281624 0.773755i −0.715546 0.698566i \(-0.753822\pi\)
0.997169 0.0751889i \(-0.0239560\pi\)
\(132\) 0 0
\(133\) 7.77752 44.1085i 0.0584776 0.331643i
\(134\) 0 0
\(135\) 108.920 30.9105i 0.806817 0.228967i
\(136\) 0 0
\(137\) 85.3702 + 15.0531i 0.623140 + 0.109876i 0.476299 0.879284i \(-0.341978\pi\)
0.146842 + 0.989160i \(0.453089\pi\)
\(138\) 0 0
\(139\) −57.5515 20.9470i −0.414040 0.150698i 0.126597 0.991954i \(-0.459594\pi\)
−0.540637 + 0.841256i \(0.681817\pi\)
\(140\) 0 0
\(141\) −187.090 208.165i −1.32688 1.47635i
\(142\) 0 0
\(143\) −25.5634 14.7590i −0.178765 0.103210i
\(144\) 0 0
\(145\) 86.4826 + 149.792i 0.596432 + 1.03305i
\(146\) 0 0
\(147\) −129.028 + 242.135i −0.877745 + 1.64718i
\(148\) 0 0
\(149\) 0.691518 0.121933i 0.00464106 0.000818344i −0.171327 0.985214i \(-0.554806\pi\)
0.175968 + 0.984396i \(0.443694\pi\)
\(150\) 0 0
\(151\) −96.5772 81.0379i −0.639584 0.536675i 0.264306 0.964439i \(-0.414857\pi\)
−0.903890 + 0.427764i \(0.859301\pi\)
\(152\) 0 0
\(153\) −34.5833 + 119.782i −0.226034 + 0.782890i
\(154\) 0 0
\(155\) −50.0494 137.510i −0.322899 0.887158i
\(156\) 0 0
\(157\) 158.053 132.622i 1.00671 0.844729i 0.0188086 0.999823i \(-0.494013\pi\)
0.987900 + 0.155095i \(0.0495682\pi\)
\(158\) 0 0
\(159\) 57.7193 + 143.236i 0.363014 + 0.900853i
\(160\) 0 0
\(161\) 318.404i 1.97766i
\(162\) 0 0
\(163\) 105.377 0.646484 0.323242 0.946316i \(-0.395227\pi\)
0.323242 + 0.946316i \(0.395227\pi\)
\(164\) 0 0
\(165\) 139.127 56.0634i 0.843191 0.339778i
\(166\) 0 0
\(167\) 134.126 + 159.846i 0.803152 + 0.957159i 0.999728 0.0233298i \(-0.00742678\pi\)
−0.196576 + 0.980489i \(0.562982\pi\)
\(168\) 0 0
\(169\) 153.049 55.7052i 0.905614 0.329617i
\(170\) 0 0
\(171\) −8.16832 33.0175i −0.0477679 0.193085i
\(172\) 0 0
\(173\) −85.3497 + 101.716i −0.493351 + 0.587953i −0.954066 0.299595i \(-0.903148\pi\)
0.460715 + 0.887548i \(0.347593\pi\)
\(174\) 0 0
\(175\) −15.2609 86.5491i −0.0872054 0.494566i
\(176\) 0 0
\(177\) −38.9287 20.7443i −0.219936 0.117199i
\(178\) 0 0
\(179\) 123.118 71.0820i 0.687808 0.397106i −0.114982 0.993368i \(-0.536681\pi\)
0.802790 + 0.596261i \(0.203348\pi\)
\(180\) 0 0
\(181\) −1.37020 + 2.37326i −0.00757019 + 0.0131119i −0.869786 0.493430i \(-0.835743\pi\)
0.862215 + 0.506542i \(0.169076\pi\)
\(182\) 0 0
\(183\) 114.277 102.708i 0.624467 0.561243i
\(184\) 0 0
\(185\) 96.1813 264.256i 0.519899 1.42841i
\(186\) 0 0
\(187\) −28.6817 + 162.662i −0.153378 + 0.869849i
\(188\) 0 0
\(189\) −23.1935 + 319.146i −0.122717 + 1.68861i
\(190\) 0 0
\(191\) −37.1032 6.54229i −0.194258 0.0342528i 0.0756728 0.997133i \(-0.475890\pi\)
−0.269930 + 0.962880i \(0.587001\pi\)
\(192\) 0 0
\(193\) 116.274 + 42.3202i 0.602455 + 0.219276i 0.625199 0.780466i \(-0.285018\pi\)
−0.0227435 + 0.999741i \(0.507240\pi\)
\(194\) 0 0
\(195\) 9.65103 29.6110i 0.0494925 0.151851i
\(196\) 0 0
\(197\) −50.1629 28.9616i −0.254634 0.147013i 0.367250 0.930122i \(-0.380299\pi\)
−0.621884 + 0.783109i \(0.713633\pi\)
\(198\) 0 0
\(199\) −155.640 269.577i −0.782112 1.35466i −0.930709 0.365761i \(-0.880809\pi\)
0.148597 0.988898i \(-0.452524\pi\)
\(200\) 0 0
\(201\) −21.5527 34.5615i −0.107227 0.171948i
\(202\) 0 0
\(203\) −481.410 + 84.8856i −2.37148 + 0.418156i
\(204\) 0 0
\(205\) −16.3452 13.7153i −0.0797328 0.0669038i
\(206\) 0 0
\(207\) −97.9451 221.071i −0.473165 1.06798i
\(208\) 0 0
