Properties

Label 300.3.c.d.151.4
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 151.4
Root \(-0.600040 - 1.28061i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.d.151.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.67986 + 1.08539i) q^{2} -1.73205i q^{3} +(1.64388 - 3.64660i) q^{4} +(1.87994 + 2.90961i) q^{6} -0.596540i q^{7} +(1.19648 + 7.91002i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-1.67986 + 1.08539i) q^{2} -1.73205i q^{3} +(1.64388 - 3.64660i) q^{4} +(1.87994 + 2.90961i) q^{6} -0.596540i q^{7} +(1.19648 + 7.91002i) q^{8} -3.00000 q^{9} +9.27963i q^{11} +(-6.31609 - 2.84728i) q^{12} +23.5117 q^{13} +(0.647476 + 1.00210i) q^{14} +(-10.5953 - 11.9891i) q^{16} -3.97751 q^{17} +(5.03959 - 3.25616i) q^{18} -7.04756i q^{19} -1.03324 q^{21} +(-10.0720 - 15.5885i) q^{22} -32.0793i q^{23} +(13.7006 - 2.07237i) q^{24} +(-39.4964 + 25.5192i) q^{26} +5.19615i q^{27} +(-2.17534 - 0.980637i) q^{28} +35.6734 q^{29} -59.2585i q^{31} +(30.8115 + 8.64000i) q^{32} +16.0728 q^{33} +(6.68167 - 4.31713i) q^{34} +(-4.93163 + 10.9398i) q^{36} +5.38761 q^{37} +(7.64932 + 11.8389i) q^{38} -40.7234i q^{39} +40.0791 q^{41} +(1.73570 - 1.12146i) q^{42} -36.1157i q^{43} +(33.8391 + 15.2545i) q^{44} +(34.8184 + 53.8888i) q^{46} +74.0131i q^{47} +(-20.7657 + 18.3517i) q^{48} +48.6441 q^{49} +6.88925i q^{51} +(38.6503 - 85.7376i) q^{52} +2.55123 q^{53} +(-5.63983 - 8.72882i) q^{54} +(4.71864 - 0.713748i) q^{56} -12.2067 q^{57} +(-59.9265 + 38.7194i) q^{58} +36.4026i q^{59} -8.73223 q^{61} +(64.3183 + 99.5461i) q^{62} +1.78962i q^{63} +(-61.1369 + 18.9284i) q^{64} +(-27.0001 + 17.4452i) q^{66} -69.7379i q^{67} +(-6.53853 + 14.5044i) q^{68} -55.5630 q^{69} -59.2170i q^{71} +(-3.58944 - 23.7301i) q^{72} +83.0019 q^{73} +(-9.05044 + 5.84763i) q^{74} +(-25.6996 - 11.5853i) q^{76} +5.53566 q^{77} +(44.2006 + 68.4098i) q^{78} +65.8705i q^{79} +9.00000 q^{81} +(-67.3274 + 43.5013i) q^{82} -129.909i q^{83} +(-1.69851 + 3.76780i) q^{84} +(39.1995 + 60.6695i) q^{86} -61.7882i q^{87} +(-73.4020 + 11.1029i) q^{88} -130.466 q^{89} -14.0256i q^{91} +(-116.980 - 52.7344i) q^{92} -102.639 q^{93} +(-80.3327 - 124.332i) q^{94} +(14.9649 - 53.3671i) q^{96} -93.1113 q^{97} +(-81.7155 + 52.7977i) q^{98} -27.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} + 10q^{4} - 6q^{6} + 20q^{8} - 24q^{9} + O(q^{10}) \) \( 8q - 4q^{2} + 10q^{4} - 6q^{6} + 20q^{8} - 24q^{9} - 16q^{13} - 20q^{14} + 34q^{16} + 12q^{18} - 48q^{21} - 68q^{22} + 18q^{24} - 36q^{26} - 28q^{28} + 64q^{29} + 76q^{32} - 92q^{34} - 30q^{36} + 112q^{37} + 40q^{38} - 16q^{41} - 108q^{42} + 172q^{44} + 152q^{46} - 48q^{48} - 56q^{49} + 128q^{52} - 352q^{53} + 18q^{54} + 116q^{56} - 144q^{57} + 204q^{58} - 176q^{61} + 56q^{62} - 110q^{64} + 108q^{66} + 184q^{68} - 96q^{69} - 60q^{72} + 240q^{73} + 132q^{74} - 24q^{76} + 288q^{77} + 240q^{78} + 72q^{81} - 40q^{82} - 36q^{84} - 200q^{86} - 140q^{88} + 80q^{89} - 144q^{92} - 144q^{93} - 96q^{94} - 174q^{96} - 432q^{97} - 660q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.67986 + 1.08539i −0.839931 + 0.542693i
\(3\) 1.73205i 0.577350i
\(4\) 1.64388 3.64660i 0.410969 0.911649i
\(5\) 0 0
\(6\) 1.87994 + 2.90961i 0.313324 + 0.484935i
\(7\) 0.596540i 0.0852199i −0.999092 0.0426100i \(-0.986433\pi\)
0.999092 0.0426100i \(-0.0135673\pi\)
\(8\) 1.19648 + 7.91002i 0.149560 + 0.988753i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 9.27963i 0.843602i 0.906688 + 0.421801i \(0.138602\pi\)
−0.906688 + 0.421801i \(0.861398\pi\)
\(12\) −6.31609 2.84728i −0.526341 0.237273i
\(13\) 23.5117 1.80859 0.904295 0.426907i \(-0.140397\pi\)
0.904295 + 0.426907i \(0.140397\pi\)
\(14\) 0.647476 + 1.00210i 0.0462483 + 0.0715789i
\(15\) 0 0
\(16\) −10.5953 11.9891i −0.662209 0.749319i
\(17\) −3.97751 −0.233971 −0.116986 0.993134i \(-0.537323\pi\)
−0.116986 + 0.993134i \(0.537323\pi\)
\(18\) 5.03959 3.25616i 0.279977 0.180898i
\(19\) 7.04756i 0.370924i −0.982651 0.185462i \(-0.940622\pi\)
0.982651 0.185462i \(-0.0593782\pi\)
\(20\) 0 0
\(21\) −1.03324 −0.0492018
\(22\) −10.0720 15.5885i −0.457817 0.708568i
\(23\) 32.0793i 1.39475i −0.716705 0.697376i \(-0.754351\pi\)
0.716705 0.697376i \(-0.245649\pi\)
\(24\) 13.7006 2.07237i 0.570857 0.0863486i
\(25\) 0 0
\(26\) −39.4964 + 25.5192i −1.51909 + 0.981509i
\(27\) 5.19615i 0.192450i
\(28\) −2.17534 0.980637i −0.0776907 0.0350227i
\(29\) 35.6734 1.23012 0.615059 0.788481i \(-0.289132\pi\)
0.615059 + 0.788481i \(0.289132\pi\)
\(30\) 0 0
\(31\) 59.2585i 1.91156i −0.294076 0.955782i \(-0.595012\pi\)
0.294076 0.955782i \(-0.404988\pi\)
\(32\) 30.8115 + 8.64000i 0.962860 + 0.270000i
\(33\) 16.0728 0.487054
\(34\) 6.68167 4.31713i 0.196520 0.126974i
\(35\) 0 0
\(36\) −4.93163 + 10.9398i −0.136990 + 0.303883i
\(37\) 5.38761 0.145611 0.0728055 0.997346i \(-0.476805\pi\)
