Properties

Label 300.3.f.b.199.14
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 199.14
Root \(0.120653 - 1.40906i\) of defining polynomial
Character \(\chi\) \(=\) 300.199
Dual form 300.3.f.b.199.13

$q$-expansion

\(f(q)\) \(=\) \(q+(1.08539 + 1.67986i) q^{2} +1.73205 q^{3} +(-1.64388 + 3.64660i) q^{4} +(1.87994 + 2.90961i) q^{6} -0.596540 q^{7} +(-7.91002 + 1.19648i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(1.08539 + 1.67986i) q^{2} +1.73205 q^{3} +(-1.64388 + 3.64660i) q^{4} +(1.87994 + 2.90961i) q^{6} -0.596540 q^{7} +(-7.91002 + 1.19648i) q^{8} +3.00000 q^{9} +9.27963i q^{11} +(-2.84728 + 6.31609i) q^{12} +23.5117i q^{13} +(-0.647476 - 1.00210i) q^{14} +(-10.5953 - 11.9891i) q^{16} +3.97751i q^{17} +(3.25616 + 5.03959i) q^{18} +7.04756i q^{19} -1.03324 q^{21} +(-15.5885 + 10.0720i) q^{22} +32.0793 q^{23} +(-13.7006 + 2.07237i) q^{24} +(-39.4964 + 25.5192i) q^{26} +5.19615 q^{27} +(0.980637 - 2.17534i) q^{28} -35.6734 q^{29} -59.2585i q^{31} +(8.64000 - 30.8115i) q^{32} +16.0728i q^{33} +(-6.68167 + 4.31713i) q^{34} +(-4.93163 + 10.9398i) q^{36} -5.38761i q^{37} +(-11.8389 + 7.64932i) q^{38} +40.7234i q^{39} +40.0791 q^{41} +(-1.12146 - 1.73570i) q^{42} +36.1157 q^{43} +(-33.8391 - 15.2545i) q^{44} +(34.8184 + 53.8888i) q^{46} +74.0131 q^{47} +(-18.3517 - 20.7657i) q^{48} -48.6441 q^{49} +6.88925i q^{51} +(-85.7376 - 38.6503i) q^{52} +2.55123i q^{53} +(5.63983 + 8.72882i) q^{54} +(4.71864 - 0.713748i) q^{56} +12.2067i q^{57} +(-38.7194 - 59.9265i) q^{58} -36.4026i q^{59} -8.73223 q^{61} +(99.5461 - 64.3183i) q^{62} -1.78962 q^{63} +(61.1369 - 18.9284i) q^{64} +(-27.0001 + 17.4452i) q^{66} -69.7379 q^{67} +(-14.5044 - 6.53853i) q^{68} +55.5630 q^{69} -59.2170i q^{71} +(-23.7301 + 3.58944i) q^{72} +83.0019i q^{73} +(9.05044 - 5.84763i) q^{74} +(-25.6996 - 11.5853i) q^{76} -5.53566i q^{77} +(-68.4098 + 44.2006i) q^{78} -65.8705i q^{79} +9.00000 q^{81} +(43.5013 + 67.3274i) q^{82} +129.909 q^{83} +(1.69851 - 3.76780i) q^{84} +(39.1995 + 60.6695i) q^{86} -61.7882 q^{87} +(-11.1029 - 73.4020i) q^{88} +130.466 q^{89} -14.0256i q^{91} +(-52.7344 + 116.980i) q^{92} -102.639i q^{93} +(80.3327 + 124.332i) q^{94} +(14.9649 - 53.3671i) q^{96} +93.1113i q^{97} +(-52.7977 - 81.7155i) q^{98} +27.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 20q^{4} - 12q^{6} + 48q^{9} + O(q^{10}) \) \( 16q - 20q^{4} - 12q^{6} + 48q^{9} + 40q^{14} + 68q^{16} - 96q^{21} - 36q^{24} - 72q^{26} - 128q^{29} + 184q^{34} - 60q^{36} - 32q^{41} - 344q^{44} + 304q^{46} + 112q^{49} - 36q^{54} + 232q^{56} - 352q^{61} + 220q^{64} + 216q^{66} + 192q^{69} - 264q^{74} - 48q^{76} + 144q^{81} + 72q^{84} - 400q^{86} - 160q^{89} + 192q^{94} - 348q^{96} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.08539 + 1.67986i 0.542693 + 0.839931i
\(3\) 1.73205 0.577350
\(4\) −1.64388 + 3.64660i −0.410969 + 0.911649i
\(5\) 0 0
\(6\) 1.87994 + 2.90961i 0.313324 + 0.484935i
\(7\) −0.596540 −0.0852199 −0.0426100 0.999092i \(-0.513567\pi\)
−0.0426100 + 0.999092i \(0.513567\pi\)
\(8\) −7.91002 + 1.19648i −0.988753 + 0.149560i
\(9\) 3.00000 0.333333
\(10\) 0 0
\(11\) 9.27963i 0.843602i 0.906688 + 0.421801i \(0.138602\pi\)
−0.906688 + 0.421801i \(0.861398\pi\)
\(12\) −2.84728 + 6.31609i −0.237273 + 0.526341i
\(13\) 23.5117i 1.80859i 0.426907 + 0.904295i \(0.359603\pi\)
−0.426907 + 0.904295i \(0.640397\pi\)
\(14\) −0.647476 1.00210i −0.0462483 0.0715789i
\(15\) 0 0
\(16\) −10.5953 11.9891i −0.662209 0.749319i
\(17\) 3.97751i 0.233971i 0.993134 + 0.116986i \(0.0373231\pi\)
−0.993134 + 0.116986i \(0.962677\pi\)
\(18\) 3.25616 + 5.03959i 0.180898 + 0.279977i
\(19\) 7.04756i 0.370924i 0.982651 + 0.185462i \(0.0593782\pi\)
−0.982651 + 0.185462i \(0.940622\pi\)
\(20\) 0 0
\(21\) −1.03324 −0.0492018
\(22\) −15.5885 + 10.0720i −0.708568 + 0.457817i
\(23\) 32.0793 1.39475 0.697376 0.716705i \(-0.254351\pi\)
0.697376 + 0.716705i \(0.254351\pi\)
\(24\) −13.7006 + 2.07237i −0.570857 + 0.0863486i
\(25\) 0 0
\(26\) −39.4964 + 25.5192i −1.51909 + 0.981509i
\(27\) 5.19615 0.192450
\(28\) 0.980637 2.17534i 0.0350227 0.0776907i
\(29\) −35.6734 −1.23012 −0.615059 0.788481i \(-0.710868\pi\)
−0.615059 + 0.788481i \(0.710868\pi\)
\(30\) 0 0
\(31\) 59.2585i 1.91156i −0.294076 0.955782i \(-0.595012\pi\)
0.294076 0.955782i \(-0.404988\pi\)
\(32\) 8.64000 30.8115i 0.270000 0.962860i
\(33\) 16.0728i 0.487054i
\(34\) −6.68167 + 4.31713i −0.196520 + 0.126974i
\(35\) 0 0
\(36\) −4.93163 + 10.9398i −0.136990 + 0.303883i
\(37\) 5.38761i 0.145611i −0.997346 0.0728055i \(-0.976805\pi\)
0.997346 0.0728055i \(-0.0231952\pi\)
\(38\) −11.8389 + 7.64932i −0.311551 + 0.201298i
\(39\) 40.7234i 1.04419i
\(40\) 0 0
\(41\) 40.0791 0.977539 0.488769 0.872413i \(-0.337446\pi\)
0.488769 + 0.872413i \(0.337446\pi\)
