Properties

Label 690.3.k.b.553.13
Level $690$
Weight $3$
Character 690.553
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
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: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 553.13
Character \(\chi\) \(=\) 690.553
Dual form 690.3.k.b.277.13

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.51369 - 2.15095i) q^{5} -2.44949 q^{6} +(-8.14300 + 8.14300i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.51369 - 2.15095i) q^{5} -2.44949 q^{6} +(-8.14300 + 8.14300i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(6.66464 - 2.36274i) q^{10} -2.98698 q^{11} +(2.44949 - 2.44949i) q^{12} +(-7.61449 - 7.61449i) q^{13} -16.2860i q^{14} +(-2.89375 - 8.16249i) q^{15} -4.00000 q^{16} +(15.0931 - 15.0931i) q^{17} +(-3.00000 - 3.00000i) q^{18} -14.0712i q^{19} +(-4.30191 + 9.02738i) q^{20} -19.9462 q^{21} +(2.98698 - 2.98698i) q^{22} +(3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(15.7468 + 19.4175i) q^{25} +15.2290 q^{26} +(-3.67423 + 3.67423i) q^{27} +(16.2860 + 16.2860i) q^{28} +49.2034i q^{29} +(11.0562 + 5.26874i) q^{30} -5.90652 q^{31} +(4.00000 - 4.00000i) q^{32} +(-3.65829 - 3.65829i) q^{33} +30.1863i q^{34} +(54.2702 - 19.2398i) q^{35} +6.00000 q^{36} +(41.6945 - 41.6945i) q^{37} +(14.0712 + 14.0712i) q^{38} -18.6516i q^{39} +(-4.72547 - 13.3293i) q^{40} -20.3143 q^{41} +(19.9462 - 19.9462i) q^{42} +(-22.1189 - 22.1189i) q^{43} +5.97396i q^{44} +(6.45286 - 13.5411i) q^{45} -6.78233 q^{46} +(60.9689 - 60.9689i) q^{47} +(-4.89898 - 4.89898i) q^{48} -83.6170i q^{49} +(-35.1643 - 3.67068i) q^{50} +36.9705 q^{51} +(-15.2290 + 15.2290i) q^{52} +(63.5049 + 63.5049i) q^{53} -7.34847i q^{54} +(13.4823 + 6.42486i) q^{55} -32.5720 q^{56} +(17.2337 - 17.2337i) q^{57} +(-49.2034 - 49.2034i) q^{58} -15.2382i q^{59} +(-16.3250 + 5.78750i) q^{60} -12.0570 q^{61} +(5.90652 - 5.90652i) q^{62} +(-24.4290 - 24.4290i) q^{63} +8.00000i q^{64} +(17.9910 + 50.7478i) q^{65} +7.31658 q^{66} +(79.9748 - 79.9748i) q^{67} +(-30.1863 - 30.1863i) q^{68} +8.30662i q^{69} +(-35.0304 + 73.5100i) q^{70} +20.4797 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-0.611855 - 0.611855i) q^{73} +83.3890i q^{74} +(-4.49564 + 43.0673i) q^{75} -28.1424 q^{76} +(24.3230 - 24.3230i) q^{77} +(18.6516 + 18.6516i) q^{78} -127.031i q^{79} +(18.0548 + 8.60381i) q^{80} -9.00000 q^{81} +(20.3143 - 20.3143i) q^{82} +(-24.8801 - 24.8801i) q^{83} +39.8924i q^{84} +(-100.590 + 35.6611i) q^{85} +44.2378 q^{86} +(-60.2616 + 60.2616i) q^{87} +(-5.97396 - 5.97396i) q^{88} +87.9111i q^{89} +(7.08821 + 19.9939i) q^{90} +124.010 q^{91} +(6.78233 - 6.78233i) q^{92} +(-7.23398 - 7.23398i) q^{93} +121.938i q^{94} +(-30.2665 + 63.5131i) q^{95} +9.79796 q^{96} +(15.5564 - 15.5564i) q^{97} +(83.6170 + 83.6170i) q^{98} -8.96095i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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
\(5\) −4.51369 2.15095i −0.902738 0.430191i
\(6\) −2.44949 −0.408248
\(7\) −8.14300 + 8.14300i −1.16329 + 1.16329i −0.179535 + 0.983752i \(0.557459\pi\)
−0.983752 + 0.179535i \(0.942541\pi\)
\(8\) 2.00000 + 2.00000i 0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 6.66464 2.36274i 0.666464 0.236274i
\(11\) −2.98698 −0.271544 −0.135772 0.990740i \(-0.543351\pi\)
−0.135772 + 0.990740i \(0.543351\pi\)
\(12\) 2.44949 2.44949i 0.204124 0.204124i
\(13\) −7.61449 7.61449i −0.585730 0.585730i 0.350742 0.936472i \(-0.385929\pi\)
−0.936472 + 0.350742i \(0.885929\pi\)
\(14\) 16.2860i 1.16329i
\(15\) −2.89375 8.16249i −0.192917 0.544166i
\(16\) −4.00000 −0.250000
\(17\) 15.0931 15.0931i 0.887831 0.887831i −0.106483 0.994315i \(-0.533959\pi\)
0.994315 + 0.106483i \(0.0339590\pi\)
\(18\) −3.00000 3.00000i −0.166667 0.166667i
\(19\) 14.0712i 0.740591i −0.928914 0.370295i \(-0.879256\pi\)
0.928914 0.370295i \(-0.120744\pi\)
\(20\) −4.30191 + 9.02738i −0.215095 + 0.451369i
\(21\) −19.9462 −0.949819
\(22\) 2.98698 2.98698i 0.135772 0.135772i
\(23\) 3.39116 + 3.39116i 0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 15.7468 + 19.4175i 0.629872 + 0.776699i
\(26\) 15.2290 0.585730
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 16.2860 + 16.2860i 0.581643 + 0.581643i
\(29\) 49.2034i 1.69667i 0.529462 + 0.848334i \(0.322394\pi\)
−0.529462 + 0.848334i \(0.677606\pi\)
\(30\) 11.0562 + 5.26874i 0.368541 + 0.175625i
\(31\) −5.90652 −0.190533 −0.0952664 0.995452i \(-0.530370\pi\)
−0.0952664 + 0.995452i \(0.530370\pi\)
\(32\) 4.00000 4.00000i 0.125000 0.125000i
\(33\) −3.65829 3.65829i −0.110857 0.110857i
\(34\) 30.1863i 0.887831i
\(35\) 54.2702 19.2398i 1.55058 0.549708i
\(36\) 6.00000 0.166667
\(37\) 41.6945 41.6945i 1.12688 1.12688i 0.136196 0.990682i \(-0.456512\pi\)
0.990682 0.136196i \(-0.0434878\pi\)
\(38\) 14.0712 + 14.0712i 0.370295 + 0.370295i
\(39\) 18.6516i 0.478246i
\(40\) −4.72547 13.3293i −0.118137 0.333232i
\(41\) −20.3143 −0.495470 −0.247735 0.968828i \(-0.579686\pi\)
−0.247735 + 0.968828i \(0.579686\pi\)
\(42\) 19.9462 19.9462i 0.474910 0.474910i
\(43\) −22.1189 22.1189i −0.514393 0.514393i 0.401477 0.915869i \(-0.368497\pi\)
−0.915869 + 0.401477i \(0.868497\pi\)
\(44\) 5.97396i 0.135772i
\(45\) 6.45286 13.5411i 0.143397 0.300913i
\(46\) −6.78233 −0.147442
\(47\) 60.9689 60.9689i 1.29721 1.29721i 0.366984 0.930227i \(-0.380391\pi\)
0.930227 0.366984i \(-0.119609\pi\)
\(48\) −4.89898 4.89898i −0.102062 0.102062i