0.0728055 + 0.997346i \(0.476805\pi\)
\(38\) 7.64932 + 11.8389i 0.201298 + 0.311551i
\(39\) 40.7234i 1.04419i
\(40\) 0 0
\(41\) 40.0791 0.977539 0.488769 0.872413i \(-0.337446\pi\)
0.488769 + 0.872413i \(0.337446\pi\)
\(42\) 1.73570 1.12146i 0.0413261 0.0267014i
\(43\) 36.1157i 0.839901i −0.907547 0.419950i \(-0.862047\pi\)
0.907547 0.419950i \(-0.137953\pi\)
\(44\) 33.8391 + 15.2545i 0.769070 + 0.346694i
\(45\) 0 0
\(46\) 34.8184 + 53.8888i 0.756922 + 1.17150i
\(47\) 74.0131i 1.57475i 0.616477 + 0.787373i \(0.288559\pi\)
−0.616477 + 0.787373i \(0.711441\pi\)
\(48\) −20.7657 + 18.3517i −0.432620 + 0.382327i
\(49\) 48.6441 0.992738
\(50\) 0 0
\(51\) 6.88925i 0.135083i
\(52\) 38.6503 85.7376i 0.743275 1.64880i
\(53\) 2.55123 0.0481364 0.0240682 0.999710i \(-0.492338\pi\)
0.0240682 + 0.999710i \(0.492338\pi\)
\(54\) −5.63983 8.72882i −0.104441 0.161645i
\(55\) 0 0
\(56\) 4.71864 0.713748i 0.0842614 0.0127455i
\(57\) −12.2067 −0.214153
\(58\) −59.9265 + 38.7194i −1.03321 + 0.667576i
\(59\) 36.4026i 0.616993i 0.951225 + 0.308497i \(0.0998259\pi\)
−0.951225 + 0.308497i \(0.900174\pi\)
\(60\) 0 0
\(61\) −8.73223 −0.143151 −0.0715757 0.997435i \(-0.522803\pi\)
−0.0715757 + 0.997435i \(0.522803\pi\)
\(62\) 64.3183 + 99.5461i 1.03739 + 1.60558i
\(63\) 1.78962i 0.0284066i
\(64\) −61.1369 + 18.9284i −0.955264 + 0.295756i
\(65\) 0 0
\(66\) −27.0001 + 17.4452i −0.409092 + 0.264321i
\(67\) 69.7379i 1.04086i −0.853903 0.520432i \(-0.825771\pi\)
0.853903 0.520432i \(-0.174229\pi\)
\(68\) −6.53853 + 14.5044i −0.0961548 + 0.213300i
\(69\) −55.5630 −0.805261
\(70\) 0 0
\(71\) 59.2170i 0.834043i −0.908897 0.417021i \(-0.863074\pi\)
0.908897 0.417021i \(-0.136926\pi\)
\(72\) −3.58944 23.7301i −0.0498534 0.329584i
\(73\) 83.0019 1.13701 0.568506 0.822679i \(-0.307522\pi\)
0.568506 + 0.822679i \(0.307522\pi\)
\(74\) −9.05044 + 5.84763i −0.122303 + 0.0790220i
\(75\) 0 0
\(76\) −25.6996 11.5853i −0.338153 0.152438i
\(77\) 5.53566 0.0718917
\(78\) 44.2006 + 68.4098i 0.566675 + 0.877048i
\(79\) 65.8705i 0.833804i 0.908951 + 0.416902i \(0.136884\pi\)
−0.908951 + 0.416902i \(0.863116\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) −67.3274 + 43.5013i −0.821065 + 0.530503i
\(83\) 129.909i 1.56517i −0.622542 0.782586i \(-0.713900\pi\)
0.622542 0.782586i \(-0.286100\pi\)
\(84\) −1.69851 + 3.76780i −0.0202204 + 0.0448547i
\(85\) 0 0
\(86\) 39.1995 + 60.6695i 0.455808 + 0.705459i
\(87\) 61.7882i 0.710209i
\(88\) −73.4020 + 11.1029i −0.834114 + 0.126169i
\(89\) −130.466 −1.46591 −0.732956 0.680277i \(-0.761860\pi\)
−0.732956 + 0.680277i \(0.761860\pi\)
\(90\) 0 0
\(91\) 14.0256i 0.154128i
\(92\) −116.980 52.7344i −1.27152 0.573200i
\(93\) −102.639 −1.10364
\(94\) −80.3327 124.332i −0.854603 1.32268i
\(95\) 0 0
\(96\) 14.9649 53.3671i 0.155885 0.555908i
\(97\) −93.1113 −0.959911 −0.479955 0.877293i \(-0.659347\pi\)
−0.479955 + 0.877293i \(0.659347\pi\)
\(98\) −81.7155 + 52.7977i −0.833831 + 0.538752i
\(99\) 27.8389i 0.281201i
\(100\) 0 0
\(101\) −3.66081 −0.0362457 −0.0181228 0.999836i \(-0.505769\pi\)
−0.0181228 + 0.999836i \(0.505769\pi\)
\(102\) −7.47749 11.5730i −0.0733087 0.113461i
\(103\) 151.417i 1.47007i 0.678032 + 0.735033i \(0.262833\pi\)
−0.678032 + 0.735033i \(0.737167\pi\)
\(104\) 28.1313 + 185.978i 0.270493 + 1.78825i
\(105\) 0 0
\(106\) −4.28571 + 2.76907i −0.0404313 + 0.0261233i
\(107\) 82.8092i 0.773918i 0.922097 + 0.386959i \(0.126474\pi\)
−0.922097 + 0.386959i \(0.873526\pi\)
\(108\) 18.9483 + 8.54183i 0.175447 + 0.0790910i
\(109\) −7.36835 −0.0675996 −0.0337998 0.999429i \(-0.510761\pi\)
−0.0337998 + 0.999429i \(0.510761\pi\)
\(110\) 0 0
\(111\) 9.33161i 0.0840685i
\(112\) −7.15197 + 6.32054i −0.0638569 + 0.0564334i
\(113\) −65.0370 −0.575549 −0.287774 0.957698i \(-0.592915\pi\)
−0.287774 + 0.957698i \(0.592915\pi\)
\(114\) 20.5056 13.2490i 0.179874 0.116219i
\(115\) 0 0
\(116\) 58.6427 130.087i 0.505540 1.12144i
\(117\) −70.5350 −0.602864
\(118\) −39.5109 61.1514i −0.334838 0.518232i
\(119\) 2.37274i 0.0199390i
\(120\) 0 0
\(121\) 34.8885 0.288335
\(122\) 14.6689 9.47784i 0.120237 0.0776872i
\(123\) 69.4190i 0.564382i
\(124\) −216.092 97.4136i −1.74268 0.785593i
\(125\) 0 0
\(126\) −1.94243 3.00631i −0.0154161 0.0238596i
\(127\) 139.469i 1.09818i 0.835763 + 0.549091i \(0.185026\pi\)
−0.835763 + 0.549091i \(0.814974\pi\)
\(128\) 82.1569 98.1542i 0.641851 0.766829i
\(129\) −62.5543 −0.484917
\(130\) 0 0
\(131\) 63.4856i 0.484623i 0.970198 + 0.242312i \(0.0779056\pi\)
−0.970198 + 0.242312i \(0.922094\pi\)
\(132\) 26.4217 58.6110i 0.200164 0.444023i
\(133\) −4.20415 −0.0316101
\(134\) 75.6925 + 117.150i 0.564870 + 0.874254i
\(135\) 0 0
\(136\) −4.75901 31.4622i −0.0349927 0.231340i
\(137\) 138.157 1.00845 0.504223 0.863573i \(-0.331779\pi\)
0.504223 + 0.863573i \(0.331779\pi\)
