Properties

Label 105.3.l.a.43.5
Level 105
Weight 3
Character 105.43
Analytic conductor 2.861
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.5
Character \(\chi\) \(=\) 105.43
Dual form 105.3.l.a.22.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.867675 + 0.867675i) q^{2} +(1.22474 + 1.22474i) q^{3} +2.49428i q^{4} +(-4.93004 + 0.833478i) q^{5} -2.12536 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-5.63493 - 5.63493i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(-0.867675 + 0.867675i) q^{2} +(1.22474 + 1.22474i) q^{3} +2.49428i q^{4} +(-4.93004 + 0.833478i) q^{5} -2.12536 q^{6} +(-1.87083 + 1.87083i) q^{7} +(-5.63493 - 5.63493i) q^{8} +3.00000i q^{9} +(3.55449 - 5.00086i) q^{10} -1.49884 q^{11} +(-3.05486 + 3.05486i) q^{12} +(2.15706 + 2.15706i) q^{13} -3.24654i q^{14} +(-7.05884 - 5.01725i) q^{15} -0.198550 q^{16} +(-2.96697 + 2.96697i) q^{17} +(-2.60303 - 2.60303i) q^{18} +34.8524i q^{19} +(-2.07893 - 12.2969i) q^{20} -4.58258 q^{21} +(1.30051 - 1.30051i) q^{22} +(-7.50682 - 7.50682i) q^{23} -13.8027i q^{24} +(23.6106 - 8.21817i) q^{25} -3.74326 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-4.66637 - 4.66637i) q^{28} +37.1782i q^{29} +(10.4781 - 1.77144i) q^{30} +47.0705 q^{31} +(22.7120 - 22.7120i) q^{32} +(-1.83570 - 1.83570i) q^{33} -5.14873i q^{34} +(7.66397 - 10.7826i) q^{35} -7.48284 q^{36} +(16.3936 - 16.3936i) q^{37} +(-30.2406 - 30.2406i) q^{38} +5.28371i q^{39} +(32.4770 + 23.0838i) q^{40} +73.4639 q^{41} +(3.97619 - 3.97619i) q^{42} +(-0.244769 - 0.244769i) q^{43} -3.73853i q^{44} +(-2.50043 - 14.7901i) q^{45} +13.0270 q^{46} +(-38.9392 + 38.9392i) q^{47} +(-0.243173 - 0.243173i) q^{48} -7.00000i q^{49} +(-13.3557 + 27.6171i) q^{50} -7.26756 q^{51} +(-5.38032 + 5.38032i) q^{52} +(-33.0957 - 33.0957i) q^{53} -6.37608i q^{54} +(7.38936 - 1.24925i) q^{55} +21.0840 q^{56} +(-42.6853 + 42.6853i) q^{57} +(-32.2586 - 32.2586i) q^{58} +31.6176i q^{59} +(12.5144 - 17.6067i) q^{60} -106.415 q^{61} +(-40.8419 + 40.8419i) q^{62} +(-5.61249 - 5.61249i) q^{63} +38.6190i q^{64} +(-12.4323 - 8.83655i) q^{65} +3.18558 q^{66} +(28.6607 - 28.6607i) q^{67} +(-7.40045 - 7.40045i) q^{68} -18.3879i q^{69} +(2.70592 + 16.0056i) q^{70} +15.8493 q^{71} +(16.9048 - 16.9048i) q^{72} +(-26.2684 - 26.2684i) q^{73} +28.4486i q^{74} +(38.9822 + 18.8518i) q^{75} -86.9316 q^{76} +(2.80408 - 2.80408i) q^{77} +(-4.58454 - 4.58454i) q^{78} -73.8402i q^{79} +(0.978860 - 0.165487i) q^{80} -9.00000 q^{81} +(-63.7428 + 63.7428i) q^{82} +(58.6690 + 58.6690i) q^{83} -11.4302i q^{84} +(12.1544 - 17.1002i) q^{85} +0.424760 q^{86} +(-45.5338 + 45.5338i) q^{87} +(8.44587 + 8.44587i) q^{88} +83.2528i q^{89} +(15.0026 + 10.6635i) q^{90} -8.07100 q^{91} +(18.7241 - 18.7241i) q^{92} +(57.6493 + 57.6493i) q^{93} -67.5732i q^{94} +(-29.0487 - 171.824i) q^{95} +55.6328 q^{96} +(-103.272 + 103.272i) q^{97} +(6.07373 + 6.07373i) q^{98} -4.49653i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} - 40q^{10} - 48q^{12} + 64q^{13} - 184q^{16} + 24q^{17} + 24q^{18} + 72q^{20} + 8q^{22} + 8q^{23} - 136q^{25} - 80q^{26} + 96q^{30} + 96q^{31} + 56q^{32} - 72q^{33} + 168q^{36} + 8q^{37} + 56q^{38} + 232q^{40} + 320q^{41} - 112q^{43} - 72q^{45} + 320q^{46} + 64q^{47} + 192q^{48} - 256q^{50} - 192q^{51} + 96q^{52} - 72q^{53} - 80q^{55} - 336q^{56} + 48q^{57} - 512q^{58} - 192q^{60} - 496q^{61} - 776q^{62} + 312q^{65} - 192q^{66} - 192q^{67} + 568q^{68} + 112q^{70} - 144q^{71} + 144q^{72} + 224q^{73} + 144q^{75} + 416q^{76} + 112q^{77} - 216q^{78} - 528q^{80} - 216q^{81} + 352q^{82} - 32q^{83} + 24q^{85} + 240q^{86} + 384q^{87} + 216q^{88} - 24q^{90} + 1304q^{92} + 376q^{95} + 168q^{96} - 816q^{97} - 56q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.867675 + 0.867675i −0.433838 + 0.433838i −0.889932 0.456094i \(-0.849248\pi\)
0.456094 + 0.889932i \(0.349248\pi\)
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i
\(4\) 2.49428i 0.623570i
\(5\) −4.93004 + 0.833478i −0.986008 + 0.166696i
\(6\) −2.12536 −0.354227
\(7\) −1.87083 + 1.87083i −0.267261 + 0.267261i
\(8\) −5.63493 5.63493i −0.704366 0.704366i
\(9\) 3.00000i 0.333333i
\(10\) 3.55449 5.00086i 0.355449 0.500086i
\(11\) −1.49884 −0.136258 −0.0681292 0.997677i \(-0.521703\pi\)
−0.0681292 + 0.997677i \(0.521703\pi\)
\(12\) −3.05486 + 3.05486i −0.254571 + 0.254571i
\(13\) 2.15706 + 2.15706i 0.165928 + 0.165928i 0.785187 0.619259i \(-0.212567\pi\)
−0.619259 + 0.785187i \(0.712567\pi\)
\(14\) 3.24654i 0.231896i
\(15\) −7.05884 5.01725i −0.470589 0.334483i
\(16\) −0.198550 −0.0124094
\(17\) −2.96697 + 2.96697i −0.174528 + 0.174528i −0.788965 0.614438i \(-0.789383\pi\)
0.614438 + 0.788965i \(0.289383\pi\)
\(18\) −2.60303 2.60303i −0.144613 0.144613i
\(19\) 34.8524i 1.83434i 0.398501 + 0.917168i \(0.369531\pi\)
−0.398501 + 0.917168i \(0.630469\pi\)
\(20\) −2.07893 12.2969i −0.103946 0.614845i
\(21\) −4.58258 −0.218218
\(22\) 1.30051 1.30051i 0.0591140 0.0591140i
\(23\) −7.50682 7.50682i −0.326383 0.326383i 0.524826 0.851209i \(-0.324130\pi\)
−0.851209 + 0.524826i \(0.824130\pi\)
\(24\) 13.8027i 0.575112i
\(25\) 23.6106 8.21817i 0.944425 0.328727i
\(26\) −3.74326 −0.143972
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) −4.66637 4.66637i −0.166656 0.166656i
\(29\) 37.1782i 1.28201i 0.767538 + 0.641004i \(0.221482\pi\)
−0.767538 + 0.641004i \(0.778518\pi\)
\(30\) 10.4781 1.77144i 0.349271 0.0590481i
\(31\) 47.0705 1.51840 0.759201 0.650856i \(-0.225590\pi\)
0.759201 + 0.650856i \(0.225590\pi\)
\(32\) 22.7120 22.7120i 0.709749 0.709749i
