Properties

Label 300.3.f.b.199.2
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 199.2
Root \(1.28061 + 0.600040i\) of defining polynomial
Character \(\chi\) \(=\) 300.199
Dual form 300.3.f.b.199.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.95141 + 0.438172i) q^{2} +1.73205 q^{3} +(3.61601 - 1.71011i) q^{4} +(-3.37994 + 0.758935i) q^{6} -6.33166 q^{7} +(-6.30701 + 4.92155i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(-1.95141 + 0.438172i) q^{2} +1.73205 q^{3} +(3.61601 - 1.71011i) q^{4} +(-3.37994 + 0.758935i) q^{6} -6.33166 q^{7} +(-6.30701 + 4.92155i) q^{8} +3.00000 q^{9} -9.27963i q^{11} +(6.26312 - 2.96199i) q^{12} -18.5674i q^{13} +(12.3557 - 2.77436i) q^{14} +(10.1511 - 12.3675i) q^{16} +13.9110i q^{17} +(-5.85423 + 1.31451i) q^{18} -17.2468i q^{19} -10.9668 q^{21} +(4.06607 + 18.1084i) q^{22} -33.7148 q^{23} +(-10.9241 + 8.52438i) q^{24} +(8.13571 + 36.2327i) q^{26} +5.19615 q^{27} +(-22.8954 + 10.8278i) q^{28} +28.6177 q^{29} -23.4939i q^{31} +(-14.3898 + 28.5820i) q^{32} -16.0728i q^{33} +(-6.09542 - 27.1461i) q^{34} +(10.8480 - 5.13032i) q^{36} -67.3338i q^{37} +(7.55706 + 33.6556i) q^{38} -32.1597i q^{39} -44.0791 q^{41} +(21.4007 - 4.80532i) q^{42} +50.2937 q^{43} +(-15.8691 - 33.5552i) q^{44} +(65.7915 - 14.7729i) q^{46} +31.1594 q^{47} +(17.5822 - 21.4212i) q^{48} -8.91003 q^{49} +24.0946i q^{51} +(-31.7522 - 67.1400i) q^{52} -81.6070i q^{53} +(-10.1398 + 2.27681i) q^{54} +(39.9338 - 31.1616i) q^{56} -29.8724i q^{57} +(-55.8449 + 12.5395i) q^{58} +19.2751i q^{59} -53.1563 q^{61} +(10.2943 + 45.8462i) q^{62} -18.9950 q^{63} +(15.5566 - 62.0805i) q^{64} +(7.04264 + 31.3646i) q^{66} +4.49911 q^{67} +(23.7893 + 50.3025i) q^{68} -58.3958 q^{69} -13.3360i q^{71} +(-18.9210 + 14.7647i) q^{72} -40.8904i q^{73} +(29.5037 + 131.396i) q^{74} +(-29.4939 - 62.3647i) q^{76} +58.7555i q^{77} +(14.0915 + 62.7568i) q^{78} +141.309i q^{79} +9.00000 q^{81} +(86.0164 - 19.3142i) q^{82} +69.8503 q^{83} +(-39.6559 + 18.7543i) q^{84} +(-98.1438 + 22.0373i) q^{86} +49.5673 q^{87} +(45.6702 + 58.5266i) q^{88} +46.3079 q^{89} +117.563i q^{91} +(-121.913 + 57.6559i) q^{92} -40.6926i q^{93} +(-60.8049 + 13.6532i) q^{94} +(-24.9239 + 49.5055i) q^{96} +68.5543i q^{97} +(17.3871 - 3.90412i) q^{98} -27.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 20q^{4} - 12q^{6} + 48q^{9} + O(q^{10}) \) \( 16q - 20q^{4} - 12q^{6} + 48q^{9} + 40q^{14} + 68q^{16} - 96q^{21} - 36q^{24} - 72q^{26} - 128q^{29} + 184q^{34} - 60q^{36} - 32q^{41} - 344q^{44} + 304q^{46} + 112q^{49} - 36q^{54} + 232q^{56} - 352q^{61} + 220q^{64} + 216q^{66} + 192q^{69} - 264q^{74} - 48q^{76} + 144q^{81} + 72q^{84} - 400q^{86} - 160q^{89} + 192q^{94} - 348q^{96} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.95141 + 0.438172i −0.975706 + 0.219086i
\(3\) 1.73205 0.577350
\(4\) 3.61601 1.71011i 0.904003 0.427526i
\(5\) 0 0
\(6\) −3.37994 + 0.758935i −0.563324 + 0.126489i
\(7\) −6.33166 −0.904523 −0.452262 0.891885i \(-0.649383\pi\)
−0.452262 + 0.891885i \(0.649383\pi\)
\(8\) −6.30701 + 4.92155i −0.788376 + 0.615194i
\(9\) 3.00000 0.333333
\(10\) 0 0
\(11\) 9.27963i 0.843602i −0.906688 0.421801i \(-0.861398\pi\)
0.906688 0.421801i \(-0.138602\pi\)
\(12\) 6.26312 2.96199i 0.521926 0.246833i
\(13\) 18.5674i 1.42826i −0.700012 0.714131i \(-0.746822\pi\)
0.700012 0.714131i \(-0.253178\pi\)
\(14\) 12.3557 2.77436i 0.882549 0.198168i
\(15\) 0 0
\(16\) 10.1511 12.3675i 0.634442 0.772970i
\(17\) 13.9110i 0.818296i 0.912468 + 0.409148i \(0.134174\pi\)
−0.912468 + 0.409148i \(0.865826\pi\)
\(18\) −5.85423 + 1.31451i −0.325235 + 0.0730286i
\(19\) 17.2468i 0.907727i −0.891071 0.453864i \(-0.850045\pi\)
0.891071 0.453864i \(-0.149955\pi\)
\(20\) 0 0
\(21\) −10.9668 −0.522227
\(22\) 4.06607 + 18.1084i 0.184821 + 0.823108i
\(23\) −33.7148 −1.46586 −0.732931 0.680303i \(-0.761848\pi\)
−0.732931 + 0.680303i \(0.761848\pi\)
\(24\) −10.9241 + 8.52438i −0.455169 + 0.355183i
\(25\) 0 0
\(26\) 8.13571 + 36.2327i 0.312912 + 1.39356i
\(27\) 5.19615 0.192450
\(28\) −22.8954 + 10.8278i −0.817692 + 0.386708i
\(29\) 28.6177 0.986817 0.493409 0.869798i \(-0.335751\pi\)
0.493409 + 0.869798i \(0.335751\pi\)
\(30\) 0 0
\(31\) 23.4939i 0.757866i −0.925424 0.378933i \(-0.876291\pi\)
0.925424 0.378933i \(-0.123709\pi\)
\(32\) −14.3898 + 28.5820i −0.449682 + 0.893189i
\(33\) 16.0728i 0.487054i
\(34\) −6.09542 27.1461i −0.179277 0.798416i
\(35\) 0 0
\(36\) 10.8480 5.13032i 0.301334 0.142509i
\(37\) 67.3338i 1.81983i −0.414793 0.909916i \(-0.636146\pi\)
0.414793 0.909916i \(-0.363854\pi\)
\(38\) 7.55706 + 33.6556i 0.198870 + 0.885674i
\(39\) 32.1597i 0.824608i
\(40\) 0 0
\(41\) −44.0791 −1.07510 −0.537550 0.843232i \(-0.680650\pi\)
−0.537550 + 0.843232i \(0.680650\pi\)
