Properties

Label 690.3.g.a.461.1
Level $690$
Weight $3$
Character 690.461
Analytic conductor $18.801$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(56\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 461.1
Character \(\chi\) \(=\) 690.461
Dual form 690.3.g.a.461.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} +(2.78199 - 1.12272i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-1.58777 - 3.93433i) q^{6} +9.71289 q^{7} +2.82843i q^{8} +(6.47899 - 6.24682i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(2.78199 - 1.12272i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-1.58777 - 3.93433i) q^{6} +9.71289 q^{7} +2.82843i q^{8} +(6.47899 - 6.24682i) q^{9} -3.16228 q^{10} +16.7924i q^{11} +(-5.56399 + 2.24544i) q^{12} +14.2200 q^{13} -13.7361i q^{14} +(-2.51048 - 6.22073i) q^{15} +4.00000 q^{16} +8.32060i q^{17} +(-8.83433 - 9.16267i) q^{18} +18.7748 q^{19} +4.47214i q^{20} +(27.0212 - 10.9049i) q^{21} +23.7480 q^{22} +4.79583i q^{23} +(3.17554 + 7.86867i) q^{24} -5.00000 q^{25} -20.1101i q^{26} +(11.0111 - 24.6527i) q^{27} -19.4258 q^{28} +8.35888i q^{29} +(-8.79744 + 3.55036i) q^{30} +12.7798 q^{31} -5.65685i q^{32} +(18.8532 + 46.7163i) q^{33} +11.7671 q^{34} -21.7187i q^{35} +(-12.9580 + 12.4936i) q^{36} -48.4043 q^{37} -26.5516i q^{38} +(39.5598 - 15.9651i) q^{39} +6.32456 q^{40} +33.7058i q^{41} +(-15.4218 - 38.2138i) q^{42} -41.8569 q^{43} -33.5848i q^{44} +(-13.9683 - 14.4875i) q^{45} +6.78233 q^{46} -25.4461i q^{47} +(11.1280 - 4.49089i) q^{48} +45.3403 q^{49} +7.07107i q^{50} +(9.34172 + 23.1479i) q^{51} -28.4399 q^{52} -64.6839i q^{53} +(-34.8642 - 15.5720i) q^{54} +37.5489 q^{55} +27.4722i q^{56} +(52.2314 - 21.0789i) q^{57} +11.8212 q^{58} -35.0667i q^{59} +(5.02097 + 12.4415i) q^{60} -57.1839 q^{61} -18.0734i q^{62} +(62.9297 - 60.6746i) q^{63} -8.00000 q^{64} -31.7968i q^{65} +(66.0668 - 26.6624i) q^{66} -61.2135 q^{67} -16.6412i q^{68} +(5.38439 + 13.3420i) q^{69} -30.7149 q^{70} -99.0489i q^{71} +(17.6687 + 18.3253i) q^{72} +1.71337 q^{73} +68.4541i q^{74} +(-13.9100 + 5.61361i) q^{75} -37.5496 q^{76} +163.103i q^{77} +(-22.5780 - 55.9461i) q^{78} +118.909 q^{79} -8.94427i q^{80} +(2.95460 - 80.9461i) q^{81} +47.6672 q^{82} -13.2505i q^{83} +(-54.0424 + 21.8098i) q^{84} +18.6054 q^{85} +59.1947i q^{86} +(9.38470 + 23.2544i) q^{87} -47.4960 q^{88} +145.864i q^{89} +(-20.4884 + 19.7542i) q^{90} +138.117 q^{91} -9.59166i q^{92} +(35.5533 - 14.3482i) q^{93} -35.9862 q^{94} -41.9818i q^{95} +(-6.35108 - 15.7373i) q^{96} -166.157 q^{97} -64.1208i q^{98} +(104.899 + 108.798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 8q^{3} - 112q^{4} + 16q^{6} - 16q^{7} + O(q^{10}) \) \( 56q - 8q^{3} - 112q^{4} + 16q^{6} - 16q^{7} + 16q^{12} + 80q^{13} - 40q^{15} + 224q^{16} - 32q^{18} - 64q^{19} + 56q^{21} - 96q^{22} - 32q^{24} - 280q^{25} + 40q^{27} + 32q^{28} - 80q^{31} + 32q^{33} + 192q^{34} + 240q^{37} - 56q^{39} - 144q^{43} - 32q^{48} + 72q^{49} - 24q^{51} - 160q^{52} + 16q^{54} - 16q^{57} + 80q^{60} + 112q^{61} - 64q^{63} - 448q^{64} + 160q^{66} + 832q^{67} + 64q^{72} - 608q^{73} + 40q^{75} + 128q^{76} - 320q^{78} + 48q^{79} - 32q^{81} - 448q^{82} - 112q^{84} + 240q^{85} + 200q^{87} + 192q^{88} + 80q^{91} - 232q^{93} + 160q^{94} + 64q^{96} - 448q^{97} + 464q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 2.78199 1.12272i 0.927332 0.374241i
\(4\) −2.00000 −0.500000
\(5\) 2.23607i 0.447214i
\(6\) −1.58777 3.93433i −0.264628 0.655722i
\(7\) 9.71289 1.38756 0.693778 0.720189i \(-0.255945\pi\)
0.693778 + 0.720189i \(0.255945\pi\)
\(8\) 2.82843i 0.353553i
\(9\) 6.47899 6.24682i 0.719888 0.694091i
\(10\) −3.16228 −0.316228
\(11\) 16.7924i 1.52658i 0.646056 + 0.763290i \(0.276417\pi\)
−0.646056 + 0.763290i \(0.723583\pi\)
\(12\) −5.56399 + 2.24544i −0.463666 + 0.187120i
\(13\) 14.2200 1.09384 0.546921 0.837184i \(-0.315800\pi\)
0.546921 + 0.837184i \(0.315800\pi\)
\(14\) 13.7361i 0.981150i
\(15\) −2.51048 6.22073i −0.167366 0.414715i
\(16\) 4.00000 0.250000
\(17\) 8.32060i 0.489447i 0.969593 + 0.244724i \(0.0786972\pi\)
−0.969593 + 0.244724i \(0.921303\pi\)
\(18\) −8.83433 9.16267i −0.490796 0.509037i
\(19\) 18.7748 0.988148 0.494074 0.869420i \(-0.335507\pi\)
0.494074 + 0.869420i \(0.335507\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 27.0212 10.9049i 1.28672 0.519280i
\(22\) 23.7480 1.07946
\(23\) 4.79583i 0.208514i
\(24\) 3.17554 + 7.86867i 0.132314 + 0.327861i
\(25\) −5.00000 −0.200000
\(26\) 20.1101i 0.773464i
\(27\) 11.0111 24.6527i 0.407818 0.913063i
\(28\) −19.4258 −0.693778
\(29\) 8.35888i 0.288237i 0.989560 + 0.144119i \(0.0460347\pi\)
−0.989560 + 0.144119i \(0.953965\pi\)
\(30\) −8.79744 + 3.55036i −0.293248 + 0.118345i
\(31\) 12.7798 0.412252 0.206126 0.978526i \(-0.433914\pi\)
0.206126 + 0.978526i \(0.433914\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 18.8532 + 46.7163i 0.571309 + 1.41565i
\(34\) 11.7671 0.346091
\(35\) 21.7187i 0.620534i
