Properties

Label 300.3.f.b.199.12
Level $300$
Weight $3$
Character 300.199
Analytic conductor $8.174$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 5 x^{14} + 12 x^{12} + 25 x^{10} + 53 x^{8} + 100 x^{6} + 192 x^{4} + 320 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{24} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 199.12
Root \(-0.422403 + 1.34966i\) of defining polynomial
Character \(\chi\) \(=\) 300.199
Dual form 300.3.f.b.199.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.696577 + 1.87477i) q^{2} -1.73205 q^{3} +(-3.02956 + 2.61185i) q^{4} +(-1.20651 - 3.24721i) q^{6} -5.46770 q^{7} +(-7.00695 - 3.86039i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(0.696577 + 1.87477i) q^{2} -1.73205 q^{3} +(-3.02956 + 2.61185i) q^{4} +(-1.20651 - 3.24721i) q^{6} -5.46770 q^{7} +(-7.00695 - 3.86039i) q^{8} +3.00000 q^{9} +11.0403i q^{11} +(5.24735 - 4.52386i) q^{12} -10.1242i q^{13} +(-3.80867 - 10.2507i) q^{14} +(2.35649 - 15.8255i) q^{16} -24.4146i q^{17} +(2.08973 + 5.62432i) q^{18} -23.7757i q^{19} +9.47033 q^{21} +(-20.6981 + 7.69043i) q^{22} -37.2526 q^{23} +(12.1364 + 6.68640i) q^{24} +(18.9806 - 7.05227i) q^{26} -5.19615 q^{27} +(16.5647 - 14.2808i) q^{28} +25.7726 q^{29} -4.83647i q^{31} +(31.3108 - 6.60580i) q^{32} -19.1224i q^{33} +(45.7719 - 17.0066i) q^{34} +(-9.08868 + 7.83555i) q^{36} +35.6493i q^{37} +(44.5741 - 16.5616i) q^{38} +17.5356i q^{39} -9.30410 q^{41} +(6.59682 + 17.7547i) q^{42} -70.0287 q^{43} +(-28.8356 - 33.4473i) q^{44} +(-25.9493 - 69.8401i) q^{46} +38.0223 q^{47} +(-4.08156 + 27.4106i) q^{48} -19.1043 q^{49} +42.2873i q^{51} +(26.4428 + 30.6718i) q^{52} -55.7762i q^{53} +(-3.61952 - 9.74162i) q^{54} +(38.3119 + 21.1075i) q^{56} +41.1808i q^{57} +(17.9526 + 48.3179i) q^{58} -55.5411i q^{59} -82.2412 q^{61} +(9.06729 - 3.36897i) q^{62} -16.4031 q^{63} +(34.1947 + 54.0992i) q^{64} +(35.8502 - 13.3202i) q^{66} -104.493 q^{67} +(63.7673 + 73.9656i) q^{68} +64.5233 q^{69} +76.7471i q^{71} +(-21.0209 - 11.5812i) q^{72} +93.5215i q^{73} +(-66.8344 + 24.8325i) q^{74} +(62.0986 + 72.0300i) q^{76} -60.3651i q^{77} +(-32.8753 + 12.2149i) q^{78} +49.3762i q^{79} +9.00000 q^{81} +(-6.48102 - 17.4431i) q^{82} +72.3768 q^{83} +(-28.6910 + 24.7351i) q^{84} +(-48.7804 - 131.288i) q^{86} -44.6395 q^{87} +(42.6199 - 77.3589i) q^{88} -115.691 q^{89} +55.3560i q^{91} +(112.859 - 97.2980i) q^{92} +8.37701i q^{93} +(26.4854 + 71.2832i) q^{94} +(-54.2318 + 11.4416i) q^{96} -72.9589i q^{97} +(-13.3076 - 35.8162i) q^{98} +33.1209i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 20q^{4} - 12q^{6} + 48q^{9} + O(q^{10}) \) \( 16q - 20q^{4} - 12q^{6} + 48q^{9} + 40q^{14} + 68q^{16} - 96q^{21} - 36q^{24} - 72q^{26} - 128q^{29} + 184q^{34} - 60q^{36} - 32q^{41} - 344q^{44} + 304q^{46} + 112q^{49} - 36q^{54} + 232q^{56} - 352q^{61} + 220q^{64} + 216q^{66} + 192q^{69} - 264q^{74} - 48q^{76} + 144q^{81} + 72q^{84} - 400q^{86} - 160q^{89} + 192q^{94} - 348q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.696577 + 1.87477i 0.348288 + 0.937387i
\(3\) −1.73205 −0.577350
\(4\) −3.02956 + 2.61185i −0.757390 + 0.652962i
\(5\) 0 0
\(6\) −1.20651 3.24721i −0.201084 0.541201i
\(7\) −5.46770 −0.781100 −0.390550 0.920582i \(-0.627715\pi\)
−0.390550 + 0.920582i \(0.627715\pi\)
\(8\) −7.00695 3.86039i −0.875869 0.482549i
\(9\) 3.00000 0.333333
\(10\) 0 0
\(11\) 11.0403i 1.00366i 0.864965 + 0.501832i \(0.167341\pi\)
−0.864965 + 0.501832i \(0.832659\pi\)
\(12\) 5.24735 4.52386i 0.437280 0.376988i
\(13\) 10.1242i 0.778784i −0.921072 0.389392i \(-0.872685\pi\)
0.921072 0.389392i \(-0.127315\pi\)
\(14\) −3.80867 10.2507i −0.272048 0.732193i
\(15\) 0 0
\(16\) 2.35649 15.8255i 0.147280 0.989095i
\(17\) 24.4146i 1.43615i −0.695964 0.718077i \(-0.745023\pi\)
0.695964 0.718077i \(-0.254977\pi\)
\(18\) 2.08973 + 5.62432i 0.116096 + 0.312462i
\(19\) 23.7757i 1.25135i −0.780082 0.625677i \(-0.784823\pi\)
0.780082 0.625677i \(-0.215177\pi\)
\(20\) 0 0
\(21\) 9.47033 0.450968
\(22\) −20.6981 + 7.69043i −0.940823 + 0.349565i
\(23\) −37.2526 −1.61968 −0.809838 0.586653i \(-0.800445\pi\)
−0.809838 + 0.586653i \(0.800445\pi\)
\(24\) 12.1364 + 6.68640i 0.505683 + 0.278600i
\(25\) 0 0
\(26\) 18.9806 7.05227i 0.730022 0.271241i
\(27\) −5.19615 −0.192450
\(28\) 16.5647 14.2808i 0.591598 0.510029i
\(29\) 25.7726 0.888712 0.444356 0.895850i \(-0.353433\pi\)
0.444356 + 0.895850i \(0.353433\pi\)
\(30\) 0 0
\(31\) 4.83647i 0.156015i −0.996953 0.0780076i \(-0.975144\pi\)
0.996953 0.0780076i \(-0.0248558\pi\)
\(32\) 31.3108 6.60580i 0.978461 0.206431i
\(33\) 19.1224i 0.579466i
\(34\) 45.7719 17.0066i 1.34623 0.500196i
\(35\) 0 0
\(36\) −9.08868 + 7.83555i −0.252463 + 0.217654i
\(37\) 35.6493i 0.963495i 0.876310 + 0.481747i \(0.159998\pi\)
−0.876310 + 0.481747i \(0.840002\pi\)
