Properties

Label 300.3.c.d.151.5
Level $300$
Weight $3$
Character 300.151
Analytic conductor $8.174$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.85100625.1
Defining polynomial: \(x^{8} - x^{7} - 2 x^{6} + x^{5} + 3 x^{4} + 2 x^{3} - 8 x^{2} - 8 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.5
Root \(1.40906 - 0.120653i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.d.151.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.438172 - 1.95141i) q^{2} -1.73205i q^{3} +(-3.61601 + 1.71011i) q^{4} +(-3.37994 + 0.758935i) q^{6} -6.33166i q^{7} +(4.92155 + 6.30701i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-0.438172 - 1.95141i) q^{2} -1.73205i q^{3} +(-3.61601 + 1.71011i) q^{4} +(-3.37994 + 0.758935i) q^{6} -6.33166i q^{7} +(4.92155 + 6.30701i) q^{8} -3.00000 q^{9} -9.27963i q^{11} +(2.96199 + 6.26312i) q^{12} -18.5674 q^{13} +(-12.3557 + 2.77436i) q^{14} +(10.1511 - 12.3675i) q^{16} -13.9110 q^{17} +(1.31451 + 5.85423i) q^{18} +17.2468i q^{19} -10.9668 q^{21} +(-18.1084 + 4.06607i) q^{22} +33.7148i q^{23} +(10.9241 - 8.52438i) q^{24} +(8.13571 + 36.2327i) q^{26} +5.19615i q^{27} +(10.8278 + 22.8954i) q^{28} -28.6177 q^{29} -23.4939i q^{31} +(-28.5820 - 14.3898i) q^{32} -16.0728 q^{33} +(6.09542 + 27.1461i) q^{34} +(10.8480 - 5.13032i) q^{36} +67.3338 q^{37} +(33.6556 - 7.55706i) q^{38} +32.1597i q^{39} -44.0791 q^{41} +(4.80532 + 21.4007i) q^{42} -50.2937i q^{43} +(15.8691 + 33.5552i) q^{44} +(65.7915 - 14.7729i) q^{46} +31.1594i q^{47} +(-21.4212 - 17.5822i) q^{48} +8.91003 q^{49} +24.0946i q^{51} +(67.1400 - 31.7522i) q^{52} -81.6070 q^{53} +(10.1398 - 2.27681i) q^{54} +(39.9338 - 31.1616i) q^{56} +29.8724 q^{57} +(12.5395 + 55.8449i) q^{58} -19.2751i q^{59} -53.1563 q^{61} +(-45.8462 + 10.2943i) q^{62} +18.9950i q^{63} +(-15.5566 + 62.0805i) q^{64} +(7.04264 + 31.3646i) q^{66} +4.49911i q^{67} +(50.3025 - 23.7893i) q^{68} +58.3958 q^{69} -13.3360i q^{71} +(-14.7647 - 18.9210i) q^{72} -40.8904 q^{73} +(-29.5037 - 131.396i) q^{74} +(-29.4939 - 62.3647i) q^{76} -58.7555 q^{77} +(62.7568 - 14.0915i) q^{78} -141.309i q^{79} +9.00000 q^{81} +(19.3142 + 86.0164i) q^{82} -69.8503i q^{83} +(39.6559 - 18.7543i) q^{84} +(-98.1438 + 22.0373i) q^{86} +49.5673i q^{87} +(58.5266 - 45.6702i) q^{88} -46.3079 q^{89} +117.563i q^{91} +(-57.6559 - 121.913i) q^{92} -40.6926 q^{93} +(60.8049 - 13.6532i) q^{94} +(-24.9239 + 49.5055i) q^{96} -68.5543 q^{97} +(-3.90412 - 17.3871i) q^{98} +27.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} + 10q^{4} - 6q^{6} + 20q^{8} - 24q^{9} + O(q^{10}) \) \( 8q - 4q^{2} + 10q^{4} - 6q^{6} + 20q^{8} - 24q^{9} - 16q^{13} - 20q^{14} + 34q^{16} + 12q^{18} - 48q^{21} - 68q^{22} + 18q^{24} - 36q^{26} - 28q^{28} + 64q^{29} + 76q^{32} - 92q^{34} - 30q^{36} + 112q^{37} + 40q^{38} - 16q^{41} - 108q^{42} + 172q^{44} + 152q^{46} - 48q^{48} - 56q^{49} + 128q^{52} - 352q^{53} + 18q^{54} + 116q^{56} - 144q^{57} + 204q^{58} - 176q^{61} + 56q^{62} - 110q^{64} + 108q^{66} + 184q^{68} - 96q^{69} - 60q^{72} + 240q^{73} + 132q^{74} - 24q^{76} + 288q^{77} + 240q^{78} + 72q^{81} - 40q^{82} - 36q^{84} - 200q^{86} - 140q^{88} + 80q^{89} - 144q^{92} - 144q^{93} - 96q^{94} - 174q^{96} - 432q^{97} - 660q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.438172 1.95141i −0.219086 0.975706i
\(3\) 1.73205i 0.577350i
\(4\) −3.61601 + 1.71011i −0.904003 + 0.427526i
\(5\) 0 0
\(6\) −3.37994 + 0.758935i −0.563324 + 0.126489i
\(7\) 6.33166i 0.904523i −0.891885 0.452262i \(-0.850617\pi\)
0.891885 0.452262i \(-0.149383\pi\)
\(8\) 4.92155 + 6.30701i 0.615194 + 0.788376i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 9.27963i 0.843602i −0.906688 0.421801i \(-0.861398\pi\)
0.906688 0.421801i \(-0.138602\pi\)
\(12\) 2.96199 + 6.26312i 0.246833 + 0.521926i
\(13\) −18.5674 −1.42826 −0.714131 0.700012i \(-0.753178\pi\)
−0.714131 + 0.700012i \(0.753178\pi\)
\(14\) −12.3557 + 2.77436i −0.882549 + 0.198168i
\(15\) 0 0
\(16\) 10.1511 12.3675i 0.634442 0.772970i
\(17\) −13.9110 −0.818296 −0.409148 0.912468i \(-0.634174\pi\)
−0.409148 + 0.912468i \(0.634174\pi\)
\(18\) 1.31451 + 5.85423i 0.0730286 + 0.325235i
\(19\) 17.2468i 0.907727i 0.891071 + 0.453864i \(0.149955\pi\)
−0.891071 + 0.453864i \(0.850045\pi\)
\(20\) 0 0
\(21\) −10.9668 −0.522227
\(22\) −18.1084 + 4.06607i −0.823108 + 0.184821i
\(23\) 33.7148i 1.46586i 0.680303 + 0.732931i \(0.261848\pi\)
−0.680303 + 0.732931i \(0.738152\pi\)
\(24\) 10.9241 8.52438i 0.455169 0.355183i
\(25\) 0 0
\(26\) 8.13571 + 36.2327i 0.312912 + 1.39356i
\(27\) 5.19615i 0.192450i
\(28\) 10.8278 + 22.8954i 0.386708 + 0.817692i
\(29\) −28.6177 −0.986817 −0.493409 0.869798i \(-0.664249\pi\)
−0.493409 + 0.869798i \(0.664249\pi\)
\(30\) 0 0
\(31\) 23.4939i 0.757866i −0.925424 0.378933i \(-0.876291\pi\)
0.925424 0.378933i \(-0.123709\pi\)