\(42\) 21.4007 4.80532i 0.509540 0.114412i
\(43\) 50.2937 1.16962 0.584811 0.811170i \(-0.301169\pi\)
0.584811 + 0.811170i \(0.301169\pi\)
\(44\) −15.8691 33.5552i −0.360662 0.762619i
\(45\) 0 0
\(46\) 65.7915 14.7729i 1.43025 0.321150i
\(47\) 31.1594 0.662967 0.331483 0.943461i \(-0.392451\pi\)
0.331483 + 0.943461i \(0.392451\pi\)
\(48\) 17.5822 21.4212i 0.366295 0.446275i
\(49\) −8.91003 −0.181837
\(50\) 0 0
\(51\) 24.0946i 0.472444i
\(52\) −31.7522 67.1400i −0.610620 1.29115i
\(53\) 81.6070i 1.53975i −0.638192 0.769877i \(-0.720318\pi\)
0.638192 0.769877i \(-0.279682\pi\)
\(54\) −10.1398 + 2.27681i −0.187775 + 0.0421631i
\(55\) 0 0
\(56\) 39.9338 31.1616i 0.713104 0.556457i
\(57\) 29.8724i 0.524077i
\(58\) −55.8449 + 12.5395i −0.962843 + 0.216198i
\(59\) 19.2751i 0.326697i 0.986568 + 0.163349i \(0.0522296\pi\)
−0.986568 + 0.163349i \(0.947770\pi\)
\(60\) 0 0
\(61\) −53.1563 −0.871415 −0.435707 0.900088i \(-0.643502\pi\)
−0.435707 + 0.900088i \(0.643502\pi\)
\(62\) 10.2943 + 45.8462i 0.166038 + 0.739455i
\(63\) −18.9950 −0.301508
\(64\) 15.5566 62.0805i 0.243072 0.970008i
\(65\) 0 0
\(66\) 7.04264 + 31.3646i 0.106707 + 0.475221i
\(67\) 4.49911 0.0671509 0.0335754 0.999436i \(-0.489311\pi\)
0.0335754 + 0.999436i \(0.489311\pi\)
\(68\) 23.7893 + 50.3025i 0.349843 + 0.739742i
\(69\) −58.3958 −0.846316
\(70\) 0 0
\(71\) 13.3360i 0.187832i −0.995580 0.0939158i \(-0.970062\pi\)
0.995580 0.0939158i \(-0.0299385\pi\)
\(72\) −18.9210 + 14.7647i −0.262792 + 0.205065i
\(73\) 40.8904i 0.560143i −0.959979 0.280071i \(-0.909642\pi\)
0.959979 0.280071i \(-0.0903581\pi\)
\(74\) 29.5037 + 131.396i 0.398699 + 1.77562i
\(75\) 0 0
\(76\) −29.4939 62.3647i −0.388077 0.820588i
\(77\) 58.7555i 0.763058i
\(78\) 14.0915 + 62.7568i 0.180660 + 0.804574i
\(79\) 141.309i 1.78872i 0.447352 + 0.894358i \(0.352367\pi\)
−0.447352 + 0.894358i \(0.647633\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 86.0164 19.3142i 1.04898 0.235539i
\(83\) 69.8503 0.841570 0.420785 0.907160i \(-0.361755\pi\)
0.420785 + 0.907160i \(0.361755\pi\)
\(84\) −39.6559 + 18.7543i −0.472095 + 0.223266i
\(85\) 0 0
\(86\) −98.1438 + 22.0373i −1.14121 + 0.256248i
\(87\) 49.5673 0.569739
\(88\) 45.6702 + 58.5266i 0.518979 + 0.665076i
\(89\) 46.3079 0.520313 0.260157 0.965566i \(-0.416226\pi\)
0.260157 + 0.965566i \(0.416226\pi\)
\(90\) 0 0
\(91\) 117.563i 1.29190i
\(92\) −121.913 + 57.6559i −1.32514 + 0.626695i
\(93\) 40.6926i 0.437554i
\(94\) −60.8049 + 13.6532i −0.646860 + 0.145247i
\(95\) 0 0
\(96\) −24.9239 + 49.5055i −0.259624 + 0.515683i
\(97\) 68.5543i 0.706745i 0.935483 + 0.353373i \(0.114965\pi\)
−0.935483 + 0.353373i \(0.885035\pi\)
\(98\) 17.3871 3.90412i 0.177420 0.0398380i
\(99\) 27.8389i 0.281201i
\(100\) 0 0
\(101\) −43.3949 −0.429653 −0.214826 0.976652i \(-0.568919\pi\)
−0.214826 + 0.976652i \(0.568919\pi\)
\(102\) −10.5576 47.0185i −0.103506 0.460966i
\(103\) 85.7919 0.832931 0.416465 0.909152i \(-0.363269\pi\)
0.416465 + 0.909152i \(0.363269\pi\)
\(104\) 91.3805 + 117.105i 0.878659 + 1.12601i
\(105\) 0 0
\(106\) 35.7579 + 159.249i 0.337338 + 1.50235i
\(107\) −183.075 −1.71098 −0.855491 0.517818i \(-0.826745\pi\)
−0.855491 + 0.517818i \(0.826745\pi\)
\(108\) 18.7893 8.88597i 0.173975 0.0822775i
\(109\) −81.4798 −0.747521 −0.373761 0.927525i \(-0.621932\pi\)
−0.373761 + 0.927525i \(0.621932\pi\)
\(110\) 0 0
\(111\) 116.625i 1.05068i
\(112\) −64.2732 + 78.3070i −0.573868 + 0.699170i
\(113\) 172.814i 1.52933i 0.644429 + 0.764664i \(0.277095\pi\)
−0.644429 + 0.764664i \(0.722905\pi\)
\(114\) 13.0892 + 58.2933i 0.114818 + 0.511344i
\(115\) 0 0
\(116\) 103.482 48.9393i 0.892086 0.421891i
\(117\) 55.7022i 0.476087i
\(118\) −8.44582 37.6137i −0.0715748 0.318760i
\(119\) 88.0800i 0.740168i
\(120\) 0 0
\(121\) 34.8885 0.288335
\(122\) 103.730 23.2916i 0.850244 0.190915i
\(123\) −76.3472 −0.620709
\(124\) −40.1770 84.9541i −0.324008 0.685113i
\(125\) 0 0
\(126\) 37.0670 8.32307i 0.294183 0.0660561i
\(127\) 22.3785 0.176208 0.0881041 0.996111i \(-0.471919\pi\)
0.0881041 + 0.996111i \(0.471919\pi\)
\(128\) −3.15546 + 127.961i −0.0246520 + 0.999696i
\(129\) 87.1113 0.675282
\(130\) 0 0
\(131\) 1.75315i 0.0133828i 0.999978 + 0.00669141i \(0.00212996\pi\)
−0.999978 + 0.00669141i \(0.997870\pi\)
\(132\) −27.4862 58.1194i −0.208228 0.440298i
\(133\) 109.201i 0.821060i
\(134\) −8.77961 + 1.97138i −0.0655195 + 0.0147118i
\(135\) 0 0
\(136\) −68.4639 87.7370i −0.503411 0.645125i
\(137\) 19.5084i 0.142397i −0.997462 0.0711987i \(-0.977318\pi\)
0.997462 0.0711987i \(-0.0226824\pi\)
\(138\) 113.954 25.5874i 0.825755 0.185416i
\(139\) 257.370i 1.85158i 0.378038 + 0.925790i \(0.376599\pi\)
−0.378038 + 0.925790i \(0.623401\pi\)
\(140\) 0 0
\(141\) 53.9697 0.382764
