Properties

Label 300.5.c.c.151.2
Level $300$
Weight $5$
Character 300.151
Analytic conductor $31.011$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(31.0109889252\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + 234752 x^{8} - 632832 x^{7} + 1884160 x^{6} - 8847360 x^{5} + 32243712 x^{4} - 113246208 x^{3} + 335544320 x^{2} - 1610612736 x + 4294967296\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.2
Root \(-1.18006 - 3.82197i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.5.c.c.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.89995 + 0.889027i) q^{2} -5.19615i q^{3} +(14.4193 - 6.93433i) q^{4} +(4.61952 + 20.2647i) q^{6} +44.0991i q^{7} +(-50.0696 + 39.8627i) q^{8} -27.0000 q^{9} +O(q^{10})\) \(q+(-3.89995 + 0.889027i) q^{2} -5.19615i q^{3} +(14.4193 - 6.93433i) q^{4} +(4.61952 + 20.2647i) q^{6} +44.0991i q^{7} +(-50.0696 + 39.8627i) q^{8} -27.0000 q^{9} -81.7783i q^{11} +(-36.0318 - 74.9247i) q^{12} -192.024 q^{13} +(-39.2053 - 171.984i) q^{14} +(159.830 - 199.976i) q^{16} +415.880 q^{17} +(105.299 - 24.0037i) q^{18} -23.6665i q^{19} +229.146 q^{21} +(72.7031 + 318.931i) q^{22} +525.030i q^{23} +(207.132 + 260.169i) q^{24} +(748.886 - 170.715i) q^{26} +140.296i q^{27} +(305.798 + 635.876i) q^{28} +254.717 q^{29} -1306.77i q^{31} +(-445.546 + 921.989i) q^{32} -424.932 q^{33} +(-1621.91 + 369.729i) q^{34} +(-389.320 + 187.227i) q^{36} -1228.10 q^{37} +(21.0402 + 92.2983i) q^{38} +997.787i q^{39} +1956.13 q^{41} +(-893.657 + 203.717i) q^{42} -2497.56i q^{43} +(-567.077 - 1179.18i) q^{44} +(-466.766 - 2047.59i) q^{46} +2009.43i q^{47} +(-1039.10 - 830.502i) q^{48} +456.271 q^{49} -2160.98i q^{51} +(-2768.85 + 1331.56i) q^{52} +20.8393 q^{53} +(-124.727 - 547.148i) q^{54} +(-1757.91 - 2208.02i) q^{56} -122.975 q^{57} +(-993.383 + 226.450i) q^{58} +2216.17i q^{59} +2191.60 q^{61} +(1161.75 + 5096.34i) q^{62} -1190.68i q^{63} +(917.936 - 3991.82i) q^{64} +(1657.22 - 377.776i) q^{66} -6567.99i q^{67} +(5996.68 - 2883.85i) q^{68} +2728.14 q^{69} -8342.55i q^{71} +(1351.88 - 1076.29i) q^{72} +6092.86 q^{73} +(4789.55 - 1091.82i) q^{74} +(-164.111 - 341.254i) q^{76} +3606.35 q^{77} +(-887.060 - 3891.32i) q^{78} -6129.92i q^{79} +729.000 q^{81} +(-7628.82 + 1739.05i) q^{82} -9941.10i q^{83} +(3304.11 - 1588.97i) q^{84} +(2220.40 + 9740.36i) q^{86} -1323.55i q^{87} +(3259.90 + 4094.61i) q^{88} +6746.75 q^{89} -8468.09i q^{91} +(3640.73 + 7570.55i) q^{92} -6790.17 q^{93} +(-1786.44 - 7836.69i) q^{94} +(4790.80 + 2315.13i) q^{96} -1534.23 q^{97} +(-1779.44 + 405.637i) q^{98} +2208.01i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + O(q^{10}) \) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + 176q^{13} + 78q^{14} - 376q^{16} - 162q^{18} - 144q^{21} - 788q^{22} + 108q^{24} + 678q^{26} + 3368q^{28} + 1728q^{29} + 2016q^{32} - 2932q^{34} - 216q^{36} - 1568q^{37} - 6990q^{38} + 1248q^{41} + 162q^{42} + 8088q^{44} + 5956q^{46} + 2088q^{48} - 10720q^{49} + 3128q^{52} - 288q^{53} - 486q^{54} - 10236q^{56} + 5616q^{57} - 16164q^{58} - 3760q^{61} - 12714q^{62} + 10544q^{64} + 8100q^{66} + 26136q^{68} + 9792q^{69} + 4860q^{72} + 11040q^{73} - 17004q^{74} - 28344q^{76} + 768q^{77} - 16830q^{78} + 11664q^{81} - 21280q^{82} + 15120q^{84} + 24414q^{86} + 52840q^{88} - 768q^{89} + 23736q^{92} - 9936q^{93} - 45156q^{94} - 11088q^{96} + 7248q^{97} - 58140q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.89995 + 0.889027i −0.974988 + 0.222257i
\(3\) 5.19615i 0.577350i
\(4\) 14.4193 6.93433i 0.901204 0.433396i
\(5\) 0 0
\(6\) 4.61952 + 20.2647i 0.128320 + 0.562910i
\(7\) 44.0991i 0.899981i 0.893033 + 0.449991i \(0.148573\pi\)
−0.893033 + 0.449991i \(0.851427\pi\)
\(8\) −50.0696 + 39.8627i −0.782338 + 0.622854i
\(9\) −27.0000 −0.333333
\(10\) 0 0
\(11\) 81.7783i 0.675853i −0.941172 0.337927i \(-0.890274\pi\)
0.941172 0.337927i \(-0.109726\pi\)
\(12\) −36.0318 74.9247i −0.250221 0.520310i
\(13\) −192.024 −1.13624 −0.568119 0.822946i \(-0.692329\pi\)
−0.568119 + 0.822946i \(0.692329\pi\)
\(14\) −39.2053 171.984i −0.200027 0.877471i
\(15\) 0 0
\(16\) 159.830 199.976i 0.624337 0.781155i
\(17\) 415.880 1.43903 0.719516 0.694476i \(-0.244364\pi\)
0.719516 + 0.694476i \(0.244364\pi\)
\(18\) 105.299 24.0037i 0.324996 0.0740856i
\(19\) 23.6665i 0.0655582i −0.999463 0.0327791i \(-0.989564\pi\)
0.999463 0.0327791i \(-0.0104358\pi\)
\(20\) 0 0
\(21\) 229.146 0.519604
\(22\) 72.7031 + 318.931i 0.150213 + 0.658949i
\(23\) 525.030i 0.992496i 0.868181 + 0.496248i \(0.165289\pi\)
−0.868181 + 0.496248i \(0.834711\pi\)
\(24\) 207.132 + 260.169i 0.359605 + 0.451683i
\(25\) 0 0
\(26\) 748.886 170.715i 1.10782 0.252537i
\(27\) 140.296i 0.192450i
\(28\) 305.798 + 635.876i 0.390048 + 0.811067i
\(29\) 254.717 0.302873 0.151437 0.988467i \(-0.451610\pi\)
0.151437 + 0.988467i \(0.451610\pi\)