\(38\) 44.5741 16.5616i 1.17300 0.435832i
\(39\) 17.5356i 0.449631i
\(40\) 0 0
\(41\) −9.30410 −0.226929 −0.113465 0.993542i \(-0.536195\pi\)
−0.113465 + 0.993542i \(0.536195\pi\)
\(42\) 6.59682 + 17.7547i 0.157067 + 0.422732i
\(43\) −70.0287 −1.62857 −0.814287 0.580462i \(-0.802872\pi\)
−0.814287 + 0.580462i \(0.802872\pi\)
\(44\) −28.8356 33.4473i −0.655355 0.760166i
\(45\) 0 0
\(46\) −25.9493 69.8401i −0.564114 1.51826i
\(47\) 38.0223 0.808984 0.404492 0.914542i \(-0.367448\pi\)
0.404492 + 0.914542i \(0.367448\pi\)
\(48\) −4.08156 + 27.4106i −0.0850324 + 0.571054i
\(49\) −19.1043 −0.389883
\(50\) 0 0
\(51\) 42.2873i 0.829164i
\(52\) 26.4428 + 30.6718i 0.508516 + 0.589843i
\(53\) 55.7762i 1.05238i −0.850366 0.526191i \(-0.823620\pi\)
0.850366 0.526191i \(-0.176380\pi\)
\(54\) −3.61952 9.74162i −0.0670281 0.180400i
\(55\) 0 0
\(56\) 38.3119 + 21.1075i 0.684141 + 0.376919i
\(57\) 41.1808i 0.722470i
\(58\) 17.9526 + 48.3179i 0.309528 + 0.833067i
\(59\) 55.5411i 0.941374i −0.882300 0.470687i \(-0.844006\pi\)
0.882300 0.470687i \(-0.155994\pi\)
\(60\) 0 0
\(61\) −82.2412 −1.34822 −0.674108 0.738633i \(-0.735472\pi\)
−0.674108 + 0.738633i \(0.735472\pi\)
\(62\) 9.06729 3.36897i 0.146247 0.0543383i
\(63\) −16.4031 −0.260367
\(64\) 34.1947 + 54.0992i 0.534293 + 0.845299i
\(65\) 0 0
\(66\) 35.8502 13.3202i 0.543184 0.201821i
\(67\) −104.493 −1.55960 −0.779802 0.626026i \(-0.784680\pi\)
−0.779802 + 0.626026i \(0.784680\pi\)
\(68\) 63.7673 + 73.9656i 0.937754 + 1.08773i
\(69\) 64.5233 0.935120
\(70\) 0 0
\(71\) 76.7471i 1.08094i 0.841362 + 0.540472i \(0.181754\pi\)
−0.841362 + 0.540472i \(0.818246\pi\)
\(72\) −21.0209 11.5812i −0.291956 0.160850i
\(73\) 93.5215i 1.28112i 0.767910 + 0.640558i \(0.221297\pi\)
−0.767910 + 0.640558i \(0.778703\pi\)
\(74\) −66.8344 + 24.8325i −0.903168 + 0.335574i
\(75\) 0 0
\(76\) 62.0986 + 72.0300i 0.817087 + 0.947764i
\(77\) 60.3651i 0.783963i
\(78\) −32.8753 + 12.2149i −0.421478 + 0.156601i
\(79\) 49.3762i 0.625016i 0.949915 + 0.312508i \(0.101169\pi\)
−0.949915 + 0.312508i \(0.898831\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) −6.48102 17.4431i −0.0790368 0.212721i
\(83\) 72.3768 0.872010 0.436005 0.899944i \(-0.356393\pi\)
0.436005 + 0.899944i \(0.356393\pi\)
\(84\) −28.6910 + 24.7351i −0.341559 + 0.294465i
\(85\) 0 0
\(86\) −48.7804 131.288i −0.567214 1.52661i
\(87\) −44.6395 −0.513098
\(88\) 42.6199 77.3589i 0.484318 0.879079i
\(89\) −115.691 −1.29990 −0.649950 0.759977i \(-0.725210\pi\)
−0.649950 + 0.759977i \(0.725210\pi\)
\(90\) 0 0
\(91\) 55.3560i 0.608308i
\(92\) 112.859 97.2980i 1.22673 1.05759i
\(93\) 8.37701i 0.0900754i
\(94\) 26.4854 + 71.2832i 0.281760 + 0.758332i
\(95\) 0 0
\(96\) −54.2318 + 11.4416i −0.564915 + 0.119183i
\(97\) 72.9589i 0.752154i −0.926588 0.376077i \(-0.877273\pi\)
0.926588 0.376077i \(-0.122727\pi\)
\(98\) −13.3076 35.8162i −0.135792 0.365471i
\(99\) 33.1209i 0.334555i
\(100\) 0 0
\(101\) 29.4092 0.291180 0.145590 0.989345i \(-0.453492\pi\)
0.145590 + 0.989345i \(0.453492\pi\)
\(102\) −79.2792 + 29.4564i −0.777247 + 0.288788i
\(103\) −28.1884 −0.273673 −0.136837 0.990594i \(-0.543694\pi\)
−0.136837 + 0.990594i \(0.543694\pi\)
\(104\) −39.0833 + 70.9397i −0.375801 + 0.682112i
\(105\) 0 0
\(106\) 104.568 38.8524i 0.986490 0.366532i
\(107\) 4.50700 0.0421215 0.0210607 0.999778i \(-0.493296\pi\)
0.0210607 + 0.999778i \(0.493296\pi\)
\(108\) 15.7421 13.5716i 0.145760 0.125663i
\(109\) −193.315 −1.77353 −0.886767 0.462217i \(-0.847054\pi\)
−0.886767 + 0.462217i \(0.847054\pi\)
\(110\) 0 0
\(111\) 61.7464i 0.556274i
\(112\) −12.8846 + 86.5292i −0.115041 + 0.772582i
\(113\) 75.5727i 0.668785i −0.942434 0.334392i \(-0.891469\pi\)
0.942434 0.334392i \(-0.108531\pi\)
\(114\) −77.2047 + 28.6856i −0.677234 + 0.251628i
\(115\) 0 0
\(116\) −78.0798 + 67.3142i −0.673102 + 0.580295i
\(117\) 30.3726i 0.259595i
\(118\) 104.127 38.6886i 0.882432 0.327870i
\(119\) 133.492i 1.12178i
\(120\) 0 0
\(121\) −0.888544 −0.00734334
\(122\) −57.2873 154.184i −0.469568 1.26380i
\(123\) 16.1152 0.131018
\(124\) 12.6321 + 14.6524i 0.101872 + 0.118164i
\(125\) 0 0
\(126\) −11.4260 30.7521i −0.0906827 0.244064i
\(127\) 131.306 1.03390 0.516951 0.856015i \(-0.327067\pi\)
0.516951 + 0.856015i \(0.327067\pi\)
\(128\) −77.6045 + 101.792i −0.606285 + 0.795247i
\(129\) 121.293 0.940258
\(130\) 0 0
\(131\) 75.7533i 0.578270i −0.957288 0.289135i \(-0.906632\pi\)
0.957288 0.289135i \(-0.0933676\pi\)
\(132\) 49.9448 + 57.9324i 0.378370 + 0.438882i
\(133\) 129.999i 0.977433i
\(134\) −72.7877 195.902i −0.543192 1.46195i
\(135\) 0 0
\(136\) −94.2500 + 171.072i −0.693014 + 1.25788i
\(137\) 66.7927i 0.487538i 0.969833 + 0.243769i \(0.0783839\pi\)
−0.969833 + 0.243769i \(0.921616\pi\)
\(138\) 44.9454 + 120.967i 0.325692 + 0.876570i