\(33\) −1.83570 1.83570i −0.0556273 0.0556273i
\(34\) 5.14873i 0.151433i
\(35\) 7.66397 10.7826i 0.218971 0.308073i
\(36\) −7.48284 −0.207857
\(37\) 16.3936 16.3936i 0.443070 0.443070i −0.449972 0.893043i \(-0.648566\pi\)
0.893043 + 0.449972i \(0.148566\pi\)
\(38\) −30.2406 30.2406i −0.795804 0.795804i
\(39\) 5.28371i 0.135480i
\(40\) 32.4770 + 23.0838i 0.811925 + 0.577096i
\(41\) 73.4639 1.79180 0.895902 0.444252i \(-0.146531\pi\)
0.895902 + 0.444252i \(0.146531\pi\)
\(42\) 3.97619 3.97619i 0.0946711 0.0946711i
\(43\) −0.244769 0.244769i −0.00569230 0.00569230i 0.704255 0.709947i \(-0.251281\pi\)
−0.709947 + 0.704255i \(0.751281\pi\)
\(44\) 3.73853i 0.0849667i
\(45\) −2.50043 14.7901i −0.0555652 0.328669i
\(46\) 13.0270 0.283195
\(47\) −38.9392 + 38.9392i −0.828494 + 0.828494i −0.987308 0.158814i \(-0.949233\pi\)
0.158814 + 0.987308i \(0.449233\pi\)
\(48\) −0.243173 0.243173i −0.00506611 0.00506611i
\(49\) 7.00000i 0.142857i
\(50\) −13.3557 + 27.6171i −0.267113 + 0.552341i
\(51\) −7.26756 −0.142501
\(52\) −5.38032 + 5.38032i −0.103468 + 0.103468i
\(53\) −33.0957 33.0957i −0.624447 0.624447i 0.322218 0.946665i \(-0.395571\pi\)
−0.946665 + 0.322218i \(0.895571\pi\)
\(54\) 6.37608i 0.118076i
\(55\) 7.38936 1.24925i 0.134352 0.0227137i
\(56\) 21.0840 0.376499
\(57\) −42.6853 + 42.6853i −0.748865 + 0.748865i
\(58\) −32.2586 32.2586i −0.556183 0.556183i
\(59\) 31.6176i 0.535891i 0.963434 + 0.267946i \(0.0863447\pi\)
−0.963434 + 0.267946i \(0.913655\pi\)
\(60\) 12.5144 17.6067i 0.208574 0.293445i
\(61\) −106.415 −1.74451 −0.872256 0.489049i \(-0.837344\pi\)
−0.872256 + 0.489049i \(0.837344\pi\)
\(62\) −40.8419 + 40.8419i −0.658740 + 0.658740i
\(63\) −5.61249 5.61249i −0.0890871 0.0890871i
\(64\) 38.6190i 0.603422i
\(65\) −12.4323 8.83655i −0.191266 0.135947i
\(66\) 3.18558 0.0482664
\(67\) 28.6607 28.6607i 0.427771 0.427771i −0.460097 0.887868i \(-0.652186\pi\)
0.887868 + 0.460097i \(0.152186\pi\)
\(68\) −7.40045 7.40045i −0.108830 0.108830i
\(69\) 18.3879i 0.266491i
\(70\) 2.70592 + 16.0056i 0.0386560 + 0.228651i
\(71\) 15.8493 0.223229 0.111615 0.993752i \(-0.464398\pi\)
0.111615 + 0.993752i \(0.464398\pi\)
\(72\) 16.9048 16.9048i 0.234789 0.234789i
\(73\) −26.2684 26.2684i −0.359841 0.359841i 0.503913 0.863754i \(-0.331893\pi\)
−0.863754 + 0.503913i \(0.831893\pi\)
\(74\) 28.4486i 0.384441i
\(75\) 38.9822 + 18.8518i 0.519762 + 0.251358i
\(76\) −86.9316 −1.14384
\(77\) 2.80408 2.80408i 0.0364166 0.0364166i
\(78\) −4.58454 4.58454i −0.0587762 0.0587762i
\(79\) 73.8402i 0.934686i −0.884076 0.467343i \(-0.845211\pi\)
0.884076 0.467343i \(-0.154789\pi\)
\(80\) 0.978860 0.165487i 0.0122358 0.00206859i
\(81\) −9.00000 −0.111111
\(82\) −63.7428 + 63.7428i −0.777352 + 0.777352i
\(83\) 58.6690 + 58.6690i 0.706856 + 0.706856i 0.965873 0.259017i \(-0.0833986\pi\)
−0.259017 + 0.965873i \(0.583399\pi\)
\(84\) 11.4302i 0.136074i
\(85\) 12.1544 17.1002i 0.142993 0.201179i
\(86\) 0.424760 0.00493907
\(87\) −45.5338 + 45.5338i −0.523377 + 0.523377i
\(88\) 8.44587 + 8.44587i 0.0959758 + 0.0959758i
\(89\) 83.2528i 0.935424i 0.883881 + 0.467712i \(0.154922\pi\)
−0.883881 + 0.467712i \(0.845078\pi\)
\(90\) 15.0026 + 10.6635i 0.166695 + 0.118483i
\(91\) −8.07100 −0.0886923
\(92\) 18.7241 18.7241i 0.203523 0.203523i
\(93\) 57.6493 + 57.6493i 0.619885 + 0.619885i
\(94\) 67.5732i 0.718864i
\(95\) −29.0487 171.824i −0.305776 1.80867i
\(96\) 55.6328 0.579508
\(97\) −103.272 + 103.272i −1.06466 + 1.06466i −0.0669049 + 0.997759i \(0.521312\pi\)
−0.997759 + 0.0669049i \(0.978688\pi\)
\(98\) 6.07373 + 6.07373i 0.0619768 + 0.0619768i
\(99\) 4.49653i 0.0454195i
\(100\) 20.4984 + 58.8915i 0.204984 + 0.588915i
\(101\) 88.5891 0.877120 0.438560 0.898702i \(-0.355489\pi\)
0.438560 + 0.898702i \(0.355489\pi\)
\(102\) 6.30588 6.30588i 0.0618224 0.0618224i
\(103\) 22.0312 + 22.0312i 0.213895 + 0.213895i 0.805920 0.592025i \(-0.201671\pi\)
−0.592025 + 0.805920i \(0.701671\pi\)
\(104\) 24.3098i 0.233748i
\(105\) 22.5923 3.81948i 0.215165 0.0363760i
\(106\) 57.4326 0.541817
\(107\) 108.746 108.746i 1.01632 1.01632i 0.0164543 0.999865i \(-0.494762\pi\)
0.999865 0.0164543i \(-0.00523781\pi\)
\(108\) −9.16457 9.16457i −0.0848571 0.0848571i
\(109\) 75.8376i 0.695758i −0.937539 0.347879i \(-0.886902\pi\)
0.937539 0.347879i \(-0.113098\pi\)
\(110\) −5.32762 + 7.49551i −0.0484329 + 0.0681410i
\(111\) 40.1560 0.361765
\(112\) 0.371453 0.371453i 0.00331655 0.00331655i
\(113\) −22.0544 22.0544i −0.195171 0.195171i 0.602755 0.797926i \(-0.294070\pi\)
−0.797926 + 0.602755i \(0.794070\pi\)
\(114\) 74.0739i 0.649771i
\(115\) 43.2657 + 30.7522i 0.376223 + 0.267410i
\(116\) −92.7329 −0.799421
\(117\) −6.47119 + 6.47119i −0.0553093 + 0.0553093i
\(118\) −27.4338 27.4338i −0.232490 0.232490i
\(119\) 11.1014i 0.0932890i
\(120\) 11.5042 + 68.0478i 0.0958687 + 0.567065i
\(121\) −118.753 −0.981434
\(122\) 92.3339 92.3339i 0.756835 0.756835i
\(123\) 89.9746 + 89.9746i 0.731501 + 0.731501i
\(124\) 117.407i 0.946830i
\(125\) −109.552 + 60.1948i −0.876414 + 0.481559i
\(126\) 9.73963 0.0772986
\(127\) 168.587 168.587i 1.32746 1.32746i 0.419880 0.907579i \(-0.362072\pi\)
0.907579 0.419880i \(-0.137928\pi\)
\(128\) 57.3391 + 57.3391i 0.447962 + 0.447962i
\(129\) 0.599559i 0.00464774i
\(130\) 18.4544 3.11993i 0.141957 0.0239994i
\(131\) 21.2016 0.161845 0.0809223 0.996720i \(-0.474213\pi\)
0.0809223 + 0.996720i \(0.474213\pi\)
\(132\) 4.57875 4.57875i 0.0346875 0.0346875i
\(133\) −65.2028 65.2028i −0.490247 0.490247i
\(134\) 49.7363i 0.371166i
