Properties

Label 690.3.g.a.461.3
Level $690$
Weight $3$
Character 690.461
Analytic conductor $18.801$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 461.3
Character \(\chi\) \(=\) 690.461
Dual form 690.3.g.a.461.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} +(-2.87483 + 0.857518i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(1.21271 + 4.06563i) q^{6} +5.06417 q^{7} +2.82843i q^{8} +(7.52932 - 4.93044i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(-2.87483 + 0.857518i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(1.21271 + 4.06563i) q^{6} +5.06417 q^{7} +2.82843i q^{8} +(7.52932 - 4.93044i) q^{9} +3.16228 q^{10} +18.8188i q^{11} +(5.74967 - 1.71504i) q^{12} -3.24812 q^{13} -7.16182i q^{14} +(-1.91747 - 6.42832i) q^{15} +4.00000 q^{16} -19.0579i q^{17} +(-6.97270 - 10.6481i) q^{18} -8.49496 q^{19} -4.47214i q^{20} +(-14.5586 + 4.34262i) q^{21} +26.6138 q^{22} -4.79583i q^{23} +(-2.42543 - 8.13125i) q^{24} -5.00000 q^{25} +4.59354i q^{26} +(-17.4176 + 20.6307i) q^{27} -10.1283 q^{28} -18.1025i q^{29} +(-9.09102 + 2.71171i) q^{30} -7.67595 q^{31} -5.65685i q^{32} +(-16.1375 - 54.1009i) q^{33} -26.9519 q^{34} +11.3238i q^{35} +(-15.0586 + 9.86089i) q^{36} +5.74178 q^{37} +12.0137i q^{38} +(9.33781 - 2.78532i) q^{39} -6.32456 q^{40} +48.7570i q^{41} +(6.14139 + 20.5890i) q^{42} +9.50005 q^{43} -37.6376i q^{44} +(11.0248 + 16.8361i) q^{45} -6.78233 q^{46} +52.9480i q^{47} +(-11.4993 + 3.43007i) q^{48} -23.3542 q^{49} +7.07107i q^{50} +(16.3425 + 54.7882i) q^{51} +6.49624 q^{52} +89.4628i q^{53} +(29.1763 + 24.6322i) q^{54} -42.0801 q^{55} +14.3236i q^{56} +(24.4216 - 7.28458i) q^{57} -25.6009 q^{58} +58.9584i q^{59} +(3.83494 + 12.8566i) q^{60} -94.2459 q^{61} +10.8554i q^{62} +(38.1298 - 24.9686i) q^{63} -8.00000 q^{64} -7.26302i q^{65} +(-76.5102 + 22.8218i) q^{66} -4.76905 q^{67} +38.1157i q^{68} +(4.11251 + 13.7872i) q^{69} +16.0143 q^{70} -16.3306i q^{71} +(13.9454 + 21.2961i) q^{72} -91.7883 q^{73} -8.12011i q^{74} +(14.3742 - 4.28759i) q^{75} +16.9899 q^{76} +95.3015i q^{77} +(-3.93904 - 13.2057i) q^{78} -110.541 q^{79} +8.94427i q^{80} +(32.3815 - 74.2458i) q^{81} +68.9528 q^{82} +15.5961i q^{83} +(29.1173 - 8.68523i) q^{84} +42.6147 q^{85} -13.4351i q^{86} +(15.5233 + 52.0418i) q^{87} -53.2276 q^{88} +98.9857i q^{89} +(23.8098 - 15.5914i) q^{90} -16.4490 q^{91} +9.59166i q^{92} +(22.0671 - 6.58227i) q^{93} +74.8798 q^{94} -18.9953i q^{95} +(4.85086 + 16.2625i) q^{96} -41.8721 q^{97} +33.0278i q^{98} +(92.7850 + 141.693i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 8q^{3} - 112q^{4} + 16q^{6} - 16q^{7} + O(q^{10}) \) \( 56q - 8q^{3} - 112q^{4} + 16q^{6} - 16q^{7} + 16q^{12} + 80q^{13} - 40q^{15} + 224q^{16} - 32q^{18} - 64q^{19} + 56q^{21} - 96q^{22} - 32q^{24} - 280q^{25} + 40q^{27} + 32q^{28} - 80q^{31} + 32q^{33} + 192q^{34} + 240q^{37} - 56q^{39} - 144q^{43} - 32q^{48} + 72q^{49} - 24q^{51} - 160q^{52} + 16q^{54} - 16q^{57} + 80q^{60} + 112q^{61} - 64q^{63} - 448q^{64} + 160q^{66} + 832q^{67} + 64q^{72} - 608q^{73} + 40q^{75} + 128q^{76} - 320q^{78} + 48q^{79} - 32q^{81} - 448q^{82} - 112q^{84} + 240q^{85} + 200q^{87} + 192q^{88} + 80q^{91} - 232q^{93} + 160q^{94} + 64q^{96} - 448q^{97} + 464q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) −2.87483 + 0.857518i −0.958278 + 0.285839i
\(4\) −2.00000 −0.500000
\(5\) 2.23607i 0.447214i
\(6\) 1.21271 + 4.06563i 0.202119 + 0.677605i
\(7\) 5.06417 0.723453 0.361726 0.932284i \(-0.382187\pi\)
0.361726 + 0.932284i \(0.382187\pi\)
\(8\) 2.82843i 0.353553i
\(9\) 7.52932 4.93044i 0.836592 0.547827i
\(10\) 3.16228 0.316228
\(11\) 18.8188i 1.71080i 0.517969 + 0.855400i \(0.326688\pi\)
−0.517969 + 0.855400i \(0.673312\pi\)
\(12\) 5.74967 1.71504i 0.479139 0.142920i
\(13\) −3.24812 −0.249856 −0.124928 0.992166i \(-0.539870\pi\)
−0.124928 + 0.992166i \(0.539870\pi\)
\(14\) 7.16182i 0.511558i
\(15\) −1.91747 6.42832i −0.127831 0.428555i
\(16\) 4.00000 0.250000
\(17\) 19.0579i 1.12105i −0.828137 0.560526i \(-0.810599\pi\)
0.828137 0.560526i \(-0.189401\pi\)
\(18\) −6.97270 10.6481i −0.387372 0.591560i
\(19\) −8.49496 −0.447103 −0.223552 0.974692i \(-0.571765\pi\)
−0.223552 + 0.974692i \(0.571765\pi\)
\(20\) 4.47214i 0.223607i
\(21\) −14.5586 + 4.34262i −0.693268 + 0.206791i
\(22\) 26.6138 1.20972
\(23\) 4.79583i 0.208514i
\(24\) −2.42543 8.13125i −0.101060 0.338802i
\(25\) −5.00000 −0.200000
\(26\) 4.59354i 0.176675i
\(27\) −17.4176 + 20.6307i −0.645096 + 0.764101i
\(28\) −10.1283 −0.361726
\(29\) 18.1025i 0.624226i −0.950045 0.312113i \(-0.898963\pi\)
0.950045 0.312113i \(-0.101037\pi\)
\(30\) −9.09102 + 2.71171i −0.303034 + 0.0903904i
\(31\) −7.67595 −0.247611 −0.123806 0.992306i \(-0.539510\pi\)
−0.123806 + 0.992306i \(0.539510\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −16.1375 54.1009i −0.489014 1.63942i