\(142\) 5.84348 + 26.0241i 0.0411512 + 0.183268i
\(143\) −172.299 −1.20489
\(144\) 30.4532 37.1026i 0.211481 0.257657i
\(145\) 0 0
\(146\) 17.9170 + 79.7940i 0.122719 + 0.546534i
\(147\) −15.4326 −0.104984
\(148\) −115.148 243.480i −0.778026 1.64513i
\(149\) 111.673 0.749486 0.374743 0.927129i \(-0.377731\pi\)
0.374743 + 0.927129i \(0.377731\pi\)
\(150\) 0 0
\(151\) 6.45275i 0.0427335i −0.999772 0.0213667i \(-0.993198\pi\)
0.999772 0.0213667i \(-0.00680176\pi\)
\(152\) 84.8811 + 108.776i 0.558428 + 0.715630i
\(153\) 41.7331i 0.272765i
\(154\) −25.7450 114.656i −0.167175 0.744520i
\(155\) 0 0
\(156\) −54.9965 116.290i −0.352542 0.745448i
\(157\) 75.9075i 0.483488i −0.970340 0.241744i \(-0.922281\pi\)
0.970340 0.241744i \(-0.0777193\pi\)
\(158\) −61.9174 275.751i −0.391882 1.74526i
\(159\) 141.347i 0.888977i
\(160\) 0 0
\(161\) 213.471 1.32591
\(162\) −17.5627 + 3.94354i −0.108412 + 0.0243429i
\(163\) 249.298 1.52944 0.764719 0.644364i \(-0.222878\pi\)
0.764719 + 0.644364i \(0.222878\pi\)
\(164\) −159.391 + 75.3799i −0.971893 + 0.459634i
\(165\) 0 0
\(166\) −136.307 + 30.6064i −0.821124 + 0.184376i
\(167\) 79.1883 0.474182 0.237091 0.971487i \(-0.423806\pi\)
0.237091 + 0.971487i \(0.423806\pi\)
\(168\) 69.1674 53.9735i 0.411711 0.321271i
\(169\) −175.749 −1.03993
\(170\) 0 0
\(171\) 51.7404i 0.302576i
\(172\) 181.863 86.0076i 1.05734 0.500044i
\(173\) 27.7204i 0.160234i 0.996785 + 0.0801168i \(0.0255293\pi\)
−0.996785 + 0.0801168i \(0.974471\pi\)
\(174\) −96.7262 + 21.7190i −0.555898 + 0.124822i
\(175\) 0 0
\(176\) −114.766 94.1982i −0.652080 0.535217i
\(177\) 33.3855i 0.188619i
\(178\) −90.3657 + 20.2908i −0.507673 + 0.113993i
\(179\) 204.324i 1.14147i −0.821133 0.570737i \(-0.806658\pi\)
0.821133 0.570737i \(-0.193342\pi\)
\(180\) 0 0
\(181\) −49.8262 −0.275283 −0.137641 0.990482i \(-0.543952\pi\)
−0.137641 + 0.990482i \(0.543952\pi\)
\(182\) −51.5126 229.413i −0.283036 1.26051i
\(183\) −92.0694 −0.503112
\(184\) 212.640 165.929i 1.15565 0.901790i
\(185\) 0 0
\(186\) 17.8303 + 79.4079i 0.0958620 + 0.426924i
\(187\) 129.089 0.690317
\(188\) 112.673 53.2859i 0.599324 0.283436i
\(189\) −32.9003 −0.174076
\(190\) 0 0
\(191\) 1.13703i 0.00595301i −0.999996 0.00297651i \(-0.999053\pi\)
0.999996 0.00297651i \(-0.000947453\pi\)
\(192\) 26.9449 107.527i 0.140338 0.560034i
\(193\) 76.6452i 0.397126i 0.980088 + 0.198563i \(0.0636274\pi\)
−0.980088 + 0.198563i \(0.936373\pi\)
\(194\) −30.0385 133.778i −0.154838 0.689575i
\(195\) 0 0
\(196\) −32.2188 + 15.2371i −0.164382 + 0.0777403i
\(197\) 134.496i 0.682719i 0.939933 + 0.341359i \(0.110887\pi\)
−0.939933 + 0.341359i \(0.889113\pi\)
\(198\) 12.1982 + 54.3251i 0.0616071 + 0.274369i
\(199\) 176.014i 0.884491i −0.896894 0.442245i \(-0.854182\pi\)
0.896894 0.442245i \(-0.145818\pi\)
\(200\) 0 0
\(201\) 7.79269 0.0387696
\(202\) 84.6813 19.0144i 0.419214 0.0941308i
\(203\) −181.198 −0.892599
\(204\) 41.2044 + 87.1264i 0.201982 + 0.427090i
\(205\) 0 0
\(206\) −167.415 + 37.5916i −0.812695 + 0.182483i
\(207\) −101.144 −0.488621
\(208\) −229.633 188.479i −1.10400 0.906150i
\(209\) −160.044 −0.765761
\(210\) 0 0
\(211\) 218.087i 1.03359i 0.856110 + 0.516793i \(0.172874\pi\)
−0.856110 + 0.516793i \(0.827126\pi\)
\(212\) −139.557 295.092i −0.658286 1.39194i
\(213\) 23.0987i 0.108445i
\(214\) 357.255 80.2183i 1.66941 0.374852i
\(215\) 0 0
\(216\) −32.7722 + 25.5731i −0.151723 + 0.118394i
\(217\) 148.755i 0.685508i
\(218\) 159.001 35.7021i 0.729361 0.163771i
\(219\) 70.8243i 0.323399i
\(220\) 0 0
\(221\) 258.292 1.16874
\(222\) 51.1020 + 227.584i 0.230189 + 1.02515i
\(223\) −328.579 −1.47345 −0.736724 0.676193i \(-0.763628\pi\)
−0.736724 + 0.676193i \(0.763628\pi\)
\(224\) 91.1115 180.972i 0.406748 0.807910i
\(225\) 0 0
\(226\) −75.7222 337.231i −0.335054 1.49217i
\(227\) 157.649 0.694491 0.347245 0.937774i \(-0.387117\pi\)
0.347245 + 0.937774i \(0.387117\pi\)
\(228\) −51.0849 108.019i −0.224057 0.473767i
\(229\) 273.148 1.19279 0.596393 0.802692i \(-0.296600\pi\)
0.596393 + 0.802692i \(0.296600\pi\)
\(230\) 0 0
\(231\) 101.767i 0.440552i
\(232\) −180.492 + 140.844i −0.777983 + 0.607084i
\(233\) 108.746i 0.466720i −0.972390 0.233360i \(-0.925028\pi\)
0.972390 0.233360i \(-0.0749721\pi\)
\(234\) 24.4071 + 108.698i 0.104304 + 0.464521i
\(235\) 0 0
\(236\) 32.9625 + 69.6992i 0.139672 + 0.295335i
\(237\) 244.754i 1.03272i
\(238\) 38.5942 + 171.880i 0.162160 + 0.722186i
\(239\) 178.994i 0.748927i −0.927242 0.374464i \(-0.877827\pi\)
0.927242 0.374464i \(-0.122173\pi\)
\(240\) 0 0
\(241\) 358.623 1.48806 0.744032 0.668144i \(-0.232911\pi\)
0.744032 + 0.668144i \(0.232911\pi\)
\(242\) −68.0819 + 15.2872i −0.281330 + 0.0631701i
\(243\) 15.5885 0.0641500
\(244\) −192.214 + 90.9029i −0.787762 + 0.372553i
\(245\) 0 0
