Properties

Label 1050.3.q.a.649.4
Level $1050$
Weight $3$
Character 1050.649
Analytic conductor $28.610$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 649.4
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1050.649
Dual form 1050.3.q.a.199.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(1.88064 + 6.74264i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(1.88064 + 6.74264i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-3.00000 - 5.19615i) q^{11} +(-1.73205 + 3.00000i) q^{12} +17.8639 q^{13} +(-2.46447 + 9.58783i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(9.37769 + 16.2426i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(14.7426 + 8.51167i) q^{19} +(-8.48528 + 8.66025i) q^{21} -8.48528i q^{22} +(-11.6531 - 6.72792i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(21.8787 + 12.6317i) q^{26} -5.19615 q^{27} +(-9.79796 + 10.0000i) q^{28} -33.9411 q^{29} +(12.7721 - 7.37396i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(5.19615 - 9.00000i) q^{33} +26.5241i q^{34} -6.00000 q^{36} +(5.17066 + 2.98528i) q^{37} +(12.0373 + 20.8492i) q^{38} +(15.4706 + 26.7958i) q^{39} +35.2354i q^{41} +(-16.5160 + 4.60660i) q^{42} +15.4853i q^{43} +(6.00000 - 10.3923i) q^{44} +(-9.51472 - 16.4800i) q^{46} +(-16.6031 + 28.7574i) q^{47} -6.92820 q^{48} +(-41.9264 + 25.3609i) q^{49} +(-16.2426 + 28.1331i) q^{51} +(17.8639 + 30.9411i) q^{52} +(-29.9161 + 17.2721i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(-19.0711 + 5.31925i) q^{56} +29.4853i q^{57} +(-41.5692 - 24.0000i) q^{58} +(-23.6985 + 13.6823i) q^{59} +(-34.9706 - 20.1903i) q^{61} +20.8567 q^{62} +(-20.3389 - 5.22792i) q^{63} -8.00000 q^{64} +(12.7279 - 7.34847i) q^{66} +(99.0707 - 57.1985i) q^{67} +(-18.7554 + 32.4853i) q^{68} -23.3062i q^{69} +18.6030 q^{71} +(-7.34847 - 4.24264i) q^{72} +(-58.5161 - 101.353i) q^{73} +(4.22183 + 7.31242i) q^{74} +34.0467i q^{76} +(29.3939 - 30.0000i) q^{77} +43.7574i q^{78} +(-44.1690 + 76.5030i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-24.9152 + 43.1543i) q^{82} -75.7601 q^{83} +(-23.4853 - 6.03668i) q^{84} +(-10.9497 + 18.9655i) q^{86} +(-29.3939 - 50.9117i) q^{87} +(14.6969 - 8.48528i) q^{88} +(18.0000 + 10.3923i) q^{89} +(33.5955 + 120.450i) q^{91} -26.9117i q^{92} +(22.1219 + 12.7721i) q^{93} +(-40.6690 + 23.4803i) q^{94} +(-8.48528 - 4.89898i) q^{96} +30.5826 q^{97} +(-69.2820 + 1.41421i) q^{98} +18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{4} - 12q^{9} + O(q^{10}) \) \( 8q + 8q^{4} - 12q^{9} - 24q^{11} - 48q^{14} - 16q^{16} + 84q^{19} + 192q^{26} + 204q^{31} - 48q^{36} - 12q^{39} + 48q^{44} - 144q^{46} + 4q^{49} - 96q^{51} - 96q^{56} + 48q^{59} - 144q^{61} - 64q^{64} + 624q^{71} + 96q^{74} + 20q^{79} - 36q^{81} - 120q^{84} - 48q^{86} + 144q^{89} - 444q^{91} + 48q^{94} + 144q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 0.707107i 0.612372 + 0.353553i
\(3\) 0.866025 + 1.50000i 0.288675 + 0.500000i
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) 1.88064 + 6.74264i 0.268662 + 0.963234i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 + 2.59808i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −3.00000 5.19615i −0.272727 0.472377i 0.696832 0.717234i \(-0.254592\pi\)
−0.969559 + 0.244857i \(0.921259\pi\)
\(12\) −1.73205 + 3.00000i −0.144338 + 0.250000i
\(13\) 17.8639 1.37414 0.687072 0.726590i \(-0.258896\pi\)
0.687072 + 0.726590i \(0.258896\pi\)
\(14\) −2.46447 + 9.58783i −0.176033 + 0.684845i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 9.37769 + 16.2426i 0.551629 + 0.955449i 0.998157 + 0.0606799i \(0.0193269\pi\)
−0.446528 + 0.894770i \(0.647340\pi\)
\(18\) −3.67423 + 2.12132i −0.204124 + 0.117851i
\(19\) 14.7426 + 8.51167i 0.775928 + 0.447983i 0.834985 0.550272i \(-0.185476\pi\)
−0.0590569 + 0.998255i \(0.518809\pi\)
\(20\) 0 0
\(21\) −8.48528 + 8.66025i −0.404061 + 0.412393i
\(22\) 8.48528i 0.385695i
\(23\) −11.6531 6.72792i −0.506657 0.292518i 0.224802 0.974405i \(-0.427827\pi\)
−0.731458 + 0.681886i \(0.761160\pi\)
\(24\) −4.24264 + 2.44949i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) 21.8787 + 12.6317i 0.841488 + 0.485833i
\(27\) −5.19615 −0.192450
\(28\) −9.79796 + 10.0000i −0.349927 + 0.357143i
\(29\) −33.9411 −1.17038 −0.585192 0.810895i \(-0.698981\pi\)
−0.585192 + 0.810895i \(0.698981\pi\)
\(30\) 0 0
\(31\) 12.7721 7.37396i 0.412003 0.237870i −0.279647 0.960103i \(-0.590218\pi\)
0.691650 + 0.722233i \(0.256884\pi\)
\(32\) −4.89898 + 2.82843i −0.153093 + 0.0883883i
\(33\) 5.19615 9.00000i 0.157459 0.272727i
\(34\) 26.5241i 0.780121i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 5.17066 + 2.98528i 0.139748 + 0.0806833i 0.568244 0.822860i \(-0.307623\pi\)
−0.428496 + 0.903544i \(0.640956\pi\)
\(38\) 12.0373 + 20.8492i 0.316771 + 0.548664i
\(39\) 15.4706 + 26.7958i 0.396681 + 0.687072i
\(40\) 0 0
\(41\) 35.2354i 0.859399i 0.902972 + 0.429700i \(0.141381\pi\)
−0.902972 + 0.429700i \(0.858619\pi\)
\(42\) −16.5160 + 4.60660i −0.393239 + 0.109681i
\(43\) 15.4853i 0.360123i 0.983655 + 0.180061i \(0.0576296\pi\)
−0.983655 + 0.180061i \(0.942370\pi\)