\(49\) 83.6170i 1.70647i
\(50\) −35.1643 3.67068i −0.703285 0.0734135i
\(51\) 36.9705 0.724911
\(52\) −15.2290 + 15.2290i −0.292865 + 0.292865i
\(53\) 63.5049 + 63.5049i 1.19821 + 1.19821i 0.974703 + 0.223502i \(0.0717490\pi\)
0.223502 + 0.974703i \(0.428251\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 13.4823 + 6.42486i 0.245133 + 0.116816i
\(56\) −32.5720 −0.581643
\(57\) 17.2337 17.2337i 0.302345 0.302345i
\(58\) −49.2034 49.2034i −0.848334 0.848334i
\(59\) 15.2382i 0.258275i −0.991627 0.129137i \(-0.958779\pi\)
0.991627 0.129137i \(-0.0412208\pi\)
\(60\) −16.3250 + 5.78750i −0.272083 + 0.0964583i
\(61\) −12.0570 −0.197655 −0.0988275 0.995105i \(-0.531509\pi\)
−0.0988275 + 0.995105i \(0.531509\pi\)
\(62\) 5.90652 5.90652i 0.0952664 0.0952664i
\(63\) −24.4290 24.4290i −0.387762 0.387762i
\(64\) 8.00000i 0.125000i
\(65\) 17.9910 + 50.7478i 0.276785 + 0.780736i
\(66\) 7.31658 0.110857
\(67\) 79.9748 79.9748i 1.19365 1.19365i 0.217620 0.976033i \(-0.430171\pi\)
0.976033 0.217620i \(-0.0698295\pi\)
\(68\) −30.1863 30.1863i −0.443916 0.443916i
\(69\) 8.30662i 0.120386i
\(70\) −35.0304 + 73.5100i −0.500435 + 1.05014i
\(71\) 20.4797 0.288446 0.144223 0.989545i \(-0.453932\pi\)
0.144223 + 0.989545i \(0.453932\pi\)
\(72\) −6.00000 + 6.00000i −0.0833333 + 0.0833333i
\(73\) −0.611855 0.611855i −0.00838158 0.00838158i 0.702904 0.711285i \(-0.251887\pi\)
−0.711285 + 0.702904i \(0.751887\pi\)
\(74\) 83.3890i 1.12688i
\(75\) −4.49564 + 43.0673i −0.0599419 + 0.574230i
\(76\) −28.1424 −0.370295
\(77\) 24.3230 24.3230i 0.315883 0.315883i
\(78\) 18.6516 + 18.6516i 0.239123 + 0.239123i
\(79\) 127.031i 1.60799i −0.594636 0.803995i \(-0.702704\pi\)
0.594636 0.803995i \(-0.297296\pi\)
\(80\) 18.0548 + 8.60381i 0.225685 + 0.107548i
\(81\) −9.00000 −0.111111
\(82\) 20.3143 20.3143i 0.247735 0.247735i
\(83\) −24.8801 24.8801i −0.299761 0.299761i 0.541159 0.840920i \(-0.317986\pi\)
−0.840920 + 0.541159i \(0.817986\pi\)
\(84\) 39.8924i 0.474910i
\(85\) −100.590 + 35.6611i −1.18342 + 0.419542i
\(86\) 44.2378 0.514393
\(87\) −60.2616 + 60.2616i −0.692662 + 0.692662i
\(88\) −5.97396 5.97396i −0.0678860 0.0678860i
\(89\) 87.9111i 0.987765i 0.869529 + 0.493883i \(0.164423\pi\)
−0.869529 + 0.493883i \(0.835577\pi\)
\(90\) 7.08821 + 19.9939i 0.0787579 + 0.222155i
\(91\) 124.010 1.36274
\(92\) 6.78233 6.78233i 0.0737210 0.0737210i
\(93\) −7.23398 7.23398i −0.0777847 0.0777847i
\(94\) 121.938i 1.29721i
\(95\) −30.2665 + 63.5131i −0.318595 + 0.668559i
\(96\) 9.79796 0.102062
\(97\) 15.5564 15.5564i 0.160375 0.160375i −0.622358 0.782733i \(-0.713825\pi\)
0.782733 + 0.622358i \(0.213825\pi\)
\(98\) 83.6170 + 83.6170i 0.853235 + 0.853235i
\(99\) 8.96095i 0.0905146i
\(100\) 38.8349 31.4936i 0.388349 0.314936i
\(101\) −136.156 −1.34808 −0.674042 0.738693i \(-0.735443\pi\)
−0.674042 + 0.738693i \(0.735443\pi\)
\(102\) −36.9705 + 36.9705i −0.362456 + 0.362456i
\(103\) 23.3277 + 23.3277i 0.226483 + 0.226483i 0.811222 0.584739i \(-0.198803\pi\)
−0.584739 + 0.811222i \(0.698803\pi\)
\(104\) 30.4579i 0.292865i
\(105\) 90.0310 + 42.9034i 0.857438 + 0.408603i
\(106\) −127.010 −1.19821
\(107\) 107.221 107.221i 1.00207 1.00207i 0.00206949 0.999998i \(-0.499341\pi\)
0.999998 0.00206949i \(-0.000658739\pi\)
\(108\) 7.34847 + 7.34847i 0.0680414 + 0.0680414i
\(109\) 59.6007i 0.546796i −0.961901 0.273398i \(-0.911852\pi\)
0.961901 0.273398i \(-0.0881475\pi\)
\(110\) −19.9072 + 7.05745i −0.180974 + 0.0641587i
\(111\) 102.130 0.920092
\(112\) 32.5720 32.5720i 0.290822 0.290822i
\(113\) 144.185 + 144.185i 1.27597 + 1.27597i 0.942901 + 0.333072i \(0.108085\pi\)
0.333072 + 0.942901i \(0.391915\pi\)
\(114\) 34.4673i 0.302345i
\(115\) −8.01243 22.6009i −0.0696733 0.196530i
\(116\) 98.4067 0.848334
\(117\) 22.8435 22.8435i 0.195243 0.195243i
\(118\) 15.2382 + 15.2382i 0.129137 + 0.129137i
\(119\) 245.807i 2.06560i
\(120\) 10.5375 22.1125i 0.0878123 0.184271i
\(121\) −112.078 −0.926264
\(122\) 12.0570 12.0570i 0.0988275 0.0988275i
\(123\) −24.8798 24.8798i −0.202275 0.202275i
\(124\) 11.8130i 0.0952664i
\(125\) −29.3101 121.515i −0.234481 0.972121i
\(126\) 48.8580 0.387762
\(127\) −19.3030 + 19.3030i −0.151992 + 0.151992i −0.779007 0.627015i \(-0.784276\pi\)
0.627015 + 0.779007i \(0.284276\pi\)
\(128\) −8.00000 8.00000i −0.0625000 0.0625000i
\(129\) 54.1800i 0.420000i
\(130\) −68.7389 32.7568i −0.528761 0.251975i
\(131\) −50.6870 −0.386923 −0.193462 0.981108i \(-0.561972\pi\)
−0.193462 + 0.981108i \(0.561972\pi\)
\(132\) −7.31658 + 7.31658i −0.0554287 + 0.0554287i
\(133\) 114.582 + 114.582i 0.861519 + 0.861519i
\(134\) 159.950i 1.19365i
\(135\) 24.4875 8.68125i 0.181389 0.0643056i
\(136\) 60.3725 0.443916
\(137\) 113.943 113.943i 0.831703 0.831703i −0.156047 0.987750i \(-0.549875\pi\)
0.987750 + 0.156047i \(0.0498751\pi\)
\(138\) −8.30662 8.30662i −0.0601929 0.0601929i
\(139\) 205.743i 1.48017i −0.672515 0.740084i \(-0.734786\pi\)
0.672515 0.740084i \(-0.265214\pi\)
\(140\) −38.4796 108.540i −0.274854 0.775289i
\(141\) 149.343 1.05917
\(142\) −20.4797 + 20.4797i −0.144223 + 0.144223i
\(143\) 22.7443 + 22.7443i 0.159051 + 0.159051i
\(144\) 12.0000i 0.0833333i
\(145\) 105.834 222.089i 0.729891 1.53165i
\(146\) 1.22371 0.00838158
\(147\) 102.410 102.410i 0.696664 0.696664i
\(148\) −83.3890 83.3890i −0.563439 0.563439i
\(149\) 51.6051i 0.346343i 0.984892 + 0.173172i \(0.0554015\pi\)
−0.984892 + 0.173172i \(0.944598\pi\)