\(42\) −1.12146 1.73570i −0.0267014 0.0413261i
\(43\) 36.1157 0.839901 0.419950 0.907547i \(-0.362047\pi\)
0.419950 + 0.907547i \(0.362047\pi\)
\(44\) −33.8391 15.2545i −0.769070 0.346694i
\(45\) 0 0
\(46\) 34.8184 + 53.8888i 0.756922 + 1.17150i
\(47\) 74.0131 1.57475 0.787373 0.616477i \(-0.211441\pi\)
0.787373 + 0.616477i \(0.211441\pi\)
\(48\) −18.3517 20.7657i −0.382327 0.432620i
\(49\) −48.6441 −0.992738
\(50\) 0 0
\(51\) 6.88925i 0.135083i
\(52\) −85.7376 38.6503i −1.64880 0.743275i
\(53\) 2.55123i 0.0481364i 0.999710 + 0.0240682i \(0.00766189\pi\)
−0.999710 + 0.0240682i \(0.992338\pi\)
\(54\) 5.63983 + 8.72882i 0.104441 + 0.161645i
\(55\) 0 0
\(56\) 4.71864 0.713748i 0.0842614 0.0127455i
\(57\) 12.2067i 0.214153i
\(58\) −38.7194 59.9265i −0.667576 1.03321i
\(59\) 36.4026i 0.616993i −0.951225 0.308497i \(-0.900174\pi\)
0.951225 0.308497i \(-0.0998259\pi\)
\(60\) 0 0
\(61\) −8.73223 −0.143151 −0.0715757 0.997435i \(-0.522803\pi\)
−0.0715757 + 0.997435i \(0.522803\pi\)
\(62\) 99.5461 64.3183i 1.60558 1.03739i
\(63\) −1.78962 −0.0284066
\(64\) 61.1369 18.9284i 0.955264 0.295756i
\(65\) 0 0
\(66\) −27.0001 + 17.4452i −0.409092 + 0.264321i
\(67\) −69.7379 −1.04086 −0.520432 0.853903i \(-0.674229\pi\)
−0.520432 + 0.853903i \(0.674229\pi\)
\(68\) −14.5044 6.53853i −0.213300 0.0961548i
\(69\) 55.5630 0.805261
\(70\) 0 0
\(71\) 59.2170i 0.834043i −0.908897 0.417021i \(-0.863074\pi\)
0.908897 0.417021i \(-0.136926\pi\)
\(72\) −23.7301 + 3.58944i −0.329584 + 0.0498534i
\(73\) 83.0019i 1.13701i 0.822679 + 0.568506i \(0.192478\pi\)
−0.822679 + 0.568506i \(0.807522\pi\)
\(74\) 9.05044 5.84763i 0.122303 0.0790220i
\(75\) 0 0
\(76\) −25.6996 11.5853i −0.338153 0.152438i
\(77\) 5.53566i 0.0718917i
\(78\) −68.4098 + 44.2006i −0.877048 + 0.566675i
\(79\) 65.8705i 0.833804i −0.908951 0.416902i \(-0.863116\pi\)
0.908951 0.416902i \(-0.136884\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 43.5013 + 67.3274i 0.530503 + 0.821065i
\(83\) 129.909 1.56517 0.782586 0.622542i \(-0.213900\pi\)
0.782586 + 0.622542i \(0.213900\pi\)
\(84\) 1.69851 3.76780i 0.0202204 0.0448547i
\(85\) 0 0
\(86\) 39.1995 + 60.6695i 0.455808 + 0.705459i
\(87\) −61.7882 −0.710209
\(88\) −11.1029 73.4020i −0.126169 0.834114i
\(89\) 130.466 1.46591 0.732956 0.680277i \(-0.238140\pi\)
0.732956 + 0.680277i \(0.238140\pi\)
\(90\) 0 0
\(91\) 14.0256i 0.154128i
\(92\) −52.7344 + 116.980i −0.573200 + 1.27152i
\(93\) 102.639i 1.10364i
\(94\) 80.3327 + 124.332i 0.854603 + 1.32268i
\(95\) 0 0
\(96\) 14.9649 53.3671i 0.155885 0.555908i
\(97\) 93.1113i 0.959911i 0.877293 + 0.479955i \(0.159347\pi\)
−0.877293 + 0.479955i \(0.840653\pi\)
\(98\) −52.7977 81.7155i −0.538752 0.833831i
\(99\) 27.8389i 0.281201i
\(100\) 0 0
\(101\) −3.66081 −0.0362457 −0.0181228 0.999836i \(-0.505769\pi\)
−0.0181228 + 0.999836i \(0.505769\pi\)
\(102\) −11.5730 + 7.47749i −0.113461 + 0.0733087i
\(103\) −151.417 −1.47007 −0.735033 0.678032i \(-0.762833\pi\)
−0.735033 + 0.678032i \(0.762833\pi\)
\(104\) −28.1313 185.978i −0.270493 1.78825i
\(105\) 0 0
\(106\) −4.28571 + 2.76907i −0.0404313 + 0.0261233i
\(107\) 82.8092 0.773918 0.386959 0.922097i \(-0.373526\pi\)
0.386959 + 0.922097i \(0.373526\pi\)
\(108\) −8.54183 + 18.9483i −0.0790910 + 0.175447i
\(109\) 7.36835 0.0675996 0.0337998 0.999429i \(-0.489239\pi\)
0.0337998 + 0.999429i \(0.489239\pi\)
\(110\) 0 0
\(111\) 9.33161i 0.0840685i
\(112\) 6.32054 + 7.15197i 0.0564334 + 0.0638569i
\(113\) 65.0370i 0.575549i −0.957698 0.287774i \(-0.907085\pi\)
0.957698 0.287774i \(-0.0929153\pi\)
\(114\) −20.5056 + 13.2490i −0.179874 + 0.116219i
\(115\) 0 0
\(116\) 58.6427 130.087i 0.505540 1.12144i
\(117\) 70.5350i 0.602864i
\(118\) 61.1514 39.5109i 0.518232 0.334838i
\(119\) 2.37274i 0.0199390i
\(120\) 0 0
\(121\) 34.8885 0.288335
\(122\) −9.47784 14.6689i −0.0776872 0.120237i
\(123\) 69.4190 0.564382
\(124\) 216.092 + 97.4136i 1.74268 + 0.785593i
\(125\) 0 0
\(126\) −1.94243 3.00631i −0.0154161 0.0238596i
\(127\) 139.469 1.09818 0.549091 0.835763i \(-0.314974\pi\)
0.549091 + 0.835763i \(0.314974\pi\)
\(128\) 98.1542 + 82.1569i 0.766829 + 0.641851i
\(129\) 62.5543 0.484917
\(130\) 0 0
\(131\) 63.4856i 0.484623i 0.970198 + 0.242312i \(0.0779056\pi\)
−0.970198 + 0.242312i \(0.922094\pi\)
\(132\) −58.6110 26.4217i −0.444023 0.200164i
\(133\) 4.20415i 0.0316101i
\(134\) −75.6925 117.150i −0.564870 0.874254i
\(135\) 0 0
\(136\) −4.75901 31.4622i −0.0349927 0.231340i
\(137\) 138.157i 1.00845i −0.863573 0.504223i \(-0.831779\pi\)
0.863573 0.504223i \(-0.168221\pi\)
\(138\) 60.3073 + 93.3382i 0.437009 + 0.676363i
\(139\) 29.9578i 0.215523i 0.994177 + 0.107762i \(0.0343684\pi\)
−0.994177 + 0.107762i \(0.965632\pi\)
\(140\) 0 0
\(141\) 128.194 0.909180
\(142\) 99.4765 64.2733i 0.700539 0.452629i