\(139\) 38.1214i 0.274255i −0.990553 0.137127i \(-0.956213\pi\)
0.990553 0.137127i \(-0.0437869\pi\)
\(140\) 0 0
\(141\) −65.8565 −0.467067
\(142\) −143.884 + 53.4602i −1.01326 + 0.376481i
\(143\) 111.774 0.781638
\(144\) 7.06946 47.4765i 0.0490935 0.329698i
\(145\) 0 0
\(146\) −175.332 + 65.1449i −1.20090 + 0.446198i
\(147\) 33.0895 0.225099
\(148\) −93.1106 108.002i −0.629126 0.729742i
\(149\) 126.717 0.850449 0.425225 0.905088i \(-0.360195\pi\)
0.425225 + 0.905088i \(0.360195\pi\)
\(150\) 0 0
\(151\) 68.4403i 0.453247i −0.973982 0.226623i \(-0.927231\pi\)
0.973982 0.226623i \(-0.0727687\pi\)
\(152\) −91.7836 + 166.595i −0.603840 + 1.09602i
\(153\) 73.2438i 0.478718i
\(154\) 113.171 42.0489i 0.734877 0.273045i
\(155\) 0 0
\(156\) −45.8004 53.1252i −0.293592 0.340546i
\(157\) 25.5777i 0.162915i 0.996677 + 0.0814577i \(0.0259575\pi\)
−0.996677 + 0.0814577i \(0.974042\pi\)
\(158\) −92.5693 + 34.3943i −0.585882 + 0.217686i
\(159\) 96.6073i 0.607593i
\(160\) 0 0
\(161\) 203.686 1.26513
\(162\) 6.26919 + 16.8730i 0.0386987 + 0.104154i
\(163\) 63.4771 0.389430 0.194715 0.980860i \(-0.437622\pi\)
0.194715 + 0.980860i \(0.437622\pi\)
\(164\) 28.1873 24.3009i 0.171874 0.148176i
\(165\) 0 0
\(166\) 50.4160 + 135.690i 0.303711 + 0.817411i
\(167\) −12.3771 −0.0741144 −0.0370572 0.999313i \(-0.511798\pi\)
−0.0370572 + 0.999313i \(0.511798\pi\)
\(168\) −66.3582 36.5592i −0.394989 0.217614i
\(169\) 66.5008 0.393496
\(170\) 0 0
\(171\) 71.3272i 0.417118i
\(172\) 212.156 182.904i 1.23347 1.06340i
\(173\) 59.3729i 0.343196i −0.985167 0.171598i \(-0.945107\pi\)
0.985167 0.171598i \(-0.0548930\pi\)
\(174\) −31.0948 83.6890i −0.178706 0.480971i
\(175\) 0 0
\(176\) 174.719 + 26.0164i 0.992720 + 0.147820i
\(177\) 96.2000i 0.543503i
\(178\) −80.5877 216.895i −0.452740 1.21851i
\(179\) 252.782i 1.41219i −0.708118 0.706094i \(-0.750455\pi\)
0.708118 0.706094i \(-0.249545\pi\)
\(180\) 0 0
\(181\) 125.373 0.692670 0.346335 0.938111i \(-0.387426\pi\)
0.346335 + 0.938111i \(0.387426\pi\)
\(182\) −103.780 + 38.5597i −0.570220 + 0.211867i
\(183\) 142.446 0.778393
\(184\) 261.027 + 143.809i 1.41862 + 0.781573i
\(185\) 0 0
\(186\) −15.7050 + 5.83523i −0.0844355 + 0.0313722i
\(187\) 269.545 1.44142
\(188\) −115.191 + 99.3084i −0.612717 + 0.528236i
\(189\) 28.4110 0.150323
\(190\) 0 0
\(191\) 97.4640i 0.510283i −0.966904 0.255141i \(-0.917878\pi\)
0.966904 0.255141i \(-0.0821220\pi\)
\(192\) −59.2270 93.7025i −0.308474 0.488034i
\(193\) 342.376i 1.77397i 0.461798 + 0.886985i \(0.347204\pi\)
−0.461798 + 0.886985i \(0.652796\pi\)
\(194\) 136.782 50.8215i 0.705060 0.261966i
\(195\) 0 0
\(196\) 57.8775 49.8974i 0.295293 0.254579i
\(197\) 74.4829i 0.378086i 0.981969 + 0.189043i \(0.0605386\pi\)
−0.981969 + 0.189043i \(0.939461\pi\)
\(198\) −62.0943 + 23.0713i −0.313608 + 0.116522i
\(199\) 178.027i 0.894606i −0.894382 0.447303i \(-0.852385\pi\)
0.894382 0.447303i \(-0.147615\pi\)
\(200\) 0 0
\(201\) 180.988 0.900438
\(202\) 20.4858 + 55.1356i 0.101415 + 0.272949i
\(203\) −140.917 −0.694173
\(204\) −110.448 128.112i −0.541413 0.628000i
\(205\) 0 0
\(206\) −19.6354 52.8468i −0.0953172 0.256538i
\(207\) −111.758 −0.539892
\(208\) −160.220 23.8575i −0.770291 0.114700i
\(209\) 262.491 1.25594
\(210\) 0 0
\(211\) 185.893i 0.881008i −0.897751 0.440504i \(-0.854800\pi\)
0.897751 0.440504i \(-0.145200\pi\)
\(212\) 145.679 + 168.978i 0.687166 + 0.797064i
\(213\) 132.930i 0.624084i
\(214\) 3.13947 + 8.44961i 0.0146704 + 0.0394842i
\(215\) 0 0
\(216\) 36.4092 + 20.0592i 0.168561 + 0.0928666i
\(217\) 26.4444i 0.121863i
\(218\) −134.659 362.422i −0.617701 1.66249i
\(219\) 161.984i 0.739653i
\(220\) 0 0
\(221\) −247.178 −1.11845
\(222\) 115.761 43.0111i 0.521444 0.193744i
\(223\) 202.724 0.909074 0.454537 0.890728i \(-0.349805\pi\)
0.454537 + 0.890728i \(0.349805\pi\)
\(224\) −171.198 + 36.1186i −0.764276 + 0.161244i
\(225\) 0 0
\(226\) 141.682 52.6422i 0.626910 0.232930i
\(227\) −51.2708 −0.225863 −0.112931 0.993603i \(-0.536024\pi\)
−0.112931 + 0.993603i \(0.536024\pi\)
\(228\) −107.558 124.760i −0.471745 0.547192i
\(229\) −337.056 −1.47186 −0.735930 0.677058i \(-0.763255\pi\)
−0.735930 + 0.677058i \(0.763255\pi\)
\(230\) 0 0
\(231\) 104.555i 0.452621i
\(232\) −180.588 99.4925i −0.778395 0.428847i
\(233\) 80.2851i 0.344571i 0.985047 + 0.172286i \(0.0551152\pi\)
−0.985047 + 0.172286i \(0.944885\pi\)
\(234\) 56.9417 21.1568i 0.243341 0.0904138i
\(235\) 0 0
\(236\) 145.065 + 168.265i 0.614682 + 0.712988i
\(237\) 85.5221i 0.360853i
\(238\) −250.267 + 92.9873i −1.05154 + 0.390703i
\(239\) 330.808i 1.38413i 0.721834 + 0.692066i \(0.243299\pi\)
−0.721834 + 0.692066i \(0.756701\pi\)
\(240\) 0 0
\(241\) −359.914 −1.49342 −0.746710 0.665150i \(-0.768368\pi\)
−0.746710 + 0.665150i \(0.768368\pi\)