\(209\) −15.4117 42.3433i −0.0737402 0.202600i
\(210\) 0 0
\(211\) −26.9821 + 22.6407i −0.127877 + 0.107302i −0.704483 0.709720i \(-0.748821\pi\)
0.576606 + 0.817022i \(0.304377\pi\)
\(212\) 0 0
\(213\) 59.7726 76.3620i 0.280623 0.358507i
\(214\) 0 0
\(215\) 194.539i 0.904832i
\(216\) 0 0
\(217\) 413.573 1.90587
\(218\) 0 0
\(219\) 17.0633 120.614i 0.0779146 0.550750i
\(220\) 0 0
\(221\) 22.0441 + 26.2711i 0.0997471 + 0.118874i
\(222\) 0 0
\(223\) 218.300 79.4546i 0.978923 0.356299i 0.197502 0.980303i \(-0.436717\pi\)
0.781421 + 0.624004i \(0.214495\pi\)
\(224\) 0 0
\(225\) −37.2194 55.3975i −0.165420 0.246211i
\(226\) 0 0
\(227\) 272.310 324.527i 1.19960 1.42963i 0.324372 0.945930i \(-0.394847\pi\)
0.875232 0.483703i \(-0.160708\pi\)
\(228\) 0 0
\(229\) 46.3777 + 263.021i 0.202523 + 1.14856i 0.901291 + 0.433215i \(0.142621\pi\)
−0.698768 + 0.715349i \(0.746268\pi\)
\(230\) 0 0
\(231\) 14.4088 + 423.681i 0.0623760 + 1.83412i
\(232\) 0 0
\(233\) 62.0180 35.8061i 0.266172 0.153674i −0.360975 0.932576i \(-0.617556\pi\)
0.627147 + 0.778901i \(0.284223\pi\)
\(234\) 0 0
\(235\) 195.611 338.808i 0.832387 1.44174i
\(236\) 0 0
\(237\) 46.1426 + 218.060i 0.194695 + 0.920086i
\(238\) 0 0
\(239\) 34.3802 94.4587i 0.143850 0.395225i −0.846754 0.531984i \(-0.821447\pi\)
0.990604 + 0.136760i \(0.0436688\pi\)
\(240\) 0 0
\(241\) −5.20365 + 29.5114i −0.0215919 + 0.122454i −0.993699 0.112085i \(-0.964247\pi\)
0.972107 + 0.234539i \(0.0753581\pi\)
\(242\) 0 0
\(243\) 82.0700 + 228.721i 0.337737 + 0.941241i
\(244\) 0 0
\(245\) −377.684 66.5958i −1.54157 0.271820i
\(246\) 0 0
\(247\) −8.79176 3.19994i −0.0355942 0.0129552i
\(248\) 0 0
\(249\) −449.939 + 95.2092i −1.80698 + 0.382366i
\(250\) 0 0
\(251\) 138.355 + 79.8791i 0.551214 + 0.318243i 0.749611 0.661878i \(-0.230240\pi\)
−0.198398 + 0.980122i \(0.563574\pi\)
\(252\) 0 0
\(253\) −160.168 277.420i −0.633077 1.09652i
\(254\) 0 0
\(255\) −174.169 + 5.92327i −0.683015 + 0.0232285i
\(256\) 0 0
\(257\) −438.482 + 77.3162i −1.70616 + 0.300841i −0.939838 0.341621i \(-0.889024\pi\)
−0.766318 + 0.642462i \(0.777913\pi\)
\(258\) 0 0
\(259\) 608.833 + 510.872i 2.35071 + 1.97248i
\(260\) 0 0
\(261\) −308.137 + 207.025i −1.18060 + 0.793199i
\(262\) 0 0
\(263\) −33.6999 92.5896i −0.128136 0.352052i 0.858990 0.511992i \(-0.171092\pi\)
−0.987127 + 0.159940i \(0.948870\pi\)
\(264\) 0 0
\(265\) −165.357 + 138.751i −0.623990 + 0.523590i
\(266\) 0 0
\(267\) 61.9853 + 8.76905i 0.232155 + 0.0328429i
\(268\) 0 0
\(269\) 46.7784i 0.173898i −0.996213 0.0869488i \(-0.972288\pi\)
0.996213 0.0869488i \(-0.0277116\pi\)
\(270\) 0 0
\(271\) −262.335 −0.968026 −0.484013 0.875061i \(-0.660821\pi\)
−0.484013 + 0.875061i \(0.660821\pi\)
\(272\) 0 0
\(273\) 69.3112 + 54.2536i 0.253887 + 0.198731i
\(274\) 0 0
\(275\) −56.8338 67.7319i −0.206669 0.246298i
\(276\) 0 0
\(277\) −321.656 + 117.073i −1.16121 + 0.422647i −0.849531 0.527539i \(-0.823115\pi\)
−0.311682 + 0.950186i \(0.600892\pi\)
\(278\) 0 0
\(279\) 287.148 127.220i 1.02921 0.455987i
\(280\) 0 0
\(281\) 164.193 195.677i 0.584316 0.696361i −0.390187 0.920736i \(-0.627590\pi\)
0.974503 + 0.224375i \(0.0720341\pi\)
\(282\) 0 0
\(283\) −8.52103 48.3252i −0.0301097 0.170760i 0.966045 0.258375i \(-0.0831868\pi\)
−0.996154 + 0.0876142i \(0.972076\pi\)
\(284\) 0 0
\(285\) 40.3417 25.1572i 0.141550 0.0882710i
\(286\) 0 0