\(36\) −12.9580 + 12.4936i −0.359944 + 0.347045i
\(37\) −48.4043 −1.30823 −0.654113 0.756397i \(-0.726958\pi\)
−0.654113 + 0.756397i \(0.726958\pi\)
\(38\) 26.5516i 0.698726i
\(39\) 39.5598 15.9651i 1.01435 0.409361i
\(40\) 6.32456 0.158114
\(41\) 33.7058i 0.822093i 0.911614 + 0.411046i \(0.134837\pi\)
−0.911614 + 0.411046i \(0.865163\pi\)
\(42\) −15.4218 38.2138i −0.367186 0.909852i
\(43\) −41.8569 −0.973417 −0.486709 0.873564i \(-0.661803\pi\)
−0.486709 + 0.873564i \(0.661803\pi\)
\(44\) 33.5848i 0.763290i
\(45\) −13.9683 14.4875i −0.310407 0.321944i
\(46\) 6.78233 0.147442
\(47\) 25.4461i 0.541406i −0.962663 0.270703i \(-0.912744\pi\)
0.962663 0.270703i \(-0.0872561\pi\)
\(48\) 11.1280 4.49089i 0.231833 0.0935602i
\(49\) 45.3403 0.925312
\(50\) 7.07107i 0.141421i
\(51\) 9.34172 + 23.1479i 0.183171 + 0.453880i
\(52\) −28.4399 −0.546921
\(53\) 64.6839i 1.22045i −0.792228 0.610225i \(-0.791079\pi\)
0.792228 0.610225i \(-0.208921\pi\)
\(54\) −34.8642 15.5720i −0.645633 0.288371i
\(55\) 37.5489 0.682707
\(56\) 27.4722i 0.490575i
\(57\) 52.2314 21.0789i 0.916341 0.369805i
\(58\) 11.8212 0.203815
\(59\) 35.0667i 0.594351i −0.954823 0.297175i \(-0.903955\pi\)
0.954823 0.297175i \(-0.0960446\pi\)
\(60\) 5.02097 + 12.4415i 0.0836828 + 0.207358i
\(61\) −57.1839 −0.937441 −0.468721 0.883347i \(-0.655285\pi\)
−0.468721 + 0.883347i \(0.655285\pi\)
\(62\) 18.0734i 0.291506i
\(63\) 62.9297 60.6746i 0.998884 0.963090i
\(64\) −8.00000 −0.125000
\(65\) 31.7968i 0.489181i
\(66\) 66.0668 26.6624i 1.00101 0.403976i
\(67\) −61.2135 −0.913634 −0.456817 0.889561i \(-0.651011\pi\)
−0.456817 + 0.889561i \(0.651011\pi\)
\(68\) 16.6412i 0.244724i
\(69\) 5.38439 + 13.3420i 0.0780346 + 0.193362i
\(70\) −30.7149 −0.438784
\(71\) 99.0489i 1.39505i −0.716558 0.697527i \(-0.754284\pi\)
0.716558 0.697527i \(-0.245716\pi\)
\(72\) 17.6687 + 18.3253i 0.245398 + 0.254519i
\(73\) 1.71337 0.0234709 0.0117354 0.999931i \(-0.496264\pi\)
0.0117354 + 0.999931i \(0.496264\pi\)
\(74\) 68.4541i 0.925055i
\(75\) −13.9100 + 5.61361i −0.185466 + 0.0748482i
\(76\) −37.5496 −0.494074
\(77\) 163.103i 2.11822i
\(78\) −22.5780 55.9461i −0.289462 0.717257i
\(79\) 118.909 1.50517 0.752586 0.658493i \(-0.228806\pi\)
0.752586 + 0.658493i \(0.228806\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 2.95460 80.9461i 0.0364765 0.999335i
\(82\) 47.6672 0.581307
\(83\) 13.2505i 0.159645i −0.996809 0.0798226i \(-0.974565\pi\)
0.996809 0.0798226i \(-0.0254354\pi\)
\(84\) −54.0424 + 21.8098i −0.643362 + 0.259640i
\(85\) 18.6054 0.218887
\(86\) 59.1947i 0.688310i
\(87\) 9.38470 + 23.2544i 0.107870 + 0.267292i
\(88\) −47.4960 −0.539728
\(89\) 145.864i 1.63892i 0.573133 + 0.819462i \(0.305728\pi\)
−0.573133 + 0.819462i \(0.694272\pi\)
\(90\) −20.4884 + 19.7542i −0.227648 + 0.219491i
\(91\) 138.117 1.51777
\(92\) 9.59166i 0.104257i
\(93\) 35.5533 14.3482i 0.382294 0.154281i
\(94\) −35.9862 −0.382832
\(95\) 41.9818i 0.441913i
\(96\) −6.35108 15.7373i −0.0661570 0.163931i
\(97\) −166.157 −1.71296 −0.856478 0.516183i \(-0.827352\pi\)
−0.856478 + 0.516183i \(0.827352\pi\)
\(98\) 64.1208i 0.654294i
\(99\) 104.899 + 108.798i 1.05958 + 1.09897i
\(100\) 10.0000 0.100000
\(101\) 101.312i 1.00309i −0.865131 0.501546i \(-0.832765\pi\)
0.865131 0.501546i \(-0.167235\pi\)
\(102\) 32.7360 13.2112i 0.320941 0.129521i
\(103\) −156.509 −1.51951 −0.759754 0.650210i \(-0.774681\pi\)
−0.759754 + 0.650210i \(0.774681\pi\)
\(104\) 40.2201i 0.386732i
\(105\) −24.3841 60.4213i −0.232229 0.575441i
\(106\) −91.4768 −0.862989
\(107\) 49.5970i 0.463523i 0.972773 + 0.231762i \(0.0744489\pi\)
−0.972773 + 0.231762i \(0.925551\pi\)
\(108\) −22.0221 + 49.3054i −0.203909 + 0.456532i
\(109\) −9.54244 −0.0875453 −0.0437727 0.999042i \(-0.513938\pi\)
−0.0437727 + 0.999042i \(0.513938\pi\)
\(110\) 53.1022i 0.482747i
\(111\) −134.661 + 54.3446i −1.21316 + 0.489591i
\(112\) 38.8516 0.346889
\(113\) 194.702i 1.72303i −0.507736 0.861513i \(-0.669517\pi\)
0.507736 0.861513i \(-0.330483\pi\)
\(114\) −29.8101 73.8664i −0.261492 0.647951i
\(115\) 10.7238 0.0932505
\(116\) 16.7178i 0.144119i
\(117\) 92.1309 88.8294i 0.787444 0.759226i
\(118\) −49.5918 −0.420269
\(119\) 80.8171i 0.679135i
\(120\) 17.5949 7.10072i 0.146624 0.0591727i
\(121\) −160.984 −1.33045
\(122\) 80.8703i 0.662871i
\(123\) 37.8423 + 93.7694i 0.307661 + 0.762353i
\(124\) −25.5596 −0.206126
\(125\) 11.1803i 0.0894427i
\(126\) −85.8069 88.9961i −0.681007 0.706318i
\(127\) 91.5991 0.721253 0.360626 0.932710i \(-0.382563\pi\)
0.360626 + 0.932710i \(0.382563\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −116.446 + 46.9937i −0.902681 + 0.364292i
\(130\) −44.9675 −0.345903
\(131\) 137.955i 1.05309i 0.850148 + 0.526544i \(0.176512\pi\)
−0.850148 + 0.526544i \(0.823488\pi\)
\(132\) −37.7064 93.4326i −0.285654 0.707823i
\(133\) 182.358 1.37111
\(134\) 86.5689i 0.646037i
\(135\) −55.1251 24.6215i −0.408334 0.182382i
\(136\) −23.5342 −0.173046