\(34\) −26.9519 −0.792703
\(35\) 11.3238i 0.323538i
\(36\) −15.0586 + 9.86089i −0.418296 + 0.273914i
\(37\) 5.74178 0.155183 0.0775917 0.996985i \(-0.475277\pi\)
0.0775917 + 0.996985i \(0.475277\pi\)
\(38\) 12.0137i 0.316150i
\(39\) 9.33781 2.78532i 0.239431 0.0714186i
\(40\) −6.32456 −0.158114
\(41\) 48.7570i 1.18920i 0.804023 + 0.594598i \(0.202689\pi\)
−0.804023 + 0.594598i \(0.797311\pi\)
\(42\) 6.14139 + 20.5890i 0.146224 + 0.490215i
\(43\) 9.50005 0.220931 0.110466 0.993880i \(-0.464766\pi\)
0.110466 + 0.993880i \(0.464766\pi\)
\(44\) 37.6376i 0.855400i
\(45\) 11.0248 + 16.8361i 0.244996 + 0.374135i
\(46\) −6.78233 −0.147442
\(47\) 52.9480i 1.12655i 0.826268 + 0.563277i \(0.190459\pi\)
−0.826268 + 0.563277i \(0.809541\pi\)
\(48\) −11.4993 + 3.43007i −0.239569 + 0.0714599i
\(49\) −23.3542 −0.476616
\(50\) 7.07107i 0.141421i
\(51\) 16.3425 + 54.7882i 0.320441 + 1.07428i
\(52\) 6.49624 0.124928
\(53\) 89.4628i 1.68798i 0.536361 + 0.843989i \(0.319799\pi\)
−0.536361 + 0.843989i \(0.680201\pi\)
\(54\) 29.1763 + 24.6322i 0.540301 + 0.456152i
\(55\) −42.0801 −0.765093
\(56\) 14.3236i 0.255779i
\(57\) 24.4216 7.28458i 0.428449 0.127800i
\(58\) −25.6009 −0.441394
\(59\) 58.9584i 0.999295i 0.866229 + 0.499648i \(0.166537\pi\)
−0.866229 + 0.499648i \(0.833463\pi\)
\(60\) 3.83494 + 12.8566i 0.0639156 + 0.214277i
\(61\) −94.2459 −1.54501 −0.772507 0.635006i \(-0.780998\pi\)
−0.772507 + 0.635006i \(0.780998\pi\)
\(62\) 10.8554i 0.175088i
\(63\) 38.1298 24.9686i 0.605234 0.396327i
\(64\) −8.00000 −0.125000
\(65\) 7.26302i 0.111739i
\(66\) −76.5102 + 22.8218i −1.15925 + 0.345785i
\(67\) −4.76905 −0.0711799 −0.0355900 0.999366i \(-0.511331\pi\)
−0.0355900 + 0.999366i \(0.511331\pi\)
\(68\) 38.1157i 0.560526i
\(69\) 4.11251 + 13.7872i 0.0596016 + 0.199815i
\(70\) 16.0143 0.228776
\(71\) 16.3306i 0.230008i −0.993365 0.115004i \(-0.963312\pi\)
0.993365 0.115004i \(-0.0366881\pi\)
\(72\) 13.9454 + 21.2961i 0.193686 + 0.295780i
\(73\) −91.7883 −1.25737 −0.628687 0.777659i \(-0.716407\pi\)
−0.628687 + 0.777659i \(0.716407\pi\)
\(74\) 8.12011i 0.109731i
\(75\) 14.3742 4.28759i 0.191656 0.0571679i
\(76\) 16.9899 0.223552
\(77\) 95.3015i 1.23768i
\(78\) −3.93904 13.2057i −0.0505006 0.169303i
\(79\) −110.541 −1.39926 −0.699628 0.714507i \(-0.746651\pi\)
−0.699628 + 0.714507i \(0.746651\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 32.3815 74.2458i 0.399771 0.916615i
\(82\) 68.9528 0.840888
\(83\) 15.5961i 0.187905i 0.995577 + 0.0939526i \(0.0299502\pi\)
−0.995577 + 0.0939526i \(0.970050\pi\)
\(84\) 29.1173 8.68523i 0.346634 0.103396i
\(85\) 42.6147 0.501349
\(86\) 13.4351i 0.156222i
\(87\) 15.5233 + 52.0418i 0.178428 + 0.598181i
\(88\) −53.2276 −0.604859
\(89\) 98.9857i 1.11220i 0.831116 + 0.556100i \(0.187703\pi\)
−0.831116 + 0.556100i \(0.812297\pi\)
\(90\) 23.8098 15.5914i 0.264553 0.173238i
\(91\) −16.4490 −0.180759
\(92\) 9.59166i 0.104257i
\(93\) 22.0671 6.58227i 0.237280 0.0707771i
\(94\) 74.8798 0.796593
\(95\) 18.9953i 0.199951i
\(96\) 4.85086 + 16.2625i 0.0505298 + 0.169401i
\(97\) −41.8721 −0.431671 −0.215835 0.976430i \(-0.569247\pi\)
−0.215835 + 0.976430i \(0.569247\pi\)
\(98\) 33.0278i 0.337019i
\(99\) 92.7850 + 141.693i 0.937222 + 1.43124i
\(100\) 10.0000 0.100000
\(101\) 17.7056i 0.175303i 0.996151 + 0.0876517i \(0.0279363\pi\)
−0.996151 + 0.0876517i \(0.972064\pi\)
\(102\) 77.4822 23.1118i 0.759629 0.226586i
\(103\) 69.5747 0.675482 0.337741 0.941239i \(-0.390337\pi\)
0.337741 + 0.941239i \(0.390337\pi\)
\(104\) 9.18708i 0.0883373i
\(105\) −9.71039 32.5541i −0.0924799 0.310039i
\(106\) 126.520 1.19358
\(107\) 56.0057i 0.523418i 0.965147 + 0.261709i \(0.0842861\pi\)
−0.965147 + 0.261709i \(0.915714\pi\)
\(108\) 34.8352 41.2615i 0.322548 0.382051i
\(109\) −23.3967 −0.214648 −0.107324 0.994224i \(-0.534228\pi\)
−0.107324 + 0.994224i \(0.534228\pi\)
\(110\) 59.5102i 0.541002i
\(111\) −16.5067 + 4.92368i −0.148709 + 0.0443575i
\(112\) 20.2567 0.180863
\(113\) 189.931i 1.68080i −0.541966 0.840401i \(-0.682320\pi\)
0.541966 0.840401i \(-0.317680\pi\)
\(114\) −10.3020 34.5373i −0.0903680 0.302959i
\(115\) 10.7238 0.0932505
\(116\) 36.2051i 0.312113i
\(117\) −24.4562 + 16.0147i −0.209027 + 0.136878i
\(118\) 83.3798 0.706609
\(119\) 96.5123i 0.811027i
\(120\) 18.1820 5.42342i 0.151517 0.0451952i
\(121\) −233.147 −1.92683
\(122\) 133.284i 1.09249i
\(123\) −41.8100 140.168i −0.339919 1.13958i
\(124\) 15.3519 0.123806
\(125\) 11.1803i 0.0894427i
\(126\) −35.3109 53.9236i −0.280245 0.427965i
\(127\) 201.992 1.59049 0.795245 0.606288i \(-0.207342\pi\)
0.795245 + 0.606288i \(0.207342\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −27.3111 + 8.14647i −0.211714 + 0.0631509i
\(130\) −10.2715 −0.0790113
\(131\) 131.815i 1.00622i −0.864223 0.503110i \(-0.832189\pi\)