\(135\) 15.0517 21.1765i 0.111494 0.156863i
\(136\) 33.4373 0.245863
\(137\) −104.237 + 104.237i −0.760851 + 0.760851i −0.976476 0.215625i \(-0.930821\pi\)
0.215625 + 0.976476i \(0.430821\pi\)
\(138\) 15.9547 + 15.9547i 0.115614 + 0.115614i
\(139\) 120.516i 0.867019i −0.901149 0.433509i \(-0.857275\pi\)
0.901149 0.433509i \(-0.142725\pi\)
\(140\) 26.8947 + 19.1161i 0.192105 + 0.136543i
\(141\) −95.3812 −0.676463
\(142\) −13.7520 + 13.7520i −0.0968452 + 0.0968452i
\(143\) −3.23310 3.23310i −0.0226091 0.0226091i
\(144\) 0.595650i 0.00413646i
\(145\) −30.9872 183.290i −0.213705 1.26407i
\(146\) 45.5849 0.312225
\(147\) 8.57321 8.57321i 0.0583212 0.0583212i
\(148\) 40.8902 + 40.8902i 0.276285 + 0.276285i
\(149\) 11.2725i 0.0756543i −0.999284 0.0378272i \(-0.987956\pi\)
0.999284 0.0378272i \(-0.0120436\pi\)
\(150\) −50.1811 + 17.4666i −0.334541 + 0.116444i
\(151\) −19.8815 −0.131666 −0.0658328 0.997831i \(-0.520970\pi\)
−0.0658328 + 0.997831i \(0.520970\pi\)
\(152\) 196.391 196.391i 1.29204 1.29204i
\(153\) −8.90091 8.90091i −0.0581759 0.0581759i
\(154\) 4.86606i 0.0315978i
\(155\) −232.059 + 39.2322i −1.49716 + 0.253111i
\(156\) −13.1790 −0.0844810
\(157\) −35.1027 + 35.1027i −0.223584 + 0.223584i −0.810006 0.586422i \(-0.800536\pi\)
0.586422 + 0.810006i \(0.300536\pi\)
\(158\) 64.0693 + 64.0693i 0.405502 + 0.405502i
\(159\) 81.0676i 0.509859i
\(160\) −93.0411 + 130.901i −0.581507 + 0.818131i
\(161\) 28.0879 0.174459
\(162\) 7.80908 7.80908i 0.0482042 0.0482042i
\(163\) 172.736 + 172.736i 1.05973 + 1.05973i 0.998099 + 0.0616300i \(0.0196299\pi\)
0.0616300 + 0.998099i \(0.480370\pi\)
\(164\) 183.240i 1.11731i
\(165\) 10.5801 + 7.52006i 0.0641218 + 0.0455761i
\(166\) −101.811 −0.613321
\(167\) 173.446 173.446i 1.03860 1.03860i 0.0393730 0.999225i \(-0.487464\pi\)
0.999225 0.0393730i \(-0.0125361\pi\)
\(168\) 25.8225 + 25.8225i 0.153705 + 0.153705i
\(169\) 159.694i 0.944936i
\(170\) 4.29136 + 25.3835i 0.0252433 + 0.149315i
\(171\) −104.557 −0.611445
\(172\) 0.610522 0.610522i 0.00354955 0.00354955i
\(173\) 13.5601 + 13.5601i 0.0783823 + 0.0783823i 0.745211 0.666829i \(-0.232349\pi\)
−0.666829 + 0.745211i \(0.732349\pi\)
\(174\) 79.0172i 0.454122i
\(175\) −28.7967 + 59.5462i −0.164552 + 0.340264i
\(176\) 0.297595 0.00169088
\(177\) −38.7235 + 38.7235i −0.218777 + 0.218777i
\(178\) −72.2364 72.2364i −0.405822 0.405822i
\(179\) 288.985i 1.61444i 0.590249 + 0.807222i \(0.299030\pi\)
−0.590249 + 0.807222i \(0.700970\pi\)
\(180\) 36.8907 6.23678i 0.204948 0.0346488i
\(181\) 20.6446 0.114059 0.0570293 0.998373i \(-0.481837\pi\)
0.0570293 + 0.998373i \(0.481837\pi\)
\(182\) 7.00300 7.00300i 0.0384780 0.0384780i
\(183\) −130.332 130.332i −0.712194 0.712194i
\(184\) 84.6007i 0.459786i
\(185\) −67.1575 + 94.4849i −0.363013 + 0.510729i
\(186\) −100.042 −0.537859
\(187\) 4.44702 4.44702i 0.0237809 0.0237809i
\(188\) −97.1253 97.1253i −0.516624 0.516624i
\(189\) 13.7477i 0.0727393i
\(190\) 174.292 + 123.882i 0.917326 + 0.652012i
\(191\) −140.214 −0.734104 −0.367052 0.930200i \(-0.619633\pi\)
−0.367052 + 0.930200i \(0.619633\pi\)
\(192\) −47.2985 + 47.2985i −0.246346 + 0.246346i
\(193\) 196.589 + 196.589i 1.01860 + 1.01860i 0.999824 + 0.0187736i \(0.00597619\pi\)
0.0187736 + 0.999824i \(0.494024\pi\)
\(194\) 179.214i 0.923783i
\(195\) −4.40385 26.0489i −0.0225839 0.133584i
\(196\) 17.4600 0.0890814
\(197\) −206.963 + 206.963i −1.05057 + 1.05057i −0.0519216 + 0.998651i \(0.516535\pi\)
−0.998651 + 0.0519216i \(0.983465\pi\)
\(198\) 3.90153 + 3.90153i 0.0197047 + 0.0197047i
\(199\) 160.567i 0.806869i −0.915009 0.403435i \(-0.867816\pi\)
0.915009 0.403435i \(-0.132184\pi\)
\(200\) −179.353 86.7354i −0.896764 0.433677i
\(201\) 70.2040 0.349274
\(202\) −76.8666 + 76.8666i −0.380528 + 0.380528i
\(203\) −69.5541 69.5541i −0.342631 0.342631i
\(204\) 18.1273i 0.0888595i
\(205\) −362.180 + 61.2306i −1.76673 + 0.298686i
\(206\) −38.2318 −0.185591
\(207\) 22.5204 22.5204i 0.108794 0.108794i
\(208\) −0.428285 0.428285i −0.00205906 0.00205906i
\(209\) 52.2383i 0.249944i
\(210\) −16.2887 + 22.9168i −0.0775653 + 0.109128i
\(211\) 265.902 1.26020 0.630099 0.776515i \(-0.283014\pi\)
0.630099 + 0.776515i \(0.283014\pi\)
\(212\) 82.5499 82.5499i 0.389386 0.389386i
\(213\) 19.4113 + 19.4113i 0.0911329 + 0.0911329i
\(214\) 188.713i 0.881835i
\(215\) 1.41073 + 1.00271i 0.00656154 + 0.00466377i
\(216\) 41.4081 0.191704
\(217\) −88.0608 + 88.0608i −0.405810 + 0.405810i
\(218\) 65.8024 + 65.8024i 0.301846 + 0.301846i
\(219\) 64.3442i 0.293809i
\(220\) 3.11599 + 18.4311i 0.0141636 + 0.0837779i
\(221\) −12.7999 −0.0579181
\(222\) −34.8423 + 34.8423i −0.156947 + 0.156947i
\(223\) 143.987 + 143.987i 0.645683 + 0.645683i 0.951947 0.306264i \(-0.0990789\pi\)
−0.306264 + 0.951947i \(0.599079\pi\)
\(224\) 84.9804i 0.379377i
\(225\) 24.6545 + 70.8319i 0.109576 + 0.314808i
\(226\) 38.2720 0.169345
\(227\) −174.471 + 174.471i −0.768596 + 0.768596i −0.977859 0.209264i \(-0.932893\pi\)
0.209264 + 0.977859i \(0.432893\pi\)
\(228\) −106.469 106.469i −0.466969 0.466969i
\(229\) 41.2978i 0.180340i −0.995926 0.0901700i \(-0.971259\pi\)
0.995926 0.0901700i \(-0.0287410\pi\)
\(230\) −64.2234 + 10.8577i −0.279232 + 0.0472073i
\(231\) 6.86856 0.0297340
\(232\) 209.497 209.497i 0.903002 0.903002i
\(233\) −72.8228 72.8228i −0.312544 0.312544i 0.533350 0.845894i \(-0.320933\pi\)
−0.845894 + 0.533350i \(0.820933\pi\)
\(234\) 11.2298i 0.0479905i
\(235\) 159.517 224.427i 0.678796 0.955008i
\(236\) −78.8631 −0.334166
\(237\) 90.4354 90.4354i 0.381584 0.381584i