\(246\) 148.985 33.4532i 0.605629 0.135989i
\(247\) −320.229 −1.29647
\(248\) 115.626 + 148.176i 0.466235 + 0.597483i
\(249\) 120.984 0.485881
\(250\) 0 0
\(251\) 306.220i 1.22000i −0.792401 0.610000i \(-0.791169\pi\)
0.792401 0.610000i \(-0.208831\pi\)
\(252\) −68.6861 + 32.4834i −0.272564 + 0.128903i
\(253\) 312.861i 1.23660i
\(254\) −43.6696 + 9.80560i −0.171927 + 0.0386047i
\(255\) 0 0
\(256\) −49.9113 251.087i −0.194966 0.980810i
\(257\) 251.062i 0.976895i −0.872593 0.488447i \(-0.837563\pi\)
0.872593 0.488447i \(-0.162437\pi\)
\(258\) −169.990 + 38.1697i −0.658876 + 0.147945i
\(259\) 426.335i 1.64608i
\(260\) 0 0
\(261\) 85.8531 0.328939
\(262\) −0.768181 3.42112i −0.00293199 0.0130577i
\(263\) −48.7645 −0.185416 −0.0927082 0.995693i \(-0.529552\pi\)
−0.0927082 + 0.995693i \(0.529552\pi\)
\(264\) 79.1031 + 101.371i 0.299633 + 0.383982i
\(265\) 0 0
\(266\) −47.8488 213.096i −0.179883 0.801113i
\(267\) 80.2076 0.300403
\(268\) 16.2688 7.69395i 0.0607046 0.0287088i
\(269\) −148.696 −0.552772 −0.276386 0.961047i \(-0.589137\pi\)
−0.276386 + 0.961047i \(0.589137\pi\)
\(270\) 0 0
\(271\) 83.3415i 0.307533i 0.988107 + 0.153767i \(0.0491404\pi\)
−0.988107 + 0.153767i \(0.950860\pi\)
\(272\) 172.045 + 141.212i 0.632519 + 0.519162i
\(273\) 203.624i 0.745877i
\(274\) 8.54805 + 38.0690i 0.0311972 + 0.138938i
\(275\) 0 0
\(276\) −211.160 + 99.8630i −0.765072 + 0.361822i
\(277\) 144.080i 0.520146i 0.965589 + 0.260073i \(0.0837466\pi\)
−0.965589 + 0.260073i \(0.916253\pi\)
\(278\) −112.772 502.234i −0.405655 1.80660i
\(279\) 70.4816i 0.252622i
\(280\) 0 0
\(281\) −343.671 −1.22303 −0.611514 0.791233i \(-0.709439\pi\)
−0.611514 + 0.791233i \(0.709439\pi\)
\(282\) −105.317 + 23.6480i −0.373465 + 0.0838581i
\(283\) 314.955 1.11292 0.556458 0.830876i \(-0.312160\pi\)
0.556458 + 0.830876i \(0.312160\pi\)
\(284\) −22.8061 48.2233i −0.0803030 0.169800i
\(285\) 0 0
\(286\) 336.225 75.4964i 1.17561 0.263973i
\(287\) 279.094 0.972453
\(288\) −43.1695 + 85.7461i −0.149894 + 0.297730i
\(289\) 95.4831 0.330391
\(290\) 0 0
\(291\) 118.740i 0.408040i
\(292\) −69.9269 147.860i −0.239476 0.506371i
\(293\) 6.55421i 0.0223693i 0.999937 + 0.0111847i \(0.00356026\pi\)
−0.999937 + 0.0111847i \(0.996440\pi\)
\(294\) 30.1154 6.76214i 0.102433 0.0230005i
\(295\) 0 0
\(296\) 331.387 + 424.674i 1.11955 + 1.43471i
\(297\) 48.2184i 0.162351i
\(298\) −217.921 + 48.9321i −0.731278 + 0.164202i
\(299\) 625.997i 2.09364i
\(300\) 0 0
\(301\) −318.443 −1.05795
\(302\) 2.82741 + 12.5920i 0.00936229 + 0.0416953i
\(303\) −75.1622 −0.248060
\(304\) −213.300 175.074i −0.701646 0.575900i
\(305\) 0 0
\(306\) −18.2863 81.4384i −0.0597590 0.266139i
\(307\) −354.559 −1.15492 −0.577458 0.816420i \(-0.695955\pi\)
−0.577458 + 0.816420i \(0.695955\pi\)
\(308\) 100.478 + 212.460i 0.326228 + 0.689807i
\(309\) 148.596 0.480893
\(310\) 0 0
\(311\) 193.387i 0.621823i 0.950439 + 0.310912i \(0.100634\pi\)
−0.950439 + 0.310912i \(0.899366\pi\)
\(312\) 158.276 + 202.831i 0.507294 + 0.650101i
\(313\) 23.5224i 0.0751514i 0.999294 + 0.0375757i \(0.0119635\pi\)
−0.999294 + 0.0375757i \(0.988036\pi\)
\(314\) 33.2605 + 148.127i 0.105925 + 0.471742i
\(315\) 0 0
\(316\) 241.653 + 510.973i 0.764724 + 1.61700i
\(317\) 214.004i 0.675092i −0.941309 0.337546i \(-0.890403\pi\)
0.941309 0.337546i \(-0.109597\pi\)
\(318\) 61.9344 + 275.827i 0.194762 + 0.867380i
\(319\) 265.562i 0.832481i
\(320\) 0 0
\(321\) −317.095 −0.987836
\(322\) −416.570 + 93.5369i −1.29369 + 0.290487i
\(323\) 239.921 0.742790
\(324\) 32.5441 15.3910i 0.100445 0.0475029i
\(325\) 0 0
\(326\) −486.483 + 109.235i −1.49228 + 0.335078i
\(327\) −141.127 −0.431582
\(328\) 278.007 216.938i 0.847583 0.661395i
\(329\) −197.291 −0.599669
\(330\) 0 0
\(331\) 412.454i 1.24609i −0.782188 0.623043i \(-0.785896\pi\)
0.782188 0.623043i \(-0.214104\pi\)
\(332\) 252.579 119.451i 0.760782 0.359793i
\(333\) 202.001i 0.606610i
\(334\) −154.529 + 34.6981i −0.462662 + 0.103886i
\(335\) 0 0
\(336\) −111.324 + 135.632i −0.331323 + 0.403666i
\(337\) 103.268i 0.306433i 0.988193 + 0.153216i \(0.0489631\pi\)
−0.988193 + 0.153216i \(0.951037\pi\)
\(338\) 342.958 77.0081i 1.01467 0.227835i
\(339\) 299.323i 0.882958i
\(340\) 0 0
\(341\) −218.014 −0.639338
\(342\) 22.6712 + 100.967i 0.0662900 + 0.295225i
\(343\) 366.667 1.06900
\(344\) −317.203 + 247.523i −0.922102 + 0.719545i
\(345\) 0 0
\(346\) −12.1463 54.0939i −0.0351049 0.156341i
\(347\) 153.211 0.441531 0.220766 0.975327i \(-0.429144\pi\)
0.220766 + 0.975327i \(0.429144\pi\)
\(348\) 179.236 84.7654i 0.515046 0.243579i
\(349\) 84.7317 0.242784 0.121392 0.992605i \(-0.461264\pi\)
0.121392 + 0.992605i \(0.461264\pi\)
\(350\) 0 0
\(351\) 96.4791i 0.274869i
\(352\) 265.231 + 133.532i 0.753496 + 0.379353i
