Properties

Label 690.3.k.a.277.12
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $40$
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.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.12
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.a.553.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.34252 - 2.47842i) q^{5} +2.44949 q^{6} +(-5.93628 - 5.93628i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.34252 - 2.47842i) q^{5} +2.44949 q^{6} +(-5.93628 - 5.93628i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-1.86410 - 6.82093i) q^{10} +11.6875 q^{11} +(2.44949 + 2.44949i) q^{12} +(-16.3131 + 16.3131i) q^{13} -11.8726i q^{14} +(-8.35390 + 2.28305i) q^{15} -4.00000 q^{16} +(2.76554 + 2.76554i) q^{17} +(3.00000 - 3.00000i) q^{18} +34.0355i q^{19} +(4.95683 - 8.68503i) q^{20} -14.5409 q^{21} +(11.6875 + 11.6875i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(12.7149 + 21.5251i) q^{25} -32.6263 q^{26} +(-3.67423 - 3.67423i) q^{27} +(11.8726 - 11.8726i) q^{28} +57.1335i q^{29} +(-10.6369 - 6.07086i) q^{30} -27.9492 q^{31} +(-4.00000 - 4.00000i) q^{32} +(14.3142 - 14.3142i) q^{33} +5.53108i q^{34} +(11.0658 + 40.4910i) q^{35} +6.00000 q^{36} +(11.9887 + 11.9887i) q^{37} +(-34.0355 + 34.0355i) q^{38} +39.9589i q^{39} +(13.6419 - 3.72820i) q^{40} -66.6724 q^{41} +(-14.5409 - 14.5409i) q^{42} +(47.1313 - 47.1313i) q^{43} +23.3749i q^{44} +(-7.43525 + 13.0275i) q^{45} +6.78233 q^{46} +(-30.7108 - 30.7108i) q^{47} +(-4.89898 + 4.89898i) q^{48} +21.4788i q^{49} +(-8.81023 + 34.2400i) q^{50} +6.77416 q^{51} +(-32.6263 - 32.6263i) q^{52} +(-31.3399 + 31.3399i) q^{53} -7.34847i q^{54} +(-50.7530 - 28.9664i) q^{55} +23.7451 q^{56} +(41.6848 + 41.6848i) q^{57} +(-57.1335 + 57.1335i) q^{58} +34.2406i q^{59} +(-4.56609 - 16.7078i) q^{60} -59.4597 q^{61} +(-27.9492 - 27.9492i) q^{62} +(-17.8088 + 17.8088i) q^{63} -8.00000i q^{64} +(111.271 - 30.4093i) q^{65} +28.6283 q^{66} +(-14.6139 - 14.6139i) q^{67} +(-5.53108 + 5.53108i) q^{68} -8.30662i q^{69} +(-29.4251 + 51.5568i) q^{70} +75.9585 q^{71} +(6.00000 + 6.00000i) q^{72} +(77.3188 - 77.3188i) q^{73} +23.9774i q^{74} +(41.9353 + 10.7903i) q^{75} -68.0709 q^{76} +(-69.3801 - 69.3801i) q^{77} +(-39.9589 + 39.9589i) q^{78} -141.674i q^{79} +(17.3701 + 9.91367i) q^{80} -9.00000 q^{81} +(-66.6724 - 66.6724i) q^{82} +(-74.9453 + 74.9453i) q^{83} -29.0817i q^{84} +(-5.15524 - 18.8636i) q^{85} +94.2626 q^{86} +(69.9740 + 69.9740i) q^{87} +(-23.3749 + 23.3749i) q^{88} +35.0157i q^{89} +(-20.4628 + 5.59230i) q^{90} +193.679 q^{91} +(6.78233 + 6.78233i) q^{92} +(-34.2306 + 34.2306i) q^{93} -61.4216i q^{94} +(84.3540 - 147.800i) q^{95} -9.79796 q^{96} +(6.39140 + 6.39140i) q^{97} +(-21.4788 + 21.4788i) q^{98} -35.0624i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \) \( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) −4.34252 2.47842i −0.868503 0.495683i
\(6\) 2.44949 0.408248
\(7\) −5.93628 5.93628i −0.848040 0.848040i 0.141849 0.989888i \(-0.454695\pi\)
−0.989888 + 0.141849i \(0.954695\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −1.86410 6.82093i −0.186410 0.682093i
\(11\) 11.6875 1.06250 0.531249 0.847216i \(-0.321723\pi\)
0.531249 + 0.847216i \(0.321723\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) −16.3131 + 16.3131i −1.25486 + 1.25486i −0.301340 + 0.953517i \(0.597434\pi\)
−0.953517 + 0.301340i \(0.902566\pi\)
\(14\) 11.8726i 0.848040i
\(15\) −8.35390 + 2.28305i −0.556927 + 0.152203i
\(16\) −4.00000 −0.250000
\(17\) 2.76554 + 2.76554i 0.162679 + 0.162679i 0.783752 0.621074i \(-0.213303\pi\)
−0.621074 + 0.783752i \(0.713303\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 34.0355i 1.79134i 0.444719 + 0.895670i \(0.353303\pi\)
−0.444719 + 0.895670i \(0.646697\pi\)
\(20\) 4.95683 8.68503i 0.247842 0.434252i
\(21\) −14.5409 −0.692422
\(22\) 11.6875 + 11.6875i 0.531249 + 0.531249i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 12.7149 + 21.5251i 0.508596 + 0.861005i
\(26\) −32.6263 −1.25486
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 11.8726 11.8726i 0.424020 0.424020i
\(29\) 57.1335i 1.97012i 0.172209 + 0.985060i \(0.444910\pi\)
−0.172209 + 0.985060i \(0.555090\pi\)
\(30\) −10.6369 6.07086i −0.354565 0.202362i
\(31\) −27.9492 −0.901586 −0.450793 0.892628i \(-0.648859\pi\)
−0.450793 + 0.892628i \(0.648859\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 14.3142 14.3142i 0.433763 0.433763i
\(34\) 5.53108i 0.162679i
\(35\) 11.0658 + 40.4910i 0.316166 + 1.15688i
\(36\) 6.00000 0.166667
\(37\) 11.9887 + 11.9887i 0.324019 + 0.324019i 0.850307 0.526288i \(-0.176416\pi\)
−0.526288 + 0.850307i \(0.676416\pi\)
\(38\) −34.0355 + 34.0355i −0.895670 + 0.895670i
\(39\) 39.9589i 1.02459i
\(40\) 13.6419 3.72820i 0.341047 0.0932050i
\(41\) −66.6724 −1.62616 −0.813078 0.582155i \(-0.802210\pi\)
−0.813078 + 0.582155i \(0.802210\pi\)
\(42\) −14.5409 14.5409i −0.346211 0.346211i
\(43\) 47.1313 47.1313i 1.09608 1.09608i 0.101211 0.994865i \(-0.467728\pi\)
0.994865 0.101211i \(-0.0322718\pi\)
\(44\) 23.3749i 0.531249i
\(45\) −7.43525 + 13.0275i −0.165228 + 0.289501i
\(46\) 6.78233 0.147442
\(47\) −30.7108 30.7108i −0.653421 0.653421i 0.300394 0.953815i \(-0.402882\pi\)
−0.953815 + 0.300394i \(0.902882\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 21.4788i 0.438343i
\(50\) −8.81023 + 34.2400i −0.176205 + 0.684801i
\(51\) 6.77416 0.132827