\(30\) 0 0
\(31\) 1306.77i 1.35980i −0.733304 0.679901i \(-0.762023\pi\)
0.733304 0.679901i \(-0.237977\pi\)
\(32\) −445.546 + 921.989i −0.435104 + 0.900380i
\(33\) −424.932 −0.390204
\(34\) −1621.91 + 369.729i −1.40304 + 0.319835i
\(35\) 0 0
\(36\) −389.320 + 187.227i −0.300401 + 0.144465i
\(37\) −1228.10 −0.897081 −0.448540 0.893763i \(-0.648056\pi\)
−0.448540 + 0.893763i \(0.648056\pi\)
\(38\) 21.0402 + 92.2983i 0.0145708 + 0.0639185i
\(39\) 997.787i 0.656007i
\(40\) 0 0
\(41\) 1956.13 1.16367 0.581835 0.813307i \(-0.302335\pi\)
0.581835 + 0.813307i \(0.302335\pi\)
\(42\) −893.657 + 203.717i −0.506608 + 0.115486i
\(43\) 2497.56i 1.35076i −0.737469 0.675381i \(-0.763979\pi\)
0.737469 0.675381i \(-0.236021\pi\)
\(44\) −567.077 1179.18i −0.292912 0.609082i
\(45\) 0 0
\(46\) −466.766 2047.59i −0.220589 0.967671i
\(47\) 2009.43i 0.909657i 0.890579 + 0.454829i \(0.150300\pi\)
−0.890579 + 0.454829i \(0.849700\pi\)
\(48\) −1039.10 830.502i −0.451000 0.360461i
\(49\) 456.271 0.190034
\(50\) 0 0
\(51\) 2160.98i 0.830825i
\(52\) −2768.85 + 1331.56i −1.02398 + 0.492441i
\(53\) 20.8393 0.00741876 0.00370938 0.999993i \(-0.498819\pi\)
0.00370938 + 0.999993i \(0.498819\pi\)
\(54\) −124.727 547.148i −0.0427733 0.187637i
\(55\) 0 0
\(56\) −1757.91 2208.02i −0.560557 0.704089i
\(57\) −122.975 −0.0378501
\(58\) −993.383 + 226.450i −0.295298 + 0.0673157i
\(59\) 2216.17i 0.636649i 0.947982 + 0.318324i \(0.103120\pi\)
−0.947982 + 0.318324i \(0.896880\pi\)
\(60\) 0 0
\(61\) 2191.60 0.588981 0.294491 0.955654i \(-0.404850\pi\)
0.294491 + 0.955654i \(0.404850\pi\)
\(62\) 1161.75 + 5096.34i 0.302225 + 1.32579i
\(63\) 1190.68i 0.299994i
\(64\) 917.936 3991.82i 0.224105 0.974565i
\(65\) 0 0
\(66\) 1657.22 377.776i 0.380444 0.0867255i
\(67\) 6567.99i 1.46313i −0.681772 0.731565i \(-0.738790\pi\)
0.681772 0.731565i \(-0.261210\pi\)
\(68\) 5996.68 2883.85i 1.29686 0.623670i
\(69\) 2728.14 0.573018
\(70\) 0 0
\(71\) 8342.55i 1.65494i −0.561510 0.827470i \(-0.689780\pi\)
0.561510 0.827470i \(-0.310220\pi\)
\(72\) 1351.88 1076.29i 0.260779 0.207618i
\(73\) 6092.86 1.14334 0.571671 0.820483i \(-0.306296\pi\)
0.571671 + 0.820483i \(0.306296\pi\)
\(74\) 4789.55 1091.82i 0.874643 0.199382i
\(75\) 0 0
\(76\) −164.111 341.254i −0.0284126 0.0590813i
\(77\) 3606.35 0.608255
\(78\) −887.060 3891.32i −0.145802 0.639600i
\(79\) 6129.92i 0.982201i −0.871103 0.491101i \(-0.836595\pi\)
0.871103 0.491101i \(-0.163405\pi\)
\(80\) 0 0
\(81\) 729.000 0.111111
\(82\) −7628.82 + 1739.05i −1.13457 + 0.258634i
\(83\) 9941.10i 1.44304i −0.692394 0.721520i \(-0.743444\pi\)
0.692394 0.721520i \(-0.256556\pi\)
\(84\) 3304.11 1588.97i 0.468269 0.225194i
\(85\) 0 0
\(86\) 2220.40 + 9740.36i 0.300216 + 1.31698i
\(87\) 1323.55i 0.174864i
\(88\) 3259.90 + 4094.61i 0.420958 + 0.528746i
\(89\) 6746.75 0.851755 0.425877 0.904781i \(-0.359965\pi\)
0.425877 + 0.904781i \(0.359965\pi\)
\(90\) 0 0
\(91\) 8468.09i 1.02259i
\(92\) 3640.73 + 7570.55i 0.430143 + 0.894441i
\(93\) −6790.17 −0.785082
\(94\) −1786.44 7836.69i −0.202178 0.886905i
\(95\) 0 0
\(96\) 4790.80 + 2315.13i 0.519835 + 0.251207i
\(97\) −1534.23 −0.163060 −0.0815301 0.996671i \(-0.525981\pi\)
−0.0815301 + 0.996671i \(0.525981\pi\)
\(98\) −1779.44 + 405.637i −0.185281 + 0.0422363i
\(99\) 2208.01i 0.225284i
\(100\) 0 0
\(101\) −8029.60 −0.787138 −0.393569 0.919295i \(-0.628760\pi\)
−0.393569 + 0.919295i \(0.628760\pi\)
\(102\) 1921.17 + 8427.71i 0.184657 + 0.810045i
\(103\) 6973.64i 0.657332i −0.944446 0.328666i \(-0.893401\pi\)
0.944446 0.328666i \(-0.106599\pi\)
\(104\) 9614.58 7654.60i 0.888922 0.707711i
\(105\) 0 0
\(106\) −81.2723 + 18.5267i −0.00723320 + 0.00164887i
\(107\) 13213.0i 1.15407i −0.816718 0.577036i \(-0.804209\pi\)
0.816718 0.577036i \(-0.195791\pi\)
\(108\) 972.859 + 2022.97i 0.0834070 + 0.173437i
\(109\) −23642.6 −1.98995 −0.994976 0.100116i \(-0.968079\pi\)
−0.994976 + 0.100116i \(0.968079\pi\)
\(110\) 0 0
\(111\) 6381.41i 0.517930i
\(112\) 8818.75 + 7048.36i 0.703025 + 0.561891i
\(113\) 20927.8 1.63896 0.819478 0.573110i \(-0.194263\pi\)
0.819478 + 0.573110i \(0.194263\pi\)
\(114\) 479.596 109.328i 0.0369034 0.00841243i
\(115\) 0 0
\(116\) 3672.82 1766.29i 0.272951 0.131264i
\(117\) 5184.66 0.378746
\(118\) −1970.24 8642.97i −0.141499 0.620725i
\(119\) 18339.9i 1.29510i
\(120\) 0 0
\(121\) 7953.32 0.543222
\(122\) −8547.13 + 1948.39i −0.574250 + 0.130905i
\(123\) 10164.4i 0.671846i
\(124\) −9061.57 18842.6i −0.589332 1.22546i
\(125\) 0 0
\(126\) 1058.54 + 4643.58i 0.0666757 + 0.292490i
\(127\) 23012.5i 1.42678i −0.700769 0.713388i \(-0.747160\pi\)
0.700769 0.713388i \(-0.252840\pi\)
\(128\) −31.0702 + 16384.0i −0.00189637 + 0.999998i
\(129\) −12977.7 −0.779863
\(130\) 0 0
\(131\) 15628.0i 0.910669i −0.890320 0.455335i \(-0.849520\pi\)
0.890320 0.455335i \(-0.150480\pi\)