\(353\) 256.065i 0.725396i −0.931907 0.362698i \(-0.881856\pi\)
0.931907 0.362698i \(-0.118144\pi\)
\(354\) −14.6286 65.1489i −0.0413237 0.184036i
\(355\) 0 0
\(356\) 167.450 79.1914i 0.470365 0.222448i
\(357\) 152.559i 0.427336i
\(358\) 89.5289 + 398.720i 0.250081 + 1.11374i
\(359\) 667.258i 1.85866i −0.369253 0.929329i \(-0.620386\pi\)
0.369253 0.929329i \(-0.379614\pi\)
\(360\) 0 0
\(361\) 63.5473 0.176031
\(362\) 97.2314 21.8324i 0.268595 0.0603106i
\(363\) 60.4287 0.166470
\(364\) 201.044 + 425.108i 0.552320 + 1.16788i
\(365\) 0 0
\(366\) 179.665 40.3422i 0.490889 0.110225i
\(367\) 245.301 0.668396 0.334198 0.942503i \(-0.391535\pi\)
0.334198 + 0.942503i \(0.391535\pi\)
\(368\) −342.242 + 416.969i −0.930005 + 1.13307i
\(369\) −132.237 −0.358367
\(370\) 0 0
\(371\) 516.708i 1.39274i
\(372\) −69.5886 147.145i −0.187066 0.395550i
\(373\) 698.787i 1.87342i −0.350101 0.936712i \(-0.613853\pi\)
0.350101 0.936712i \(-0.386147\pi\)
\(374\) −251.906 + 56.5632i −0.673546 + 0.151239i
\(375\) 0 0
\(376\) −196.523 + 153.353i −0.522667 + 0.407853i
\(377\) 531.357i 1.40943i
\(378\) 64.2020 14.4160i 0.169847 0.0381375i
\(379\) 208.691i 0.550636i 0.961353 + 0.275318i \(0.0887831\pi\)
−0.961353 + 0.275318i \(0.911217\pi\)
\(380\) 0 0
\(381\) 38.7606 0.101734
\(382\) 0.498212 + 2.21880i 0.00130422 + 0.00580839i
\(383\) 156.524 0.408680 0.204340 0.978900i \(-0.434495\pi\)
0.204340 + 0.978900i \(0.434495\pi\)
\(384\) −5.46541 + 221.635i −0.0142328 + 0.577175i
\(385\) 0 0
\(386\) −33.5838 149.566i −0.0870046 0.387478i
\(387\) 150.881 0.389874
\(388\) 117.235 + 247.893i 0.302152 + 0.638900i
\(389\) −386.588 −0.993801 −0.496900 0.867808i \(-0.665529\pi\)
−0.496900 + 0.867808i \(0.665529\pi\)
\(390\) 0 0
\(391\) 469.008i 1.19951i
\(392\) 56.1956 43.8512i 0.143356 0.111865i
\(393\) 3.03655i 0.00772658i
\(394\) −58.9322 262.456i −0.149574 0.666133i
\(395\) 0 0
\(396\) −47.6074 100.666i −0.120221 0.254206i
\(397\) 561.155i 1.41349i −0.707470 0.706744i \(-0.750163\pi\)
0.707470 0.706744i \(-0.249837\pi\)
\(398\) 77.1242 + 343.475i 0.193779 + 0.863002i
\(399\) 189.142i 0.474039i
\(400\) 0 0
\(401\) 16.9333 0.0422276 0.0211138 0.999777i \(-0.493279\pi\)
0.0211138 + 0.999777i \(0.493279\pi\)
\(402\) −15.2067 + 3.41453i −0.0378277 + 0.00849387i
\(403\) −436.220 −1.08243
\(404\) −156.917 + 74.2099i −0.388407 + 0.183688i
\(405\) 0 0
\(406\) 353.591 79.3957i 0.870914 0.195556i
\(407\) −624.832 −1.53521
\(408\) −118.583 151.965i −0.290644 0.372463i
\(409\) −258.490 −0.632006 −0.316003 0.948758i \(-0.602341\pi\)
−0.316003 + 0.948758i \(0.602341\pi\)
\(410\) 0 0
\(411\) 33.7896i 0.0822132i
\(412\) 310.224 146.713i 0.752972 0.356100i
\(413\) 122.044i 0.295505i
\(414\) 197.374 44.3186i 0.476750 0.107050i
\(415\) 0 0
\(416\) 530.694 + 267.182i 1.27571 + 0.642264i
\(417\) 445.777i 1.06901i
\(418\) 312.312 70.1267i 0.747157 0.167767i
\(419\) 258.917i 0.617941i 0.951072 + 0.308970i \(0.0999844\pi\)
−0.951072 + 0.308970i \(0.900016\pi\)
\(420\) 0 0
\(421\) 97.4654 0.231509 0.115755 0.993278i \(-0.463071\pi\)
0.115755 + 0.993278i \(0.463071\pi\)
\(422\) −95.5594 425.577i −0.226444 1.00848i
\(423\) 93.4783 0.220989
\(424\) 401.633 + 514.696i 0.947248 + 1.21390i
\(425\) 0 0
\(426\) 10.1212 + 45.0751i 0.0237587 + 0.105810i
\(427\) 336.568 0.788215
\(428\) −662.002 + 313.078i −1.54673 + 0.731490i
\(429\) −298.430 −0.695641
\(430\) 0 0
\(431\) 389.968i 0.904799i −0.891815 0.452399i \(-0.850568\pi\)
0.891815 0.452399i \(-0.149432\pi\)
\(432\) 52.7465 64.2635i 0.122098 0.148758i
\(433\) 275.893i 0.637166i −0.947895 0.318583i \(-0.896793\pi\)
0.947895 0.318583i \(-0.103207\pi\)
\(434\) −65.1803 290.283i −0.150185 0.668854i
\(435\) 0 0
\(436\) −294.632 + 139.339i −0.675761 + 0.319585i
\(437\) 581.473i 1.33060i
\(438\) 31.0332 + 138.207i 0.0708520 + 0.315542i
\(439\) 446.143i 1.01627i −0.861277 0.508136i \(-0.830335\pi\)
0.861277 0.508136i \(-0.169665\pi\)
\(440\) 0 0
\(441\) −26.7301 −0.0606125
\(442\) −504.034 + 113.176i −1.14035 + 0.256055i
\(443\) 794.679 1.79386 0.896929 0.442174i \(-0.145793\pi\)
0.896929 + 0.442174i \(0.145793\pi\)
\(444\) −199.442 421.719i −0.449194 0.949818i
\(445\) 0 0
\(446\) 641.193 143.974i 1.43765 0.322812i
\(447\) 193.424 0.432716
\(448\) −98.4993 + 393.073i −0.219865 + 0.877395i
\(449\) 750.226 1.67088 0.835441 0.549581i \(-0.185212\pi\)
0.835441 + 0.549581i \(0.185212\pi\)
\(450\) 0 0
\(451\) 409.037i 0.906957i
\(452\) 295.530 + 624.898i 0.653828 + 1.38252i
\(453\) 11.1765i 0.0246722i
\(454\) −307.639 + 69.0775i −0.677619 + 0.152153i
\(455\) 0 0
\(456\) 147.018 + 188.405i 0.322409 + 0.413169i
\(457\) 101.092i 0.221209i 0.993865 + 0.110604i \(0.0352787\pi\)
−0.993865 + 0.110604i \(0.964721\pi\)
\(458\) −533.024 + 119.686i −1.16381 + 0.261323i