\(238\) 9.63240 + 9.63240i 0.0404723 + 0.0404723i
\(239\) 418.650i 1.75168i −0.482606 0.875838i \(-0.660310\pi\)
0.482606 0.875838i \(-0.339690\pi\)
\(240\) 1.40153 + 0.996174i 0.00583972 + 0.00415073i
\(241\) 371.820 1.54282 0.771410 0.636338i \(-0.219552\pi\)
0.771410 + 0.636338i \(0.219552\pi\)
\(242\) 103.039 103.039i 0.425783 0.425783i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 265.429i 1.08783i
\(245\) 5.83435 + 34.5103i 0.0238137 + 0.140858i
\(246\) −156.137 −0.634705
\(247\) −75.1788 + 75.1788i −0.304368 + 0.304368i
\(248\) −265.238 265.238i −1.06951 1.06951i
\(249\) 143.709i 0.577145i
\(250\) 42.8257 147.285i 0.171303 0.589140i
\(251\) 469.550 1.87072 0.935358 0.353702i \(-0.115077\pi\)
0.935358 + 0.353702i \(0.115077\pi\)
\(252\) 13.9991 13.9991i 0.0555520 0.0555520i
\(253\) 11.2515 + 11.2515i 0.0444725 + 0.0444725i
\(254\) 292.558i 1.15180i
\(255\) 35.8294 6.05736i 0.140507 0.0237543i
\(256\) −253.980 −0.992108
\(257\) 215.003 215.003i 0.836589 0.836589i −0.151819 0.988408i \(-0.548513\pi\)
0.988408 + 0.151819i \(0.0485131\pi\)
\(258\) 0.520222 + 0.520222i 0.00201637 + 0.00201637i
\(259\) 61.3393i 0.236831i
\(260\) 22.0408 31.0096i 0.0847724 0.119268i
\(261\) −111.535 −0.427336
\(262\) −18.3961 + 18.3961i −0.0702142 + 0.0702142i
\(263\) 95.9799 + 95.9799i 0.364943 + 0.364943i 0.865629 0.500686i \(-0.166919\pi\)
−0.500686 + 0.865629i \(0.666919\pi\)
\(264\) 20.6881i 0.0783639i
\(265\) 190.748 + 135.579i 0.719803 + 0.511617i
\(266\) 113.150 0.425375
\(267\) −101.963 + 101.963i −0.381885 + 0.381885i
\(268\) 71.4877 + 71.4877i 0.266745 + 0.266745i
\(269\) 53.9055i 0.200392i −0.994968 0.100196i \(-0.968053\pi\)
0.994968 0.100196i \(-0.0319470\pi\)
\(270\) 5.31433 + 31.4344i 0.0196827 + 0.116424i
\(271\) −163.641 −0.603843 −0.301921 0.953333i \(-0.597628\pi\)
−0.301921 + 0.953333i \(0.597628\pi\)
\(272\) 0.589092 0.589092i 0.00216578 0.00216578i
\(273\) −9.88491 9.88491i −0.0362085 0.0362085i
\(274\) 180.887i 0.660171i
\(275\) −35.3886 + 12.3177i −0.128686 + 0.0447918i
\(276\) 45.8645 0.166176
\(277\) 25.4139 25.4139i 0.0917470 0.0917470i −0.659744 0.751491i \(-0.729335\pi\)
0.751491 + 0.659744i \(0.229335\pi\)
\(278\) 104.568 + 104.568i 0.376145 + 0.376145i
\(279\) 141.211i 0.506134i
\(280\) −103.945 + 17.5730i −0.371231 + 0.0627608i
\(281\) 113.158 0.402698 0.201349 0.979520i \(-0.435468\pi\)
0.201349 + 0.979520i \(0.435468\pi\)
\(282\) 82.7599 82.7599i 0.293475 0.293475i
\(283\) 351.039 + 351.039i 1.24042 + 1.24042i 0.959827 + 0.280593i \(0.0905312\pi\)
0.280593 + 0.959827i \(0.409469\pi\)
\(284\) 39.5325i 0.139199i
\(285\) 174.863 246.017i 0.613554 0.863219i
\(286\) 5.61056 0.0196174
\(287\) −137.438 + 137.438i −0.478880 + 0.478880i
\(288\) 68.1359 + 68.1359i 0.236583 + 0.236583i
\(289\) 271.394i 0.939080i
\(290\) 185.923 + 132.149i 0.641115 + 0.455688i
\(291\) −252.965 −0.869295
\(292\) 65.5207 65.5207i 0.224386 0.224386i
\(293\) −86.4775 86.4775i −0.295145 0.295145i 0.543964 0.839109i \(-0.316923\pi\)
−0.839109 + 0.543964i \(0.816923\pi\)
\(294\) 14.8775i 0.0506038i
\(295\) −26.3526 155.876i −0.0893307 0.528393i
\(296\) −184.753 −0.624167
\(297\) 5.50710 5.50710i 0.0185424 0.0185424i
\(298\) 9.78086 + 9.78086i 0.0328217 + 0.0328217i
\(299\) 32.3854i 0.108312i
\(300\) −47.0218 + 97.2324i −0.156739 + 0.324108i
\(301\) 0.915841 0.00304266
\(302\) 17.2507 17.2507i 0.0571215 0.0571215i
\(303\) 108.499 + 108.499i 0.358083 + 0.358083i
\(304\) 6.91994i 0.0227630i
\(305\) 524.632 88.6948i 1.72010 0.290803i
\(306\) 15.4462 0.0504778
\(307\) −113.083 + 113.083i −0.368348 + 0.368348i −0.866874 0.498526i \(-0.833875\pi\)
0.498526 + 0.866874i \(0.333875\pi\)
\(308\) 6.99416 + 6.99416i 0.0227083 + 0.0227083i
\(309\) 53.9651i 0.174644i
\(310\) 167.311 235.393i 0.539714 0.759332i
\(311\) −73.9659 −0.237832 −0.118916 0.992904i \(-0.537942\pi\)
−0.118916 + 0.992904i \(0.537942\pi\)
\(312\) 29.7733 29.7733i 0.0954272 0.0954272i
\(313\) −324.281 324.281i −1.03604 1.03604i −0.999326 0.0367164i \(-0.988310\pi\)
−0.0367164 0.999326i \(-0.511690\pi\)
\(314\) 60.9154i 0.193998i
\(315\) 32.3477 + 22.9919i 0.102691 + 0.0729902i
\(316\) 184.178 0.582842
\(317\) −151.033 + 151.033i −0.476445 + 0.476445i −0.903993 0.427547i \(-0.859378\pi\)
0.427547 + 0.903993i \(0.359378\pi\)
\(318\) 70.3403 + 70.3403i 0.221196 + 0.221196i
\(319\) 55.7243i 0.174684i
\(320\) −32.1881 190.393i −0.100588 0.594980i
\(321\) 266.373 0.829821
\(322\) −24.3712 + 24.3712i −0.0756870 + 0.0756870i
\(323\) −103.406 103.406i −0.320142 0.320142i
\(324\) 22.4485i 0.0692855i
\(325\) 68.6568 + 33.2025i 0.211252 + 0.102162i
\(326\) −299.757 −0.919501
\(327\) 92.8818 92.8818i 0.284042 0.284042i
\(328\) −413.964 413.964i −1.26208 1.26208i
\(329\) 145.697i 0.442849i
\(330\) −15.7051 + 2.65511i −0.0475911 + 0.00804580i
\(331\) −181.099 −0.547128 −0.273564 0.961854i \(-0.588202\pi\)
−0.273564 + 0.961854i \(0.588202\pi\)
\(332\) −146.337 + 146.337i −0.440774 + 0.440774i
\(333\) 49.1808 + 49.1808i 0.147690 + 0.147690i
\(334\) 300.989i 0.901165i
\(335\) −117.410 + 165.186i −0.350478 + 0.493093i
\(336\) 0.909871 0.00270795
\(337\) −388.741 + 388.741i −1.15353 + 1.15353i −0.167693 + 0.985839i \(0.553632\pi\)
−0.985839 + 0.167693i \(0.946368\pi\)
\(338\) 138.563 + 138.563i 0.409949 + 0.409949i
\(339\) 54.0219i 0.159357i
\(340\) 42.6527 + 30.3164i 0.125449 + 0.0891660i
\(341\) −70.5512 −0.206895
\(342\) 90.7217 90.7217i 0.265268 0.265268i
\(343\) 13.0958 + 13.0958i 0.0381802 + 0.0381802i
\(344\) 2.75851i 0.00801892i