\(52\) −32.6263 32.6263i −0.627428 0.627428i
\(53\) −31.3399 + 31.3399i −0.591318 + 0.591318i −0.937987 0.346669i \(-0.887313\pi\)
0.346669 + 0.937987i \(0.387313\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −50.7530 28.9664i −0.922782 0.526662i
\(56\) 23.7451 0.424020
\(57\) 41.6848 + 41.6848i 0.731311 + 0.731311i
\(58\) −57.1335 + 57.1335i −0.985060 + 0.985060i
\(59\) 34.2406i 0.580348i 0.956974 + 0.290174i \(0.0937133\pi\)
−0.956974 + 0.290174i \(0.906287\pi\)
\(60\) −4.56609 16.7078i −0.0761016 0.278463i
\(61\) −59.4597 −0.974750 −0.487375 0.873193i \(-0.662045\pi\)
−0.487375 + 0.873193i \(0.662045\pi\)
\(62\) −27.9492 27.9492i −0.450793 0.450793i
\(63\) −17.8088 + 17.8088i −0.282680 + 0.282680i
\(64\) 8.00000i 0.125000i
\(65\) 111.271 30.4093i 1.71186 0.467836i
\(66\) 28.6283 0.433763
\(67\) −14.6139 14.6139i −0.218118 0.218118i 0.589587 0.807705i \(-0.299291\pi\)
−0.807705 + 0.589587i \(0.799291\pi\)
\(68\) −5.53108 + 5.53108i −0.0813394 + 0.0813394i
\(69\) 8.30662i 0.120386i
\(70\) −29.4251 + 51.5568i −0.420359 + 0.736525i
\(71\) 75.9585 1.06984 0.534919 0.844903i \(-0.320342\pi\)
0.534919 + 0.844903i \(0.320342\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) 77.3188 77.3188i 1.05916 1.05916i 0.0610249 0.998136i \(-0.480563\pi\)
0.998136 0.0610249i \(-0.0194369\pi\)
\(74\) 23.9774i 0.324019i
\(75\) 41.9353 + 10.7903i 0.559137 + 0.143870i
\(76\) −68.0709 −0.895670
\(77\) −69.3801 69.3801i −0.901040 0.901040i
\(78\) −39.9589 + 39.9589i −0.512293 + 0.512293i
\(79\) 141.674i 1.79335i −0.442692 0.896674i \(-0.645977\pi\)
0.442692 0.896674i \(-0.354023\pi\)
\(80\) 17.3701 + 9.91367i 0.217126 + 0.123921i
\(81\) −9.00000 −0.111111
\(82\) −66.6724 66.6724i −0.813078 0.813078i
\(83\) −74.9453 + 74.9453i −0.902955 + 0.902955i −0.995691 0.0927358i \(-0.970439\pi\)
0.0927358 + 0.995691i \(0.470439\pi\)
\(84\) 29.0817i 0.346211i
\(85\) −5.15524 18.8636i −0.0606499 0.221924i
\(86\) 94.2626 1.09608
\(87\) 69.9740 + 69.9740i 0.804298 + 0.804298i
\(88\) −23.3749 + 23.3749i −0.265624 + 0.265624i
\(89\) 35.0157i 0.393435i 0.980460 + 0.196718i \(0.0630282\pi\)
−0.980460 + 0.196718i \(0.936972\pi\)
\(90\) −20.4628 + 5.59230i −0.227364 + 0.0621367i
\(91\) 193.679 2.12834
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) −34.2306 + 34.2306i −0.368071 + 0.368071i
\(94\) 61.4216i 0.653421i
\(95\) 84.3540 147.800i 0.887937 1.55578i
\(96\) −9.79796 −0.102062
\(97\) 6.39140 + 6.39140i 0.0658907 + 0.0658907i 0.739284 0.673394i \(-0.235164\pi\)
−0.673394 + 0.739284i \(0.735164\pi\)
\(98\) −21.4788 + 21.4788i −0.219171 + 0.219171i
\(99\) 35.0624i 0.354166i
\(100\) −43.0503 + 25.4298i −0.430503 + 0.254298i
\(101\) −32.1722 −0.318536 −0.159268 0.987235i \(-0.550913\pi\)
−0.159268 + 0.987235i \(0.550913\pi\)
\(102\) 6.77416 + 6.77416i 0.0664133 + 0.0664133i
\(103\) −68.4939 + 68.4939i −0.664989 + 0.664989i −0.956552 0.291563i \(-0.905825\pi\)
0.291563 + 0.956552i \(0.405825\pi\)
\(104\) 65.2526i 0.627428i
\(105\) 63.1439 + 36.0383i 0.601370 + 0.343222i
\(106\) −62.6797 −0.591318
\(107\) 22.3110 + 22.3110i 0.208514 + 0.208514i 0.803636 0.595122i \(-0.202896\pi\)
−0.595122 + 0.803636i \(0.702896\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 190.368i 1.74650i 0.487275 + 0.873249i \(0.337991\pi\)
−0.487275 + 0.873249i \(0.662009\pi\)
\(110\) −21.7866 79.7195i −0.198060 0.724722i
\(111\) 29.3662 0.264560
\(112\) 23.7451 + 23.7451i 0.212010 + 0.212010i
\(113\) −61.7629 + 61.7629i −0.546574 + 0.546574i −0.925448 0.378874i \(-0.876311\pi\)
0.378874 + 0.925448i \(0.376311\pi\)
\(114\) 83.3695i 0.731311i
\(115\) −23.1309 + 6.32147i −0.201138 + 0.0549693i
\(116\) −114.267 −0.985060
\(117\) 48.9394 + 48.9394i 0.418286 + 0.418286i
\(118\) −34.2406 + 34.2406i −0.290174 + 0.290174i
\(119\) 32.8340i 0.275916i
\(120\) 12.1417 21.2739i 0.101181 0.177282i
\(121\) 15.5970 0.128900
\(122\) −59.4597 59.4597i −0.487375 0.487375i
\(123\) −81.6567 + 81.6567i −0.663875 + 0.663875i
\(124\) 55.8983i 0.450793i
\(125\) −1.86642 124.986i −0.0149314 0.999889i
\(126\) −35.6177 −0.282680
\(127\) −35.6620 35.6620i −0.280803 0.280803i 0.552626 0.833429i \(-0.313626\pi\)
−0.833429 + 0.552626i \(0.813626\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 115.448i 0.894942i
\(130\) 141.680 + 80.8615i 1.08985 + 0.622012i
\(131\) −54.4939 −0.415984 −0.207992 0.978131i \(-0.566693\pi\)
−0.207992 + 0.978131i \(0.566693\pi\)
\(132\) 28.6283 + 28.6283i 0.216881 + 0.216881i
\(133\) 202.044 202.044i 1.51913 1.51913i
\(134\) 29.2279i 0.218118i
\(135\) 6.84914 + 25.0617i 0.0507344 + 0.185642i
\(136\) −11.0622 −0.0813394
\(137\) −59.6809 59.6809i −0.435627 0.435627i 0.454910 0.890537i \(-0.349671\pi\)
−0.890537 + 0.454910i \(0.849671\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 75.7410i 0.544899i 0.962170 + 0.272450i \(0.0878338\pi\)
−0.962170 + 0.272450i \(0.912166\pi\)
\(140\) −80.9819 + 22.1316i −0.578442 + 0.158083i
\(141\) −75.2258 −0.533516
\(142\) 75.9585 + 75.9585i 0.534919 + 0.534919i
\(143\) −190.659 + 190.659i −1.33328 + 1.33328i
\(144\) 12.0000i 0.0833333i
\(145\) 141.601 248.103i 0.976556 1.71106i
\(146\) 154.638 1.05916
\(147\) 26.3060 + 26.3060i 0.178953 + 0.178953i
\(148\) −23.9774 + 23.9774i −0.162010 + 0.162010i
\(149\) 122.794i 0.824124i 0.911156 + 0.412062i \(0.135191\pi\)
−0.911156 + 0.412062i \(0.864809\pi\)
\(150\) 31.1450 + 52.7256i 0.207633 + 0.351504i