\(32\) −28.5820 14.3898i −0.893189 0.449682i
\(33\) −16.0728 −0.487054
\(34\) 6.09542 + 27.1461i 0.179277 + 0.798416i
\(35\) 0 0
\(36\) 10.8480 5.13032i 0.301334 0.142509i
\(37\) 67.3338 1.81983 0.909916 0.414793i \(-0.136146\pi\)
0.909916 + 0.414793i \(0.136146\pi\)
\(38\) 33.6556 7.55706i 0.885674 0.198870i
\(39\) 32.1597i 0.824608i
\(40\) 0 0
\(41\) −44.0791 −1.07510 −0.537550 0.843232i \(-0.680650\pi\)
−0.537550 + 0.843232i \(0.680650\pi\)
\(42\) 4.80532 + 21.4007i 0.114412 + 0.509540i
\(43\) 50.2937i 1.16962i −0.811170 0.584811i \(-0.801169\pi\)
0.811170 0.584811i \(-0.198831\pi\)
\(44\) 15.8691 + 33.5552i 0.360662 + 0.762619i
\(45\) 0 0
\(46\) 65.7915 14.7729i 1.43025 0.321150i
\(47\) 31.1594i 0.662967i 0.943461 + 0.331483i \(0.107549\pi\)
−0.943461 + 0.331483i \(0.892451\pi\)
\(48\) −21.4212 17.5822i −0.446275 0.366295i
\(49\) 8.91003 0.181837
\(50\) 0 0
\(51\) 24.0946i 0.472444i
\(52\) 67.1400 31.7522i 1.29115 0.610620i
\(53\) −81.6070 −1.53975 −0.769877 0.638192i \(-0.779682\pi\)
−0.769877 + 0.638192i \(0.779682\pi\)
\(54\) 10.1398 2.27681i 0.187775 0.0421631i
\(55\) 0 0
\(56\) 39.9338 31.1616i 0.713104 0.556457i
\(57\) 29.8724 0.524077
\(58\) 12.5395 + 55.8449i 0.216198 + 0.962843i
\(59\) 19.2751i 0.326697i −0.986568 0.163349i \(-0.947770\pi\)
0.986568 0.163349i \(-0.0522296\pi\)
\(60\) 0 0
\(61\) −53.1563 −0.871415 −0.435707 0.900088i \(-0.643502\pi\)
−0.435707 + 0.900088i \(0.643502\pi\)
\(62\) −45.8462 + 10.2943i −0.739455 + 0.166038i
\(63\) 18.9950i 0.301508i
\(64\) −15.5566 + 62.0805i −0.243072 + 0.970008i
\(65\) 0 0
\(66\) 7.04264 + 31.3646i 0.106707 + 0.475221i
\(67\) 4.49911i 0.0671509i 0.999436 + 0.0335754i \(0.0106894\pi\)
−0.999436 + 0.0335754i \(0.989311\pi\)
\(68\) 50.3025 23.7893i 0.739742 0.349843i
\(69\) 58.3958 0.846316
\(70\) 0 0
\(71\) 13.3360i 0.187832i −0.995580 0.0939158i \(-0.970062\pi\)
0.995580 0.0939158i \(-0.0299385\pi\)
\(72\) −14.7647 18.9210i −0.205065 0.262792i
\(73\) −40.8904 −0.560143 −0.280071 0.959979i \(-0.590358\pi\)
−0.280071 + 0.959979i \(0.590358\pi\)
\(74\) −29.5037 131.396i −0.398699 1.77562i
\(75\) 0 0
\(76\) −29.4939 62.3647i −0.388077 0.820588i
\(77\) −58.7555 −0.763058
\(78\) 62.7568 14.0915i 0.804574 0.180660i
\(79\) 141.309i 1.78872i −0.447352 0.894358i \(-0.647633\pi\)
0.447352 0.894358i \(-0.352367\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 19.3142 + 86.0164i 0.235539 + 1.04898i
\(83\) 69.8503i 0.841570i −0.907160 0.420785i \(-0.861755\pi\)
0.907160 0.420785i \(-0.138245\pi\)
\(84\) 39.6559 18.7543i 0.472095 0.223266i
\(85\) 0 0
\(86\) −98.1438 + 22.0373i −1.14121 + 0.256248i
\(87\) 49.5673i 0.569739i
\(88\) 58.5266 45.6702i 0.665076 0.518979i
\(89\) −46.3079 −0.520313 −0.260157 0.965566i \(-0.583774\pi\)
−0.260157 + 0.965566i \(0.583774\pi\)
\(90\) 0 0
\(91\) 117.563i 1.29190i
\(92\) −57.6559 121.913i −0.626695 1.32514i
\(93\) −40.6926 −0.437554
\(94\) 60.8049 13.6532i 0.646860 0.145247i
\(95\) 0 0
\(96\) −24.9239 + 49.5055i −0.259624 + 0.515683i
\(97\) −68.5543 −0.706745 −0.353373 0.935483i \(-0.614965\pi\)
−0.353373 + 0.935483i \(0.614965\pi\)
\(98\) −3.90412 17.3871i −0.0398380 0.177420i
\(99\) 27.8389i 0.281201i
\(100\) 0 0
\(101\) −43.3949 −0.429653 −0.214826 0.976652i \(-0.568919\pi\)
−0.214826 + 0.976652i \(0.568919\pi\)
\(102\) 47.0185 10.5576i 0.460966 0.103506i
\(103\) 85.7919i 0.832931i −0.909152 0.416465i \(-0.863269\pi\)
0.909152 0.416465i \(-0.136731\pi\)
\(104\) −91.3805 117.105i −0.878659 1.12601i
\(105\) 0 0
\(106\) 35.7579 + 159.249i 0.337338 + 1.50235i
\(107\) 183.075i 1.71098i −0.517818 0.855491i \(-0.673255\pi\)
0.517818 0.855491i \(-0.326745\pi\)
\(108\) −8.88597 18.7893i −0.0822775 0.173975i
\(109\) 81.4798 0.747521 0.373761 0.927525i \(-0.378068\pi\)
0.373761 + 0.927525i \(0.378068\pi\)
\(110\) 0 0
\(111\) 116.625i 1.05068i
\(112\) −78.3070 64.2732i −0.699170 0.573868i
\(113\) 172.814 1.52933 0.764664 0.644429i \(-0.222905\pi\)
0.764664 + 0.644429i \(0.222905\pi\)
\(114\) −13.0892 58.2933i −0.114818 0.511344i
\(115\) 0 0
\(116\) 103.482 48.9393i 0.892086 0.421891i
\(117\) 55.7022 0.476087
\(118\) −37.6137 + 8.44582i −0.318760 + 0.0715748i
\(119\) 88.0800i 0.740168i
\(120\) 0 0
\(121\) 34.8885 0.288335
\(122\) 23.2916 + 103.730i 0.190915 + 0.850244i
\(123\) 76.3472i 0.620709i
\(124\) 40.1770 + 84.9541i 0.324008 + 0.685113i
\(125\) 0 0
\(126\) 37.0670 8.32307i 0.294183 0.0660561i
\(127\) 22.3785i 0.176208i 0.996111 + 0.0881041i \(0.0280808\pi\)
−0.996111 + 0.0881041i \(0.971919\pi\)
\(128\) 127.961 + 3.15546i 0.999696 + 0.0246520i
\(129\) −87.1113 −0.675282
\(130\) 0 0
\(131\) 1.75315i 0.0133828i 0.999978 + 0.00669141i \(0.00212996\pi\)
−0.999978 + 0.00669141i \(0.997870\pi\)
\(132\) 58.1194 27.4862i 0.440298 0.208228i
\(133\) 109.201 0.821060
\(134\) 8.77961 1.97138i 0.0655195 0.0147118i