\(150\) −38.5716 47.5629i −0.257144 0.317086i
\(151\) 113.345 0.750629 0.375314 0.926898i \(-0.377535\pi\)
0.375314 + 0.926898i \(0.377535\pi\)
\(152\) 28.1424 28.1424i 0.185148 0.185148i
\(153\) 45.2794 + 45.2794i 0.295944 + 0.295944i
\(154\) 48.6460i 0.315883i
\(155\) 26.6602 + 12.7046i 0.172001 + 0.0819654i
\(156\) −37.3032 −0.239123
\(157\) −160.914 + 160.914i −1.02493 + 1.02493i −0.0252486 + 0.999681i \(0.508038\pi\)
−0.999681 + 0.0252486i \(0.991962\pi\)
\(158\) 127.031 + 127.031i 0.803995 + 0.803995i
\(159\) 155.555i 0.978331i
\(160\) −26.6586 + 9.45095i −0.166616 + 0.0590684i
\(161\) −55.2285 −0.343034
\(162\) 9.00000 9.00000i 0.0555556 0.0555556i
\(163\) −122.176 122.176i −0.749545 0.749545i 0.224848 0.974394i \(-0.427811\pi\)
−0.974394 + 0.224848i \(0.927811\pi\)
\(164\) 40.6286i 0.247735i
\(165\) 8.64358 + 24.3812i 0.0523853 + 0.147765i
\(166\) 49.7603 0.299761
\(167\) −126.535 + 126.535i −0.757695 + 0.757695i −0.975902 0.218207i \(-0.929979\pi\)
0.218207 + 0.975902i \(0.429979\pi\)
\(168\) −39.8924 39.8924i −0.237455 0.237455i
\(169\) 53.0392i 0.313841i
\(170\) 64.9293 136.251i 0.381937 0.801479i
\(171\) 42.2137 0.246864
\(172\) −44.2378 + 44.2378i −0.257196 + 0.257196i
\(173\) −116.139 116.139i −0.671324 0.671324i 0.286697 0.958021i \(-0.407443\pi\)
−0.958021 + 0.286697i \(0.907443\pi\)
\(174\) 120.523i 0.692662i
\(175\) −286.343 29.8903i −1.63624 0.170802i
\(176\) 11.9479 0.0678860
\(177\) 18.6629 18.6629i 0.105440 0.105440i
\(178\) −87.9111 87.9111i −0.493883 0.493883i
\(179\) 127.573i 0.712696i −0.934353 0.356348i \(-0.884022\pi\)
0.934353 0.356348i \(-0.115978\pi\)
\(180\) −27.0821 12.9057i −0.150456 0.0716984i
\(181\) −321.120 −1.77414 −0.887072 0.461630i \(-0.847265\pi\)
−0.887072 + 0.461630i \(0.847265\pi\)
\(182\) −124.010 + 124.010i −0.681371 + 0.681371i
\(183\) −14.7667 14.7667i −0.0806923 0.0806923i
\(184\) 13.5647i 0.0737210i
\(185\) −277.879 + 98.5131i −1.50205 + 0.532503i
\(186\) 14.4680 0.0777847
\(187\) −45.0829 + 45.0829i −0.241085 + 0.241085i
\(188\) −121.938 121.938i −0.648605 0.648605i
\(189\) 59.8386i 0.316606i
\(190\) −33.2466 93.7797i −0.174982 0.493577i
\(191\) 91.9988 0.481669 0.240835 0.970566i \(-0.422579\pi\)
0.240835 + 0.970566i \(0.422579\pi\)
\(192\) −9.79796 + 9.79796i −0.0510310 + 0.0510310i
\(193\) −73.1687 73.1687i −0.379113 0.379113i 0.491669 0.870782i \(-0.336387\pi\)
−0.870782 + 0.491669i \(0.836387\pi\)
\(194\) 31.1128i 0.160375i
\(195\) −40.1187 + 84.1876i −0.205737 + 0.431731i
\(196\) −167.234 −0.853235
\(197\) 71.2245 71.2245i 0.361546 0.361546i −0.502836 0.864382i \(-0.667710\pi\)
0.864382 + 0.502836i \(0.167710\pi\)
\(198\) 8.96095 + 8.96095i 0.0452573 + 0.0452573i
\(199\) 272.364i 1.36866i 0.729171 + 0.684331i \(0.239906\pi\)
−0.729171 + 0.684331i \(0.760094\pi\)
\(200\) −7.34135 + 70.3285i −0.0367068 + 0.351643i
\(201\) 195.897 0.974614
\(202\) 136.156 136.156i 0.674042 0.674042i
\(203\) −400.663 400.663i −1.97371 1.97371i
\(204\) 73.9410i 0.362456i
\(205\) 91.6924 + 43.6951i 0.447280 + 0.213147i
\(206\) −46.6554 −0.226483
\(207\) −10.1735 + 10.1735i −0.0491473 + 0.0491473i
\(208\) 30.4579 + 30.4579i 0.146432 + 0.146432i
\(209\) 42.0305i 0.201103i
\(210\) −132.934 + 47.1276i −0.633021 + 0.224417i
\(211\) 317.005 1.50239 0.751197 0.660078i \(-0.229477\pi\)
0.751197 + 0.660078i \(0.229477\pi\)
\(212\) 127.010 127.010i 0.599103 0.599103i
\(213\) 25.0824 + 25.0824i 0.117758 + 0.117758i
\(214\) 214.442i 1.00207i
\(215\) 52.2611 + 147.414i 0.243075 + 0.685649i
\(216\) −14.6969 −0.0680414
\(217\) 48.0968 48.0968i 0.221644 0.221644i
\(218\) 59.6007 + 59.6007i 0.273398 + 0.273398i
\(219\) 1.49873i 0.00684353i
\(220\) 12.8497 26.9646i 0.0584078 0.122566i
\(221\) −229.853 −1.04006
\(222\) −102.130 + 102.130i −0.460046 + 0.460046i
\(223\) −16.1528 16.1528i −0.0724339 0.0724339i 0.669962 0.742396i \(-0.266310\pi\)
−0.742396 + 0.669962i \(0.766310\pi\)
\(224\) 65.1440i 0.290822i
\(225\) −58.2524 + 47.2404i −0.258900 + 0.209957i
\(226\) −288.370 −1.27597
\(227\) 219.388 219.388i 0.966466 0.966466i −0.0329895 0.999456i \(-0.510503\pi\)
0.999456 + 0.0329895i \(0.0105028\pi\)
\(228\) −34.4673 34.4673i −0.151172 0.151172i
\(229\) 314.913i 1.37517i 0.726105 + 0.687583i \(0.241328\pi\)
−0.726105 + 0.687583i \(0.758672\pi\)
\(230\) 30.6133 + 14.5885i 0.133101 + 0.0634282i
\(231\) 59.5790 0.257918
\(232\) −98.4067 + 98.4067i −0.424167 + 0.424167i
\(233\) 20.1806 + 20.1806i 0.0866119 + 0.0866119i 0.749085 0.662473i \(-0.230493\pi\)
−0.662473 + 0.749085i \(0.730493\pi\)
\(234\) 45.6869i 0.195243i
\(235\) −406.336 + 144.054i −1.72909 + 0.612994i
\(236\) −30.4764 −0.129137
\(237\) 155.581 155.581i 0.656459 0.656459i
\(238\) −245.807 245.807i −1.03280 1.03280i
\(239\) 363.636i 1.52149i −0.649051 0.760745i \(-0.724834\pi\)
0.649051 0.760745i \(-0.275166\pi\)
\(240\) 11.5750 + 32.6500i 0.0482292 + 0.136041i
\(241\) 53.3378 0.221319 0.110659 0.993858i \(-0.464704\pi\)
0.110659 + 0.993858i \(0.464704\pi\)
\(242\) 112.078 112.078i 0.463132 0.463132i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 24.1139i 0.0988275i
\(245\) −179.856 + 377.421i −0.734108 + 1.54050i
\(246\) 49.7596 0.202275
\(247\) −107.145 + 107.145i −0.433786 + 0.433786i
\(248\) −11.8130 11.8130i −0.0476332 0.0476332i
\(249\) 60.9437i 0.244754i
\(250\) 150.825 + 92.2050i 0.603301 + 0.368820i
\(251\) 165.873 0.660850 0.330425 0.943832i \(-0.392808\pi\)
0.330425 + 0.943832i \(0.392808\pi\)