\(143\) −218.180 −1.52573
\(144\) −31.7860 35.9673i −0.220736 0.249773i
\(145\) 0 0
\(146\) −139.432 + 90.0891i −0.955012 + 0.617048i
\(147\) −84.2541 −0.573157
\(148\) 19.6464 + 8.85655i 0.132746 + 0.0598416i
\(149\) 47.3823 0.318002 0.159001 0.987278i \(-0.449173\pi\)
0.159001 + 0.987278i \(0.449173\pi\)
\(150\) 0 0
\(151\) 109.604i 0.725852i 0.931818 + 0.362926i \(0.118222\pi\)
−0.931818 + 0.362926i \(0.881778\pi\)
\(152\) −8.43227 55.7463i −0.0554755 0.366752i
\(153\) 11.9325i 0.0779904i
\(154\) 9.29915 6.00833i 0.0603841 0.0390151i
\(155\) 0 0
\(156\) −148.502 66.9442i −0.951936 0.429130i
\(157\) 177.588i 1.13113i −0.824703 0.565566i \(-0.808658\pi\)
0.824703 0.565566i \(-0.191342\pi\)
\(158\) 110.653 71.4950i 0.700338 0.452500i
\(159\) 4.41886i 0.0277916i
\(160\) 0 0
\(161\) −19.1366 −0.118861
\(162\) 9.76847 + 15.1188i 0.0602992 + 0.0933257i
\(163\) −96.8778 −0.594342 −0.297171 0.954824i \(-0.596043\pi\)
−0.297171 + 0.954824i \(0.596043\pi\)
\(164\) −65.8850 + 146.152i −0.401738 + 0.891173i
\(165\) 0 0
\(166\) 141.002 + 218.230i 0.849408 + 1.31464i
\(167\) −152.605 −0.913801 −0.456901 0.889518i \(-0.651040\pi\)
−0.456901 + 0.889518i \(0.651040\pi\)
\(168\) 8.17292 1.23625i 0.0486484 0.00735862i
\(169\) −383.799 −2.27100
\(170\) 0 0
\(171\) 21.1427i 0.123641i
\(172\) −59.3698 + 131.700i −0.345173 + 0.765695i
\(173\) 155.773i 0.900422i −0.892922 0.450211i \(-0.851349\pi\)
0.892922 0.450211i \(-0.148651\pi\)
\(174\) −67.0640 103.796i −0.385425 0.596527i
\(175\) 0 0
\(176\) 111.254 98.3209i 0.632127 0.558641i
\(177\) 63.0512i 0.356221i
\(178\) 141.606 + 219.165i 0.795540 + 1.23126i
\(179\) 126.001i 0.703915i 0.936016 + 0.351957i \(0.114484\pi\)
−0.936016 + 0.351957i \(0.885516\pi\)
\(180\) 0 0
\(181\) −346.725 −1.91561 −0.957803 0.287424i \(-0.907201\pi\)
−0.957803 + 0.287424i \(0.907201\pi\)
\(182\) 23.5612 15.2232i 0.129457 0.0836442i
\(183\) −15.1247 −0.0826485
\(184\) −253.748 + 38.3823i −1.37906 + 0.208599i
\(185\) 0 0
\(186\) 172.419 111.403i 0.926983 0.598939i
\(187\) −36.9098 −0.197379
\(188\) −121.668 + 269.896i −0.647171 + 1.43562i
\(189\) −3.09971 −0.0164006
\(190\) 0 0
\(191\) 133.159i 0.697167i 0.937278 + 0.348584i \(0.113337\pi\)
−0.937278 + 0.348584i \(0.886663\pi\)
\(192\) 105.892 32.7849i 0.551522 0.170755i
\(193\) 136.246i 0.705940i 0.935635 + 0.352970i \(0.114828\pi\)
−0.935635 + 0.352970i \(0.885172\pi\)
\(194\) −156.414 + 101.062i −0.806259 + 0.520937i
\(195\) 0 0
\(196\) 79.9649 177.386i 0.407984 0.905029i
\(197\) 74.8945i 0.380175i 0.981767 + 0.190087i \(0.0608772\pi\)
−0.981767 + 0.190087i \(0.939123\pi\)
\(198\) −46.7655 + 30.2159i −0.236189 + 0.152606i
\(199\) 251.605i 1.26434i −0.774828 0.632172i \(-0.782164\pi\)
0.774828 0.632172i \(-0.217836\pi\)
\(200\) 0 0
\(201\) −120.790 −0.600943
\(202\) −3.97339 6.14966i −0.0196703 0.0304439i
\(203\) 21.2806 0.104831
\(204\) −25.1223 11.3251i −0.123149 0.0555150i
\(205\) 0 0
\(206\) −164.346 254.359i −0.797794 1.23475i
\(207\) 96.2379 0.464917
\(208\) 281.884 249.114i 1.35521 1.19767i
\(209\) −65.3987 −0.312913
\(210\) 0 0
\(211\) 228.203i 1.08153i 0.841173 + 0.540766i \(0.181865\pi\)
−0.841173 + 0.540766i \(0.818135\pi\)
\(212\) −9.30331 4.19390i −0.0438835 0.0197826i
\(213\) 102.567i 0.481535i
\(214\) 89.8799 + 139.108i 0.420000 + 0.650038i
\(215\) 0 0
\(216\) −41.1017 + 6.21710i −0.190286 + 0.0287829i
\(217\) 35.3500i 0.162903i
\(218\) 7.99751 + 12.3778i 0.0366858 + 0.0567790i
\(219\) 143.763i 0.656454i
\(220\) 0 0
\(221\) −93.5179 −0.423158
\(222\) 15.6758 10.1284i 0.0706118 0.0456234i
\(223\) −85.9549 −0.385448 −0.192724 0.981253i \(-0.561732\pi\)
−0.192724 + 0.981253i \(0.561732\pi\)
\(224\) −5.15410 + 18.3803i −0.0230094 + 0.0820549i
\(225\) 0 0
\(226\) 109.253 70.5902i 0.483421 0.312346i
\(227\) −282.357 −1.24386 −0.621932 0.783071i \(-0.713652\pi\)
−0.621932 + 0.783071i \(0.713652\pi\)
\(228\) −44.5130 20.0663i −0.195233 0.0880103i
\(229\) −138.263 −0.603768 −0.301884 0.953345i \(-0.597615\pi\)
−0.301884 + 0.953345i \(0.597615\pi\)
\(230\) 0 0
\(231\) 9.58805i 0.0415067i
\(232\) 282.178 42.6826i 1.21628 0.183977i
\(233\) 0.522939i 0.00224438i 0.999999 + 0.00112219i \(0.000357204\pi\)
−0.999999 + 0.00112219i \(0.999643\pi\)
\(234\) −118.489 + 76.5577i −0.506364 + 0.327170i
\(235\) 0 0
\(236\) 132.746 + 59.8413i 0.562482 + 0.253565i
\(237\) 114.091i 0.481397i
\(238\) 3.98588 2.57534i 0.0167474 0.0108208i
\(239\) 73.6928i 0.308338i −0.988044 0.154169i \(-0.950730\pi\)
0.988044 0.154169i \(-0.0492700\pi\)
\(240\) 0 0
\(241\) 31.3705 0.130168 0.0650840 0.997880i \(-0.479268\pi\)
0.0650840 + 0.997880i \(0.479268\pi\)
\(242\) 37.8675 + 58.6080i 0.156477 + 0.242182i
\(243\) 15.5885 0.0641500
\(244\) 14.3547 31.8429i 0.0588307 0.130504i
\(245\) 0 0