\(151\) −97.6700 −0.646821 −0.323410 0.946259i \(-0.604829\pi\)
−0.323410 + 0.946259i \(0.604829\pi\)
\(152\) −68.0709 68.0709i −0.447835 0.447835i
\(153\) 8.29661 8.29661i 0.0542262 0.0542262i
\(154\) 138.760i 0.901040i
\(155\) 121.370 + 69.2697i 0.783031 + 0.446901i
\(156\) −79.9177 −0.512293
\(157\) −8.25080 8.25080i −0.0525528 0.0525528i 0.680342 0.732895i \(-0.261831\pi\)
−0.732895 + 0.680342i \(0.761831\pi\)
\(158\) 141.674 141.674i 0.896674 0.896674i
\(159\) 76.7667i 0.482809i
\(160\) 7.45640 + 27.2837i 0.0466025 + 0.170523i
\(161\) −40.2618 −0.250073
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) 196.824 196.824i 1.20751 1.20751i 0.235682 0.971830i \(-0.424268\pi\)
0.971830 0.235682i \(-0.0757323\pi\)
\(164\) 133.345i 0.813078i
\(165\) −97.6360 + 26.6830i −0.591733 + 0.161715i
\(166\) −149.891 −0.902955
\(167\) −33.1032 33.1032i −0.198223 0.198223i 0.601015 0.799238i \(-0.294763\pi\)
−0.799238 + 0.601015i \(0.794763\pi\)
\(168\) 29.0817 29.0817i 0.173105 0.173105i
\(169\) 363.237i 2.14933i
\(170\) 13.7083 24.0188i 0.0806371 0.141287i
\(171\) 102.106 0.597113
\(172\) 94.2626 + 94.2626i 0.548038 + 0.548038i
\(173\) −129.709 + 129.709i −0.749764 + 0.749764i −0.974435 0.224670i \(-0.927869\pi\)
0.224670 + 0.974435i \(0.427869\pi\)
\(174\) 139.948i 0.804298i
\(175\) 52.3000 203.258i 0.298857 1.16148i
\(176\) −46.7499 −0.265624
\(177\) 41.9359 + 41.9359i 0.236926 + 0.236926i
\(178\) −35.0157 + 35.0157i −0.196718 + 0.196718i
\(179\) 117.226i 0.654893i 0.944870 + 0.327447i \(0.106188\pi\)
−0.944870 + 0.327447i \(0.893812\pi\)
\(180\) −26.0551 14.8705i −0.144751 0.0826139i
\(181\) −84.0690 −0.464470 −0.232235 0.972660i \(-0.574604\pi\)
−0.232235 + 0.972660i \(0.574604\pi\)
\(182\) 193.679 + 193.679i 1.06417 + 1.06417i
\(183\) −72.8230 + 72.8230i −0.397940 + 0.397940i
\(184\) 13.5647i 0.0737210i
\(185\) −22.3481 81.7742i −0.120801 0.442022i
\(186\) −68.4612 −0.368071
\(187\) 32.3221 + 32.3221i 0.172846 + 0.172846i
\(188\) 61.4216 61.4216i 0.326711 0.326711i
\(189\) 43.6226i 0.230807i
\(190\) 232.154 63.4455i 1.22186 0.333924i
\(191\) 29.5286 0.154600 0.0772999 0.997008i \(-0.475370\pi\)
0.0772999 + 0.997008i \(0.475370\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) 21.3978 21.3978i 0.110869 0.110869i −0.649496 0.760365i \(-0.725020\pi\)
0.760365 + 0.649496i \(0.225020\pi\)
\(194\) 12.7828i 0.0658907i
\(195\) 99.0347 173.522i 0.507870 0.889857i
\(196\) −42.9576 −0.219171
\(197\) −63.6996 63.6996i −0.323348 0.323348i 0.526702 0.850050i \(-0.323428\pi\)
−0.850050 + 0.526702i \(0.823428\pi\)
\(198\) 35.0624 35.0624i 0.177083 0.177083i
\(199\) 270.574i 1.35967i 0.733366 + 0.679834i \(0.237948\pi\)
−0.733366 + 0.679834i \(0.762052\pi\)
\(200\) −68.4801 17.6205i −0.342400 0.0881023i
\(201\) −35.7967 −0.178093
\(202\) −32.1722 32.1722i −0.159268 0.159268i
\(203\) 339.160 339.160i 1.67074 1.67074i
\(204\) 13.5483i 0.0664133i
\(205\) 289.526 + 165.242i 1.41232 + 0.806058i
\(206\) −136.988 −0.664989
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) 65.2526 65.2526i 0.313714 0.313714i
\(209\) 397.788i 1.90329i
\(210\) 27.1056 + 99.1822i 0.129074 + 0.472296i
\(211\) −344.189 −1.63123 −0.815614 0.578597i \(-0.803600\pi\)
−0.815614 + 0.578597i \(0.803600\pi\)
\(212\) −62.6797 62.6797i −0.295659 0.295659i
\(213\) 93.0298 93.0298i 0.436760 0.436760i
\(214\) 44.6219i 0.208514i
\(215\) −321.479 + 87.8574i −1.49525 + 0.408639i
\(216\) 14.6969 0.0680414
\(217\) 165.914 + 165.914i 0.764581 + 0.764581i
\(218\) −190.368 + 190.368i −0.873249 + 0.873249i
\(219\) 189.392i 0.864801i
\(220\) 57.9328 101.506i 0.263331 0.461391i
\(221\) −90.2292 −0.408277
\(222\) 29.3662 + 29.3662i 0.132280 + 0.132280i
\(223\) 46.6839 46.6839i 0.209345 0.209345i −0.594644 0.803989i \(-0.702707\pi\)
0.803989 + 0.594644i \(0.202707\pi\)
\(224\) 47.4902i 0.212010i
\(225\) 64.5754 38.1447i 0.287002 0.169532i
\(226\) −123.526 −0.546574
\(227\) 269.016 + 269.016i 1.18509 + 1.18509i 0.978408 + 0.206684i \(0.0662672\pi\)
0.206684 + 0.978408i \(0.433733\pi\)
\(228\) −83.3695 + 83.3695i −0.365656 + 0.365656i
\(229\) 149.901i 0.654588i −0.944923 0.327294i \(-0.893863\pi\)
0.944923 0.327294i \(-0.106137\pi\)
\(230\) −29.4524 16.8094i −0.128054 0.0730845i
\(231\) −169.946 −0.735696
\(232\) −114.267 114.267i −0.492530 0.492530i
\(233\) 141.005 141.005i 0.605172 0.605172i −0.336508 0.941680i \(-0.609246\pi\)
0.941680 + 0.336508i \(0.109246\pi\)
\(234\) 97.8788i 0.418286i
\(235\) 57.2480 + 209.476i 0.243608 + 0.891388i
\(236\) −68.4811 −0.290174
\(237\) −173.515 173.515i −0.732131 0.732131i
\(238\) 32.8340 32.8340i 0.137958 0.137958i
\(239\) 264.006i 1.10463i −0.833636 0.552315i \(-0.813745\pi\)
0.833636 0.552315i \(-0.186255\pi\)
\(240\) 33.4156 9.13219i 0.139232 0.0380508i
\(241\) 193.299 0.802070 0.401035 0.916063i \(-0.368651\pi\)
0.401035 + 0.916063i \(0.368651\pi\)
\(242\) 15.5970 + 15.5970i 0.0644502 + 0.0644502i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 118.919i 0.487375i
\(245\) 53.2334 93.2720i 0.217279 0.380702i
\(246\) −163.313 −0.663875
\(247\) −555.225 555.225i −2.24788 2.24788i
\(248\) 55.8983 55.8983i 0.225397 0.225397i
\(249\) 183.578i 0.737260i
\(250\) 123.120 126.852i 0.492479 0.507410i
\(251\) 408.680 1.62821 0.814104 0.580718i \(-0.197228\pi\)
0.814104 + 0.580718i \(0.197228\pi\)
\(252\) −35.6177 35.6177i −0.141340 0.141340i