\(135\) 0 0
\(136\) −68.4639 87.7370i −0.503411 0.645125i
\(137\) 19.5084 0.142397 0.0711987 0.997462i \(-0.477318\pi\)
0.0711987 + 0.997462i \(0.477318\pi\)
\(138\) −25.5874 113.954i −0.185416 0.825755i
\(139\) 257.370i 1.85158i −0.378038 0.925790i \(-0.623401\pi\)
0.378038 0.925790i \(-0.376599\pi\)
\(140\) 0 0
\(141\) 53.9697 0.382764
\(142\) −26.0241 + 5.84348i −0.183268 + 0.0411512i
\(143\) 172.299i 1.20489i
\(144\) −30.4532 + 37.1026i −0.211481 + 0.257657i
\(145\) 0 0
\(146\) 17.9170 + 79.7940i 0.122719 + 0.546534i
\(147\) 15.4326i 0.104984i
\(148\) −243.480 + 115.148i −1.64513 + 0.778026i
\(149\) −111.673 −0.749486 −0.374743 0.927129i \(-0.622269\pi\)
−0.374743 + 0.927129i \(0.622269\pi\)
\(150\) 0 0
\(151\) 6.45275i 0.0427335i −0.999772 0.0213667i \(-0.993198\pi\)
0.999772 0.0213667i \(-0.00680176\pi\)
\(152\) −108.776 + 84.8811i −0.715630 + 0.558428i
\(153\) 41.7331 0.272765
\(154\) 25.7450 + 114.656i 0.167175 + 0.744520i
\(155\) 0 0
\(156\) −54.9965 116.290i −0.352542 0.745448i
\(157\) 75.9075 0.483488 0.241744 0.970340i \(-0.422281\pi\)
0.241744 + 0.970340i \(0.422281\pi\)
\(158\) −275.751 + 61.9174i −1.74526 + 0.391882i
\(159\) 141.347i 0.888977i
\(160\) 0 0
\(161\) 213.471 1.32591
\(162\) −3.94354 17.5627i −0.0243429 0.108412i
\(163\) 249.298i 1.52944i −0.644364 0.764719i \(-0.722878\pi\)
0.644364 0.764719i \(-0.277122\pi\)
\(164\) 159.391 75.3799i 0.971893 0.459634i
\(165\) 0 0
\(166\) −136.307 + 30.6064i −0.821124 + 0.184376i
\(167\) 79.1883i 0.474182i 0.971487 + 0.237091i \(0.0761939\pi\)
−0.971487 + 0.237091i \(0.923806\pi\)
\(168\) −53.9735 69.1674i −0.321271 0.411711i
\(169\) 175.749 1.03993
\(170\) 0 0
\(171\) 51.7404i 0.302576i
\(172\) 86.0076 + 181.863i 0.500044 + 1.05734i
\(173\) 27.7204 0.160234 0.0801168 0.996785i \(-0.474471\pi\)
0.0801168 + 0.996785i \(0.474471\pi\)
\(174\) 96.7262 21.7190i 0.555898 0.124822i
\(175\) 0 0
\(176\) −114.766 94.1982i −0.652080 0.535217i
\(177\) −33.3855 −0.188619
\(178\) 20.2908 + 90.3657i 0.113993 + 0.507673i
\(179\) 204.324i 1.14147i 0.821133 + 0.570737i \(0.193342\pi\)
−0.821133 + 0.570737i \(0.806658\pi\)
\(180\) 0 0
\(181\) −49.8262 −0.275283 −0.137641 0.990482i \(-0.543952\pi\)
−0.137641 + 0.990482i \(0.543952\pi\)
\(182\) 229.413 51.5126i 1.26051 0.283036i
\(183\) 92.0694i 0.503112i
\(184\) −212.640 + 165.929i −1.15565 + 0.901790i
\(185\) 0 0
\(186\) 17.8303 + 79.4079i 0.0958620 + 0.426924i
\(187\) 129.089i 0.690317i
\(188\) −53.2859 112.673i −0.283436 0.599324i
\(189\) 32.9003 0.174076
\(190\) 0 0
\(191\) 1.13703i 0.00595301i −0.999996 0.00297651i \(-0.999053\pi\)
0.999996 0.00297651i \(-0.000947453\pi\)
\(192\) 107.527 + 26.9449i 0.560034 + 0.140338i
\(193\) 76.6452 0.397126 0.198563 0.980088i \(-0.436373\pi\)
0.198563 + 0.980088i \(0.436373\pi\)
\(194\) 30.0385 + 133.778i 0.154838 + 0.689575i
\(195\) 0 0
\(196\) −32.2188 + 15.2371i −0.164382 + 0.0777403i
\(197\) −134.496 −0.682719 −0.341359 0.939933i \(-0.610887\pi\)
−0.341359 + 0.939933i \(0.610887\pi\)
\(198\) 54.3251 12.1982i 0.274369 0.0616071i
\(199\) 176.014i 0.884491i 0.896894 + 0.442245i \(0.145818\pi\)
−0.896894 + 0.442245i \(0.854182\pi\)
\(200\) 0 0
\(201\) 7.79269 0.0387696
\(202\) 19.0144 + 84.6813i 0.0941308 + 0.419214i
\(203\) 181.198i 0.892599i
\(204\) −41.2044 87.1264i −0.201982 0.427090i
\(205\) 0 0
\(206\) −167.415 + 37.5916i −0.812695 + 0.182483i
\(207\) 101.144i 0.488621i
\(208\) −188.479 + 229.633i −0.906150 + 1.10400i
\(209\) 160.044 0.765761
\(210\) 0 0
\(211\) 218.087i 1.03359i 0.856110 + 0.516793i \(0.172874\pi\)
−0.856110 + 0.516793i \(0.827126\pi\)
\(212\) 295.092 139.557i 1.39194 0.658286i
\(213\) −23.0987 −0.108445
\(214\) −357.255 + 80.2183i −1.66941 + 0.374852i
\(215\) 0 0
\(216\) −32.7722 + 25.5731i −0.151723 + 0.118394i
\(217\) −148.755 −0.685508
\(218\) −35.7021 159.001i −0.163771 0.729361i
\(219\) 70.8243i 0.323399i
\(220\) 0 0
\(221\) 258.292 1.16874
\(222\) −227.584 + 51.1020i −1.02515 + 0.230189i
\(223\) 328.579i 1.47345i 0.676193 + 0.736724i \(0.263628\pi\)
−0.676193 + 0.736724i \(0.736372\pi\)
\(224\) −91.1115 + 180.972i −0.406748 + 0.807910i
\(225\) 0 0
\(226\) −75.7222 337.231i −0.335054 1.49217i
\(227\) 157.649i 0.694491i 0.937774 + 0.347245i \(0.112883\pi\)
−0.937774 + 0.347245i \(0.887117\pi\)
\(228\) −108.019 + 51.0849i −0.473767 + 0.224057i
\(229\) −273.148 −1.19279 −0.596393 0.802692i \(-0.703400\pi\)
−0.596393 + 0.802692i \(0.703400\pi\)
\(230\) 0 0
\(231\) 101.767i 0.440552i
\(232\) −140.844 180.492i −0.607084 0.777983i
\(233\) −108.746 −0.466720 −0.233360 0.972390i \(-0.574972\pi\)
−0.233360 + 0.972390i \(0.574972\pi\)
\(234\) −24.4071 108.698i −0.104304 0.464521i
\(235\) 0 0
\(236\) 32.9625 + 69.6992i 0.139672 + 0.295335i
\(237\) −244.754 −1.03272
\(238\) 171.880 38.5942i 0.722186 0.162160i