\(345\) 15.3259 + 90.6530i 0.0444229 + 0.262762i
\(346\) −23.5316 −0.0680104
\(347\) 16.1754 16.1754i 0.0466151 0.0466151i −0.683415 0.730030i \(-0.739506\pi\)
0.730030 + 0.683415i \(0.239506\pi\)
\(348\) −113.574 113.574i −0.326362 0.326362i
\(349\) 249.140i 0.713868i 0.934130 + 0.356934i \(0.116178\pi\)
−0.934130 + 0.356934i \(0.883822\pi\)
\(350\) −26.6806 76.6529i −0.0762304 0.219008i
\(351\) −15.8511 −0.0451599
\(352\) −34.0417 + 34.0417i −0.0967094 + 0.0967094i
\(353\) −315.334 315.334i −0.893298 0.893298i 0.101534 0.994832i \(-0.467625\pi\)
−0.994832 + 0.101534i \(0.967625\pi\)
\(354\) 67.1988i 0.189827i
\(355\) −78.1376 + 13.2100i −0.220106 + 0.0372113i
\(356\) −207.656 −0.583302
\(357\) 13.5964 13.5964i 0.0380851 0.0380851i
\(358\) −250.745 250.745i −0.700406 0.700406i
\(359\) 84.4547i 0.235250i −0.993058 0.117625i \(-0.962472\pi\)
0.993058 0.117625i \(-0.0375281\pi\)
\(360\) −69.2515 + 97.4310i −0.192365 + 0.270642i
\(361\) −853.689 −2.36479
\(362\) −17.9128 + 17.9128i −0.0494829 + 0.0494829i
\(363\) −145.443 145.443i −0.400669 0.400669i
\(364\) 20.1313i 0.0553058i
\(365\) 151.398 + 107.610i 0.414790 + 0.294822i
\(366\) 226.171 0.617953
\(367\) −199.907 + 199.907i −0.544707 + 0.544707i −0.924905 0.380198i \(-0.875856\pi\)
0.380198 + 0.924905i \(0.375856\pi\)
\(368\) 1.49048 + 1.49048i 0.00405021 + 0.00405021i
\(369\) 220.392i 0.597268i
\(370\) −23.7113 140.253i −0.0640847 0.379062i
\(371\) 123.833 0.333781
\(372\) −143.793 + 143.793i −0.386542 + 0.386542i
\(373\) −392.541 392.541i −1.05239 1.05239i −0.998550 0.0538401i \(-0.982854\pi\)
−0.0538401 0.998550i \(-0.517146\pi\)
\(374\) 7.71714i 0.0206341i
\(375\) −207.896 60.4496i −0.554390 0.161199i
\(376\) 438.839 1.16713
\(377\) −80.1958 + 80.1958i −0.212721 + 0.212721i
\(378\) 11.9286 + 11.9286i 0.0315570 + 0.0315570i
\(379\) 360.732i 0.951798i 0.879500 + 0.475899i \(0.157877\pi\)
−0.879500 + 0.475899i \(0.842123\pi\)
\(380\) 428.576 72.4556i 1.12783 0.190673i
\(381\) 412.953 1.08387
\(382\) 121.660 121.660i 0.318482 0.318482i
\(383\) 337.526 + 337.526i 0.881268 + 0.881268i 0.993664 0.112395i \(-0.0358523\pi\)
−0.112395 + 0.993664i \(0.535852\pi\)
\(384\) 140.452i 0.365759i
\(385\) −11.4871 + 16.1614i −0.0298366 + 0.0419776i
\(386\) −341.151 −0.883812
\(387\) 0.734307 0.734307i 0.00189743 0.00189743i
\(388\) −257.590 257.590i −0.663893 0.663893i
\(389\) 585.722i 1.50571i 0.658185 + 0.752856i \(0.271324\pi\)
−0.658185 + 0.752856i \(0.728676\pi\)
\(390\) 26.4231 + 18.7809i 0.0677515 + 0.0481561i
\(391\) 44.5450 0.113926
\(392\) −39.4445 + 39.4445i −0.100624 + 0.100624i
\(393\) 25.9666 + 25.9666i 0.0660728 + 0.0660728i
\(394\) 359.153i 0.911556i
\(395\) 61.5442 + 364.035i 0.155808 + 0.921608i
\(396\) 11.2156 0.0283222
\(397\) −165.106 + 165.106i −0.415883 + 0.415883i −0.883782 0.467899i \(-0.845011\pi\)
0.467899 + 0.883782i \(0.345011\pi\)
\(398\) 139.320 + 139.320i 0.350050 + 0.350050i
\(399\) 159.714i 0.400285i
\(400\) −4.68789 + 1.63172i −0.0117197 + 0.00407929i
\(401\) 593.726 1.48061 0.740307 0.672269i \(-0.234680\pi\)
0.740307 + 0.672269i \(0.234680\pi\)
\(402\) −60.9143 + 60.9143i −0.151528 + 0.151528i
\(403\) 101.534 + 101.534i 0.251945 + 0.251945i
\(404\) 220.966i 0.546946i
\(405\) 44.3704 7.50130i 0.109556 0.0185217i
\(406\) 120.701 0.297292
\(407\) −24.5714 + 24.5714i −0.0603721 + 0.0603721i
\(408\) 40.9522 + 40.9522i 0.100373 + 0.100373i
\(409\) 354.736i 0.867324i −0.901076 0.433662i \(-0.857221\pi\)
0.901076 0.433662i \(-0.142779\pi\)
\(410\) 261.127 367.383i 0.636894 0.896056i
\(411\) −255.326 −0.621232
\(412\) −54.9519 + 54.9519i −0.133378 + 0.133378i
\(413\) −59.1511 59.1511i −0.143223 0.143223i
\(414\) 39.0809i 0.0943982i
\(415\) −338.140 240.341i −0.814795 0.579136i
\(416\) 97.9824 0.235535
\(417\) 147.601 147.601i 0.353959 0.353959i
\(418\) 45.3258 + 45.3258i 0.108435 + 0.108435i
\(419\) 107.473i 0.256498i −0.991742 0.128249i \(-0.959064\pi\)
0.991742 0.128249i \(-0.0409356\pi\)
\(420\) 9.52684 + 56.3515i 0.0226830 + 0.134170i
\(421\) 572.426 1.35968 0.679841 0.733359i \(-0.262049\pi\)
0.679841 + 0.733359i \(0.262049\pi\)
\(422\) −230.716 + 230.716i −0.546721 + 0.546721i
\(423\) −116.818 116.818i −0.276165 0.276165i
\(424\) 372.984i 0.879678i
\(425\) −45.6690 + 94.4351i −0.107456 + 0.222200i
\(426\) −33.6854 −0.0790738
\(427\) 199.085 199.085i 0.466241 0.466241i
\(428\) 271.243 + 271.243i 0.633746 + 0.633746i
\(429\) 7.91945i 0.0184603i
\(430\) −2.09408 + 0.354028i −0.00486996 + 0.000823321i
\(431\) 346.647 0.804285 0.402142 0.915577i \(-0.368266\pi\)
0.402142 + 0.915577i \(0.368266\pi\)
\(432\) 0.729519 0.729519i 0.00168870 0.00168870i
\(433\) −103.330 103.330i −0.238637 0.238637i 0.577649 0.816285i \(-0.303970\pi\)
−0.816285 + 0.577649i \(0.803970\pi\)
\(434\) 152.816i 0.352111i
\(435\) 186.532 262.435i 0.428810 0.603299i
\(436\) 189.160 0.433854
\(437\) 261.630 261.630i 0.598697 0.598697i
\(438\) 55.8298 + 55.8298i 0.127465 + 0.127465i
\(439\) 324.757i 0.739766i 0.929078 + 0.369883i \(0.120602\pi\)
−0.929078 + 0.369883i \(0.879398\pi\)
\(440\) −48.6779 34.5990i −0.110632 0.0786342i
\(441\) 21.0000 0.0476190
\(442\) 11.1061 11.1061i 0.0251270 0.0251270i
\(443\) −226.450 226.450i −0.511173 0.511173i 0.403713 0.914886i \(-0.367720\pi\)
−0.914886 + 0.403713i \(0.867720\pi\)
\(444\) 100.160i 0.225586i
\(445\) −69.3894 410.440i −0.155931 0.922336i
\(446\) −249.868 −0.560243
\(447\) 13.8059 13.8059i 0.0308857 0.0308857i
\(448\) −72.2496 72.2496i −0.161271 0.161271i