\(138\) 93.3382 60.3073i 0.676363 0.437009i
\(139\) 29.9578i 0.215523i −0.994177 0.107762i \(-0.965632\pi\)
0.994177 0.107762i \(-0.0343684\pi\)
\(140\) 0 0
\(141\) 128.194 0.909180
\(142\) 64.2733 + 99.4765i 0.452629 + 0.700539i
\(143\) 218.180i 1.52573i
\(144\) 31.7860 + 35.9673i 0.220736 + 0.249773i
\(145\) 0 0
\(146\) −139.432 + 90.0891i −0.955012 + 0.617048i
\(147\) 84.2541i 0.573157i
\(148\) 8.85655 19.6464i 0.0598416 0.132746i
\(149\) −47.3823 −0.318002 −0.159001 0.987278i \(-0.550827\pi\)
−0.159001 + 0.987278i \(0.550827\pi\)
\(150\) 0 0
\(151\) 109.604i 0.725852i 0.931818 + 0.362926i \(0.118222\pi\)
−0.931818 + 0.362926i \(0.881778\pi\)
\(152\) 55.7463 8.43227i 0.366752 0.0554755i
\(153\) 11.9325 0.0779904
\(154\) −9.29915 + 6.00833i −0.0603841 + 0.0390151i
\(155\) 0 0
\(156\) −148.502 66.9442i −0.951936 0.429130i
\(157\) 177.588 1.13113 0.565566 0.824703i \(-0.308658\pi\)
0.565566 + 0.824703i \(0.308658\pi\)
\(158\) −71.4950 110.653i −0.452500 0.700338i
\(159\) 4.41886i 0.0277916i
\(160\) 0 0
\(161\) −19.1366 −0.118861
\(162\) −15.1188 + 9.76847i −0.0933257 + 0.0602992i
\(163\) 96.8778i 0.594342i 0.954824 + 0.297171i \(0.0960432\pi\)
−0.954824 + 0.297171i \(0.903957\pi\)
\(164\) 65.8850 146.152i 0.401738 0.891173i
\(165\) 0 0
\(166\) 141.002 + 218.230i 0.849408 + 1.31464i
\(167\) 152.605i 0.913801i −0.889518 0.456901i \(-0.848960\pi\)
0.889518 0.456901i \(-0.151040\pi\)
\(168\) −1.23625 8.17292i −0.00735862 0.0486484i
\(169\) 383.799 2.27100
\(170\) 0 0
\(171\) 21.1427i 0.123641i
\(172\) −131.700 59.3698i −0.765695 0.345173i
\(173\) −155.773 −0.900422 −0.450211 0.892922i \(-0.648651\pi\)
−0.450211 + 0.892922i \(0.648651\pi\)
\(174\) 67.0640 + 103.796i 0.385425 + 0.596527i
\(175\) 0 0
\(176\) 111.254 98.3209i 0.632127 0.558641i
\(177\) 63.0512 0.356221
\(178\) 219.165 141.606i 1.23126 0.795540i
\(179\) 126.001i 0.703915i −0.936016 0.351957i \(-0.885516\pi\)
0.936016 0.351957i \(-0.114484\pi\)
\(180\) 0 0
\(181\) −346.725 −1.91561 −0.957803 0.287424i \(-0.907201\pi\)
−0.957803 + 0.287424i \(0.907201\pi\)
\(182\) 15.2232 + 23.5612i 0.0836442 + 0.129457i
\(183\) 15.1247i 0.0826485i
\(184\) 253.748 38.3823i 1.37906 0.208599i
\(185\) 0 0
\(186\) 172.419 111.403i 0.926983 0.598939i
\(187\) 36.9098i 0.197379i
\(188\) 269.896 + 121.668i 1.43562 + 0.647171i
\(189\) 3.09971 0.0164006
\(190\) 0 0
\(191\) 133.159i 0.697167i 0.937278 + 0.348584i \(0.113337\pi\)
−0.937278 + 0.348584i \(0.886663\pi\)
\(192\) 32.7849 + 105.892i 0.170755 + 0.551522i
\(193\) 136.246 0.705940 0.352970 0.935635i \(-0.385172\pi\)
0.352970 + 0.935635i \(0.385172\pi\)
\(194\) 156.414 101.062i 0.806259 0.520937i
\(195\) 0 0
\(196\) 79.9649 177.386i 0.407984 0.905029i
\(197\) −74.8945 −0.380175 −0.190087 0.981767i \(-0.560877\pi\)
−0.190087 + 0.981767i \(0.560877\pi\)
\(198\) 30.2159 + 46.7655i 0.152606 + 0.236189i
\(199\) 251.605i 1.26434i 0.774828 + 0.632172i \(0.217836\pi\)
−0.774828 + 0.632172i \(0.782164\pi\)
\(200\) 0 0
\(201\) −120.790 −0.600943
\(202\) 6.14966 3.97339i 0.0304439 0.0196703i
\(203\) 21.2806i 0.104831i
\(204\) 25.1223 + 11.3251i 0.123149 + 0.0555150i
\(205\) 0 0
\(206\) −164.346 254.359i −0.797794 1.23475i
\(207\) 96.2379i 0.464917i
\(208\) −249.114 281.884i −1.19767 1.35521i
\(209\) 65.3987 0.312913
\(210\) 0 0
\(211\) 228.203i 1.08153i 0.841173 + 0.540766i \(0.181865\pi\)
−0.841173 + 0.540766i \(0.818135\pi\)
\(212\) 4.19390 9.30331i 0.0197826 0.0438835i
\(213\) −102.567 −0.481535
\(214\) −89.8799 139.108i −0.420000 0.650038i
\(215\) 0 0
\(216\) −41.1017 + 6.21710i −0.190286 + 0.0287829i
\(217\) −35.3500 −0.162903
\(218\) 12.3778 7.99751i 0.0567790 0.0366858i
\(219\) 143.763i 0.656454i
\(220\) 0 0
\(221\) −93.5179 −0.423158
\(222\) 10.1284 + 15.6758i 0.0456234 + 0.0706118i
\(223\) 85.9549i 0.385448i 0.981253 + 0.192724i \(0.0617322\pi\)
−0.981253 + 0.192724i \(0.938268\pi\)
\(224\) 5.15410 18.3803i 0.0230094 0.0820549i
\(225\) 0 0
\(226\) 109.253 70.5902i 0.483421 0.312346i
\(227\) 282.357i 1.24386i −0.783071 0.621932i \(-0.786348\pi\)
0.783071 0.621932i \(-0.213652\pi\)
\(228\) −20.0663 + 44.5130i −0.0880103 + 0.195233i
\(229\) 138.263 0.603768 0.301884 0.953345i \(-0.402385\pi\)
0.301884 + 0.953345i \(0.402385\pi\)
\(230\) 0 0
\(231\) 9.58805i 0.0415067i
\(232\) 42.6826 + 282.178i 0.183977 + 1.21628i
\(233\) 0.522939 0.00224438 0.00112219 0.999999i \(-0.499643\pi\)
0.00112219 + 0.999999i \(0.499643\pi\)
\(234\) 118.489 76.5577i 0.506364 0.327170i
\(235\) 0 0
\(236\) 132.746 + 59.8413i 0.562482 + 0.253565i
\(237\) 114.091 0.481397
\(238\) −2.57534 3.98588i −0.0108208 0.0167474i
\(239\) 73.6928i 0.308338i 0.988044 + 0.154169i \(0.0492700\pi\)
−0.988044 + 0.154169i \(0.950730\pi\)
\(240\) 0 0
\(241\) 31.3705 0.130168 0.0650840 0.997880i \(-0.479268\pi\)