\(252\) −48.8580 + 48.8580i −0.193881 + 0.193881i
\(253\) −10.1294 10.1294i −0.0400370 0.0400370i
\(254\) 38.6059i 0.151992i
\(255\) −166.873 79.5218i −0.654405 0.311850i
\(256\) 16.0000 0.0625000
\(257\) −256.875 + 256.875i −0.999515 + 0.999515i −1.00000 0.000484450i \(-0.999846\pi\)
0.000484450 1.00000i \(0.499846\pi\)
\(258\) 54.1800 + 54.1800i 0.210000 + 0.210000i
\(259\) 679.037i 2.62176i
\(260\) 101.496 35.9821i 0.390368 0.138393i
\(261\) −147.610 −0.565556
\(262\) 50.6870 50.6870i 0.193462 0.193462i
\(263\) −29.0957 29.0957i −0.110630 0.110630i 0.649625 0.760255i \(-0.274926\pi\)
−0.760255 + 0.649625i \(0.774926\pi\)
\(264\) 14.6332i 0.0554287i
\(265\) −150.045 423.237i −0.566209 1.59712i
\(266\) −229.164 −0.861519
\(267\) −107.669 + 107.669i −0.403253 + 0.403253i
\(268\) −159.950 159.950i −0.596827 0.596827i
\(269\) 92.9336i 0.345478i −0.984968 0.172739i \(-0.944738\pi\)
0.984968 0.172739i \(-0.0552618\pi\)
\(270\) −15.8062 + 33.1687i −0.0585415 + 0.122847i
\(271\) −355.672 −1.31244 −0.656221 0.754568i \(-0.727846\pi\)
−0.656221 + 0.754568i \(0.727846\pi\)
\(272\) −60.3725 + 60.3725i −0.221958 + 0.221958i
\(273\) 151.880 + 151.880i 0.556337 + 0.556337i
\(274\) 227.887i 0.831703i
\(275\) −47.0354 57.9997i −0.171038 0.210908i
\(276\) 16.6132 0.0601929
\(277\) 91.3940 91.3940i 0.329942 0.329942i −0.522622 0.852564i \(-0.675046\pi\)
0.852564 + 0.522622i \(0.175046\pi\)
\(278\) 205.743 + 205.743i 0.740084 + 0.740084i
\(279\) 17.7196i 0.0635109i
\(280\) 147.020 + 70.0609i 0.525071 + 0.250217i
\(281\) 203.040 0.722564 0.361282 0.932457i \(-0.382339\pi\)
0.361282 + 0.932457i \(0.382339\pi\)
\(282\) −149.343 + 149.343i −0.529584 + 0.529584i
\(283\) −127.646 127.646i −0.451046 0.451046i 0.444656 0.895702i \(-0.353326\pi\)
−0.895702 + 0.444656i \(0.853326\pi\)
\(284\) 40.9594i 0.144223i
\(285\) −114.856 + 40.7186i −0.403004 + 0.142872i
\(286\) −45.4887 −0.159051
\(287\) 165.419 165.419i 0.576374 0.576374i
\(288\) 12.0000 + 12.0000i 0.0416667 + 0.0416667i
\(289\) 166.605i 0.576489i
\(290\) 116.255 + 327.923i 0.400878 + 1.13077i
\(291\) 38.1052 0.130946
\(292\) −1.22371 + 1.22371i −0.00419079 + 0.00419079i
\(293\) −19.7725 19.7725i −0.0674828 0.0674828i 0.672560 0.740043i \(-0.265195\pi\)
−0.740043 + 0.672560i \(0.765195\pi\)
\(294\) 204.819i 0.696664i
\(295\) −32.7767 + 68.7806i −0.111107 + 0.233155i
\(296\) 166.778 0.563439
\(297\) 10.9749 10.9749i 0.0369524 0.0369524i
\(298\) −51.6051 51.6051i −0.173172 0.173172i
\(299\) 51.6440i 0.172722i
\(300\) 86.1345 + 8.99128i 0.287115 + 0.0299709i
\(301\) 360.228 1.19677
\(302\) −113.345 + 113.345i −0.375314 + 0.375314i
\(303\) −166.757 166.757i −0.550353 0.550353i
\(304\) 56.2849i 0.185148i
\(305\) 54.4214 + 25.9339i 0.178431 + 0.0850293i
\(306\) −90.5588 −0.295944
\(307\) 22.7462 22.7462i 0.0740918 0.0740918i −0.669090 0.743182i \(-0.733316\pi\)
0.743182 + 0.669090i \(0.233316\pi\)
\(308\) −48.6460 48.6460i −0.157942 0.157942i
\(309\) 57.1410i 0.184922i
\(310\) −39.3648 + 13.9555i −0.126983 + 0.0450179i
\(311\) 58.8069 0.189090 0.0945449 0.995521i \(-0.469860\pi\)
0.0945449 + 0.995521i \(0.469860\pi\)
\(312\) 37.3032 37.3032i 0.119562 0.119562i
\(313\) −321.959 321.959i −1.02862 1.02862i −0.999578 0.0290452i \(-0.990753\pi\)
−0.0290452 0.999578i \(-0.509247\pi\)
\(314\) 321.828i 1.02493i
\(315\) 57.7193 + 162.811i 0.183236 + 0.516859i
\(316\) −254.062 −0.803995
\(317\) 65.2518 65.2518i 0.205842 0.205842i −0.596656 0.802497i \(-0.703504\pi\)
0.802497 + 0.596656i \(0.203504\pi\)
\(318\) −155.555 155.555i −0.489165 0.489165i
\(319\) 146.970i 0.460720i
\(320\) 17.2076 36.1095i 0.0537738 0.112842i
\(321\) 262.637 0.818185
\(322\) 55.2285 55.2285i 0.171517 0.171517i
\(323\) −212.379 212.379i −0.657520 0.657520i
\(324\) 18.0000i 0.0555556i
\(325\) 27.9503 267.758i 0.0860010 0.823870i
\(326\) 244.352 0.749545
\(327\) 72.9957 72.9957i 0.223228 0.223228i
\(328\) −40.6286 40.6286i −0.123868 0.123868i
\(329\) 992.940i 3.01806i
\(330\) −33.0248 15.7376i −0.100075 0.0476898i
\(331\) −498.721 −1.50671 −0.753355 0.657614i \(-0.771566\pi\)
−0.753355 + 0.657614i \(0.771566\pi\)
\(332\) −49.7603 + 49.7603i −0.149880 + 0.149880i
\(333\) 125.083 + 125.083i 0.375626 + 0.375626i
\(334\) 253.070i 0.757695i
\(335\) −533.004 + 188.959i −1.59106 + 0.564058i
\(336\) 79.7848 0.237455
\(337\) 253.715 253.715i 0.752863 0.752863i −0.222149 0.975013i \(-0.571307\pi\)
0.975013 + 0.222149i \(0.0713072\pi\)
\(338\) 53.0392 + 53.0392i 0.156921 + 0.156921i
\(339\) 353.180i 1.04183i
\(340\) 71.3222 + 201.181i 0.209771 + 0.591708i
\(341\) 17.6427 0.0517380
\(342\) −42.2137 + 42.2137i −0.123432 + 0.123432i
\(343\) 281.887 + 281.887i 0.821827 + 0.821827i
\(344\) 88.4755i 0.257196i
\(345\) 17.8672 37.4935i 0.0517889 0.108677i
\(346\) 232.278 0.671324
\(347\) 350.383 350.383i 1.00975 1.00975i 0.00979723 0.999952i \(-0.496881\pi\)
0.999952 0.00979723i \(-0.00311860\pi\)
\(348\) 120.523 + 120.523i 0.346331 + 0.346331i
\(349\) 501.750i 1.43768i −0.695176 0.718840i \(-0.744673\pi\)
0.695176 0.718840i \(-0.255327\pi\)
\(350\) 316.233 256.453i 0.903523 0.732721i
\(351\) 55.9548 0.159415
\(352\) −11.9479 + 11.9479i −0.0339430 + 0.0339430i
\(353\) 83.9266 + 83.9266i 0.237752 + 0.237752i 0.815919 0.578166i \(-0.196232\pi\)
−0.578166 + 0.815919i \(0.696232\pi\)
\(354\) 37.3259i 0.105440i
\(355\) −92.4390 44.0509i −0.260391 0.124087i
\(356\) 175.822 0.493883
