Properties

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

$q$-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 \(0.138602\pi\)
−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 \(-0.640397\pi\)
0.426907 0.904295i \(-0.359603\pi\)
\(14\) −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 \(-0.962677\pi\)
0.993134 0.116986i \(-0.0373231\pi\)
\(18\) −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 \(-0.745649\pi\)
−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 \(-0.595012\pi\)
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 \(0.0231952\pi\)
−0.997346 + 0.0728055i \(0.976805\pi\)
\(38\) 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 \(-0.992338\pi\)
0.999710 0.0240682i \(-0.00766189\pi\)
\(54\) 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 \(-0.325771\pi\)
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 \(-0.863074\pi\)
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 \(-0.807522\pi\)
0.822679 0.568506i \(-0.192478\pi\)
\(74\) 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 \(-0.786100\pi\)
−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 \(-0.840653\pi\)
0.877293 0.479955i \(-0.159347\pi\)
\(98\) 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 \(0.0929153\pi\)
−0.957698 + 0.287774i \(0.907085\pi\)
\(114\) −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 \(0.0779056\pi\)
−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 \(0.168221\pi\)
−0.863573 + 0.504223i \(0.831779\pi\)
\(138\) −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 \(0.191342\pi\)
−0.824703 + 0.565566i \(0.808658\pi\)
\(158\) −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 \(0.148651\pi\)
−0.892922 + 0.450211i \(0.851349\pi\)
\(174\) −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 \(-0.885172\pi\)
0.935635 0.352970i \(-0.114828\pi\)
\(194\) −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 \(-0.939123\pi\)
0.981767 0.190087i \(-0.0608772\pi\)
\(198\) 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 \(-0.438268\pi\)
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 \(-0.999643\pi\)
0.999999 0.00112219i \(-0.000357204\pi\)
\(234\) −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 \(-0.842586\pi\)
0.880192 0.474618i \(-0.157414\pi\)
\(258\) −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 \(-0.789870\pi\)
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 \(0.0729851\pi\)
−0.973828 + 0.227286i \(0.927015\pi\)
\(278\) 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 \(0.0557779\pi\)
−0.984686 + 0.174336i \(0.944222\pi\)
\(294\) −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 \(-0.950966\pi\)
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 \(0.341953\pi\)
−0.476368 + 0.879246i \(0.658047\pi\)
\(314\) 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 \(-0.756266\pi\)
0.720889 0.693051i \(-0.243734\pi\)
\(318\) 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 \(-0.972174\pi\)
0.996182 0.0873052i \(-0.0278255\pi\)
\(338\) 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 \(-0.866218\pi\)
0.912971 0.408024i \(-0.133782\pi\)
\(354\) 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 \(-0.497361\pi\)
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 \(-0.911504\pi\)
0.961601 0.274451i \(-0.0884963\pi\)
\(374\) −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 \(-0.357421\pi\)
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 \(0.147746\pi\)
−0.894199 + 0.447669i \(0.852254\pi\)
\(398\) −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 \(0.0197776\pi\)
−0.998070 + 0.0620931i \(0.980222\pi\)
\(434\) −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 \(-0.660852\pi\)
−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 \(-0.682040\pi\)
0.541228 0.840876i \(-0.317960\pi\)
\(458\) 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 \(0.0665778\pi\)
−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 \(-0.432579\pi\)
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 \(-0.703208\pi\)
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 \(-0.477554\pi\)
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 \(-0.946110\pi\)
0.985703 0.168492i \(-0.0538898\pi\)
\(558\) −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 \(0.305970\pi\)
−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 \(0.156513\pi\)
−0.881532 + 0.472125i \(0.843487\pi\)
\(578\) −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 \(0.158748\pi\)
−0.878194 + 0.478304i \(0.841252\pi\)
\(594\) −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 \(-0.641769\pi\)
−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 \(0.316047\pi\)
−0.546270 + 0.837609i \(0.683953\pi\)
\(614\) 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 \(0.126954\pi\)
−0.921512 + 0.388349i \(0.873046\pi\)
\(618\) 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 \(-0.348185\pi\)
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 \(0.0216097\pi\)
−0.997696 + 0.0678369i \(0.978390\pi\)
\(654\) 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 \(0.0285721\pi\)
−0.995974 + 0.0896415i \(0.971428\pi\)
\(674\) −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 \(0.0517583\pi\)
−0.986809 + 0.161888i \(0.948242\pi\)
\(678\) −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 \(-0.974744\pi\)
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 \(-0.461997\pi\)
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 \(0.0608891\pi\)
−0.981760 + 0.190124i \(0.939111\pi\)
\(734\) −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 \(-0.170475\pi\)
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 \(0.282673\pi\)
−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 \(-0.752017\pi\)
0.711574 0.702611i \(-0.247983\pi\)
\(758\) 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 \(-0.838695\pi\)
0.874324 0.485342i \(-0.161305\pi\)
\(774\) 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 0.851