0.864223 0.503110i \(-0.167811\pi\)
\(132\) 32.2749 + 108.202i 0.244507 + 0.819710i
\(133\) −43.0199 −0.323458
\(134\) 6.74446i 0.0503318i
\(135\) −46.1317 38.9469i −0.341716 0.288496i
\(136\) 53.9038 0.396351
\(137\) 69.1354i 0.504638i −0.967644 0.252319i \(-0.918807\pi\)
0.967644 0.252319i \(-0.0811932\pi\)
\(138\) 19.4981 5.81597i 0.141290 0.0421447i
\(139\) 51.2040 0.368374 0.184187 0.982891i \(-0.441035\pi\)
0.184187 + 0.982891i \(0.441035\pi\)
\(140\) 22.6476i 0.161769i
\(141\) −45.4039 152.217i −0.322013 1.07955i
\(142\) −23.0949 −0.162640
\(143\) 61.1257i 0.427453i
\(144\) 30.1173 19.7218i 0.209148 0.136957i
\(145\) 40.4785 0.279162
\(146\) 129.808i 0.889097i
\(147\) 67.1394 20.0267i 0.456731 0.136236i
\(148\) −11.4836 −0.0775917
\(149\) 219.870i 1.47564i 0.674998 + 0.737820i \(0.264144\pi\)
−0.674998 + 0.737820i \(0.735856\pi\)
\(150\) −6.06357 20.3281i −0.0404238 0.135521i
\(151\) −214.804 −1.42255 −0.711273 0.702916i \(-0.751881\pi\)
−0.711273 + 0.702916i \(0.751881\pi\)
\(152\) 24.0274i 0.158075i
\(153\) −93.9638 143.493i −0.614142 0.937862i
\(154\) 134.777 0.875174
\(155\) 17.1640i 0.110735i
\(156\) −18.6756 + 5.57065i −0.119715 + 0.0357093i
\(157\) 99.1915 0.631793 0.315896 0.948794i \(-0.397695\pi\)
0.315896 + 0.948794i \(0.397695\pi\)
\(158\) 156.329i 0.989423i
\(159\) −76.7160 257.191i −0.482491 1.61755i
\(160\) 12.6491 0.0790569
\(161\) 24.2869i 0.150850i
\(162\) −104.999 45.7943i −0.648145 0.282681i
\(163\) −123.345 −0.756716 −0.378358 0.925659i \(-0.623511\pi\)
−0.378358 + 0.925659i \(0.623511\pi\)
\(164\) 97.5140i 0.594598i
\(165\) 120.973 36.0845i 0.733171 0.218694i
\(166\) 22.0563 0.132869
\(167\) 11.3950i 0.0682337i −0.999418 0.0341169i \(-0.989138\pi\)
0.999418 0.0341169i \(-0.0108618\pi\)
\(168\) −12.2828 41.1780i −0.0731118 0.245107i
\(169\) −158.450 −0.937572
\(170\) 60.2663i 0.354508i
\(171\) −63.9613 + 41.8839i −0.374043 + 0.244935i
\(172\) −19.0001 −0.110466
\(173\) 59.2460i 0.342462i −0.985231 0.171231i \(-0.945225\pi\)
0.985231 0.171231i \(-0.0547745\pi\)
\(174\) 73.5982 21.9532i 0.422978 0.126168i
\(175\) −25.3208 −0.144691
\(176\) 75.2752i 0.427700i
\(177\) −50.5579 169.496i −0.285638 0.957602i
\(178\) 139.987 0.786444
\(179\) 137.958i 0.770712i 0.922768 + 0.385356i \(0.125921\pi\)
−0.922768 + 0.385356i \(0.874079\pi\)
\(180\) −22.0496 33.6722i −0.122498 0.187068i
\(181\) −272.565 −1.50588 −0.752941 0.658088i \(-0.771366\pi\)
−0.752941 + 0.658088i \(0.771366\pi\)
\(182\) 23.2625i 0.127816i
\(183\) 270.941 80.8176i 1.48055 0.441626i
\(184\) 13.5647 0.0737210
\(185\) 12.8390i 0.0694001i
\(186\) −9.30874 31.2076i −0.0500470 0.167783i
\(187\) 358.646 1.91789
\(188\) 105.896i 0.563277i
\(189\) −88.2057 + 104.478i −0.466697 + 0.552791i
\(190\) −26.8634 −0.141386
\(191\) 85.7231i 0.448812i 0.974496 + 0.224406i \(0.0720442\pi\)
−0.974496 + 0.224406i \(0.927956\pi\)
\(192\) 22.9987 6.86015i 0.119785 0.0357299i
\(193\) 197.316 1.02236 0.511182 0.859472i \(-0.329208\pi\)
0.511182 + 0.859472i \(0.329208\pi\)
\(194\) 59.2160i 0.305237i
\(195\) 6.22817 + 20.8800i 0.0319394 + 0.107077i
\(196\) 46.7084 0.238308
\(197\) 196.588i 0.997910i 0.866628 + 0.498955i \(0.166283\pi\)
−0.866628 + 0.498955i \(0.833717\pi\)
\(198\) 200.384 131.218i 1.01204 0.662716i
\(199\) −13.6075 −0.0683794 −0.0341897 0.999415i \(-0.510885\pi\)
−0.0341897 + 0.999415i \(0.510885\pi\)
\(200\) 14.1421i 0.0707107i
\(201\) 13.7102 4.08955i 0.0682101 0.0203460i
\(202\) 25.0396 0.123958
\(203\) 91.6743i 0.451598i
\(204\) −32.6850 109.576i −0.160220 0.537139i
\(205\) −109.024 −0.531824
\(206\) 98.3935i 0.477638i
\(207\) −23.6456 36.1094i −0.114230 0.174441i
\(208\) −12.9925 −0.0624639
\(209\) 159.865i 0.764904i
\(210\) −46.0384 + 13.7326i −0.219231 + 0.0653932i
\(211\) 318.759 1.51071 0.755353 0.655318i \(-0.227465\pi\)
0.755353 + 0.655318i \(0.227465\pi\)
\(212\) 178.926i 0.843989i
\(213\) 14.0038 + 46.9477i 0.0657454 + 0.220412i
\(214\) 79.2041 0.370113
\(215\) 21.2428i 0.0988035i
\(216\) −58.3525 49.2644i −0.270151 0.228076i
\(217\) −38.8723 −0.179135
\(218\) 33.0879i 0.151779i
\(219\) 263.876 78.7101i 1.20491 0.359407i
\(220\) 84.1602 0.382546
\(221\) 61.9023i 0.280101i
\(222\) 6.96314 + 23.3439i 0.0313655 + 0.105153i
\(223\) −109.529 −0.491161 −0.245580 0.969376i \(-0.578979\pi\)
−0.245580 + 0.969376i \(0.578979\pi\)
\(224\) 28.6473i 0.127890i
\(225\) −37.6466 + 24.6522i −0.167318 + 0.109565i
\(226\) −268.602 −1.18851
\(227\) 123.236i 0.542891i 0.962454 + 0.271446i \(0.0875018\pi\)
−0.962454 + 0.271446i \(0.912498\pi\)
\(228\) −48.8432 + 14.5692i −0.214224 + 0.0638999i
\(229\) −408.810 −1.78520 −0.892598 0.450853i \(-0.851120\pi\)
−0.892598 + 0.450853i \(0.851120\pi\)
\(230\) 15.1658i 0.0659380i
\(231\) −81.7228 273.976i −0.353778 1.18604i
\(232\) 51.2017 0.220697