0.0650840 + 0.997880i \(0.479268\pi\)
\(242\) −58.6080 + 37.8675i −0.242182 + 0.156477i
\(243\) 15.5885i 0.0641500i
\(244\) −14.3547 + 31.8429i −0.0588307 + 0.130504i
\(245\) 0 0
\(246\) 75.3464 + 116.614i 0.306286 + 0.474042i
\(247\) 165.700i 0.670850i
\(248\) 468.736 70.9016i 1.89006 0.285894i
\(249\) −225.010 −0.903653
\(250\) 0 0
\(251\) 78.7478i 0.313736i 0.987620 + 0.156868i \(0.0501398\pi\)
−0.987620 + 0.156868i \(0.949860\pi\)
\(252\) 6.52602 + 2.94191i 0.0258969 + 0.0116742i
\(253\) 297.684 1.17662
\(254\) −151.378 234.289i −0.595975 0.922397i
\(255\) 0 0
\(256\) −31.4772 + 254.057i −0.122958 + 0.992412i
\(257\) −243.954 −0.949236 −0.474618 0.880192i \(-0.657414\pi\)
−0.474618 + 0.880192i \(0.657414\pi\)
\(258\) 105.083 67.8956i 0.407297 0.263161i
\(259\) 3.21392i 0.0124090i
\(260\) 0 0
\(261\) −107.020 −0.410039
\(262\) −68.9064 106.647i −0.263002 0.407050i
\(263\) 102.737i 0.390635i −0.980740 0.195317i \(-0.937426\pi\)
0.980740 0.195317i \(-0.0625737\pi\)
\(264\) 19.2308 + 127.136i 0.0728439 + 0.481576i
\(265\) 0 0
\(266\) 7.06239 4.56312i 0.0265503 0.0171546i
\(267\) 225.974i 0.846344i
\(268\) −254.306 114.640i −0.948903 0.427763i
\(269\) −123.646 −0.459651 −0.229825 0.973232i \(-0.573816\pi\)
−0.229825 + 0.973232i \(0.573816\pi\)
\(270\) 0 0
\(271\) 332.371i 1.22646i −0.789904 0.613230i \(-0.789870\pi\)
0.789904 0.613230i \(-0.210130\pi\)
\(272\) 42.1431 + 47.6868i 0.154938 + 0.175319i
\(273\) −24.2931 −0.0889858
\(274\) −232.085 + 149.954i −0.847026 + 0.547277i
\(275\) 0 0
\(276\) −91.3386 + 202.616i −0.330937 + 0.734115i
\(277\) 125.916 0.454571 0.227286 0.973828i \(-0.427015\pi\)
0.227286 + 0.973828i \(0.427015\pi\)
\(278\) 32.5157 + 50.3249i 0.116963 + 0.181025i
\(279\) 177.775i 0.637188i
\(280\) 0 0
\(281\) 52.5628 0.187056 0.0935281 0.995617i \(-0.470186\pi\)
0.0935281 + 0.995617i \(0.470186\pi\)
\(282\) −215.349 + 139.140i −0.763649 + 0.493405i
\(283\) 199.288i 0.704199i 0.935963 + 0.352100i \(0.114532\pi\)
−0.935963 + 0.352100i \(0.885468\pi\)
\(284\) −215.941 97.3454i −0.760355 0.342766i
\(285\) 0 0
\(286\) −236.809 366.512i −0.828004 1.28151i
\(287\) 23.9088i 0.0833058i
\(288\) −92.4346 25.9200i −0.320953 0.0900001i
\(289\) −273.179 −0.945258
\(290\) 0 0
\(291\) 161.274i 0.554205i
\(292\) 136.445 302.674i 0.467276 1.03656i
\(293\) −102.161 −0.348672 −0.174336 0.984686i \(-0.555778\pi\)
−0.174336 + 0.984686i \(0.555778\pi\)
\(294\) 91.4482 + 141.535i 0.311048 + 0.481413i
\(295\) 0 0
\(296\) 6.44617 + 42.6161i 0.0217776 + 0.143973i
\(297\) −48.2184 −0.162351
\(298\) 79.5957 51.4281i 0.267100 0.172577i
\(299\) 754.238i 2.52254i
\(300\) 0 0
\(301\) −21.5445 −0.0715763
\(302\) −118.962 184.119i −0.393915 0.609666i
\(303\) 6.34071i 0.0209264i
\(304\) −84.4939 + 74.6713i −0.277941 + 0.245629i
\(305\) 0 0
\(306\) −20.0450 + 12.9514i −0.0655065 + 0.0423248i
\(307\) 328.391i 1.06968i 0.844954 + 0.534839i \(0.179628\pi\)
−0.844954 + 0.534839i \(0.820372\pi\)
\(308\) 9.09994 20.1863i 0.0295453 0.0655401i
\(309\) 262.262 0.848743
\(310\) 0 0
\(311\) 95.4377i 0.306874i −0.988158 0.153437i \(-0.950966\pi\)
0.988158 0.153437i \(-0.0490342\pi\)
\(312\) 322.123 48.7248i 1.03245 0.156169i
\(313\) −550.408 −1.75849 −0.879246 0.476368i \(-0.841953\pi\)
−0.879246 + 0.476368i \(0.841953\pi\)
\(314\) −298.323 + 192.751i −0.950073 + 0.613858i
\(315\) 0 0
\(316\) 240.203 + 108.283i 0.760137 + 0.342668i
\(317\) −439.394 −1.38610 −0.693051 0.720889i \(-0.743734\pi\)
−0.693051 + 0.720889i \(0.743734\pi\)
\(318\) 4.79617 + 7.42307i 0.0150823 + 0.0233430i
\(319\) 331.036i 1.03773i
\(320\) 0 0
\(321\) 143.430 0.446822
\(322\) 32.1468 20.7706i 0.0998348 0.0645048i
\(323\) 28.0317i 0.0867855i
\(324\) 14.7949 32.8194i 0.0456632 0.101294i
\(325\) 0 0
\(326\) −105.150 162.741i −0.322545 0.499206i
\(327\) 12.7624i 0.0390286i
\(328\) 47.9539 + 317.026i 0.146201 + 0.966544i
\(329\) 44.1517 0.134200
\(330\) 0 0
\(331\) 479.922i 1.44992i −0.688794 0.724958i \(-0.741859\pi\)
0.688794 0.724958i \(-0.258141\pi\)
\(332\) −473.727 213.555i −1.42689 0.643237i
\(333\) −16.1628 −0.0485370
\(334\) 165.635 + 256.355i 0.495913 + 0.767530i
\(335\) 0 0
\(336\) 10.9475 + 12.3876i 0.0325819 + 0.0368678i
\(337\) −58.8437 −0.174610 −0.0873052 0.996182i \(-0.527826\pi\)
−0.0873052 + 0.996182i \(0.527826\pi\)
\(338\) −644.730 + 416.570i −1.90748 + 1.23246i
\(339\) 112.647i 0.332293i
\(340\) 0 0
\(341\) 549.897 1.61260
\(342\) −22.9480 35.5168i −0.0670993 0.103850i
\(343\) 58.2486i 0.169821i
\(344\) 285.676 43.2118i 0.830454 0.125616i
\(345\) 0 0
\(346\) 261.677 169.074i 0.756293 0.488653i
\(347\) 12.1484i 0.0350099i −0.999847 0.0175049i \(-0.994428\pi\)
0.999847 0.0175049i \(-0.00557228\pi\)
\(348\) −225.317 101.572i −0.647462 0.291874i
\(349\) −30.9277 −0.0886180 −0.0443090 0.999018i \(-0.514109\pi\)