\(253\) 39.6341 39.6341i 0.156657 0.156657i
\(254\) 71.3239i 0.280803i
\(255\) −29.4169 16.7892i −0.115360 0.0658399i
\(256\) 16.0000 0.0625000
\(257\) 26.8280 + 26.8280i 0.104389 + 0.104389i 0.757372 0.652983i \(-0.226483\pi\)
−0.652983 + 0.757372i \(0.726483\pi\)
\(258\) 115.448 115.448i 0.447471 0.447471i
\(259\) 142.337i 0.549562i
\(260\) 60.8186 + 222.542i 0.233918 + 0.855929i
\(261\) 171.401 0.656707
\(262\) −54.4939 54.4939i −0.207992 0.207992i
\(263\) −85.7865 + 85.7865i −0.326185 + 0.326185i −0.851134 0.524949i \(-0.824084\pi\)
0.524949 + 0.851134i \(0.324084\pi\)
\(264\) 57.2567i 0.216881i
\(265\) 213.767 58.4206i 0.806668 0.220455i
\(266\) 404.088 1.51913
\(267\) 42.8853 + 42.8853i 0.160619 + 0.160619i
\(268\) 29.2279 29.2279i 0.109059 0.109059i
\(269\) 252.246i 0.937718i 0.883273 + 0.468859i \(0.155335\pi\)
−0.883273 + 0.468859i \(0.844665\pi\)
\(270\) −18.2126 + 31.9108i −0.0674540 + 0.118188i
\(271\) 468.292 1.72802 0.864008 0.503478i \(-0.167947\pi\)
0.864008 + 0.503478i \(0.167947\pi\)
\(272\) −11.0622 11.0622i −0.0406697 0.0406697i
\(273\) 237.207 237.207i 0.868890 0.868890i
\(274\) 119.362i 0.435627i
\(275\) 148.605 + 251.574i 0.540382 + 0.914816i
\(276\) 16.6132 0.0601929
\(277\) 338.293 + 338.293i 1.22127 + 1.22127i 0.967180 + 0.254093i \(0.0817771\pi\)
0.254093 + 0.967180i \(0.418223\pi\)
\(278\) −75.7410 + 75.7410i −0.272450 + 0.272450i
\(279\) 83.8475i 0.300529i
\(280\) −103.114 58.8503i −0.368263 0.210180i
\(281\) −49.4745 −0.176066 −0.0880330 0.996118i \(-0.528058\pi\)
−0.0880330 + 0.996118i \(0.528058\pi\)
\(282\) −75.2258 75.2258i −0.266758 0.266758i
\(283\) −29.5290 + 29.5290i −0.104343 + 0.104343i −0.757351 0.653008i \(-0.773507\pi\)
0.653008 + 0.757351i \(0.273507\pi\)
\(284\) 151.917i 0.534919i
\(285\) −77.7045 284.329i −0.272647 0.997645i
\(286\) −381.319 −1.33328
\(287\) 395.786 + 395.786i 1.37904 + 1.37904i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 273.704i 0.947071i
\(290\) 389.704 106.503i 1.34381 0.367250i
\(291\) 15.6557 0.0537995
\(292\) 154.638 + 154.638i 0.529581 + 0.529581i
\(293\) 131.570 131.570i 0.449045 0.449045i −0.445992 0.895037i \(-0.647149\pi\)
0.895037 + 0.445992i \(0.147149\pi\)
\(294\) 52.6121i 0.178953i
\(295\) 84.8624 148.690i 0.287669 0.504035i
\(296\) −47.9548 −0.162010
\(297\) −42.9425 42.9425i −0.144588 0.144588i
\(298\) −122.794 + 122.794i −0.412062 + 0.412062i
\(299\) 110.641i 0.370037i
\(300\) −21.5806 + 83.8706i −0.0719352 + 0.279569i
\(301\) −559.569 −1.85903
\(302\) −97.6700 97.6700i −0.323410 0.323410i
\(303\) −39.4027 + 39.4027i −0.130042 + 0.130042i
\(304\) 136.142i 0.447835i
\(305\) 258.205 + 147.366i 0.846573 + 0.483167i
\(306\) 16.5932 0.0542262
\(307\) −244.537 244.537i −0.796538 0.796538i 0.186010 0.982548i \(-0.440444\pi\)
−0.982548 + 0.186010i \(0.940444\pi\)
\(308\) 138.760 138.760i 0.450520 0.450520i
\(309\) 167.775i 0.542961i
\(310\) 52.1000 + 190.639i 0.168065 + 0.614966i
\(311\) 292.121 0.939297 0.469648 0.882853i \(-0.344381\pi\)
0.469648 + 0.882853i \(0.344381\pi\)
\(312\) −79.9177 79.9177i −0.256147 0.256147i
\(313\) 221.693 221.693i 0.708286 0.708286i −0.257889 0.966175i \(-0.583027\pi\)
0.966175 + 0.257889i \(0.0830269\pi\)
\(314\) 16.5016i 0.0525528i
\(315\) 121.473 33.1974i 0.385628 0.105389i
\(316\) 283.349 0.896674
\(317\) −270.588 270.588i −0.853591 0.853591i 0.136982 0.990573i \(-0.456260\pi\)
−0.990573 + 0.136982i \(0.956260\pi\)
\(318\) −76.7667 + 76.7667i −0.241405 + 0.241405i
\(319\) 667.746i 2.09325i
\(320\) −19.8273 + 34.7401i −0.0619604 + 0.108563i
\(321\) 54.6505 0.170251
\(322\) −40.2618 40.2618i −0.125037 0.125037i
\(323\) −94.1264 + 94.1264i −0.291413 + 0.291413i
\(324\) 18.0000i 0.0555556i
\(325\) −558.562 143.723i −1.71865 0.442223i
\(326\) 393.649 1.20751
\(327\) 233.153 + 233.153i 0.713005 + 0.713005i
\(328\) 133.345 133.345i 0.406539 0.406539i
\(329\) 364.616i 1.10825i
\(330\) −124.319 70.9530i −0.376724 0.215009i
\(331\) −279.894 −0.845601 −0.422801 0.906223i \(-0.638953\pi\)
−0.422801 + 0.906223i \(0.638953\pi\)
\(332\) −149.891 149.891i −0.451477 0.451477i
\(333\) 35.9661 35.9661i 0.108006 0.108006i
\(334\) 66.2064i 0.198223i
\(335\) 27.2418 + 99.6806i 0.0813189 + 0.297554i
\(336\) 58.1634 0.173105
\(337\) 291.255 + 291.255i 0.864258 + 0.864258i 0.991829 0.127571i \(-0.0407181\pi\)
−0.127571 + 0.991829i \(0.540718\pi\)
\(338\) 363.237 363.237i 1.07467 1.07467i
\(339\) 151.288i 0.446276i
\(340\) 37.7271 10.3105i 0.110962 0.0303249i
\(341\) −326.655 −0.957933
\(342\) 102.106 + 102.106i 0.298557 + 0.298557i
\(343\) −163.374 + 163.374i −0.476308 + 0.476308i
\(344\) 188.525i 0.548038i
\(345\) −20.5873 + 36.0717i −0.0596733 + 0.104556i
\(346\) −259.418 −0.749764
\(347\) −126.085 126.085i −0.363356 0.363356i 0.501691 0.865047i \(-0.332711\pi\)
−0.865047 + 0.501691i \(0.832711\pi\)
\(348\) −139.948 + 139.948i −0.402149 + 0.402149i
\(349\) 370.710i 1.06221i −0.847307 0.531104i \(-0.821777\pi\)
0.847307 0.531104i \(-0.178223\pi\)
\(350\) 255.558 150.958i 0.730167 0.431310i
\(351\) 119.877 0.341529
\(352\) −46.7499 46.7499i −0.132812 0.132812i
\(353\) −115.425 + 115.425i −0.326984 + 0.326984i −0.851439 0.524454i \(-0.824269\pi\)
0.524454 + 0.851439i \(0.324269\pi\)
\(354\) 83.8719i 0.236926i
\(355\) −329.851 188.257i −0.929158 0.530301i
\(356\) −70.0315 −0.196718
\(357\) −40.2133 40.2133i −0.112642 0.112642i
\(358\) −117.226 + 117.226i −0.327447 + 0.327447i