\(239\) 178.994i 0.748927i 0.927242 + 0.374464i \(0.122173\pi\)
−0.927242 + 0.374464i \(0.877827\pi\)
\(240\) 0 0
\(241\) 358.623 1.48806 0.744032 0.668144i \(-0.232911\pi\)
0.744032 + 0.668144i \(0.232911\pi\)
\(242\) −15.2872 68.0819i −0.0631701 0.281330i
\(243\) 15.5885i 0.0641500i
\(244\) 192.214 90.9029i 0.787762 0.372553i
\(245\) 0 0
\(246\) 148.985 33.4532i 0.605629 0.135989i
\(247\) 320.229i 1.29647i
\(248\) 148.176 115.626i 0.597483 0.466235i
\(249\) −120.984 −0.485881
\(250\) 0 0
\(251\) 306.220i 1.22000i −0.792401 0.610000i \(-0.791169\pi\)
0.792401 0.610000i \(-0.208831\pi\)
\(252\) −32.4834 68.6861i −0.128903 0.272564i
\(253\) 312.861 1.23660
\(254\) 43.6696 9.80560i 0.171927 0.0386047i
\(255\) 0 0
\(256\) −49.9113 251.087i −0.194966 0.980810i
\(257\) 251.062 0.976895 0.488447 0.872593i \(-0.337563\pi\)
0.488447 + 0.872593i \(0.337563\pi\)
\(258\) 38.1697 + 169.990i 0.147945 + 0.658876i
\(259\) 426.335i 1.64608i
\(260\) 0 0
\(261\) 85.8531 0.328939
\(262\) 3.42112 0.768181i 0.0130577 0.00293199i
\(263\) 48.7645i 0.185416i 0.995693 + 0.0927082i \(0.0295524\pi\)
−0.995693 + 0.0927082i \(0.970448\pi\)
\(264\) −79.1031 101.371i −0.299633 0.383982i
\(265\) 0 0
\(266\) −47.8488 213.096i −0.179883 0.801113i
\(267\) 80.2076i 0.300403i
\(268\) −7.69395 16.2688i −0.0287088 0.0607046i
\(269\) 148.696 0.552772 0.276386 0.961047i \(-0.410863\pi\)
0.276386 + 0.961047i \(0.410863\pi\)
\(270\) 0 0
\(271\) 83.3415i 0.307533i 0.988107 + 0.153767i \(0.0491404\pi\)
−0.988107 + 0.153767i \(0.950860\pi\)
\(272\) −141.212 + 172.045i −0.519162 + 0.632519i
\(273\) 203.624 0.745877
\(274\) −8.54805 38.0690i −0.0311972 0.138938i
\(275\) 0 0
\(276\) −211.160 + 99.8630i −0.765072 + 0.361822i
\(277\) −144.080 −0.520146 −0.260073 0.965589i \(-0.583747\pi\)
−0.260073 + 0.965589i \(0.583747\pi\)
\(278\) −502.234 + 112.772i −1.80660 + 0.405655i
\(279\) 70.4816i 0.252622i
\(280\) 0 0
\(281\) −343.671 −1.22303 −0.611514 0.791233i \(-0.709439\pi\)
−0.611514 + 0.791233i \(0.709439\pi\)
\(282\) −23.6480 105.317i −0.0838581 0.373465i
\(283\) 314.955i 1.11292i −0.830876 0.556458i \(-0.812160\pi\)
0.830876 0.556458i \(-0.187840\pi\)
\(284\) 22.8061 + 48.2233i 0.0803030 + 0.169800i
\(285\) 0 0
\(286\) 336.225 75.4964i 1.17561 0.263973i
\(287\) 279.094i 0.972453i
\(288\) 85.7461 + 43.1695i 0.297730 + 0.149894i
\(289\) −95.4831 −0.330391
\(290\) 0 0
\(291\) 118.740i 0.408040i
\(292\) 147.860 69.9269i 0.506371 0.239476i
\(293\) 6.55421 0.0223693 0.0111847 0.999937i \(-0.496440\pi\)
0.0111847 + 0.999937i \(0.496440\pi\)
\(294\) −30.1154 + 6.76214i −0.102433 + 0.0230005i
\(295\) 0 0
\(296\) 331.387 + 424.674i 1.11955 + 1.43471i
\(297\) 48.2184 0.162351
\(298\) 48.9321 + 217.921i 0.164202 + 0.731278i
\(299\) 625.997i 2.09364i
\(300\) 0 0
\(301\) −318.443 −1.05795
\(302\) −12.5920 + 2.82741i −0.0416953 + 0.00936229i
\(303\) 75.1622i 0.248060i
\(304\) 213.300 + 175.074i 0.701646 + 0.575900i
\(305\) 0 0
\(306\) −18.2863 81.4384i −0.0597590 0.266139i
\(307\) 354.559i 1.15492i −0.816420 0.577458i \(-0.804045\pi\)
0.816420 0.577458i \(-0.195955\pi\)
\(308\) 212.460 100.478i 0.689807 0.326228i
\(309\) −148.596 −0.480893
\(310\) 0 0
\(311\) 193.387i 0.621823i 0.950439 + 0.310912i \(0.100634\pi\)
−0.950439 + 0.310912i \(0.899366\pi\)
\(312\) −202.831 + 158.276i −0.650101 + 0.507294i
\(313\) 23.5224 0.0751514 0.0375757 0.999294i \(-0.488036\pi\)
0.0375757 + 0.999294i \(0.488036\pi\)
\(314\) −33.2605 148.127i −0.105925 0.471742i
\(315\) 0 0
\(316\) 241.653 + 510.973i 0.764724 + 1.61700i
\(317\) 214.004 0.675092 0.337546 0.941309i \(-0.390403\pi\)
0.337546 + 0.941309i \(0.390403\pi\)
\(318\) 275.827 61.9344i 0.867380 0.194762i
\(319\) 265.562i 0.832481i
\(320\) 0 0
\(321\) −317.095 −0.987836
\(322\) −93.5369 416.570i −0.290487 1.29369i
\(323\) 239.921i 0.742790i
\(324\) −32.5441 + 15.3910i −0.100445 + 0.0475029i
\(325\) 0 0
\(326\) −486.483 + 109.235i −1.49228 + 0.335078i
\(327\) 141.127i 0.431582i
\(328\) −216.938 278.007i −0.661395 0.847583i
\(329\) 197.291 0.599669
\(330\) 0 0
\(331\) 412.454i 1.24609i −0.782188 0.623043i \(-0.785896\pi\)
0.782188 0.623043i \(-0.214104\pi\)
\(332\) 119.451 + 252.579i 0.359793 + 0.760782i
\(333\) −202.001 −0.606610
\(334\) 154.529 34.6981i 0.462662 0.103886i
\(335\) 0 0
\(336\) −111.324 + 135.632i −0.331323 + 0.403666i
\(337\) −103.268 −0.306433 −0.153216 0.988193i \(-0.548963\pi\)
−0.153216 + 0.988193i \(0.548963\pi\)
\(338\) −77.0081 342.958i −0.227835 1.01467i
\(339\) 299.323i 0.882958i
\(340\) 0 0
\(341\) −218.014 −0.639338
\(342\) −100.967 + 22.6712i −0.295225 + 0.0662900i
\(343\) 366.667i 1.06900i
\(344\) 317.203 247.523i 0.922102 0.719545i
\(345\) 0 0
\(346\) −12.1463 54.0939i −0.0351049 0.156341i
\(347\) 153.211i 0.441531i 0.975327 + 0.220766i \(0.0708556\pi\)
−0.975327 + 0.220766i \(0.929144\pi\)
