Properties

Label 105.3.l.a.22.5
Level 105
Weight 3
Character 105.22
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 22.5
Character \(\chi\) \(=\) 105.22
Dual form 105.3.l.a.43.5

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.867675 0.867675i −0.433838 0.433838i 0.456094 0.889932i \(-0.349248\pi\)
−0.889932 + 0.456094i \(0.849248\pi\)
\(3\) 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 −0.619259 0.785187i \(-0.712567\pi\)
0.785187 + 0.619259i \(0.212567\pi\)
\(14\) 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 0.614438 0.788965i \(-0.289383\pi\)
−0.788965 + 0.614438i \(0.789383\pi\)
\(18\) −2.60303 + 2.60303i −0.144613 + 0.144613i
\(19\) 34.8524i 1.83434i −0.398501 0.917168i \(-0.630469\pi\)
0.398501 0.917168i \(-0.369531\pi\)
\(20\) −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 −0.851209 0.524826i \(-0.824130\pi\)
0.524826 + 0.851209i \(0.324130\pi\)
\(24\) 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 \(-0.778518\pi\)
0.767538 0.641004i \(-0.221482\pi\)
\(30\) 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 0.893043 0.449972i \(-0.148566\pi\)
−0.449972 + 0.893043i \(0.648566\pi\)
\(38\) −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 −0.709947 0.704255i \(-0.751281\pi\)
0.704255 + 0.709947i \(0.251281\pi\)
\(44\) 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 0.158814 0.987308i \(-0.449233\pi\)
−0.987308 + 0.158814i \(0.949233\pi\)
\(48\) −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 −0.946665 0.322218i \(-0.895571\pi\)
0.322218 + 0.946665i \(0.395571\pi\)
\(54\) 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 \(-0.913655\pi\)
0.963434 0.267946i \(-0.0863447\pi\)
\(60\) 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 0.887868 0.460097i \(-0.152186\pi\)
−0.460097 + 0.887868i \(0.652186\pi\)
\(68\) −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 −0.863754 0.503913i \(-0.831893\pi\)
0.503913 + 0.863754i \(0.331893\pi\)
\(74\) 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 \(0.154789\pi\)
−0.884076 + 0.467343i \(0.845211\pi\)
\(80\) 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 −0.259017 0.965873i \(-0.583399\pi\)
0.965873 + 0.259017i \(0.0833986\pi\)
\(84\) 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 \(-0.845078\pi\)
0.883881 0.467712i \(-0.154922\pi\)
\(90\) 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 −0.997759 0.0669049i \(-0.978688\pi\)
−0.0669049 0.997759i \(-0.521312\pi\)
\(98\) 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 −0.592025 0.805920i \(-0.701671\pi\)
0.805920 + 0.592025i \(0.201671\pi\)
\(104\) 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 0.999865 + 0.0164543i \(0.00523781\pi\)
0.0164543 + 0.999865i \(0.494762\pi\)
\(108\) −9.16457 + 9.16457i −0.0848571 + 0.0848571i
\(109\) 75.8376i 0.695758i 0.937539 + 0.347879i \(0.113098\pi\)
−0.937539 + 0.347879i \(0.886902\pi\)
\(110\) −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 −0.797926 0.602755i \(-0.794070\pi\)
0.602755 + 0.797926i \(0.294070\pi\)
\(114\) 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 0.907579 + 0.419880i \(0.137928\pi\)
0.419880 + 0.907579i \(0.362072\pi\)
\(128\) 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 0.215625 0.976476i \(-0.430821\pi\)
−0.976476 + 0.215625i \(0.930821\pi\)
\(138\) 15.9547 15.9547i 0.115614 0.115614i
\(139\) 120.516i 0.867019i 0.901149 + 0.433509i \(0.142725\pi\)
−0.901149 + 0.433509i \(0.857275\pi\)
\(140\) 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 \(0.0120436\pi\)
−0.999284 + 0.0378272i \(0.987956\pi\)
\(150\) −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 0.586422 0.810006i \(-0.300536\pi\)
−0.810006 + 0.586422i \(0.800536\pi\)
\(158\) 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 0.0616300 0.998099i \(-0.480370\pi\)
0.998099 0.0616300i \(-0.0196299\pi\)
\(164\) 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 0.999225 + 0.0393730i \(0.0125361\pi\)
0.0393730 + 0.999225i \(0.487464\pi\)
\(168\) 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 −0.666829 0.745211i \(-0.732349\pi\)
0.745211 + 0.666829i \(0.232349\pi\)
\(174\) 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 \(-0.700970\pi\)
0.590249 0.807222i \(-0.299030\pi\)
\(180\) 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 0.0187736 0.999824i \(-0.494024\pi\)
0.999824 0.0187736i \(-0.00597619\pi\)
\(194\) 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 −0.998651 0.0519216i \(-0.983465\pi\)
−0.0519216 0.998651i \(-0.516535\pi\)
\(198\) 3.90153 3.90153i 0.0197047 0.0197047i