\(357\) −301.051 + 301.051i −0.843279 + 0.843279i
\(358\) 127.573 + 127.573i 0.356348 + 0.356348i
\(359\) 68.1546i 0.189846i −0.995485 0.0949228i \(-0.969740\pi\)
0.995485 0.0949228i \(-0.0302604\pi\)
\(360\) 39.9879 14.1764i 0.111077 0.0393789i
\(361\) 163.001 0.451525
\(362\) 321.120 321.120i 0.887072 0.887072i
\(363\) −137.267 137.267i −0.378146 0.378146i
\(364\) 248.019i 0.681371i
\(365\) 1.44565 + 4.07780i 0.00396069 + 0.0111720i
\(366\) 29.5334 0.0806923
\(367\) 91.7002 91.7002i 0.249864 0.249864i −0.571051 0.820915i \(-0.693464\pi\)
0.820915 + 0.571051i \(0.193464\pi\)
\(368\) −13.5647 13.5647i −0.0368605 0.0368605i
\(369\) 60.9428i 0.165157i
\(370\) 179.366 376.392i 0.484772 1.01728i
\(371\) −1034.24 −2.78771
\(372\) −14.4680 + 14.4680i −0.0388924 + 0.0388924i
\(373\) 23.7795 + 23.7795i 0.0637519 + 0.0637519i 0.738264 0.674512i \(-0.235646\pi\)
−0.674512 + 0.738264i \(0.735646\pi\)
\(374\) 90.1659i 0.241085i
\(375\) 112.928 184.722i 0.301140 0.492593i
\(376\) 243.876 0.648605
\(377\) 374.658 374.658i 0.993789 0.993789i
\(378\) 59.8386 + 59.8386i 0.158303 + 0.158303i
\(379\) 178.495i 0.470964i −0.971879 0.235482i \(-0.924333\pi\)
0.971879 0.235482i \(-0.0756669\pi\)
\(380\) 127.026 + 60.5331i 0.334280 + 0.159298i
\(381\) −47.2824 −0.124101
\(382\) −91.9988 + 91.9988i −0.240835 + 0.240835i
\(383\) 111.563 + 111.563i 0.291288 + 0.291288i 0.837589 0.546301i \(-0.183964\pi\)
−0.546301 + 0.837589i \(0.683964\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −162.104 + 57.4689i −0.421050 + 0.149270i
\(386\) 146.337 0.379113
\(387\) 66.3566 66.3566i 0.171464 0.171464i
\(388\) −31.1128 31.1128i −0.0801876 0.0801876i
\(389\) 765.523i 1.96792i 0.178377 + 0.983962i \(0.442915\pi\)
−0.178377 + 0.983962i \(0.557085\pi\)
\(390\) −44.0688 124.306i −0.112997 0.318734i
\(391\) 102.367 0.261807
\(392\) 167.234 167.234i 0.426618 0.426618i
\(393\) −62.0786 62.0786i −0.157961 0.157961i
\(394\) 142.449i 0.361546i
\(395\) −273.238 + 573.380i −0.691742 + 1.45159i
\(396\) −17.9219 −0.0452573
\(397\) −68.4982 + 68.4982i −0.172540 + 0.172540i −0.788094 0.615555i \(-0.788932\pi\)
0.615555 + 0.788094i \(0.288932\pi\)
\(398\) −272.364 272.364i −0.684331 0.684331i
\(399\) 280.668i 0.703427i
\(400\) −62.9872 77.6699i −0.157468 0.194175i
\(401\) 603.687 1.50545 0.752727 0.658333i \(-0.228738\pi\)
0.752727 + 0.658333i \(0.228738\pi\)
\(402\) −195.897 + 195.897i −0.487307 + 0.487307i
\(403\) 44.9751 + 44.9751i 0.111601 + 0.111601i
\(404\) 272.313i 0.674042i
\(405\) 40.6232 + 19.3586i 0.100304 + 0.0477990i
\(406\) 801.326 1.97371
\(407\) −124.541 + 124.541i −0.305997 + 0.305997i
\(408\) 73.9410 + 73.9410i 0.181228 + 0.181228i
\(409\) 410.613i 1.00394i 0.864884 + 0.501972i \(0.167392\pi\)
−0.864884 + 0.501972i \(0.832608\pi\)
\(410\) −135.387 + 47.9973i −0.330213 + 0.117067i
\(411\) 279.103 0.679082
\(412\) 46.6554 46.6554i 0.113241 0.113241i
\(413\) 124.085 + 124.085i 0.300448 + 0.300448i
\(414\) 20.3470i 0.0491473i
\(415\) 58.7852 + 165.817i 0.141651 + 0.399560i
\(416\) −60.9159 −0.146432
\(417\) 251.983 251.983i 0.604276 0.604276i
\(418\) −42.0305 42.0305i −0.100551 0.100551i
\(419\) 426.786i 1.01858i −0.860594 0.509292i \(-0.829907\pi\)
0.860594 0.509292i \(-0.170093\pi\)
\(420\) 85.8067 180.062i 0.204302 0.428719i
\(421\) 589.186 1.39949 0.699746 0.714392i \(-0.253297\pi\)
0.699746 + 0.714392i \(0.253297\pi\)
\(422\) −317.005 + 317.005i −0.751197 + 0.751197i
\(423\) 182.907 + 182.907i 0.432404 + 0.432404i
\(424\) 254.020i 0.599103i
\(425\) 530.739 + 55.4020i 1.24880 + 0.130358i
\(426\) −50.1648 −0.117758
\(427\) 98.1798 98.1798i 0.229929 0.229929i
\(428\) −214.442 214.442i −0.501034 0.501034i
\(429\) 55.7120i 0.129865i
\(430\) −199.676 95.1534i −0.464362 0.221287i
\(431\) 507.800 1.17819 0.589095 0.808064i \(-0.299484\pi\)
0.589095 + 0.808064i \(0.299484\pi\)
\(432\) 14.6969 14.6969i 0.0340207 0.0340207i
\(433\) 97.8860 + 97.8860i 0.226065 + 0.226065i 0.811046 0.584982i \(-0.198898\pi\)
−0.584982 + 0.811046i \(0.698898\pi\)
\(434\) 96.1936i 0.221644i
\(435\) 401.622 142.382i 0.923269 0.327315i
\(436\) −119.201 −0.273398
\(437\) 47.7178 47.7178i 0.109194 0.109194i
\(438\) 1.49873 + 1.49873i 0.00342176 + 0.00342176i
\(439\) 45.5200i 0.103690i 0.998655 + 0.0518451i \(0.0165102\pi\)
−0.998655 + 0.0518451i \(0.983490\pi\)
\(440\) 14.1149 + 39.8143i 0.0320793 + 0.0904872i
\(441\) 250.851 0.568823
\(442\) 229.853 229.853i 0.520029 0.520029i
\(443\) −204.022 204.022i −0.460547 0.460547i 0.438288 0.898835i \(-0.355585\pi\)
−0.898835 + 0.438288i \(0.855585\pi\)
\(444\) 204.260i 0.460046i
\(445\) 189.093 396.803i 0.424927 0.891693i
\(446\) 32.3055 0.0724339
\(447\) −63.2031 + 63.2031i −0.141394 + 0.141394i
\(448\) −65.1440 65.1440i −0.145411 0.145411i
\(449\) 699.112i 1.55704i −0.627618 0.778521i \(-0.715970\pi\)
0.627618 0.778521i \(-0.284030\pi\)
\(450\) 11.0120 105.493i 0.0244712 0.234428i
\(451\) 60.6784 0.134542
\(452\) 288.370 288.370i 0.637987 0.637987i
\(453\) 138.819 + 138.819i 0.306443 + 0.306443i
\(454\) 438.776i 0.966466i
\(455\) −559.741 266.739i −1.23020 0.586239i
\(456\) 68.9346 0.151172
\(457\) 175.228 175.228i 0.383432 0.383432i −0.488905 0.872337i \(-0.662604\pi\)
0.872337 + 0.488905i \(0.162604\pi\)
\(458\) −314.913 314.913i −0.687583 0.687583i
\(459\) 110.911i 0.241637i
\(460\) −45.2018 + 16.0249i −0.0982648 + 0.0348367i
\(461\) 233.765 0.507083 0.253542 0.967324i \(-0.418405\pi\)