\(287\) 52.2243 30.1517i 0.181966 0.105058i
\(288\) 0 0
\(289\) −48.5508 + 84.0925i −0.167996 + 0.290978i
\(290\) 0 0
\(291\) 136.102 + 44.3592i 0.467703 + 0.152437i
\(292\) 0 0
\(293\) −105.146 + 288.885i −0.358859 + 0.985956i 0.620567 + 0.784153i \(0.286902\pi\)
−0.979426 + 0.201803i \(0.935320\pi\)
\(294\) 0 0
\(295\) 10.7068 60.7212i 0.0362942 0.205835i
\(296\) 0 0
\(297\) 140.334 + 289.734i 0.472504 + 0.975535i
\(298\) 0 0
\(299\) −65.5012 11.5496i −0.219067 0.0386275i
\(300\) 0 0
\(301\) −516.651 188.046i −1.71645 0.624736i
\(302\) 0 0
\(303\) −95.2562 105.987i −0.314377 0.349791i
\(304\) 0 0
\(305\) 185.997 + 107.385i 0.609825 + 0.352083i
\(306\) 0 0
\(307\) 139.540 + 241.691i 0.454528 + 0.787266i 0.998661 0.0517333i \(-0.0164746\pi\)
−0.544133 + 0.838999i \(0.683141\pi\)
\(308\) 0 0
\(309\) 148.734 279.115i 0.481341 0.903285i
\(310\) 0 0
\(311\) −296.031 + 52.1983i −0.951869 + 0.167840i −0.627958 0.778247i \(-0.716109\pi\)
−0.323911 + 0.946087i \(0.604998\pi\)
\(312\) 0 0
\(313\) −187.281 157.148i −0.598342 0.502069i 0.292570 0.956244i \(-0.405490\pi\)
−0.890912 + 0.454175i \(0.849934\pi\)
\(314\) 0 0
\(315\) −434.188 + 107.415i −1.37838 + 0.341001i
\(316\) 0 0
\(317\) 107.090 + 294.227i 0.337823 + 0.928161i 0.986011 + 0.166681i \(0.0533049\pi\)
−0.648188 + 0.761480i \(0.724473\pi\)
\(318\) 0 0
\(319\) −376.744 + 316.126i −1.18102 + 0.990990i
\(320\) 0 0
\(321\) −212.682 527.791i −0.662562 1.64421i
\(322\) 0 0
\(323\) 52.3524i 0.162082i
\(324\) 0 0
\(325\) −18.3582 −0.0564868
\(326\) 0 0
\(327\) 241.342 97.2527i 0.738048 0.297409i
\(328\) 0 0
\(329\) 710.715 + 846.997i 2.16023 + 2.57446i
\(330\) 0 0
\(331\) 404.100 147.080i 1.22085 0.444352i 0.350393 0.936603i \(-0.386048\pi\)
0.870453 + 0.492251i \(0.163826\pi\)
\(332\) 0 0
\(333\) 579.870 + 167.419i 1.74135 + 0.502760i
\(334\) 0 0
\(335\) 36.5963 43.6137i 0.109243 0.130190i
\(336\) 0 0
\(337\) −85.6983 486.019i −0.254297 1.44219i −0.797870 0.602830i \(-0.794040\pi\)
0.543572 0.839363i \(-0.317071\pi\)
\(338\) 0 0
\(339\) −410.975 219.000i −1.21232 0.646017i
\(340\) 0 0
\(341\) 360.339 208.042i 1.05671 0.610093i
\(342\) 0 0
\(343\) 251.581 435.751i 0.733473 1.27041i
\(344\) 0 0
\(345\) 251.376 225.926i 0.728626 0.654857i
\(346\) 0 0
\(347\) 177.696 488.217i 0.512093 1.40696i −0.366958 0.930238i \(-0.619601\pi\)
0.879051 0.476727i \(-0.158177\pi\)
\(348\) 0 0
\(349\) −42.2124 + 239.399i −0.120952 + 0.685956i 0.862677 + 0.505755i \(0.168786\pi\)
−0.983630 + 0.180201i \(0.942325\pi\)
\(350\) 0 0
\(351\) 64.8126 + 16.3479i 0.184651 + 0.0465751i
\(352\) 0 0
\(353\) −631.952 111.430i −1.79023 0.315666i −0.822711 0.568460i \(-0.807540\pi\)
−0.967520 + 0.252793i \(0.918651\pi\)
\(354\) 0 0
\(355\) 127.375 + 46.3607i 0.358803 + 0.130593i
\(356\) 0 0
\(357\) 152.625 468.279i 0.427520 1.31171i
\(358\) 0 0
\(359\) 287.633 + 166.065i 0.801207 + 0.462577i 0.843893 0.536511i \(-0.180258\pi\)
−0.0426860 + 0.999089i \(0.513592\pi\)
\(360\) 0 0
\(361\) 173.359 + 300.266i 0.480218 + 0.831762i
\(362\) 0 0
\(363\) 33.6004 + 53.8810i 0.0925631 + 0.148433i
\(364\) 0 0
\(365\) 167.686 29.5676i 0.459414 0.0810070i
\(366\) 0 0
\(367\) 54.4378 + 45.6788i 0.148332 + 0.124465i 0.713934 0.700213i \(-0.246912\pi\)
−0.565602 + 0.824678i \(0.691356\pi\)
\(368\) 0 0
\(369\) 26.9849 36.9995i 0.0731297 0.100270i
\(370\) 0 0
\(371\) −208.654 573.271i −0.562409 1.54521i