\(132\) −6127.21 + 2946.62i −0.351653 + 0.169113i
\(133\) 1043.67 0.0590012
\(134\) 5839.12 + 25614.9i 0.325191 + 1.42653i
\(135\) 0 0
\(136\) −20823.0 + 16578.1i −1.12581 + 0.896307i
\(137\) 12124.8 0.645999 0.323000 0.946399i \(-0.395309\pi\)
0.323000 + 0.946399i \(0.395309\pi\)
\(138\) −10639.6 + 2425.39i −0.558685 + 0.127357i
\(139\) 21661.2i 1.12112i 0.828112 + 0.560562i \(0.189415\pi\)
−0.828112 + 0.560562i \(0.810585\pi\)
\(140\) 0 0
\(141\) 10441.3 0.525191
\(142\) 7416.75 + 32535.5i 0.367822 + 1.61355i
\(143\) 15703.4i 0.767930i
\(144\) −4315.41 + 5399.35i −0.208112 + 0.260385i
\(145\) 0 0
\(146\) −23761.9 + 5416.72i −1.11474 + 0.254115i
\(147\) 2370.85i 0.109716i
\(148\) −17708.3 + 8516.07i −0.808453 + 0.388791i
\(149\) 7153.57 0.322218 0.161109 0.986937i \(-0.448493\pi\)
0.161109 + 0.986937i \(0.448493\pi\)
\(150\) 0 0
\(151\) 6696.21i 0.293680i −0.989160 0.146840i \(-0.953090\pi\)
0.989160 0.146840i \(-0.0469103\pi\)
\(152\) 943.411 + 1184.97i 0.0408332 + 0.0512887i
\(153\) −11228.8 −0.479677
\(154\) −14064.6 + 3206.14i −0.593042 + 0.135189i
\(155\) 0 0
\(156\) 6918.98 + 14387.4i 0.284311 + 0.591196i
\(157\) −35186.7 −1.42751 −0.713756 0.700394i \(-0.753007\pi\)
−0.713756 + 0.700394i \(0.753007\pi\)
\(158\) 5449.66 + 23906.4i 0.218301 + 0.957635i
\(159\) 108.284i 0.00428322i
\(160\) 0 0
\(161\) −23153.3 −0.893227
\(162\) −2843.07 + 648.101i −0.108332 + 0.0246952i
\(163\) 37194.0i 1.39990i 0.714191 + 0.699951i \(0.246795\pi\)
−0.714191 + 0.699951i \(0.753205\pi\)
\(164\) 28206.0 13564.5i 1.04870 0.504330i
\(165\) 0 0
\(166\) 8837.91 + 38769.8i 0.320725 + 1.40695i
\(167\) 52749.4i 1.89140i −0.325035 0.945702i \(-0.605376\pi\)
0.325035 0.945702i \(-0.394624\pi\)
\(168\) −11473.2 + 9134.35i −0.406506 + 0.323638i
\(169\) 8312.32 0.291037
\(170\) 0 0
\(171\) 638.996i 0.0218527i
\(172\) −17318.9 36013.0i −0.585414 1.21731i
\(173\) −23695.1 −0.791711 −0.395855 0.918313i \(-0.629552\pi\)
−0.395855 + 0.918313i \(0.629552\pi\)
\(174\) 1176.67 + 5161.77i 0.0388647 + 0.170490i
\(175\) 0 0
\(176\) −16353.7 13070.6i −0.527946 0.421960i
\(177\) 11515.6 0.367569
\(178\) −26312.0 + 5998.05i −0.830451 + 0.189308i
\(179\) 39705.3i 1.23920i 0.784917 + 0.619601i \(0.212706\pi\)
−0.784917 + 0.619601i \(0.787294\pi\)
\(180\) 0 0
\(181\) 37853.5 1.15545 0.577723 0.816233i \(-0.303941\pi\)
0.577723 + 0.816233i \(0.303941\pi\)
\(182\) 7528.37 + 33025.2i 0.227278 + 0.997016i
\(183\) 11387.9i 0.340048i
\(184\) −20929.1 26288.1i −0.618180 0.776467i
\(185\) 0 0
\(186\) 26481.4 6036.65i 0.765446 0.174490i
\(187\) 34010.0i 0.972574i
\(188\) 13934.1 + 28974.5i 0.394241 + 0.819787i
\(189\) −6186.93 −0.173201
\(190\) 0 0
\(191\) 9912.58i 0.271719i 0.990728 + 0.135860i \(0.0433796\pi\)
−0.990728 + 0.135860i \(0.956620\pi\)
\(192\) −20742.1 4769.73i −0.562665 0.129387i
\(193\) −33480.7 −0.898836 −0.449418 0.893322i \(-0.648369\pi\)
−0.449418 + 0.893322i \(0.648369\pi\)
\(194\) 5983.44 1363.97i 0.158982 0.0362412i
\(195\) 0 0
\(196\) 6579.09 3163.93i 0.171259 0.0823598i
\(197\) 47603.7 1.22662 0.613308 0.789844i \(-0.289839\pi\)
0.613308 + 0.789844i \(0.289839\pi\)
\(198\) −1962.98 8611.15i −0.0500710 0.219650i
\(199\) 36097.0i 0.911518i 0.890103 + 0.455759i \(0.150632\pi\)
−0.890103 + 0.455759i \(0.849368\pi\)
\(200\) 0 0
\(201\) −34128.3 −0.844738
\(202\) 31315.1 7138.53i 0.767451 0.174947i
\(203\) 11232.8i 0.272580i
\(204\) −14984.9 31159.7i −0.360076 0.748743i
\(205\) 0 0
\(206\) 6199.76 + 27196.9i 0.146097 + 0.640891i
\(207\) 14175.8i 0.330832i
\(208\) −30691.3 + 38400.2i −0.709395 + 0.887579i
\(209\) −1935.41 −0.0443077
\(210\) 0 0
\(211\) 38188.8i 0.857770i 0.903359 + 0.428885i \(0.141093\pi\)
−0.903359 + 0.428885i \(0.858907\pi\)
\(212\) 300.487 144.507i 0.00668582 0.00321526i
\(213\) −43349.2 −0.955480
\(214\) 11746.7 + 51530.0i 0.256501 + 1.12521i
\(215\) 0 0
\(216\) −5592.58 7024.57i −0.119868 0.150561i
\(217\) 57627.3 1.22380
\(218\) 92205.1 21018.9i 1.94018 0.442280i
\(219\) 31659.5i 0.660108i
\(220\) 0 0
\(221\) −79859.1 −1.63508
\(222\) −5673.25 24887.2i −0.115113 0.504976i
\(223\) 57730.2i 1.16090i −0.814297 0.580448i \(-0.802877\pi\)
0.814297 0.580448i \(-0.197123\pi\)
\(224\) −40658.9 19648.2i −0.810325 0.391585i
\(225\) 0 0
\(226\) −81617.6 + 18605.4i −1.59796 + 0.364269i
\(227\) 71760.8i 1.39263i 0.717737 + 0.696314i \(0.245178\pi\)
−0.717737 + 0.696314i \(0.754822\pi\)
\(228\) −1773.21 + 852.748i −0.0341106 + 0.0164040i
\(229\) 39466.1 0.752581 0.376290 0.926502i \(-0.377200\pi\)
0.376290 + 0.926502i \(0.377200\pi\)
\(230\) 0 0
\(231\) 18739.1i 0.351176i
\(232\) −12753.6 + 10153.7i −0.236949 + 0.188646i
\(233\) 106708. 1.96556 0.982781 0.184775i \(-0.0591555\pi\)
0.982781 + 0.184775i \(0.0591555\pi\)
\(234\) −20219.9 + 4609.30i −0.369273 + 0.0841789i
\(235\) 0 0