\(449\) 221.579i 0.493494i −0.969080 0.246747i \(-0.920638\pi\)
0.969080 0.246747i \(-0.0793617\pi\)
\(450\) −82.8512 40.0670i −0.184114 0.0890377i
\(451\) −110.111 −0.244148
\(452\) 55.0097 55.0097i 0.121703 0.121703i
\(453\) −24.3498 24.3498i −0.0537523 0.0537523i
\(454\) 302.769i 0.666891i
\(455\) 39.7903 6.72700i 0.0874513 0.0147846i
\(456\) 481.057 1.05495
\(457\) 631.757 631.757i 1.38240 1.38240i 0.542064 0.840337i \(-0.317643\pi\)
0.840337 0.542064i \(-0.182357\pi\)
\(458\) 35.8331 + 35.8331i 0.0782382 + 0.0782382i
\(459\) 21.8027i 0.0475004i
\(460\) −76.7045 + 107.917i −0.166749 + 0.234602i
\(461\) 10.7536 0.0233266 0.0116633 0.999932i \(-0.496287\pi\)
0.0116633 + 0.999932i \(0.496287\pi\)
\(462\) −5.95968 + 5.95968i −0.0128997 + 0.0128997i
\(463\) −87.0943 87.0943i −0.188109 0.188109i 0.606769 0.794878i \(-0.292465\pi\)
−0.794878 + 0.606769i \(0.792465\pi\)
\(464\) 7.38174i 0.0159089i
\(465\) −332.263 236.164i −0.714544 0.507880i
\(466\) 126.373 0.271187
\(467\) −168.883 + 168.883i −0.361633 + 0.361633i −0.864414 0.502781i \(-0.832310\pi\)
0.502781 + 0.864414i \(0.332310\pi\)
\(468\) −16.1410 16.1410i −0.0344892 0.0344892i
\(469\) 107.238i 0.228653i
\(470\) 56.3208 + 333.139i 0.119831 + 0.708806i
\(471\) −85.9836 −0.182555
\(472\) 178.163 178.163i 0.377463 0.377463i
\(473\) 0.366870 + 0.366870i 0.000775624 + 0.000775624i
\(474\) 156.937i 0.331091i
\(475\) 286.423 + 822.887i 0.602995 + 1.73239i
\(476\) 27.6900 0.0581722
\(477\) 99.2871 99.2871i 0.208149 0.208149i
\(478\) 363.253 + 363.253i 0.759943 + 0.759943i
\(479\) 591.385i 1.23462i −0.786718 0.617312i \(-0.788221\pi\)
0.786718 0.617312i \(-0.211779\pi\)
\(480\) −274.272 + 46.3687i −0.571400 + 0.0966014i
\(481\) 70.7241 0.147036
\(482\) −322.619 + 322.619i −0.669334 + 0.669334i
\(483\) 34.4006 + 34.4006i 0.0712227 + 0.0712227i
\(484\) 296.204i 0.611992i
\(485\) 423.062 595.213i 0.872293 1.22724i
\(486\) 19.1283 0.0393585
\(487\) 454.628 454.628i 0.933527 0.933527i −0.0643972 0.997924i \(-0.520512\pi\)
0.997924 + 0.0643972i \(0.0205125\pi\)
\(488\) 599.642 + 599.642i 1.22877 + 1.22877i
\(489\) 423.115i 0.865265i
\(490\) −35.0060 24.8814i −0.0714409 0.0507784i
\(491\) −267.659 −0.545130 −0.272565 0.962137i \(-0.587872\pi\)
−0.272565 + 0.962137i \(0.587872\pi\)
\(492\) −224.422 + 224.422i −0.456142 + 0.456142i
\(493\) −110.307 110.307i −0.223746 0.223746i
\(494\) 130.462i 0.264092i
\(495\) 3.74776 + 22.1681i 0.00757123 + 0.0447840i
\(496\) −9.34584 −0.0188424
\(497\) −29.6513 + 29.6513i −0.0596605 + 0.0596605i
\(498\) −124.693 124.693i −0.250387 0.250387i
\(499\) 598.541i 1.19948i 0.800194 + 0.599741i \(0.204730\pi\)
−0.800194 + 0.599741i \(0.795270\pi\)
\(500\) −150.143 273.253i −0.300286 0.546505i
\(501\) 424.854 0.848011
\(502\) −407.417 + 407.417i −0.811587 + 0.811587i
\(503\) −597.424 597.424i −1.18772 1.18772i −0.977696 0.210027i \(-0.932645\pi\)
−0.210027 0.977696i \(-0.567355\pi\)
\(504\) 63.2519i 0.125500i
\(505\) −436.748 + 73.8371i −0.864848 + 0.146212i
\(506\) −19.5254 −0.0385877
\(507\) 195.585 195.585i 0.385768 0.385768i
\(508\) 420.504 + 420.504i 0.827764 + 0.827764i
\(509\) 734.407i 1.44284i −0.692496 0.721422i \(-0.743489\pi\)
0.692496 0.721422i \(-0.256511\pi\)
\(510\) −25.8325 + 36.3441i −0.0506519 + 0.0712629i
\(511\) 98.2873 0.192343
\(512\) −8.98472 + 8.98472i −0.0175483 + 0.0175483i
\(513\) −128.056 128.056i −0.249622 0.249622i
\(514\) 373.106i 0.725888i
\(515\) −126.977 90.2521i −0.246557 0.175247i
\(516\) 1.49547 0.00289819
\(517\) 58.3638 58.3638i 0.112889 0.112889i
\(518\) −53.2225 53.2225i −0.102746 0.102746i
\(519\) 33.2154i 0.0639989i
\(520\) 20.2617 + 119.848i 0.0389648 + 0.230477i
\(521\) 207.188 0.397674 0.198837 0.980033i \(-0.436284\pi\)
0.198837 + 0.980033i \(0.436284\pi\)
\(522\) 96.7759 96.7759i 0.185394 0.185394i
\(523\) 143.359 + 143.359i 0.274110 + 0.274110i 0.830752 0.556642i \(-0.187911\pi\)
−0.556642 + 0.830752i \(0.687911\pi\)
\(524\) 52.8828i 0.100921i
\(525\) −108.197 + 37.6604i −0.206090 + 0.0717340i
\(526\) −166.559 −0.316652
\(527\) −139.657 + 139.657i −0.265003 + 0.265003i
\(528\) 0.364478 + 0.364478i 0.000690300 + 0.000690300i
\(529\) 416.295i 0.786948i
\(530\) −283.145 + 47.8688i −0.534236 + 0.0903186i
\(531\) −94.8527 −0.178630
\(532\) 162.634 162.634i 0.305703 0.305703i
\(533\) 158.466 + 158.466i 0.297310 + 0.297310i
\(534\) 176.942i 0.331352i
\(535\) −445.485 + 626.760i −0.832683 + 1.17151i
\(536\) −323.001 −0.602614
\(537\) −353.933 + 353.933i −0.659094 + 0.659094i
\(538\) 46.7724 + 46.7724i 0.0869376 + 0.0869376i
\(539\) 10.4919i 0.0194655i
\(540\) 52.8202 + 37.5432i 0.0978151 + 0.0695245i
\(541\) −22.1387 −0.0409219 −0.0204609 0.999791i \(-0.506513\pi\)
−0.0204609 + 0.999791i \(0.506513\pi\)
\(542\) 141.988 141.988i 0.261970 0.261970i
\(543\) 25.2844 + 25.2844i 0.0465642 + 0.0465642i
\(544\) 134.772i 0.247742i
\(545\) 63.2090 + 373.883i 0.115980 + 0.686023i
\(546\) 17.1538 0.0314172
\(547\) 113.508 113.508i 0.207509 0.207509i −0.595699 0.803208i \(-0.703125\pi\)
0.803208 + 0.595699i \(0.203125\pi\)
\(548\) −259.995 259.995i −0.474444 0.474444i
\(549\) 319.246i 0.581504i
\(550\) 20.0180 41.3936i 0.0363964 0.0752612i
\(551\) −1295.75 −2.35163
\(552\) −103.614 + 103.614i −0.187707 + 0.187707i
\(553\) 138.142 + 138.142i 0.249805 + 0.249805i
\(554\) 44.1020i 0.0796066i
\(555\) −197.971 + 33.4691i −0.356704 + 0.0603047i
\(556\) 300.600 0.540647
\(557\) −229.622 + 229.622i −0.412248 + 0.412248i −0.882521 0.470273i \(-0.844155\pi\)
0.470273 + 0.882521i \(0.344155\pi\)