\(459\) 72.2839i 0.157481i
\(460\) 0 0
\(461\) −4.48690 −0.00973297 −0.00486648 0.999988i \(-0.501549\pi\)
−0.00486648 + 0.999988i \(0.501549\pi\)
\(462\) −44.5916 198.590i −0.0965186 0.429849i
\(463\) −515.108 −1.11254 −0.556272 0.831000i \(-0.687769\pi\)
−0.556272 + 0.831000i \(0.687769\pi\)
\(464\) 290.500 353.930i 0.626079 0.762780i
\(465\) 0 0
\(466\) 47.6493 + 212.208i 0.102252 + 0.455382i
\(467\) −295.498 −0.632758 −0.316379 0.948633i \(-0.602467\pi\)
−0.316379 + 0.948633i \(0.602467\pi\)
\(468\) −95.2567 201.420i −0.203540 0.430384i
\(469\) −28.4869 −0.0607396
\(470\) 0 0
\(471\) 131.476i 0.279142i
\(472\) −94.8637 121.568i −0.200982 0.257560i
\(473\) 466.707i 0.986696i
\(474\) −107.244 477.615i −0.226253 1.00763i
\(475\) 0 0
\(476\) −150.626 318.498i −0.316441 0.669114i
\(477\) 244.821i 0.513251i
\(478\) 78.4299 + 349.290i 0.164079 + 0.730732i
\(479\) 273.155i 0.570260i 0.958489 + 0.285130i \(0.0920368\pi\)
−0.958489 + 0.285130i \(0.907963\pi\)
\(480\) 0 0
\(481\) −1250.21 −2.59920
\(482\) −699.822 + 157.139i −1.45191 + 0.326014i
\(483\) 369.743 0.765512
\(484\) 126.157 59.6631i 0.260656 0.123271i
\(485\) 0 0
\(486\) −30.4195 + 6.83042i −0.0625915 + 0.0140544i
\(487\) 357.751 0.734601 0.367301 0.930102i \(-0.380282\pi\)
0.367301 + 0.930102i \(0.380282\pi\)
\(488\) 335.257 261.612i 0.687002 0.536089i
\(489\) 431.797 0.883021
\(490\) 0 0
\(491\) 422.379i 0.860242i 0.902771 + 0.430121i \(0.141529\pi\)
−0.902771 + 0.430121i \(0.858471\pi\)
\(492\) −276.072 + 130.562i −0.561123 + 0.265370i
\(493\) 398.102i 0.807509i
\(494\) 624.898 140.315i 1.26498 0.284039i
\(495\) 0 0
\(496\) −290.561 238.488i −0.585808 0.480822i
\(497\) 84.4394i 0.169898i
\(498\) −236.090 + 53.0119i −0.474076 + 0.106450i
\(499\) 207.096i 0.415021i −0.978233 0.207511i \(-0.933464\pi\)
0.978233 0.207511i \(-0.0665362\pi\)
\(500\) 0 0
\(501\) 137.158 0.273769
\(502\) 134.177 + 597.562i 0.267285 + 1.19036i
\(503\) −702.853 −1.39732 −0.698661 0.715452i \(-0.746221\pi\)
−0.698661 + 0.715452i \(0.746221\pi\)
\(504\) 119.802 93.4849i 0.237701 0.185486i
\(505\) 0 0
\(506\) −137.087 610.520i −0.270923 1.20656i
\(507\) −304.406 −0.600406
\(508\) 80.9207 38.2695i 0.159293 0.0753337i
\(509\) 389.029 0.764300 0.382150 0.924100i \(-0.375184\pi\)
0.382150 + 0.924100i \(0.375184\pi\)
\(510\) 0 0
\(511\) 258.904i 0.506662i
\(512\) 207.417 + 468.105i 0.405111 + 0.914267i
\(513\) 89.6171i 0.174692i
\(514\) 110.008 + 489.925i 0.214024 + 0.953162i
\(515\) 0 0
\(516\) 314.996 148.970i 0.610457 0.288701i
\(517\) 289.148i 0.559280i
\(518\) −186.808 831.954i −0.360633 1.60609i
\(519\) 48.0132i 0.0925109i
\(520\) 0 0
\(521\) −151.753 −0.291273 −0.145637 0.989338i \(-0.546523\pi\)
−0.145637 + 0.989338i \(0.546523\pi\)
\(522\) −167.535 + 37.6184i −0.320948 + 0.0720659i
\(523\) −557.762 −1.06647 −0.533234 0.845968i \(-0.679023\pi\)
−0.533234 + 0.845968i \(0.679023\pi\)
\(524\) 2.99807 + 6.33941i 0.00572151 + 0.0120981i
\(525\) 0 0
\(526\) 95.1596 21.3672i 0.180912 0.0406221i
\(527\) 326.824 0.620159
\(528\) −198.781 163.156i −0.376478 0.309008i
\(529\) 607.689 1.14875
\(530\) 0 0
\(531\) 57.8254i 0.108899i
\(532\) 186.745 + 394.872i 0.351025 + 0.742241i
\(533\) 818.435i 1.53552i
\(534\) −156.518 + 35.1447i −0.293105 + 0.0658141i
\(535\) 0 0
\(536\) −28.3759 + 22.1426i −0.0529401 + 0.0413108i
\(537\) 353.899i 0.659030i
\(538\) 290.166 65.1542i 0.539342 0.121104i
\(539\) 82.6818i 0.153398i
\(540\) 0 0
\(541\) 340.979 0.630275 0.315137 0.949046i \(-0.397949\pi\)
0.315137 + 0.949046i \(0.397949\pi\)
\(542\) −36.5179 162.633i −0.0673761 0.300062i
\(543\) −86.3015 −0.158935
\(544\) −397.606 200.177i −0.730893 0.367973i
\(545\) 0 0
\(546\) −89.2224 397.355i −0.163411 0.727756i
\(547\) −113.651 −0.207771 −0.103885 0.994589i \(-0.533128\pi\)
−0.103885 + 0.994589i \(0.533128\pi\)
\(548\) −33.3615 70.5428i −0.0608787 0.128728i
\(549\) −159.469 −0.290472
\(550\) 0 0
\(551\) 493.564i 0.895761i
\(552\) 368.303 287.398i 0.667215 0.520649i
\(553\) 894.718i 1.61794i
\(554\) −63.1319 281.160i −0.113957 0.507509i
\(555\) 0 0
\(556\) 440.129 + 930.651i 0.791599 + 1.67383i
\(557\) 233.232i 0.418728i 0.977838 + 0.209364i \(0.0671394\pi\)
−0.977838 + 0.209364i \(0.932861\pi\)
\(558\) 30.8830 + 137.539i 0.0553459 + 0.246485i
\(559\) 933.825i 1.67053i
\(560\) 0 0
\(561\) 223.589 0.398554
\(562\) 670.644 150.587i 1.19332 0.267948i
\(563\) 167.786 0.298021 0.149011 0.988836i \(-0.452391\pi\)
0.149011 + 0.988836i \(0.452391\pi\)
\(564\) 195.155 92.2939i 0.346020 0.163642i
\(565\) 0 0
\(566\) −614.607 + 138.004i −1.08588 + 0.243824i
\(567\) −56.9850 −0.100503
\(568\) 65.6341 + 84.1105i 0.115553 + 0.148082i
\(569\) −381.089 −0.669752 −0.334876 0.942262i \(-0.608694\pi\)
−0.334876 + 0.942262i \(0.608694\pi\)