\(348\) −84.7654 179.236i −0.243579 0.515046i
\(349\) −84.7317 −0.242784 −0.121392 0.992605i \(-0.538736\pi\)
−0.121392 + 0.992605i \(0.538736\pi\)
\(350\) 0 0
\(351\) 96.4791i 0.274869i
\(352\) −133.532 + 265.231i −0.379353 + 0.753496i
\(353\) −256.065 −0.725396 −0.362698 0.931907i \(-0.618144\pi\)
−0.362698 + 0.931907i \(0.618144\pi\)
\(354\) 14.6286 + 65.1489i 0.0413237 + 0.184036i
\(355\) 0 0
\(356\) 167.450 79.1914i 0.470365 0.222448i
\(357\) 152.559 0.427336
\(358\) 398.720 89.5289i 1.11374 0.250081i
\(359\) 667.258i 1.85866i 0.369253 + 0.929329i \(0.379614\pi\)
−0.369253 + 0.929329i \(0.620386\pi\)
\(360\) 0 0
\(361\) 63.5473 0.176031
\(362\) 21.8324 + 97.2314i 0.0603106 + 0.268595i
\(363\) 60.4287i 0.166470i
\(364\) −201.044 425.108i −0.552320 1.16788i
\(365\) 0 0
\(366\) 179.665 40.3422i 0.490889 0.110225i
\(367\) 245.301i 0.668396i 0.942503 + 0.334198i \(0.108465\pi\)
−0.942503 + 0.334198i \(0.891535\pi\)
\(368\) 416.969 + 342.242i 1.13307 + 0.930005i
\(369\) 132.237 0.358367
\(370\) 0 0
\(371\) 516.708i 1.39274i
\(372\) 147.145 69.5886i 0.395550 0.187066i
\(373\) −698.787 −1.87342 −0.936712 0.350101i \(-0.886147\pi\)
−0.936712 + 0.350101i \(0.886147\pi\)
\(374\) 251.906 56.5632i 0.673546 0.151239i
\(375\) 0 0
\(376\) −196.523 + 153.353i −0.522667 + 0.407853i
\(377\) 531.357 1.40943
\(378\) −14.4160 64.2020i −0.0381375 0.169847i
\(379\) 208.691i 0.550636i −0.961353 0.275318i \(-0.911217\pi\)
0.961353 0.275318i \(-0.0887831\pi\)
\(380\) 0 0
\(381\) 38.7606 0.101734
\(382\) −2.21880 + 0.498212i −0.00580839 + 0.00130422i
\(383\) 156.524i 0.408680i −0.978900 0.204340i \(-0.934495\pi\)
0.978900 0.204340i \(-0.0655048\pi\)
\(384\) 5.46541 221.635i 0.0142328 0.577175i
\(385\) 0 0
\(386\) −33.5838 149.566i −0.0870046 0.387478i
\(387\) 150.881i 0.389874i
\(388\) 247.893 117.235i 0.638900 0.302152i
\(389\) 386.588 0.993801 0.496900 0.867808i \(-0.334471\pi\)
0.496900 + 0.867808i \(0.334471\pi\)
\(390\) 0 0
\(391\) 469.008i 1.19951i
\(392\) 43.8512 + 56.1956i 0.111865 + 0.143356i
\(393\) 3.03655 0.00772658
\(394\) 58.9322 + 262.456i 0.149574 + 0.666133i
\(395\) 0 0
\(396\) −47.6074 100.666i −0.120221 0.254206i
\(397\) 561.155 1.41349 0.706744 0.707470i \(-0.250163\pi\)
0.706744 + 0.707470i \(0.250163\pi\)
\(398\) 343.475 77.1242i 0.863002 0.193779i
\(399\) 189.142i 0.474039i
\(400\) 0 0
\(401\) 16.9333 0.0422276 0.0211138 0.999777i \(-0.493279\pi\)
0.0211138 + 0.999777i \(0.493279\pi\)
\(402\) −3.41453 15.2067i −0.00849387 0.0378277i
\(403\) 436.220i 1.08243i
\(404\) 156.917 74.2099i 0.388407 0.183688i
\(405\) 0 0
\(406\) 353.591 79.3957i 0.870914 0.195556i
\(407\) 624.832i 1.53521i
\(408\) −151.965 + 118.583i −0.372463 + 0.290644i
\(409\) 258.490 0.632006 0.316003 0.948758i \(-0.397659\pi\)
0.316003 + 0.948758i \(0.397659\pi\)
\(410\) 0 0
\(411\) 33.7896i 0.0822132i
\(412\) 146.713 + 310.224i 0.356100 + 0.752972i
\(413\) −122.044 −0.295505
\(414\) −197.374 + 44.3186i −0.476750 + 0.107050i
\(415\) 0 0
\(416\) 530.694 + 267.182i 1.27571 + 0.642264i
\(417\) −445.777 −1.06901
\(418\) −70.1267 312.312i −0.167767 0.747157i
\(419\) 258.917i 0.617941i −0.951072 0.308970i \(-0.900016\pi\)
0.951072 0.308970i \(-0.0999844\pi\)
\(420\) 0 0
\(421\) 97.4654 0.231509 0.115755 0.993278i \(-0.463071\pi\)
0.115755 + 0.993278i \(0.463071\pi\)
\(422\) 425.577 95.5594i 1.00848 0.226444i
\(423\) 93.4783i 0.220989i
\(424\) −401.633 514.696i −0.947248 1.21390i
\(425\) 0 0
\(426\) 10.1212 + 45.0751i 0.0237587 + 0.105810i
\(427\) 336.568i 0.788215i
\(428\) 313.078 + 662.002i 0.731490 + 1.54673i
\(429\) 298.430 0.695641
\(430\) 0 0
\(431\) 389.968i 0.904799i −0.891815 0.452399i \(-0.850568\pi\)
0.891815 0.452399i \(-0.149432\pi\)
\(432\) 64.2635 + 52.7465i 0.148758 + 0.122098i
\(433\) −275.893 −0.637166 −0.318583 0.947895i \(-0.603207\pi\)
−0.318583 + 0.947895i \(0.603207\pi\)
\(434\) 65.1803 + 290.283i 0.150185 + 0.668854i
\(435\) 0 0
\(436\) −294.632 + 139.339i −0.675761 + 0.319585i
\(437\) −581.473 −1.33060
\(438\) 138.207 31.0332i 0.315542 0.0708520i
\(439\) 446.143i 1.01627i 0.861277 + 0.508136i \(0.169665\pi\)
−0.861277 + 0.508136i \(0.830335\pi\)
\(440\) 0 0
\(441\) −26.7301 −0.0606125
\(442\) −113.176 504.034i −0.256055 1.14035i
\(443\) 794.679i 1.79386i −0.442174 0.896929i \(-0.645793\pi\)
0.442174 0.896929i \(-0.354207\pi\)
\(444\) 199.442 + 421.719i 0.449194 + 0.949818i
\(445\) 0 0
\(446\) 641.193 143.974i 1.43765 0.322812i
\(447\) 193.424i 0.432716i
\(448\) 393.073 + 98.4993i 0.877395 + 0.219865i
\(449\) −750.226 −1.67088 −0.835441 0.549581i \(-0.814788\pi\)
−0.835441 + 0.549581i \(0.814788\pi\)
\(450\) 0 0
\(451\) 409.037i 0.906957i
\(452\) −624.898 + 295.530i −1.38252 + 0.653828i
\(453\) −11.1765 −0.0246722
\(454\) 307.639 69.0775i 0.677619 0.152153i
\(455\) 0 0