\(137\) 60.6857i 0.442961i −0.975165 0.221481i \(-0.928911\pi\)
0.975165 0.221481i \(-0.0710889\pi\)
\(138\) 18.8684 7.61467i 0.136728 0.0551788i
\(139\) 107.481 0.773243 0.386622 0.922238i \(-0.373642\pi\)
0.386622 + 0.922238i \(0.373642\pi\)
\(140\) 43.4374i 0.310267i
\(141\) −28.5689 70.7908i −0.202616 0.502063i
\(142\) −140.076 −0.986453
\(143\) 238.787i 1.66984i
\(144\) 25.9160 24.9873i 0.179972 0.173523i
\(145\) 18.6910 0.128904
\(146\) 2.42308i 0.0165964i
\(147\) 126.136 50.9045i 0.858071 0.346289i
\(148\) 96.8087 0.654113
\(149\) 34.1446i 0.229158i 0.993414 + 0.114579i \(0.0365520\pi\)
−0.993414 + 0.114579i \(0.963448\pi\)
\(150\) 7.93885 + 19.6717i 0.0529256 + 0.131144i
\(151\) −153.941 −1.01947 −0.509737 0.860330i \(-0.670257\pi\)
−0.509737 + 0.860330i \(0.670257\pi\)
\(152\) 53.1032i 0.349363i
\(153\) 51.9773 + 53.9091i 0.339721 + 0.352347i
\(154\) 230.662 1.49780
\(155\) 28.5765i 0.184364i
\(156\) −79.1197 + 31.9301i −0.507177 + 0.204680i
\(157\) 68.3351 0.435255 0.217628 0.976032i \(-0.430168\pi\)
0.217628 + 0.976032i \(0.430168\pi\)
\(158\) 168.162i 1.06432i
\(159\) −72.6220 179.950i −0.456742 1.13176i
\(160\) −12.6491 −0.0790569
\(161\) 46.5814i 0.289325i
\(162\) −114.475 4.17844i −0.706636 0.0257928i
\(163\) 160.804 0.986527 0.493264 0.869880i \(-0.335804\pi\)
0.493264 + 0.869880i \(0.335804\pi\)
\(164\) 67.4116i 0.411046i
\(165\) 104.461 42.1570i 0.633096 0.255497i
\(166\) −18.7391 −0.112886
\(167\) 203.880i 1.22084i −0.792078 0.610420i \(-0.791001\pi\)
0.792078 0.610420i \(-0.208999\pi\)
\(168\) 30.8437 + 76.4275i 0.183593 + 0.454926i
\(169\) 33.2072 0.196492
\(170\) 26.3120i 0.154777i
\(171\) 121.642 117.283i 0.711356 0.685864i
\(172\) 83.7139 0.486709
\(173\) 38.3584i 0.221725i 0.993836 + 0.110863i \(0.0353613\pi\)
−0.993836 + 0.110863i \(0.964639\pi\)
\(174\) 32.8866 13.2720i 0.189004 0.0762757i
\(175\) −48.5645 −0.277511
\(176\) 67.1695i 0.381645i
\(177\) −39.3702 97.5553i −0.222430 0.551160i
\(178\) 206.283 1.15889
\(179\) 36.4722i 0.203755i −0.994797 0.101878i \(-0.967515\pi\)
0.994797 0.101878i \(-0.0324850\pi\)
\(180\) 27.9366 + 28.9749i 0.155203 + 0.160972i
\(181\) −340.697 −1.88231 −0.941153 0.337981i \(-0.890256\pi\)
−0.941153 + 0.337981i \(0.890256\pi\)
\(182\) 195.327i 1.07322i
\(183\) −159.085 + 64.2016i −0.869319 + 0.350829i
\(184\) −13.5647 −0.0737210
\(185\) 108.235i 0.585056i
\(186\) −20.2914 50.2800i −0.109093 0.270323i
\(187\) −139.723 −0.747180
\(188\) 50.8921i 0.270703i
\(189\) 106.949 239.449i 0.565870 1.26693i
\(190\) −59.3712 −0.312480
\(191\) 187.221i 0.980216i 0.871662 + 0.490108i \(0.163043\pi\)
−0.871662 + 0.490108i \(0.836957\pi\)
\(192\) −22.2560 + 8.98178i −0.115916 + 0.0467801i
\(193\) 375.100 1.94352 0.971760 0.235970i \(-0.0758266\pi\)
0.971760 + 0.235970i \(0.0758266\pi\)
\(194\) 234.981i 1.21124i
\(195\) −35.6990 88.4585i −0.183072 0.453633i
\(196\) −90.6806 −0.462656
\(197\) 199.478i 1.01258i 0.862363 + 0.506290i \(0.168984\pi\)
−0.862363 + 0.506290i \(0.831016\pi\)
\(198\) 153.863 148.349i 0.777086 0.749240i
\(199\) 331.088 1.66376 0.831880 0.554955i \(-0.187265\pi\)
0.831880 + 0.554955i \(0.187265\pi\)
\(200\) 14.1421i 0.0707107i
\(201\) −170.296 + 68.7257i −0.847242 + 0.341919i
\(202\) −143.277 −0.709293
\(203\) 81.1889i 0.399945i
\(204\) −18.6834 46.2957i −0.0915855 0.226940i
\(205\) 75.3685 0.367651
\(206\) 221.338i 1.07445i
\(207\) 29.9587 + 31.0721i 0.144728 + 0.150107i
\(208\) 56.8798 0.273461
\(209\) 315.274i 1.50849i
\(210\) −85.4486 + 34.4843i −0.406898 + 0.164211i
\(211\) −327.623 −1.55272 −0.776358 0.630293i \(-0.782935\pi\)
−0.776358 + 0.630293i \(0.782935\pi\)
\(212\) 129.368i 0.610225i
\(213\) −111.204 275.553i −0.522086 1.29368i
\(214\) 70.1407 0.327760
\(215\) 93.5950i 0.435325i
\(216\) 69.7284 + 31.1440i 0.322817 + 0.144185i
\(217\) 124.129 0.572022
\(218\) 13.4950i 0.0619039i
\(219\) 4.76660 1.92364i 0.0217653 0.00878376i
\(220\) −75.0978 −0.341354
\(221\) 118.319i 0.535378i
\(222\) 76.8549 + 190.439i 0.346193 + 0.857833i
\(223\) −397.757 −1.78366 −0.891832 0.452367i \(-0.850580\pi\)
−0.891832 + 0.452367i \(0.850580\pi\)
\(224\) 54.9444i 0.245288i
\(225\) −32.3949 + 31.2341i −0.143978 + 0.138818i
\(226\) −275.350 −1.21836
\(227\) 76.3503i 0.336345i 0.985758 + 0.168172i \(0.0537865\pi\)
−0.985758 + 0.168172i \(0.946213\pi\)
\(228\) −104.463 + 42.1578i −0.458171 + 0.184903i
\(229\) −95.0705 −0.415155 −0.207578 0.978219i \(-0.566558\pi\)
−0.207578 + 0.978219i \(0.566558\pi\)
\(230\) 15.1658i 0.0659380i
\(231\) 183.119 + 453.751i 0.792723 + 1.96429i
\(232\) −23.6425 −0.101907
\(233\) 372.400i 1.59828i 0.601144 + 0.799141i \(0.294712\pi\)
−0.601144 + 0.799141i \(0.705288\pi\)
\(234\) −125.624 130.293i −0.536854 0.556807i
\(235\) −56.8991 −0.242124
\(236\) 70.1334i 0.297175i
\(237\) 330.803 133.501i 1.39579 0.563297i
\(238\) 114.293 0.480221
\(239\) 337.680i 1.41289i 0.707770 + 0.706443i \(0.249701\pi\)
−0.707770 + 0.706443i \(0.750299\pi\)
\(240\) −10.0419 24.8829i −0.0418414 0.103679i