−0.0443090 + 0.999018i \(0.514109\pi\)
\(350\) 0 0
\(351\) 122.170i 0.348063i
\(352\) −80.1760 + 285.919i −0.227773 + 0.812271i
\(353\) 288.065 0.816048 0.408024 0.912971i \(-0.366218\pi\)
0.408024 + 0.912971i \(0.366218\pi\)
\(354\) −105.917 + 68.4348i −0.299201 + 0.193319i
\(355\) 0 0
\(356\) −214.470 + 475.757i −0.602444 + 1.33640i
\(357\) 4.10971 0.0115118
\(358\) 136.759 + 211.664i 0.382010 + 0.591240i
\(359\) 663.911i 1.84933i 0.380776 + 0.924667i \(0.375657\pi\)
−0.380776 + 0.924667i \(0.624343\pi\)
\(360\) 0 0
\(361\) 311.332 0.862415
\(362\) 582.450 376.330i 1.60898 1.03959i
\(363\) 60.4287i 0.166470i
\(364\) −51.1459 23.0564i −0.140511 0.0633418i
\(365\) 0 0
\(366\) −16.4161 25.4074i −0.0448527 0.0694190i
\(367\) 6.08529i 0.0165812i −0.999966 0.00829059i \(-0.997361\pi\)
0.999966 0.00829059i \(-0.00263901\pi\)
\(368\) −384.602 + 339.891i −1.04511 + 0.923618i
\(369\) −120.237 −0.325846
\(370\) 0 0
\(371\) 1.52191i 0.00410218i
\(372\) −168.725 + 374.282i −0.453562 + 1.00613i
\(373\) 204.741 0.548903 0.274451 0.961601i \(-0.411504\pi\)
0.274451 + 0.961601i \(0.411504\pi\)
\(374\) 40.0614 + 62.0034i 0.107116 + 0.165784i
\(375\) 0 0
\(376\) −585.445 + 88.5552i −1.55703 + 0.235519i
\(377\) 838.742 2.22478
\(378\) −5.20709 + 3.36438i −0.0137754 + 0.00890048i
\(379\) 402.331i 1.06156i −0.847510 0.530780i \(-0.821899\pi\)
0.847510 0.530780i \(-0.178101\pi\)
\(380\) 0 0
\(381\) 241.568 0.634036
\(382\) −144.529 223.689i −0.378348 0.585573i
\(383\) 331.751i 0.866191i 0.901348 + 0.433096i \(0.142579\pi\)
−0.901348 + 0.433096i \(0.857421\pi\)
\(384\) −170.008 142.300i −0.442729 0.370573i
\(385\) 0 0
\(386\) −228.875 + 147.880i −0.592941 + 0.383109i
\(387\) 108.347i 0.279967i
\(388\) −153.063 + 339.540i −0.394493 + 0.875102i
\(389\) −623.310 −1.60234 −0.801169 0.598438i \(-0.795788\pi\)
−0.801169 + 0.598438i \(0.795788\pi\)
\(390\) 0 0
\(391\) 127.596i 0.326332i
\(392\) 58.2018 + 384.776i 0.148474 + 0.981572i
\(393\) 109.960 0.279797
\(394\) 125.812 81.2894i 0.319321 0.206318i
\(395\) 0 0
\(396\) −101.517 45.7636i −0.256357 0.115565i
\(397\) 355.449 0.895338 0.447669 0.894199i \(-0.352254\pi\)
0.447669 + 0.894199i \(0.352254\pi\)
\(398\) −273.088 422.661i −0.686151 1.06196i
\(399\) 7.28180i 0.0182501i
\(400\) 0 0
\(401\) −542.927 −1.35393 −0.676966 0.736014i \(-0.736706\pi\)
−0.676966 + 0.736014i \(0.736706\pi\)
\(402\) 202.910 131.103i 0.504751 0.326128i
\(403\) 1393.27i 3.45724i
\(404\) −6.01792 + 13.3495i −0.0148958 + 0.0330433i
\(405\) 0 0
\(406\) 23.0977 + 35.7485i 0.0568908 + 0.0880505i
\(407\) 49.9950i 0.122838i
\(408\) −54.4941 + 8.24285i −0.133564 + 0.0202031i
\(409\) −108.497 −0.265273 −0.132636 0.991165i \(-0.542344\pi\)
−0.132636 + 0.991165i \(0.542344\pi\)
\(410\) 0 0
\(411\) 239.295i 0.582227i
\(412\) 552.156 + 248.910i 1.34018 + 0.604151i
\(413\) 21.7156 0.0525801
\(414\) −104.455 161.666i −0.252307 0.390499i
\(415\) 0 0
\(416\) 724.431 + 203.141i 1.74142 + 0.488320i
\(417\) −51.8884 −0.124433
\(418\) −109.861 + 70.9828i −0.262825 + 0.169815i
\(419\) 172.176i 0.410921i −0.978665 0.205460i \(-0.934131\pi\)
0.978665 0.205460i \(-0.0658691\pi\)
\(420\) 0 0
\(421\) 478.522 1.13663 0.568316 0.822810i \(-0.307595\pi\)
0.568316 + 0.822810i \(0.307595\pi\)
\(422\) −247.688 383.350i −0.586940 0.908412i
\(423\) 222.039i 0.524915i
\(424\) 3.05250 + 20.1803i 0.00719929 + 0.0475950i
\(425\) 0 0
\(426\) 172.298 111.325i 0.404456 0.261326i
\(427\) 5.20912i 0.0121993i
\(428\) 301.972 + 136.128i 0.705541 + 0.318056i
\(429\) 377.898 0.880882
\(430\) 0 0
\(431\) 290.722i 0.674530i −0.941410 0.337265i \(-0.890498\pi\)
0.941410 0.337265i \(-0.109502\pi\)
\(432\) 62.2972 55.0550i 0.144207 0.127442i
\(433\) −53.7726 −0.124186 −0.0620931 0.998070i \(-0.519778\pi\)
−0.0620931 + 0.998070i \(0.519778\pi\)
\(434\) 59.3832 38.3684i 0.136828 0.0884065i
\(435\) 0 0
\(436\) −12.1127 + 26.8694i −0.0277813 + 0.0616271i
\(437\) −226.081 −0.517347
\(438\) 156.039 + 241.503i 0.356253 + 0.551376i
\(439\) 328.657i 0.748650i 0.927298 + 0.374325i \(0.122126\pi\)
−0.927298 + 0.374325i \(0.877874\pi\)
\(440\) 0 0
\(441\) −145.932 −0.330913
\(442\) 157.097 101.503i 0.355424 0.229645i
\(443\) 428.910i 0.968194i −0.875014 0.484097i \(-0.839148\pi\)
0.875014 0.484097i \(-0.160852\pi\)
\(444\) −34.0286 15.3400i −0.0766410 0.0345496i
\(445\) 0 0
\(446\) −93.2942 144.392i −0.209180 0.323750i
\(447\) 82.0685i 0.183599i
\(448\) 11.2915 + 36.4706i 0.0252043 + 0.0814075i
\(449\) 409.229 0.911423 0.455711 0.890128i \(-0.349385\pi\)
0.455711 + 0.890128i \(0.349385\pi\)
\(450\) 0 0
\(451\) 371.919i 0.824654i
\(452\) −106.913 + 237.164i −0.236533 + 0.524698i
\(453\) 189.839 0.419071
\(454\) 306.466 + 474.321i 0.675036 + 1.04476i
\(455\) 0 0
\(456\) −14.6051 96.5555i −0.0320288 0.211745i