\(233\) 310.433i 1.33233i 0.745804 + 0.666165i \(0.232065\pi\)
−0.745804 + 0.666165i \(0.767935\pi\)
\(234\) 22.6482 + 34.5862i 0.0967871 + 0.147804i
\(235\) −118.395 −0.503810
\(236\) 117.917i 0.499648i
\(237\) 317.787 94.7911i 1.34088 0.399963i
\(238\) −136.489 −0.573483
\(239\) 306.119i 1.28083i −0.768028 0.640417i \(-0.778762\pi\)
0.768028 0.640417i \(-0.221238\pi\)
\(240\) −7.66988 25.7133i −0.0319578 0.107139i
\(241\) −336.911 −1.39797 −0.698986 0.715136i \(-0.746365\pi\)
−0.698986 + 0.715136i \(0.746365\pi\)
\(242\) 329.720i 1.36248i
\(243\) −29.4241 + 241.212i −0.121087 + 0.992642i
\(244\) 188.492 0.772507
\(245\) 52.2216i 0.213149i
\(246\) −198.228 + 59.1283i −0.805804 + 0.240359i
\(247\) 27.5927 0.111711
\(248\) 21.7109i 0.0875439i
\(249\) −13.3740 44.8363i −0.0537107 0.180065i
\(250\) −15.8114 −0.0632456
\(251\) 384.416i 1.53154i 0.643115 + 0.765770i \(0.277642\pi\)
−0.643115 + 0.765770i \(0.722358\pi\)
\(252\) −76.2595 + 49.9372i −0.302617 + 0.198163i
\(253\) 90.2518 0.356726
\(254\) 285.660i 1.12465i
\(255\) −122.510 + 36.5429i −0.480432 + 0.143305i
\(256\) 16.0000 0.0625000
\(257\) 291.537i 1.13439i −0.823585 0.567193i \(-0.808029\pi\)
0.823585 0.567193i \(-0.191971\pi\)
\(258\) 11.5208 + 38.6237i 0.0446544 + 0.149704i
\(259\) 29.0774 0.112268
\(260\) 14.5260i 0.0558694i
\(261\) −89.2536 136.300i −0.341968 0.522222i
\(262\) −186.414 −0.711504
\(263\) 48.4412i 0.184187i 0.995750 + 0.0920935i \(0.0293559\pi\)
−0.995750 + 0.0920935i \(0.970644\pi\)
\(264\) 153.020 45.6436i 0.579623 0.172893i
\(265\) −200.045 −0.754887
\(266\) 60.8393i 0.228719i
\(267\) −84.8821 284.567i −0.317910 1.06580i
\(268\) 9.53811 0.0355900
\(269\) 200.718i 0.746165i 0.927798 + 0.373082i \(0.121699\pi\)
−0.927798 + 0.373082i \(0.878301\pi\)
\(270\) −55.0793 + 65.2401i −0.203997 + 0.241630i
\(271\) 394.542 1.45587 0.727936 0.685645i \(-0.240480\pi\)
0.727936 + 0.685645i \(0.240480\pi\)
\(272\) 76.2315i 0.280263i
\(273\) 47.2882 14.1054i 0.173217 0.0516680i
\(274\) −97.7722 −0.356833
\(275\) 94.0940i 0.342160i
\(276\) −8.22503 27.5744i −0.0298008 0.0999073i
\(277\) 167.087 0.603204 0.301602 0.953434i \(-0.402479\pi\)
0.301602 + 0.953434i \(0.402479\pi\)
\(278\) 72.4133i 0.260480i
\(279\) −57.7948 + 37.8459i −0.207150 + 0.135648i
\(280\) −32.0286 −0.114388
\(281\) 282.594i 1.00567i −0.864381 0.502837i \(-0.832290\pi\)
0.864381 0.502837i \(-0.167710\pi\)
\(282\) −215.267 + 64.2108i −0.763357 + 0.227698i
\(283\) −116.160 −0.410461 −0.205230 0.978714i \(-0.565794\pi\)
−0.205230 + 0.978714i \(0.565794\pi\)
\(284\) 32.6612i 0.115004i
\(285\) 16.2888 + 54.6083i 0.0571538 + 0.191608i
\(286\) −86.4448 −0.302255
\(287\) 246.914i 0.860327i
\(288\) −27.8908 42.5923i −0.0968431 0.147890i
\(289\) −74.2025 −0.256756
\(290\) 57.2453i 0.197398i
\(291\) 120.375 35.9061i 0.413660 0.123389i
\(292\) 183.577 0.628687
\(293\) 437.333i 1.49261i −0.665607 0.746303i \(-0.731827\pi\)
0.665607 0.746303i \(-0.268173\pi\)
\(294\) −28.3220 94.9495i −0.0963332 0.322957i
\(295\) −131.835 −0.446898
\(296\) 16.2402i 0.0548656i
\(297\) −388.246 327.778i −1.30722 1.10363i
\(298\) 310.943 1.04343
\(299\) 15.5774i 0.0520985i
\(300\) −28.7483 + 8.57518i −0.0958278 + 0.0285839i
\(301\) 48.1099 0.159833
\(302\) 303.779i 1.00589i
\(303\) −15.1829 50.9008i −0.0501086 0.167989i
\(304\) −33.9798 −0.111776
\(305\) 210.740i 0.690951i
\(306\) −202.930 + 132.885i −0.663169 + 0.434264i
\(307\) 72.6694 0.236708 0.118354 0.992971i \(-0.462238\pi\)
0.118354 + 0.992971i \(0.462238\pi\)
\(308\) 190.603i 0.618841i
\(309\) −200.016 + 59.6616i −0.647300 + 0.193080i
\(310\) −24.2735 −0.0783016
\(311\) 260.179i 0.836589i 0.908312 + 0.418294i \(0.137372\pi\)
−0.908312 + 0.418294i \(0.862628\pi\)
\(312\) 7.87809 + 26.4113i 0.0252503 + 0.0846516i
\(313\) 376.440 1.20268 0.601342 0.798992i \(-0.294633\pi\)
0.601342 + 0.798992i \(0.294633\pi\)
\(314\) 140.278i 0.446745i
\(315\) 55.8315 + 85.2607i 0.177243 + 0.270669i
\(316\) 221.082 0.699628
\(317\) 312.850i 0.986907i −0.869772 0.493454i \(-0.835734\pi\)
0.869772 0.493454i \(-0.164266\pi\)
\(318\) −363.722 + 108.493i −1.14378 + 0.341172i
\(319\) 340.668 1.06792
\(320\) 17.8885i 0.0559017i
\(321\) −48.0260 161.007i −0.149614 0.501580i
\(322\) −34.3469 −0.106667
\(323\) 161.896i 0.501225i
\(324\) −64.7629 + 148.492i −0.199886 + 0.458308i
\(325\) 16.2406 0.0499711
\(326\) 174.436i 0.535079i
\(327\) 67.2615 20.0631i 0.205693 0.0613550i
\(328\) −137.906 −0.420444
\(329\) 268.138i 0.815008i
\(330\) −51.0311 171.082i −0.154640 0.518430i
\(331\) 104.128 0.314585 0.157292 0.987552i \(-0.449723\pi\)
0.157292 + 0.987552i \(0.449723\pi\)
\(332\) 31.1923i 0.0939526i
\(333\) 43.2317 28.3095i 0.129825 0.0850136i
\(334\) −16.1150 −0.0482485
\(335\) 10.6639i 0.0318326i
\(336\) −58.2345 + 17.3705i −0.173317 + 0.0516978i