\(236\) 15367.7 + 31955.6i 0.275921 + 0.573750i
\(237\) −31852.0 −0.567074
\(238\) −16304.7 71524.9i −0.287845 1.26271i
\(239\) 32704.8i 0.572554i −0.958147 0.286277i \(-0.907582\pi\)
0.958147 0.286277i \(-0.0924177\pi\)
\(240\) 0 0
\(241\) 93720.2 1.61361 0.806806 0.590816i \(-0.201194\pi\)
0.806806 + 0.590816i \(0.201194\pi\)
\(242\) −31017.6 + 7070.72i −0.529635 + 0.120735i
\(243\) 3788.00i 0.0641500i
\(244\) 31601.2 15197.3i 0.530792 0.255262i
\(245\) 0 0
\(246\) 9036.39 + 39640.5i 0.149322 + 0.655041i
\(247\) 4544.55i 0.0744898i
\(248\) 52091.3 + 65429.5i 0.846958 + 1.06382i
\(249\) −51655.5 −0.833139
\(250\) 0 0
\(251\) 2858.44i 0.0453714i −0.999743 0.0226857i \(-0.992778\pi\)
0.999743 0.0226857i \(-0.00722170\pi\)
\(252\) −8256.53 17168.7i −0.130016 0.270356i
\(253\) 42936.0 0.670781
\(254\) 20458.7 + 89747.5i 0.317111 + 1.39109i
\(255\) 0 0
\(256\) −14444.6 63924.3i −0.220407 0.975408i
\(257\) 34273.0 0.518902 0.259451 0.965756i \(-0.416458\pi\)
0.259451 + 0.965756i \(0.416458\pi\)
\(258\) 50612.4 11537.5i 0.760357 0.173330i
\(259\) 54158.2i 0.807356i
\(260\) 0 0
\(261\) −6877.35 −0.100958
\(262\) 13893.7 + 60948.4i 0.202402 + 0.887892i
\(263\) 50691.6i 0.732866i 0.930444 + 0.366433i \(0.119421\pi\)
−0.930444 + 0.366433i \(0.880579\pi\)
\(264\) 21276.2 16938.9i 0.305271 0.243040i
\(265\) 0 0
\(266\) −4070.27 + 927.853i −0.0575254 + 0.0131134i
\(267\) 35057.1i 0.491761i
\(268\) −45544.6 94705.6i −0.634114 1.31858i
\(269\) 42022.9 0.580740 0.290370 0.956914i \(-0.406222\pi\)
0.290370 + 0.956914i \(0.406222\pi\)
\(270\) 0 0
\(271\) 101170.i 1.37757i 0.724965 + 0.688786i \(0.241856\pi\)
−0.724965 + 0.688786i \(0.758144\pi\)
\(272\) 66470.2 83166.0i 0.898440 1.12411i
\(273\) −44001.5 −0.590394
\(274\) −47286.0 + 10779.2i −0.629841 + 0.143578i
\(275\) 0 0
\(276\) 39337.7 18917.8i 0.516406 0.248343i
\(277\) −129724. −1.69067 −0.845337 0.534234i \(-0.820600\pi\)
−0.845337 + 0.534234i \(0.820600\pi\)
\(278\) −19257.4 84477.8i −0.249177 1.09308i
\(279\) 35282.8i 0.453267i
\(280\) 0 0
\(281\) −10671.3 −0.135147 −0.0675733 0.997714i \(-0.521526\pi\)
−0.0675733 + 0.997714i \(0.521526\pi\)
\(282\) −40720.7 + 9282.62i −0.512055 + 0.116727i
\(283\) 98529.3i 1.23025i −0.788431 0.615124i \(-0.789106\pi\)
0.788431 0.615124i \(-0.210894\pi\)
\(284\) −57850.0 120293.i −0.717243 1.49144i
\(285\) 0 0
\(286\) −13960.8 61242.6i −0.170678 0.748723i
\(287\) 86263.6i 1.04728i
\(288\) 12029.7 24893.7i 0.145035 0.300127i
\(289\) 89435.3 1.07081
\(290\) 0 0
\(291\) 7972.11i 0.0941428i
\(292\) 87854.6 42249.9i 1.03038 0.495519i
\(293\) 11135.2 0.129707 0.0648536 0.997895i \(-0.479342\pi\)
0.0648536 + 0.997895i \(0.479342\pi\)
\(294\) 2107.75 + 9246.22i 0.0243851 + 0.106972i
\(295\) 0 0
\(296\) 61490.7 48955.5i 0.701820 0.558751i
\(297\) 11473.2 0.130068
\(298\) −27898.6 + 6359.72i −0.314159 + 0.0716152i
\(299\) 100819.i 1.12771i
\(300\) 0 0
\(301\) 110140. 1.21566
\(302\) 5953.11 + 26114.9i 0.0652725 + 0.286335i
\(303\) 41723.0i 0.454455i
\(304\) −4732.73 3782.62i −0.0512112 0.0409304i
\(305\) 0 0
\(306\) 43791.7 9982.68i 0.467680 0.106612i
\(307\) 132222.i 1.40290i 0.712721 + 0.701448i \(0.247463\pi\)
−0.712721 + 0.701448i \(0.752537\pi\)
\(308\) 52000.8 25007.6i 0.548162 0.263615i
\(309\) −36236.1 −0.379511
\(310\) 0 0
\(311\) 112364.i 1.16173i −0.813999 0.580867i \(-0.802714\pi\)
0.813999 0.580867i \(-0.197286\pi\)
\(312\) −39774.5 49958.8i −0.408597 0.513220i
\(313\) 44150.3 0.450656 0.225328 0.974283i \(-0.427655\pi\)
0.225328 + 0.974283i \(0.427655\pi\)
\(314\) 137227. 31282.0i 1.39181 0.317274i
\(315\) 0 0
\(316\) −42506.9 88388.9i −0.425682 0.885164i
\(317\) −48209.0 −0.479744 −0.239872 0.970805i \(-0.577105\pi\)
−0.239872 + 0.970805i \(0.577105\pi\)
\(318\) 96.2676 + 422.303i 0.000951976 + 0.00417609i
\(319\) 20830.3i 0.204698i
\(320\) 0 0
\(321\) −68656.6 −0.666304
\(322\) 90297.0 20584.0i 0.870886 0.198526i
\(323\) 9842.44i 0.0943404i
\(324\) 10511.6 5055.13i 0.100134 0.0481551i
\(325\) 0 0
\(326\) −33066.5 145055.i −0.311138 1.36489i
\(327\) 122851.i 1.14890i
\(328\) −97942.7 + 77976.6i −0.910384 + 0.724797i
\(329\) −88614.2 −0.818675
\(330\) 0 0
\(331\) 88854.4i 0.811004i −0.914094 0.405502i \(-0.867097\pi\)
0.914094 0.405502i \(-0.132903\pi\)
\(332\) −68934.8 143343.i −0.625407 1.30047i
\(333\) 33158.8 0.299027
\(334\) 46895.6 + 205720.i 0.420377 + 1.84410i
\(335\) 0 0
\(336\) 36624.4 45823.6i 0.324408 0.405892i
\(337\) −144878. −1.27569 −0.637843 0.770166i \(-0.720173\pi\)
−0.637843 + 0.770166i \(0.720173\pi\)
\(338\) −32417.6 + 7389.88i −0.283758 + 0.0646850i
\(339\) 108744.i 0.946252i
\(340\) 0 0
\(341\) −106865. −0.919026
\(342\) −568.085 2492.05i −0.00485692 0.0213062i
\(343\) 126003.i 1.07101i
\(344\) 99559.4 + 125052.i 0.841328 + 1.05675i
\(345\) 0 0
\(346\) 92409.8 21065.6i 0.771908 0.175963i