\(44\) 6.00000 10.3923i 0.136364 0.236189i
\(45\) 0 0
\(46\) −9.51472 16.4800i −0.206842 0.358260i
\(47\) −16.6031 + 28.7574i −0.353257 + 0.611859i −0.986818 0.161834i \(-0.948259\pi\)
0.633561 + 0.773693i \(0.281592\pi\)
\(48\) −6.92820 −0.144338
\(49\) −41.9264 + 25.3609i −0.855641 + 0.517570i
\(50\) 0 0
\(51\) −16.2426 + 28.1331i −0.318483 + 0.551629i
\(52\) 17.8639 + 30.9411i 0.343536 + 0.595022i
\(53\) −29.9161 + 17.2721i −0.564455 + 0.325888i −0.754932 0.655803i \(-0.772330\pi\)
0.190477 + 0.981692i \(0.438997\pi\)
\(54\) −6.36396 3.67423i −0.117851 0.0680414i
\(55\) 0 0
\(56\) −19.0711 + 5.31925i −0.340555 + 0.0949865i
\(57\) 29.4853i 0.517286i
\(58\) −41.5692 24.0000i −0.716711 0.413793i
\(59\) −23.6985 + 13.6823i −0.401669 + 0.231904i −0.687204 0.726465i \(-0.741162\pi\)
0.285535 + 0.958368i \(0.407829\pi\)
\(60\) 0 0
\(61\) −34.9706 20.1903i −0.573288 0.330988i 0.185174 0.982706i \(-0.440715\pi\)
−0.758461 + 0.651718i \(0.774049\pi\)
\(62\) 20.8567 0.336399
\(63\) −20.3389 5.22792i −0.322839 0.0829829i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 12.7279 7.34847i 0.192847 0.111340i
\(67\) 99.0707 57.1985i 1.47867 0.853709i 0.478958 0.877838i \(-0.341015\pi\)
0.999709 + 0.0241291i \(0.00768127\pi\)
\(68\) −18.7554 + 32.4853i −0.275814 + 0.477725i
\(69\) 23.3062i 0.337771i
\(70\) 0 0
\(71\) 18.6030 0.262015 0.131007 0.991381i \(-0.458179\pi\)
0.131007 + 0.991381i \(0.458179\pi\)
\(72\) −7.34847 4.24264i −0.102062 0.0589256i
\(73\) −58.5161 101.353i −0.801590 1.38839i −0.918569 0.395260i \(-0.870654\pi\)
0.116979 0.993134i \(-0.462679\pi\)
\(74\) 4.22183 + 7.31242i 0.0570517 + 0.0988164i
\(75\) 0 0
\(76\) 34.0467i 0.447983i
\(77\) 29.3939 30.0000i 0.381739 0.389610i
\(78\) 43.7574i 0.560992i
\(79\) −44.1690 + 76.5030i −0.559102 + 0.968393i 0.438470 + 0.898746i \(0.355521\pi\)
−0.997572 + 0.0696469i \(0.977813\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) −24.9152 + 43.1543i −0.303843 + 0.526272i
\(83\) −75.7601 −0.912772 −0.456386 0.889782i \(-0.650856\pi\)
−0.456386 + 0.889782i \(0.650856\pi\)
\(84\) −23.4853 6.03668i −0.279587 0.0718653i
\(85\) 0 0
\(86\) −10.9497 + 18.9655i −0.127323 + 0.220529i
\(87\) −29.3939 50.9117i −0.337861 0.585192i
\(88\) 14.6969 8.48528i 0.167011 0.0964237i
\(89\) 18.0000 + 10.3923i 0.202247 + 0.116767i 0.597703 0.801717i \(-0.296080\pi\)
−0.395456 + 0.918485i \(0.629413\pi\)
\(90\) 0 0
\(91\) 33.5955 + 120.450i 0.369181 + 1.32362i
\(92\) 26.9117i 0.292518i
\(93\) 22.1219 + 12.7721i 0.237870 + 0.137334i
\(94\) −40.6690 + 23.4803i −0.432649 + 0.249790i
\(95\) 0 0
\(96\) −8.48528 4.89898i −0.0883883 0.0510310i
\(97\) 30.5826 0.315284 0.157642 0.987496i \(-0.449611\pi\)
0.157642 + 0.987496i \(0.449611\pi\)
\(98\) −69.2820 + 1.41421i −0.706960 + 0.0144308i
\(99\) 18.0000 0.181818
\(100\) 0 0
\(101\) 110.823 63.9839i 1.09726 0.633504i 0.161761 0.986830i \(-0.448283\pi\)
0.935500 + 0.353326i \(0.114949\pi\)
\(102\) −39.7862 + 22.9706i −0.390061 + 0.225202i
\(103\) 40.4781 70.1102i 0.392992 0.680681i −0.599851 0.800112i \(-0.704774\pi\)
0.992843 + 0.119430i \(0.0381068\pi\)
\(104\) 50.5266i 0.485833i
\(105\) 0 0
\(106\) −48.8528 −0.460876
\(107\) 146.753 + 84.7279i 1.37152 + 0.791850i 0.991120 0.132971i \(-0.0424516\pi\)
0.380404 + 0.924820i \(0.375785\pi\)
\(108\) −5.19615 9.00000i −0.0481125 0.0833333i
\(109\) 89.4706 + 154.968i 0.820831 + 1.42172i 0.905064 + 0.425275i \(0.139823\pi\)
−0.0842335 + 0.996446i \(0.526844\pi\)
\(110\) 0 0
\(111\) 10.3413i 0.0931650i
\(112\) −27.1185 6.97056i −0.242129 0.0622372i
\(113\) 17.3970i 0.153955i −0.997033 0.0769777i \(-0.975473\pi\)
0.997033 0.0769777i \(-0.0245270\pi\)
\(114\) −20.8492 + 36.1119i −0.182888 + 0.316771i
\(115\) 0 0
\(116\) −33.9411 58.7878i −0.292596 0.506791i
\(117\) −26.7958 + 46.4117i −0.229024 + 0.396681i
\(118\) −38.6995 −0.327962
\(119\) −91.8823 + 93.7769i −0.772120 + 0.788041i
\(120\) 0 0
\(121\) 42.5000 73.6122i 0.351240 0.608365i
\(122\) −28.5533 49.4558i −0.234044 0.405376i
\(123\) −52.8530 + 30.5147i −0.429700 + 0.248087i
\(124\) 25.5442 + 14.7479i 0.206001 + 0.118935i
\(125\) 0 0
\(126\) −21.2132 20.7846i −0.168359 0.164957i
\(127\) 167.426i 1.31832i −0.752004 0.659159i \(-0.770912\pi\)
0.752004 0.659159i \(-0.229088\pi\)
\(128\) −9.79796 5.65685i −0.0765466 0.0441942i
\(129\) −23.2279 + 13.4106i −0.180061 + 0.103959i
\(130\) 0 0
\(131\) −1.54416 0.891519i −0.0117874 0.00680549i 0.494095 0.869408i \(-0.335500\pi\)
−0.505882 + 0.862603i \(0.668833\pi\)
\(132\) 20.7846 0.157459
\(133\) −29.6656 + 115.412i −0.223049 + 0.867757i
\(134\) 161.782 1.20733
\(135\) 0 0
\(136\) −45.9411 + 26.5241i −0.337802 + 0.195030i
\(137\) −87.4431 + 50.4853i −0.638271 + 0.368506i −0.783948 0.620826i \(-0.786797\pi\)
0.145677 + 0.989332i \(0.453464\pi\)
\(138\) 16.4800 28.5442i 0.119420 0.206842i
\(139\) 140.542i 1.01110i 0.862799 + 0.505548i \(0.168710\pi\)
−0.862799 + 0.505548i \(0.831290\pi\)
\(140\) 0 0
\(141\) −57.5147 −0.407906
\(142\) 22.7840 + 13.1543i 0.160450 + 0.0926361i
\(143\) −53.5916 92.8234i −0.374766 0.649115i