\(457\) −768.561 −1.68175 −0.840876 0.541228i \(-0.817960\pi\)
−0.840876 + 0.541228i \(0.817960\pi\)
\(458\) −232.262 + 150.068i −0.507123 + 0.327660i
\(459\) 20.6677i 0.0450278i
\(460\) 0 0
\(461\) −316.563 −0.686687 −0.343343 0.939210i \(-0.611559\pi\)
−0.343343 + 0.939210i \(0.611559\pi\)
\(462\) 10.4067 + 16.1066i 0.0225254 + 0.0348628i
\(463\) 491.208i 1.06093i 0.847708 + 0.530463i \(0.177982\pi\)
−0.847708 + 0.530463i \(0.822018\pi\)
\(464\) −377.972 427.692i −0.814596 0.921751i
\(465\) 0 0
\(466\) −0.878466 + 0.567591i −0.00188512 + 0.00121801i
\(467\) 410.393i 0.878785i 0.898295 + 0.439393i \(0.144806\pi\)
−0.898295 + 0.439393i \(0.855194\pi\)
\(468\) −115.951 + 257.213i −0.247758 + 0.549600i
\(469\) −41.6014 −0.0887024
\(470\) 0 0
\(471\) 307.591i 0.653060i
\(472\) −287.945 + 43.5550i −0.610054 + 0.0922776i
\(473\) 335.141 0.708542
\(474\) −191.657 + 123.833i −0.404341 + 0.261251i
\(475\) 0 0
\(476\) 8.65243 + 3.90049i 0.0181774 + 0.00819431i
\(477\) −7.65369 −0.0160455
\(478\) −79.9851 123.794i −0.167333 0.258983i
\(479\) 198.918i 0.415277i −0.978206 0.207638i \(-0.933422\pi\)
0.978206 0.207638i \(-0.0665778\pi\)
\(480\) 0 0
\(481\) 126.672 0.263351
\(482\) −52.6981 + 34.0491i −0.109332 + 0.0706413i
\(483\) 33.1455i 0.0686242i
\(484\) 57.3524 127.224i 0.118497 0.262860i
\(485\) 0 0
\(486\) 16.9195 + 26.1865i 0.0348138 + 0.0538816i
\(487\) 204.762i 0.420456i −0.977652 0.210228i \(-0.932579\pi\)
0.977652 0.210228i \(-0.0674206\pi\)
\(488\) −10.4479 69.0721i −0.0214097 0.141541i
\(489\) 167.797 0.343144
\(490\) 0 0
\(491\) 788.598i 1.60611i −0.595908 0.803053i \(-0.703208\pi\)
0.595908 0.803053i \(-0.296792\pi\)
\(492\) −253.143 114.116i −0.514519 0.231944i
\(493\) −141.891 −0.287812
\(494\) 179.848 + 278.353i 0.364066 + 0.563468i
\(495\) 0 0
\(496\) −710.456 + 627.864i −1.43237 + 1.26586i
\(497\) −35.3253 −0.0710771
\(498\) 377.985 244.222i 0.759006 0.490406i
\(499\) 740.385i 1.48374i −0.670545 0.741869i \(-0.733940\pi\)
0.670545 0.741869i \(-0.266060\pi\)
\(500\) 0 0
\(501\) −264.319 −0.527583
\(502\) −85.4717 132.285i −0.170262 0.263517i
\(503\) 70.8800i 0.140914i 0.997515 + 0.0704572i \(0.0224458\pi\)
−0.997515 + 0.0704572i \(0.977554\pi\)
\(504\) −14.1559 + 2.14124i −0.0280871 + 0.00424850i
\(505\) 0 0
\(506\) −500.068 + 323.102i −0.988277 + 0.638541i
\(507\) 664.760i 1.31116i
\(508\) 508.588 + 229.270i 1.00116 + 0.451318i
\(509\) 522.642 1.02680 0.513400 0.858149i \(-0.328386\pi\)
0.513400 + 0.858149i \(0.328386\pi\)
\(510\) 0 0
\(511\) 49.5139i 0.0968961i
\(512\) −222.873 460.946i −0.435299 0.900286i
\(513\) 36.6202 0.0713844
\(514\) 409.809 264.784i 0.797293 0.515144i
\(515\) 0 0
\(516\) −102.831 + 228.110i −0.199286 + 0.442074i
\(517\) −686.813 −1.32846
\(518\) 3.48834 + 5.39894i 0.00673425 + 0.0104227i
\(519\) 269.807i 0.519859i
\(520\) 0 0
\(521\) 304.082 0.583650 0.291825 0.956472i \(-0.405738\pi\)
0.291825 + 0.956472i \(0.405738\pi\)
\(522\) 179.779 116.158i 0.344405 0.222525i
\(523\) 174.416i 0.333491i −0.986000 0.166746i \(-0.946674\pi\)
0.986000 0.166746i \(-0.0533259\pi\)
\(524\) 231.507 + 104.362i 0.441806 + 0.199165i
\(525\) 0 0
\(526\) 111.509 + 172.584i 0.211995 + 0.328106i
\(527\) 235.701i 0.447251i
\(528\) −170.297 192.698i −0.322532 0.364959i
\(529\) −500.081 −0.945333
\(530\) 0 0
\(531\) 109.208i 0.205664i
\(532\) −6.91109 + 15.3308i −0.0129908 + 0.0288174i
\(533\) 942.327 1.76797
\(534\) −245.269 379.605i −0.459305 0.710871i
\(535\) 0 0
\(536\) 551.628 83.4401i 1.02916 0.155672i
\(537\) −218.240 −0.406405
\(538\) 207.708 134.204i 0.386075 0.249449i
\(539\) 451.399i 0.837476i
\(540\) 0 0
\(541\) −262.199 −0.484655 −0.242328 0.970194i \(-0.577911\pi\)
−0.242328 + 0.970194i \(0.577911\pi\)
\(542\) 360.750 + 558.337i 0.665591 + 1.03014i
\(543\) 600.545i 1.10598i
\(544\) −122.553 34.3657i −0.225281 0.0631722i
\(545\) 0 0
\(546\) 40.8091 26.3674i 0.0747420 0.0482920i
\(547\) 146.179i 0.267237i 0.991033 + 0.133619i \(0.0426598\pi\)
−0.991033 + 0.133619i \(0.957340\pi\)
\(548\) 227.113 503.804i 0.414440 0.919350i
\(549\) 26.1967 0.0477171
\(550\) 0 0
\(551\) 251.411i 0.456281i
\(552\) −66.4800 439.504i −0.120435 0.796203i
\(553\) 39.2944 0.0710568
\(554\) −211.522 + 136.668i −0.381809 + 0.246693i
\(555\) 0 0
\(556\) −109.244 49.2468i −0.196482 0.0885734i
\(557\) −187.700 −0.336984 −0.168492 0.985703i \(-0.553890\pi\)
−0.168492 + 0.985703i \(0.553890\pi\)
\(558\) −192.955 298.638i −0.345797 0.535194i
\(559\) 849.142i 1.51904i
\(560\) 0 0
\(561\) −63.9296 −0.113957
\(562\) −88.2982 + 57.0509i −0.157114 + 0.101514i
\(563\) 447.848i 0.795467i −0.917501 0.397734i \(-0.869797\pi\)
0.917501 0.397734i \(-0.130203\pi\)
\(564\) 210.736 467.473i 0.373645 0.828853i
\(565\) 0 0
\(566\) −216.305 334.777i −0.382164 0.591479i
\(567\) 5.36886i 0.00946888i
\(568\) 468.408 70.8520i 0.824662 0.124740i