\(558\) −122.526 122.526i −0.219580 0.219580i
\(559\) 1.05596i 0.00188902i
\(560\) −1.52168 + 2.14088i −0.00271729 + 0.00382300i
\(561\) 10.8929 0.0194170
\(562\) −98.1844 + 98.1844i −0.174705 + 0.174705i
\(563\) 92.9885 + 92.9885i 0.165166 + 0.165166i 0.784851 0.619685i \(-0.212740\pi\)
−0.619685 + 0.784851i \(0.712740\pi\)
\(564\) 237.907i 0.421822i
\(565\) 127.111 + 90.3471i 0.224975 + 0.159906i
\(566\) −609.175 −1.07628
\(567\) 16.8375 16.8375i 0.0296957 0.0296957i
\(568\) −89.3094 89.3094i −0.157235 0.157235i
\(569\) 388.149i 0.682160i −0.940034 0.341080i \(-0.889207\pi\)
0.940034 0.341080i \(-0.110793\pi\)
\(570\) 61.7390 + 365.188i 0.108314 + 0.640680i
\(571\) −488.529 −0.855568 −0.427784 0.903881i \(-0.640706\pi\)
−0.427784 + 0.903881i \(0.640706\pi\)
\(572\) 8.06426 8.06426i 0.0140984 0.0140984i
\(573\) −171.726 171.726i −0.299697 0.299697i
\(574\) 238.504i 0.415512i
\(575\) −238.933 115.548i −0.415536 0.200954i
\(576\) −115.857 −0.201141
\(577\) 365.601 365.601i 0.633624 0.633624i −0.315351 0.948975i \(-0.602122\pi\)
0.948975 + 0.315351i \(0.102122\pi\)
\(578\) −235.482 235.482i −0.407408 0.407408i
\(579\) 481.543i 0.831681i
\(580\) 457.177 77.2909i 0.788236 0.133260i
\(581\) −219.519 −0.377830
\(582\) 219.491 219.491i 0.377133 0.377133i
\(583\) 49.6053 + 49.6053i 0.0850862 + 0.0850862i
\(584\) 296.041i 0.506919i
\(585\) 26.5097 37.2969i 0.0453156 0.0637553i
\(586\) 150.069 0.256090
\(587\) 410.771 410.771i 0.699780 0.699780i −0.264583 0.964363i \(-0.585234\pi\)
0.964363 + 0.264583i \(0.0852343\pi\)
\(588\) 21.3840 + 21.3840i 0.0363673 + 0.0363673i
\(589\) 1640.52i 2.78526i
\(590\) 158.115 + 112.384i 0.267992 + 0.190482i
\(591\) −506.953 −0.857789
\(592\) −3.25495 + 3.25495i −0.00549823 + 0.00549823i
\(593\) 776.361 + 776.361i 1.30921 + 1.30921i 0.921986 + 0.387224i \(0.126566\pi\)
0.387224 + 0.921986i \(0.373434\pi\)
\(594\) 9.55675i 0.0160888i
\(595\) 9.25277 + 54.7303i 0.0155509 + 0.0919837i
\(596\) 28.1167 0.0471757
\(597\) 196.654 196.654i 0.329403 0.329403i
\(598\) 28.1000 + 28.1000i 0.0469899 + 0.0469899i
\(599\) 573.555i 0.957521i −0.877946 0.478760i \(-0.841086\pi\)
0.877946 0.478760i \(-0.158914\pi\)
\(600\) −113.433 325.890i −0.189055 0.543150i
\(601\) 345.953 0.575628 0.287814 0.957686i \(-0.407071\pi\)
0.287814 + 0.957686i \(0.407071\pi\)
\(602\) −0.794653 + 0.794653i −0.00132002 + 0.00132002i
\(603\) 85.9820 + 85.9820i 0.142590 + 0.142590i
\(604\) 49.5901i 0.0821028i
\(605\) 585.460 98.9784i 0.967702 0.163601i
\(606\) −188.284 −0.310700
\(607\) 627.891 627.891i 1.03442 1.03442i 0.0350309 0.999386i \(-0.488847\pi\)
0.999386 0.0350309i \(-0.0111530\pi\)
\(608\) 791.567 + 791.567i 1.30192 + 1.30192i
\(609\) 170.372i 0.279757i
\(610\) −378.252 + 532.168i −0.620085 + 0.872407i
\(611\) −167.989 −0.274941
\(612\) 22.2014 22.2014i 0.0362767 0.0362767i
\(613\) 114.845 + 114.845i 0.187349 + 0.187349i 0.794549 0.607200i \(-0.207707\pi\)
−0.607200 + 0.794549i \(0.707707\pi\)
\(614\) 196.238i 0.319606i
\(615\) −518.570 368.587i −0.843204 0.599328i
\(616\) −31.6016 −0.0513012
\(617\) −271.304 + 271.304i −0.439715 + 0.439715i −0.891916 0.452201i \(-0.850639\pi\)
0.452201 + 0.891916i \(0.350639\pi\)
\(618\) −46.8242 46.8242i −0.0757673 0.0757673i
\(619\) 346.221i 0.559323i −0.960099 0.279662i \(-0.909778\pi\)
0.960099 0.279662i \(-0.0902223\pi\)
\(620\) −97.8561 578.821i −0.157832 0.933582i
\(621\) 55.1636 0.0888303
\(622\) 64.1784 64.1784i 0.103181 0.103181i
\(623\) −155.752 155.752i −0.250003 0.250003i
\(624\) 1.04908i 0.00168122i
\(625\) 489.923 388.072i 0.783878 0.620915i
\(626\) 562.741 0.898948
\(627\) 63.9786 63.9786i 0.102039 0.102039i
\(628\) −87.5558 87.5558i −0.139420 0.139420i
\(629\) 97.2787i 0.154656i
\(630\) −48.0168 + 8.11777i −0.0762171 + 0.0128853i
\(631\) −828.209 −1.31253 −0.656267 0.754528i \(-0.727866\pi\)
−0.656267 + 0.754528i \(0.727866\pi\)
\(632\) −416.084 + 416.084i −0.658361 + 0.658361i
\(633\) 325.662 + 325.662i 0.514474 + 0.514474i
\(634\) 262.096i 0.413400i
\(635\) −690.629 + 971.657i −1.08760 + 1.53017i
\(636\) 202.205 0.317933
\(637\) 15.0994 15.0994i 0.0237040 0.0237040i
\(638\) 48.3506 + 48.3506i 0.0757847 + 0.0757847i
\(639\) 47.5478i 0.0744097i
\(640\) −330.475 234.893i −0.516368 0.367021i
\(641\) −167.603 −0.261471 −0.130736 0.991417i \(-0.541734\pi\)
−0.130736 + 0.991417i \(0.541734\pi\)
\(642\) −231.125 + 231.125i −0.360007 + 0.360007i
\(643\) 442.638 + 442.638i 0.688395 + 0.688395i 0.961877 0.273482i \(-0.0881755\pi\)
−0.273482 + 0.961877i \(0.588176\pi\)
\(644\) 70.0592i 0.108788i
\(645\) 0.499719 + 2.95585i 0.000774759 + 0.00458271i
\(646\) 179.446 0.277780
\(647\) −494.631 + 494.631i −0.764500 + 0.764500i −0.977132 0.212632i \(-0.931796\pi\)
0.212632 + 0.977132i \(0.431796\pi\)
\(648\) 50.7143 + 50.7143i 0.0782628 + 0.0782628i
\(649\) 47.3898i 0.0730197i
\(650\) −88.3808 + 30.7627i −0.135970 + 0.0473273i
\(651\) −215.704 −0.331342
\(652\) −430.851 + 430.851i −0.660815 + 0.660815i
\(653\) −106.722 106.722i −0.163434 0.163434i 0.620652 0.784086i \(-0.286868\pi\)
−0.784086 + 0.620652i \(0.786868\pi\)
\(654\) 161.182i 0.246456i
\(655\) −104.525 + 17.6711i −0.159580 + 0.0269788i
\(656\) −14.5863 −0.0222352
\(657\) 78.8052 78.8052i 0.119947 0.119947i
\(658\) 126.418 + 126.418i 0.192124 + 0.192124i
\(659\) 712.593i 1.08132i −0.841240 0.540662i \(-0.818174\pi\)
0.841240 0.540662i \(-0.181826\pi\)
\(660\) −18.7571 + 26.3897i −0.0284199 + 0.0399844i
\(661\) −1217.06 −1.84123 −0.920617 0.390466i \(-0.872314\pi\)
−0.920617 + 0.390466i \(0.872314\pi\)