0.253542 + 0.967324i \(0.418405\pi\)
\(462\) −59.5790 + 59.5790i −0.128959 + 0.128959i
\(463\) 295.945 + 295.945i 0.639190 + 0.639190i 0.950356 0.311166i \(-0.100719\pi\)
−0.311166 + 0.950356i \(0.600719\pi\)
\(464\) 196.813i 0.424167i
\(465\) 17.0920 + 48.2119i 0.0367570 + 0.103681i
\(466\) −40.3611 −0.0866119
\(467\) −40.8201 + 40.8201i −0.0874092 + 0.0874092i −0.749459 0.662050i \(-0.769687\pi\)
0.662050 + 0.749459i \(0.269687\pi\)
\(468\) −45.6869 45.6869i −0.0976216 0.0976216i
\(469\) 1302.47i 2.77712i
\(470\) 262.283 550.390i 0.558048 1.17104i
\(471\) −394.157 −0.836852
\(472\) 30.4764 30.4764i 0.0645687 0.0645687i
\(473\) 66.0687 + 66.0687i 0.139680 + 0.139680i
\(474\) 311.162i 0.656459i
\(475\) 273.228 221.577i 0.575216 0.466477i
\(476\) 491.614 1.03280
\(477\) −190.515 + 190.515i −0.399402 + 0.399402i
\(478\) 363.636 + 363.636i 0.760745 + 0.760745i
\(479\) 145.106i 0.302935i −0.988462 0.151467i \(-0.951600\pi\)
0.988462 0.151467i \(-0.0483999\pi\)
\(480\) −44.2250 21.0750i −0.0921353 0.0439062i
\(481\) −634.964 −1.32009
\(482\) −53.3378 + 53.3378i −0.110659 + 0.110659i
\(483\) −67.6409 67.6409i −0.140043 0.140043i
\(484\) 224.156i 0.463132i
\(485\) −103.678 + 36.7556i −0.213769 + 0.0757848i
\(486\) 22.0454 0.0453609
\(487\) −9.52353 + 9.52353i −0.0195555 + 0.0195555i −0.716817 0.697261i \(-0.754402\pi\)
0.697261 + 0.716817i \(0.254402\pi\)
\(488\) −24.1139 24.1139i −0.0494137 0.0494137i
\(489\) 299.269i 0.612001i
\(490\) −197.565 557.278i −0.403194 1.13730i
\(491\) −436.381 −0.888759 −0.444379 0.895839i \(-0.646576\pi\)
−0.444379 + 0.895839i \(0.646576\pi\)
\(492\) −49.7596 + 49.7596i −0.101137 + 0.101137i
\(493\) 742.633 + 742.633i 1.50635 + 1.50635i
\(494\) 214.290i 0.433786i
\(495\) −19.2746 + 40.4469i −0.0389385 + 0.0817110i
\(496\) 23.6261 0.0476332
\(497\) −166.766 + 166.766i −0.335546 + 0.335546i
\(498\) 60.9437 + 60.9437i 0.122377 + 0.122377i
\(499\) 521.427i 1.04494i −0.852656 0.522472i \(-0.825010\pi\)
0.852656 0.522472i \(-0.174990\pi\)
\(500\) −243.030 + 58.6202i −0.486060 + 0.117240i
\(501\) −309.946 −0.618655
\(502\) −165.873 + 165.873i −0.330425 + 0.330425i
\(503\) −487.805 487.805i −0.969791 0.969791i 0.0297662 0.999557i \(-0.490524\pi\)
−0.999557 + 0.0297662i \(0.990524\pi\)
\(504\) 97.7161i 0.193881i
\(505\) 614.568 + 292.866i 1.21697 + 0.579933i
\(506\) 20.2587 0.0400370
\(507\) 64.9595 64.9595i 0.128125 0.128125i
\(508\) 38.6059 + 38.6059i 0.0759959 + 0.0759959i
\(509\) 57.1963i 0.112370i 0.998420 + 0.0561850i \(0.0178937\pi\)
−0.998420 + 0.0561850i \(0.982106\pi\)
\(510\) 246.395 87.3515i 0.483128 0.171277i
\(511\) 9.96468 0.0195004
\(512\) −16.0000 + 16.0000i −0.0312500 + 0.0312500i
\(513\) 51.7010 + 51.7010i 0.100782 + 0.100782i
\(514\) 513.751i 0.999515i
\(515\) −55.1172 155.471i −0.107024 0.301885i
\(516\) −108.360 −0.210000
\(517\) −182.113 + 182.113i −0.352250 + 0.352250i
\(518\) −679.037 679.037i −1.31088 1.31088i
\(519\) 284.481i 0.548134i
\(520\) −65.5136 + 137.478i −0.125988 + 0.264380i
\(521\) −216.280 −0.415124 −0.207562 0.978222i \(-0.566553\pi\)
−0.207562 + 0.978222i \(0.566553\pi\)
\(522\) 147.610 147.610i 0.282778 0.282778i
\(523\) 733.496 + 733.496i 1.40248 + 1.40248i 0.792143 + 0.610335i \(0.208965\pi\)
0.610335 + 0.792143i \(0.291035\pi\)
\(524\) 101.374i 0.193462i
\(525\) −314.089 387.305i −0.598265 0.737724i
\(526\) 58.1915 0.110630
\(527\) −89.1479 + 89.1479i −0.169161 + 0.169161i
\(528\) 14.6332 + 14.6332i 0.0277143 + 0.0277143i
\(529\) 23.0000i 0.0434783i
\(530\) 573.283 + 273.192i 1.08167 + 0.515457i
\(531\) 45.7147 0.0860916
\(532\) 229.164 229.164i 0.430760 0.430760i
\(533\) 154.683 + 154.683i 0.290212 + 0.290212i
\(534\) 215.337i 0.403253i
\(535\) −714.591 + 253.335i −1.33568 + 0.473524i
\(536\) 319.899 0.596827
\(537\) 156.244 156.244i 0.290957 0.290957i
\(538\) 92.9336 + 92.9336i 0.172739 + 0.172739i
\(539\) 249.763i 0.463381i
\(540\) −17.3625 48.9749i −0.0321528 0.0906943i
\(541\) 740.869 1.36944 0.684721 0.728805i \(-0.259924\pi\)
0.684721 + 0.728805i \(0.259924\pi\)
\(542\) 355.672 355.672i 0.656221 0.656221i
\(543\) −393.290 393.290i −0.724292 0.724292i
\(544\) 120.745i 0.221958i
\(545\) −128.198 + 269.019i −0.235226 + 0.493613i
\(546\) −303.760 −0.556337
\(547\) −353.243 + 353.243i −0.645782 + 0.645782i −0.951971 0.306189i \(-0.900946\pi\)
0.306189 + 0.951971i \(0.400946\pi\)
\(548\) −227.887 227.887i −0.415851 0.415851i
\(549\) 36.1709i 0.0658850i
\(550\) 105.035 + 10.9642i 0.190973 + 0.0199350i
\(551\) 692.351 1.25654
\(552\) −16.6132 + 16.6132i −0.0300965 + 0.0300965i
\(553\) 1034.42 + 1034.42i 1.87055 + 1.87055i
\(554\) 182.788i 0.329942i
\(555\) −460.984 219.677i −0.830602 0.395815i
\(556\) −411.487 −0.740084
\(557\) −666.199 + 666.199i −1.19605 + 1.19605i −0.220708 + 0.975340i \(0.570837\pi\)
−0.975340 + 0.220708i \(0.929163\pi\)
\(558\) 17.7196 + 17.7196i 0.0317555 + 0.0317555i
\(559\) 336.848i 0.602590i
\(560\) −217.081 + 76.9591i −0.387644 + 0.137427i
\(561\) −110.430 −0.196845
\(562\) −203.040 + 203.040i −0.361282 + 0.361282i
\(563\) −629.280 629.280i −1.11773 1.11773i −0.992074 0.125652i \(-0.959898\pi\)
−0.125652 0.992074i \(-0.540102\pi\)
\(564\) 298.685i 0.529584i
\(565\) −340.671 960.942i −0.602958 1.70078i
\(566\) 255.292 0.451046
\(567\) 73.2870 73.2870i 0.129254 0.129254i
\(568\) 40.9594 + 40.9594i 0.0721116 + 0.0721116i
\(569\) 379.634i 0.667194i 0.942716 + 0.333597i \(0.108263\pi\)