\(337\) 114.015 0.338324 0.169162 0.985588i \(-0.445894\pi\)
0.169162 + 0.985588i \(0.445894\pi\)
\(338\) 224.082i 0.662964i
\(339\) 162.869 + 546.018i 0.480439 + 1.61067i
\(340\) −85.2294 −0.250675
\(341\) 144.452i 0.423614i
\(342\) 59.2328 + 90.4549i 0.173195 + 0.264488i
\(343\) −366.414 −1.06826
\(344\) 26.8702i 0.0781111i
\(345\) −30.8291 + 9.19586i −0.0893598 + 0.0266547i
\(346\) −83.7865 −0.242157
\(347\) 15.3420i 0.0442131i −0.999756 0.0221066i \(-0.992963\pi\)
0.999756 0.0221066i \(-0.00703731\pi\)
\(348\) −31.0465 104.084i −0.0892142 0.299091i
\(349\) 645.031 1.84823 0.924113 0.382119i \(-0.124806\pi\)
0.924113 + 0.382119i \(0.124806\pi\)
\(350\) 35.8091i 0.102312i
\(351\) 56.5745 67.0111i 0.161181 0.190915i
\(352\) 106.455 0.302429
\(353\) 261.860i 0.741813i −0.928670 0.370907i \(-0.879047\pi\)
0.928670 0.370907i \(-0.120953\pi\)
\(354\) −239.703 + 71.4997i −0.677127 + 0.201977i
\(355\) 36.5163 0.102863
\(356\) 197.971i 0.556100i
\(357\) 82.7610 + 277.457i 0.231824 + 0.777189i
\(358\) 195.101 0.544976
\(359\) 500.283i 1.39354i 0.717292 + 0.696772i \(0.245381\pi\)
−0.717292 + 0.696772i \(0.754619\pi\)
\(360\) −47.6196 + 31.1829i −0.132277 + 0.0866191i
\(361\) −288.836 −0.800099
\(362\) 385.465i 1.06482i
\(363\) 670.258 199.928i 1.84644 0.550765i
\(364\) 32.8981 0.0903793
\(365\) 205.245i 0.562315i
\(366\) −114.293 383.169i −0.312277 1.04691i
\(367\) 664.129 1.80962 0.904809 0.425819i \(-0.140014\pi\)
0.904809 + 0.425819i \(0.140014\pi\)
\(368\) 19.1833i 0.0521286i
\(369\) 240.394 + 367.107i 0.651474 + 0.994871i
\(370\) 18.1571 0.0490733
\(371\) 453.055i 1.22117i
\(372\) −44.1342 + 13.1645i −0.118640 + 0.0353886i
\(373\) −120.804 −0.323871 −0.161936 0.986801i \(-0.551774\pi\)
−0.161936 + 0.986801i \(0.551774\pi\)
\(374\) 507.202i 1.35616i
\(375\) 9.58735 + 32.1416i 0.0255663 + 0.0857109i
\(376\) −149.760 −0.398297
\(377\) 58.7993i 0.155966i
\(378\) 147.754 + 124.742i 0.390882 + 0.330004i
\(379\) 346.819 0.915089 0.457545 0.889187i \(-0.348729\pi\)
0.457545 + 0.889187i \(0.348729\pi\)
\(380\) 37.9906i 0.0999753i
\(381\) −580.694 + 173.212i −1.52413 + 0.454625i
\(382\) 121.231 0.317358
\(383\) 340.037i 0.887825i 0.896070 + 0.443913i \(0.146410\pi\)
−0.896070 + 0.443913i \(0.853590\pi\)
\(384\) −9.70171 32.5250i −0.0252649 0.0847006i
\(385\) −213.101 −0.553508
\(386\) 279.047i 0.722921i
\(387\) 71.5290 46.8395i 0.184829 0.121032i
\(388\) 83.7441 0.215835
\(389\) 182.872i 0.470108i −0.971982 0.235054i \(-0.924473\pi\)
0.971982 0.235054i \(-0.0755267\pi\)
\(390\) 29.5287 8.80797i 0.0757147 0.0225845i
\(391\) −91.3983 −0.233755
\(392\) 66.0557i 0.168509i
\(393\) 113.034 + 378.945i 0.287617 + 0.964237i
\(394\) 278.018 0.705629
\(395\) 247.178i 0.625766i
\(396\) −185.570 283.386i −0.468611 0.715620i
\(397\) 148.814 0.374845 0.187423 0.982279i \(-0.439987\pi\)
0.187423 + 0.982279i \(0.439987\pi\)
\(398\) 19.2439i 0.0483515i
\(399\) 123.675 36.8904i 0.309962 0.0924570i
\(400\) −20.0000 −0.0500000
\(401\) 597.537i 1.49012i −0.666999 0.745058i \(-0.732422\pi\)
0.666999 0.745058i \(-0.267578\pi\)
\(402\) −5.78350 19.3892i −0.0143868 0.0482318i
\(403\) 24.9324 0.0618671
\(404\) 35.4113i 0.0876517i
\(405\) 166.019 + 72.4071i 0.409923 + 0.178783i
\(406\) −129.647 −0.319328
\(407\) 108.053i 0.265488i
\(408\) −154.964 + 46.2235i −0.379815 + 0.113293i
\(409\) −272.829 −0.667065 −0.333532 0.942739i \(-0.608241\pi\)
−0.333532 + 0.942739i \(0.608241\pi\)
\(410\) 154.183i 0.376057i
\(411\) 59.2849 + 198.753i 0.144245 + 0.483583i
\(412\) −139.149 −0.337741
\(413\) 298.575i 0.722943i
\(414\) −51.0664 + 33.4399i −0.123349 + 0.0807727i
\(415\) −34.8740 −0.0840337
\(416\) 18.3742i 0.0441686i
\(417\) −147.203 + 43.9083i −0.353004 + 0.105296i
\(418\) −226.083 −0.540869
\(419\) 262.152i 0.625661i −0.949809 0.312831i \(-0.898723\pi\)
0.949809 0.312831i \(-0.101277\pi\)
\(420\) 19.4208 + 65.1082i 0.0462399 + 0.155020i
\(421\) 630.483 1.49758 0.748792 0.662806i \(-0.230634\pi\)
0.748792 + 0.662806i \(0.230634\pi\)
\(422\) 450.794i 1.06823i
\(423\) 261.057 + 398.663i 0.617156 + 0.942465i
\(424\) −253.039 −0.596790
\(425\) 95.2894i 0.224210i
\(426\) 66.3940 19.8043i 0.155855 0.0464890i
\(427\) −477.277 −1.11774
\(428\) 112.011i 0.261709i
\(429\) 52.4164 + 175.726i 0.122183 + 0.409618i
\(430\) 30.0418 0.0698646
\(431\) 69.6557i 0.161614i 0.996730 + 0.0808071i \(0.0257498\pi\)
−0.996730 + 0.0808071i \(0.974250\pi\)
\(432\) −69.6704 + 82.5229i −0.161274 + 0.191025i
\(433\) −372.470 −0.860209 −0.430104 0.902779i \(-0.641523\pi\)
−0.430104 + 0.902779i \(0.641523\pi\)
\(434\) 54.9738i 0.126668i
\(435\) −116.369 + 34.7111i −0.267515 + 0.0797956i
\(436\) 46.7934 0.107324
\(437\) 40.7404i 0.0932274i
\(438\) −111.313 373.177i −0.254139 0.852002i
\(439\) 337.965 0.769851 0.384926 0.922948i \(-0.374227\pi\)