\(241\) 127.860 0.530539 0.265270 0.964174i \(-0.414539\pi\)
0.265270 + 0.964174i \(0.414539\pi\)
\(242\) 227.666i 0.940768i
\(243\) −82.6603 228.509i −0.340166 0.940365i
\(244\) 114.368 0.468721
\(245\) 101.384i 0.413812i
\(246\) 132.610 53.5170i 0.539065 0.217549i
\(247\) 266.977 1.08088
\(248\) 36.1467i 0.145753i
\(249\) −14.8767 36.8630i −0.0597457 0.148044i
\(250\) 15.8114 0.0632456
\(251\) 117.132i 0.466662i −0.972397 0.233331i \(-0.925037\pi\)
0.972397 0.233331i \(-0.0749625\pi\)
\(252\) −125.859 + 121.349i −0.499442 + 0.481545i
\(253\) −80.5334 −0.318314
\(254\) 129.541i 0.510003i
\(255\) 51.7602 20.8887i 0.202981 0.0819166i
\(256\) 16.0000 0.0625000
\(257\) 95.1801i 0.370351i 0.982706 + 0.185175i \(0.0592853\pi\)
−0.982706 + 0.185175i \(0.940715\pi\)
\(258\) 66.4592 + 164.679i 0.257594 + 0.638292i
\(259\) −470.146 −1.81524
\(260\) 63.5936i 0.244591i
\(261\) 52.2164 + 54.1571i 0.200063 + 0.207498i
\(262\) 195.097 0.744646
\(263\) 189.537i 0.720673i 0.932822 + 0.360336i \(0.117338\pi\)
−0.932822 + 0.360336i \(0.882662\pi\)
\(264\) −132.134 + 53.3248i −0.500506 + 0.201988i
\(265\) −144.638 −0.545802
\(266\) 257.893i 0.969522i
\(267\) 163.765 + 405.794i 0.613352 + 1.51983i
\(268\) 122.427 0.456817
\(269\) 44.1590i 0.164160i −0.996626 0.0820799i \(-0.973844\pi\)
0.996626 0.0820799i \(-0.0261563\pi\)
\(270\) −34.8201 + 77.9587i −0.128963 + 0.288736i
\(271\) −198.521 −0.732548 −0.366274 0.930507i \(-0.619367\pi\)
−0.366274 + 0.930507i \(0.619367\pi\)
\(272\) 33.2824i 0.122362i
\(273\) 384.240 155.067i 1.40747 0.568011i
\(274\) −85.8225 −0.313221
\(275\) 83.9619i 0.305316i
\(276\) −10.7688 26.6840i −0.0390173 0.0966810i
\(277\) 516.578 1.86490 0.932452 0.361295i \(-0.117665\pi\)
0.932452 + 0.361295i \(0.117665\pi\)
\(278\) 152.001i 0.546766i
\(279\) 82.8002 79.8330i 0.296775 0.286140i
\(280\) 61.4297 0.219392
\(281\) 263.794i 0.938769i 0.882994 + 0.469385i \(0.155524\pi\)
−0.882994 + 0.469385i \(0.844476\pi\)
\(282\) −100.113 + 40.4025i −0.355012 + 0.143271i
\(283\) 100.543 0.355277 0.177639 0.984096i \(-0.443154\pi\)
0.177639 + 0.984096i \(0.443154\pi\)
\(284\) 198.098i 0.697527i
\(285\) −47.1339 116.793i −0.165382 0.409800i
\(286\) 337.696 1.18075
\(287\) 327.381i 1.14070i
\(288\) −35.3373 36.6507i −0.122699 0.127259i
\(289\) 219.768 0.760442
\(290\) 26.4331i 0.0911486i
\(291\) −462.247 + 186.548i −1.58848 + 0.641058i
\(292\) −3.42675 −0.0117354
\(293\) 334.768i 1.14255i 0.820758 + 0.571276i \(0.193551\pi\)
−0.820758 + 0.571276i \(0.806449\pi\)
\(294\) −71.9899 178.384i −0.244864 0.606748i
\(295\) −78.4115 −0.265802
\(296\) 136.908i 0.462527i
\(297\) 413.978 + 184.902i 1.39386 + 0.622566i
\(298\) 48.2878 0.162039
\(299\) 68.1965i 0.228082i
\(300\) 27.8199 11.2272i 0.0927332 0.0374241i
\(301\) −406.552 −1.35067
\(302\) 217.705i 0.720878i
\(303\) −113.746 281.850i −0.375398 0.930199i
\(304\) 75.0993 0.247037
\(305\) 127.867i 0.419236i
\(306\) 76.2389 73.5069i 0.249147 0.240219i
\(307\) −273.175 −0.889819 −0.444910 0.895575i \(-0.646764\pi\)
−0.444910 + 0.895575i \(0.646764\pi\)
\(308\) 326.205i 1.05911i
\(309\) −435.408 + 175.717i −1.40909 + 0.568662i
\(310\) −40.4133 −0.130365
\(311\) 364.172i 1.17097i −0.810683 0.585485i \(-0.800904\pi\)
0.810683 0.585485i \(-0.199096\pi\)
\(312\) 45.1560 + 111.892i 0.144731 + 0.358629i
\(313\) −499.143 −1.59471 −0.797354 0.603512i \(-0.793767\pi\)
−0.797354 + 0.603512i \(0.793767\pi\)
\(314\) 96.6404i 0.307772i
\(315\) −135.673 140.715i −0.430707 0.446715i
\(316\) −237.817 −0.752586
\(317\) 609.173i 1.92168i −0.277099 0.960841i \(-0.589373\pi\)
0.277099 0.960841i \(-0.410627\pi\)
\(318\) −254.488 + 102.703i −0.800277 + 0.322966i
\(319\) −140.366 −0.440017
\(320\) 17.8885i 0.0559017i
\(321\) 55.6836 + 137.979i 0.173469 + 0.429840i
\(322\) 65.8760 0.204584
\(323\) 156.218i 0.483646i
\(324\) −5.90920 + 161.892i −0.0182383 + 0.499667i
\(325\) −71.0998 −0.218769
\(326\) 227.411i 0.697580i
\(327\) −26.5470 + 10.7135i −0.0811835 + 0.0327630i
\(328\) −95.3344 −0.290654
\(329\) 247.155i 0.751231i
\(330\) −59.6190 147.730i −0.180664 0.447667i
\(331\) 212.610 0.642326 0.321163 0.947024i \(-0.395926\pi\)
0.321163 + 0.947024i \(0.395926\pi\)
\(332\) 26.5011i 0.0798226i
\(333\) −313.611 + 302.373i −0.941775 + 0.908027i
\(334\) −288.330 −0.863265
\(335\) 136.877i 0.408589i
\(336\) 108.085 43.6195i 0.321681 0.129820i
\(337\) 186.428 0.553199 0.276600 0.960985i \(-0.410792\pi\)
0.276600 + 0.960985i \(0.410792\pi\)
\(338\) 46.9620i 0.138941i
\(339\) −218.596 541.660i −0.644826 1.59782i
\(340\) −37.2109 −0.109444
\(341\) 214.603i 0.629335i
\(342\) −165.863 172.028i −0.484979 0.503005i
\(343\) −35.5465 −0.103634
\(344\) 118.389i 0.344155i
\(345\) 29.8336 12.0399i 0.0864741 0.0348981i
\(346\) 54.2470 0.156783
\(347\) 144.932i 0.417672i 0.977951 + 0.208836i \(0.0669674\pi\)
−0.977951 + 0.208836i \(0.933033\pi\)
\(348\) −18.7694 46.5087i −0.0539351 0.133646i