−0.942716 + 0.333597i \(0.891737\pi\)
\(570\) 74.1376 155.575i 0.130066 0.272938i
\(571\) 719.736 1.26048 0.630242 0.776399i \(-0.282956\pi\)
0.630242 + 0.776399i \(0.282956\pi\)
\(572\) 45.4887 45.4887i 0.0795257 0.0795257i
\(573\) 112.675 + 112.675i 0.196641 + 0.196641i
\(574\) 330.839i 0.576374i
\(575\) −12.4479 + 119.248i −0.0216485 + 0.207388i
\(576\) −24.0000 −0.0416667
\(577\) 391.579 391.579i 0.678647 0.678647i −0.281047 0.959694i \(-0.590682\pi\)
0.959694 + 0.281047i \(0.0906818\pi\)
\(578\) 166.605 + 166.605i 0.288245 + 0.288245i
\(579\) 179.226i 0.309544i
\(580\) −444.177 211.668i −0.765823 0.364945i
\(581\) 405.198 0.697415
\(582\) −38.1052 + 38.1052i −0.0654729 + 0.0654729i
\(583\) −189.688 189.688i −0.325365 0.325365i
\(584\) 2.44742i 0.00419079i
\(585\) −152.244 + 53.9731i −0.260245 + 0.0922617i
\(586\) 39.5449 0.0674828
\(587\) −525.796 + 525.796i −0.895734 + 0.895734i −0.995055 0.0993214i \(-0.968333\pi\)
0.0993214 + 0.995055i \(0.468333\pi\)
\(588\) −204.819 204.819i −0.348332 0.348332i
\(589\) 83.1119i 0.141107i
\(590\) −36.0039 101.557i −0.0610236 0.172131i
\(591\) 174.464 0.295201
\(592\) −166.778 + 166.778i −0.281720 + 0.281720i
\(593\) 376.688 + 376.688i 0.635225 + 0.635225i 0.949374 0.314149i \(-0.101719\pi\)
−0.314149 + 0.949374i \(0.601719\pi\)
\(594\) 21.9497i 0.0369524i
\(595\) 528.719 1109.50i 0.888604 1.86470i
\(596\) 103.210 0.173172
\(597\) −333.576 + 333.576i −0.558754 + 0.558754i
\(598\) 51.6440 + 51.6440i 0.0863611 + 0.0863611i
\(599\) 1066.37i 1.78025i 0.455713 + 0.890127i \(0.349384\pi\)
−0.455713 + 0.890127i \(0.650616\pi\)
\(600\) −95.1258 + 77.1432i −0.158543 + 0.128572i
\(601\) −199.265 −0.331555 −0.165777 0.986163i \(-0.553013\pi\)
−0.165777 + 0.986163i \(0.553013\pi\)
\(602\) −360.228 + 360.228i −0.598386 + 0.598386i
\(603\) 239.924 + 239.924i 0.397885 + 0.397885i
\(604\) 226.690i 0.375314i
\(605\) 505.885 + 241.074i 0.836174 + 0.398470i
\(606\) 333.514 0.550353
\(607\) 210.101 210.101i 0.346131 0.346131i −0.512536 0.858666i \(-0.671294\pi\)
0.858666 + 0.512536i \(0.171294\pi\)
\(608\) −56.2849 56.2849i −0.0925738 0.0925738i
\(609\) 981.420i 1.61153i
\(610\) −80.3553 + 28.4874i −0.131730 + 0.0467007i
\(611\) −928.494 −1.51963
\(612\) 90.5588 90.5588i 0.147972 0.147972i
\(613\) 105.165 + 105.165i 0.171557 + 0.171557i 0.787663 0.616106i \(-0.211291\pi\)
−0.616106 + 0.787663i \(0.711291\pi\)
\(614\) 45.4924i 0.0740918i
\(615\) 58.7844 + 165.815i 0.0955845 + 0.269618i
\(616\) 97.2920 0.157942
\(617\) −224.661 + 224.661i −0.364118 + 0.364118i −0.865326 0.501209i \(-0.832889\pi\)
0.501209 + 0.865326i \(0.332889\pi\)
\(618\) −57.1410 57.1410i −0.0924611 0.0924611i
\(619\) 975.230i 1.57549i −0.616000 0.787746i \(-0.711248\pi\)
0.616000 0.787746i \(-0.288752\pi\)
\(620\) 25.4093 53.3204i 0.0409827 0.0860006i
\(621\) −24.9199 −0.0401286
\(622\) −58.8069 + 58.8069i −0.0945449 + 0.0945449i
\(623\) −715.860 715.860i −1.14905 1.14905i
\(624\) 74.6064i 0.119562i
\(625\) −129.077 + 611.526i −0.206523 + 0.978442i
\(626\) 643.918 1.02862
\(627\) −51.4766 + 51.4766i −0.0820999 + 0.0820999i
\(628\) 321.828 + 321.828i 0.512465 + 0.512465i
\(629\) 1258.60i 2.00096i
\(630\) −220.530 105.091i −0.350048 0.166812i
\(631\) −847.237 −1.34269 −0.671344 0.741146i \(-0.734283\pi\)
−0.671344 + 0.741146i \(0.734283\pi\)
\(632\) 254.062 254.062i 0.401997 0.401997i
\(633\) 388.250 + 388.250i 0.613350 + 0.613350i
\(634\) 130.504i 0.205842i
\(635\) 128.647 45.6078i 0.202594 0.0718233i
\(636\) 311.109 0.489165
\(637\) −636.701 + 636.701i −0.999530 + 0.999530i
\(638\) 146.970 + 146.970i 0.230360 + 0.230360i
\(639\) 61.4391i 0.0961488i
\(640\) 18.9019 + 53.3171i 0.0295342 + 0.0833080i
\(641\) −927.911 −1.44760 −0.723799 0.690010i \(-0.757606\pi\)
−0.723799 + 0.690010i \(0.757606\pi\)
\(642\) −262.637 + 262.637i −0.409092 + 0.409092i
\(643\) 424.937 + 424.937i 0.660867 + 0.660867i 0.955584 0.294718i \(-0.0952256\pi\)
−0.294718 + 0.955584i \(0.595226\pi\)
\(644\) 110.457i 0.171517i
\(645\) −116.539 + 244.552i −0.180680 + 0.379150i
\(646\) 424.758 0.657520
\(647\) −67.6741 + 67.6741i −0.104597 + 0.104597i −0.757468 0.652872i \(-0.773564\pi\)
0.652872 + 0.757468i \(0.273564\pi\)
\(648\) −18.0000 18.0000i −0.0277778 0.0277778i
\(649\) 45.5163i 0.0701330i
\(650\) 239.808 + 295.708i 0.368935 + 0.454936i
\(651\) 117.813 0.180972
\(652\) −244.352 + 244.352i −0.374773 + 0.374773i
\(653\) 412.106 + 412.106i 0.631097 + 0.631097i 0.948343 0.317246i \(-0.102758\pi\)
−0.317246 + 0.948343i \(0.602758\pi\)
\(654\) 145.991i 0.223228i
\(655\) 228.785 + 109.025i 0.349290 + 0.166451i
\(656\) 81.2571 0.123868
\(657\) 1.83557 1.83557i 0.00279386 0.00279386i
\(658\) −992.940 992.940i −1.50903 1.50903i
\(659\) 677.303i 1.02777i −0.857858 0.513887i \(-0.828205\pi\)
0.857858 0.513887i \(-0.171795\pi\)
\(660\) 48.7624 17.2872i 0.0738824 0.0261927i
\(661\) −136.925 −0.207148 −0.103574 0.994622i \(-0.533028\pi\)
−0.103574 + 0.994622i \(0.533028\pi\)
\(662\) 498.721 498.721i 0.753355 0.753355i
\(663\) −281.511 281.511i −0.424602 0.424602i
\(664\) 99.5206i 0.149880i
\(665\) −270.727 763.648i −0.407109 1.14834i
\(666\) −250.167 −0.375626
\(667\) −166.857 + 166.857i −0.250160 + 0.250160i
\(668\) 253.070 + 253.070i 0.378847 + 0.378847i
\(669\) 39.5660i 0.0591420i
\(670\) 344.044 721.963i 0.513499 1.07756i
\(671\) 36.0139 0.0536720
\(672\) −79.7848 + 79.7848i −0.118727 + 0.118727i