\(372\) 0 0
\(373\) 251.356 210.913i 0.673878 0.565450i −0.240333 0.970691i \(-0.577257\pi\)
0.914210 + 0.405240i \(0.132812\pi\)
\(374\) 0 0
\(375\) 251.355 321.116i 0.670279 0.856309i
\(376\) 0 0
\(377\) 102.114i 0.270858i
\(378\) 0 0
\(379\) −77.9266 −0.205611 −0.102806 0.994701i \(-0.532782\pi\)
−0.102806 + 0.994701i \(0.532782\pi\)
\(380\) 0 0
\(381\) 84.2925 595.834i 0.221240 1.56387i
\(382\) 0 0
\(383\) 132.591 + 158.016i 0.346192 + 0.412575i 0.910842 0.412755i \(-0.135433\pi\)
−0.564651 + 0.825330i \(0.690989\pi\)
\(384\) 0 0
\(385\) −556.826 + 202.668i −1.44630 + 0.526410i
\(386\) 0 0
\(387\) −416.562 + 28.3663i −1.07639 + 0.0732979i
\(388\) 0 0
\(389\) −6.12284 + 7.29692i −0.0157400 + 0.0187582i −0.773857 0.633360i \(-0.781675\pi\)
0.758117 + 0.652119i \(0.226120\pi\)
\(390\) 0 0
\(391\) 64.6270 + 366.518i 0.165287 + 0.937386i
\(392\) 0 0
\(393\) 10.9989 + 323.414i 0.0279871 + 0.822937i
\(394\) 0 0
\(395\) −269.813 + 155.777i −0.683071 + 0.394371i
\(396\) 0 0
\(397\) −38.5291 + 66.7344i −0.0970507 + 0.168097i −0.910463 0.413591i \(-0.864274\pi\)
0.813412 + 0.581688i \(0.197608\pi\)
\(398\) 0 0
\(399\) 27.8167 + 131.456i 0.0697160 + 0.329464i
\(400\) 0 0
\(401\) −113.749 + 312.524i −0.283664 + 0.779361i 0.713253 + 0.700906i \(0.247221\pi\)
−0.996918 + 0.0784548i \(0.975001\pi\)
\(402\) 0 0
\(403\) 15.0017 85.0791i 0.0372252 0.211114i
\(404\) 0 0
\(405\) −268.419 + 208.142i −0.662764 + 0.513930i
\(406\) 0 0
\(407\) 787.452 + 138.849i 1.93477 + 0.341152i
\(408\) 0 0
\(409\) −395.056 143.789i −0.965906 0.351561i −0.189561 0.981869i \(-0.560706\pi\)
−0.776345 + 0.630308i \(0.782929\pi\)
\(410\) 0 0
\(411\) −254.428 + 53.8381i −0.619046 + 0.130993i
\(412\) 0 0
\(413\) 150.912 + 87.1293i 0.365405 + 0.210967i
\(414\) 0 0
\(415\) −321.425 556.724i −0.774517 1.34150i
\(416\) 0 0
\(417\) 183.629 6.24499i 0.440357 0.0149760i
\(418\) 0 0
\(419\) −154.222 + 27.1934i −0.368071 + 0.0649008i −0.354624 0.935009i \(-0.615391\pi\)
−0.0134462 + 0.999910i \(0.504280\pi\)
\(420\) 0 0
\(421\) 19.9240 + 16.7182i 0.0473253 + 0.0397107i 0.666144 0.745824i \(-0.267944\pi\)
−0.618818 + 0.785534i \(0.712388\pi\)
\(422\) 0 0
\(423\) 754.005 + 369.455i 1.78252 + 0.873415i
\(424\) 0 0
\(425\) 35.1341 + 96.5300i 0.0826684 + 0.227129i
\(426\) 0 0
\(427\) −464.980 + 390.164i −1.08894 + 0.913733i
\(428\) 0 0
\(429\) 87.6811 + 12.4042i 0.204385 + 0.0289143i
\(430\) 0 0
\(431\) 209.889i 0.486982i 0.969903 + 0.243491i \(0.0782927\pi\)
−0.969903 + 0.243491i \(0.921707\pi\)
\(432\) 0 0
\(433\) −405.331 −0.936100 −0.468050 0.883702i \(-0.655043\pi\)
−0.468050 + 0.883702i \(0.655043\pi\)
\(434\) 0 0
\(435\) −408.604 319.836i −0.939320 0.735256i
\(436\) 0 0
\(437\) −65.2644 77.7791i −0.149347 0.177984i
\(438\) 0 0
\(439\) 119.203 43.3863i 0.271533 0.0988299i −0.202665 0.979248i \(-0.564960\pi\)
0.474198 + 0.880418i \(0.342738\pi\)
\(440\) 0 0
\(441\) 87.5290 818.436i 0.198478 1.85586i
\(442\) 0 0
\(443\) −226.993 + 270.519i −0.512399 + 0.610653i −0.958766 0.284197i \(-0.908273\pi\)
0.446367 + 0.894850i \(0.352718\pi\)
\(444\) 0 0
\(445\) 15.1952 + 86.1760i 0.0341464 + 0.193654i
\(446\) 0 0
\(447\) −1.78748 + 1.11468i −0.00399883 + 0.00249369i
\(448\) 0 0
\(449\) 422.525 243.945i 0.941036 0.543307i 0.0507511 0.998711i \(-0.483838\pi\)
0.890285 + 0.455404i \(0.150505\pi\)
\(450\) 0 0