\(349\) 217.428 0.623003 0.311502 0.950246i \(-0.399168\pi\)
0.311502 + 0.950246i \(0.399168\pi\)
\(350\) 68.6805i 0.196230i
\(351\) 156.577 350.560i 0.446088 0.998748i
\(352\) 94.9921 0.269864
\(353\) 252.766i 0.716052i −0.933712 0.358026i \(-0.883450\pi\)
0.933712 0.358026i \(-0.116550\pi\)
\(354\) −137.964 + 55.6778i −0.389729 + 0.157282i
\(355\) −221.480 −0.623887
\(356\) 291.729i 0.819462i
\(357\) 90.7352 + 224.833i 0.254160 + 0.629784i
\(358\) −51.5795 −0.144077
\(359\) 310.853i 0.865887i −0.901421 0.432943i \(-0.857475\pi\)
0.901421 0.432943i \(-0.142525\pi\)
\(360\) 40.9767 39.5083i 0.113824 0.109745i
\(361\) −8.50620 −0.0235629
\(362\) 481.819i 1.33099i
\(363\) −447.857 + 180.740i −1.23377 + 0.497907i
\(364\) −276.234 −0.758884
\(365\) 3.83122i 0.0104965i
\(366\) 90.7948 + 224.981i 0.248073 + 0.614701i
\(367\) 578.070 1.57512 0.787561 0.616237i \(-0.211344\pi\)
0.787561 + 0.616237i \(0.211344\pi\)
\(368\) 19.1833i 0.0521286i
\(369\) 210.554 + 218.380i 0.570607 + 0.591814i
\(370\) 153.068 0.413697
\(371\) 628.267i 1.69344i
\(372\) −71.1067 + 28.6963i −0.191147 + 0.0771407i
\(373\) 547.166 1.46693 0.733466 0.679726i \(-0.237901\pi\)
0.733466 + 0.679726i \(0.237901\pi\)
\(374\) 197.598i 0.528336i
\(375\) 12.5524 + 31.1036i 0.0334731 + 0.0829431i
\(376\) 71.9723 0.191416
\(377\) 118.863i 0.315286i
\(378\) −338.632 151.249i −0.895852 0.400130i
\(379\) −176.439 −0.465539 −0.232769 0.972532i \(-0.574779\pi\)
−0.232769 + 0.972532i \(0.574779\pi\)
\(380\) 83.9635i 0.220957i
\(381\) 254.828 102.840i 0.668841 0.269922i
\(382\) 264.771 0.693118
\(383\) 102.841i 0.268513i −0.990947 0.134257i \(-0.957135\pi\)
0.990947 0.134257i \(-0.0428646\pi\)
\(384\) 12.7022 + 31.4747i 0.0330785 + 0.0819653i
\(385\) 364.708 0.947295
\(386\) 530.471i 1.37428i
\(387\) −271.191 + 261.473i −0.700751 + 0.675640i
\(388\) 332.314 0.856478
\(389\) 225.716i 0.580248i 0.956989 + 0.290124i \(0.0936965\pi\)
−0.956989 + 0.290124i \(0.906304\pi\)
\(390\) −125.099 + 50.4860i −0.320767 + 0.129451i
\(391\) −39.9042 −0.102057
\(392\) 128.242i 0.327147i
\(393\) 154.885 + 383.789i 0.394108 + 0.976562i
\(394\) 282.105 0.716002
\(395\) 265.888i 0.673134i
\(396\) −209.798 217.595i −0.529792 0.549483i
\(397\) 267.452 0.673682 0.336841 0.941562i \(-0.390642\pi\)
0.336841 + 0.941562i \(0.390642\pi\)
\(398\) 468.230i 1.17646i
\(399\) 507.318 204.737i 1.27147 0.513126i
\(400\) −20.0000 −0.0500000
\(401\) 440.820i 1.09930i −0.835395 0.549651i \(-0.814761\pi\)
0.835395 0.549651i \(-0.185239\pi\)
\(402\) 97.1929 + 240.834i 0.241773 + 0.599090i
\(403\) 181.728 0.450938
\(404\) 202.625i 0.501546i
\(405\) −181.001 6.60669i −0.446916 0.0163128i
\(406\) 114.818 0.282804
\(407\) 812.824i 1.99711i
\(408\) −65.4720 + 26.4224i −0.160471 + 0.0647607i
\(409\) 62.7728 0.153479 0.0767393 0.997051i \(-0.475549\pi\)
0.0767393 + 0.997051i \(0.475549\pi\)
\(410\) 106.587i 0.259969i
\(411\) −68.1332 168.827i −0.165774 0.410772i
\(412\) 313.019 0.759754
\(413\) 340.599i 0.824695i
\(414\) 43.9426 42.3680i 0.106142 0.102338i
\(415\) −29.6291 −0.0713955
\(416\) 80.4402i 0.193366i
\(417\) 299.011 120.671i 0.717053 0.289379i
\(418\) 445.865 1.06666
\(419\) 678.217i 1.61866i −0.587357 0.809328i \(-0.699832\pi\)
0.587357 0.809328i \(-0.300168\pi\)
\(420\) 48.7681 + 120.843i 0.116115 + 0.287720i
\(421\) 104.952 0.249293 0.124646 0.992201i \(-0.460220\pi\)
0.124646 + 0.992201i \(0.460220\pi\)
\(422\) 463.329i 1.09794i
\(423\) −158.957 164.865i −0.375785 0.389751i
\(424\) 182.954 0.431494
\(425\) 41.6030i 0.0978894i
\(426\) −389.691 + 157.267i −0.914769 + 0.369171i
\(427\) −555.421 −1.30075
\(428\) 99.1940i 0.231762i
\(429\) 268.091 + 664.304i 0.624922 + 1.54849i
\(430\) 132.363 0.307822
\(431\) 155.310i 0.360349i 0.983635 + 0.180174i \(0.0576662\pi\)
−0.983635 + 0.180174i \(0.942334\pi\)
\(432\) 44.0443 98.6109i 0.101954 0.228266i
\(433\) −618.290 −1.42792 −0.713961 0.700185i \(-0.753101\pi\)
−0.713961 + 0.700185i \(0.753101\pi\)
\(434\) 175.545i 0.404481i
\(435\) 51.9983 20.9848i 0.119536 0.0482410i
\(436\) 19.0849 0.0437727
\(437\) 90.0409i 0.206043i
\(438\) −2.72044 6.74099i −0.00621106 0.0153904i
\(439\) −103.321 −0.235356 −0.117678 0.993052i \(-0.537545\pi\)
−0.117678 + 0.993052i \(0.537545\pi\)
\(440\) 106.204i 0.241374i
\(441\) 293.759 283.232i 0.666121 0.642250i
\(442\) 167.328 0.378570
\(443\) 190.496i 0.430013i −0.976613 0.215006i \(-0.931023\pi\)
0.976613 0.215006i \(-0.0689772\pi\)
\(444\) 269.321 108.689i 0.606579 0.244796i
\(445\) 326.162 0.732949
\(446\) 562.513i 1.26124i
\(447\) 38.3349 + 94.9901i 0.0857604 + 0.212506i
\(448\) −77.7031 −0.173445
\(449\) 2.15568i 0.00480107i 0.999997 + 0.00240053i \(0.000764114\pi\)
−0.999997 + 0.00240053i \(0.999236\pi\)
\(450\) 44.1717 + 45.8134i 0.0981592 + 0.101807i
\(451\) −566.001 −1.25499
\(452\) 389.404i 0.861513i
\(453\) −428.262 + 172.833i −0.945391 + 0.381529i
\(454\) 107.976 0.237832
\(455\) 308.839i 0.678767i
\(456\) 59.6202 + 147.733i 0.130746 + 0.323976i