\(359\) 201.226i 0.560518i 0.959924 + 0.280259i \(0.0904204\pi\)
−0.959924 + 0.280259i \(0.909580\pi\)
\(360\) −11.1846 40.9256i −0.0310683 0.113682i
\(361\) −797.412 −2.20890
\(362\) −84.0690 84.0690i −0.232235 0.232235i
\(363\) 19.1023 19.1023i 0.0526234 0.0526234i
\(364\) 387.357i 1.06417i
\(365\) −527.386 + 144.130i −1.44489 + 0.394876i
\(366\) −145.646 −0.397940
\(367\) −121.905 121.905i −0.332167 0.332167i 0.521242 0.853409i \(-0.325469\pi\)
−0.853409 + 0.521242i \(0.825469\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 200.017i 0.542052i
\(370\) 59.4260 104.122i 0.160611 0.281412i
\(371\) 372.084 1.00292
\(372\) −68.4612 68.4612i −0.184035 0.184035i
\(373\) 190.337 190.337i 0.510288 0.510288i −0.404327 0.914615i \(-0.632494\pi\)
0.914615 + 0.404327i \(0.132494\pi\)
\(374\) 64.6443i 0.172846i
\(375\) −155.362 150.790i −0.414298 0.402107i
\(376\) 122.843 0.326711
\(377\) −932.027 932.027i −2.47222 2.47222i
\(378\) −43.6226 + 43.6226i −0.115404 + 0.115404i
\(379\) 8.74600i 0.0230765i 0.999933 + 0.0115383i \(0.00367282\pi\)
−0.999933 + 0.0115383i \(0.996327\pi\)
\(380\) 295.599 + 168.708i 0.777892 + 0.443969i
\(381\) −87.3536 −0.229275
\(382\) 29.5286 + 29.5286i 0.0772999 + 0.0772999i
\(383\) 4.52817 4.52817i 0.0118229 0.0118229i −0.701171 0.712994i \(-0.747339\pi\)
0.712994 + 0.701171i \(0.247339\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 129.331 + 473.237i 0.335926 + 1.22919i
\(386\) 42.7956 0.110869
\(387\) −141.394 141.394i −0.365359 0.365359i
\(388\) −12.7828 + 12.7828i −0.0329454 + 0.0329454i
\(389\) 647.329i 1.66408i −0.554713 0.832042i \(-0.687172\pi\)
0.554713 0.832042i \(-0.312828\pi\)
\(390\) 272.557 74.4873i 0.698863 0.190993i
\(391\) 18.7568 0.0479713
\(392\) −42.9576 42.9576i −0.109586 0.109586i
\(393\) −66.7412 + 66.7412i −0.169825 + 0.169825i
\(394\) 127.399i 0.323348i
\(395\) −351.128 + 615.224i −0.888932 + 1.55753i
\(396\) 70.1248 0.177083
\(397\) −457.813 457.813i −1.15318 1.15318i −0.985911 0.167272i \(-0.946504\pi\)
−0.167272 0.985911i \(-0.553496\pi\)
\(398\) −270.574 + 270.574i −0.679834 + 0.679834i
\(399\) 494.905i 1.24036i
\(400\) −50.8596 86.1005i −0.127149 0.215251i
\(401\) −419.534 −1.04622 −0.523109 0.852266i \(-0.675228\pi\)
−0.523109 + 0.852266i \(0.675228\pi\)
\(402\) −35.7967 35.7967i −0.0890464 0.0890464i
\(403\) 455.939 455.939i 1.13136 1.13136i
\(404\) 64.3444i 0.159268i
\(405\) 39.0826 + 22.3058i 0.0965004 + 0.0550759i
\(406\) 678.321 1.67074
\(407\) 140.118 + 140.118i 0.344269 + 0.344269i
\(408\) −13.5483 + 13.5483i −0.0332067 + 0.0332067i
\(409\) 168.996i 0.413194i 0.978426 + 0.206597i \(0.0662389\pi\)
−0.978426 + 0.206597i \(0.933761\pi\)
\(410\) 124.284 + 454.768i 0.303132 + 1.10919i
\(411\) −146.188 −0.355688
\(412\) −136.988 136.988i −0.332494 0.332494i
\(413\) 203.261 203.261i 0.492159 0.492159i
\(414\) 20.3470i 0.0491473i
\(415\) 511.197 139.705i 1.23180 0.336640i
\(416\) 130.505 0.313714
\(417\) 92.7634 + 92.7634i 0.222454 + 0.222454i
\(418\) −397.788 + 397.788i −0.951647 + 0.951647i
\(419\) 688.224i 1.64254i 0.570540 + 0.821270i \(0.306734\pi\)
−0.570540 + 0.821270i \(0.693266\pi\)
\(420\) −72.0766 + 126.288i −0.171611 + 0.300685i
\(421\) −4.67524 −0.0111051 −0.00555255 0.999985i \(-0.501767\pi\)
−0.00555255 + 0.999985i \(0.501767\pi\)
\(422\) −344.189 344.189i −0.815614 0.815614i
\(423\) −92.1324 + 92.1324i −0.217807 + 0.217807i
\(424\) 125.359i 0.295659i
\(425\) −24.3650 + 94.6921i −0.0573295 + 0.222805i
\(426\) 186.060 0.436760
\(427\) 352.969 + 352.969i 0.826626 + 0.826626i
\(428\) −44.6219 + 44.6219i −0.104257 + 0.104257i
\(429\) 467.018i 1.08862i
\(430\) −409.337 233.622i −0.951946 0.543307i
\(431\) −273.490 −0.634549 −0.317274 0.948334i \(-0.602768\pi\)
−0.317274 + 0.948334i \(0.602768\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) 559.711 559.711i 1.29264 1.29264i 0.359484 0.933151i \(-0.382953\pi\)
0.933151 0.359484i \(-0.117047\pi\)
\(434\) 331.828i 0.764581i
\(435\) −130.438 477.288i −0.299859 1.09721i
\(436\) −380.736 −0.873249
\(437\) 115.420 + 115.420i 0.264119 + 0.264119i
\(438\) 189.392 189.392i 0.432401 0.432401i
\(439\) 331.061i 0.754126i 0.926188 + 0.377063i \(0.123066\pi\)
−0.926188 + 0.377063i \(0.876934\pi\)
\(440\) 159.439 43.5732i 0.362361 0.0990300i
\(441\) 64.4364 0.146114
\(442\) −90.2292 90.2292i −0.204138 0.204138i
\(443\) −302.093 + 302.093i −0.681926 + 0.681926i −0.960434 0.278508i \(-0.910160\pi\)
0.278508 + 0.960434i \(0.410160\pi\)
\(444\) 58.7324i 0.132280i
\(445\) 86.7836 152.056i 0.195019 0.341700i
\(446\) 93.3678 0.209345
\(447\) 150.392 + 150.392i 0.336447 + 0.336447i
\(448\) −47.4902 + 47.4902i −0.106005 + 0.106005i
\(449\) 49.8135i 0.110943i 0.998460 + 0.0554716i \(0.0176662\pi\)
−0.998460 + 0.0554716i \(0.982334\pi\)
\(450\) 102.720 + 26.4307i 0.228267 + 0.0587349i
\(451\) −779.231 −1.72779
\(452\) −123.526 123.526i −0.273287 0.273287i
\(453\) −119.621 + 119.621i −0.264064 + 0.264064i
\(454\) 538.032i 1.18509i
\(455\) −841.053 480.016i −1.84847 1.05498i
\(456\) −166.739 −0.365656
\(457\) 599.809 + 599.809i 1.31249 + 1.31249i 0.919573 + 0.392919i \(0.128535\pi\)
0.392919 + 0.919573i \(0.371465\pi\)
\(458\) 149.901 149.901i 0.327294 0.327294i
\(459\) 20.3225i 0.0442755i
\(460\) −12.6429 46.2618i −0.0274847 0.100569i
\(461\) −42.9308 −0.0931255 −0.0465627 0.998915i \(-0.514827\pi\)
−0.0465627 + 0.998915i \(0.514827\pi\)