\(246\) 75.3464 + 116.614i 0.306286 + 0.474042i
\(247\) −165.700 −0.670850
\(248\) 70.9016 + 468.736i 0.285894 + 1.89006i
\(249\) 225.010 0.903653
\(250\) 0 0
\(251\) 78.7478i 0.313736i 0.987620 + 0.156868i \(0.0501398\pi\)
−0.987620 + 0.156868i \(0.949860\pi\)
\(252\) 2.94191 6.52602i 0.0116742 0.0258969i
\(253\) 297.684i 1.17662i
\(254\) 151.378 + 234.289i 0.595975 + 0.922397i
\(255\) 0 0
\(256\) −31.4772 + 254.057i −0.122958 + 0.992412i
\(257\) 243.954i 0.949236i 0.880192 + 0.474618i \(0.157414\pi\)
−0.880192 + 0.474618i \(0.842586\pi\)
\(258\) 67.8956 + 105.083i 0.263161 + 0.407297i
\(259\) 3.21392i 0.0124090i
\(260\) 0 0
\(261\) −107.020 −0.410039
\(262\) −106.647 + 68.9064i −0.407050 + 0.263002i
\(263\) 102.737 0.390635 0.195317 0.980740i \(-0.437426\pi\)
0.195317 + 0.980740i \(0.437426\pi\)
\(264\) −19.2308 127.136i −0.0728439 0.481576i
\(265\) 0 0
\(266\) 7.06239 4.56312i 0.0265503 0.0171546i
\(267\) 225.974 0.846344
\(268\) 114.640 254.306i 0.427763 0.948903i
\(269\) 123.646 0.459651 0.229825 0.973232i \(-0.426184\pi\)
0.229825 + 0.973232i \(0.426184\pi\)
\(270\) 0 0
\(271\) 332.371i 1.22646i −0.789904 0.613230i \(-0.789870\pi\)
0.789904 0.613230i \(-0.210130\pi\)
\(272\) 47.6868 42.1431i 0.175319 0.154938i
\(273\) 24.2931i 0.0889858i
\(274\) 232.085 149.954i 0.847026 0.547277i
\(275\) 0 0
\(276\) −91.3386 + 202.616i −0.330937 + 0.734115i
\(277\) 125.916i 0.454571i −0.973828 0.227286i \(-0.927015\pi\)
0.973828 0.227286i \(-0.0729851\pi\)
\(278\) −50.3249 + 32.5157i −0.181025 + 0.116963i
\(279\) 177.775i 0.637188i
\(280\) 0 0
\(281\) 52.5628 0.187056 0.0935281 0.995617i \(-0.470186\pi\)
0.0935281 + 0.995617i \(0.470186\pi\)
\(282\) 139.140 + 215.349i 0.493405 + 0.763649i
\(283\) −199.288 −0.704199 −0.352100 0.935963i \(-0.614532\pi\)
−0.352100 + 0.935963i \(0.614532\pi\)
\(284\) 215.941 + 97.3454i 0.760355 + 0.342766i
\(285\) 0 0
\(286\) −236.809 366.512i −0.828004 1.28151i
\(287\) −23.9088 −0.0833058
\(288\) 25.9200 92.4346i 0.0900001 0.320953i
\(289\) 273.179 0.945258
\(290\) 0 0
\(291\) 161.274i 0.554205i
\(292\) −302.674 136.445i −1.03656 0.467276i
\(293\) 102.161i 0.348672i −0.984686 0.174336i \(-0.944222\pi\)
0.984686 0.174336i \(-0.0557779\pi\)
\(294\) −91.4482 141.535i −0.311048 0.481413i
\(295\) 0 0
\(296\) 6.44617 + 42.6161i 0.0217776 + 0.143973i
\(297\) 48.2184i 0.162351i
\(298\) 51.4281 + 79.5957i 0.172577 + 0.267100i
\(299\) 754.238i 2.52254i
\(300\) 0 0
\(301\) −21.5445 −0.0715763
\(302\) −184.119 + 118.962i −0.609666 + 0.393915i
\(303\) −6.34071 −0.0209264
\(304\) 84.4939 74.6713i 0.277941 0.245629i
\(305\) 0 0
\(306\) −20.0450 + 12.9514i −0.0655065 + 0.0423248i
\(307\) 328.391 1.06968 0.534839 0.844954i \(-0.320372\pi\)
0.534839 + 0.844954i \(0.320372\pi\)
\(308\) 20.1863 + 9.09994i 0.0655401 + 0.0295453i
\(309\) −262.262 −0.848743
\(310\) 0 0
\(311\) 95.4377i 0.306874i −0.988158 0.153437i \(-0.950966\pi\)
0.988158 0.153437i \(-0.0490342\pi\)
\(312\) −48.7248 322.123i −0.156169 1.03245i
\(313\) 550.408i 1.75849i −0.476368 0.879246i \(-0.658047\pi\)
0.476368 0.879246i \(-0.341953\pi\)
\(314\) 298.323 192.751i 0.950073 0.613858i
\(315\) 0 0
\(316\) 240.203 + 108.283i 0.760137 + 0.342668i
\(317\) 439.394i 1.38610i 0.720889 + 0.693051i \(0.243734\pi\)
−0.720889 + 0.693051i \(0.756266\pi\)
\(318\) −7.42307 + 4.79617i −0.0233430 + 0.0150823i
\(319\) 331.036i 1.03773i
\(320\) 0 0
\(321\) 143.430 0.446822
\(322\) −20.7706 32.1468i −0.0645048 0.0998348i
\(323\) −28.0317 −0.0867855
\(324\) −14.7949 + 32.8194i −0.0456632 + 0.101294i
\(325\) 0 0
\(326\) −105.150 162.741i −0.322545 0.499206i
\(327\) 12.7624 0.0390286
\(328\) −317.026 + 47.9539i −0.966544 + 0.146201i
\(329\) −44.1517 −0.134200
\(330\) 0 0
\(331\) 479.922i 1.44992i −0.688794 0.724958i \(-0.741859\pi\)
0.688794 0.724958i \(-0.258141\pi\)
\(332\) −213.555 + 473.727i −0.643237 + 1.42689i
\(333\) 16.1628i 0.0485370i
\(334\) −165.635 256.355i −0.495913 0.767530i
\(335\) 0 0
\(336\) 10.9475 + 12.3876i 0.0325819 + 0.0368678i
\(337\) 58.8437i 0.174610i 0.996182 + 0.0873052i \(0.0278255\pi\)
−0.996182 + 0.0873052i \(0.972174\pi\)
\(338\) −416.570 644.730i −1.23246 1.90748i
\(339\) 112.647i 0.332293i
\(340\) 0 0
\(341\) 549.897 1.61260
\(342\) −35.5168 + 22.9480i −0.103850 + 0.0670993i
\(343\) 58.2486 0.169821
\(344\) −285.676 + 43.2118i −0.830454 + 0.125616i
\(345\) 0 0
\(346\) 261.677 169.074i 0.756293 0.488653i
\(347\) −12.1484 −0.0350099 −0.0175049 0.999847i \(-0.505572\pi\)
−0.0175049 + 0.999847i \(0.505572\pi\)
\(348\) 101.572 225.317i 0.291874 0.647462i
\(349\) 30.9277 0.0886180 0.0443090 0.999018i \(-0.485891\pi\)
0.0443090 + 0.999018i \(0.485891\pi\)
\(350\) 0 0
\(351\) 122.170i 0.348063i
\(352\) 285.919 + 80.1760i 0.812271 + 0.227773i