\(457\) −400.938 −0.877326 −0.438663 0.898652i \(-0.644548\pi\)
−0.438663 + 0.898652i \(0.644548\pi\)
\(458\) 134.450i 0.293559i
\(459\) 205.125 + 91.6187i 0.446896 + 0.199605i
\(460\) −21.4476 −0.0466252
\(461\) 416.867i 0.904266i −0.891951 0.452133i \(-0.850663\pi\)
0.891951 0.452133i \(-0.149337\pi\)
\(462\) 641.700 258.969i 1.38896 0.560540i
\(463\) −211.974 −0.457827 −0.228913 0.973447i \(-0.573517\pi\)
−0.228913 + 0.973447i \(0.573517\pi\)
\(464\) 33.4355i 0.0720593i
\(465\) −32.0835 79.4997i −0.0689967 0.170967i
\(466\) 526.652 1.13016
\(467\) 536.033i 1.14782i −0.818918 0.573911i \(-0.805426\pi\)
0.818918 0.573911i \(-0.194574\pi\)
\(468\) −184.262 + 177.659i −0.393722 + 0.379613i
\(469\) −594.560 −1.26772
\(470\) 80.4675i 0.171208i
\(471\) 190.108 76.7214i 0.403626 0.162890i
\(472\) 99.1836 0.210135
\(473\) 702.878i 1.48600i
\(474\) −188.800 467.826i −0.398311 0.986976i
\(475\) −93.8741 −0.197630
\(476\) 161.634i 0.339568i
\(477\) −404.068 419.086i −0.847103 0.878587i
\(478\) 477.551 0.999061
\(479\) 143.758i 0.300120i −0.988677 0.150060i \(-0.952053\pi\)
0.988677 0.150060i \(-0.0479467\pi\)
\(480\) −35.1898 + 14.2014i −0.0733120 + 0.0295863i
\(481\) −688.307 −1.43099
\(482\) 180.821i 0.375148i
\(483\) 52.2980 + 129.589i 0.108277 + 0.268301i
\(484\) 321.968 0.665223
\(485\) 371.538i 0.766058i
\(486\) −323.160 + 116.899i −0.664939 + 0.240534i
\(487\) −454.474 −0.933211 −0.466605 0.884466i \(-0.654523\pi\)
−0.466605 + 0.884466i \(0.654523\pi\)
\(488\) 161.741i 0.331435i
\(489\) 447.356 180.538i 0.914838 0.369199i
\(490\) −143.379 −0.292609
\(491\) 414.443i 0.844079i −0.906577 0.422039i \(-0.861314\pi\)
0.906577 0.422039i \(-0.138686\pi\)
\(492\) −75.6845 187.539i −0.153830 0.381176i
\(493\) −69.5509 −0.141077
\(494\) 377.563i 0.764297i
\(495\) 243.279 234.561i 0.491473 0.473861i
\(496\) 51.1192 0.103063
\(497\) 962.051i 1.93572i
\(498\) −52.1321 + 21.0388i −0.104683 + 0.0422466i
\(499\) −408.192 −0.818021 −0.409010 0.912530i \(-0.634126\pi\)
−0.409010 + 0.912530i \(0.634126\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −228.901 567.194i −0.456888 1.13212i
\(502\) −165.650 −0.329980
\(503\) 541.009i 1.07556i 0.843084 + 0.537782i \(0.180738\pi\)
−0.843084 + 0.537782i \(0.819262\pi\)
\(504\) 171.614 + 177.992i 0.340504 + 0.353159i
\(505\) −226.541 −0.448596
\(506\) 113.891i 0.225082i
\(507\) 92.3821 37.2824i 0.182213 0.0735353i
\(508\) −183.198 −0.360626
\(509\) 508.935i 0.999872i 0.866062 + 0.499936i \(0.166643\pi\)
−0.866062 + 0.499936i \(0.833357\pi\)
\(510\) −29.5411 73.2000i −0.0579238 0.143529i
\(511\) 16.6418 0.0325672
\(512\) 22.6274i 0.0441942i
\(513\) 206.731 462.850i 0.402984 0.902242i
\(514\) 134.605 0.261877
\(515\) 349.966i 0.679545i
\(516\) 232.892 93.9874i 0.451340 0.182146i
\(517\) 427.300 0.826499
\(518\) 664.887i 1.28357i
\(519\) 43.0659 + 106.713i 0.0829786 + 0.205613i
\(520\) 89.9349 0.172952
\(521\) 326.505i 0.626689i 0.949640 + 0.313344i \(0.101449\pi\)
−0.949640 + 0.313344i \(0.898551\pi\)
\(522\) 76.5897 73.8451i 0.146724 0.141466i
\(523\) 651.561 1.24581 0.622907 0.782296i \(-0.285951\pi\)
0.622907 + 0.782296i \(0.285951\pi\)
\(524\) 275.909i 0.526544i
\(525\) −135.106 + 54.5244i −0.257345 + 0.103856i
\(526\) 268.046 0.509592
\(527\) 106.336i 0.201775i
\(528\) 75.4127 + 186.865i 0.142827 + 0.353911i
\(529\) −23.0000 −0.0434783
\(530\) 204.548i 0.385940i
\(531\) −219.055 227.197i −0.412533 0.427866i
\(532\) −364.716 −0.685556
\(533\) 479.295i 0.899240i
\(534\) 573.879 231.599i 1.07468 0.433706i
\(535\) 110.902 0.207294
\(536\) 173.138i 0.323018i
\(537\) −40.9482 101.465i −0.0762535 0.188949i
\(538\) −62.4502 −0.116078
\(539\) 761.371i 1.41256i
\(540\) 110.250 + 49.2430i 0.204167 + 0.0911908i
\(541\) −561.296 −1.03752 −0.518758 0.854921i \(-0.673605\pi\)
−0.518758 + 0.854921i \(0.673605\pi\)
\(542\) 280.751i 0.517990i
\(543\) −947.818 + 382.509i −1.74552 + 0.704436i
\(544\) 47.0684 0.0865228
\(545\) 21.3375i 0.0391514i
\(546\) −219.298 543.398i −0.401644 0.995235i
\(547\) −539.069 −0.985500 −0.492750 0.870171i \(-0.664008\pi\)
−0.492750 + 0.870171i \(0.664008\pi\)
\(548\) 121.371i 0.221481i
\(549\) −370.494 + 357.217i −0.674852 + 0.650669i
\(550\) −118.740 −0.215891
\(551\) 156.936i 0.284821i
\(552\) −37.7368 + 15.2293i −0.0683638 + 0.0275894i
\(553\) 1154.95 2.08851
\(554\) 730.552i 1.31869i
\(555\) 121.518 + 301.110i 0.218952 + 0.542541i
\(556\) −214.962 −0.386622
\(557\) 613.984i 1.10231i 0.834404 + 0.551153i \(0.185812\pi\)
−0.834404 + 0.551153i \(0.814188\pi\)
\(558\) −112.901 117.097i −0.202331 0.209851i
\(559\) −595.204 −1.06477
\(560\) 86.8747i 0.155133i
\(561\) −388.708 + 156.870i −0.692884 + 0.279625i
\(562\) 373.061 0.663810
\(563\) 522.289i 0.927689i −0.885917 0.463844i \(-0.846470\pi\)
0.885917 0.463844i \(-0.153530\pi\)
\(564\) 57.1377 + 141.582i 0.101308 + 0.251031i
\(565\) −435.367 −0.770560
\(566\) 142.190i 0.251219i
\(567\) 28.6977 786.221i 0.0506132 1.38663i