\(347\) 72849.3i 0.605016i 0.953147 + 0.302508i \(0.0978238\pi\)
−0.953147 + 0.302508i \(0.902176\pi\)
\(348\) −9177.90 19084.6i −0.0757853 0.157588i
\(349\) 123918. 1.01738 0.508692 0.860948i \(-0.330129\pi\)
0.508692 + 0.860948i \(0.330129\pi\)
\(350\) 0 0
\(351\) 26940.3i 0.218669i
\(352\) 75398.7 + 36436.0i 0.608525 + 0.294066i
\(353\) −185296. −1.48702 −0.743508 0.668727i \(-0.766840\pi\)
−0.743508 + 0.668727i \(0.766840\pi\)
\(354\) −44910.2 + 10237.7i −0.358376 + 0.0816948i
\(355\) 0 0
\(356\) 97283.2 46784.2i 0.767605 0.369147i
\(357\) 95297.1 0.747727
\(358\) −35299.1 154849.i −0.275421 1.20821i
\(359\) 98151.3i 0.761565i −0.924665 0.380783i \(-0.875655\pi\)
0.924665 0.380783i \(-0.124345\pi\)
\(360\) 0 0
\(361\) 129761. 0.995702
\(362\) −147627. + 33652.8i −1.12655 + 0.256806i
\(363\) 41326.6i 0.313630i
\(364\) −58720.5 122104.i −0.443187 0.921565i
\(365\) 0 0
\(366\) 10124.1 + 44412.2i 0.0755781 + 0.331543i
\(367\) 119078.i 0.884096i 0.896991 + 0.442048i \(0.145748\pi\)
−0.896991 + 0.442048i \(0.854252\pi\)
\(368\) 104993. + 83915.7i 0.775293 + 0.619651i
\(369\) −52815.5 −0.387890
\(370\) 0 0
\(371\) 918.994i 0.00667675i
\(372\) −97909.3 + 47085.3i −0.707519 + 0.340251i
\(373\) 101781. 0.731558 0.365779 0.930702i \(-0.380803\pi\)
0.365779 + 0.930702i \(0.380803\pi\)
\(374\) 30235.8 + 132637.i 0.216161 + 0.948249i
\(375\) 0 0
\(376\) −80101.4 100612.i −0.566584 0.711660i
\(377\) −48911.8 −0.344136
\(378\) 24128.7 5500.35i 0.168869 0.0384952i
\(379\) 53693.3i 0.373802i −0.982379 0.186901i \(-0.940156\pi\)
0.982379 0.186901i \(-0.0598444\pi\)
\(380\) 0 0
\(381\) −119576. −0.823749
\(382\) −8812.56 38658.6i −0.0603914 0.264923i
\(383\) 36473.1i 0.248642i 0.992242 + 0.124321i \(0.0396753\pi\)
−0.992242 + 0.124321i \(0.960325\pi\)
\(384\) 85133.6 + 161.445i 0.577349 + 0.00109487i
\(385\) 0 0
\(386\) 130573. 29765.3i 0.876355 0.199772i
\(387\) 67434.1i 0.450254i
\(388\) −22122.5 + 10638.9i −0.146950 + 0.0706695i
\(389\) −95226.4 −0.629300 −0.314650 0.949208i \(-0.601887\pi\)
−0.314650 + 0.949208i \(0.601887\pi\)
\(390\) 0 0
\(391\) 218350.i 1.42823i
\(392\) −22845.3 + 18188.2i −0.148671 + 0.118363i
\(393\) −81205.5 −0.525775
\(394\) −185652. + 42321.0i −1.19594 + 0.272624i
\(395\) 0 0
\(396\) 15311.1 + 31837.9i 0.0976373 + 0.203027i
\(397\) −116517. −0.739282 −0.369641 0.929175i \(-0.620519\pi\)
−0.369641 + 0.929175i \(0.620519\pi\)
\(398\) −32091.2 140777.i −0.202591 0.888719i
\(399\) 5423.08i 0.0340643i
\(400\) 0 0
\(401\) 13995.3 0.0870350 0.0435175 0.999053i \(-0.486144\pi\)
0.0435175 + 0.999053i \(0.486144\pi\)
\(402\) 133099. 30341.0i 0.823610 0.187749i
\(403\) 250931.i 1.54506i
\(404\) −115781. + 55679.9i −0.709372 + 0.341142i
\(405\) 0 0
\(406\) −9986.24 43807.3i −0.0605829 0.265763i
\(407\) 100432.i 0.606295i
\(408\) 86142.3 + 108199.i 0.517483 + 0.649986i
\(409\) −213064. −1.27369 −0.636845 0.770992i \(-0.719761\pi\)
−0.636845 + 0.770992i \(0.719761\pi\)
\(410\) 0 0
\(411\) 63002.1i 0.372968i
\(412\) −48357.5 100555.i −0.284885 0.592390i
\(413\) −97731.2 −0.572972
\(414\) 12602.7 + 55285.0i 0.0735296 + 0.322557i
\(415\) 0 0
\(416\) 85555.7 177044.i 0.494382 1.02305i
\(417\) 112555. 0.647281
\(418\) 7547.99 1720.63i 0.0431995 0.00984770i
\(419\) 180964.i 1.03078i 0.856957 + 0.515389i \(0.172352\pi\)
−0.856957 + 0.515389i \(0.827648\pi\)
\(420\) 0 0
\(421\) 160722. 0.906799 0.453399 0.891307i \(-0.350211\pi\)
0.453399 + 0.891307i \(0.350211\pi\)
\(422\) −33950.9 148934.i −0.190645 0.836315i
\(423\) 54254.7i 0.303219i
\(424\) −1043.42 + 830.710i −0.00580398 + 0.00462081i
\(425\) 0 0
\(426\) 169060. 38538.6i 0.931581 0.212362i
\(427\) 96647.5i 0.530072i
\(428\) −91623.1 190521.i −0.500170 1.04005i
\(429\) 81597.3 0.443365
\(430\) 0 0
\(431\) 314539.i 1.69325i 0.532193 + 0.846623i \(0.321368\pi\)
−0.532193 + 0.846623i \(0.678632\pi\)
\(432\) 28055.8 + 22423.6i 0.150333 + 0.120154i
\(433\) 289159. 1.54227 0.771135 0.636671i \(-0.219689\pi\)
0.771135 + 0.636671i \(0.219689\pi\)
\(434\) −224744. + 51232.3i −1.19319 + 0.271997i
\(435\) 0 0
\(436\) −340909. + 163946.i −1.79335 + 0.862436i
\(437\) 12425.6 0.0650662
\(438\) 28146.1 + 123470.i 0.146714 + 0.643598i
\(439\) 26053.1i 0.135185i −0.997713 0.0675927i \(-0.978468\pi\)
0.997713 0.0675927i \(-0.0215318\pi\)
\(440\) 0 0
\(441\) −12319.3 −0.0633446
\(442\) 311447. 70996.9i 1.59419 0.363408i
\(443\) 257150.i 1.31033i −0.755487 0.655163i \(-0.772600\pi\)
0.755487 0.655163i \(-0.227400\pi\)
\(444\) 44250.8 + 92015.3i 0.224468 + 0.466760i
\(445\) 0 0
\(446\) 51323.8 + 225145.i 0.258017 + 1.13186i
\(447\) 37171.0i 0.186033i
\(448\) 176036. + 40480.1i 0.877090 + 0.201691i
\(449\) 134951. 0.669397 0.334698 0.942325i \(-0.391366\pi\)
0.334698 + 0.942325i \(0.391366\pi\)
\(450\) 0 0
\(451\) 159969.i 0.786471i
\(452\) 301764. 145120.i 1.47703 0.710316i