\(353\) 288.065i 0.816048i 0.912971 + 0.408024i \(0.133782\pi\)
−0.912971 + 0.408024i \(0.866218\pi\)
\(354\) 105.917 68.4348i 0.299201 0.193319i
\(355\) 0 0
\(356\) −214.470 + 475.757i −0.602444 + 1.33640i
\(357\) 4.10971i 0.0115118i
\(358\) −211.664 + 136.759i −0.591240 + 0.382010i
\(359\) 663.911i 1.84933i −0.380776 0.924667i \(-0.624343\pi\)
0.380776 0.924667i \(-0.375657\pi\)
\(360\) 0 0
\(361\) 311.332 0.862415
\(362\) −376.330 582.450i −1.03959 1.60898i
\(363\) 60.4287 0.166470
\(364\) 51.1459 + 23.0564i 0.140511 + 0.0633418i
\(365\) 0 0
\(366\) −16.4161 25.4074i −0.0448527 0.0694190i
\(367\) −6.08529 −0.0165812 −0.00829059 0.999966i \(-0.502639\pi\)
−0.00829059 + 0.999966i \(0.502639\pi\)
\(368\) −339.891 384.602i −0.923618 1.04511i
\(369\) 120.237 0.325846
\(370\) 0 0
\(371\) 1.52191i 0.00410218i
\(372\) 374.282 + 168.725i 1.00613 + 0.453562i
\(373\) 204.741i 0.548903i 0.961601 + 0.274451i \(0.0884963\pi\)
−0.961601 + 0.274451i \(0.911504\pi\)
\(374\) −40.0614 62.0034i −0.107116 0.165784i
\(375\) 0 0
\(376\) −585.445 + 88.5552i −1.55703 + 0.235519i
\(377\) 838.742i 2.22478i
\(378\) −3.36438 5.20709i −0.00890048 0.0137754i
\(379\) 402.331i 1.06156i 0.847510 + 0.530780i \(0.178101\pi\)
−0.847510 + 0.530780i \(0.821899\pi\)
\(380\) 0 0
\(381\) 241.568 0.634036
\(382\) −223.689 + 144.529i −0.585573 + 0.378348i
\(383\) −331.751 −0.866191 −0.433096 0.901348i \(-0.642579\pi\)
−0.433096 + 0.901348i \(0.642579\pi\)
\(384\) 170.008 + 142.300i 0.442729 + 0.370573i
\(385\) 0 0
\(386\) −228.875 + 147.880i −0.592941 + 0.383109i
\(387\) 108.347 0.279967
\(388\) −339.540 153.063i −0.875102 0.394493i
\(389\) 623.310 1.60234 0.801169 0.598438i \(-0.204212\pi\)
0.801169 + 0.598438i \(0.204212\pi\)
\(390\) 0 0
\(391\) 127.596i 0.326332i
\(392\) 384.776 58.2018i 0.981572 0.148474i
\(393\) 109.960i 0.279797i
\(394\) −125.812 + 81.2894i −0.319321 + 0.206318i
\(395\) 0 0
\(396\) −101.517 45.7636i −0.256357 0.115565i
\(397\) 355.449i 0.895338i −0.894199 0.447669i \(-0.852254\pi\)
0.894199 0.447669i \(-0.147746\pi\)
\(398\) 422.661 273.088i 1.06196 0.686151i
\(399\) 7.28180i 0.0182501i
\(400\) 0 0
\(401\) −542.927 −1.35393 −0.676966 0.736014i \(-0.736706\pi\)
−0.676966 + 0.736014i \(0.736706\pi\)
\(402\) −131.103 202.910i −0.326128 0.504751i
\(403\) 1393.27 3.45724
\(404\) 6.01792 13.3495i 0.0148958 0.0330433i
\(405\) 0 0
\(406\) 23.0977 + 35.7485i 0.0568908 + 0.0880505i
\(407\) 49.9950 0.122838
\(408\) −8.24285 54.4941i −0.0202031 0.133564i
\(409\) 108.497 0.265273 0.132636 0.991165i \(-0.457656\pi\)
0.132636 + 0.991165i \(0.457656\pi\)
\(410\) 0 0
\(411\) 239.295i 0.582227i
\(412\) 248.910 552.156i 0.604151 1.34018i
\(413\) 21.7156i 0.0525801i
\(414\) 104.455 + 161.666i 0.252307 + 0.390499i
\(415\) 0 0
\(416\) 724.431 + 203.141i 1.74142 + 0.488320i
\(417\) 51.8884i 0.124433i
\(418\) −70.9828 109.861i −0.169815 0.262825i
\(419\) 172.176i 0.410921i 0.978665 + 0.205460i \(0.0658691\pi\)
−0.978665 + 0.205460i \(0.934131\pi\)
\(420\) 0 0
\(421\) 478.522 1.13663 0.568316 0.822810i \(-0.307595\pi\)
0.568316 + 0.822810i \(0.307595\pi\)
\(422\) −383.350 + 247.688i −0.908412 + 0.586940i
\(423\) 222.039 0.524915
\(424\) −3.05250 20.1803i −0.00719929 0.0475950i
\(425\) 0 0
\(426\) 172.298 111.325i 0.404456 0.261326i
\(427\) 5.20912 0.0121993
\(428\) −136.128 + 301.972i −0.318056 + 0.705541i
\(429\) −377.898 −0.880882
\(430\) 0 0
\(431\) 290.722i 0.674530i −0.941410 0.337265i \(-0.890498\pi\)
0.941410 0.337265i \(-0.109502\pi\)
\(432\) −55.0550 62.2972i −0.127442 0.144207i
\(433\) 53.7726i 0.124186i −0.998070 0.0620931i \(-0.980222\pi\)
0.998070 0.0620931i \(-0.0197776\pi\)
\(434\) −59.3832 + 38.3684i −0.136828 + 0.0884065i
\(435\) 0 0
\(436\) −12.1127 + 26.8694i −0.0277813 + 0.0616271i
\(437\) 226.081i 0.517347i
\(438\) −241.503 + 156.039i −0.551376 + 0.356253i
\(439\) 328.657i 0.748650i −0.927298 0.374325i \(-0.877874\pi\)
0.927298 0.374325i \(-0.122126\pi\)
\(440\) 0 0
\(441\) −145.932 −0.330913
\(442\) −101.503 157.097i −0.229645 0.355424i
\(443\) 428.910 0.968194 0.484097 0.875014i \(-0.339148\pi\)
0.484097 + 0.875014i \(0.339148\pi\)
\(444\) 34.0286 + 15.3400i 0.0766410 + 0.0345496i
\(445\) 0 0
\(446\) −93.2942 144.392i −0.209180 0.323750i
\(447\) 82.0685 0.183599
\(448\) −36.4706 + 11.2915i −0.0814075 + 0.0252043i
\(449\) −409.229 −0.911423 −0.455711 0.890128i \(-0.650615\pi\)
−0.455711 + 0.890128i \(0.650615\pi\)
\(450\) 0 0
\(451\) 371.919i 0.824654i
\(452\) 237.164 + 106.913i 0.524698 + 0.236533i
\(453\) 189.839i 0.419071i
\(454\) −306.466 474.321i −0.675036 1.04476i
\(455\) 0 0
\(456\) −14.6051 96.5555i −0.0320288 0.211745i
\(457\) 768.561i 1.68175i 0.541228 + 0.840876i \(0.317960\pi\)
−0.541228 + 0.840876i \(0.682040\pi\)
\(458\) −150.068 232.262i −0.327660 0.507123i