0.384926 + 0.922948i \(0.374227\pi\)
\(440\) 119.020i 0.270501i
\(441\) −175.841 + 115.147i −0.398733 + 0.261103i
\(442\) 87.5431 0.198061
\(443\) 715.113i 1.61425i 0.590380 + 0.807126i \(0.298978\pi\)
−0.590380 + 0.807126i \(0.701022\pi\)
\(444\) 33.0133 9.84737i 0.0743543 0.0221788i
\(445\) −221.339 −0.497391
\(446\) 154.897i 0.347303i
\(447\) −188.543 632.090i −0.421796 1.41407i
\(448\) −40.5133 −0.0904316
\(449\) 684.244i 1.52393i 0.647619 + 0.761964i \(0.275765\pi\)
−0.647619 + 0.761964i \(0.724235\pi\)
\(450\) 34.8635 + 53.2404i 0.0774744 + 0.118312i
\(451\) −917.548 −2.03448
\(452\) 379.861i 0.840401i
\(453\) 617.527 184.199i 1.36319 0.406620i
\(454\) 174.283 0.383882
\(455\) 36.7812i 0.0808377i
\(456\) 20.6039 + 69.0747i 0.0451840 + 0.151480i
\(457\) 277.770 0.607813 0.303906 0.952702i \(-0.401709\pi\)
0.303906 + 0.952702i \(0.401709\pi\)
\(458\) 578.145i 1.26232i
\(459\) 393.178 + 331.942i 0.856597 + 0.723186i
\(460\) −21.4476 −0.0466252
\(461\) 51.6571i 0.112054i 0.998429 + 0.0560272i \(0.0178433\pi\)
−0.998429 + 0.0560272i \(0.982157\pi\)
\(462\) −387.461 + 115.574i −0.838659 + 0.250159i
\(463\) 274.835 0.593595 0.296798 0.954940i \(-0.404081\pi\)
0.296798 + 0.954940i \(0.404081\pi\)
\(464\) 72.4102i 0.156056i
\(465\) 14.7184 + 49.3435i 0.0316525 + 0.106115i
\(466\) 439.018 0.942100
\(467\) 908.495i 1.94539i −0.232096 0.972693i \(-0.574558\pi\)
0.232096 0.972693i \(-0.425442\pi\)
\(468\) 48.9123 32.0294i 0.104514 0.0684388i
\(469\) −24.1513 −0.0514953
\(470\) 167.436i 0.356247i
\(471\) −285.159 + 85.0585i −0.605433 + 0.180591i
\(472\) −166.760 −0.353304
\(473\) 178.779i 0.377969i
\(474\) −134.055 449.419i −0.282816 0.948142i
\(475\) 42.4748 0.0894206
\(476\) 193.025i 0.405514i
\(477\) 441.091 + 673.595i 0.924720 + 1.41215i
\(478\) −432.918 −0.905686
\(479\) 59.4517i 0.124116i 0.998073 + 0.0620582i \(0.0197664\pi\)
−0.998073 + 0.0620582i \(0.980234\pi\)
\(480\) −36.3641 + 10.8468i −0.0757585 + 0.0225976i
\(481\) −18.6500 −0.0387734
\(482\) 476.464i 0.988515i
\(483\) 20.8265 + 69.8208i 0.0431190 + 0.144556i
\(484\) 466.294 0.963417
\(485\) 93.6288i 0.193049i
\(486\) 341.125 + 41.6120i 0.701904 + 0.0856213i
\(487\) 706.752 1.45124 0.725618 0.688097i \(-0.241554\pi\)
0.725618 + 0.688097i \(0.241554\pi\)
\(488\) 266.568i 0.546245i
\(489\) 354.595 105.770i 0.725144 0.216299i
\(490\) −73.8525 −0.150719
\(491\) 785.728i 1.60026i −0.599827 0.800130i \(-0.704764\pi\)
0.599827 0.800130i \(-0.295236\pi\)
\(492\) 83.6201 + 280.337i 0.169960 + 0.569790i
\(493\) −344.996 −0.699789
\(494\) 39.0219i 0.0789917i
\(495\) −316.835 + 207.474i −0.640070 + 0.419139i
\(496\) −30.7038 −0.0619029
\(497\) 82.7008i 0.166400i
\(498\) −63.4080 + 18.9136i −0.127325 + 0.0379792i
\(499\) 628.387 1.25929 0.629646 0.776882i \(-0.283200\pi\)
0.629646 + 0.776882i \(0.283200\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) 9.77145 + 32.7588i 0.0195039 + 0.0653868i
\(502\) 543.647 1.08296
\(503\) 436.393i 0.867581i 0.901014 + 0.433791i \(0.142824\pi\)
−0.901014 + 0.433791i \(0.857176\pi\)
\(504\) 70.6219 + 107.847i 0.140123 + 0.213983i
\(505\) −39.5910 −0.0783981
\(506\) 127.635i 0.252244i
\(507\) 455.516 135.874i 0.898454 0.267995i
\(508\) −403.984 −0.795245
\(509\) 152.541i 0.299687i 0.988710 + 0.149844i \(0.0478771\pi\)
−0.988710 + 0.149844i \(0.952123\pi\)
\(510\) 51.6794 + 173.255i 0.101332 + 0.339717i
\(511\) −464.831 −0.909650
\(512\) 22.6274i 0.0441942i
\(513\) 147.962 175.257i 0.288425 0.341632i
\(514\) −412.296 −0.802133
\(515\) 155.574i 0.302085i
\(516\) 54.6221 16.2929i 0.105857 0.0315755i
\(517\) −996.417 −1.92731
\(518\) 41.1216i 0.0793853i
\(519\) 50.8045 + 170.322i 0.0978893 + 0.328174i
\(520\) 20.5429 0.0395056
\(521\) 686.243i 1.31717i 0.752508 + 0.658583i \(0.228844\pi\)
−0.752508 + 0.658583i \(0.771156\pi\)
\(522\) −192.757 + 126.224i −0.369267 + 0.241808i
\(523\) −759.604 −1.45240 −0.726199 0.687485i \(-0.758715\pi\)
−0.726199 + 0.687485i \(0.758715\pi\)
\(524\) 263.629i 0.503110i
\(525\) 72.7932 21.7131i 0.138654 0.0413583i
\(526\) 68.5062 0.130240
\(527\) 146.287i 0.277585i
\(528\) −64.5498 216.404i −0.122253 0.409855i
\(529\) −23.0000 −0.0434783
\(530\) 282.906i 0.533785i
\(531\) 290.691 + 443.917i 0.547441 + 0.836002i
\(532\) 86.0398 0.161729
\(533\) 158.369i 0.297127i
\(534\) −402.439 + 120.041i −0.753631 + 0.224797i
\(535\) −125.233 −0.234080
\(536\) 13.4889i 0.0251659i
\(537\) −118.301 396.605i −0.220300 0.738556i
\(538\) 283.859 0.527618
\(539\) 439.498i 0.815395i
\(540\) 92.2634 + 77.8939i 0.170858 + 0.144248i
\(541\) 913.857 1.68920 0.844600 0.535399i \(-0.179839\pi\)
0.844600 + 0.535399i \(0.179839\pi\)
\(542\) 557.966i 1.02946i
\(543\) 783.578 233.729i 1.44305 0.430441i
\(544\) −107.808 −0.198176
\(545\) 52.3166i 0.0959937i
\(546\) −19.9480 66.8757i −0.0365348 0.122483i