\(451\) 30.3348 52.5414i 0.0672611 0.116500i
\(452\) 0 0
\(453\) 359.600 + 117.203i 0.793819 + 0.258727i
\(454\) 0 0
\(455\) −42.0800 + 115.614i −0.0924836 + 0.254096i
\(456\) 0 0
\(457\) −43.5060 + 246.735i −0.0951992 + 0.539901i 0.899487 + 0.436948i \(0.143941\pi\)
−0.994686 + 0.102954i \(0.967171\pi\)
\(458\) 0 0
\(459\) −38.0795 372.080i −0.0829618 0.810633i
\(460\) 0 0
\(461\) 455.801 + 80.3699i 0.988721 + 0.174338i 0.644545 0.764567i \(-0.277047\pi\)
0.344177 + 0.938905i \(0.388158\pi\)
\(462\) 0 0
\(463\) −406.424 147.926i −0.877806 0.319495i −0.136482 0.990643i \(-0.543580\pi\)
−0.741324 + 0.671147i \(0.765802\pi\)
\(464\) 0 0
\(465\) 293.453 + 326.511i 0.631083 + 0.702174i
\(466\) 0 0
\(467\) 55.4592 + 32.0194i 0.118756 + 0.0685640i 0.558202 0.829705i \(-0.311492\pi\)
−0.439445 + 0.898269i \(0.644825\pi\)
\(468\) 0 0
\(469\) 80.4534 + 139.349i 0.171542 + 0.297120i
\(470\) 0 0
\(471\) −291.087 + 546.254i −0.618020 + 1.15978i
\(472\) 0 0
\(473\) −544.743 + 96.0528i −1.15168 + 0.203071i
\(474\) 0 0
\(475\) −21.4682 18.0140i −0.0451962 0.0379241i
\(476\) 0 0
\(477\) −321.216 333.844i −0.673409 0.699883i
\(478\) 0 0
\(479\) −59.8876 164.540i −0.125026 0.343507i 0.861350 0.508012i \(-0.169620\pi\)
−0.986376 + 0.164505i \(0.947397\pi\)
\(480\) 0 0
\(481\) 127.180 106.716i 0.264407 0.221864i
\(482\) 0 0
\(483\) 357.022 + 885.982i 0.739175 + 1.83433i
\(484\) 0 0
\(485\) 200.092i 0.412560i
\(486\) 0 0
\(487\) −28.7536 −0.0590424 −0.0295212 0.999564i \(-0.509398\pi\)
−0.0295212 + 0.999564i \(0.509398\pi\)
\(488\) 0 0
\(489\) −293.219 + 118.158i −0.599630 + 0.241631i
\(490\) 0 0
\(491\) −496.568 591.786i −1.01134 1.20527i −0.978593 0.205804i \(-0.934019\pi\)
−0.0327461 0.999464i \(-0.510425\pi\)
\(492\) 0 0
\(493\) 536.927 195.425i 1.08910 0.396401i
\(494\) 0 0
\(495\) −324.267 + 312.001i −0.655085 + 0.630306i
\(496\) 0 0
\(497\) −246.247 + 293.466i −0.495467 + 0.590474i
\(498\) 0 0
\(499\) 101.012 + 572.868i 0.202429 + 1.14803i 0.901435 + 0.432915i \(0.142515\pi\)
−0.699006 + 0.715116i \(0.746374\pi\)
\(500\) 0 0
\(501\) −552.449 294.388i −1.10269 0.587601i
\(502\) 0 0
\(503\) −491.674 + 283.868i −0.977484 + 0.564351i −0.901510 0.432759i \(-0.857540\pi\)
−0.0759745 + 0.997110i \(0.524207\pi\)
\(504\) 0 0
\(505\) 99.5946 172.503i 0.197217 0.341590i
\(506\) 0 0
\(507\) −363.408 + 326.615i −0.716782 + 0.644212i
\(508\) 0 0
\(509\) 175.613 482.494i 0.345016 0.947925i −0.638899 0.769291i \(-0.720610\pi\)
0.983916 0.178634i \(-0.0571679\pi\)
\(510\) 0 0
\(511\) −83.5643 + 473.917i −0.163531 + 0.927430i
\(512\) 0 0
\(513\) 59.7510 + 82.7146i 0.116474 + 0.161237i
\(514\) 0 0
\(515\) 435.366 + 76.7667i 0.845370 + 0.149062i
\(516\) 0 0
\(517\) 1045.30 + 380.459i 2.02186 + 0.735898i
\(518\) 0 0
\(519\) 123.439 378.733i 0.237841 0.729737i
\(520\) 0 0
\(521\) −616.698 356.051i −1.18368 0.683398i −0.226817 0.973937i \(-0.572832\pi\)
−0.956863 + 0.290539i \(0.906165\pi\)
\(522\) 0 0
\(523\) 101.608 + 175.990i 0.194279 + 0.336502i 0.946664 0.322222i \(-0.104430\pi\)
−0.752385 + 0.658724i \(0.771096\pi\)
\(524\) 0 0
\(525\) 139.511 + 223.717i 0.265735 + 0.426128i
\(526\) 0 0
\(527\) −476.068 + 83.9437i −0.903355 + 0.159286i
\(528\) 0 0
\(529\) −147.693 123.929i −0.279193 0.234271i
\(530\) 0 0
\(531\) 131.582 + 14.0723i 0.247801 + 0.0265015i
\(532\) 0 0
\(533\) −4.30837 11.8372i −0.00808325 0.0222085i
\(534\) 0 0