\(459\) 20.6677i 0.0450278i
\(460\) 0 0
\(461\) −316.563 −0.686687 −0.343343 0.939210i \(-0.611559\pi\)
−0.343343 + 0.939210i \(0.611559\pi\)
\(462\) 16.1066 10.4067i 0.0348628 0.0225254i
\(463\) −491.208 −1.06093 −0.530463 0.847708i \(-0.677982\pi\)
−0.530463 + 0.847708i \(0.677982\pi\)
\(464\) 377.972 + 427.692i 0.814596 + 0.921751i
\(465\) 0 0
\(466\) −0.878466 + 0.567591i −0.00188512 + 0.00121801i
\(467\) 410.393 0.878785 0.439393 0.898295i \(-0.355194\pi\)
0.439393 + 0.898295i \(0.355194\pi\)
\(468\) −257.213 115.951i −0.549600 0.247758i
\(469\) 41.6014 0.0887024
\(470\) 0 0
\(471\) 307.591i 0.653060i
\(472\) 43.5550 + 287.945i 0.0922776 + 0.610054i
\(473\) 335.141i 0.708542i
\(474\) 191.657 123.833i 0.404341 0.261251i
\(475\) 0 0
\(476\) 8.65243 + 3.90049i 0.0181774 + 0.00819431i
\(477\) 7.65369i 0.0160455i
\(478\) 123.794 79.9851i 0.258983 0.167333i
\(479\) 198.918i 0.415277i 0.978206 + 0.207638i \(0.0665778\pi\)
−0.978206 + 0.207638i \(0.933422\pi\)
\(480\) 0 0
\(481\) 126.672 0.263351
\(482\) 34.0491 + 52.6981i 0.0706413 + 0.109332i
\(483\) −33.1455 −0.0686242
\(484\) −57.3524 + 127.224i −0.118497 + 0.262860i
\(485\) 0 0
\(486\) 16.9195 + 26.1865i 0.0348138 + 0.0538816i
\(487\) −204.762 −0.420456 −0.210228 0.977652i \(-0.567421\pi\)
−0.210228 + 0.977652i \(0.567421\pi\)
\(488\) 69.0721 10.4479i 0.141541 0.0214097i
\(489\) −167.797 −0.343144
\(490\) 0 0
\(491\) 788.598i 1.60611i −0.595908 0.803053i \(-0.703208\pi\)
0.595908 0.803053i \(-0.296792\pi\)
\(492\) −114.116 + 253.143i −0.231944 + 0.514519i
\(493\) 141.891i 0.287812i
\(494\) −179.848 278.353i −0.364066 0.563468i
\(495\) 0 0
\(496\) −710.456 + 627.864i −1.43237 + 1.26586i
\(497\) 35.3253i 0.0710771i
\(498\) 244.222 + 377.985i 0.490406 + 0.759006i
\(499\) 740.385i 1.48374i 0.670545 + 0.741869i \(0.266060\pi\)
−0.670545 + 0.741869i \(0.733940\pi\)
\(500\) 0 0
\(501\) −264.319 −0.527583
\(502\) −132.285 + 85.4717i −0.263517 + 0.170262i
\(503\) −70.8800 −0.140914 −0.0704572 0.997515i \(-0.522446\pi\)
−0.0704572 + 0.997515i \(0.522446\pi\)
\(504\) 14.1559 2.14124i 0.0280871 0.00424850i
\(505\) 0 0
\(506\) −500.068 + 323.102i −0.988277 + 0.638541i
\(507\) −664.760 −1.31116
\(508\) −229.270 + 508.588i −0.451318 + 1.00116i
\(509\) −522.642 −1.02680 −0.513400 0.858149i \(-0.671614\pi\)
−0.513400 + 0.858149i \(0.671614\pi\)
\(510\) 0 0
\(511\) 49.5139i 0.0968961i
\(512\) −460.946 + 222.873i −0.900286 + 0.435299i
\(513\) 36.6202i 0.0713844i
\(514\) −409.809 + 264.784i −0.797293 + 0.515144i
\(515\) 0 0
\(516\) −102.831 + 228.110i −0.199286 + 0.442074i
\(517\) 686.813i 1.32846i
\(518\) −5.39894 + 3.48834i −0.0104227 + 0.00673425i
\(519\) 269.807i 0.519859i
\(520\) 0 0
\(521\) 304.082 0.583650 0.291825 0.956472i \(-0.405738\pi\)
0.291825 + 0.956472i \(0.405738\pi\)
\(522\) −116.158 179.779i −0.222525 0.344405i
\(523\) 174.416 0.333491 0.166746 0.986000i \(-0.446674\pi\)
0.166746 + 0.986000i \(0.446674\pi\)
\(524\) −231.507 104.362i −0.441806 0.199165i
\(525\) 0 0
\(526\) 111.509 + 172.584i 0.211995 + 0.328106i
\(527\) 235.701 0.447251
\(528\) 192.698 170.297i 0.364959 0.322532i
\(529\) 500.081 0.945333
\(530\) 0 0
\(531\) 109.208i 0.205664i
\(532\) 15.3308 + 6.91109i 0.0288174 + 0.0129908i
\(533\) 942.327i 1.76797i
\(534\) 245.269 + 379.605i 0.459305 + 0.710871i
\(535\) 0 0
\(536\) 551.628 83.4401i 1.02916 0.155672i
\(537\) 218.240i 0.406405i
\(538\) 134.204 + 207.708i 0.249449 + 0.386075i
\(539\) 451.399i 0.837476i
\(540\) 0 0
\(541\) −262.199 −0.484655 −0.242328 0.970194i \(-0.577911\pi\)
−0.242328 + 0.970194i \(0.577911\pi\)
\(542\) 558.337 360.750i 1.03014 0.665591i
\(543\) −600.545 −1.10598
\(544\) 122.553 + 34.3657i 0.225281 + 0.0631722i
\(545\) 0 0
\(546\) 40.8091 26.3674i 0.0747420 0.0482920i
\(547\) 146.179 0.267237 0.133619 0.991033i \(-0.457340\pi\)
0.133619 + 0.991033i \(0.457340\pi\)
\(548\) 503.804 + 227.113i 0.919350 + 0.414440i
\(549\) −26.1967 −0.0477171
\(550\) 0 0
\(551\) 251.411i 0.456281i
\(552\) −439.504 + 66.4800i −0.796203 + 0.120435i
\(553\) 39.2944i 0.0710568i
\(554\) 211.522 136.668i 0.381809 0.246693i
\(555\) 0 0
\(556\) −109.244 49.2468i −0.196482 0.0885734i
\(557\) 187.700i 0.336984i 0.985703 + 0.168492i \(0.0538898\pi\)
−0.985703 + 0.168492i \(0.946110\pi\)
\(558\) 298.638 192.955i 0.535194 0.345797i
\(559\) 849.142i 1.51904i
\(560\) 0 0
\(561\) −63.9296 −0.113957
\(562\) 57.0509 + 88.2982i 0.101514 + 0.157114i
\(563\) 447.848 0.795467 0.397734 0.917501i \(-0.369797\pi\)
0.397734 + 0.917501i \(0.369797\pi\)
\(564\) −210.736 + 467.473i −0.373645 + 0.828853i
\(565\) 0 0
\(566\) −216.305 334.777i −0.382164 0.591479i
\(567\) −5.36886 −0.00946888
\(568\) 70.8520 + 468.408i 0.124740 + 0.824662i
\(569\) −1078.91 −1.89615 −0.948077 0.318042i \(-0.896975\pi\)
