Properties

Label 690.3.k.b.277.13
Level $690$
Weight $3$
Character 690.277
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 277.13
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.13

$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

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

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
\(5\) −4.51369 + 2.15095i −0.902738 + 0.430191i
\(6\) −2.44949 −0.408248
\(7\) −8.14300 8.14300i −1.16329 1.16329i −0.983752 0.179535i \(-0.942541\pi\)
−0.179535 0.983752i \(-0.557459\pi\)
\(8\) 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 −0.936472 0.350742i \(-0.885929\pi\)
0.350742 + 0.936472i \(0.385929\pi\)
\(14\) 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 0.994315 0.106483i \(-0.0339590\pi\)
−0.106483 + 0.994315i \(0.533959\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 14.0712i 0.740591i 0.928914 + 0.370295i \(0.120744\pi\)
−0.928914 + 0.370295i \(0.879256\pi\)
\(20\) −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 \(-0.677606\pi\)
0.529462 0.848334i \(-0.322394\pi\)
\(30\) 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 0.990682 + 0.136196i \(0.0434878\pi\)
0.136196 + 0.990682i \(0.456512\pi\)
\(38\) 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 −0.915869 0.401477i \(-0.868497\pi\)
0.401477 + 0.915869i \(0.368497\pi\)
\(44\) 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 0.930227 + 0.366984i \(0.119609\pi\)
0.366984 + 0.930227i \(0.380391\pi\)
\(48\) −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 0.223502 0.974703i \(-0.428251\pi\)
0.974703 0.223502i \(-0.0717490\pi\)
\(54\) 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 \(0.0412208\pi\)
−0.991627 + 0.129137i \(0.958779\pi\)
\(60\) −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 0.976033 + 0.217620i \(0.0698295\pi\)
0.217620 + 0.976033i \(0.430171\pi\)
\(68\) −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 −0.711285 0.702904i \(-0.751887\pi\)
0.702904 + 0.711285i \(0.251887\pi\)
\(74\) 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 \(0.297296\pi\)
−0.594636 + 0.803995i \(0.702704\pi\)
\(80\) 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 −0.840920 0.541159i \(-0.817986\pi\)
0.541159 + 0.840920i \(0.317986\pi\)
\(84\) 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 \(-0.835577\pi\)
0.869529 0.493883i \(-0.164423\pi\)
\(90\) 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 0.782733 0.622358i \(-0.213825\pi\)
−0.622358 + 0.782733i \(0.713825\pi\)
\(98\) 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 −0.584739 0.811222i \(-0.698803\pi\)
0.811222 + 0.584739i \(0.198803\pi\)
\(104\) 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 0.999998 + 0.00206949i \(0.000658739\pi\)
0.00206949 + 0.999998i \(0.499341\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 59.6007i 0.546796i 0.961901 + 0.273398i \(0.0881475\pi\)
−0.961901 + 0.273398i \(0.911852\pi\)
\(110\) −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 0.333072 0.942901i \(-0.391915\pi\)
0.942901 0.333072i \(-0.108085\pi\)
\(114\) 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 0.627015 0.779007i \(-0.284276\pi\)
−0.779007 + 0.627015i \(0.784276\pi\)
\(128\) −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 0.987750 0.156047i \(-0.0498751\pi\)
−0.156047 + 0.987750i \(0.549875\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 205.743i 1.48017i 0.672515 + 0.740084i \(0.265214\pi\)
−0.672515 + 0.740084i \(0.734786\pi\)
\(140\) −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 \(-0.944598\pi\)
0.984892 0.173172i \(-0.0554015\pi\)
\(150\) −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 −0.999681 0.0252486i \(-0.991962\pi\)
−0.0252486 0.999681i \(-0.508038\pi\)
\(158\) 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 −0.974394 0.224848i \(-0.927811\pi\)
0.224848 + 0.974394i \(0.427811\pi\)
\(164\) 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 0.218207 0.975902i \(-0.429979\pi\)
−0.975902 + 0.218207i \(0.929979\pi\)
\(168\) −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 −0.958021 0.286697i \(-0.907443\pi\)
0.286697 + 0.958021i \(0.407443\pi\)
\(174\) 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 \(0.115978\pi\)
−0.934353 + 0.356348i \(0.884022\pi\)
\(180\) −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 −0.870782 0.491669i \(-0.836387\pi\)
0.491669 + 0.870782i \(0.336387\pi\)
\(194\) 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 0.864382 0.502836i \(-0.167710\pi\)
−0.502836 + 0.864382i \(0.667710\pi\)
\(198\) 8.96095 8.96095i 0.0452573 0.0452573i