\(535\) 609.304 511.267i 1.13889 0.955639i
\(536\) 0 0
\(537\) −262.881 + 335.841i −0.489536 + 0.625402i
\(538\) 0 0
\(539\) 1090.46i 2.02312i
\(540\) 0 0
\(541\) 96.3158 0.178033 0.0890165 0.996030i \(-0.471628\pi\)
0.0890165 + 0.996030i \(0.471628\pi\)
\(542\) 0 0
\(543\) 1.15159 8.14017i 0.00212079 0.0149911i
\(544\) 0 0
\(545\) 233.786 + 278.615i 0.428965 + 0.511220i
\(546\) 0 0
\(547\) 242.175 88.1443i 0.442732 0.161141i −0.111028 0.993817i \(-0.535414\pi\)
0.553761 + 0.832676i \(0.313192\pi\)
\(548\) 0 0
\(549\) −202.821 + 413.929i −0.369437 + 0.753969i
\(550\) 0 0
\(551\) −100.199 + 119.412i −0.181849 + 0.216719i
\(552\) 0 0
\(553\) −152.900 867.139i −0.276492 1.56806i
\(554\) 0 0
\(555\) 28.6748 + 843.159i 0.0516662 + 1.51920i
\(556\) 0 0
\(557\) −251.062 + 144.951i −0.450740 + 0.260235i −0.708143 0.706069i \(-0.750467\pi\)
0.257403 + 0.966304i \(0.417133\pi\)
\(558\) 0 0
\(559\) −57.4250 + 99.4630i −0.102728 + 0.177930i
\(560\) 0 0
\(561\) −102.581 484.779i −0.182855 0.864133i
\(562\) 0 0
\(563\) 20.9437 57.5424i 0.0372002 0.102207i −0.919702 0.392617i \(-0.871570\pi\)
0.956902 + 0.290411i \(0.0937919\pi\)
\(564\) 0 0
\(565\) 113.033 641.041i 0.200058 1.13459i
\(566\) 0 0
\(567\) −293.317 914.055i −0.517313 1.61209i
\(568\) 0 0
\(569\) −482.543 85.0854i −0.848055 0.149535i −0.267300 0.963613i \(-0.586131\pi\)
−0.580755 + 0.814079i \(0.697242\pi\)
\(570\) 0 0
\(571\) 717.627 + 261.195i 1.25679 + 0.457434i 0.882690 0.469955i \(-0.155730\pi\)
0.374099 + 0.927389i \(0.377952\pi\)
\(572\) 0 0
\(573\) 110.578 23.3989i 0.192981 0.0408357i
\(574\) 0 0
\(575\) −172.536 99.6138i −0.300063 0.173241i
\(576\) 0 0
\(577\) 130.453 + 225.951i 0.226088 + 0.391595i 0.956645 0.291256i \(-0.0940730\pi\)
−0.730557 + 0.682851i \(0.760740\pi\)
\(578\) 0 0
\(579\) −370.994 + 12.6170i −0.640749 + 0.0217911i
\(580\) 0 0
\(581\) 1789.23 315.489i 3.07957 0.543011i
\(582\) 0 0
\(583\) −470.172 394.521i −0.806470 0.676709i
\(584\) 0 0
\(585\) 6.34768 + 93.2164i 0.0108507 + 0.159344i
\(586\) 0 0
\(587\) −96.4128 264.892i −0.164247 0.451264i 0.830079 0.557646i \(-0.188295\pi\)
−0.994325 + 0.106382i \(0.966073\pi\)
\(588\) 0 0
\(589\) 101.027 84.7716i 0.171523 0.143925i
\(590\) 0 0
\(591\) 172.056 + 24.3408i 0.291127 + 0.0411857i
\(592\) 0 0
\(593\) 248.742i 0.419463i 0.977759 + 0.209731i \(0.0672590\pi\)
−0.977759 + 0.209731i \(0.932741\pi\)
\(594\) 0 0
\(595\) 688.447 1.15705
\(596\) 0 0
\(597\) 735.354 + 575.601i 1.23175 + 0.964155i
\(598\) 0 0
\(599\) −204.393 243.586i −0.341224 0.406655i 0.567956 0.823059i \(-0.307734\pi\)
−0.909179 + 0.416404i \(0.863290\pi\)
\(600\) 0 0
\(601\) −775.786 + 282.363i −1.29083 + 0.469822i −0.893998 0.448071i \(-0.852111\pi\)
−0.396828 + 0.917893i \(0.629889\pi\)
\(602\) 0 0
\(603\) 98.7253 + 72.0033i 0.163724 + 0.119408i
\(604\) 0 0
\(605\) −57.0532 + 67.9933i −0.0943027 + 0.112386i
\(606\) 0 0
\(607\) −70.3046 398.717i −0.115823 0.656865i −0.986339 0.164726i \(-0.947326\pi\)
0.870516 0.492139i \(-0.163785\pi\)
\(608\) 0 0
\(609\) 1244.38 775.999i 2.04331 1.27422i
\(610\) 0 0
\(611\) 200.022 115.483i 0.327369 0.189006i
\(612\) 0 0
\(613\) −309.729 + 536.467i −0.505268 + 0.875150i 0.494713 + 0.869056i \(0.335273\pi\)
−0.999981 + 0.00609364i \(0.998060\pi\)
\(614\) 0 0
\(615\) 60.8606 + 19.8361i 0.0989603 + 0.0322538i
\(616\) 0 0