\(144\) −6.00000 10.3923i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) 165.508i 1.13362i
\(147\) −74.3507 40.9264i −0.505787 0.278411i
\(148\) 11.9411i 0.0806833i
\(149\) 91.4558 158.406i 0.613798 1.06313i −0.376797 0.926296i \(-0.622974\pi\)
0.990594 0.136833i \(-0.0436922\pi\)
\(150\) 0 0
\(151\) 144.397 + 250.103i 0.956271 + 1.65631i 0.731432 + 0.681915i \(0.238852\pi\)
0.224840 + 0.974396i \(0.427814\pi\)
\(152\) −24.0746 + 41.6985i −0.158386 + 0.274332i
\(153\) −56.2662 −0.367753
\(154\) 57.2132 15.9577i 0.371514 0.103622i
\(155\) 0 0
\(156\) −30.9411 + 53.5916i −0.198341 + 0.343536i
\(157\) −93.5307 162.000i −0.595737 1.03185i −0.993442 0.114334i \(-0.963527\pi\)
0.397705 0.917513i \(-0.369807\pi\)
\(158\) −108.192 + 62.4645i −0.684757 + 0.395345i
\(159\) −51.8162 29.9161i −0.325888 0.188152i
\(160\) 0 0
\(161\) 23.4487 91.2255i 0.145644 0.566618i
\(162\) 12.7279i 0.0785674i
\(163\) −13.9074 8.02944i −0.0853214 0.0492604i 0.456732 0.889604i \(-0.349020\pi\)
−0.542054 + 0.840344i \(0.682353\pi\)
\(164\) −61.0294 + 35.2354i −0.372131 + 0.214850i
\(165\) 0 0
\(166\) −92.7868 53.5705i −0.558957 0.322714i
\(167\) −176.117 −1.05459 −0.527297 0.849681i \(-0.676794\pi\)
−0.527297 + 0.849681i \(0.676794\pi\)
\(168\) −24.4949 24.0000i −0.145803 0.142857i
\(169\) 150.118 0.888271
\(170\) 0 0
\(171\) −44.2279 + 25.5350i −0.258643 + 0.149328i
\(172\) −26.8213 + 15.4853i −0.155938 + 0.0900307i
\(173\) 115.576 200.184i 0.668070 1.15713i −0.310373 0.950615i \(-0.600454\pi\)
0.978443 0.206517i \(-0.0662128\pi\)
\(174\) 83.1384i 0.477807i
\(175\) 0 0
\(176\) 24.0000 0.136364
\(177\) −41.0470 23.6985i −0.231904 0.133890i
\(178\) 14.6969 + 25.4558i 0.0825671 + 0.143010i
\(179\) −42.6396 73.8540i −0.238210 0.412592i 0.721991 0.691903i \(-0.243227\pi\)
−0.960201 + 0.279311i \(0.909894\pi\)
\(180\) 0 0
\(181\) 5.58655i 0.0308649i −0.999881 0.0154325i \(-0.995087\pi\)
0.999881 0.0154325i \(-0.00491250\pi\)
\(182\) −44.0249 + 171.276i −0.241895 + 0.941075i
\(183\) 69.9411i 0.382192i
\(184\) 19.0294 32.9600i 0.103421 0.179130i
\(185\) 0 0
\(186\) 18.0624 + 31.2851i 0.0971099 + 0.168199i
\(187\) 56.2662 97.4558i 0.300889 0.521154i
\(188\) −66.4123 −0.353257
\(189\) −9.77208 35.0358i −0.0517041 0.185375i
\(190\) 0 0
\(191\) −92.6985 + 160.558i −0.485332 + 0.840620i −0.999858 0.0168547i \(-0.994635\pi\)
0.514526 + 0.857475i \(0.327968\pi\)
\(192\) −6.92820 12.0000i −0.0360844 0.0625000i
\(193\) 197.275 113.897i 1.02215 0.590140i 0.107425 0.994213i \(-0.465739\pi\)
0.914727 + 0.404073i \(0.132406\pi\)
\(194\) 37.4558 + 21.6251i 0.193071 + 0.111470i
\(195\) 0 0
\(196\) −85.8528 47.2577i −0.438025 0.241111i
\(197\) 123.161i 0.625185i −0.949887 0.312593i \(-0.898803\pi\)
0.949887 0.312593i \(-0.101197\pi\)
\(198\) 22.0454 + 12.7279i 0.111340 + 0.0642824i
\(199\) −5.39697 + 3.11594i −0.0271205 + 0.0156580i −0.513499 0.858090i \(-0.671651\pi\)
0.486378 + 0.873748i \(0.338318\pi\)
\(200\) 0 0
\(201\) 171.595 + 99.0707i 0.853709 + 0.492889i
\(202\) 180.974 0.895910
\(203\) −63.8309 228.853i −0.314438 1.12735i
\(204\) −64.9706 −0.318483
\(205\) 0 0
\(206\) 99.1508 57.2447i 0.481314 0.277887i
\(207\) 34.9593 20.1838i 0.168886 0.0975061i
\(208\) −35.7277 + 61.8823i −0.171768 + 0.297511i
\(209\) 102.140i 0.488708i
\(210\) 0 0
\(211\) −124.912 −0.591999 −0.295999 0.955188i \(-0.595653\pi\)
−0.295999 + 0.955188i \(0.595653\pi\)
\(212\) −59.8322 34.5442i −0.282228 0.162944i
\(213\) 16.1107 + 27.9045i 0.0756371 + 0.131007i
\(214\) 119.823 + 207.540i 0.559922 + 0.969814i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 73.7396 + 72.2498i 0.339814 + 0.332948i
\(218\) 253.061i 1.16083i
\(219\) 101.353 175.548i 0.462798 0.801590i
\(220\) 0 0
\(221\) 167.522 + 290.156i 0.758017 + 1.31292i
\(222\) −7.31242 + 12.6655i −0.0329388 + 0.0570517i
\(223\) 228.631 1.02525 0.512625 0.858613i \(-0.328673\pi\)
0.512625 + 0.858613i \(0.328673\pi\)
\(224\) −28.2843 27.7128i −0.126269 0.123718i
\(225\) 0 0
\(226\) 12.3015 21.3068i 0.0544315 0.0942781i
\(227\) 84.7685 + 146.823i 0.373430 + 0.646799i 0.990091 0.140430i \(-0.0448484\pi\)
−0.616661 + 0.787229i \(0.711515\pi\)
\(228\) −51.0700 + 29.4853i −0.223991 + 0.129321i
\(229\) −30.0442 17.3460i −0.131197 0.0757467i 0.432965 0.901411i \(-0.357467\pi\)
−0.564162 + 0.825664i \(0.690801\pi\)
\(230\) 0 0
\(231\) 70.4558 + 18.1101i 0.305004 + 0.0783985i
\(232\) 96.0000i 0.413793i
\(233\) 220.391 + 127.243i 0.945883 + 0.546106i 0.891800 0.452431i \(-0.149443\pi\)
0.0540833 + 0.998536i \(0.482776\pi\)
\(234\) −65.6360 + 37.8950i −0.280496 + 0.161944i
\(235\) 0 0
\(236\) −47.3970 27.3647i −0.200835 0.115952i
\(237\) −153.006 −0.645595
\(238\) −178.843 + 49.8823i −0.751440 + 0.209589i
\(239\) −197.147 −0.824884 −0.412442 0.910984i \(-0.635324\pi\)
−0.412442 + 0.910984i \(0.635324\pi\)
\(240\) 0 0
\(241\) 76.6173 44.2350i 0.317914 0.183548i −0.332548 0.943086i \(-0.607908\pi\)
0.650462 + 0.759538i \(0.274575\pi\)
\(242\) 104.103 60.1041i 0.430179 0.248364i
\(243\) 7.79423 13.5000i 0.0320750 0.0555556i
\(244\) 80.7611i 0.330988i
\(245\) 0 0
\(246\) −86.3087 −0.350848