\(242\) −0.618939 1.66582i −0.00255760 0.00688355i
\(243\) −15.5885 −0.0641500
\(244\) 249.155 214.802i 1.02113 0.880334i
\(245\) 0 0
\(246\) 11.2255 + 30.2123i 0.0456319 + 0.122814i
\(247\) −240.710 −0.974534
\(248\) −18.6707 + 33.8889i −0.0752850 + 0.136649i
\(249\) −125.360 −0.503455
\(250\) 0 0
\(251\) 312.213i 1.24388i −0.783067 0.621938i \(-0.786346\pi\)
0.783067 0.621938i \(-0.213654\pi\)
\(252\) 49.6942 42.8424i 0.197199 0.170010i
\(253\) 411.280i 1.62561i
\(254\) 91.4645 + 246.169i 0.360096 + 0.969167i
\(255\) 0 0
\(256\) −244.894 74.5853i −0.956617 0.291349i
\(257\) 80.2592i 0.312293i 0.987734 + 0.156146i \(0.0499072\pi\)
−0.987734 + 0.156146i \(0.950093\pi\)
\(258\) 84.4901 + 227.398i 0.327481 + 0.881386i
\(259\) 194.920i 0.752586i
\(260\) 0 0
\(261\) 77.3179 0.296237
\(262\) 142.020 52.7680i 0.542063 0.201405i
\(263\) 487.967 1.85539 0.927694 0.373342i \(-0.121788\pi\)
0.927694 + 0.373342i \(0.121788\pi\)
\(264\) −73.8199 + 133.990i −0.279621 + 0.507536i
\(265\) 0 0
\(266\) −243.718 + 90.5540i −0.916233 + 0.340428i
\(267\) 200.383 0.750498
\(268\) 316.569 272.921i 1.18123 1.01836i
\(269\) 309.553 1.15076 0.575378 0.817888i \(-0.304855\pi\)
0.575378 + 0.817888i \(0.304855\pi\)
\(270\) 0 0
\(271\) 48.9693i 0.180698i −0.995910 0.0903492i \(-0.971202\pi\)
0.995910 0.0903492i \(-0.0287983\pi\)
\(272\) −386.374 57.5327i −1.42049 0.211517i
\(273\) 95.8794i 0.351207i
\(274\) −125.221 + 46.5262i −0.457012 + 0.169804i
\(275\) 0 0
\(276\) −195.477 + 168.525i −0.708251 + 0.610598i
\(277\) 199.644i 0.720736i −0.932810 0.360368i \(-0.882651\pi\)
0.932810 0.360368i \(-0.117349\pi\)
\(278\) 71.4690 26.5545i 0.257083 0.0955197i
\(279\) 14.5094i 0.0520051i
\(280\) 0 0
\(281\) 61.1598 0.217650 0.108825 0.994061i \(-0.465291\pi\)
0.108825 + 0.994061i \(0.465291\pi\)
\(282\) −45.8741 123.466i −0.162674 0.437823i
\(283\) −432.506 −1.52829 −0.764145 0.645044i \(-0.776839\pi\)
−0.764145 + 0.645044i \(0.776839\pi\)
\(284\) −200.452 232.510i −0.705816 0.818697i
\(285\) 0 0
\(286\) 77.8593 + 209.551i 0.272235 + 0.732697i
\(287\) 50.8720 0.177254
\(288\) 93.9323 19.8174i 0.326154 0.0688105i
\(289\) −307.073 −1.06254
\(290\) 0 0
\(291\) 126.369i 0.434256i
\(292\) −244.264 283.329i −0.836521 0.970305i
\(293\) 283.234i 0.966668i 0.875436 + 0.483334i \(0.160574\pi\)
−0.875436 + 0.483334i \(0.839426\pi\)
\(294\) 23.0494 + 62.0354i 0.0783993 + 0.211005i
\(295\) 0 0
\(296\) 137.620 249.793i 0.464933 0.843895i
\(297\) 57.3672i 0.193155i
\(298\) 88.2681 + 237.566i 0.296202 + 0.797200i
\(299\) 377.152i 1.26138i
\(300\) 0 0
\(301\) 382.896 1.27208
\(302\) 128.310 47.6739i 0.424868 0.157861i
\(303\) −50.9382 −0.168113
\(304\) −376.263 56.0272i −1.23771 0.184300i
\(305\) 0 0
\(306\) 137.316 51.0199i 0.448744 0.166732i
\(307\) −100.077 −0.325983 −0.162992 0.986627i \(-0.552114\pi\)
−0.162992 + 0.986627i \(0.552114\pi\)
\(308\) 157.665 + 182.880i 0.511898 + 0.593766i
\(309\) 48.8237 0.158005
\(310\) 0 0
\(311\) 404.185i 1.29963i 0.760092 + 0.649815i \(0.225154\pi\)
−0.760092 + 0.649815i \(0.774846\pi\)
\(312\) 67.6943 122.871i 0.216969 0.393818i
\(313\) 128.579i 0.410795i 0.978679 + 0.205398i \(0.0658487\pi\)
−0.978679 + 0.205398i \(0.934151\pi\)
\(314\) −47.9525 + 17.8168i −0.152715 + 0.0567415i
\(315\) 0 0
\(316\) −128.963 149.588i −0.408112 0.473381i
\(317\) 85.9315i 0.271077i 0.990772 + 0.135539i \(0.0432765\pi\)
−0.990772 + 0.135539i \(0.956724\pi\)
\(318\) −181.117 + 67.2944i −0.569550 + 0.211618i
\(319\) 284.538i 0.891969i
\(320\) 0 0
\(321\) −7.80635 −0.0243189
\(322\) 141.883 + 381.865i 0.440630 + 1.18592i
\(323\) −580.475 −1.79714
\(324\) −27.2661 + 23.5066i −0.0841545 + 0.0725514i
\(325\) 0 0
\(326\) 44.2167 + 119.005i 0.135634 + 0.365047i
\(327\) 334.832 1.02395
\(328\) 65.1934 + 35.9175i 0.198760 + 0.109505i
\(329\) −207.894 −0.631898
\(330\) 0 0
\(331\) 183.391i 0.554052i −0.960862 0.277026i \(-0.910651\pi\)
0.960862 0.277026i \(-0.0893488\pi\)
\(332\) −219.270 + 189.037i −0.660452 + 0.569390i
\(333\) 106.948i 0.321165i
\(334\) −8.62160 23.2043i −0.0258132 0.0694739i
\(335\) 0 0
\(336\) 22.3167 149.873i 0.0664188 0.446050i
\(337\) 168.130i 0.498901i 0.968388 + 0.249451i \(0.0802500\pi\)
−0.968388 + 0.249451i \(0.919750\pi\)
\(338\) 46.3229 + 124.674i 0.137050 + 0.368858i
\(339\) 130.896i 0.386123i
\(340\) 0 0
\(341\) 53.3962 0.156587
\(342\) 133.722 49.6849i 0.391001 0.145277i
\(343\) 372.374 1.08564
\(344\) 490.688 + 270.338i 1.42642 + 0.785867i
\(345\) 0 0
\(346\) 111.311 41.3578i 0.321708 0.119531i
\(347\) −137.414 −0.396006 −0.198003 0.980201i \(-0.563446\pi\)
−0.198003 + 0.980201i \(0.563446\pi\)
\(348\) 135.238 116.592i 0.388615 0.335034i
\(349\) 13.4893 0.0386513 0.0193256 0.999813i \(-0.493848\pi\)
0.0193256 + 0.999813i \(0.493848\pi\)
\(350\) 0 0
\(351\) 52.6068i 0.149877i