\(617\) 275.916 758.074i 0.447190 1.22865i −0.487481 0.873133i \(-0.662084\pi\)
0.934672 0.355512i \(-0.115694\pi\)
\(618\) 0 0
\(619\) 155.014 879.129i 0.250427 1.42024i −0.557118 0.830434i \(-0.688093\pi\)
0.807544 0.589807i \(-0.200796\pi\)
\(620\) 0 0
\(621\) 520.423 + 505.323i 0.838041 + 0.813725i
\(622\) 0 0
\(623\) −243.552 42.9448i −0.390934 0.0689322i
\(624\) 0 0
\(625\) 361.427 + 131.549i 0.578283 + 0.210478i
\(626\) 0 0
\(627\) 90.3632 + 100.543i 0.144120 + 0.160355i
\(628\) 0 0
\(629\) −804.527 464.494i −1.27906 0.738464i
\(630\) 0 0
\(631\) 415.342 + 719.393i 0.658228 + 1.14008i 0.981074 + 0.193633i \(0.0620271\pi\)
−0.322846 + 0.946452i \(0.604640\pi\)
\(632\) 0 0
\(633\) 49.6931 93.2541i 0.0785041 0.147321i
\(634\) 0 0
\(635\) 828.368 146.064i 1.30452 0.230021i
\(636\) 0 0
\(637\) −173.442 145.535i −0.272280 0.228470i
\(638\) 0 0
\(639\) −80.6982 + 279.505i −0.126288 + 0.437410i
\(640\) 0 0
\(641\) 243.303 + 668.469i 0.379567 + 1.04285i 0.971536 + 0.236892i \(0.0761287\pi\)
−0.591969 + 0.805961i \(0.701649\pi\)
\(642\) 0 0
\(643\) 693.699 582.082i 1.07885 0.905260i 0.0830225 0.996548i \(-0.473543\pi\)
0.995825 + 0.0912875i \(0.0290982\pi\)
\(644\) 0 0
\(645\) −218.134 541.319i −0.338192 0.839254i
\(646\) 0 0
\(647\) 175.592i 0.271394i −0.990750 0.135697i \(-0.956673\pi\)
0.990750 0.135697i \(-0.0433273\pi\)
\(648\) 0 0
\(649\) 175.316 0.270133
\(650\) 0 0
\(651\) −1150.80 + 463.733i −1.76774 + 0.712340i
\(652\) 0 0
\(653\) −649.581 774.140i −0.994764 1.18551i −0.982628 0.185587i \(-0.940581\pi\)
−0.0121359 0.999926i \(-0.503863\pi\)
\(654\) 0 0
\(655\) −425.050 + 154.705i −0.648931 + 0.236191i
\(656\) 0 0
\(657\) 87.7632 + 354.751i 0.133582 + 0.539956i
\(658\) 0 0
\(659\) −168.977 + 201.379i −0.256414 + 0.305582i −0.878859 0.477081i \(-0.841695\pi\)
0.622445 + 0.782663i \(0.286139\pi\)
\(660\) 0 0
\(661\) 86.6822 + 491.599i 0.131138 + 0.743721i 0.977472 + 0.211067i \(0.0676939\pi\)
−0.846334 + 0.532653i \(0.821195\pi\)
\(662\) 0 0
\(663\) −90.7968 48.3837i −0.136948 0.0729769i
\(664\) 0 0
\(665\) −162.655 + 93.9086i −0.244593 + 0.141216i
\(666\) 0 0
\(667\) −554.080 + 959.694i −0.830704 + 1.43882i
\(668\) 0 0
\(669\) −518.344 + 465.865i −0.774804 + 0.696360i
\(670\) 0 0
\(671\) −208.862 + 573.844i −0.311270 + 0.855208i
\(672\) 0 0
\(673\) 155.048 879.320i 0.230383 1.30657i −0.621739 0.783225i \(-0.713573\pi\)
0.852122 0.523343i \(-0.175316\pi\)
\(674\) 0 0
\(675\) 165.682 + 112.414i 0.245455 + 0.166539i
\(676\) 0 0
\(677\) −308.774 54.4452i −0.456092 0.0804213i −0.0591175 0.998251i \(-0.518829\pi\)
−0.396974 + 0.917830i \(0.629940\pi\)
\(678\) 0 0
\(679\) −531.398 193.413i −0.782619 0.284850i
\(680\) 0 0
\(681\) −393.836 + 1208.36i −0.578320 + 1.77439i
\(682\) 0 0
\(683\) −421.298 243.237i −0.616835 0.356130i 0.158801 0.987311i \(-0.449237\pi\)
−0.775636 + 0.631181i \(0.782571\pi\)
\(684\) 0 0
\(685\) −181.756 314.811i −0.265338 0.459579i
\(686\) 0 0
\(687\) −423.971 679.873i −0.617134 0.989626i
\(688\) 0 0
\(689\) −125.500 + 22.1291i −0.182149 + 0.0321177i
\(690\) 0 0
\(691\) 473.285 + 397.134i 0.684928 + 0.574723i 0.917442 0.397870i \(-0.130251\pi\)
−0.232513 + 0.972593i \(0.574695\pi\)
\(692\) 0 0
\(693\) −515.161 1162.77i −0.743378 1.67787i
\(694\) 0 0
\(695\) 87.8391 + 241.336i 0.126387 + 0.347246i
\(696\) 0 0
\(697\) −53.9960 + 45.3080i −0.0774692 + 0.0650044i
\(698\) 0 0