\(453\) −34794.5 −0.169556
\(454\) −63797.3 279864.i −0.309521 1.35780i
\(455\) 0 0
\(456\) 6157.30 4902.11i 0.0296115 0.0235751i
\(457\) −57157.1 −0.273677 −0.136838 0.990593i \(-0.543694\pi\)
−0.136838 + 0.990593i \(0.543694\pi\)
\(458\) −153916. + 35086.4i −0.733757 + 0.167266i
\(459\) 58346.4i 0.276942i
\(460\) 0 0
\(461\) −255702. −1.20319 −0.601593 0.798803i \(-0.705467\pi\)
−0.601593 + 0.798803i \(0.705467\pi\)
\(462\) 16659.6 + 73081.7i 0.0780513 + 0.342393i
\(463\) 79969.9i 0.373048i 0.982450 + 0.186524i \(0.0597222\pi\)
−0.982450 + 0.186524i \(0.940278\pi\)
\(464\) 40711.4 50937.1i 0.189095 0.236591i
\(465\) 0 0
\(466\) −416158. + 94866.7i −1.91640 + 0.436859i
\(467\) 6899.37i 0.0316356i 0.999875 + 0.0158178i \(0.00503517\pi\)
−0.999875 + 0.0158178i \(0.994965\pi\)
\(468\) 74758.9 35952.1i 0.341327 0.164147i
\(469\) 289642. 1.31679
\(470\) 0 0
\(471\) 182836.i 0.824175i
\(472\) −88342.6 110963.i −0.396539 0.498074i
\(473\) −204246. −0.912917
\(474\) 124221. 28317.3i 0.552891 0.126036i
\(475\) 0 0
\(476\) 127175. + 264448.i 0.561291 + 1.16715i
\(477\) −562.661 −0.00247292
\(478\) 29075.5 + 127547.i 0.127254 + 0.558233i
\(479\) 210368.i 0.916870i −0.888728 0.458435i \(-0.848410\pi\)
0.888728 0.458435i \(-0.151590\pi\)
\(480\) 0 0
\(481\) 235826. 1.01930
\(482\) −365504. + 83319.8i −1.57325 + 0.358636i
\(483\) 120308.i 0.515705i
\(484\) 114681. 55150.9i 0.489554 0.235430i
\(485\) 0 0
\(486\) 3367.63 + 14773.0i 0.0142578 + 0.0625455i
\(487\) 278872.i 1.17584i −0.808920 0.587919i \(-0.799947\pi\)
0.808920 0.587919i \(-0.200053\pi\)
\(488\) −109733. + 87363.0i −0.460782 + 0.366849i
\(489\) 193266. 0.808234
\(490\) 0 0
\(491\) 138823.i 0.575836i 0.957655 + 0.287918i \(0.0929630\pi\)
−0.957655 + 0.287918i \(0.907037\pi\)
\(492\) −70483.0 146562.i −0.291175 0.605470i
\(493\) 105932. 0.435844
\(494\) −4040.23 17723.5i −0.0165559 0.0726266i
\(495\) 0 0
\(496\) −261322. 208861.i −1.06222 0.848974i
\(497\) 367899. 1.48941
\(498\) 201454. 45923.1i 0.812301 0.185171i
\(499\) 95898.1i 0.385131i −0.981284 0.192566i \(-0.938319\pi\)
0.981284 0.192566i \(-0.0616808\pi\)
\(500\) 0 0
\(501\) −274094. −1.09200
\(502\) 2541.23 + 11147.8i 0.0100841 + 0.0442365i
\(503\) 134868.i 0.533056i 0.963827 + 0.266528i \(0.0858766\pi\)
−0.963827 + 0.266528i \(0.914123\pi\)
\(504\) 47463.5 + 59616.7i 0.186852 + 0.234696i
\(505\) 0 0
\(506\) −167449. + 38171.3i −0.654004 + 0.149086i
\(507\) 43192.1i 0.168031i
\(508\) −159576. 331823.i −0.618358 1.28582i
\(509\) −14376.3 −0.0554894 −0.0277447 0.999615i \(-0.508833\pi\)
−0.0277447 + 0.999615i \(0.508833\pi\)
\(510\) 0 0
\(511\) 268690.i 1.02899i
\(512\) 113164. + 236460.i 0.431686 + 0.902024i
\(513\) 3320.32 0.0126167
\(514\) −133663. + 30469.6i −0.505923 + 0.115329i
\(515\) 0 0
\(516\) −187129. + 89991.6i −0.702816 + 0.337989i
\(517\) 164328. 0.614795
\(518\) 48148.2 + 211215.i 0.179440 + 0.787163i
\(519\) 123123.i 0.457094i
\(520\) 0 0
\(521\) 235843. 0.868856 0.434428 0.900706i \(-0.356950\pi\)
0.434428 + 0.900706i \(0.356950\pi\)
\(522\) 26821.3 6114.15i 0.0984327 0.0224386i
\(523\) 104237.i 0.381083i 0.981679 + 0.190541i \(0.0610243\pi\)
−0.981679 + 0.190541i \(0.938976\pi\)
\(524\) −108370. 225344.i −0.394680 0.820699i
\(525\) 0 0
\(526\) −45066.2 197695.i −0.162885 0.714536i
\(527\) 543459.i 1.95680i
\(528\) −67917.0 + 84976.2i −0.243619 + 0.304810i
\(529\) 4184.37 0.0149527
\(530\) 0 0
\(531\) 59836.7i 0.212216i
\(532\) 15049.0 7237.16i 0.0531721 0.0255708i
\(533\) −375625. −1.32221
\(534\) 31166.8 + 136721.i 0.109297 + 0.479461i
\(535\) 0 0
\(536\) 261818. + 328857.i 0.911317 + 1.14466i
\(537\) 206315. 0.715454
\(538\) −163887. + 37359.5i −0.566215 + 0.129073i
\(539\) 37313.0i 0.128435i
\(540\) 0 0
\(541\) −415208. −1.41864 −0.709318 0.704889i \(-0.750997\pi\)
−0.709318 + 0.704889i \(0.750997\pi\)
\(542\) −89943.1 394559.i −0.306175 1.34312i
\(543\) 196693.i 0.667097i
\(544\) −185294. + 383437.i −0.626128 + 1.29568i
\(545\) 0 0
\(546\) 171604. 39118.5i 0.575628 0.131219i
\(547\) 438329.i 1.46496i −0.680789 0.732480i \(-0.738363\pi\)
0.680789 0.732480i \(-0.261637\pi\)
\(548\) 174830. 84077.0i 0.582177 0.279973i
\(549\) −59173.2 −0.196327
\(550\) 0 0
\(551\) 6028.25i 0.0198558i
\(552\) −136597. + 108751.i −0.448293 + 0.356906i
\(553\) 270324. 0.883963
\(554\) 505916. 115328.i 1.64839 0.375764i
\(555\) 0 0
\(556\) 150206. + 312339.i 0.485890 + 1.01036i
\(557\) −93371.4 −0.300956 −0.150478 0.988613i \(-0.548081\pi\)
−0.150478 + 0.988613i \(0.548081\pi\)
\(558\) −31367.3 137601.i −0.100742 0.441930i
\(559\) 479592.i 1.53479i
\(560\) 0 0
\(561\) −176721. −0.561516
\(562\) 41617.6 9487.08i 0.131766 0.0300372i
\(563\) 460554.i 1.45299i −0.687170 0.726497i \(-0.741147\pi\)
0.687170 0.726497i \(-0.258853\pi\)
\(564\) 150556. 72403.5i 0.473304 0.227615i