\(456\) 147.018 + 188.405i 0.322409 + 0.413169i
\(457\) −101.092 −0.221209 −0.110604 0.993865i \(-0.535279\pi\)
−0.110604 + 0.993865i \(0.535279\pi\)
\(458\) 119.686 + 533.024i 0.261323 + 1.16381i
\(459\) 72.2839i 0.157481i
\(460\) 0 0
\(461\) −4.48690 −0.00973297 −0.00486648 0.999988i \(-0.501549\pi\)
−0.00486648 + 0.999988i \(0.501549\pi\)
\(462\) 198.590 44.5916i 0.429849 0.0965186i
\(463\) 515.108i 1.11254i 0.831000 + 0.556272i \(0.187769\pi\)
−0.831000 + 0.556272i \(0.812231\pi\)
\(464\) −290.500 + 353.930i −0.626079 + 0.762780i
\(465\) 0 0
\(466\) 47.6493 + 212.208i 0.102252 + 0.455382i
\(467\) 295.498i 0.632758i −0.948633 0.316379i \(-0.897533\pi\)
0.948633 0.316379i \(-0.102467\pi\)
\(468\) −201.420 + 95.2567i −0.430384 + 0.203540i
\(469\) 28.4869 0.0607396
\(470\) 0 0
\(471\) 131.476i 0.279142i
\(472\) 121.568 94.8637i 0.257560 0.200982i
\(473\) −466.707 −0.986696
\(474\) 107.244 + 477.615i 0.226253 + 1.00763i
\(475\) 0 0
\(476\) −150.626 318.498i −0.316441 0.669114i
\(477\) 244.821 0.513251
\(478\) 349.290 78.4299i 0.730732 0.164079i
\(479\) 273.155i 0.570260i −0.958489 0.285130i \(-0.907963\pi\)
0.958489 0.285130i \(-0.0920368\pi\)
\(480\) 0 0
\(481\) −1250.21 −2.59920
\(482\) −157.139 699.822i −0.326014 1.45191i
\(483\) 369.743i 0.765512i
\(484\) −126.157 + 59.6631i −0.260656 + 0.123271i
\(485\) 0 0
\(486\) −30.4195 + 6.83042i −0.0625915 + 0.0140544i
\(487\) 357.751i 0.734601i 0.930102 + 0.367301i \(0.119718\pi\)
−0.930102 + 0.367301i \(0.880282\pi\)
\(488\) −261.612 335.257i −0.536089 0.687002i
\(489\) −431.797 −0.883021
\(490\) 0 0
\(491\) 422.379i 0.860242i 0.902771 + 0.430121i \(0.141529\pi\)
−0.902771 + 0.430121i \(0.858471\pi\)
\(492\) −130.562 276.072i −0.265370 0.561123i
\(493\) 398.102 0.807509
\(494\) −624.898 + 140.315i −1.26498 + 0.284039i
\(495\) 0 0
\(496\) −290.561 238.488i −0.585808 0.480822i
\(497\) −84.4394 −0.169898
\(498\) 53.0119 + 236.090i 0.106450 + 0.474076i
\(499\) 207.096i 0.415021i 0.978233 + 0.207511i \(0.0665362\pi\)
−0.978233 + 0.207511i \(0.933464\pi\)
\(500\) 0 0
\(501\) 137.158 0.273769
\(502\) −597.562 + 134.177i −1.19036 + 0.267285i
\(503\) 702.853i 1.39732i 0.715452 + 0.698661i \(0.246221\pi\)
−0.715452 + 0.698661i \(0.753779\pi\)
\(504\) −119.802 + 93.4849i −0.237701 + 0.185486i
\(505\) 0 0
\(506\) −137.087 610.520i −0.270923 1.20656i
\(507\) 304.406i 0.600406i
\(508\) −38.2695 80.9207i −0.0753337 0.159293i
\(509\) −389.029 −0.764300 −0.382150 0.924100i \(-0.624816\pi\)
−0.382150 + 0.924100i \(0.624816\pi\)
\(510\) 0 0
\(511\) 258.904i 0.506662i
\(512\) −468.105 + 207.417i −0.914267 + 0.405111i
\(513\) −89.6171 −0.174692
\(514\) −110.008 489.925i −0.214024 0.953162i
\(515\) 0 0
\(516\) 314.996 148.970i 0.610457 0.288701i
\(517\) 289.148 0.559280
\(518\) −831.954 + 186.808i −1.60609 + 0.360633i
\(519\) 48.0132i 0.0925109i
\(520\) 0 0
\(521\) −151.753 −0.291273 −0.145637 0.989338i \(-0.546523\pi\)
−0.145637 + 0.989338i \(0.546523\pi\)
\(522\) −37.6184 167.535i −0.0720659 0.320948i
\(523\) 557.762i 1.06647i 0.845968 + 0.533234i \(0.179023\pi\)
−0.845968 + 0.533234i \(0.820977\pi\)
\(524\) −2.99807 6.33941i −0.00572151 0.0120981i
\(525\) 0 0
\(526\) 95.1596 21.3672i 0.180912 0.0406221i
\(527\) 326.824i 0.620159i
\(528\) −163.156 + 198.781i −0.309008 + 0.376478i
\(529\) −607.689 −1.14875
\(530\) 0 0
\(531\) 57.8254i 0.108899i
\(532\) −394.872 + 186.745i −0.742241 + 0.351025i
\(533\) 818.435 1.53552
\(534\) 156.518 35.1447i 0.293105 0.0658141i
\(535\) 0 0
\(536\) −28.3759 + 22.1426i −0.0529401 + 0.0413108i
\(537\) 353.899 0.659030
\(538\) −65.1542 290.166i −0.121104 0.539342i
\(539\) 82.6818i 0.153398i
\(540\) 0 0
\(541\) 340.979 0.630275 0.315137 0.949046i \(-0.397949\pi\)
0.315137 + 0.949046i \(0.397949\pi\)
\(542\) 162.633 36.5179i 0.300062 0.0673761i
\(543\) 86.3015i 0.158935i
\(544\) 397.606 + 200.177i 0.730893 + 0.367973i
\(545\) 0 0
\(546\) −89.2224 397.355i −0.163411 0.727756i
\(547\) 113.651i 0.207771i −0.994589 0.103885i \(-0.966872\pi\)
0.994589 0.103885i \(-0.0331275\pi\)
\(548\) −70.5428 + 33.3615i −0.128728 + 0.0608787i
\(549\) 159.469 0.290472
\(550\) 0 0
\(551\) 493.564i 0.895761i
\(552\) 287.398 + 368.303i 0.520649 + 0.667215i
\(553\) −894.718 −1.61794
\(554\) 63.1319 + 281.160i 0.113957 + 0.507509i
\(555\) 0 0
\(556\) 440.129 + 930.651i 0.791599 + 1.67383i
\(557\) −233.232 −0.418728 −0.209364 0.977838i \(-0.567139\pi\)
−0.209364 + 0.977838i \(0.567139\pi\)
\(558\) 137.539 30.8830i 0.246485 0.0553459i
\(559\) 933.825i 1.67053i
\(560\) 0 0
\(561\) 223.589 0.398554
\(562\) 150.587 + 670.644i 0.267948 + 1.19332i
\(563\) 167.786i 0.298021i −0.988836 0.149011i \(-0.952391\pi\)
0.988836 0.149011i \(-0.0476088\pi\)
\(564\) −195.155 + 92.2939i −0.346020 + 0.163642i
\(565\) 0 0
\(566\) −614.607 + 138.004i −1.08588 + 0.243824i