\(199\) 160.567i 0.806869i 0.915009 + 0.403435i \(0.132184\pi\)
−0.915009 + 0.403435i \(0.867816\pi\)
\(200\) −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 −0.306264 0.951947i \(-0.599079\pi\)
0.951947 + 0.306264i \(0.0990789\pi\)
\(224\) 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 0.209264 0.977859i \(-0.432893\pi\)
−0.977859 + 0.209264i \(0.932893\pi\)
\(228\) −106.469 + 106.469i −0.466969 + 0.466969i
\(229\) 41.2978i 0.180340i 0.995926 + 0.0901700i \(0.0287410\pi\)
−0.995926 + 0.0901700i \(0.971259\pi\)
\(230\) −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 −0.845894 0.533350i \(-0.820933\pi\)
0.533350 + 0.845894i \(0.320933\pi\)
\(234\) 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 \(0.339690\pi\)
−0.482606 + 0.875838i \(0.660310\pi\)
\(240\) 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 0.988408 0.151819i \(-0.0485131\pi\)
−0.151819 + 0.988408i \(0.548513\pi\)
\(258\) 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 −0.500686 0.865629i \(-0.666919\pi\)
0.865629 + 0.500686i \(0.166919\pi\)
\(264\) 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 \(0.0319470\pi\)
−0.994968 + 0.100196i \(0.968053\pi\)
\(270\) 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 0.751491 0.659744i \(-0.229335\pi\)
−0.659744 + 0.751491i \(0.729335\pi\)
\(278\) 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 0.280593 0.959827i \(-0.409469\pi\)
0.959827 0.280593i \(-0.0905312\pi\)
\(284\) 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 −0.839109 0.543964i \(-0.816923\pi\)
0.543964 + 0.839109i \(0.316923\pi\)
\(294\) 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 0.498526 0.866874i \(-0.333875\pi\)
−0.866874 + 0.498526i \(0.833875\pi\)
\(308\) 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 −0.0367164 + 0.999326i \(0.511690\pi\)
−0.999326 + 0.0367164i \(0.988310\pi\)
\(314\) 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 0.427547 0.903993i \(-0.359378\pi\)
−0.903993 + 0.427547i \(0.859378\pi\)
\(318\) 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 −0.985839 0.167693i \(-0.946368\pi\)
−0.167693 0.985839i \(-0.553632\pi\)
\(338\) 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 0.730030 0.683415i \(-0.239506\pi\)
−0.683415 + 0.730030i \(0.739506\pi\)
\(348\) −113.574 + 113.574i −0.326362 + 0.326362i
\(349\) 249.140i 0.713868i −0.934130 0.356934i \(-0.883822\pi\)
0.934130 0.356934i \(-0.116178\pi\)
\(350\) −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 −0.994832 0.101534i \(-0.967625\pi\)
0.101534 + 0.994832i \(0.467625\pi\)
\(354\) 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 \(0.0375281\pi\)
−0.993058 + 0.117625i \(0.962472\pi\)
\(360\) −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 0.380198 0.924905i \(-0.375856\pi\)
−0.924905 + 0.380198i \(0.875856\pi\)
\(368\) 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 −0.0538401 + 0.998550i \(0.517146\pi\)
−0.998550 + 0.0538401i \(0.982854\pi\)
\(374\) 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 \(-0.842123\pi\)
0.879500 0.475899i \(-0.157877\pi\)
\(380\) 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 −0.112395 0.993664i \(-0.535852\pi\)
0.993664 + 0.112395i \(0.0358523\pi\)
\(384\) 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 \(-0.728676\pi\)
0.658185 0.752856i \(-0.271324\pi\)
\(390\) 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 0.467899 0.883782i \(-0.345011\pi\)
−0.883782 + 0.467899i \(0.845011\pi\)
\(398\) 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 \(0.142779\pi\)
−0.901076 + 0.433662i \(0.857221\pi\)
\(410\) 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 \(0.0409356\pi\)
−0.991742 + 0.128249i \(0.959064\pi\)
\(420\) 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 −0.816285 0.577649i \(-0.803970\pi\)
0.577649 + 0.816285i \(0.303970\pi\)
\(434\) 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 \(-0.879398\pi\)
0.929078 0.369883i \(-0.120602\pi\)
\(440\) −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 −0.914886 0.403713i \(-0.867720\pi\)
0.403713 + 0.914886i \(0.367720\pi\)
\(444\) 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 \(0.0793617\pi\)
−0.969080 + 0.246747i \(0.920638\pi\)
\(450\) −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 0.840337 + 0.542064i \(0.182357\pi\)
0.542064 + 0.840337i \(0.317643\pi\)
\(458\) 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 −0.794878 0.606769i \(-0.792465\pi\)
0.606769 + 0.794878i \(0.292465\pi\)
\(464\) 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 0.502781 0.864414i \(-0.332310\pi\)