\(247\) 263.361 + 152.051i 1.06624 + 0.615592i
\(248\) 20.8567 + 36.1249i 0.0840997 + 0.145665i
\(249\) −65.6102 113.640i −0.263495 0.456386i
\(250\) 0 0
\(251\) 215.903i 0.860172i −0.902788 0.430086i \(-0.858483\pi\)
0.902788 0.430086i \(-0.141517\pi\)
\(252\) −11.2838 40.4558i −0.0447771 0.160539i
\(253\) 80.7351i 0.319111i
\(254\) 118.388 205.055i 0.466096 0.807302i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −2.15232 + 3.72792i −0.00837477 + 0.0145055i −0.870182 0.492730i \(-0.835999\pi\)
0.861808 + 0.507235i \(0.169332\pi\)
\(258\) −37.9310 −0.147020
\(259\) −10.4045 + 40.4781i −0.0401720 + 0.156286i
\(260\) 0 0
\(261\) 50.9117 88.1816i 0.195064 0.337861i
\(262\) −1.26080 2.18377i −0.00481221 0.00833499i
\(263\) 244.805 141.338i 0.930817 0.537407i 0.0437468 0.999043i \(-0.486071\pi\)
0.887070 + 0.461635i \(0.152737\pi\)
\(264\) 25.4558 + 14.6969i 0.0964237 + 0.0556702i
\(265\) 0 0
\(266\) −117.941 + 120.373i −0.443388 + 0.452531i
\(267\) 36.0000i 0.134831i
\(268\) 198.141 + 114.397i 0.739333 + 0.426854i
\(269\) 330.765 190.967i 1.22961 0.709914i 0.262660 0.964888i \(-0.415400\pi\)
0.966948 + 0.254974i \(0.0820669\pi\)
\(270\) 0 0
\(271\) −73.0294 42.1636i −0.269481 0.155585i 0.359171 0.933272i \(-0.383060\pi\)
−0.628652 + 0.777687i \(0.716393\pi\)
\(272\) −75.0215 −0.275814
\(273\) −151.580 + 154.706i −0.555238 + 0.566687i
\(274\) −142.794 −0.521146
\(275\) 0 0
\(276\) 40.3675 23.3062i 0.146259 0.0844428i
\(277\) 118.747 68.5589i 0.428691 0.247505i −0.270098 0.962833i \(-0.587056\pi\)
0.698789 + 0.715328i \(0.253723\pi\)
\(278\) −99.3784 + 172.128i −0.357476 + 0.619167i
\(279\) 44.2438i 0.158580i
\(280\) 0 0
\(281\) −325.103 −1.15695 −0.578474 0.815701i \(-0.696352\pi\)
−0.578474 + 0.815701i \(0.696352\pi\)
\(282\) −70.4409 40.6690i −0.249790 0.144216i
\(283\) 97.2876 + 168.507i 0.343773 + 0.595432i 0.985130 0.171811i \(-0.0549617\pi\)
−0.641357 + 0.767242i \(0.721628\pi\)
\(284\) 18.6030 + 32.2214i 0.0655036 + 0.113456i
\(285\) 0 0
\(286\) 151.580i 0.530000i
\(287\) −237.579 + 66.2649i −0.827803 + 0.230888i
\(288\) 16.9706i 0.0589256i
\(289\) −31.3823 + 54.3557i −0.108589 + 0.188082i
\(290\) 0 0
\(291\) 26.4853 + 45.8739i 0.0910147 + 0.157642i
\(292\) 117.032 202.706i 0.400795 0.694197i
\(293\) 239.702 0.818095 0.409048 0.912513i \(-0.365861\pi\)
0.409048 + 0.912513i \(0.365861\pi\)
\(294\) −62.1213 102.698i −0.211297 0.349314i
\(295\) 0 0
\(296\) −8.44365 + 14.6248i −0.0285258 + 0.0494082i
\(297\) 15.5885 + 27.0000i 0.0524864 + 0.0909091i
\(298\) 224.020 129.338i 0.751745 0.434020i
\(299\) −208.169 120.187i −0.696219 0.401962i
\(300\) 0 0
\(301\) −104.412 + 29.1222i −0.346883 + 0.0967515i
\(302\) 408.416i 1.35237i
\(303\) 191.952 + 110.823i 0.633504 + 0.365754i
\(304\) −58.9706 + 34.0467i −0.193982 + 0.111996i
\(305\) 0 0
\(306\) −68.9117 39.7862i −0.225202 0.130020i
\(307\) 540.272 1.75984 0.879921 0.475120i \(-0.157595\pi\)
0.879921 + 0.475120i \(0.157595\pi\)
\(308\) 81.3554 + 20.9117i 0.264141 + 0.0678951i
\(309\) 140.220 0.453788
\(310\) 0 0
\(311\) 350.044 202.098i 1.12554 0.649832i 0.182732 0.983163i \(-0.441506\pi\)
0.942810 + 0.333330i \(0.108172\pi\)
\(312\) −75.7900 + 43.7574i −0.242917 + 0.140248i
\(313\) 65.6482 113.706i 0.209739 0.363278i −0.741893 0.670518i \(-0.766072\pi\)
0.951632 + 0.307240i \(0.0994053\pi\)
\(314\) 264.545i 0.842500i
\(315\) 0 0
\(316\) −176.676 −0.559102
\(317\) −81.3554 46.9706i −0.256642 0.148172i 0.366160 0.930552i \(-0.380672\pi\)
−0.622802 + 0.782380i \(0.714006\pi\)
\(318\) −42.3078 73.2792i −0.133043 0.230438i
\(319\) 101.823 + 176.363i 0.319196 + 0.552863i
\(320\) 0 0
\(321\) 293.506i 0.914349i
\(322\) 93.2248 95.1472i 0.289518 0.295488i
\(323\) 319.279i 0.988481i
\(324\) 9.00000 15.5885i 0.0277778 0.0481125i
\(325\) 0 0
\(326\) −11.3553 19.6680i −0.0348323 0.0603314i
\(327\) −154.968 + 268.412i −0.473907 + 0.820831i
\(328\) −99.6607 −0.303843
\(329\) −225.125 57.8664i −0.684270 0.175886i
\(330\) 0 0
\(331\) 130.684 226.351i 0.394815 0.683840i −0.598263 0.801300i \(-0.704142\pi\)
0.993078 + 0.117460i \(0.0374754\pi\)
\(332\) −75.7601 131.220i −0.228193 0.395242i
\(333\) −15.5120 + 8.95584i −0.0465825 + 0.0268944i
\(334\) −215.698 124.534i −0.645804 0.372855i
\(335\) 0 0
\(336\) −13.0294 46.7144i −0.0387781 0.139031i
\(337\) 136.265i 0.404347i −0.979350 0.202173i \(-0.935200\pi\)
0.979350 0.202173i \(-0.0648005\pi\)
\(338\) 183.856 + 106.149i 0.543952 + 0.314051i
\(339\) 26.0955 15.0662i 0.0769777 0.0444431i
\(340\) 0 0
\(341\) −76.6325 44.2438i −0.224729 0.129747i
\(342\) −72.2239 −0.211181
\(343\) −249.848 235.000i −0.728420 0.685131i
\(344\) −43.7990 −0.127323
\(345\) 0 0
\(346\) 283.103 163.449i 0.818216 0.472397i
\(347\) 279.026 161.095i 0.804108 0.464252i −0.0407975 0.999167i \(-0.512990\pi\)
0.844906 + 0.534915i \(0.179657\pi\)
\(348\) 58.7878 101.823i 0.168930 0.292596i
\(349\) 346.495i 0.992821i −0.868088 0.496411i \(-0.834651\pi\)
0.868088 0.496411i \(-0.165349\pi\)
\(350\) 0 0
\(351\) −92.8234 −0.264454
\(352\) 29.3939 + 16.9706i 0.0835053 + 0.0482118i