\(565\) 0 0
\(566\) 87595.2 + 384259.i 0.273431 + 1.19948i
\(567\) 32148.2i 0.0999979i
\(568\) 332556. + 417708.i 1.03079 + 1.29472i
\(569\) −451247. −1.39376 −0.696882 0.717186i \(-0.745430\pi\)
−0.696882 + 0.717186i \(0.745430\pi\)
\(570\) 0 0
\(571\) 5267.14i 0.0161548i −0.999967 0.00807742i \(-0.997429\pi\)
0.999967 0.00807742i \(-0.00257115\pi\)
\(572\) 108893. + 226432.i 0.332818 + 0.692062i
\(573\) 51507.3 0.156877
\(574\) −76690.6 336424.i −0.232766 1.02109i
\(575\) 0 0
\(576\) −24784.3 + 107779.i −0.0747018 + 0.324855i
\(577\) −532802. −1.60035 −0.800174 0.599768i \(-0.795259\pi\)
−0.800174 + 0.599768i \(0.795259\pi\)
\(578\) −348794. + 79510.4i −1.04403 + 0.237995i
\(579\) 173971.i 0.518943i
\(580\) 0 0
\(581\) 438393. 1.29871
\(582\) −7087.42 31090.8i −0.0209239 0.0917881i
\(583\) 1704.20i 0.00501399i
\(584\) −305067. + 242878.i −0.894479 + 0.712135i
\(585\) 0 0
\(586\) −43426.9 + 9899.52i −0.126463 + 0.0288283i
\(587\) 474104.i 1.37593i 0.725742 + 0.687967i \(0.241497\pi\)
−0.725742 + 0.687967i \(0.758503\pi\)
\(588\) −16440.3 34186.0i −0.0475504 0.0988765i
\(589\) −30926.7 −0.0891462
\(590\) 0 0
\(591\) 247356.i 0.708187i
\(592\) −196288. + 245591.i −0.560080 + 0.700760i
\(593\) −389837. −1.10860 −0.554299 0.832318i \(-0.687013\pi\)
−0.554299 + 0.832318i \(0.687013\pi\)
\(594\) −44744.8 + 10200.0i −0.126815 + 0.0289085i
\(595\) 0 0
\(596\) 103149. 49605.2i 0.290384 0.139648i
\(597\) 187566. 0.526265
\(598\) 89630.4 + 393187.i 0.250642 + 1.09951i
\(599\) 298392.i 0.831637i 0.909448 + 0.415818i \(0.136505\pi\)
−0.909448 + 0.415818i \(0.863495\pi\)
\(600\) 0 0
\(601\) −104029. −0.288009 −0.144004 0.989577i \(-0.545998\pi\)
−0.144004 + 0.989577i \(0.545998\pi\)
\(602\) −429541. + 97917.5i −1.18525 + 0.270189i
\(603\) 177336.i 0.487710i
\(604\) −46433.7 96554.4i −0.127280 0.264666i
\(605\) 0 0
\(606\) −37092.9 162718.i −0.101006 0.443088i
\(607\) 335077.i 0.909425i −0.890638 0.454712i \(-0.849742\pi\)
0.890638 0.454712i \(-0.150258\pi\)
\(608\) 21820.3 + 10544.5i 0.0590273 + 0.0285246i
\(609\) 58367.2 0.157374
\(610\) 0 0
\(611\) 385860.i 1.03359i
\(612\) −161910. + 77863.9i −0.432287 + 0.207890i
\(613\) 205373. 0.546539 0.273270 0.961937i \(-0.411895\pi\)
0.273270 + 0.961937i \(0.411895\pi\)
\(614\) −117549. 515658.i −0.311803 1.36781i
\(615\) 0 0
\(616\) −180568. + 143759.i −0.475861 + 0.378854i
\(617\) 117370. 0.308309 0.154155 0.988047i \(-0.450735\pi\)
0.154155 + 0.988047i \(0.450735\pi\)
\(618\) 141319. 32214.9i 0.370019 0.0843489i
\(619\) 152525.i 0.398069i 0.979992 + 0.199035i \(0.0637807\pi\)
−0.979992 + 0.199035i \(0.936219\pi\)
\(620\) 0 0
\(621\) −73659.7 −0.191006
\(622\) 99894.7 + 438215.i 0.258203 + 1.13268i
\(623\) 297526.i 0.766563i
\(624\) 199533. + 159477.i 0.512444 + 0.409570i
\(625\) 0 0
\(626\) −172184. + 39250.8i −0.439384 + 0.100161i
\(627\) 10056.7i 0.0255811i
\(628\) −507367. + 243996.i −1.28648 + 0.618677i
\(629\) −510744. −1.29093
\(630\) 0 0
\(631\) 420163.i 1.05526i −0.849475 0.527629i \(-0.823081\pi\)
0.849475 0.527629i \(-0.176919\pi\)
\(632\) 244355. + 306923.i 0.611768 + 0.768413i
\(633\) 198435. 0.495234
\(634\) 188013. 42859.1i 0.467745 0.106626i
\(635\) 0 0
\(636\) −750.878 1561.38i −0.00185633 0.00386006i
\(637\) −87615.1 −0.215924
\(638\) 18518.7 + 81237.1i 0.0454955 + 0.199578i
\(639\) 225249.i 0.551646i
\(640\) 0 0
\(641\) −633476. −1.54175 −0.770875 0.636986i \(-0.780181\pi\)
−0.770875 + 0.636986i \(0.780181\pi\)
\(642\) 267758. 61037.6i 0.649639 0.148091i
\(643\) 463320.i 1.12062i −0.828282 0.560311i \(-0.810682\pi\)
0.828282 0.560311i \(-0.189318\pi\)
\(644\) −333854. + 160553.i −0.804980 + 0.387121i
\(645\) 0 0
\(646\) 8750.19 + 38385.0i 0.0209678 + 0.0919807i
\(647\) 556505.i 1.32941i −0.747104 0.664707i \(-0.768556\pi\)
0.747104 0.664707i \(-0.231444\pi\)
\(648\) −36500.8 + 29059.9i −0.0869264 + 0.0692060i
\(649\) 181235. 0.430281
\(650\) 0 0
\(651\) 299440.i 0.706559i
\(652\) 257915. + 536310.i 0.606711 + 1.26160i
\(653\) 116848. 0.274029 0.137015 0.990569i \(-0.456249\pi\)
0.137015 + 0.990569i \(0.456249\pi\)
\(654\) −109218. 479112.i −0.255351 1.12016i
\(655\) 0 0
\(656\) 312649. 391179.i 0.726522 0.909008i
\(657\) −164507. −0.381114
\(658\) 345591. 78780.4i 0.798198 0.181956i
\(659\) 8238.25i 0.0189699i 0.999955 + 0.00948493i \(0.00301919\pi\)
−0.999955 + 0.00948493i \(0.996981\pi\)
\(660\) 0 0
\(661\) 846034. 1.93635 0.968177 0.250265i \(-0.0805178\pi\)
0.968177 + 0.250265i \(0.0805178\pi\)
\(662\) 78993.9 + 346528.i 0.180251 + 0.790719i
\(663\) 414960.i 0.944016i
\(664\) 396279. + 497747.i 0.898803 + 1.12894i
\(665\) 0 0
\(666\) −129318. + 29479.1i −0.291548 + 0.0664608i
\(667\) 133734.i 0.300601i
\(668\) −365781. 760607.i −0.819726 1.70454i
\(669\) −299975. −0.670244
\(670\) 0 0
\(671\) 179225.i 0.398065i