\(199\) 272.364i 1.36866i −0.729171 0.684331i \(-0.760094\pi\)
0.729171 0.684331i \(-0.239906\pi\)
\(200\) −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 −0.742396 0.669962i \(-0.766310\pi\)
0.669962 + 0.742396i \(0.266310\pi\)
\(224\) 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 0.999456 0.0329895i \(-0.0105028\pi\)
−0.0329895 + 0.999456i \(0.510503\pi\)
\(228\) −34.4673 + 34.4673i −0.151172 + 0.151172i
\(229\) 314.913i 1.37517i −0.726105 0.687583i \(-0.758672\pi\)
0.726105 0.687583i \(-0.241328\pi\)
\(230\) 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 −0.662473 0.749085i \(-0.730493\pi\)
0.749085 + 0.662473i \(0.230493\pi\)
\(234\) 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 \(0.275166\pi\)
−0.649051 + 0.760745i \(0.724834\pi\)
\(240\) 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 0.000484450 1.00000i \(-0.499846\pi\)
−1.00000 0.000484450i \(0.999846\pi\)
\(258\) 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 −0.760255 0.649625i \(-0.774926\pi\)
0.649625 + 0.760255i \(0.274926\pi\)
\(264\) 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 \(0.0552618\pi\)
−0.984968 + 0.172739i \(0.944738\pi\)
\(270\) −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 0.852564 0.522622i \(-0.175046\pi\)
−0.522622 + 0.852564i \(0.675046\pi\)
\(278\) 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 −0.895702 0.444656i \(-0.853326\pi\)
0.444656 + 0.895702i \(0.353326\pi\)
\(284\) 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 −0.740043 0.672560i \(-0.765195\pi\)
0.672560 + 0.740043i \(0.265195\pi\)
\(294\) 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 0.743182 0.669090i \(-0.233316\pi\)
−0.669090 + 0.743182i \(0.733316\pi\)
\(308\) −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 −0.0290452 + 0.999578i \(0.509247\pi\)
−0.999578 + 0.0290452i \(0.990753\pi\)
\(314\) 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 0.802497 0.596656i \(-0.203504\pi\)
−0.596656 + 0.802497i \(0.703504\pi\)
\(318\) −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 0.975013 0.222149i \(-0.0713072\pi\)
−0.222149 + 0.975013i \(0.571307\pi\)
\(338\) 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 0.999952 + 0.00979723i \(0.00311860\pi\)
0.00979723 + 0.999952i \(0.496881\pi\)
\(348\) 120.523 120.523i 0.346331 0.346331i
\(349\) 501.750i 1.43768i 0.695176 + 0.718840i \(0.255327\pi\)
−0.695176 + 0.718840i \(0.744673\pi\)
\(350\) 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 −0.578166 0.815919i \(-0.696232\pi\)
0.815919 + 0.578166i \(0.196232\pi\)
\(354\) 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 \(0.0302604\pi\)
−0.995485 + 0.0949228i \(0.969740\pi\)
\(360\) 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 0.820915 0.571051i \(-0.193464\pi\)
−0.571051 + 0.820915i \(0.693464\pi\)
\(368\) −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 −0.674512 0.738264i \(-0.735646\pi\)
0.738264 + 0.674512i \(0.235646\pi\)
\(374\) 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 \(0.0756669\pi\)
−0.971879 + 0.235482i \(0.924333\pi\)
\(380\) 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 −0.546301 0.837589i \(-0.683964\pi\)
0.837589 + 0.546301i \(0.183964\pi\)
\(384\) 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 \(-0.557085\pi\)
0.178377 0.983962i \(-0.442915\pi\)
\(390\) −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 0.615555 0.788094i \(-0.288932\pi\)
−0.788094 + 0.615555i \(0.788932\pi\)
\(398\) −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 \(-0.832608\pi\)
0.864884 0.501972i \(-0.167392\pi\)
\(410\) −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 \(0.170093\pi\)
−0.860594 + 0.509292i \(0.829907\pi\)
\(420\) 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 −0.584982 0.811046i \(-0.698898\pi\)
0.811046 + 0.584982i \(0.198898\pi\)
\(434\) 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 \(-0.983490\pi\)
0.998655 0.0518451i \(-0.0165102\pi\)
\(440\) 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 −0.898835 0.438288i \(-0.855585\pi\)
0.438288 + 0.898835i \(0.355585\pi\)
\(444\) 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 \(0.284030\pi\)
−0.627618 + 0.778521i \(0.715970\pi\)
\(450\) 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 0.872337 0.488905i \(-0.162604\pi\)
−0.488905 + 0.872337i \(0.662604\pi\)
\(458\) −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 −0.311166 0.950356i \(-0.600719\pi\)
0.950356 + 0.311166i \(0.100719\pi\)
\(464\) 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 0.662050 0.749459i \(-0.269687\pi\)