\(353\) −310.296 537.448i −0.879025 1.52252i −0.852413 0.522869i \(-0.824862\pi\)
−0.0266116 0.999646i \(-0.508472\pi\)
\(354\) −33.5147 58.0492i −0.0946743 0.163981i
\(355\) 0 0
\(356\) 41.5692i 0.116767i
\(357\) −220.238 56.6102i −0.616912 0.158572i
\(358\) 120.603i 0.336880i
\(359\) 10.1177 17.5245i 0.0281831 0.0488146i −0.851590 0.524209i \(-0.824361\pi\)
0.879773 + 0.475394i \(0.157695\pi\)
\(360\) 0 0
\(361\) −35.6030 61.6663i −0.0986234 0.170821i
\(362\) 3.95029 6.84210i 0.0109124 0.0189008i
\(363\) 147.224 0.405577
\(364\) −175.029 + 178.639i −0.480850 + 0.490766i
\(365\) 0 0
\(366\) 49.4558 85.6600i 0.135125 0.234044i
\(367\) 155.787 + 269.831i 0.424488 + 0.735234i 0.996372 0.0850998i \(-0.0271209\pi\)
−0.571885 + 0.820334i \(0.693788\pi\)
\(368\) 46.6124 26.9117i 0.126664 0.0731296i
\(369\) −91.5442 52.8530i −0.248087 0.143233i
\(370\) 0 0
\(371\) −172.721 169.231i −0.465555 0.456149i
\(372\) 51.0883i 0.137334i
\(373\) 590.094 + 340.691i 1.58202 + 0.913380i 0.994564 + 0.104125i \(0.0332043\pi\)
0.587457 + 0.809255i \(0.300129\pi\)
\(374\) 137.823 79.5724i 0.368512 0.212760i
\(375\) 0 0
\(376\) −81.3381 46.9606i −0.216325 0.124895i
\(377\) −606.320 −1.60828
\(378\) 12.8057 49.8198i 0.0338776 0.131798i
\(379\) 624.779 1.64849 0.824246 0.566231i \(-0.191599\pi\)
0.824246 + 0.566231i \(0.191599\pi\)
\(380\) 0 0
\(381\) 251.140 144.996i 0.659159 0.380566i
\(382\) −227.064 + 131.095i −0.594408 + 0.343182i
\(383\) −69.1502 + 119.772i −0.180549 + 0.312720i −0.942068 0.335423i \(-0.891121\pi\)
0.761519 + 0.648143i \(0.224454\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) 322.149 0.834584
\(387\) −40.2319 23.2279i −0.103959 0.0600205i
\(388\) 30.5826 + 52.9706i 0.0788211 + 0.136522i
\(389\) −281.787 488.069i −0.724388 1.25468i −0.959226 0.282642i \(-0.908789\pi\)
0.234838 0.972035i \(-0.424544\pi\)
\(390\) 0 0
\(391\) 252.370i 0.645446i
\(392\) −71.7315 118.586i −0.182989 0.302515i
\(393\) 3.08831i 0.00785830i
\(394\) 87.0883 150.841i 0.221036 0.382846i
\(395\) 0 0
\(396\) 18.0000 + 31.1769i 0.0454545 + 0.0787296i
\(397\) −226.669 + 392.603i −0.570955 + 0.988923i 0.425513 + 0.904952i \(0.360094\pi\)
−0.996468 + 0.0839711i \(0.973240\pi\)
\(398\) −8.81321 −0.0221438
\(399\) −198.809 + 55.4511i −0.498267 + 0.138975i
\(400\) 0 0
\(401\) 137.875 238.807i 0.343828 0.595528i −0.641312 0.767280i \(-0.721610\pi\)
0.985140 + 0.171752i \(0.0549429\pi\)
\(402\) 140.107 + 242.673i 0.348525 + 0.603663i
\(403\) 228.159 131.727i 0.566151 0.326867i
\(404\) 221.647 + 127.968i 0.548631 + 0.316752i
\(405\) 0 0
\(406\) 83.6468 325.422i 0.206026 0.801531i
\(407\) 35.8234i 0.0880181i
\(408\) −79.5724 45.9411i −0.195030 0.112601i
\(409\) 377.441 217.916i 0.922839 0.532801i 0.0382993 0.999266i \(-0.487806\pi\)
0.884540 + 0.466465i \(0.154473\pi\)
\(410\) 0 0
\(411\) −151.456 87.4431i −0.368506 0.212757i
\(412\) 161.913 0.392992
\(413\) −136.823 134.059i −0.331291 0.324598i
\(414\) 57.0883 0.137894
\(415\) 0 0
\(416\) −87.5147 + 50.5266i −0.210372 + 0.121458i
\(417\) −210.813 + 121.713i −0.505548 + 0.291878i
\(418\) 72.2239 125.095i 0.172784 0.299271i
\(419\) 301.257i 0.718991i 0.933147 + 0.359496i \(0.117051\pi\)
−0.933147 + 0.359496i \(0.882949\pi\)
\(420\) 0 0
\(421\) −203.794 −0.484071 −0.242036 0.970267i \(-0.577815\pi\)
−0.242036 + 0.970267i \(0.577815\pi\)
\(422\) −152.985 88.3259i −0.362524 0.209303i
\(423\) −49.8092 86.2721i −0.117752 0.203953i
\(424\) −48.8528 84.6156i −0.115219 0.199565i
\(425\) 0 0
\(426\) 45.5679i 0.106967i
\(427\) 70.3688 273.765i 0.164798 0.641135i
\(428\) 338.912i 0.791850i
\(429\) 92.8234 160.775i 0.216372 0.374766i
\(430\) 0 0
\(431\) 197.860 + 342.703i 0.459072 + 0.795136i 0.998912 0.0466317i \(-0.0148487\pi\)
−0.539840 + 0.841767i \(0.681515\pi\)
\(432\) 10.3923 18.0000i 0.0240563 0.0416667i
\(433\) 44.2685 0.102237 0.0511184 0.998693i \(-0.483721\pi\)
0.0511184 + 0.998693i \(0.483721\pi\)
\(434\) 39.2239 + 140.629i 0.0903777 + 0.324031i
\(435\) 0 0
\(436\) −178.941 + 309.935i −0.410415 + 0.710860i
\(437\) −114.532 198.375i −0.262086 0.453947i
\(438\) 248.263 143.335i 0.566810 0.327248i
\(439\) −344.558 198.931i −0.784871 0.453146i 0.0532827 0.998579i \(-0.483032\pi\)
−0.838154 + 0.545434i \(0.816365\pi\)
\(440\) 0 0
\(441\) −3.00000 146.969i −0.00680272 0.333264i
\(442\) 473.823i 1.07200i
\(443\) 102.662 + 59.2721i 0.231743 + 0.133797i 0.611376 0.791340i \(-0.290616\pi\)
−0.379633 + 0.925137i \(0.623950\pi\)
\(444\) −17.9117 + 10.3413i −0.0403416 + 0.0232913i
\(445\) 0 0
\(446\) 280.014 + 161.666i 0.627835 + 0.362481i
\(447\) 316.812 0.708752
\(448\) −15.0451 53.9411i −0.0335828 0.120404i
\(449\) −713.897 −1.58997 −0.794985 0.606629i \(-0.792521\pi\)
−0.794985 + 0.606629i \(0.792521\pi\)
\(450\) 0 0
\(451\) 183.088 105.706i 0.405961 0.234382i
\(452\) 30.1324 17.3970i 0.0666647 0.0384889i
\(453\) −250.103 + 433.191i −0.552104 + 0.956271i
\(454\) 239.762i 0.528109i
\(455\) 0 0
\(456\) −83.3970 −0.182888
\(457\) −108.406 62.5883i −0.237213 0.136955i 0.376682 0.926342i \(-0.377065\pi\)
−0.613895 + 0.789388i \(0.710398\pi\)
\(458\) −24.5310 42.4889i −0.0535610 0.0927704i