\(673\) 519.433 + 519.433i 0.771817 + 0.771817i 0.978424 0.206607i \(-0.0662423\pi\)
−0.206607 + 0.978424i \(0.566242\pi\)
\(674\) 507.430i 0.752863i
\(675\) −129.202 13.4869i −0.191410 0.0199806i
\(676\) −106.078 −0.156921
\(677\) 706.858 706.858i 1.04410 1.04410i 0.0451224 0.998981i \(-0.485632\pi\)
0.998981 0.0451224i \(-0.0143678\pi\)
\(678\) −353.180 353.180i −0.520914 0.520914i
\(679\) 253.351i 0.373124i
\(680\) −272.503 129.859i −0.400740 0.190968i
\(681\) 537.388 0.789116
\(682\) −17.6427 + 17.6427i −0.0258690 + 0.0258690i
\(683\) −317.830 317.830i −0.465344 0.465344i 0.435059 0.900402i \(-0.356728\pi\)
−0.900402 + 0.435059i \(0.856728\pi\)
\(684\) 84.4273i 0.123432i
\(685\) −759.391 + 269.218i −1.10860 + 0.393019i
\(686\) −563.773 −0.821827
\(687\) −385.688 + 385.688i −0.561410 + 0.561410i
\(688\) 88.4755 + 88.4755i 0.128598 + 0.128598i
\(689\) 967.114i 1.40365i
\(690\) 19.6264 + 55.3607i 0.0284440 + 0.0802329i
\(691\) 791.492 1.14543 0.572715 0.819755i \(-0.305890\pi\)
0.572715 + 0.819755i \(0.305890\pi\)
\(692\) −232.278 + 232.278i −0.335662 + 0.335662i
\(693\) 72.9690 + 72.9690i 0.105294 + 0.105294i
\(694\) 700.766i 1.00975i
\(695\) −442.544 + 928.662i −0.636754 + 1.33620i
\(696\) −241.046 −0.346331
\(697\) −306.606 + 306.606i −0.439894 + 0.439894i
\(698\) 501.750 + 501.750i 0.718840 + 0.718840i
\(699\) 49.4321i 0.0707183i
\(700\) −59.7807 + 572.686i −0.0854009 + 0.818122i
\(701\) 672.284 0.959036 0.479518 0.877532i \(-0.340812\pi\)
0.479518 + 0.877532i \(0.340812\pi\)
\(702\) −55.9548 + 55.9548i −0.0797077 + 0.0797077i
\(703\) −586.693 586.693i −0.834556 0.834556i
\(704\) 23.8959i 0.0339430i
\(705\) −674.087 321.229i −0.956152 0.455644i
\(706\) −167.853 −0.237752
\(707\) 1108.72 1108.72i 1.56821 1.56821i
\(708\) −37.3259 37.3259i −0.0527201 0.0527201i
\(709\) 1080.93i 1.52459i −0.647232 0.762293i \(-0.724074\pi\)
0.647232 0.762293i \(-0.275926\pi\)
\(710\) 136.490 48.3881i 0.192239 0.0681523i
\(711\) 381.094 0.535997
\(712\) −175.822 + 175.822i −0.246941 + 0.246941i
\(713\) −20.0300 20.0300i −0.0280925 0.0280925i
\(714\) 602.102i 0.843279i
\(715\) −53.7389 151.583i −0.0751593 0.212004i
\(716\) −255.145 −0.356348
\(717\) 445.361 445.361i 0.621146 0.621146i
\(718\) 68.1546 + 68.1546i 0.0949228 + 0.0949228i
\(719\) 44.1508i 0.0614059i −0.999529 0.0307029i \(-0.990225\pi\)
0.999529 0.0307029i \(-0.00977458\pi\)
\(720\) −25.8114 + 54.1643i −0.0358492 + 0.0752282i
\(721\) −379.915 −0.526928
\(722\) −163.001 + 163.001i −0.225763 + 0.225763i
\(723\) 65.3252 + 65.3252i 0.0903529 + 0.0903529i
\(724\) 642.240i 0.887072i
\(725\) −955.405 + 774.795i −1.31780 + 1.06868i
\(726\) 274.534 0.378146
\(727\) −577.116 + 577.116i −0.793832 + 0.793832i −0.982115 0.188283i \(-0.939708\pi\)
0.188283 + 0.982115i \(0.439708\pi\)
\(728\) 248.019 + 248.019i 0.340686 + 0.340686i
\(729\) 27.0000i 0.0370370i
\(730\) −5.52345 2.63214i −0.00756637 0.00360568i
\(731\) −667.686 −0.913388
\(732\) −29.5334 + 29.5334i −0.0403462 + 0.0403462i
\(733\) −427.263 427.263i −0.582896 0.582896i 0.352802 0.935698i \(-0.385229\pi\)
−0.935698 + 0.352802i \(0.885229\pi\)
\(734\) 183.400i 0.249864i
\(735\) −682.523 + 241.967i −0.928603 + 0.329207i
\(736\) 27.1293 0.0368605
\(737\) −238.883 + 238.883i −0.324129 + 0.324129i
\(738\) 60.9428 + 60.9428i 0.0825784 + 0.0825784i
\(739\) 326.041i 0.441192i −0.975365 0.220596i \(-0.929200\pi\)
0.975365 0.220596i \(-0.0708003\pi\)
\(740\) 197.026 + 555.758i 0.266252 + 0.751024i
\(741\) −262.451 −0.354185
\(742\) 1034.24 1034.24i 1.39386 1.39386i
\(743\) 786.240 + 786.240i 1.05820 + 1.05820i 0.998199 + 0.0599978i \(0.0191094\pi\)
0.0599978 + 0.998199i \(0.480891\pi\)
\(744\) 28.9359i 0.0388924i
\(745\) 111.000 232.930i 0.148994 0.312657i
\(746\) −47.5589 −0.0637519
\(747\) 74.6404 74.6404i 0.0999202 0.0999202i
\(748\) 90.1659 + 90.1659i 0.120543 + 0.120543i
\(749\) 1746.21i 2.33138i
\(750\) 71.7948 + 297.650i 0.0957264 + 0.396867i
\(751\) −856.133 −1.13999 −0.569995 0.821648i \(-0.693055\pi\)
−0.569995 + 0.821648i \(0.693055\pi\)
\(752\) −243.876 + 243.876i −0.324303 + 0.324303i
\(753\) 203.153 + 203.153i 0.269791 + 0.269791i
\(754\) 749.317i 0.993789i
\(755\) −511.604 243.800i −0.677621 0.322914i
\(756\) −119.677 −0.158303
\(757\) 534.371 534.371i 0.705906 0.705906i −0.259765 0.965672i \(-0.583645\pi\)
0.965672 + 0.259765i \(0.0836452\pi\)
\(758\) 178.495 + 178.495i 0.235482 + 0.235482i
\(759\) 24.8117i 0.0326900i
\(760\) −187.559 + 66.4932i −0.246789 + 0.0874911i
\(761\) 84.8082 0.111443 0.0557216 0.998446i \(-0.482254\pi\)
0.0557216 + 0.998446i \(0.482254\pi\)
\(762\) 47.2824 47.2824i 0.0620504 0.0620504i
\(763\) 485.329 + 485.329i 0.636080 + 0.636080i
\(764\) 183.998i 0.240835i
\(765\) −106.983 301.771i −0.139847 0.394472i
\(766\) −223.127 −0.291288
\(767\) −116.031 + 116.031i −0.151279 + 0.151279i
\(768\) 19.5959 + 19.5959i 0.0255155 + 0.0255155i
\(769\) 662.469i 0.861468i −0.902479 0.430734i \(-0.858255\pi\)
0.902479 0.430734i \(-0.141745\pi\)
\(770\) 104.635 219.573i 0.135890 0.285160i
\(771\) −629.214 −0.816101
\(772\) −146.337 + 146.337i −0.189556 + 0.189556i
\(773\) 608.097 + 608.097i 0.786671 + 0.786671i 0.980947 0.194276i \(-0.0622358\pi\)
−0.194276 + 0.980947i \(0.562236\pi\)
\(774\) 132.713i 0.171464i
\(775\) −93.0087 114.690i −0.120011 0.147987i
\(776\) 62.2255 0.0801876
\(777\) −831.647 + 831.647i −1.07033 + 1.07033i
\(778\) −765.523 765.523i −0.983962 0.983962i
\(779\)