\(462\) −169.946 169.946i −0.367848 0.367848i
\(463\) −94.7288 + 94.7288i −0.204598 + 0.204598i −0.801967 0.597369i \(-0.796213\pi\)
0.597369 + 0.801967i \(0.296213\pi\)
\(464\) 228.534i 0.492530i
\(465\) 233.485 63.8093i 0.502118 0.137224i
\(466\) 282.010 0.605172
\(467\) 242.603 + 242.603i 0.519493 + 0.519493i 0.917418 0.397925i \(-0.130270\pi\)
−0.397925 + 0.917418i \(0.630270\pi\)
\(468\) −97.8788 + 97.8788i −0.209143 + 0.209143i
\(469\) 173.505i 0.369946i
\(470\) −152.228 + 266.724i −0.323890 + 0.567498i
\(471\) −20.2102 −0.0429092
\(472\) −68.4811 68.4811i −0.145087 0.145087i
\(473\) 550.845 550.845i 1.16458 1.16458i
\(474\) 347.030i 0.732131i
\(475\) −732.618 + 432.757i −1.54235 + 0.911068i
\(476\) 65.6680 0.137958
\(477\) 94.0196 + 94.0196i 0.197106 + 0.197106i
\(478\) 264.006 264.006i 0.552315 0.552315i
\(479\) 246.825i 0.515291i 0.966239 + 0.257646i \(0.0829467\pi\)
−0.966239 + 0.257646i \(0.917053\pi\)
\(480\) 42.5478 + 24.2834i 0.0886412 + 0.0505905i
\(481\) −391.147 −0.813195
\(482\) 193.299 + 193.299i 0.401035 + 0.401035i
\(483\) −49.3104 + 49.3104i −0.102092 + 0.102092i
\(484\) 31.1939i 0.0644502i
\(485\) −11.9142 43.5953i −0.0245654 0.0898872i
\(486\) −22.0454 −0.0453609
\(487\) 110.009 + 110.009i 0.225890 + 0.225890i 0.810973 0.585083i \(-0.198938\pi\)
−0.585083 + 0.810973i \(0.698938\pi\)
\(488\) 118.919 118.919i 0.243687 0.243687i
\(489\) 482.119i 0.985929i
\(490\) 146.505 40.0386i 0.298991 0.0817115i
\(491\) −269.756 −0.549400 −0.274700 0.961530i \(-0.588579\pi\)
−0.274700 + 0.961530i \(0.588579\pi\)
\(492\) −163.313 163.313i −0.331938 0.331938i
\(493\) −158.005 + 158.005i −0.320497 + 0.320497i
\(494\) 1110.45i 2.24788i
\(495\) −86.8993 + 152.259i −0.175554 + 0.307594i
\(496\) 111.797 0.225397
\(497\) −450.911 450.911i −0.907266 0.907266i
\(498\) −183.578 + 183.578i −0.368630 + 0.368630i
\(499\) 349.467i 0.700334i 0.936687 + 0.350167i \(0.113875\pi\)
−0.936687 + 0.350167i \(0.886125\pi\)
\(500\) 249.972 3.73284i 0.499944 0.00746568i
\(501\) −81.0859 −0.161848
\(502\) 408.680 + 408.680i 0.814104 + 0.814104i
\(503\) −343.643 + 343.643i −0.683187 + 0.683187i −0.960717 0.277530i \(-0.910484\pi\)
0.277530 + 0.960717i \(0.410484\pi\)
\(504\) 71.2353i 0.141340i
\(505\) 139.708 + 79.7361i 0.276650 + 0.157893i
\(506\) 79.2683 0.156657
\(507\) −444.873 444.873i −0.877461 0.877461i
\(508\) 71.3239 71.3239i 0.140401 0.140401i
\(509\) 603.575i 1.18581i 0.805274 + 0.592903i \(0.202018\pi\)
−0.805274 + 0.592903i \(0.797982\pi\)
\(510\) −12.6277 46.2061i −0.0247602 0.0906001i
\(511\) −917.971 −1.79642
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 125.054 125.054i 0.243770 0.243770i
\(514\) 53.6559i 0.104389i
\(515\) 467.192 127.679i 0.907169 0.247921i
\(516\) 230.895 0.447471
\(517\) −358.931 358.931i −0.694258 0.694258i
\(518\) 142.337 142.337i 0.274781 0.274781i
\(519\) 317.721i 0.612180i
\(520\) −161.723 + 283.360i −0.311006 + 0.544924i
\(521\) −572.281 −1.09843 −0.549214 0.835681i \(-0.685073\pi\)
−0.549214 + 0.835681i \(0.685073\pi\)
\(522\) 171.401 + 171.401i 0.328353 + 0.328353i
\(523\) 360.248 360.248i 0.688810 0.688810i −0.273159 0.961969i \(-0.588069\pi\)
0.961969 + 0.273159i \(0.0880685\pi\)
\(524\) 108.988i 0.207992i
\(525\) −184.885 312.994i −0.352163 0.596179i
\(526\) −171.573 −0.326185
\(527\) −77.2945 77.2945i −0.146669 0.146669i
\(528\) −57.2567 + 57.2567i −0.108441 + 0.108441i
\(529\) 23.0000i 0.0434783i
\(530\) 272.188 + 155.346i 0.513562 + 0.293107i
\(531\) 102.722 0.193449
\(532\) 404.088 + 404.088i 0.759564 + 0.759564i
\(533\) 1087.64 1087.64i 2.04059 2.04059i
\(534\) 85.7707i 0.160619i
\(535\) −41.5899 152.182i −0.0777381 0.284452i
\(536\) 58.4557 0.109059
\(537\) 143.572 + 143.572i 0.267359 + 0.267359i
\(538\) −252.246 + 252.246i −0.468859 + 0.468859i
\(539\) 251.033i 0.465738i
\(540\) −50.1234 + 13.6983i −0.0928211 + 0.0253672i
\(541\) 536.996 0.992598 0.496299 0.868152i \(-0.334692\pi\)
0.496299 + 0.868152i \(0.334692\pi\)
\(542\) 468.292 + 468.292i 0.864008 + 0.864008i
\(543\) −102.963 + 102.963i −0.189619 + 0.189619i
\(544\) 22.1243i 0.0406697i
\(545\) 471.812 826.677i 0.865710 1.51684i
\(546\) 474.414 0.868890
\(547\) 332.299 + 332.299i 0.607493 + 0.607493i 0.942290 0.334797i \(-0.108668\pi\)
−0.334797 + 0.942290i \(0.608668\pi\)
\(548\) 119.362 119.362i 0.217814 0.217814i
\(549\) 178.379i 0.324917i
\(550\) −102.969 + 400.179i −0.187217 + 0.727599i
\(551\) −1944.56 −3.52916
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) −841.019 + 841.019i −1.52083 + 1.52083i
\(554\) 676.585i 1.22127i
\(555\) −127.523 72.7817i −0.229772 0.131138i
\(556\) −151.482 −0.272450
\(557\) −466.722 466.722i −0.837921 0.837921i 0.150664 0.988585i \(-0.451859\pi\)
−0.988585 + 0.150664i \(0.951859\pi\)
\(558\) −83.8475 + 83.8475i −0.150264 + 0.150264i
\(559\) 1537.72i 2.75084i
\(560\) −44.2633 161.964i −0.0790415 0.289221i
\(561\) 79.1728 0.141128
\(562\) −49.4745 49.4745i −0.0880330 0.0880330i
\(563\) −575.407 + 575.407i −1.02204 + 1.02204i −0.0222862 + 0.999752i \(0.507095\pi\)
−0.999752 + 0.0222862i \(0.992905\pi\)
\(564\) 150.452i 0.266758i
\(565\) 421.281 115.132i 0.745629 0.203774i
\(566\) −59.0580 −0.104343
\(567\) 53.4265 + 53.4265i 0.0942266 + 0.0942266i
\(568\) −151.917 + 151.917i −0.267460 + 0.267460i
\(569\) 90.6448i 0.159305i −0.996823 0.0796527i \(-0.974619\pi\)
0.996823 0.0796527i \(-0.0253811\pi\)