\(459\) −48.7279 84.3992i −0.106161 0.183876i
\(460\) 0 0
\(461\) 655.767i 1.42249i 0.702945 + 0.711244i \(0.251868\pi\)
−0.702945 + 0.711244i \(0.748132\pi\)
\(462\) 73.4847 + 72.0000i 0.159058 + 0.155844i
\(463\) 869.396i 1.87775i 0.344265 + 0.938873i \(0.388128\pi\)
−0.344265 + 0.938873i \(0.611872\pi\)
\(464\) 67.8823 117.576i 0.146298 0.253395i
\(465\) 0 0
\(466\) 179.948 + 311.680i 0.386155 + 0.668840i
\(467\) −133.686 + 231.551i −0.286266 + 0.495827i −0.972915 0.231162i \(-0.925747\pi\)
0.686649 + 0.726989i \(0.259081\pi\)
\(468\) −107.183 −0.229024
\(469\) 571.985 + 560.428i 1.21958 + 1.19494i
\(470\) 0 0
\(471\) 162.000 280.592i 0.343949 0.595737i
\(472\) −38.6995 67.0294i −0.0819904 0.142012i
\(473\) 80.4639 46.4558i 0.170114 0.0982153i
\(474\) −187.393 108.192i −0.395345 0.228252i
\(475\) 0 0
\(476\) −254.309 65.3678i −0.534262 0.137327i
\(477\) 103.632i 0.217259i
\(478\) −241.455 139.404i −0.505136 0.291640i
\(479\) −235.331 + 135.868i −0.491296 + 0.283650i −0.725112 0.688631i \(-0.758212\pi\)
0.233816 + 0.972281i \(0.424879\pi\)
\(480\) 0 0
\(481\) 92.3680 + 53.3287i 0.192033 + 0.110870i
\(482\) 125.116 0.259576
\(483\) 157.145 43.8305i 0.325353 0.0907464i
\(484\) 170.000 0.351240
\(485\) 0 0
\(486\) 19.0919 11.0227i 0.0392837 0.0226805i
\(487\) 486.285 280.757i 0.998532 0.576503i 0.0907186 0.995877i \(-0.471084\pi\)
0.907814 + 0.419374i \(0.137750\pi\)
\(488\) 57.1067 98.9117i 0.117022 0.202688i
\(489\) 27.8148i 0.0568810i
\(490\) 0 0
\(491\) −406.441 −0.827781 −0.413891 0.910327i \(-0.635830\pi\)
−0.413891 + 0.910327i \(0.635830\pi\)
\(492\) −105.706 61.0294i −0.214850 0.124044i
\(493\) −318.289 551.294i −0.645618 1.11824i
\(494\) 215.033 + 372.448i 0.435289 + 0.753944i
\(495\) 0 0
\(496\) 58.9917i 0.118935i
\(497\) 34.9856 + 125.434i 0.0703935 + 0.252381i
\(498\) 185.574i 0.372638i
\(499\) −185.713 + 321.665i −0.372171 + 0.644619i −0.989899 0.141773i \(-0.954720\pi\)
0.617728 + 0.786391i \(0.288053\pi\)
\(500\) 0 0
\(501\) −152.522 264.176i −0.304435 0.527297i
\(502\) 152.667 264.426i 0.304117 0.526746i
\(503\) −64.6292 −0.128488 −0.0642438 0.997934i \(-0.520464\pi\)
−0.0642438 + 0.997934i \(0.520464\pi\)
\(504\) 14.7868 57.5270i 0.0293389 0.114141i
\(505\) 0 0
\(506\) −57.0883 + 98.8799i −0.112823 + 0.195415i
\(507\) 130.006 + 225.177i 0.256422 + 0.444135i
\(508\) 289.991 167.426i 0.570849 0.329580i
\(509\) −871.889 503.385i −1.71294 0.988969i −0.930534 0.366205i \(-0.880657\pi\)
−0.782410 0.622764i \(-0.786010\pi\)
\(510\) 0 0
\(511\) 573.338 585.161i 1.12199 1.14513i
\(512\) 22.6274i 0.0441942i
\(513\) −76.6050 44.2279i −0.149328 0.0862143i
\(514\) −5.27208 + 3.04384i −0.0102570 + 0.00592186i
\(515\) 0 0
\(516\) −46.4558 26.8213i −0.0900307 0.0519793i
\(517\) 199.237 0.385371
\(518\) −41.3653 + 42.2183i −0.0798557 + 0.0815024i
\(519\) 400.368 0.771421
\(520\) 0 0
\(521\) −322.294 + 186.077i −0.618607 + 0.357153i −0.776327 0.630331i \(-0.782919\pi\)
0.157719 + 0.987484i \(0.449586\pi\)
\(522\) 124.708 72.0000i 0.238904 0.137931i
\(523\) 318.642 551.904i 0.609258 1.05527i −0.382105 0.924119i \(-0.624801\pi\)
0.991363 0.131147i \(-0.0418660\pi\)
\(524\) 3.56608i 0.00680549i
\(525\) 0 0
\(526\) 399.765 0.760009
\(527\) 239.545 + 138.302i 0.454545 + 0.262432i
\(528\) 20.7846 + 36.0000i 0.0393648 + 0.0681818i
\(529\) −173.970 301.325i −0.328866 0.569613i
\(530\) 0 0
\(531\) 82.0940i 0.154603i
\(532\) −229.564 + 64.0294i −0.431512 + 0.120356i
\(533\) 629.440i 1.18094i
\(534\) −25.4558 + 44.0908i −0.0476701 + 0.0825671i
\(535\) 0 0
\(536\) 161.782 + 280.214i 0.301832 + 0.522788i
\(537\) 73.8540 127.919i 0.137531 0.238210i
\(538\) 540.136 1.00397
\(539\) 257.558 + 141.773i 0.477845 + 0.263030i
\(540\) 0 0
\(541\) −110.412 + 191.239i −0.204088 + 0.353491i −0.949842 0.312731i \(-0.898756\pi\)
0.745754 + 0.666222i \(0.232090\pi\)
\(542\) −59.6283 103.279i −0.110015 0.190552i
\(543\) 8.37983 4.83810i 0.0154325 0.00890994i
\(544\) −91.8823 53.0482i −0.168901 0.0975152i
\(545\) 0 0
\(546\) −295.040 + 82.2917i −0.540367 + 0.150717i
\(547\) 160.676i 0.293741i 0.989156 + 0.146870i \(0.0469200\pi\)
−0.989156 + 0.146870i \(0.953080\pi\)
\(548\) −174.886 100.971i −0.319135 0.184253i
\(549\) 104.912 60.5708i 0.191096 0.110329i
\(550\) 0 0
\(551\) −500.382 288.896i −0.908134 0.524311i
\(552\) 65.9199 0.119420
\(553\) −598.898 153.942i −1.08300 0.278375i
\(554\) 193.914 0.350025
\(555\) 0 0
\(556\) −243.426 + 140.542i −0.437817 + 0.252774i
\(557\) 410.802 237.177i 0.737526 0.425811i −0.0836431 0.996496i \(-0.526656\pi\)
0.821169 + 0.570685i \(0.193322\pi\)
\(558\) −31.2851 + 54.1873i −0.0560664 + 0.0971099i
\(559\) 276.627i 0.494860i
\(560\) 0 0
\(561\) 194.912 0.347436
\(562\) −398.168 229.882i −0.708484 0.409043i
\(563\) −248.434 430.301i −0.441269 0.764300i 0.556515 0.830837i \(-0.312138\pi\)
−0.997784 + 0.0665378i \(0.978805\pi\)
\(564\) −57.5147 99.6184i −0.101976 0.176628i
\(565\) 0 0
\(566\) 275.171i 0.486168i
\(567\) 44.0908 45.0000i 0.0777616 0.0793651i
\(568\) 52.6173i 0.0926361i