\(352\) 72.9301 + 345.681i 0.207188 + 0.982047i
\(353\) 243.547i 0.689935i −0.938615 0.344968i \(-0.887890\pi\)
0.938615 0.344968i \(-0.112110\pi\)
\(354\) −180.353 + 67.0107i −0.509473 + 0.189296i
\(355\) 0 0
\(356\) 350.493 302.168i 0.984532 0.848786i
\(357\) 231.215i 0.647660i
\(358\) 473.909 176.082i 1.32377 0.491849i
\(359\) 17.9166i 0.0499068i 0.999689 + 0.0249534i \(0.00794374\pi\)
−0.999689 + 0.0249534i \(0.992056\pi\)
\(360\) 0 0
\(361\) −204.285 −0.565887
\(362\) 87.3321 + 235.047i 0.241249 + 0.649300i
\(363\) 1.53900 0.00423968
\(364\) −144.582 167.704i −0.397202 0.460727i
\(365\) 0 0
\(366\) 99.2245 + 267.054i 0.271105 + 0.729656i
\(367\) −238.417 −0.649637 −0.324818 0.945776i \(-0.605303\pi\)
−0.324818 + 0.945776i \(0.605303\pi\)
\(368\) −87.7852 + 589.541i −0.238547 + 1.60201i
\(369\) −27.9123 −0.0756431
\(370\) 0 0
\(371\) 304.968i 0.822016i
\(372\) −21.8795 25.3787i −0.0588158 0.0682222i
\(373\) 181.271i 0.485981i 0.970029 + 0.242990i \(0.0781283\pi\)
−0.970029 + 0.242990i \(0.921872\pi\)
\(374\) 187.759 + 505.336i 0.502029 + 1.35117i
\(375\) 0 0
\(376\) −266.420 146.781i −0.708564 0.390375i
\(377\) 260.927i 0.692114i
\(378\) 19.7904 + 53.2642i 0.0523557 + 0.140911i
\(379\) 306.206i 0.807931i −0.914774 0.403965i \(-0.867632\pi\)
0.914774 0.403965i \(-0.132368\pi\)
\(380\) 0 0
\(381\) −227.428 −0.596924
\(382\) 182.723 67.8912i 0.478333 0.177726i
\(383\) −144.027 −0.376050 −0.188025 0.982164i \(-0.560209\pi\)
−0.188025 + 0.982164i \(0.560209\pi\)
\(384\) 134.415 176.308i 0.350039 0.459136i
\(385\) 0 0
\(386\) −641.878 + 238.491i −1.66290 + 0.617853i
\(387\) −210.086 −0.542858
\(388\) 190.558 + 221.034i 0.491128 + 0.569674i
\(389\) −14.0099 −0.0360152 −0.0180076 0.999838i \(-0.505732\pi\)
−0.0180076 + 0.999838i \(0.505732\pi\)
\(390\) 0 0
\(391\) 909.506i 2.32610i
\(392\) 133.863 + 73.7499i 0.341486 + 0.188138i
\(393\) 131.209i 0.333864i
\(394\) −139.639 + 51.8831i −0.354413 + 0.131683i
\(395\) 0 0
\(396\) −86.5069 100.342i −0.218452 0.253389i
\(397\) 39.1084i 0.0985098i 0.998786 + 0.0492549i \(0.0156847\pi\)
−0.998786 + 0.0492549i \(0.984315\pi\)
\(398\) 333.760 124.009i 0.838592 0.311581i
\(399\) 225.164i 0.564321i
\(400\) 0 0
\(401\) −121.067 −0.301913 −0.150957 0.988540i \(-0.548235\pi\)
−0.150957 + 0.988540i \(0.548235\pi\)
\(402\) 126.072 + 339.312i 0.313612 + 0.844059i
\(403\) −48.9653 −0.121502
\(404\) −89.0970 + 76.8124i −0.220537 + 0.190130i
\(405\) 0 0
\(406\) −98.1595 264.188i −0.241772 0.650709i
\(407\) −393.579 −0.967026
\(408\) 163.246 296.305i 0.400112 0.726239i
\(409\) 541.795 1.32468 0.662342 0.749202i \(-0.269563\pi\)
0.662342 + 0.749202i \(0.269563\pi\)
\(410\) 0 0
\(411\) 115.688i 0.281480i
\(412\) 85.3983 73.6237i 0.207278 0.178698i
\(413\) 303.682i 0.735307i
\(414\) −77.8478 209.520i −0.188038 0.506088i
\(415\) 0 0
\(416\) −66.8784 316.996i −0.160765 0.762009i
\(417\) 66.0282i 0.158341i
\(418\) 182.845 + 492.112i 0.437429 + 1.17730i
\(419\) 687.825i 1.64159i −0.571224 0.820794i \(-0.693531\pi\)
0.571224 0.820794i \(-0.306469\pi\)
\(420\) 0 0
\(421\) −454.396 −1.07932 −0.539662 0.841882i \(-0.681448\pi\)
−0.539662 + 0.841882i \(0.681448\pi\)
\(422\) 348.507 129.489i 0.825846 0.306845i
\(423\) 114.067 0.269661
\(424\) −215.318 + 390.821i −0.507826 + 0.921749i
\(425\) 0 0
\(426\) 249.214 92.5959i 0.585008 0.217361i
\(427\) 449.670 1.05309
\(428\) −13.6542 + 11.7716i −0.0319024 + 0.0275037i
\(429\) −193.599 −0.451279
\(430\) 0 0
\(431\) 466.145i 1.08154i 0.841169 + 0.540772i \(0.181868\pi\)
−0.841169 + 0.540772i \(0.818132\pi\)
\(432\) −12.2447 + 82.2318i −0.0283441 + 0.190351i
\(433\) 457.094i 1.05565i −0.849355 0.527823i \(-0.823009\pi\)
0.849355 0.527823i \(-0.176991\pi\)
\(434\) −49.5772 + 18.4205i −0.114233 + 0.0424436i
\(435\) 0 0
\(436\) 585.660 504.910i 1.34326 1.15805i
\(437\) 885.706i 2.02679i
\(438\) 303.684 112.834i 0.693341 0.257613i
\(439\) 777.467i 1.77100i 0.464644 + 0.885498i \(0.346182\pi\)
−0.464644 + 0.885498i \(0.653818\pi\)
\(440\) 0 0
\(441\) −57.3128 −0.129961
\(442\) −172.178 463.403i −0.389544 1.04842i
\(443\) −247.484 −0.558654 −0.279327 0.960196i \(-0.590111\pi\)
−0.279327 + 0.960196i \(0.590111\pi\)
\(444\) 161.272 + 187.065i 0.363226 + 0.421316i
\(445\) 0 0
\(446\) 141.213 + 380.061i 0.316620 + 0.852155i
\(447\) −219.480 −0.491007
\(448\) −186.967 295.798i −0.417336 0.660263i
\(449\) −412.508 −0.918726 −0.459363 0.888249i \(-0.651922\pi\)
−0.459363 + 0.888249i \(0.651922\pi\)
\(450\) 0 0
\(451\) 102.720i 0.227761i
\(452\) 197.384 + 228.952i 0.436691 + 0.506531i
\(453\) 118.542i 0.261682i
\(454\) −35.7141 96.1213i −0.0786654 0.211721i
\(455\) 0 0
\(456\) 158.974 288.552i 0.348627 0.632789i
\(457\) 745.400i 1.63107i −0.578706 0.815537i \(-0.696442\pi\)
0.578706 0.815537i \(-0.303558\pi\)