\(567\) 56.9850i 0.100503i
\(568\) 84.1105 65.6341i 0.148082 0.115553i
\(569\) 381.089 0.669752 0.334876 0.942262i \(-0.391306\pi\)
0.334876 + 0.942262i \(0.391306\pi\)
\(570\) 0 0
\(571\) 453.871i 0.794870i −0.917630 0.397435i \(-0.869900\pi\)
0.917630 0.397435i \(-0.130100\pi\)
\(572\) −294.649 623.034i −0.515120 1.08922i
\(573\) −1.96939 −0.00343697
\(574\) 544.627 122.291i 0.948828 0.213051i
\(575\) 0 0
\(576\) 46.6699 186.242i 0.0810241 0.323336i
\(577\) −688.294 −1.19288 −0.596442 0.802656i \(-0.703419\pi\)
−0.596442 + 0.802656i \(0.703419\pi\)
\(578\) 41.8380 + 186.327i 0.0723841 + 0.322365i
\(579\) 132.753i 0.229281i
\(580\) 0 0
\(581\) −442.269 −0.761220
\(582\) 231.710 52.0283i 0.398127 0.0893957i
\(583\) 757.282i 1.29894i
\(584\) −201.244 257.896i −0.344597 0.441603i
\(585\) 0 0
\(586\) −2.87187 12.7900i −0.00490080 0.0218259i
\(587\) 249.163i 0.424468i 0.977219 + 0.212234i \(0.0680739\pi\)
−0.977219 + 0.212234i \(0.931926\pi\)
\(588\) 26.3914 + 55.8046i 0.0448834 + 0.0949057i
\(589\) 405.194 0.687936
\(590\) 0 0
\(591\) 232.953i 0.394168i
\(592\) 683.510 832.752i 1.15458 1.40668i
\(593\) 163.937 0.276454 0.138227 0.990401i \(-0.455860\pi\)
0.138227 + 0.990401i \(0.455860\pi\)
\(594\) −21.1279 94.0938i −0.0355689 0.158407i
\(595\) 0 0
\(596\) 403.812 190.973i 0.677538 0.320425i
\(597\) 304.865 0.510661
\(598\) −1221.58 + 274.294i −2.04277 + 0.458686i
\(599\) 170.412i 0.284494i −0.989831 0.142247i \(-0.954567\pi\)
0.989831 0.142247i \(-0.0454327\pi\)
\(600\) 0 0
\(601\) 1119.87 1.86335 0.931674 0.363295i \(-0.118348\pi\)
0.931674 + 0.363295i \(0.118348\pi\)
\(602\) 139.533 + 621.413i 0.231782 + 1.03225i
\(603\) 13.4973i 0.0223836i
\(604\) 11.0349 + 23.3332i 0.0182697 + 0.0386312i
\(605\) 0 0
\(606\) 146.672 32.9339i 0.242034 0.0543464i
\(607\) 660.957i 1.08889i 0.838796 + 0.544445i \(0.183260\pi\)
−0.838796 + 0.544445i \(0.816740\pi\)
\(608\) 248.179 492.949i 0.408189 0.810772i
\(609\) 313.844 0.515342
\(610\) 0 0
\(611\) 578.550i 0.946890i
\(612\) −150.907 + 71.3680i −0.246581 + 0.116614i
\(613\) 179.315 0.292520 0.146260 0.989246i \(-0.453276\pi\)
0.146260 + 0.989246i \(0.453276\pi\)
\(614\) −691.891 + 155.358i −1.12686 + 0.253026i
\(615\) 0 0
\(616\) −289.168 370.571i −0.469429 0.601576i
\(617\) 63.6752 0.103201 0.0516007 0.998668i \(-0.483568\pi\)
0.0516007 + 0.998668i \(0.483568\pi\)
\(618\) 65.1105 + 289.972i 0.105357 + 0.469210i
\(619\) 872.350i 1.40929i 0.709561 + 0.704644i \(0.248893\pi\)
−0.709561 + 0.704644i \(0.751107\pi\)
\(620\) 0 0
\(621\) −175.187 −0.282105
\(622\) 377.378 84.7367i 0.606716 0.136233i
\(623\) 293.206i 0.470636i
\(624\) 397.736 + 326.456i 0.637397 + 0.523166i
\(625\) 0 0
\(626\) −10.3068 45.9019i −0.0164646 0.0733257i
\(627\) 277.204i 0.442112i
\(628\) −274.483 + 129.810i −0.437074 + 0.206704i
\(629\) −936.682 −1.48916
\(630\) 0 0
\(631\) 340.783i 0.540068i −0.962851 0.270034i \(-0.912965\pi\)
0.962851 0.270034i \(-0.0870349\pi\)
\(632\) 891.234 695.458i 1.41018 1.10041i
\(633\) 377.737 0.596742
\(634\) −93.7705 417.610i −0.147903 0.658691i
\(635\) 0 0
\(636\) −241.719 511.114i −0.380061 0.803638i
\(637\) −165.436 −0.259712
\(638\) 518.220 116.362i 0.812257 0.182385i
\(639\) 40.0081i 0.0626105i
\(640\) 0 0
\(641\) 766.210 1.19534 0.597668 0.801744i \(-0.296094\pi\)
0.597668 + 0.801744i \(0.296094\pi\)
\(642\) 138.942 + 618.783i 0.216421 + 0.963837i
\(643\) 1163.47i 1.80943i −0.426014 0.904717i \(-0.640083\pi\)
0.426014 0.904717i \(-0.359917\pi\)
\(644\) −771.913 + 365.058i −1.19862 + 0.566860i
\(645\) 0 0
\(646\) −468.185 + 105.127i −0.724744 + 0.162735i
\(647\) 740.530i 1.14456i −0.820059 0.572279i \(-0.806059\pi\)
0.820059 0.572279i \(-0.193941\pi\)
\(648\) 44.2940 + 56.7630i 0.0683549 + 0.0875973i
\(649\) −178.866 −0.275603
\(650\) 0 0
\(651\) 257.652i 0.395778i
\(652\) 426.326 + 901.465i 0.653875 + 1.38262i
\(653\) −109.569 −0.167793 −0.0838967 0.996474i \(-0.526737\pi\)
−0.0838967 + 0.996474i \(0.526737\pi\)
\(654\) −275.397 + 61.8379i −0.421097 + 0.0945534i
\(655\) 0 0
\(656\) −447.450 + 545.149i −0.682089 + 0.831020i
\(657\) 122.671 0.186714
\(658\) −86.4473 384.996i −0.131379 0.585100i
\(659\) 723.214i 1.09744i −0.836006 0.548721i \(-0.815115\pi\)
0.836006 0.548721i \(-0.184885\pi\)
\(660\) 0 0
\(661\) 700.333 1.05951 0.529753 0.848152i \(-0.322285\pi\)
0.529753 + 0.848152i \(0.322285\pi\)
\(662\) −804.868 + 180.726i −1.21581 + 0.273000i
\(663\) 447.375i 0.674773i
\(664\) 440.546 343.772i 0.663473 0.517729i
\(665\) 0 0
\(666\) 88.5112 + 394.188i 0.132900 + 0.591873i
\(667\) 964.841i 1.44654i
\(668\) −135.420 286.346i −0.202725 0.428662i
\(669\) 569.116 0.850696
\(670\) 0 0
\(671\) 493.271i 0.735128i
\(672\) 313.452 + 157.810i 0.466447 + 0.234836i
\(673\) 1221.18 1.81454 0.907269 0.420552i \(-0.138163\pi\)
0.907269 + 0.420552i \(0.138163\pi\)