\(569\) 392.647 680.084i 0.690065 1.19523i −0.281752 0.959487i \(-0.590915\pi\)
0.971816 0.235740i \(-0.0757512\pi\)
\(570\) 0 0
\(571\) 357.521 + 619.245i 0.626132 + 1.08449i 0.988321 + 0.152388i \(0.0486963\pi\)
−0.362189 + 0.932105i \(0.617970\pi\)
\(572\) 107.183 185.647i 0.187383 0.324557i
\(573\) −321.117 −0.560414
\(574\) −337.831 86.8364i −0.588555 0.151283i
\(575\) 0 0
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) −386.315 669.117i −0.669524 1.15965i −0.978038 0.208429i \(-0.933165\pi\)
0.308514 0.951220i \(-0.400168\pi\)
\(578\) −76.8705 + 44.3812i −0.132994 + 0.0767841i
\(579\) 341.691 + 197.275i 0.590140 + 0.340717i
\(580\) 0 0
\(581\) −142.477 510.823i −0.245228 0.879214i
\(582\) 74.9117i 0.128714i
\(583\) 179.497 + 103.632i 0.307885 + 0.177757i
\(584\) 286.669 165.508i 0.490872 0.283405i
\(585\) 0 0
\(586\) 293.574 + 169.495i 0.500979 + 0.289240i
\(587\) −436.477 −0.743572 −0.371786 0.928318i \(-0.621254\pi\)
−0.371786 + 0.928318i \(0.621254\pi\)
\(588\) −3.46410 169.706i −0.00589133 0.288615i
\(589\) 251.059 0.426246
\(590\) 0 0
\(591\) 184.742 106.661i 0.312593 0.180475i
\(592\) −20.6826 + 11.9411i −0.0349369 + 0.0201708i
\(593\) −417.076 + 722.397i −0.703332 + 1.21821i 0.263958 + 0.964534i \(0.414972\pi\)
−0.967290 + 0.253673i \(0.918361\pi\)
\(594\) 44.0908i 0.0742270i
\(595\) 0 0
\(596\) 365.823 0.613798
\(597\) −9.34783 5.39697i −0.0156580 0.00904015i
\(598\) −169.970 294.396i −0.284230 0.492301i
\(599\) 436.794 + 756.549i 0.729205 + 1.26302i 0.957220 + 0.289363i \(0.0934434\pi\)
−0.228014 + 0.973658i \(0.573223\pi\)
\(600\) 0 0
\(601\) 198.982i 0.331085i 0.986203 + 0.165542i \(0.0529375\pi\)
−0.986203 + 0.165542i \(0.947063\pi\)
\(602\) −148.470 38.1630i −0.246628 0.0633936i
\(603\) 343.191i 0.569139i
\(604\) −288.794 + 500.206i −0.478136 + 0.828155i
\(605\) 0 0
\(606\) 156.728 + 271.461i 0.258627 + 0.447955i
\(607\) 79.4748 137.654i 0.130930 0.226778i −0.793105 0.609085i \(-0.791537\pi\)
0.924035 + 0.382307i \(0.124870\pi\)
\(608\) −96.2985 −0.158386
\(609\) 288.000 293.939i 0.472906 0.482658i
\(610\) 0 0
\(611\) −296.595 + 513.718i −0.485426 + 0.840782i
\(612\) −56.2662 97.4558i −0.0919382 0.159242i
\(613\) −618.979 + 357.368i −1.00975 + 0.582981i −0.911119 0.412143i \(-0.864781\pi\)
−0.0986338 + 0.995124i \(0.531447\pi\)
\(614\) 661.695 + 382.030i 1.07768 + 0.622198i
\(615\) 0 0
\(616\) 84.8528 + 83.1384i 0.137748 + 0.134965i
\(617\) 639.381i 1.03627i 0.855298 + 0.518137i \(0.173374\pi\)
−0.855298 + 0.518137i \(0.826626\pi\)
\(618\) 171.734 + 99.1508i 0.277887 + 0.160438i
\(619\) −148.978 + 86.0126i −0.240676 + 0.138954i −0.615487 0.788147i \(-0.711041\pi\)
0.374812 + 0.927101i \(0.377707\pi\)
\(620\) 0 0
\(621\) 60.5513 + 34.9593i 0.0975061 + 0.0562952i
\(622\) 571.619 0.919002
\(623\) −36.2201 + 140.912i −0.0581382 + 0.226182i
\(624\) −123.765 −0.198341
\(625\) 0 0
\(626\) 160.805 92.8406i 0.256876 0.148308i
\(627\) 153.210 88.4558i 0.244354 0.141078i
\(628\) 187.061 324.000i 0.297869 0.515924i
\(629\) 111.980i 0.178029i
\(630\) 0 0
\(631\) −1141.06 −1.80833 −0.904166 0.427180i \(-0.859507\pi\)
−0.904166 + 0.427180i \(0.859507\pi\)
\(632\) −216.383 124.929i −0.342379 0.197672i
\(633\) −108.177 187.368i −0.170895 0.295999i
\(634\) −66.4264 115.054i −0.104774 0.181473i
\(635\) 0 0
\(636\) 119.664i 0.188152i
\(637\) −748.968 + 453.044i −1.17577 + 0.711215i
\(638\) 288.000i 0.451411i
\(639\) −27.9045 + 48.3321i −0.0436691 + 0.0756371i
\(640\) 0 0
\(641\) −114.551 198.409i −0.178707 0.309530i 0.762731 0.646716i \(-0.223858\pi\)
−0.941438 + 0.337186i \(0.890525\pi\)
\(642\) −207.540 + 359.470i −0.323271 + 0.559922i
\(643\) −707.670 −1.10058 −0.550288 0.834975i \(-0.685482\pi\)
−0.550288 + 0.834975i \(0.685482\pi\)
\(644\) 181.456 50.6111i 0.281764 0.0785887i
\(645\) 0 0
\(646\) −225.765 + 391.036i −0.349481 + 0.605318i
\(647\) −589.687 1021.37i −0.911417 1.57862i −0.812064 0.583568i \(-0.801656\pi\)
−0.0993530 0.995052i \(-0.531677\pi\)
\(648\) 22.0454 12.7279i 0.0340207 0.0196419i
\(649\) 142.191 + 82.0940i 0.219092 + 0.126493i
\(650\) 0 0
\(651\) −44.5143 + 173.180i −0.0683783 + 0.266021i
\(652\) 32.1177i 0.0492604i
\(653\) 134.029 + 77.3818i 0.205252 + 0.118502i 0.599103 0.800672i \(-0.295524\pi\)
−0.393851 + 0.919174i \(0.628857\pi\)
\(654\) −379.591 + 219.157i −0.580415 + 0.335103i
\(655\) 0 0
\(656\) −122.059 70.4707i −0.186065 0.107425i
\(657\) 351.096 0.534393
\(658\) −234.803 230.059i −0.356843 0.349634i
\(659\) −591.308 −0.897280 −0.448640 0.893712i \(-0.648092\pi\)
−0.448640 + 0.893712i \(0.648092\pi\)
\(660\) 0 0
\(661\) 140.441 81.0837i 0.212468 0.122668i −0.389990 0.920819i \(-0.627522\pi\)
0.602458 + 0.798151i \(0.294188\pi\)
\(662\) 320.109 184.815i 0.483548 0.279176i
\(663\) −290.156 + 502.566i −0.437642 + 0.758017i
\(664\) 214.282i 0.322714i
\(665\) 0 0
\(666\) −25.3310 −0.0380345
\(667\) 395.519 + 228.353i 0.592983 + 0.342359i
\(668\) −176.117 305.044i −0.263648 0.456652i
\(669\) 198.000 + 342.946i 0.295964 + 0.512625i
\(670\) 0 0
\(671\) 242.283i 0.361078i
\(672\) 17.0743 66.4264i 0.0254082 0.0988488i