\(570\) 206.624 362.033i 0.362499 0.635146i
\(571\) 876.900 1.53573 0.767863 0.640614i \(-0.221320\pi\)
0.767863 + 0.640614i \(0.221320\pi\)
\(572\) −381.319 381.319i −0.666641 0.666641i
\(573\) 36.1649 36.1649i 0.0631151 0.0631151i
\(574\) 791.572i 1.37904i
\(575\) 116.114 + 29.8769i 0.201937 + 0.0519599i
\(576\) −24.0000 −0.0416667
\(577\) −570.461 570.461i −0.988668 0.988668i 0.0112686 0.999937i \(-0.496413\pi\)
−0.999937 + 0.0112686i \(0.996413\pi\)
\(578\) 273.704 273.704i 0.473536 0.473536i
\(579\) 52.4137i 0.0905245i
\(580\) 496.206 + 283.201i 0.855528 + 0.488278i
\(581\) 889.792 1.53148
\(582\) 15.6557 + 15.6557i 0.0268998 + 0.0268998i
\(583\) −366.284 + 366.284i −0.628274 + 0.628274i
\(584\) 309.275i 0.529581i
\(585\) −91.2280 333.812i −0.155945 0.570620i
\(586\) 263.140 0.449045
\(587\) −476.810 476.810i −0.812283 0.812283i 0.172693 0.984976i \(-0.444753\pi\)
−0.984976 + 0.172693i \(0.944753\pi\)
\(588\) −52.6121 + 52.6121i −0.0894764 + 0.0894764i
\(589\) 951.263i 1.61505i
\(590\) 233.553 63.8278i 0.395852 0.108183i
\(591\) −156.031 −0.264013
\(592\) −47.9548 47.9548i −0.0810048 0.0810048i
\(593\) −464.944 + 464.944i −0.784053 + 0.784053i −0.980512 0.196459i \(-0.937056\pi\)
0.196459 + 0.980512i \(0.437056\pi\)
\(594\) 85.8850i 0.144588i
\(595\) −81.3764 + 142.582i −0.136767 + 0.239634i
\(596\) −245.589 −0.412062
\(597\) 331.384 + 331.384i 0.555082 + 0.555082i
\(598\) −110.641 + 110.641i −0.185019 + 0.185019i
\(599\) 1081.33i 1.80523i 0.430445 + 0.902617i \(0.358357\pi\)
−0.430445 + 0.902617i \(0.641643\pi\)
\(600\) −105.451 + 62.2900i −0.175752 + 0.103817i
\(601\) 486.380 0.809285 0.404642 0.914475i \(-0.367396\pi\)
0.404642 + 0.914475i \(0.367396\pi\)
\(602\) −559.569 559.569i −0.929516 0.929516i
\(603\) −43.8418 + 43.8418i −0.0727061 + 0.0727061i
\(604\) 195.340i 0.323410i
\(605\) −67.7300 38.6557i −0.111950 0.0638938i
\(606\) −78.8054 −0.130042
\(607\) 476.578 + 476.578i 0.785136 + 0.785136i 0.980693 0.195556i \(-0.0626512\pi\)
−0.195556 + 0.980693i \(0.562651\pi\)
\(608\) 136.142 136.142i 0.223917 0.223917i
\(609\) 830.770i 1.36415i
\(610\) 110.839 + 405.571i 0.181703 + 0.664870i
\(611\) 1001.98 1.63990
\(612\) 16.5932 + 16.5932i 0.0271131 + 0.0271131i
\(613\) −65.0705 + 65.0705i −0.106151 + 0.106151i −0.758187 0.652037i \(-0.773915\pi\)
0.652037 + 0.758187i \(0.273915\pi\)
\(614\) 489.074i 0.796538i
\(615\) 556.975 152.216i 0.905650 0.247506i
\(616\) 277.520 0.450520
\(617\) −573.526 573.526i −0.929539 0.929539i 0.0681366 0.997676i \(-0.478295\pi\)
−0.997676 + 0.0681366i \(0.978295\pi\)
\(618\) −167.775 + 167.775i −0.271481 + 0.271481i
\(619\) 59.7320i 0.0964976i −0.998835 0.0482488i \(-0.984636\pi\)
0.998835 0.0482488i \(-0.0153640\pi\)
\(620\) −138.539 + 242.739i −0.223451 + 0.391515i
\(621\) −24.9199 −0.0401286
\(622\) 292.121 + 292.121i 0.469648 + 0.469648i
\(623\) 207.863 207.863i 0.333649 0.333649i
\(624\) 159.835i 0.256147i
\(625\) −301.663 + 547.380i −0.482660 + 0.875808i
\(626\) 443.387 0.708286
\(627\) 487.189 + 487.189i 0.777016 + 0.777016i
\(628\) 16.5016 16.5016i 0.0262764 0.0262764i
\(629\) 66.3104i 0.105422i
\(630\) 154.670 + 88.2754i 0.245508 + 0.140120i
\(631\) 394.424 0.625077 0.312539 0.949905i \(-0.398821\pi\)
0.312539 + 0.949905i \(0.398821\pi\)
\(632\) 283.349 + 283.349i 0.448337 + 0.448337i
\(633\) −421.544 + 421.544i −0.665946 + 0.665946i
\(634\) 541.177i 0.853591i
\(635\) 66.4775 + 243.248i 0.104689 + 0.383067i
\(636\) −153.533 −0.241405
\(637\) −350.387 350.387i −0.550058 0.550058i
\(638\) −667.746 + 667.746i −1.04662 + 1.04662i
\(639\) 227.876i 0.356613i
\(640\) −54.5675 + 14.9128i −0.0852617 + 0.0233012i
\(641\) 1137.01 1.77381 0.886905 0.461951i \(-0.152850\pi\)
0.886905 + 0.461951i \(0.152850\pi\)
\(642\) 54.6505 + 54.6505i 0.0851254 + 0.0851254i
\(643\) −208.084 + 208.084i −0.323614 + 0.323614i −0.850152 0.526538i \(-0.823490\pi\)
0.526538 + 0.850152i \(0.323490\pi\)
\(644\) 80.5236i 0.125037i
\(645\) −286.127 + 501.333i −0.443608 + 0.777261i
\(646\) −188.253 −0.291413
\(647\) 336.574 + 336.574i 0.520207 + 0.520207i 0.917634 0.397427i \(-0.130097\pi\)
−0.397427 + 0.917634i \(0.630097\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 400.185i 0.616619i
\(650\) −414.840 702.285i −0.638215 1.08044i
\(651\) 406.405 0.624278
\(652\) 393.649 + 393.649i 0.603756 + 0.603756i
\(653\) −29.6916 + 29.6916i −0.0454695 + 0.0454695i −0.729476 0.684006i \(-0.760236\pi\)
0.684006 + 0.729476i \(0.260236\pi\)
\(654\) 466.305i 0.713005i
\(655\) 236.641 + 135.059i 0.361284 + 0.206196i
\(656\) 266.690 0.406539
\(657\) −231.956 231.956i −0.353054 0.353054i
\(658\) −364.616 + 364.616i −0.554127 + 0.554127i
\(659\) 1060.05i 1.60858i 0.594240 + 0.804288i \(0.297453\pi\)
−0.594240 + 0.804288i \(0.702547\pi\)
\(660\) −53.3661 195.272i −0.0808577 0.295867i
\(661\) 339.496 0.513609 0.256805 0.966463i \(-0.417330\pi\)
0.256805 + 0.966463i \(0.417330\pi\)
\(662\) −279.894 279.894i −0.422801 0.422801i
\(663\) −110.508 + 110.508i −0.166678 + 0.166678i
\(664\) 299.781i 0.451477i
\(665\) −1378.13 + 376.630i −2.07237 + 0.566361i
\(666\) 71.9322 0.108006
\(667\) 193.749 + 193.749i 0.290478 + 0.290478i
\(668\) 66.2064 66.2064i 0.0991113 0.0991113i
\(669\) 114.352i 0.170929i
\(670\) −72.4388 + 126.922i −0.108118 + 0.189436i
\(671\) −694.934 −1.03567
\(672\) 58.1634 + 58.1634i 0.0865527 + 0.0865527i