\(568\) 280.153 0.493226
\(569\) 835.117i 1.46769i 0.679316 + 0.733846i \(0.262277\pi\)
−0.679316 + 0.733846i \(0.737723\pi\)
\(570\) −165.170 + 66.6574i −0.289773 + 0.116943i
\(571\) −973.842 −1.70550 −0.852752 0.522316i \(-0.825068\pi\)
−0.852752 + 0.522316i \(0.825068\pi\)
\(572\) 477.574i 0.834919i
\(573\) 210.198 + 520.849i 0.366837 + 0.908986i
\(574\) 462.986 0.806596
\(575\) 23.9792i 0.0417029i
\(576\) −51.8319 + 49.9745i −0.0899860 + 0.0867613i
\(577\) 556.066 0.963719 0.481859 0.876249i \(-0.339962\pi\)
0.481859 + 0.876249i \(0.339962\pi\)
\(578\) 310.798i 0.537713i
\(579\) 1043.52 421.133i 1.80229 0.727345i
\(580\) −37.3821 −0.0644518
\(581\) 128.701i 0.221517i
\(582\) 263.819 + 653.716i 0.453297 + 1.12322i
\(583\) 1086.20 1.86312
\(584\) 4.84616i 0.00829821i
\(585\) −198.629 206.011i −0.339536 0.352156i
\(586\) 473.433 0.807906
\(587\) 455.905i 0.776669i −0.921519 0.388334i \(-0.873051\pi\)
0.921519 0.388334i \(-0.126949\pi\)
\(588\) −252.273 + 101.809i −0.429035 + 0.173145i
\(589\) 239.938 0.407366
\(590\) 110.891i 0.187950i
\(591\) 223.959 + 554.948i 0.378949 + 0.938998i
\(592\) −193.617 −0.327056
\(593\) 1016.74i 1.71457i −0.514842 0.857285i \(-0.672149\pi\)
0.514842 0.857285i \(-0.327851\pi\)
\(594\) 261.491 585.453i 0.440221 0.985611i
\(595\) 180.713 0.303719
\(596\) 68.2892i 0.114579i
\(597\) 921.086 371.720i 1.54286 0.622647i
\(598\) 96.4444 0.161278
\(599\) 6.66161i 0.0111212i 0.999985 + 0.00556061i \(0.00177001\pi\)
−0.999985 + 0.00556061i \(0.998230\pi\)
\(600\) −15.8777 39.3433i −0.0264628 0.0655722i
\(601\) 451.786 0.751724 0.375862 0.926676i \(-0.377347\pi\)
0.375862 + 0.926676i \(0.377347\pi\)
\(602\) 574.951i 0.955069i
\(603\) −396.601 + 382.389i −0.657714 + 0.634145i
\(604\) 307.881 0.509737
\(605\) 359.971i 0.594994i
\(606\) −398.596 + 160.861i −0.657750 + 0.265446i
\(607\) −263.050 −0.433361 −0.216680 0.976243i \(-0.569523\pi\)
−0.216680 + 0.976243i \(0.569523\pi\)
\(608\) 106.206i 0.174682i
\(609\) 91.1526 + 225.867i 0.149676 + 0.370882i
\(610\) 180.831 0.296445
\(611\) 361.842i 0.592213i
\(612\) −103.955 107.818i −0.169860 0.176173i
\(613\) 613.976 1.00159 0.500796 0.865565i \(-0.333041\pi\)
0.500796 + 0.865565i \(0.333041\pi\)
\(614\) 386.327i 0.629197i
\(615\) 209.675 84.6179i 0.340934 0.137590i
\(616\) −461.324 −0.748902
\(617\) 1142.79i 1.85217i −0.377316 0.926084i \(-0.623153\pi\)
0.377316 0.926084i \(-0.376847\pi\)
\(618\) 248.501 + 615.760i 0.402105 + 0.996376i
\(619\) −590.671 −0.954234 −0.477117 0.878840i \(-0.658318\pi\)
−0.477117 + 0.878840i \(0.658318\pi\)
\(620\) 57.1530i 0.0921822i
\(621\) 118.230 + 52.8073i 0.190387 + 0.0850358i
\(622\) −515.017 −0.828001
\(623\) 1416.76i 2.27410i
\(624\) 158.239 63.8603i 0.253589 0.102340i
\(625\) 25.0000 0.0400000
\(626\) 705.895i 1.12763i
\(627\) 353.965 + 877.090i 0.564538 + 1.39887i
\(628\) −136.670 −0.217628
\(629\) 402.753i 0.640307i
\(630\) −199.001 + 191.870i −0.315875 + 0.304556i
\(631\) 316.818 0.502089 0.251044 0.967976i \(-0.419226\pi\)
0.251044 + 0.967976i \(0.419226\pi\)
\(632\) 336.324i 0.532159i
\(633\) −911.445 + 367.830i −1.43988 + 0.581089i
\(634\) −861.501 −1.35883
\(635\) 204.822i 0.322554i
\(636\) 145.244 + 359.900i 0.228371 + 0.565881i
\(637\) 644.737 1.01215
\(638\) 198.507i 0.311139i
\(639\) −618.740 641.737i −0.968294 1.00428i
\(640\) 25.2982 0.0395285
\(641\) 617.453i 0.963265i 0.876373 + 0.481633i \(0.159956\pi\)
−0.876373 + 0.481633i \(0.840044\pi\)
\(642\) 195.131 78.7486i 0.303943 0.122661i
\(643\) −465.627 −0.724148 −0.362074 0.932149i \(-0.617931\pi\)
−0.362074 + 0.932149i \(0.617931\pi\)
\(644\) 93.1628i 0.144663i
\(645\) 105.081 + 260.381i 0.162917 + 0.403691i
\(646\) 220.925 0.341990
\(647\) 439.316i 0.679005i 0.940605 + 0.339503i \(0.110259\pi\)
−0.940605 + 0.339503i \(0.889741\pi\)
\(648\) 228.950 + 8.35687i 0.353318 + 0.0128964i
\(649\) 588.853 0.907324
\(650\) 100.550i 0.154693i
\(651\) 345.326 139.362i 0.530454 0.214074i
\(652\) −321.608 −0.493264
\(653\) 1275.64i 1.95350i −0.214377 0.976751i \(-0.568772\pi\)
0.214377 0.976751i \(-0.431228\pi\)
\(654\) 15.1512 + 37.5431i 0.0231670 + 0.0574054i
\(655\) 308.476 0.470955
\(656\) 134.823i 0.205523i
\(657\) 11.1009 10.7031i 0.0168964 0.0162909i
\(658\) −349.530 −0.531200
\(659\) 1058.48i 1.60619i 0.595851 + 0.803095i \(0.296815\pi\)
−0.595851 + 0.803095i \(0.703185\pi\)
\(660\) −208.922 + 84.3140i −0.316548 + 0.127748i
\(661\) 74.3586 0.112494 0.0562470 0.998417i \(-0.482087\pi\)
0.0562470 + 0.998417i \(0.482087\pi\)
\(662\) 300.676i 0.454193i
\(663\) 132.839 + 329.162i 0.200360 + 0.496473i
\(664\) 37.4782 0.0564431
\(665\) 407.764i 0.613180i
\(666\) 427.620 + 443.513i 0.642072 + 0.665936i
\(667\) −40.0878 −0.0601016
\(668\) 407.761i 0.610420i
\(669\) −1106.56 + 446.571i −1.65405 + 0.667520i
\(670\) 193.574 0.288916
\(671\) 960.254i 1.43108i
\(672\) −61.6873 152.855i −0.0917966 0.227463i
\(673\) 495.673 0.736513 0.368256 0.929724i \(-0.379955\pi\)