\(699\) −132.421 + 169.173i −0.189443 + 0.242022i
\(700\) 0 0
\(701\) 297.109i 0.423836i 0.977287 + 0.211918i \(0.0679709\pi\)
−0.977287 + 0.211918i \(0.932029\pi\)
\(702\) 0 0
\(703\) 253.440 0.360512
\(704\) 0 0
\(705\) −164.401 + 1162.09i −0.233193 + 1.64836i
\(706\) 0 0
\(707\) 361.858 + 431.246i 0.511822 + 0.609966i
\(708\) 0 0
\(709\) 827.896 301.330i 1.16770 0.425006i 0.315855 0.948807i \(-0.397709\pi\)
0.851841 + 0.523801i \(0.175486\pi\)
\(710\) 0 0
\(711\) −372.903 555.030i −0.524477 0.780634i
\(712\) 0 0
\(713\) 602.640 718.198i 0.845217 1.00729i
\(714\) 0 0
\(715\) 21.4943 + 121.900i 0.0300619 + 0.170490i
\(716\) 0 0
\(717\) 10.2498 + 301.388i 0.0142955 + 0.420346i
\(718\) 0 0
\(719\) −1021.09 + 589.526i −1.42015 + 0.819925i −0.996311 0.0858124i \(-0.972651\pi\)
−0.423840 + 0.905737i \(0.639318\pi\)
\(720\) 0 0
\(721\) −624.709 + 1082.03i −0.866448 + 1.50073i
\(722\) 0 0
\(723\) −18.6111 87.9524i −0.0257415 0.121649i
\(724\) 0 0
\(725\) −104.613 + 287.422i −0.144294 + 0.396445i
\(726\) 0 0
\(727\) −111.710 + 633.537i −0.153658 + 0.871441i 0.806344 + 0.591447i \(0.201443\pi\)
−0.960002 + 0.279993i \(0.909668\pi\)
\(728\) 0 0
\(729\) −484.828 544.411i −0.665059 0.746791i
\(730\) 0 0
\(731\) 632.890 + 111.596i 0.865787 + 0.152662i
\(732\) 0 0
\(733\) −177.435 64.5811i −0.242067 0.0881052i 0.218138 0.975918i \(-0.430002\pi\)
−0.460205 + 0.887813i \(0.652224\pi\)
\(734\) 0 0
\(735\) 1125.61 238.183i 1.53144 0.324059i
\(736\) 0 0
\(737\) 140.195 + 80.9418i 0.190224 + 0.109826i
\(738\) 0 0
\(739\) −455.604 789.129i −0.616514 1.06783i −0.990117 0.140244i \(-0.955211\pi\)
0.373603 0.927589i \(-0.378122\pi\)
\(740\) 0 0
\(741\) 28.0518 0.954005i 0.0378566 0.00128746i
\(742\) 0 0
\(743\) 293.238 51.7058i 0.394668 0.0695906i 0.0272075 0.999630i \(-0.491339\pi\)
0.367460 + 0.930039i \(0.380227\pi\)
\(744\) 0 0
\(745\) −2.25565 1.89271i −0.00302771 0.00254055i
\(746\) 0 0
\(747\) 1145.23 769.437i 1.53311 1.03004i
\(748\) 0 0
\(749\) 768.841 + 2112.37i 1.02649 + 2.82026i
\(750\) 0 0
\(751\) −4.07029 + 3.41538i −0.00541983 + 0.00454777i −0.645494 0.763766i \(-0.723348\pi\)
0.640074 + 0.768314i \(0.278904\pi\)
\(752\) 0 0
\(753\) −474.549 67.1344i −0.630212 0.0891560i
\(754\) 0 0
\(755\) 528.671i 0.700227i
\(756\) 0 0
\(757\) −678.131 −0.895813 −0.447907 0.894080i \(-0.647830\pi\)
−0.447907 + 0.894080i \(0.647830\pi\)
\(758\) 0 0
\(759\) 756.747 + 592.347i 0.997032 + 0.780430i
\(760\) 0 0
\(761\) −587.824 700.542i −0.772436 0.920554i 0.226129 0.974097i \(-0.427393\pi\)
−0.998566 + 0.0535434i \(0.982948\pi\)
\(762\) 0 0
\(763\) −965.920 + 351.566i −1.26595 + 0.460768i
\(764\) 0 0
\(765\) 477.996 211.775i 0.624832 0.276830i
\(766\) 0 0
\(767\) 23.3981 27.8848i 0.0305060 0.0363557i
\(768\) 0 0
\(769\) 61.7617 + 350.268i 0.0803143 + 0.455485i 0.998270 + 0.0588015i \(0.0187279\pi\)
−0.917955 + 0.396684i \(0.870161\pi\)
\(770\) 0 0
\(771\) 1133.42 706.801i 1.47006 0.916733i
\(772\) 0 0
\(773\) −630.397 + 363.960i −0.815520 + 0.470841i −0.848869 0.528603i \(-0.822716\pi\)
0.0333493 + 0.999444i \(0.489383\pi\)
\(774\) 0 0
\(775\) 129.388 224.106i 0.166952 0.289169i
\(776\) 0 0
\(777\) −2266.96 738.862i −2.91757 0.950917i
\(778\) 0 0
\(779\) 6.57695 18.0700i 0.00844281 0.0231964i
\(780\) 0 0
\(781\) −66.9271 + 379.562i −0.0856941 + 0.485995i
\(782\) 0 0
\(783\) 625.279 921.571i 0.798568 1.17697i
\(784\) 0