\(547\) 343.498 0.627967 0.313983 0.949428i \(-0.398336\pi\)
0.313983 + 0.949428i \(0.398336\pi\)
\(548\) 138.271i 0.252319i
\(549\) −709.608 + 464.674i −1.29255 + 0.846401i
\(550\) −133.069 −0.241944
\(551\) 153.780i 0.279093i
\(552\) −38.9961 + 11.6319i −0.0706452 + 0.0210724i
\(553\) −559.799 −1.01230
\(554\) 236.297i 0.426529i
\(555\) −11.0097 36.9100i −0.0198373 0.0665045i
\(556\) −102.408 −0.184187
\(557\) 332.247i 0.596493i −0.954489 0.298247i \(-0.903598\pi\)
0.954489 0.298247i \(-0.0964017\pi\)
\(558\) 53.5221 + 81.7341i 0.0959178 + 0.146477i
\(559\) −30.8573 −0.0552009
\(560\) 45.2953i 0.0808845i
\(561\) −1031.05 + 307.546i −1.83787 + 0.548210i
\(562\) −399.649 −0.711119
\(563\) 741.449i 1.31696i 0.752598 + 0.658481i \(0.228801\pi\)
−0.752598 + 0.658481i \(0.771199\pi\)
\(564\) 90.8078 + 304.433i 0.161007 + 0.539775i
\(565\) 424.698 0.751677
\(566\) 164.276i 0.290240i
\(567\) 163.985 375.993i 0.289215 0.663128i
\(568\) 46.1898 0.0813201
\(569\) 299.724i 0.526755i −0.964693 0.263378i \(-0.915163\pi\)
0.964693 0.263378i \(-0.0848366\pi\)
\(570\) 77.2278 23.0359i 0.135487 0.0404138i
\(571\) −599.952 −1.05070 −0.525352 0.850885i \(-0.676066\pi\)
−0.525352 + 0.850885i \(0.676066\pi\)
\(572\) 122.251i 0.213726i
\(573\) −73.5092 246.440i −0.128288 0.430087i
\(574\) 349.189 0.608343
\(575\) 23.9792i 0.0417029i
\(576\) −60.2346 + 39.4435i −0.104574 + 0.0684784i
\(577\) −687.038 −1.19071 −0.595354 0.803464i \(-0.702988\pi\)
−0.595354 + 0.803464i \(0.702988\pi\)
\(578\) 104.938i 0.181554i
\(579\) −567.252 + 169.202i −0.979709 + 0.292232i
\(580\) −80.9570 −0.139581
\(581\) 78.9814i 0.135940i
\(582\) −50.7788 170.236i −0.0872489 0.292502i
\(583\) −1683.58 −2.88779
\(584\) 259.616i 0.444549i
\(585\) −35.8099 54.6856i −0.0612135 0.0934797i
\(586\) −618.483 −1.05543
\(587\) 124.548i 0.212177i 0.994357 + 0.106089i \(0.0338328\pi\)
−0.994357 + 0.106089i \(0.966167\pi\)
\(588\) −134.279 + 40.0533i −0.228365 + 0.0681179i
\(589\) 65.2069 0.110708
\(590\) 186.443i 0.316005i
\(591\) −168.578 565.159i −0.285242 0.956275i
\(592\) 22.9671 0.0387958
\(593\) 289.161i 0.487625i 0.969822 + 0.243812i \(0.0783981\pi\)
−0.969822 + 0.243812i \(0.921602\pi\)
\(594\) −463.548 + 549.062i −0.780385 + 0.924347i
\(595\) 215.808 0.362703
\(596\) 439.740i 0.737820i
\(597\) 39.1193 11.6687i 0.0655264 0.0195455i
\(598\) 22.0298 0.0368392
\(599\) 162.616i 0.271479i 0.990745 + 0.135739i \(0.0433410\pi\)
−0.990745 + 0.135739i \(0.956659\pi\)
\(600\) 12.1271 + 40.6563i 0.0202119 + 0.0677605i
\(601\) 815.650 1.35715 0.678577 0.734529i \(-0.262597\pi\)
0.678577 + 0.734529i \(0.262597\pi\)
\(602\) 68.0376i 0.113019i
\(603\) −35.9078 + 23.5136i −0.0595485 + 0.0389943i
\(604\) 429.609 0.711273
\(605\) 521.332i 0.861707i
\(606\) −71.9845 + 21.4719i −0.118786 + 0.0354322i
\(607\) −771.203 −1.27052 −0.635258 0.772300i \(-0.719106\pi\)
−0.635258 + 0.772300i \(0.719106\pi\)
\(608\) 48.0547i 0.0790374i
\(609\) 78.6124 + 263.548i 0.129084 + 0.432756i
\(610\) −298.032 −0.488576
\(611\) 171.982i 0.281476i
\(612\) 187.928 + 286.986i 0.307071 + 0.468931i
\(613\) 149.236 0.243451 0.121726 0.992564i \(-0.461157\pi\)
0.121726 + 0.992564i \(0.461157\pi\)
\(614\) 102.770i 0.167378i
\(615\) 313.426 93.4901i 0.509635 0.152016i
\(616\) −269.553 −0.437587
\(617\) 91.1721i 0.147767i −0.997267 0.0738834i \(-0.976461\pi\)
0.997267 0.0738834i \(-0.0235393\pi\)
\(618\) 84.3742 + 282.865i 0.136528 + 0.457710i
\(619\) 278.475 0.449879 0.224940 0.974373i \(-0.427782\pi\)
0.224940 + 0.974373i \(0.427782\pi\)
\(620\) 34.3279i 0.0553676i
\(621\) 98.9415 + 83.5319i 0.159326 + 0.134512i
\(622\) 367.949 0.591558
\(623\) 501.280i 0.804623i
\(624\) 37.3512 11.1413i 0.0598577 0.0178546i
\(625\) 25.0000 0.0400000
\(626\) 532.366i 0.850425i
\(627\) 137.087 + 459.585i 0.218640 + 0.732990i
\(628\) −198.383 −0.315896
\(629\) 109.426i 0.173968i
\(630\) 120.577 78.9576i 0.191392 0.125330i
\(631\) −488.140 −0.773597 −0.386798 0.922164i \(-0.626419\pi\)
−0.386798 + 0.922164i \(0.626419\pi\)
\(632\) 312.658i 0.494712i
\(633\) −916.379 + 273.342i −1.44768 + 0.431820i
\(634\) −442.436 −0.697849
\(635\) 451.668i 0.711289i
\(636\) 153.432 + 514.381i 0.241245 + 0.808776i
\(637\) 75.8573 0.119085
\(638\) 481.777i 0.755137i
\(639\) −80.5170 122.958i −0.126005 0.192423i
\(640\) −25.2982 −0.0395285
\(641\) 353.083i 0.550832i 0.961325 + 0.275416i \(0.0888155\pi\)
−0.961325 + 0.275416i \(0.911184\pi\)
\(642\) −227.698 + 67.9190i −0.354671 + 0.105793i
\(643\) 675.054 1.04985 0.524926 0.851148i \(-0.324093\pi\)
0.524926 + 0.851148i \(0.324093\pi\)
\(644\) 48.5738i 0.0754251i
\(645\) −18.2161 61.0694i −0.0282419 0.0946812i
\(646\) 228.955 0.354420
\(647\) 752.235i 1.16265i −0.813671 0.581325i \(-0.802534\pi\)
0.813671 0.581325i \(-0.197466\pi\)