0.368256 + 0.929724i \(0.379955\pi\)
\(674\) 263.649i 0.391171i
\(675\) −55.0554 + 123.264i −0.0815635 + 0.182613i
\(676\) −66.4143 −0.0982460
\(677\) 179.621i 0.265319i 0.991162 + 0.132660i \(0.0423517\pi\)
−0.991162 + 0.132660i \(0.957648\pi\)
\(678\) −766.022 + 309.142i −1.12983 + 0.455961i
\(679\) −1613.86 −2.37682
\(680\) 52.6241i 0.0773884i
\(681\) 85.7201 + 212.406i 0.125874 + 0.311903i
\(682\) 303.495 0.445007
\(683\) 144.842i 0.212067i −0.994363 0.106034i \(-0.966185\pi\)
0.994363 0.106034i \(-0.0338151\pi\)
\(684\) −243.284 + 234.566i −0.355678 + 0.342932i
\(685\) −135.697 −0.198098
\(686\) 50.2704i 0.0732804i
\(687\) −264.486 + 106.738i −0.384986 + 0.155368i
\(688\) −167.428 −0.243354
\(689\) 919.802i 1.33498i
\(690\) −17.0269 42.1910i −0.0246767 0.0611464i
\(691\) −877.963 −1.27057 −0.635284 0.772278i \(-0.719117\pi\)
−0.635284 + 0.772278i \(0.719117\pi\)
\(692\) 76.7169i 0.110863i
\(693\) 1018.87 + 1056.74i 1.47023 + 1.52488i
\(694\) 204.965 0.295338
\(695\) 240.334i 0.345805i
\(696\) −65.7733 + 26.5439i −0.0945018 + 0.0381379i
\(697\) −280.452 −0.402371
\(698\) 307.490i 0.440530i
\(699\) 418.101 + 1036.01i 0.598142 + 1.48214i
\(700\) 97.1289 0.138756
\(701\) 1173.42i 1.67393i 0.547259 + 0.836964i \(0.315671\pi\)
−0.547259 + 0.836964i \(0.684329\pi\)
\(702\) −495.767 221.433i −0.706221 0.315432i
\(703\) −908.783 −1.29272
\(704\) 134.339i 0.190823i
\(705\) −158.293 + 63.8819i −0.224529 + 0.0906127i
\(706\) −357.466 −0.506325
\(707\) 984.035i 1.39185i
\(708\) 78.7403 + 195.111i 0.111215 + 0.275580i
\(709\) 1123.63 1.58481 0.792407 0.609993i \(-0.208828\pi\)
0.792407 + 0.609993i \(0.208828\pi\)
\(710\) 313.220i 0.441155i
\(711\) 770.408 742.800i 1.08356 1.04473i
\(712\) −412.566 −0.579447
\(713\) 61.2898i 0.0859604i
\(714\) 317.961 128.319i 0.445324 0.179718i
\(715\) 533.944 0.746775
\(716\) 72.9444i 0.101878i
\(717\) 379.120 + 939.423i 0.528759 + 1.31021i
\(718\) −439.613 −0.612274
\(719\) 1040.78i 1.44753i 0.690044 + 0.723767i \(0.257591\pi\)
−0.690044 + 0.723767i \(0.742409\pi\)
\(720\) −55.8732 57.9498i −0.0776017 0.0804859i
\(721\) −1520.16 −2.10840
\(722\) 12.0296i 0.0166615i
\(723\) 355.706 143.551i 0.491986 0.198549i
\(724\) 681.395 0.941153
\(725\) 41.7944i 0.0576475i
\(726\) 255.606 + 633.365i 0.352074 + 0.872404i
\(727\) 501.507 0.689831 0.344916 0.938634i \(-0.387908\pi\)
0.344916 + 0.938634i \(0.387908\pi\)
\(728\) 390.654i 0.536612i
\(729\) −486.512 542.906i −0.667370 0.744727i
\(730\) −5.41817 −0.00742215
\(731\) 348.275i 0.476436i
\(732\) 318.171 128.403i 0.434659 0.175414i
\(733\) −110.721 −0.151052 −0.0755261 0.997144i \(-0.524064\pi\)
−0.0755261 + 0.997144i \(0.524064\pi\)
\(734\) 817.514i 1.11378i
\(735\) −113.826 282.050i −0.154865 0.383741i
\(736\) 27.1293 0.0368605
\(737\) 1027.92i 1.39474i
\(738\) 308.835 297.768i 0.418476 0.403480i
\(739\) −637.166 −0.862200 −0.431100 0.902304i \(-0.641874\pi\)
−0.431100 + 0.902304i \(0.641874\pi\)
\(740\) 216.471i 0.292528i
\(741\) 742.729 299.741i 1.00233 0.404509i
\(742\) −888.504 −1.19745
\(743\) 174.168i 0.234412i −0.993108 0.117206i \(-0.962606\pi\)
0.993108 0.117206i \(-0.0373937\pi\)
\(744\) 40.5827 + 100.560i 0.0545467 + 0.135161i
\(745\) 76.3497 0.102483
\(746\) 773.809i 1.03728i
\(747\) −82.7737 85.8502i −0.110808 0.114927i
\(748\) 279.445 0.373590
\(749\) 481.730i 0.643164i
\(750\) 43.9872 17.7518i 0.0586496 0.0236691i
\(751\) 1041.90 1.38735 0.693676 0.720287i \(-0.255990\pi\)
0.693676 + 0.720287i \(0.255990\pi\)
\(752\) 101.784i 0.135351i
\(753\) −131.507 325.861i −0.174644 0.432750i
\(754\) 168.098 0.222941
\(755\) 344.222i 0.455923i
\(756\) −213.899 + 478.898i −0.282935 + 0.633463i
\(757\) 1352.49 1.78664 0.893321 0.449419i \(-0.148369\pi\)
0.893321 + 0.449419i \(0.148369\pi\)
\(758\) 249.523i 0.329186i
\(759\) −224.044 + 90.4167i −0.295183 + 0.119126i
\(760\) 118.742 0.156240
\(761\) 786.105i 1.03299i 0.856290 + 0.516495i \(0.172763\pi\)
−0.856290 + 0.516495i \(0.827237\pi\)
\(762\) −145.438 360.382i −0.190864 0.472942i
\(763\) −92.6847 −0.121474
\(764\) 374.443i 0.490108i
\(765\) 120.544 116.225i 0.157574 0.151928i
\(766\) −145.438 −0.189867
\(767\) 498.647i 0.650126i
\(768\) 44.5119 17.9636i 0.0579582 0.0233900i
\(769\) 273.919 0.356202 0.178101 0.984012i \(-0.443005\pi\)
0.178101 + 0.984012i \(0.443005\pi\)
\(770\) 515.776i 0.669839i
\(771\) 106.861 + 264.790i 0.138600 + 0.343438i
\(772\) −750.199 −0.971760
\(773\) 396.276i 0.512647i 0.966591 + 0.256324i \(0.0825113\pi\)
−0.966591 + 0.256324i \(0.917489\pi\)
\(774\) 369.778 + 383.522i 0.477749 + 0.495506i
\(775\) −63.8990 −0.0824503
\(776\) 469.962i 0.605622i
\(777\) −1307.94 + 527.843i −1.68333 + 0.679335i
\(778\) 319.211 0.410297
\(779\) 632.820i 0.812350i
\(780\) 71.3979 + 176.917i 0.0915358 + 0.226817i
\(781\) 1663.27 2.12966
\(782\) 56.4331i 0.0721650i
\(783\) 206.069 + 92.0403i 0.263179 + 0.117548i
\(784\) 181.361 0.231328
\(785\) 152.802i 0.194652i
\(786\) 542.759 219.040i