\(458\) −234.785 631.904i −0.512631 1.37970i
\(459\) 126.862i 0.276388i
\(460\) 0 0
\(461\) 81.6151 0.177039 0.0885196 0.996074i \(-0.471786\pi\)
0.0885196 + 0.996074i \(0.471786\pi\)
\(462\) −196.018 + 72.8309i −0.424281 + 0.157643i
\(463\) −292.248 −0.631205 −0.315603 0.948891i \(-0.602207\pi\)
−0.315603 + 0.948891i \(0.602207\pi\)
\(464\) 60.7329 407.865i 0.130890 0.879020i
\(465\) 0 0
\(466\) −150.517 + 55.9248i −0.322997 + 0.120010i
\(467\) −51.4163 −0.110099 −0.0550495 0.998484i \(-0.517532\pi\)
−0.0550495 + 0.998484i \(0.517532\pi\)
\(468\) 79.3285 + 92.0155i 0.169505 + 0.196614i
\(469\) 571.339 1.21821
\(470\) 0 0
\(471\) 44.3019i 0.0940592i
\(472\) −214.410 + 389.174i −0.454259 + 0.824520i
\(473\) 773.139i 1.63454i
\(474\) 160.335 59.5727i 0.338259 0.125681i
\(475\) 0 0
\(476\) −348.660 404.422i −0.732480 0.849625i
\(477\) 167.329i 0.350794i
\(478\) −620.190 + 230.433i −1.29747 + 0.482077i
\(479\) 122.593i 0.255935i 0.991778 + 0.127967i \(0.0408453\pi\)
−0.991778 + 0.127967i \(0.959155\pi\)
\(480\) 0 0
\(481\) 360.920 0.750354
\(482\) −250.708 674.758i −0.520141 1.39991i
\(483\) −352.794 −0.730423
\(484\) 2.69190 2.32074i 0.00556177 0.00479492i
\(485\) 0 0
\(486\) −10.8586 29.2248i −0.0223427 0.0601334i
\(487\) 65.9859 0.135495 0.0677474 0.997703i \(-0.478419\pi\)
0.0677474 + 0.997703i \(0.478419\pi\)
\(488\) 576.260 + 317.483i 1.18086 + 0.650580i
\(489\) −109.946 −0.224837
\(490\) 0 0
\(491\) 361.163i 0.735567i −0.929911 0.367783i \(-0.880117\pi\)
0.929911 0.367783i \(-0.119883\pi\)
\(492\) −48.8219 + 42.0904i −0.0992315 + 0.0855496i
\(493\) 629.229i 1.27633i
\(494\) −167.673 451.277i −0.339419 0.913516i
\(495\) 0 0
\(496\) −76.5396 11.3971i −0.154314 0.0229780i
\(497\) 419.630i 0.844326i
\(498\) −87.3231 235.022i −0.175348 0.471933i
\(499\) 711.138i 1.42513i −0.701608 0.712564i \(-0.747534\pi\)
0.701608 0.712564i \(-0.252466\pi\)
\(500\) 0 0
\(501\) 21.4378 0.0427900
\(502\) 585.328 217.480i 1.16599 0.433227i
\(503\) −353.756 −0.703292 −0.351646 0.936133i \(-0.614378\pi\)
−0.351646 + 0.936133i \(0.614378\pi\)
\(504\) 114.936 + 63.3224i 0.228047 + 0.125640i
\(505\) 0 0
\(506\) 771.057 286.488i 1.52383 0.566182i
\(507\) −115.183 −0.227185
\(508\) −397.799 + 342.951i −0.783068 + 0.675100i
\(509\) −478.049 −0.939192 −0.469596 0.882881i \(-0.655600\pi\)
−0.469596 + 0.882881i \(0.655600\pi\)
\(510\) 0 0
\(511\) 511.348i 1.00068i
\(512\) −30.7568 511.075i −0.0600720 0.998194i
\(513\) 123.542i 0.240823i
\(514\) −150.468 + 55.9067i −0.292739 + 0.108768i
\(515\) 0 0
\(516\) −367.466 + 316.800i −0.712142 + 0.613953i
\(517\) 419.778i 0.811949i
\(518\) 365.431 135.777i 0.705464 0.262117i
\(519\) 102.837i 0.198144i
\(520\) 0 0
\(521\) −35.7365 −0.0685921 −0.0342960 0.999412i \(-0.510919\pi\)
−0.0342960 + 0.999412i \(0.510919\pi\)
\(522\) 53.8579 + 144.954i 0.103176 + 0.277689i
\(523\) −733.562 −1.40260 −0.701302 0.712864i \(-0.747398\pi\)
−0.701302 + 0.712864i \(0.747398\pi\)
\(524\) 197.856 + 229.499i 0.377588 + 0.437976i
\(525\) 0 0
\(526\) 339.906 + 914.828i 0.646210 + 1.73922i
\(527\) −118.081 −0.224062
\(528\) −302.622 45.0617i −0.573147 0.0853441i
\(529\) 858.753 1.62335
\(530\) 0 0
\(531\) 166.623i 0.313791i
\(532\) −339.537 393.839i −0.638227 0.740298i
\(533\) 94.1965i 0.176729i
\(534\) 139.582 + 375.673i 0.261390 + 0.703507i
\(535\) 0 0
\(536\) 732.181 + 403.386i 1.36601 + 0.752585i
\(537\) 437.831i 0.815327i
\(538\) 215.628 + 580.342i 0.400795 + 1.07870i
\(539\) 210.917i 0.391312i
\(540\) 0 0
\(541\) 608.939 1.12558 0.562790 0.826600i \(-0.309728\pi\)
0.562790 + 0.826600i \(0.309728\pi\)
\(542\) 91.8064 34.1109i 0.169384 0.0629352i
\(543\) −217.153 −0.399913
\(544\) −161.278 764.440i −0.296467 1.40522i
\(545\) 0 0
\(546\) 179.752 66.7874i 0.329217 0.122321i
\(547\) −78.5868 −0.143669 −0.0718344 0.997417i \(-0.522885\pi\)
−0.0718344 + 0.997417i \(0.522885\pi\)
\(548\) −174.452 202.353i −0.318344 0.369257i
\(549\) −246.724 −0.449405
\(550\) 0 0
\(551\) 612.763i 1.11209i
\(552\) −452.112 249.085i −0.819043 0.451242i
\(553\) 269.974i 0.488200i
\(554\) 374.287 139.067i 0.675609 0.251024i
\(555\) 0 0
\(556\) 99.5673 + 115.491i 0.179078 + 0.207718i
\(557\) 928.488i 1.66694i −0.552561 0.833472i \(-0.686349\pi\)
0.552561 0.833472i \(-0.313651\pi\)
\(558\) 27.2019 10.1069i 0.0487489 0.0181128i
\(559\) 708.984i 1.26831i
\(560\) 0 0
\(561\) −466.866 −0.832202
\(562\) 42.6025 + 114.661i 0.0758051 + 0.204023i
\(563\) 447.978 0.795697 0.397849 0.917451i \(-0.369757\pi\)
0.397849 + 0.917451i \(0.369757\pi\)
\(564\) 199.516 172.007i 0.353752 0.304977i
\(565\) 0 0
\(566\) −301.274 810.852i −0.532286 1.43260i
\(567\) −49.2093 −0.0867889
\(568\) 296.274 537.763i 0.521609 0.946766i
\(569\) −571.441 −1.00429 −0.502145 0.864783i \(-0.667456\pi\)
−0.502145 + 0.864783i \(0.667456\pi\)