\(570\) 0 0
\(571\) 453.871i 0.794870i −0.917630 0.397435i \(-0.869900\pi\)
0.917630 0.397435i \(-0.130100\pi\)
\(572\) −623.034 + 294.649i −1.08922 + 0.515120i
\(573\) 1.96939i 0.00343697i
\(574\) −544.627 + 122.291i −0.948828 + 0.213051i
\(575\) 0 0
\(576\) 46.6699 186.242i 0.0810241 0.323336i
\(577\) 688.294i 1.19288i 0.802656 + 0.596442i \(0.203419\pi\)
−0.802656 + 0.596442i \(0.796581\pi\)
\(578\) −186.327 + 41.8380i −0.322365 + 0.0723841i
\(579\) 132.753i 0.229281i
\(580\) 0 0
\(581\) −442.269 −0.761220
\(582\) −52.0283 231.710i −0.0893957 0.398127i
\(583\) −757.282 −1.29894
\(584\) 201.244 + 257.896i 0.344597 + 0.441603i
\(585\) 0 0
\(586\) −2.87187 12.7900i −0.00490080 0.0218259i
\(587\) 249.163 0.424468 0.212234 0.977219i \(-0.431926\pi\)
0.212234 + 0.977219i \(0.431926\pi\)
\(588\) −55.8046 + 26.3914i −0.0949057 + 0.0448834i
\(589\) −405.194 −0.687936
\(590\) 0 0
\(591\) 232.953i 0.394168i
\(592\) −832.752 683.510i −1.40668 1.15458i
\(593\) 163.937i 0.276454i 0.990401 + 0.138227i \(0.0441404\pi\)
−0.990401 + 0.138227i \(0.955860\pi\)
\(594\) 21.1279 + 94.0938i 0.0355689 + 0.158407i
\(595\) 0 0
\(596\) 403.812 190.973i 0.677538 0.320425i
\(597\) 304.865i 0.510661i
\(598\) −274.294 1221.58i −0.458686 2.04277i
\(599\) 170.412i 0.284494i 0.989831 + 0.142247i \(0.0454327\pi\)
−0.989831 + 0.142247i \(0.954567\pi\)
\(600\) 0 0
\(601\) 1119.87 1.86335 0.931674 0.363295i \(-0.118348\pi\)
0.931674 + 0.363295i \(0.118348\pi\)
\(602\) 621.413 139.533i 1.03225 0.231782i
\(603\) 13.4973 0.0223836
\(604\) −11.0349 23.3332i −0.0182697 0.0386312i
\(605\) 0 0
\(606\) 146.672 32.9339i 0.242034 0.0543464i
\(607\) 660.957 1.08889 0.544445 0.838796i \(-0.316740\pi\)
0.544445 + 0.838796i \(0.316740\pi\)
\(608\) 492.949 + 248.179i 0.810772 + 0.408189i
\(609\) −313.844 −0.515342
\(610\) 0 0
\(611\) 578.550i 0.946890i
\(612\) 71.3680 + 150.907i 0.116614 + 0.246581i
\(613\) 179.315i 0.292520i 0.989246 + 0.146260i \(0.0467236\pi\)
−0.989246 + 0.146260i \(0.953276\pi\)
\(614\) 691.891 155.358i 1.12686 0.253026i
\(615\) 0 0
\(616\) −289.168 370.571i −0.469429 0.601576i
\(617\) 63.6752i 0.103201i −0.998668 0.0516007i \(-0.983568\pi\)
0.998668 0.0516007i \(-0.0164323\pi\)
\(618\) −289.972 + 65.1105i −0.469210 + 0.105357i
\(619\) 872.350i 1.40929i −0.709561 0.704644i \(-0.751107\pi\)
0.709561 0.704644i \(-0.248893\pi\)
\(620\) 0 0
\(621\) −175.187 −0.282105
\(622\) −84.7367 377.378i −0.136233 0.606716i
\(623\) −293.206 −0.470636
\(624\) −397.736 326.456i −0.637397 0.523166i
\(625\) 0 0
\(626\) −10.3068 45.9019i −0.0164646 0.0733257i
\(627\) −277.204 −0.442112
\(628\) −129.810 274.483i −0.206704 0.437074i
\(629\) 936.682 1.48916
\(630\) 0 0
\(631\) 340.783i 0.540068i −0.962851 0.270034i \(-0.912965\pi\)
0.962851 0.270034i \(-0.0870349\pi\)
\(632\) −695.458 891.234i −1.10041 1.41018i
\(633\) 377.737i 0.596742i
\(634\) 93.7705 + 417.610i 0.147903 + 0.658691i
\(635\) 0 0
\(636\) −241.719 511.114i −0.380061 0.803638i
\(637\) 165.436i 0.259712i
\(638\) 116.362 + 518.220i 0.182385 + 0.812257i
\(639\) 40.0081i 0.0626105i
\(640\) 0 0
\(641\) 766.210 1.19534 0.597668 0.801744i \(-0.296094\pi\)
0.597668 + 0.801744i \(0.296094\pi\)
\(642\) 618.783 138.942i 0.963837 0.216421i
\(643\) 1163.47 1.80943 0.904717 0.426014i \(-0.140083\pi\)
0.904717 + 0.426014i \(0.140083\pi\)
\(644\) 771.913 365.058i 1.19862 0.566860i
\(645\) 0 0
\(646\) −468.185 + 105.127i −0.724744 + 0.162735i
\(647\) −740.530 −1.14456 −0.572279 0.820059i \(-0.693941\pi\)
−0.572279 + 0.820059i \(0.693941\pi\)
\(648\) −56.7630 + 44.2940i −0.0875973 + 0.0683549i
\(649\) 178.866 0.275603
\(650\) 0 0
\(651\) 257.652i 0.395778i
\(652\) 901.465 426.326i 1.38262 0.653875i
\(653\) 109.569i 0.167793i −0.996474 0.0838967i \(-0.973263\pi\)
0.996474 0.0838967i \(-0.0267366\pi\)
\(654\) 275.397 61.8379i 0.421097 0.0945534i
\(655\) 0 0
\(656\) −447.450 + 545.149i −0.682089 + 0.831020i
\(657\) 122.671i 0.186714i
\(658\) 384.996 86.4473i 0.585100 0.131379i
\(659\) 723.214i 1.09744i 0.836006 + 0.548721i \(0.184885\pi\)
−0.836006 + 0.548721i \(0.815115\pi\)
\(660\) 0 0
\(661\) 700.333 1.05951 0.529753 0.848152i \(-0.322285\pi\)
0.529753 + 0.848152i \(0.322285\pi\)
\(662\) 180.726 + 804.868i 0.273000 + 1.21581i
\(663\) 447.375 0.674773
\(664\) −440.546 + 343.772i −0.663473 + 0.517729i
\(665\) 0 0
\(666\) 88.5112 + 394.188i 0.132900 + 0.591873i
\(667\) −964.841 −1.44654
\(668\) 286.346 135.420i 0.428662 0.202725i
\(669\) −569.116 −0.850696
\(670\) 0 0
\(671\) 493.271i 0.735128i
\(672\) 157.810 313.452i 0.234836 0.466447i
\(673\) 1221.18i 1.81454i 0.420552 + 0.907269i \(0.361837\pi\)
−0.420552 + 0.907269i \(0.638163\pi\)
\(674\) −45.2490 201.518i −0.0671350 0.298988i
\(675\) 0 0