\(673\) −652.029 + 652.029i −0.968839 + 0.968839i −0.999529 0.0306899i \(-0.990230\pi\)
0.0306899 + 0.999529i \(0.490230\pi\)
\(674\) 582.510i 0.864258i
\(675\) 32.3709 125.806i 0.0479568 0.186379i
\(676\) 726.474 1.07467
\(677\) 784.901 + 784.901i 1.15938 + 1.15938i 0.984609 + 0.174771i \(0.0559187\pi\)
0.174771 + 0.984609i \(0.444081\pi\)
\(678\) −151.288 + 151.288i −0.223138 + 0.223138i
\(679\) 75.8822i 0.111756i
\(680\) 48.0376 + 27.4166i 0.0706435 + 0.0403186i
\(681\) 658.952 0.967623
\(682\) −326.655 326.655i −0.478966 0.478966i
\(683\) 726.204 726.204i 1.06326 1.06326i 0.0653967 0.997859i \(-0.479169\pi\)
0.997859 0.0653967i \(-0.0208313\pi\)
\(684\) 204.213i 0.298557i
\(685\) 111.251 + 407.080i 0.162410 + 0.594277i
\(686\) −326.747 −0.476308
\(687\) −183.590 183.590i −0.267234 0.267234i
\(688\) −188.525 + 188.525i −0.274019 + 0.274019i
\(689\) 1022.50i 1.48404i
\(690\) −56.6589 + 15.4844i −0.0821144 + 0.0224411i
\(691\) −41.6811 −0.0603199 −0.0301600 0.999545i \(-0.509602\pi\)
−0.0301600 + 0.999545i \(0.509602\pi\)
\(692\) −259.418 259.418i −0.374882 0.374882i
\(693\) −208.140 + 208.140i −0.300347 + 0.300347i
\(694\) 252.169i 0.363356i
\(695\) 187.718 328.906i 0.270097 0.473247i
\(696\) −279.896 −0.402149
\(697\) −184.385 184.385i −0.264541 0.264541i
\(698\) 370.710 370.710i 0.531104 0.531104i
\(699\) 345.390i 0.494121i
\(700\) 406.517 + 104.600i 0.580738 + 0.149429i
\(701\) 376.669 0.537331 0.268666 0.963234i \(-0.413417\pi\)
0.268666 + 0.963234i \(0.413417\pi\)
\(702\) 119.877 + 119.877i 0.170764 + 0.170764i
\(703\) −408.041 + 408.041i −0.580428 + 0.580428i
\(704\) 93.4998i 0.132812i
\(705\) 326.669 + 186.441i 0.463360 + 0.264455i
\(706\) −230.851 −0.326984
\(707\) 190.983 + 190.983i 0.270132 + 0.270132i
\(708\) −83.8719 + 83.8719i −0.118463 + 0.118463i
\(709\) 34.6689i 0.0488983i −0.999701 0.0244491i \(-0.992217\pi\)
0.999701 0.0244491i \(-0.00778318\pi\)
\(710\) −141.594 518.108i −0.199429 0.729730i
\(711\) −425.023 −0.597782
\(712\) −70.0315 70.0315i −0.0983588 0.0983588i
\(713\) −94.7802 + 94.7802i −0.132932 + 0.132932i
\(714\) 80.4266i 0.112642i
\(715\) 1300.47 355.408i 1.81885 0.497074i
\(716\) −234.452 −0.327447
\(717\) −323.340 323.340i −0.450963 0.450963i
\(718\) −201.226 + 201.226i −0.280259 + 0.280259i
\(719\) 299.243i 0.416194i −0.978108 0.208097i \(-0.933273\pi\)
0.978108 0.208097i \(-0.0667270\pi\)
\(720\) 29.7410 52.1102i 0.0413069 0.0723753i
\(721\) 813.197 1.12787
\(722\) −797.412 797.412i −1.10445 1.10445i
\(723\) 236.742 236.742i 0.327444 0.327444i
\(724\) 168.138i 0.232235i
\(725\) −1229.81 + 726.447i −1.69628 + 1.00200i
\(726\) 38.2046 0.0526234
\(727\) 434.804 + 434.804i 0.598079 + 0.598079i 0.939801 0.341722i \(-0.111010\pi\)
−0.341722 + 0.939801i \(0.611010\pi\)
\(728\) −387.357 + 387.357i −0.532084 + 0.532084i
\(729\) 27.0000i 0.0370370i
\(730\) −671.516 383.256i −0.919885 0.525009i
\(731\) 260.687 0.356617
\(732\) −145.646 145.646i −0.198970 0.198970i
\(733\) 215.359 215.359i 0.293806 0.293806i −0.544776 0.838582i \(-0.683385\pi\)
0.838582 + 0.544776i \(0.183385\pi\)
\(734\) 243.811i 0.332167i
\(735\) −49.0371 179.432i −0.0667171 0.244125i
\(736\) −27.1293 −0.0368605
\(737\) −170.800 170.800i −0.231750 0.231750i
\(738\) −200.017 + 200.017i −0.271026 + 0.271026i
\(739\) 21.9856i 0.0297504i −0.999889 0.0148752i \(-0.995265\pi\)
0.999889 0.0148752i \(-0.00473510\pi\)
\(740\) 163.548 44.6963i 0.221011 0.0604004i
\(741\) −1360.02 −1.83538
\(742\) 372.084 + 372.084i 0.501461 + 0.501461i
\(743\) 229.362 229.362i 0.308697 0.308697i −0.535707 0.844404i \(-0.679955\pi\)
0.844404 + 0.535707i \(0.179955\pi\)
\(744\) 136.922i 0.184035i
\(745\) 304.336 533.237i 0.408504 0.715754i
\(746\) 380.675 0.510288
\(747\) 224.836 + 224.836i 0.300985 + 0.300985i
\(748\) −64.6443 + 64.6443i −0.0864228 + 0.0864228i
\(749\) 264.888i 0.353656i
\(750\) −4.57177 306.152i −0.00609570 0.408203i
\(751\) −433.258 −0.576908 −0.288454 0.957494i \(-0.593141\pi\)
−0.288454 + 0.957494i \(0.593141\pi\)
\(752\) 122.843 + 122.843i 0.163355 + 0.163355i
\(753\) 500.529 500.529i 0.664714 0.664714i
\(754\) 1864.05i 2.47222i
\(755\) 424.133 + 242.067i 0.561766 + 0.320618i
\(756\) −87.2451 −0.115404
\(757\) −707.838 707.838i −0.935057 0.935057i 0.0629594 0.998016i \(-0.479946\pi\)
−0.998016 + 0.0629594i \(0.979946\pi\)
\(758\) −8.74600 + 8.74600i −0.0115383 + 0.0115383i
\(759\) 97.0834i 0.127910i
\(760\) 126.891 + 464.307i 0.166962 + 0.610930i
\(761\) 211.795 0.278311 0.139155 0.990271i \(-0.455561\pi\)
0.139155 + 0.990271i \(0.455561\pi\)
\(762\) −87.3536 87.3536i −0.114637 0.114637i
\(763\) 1130.08 1130.08i 1.48110 1.48110i
\(764\) 59.0571i 0.0772999i
\(765\) −56.5907 + 15.4657i −0.0739747 + 0.0202166i
\(766\) 9.05634 0.0118229
\(767\) −558.571 558.571i −0.728254 0.728254i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 67.3997i 0.0876459i 0.999039 + 0.0438230i \(0.0139538\pi\)
−0.999039 + 0.0438230i \(0.986046\pi\)
\(770\) −343.905 + 602.568i −0.446630 + 0.782556i
\(771\) 65.7148 0.0852332
\(772\) 42.7956 + 42.7956i 0.0554347 + 0.0554347i
\(773\) 994.512 994.512i 1.28656 1.28656i 0.349699 0.936862i \(-0.386284\pi\)
0.936862 0.349699i \(-0.113716\pi\)
\(774\) 282.788i 0.365359i
\(775\) −355.371 601.610i −0.458543 0.776270i
\(776\) −25.5656 −0.0329454
\(777\) −174.326 174.326i −0.224358 0.224358i
\(778\) 647.329 647.329i 0.832042 0.832042i
\(779\) 2269.22i