−0.864414 + 0.502781i \(0.832310\pi\)
\(468\) −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 \(0.211779\pi\)
−0.786718 + 0.617312i \(0.788221\pi\)
\(480\) −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 0.997924 0.0643972i \(-0.0205125\pi\)
−0.0643972 + 0.997924i \(0.520512\pi\)
\(488\) 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 \(-0.795270\pi\)
0.800194 0.599741i \(-0.204730\pi\)
\(500\) −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 −0.210027 + 0.977696i \(0.567355\pi\)
−0.977696 + 0.210027i \(0.932645\pi\)
\(504\) 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 \(0.256511\pi\)
−0.692496 + 0.721422i \(0.743489\pi\)
\(510\) −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 −0.556642 0.830752i \(-0.687911\pi\)
0.830752 + 0.556642i \(0.187911\pi\)
\(524\) 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 0.803208 0.595699i \(-0.203125\pi\)
−0.595699 + 0.803208i \(0.703125\pi\)
\(548\) −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 0.470273 0.882521i \(-0.344155\pi\)
−0.882521 + 0.470273i \(0.844155\pi\)
\(558\) −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 −0.619685 0.784851i \(-0.712740\pi\)
0.784851 + 0.619685i \(0.212740\pi\)
\(564\) 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 \(0.110793\pi\)
−0.940034 + 0.341080i \(0.889207\pi\)
\(570\) 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 0.948975 0.315351i \(-0.102122\pi\)
−0.315351 + 0.948975i \(0.602122\pi\)
\(578\) −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 0.964363 0.264583i \(-0.0852343\pi\)
−0.264583 + 0.964363i \(0.585234\pi\)
\(588\) 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 0.387224 0.921986i \(-0.373434\pi\)
0.921986 0.387224i \(-0.126566\pi\)
\(594\) 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 \(0.158914\pi\)
−0.877946 + 0.478760i \(0.841086\pi\)
\(600\) −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 0.999386 + 0.0350309i \(0.0111530\pi\)
0.0350309 + 0.999386i \(0.488847\pi\)
\(608\) 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 −0.607200 0.794549i \(-0.707707\pi\)
0.794549 + 0.607200i \(0.207707\pi\)
\(614\) 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 0.452201 0.891916i \(-0.350639\pi\)
−0.891916 + 0.452201i \(0.850639\pi\)
\(618\) −46.8242 + 46.8242i −0.0757673 + 0.0757673i
\(619\) 346.221i 0.559323i 0.960099 + 0.279662i \(0.0902223\pi\)
−0.960099 + 0.279662i \(0.909778\pi\)
\(620\) −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 −0.273482 0.961877i \(-0.588176\pi\)
0.961877 + 0.273482i \(0.0881755\pi\)
\(644\) 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 0.212632 0.977132i \(-0.431796\pi\)
−0.977132 + 0.212632i \(0.931796\pi\)
\(648\) 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 −0.784086 0.620652i \(-0.786868\pi\)
0.620652 + 0.784086i \(0.286868\pi\)
\(654\) 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 \(0.181826\pi\)
−0.841240 + 0.540662i \(0.818174\pi\)
\(660\) −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 −0.984756 0.173940i \(-0.944350\pi\)
0.173940 + 0.984756i \(0.444350\pi\)
\(674\) 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 0.891849 0.452333i \(-0.149408\pi\)
−0.452333 + 0.891849i \(0.649408\pi\)
\(678\) 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 −0.582996 0.812475i \(-0.698120\pi\)
0.812475 + 0.582996i \(0.198120\pi\)
\(684\) 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 \(-0.915911\pi\)
0.965309 0.261111i \(-0.0840889\pi\)
\(710\) 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 \(0.210710\pi\)
−0.788786 + 0.614668i \(0.789290\pi\)
\(720\) 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 0.501694 0.865045i \(-0.332710\pi\)
−0.865045 + 0.501694i \(0.832710\pi\)
\(728\) 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 −0.897960 0.440076i \(-0.854951\pi\)
0.440076 + 0.897960i \(0.354951\pi\)
\(734\) 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 \(0.138460\pi\)
−0.906877 + 0.421396i \(0.861540\pi\)
\(740\) −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 −0.145988 0.989286i \(-0.546636\pi\)
0.989286 + 0.145988i \(0.0466360\pi\)
\(744\) 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 0.560301 0.828289i \(-0.310685\pi\)
−0.828289 + 0.560301i \(0.810685\pi\)
\(758\) −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 \(0.0553329\pi\)
−0.984929 + 0.172959i \(0.944667\pi\)
\(770\) −4.05575 + 23.9899i −0.00526721 + 0.0311557i
\(771\) 526.649 0.683072
\(772\) −490.349 490.349i −0.635167 0.635167i