\(662\) 157.135 157.135i 0.237365 0.237365i
\(663\) −15.6766 15.6766i −0.0236450 0.0236450i
\(664\) 661.191i 0.995770i
\(665\) 375.798 + 267.108i 0.565110 + 0.401666i
\(666\) −85.3459 −0.128147
\(667\) 279.090 279.090i 0.418426 0.418426i
\(668\) 432.622 + 432.622i 0.647638 + 0.647638i
\(669\) 352.696i 0.527198i
\(670\) −41.4541 245.202i −0.0618718 0.365973i
\(671\) 159.500 0.237705
\(672\) −104.079 + 104.079i −0.154880 + 0.154880i
\(673\) −545.679 545.679i −0.810816 0.810816i 0.173940 0.984756i \(-0.444350\pi\)
−0.984756 + 0.173940i \(0.944350\pi\)
\(674\) 674.601i 1.00089i
\(675\) −56.5555 + 116.946i −0.0837859 + 0.173254i
\(676\) 398.322 0.589234
\(677\) 297.552 297.552i 0.439515 0.439515i −0.452333 0.891849i \(-0.649408\pi\)
0.891849 + 0.452333i \(0.149408\pi\)
\(678\) 46.8735 + 46.8735i 0.0691349 + 0.0691349i
\(679\) 386.410i 0.569087i
\(680\) −164.847 + 27.8693i −0.242423 + 0.0409842i
\(681\) −427.365 −0.627556
\(682\) 61.2155 61.2155i 0.0897589 0.0897589i
\(683\) 156.734 + 156.734i 0.229479 + 0.229479i 0.812475 0.582996i \(-0.198120\pi\)
−0.582996 + 0.812475i \(0.698120\pi\)
\(684\) 260.795i 0.381279i
\(685\) 427.012 600.770i 0.623375 0.877036i
\(686\) −22.7258 −0.0331280
\(687\) 50.5793 50.5793i 0.0736235 0.0736235i
\(688\) 0.0485989 + 0.0485989i 7.06379e−5 + 7.06379e-5i
\(689\) 142.779i 0.207227i
\(690\) −91.9552 65.3594i −0.133268 0.0947238i
\(691\) 330.267 0.477955 0.238977 0.971025i \(-0.423188\pi\)
0.238977 + 0.971025i \(0.423188\pi\)
\(692\) −33.8228 + 33.8228i −0.0488769 + 0.0488769i
\(693\) 8.41224 + 8.41224i 0.0121389 + 0.0121389i
\(694\) 28.0700i 0.0404468i
\(695\) 100.447 + 594.147i 0.144528 + 0.854888i
\(696\) 513.160 0.737298
\(697\) −217.965 + 217.965i −0.312719 + 0.312719i
\(698\) −216.172 216.172i −0.309703 0.309703i
\(699\) 178.379i 0.255191i
\(700\) −148.525 71.8269i −0.212178 0.102610i
\(701\) 1362.28 1.94334 0.971671 0.236336i \(-0.0759465\pi\)
0.971671 + 0.236336i \(0.0759465\pi\)
\(702\) 13.7536 13.7536i 0.0195921 0.0195921i
\(703\) 571.356 + 571.356i 0.812740 + 0.812740i
\(704\) 57.8839i 0.0822214i
\(705\) 470.233 79.4982i 0.666998 0.112763i
\(706\) 547.215 0.775093
\(707\) −165.735 + 165.735i −0.234420 + 0.234420i
\(708\) −96.5871 96.5871i −0.136423 0.136423i
\(709\) 370.256i 0.522222i 0.965309 + 0.261111i \(0.0840889\pi\)
−0.965309 + 0.261111i \(0.915911\pi\)
\(710\) 56.3360 79.2600i 0.0793465 0.111634i
\(711\) 221.521 0.311562
\(712\) 469.123 469.123i 0.658881 0.658881i
\(713\) −353.349 353.349i −0.495581 0.495581i
\(714\) 23.5945i 0.0330455i
\(715\) 18.6340 + 13.2446i 0.0260616 + 0.0185239i
\(716\) −720.810 −1.00672
\(717\) 512.740 512.740i 0.715119 0.715119i
\(718\) 73.2793 + 73.2793i 0.102060 + 0.102060i
\(719\) 883.893i 1.22934i −0.788786 0.614668i \(-0.789290\pi\)
0.788786 0.614668i \(-0.210710\pi\)
\(720\) 0.496461 + 2.93658i 0.000689530 + 0.00407858i
\(721\) −82.4331 −0.114332
\(722\) 740.725 740.725i 1.02593 1.02593i
\(723\) 455.384 + 455.384i 0.629854 + 0.629854i
\(724\) 51.4934i 0.0711235i
\(725\) 305.537 + 877.801i 0.421430 + 1.21076i
\(726\) 252.394 0.347650
\(727\) −264.156 + 264.156i −0.363351 + 0.363351i −0.865045 0.501694i \(-0.832710\pi\)
0.501694 + 0.865045i \(0.332710\pi\)
\(728\) 45.4795 + 45.4795i 0.0624718 + 0.0624718i
\(729\) 27.0000i 0.0370370i
\(730\) −224.735 + 37.9940i −0.307857 + 0.0520466i
\(731\) 1.45244 0.00198693
\(732\) 325.083 325.083i 0.444103 0.444103i
\(733\) −335.629 335.629i −0.457884 0.457884i 0.440076 0.897960i \(-0.354951\pi\)
−0.897960 + 0.440076i \(0.854951\pi\)
\(734\) 346.909i 0.472628i
\(735\) −35.1207 + 49.4119i −0.0477833 + 0.0672271i
\(736\) −340.989 −0.463301
\(737\) −42.9578 + 42.9578i −0.0582874 + 0.0582874i
\(738\) −191.229 191.229i −0.259117 0.259117i
\(739\) 622.823i 0.842791i −0.906877 0.421396i \(-0.861540\pi\)
0.906877 0.421396i \(-0.138460\pi\)
\(740\) −235.672 167.509i −0.318475 0.226364i
\(741\) −184.150 −0.248515
\(742\) −107.447 + 107.447i −0.144807 + 0.144807i
\(743\) 626.571 + 626.571i 0.843299 + 0.843299i 0.989286 0.145988i \(-0.0466360\pi\)
−0.145988 + 0.989286i \(0.546636\pi\)
\(744\) 649.699i 0.873251i
\(745\) 9.39538 + 55.5739i 0.0126112 + 0.0745958i
\(746\) 681.197 0.913132
\(747\) −176.007 + 176.007i −0.235619 + 0.235619i
\(748\) 11.0921 + 11.0921i 0.0148290 + 0.0148290i
\(749\) 406.891i 0.543245i
\(750\) 232.837 127.936i 0.310449 0.170581i
\(751\) 953.276 1.26934 0.634671 0.772783i \(-0.281136\pi\)
0.634671 + 0.772783i \(0.281136\pi\)
\(752\) 7.73138 7.73138i 0.0102811 0.0102811i
\(753\) 575.079 + 575.079i 0.763717 + 0.763717i
\(754\) 139.168i 0.184573i
\(755\) 98.0167 16.5708i 0.129823 0.0219481i
\(756\) 34.2907 0.0453580
\(757\) −202.867 + 202.867i −0.267988 + 0.267988i −0.828289 0.560301i \(-0.810685\pi\)
0.560301 + 0.828289i \(0.310685\pi\)
\(758\) −312.998 312.998i −0.412926 0.412926i
\(759\) 27.5605i 0.0363116i
\(760\) −804.527 + 1131.90i −1.05859 + 1.48934i
\(761\) −721.550 −0.948160 −0.474080 0.880482i \(-0.657219\pi\)
−0.474080 + 0.880482i \(0.657219\pi\)
\(762\) −358.309 + 358.309i −0.470222 + 0.470222i
\(763\) 141.879 + 141.879i 0.185949 + 0.185949i
\(764\) 349.733i 0.457765i
\(765\) 51.3006 + 36.4632i 0.0670596 + 0.0476643i
\(766\) −585.725 −0.764655
\(767\) −68.2011 + 68.2011i −0.0889193 + 0.0889193i
\(768\) −311.060 311.060i −0.405026 0.405026i
\(769\) 266.011i 0.345918i −0.984929 0.172959i \(-0.944667\pi\)
0.984929 0.172959i \(-0.0553329\pi\)
\(770\) −4.05575 23.9899i −0.00526721 0.0311557i
\(771\) 526.649 0.683072
\(772\) −490.349 + 490.349i −0.635167 +