\(672\) −102095. + 211270.i −0.226082 + 0.467842i
\(673\) −250.046 −0.000552065 −0.000276032 1.00000i \(-0.500088\pi\)
−0.000276032 1.00000i \(0.500088\pi\)
\(674\) 565019. 128801.i 1.24378 0.283530i
\(675\) 0 0
\(676\) 119857. 57640.3i 0.262284 0.126134i
\(677\) −241924. −0.527838 −0.263919 0.964545i \(-0.585015\pi\)
−0.263919 + 0.964545i \(0.585015\pi\)
\(678\) 96676.6 + 424097.i 0.210311 + 0.922584i
\(679\) 67658.3i 0.146751i
\(680\) 0 0
\(681\) 372880. 0.804035
\(682\) 416770. 95006.2i 0.896040 0.204260i
\(683\) 10868.8i 0.0232991i −0.999932 0.0116495i \(-0.996292\pi\)
0.999932 0.0116495i \(-0.00370825\pi\)
\(684\) 4431.01 + 9213.85i 0.00947088 + 0.0196938i
\(685\) 0 0
\(686\) −112020. 491406.i −0.238039 1.04422i
\(687\) 205072.i 0.434503i
\(688\) −499451. 399185.i −1.05516 0.843331i
\(689\) −4001.65 −0.00842948
\(690\) 0 0
\(691\) 318000.i 0.665995i −0.942928 0.332998i \(-0.891940\pi\)
0.942928 0.332998i \(-0.108060\pi\)
\(692\) −341666. + 164310.i −0.713493 + 0.343124i
\(693\) −97371.3 −0.202752
\(694\) −64765.0 284109.i −0.134469 0.589883i
\(695\) 0 0
\(696\) 52760.1 + 66269.5i 0.108915 + 0.136803i
\(697\) 813516. 1.67456
\(698\) −483276. + 110167.i −0.991938 + 0.226121i
\(699\) 554473.i 1.13482i
\(700\) 0 0
\(701\) 963668. 1.96106 0.980531 0.196365i \(-0.0629136\pi\)
0.980531 + 0.196365i \(0.0629136\pi\)
\(702\) 23950.6 + 105066.i 0.0486007 + 0.213200i
\(703\) 29064.9i 0.0588110i
\(704\) −326444. 75067.2i −0.658663 0.151462i
\(705\) 0 0
\(706\) 722644. 164733.i 1.44982 0.330500i
\(707\) 354098.i 0.708410i
\(708\) 166046. 79852.8i 0.331255 0.159303i
\(709\) −135081. −0.268721 −0.134361 0.990932i \(-0.542898\pi\)
−0.134361 + 0.990932i \(0.542898\pi\)
\(710\) 0 0
\(711\) 165508.i 0.327400i
\(712\) −337807. + 268943.i −0.666360 + 0.530519i
\(713\) 686093. 1.34960
\(714\) −371654. + 84721.7i −0.729025 + 0.166187i
\(715\) 0 0
\(716\) 275329. + 572521.i 0.537065 + 1.11677i
\(717\) −169939. −0.330564
\(718\) 87259.2 + 382785.i 0.169263 + 0.742517i
\(719\) 471123.i 0.911332i 0.890151 + 0.455666i \(0.150599\pi\)
−0.890151 + 0.455666i \(0.849401\pi\)
\(720\) 0 0
\(721\) 307531. 0.591587
\(722\) −506061. + 115361.i −0.970798 + 0.221302i
\(723\) 486985.i 0.931620i
\(724\) 545820. 262489.i 1.04129 0.500765i
\(725\) 0 0
\(726\) 36740.5 + 161172.i 0.0697063 + 0.305785i
\(727\) 27020.9i 0.0511248i −0.999673 0.0255624i \(-0.991862\pi\)
0.999673 0.0255624i \(-0.00813765\pi\)
\(728\) 337561. + 423994.i 0.636926 + 0.800013i
\(729\) −19683.0 −0.0370370
\(730\) 0 0
\(731\) 1.03869e6i 1.94379i
\(732\) −78967.3 164205.i −0.147375 0.306453i
\(733\) −203765. −0.379246 −0.189623 0.981857i \(-0.560727\pi\)
−0.189623 + 0.981857i \(0.560727\pi\)
\(734\) −105864. 464399.i −0.196496 0.861983i
\(735\) 0 0
\(736\) −484072. 233925.i −0.893623 0.431839i
\(737\) −537119. −0.988861
\(738\) 205978. 46954.4i 0.378188 0.0862112i
\(739\) 311174.i 0.569789i −0.958559 0.284894i \(-0.908042\pi\)
0.958559 0.284894i \(-0.0919585\pi\)
\(740\) 0 0
\(741\) 23614.2 0.0430067
\(742\) −817.011 3584.03i −0.00148395 0.00650975i
\(743\) 459748.i 0.832803i −0.909181 0.416401i \(-0.863291\pi\)
0.909181 0.416401i \(-0.136709\pi\)
\(744\) 339981. 270674.i 0.614199 0.488992i
\(745\) 0 0
\(746\) −396941. + 90486.0i −0.713260 + 0.162594i
\(747\) 268410.i 0.481013i
\(748\) −235836. 490398.i −0.421509 0.876488i
\(749\) 582680. 1.03864
\(750\) 0 0
\(751\) 201657.i 0.357547i −0.983890 0.178774i \(-0.942787\pi\)
0.983890 0.178774i \(-0.0572130\pi\)
\(752\) 401838. + 321168.i 0.710584 + 0.567932i
\(753\) −14852.9 −0.0261952
\(754\) 190754. 43483.9i 0.335529 0.0764867i
\(755\) 0 0
\(756\) −89211.0 + 42902.2i −0.156090 + 0.0750647i
\(757\) 409395. 0.714415 0.357208 0.934025i \(-0.383729\pi\)
0.357208 + 0.934025i \(0.383729\pi\)
\(758\) 47734.8 + 209401.i 0.0830801 + 0.364453i
\(759\) 223102.i 0.387276i
\(760\) 0 0
\(761\) −626699. −1.08216 −0.541078 0.840972i \(-0.681984\pi\)
−0.541078 + 0.840972i \(0.681984\pi\)
\(762\) 466342. 106307.i 0.803146 0.183084i
\(763\) 1.04262e6i 1.79092i
\(764\) 68737.1 + 142932.i 0.117762 + 0.244874i
\(765\) 0 0
\(766\) −32425.6 142243.i −0.0552624 0.242423i
\(767\) 425559.i 0.723384i
\(768\) −332161. + 75056.5i −0.563152 + 0.127252i
\(769\) 203601. 0.344292 0.172146 0.985071i \(-0.444930\pi\)
0.172146 + 0.985071i \(0.444930\pi\)
\(770\) 0 0
\(771\) 178087.i 0.299588i
\(772\) −482768. + 232167.i −0.810035 + 0.389552i
\(773\) 197131. 0.329910 0.164955 0.986301i \(-0.447252\pi\)
0.164955 + 0.986301i \(0.447252\pi\)
\(774\) −59950.8 262990.i −0.100072 0.438992i
\(775\) 0 0
\(776\) 76818.5 61158.6i 0.127568 0.101563i
\(777\) −281415. −0.466127
\(778\) 371378. 84658.8i 0.613560 0.139866i
\(779\) 46294.8i 0.0762882i
\(780\) 0 0
\(781\) −682239. −1.11850
\(782\) −194119. 851553.i −0.317434 1.39251i
\(783\) 35735.7i 0.0582880i