−0.749459 + 0.662050i \(0.769687\pi\)
\(468\) −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 \(0.0483999\pi\)
−0.988462 + 0.151467i \(0.951600\pi\)
\(480\) −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 0.697261 0.716817i \(-0.254402\pi\)
−0.716817 + 0.697261i \(0.754402\pi\)
\(488\) −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 \(0.174990\pi\)
−0.852656 + 0.522472i \(0.825010\pi\)
\(500\) −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 −0.999557 0.0297662i \(-0.990524\pi\)
0.0297662 + 0.999557i \(0.490524\pi\)
\(504\) 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 \(-0.982106\pi\)
0.998420 0.0561850i \(-0.0178937\pi\)
\(510\) 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 0.610335 0.792143i \(-0.291035\pi\)
0.792143 0.610335i \(-0.208965\pi\)
\(524\) 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 0.306189 0.951971i \(-0.400946\pi\)
−0.951971 + 0.306189i \(0.900946\pi\)
\(548\) −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 −0.975340 0.220708i \(-0.929163\pi\)
−0.220708 0.975340i \(-0.570837\pi\)
\(558\) 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 −0.125652 + 0.992074i \(0.540102\pi\)
−0.992074 + 0.125652i \(0.959898\pi\)
\(564\) 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 \(-0.891737\pi\)
0.942716 0.333597i \(-0.108263\pi\)
\(570\) 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 0.959694 0.281047i \(-0.0906818\pi\)
−0.281047 + 0.959694i \(0.590682\pi\)
\(578\) 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 0.0993214 0.995055i \(-0.468333\pi\)
−0.995055 + 0.0993214i \(0.968333\pi\)
\(588\) −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 −0.314149 0.949374i \(-0.601719\pi\)
0.949374 + 0.314149i \(0.101719\pi\)
\(594\) 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 \(-0.650616\pi\)
0.455713 0.890127i \(-0.349384\pi\)
\(600\) −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 0.858666 0.512536i \(-0.171294\pi\)
−0.512536 + 0.858666i \(0.671294\pi\)
\(608\) −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 −0.616106 0.787663i \(-0.711291\pi\)
0.787663 + 0.616106i \(0.211291\pi\)
\(614\) 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 0.501209 0.865326i \(-0.332889\pi\)
−0.865326 + 0.501209i \(0.832889\pi\)
\(618\) −57.1410 + 57.1410i −0.0924611 + 0.0924611i
\(619\) 975.230i 1.57549i 0.616000 + 0.787746i \(0.288752\pi\)
−0.616000 + 0.787746i \(0.711248\pi\)
\(620\) 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 −0.294718 0.955584i \(-0.595226\pi\)
0.955584 + 0.294718i \(0.0952256\pi\)
\(644\) 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 0.652872 0.757468i \(-0.273564\pi\)
−0.757468 + 0.652872i \(0.773564\pi\)
\(648\) −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 −0.317246 0.948343i \(-0.602758\pi\)
0.948343 + 0.317246i \(0.102758\pi\)
\(654\) 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 \(0.171795\pi\)
−0.857858 + 0.513887i \(0.828205\pi\)
\(660\) 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 −0.206607 0.978424i \(-0.566242\pi\)
0.978424 + 0.206607i \(0.0662423\pi\)
\(674\) 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 0.998981 + 0.0451224i \(0.0143678\pi\)
0.0451224 + 0.998981i \(0.485632\pi\)
\(678\) −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 −0.900402 0.435059i \(-0.856728\pi\)
0.435059 + 0.900402i \(0.356728\pi\)
\(684\) 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 \(0.275926\pi\)
−0.647232 + 0.762293i \(0.724074\pi\)
\(710\) 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 \(0.00977458\pi\)
−0.999529 + 0.0307029i \(0.990225\pi\)
\(720\) −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 0.188283 0.982115i \(-0.439708\pi\)
−0.982115 + 0.188283i \(0.939708\pi\)
\(728\) 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 −0.935698 0.352802i \(-0.885229\pi\)
0.352802 + 0.935698i \(0.385229\pi\)
\(734\) 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 \(0.0708003\pi\)
−0.975365 + 0.220596i \(0.929200\pi\)
\(740\) 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 0.0599978 0.998199i \(-0.480891\pi\)
0.998199 0.0599978i \(-0.0191094\pi\)
\(744\) 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 0.965672 0.259765i \(-0.0836452\pi\)
−0.259765 + 0.965672i \(0.583645\pi\)
\(758\) 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 \(0.141745\pi\)
−0.902479 + 0.430734i \(0.858255\pi\)
\(770\) 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 −0.194276 0.980947i \(-0.562236\pi\)
0.980947 + 0.194276i \(0.0622358\pi\)
\(774\) 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
\(779\)