\(674\) 45.2490 + 201.518i 0.0671350 + 0.298988i
\(675\) 0 0
\(676\) −635.509 + 300.549i −0.940103 + 0.444599i
\(677\) −989.373 −1.46141 −0.730704 0.682695i \(-0.760808\pi\)
−0.730704 + 0.682695i \(0.760808\pi\)
\(678\) −584.102 + 131.155i −0.861507 + 0.193444i
\(679\) 434.063i 0.639268i
\(680\) 0 0
\(681\) 273.057 0.400965
\(682\) 95.5276 + 425.435i 0.140070 + 0.623806i
\(683\) 307.312i 0.449945i −0.974365 0.224972i \(-0.927771\pi\)
0.974365 0.224972i \(-0.0722292\pi\)
\(684\) 88.4816 + 187.094i 0.129359 + 0.273529i
\(685\) 0 0
\(686\) −715.518 + 160.663i −1.04303 + 0.234203i
\(687\) 473.107i 0.688656i
\(688\) −622.009 510.536i −0.904083 0.742058i
\(689\) 1515.23 2.19917
\(690\) 0 0
\(691\) 893.378i 1.29288i 0.762966 + 0.646438i \(0.223742\pi\)
−0.762966 + 0.646438i \(0.776258\pi\)
\(692\) −100.237 + 47.4048i −0.144852 + 0.0685041i
\(693\) 176.266 0.254353
\(694\) 298.978 67.1329i 0.430805 0.0967332i
\(695\) 0 0
\(696\) −312.621 + 243.948i −0.449169 + 0.350500i
\(697\) 613.186 0.879750
\(698\) 37.1270 + 165.346i 0.0531906 + 0.236886i
\(699\) 188.353i 0.269461i
\(700\) 0 0
\(701\) 1127.42 1.60830 0.804149 0.594428i \(-0.202622\pi\)
0.804149 + 0.594428i \(0.202622\pi\)
\(702\) −188.270 + 42.2744i −0.268191 + 0.0602199i
\(703\) 1161.29i 1.65191i
\(704\) 576.084 + 144.360i 0.818301 + 0.205056i
\(705\) 0 0
\(706\) 112.200 + 499.688i 0.158924 + 0.707773i
\(707\) 274.762i 0.388631i
\(708\) 120.722 57.0928i 0.170512 0.0806395i
\(709\) 1093.27 1.54199 0.770997 0.636839i \(-0.219758\pi\)
0.770997 + 0.636839i \(0.219758\pi\)
\(710\) 0 0
\(711\) 423.926i 0.596239i
\(712\) −227.907 292.064i −0.320094 0.410202i
\(713\) 792.091 1.11093
\(714\) −66.8470 297.705i −0.0936233 0.416954i
\(715\) 0 0
\(716\) −349.415 738.837i −0.488010 1.03190i
\(717\) 310.026 0.432393
\(718\) 1302.10 292.374i 1.81350 0.407206i
\(719\) 769.690i 1.07050i −0.844693 0.535251i \(-0.820217\pi\)
0.844693 0.535251i \(-0.179783\pi\)
\(720\) 0 0
\(721\) −543.205 −0.753405
\(722\) −27.8446 124.007i −0.0385660 0.171755i
\(723\) 621.154i 0.859134i
\(724\) 180.172 85.2081i 0.248857 0.117691i
\(725\) 0 0
\(726\) −117.921 + 26.4782i −0.162426 + 0.0364713i
\(727\) 295.050i 0.405846i −0.979195 0.202923i \(-0.934956\pi\)
0.979195 0.202923i \(-0.0650441\pi\)
\(728\) −741.468 + 578.591i −1.01850 + 0.794767i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 699.638i 0.957097i
\(732\) −157.448 332.924i −0.215094 0.454814i
\(733\) −261.200 −0.356344 −0.178172 0.983999i \(-0.557018\pi\)
−0.178172 + 0.983999i \(0.557018\pi\)
\(734\) 478.684 107.484i 0.652158 0.146436i
\(735\) 0 0
\(736\) 485.150 963.638i 0.659172 1.30929i
\(737\) 41.7501 0.0566487
\(738\) −57.9426 258.049i −0.0785130 0.349660i
\(739\) 482.679i 0.653151i −0.945171 0.326576i \(-0.894105\pi\)
0.945171 0.326576i \(-0.105895\pi\)
\(740\) 0 0
\(741\) −554.652 −0.748519
\(742\) 1008.31 226.407i 1.35891 0.305130i
\(743\) 23.7067i 0.0319067i 0.999873 + 0.0159534i \(0.00507833\pi\)
−0.999873 + 0.0159534i \(0.994922\pi\)
\(744\) −200.271 256.648i −0.269181 0.344957i
\(745\) 0 0
\(746\) 306.189 + 1363.62i 0.410441 + 1.82791i
\(747\) 209.551i 0.280523i
\(748\) −220.756 466.788i −0.295129 0.624048i
\(749\) −1159.17 −1.54762
\(750\) 0 0
\(751\) 395.508i 0.526642i −0.964708 0.263321i \(-0.915182\pi\)
0.964708 0.263321i \(-0.0848179\pi\)
\(752\) 385.365 + 316.302i 0.512453 + 0.420614i
\(753\) −530.389 −0.704368
\(754\) −232.825 1036.90i −0.308787 1.37519i
\(755\) 0 0
\(756\) −118.968 + 56.2630i −0.157365 + 0.0744219i
\(757\) −393.940 −0.520396 −0.260198 0.965555i \(-0.583788\pi\)
−0.260198 + 0.965555i \(0.583788\pi\)
\(758\) −407.242 + 91.4425i −0.537259 + 0.120637i
\(759\) 541.891i 0.713954i
\(760\) 0 0
\(761\) −369.354 −0.485354 −0.242677 0.970107i \(-0.578025\pi\)
−0.242677 + 0.970107i \(0.578025\pi\)
\(762\) −16.9838 75.6379i −0.0222885 0.0992623i
\(763\) 515.903i 0.676150i
\(764\) 1.94443 + 4.11150i 0.00254507 + 0.00538154i
\(765\) 0 0
\(766\) −305.444 + 68.5846i −0.398751 + 0.0895360i
\(767\) 357.890i 0.466610i
\(768\) −434.896 + 86.4490i −0.566271 + 0.112564i
\(769\) −873.491 −1.13588 −0.567940 0.823070i \(-0.692259\pi\)
−0.567940 + 0.823070i \(0.692259\pi\)
\(770\) 0 0
\(771\) 434.852i 0.564010i
\(772\) −277.150 + 131.071i −0.359003 + 0.169782i
\(773\) 1176.93 1.52254 0.761272 0.648432i \(-0.224575\pi\)
0.761272 + 0.648432i \(0.224575\pi\)
\(774\) 294.431 66.1119i 0.380402 0.0854159i
\(775\) 0 0
\(776\) −337.394 432.372i −0.434786 0.557181i
\(777\) −738.433 −0.950365
\(778\) −169.392 754.393i −0.217728 0.969657i
\(779\) 760.224i 0.975897i
\(780\) 0 0
\(781\) −123.754 −0.158455
\(782\) −915.228 + 205.506i −1.17037 + 0.262795i
\(783\) 148.702i 0.189913i
\(784\) 90.4464 110.195i 0.115365 0.140555i
\(785\) 0 0
\(786\) −1.33053 5.92555i −0.00169278 0.00753887i
\(787\)