Properties

Label 300.3.f.b.199.4
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 199.4
Root \(-0.120653 - 1.40906i\) of defining polynomial
Character \(\chi\) \(=\) 300.199
Dual form 300.3.f.b.199.3

$q$-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 \(-0.486433\pi\)
0.0426100 + 0.999092i \(0.486433\pi\)
\(8\) 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 \(-0.861398\pi\)
0.906688 0.421801i \(-0.138602\pi\)
\(12\) 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 \(-0.940622\pi\)
0.982651 0.185462i \(-0.0593782\pi\)
\(20\) 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 \(-0.745649\pi\)
−0.697376 + 0.716705i \(0.745649\pi\)
\(24\) −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 \(0.404988\pi\)
−0.294076 + 0.955782i \(0.595012\pi\)
\(32\) −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 \(-0.637953\pi\)
−0.419950 + 0.907547i \(0.637953\pi\)
\(44\) −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 \(-0.788559\pi\)
−0.787373 + 0.616477i \(0.788559\pi\)
\(48\) 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 \(0.0998259\pi\)
−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 \(0.522803\pi\)
\(62\) −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 \(-0.325771\pi\)
0.520432 + 0.853903i \(0.325771\pi\)
\(68\) 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 \(0.136926\pi\)
−0.908897 + 0.417021i \(0.863074\pi\)
\(72\) 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 \(0.136884\pi\)
−0.908951 + 0.416902i \(0.863116\pi\)
\(80\) 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 \(-0.786100\pi\)
−0.782586 + 0.622542i \(0.786100\pi\)
\(84\) 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 \(-0.237167\pi\)
0.735033 + 0.678032i \(0.237167\pi\)
\(104\) −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 \(-0.626474\pi\)
−0.386959 + 0.922097i \(0.626474\pi\)
\(108\) 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 \(-0.685026\pi\)
−0.549091 + 0.835763i \(0.685026\pi\)
\(128\) −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 \(-0.922094\pi\)
0.970198 0.242312i \(-0.0779056\pi\)
\(132\) 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 \(-0.965632\pi\)
0.994177 0.107762i \(-0.0343684\pi\)
\(140\) 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 \(-0.881778\pi\)
0.931818 0.362926i \(-0.118222\pi\)
\(152\) 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 \(-0.403957\pi\)
0.297171 + 0.954824i \(0.403957\pi\)
\(164\) −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 \(-0.348960\pi\)
0.456901 + 0.889518i \(0.348960\pi\)
\(168\) −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 \(-0.885516\pi\)
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 \(0.907201\pi\)
\(182\) −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 \(-0.886663\pi\)
0.937278 0.348584i \(-0.113337\pi\)
\(192\) −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 \(0.217836\pi\)
−0.774828 + 0.632172i \(0.782164\pi\)
\(200\) 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 \(-0.818135\pi\)
0.841173 0.540766i \(-0.181865\pi\)
\(212\) 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 \(-0.438268\pi\)
0.192724 + 0.981253i \(0.438268\pi\)
\(224\) −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 \(-0.286348\pi\)
0.621932 + 0.783071i \(0.286348\pi\)
\(228\) 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 \(0.0492700\pi\)
−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 \(0.479268\pi\)
\(242\) −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 \(-0.949860\pi\)
0.987620 0.156868i \(-0.0501398\pi\)
\(252\) −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 \(-0.562574\pi\)
−0.195317 + 0.980740i \(0.562574\pi\)
\(264\) −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 \(0.210130\pi\)
−0.789904 + 0.613230i \(0.789870\pi\)
\(272\) −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 \(-0.385468\pi\)
0.352100 + 0.935963i \(0.385468\pi\)
\(284\) 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 \(-0.679628\pi\)
−0.534839 + 0.844954i \(0.679628\pi\)
\(308\) −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 \(0.0490342\pi\)
−0.988158 + 0.153437i \(0.950966\pi\)
\(312\) 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 \(0.258141\pi\)
−0.688794 + 0.724958i \(0.741859\pi\)