\(676\) −635.509 + 300.549i −0.940103 + 0.444599i
\(677\) 989.373i 1.46141i 0.682695 + 0.730704i \(0.260808\pi\)
−0.682695 + 0.730704i \(0.739192\pi\)
\(678\) −131.155 584.102i −0.193444 0.861507i
\(679\) 434.063i 0.639268i
\(680\) 0 0
\(681\) 273.057 0.400965
\(682\) 425.435 95.5276i 0.623806 0.140070i
\(683\) 307.312 0.449945 0.224972 0.974365i \(-0.427771\pi\)
0.224972 + 0.974365i \(0.427771\pi\)
\(684\) −88.4816 187.094i −0.129359 0.273529i
\(685\) 0 0
\(686\) −715.518 + 160.663i −1.04303 + 0.234203i
\(687\) 473.107 0.688656
\(688\) 510.536 622.009i 0.742058 0.904083i
\(689\) −1515.23 −2.19917
\(690\) 0 0
\(691\) 893.378i 1.29288i 0.762966 + 0.646438i \(0.223742\pi\)
−0.762966 + 0.646438i \(0.776258\pi\)
\(692\) 47.4048 + 100.237i 0.0685041 + 0.144852i
\(693\) 176.266i 0.254353i
\(694\) −298.978 + 67.1329i −0.430805 + 0.0967332i
\(695\) 0 0
\(696\) −312.621 + 243.948i −0.449169 + 0.350500i
\(697\) 613.186i 0.879750i
\(698\) −165.346 + 37.1270i −0.236886 + 0.0531906i
\(699\) 188.353i 0.269461i
\(700\) 0 0
\(701\) 1127.42 1.60830 0.804149 0.594428i \(-0.202622\pi\)
0.804149 + 0.594428i \(0.202622\pi\)
\(702\) 42.2744 + 188.270i 0.0602199 + 0.268191i
\(703\) −1161.29 −1.65191
\(704\) −576.084 144.360i −0.818301 0.205056i
\(705\) 0 0
\(706\) 112.200 + 499.688i 0.158924 + 0.707773i
\(707\) 274.762 0.388631
\(708\) 57.0928 + 120.722i 0.0806395 + 0.170512i
\(709\) −1093.27 −1.54199 −0.770997 0.636839i \(-0.780242\pi\)
−0.770997 + 0.636839i \(0.780242\pi\)
\(710\) 0 0
\(711\) 423.926i 0.596239i
\(712\) −292.064 + 227.907i −0.410202 + 0.320094i
\(713\) 792.091i 1.11093i
\(714\) 66.8470 + 297.705i 0.0936233 + 0.416954i
\(715\) 0 0
\(716\) −349.415 738.837i −0.488010 1.03190i
\(717\) 310.026i 0.432393i
\(718\) 292.374 + 1302.10i 0.407206 + 1.81350i
\(719\) 769.690i 1.07050i 0.844693 + 0.535251i \(0.179783\pi\)
−0.844693 + 0.535251i \(0.820217\pi\)
\(720\) 0 0
\(721\) −543.205 −0.753405
\(722\) −124.007 + 27.8446i −0.171755 + 0.0385660i
\(723\) 621.154 0.859134
\(724\) −180.172 + 85.2081i −0.248857 + 0.117691i
\(725\) 0 0
\(726\) −117.921 + 26.4782i −0.162426 + 0.0364713i
\(727\) −295.050 −0.405846 −0.202923 0.979195i \(-0.565044\pi\)
−0.202923 + 0.979195i \(0.565044\pi\)
\(728\) −578.591 741.468i −0.794767 1.01850i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 699.638i 0.957097i
\(732\) −332.924 + 157.448i −0.454814 + 0.215094i
\(733\) 261.200i 0.356344i −0.983999 0.178172i \(-0.942982\pi\)
0.983999 0.178172i \(-0.0570184\pi\)
\(734\) −478.684 + 107.484i −0.652158 + 0.146436i
\(735\) 0 0
\(736\) 485.150 963.638i 0.659172 1.30929i
\(737\) 41.7501i 0.0566487i
\(738\) 258.049 57.9426i 0.349660 0.0785130i
\(739\) 482.679i 0.653151i 0.945171 + 0.326576i \(0.105895\pi\)
−0.945171 + 0.326576i \(0.894105\pi\)
\(740\) 0 0
\(741\) −554.652 −0.748519
\(742\) −226.407 1008.31i −0.305130 1.35891i
\(743\) −23.7067 −0.0319067 −0.0159534 0.999873i \(-0.505078\pi\)
−0.0159534 + 0.999873i \(0.505078\pi\)
\(744\) 200.271 + 256.648i 0.269181 + 0.344957i
\(745\) 0 0
\(746\) 306.189 + 1363.62i 0.410441 + 1.82791i
\(747\) 209.551 0.280523
\(748\) 466.788 220.756i 0.624048 0.295129i
\(749\) 1159.17 1.54762
\(750\) 0 0
\(751\) 395.508i 0.526642i −0.964708 0.263321i \(-0.915182\pi\)
0.964708 0.263321i \(-0.0848179\pi\)
\(752\) 316.302 385.365i 0.420614 0.512453i
\(753\) 530.389i 0.704368i
\(754\) 232.825 + 1036.90i 0.308787 + 1.37519i
\(755\) 0 0
\(756\) −118.968 + 56.2630i −0.157365 + 0.0744219i
\(757\) 393.940i 0.520396i 0.965555 + 0.260198i \(0.0837879\pi\)
−0.965555 + 0.260198i \(0.916212\pi\)
\(758\) −91.4425 407.242i −0.120637 0.537259i
\(759\) 541.891i 0.713954i
\(760\) 0 0
\(761\) −369.354 −0.485354 −0.242677 0.970107i \(-0.578025\pi\)
−0.242677 + 0.970107i \(0.578025\pi\)
\(762\) −75.6379 + 16.9838i −0.0992623 + 0.0222885i
\(763\) 515.903 0.676150
\(764\) −1.94443 4.11150i −0.00254507 0.00538154i
\(765\) 0 0
\(766\) −305.444 + 68.5846i −0.398751 + 0.0895360i
\(767\) 357.890 0.466610
\(768\) −86.4490 434.896i −0.112564 0.566271i
\(769\) 873.491 1.13588 0.567940 0.823070i \(-0.307741\pi\)
0.567940 + 0.823070i \(0.307741\pi\)
\(770\) 0 0
\(771\) 434.852i 0.564010i
\(772\) 131.071 + 277.150i 0.169782 + 0.359003i
\(773\) 1176.93i 1.52254i 0.648432 + 0.761272i \(0.275425\pi\)
−0.648432 + 0.761272i \(0.724575\pi\)
\(774\) −294.431 + 66.1119i −0.380402 + 0.0854159i
\(775\) 0 0
\(776\) −337.394 432.372i −0.434786 0.557181i
\(777\) 738.433i 0.950365i
\(778\) 754.393 169.392i 0.969657 0.217728i
\(779\) 760.224i 0.975897i
\(780\) 0 0
\(781\) −123.754 −0.158455
\(782\) 205.506 + 915.228i 0.262795 + 1.17037i
\(783\) 148.702 0.189913
\(784\) −90.4464 + 110.195i −0.115365 + 0.140555i
\(785\) 0 0
\(786\) −1.33053 5.92555i −0.00169278 0.00753887i
\(787\) 603.482 0.766814 0.