−0.948077 + 0.318042i \(0.896975\pi\)
\(570\) 0 0
\(571\) 936.324i 1.63980i 0.572509 + 0.819899i \(0.305970\pi\)
−0.572509 + 0.819899i \(0.694030\pi\)
\(572\) 358.660 795.613i 0.627028 1.39093i
\(573\) 230.638i 0.402510i
\(574\) −25.9502 40.1634i −0.0452095 0.0699711i
\(575\) 0 0
\(576\) 183.411 56.7851i 0.318421 0.0985853i
\(577\) 544.832i 0.944250i −0.881532 0.472125i \(-0.843487\pi\)
0.881532 0.472125i \(-0.156513\pi\)
\(578\) 296.505 + 458.904i 0.512985 + 0.793951i
\(579\) 235.986i 0.407575i
\(580\) 0 0
\(581\) −77.4960 −0.133384
\(582\) −270.917 + 175.044i −0.465494 + 0.300763i
\(583\) −23.6745 −0.0406080
\(584\) −99.3101 656.547i −0.170052 1.12422i
\(585\) 0 0
\(586\) 171.616 110.884i 0.292861 0.189222i
\(587\) −337.889 −0.575619 −0.287810 0.957688i \(-0.592927\pi\)
−0.287810 + 0.957688i \(0.592927\pi\)
\(588\) 138.503 307.241i 0.235550 0.522519i
\(589\) 417.628 0.709045
\(590\) 0 0
\(591\) 129.721i 0.219494i
\(592\) −64.5926 + 57.0836i −0.109109 + 0.0964249i
\(593\) 567.269i 0.956608i −0.878194 0.478304i \(-0.841252\pi\)
0.878194 0.478304i \(-0.158748\pi\)
\(594\) −81.0002 + 52.3355i −0.136364 + 0.0881069i
\(595\) 0 0
\(596\) −77.8906 + 172.784i −0.130689 + 0.289906i
\(597\) 435.792i 0.729969i
\(598\) −1267.02 + 818.640i −2.11876 + 1.36896i
\(599\) 762.966i 1.27373i −0.770974 0.636867i \(-0.780230\pi\)
0.770974 0.636867i \(-0.219770\pi\)
\(600\) 0 0
\(601\) −790.102 −1.31464 −0.657322 0.753609i \(-0.728311\pi\)
−0.657322 + 0.753609i \(0.728311\pi\)
\(602\) −23.3841 36.1917i −0.0388440 0.0601192i
\(603\) −209.214 −0.346955
\(604\) −399.680 180.175i −0.661722 0.298302i
\(605\) 0 0
\(606\) −6.88212 10.6515i −0.0113566 0.0175768i
\(607\) 522.994 0.861605 0.430802 0.902446i \(-0.358231\pi\)
0.430802 + 0.902446i \(0.358231\pi\)
\(608\) 217.146 + 60.8909i 0.357148 + 0.100150i
\(609\) 36.8591 0.0605240
\(610\) 0 0
\(611\) 1740.17i 2.84807i
\(612\) −43.5131 19.6156i −0.0710999 0.0320516i
\(613\) 1026.91i 1.67522i −0.546270 0.837609i \(-0.683953\pi\)
0.546270 0.837609i \(-0.316047\pi\)
\(614\) 356.431 + 551.652i 0.580506 + 0.898455i
\(615\) 0 0
\(616\) 6.62332 + 43.7872i 0.0107521 + 0.0710831i
\(617\) 479.223i 0.776698i −0.921512 0.388349i \(-0.873046\pi\)
0.921512 0.388349i \(-0.126954\pi\)
\(618\) −284.655 440.563i −0.460607 0.712886i
\(619\) 507.654i 0.820119i 0.912059 + 0.410059i \(0.134492\pi\)
−0.912059 + 0.410059i \(0.865508\pi\)
\(620\) 0 0
\(621\) 166.689 0.268420
\(622\) 160.322 103.587i 0.257753 0.166538i
\(623\) −77.8282 −0.124925
\(624\) 488.237 431.479i 0.782432 0.691473i
\(625\) 0 0
\(626\) 924.609 597.405i 1.47701 0.954321i
\(627\) −113.274 −0.180660
\(628\) 647.591 + 291.932i 1.03120 + 0.464860i
\(629\) 21.4293 0.0340688
\(630\) 0 0
\(631\) 460.186i 0.729297i −0.931145 0.364648i \(-0.881189\pi\)
0.931145 0.364648i \(-0.118811\pi\)
\(632\) 78.8128 + 521.037i 0.124704 + 0.824426i
\(633\) 395.259i 0.624423i
\(634\) −738.122 + 476.912i −1.16423 + 0.752228i
\(635\) 0 0
\(636\) −16.1138 7.26405i −0.0253362 0.0114215i
\(637\) 1143.71i 1.79546i
\(638\) 556.095 359.302i 0.871622 0.563169i
\(639\) 177.651i 0.278014i
\(640\) 0 0
\(641\) 250.774 0.391223 0.195612 0.980681i \(-0.437331\pi\)
0.195612 + 0.980681i \(0.437331\pi\)
\(642\) 155.677 + 240.942i 0.242487 + 0.375299i
\(643\) −590.355 −0.918126 −0.459063 0.888404i \(-0.651815\pi\)
−0.459063 + 0.888404i \(0.651815\pi\)
\(644\) 31.4581 69.7834i 0.0488480 0.108359i
\(645\) 0 0
\(646\) −30.4252 47.0894i −0.0470979 0.0728939i
\(647\) 319.341 0.493572 0.246786 0.969070i \(-0.420626\pi\)
0.246786 + 0.969070i \(0.420626\pi\)
\(648\) −71.1902 + 10.7683i −0.109861 + 0.0166178i
\(649\) 337.803 0.520497
\(650\) 0 0
\(651\) 61.2280i 0.0940523i
\(652\) 159.255 353.274i 0.244256 0.541832i
\(653\) 88.5949i 0.135674i −0.997696 0.0678369i \(-0.978390\pi\)
0.997696 0.0678369i \(-0.0216097\pi\)
\(654\) 13.8521 + 21.4390i 0.0211806 + 0.0327814i
\(655\) 0 0
\(656\) −424.652 480.512i −0.647335 0.732488i
\(657\) 249.006i 0.379004i
\(658\) −47.9216 74.1688i −0.0728292 0.112719i
\(659\) 758.423i 1.15087i −0.817847 0.575435i \(-0.804833\pi\)
0.817847 0.575435i \(-0.195167\pi\)
\(660\) 0 0
\(661\) 527.327 0.797771 0.398885 0.917001i \(-0.369397\pi\)
0.398885 + 0.917001i \(0.369397\pi\)
\(662\) 806.203 520.900i 1.21783 0.786859i
\(663\) −161.978 −0.244310
\(664\) −1027.59 + 155.434i −1.54757 + 0.234087i
\(665\) 0 0
\(666\) 27.1513 17.5429i 0.0407677 0.0263407i
\(667\) −1144.38 −1.71571
\(668\) 250.863 556.488i 0.375544 0.833066i
\(669\) −148.878 −0.222538
\(670\) 0 0
\(671\) 81.0318i 0.120763i
\(672\) −8.92717 + 31.8356i −0.0132845 + 0.0473744i
\(673\) 120.657i 0.179283i −0.995974 0.0896415i \(-0.971428\pi\)
0.995974 0.0896415i \(-0.0285721\pi\)
\(674\) −98.8493 + 63.8681i −0.146661 + 0.0947598i
\(675\) 0 0