\(569\) 1078.91 1.89615 0.948077 0.318042i \(-0.103025\pi\)
0.948077 + 0.318042i \(0.103025\pi\)
\(570\) 0 0
\(571\) 936.324i 1.63980i 0.572509 + 0.819899i \(0.305970\pi\)
−0.572509 + 0.819899i \(0.694030\pi\)
\(572\) 795.613 + 358.660i 1.39093 + 0.627028i
\(573\) 230.638 0.402510
\(574\) 25.9502 + 40.1634i 0.0452095 + 0.0699711i
\(575\) 0 0
\(576\) 183.411 56.7851i 0.318421 0.0985853i
\(577\) 544.832 0.944250 0.472125 0.881532i \(-0.343487\pi\)
0.472125 + 0.881532i \(0.343487\pi\)
\(578\) 458.904 296.505i 0.793951 0.512985i
\(579\) 235.986i 0.407575i
\(580\) 0 0
\(581\) −77.4960 −0.133384
\(582\) −175.044 270.917i −0.300763 0.465494i
\(583\) 23.6745i 0.0406080i
\(584\) 99.3101 + 656.547i 0.170052 + 1.12422i
\(585\) 0 0
\(586\) 171.616 110.884i 0.292861 0.189222i
\(587\) 337.889i 0.575619i −0.957688 0.287810i \(-0.907073\pi\)
0.957688 0.287810i \(-0.0929271\pi\)
\(588\) −307.241 138.503i −0.522519 0.235550i
\(589\) −417.628 −0.709045
\(590\) 0 0
\(591\) 129.721i 0.219494i
\(592\) −57.0836 64.5926i −0.0964249 0.109109i
\(593\) −567.269 −0.956608 −0.478304 0.878194i \(-0.658748\pi\)
−0.478304 + 0.878194i \(0.658748\pi\)
\(594\) 81.0002 52.3355i 0.136364 0.0881069i
\(595\) 0 0
\(596\) −77.8906 + 172.784i −0.130689 + 0.289906i
\(597\) 435.792 0.729969
\(598\) 818.640 + 1267.02i 1.36896 + 2.11876i
\(599\) 762.966i 1.27373i 0.770974 + 0.636867i \(0.219770\pi\)
−0.770974 + 0.636867i \(0.780230\pi\)
\(600\) 0 0
\(601\) −790.102 −1.31464 −0.657322 0.753609i \(-0.728311\pi\)
−0.657322 + 0.753609i \(0.728311\pi\)
\(602\) 36.1917 23.3841i 0.0601192 0.0388440i
\(603\) 209.214i 0.346955i
\(604\) 399.680 + 180.175i 0.661722 + 0.298302i
\(605\) 0 0
\(606\) −6.88212 10.6515i −0.0113566 0.0175768i
\(607\) 522.994i 0.861605i 0.902446 + 0.430802i \(0.141769\pi\)
−0.902446 + 0.430802i \(0.858231\pi\)
\(608\) 60.8909 217.146i 0.100150 0.357148i
\(609\) −36.8591 −0.0605240
\(610\) 0 0
\(611\) 1740.17i 2.84807i
\(612\) 19.6156 43.5131i 0.0320516 0.0710999i
\(613\) −1026.91 −1.67522 −0.837609 0.546270i \(-0.816047\pi\)
−0.837609 + 0.546270i \(0.816047\pi\)
\(614\) −356.431 551.652i −0.580506 0.898455i
\(615\) 0 0
\(616\) 6.62332 + 43.7872i 0.0107521 + 0.0710831i
\(617\) 479.223 0.776698 0.388349 0.921512i \(-0.373046\pi\)
0.388349 + 0.921512i \(0.373046\pi\)
\(618\) −440.563 + 284.655i −0.712886 + 0.460607i
\(619\) 507.654i 0.820119i −0.912059 0.410059i \(-0.865508\pi\)
0.912059 0.410059i \(-0.134492\pi\)
\(620\) 0 0
\(621\) 166.689 0.268420
\(622\) 103.587 + 160.322i 0.166538 + 0.257753i
\(623\) 77.8282i 0.124925i
\(624\) −488.237 + 431.479i −0.782432 + 0.691473i
\(625\) 0 0
\(626\) 924.609 597.405i 1.47701 0.954321i
\(627\) 113.274i 0.180660i
\(628\) 291.932 647.591i 0.464860 1.03120i
\(629\) −21.4293 −0.0340688
\(630\) 0 0
\(631\) 460.186i 0.729297i −0.931145 0.364648i \(-0.881189\pi\)
0.931145 0.364648i \(-0.118811\pi\)
\(632\) −521.037 + 78.8128i −0.824426 + 0.124704i
\(633\) 395.259 0.624423
\(634\) 738.122 476.912i 1.16423 0.752228i
\(635\) 0 0
\(636\) −16.1138 7.26405i −0.0253362 0.0114215i
\(637\) 1143.71 1.79546
\(638\) −359.302 556.095i −0.563169 0.871622i
\(639\) 177.651i 0.278014i
\(640\) 0 0
\(641\) 250.774 0.391223 0.195612 0.980681i \(-0.437331\pi\)
0.195612 + 0.980681i \(0.437331\pi\)
\(642\) −240.942 + 155.677i −0.375299 + 0.242487i
\(643\) 590.355i 0.918126i 0.888404 + 0.459063i \(0.151815\pi\)
−0.888404 + 0.459063i \(0.848185\pi\)
\(644\) −31.4581 + 69.7834i −0.0488480 + 0.108359i
\(645\) 0 0
\(646\) −30.4252 47.0894i −0.0470979 0.0728939i
\(647\) 319.341i 0.493572i 0.969070 + 0.246786i \(0.0793744\pi\)
−0.969070 + 0.246786i \(0.920626\pi\)
\(648\) 10.7683 + 71.1902i 0.0166178 + 0.109861i
\(649\) −337.803 −0.520497
\(650\) 0 0
\(651\) 61.2280i 0.0940523i
\(652\) 353.274 + 159.255i 0.541832 + 0.244256i
\(653\) −88.5949 −0.135674 −0.0678369 0.997696i \(-0.521610\pi\)
−0.0678369 + 0.997696i \(0.521610\pi\)
\(654\) −13.8521 21.4390i −0.0211806 0.0327814i
\(655\) 0 0
\(656\) −424.652 480.512i −0.647335 0.732488i
\(657\) −249.006 −0.379004
\(658\) −74.1688 + 47.9216i −0.112719 + 0.0728292i
\(659\) 758.423i 1.15087i 0.817847 + 0.575435i \(0.195167\pi\)
−0.817847 + 0.575435i \(0.804833\pi\)
\(660\) 0 0
\(661\) 527.327 0.797771 0.398885 0.917001i \(-0.369397\pi\)
0.398885 + 0.917001i \(0.369397\pi\)
\(662\) 520.900 + 806.203i 0.786859 + 1.21783i
\(663\) 161.978i 0.244310i
\(664\) 1027.59 155.434i 1.54757 0.234087i
\(665\) 0 0
\(666\) 27.1513 17.5429i 0.0407677 0.0263407i
\(667\) 1144.38i 1.71571i
\(668\) −556.488 250.863i −0.833066 0.375544i
\(669\) 148.878 0.222538
\(670\) 0 0
\(671\) 81.0318i 0.120763i
\(672\) −31.8356 8.92717i −0.0473744 0.0132845i
\(673\) −120.657 −0.179283 −0.0896415 0.995974i \(-0.528572\pi\)
−0.0896415 + 0.995974i \(0.528572\pi\)