\(570\) 0 0
\(571\) 990.801i 1.73520i 0.497260 + 0.867602i \(0.334340\pi\)
−0.497260 + 0.867602i \(0.665660\pi\)
\(572\) −338.627 + 291.937i −0.592005 + 0.510380i
\(573\) 168.813i 0.294612i
\(574\) 35.4363 + 95.3736i 0.0617357 + 0.166156i
\(575\) 0 0
\(576\) 102.584 + 162.298i 0.178098 + 0.281766i
\(577\) 826.638i 1.43265i 0.697768 + 0.716324i \(0.254177\pi\)
−0.697768 + 0.716324i \(0.745823\pi\)
\(578\) −213.900 575.693i −0.370069 0.996008i
\(579\) 593.013i 1.02420i
\(580\) 0 0
\(581\) −395.735 −0.681127
\(582\) −236.913 + 88.0254i −0.407066 + 0.151246i
\(583\) 615.787 1.05624
\(584\) 361.030 655.301i 0.618202 1.12209i
\(585\) 0 0
\(586\) −530.999 + 197.294i −0.906142 + 0.336679i
\(587\) 900.009 1.53323 0.766617 0.642104i \(-0.221938\pi\)
0.766617 + 0.642104i \(0.221938\pi\)
\(588\) −100.247 + 86.4249i −0.170488 + 0.146981i
\(589\) −114.991 −0.195230
\(590\) 0 0
\(591\) 129.008i 0.218288i
\(592\) 564.169 + 84.0071i 0.952987 + 0.141904i
\(593\) 704.088i 1.18733i 0.804711 + 0.593666i \(0.202320\pi\)
−0.804711 + 0.593666i \(0.797680\pi\)
\(594\) 107.551 39.9606i 0.181061 0.0672738i
\(595\) 0 0
\(596\) −383.897 + 330.965i −0.644122 + 0.555311i
\(597\) 308.351i 0.516501i
\(598\) −707.075 + 262.715i −1.18240 + 0.439323i
\(599\) 376.098i 0.627876i −0.949444 0.313938i \(-0.898352\pi\)
0.949444 0.313938i \(-0.101648\pi\)
\(600\) 0 0
\(601\) 430.191 0.715791 0.357896 0.933762i \(-0.383494\pi\)
0.357896 + 0.933762i \(0.383494\pi\)
\(602\) 266.716 + 717.844i 0.443051 + 1.19243i
\(603\) −313.480 −0.519868
\(604\) 178.756 + 207.344i 0.295953 + 0.343285i
\(605\) 0 0
\(606\) −35.4824 95.4977i −0.0585518 0.157587i
\(607\) −93.4019 −0.153875 −0.0769373 0.997036i \(-0.524514\pi\)
−0.0769373 + 0.997036i \(0.524514\pi\)
\(608\) −157.058 744.436i −0.258319 1.22440i
\(609\) 244.075 0.400781
\(610\) 0 0
\(611\) 384.944i 0.630024i
\(612\) 191.302 + 221.897i 0.312585 + 0.362576i
\(613\) 156.506i 0.255312i 0.991818 + 0.127656i \(0.0407454\pi\)
−0.991818 + 0.127656i \(0.959255\pi\)
\(614\) −69.7113 187.622i −0.113536 0.305573i
\(615\) 0 0
\(616\) −233.033 + 422.976i −0.378301 + 0.686649i
\(617\) 553.493i 0.897072i −0.893765 0.448536i \(-0.851946\pi\)
0.893765 0.448536i \(-0.148054\pi\)
\(618\) 34.0094 + 91.5334i 0.0550314 + 0.148112i
\(619\) 14.4398i 0.0233276i −0.999932 0.0116638i \(-0.996287\pi\)
0.999932 0.0116638i \(-0.00371278\pi\)
\(620\) 0 0
\(621\) 193.570 0.311707
\(622\) −757.756 + 281.546i −1.21826 + 0.452646i
\(623\) 632.564 1.01535
\(624\) 277.510 + 41.3224i 0.444728 + 0.0662219i
\(625\) 0 0
\(626\) −241.056 + 89.5651i −0.385074 + 0.143075i
\(627\) −454.649 −0.725117
\(628\) −66.8051 77.4893i −0.106378 0.123391i
\(629\) 870.364 1.38373
\(630\) 0 0
\(631\) 352.389i 0.558460i 0.960224 + 0.279230i \(0.0900793\pi\)
−0.960224 + 0.279230i \(0.909921\pi\)
\(632\) 190.612 345.977i 0.301601 0.547432i
\(633\) 321.976i 0.508650i
\(634\) −161.102 + 59.8579i −0.254104 + 0.0944130i
\(635\) 0 0
\(636\) −252.324 292.678i −0.396735 0.460185i
\(637\) 193.415i 0.303634i
\(638\) −533.445 + 198.203i −0.836120 + 0.310662i
\(639\) 230.241i 0.360315i
\(640\) 0 0
\(641\) −545.742 −0.851391 −0.425696 0.904866i \(-0.639971\pi\)
−0.425696 + 0.904866i \(0.639971\pi\)
\(642\) −5.43772 14.6352i −0.00846997 0.0227962i
\(643\) 757.447 1.17799 0.588995 0.808137i \(-0.299524\pi\)
0.588995 + 0.808137i \(0.299524\pi\)
\(644\) −617.079 + 531.997i −0.958197 + 0.826082i
\(645\) 0 0
\(646\) −404.345 1088.26i −0.625922 1.68461i
\(647\) 1161.36 1.79500 0.897499 0.441016i \(-0.145382\pi\)
0.897499 + 0.441016i \(0.145382\pi\)
\(648\) −63.0626 34.7435i −0.0973188 0.0536166i
\(649\) 613.191 0.944824
\(650\) 0 0
\(651\) 45.8030i 0.0703579i
\(652\) −192.308 + 165.793i −0.294950 + 0.254283i
\(653\) 621.231i 0.951348i 0.879622 + 0.475674i \(0.157796\pi\)
−0.879622 + 0.475674i \(0.842204\pi\)
\(654\) 233.236 + 627.734i 0.356630 + 0.959838i
\(655\) 0 0
\(656\) −21.9250 + 147.242i −0.0334223 + 0.224455i
\(657\) 280.565i 0.427039i
\(658\) −144.814 389.755i −0.220083 0.592333i
\(659\) 736.047i 1.11692i −0.829533 0.558458i \(-0.811393\pi\)
0.829533 0.558458i \(-0.188607\pi\)
\(660\) 0 0
\(661\) 383.845 0.580704 0.290352 0.956920i \(-0.406228\pi\)
0.290352 + 0.956920i \(0.406228\pi\)
\(662\) 343.817 127.746i 0.519362 0.192970i
\(663\) 428.125 0.645739
\(664\) −507.141 279.403i −0.763766 0.420788i
\(665\) 0 0
\(666\) −200.503 + 74.4974i −0.301056 + 0.111858i
\(667\) −960.096 −1.43942
\(668\) 37.4972 32.3271i 0.0561335 0.0483939i
\(669\) −351.128 −0.524854
\(670\) 0 0
\(671\) 907.968i 1.35316i
\(672\) 296.523 62.5592i 0.441255 0.0930940i
\(673\) 984.464i 1.46280i −0.681949 0.731400i \(-0.738867\pi\)
0.681949 0.731400i \(-0.261133\pi\)
\(674\) −315.205 + 117.115i −0.467664 + 0.173761i
\(675\) 0 0