\(676\) 630.918 1399.56i 0.933311 2.07036i
\(677\) 219.196i 0.323776i −0.986809 0.161888i \(-0.948242\pi\)
0.986809 0.161888i \(-0.0517583\pi\)
\(678\) 189.232 122.266i 0.279103 0.180333i
\(679\) 55.5446i 0.0818035i
\(680\) 0 0
\(681\) −489.057 −0.718145
\(682\) 596.850 + 923.751i 0.875146 + 1.35447i
\(683\) −205.502 −0.300881 −0.150441 0.988619i \(-0.548069\pi\)
−0.150441 + 0.988619i \(0.548069\pi\)
\(684\) −77.0988 34.7559i −0.112718 0.0508128i
\(685\) 0 0
\(686\) 63.2222 + 97.8496i 0.0921606 + 0.142638i
\(687\) −239.478 −0.348585
\(688\) −382.659 432.995i −0.556190 0.629354i
\(689\) −59.9837 −0.0870591
\(690\) 0 0
\(691\) 109.536i 0.158519i −0.996854 0.0792593i \(-0.974744\pi\)
0.996854 0.0792593i \(-0.0252555\pi\)
\(692\) 568.042 + 256.071i 0.820869 + 0.370045i
\(693\) 16.6070i 0.0239639i
\(694\) −13.1857 20.4077i −0.0189996 0.0294059i
\(695\) 0 0
\(696\) 488.746 73.9284i 0.702221 0.106219i
\(697\) 159.415i 0.228716i
\(698\) 33.5685 + 51.9543i 0.0480924 + 0.0744331i
\(699\) 0.905758i 0.00129579i
\(700\) 0 0
\(701\) 168.847 0.240865 0.120433 0.992721i \(-0.461572\pi\)
0.120433 + 0.992721i \(0.461572\pi\)
\(702\) −205.229 + 132.602i −0.292349 + 0.188892i
\(703\) 37.9695 0.0540106
\(704\) 175.648 + 567.327i 0.249500 + 0.805863i
\(705\) 0 0
\(706\) −483.909 + 312.661i −0.685424 + 0.442863i
\(707\) 2.18382 0.00308885
\(708\) 229.922 + 103.648i 0.324749 + 0.146396i
\(709\) 554.846 0.782576 0.391288 0.920268i \(-0.372030\pi\)
0.391288 + 0.920268i \(0.372030\pi\)
\(710\) 0 0
\(711\) 197.612i 0.277935i
\(712\) −1031.99 + 156.100i −1.44942 + 0.219242i
\(713\) 1900.97i 2.66616i
\(714\) 6.90374 4.46062i 0.00966911 0.00624737i
\(715\) 0 0
\(716\) −459.474 207.130i −0.641723 0.289287i
\(717\) 127.640i 0.178019i
\(718\) 1115.28 720.600i 1.55331 1.00362i
\(719\) 377.485i 0.525014i −0.964930 0.262507i \(-0.915451\pi\)
0.964930 0.262507i \(-0.0845494\pi\)
\(720\) 0 0
\(721\) 90.3261 0.125279
\(722\) 337.915 + 522.995i 0.468027 + 0.724369i
\(723\) 54.3353 0.0751525
\(724\) 569.972 1264.37i 0.787255 1.74636i
\(725\) 0 0
\(726\) 65.5885 + 101.512i 0.0903423 + 0.139824i
\(727\) −173.183 −0.238216 −0.119108 0.992881i \(-0.538003\pi\)
−0.119108 + 0.992881i \(0.538003\pi\)
\(728\) 16.7814 + 110.943i 0.0230514 + 0.152394i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 143.651i 0.196513i
\(732\) 24.8631 55.1536i 0.0339659 0.0753464i
\(733\) 278.722i 0.380249i −0.981760 0.190124i \(-0.939111\pi\)
0.981760 0.190124i \(-0.0608891\pi\)
\(734\) −6.60489 10.2225i −0.00899849 0.0139270i
\(735\) 0 0
\(736\) 277.165 988.412i 0.376583 1.34295i
\(737\) 647.142i 0.878075i
\(738\) 130.504 + 201.982i 0.176834 + 0.273688i
\(739\) 521.363i 0.705498i −0.935718 0.352749i \(-0.885247\pi\)
0.935718 0.352749i \(-0.114753\pi\)
\(740\) 0 0
\(741\) −287.001 −0.387315
\(742\) 2.55660 1.65186i 0.00344555 0.00222622i
\(743\) −1277.93 −1.71996 −0.859981 0.510326i \(-0.829525\pi\)
−0.859981 + 0.510326i \(0.829525\pi\)
\(744\) 122.805 + 811.874i 0.165061 + 1.09123i
\(745\) 0 0
\(746\) −343.936 + 222.223i −0.461041 + 0.297886i
\(747\) 389.728 0.521724
\(748\) 60.6751 134.595i 0.0811164 0.179940i
\(749\) −49.3989 −0.0659532
\(750\) 0 0
\(751\) 1165.31i 1.55168i 0.630930 + 0.775840i \(0.282673\pi\)
−0.630930 + 0.775840i \(0.717327\pi\)
\(752\) −784.194 887.350i −1.04281 1.17999i
\(753\) 136.395i 0.181136i
\(754\) 1408.97 910.359i 1.86866 1.20737i
\(755\) 0 0
\(756\) 5.09554 11.3034i 0.00674013 0.0149516i
\(757\) 1063.75i 1.40522i 0.711574 + 0.702611i \(0.247983\pi\)
−0.711574 + 0.702611i \(0.752017\pi\)
\(758\) −675.861 + 436.685i −0.891638 + 0.576101i
\(759\) 515.604i 0.679320i
\(760\) 0 0
\(761\) −677.847 −0.890732 −0.445366 0.895349i \(-0.646926\pi\)
−0.445366 + 0.895349i \(0.646926\pi\)
\(762\) 262.194 + 405.800i 0.344087 + 0.532546i
\(763\) −4.39551 −0.00576083
\(764\) −485.577 218.897i −0.635572 0.286514i
\(765\) 0 0
\(766\) −360.078 557.296i −0.470076 0.727541i
\(767\) 855.887 1.11589
\(768\) −54.5201 + 440.040i −0.0709898 + 0.572969i
\(769\) 1289.59 1.67697 0.838486 0.544922i \(-0.183441\pi\)
0.838486 + 0.544922i \(0.183441\pi\)
\(770\) 0 0
\(771\) 422.540i 0.548042i
\(772\) −496.836 223.972i −0.643570 0.290119i
\(773\) 750.339i 0.970684i 0.874324 + 0.485342i \(0.161305\pi\)
−0.874324 + 0.485342i \(0.838695\pi\)
\(774\) 117.599 + 182.008i 0.151936 + 0.235153i
\(775\) 0 0
\(776\) −111.406 736.513i −0.143564 0.949114i
\(777\) 5.56667i 0.00716432i
\(778\) 676.532 + 1047.07i 0.869578 + 1.34585i
\(779\) 282.460i 0.362593i
\(780\) 0 0
\(781\) 549.512 0.703600
\(782\) −214.343 + 138.491i −0.274096 + 0.177098i
\(783\) −185.365 −0.236736
\(784\) 515.402 + 583.200i 0.657400 + 0.743877i
\(785\) 0 0
\(786\) −184.718 + 119.349i −0.235011 + 0.151844i
\(787\) −825.185 −1.04852 −0.524260 0.851558i