\(674\) 98.8493 63.8681i 0.146661 0.0947598i
\(675\) 0 0
\(676\) 630.918 1399.56i 0.933311 2.07036i
\(677\) 219.196 0.323776 0.161888 0.986809i \(-0.448242\pi\)
0.161888 + 0.986809i \(0.448242\pi\)
\(678\) −122.266 189.232i −0.180333 0.279103i
\(679\) 55.5446i 0.0818035i
\(680\) 0 0
\(681\) −489.057 −0.718145
\(682\) −923.751 + 596.850i −1.35447 + 0.875146i
\(683\) 205.502i 0.300881i 0.988619 + 0.150441i \(0.0480693\pi\)
−0.988619 + 0.150441i \(0.951931\pi\)
\(684\) 77.0988 + 34.7559i 0.112718 + 0.0508128i
\(685\) 0 0
\(686\) 63.2222 + 97.8496i 0.0921606 + 0.142638i
\(687\) 239.478i 0.348585i
\(688\) −432.995 + 382.659i −0.629354 + 0.556190i
\(689\) 59.9837 0.0870591
\(690\) 0 0
\(691\) 109.536i 0.158519i −0.996854 0.0792593i \(-0.974744\pi\)
0.996854 0.0792593i \(-0.0252555\pi\)
\(692\) −256.071 + 568.042i −0.370045 + 0.820869i
\(693\) −16.6070 −0.0239639
\(694\) 13.1857 + 20.4077i 0.0189996 + 0.0294059i
\(695\) 0 0
\(696\) 488.746 73.9284i 0.702221 0.106219i
\(697\) −159.415 −0.228716
\(698\) 51.9543 33.5685i 0.0744331 0.0480924i
\(699\) 0.905758i 0.00129579i
\(700\) 0 0
\(701\) 168.847 0.240865 0.120433 0.992721i \(-0.461572\pi\)
0.120433 + 0.992721i \(0.461572\pi\)
\(702\) −132.602 205.229i −0.188892 0.292349i
\(703\) 37.9695i 0.0540106i
\(704\) −175.648 567.327i −0.249500 0.805863i
\(705\) 0 0
\(706\) −483.909 + 312.661i −0.685424 + 0.442863i
\(707\) 2.18382i 0.00308885i
\(708\) 103.648 229.922i 0.146396 0.324749i
\(709\) −554.846 −0.782576 −0.391288 0.920268i \(-0.627970\pi\)
−0.391288 + 0.920268i \(0.627970\pi\)
\(710\) 0 0
\(711\) 197.612i 0.277935i
\(712\) −156.100 1031.99i −0.219242 1.44942i
\(713\) −1900.97 −2.66616
\(714\) −6.90374 + 4.46062i −0.00966911 + 0.00624737i
\(715\) 0 0
\(716\) −459.474 207.130i −0.641723 0.289287i
\(717\) 127.640 0.178019
\(718\) −720.600 1115.28i −1.00362 1.55331i
\(719\) 377.485i 0.525014i 0.964930 + 0.262507i \(0.0845494\pi\)
−0.964930 + 0.262507i \(0.915451\pi\)
\(720\) 0 0
\(721\) 90.3261 0.125279
\(722\) −522.995 + 337.915i −0.724369 + 0.468027i
\(723\) 54.3353i 0.0751525i
\(724\) −569.972 + 1264.37i −0.787255 + 1.74636i
\(725\) 0 0
\(726\) 65.5885 + 101.512i 0.0903423 + 0.139824i
\(727\) 173.183i 0.238216i −0.992881 0.119108i \(-0.961997\pi\)
0.992881 0.119108i \(-0.0380035\pi\)
\(728\) 110.943 16.7814i 0.152394 0.0230514i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 143.651i 0.196513i
\(732\) 55.1536 + 24.8631i 0.0753464 + 0.0339659i
\(733\) −278.722 −0.380249 −0.190124 0.981760i \(-0.560889\pi\)
−0.190124 + 0.981760i \(0.560889\pi\)
\(734\) 6.60489 + 10.2225i 0.00899849 + 0.0139270i
\(735\) 0 0
\(736\) 277.165 988.412i 0.376583 1.34295i
\(737\) 647.142 0.878075
\(738\) 201.982 130.504i 0.273688 0.176834i
\(739\) 521.363i 0.705498i 0.935718 + 0.352749i \(0.114753\pi\)
−0.935718 + 0.352749i \(0.885247\pi\)
\(740\) 0 0
\(741\) −287.001 −0.387315
\(742\) 1.65186 + 2.55660i 0.00222622 + 0.00344555i
\(743\) 1277.93i 1.71996i 0.510326 + 0.859981i \(0.329525\pi\)
−0.510326 + 0.859981i \(0.670475\pi\)
\(744\) −122.805 811.874i −0.165061 1.09123i
\(745\) 0 0
\(746\) −343.936 + 222.223i −0.461041 + 0.297886i
\(747\) 389.728i 0.521724i
\(748\) −134.595 60.6751i −0.179940 0.0811164i
\(749\) 49.3989 0.0659532
\(750\) 0 0
\(751\) 1165.31i 1.55168i 0.630930 + 0.775840i \(0.282673\pi\)
−0.630930 + 0.775840i \(0.717327\pi\)
\(752\) 887.350 784.194i 1.17999 1.04281i
\(753\) 136.395 0.181136
\(754\) −1408.97 + 910.359i −1.86866 + 1.20737i
\(755\) 0 0
\(756\) 5.09554 11.3034i 0.00674013 0.0149516i
\(757\) −1063.75 −1.40522 −0.702611 0.711574i \(-0.747983\pi\)
−0.702611 + 0.711574i \(0.747983\pi\)
\(758\) 436.685 + 675.861i 0.576101 + 0.891638i
\(759\) 515.604i 0.679320i
\(760\) 0 0
\(761\) −677.847 −0.890732 −0.445366 0.895349i \(-0.646926\pi\)
−0.445366 + 0.895349i \(0.646926\pi\)
\(762\) −405.800 + 262.194i −0.532546 + 0.344087i
\(763\) 4.39551i 0.00576083i
\(764\) 485.577 + 218.897i 0.635572 + 0.286514i
\(765\) 0 0
\(766\) −360.078 557.296i −0.470076 0.727541i
\(767\) 855.887i 1.11589i
\(768\) 440.040 + 54.5201i 0.572969 + 0.0709898i
\(769\) −1289.59 −1.67697 −0.838486 0.544922i \(-0.816559\pi\)
−0.838486 + 0.544922i \(0.816559\pi\)
\(770\) 0 0
\(771\) 422.540i 0.548042i
\(772\) 223.972 496.836i 0.290119 0.643570i
\(773\) 750.339 0.970684 0.485342 0.874324i \(-0.338695\pi\)
0.485342 + 0.874324i \(0.338695\pi\)
\(774\) −117.599 182.008i −0.151936 0.235153i
\(775\) 0 0
\(776\) −111.406 736.513i −0.143564 0.949114i
\(777\) −5.56667 −0.00716432
\(778\) 1047.07 676.532i 1.34585 0.869578i
\(779\) 282.460i 0.362593i
\(780\) 0 0
\(781\) 549.512 0.703600
\(782\) −138.491 214.343i −0.177098 0.274096i
\(783\) 185.365i 0.236736i
\(784\) −515.402 583.200i −0.657400 0.743877i
\(785\) 0 0
\(786\) −184.718 + 119.349i −0.235011 + 0.151844i
\(787\) 825.185i