\(676\) −201.468 + 173.690i −0.298030 + 0.256938i
\(677\) 673.154i 0.994319i 0.867659 + 0.497160i \(0.165624\pi\)
−0.867659 + 0.497160i \(0.834376\pi\)
\(678\) −245.400 + 91.1789i −0.361947 + 0.134482i
\(679\) 398.918i 0.587507i
\(680\) 0 0
\(681\) 88.8037 0.130402
\(682\) 37.1945 + 100.106i 0.0545374 + 0.146783i
\(683\) 291.192 0.426343 0.213171 0.977015i \(-0.431621\pi\)
0.213171 + 0.977015i \(0.431621\pi\)
\(684\) 186.296 + 216.090i 0.272362 + 0.315921i
\(685\) 0 0
\(686\) 259.387 + 698.117i 0.378115 + 1.01766i
\(687\) 583.798 0.849778
\(688\) −165.022 + 1108.24i −0.239857 + 1.61081i
\(689\) −564.689 −0.819578
\(690\) 0 0
\(691\) 943.693i 1.36569i −0.730563 0.682846i \(-0.760742\pi\)
0.730563 0.682846i \(-0.239258\pi\)
\(692\) 155.073 + 179.874i 0.224094 + 0.259933i
\(693\) 181.095i 0.261321i
\(694\) −95.7193 257.620i −0.137924 0.371211i
\(695\) 0 0
\(696\) 312.787 + 172.326i 0.449406 + 0.247595i
\(697\) 227.156i 0.325905i
\(698\) 9.39633 + 25.2894i 0.0134618 + 0.0362312i
\(699\) 139.058i 0.198938i
\(700\) 0 0
\(701\) 885.681 1.26345 0.631727 0.775191i \(-0.282346\pi\)
0.631727 + 0.775191i \(0.282346\pi\)
\(702\) −98.6259 + 36.6447i −0.140493 + 0.0522004i
\(703\) 847.588 1.20567
\(704\) −597.272 + 377.521i −0.848397 + 0.536251i
\(705\) 0 0
\(706\) 456.596 169.649i 0.646737 0.240296i
\(707\) −160.801 −0.227441
\(708\) −251.260 291.444i −0.354887 0.411644i
\(709\) 286.183 0.403644 0.201822 0.979422i \(-0.435314\pi\)
0.201822 + 0.979422i \(0.435314\pi\)
\(710\) 0 0
\(711\) 148.129i 0.208339i
\(712\) 810.642 + 446.613i 1.13854 + 0.627266i
\(713\) 180.171i 0.252694i
\(714\) 433.475 161.059i 0.607108 0.225572i
\(715\) 0 0
\(716\) 660.228 + 765.818i 0.922106 + 1.06958i
\(717\) 572.976i 0.799129i
\(718\) −33.5895 + 12.4803i −0.0467820 + 0.0173820i
\(719\) 666.163i 0.926513i 0.886224 + 0.463257i \(0.153319\pi\)
−0.886224 + 0.463257i \(0.846681\pi\)
\(720\) 0 0
\(721\) 154.125 0.213766
\(722\) −142.300 382.989i −0.197092 0.530455i
\(723\) 623.389 0.862226
\(724\) −379.826 + 327.456i −0.524622 + 0.452287i
\(725\) 0 0
\(726\) 1.07203 + 2.88528i 0.00147663 + 0.00397422i
\(727\) 856.270 1.17781 0.588907 0.808201i \(-0.299559\pi\)
0.588907 + 0.808201i \(0.299559\pi\)
\(728\) 213.696 387.877i 0.293538 0.532798i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 1709.72i 2.33888i
\(732\) −431.549 + 372.047i −0.589547 + 0.508261i
\(733\) 769.487i 1.04978i 0.851171 + 0.524889i \(0.175893\pi\)
−0.851171 + 0.524889i \(0.824107\pi\)
\(734\) −166.076 446.978i −0.226261 0.608961i
\(735\) 0 0
\(736\) −1166.41 + 246.083i −1.58479 + 0.334352i
\(737\) 1153.64i 1.56532i
\(738\) −19.4431 52.3293i −0.0263456 0.0709069i
\(739\) 1156.70i 1.56522i 0.622511 + 0.782611i \(0.286113\pi\)
−0.622511 + 0.782611i \(0.713887\pi\)
\(740\) 0 0
\(741\) 416.922 0.562647
\(742\) −571.746 + 212.433i −0.770547 + 0.286298i
\(743\) 426.794 0.574421 0.287210 0.957868i \(-0.407272\pi\)
0.287210 + 0.957868i \(0.407272\pi\)
\(744\) 32.3386 58.6973i 0.0434658 0.0788942i
\(745\) 0 0
\(746\) −339.842 + 126.269i −0.455552 + 0.169261i
\(747\) 217.130 0.290670
\(748\) −816.603 + 704.011i −1.09172 + 0.941191i
\(749\) −24.6429 −0.0329011
\(750\) 0 0
\(751\) 1222.03i 1.62721i −0.581420 0.813604i \(-0.697503\pi\)
0.581420 0.813604i \(-0.302497\pi\)
\(752\) 89.5990 601.722i 0.119148 0.800162i
\(753\) 540.768i 0.718152i
\(754\) 489.179 181.756i 0.648779 0.241055i
\(755\) 0 0
\(756\) −86.0729 + 74.2053i −0.113853 + 0.0981551i
\(757\) 1312.95i 1.73442i −0.497945 0.867209i \(-0.665912\pi\)
0.497945 0.867209i \(-0.334088\pi\)
\(758\) 574.067 213.296i 0.757344 0.281393i
\(759\) 712.358i 0.938548i
\(760\) 0 0
\(761\) −189.584 −0.249124 −0.124562 0.992212i \(-0.539753\pi\)
−0.124562 + 0.992212i \(0.539753\pi\)
\(762\) −158.421 426.376i −0.207902 0.559549i
\(763\) 1056.99 1.38531
\(764\) 254.561 + 295.273i 0.333195 + 0.386483i
\(765\) 0 0
\(766\) −100.326 270.019i −0.130974 0.352505i
\(767\) −562.308 −0.733127
\(768\) 424.169 + 129.185i 0.552303 + 0.168210i
\(769\) −254.995 −0.331594 −0.165797 0.986160i \(-0.553020\pi\)
−0.165797 + 0.986160i \(0.553020\pi\)
\(770\) 0 0
\(771\) 139.013i 0.180302i
\(772\) −894.235 1037.25i −1.15834 1.34359i
\(773\) 23.2536i 0.0300823i −0.999887 0.0150411i \(-0.995212\pi\)
0.999887 0.0150411i \(-0.00478793\pi\)
\(774\) −146.341 393.864i −0.189071 0.508869i
\(775\) 0 0
\(776\) −281.650 + 511.220i −0.362951 + 0.658788i
\(777\) 337.611i 0.434506i
\(778\) −9.75897 26.2654i −0.0125437 0.0337602i
\(779\) 221.212i 0.283969i
\(780\) 0 0
\(781\) −847.312 −1.08491
\(782\) −1705.12 + 633.541i −2.18046 + 0.810155i
\(783\) −133.919 −0.171033
\(784\) −45.0189 + 302.335i −0.0574221 + 0.385631i
\(785\) 0 0
\(786\) −245.987 + 91.3969i −0.312960 + 0.116281i
\(787\) −220.593 −0.280296 −0.140148 0.990131i \(-0.544758\pi\)