\(332\) 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 \(-0.494428\pi\)
0.0175049 + 0.999847i \(0.494428\pi\)
\(348\) −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 \(0.375657\pi\)
−0.380776 + 0.924667i \(0.624343\pi\)
\(360\) 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 \(-0.497361\pi\)
0.00829059 + 0.999966i \(0.497361\pi\)
\(368\) 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 \(-0.821899\pi\)
0.847510 0.530780i \(-0.178101\pi\)
\(380\) 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 \(-0.357421\pi\)
0.433096 + 0.901348i \(0.357421\pi\)
\(384\) 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 \(-0.934131\pi\)
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 \(0.307595\pi\)
\(422\) 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 \(0.109502\pi\)
−0.941410 + 0.337265i \(0.890498\pi\)
\(432\) 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 \(0.122126\pi\)
−0.927298 + 0.374325i \(0.877874\pi\)
\(440\) 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 \(-0.660852\pi\)
−0.484097 + 0.875014i \(0.660852\pi\)
\(444\) 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 \(-0.322018\pi\)
0.530463 + 0.847708i \(0.322018\pi\)
\(464\) 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 \(-0.644806\pi\)
−0.439393 + 0.898295i \(0.644806\pi\)
\(468\) 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 \(-0.933422\pi\)
0.978206 0.207638i \(-0.0665778\pi\)
\(480\) 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 \(-0.432579\pi\)
0.210228 + 0.977652i \(0.432579\pi\)
\(488\) −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 \(0.296792\pi\)
−0.595908 + 0.803053i \(0.703208\pi\)
\(492\) 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 \(-0.733940\pi\)
0.670545 0.741869i \(-0.266060\pi\)
\(500\) 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 \(-0.477554\pi\)
0.0704572 + 0.997515i \(0.477554\pi\)
\(504\) 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 \(-0.553326\pi\)
−0.166746 + 0.986000i \(0.553326\pi\)
\(524\) −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 \(-0.542660\pi\)
−0.133619 + 0.991033i \(0.542660\pi\)
\(548\) −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 \(-0.630203\pi\)
−0.397734 + 0.917501i \(0.630203\pi\)
\(564\) −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 \(-0.694030\pi\)
0.572509 0.819899i \(-0.305970\pi\)
\(572\) −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 \(-0.407073\pi\)
0.287810 + 0.957688i \(0.407073\pi\)
\(588\) −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 \(0.219770\pi\)
−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 \(0.728311\pi\)
\(602\) 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 \(-0.641769\pi\)
−0.430802 + 0.902446i \(0.641769\pi\)
\(608\) −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 \(-0.865508\pi\)
0.912059 0.410059i \(-0.134492\pi\)
\(620\) 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 \(0.118811\pi\)
−0.931145 + 0.364648i \(0.881189\pi\)
\(632\) −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 \(-0.348185\pi\)
0.459063 + 0.888404i \(0.348185\pi\)
\(644\) 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 \(-0.579374\pi\)
−0.246786 + 0.969070i \(0.579374\pi\)
\(648\) 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 \(0.195167\pi\)
−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 \(0.369397\pi\)
\(662\) −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 \(-0.451931\pi\)
0.150441 + 0.988619i \(0.451931\pi\)
\(684\) −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 \(0.0252555\pi\)
−0.996854 + 0.0792593i \(0.974744\pi\)
\(692\) −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 \(0.0845494\pi\)
−0.964930 + 0.262507i \(0.915451\pi\)
\(720\) 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 \(-0.461997\pi\)
0.119108 + 0.992881i \(0.461997\pi\)
\(728\) −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 \(0.114753\pi\)
−0.935718 + 0.352749i \(0.885247\pi\)
\(740\) 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 \(-0.170475\pi\)
0.859981 + 0.510326i \(0.170475\pi\)
\(744\) 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 \(-0.717327\pi\)
0.630930 0.775840i \(-0.282673\pi\)
\(752\) 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 \(-0.324342\pi\)