\(673\) 42.3238i 0.0628883i 0.999506 + 0.0314441i \(0.0100106\pi\)
−0.999506 + 0.0314441i \(0.989989\pi\)
\(674\) 96.3539 166.890i 0.142958 0.247611i
\(675\) 0 0
\(676\) 150.118 + 260.012i 0.222068 + 0.384632i
\(677\) 248.677 430.721i 0.367322 0.636220i −0.621824 0.783157i \(-0.713608\pi\)
0.989146 + 0.146937i \(0.0469415\pi\)
\(678\) 42.6137 0.0628521
\(679\) 57.5147 + 206.207i 0.0847050 + 0.303693i
\(680\) 0 0
\(681\) −146.823 + 254.306i −0.215600 + 0.373430i
\(682\) −62.5701 108.375i −0.0917451 0.158907i
\(683\) 1053.23 608.080i 1.54206 0.890308i 0.543350 0.839506i \(-0.317156\pi\)
0.998709 0.0508015i \(-0.0161776\pi\)
\(684\) −88.4558 51.0700i −0.129321 0.0746638i
\(685\) 0 0
\(686\) −139.830 464.484i −0.203834 0.677091i
\(687\) 60.0883i 0.0874648i
\(688\) −53.6426 30.9706i −0.0779689 0.0450154i
\(689\) −534.418 + 308.546i −0.775642 + 0.447817i
\(690\) 0 0
\(691\) −932.182 538.196i −1.34903 0.778865i −0.360921 0.932596i \(-0.617538\pi\)
−0.988113 + 0.153731i \(0.950871\pi\)
\(692\) 462.305 0.668070
\(693\) 33.8515 + 121.368i 0.0488477 + 0.175134i
\(694\) 455.647 0.656552
\(695\) 0 0
\(696\) 144.000 83.1384i 0.206897 0.119452i
\(697\) −572.315 + 330.426i −0.821112 + 0.474069i
\(698\) 245.009 424.368i 0.351015 0.607976i
\(699\) 440.781i 0.630589i
\(700\) 0 0
\(701\) −695.897 −0.992720 −0.496360 0.868117i \(-0.665330\pi\)
−0.496360 + 0.868117i \(0.665330\pi\)
\(702\) −113.685 65.6360i −0.161944 0.0934986i
\(703\) 50.8194 + 88.0219i 0.0722894 + 0.125209i
\(704\) 24.0000 + 41.5692i 0.0340909 + 0.0590472i
\(705\) 0 0
\(706\) 877.649i 1.24313i
\(707\) 639.839 + 626.912i 0.905006 + 0.886721i
\(708\) 94.7939i 0.133890i
\(709\) 127.412 220.684i 0.179707 0.311261i −0.762073 0.647491i \(-0.775818\pi\)
0.941780 + 0.336229i \(0.109152\pi\)
\(710\) 0 0
\(711\) −132.507 229.509i −0.186367 0.322798i
\(712\) −29.3939 + 50.9117i −0.0412835 + 0.0715052i
\(713\) −198.446 −0.278325
\(714\) −229.706 225.065i −0.321717 0.315217i
\(715\) 0 0
\(716\) 85.2792 147.708i 0.119105 0.206296i
\(717\) −170.734 295.721i −0.238123 0.412442i
\(718\) 24.7833 14.3087i 0.0345172 0.0199285i
\(719\) 964.925 + 557.100i 1.34204 + 0.774826i 0.987106 0.160066i \(-0.0511709\pi\)
0.354931 + 0.934892i \(0.384504\pi\)
\(720\) 0 0
\(721\) 548.852 + 141.078i 0.761238 + 0.195669i
\(722\) 100.701i 0.139474i
\(723\) 132.705 + 76.6173i 0.183548 + 0.105971i
\(724\) 9.67619 5.58655i 0.0133649 0.00771623i
\(725\) 0 0
\(726\) 180.312 + 104.103i 0.248364 + 0.143393i
\(727\) −398.345 −0.547930 −0.273965 0.961740i \(-0.588335\pi\)
−0.273965 + 0.961740i \(0.588335\pi\)
\(728\) −340.683 + 95.0223i −0.467971 + 0.130525i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) −251.522 + 145.216i −0.344079 + 0.198654i
\(732\) 121.142 69.9411i 0.165494 0.0955480i
\(733\) −472.569 + 818.514i −0.644706 + 1.11666i 0.339663 + 0.940547i \(0.389687\pi\)
−0.984369 + 0.176116i \(0.943646\pi\)
\(734\) 440.632i 0.600316i
\(735\) 0 0
\(736\) 76.1177 0.103421
\(737\) −594.424 343.191i −0.806546 0.465659i
\(738\) −74.7455 129.463i −0.101281 0.175424i
\(739\) 96.3162 + 166.825i 0.130333 + 0.225744i 0.923805 0.382863i \(-0.125062\pi\)
−0.793472 + 0.608607i \(0.791729\pi\)
\(740\) 0 0
\(741\) 526.721i 0.710825i
\(742\) −91.8744 329.397i −0.123820 0.443931i
\(743\) 911.616i 1.22694i −0.789718 0.613470i \(-0.789773\pi\)
0.789718 0.613470i \(-0.210227\pi\)
\(744\) −36.1249 + 62.5701i −0.0485550 + 0.0840997i
\(745\) 0 0
\(746\) 481.810 + 834.519i 0.645858 + 1.11866i
\(747\) 113.640 196.831i 0.152129 0.263495i
\(748\) 225.065 0.300889
\(749\) −295.301 + 1148.85i −0.394260 + 1.53384i
\(750\) 0 0
\(751\) 195.831 339.189i 0.260760 0.451650i −0.705684 0.708527i \(-0.749360\pi\)
0.966444 + 0.256877i \(0.0826935\pi\)
\(752\) −66.4123 115.029i −0.0883142 0.152965i
\(753\) 323.855 186.978i 0.430086 0.248310i
\(754\) −742.587 428.733i −0.984863 0.568611i
\(755\) 0 0
\(756\) 50.9117 51.9615i 0.0673435 0.0687322i
\(757\) 152.823i 0.201879i 0.994893 + 0.100940i \(0.0321849\pi\)
−0.994893 + 0.100940i \(0.967815\pi\)
\(758\) 765.195 + 441.785i 1.00949 + 0.582830i
\(759\) −121.103 + 69.9186i −0.159555 + 0.0921194i
\(760\) 0 0
\(761\) −109.331 63.1223i −0.143667 0.0829465i 0.426443 0.904514i \(-0.359766\pi\)
−0.570111 + 0.821568i \(0.693100\pi\)
\(762\) 410.109 0.538201
\(763\) −876.629 + 894.706i −1.14892 + 1.17262i
\(764\) −370.794 −0.485332
\(765\) 0 0
\(766\) −169.383 + 97.7931i −0.221126 + 0.127667i
\(767\) −423.347 + 244.419i −0.551951 + 0.318669i
\(768\) 13.8564 24.0000i 0.0180422 0.0312500i
\(769\) 369.148i 0.480037i 0.970768 + 0.240018i \(0.0771535\pi\)
−0.970768 + 0.240018i \(0.922847\pi\)
\(770\) 0 0
\(771\) −7.45584 −0.00967036
\(772\) 394.551 + 227.794i 0.511076 + 0.295070i
\(773\) −701.853 1215.65i −0.907961 1.57263i −0.816893 0.576789i \(-0.804305\pi\)
−0.0910674 0.995845i \(-0.529028\pi\)
\(774\) −32.8492 56.8966i −0.0424409 0.0735098i
\(775\) 0 0
\(776\) 86.5006i 0.111470i
\(777\) −69.7278 + 19.4483i −0.0897398 + 0.0250299i
\(778\) 797.013i 1.02444i
\(779\) −299.912 + 519.462i −0.384996 + 0.666832i
\(780\) 0 0
\(781\) −55.8091 96.6642i −0.0714585 0.123770i