\(648\) 209.999 + 91.5886i 0.324072 + 0.141340i
\(649\) −1109.53 −1.70959
\(650\) 22.9677i 0.0353349i
\(651\) 111.751 33.3337i 0.171661 0.0512039i
\(652\) 246.689 0.378358
\(653\) 90.4569i 0.138525i 0.997598 + 0.0692626i \(0.0220646\pi\)
−0.997598 + 0.0692626i \(0.977935\pi\)
\(654\) −28.3735 95.1222i −0.0433845 0.145447i
\(655\) 294.747 0.449995
\(656\) 195.028i 0.297299i
\(657\) −691.104 + 452.557i −1.05191 + 0.688823i
\(658\) 379.204 0.576298
\(659\) 352.118i 0.534322i −0.963652 0.267161i \(-0.913915\pi\)
0.963652 0.267161i \(-0.0860855\pi\)
\(660\) −241.946 + 72.1689i −0.366586 + 0.109347i
\(661\) 699.250 1.05787 0.528933 0.848664i \(-0.322592\pi\)
0.528933 + 0.848664i \(0.322592\pi\)
\(662\) 147.259i 0.222445i
\(663\) −53.0824 177.959i −0.0800639 0.268414i
\(664\) −44.1125 −0.0664345
\(665\) 96.1954i 0.144655i
\(666\) −40.0357 61.1389i −0.0601137 0.0918002i
\(667\) −86.8168 −0.130160
\(668\) 22.7901i 0.0341169i
\(669\) 314.877 93.9230i 0.470668 0.140393i
\(670\) −15.0811 −0.0225091
\(671\) 1773.59i 2.64321i
\(672\) 24.5656 + 82.3561i 0.0365559 + 0.122554i
\(673\) 677.167 1.00619 0.503096 0.864231i \(-0.332194\pi\)
0.503096 + 0.864231i \(0.332194\pi\)
\(674\) 161.242i 0.239231i
\(675\) 87.0880 103.154i 0.129019 0.152820i
\(676\) 316.899 0.468786
\(677\) 615.623i 0.909340i 0.890660 + 0.454670i \(0.150243\pi\)
−0.890660 + 0.454670i \(0.849757\pi\)
\(678\) 772.187 230.331i 1.13892 0.339722i
\(679\) −212.047 −0.312293
\(680\) 120.533i 0.177254i
\(681\) −105.677 354.284i −0.155180 0.520241i
\(682\) −204.286 −0.299540
\(683\) 221.790i 0.324729i −0.986731 0.162364i \(-0.948088\pi\)
0.986731 0.162364i \(-0.0519120\pi\)
\(684\) 127.923 83.7678i 0.187021 0.122468i
\(685\) 154.591 0.225681
\(686\) 518.187i 0.755375i
\(687\) 1175.26 350.562i 1.71071 0.510280i
\(688\) 38.0002 0.0552329
\(689\) 290.586i 0.421751i
\(690\) 13.0049 + 43.5990i 0.0188477 + 0.0631869i
\(691\) −61.9651 −0.0896745 −0.0448373 0.998994i \(-0.514277\pi\)
−0.0448373 + 0.998994i \(0.514277\pi\)
\(692\) 118.492i 0.171231i
\(693\) 469.879 + 717.556i 0.678036 + 1.03543i
\(694\) −21.6968 −0.0312634
\(695\) 114.496i 0.164742i
\(696\) −147.196 + 43.9064i −0.211489 + 0.0630839i
\(697\) 929.205 1.33315
\(698\) 912.211i 1.30689i
\(699\) −266.202 892.443i −0.380833 1.27674i
\(700\) 50.6417 0.0723453
\(701\) 420.912i 0.600445i −0.953869 0.300223i \(-0.902939\pi\)
0.953869 0.300223i \(-0.0970610\pi\)
\(702\) −94.7681 80.0084i −0.134997 0.113972i
\(703\) −48.7762 −0.0693829
\(704\) 150.550i 0.213850i
\(705\) 340.367 101.526i 0.482790 0.144009i
\(706\) −370.326 −0.524541
\(707\) 89.6644i 0.126824i
\(708\) 101.116 + 338.991i 0.142819 + 0.478801i
\(709\) −560.407 −0.790418 −0.395209 0.918591i \(-0.629328\pi\)
−0.395209 + 0.918591i \(0.629328\pi\)
\(710\) 51.6418i 0.0727350i
\(711\) −832.301 + 545.017i −1.17061 + 0.766550i
\(712\) −279.974 −0.393222
\(713\) 36.8126i 0.0516306i
\(714\) 392.383 117.042i 0.549556 0.163924i
\(715\) 136.681 0.191163
\(716\) 275.915i 0.385356i
\(717\) 262.503 + 880.041i 0.366113 + 1.22739i
\(718\) 707.506 0.985385
\(719\) 60.7661i 0.0845148i −0.999107 0.0422574i \(-0.986545\pi\)
0.999107 0.0422574i \(-0.0134550\pi\)
\(720\) 44.0992 + 67.3443i 0.0612489 + 0.0935338i
\(721\) 352.338 0.488680
\(722\) 408.475i 0.565755i
\(723\) 968.563 288.907i 1.33964 0.399595i
\(724\) 545.130 0.752941
\(725\) 90.5127i 0.124845i
\(726\) −282.741 947.889i −0.389450 1.30563i
\(727\) −305.359 −0.420026 −0.210013 0.977699i \(-0.567351\pi\)
−0.210013 + 0.977699i \(0.567351\pi\)
\(728\) 46.5249i 0.0639078i
\(729\) −122.254 718.676i −0.167701 0.985838i
\(730\) −290.260 −0.397616
\(731\) 181.051i 0.247675i
\(732\) −541.882 + 161.635i −0.740276 + 0.220813i
\(733\) −820.155 −1.11890 −0.559451 0.828864i \(-0.688988\pi\)
−0.559451 + 0.828864i \(0.688988\pi\)
\(734\) 939.221i 1.27959i
\(735\) 44.7810 + 150.128i 0.0609265 + 0.204256i
\(736\) −27.1293 −0.0368605
\(737\) 89.7478i 0.121775i
\(738\) 519.168 339.968i 0.703480 0.460661i
\(739\) −442.131 −0.598282 −0.299141 0.954209i \(-0.596700\pi\)
−0.299141 + 0.954209i \(0.596700\pi\)
\(740\) 25.6780i 0.0347000i
\(741\) −79.3243 + 23.6612i −0.107050 + 0.0319315i
\(742\) 640.716 0.863499
\(743\) 604.855i 0.814072i 0.913412 + 0.407036i \(0.133438\pi\)
−0.913412 + 0.407036i \(0.866562\pi\)
\(744\) 18.6175 + 62.4151i 0.0250235 + 0.0838913i
\(745\) −491.645 −0.659926
\(746\) 170.843i 0.229012i
\(747\) 76.8958 + 117.428i 0.102940 + 0.157200i
\(748\) −717.292 −0.958947
\(749\) 283.623i 0.378668i
\(750\) 45.4551 13.5586i 0.0606068 0.0180781i
\(751\) 1199.13 1.59671 0.798355 0.602187i \(-0.205704\pi\)
0.798355 + 0.602187i \(0.205704\pi\)
\(752\) 211.792i 0.281638i
\(753\) −329.644 1105.13i −0.437774 1.46764i
\(754\) 83.1547 0.110285
\(755\) 480.317i 0.636182i
\(756\) 176.411 208.955i 0.233348 0.276396i
\(757\) 561.572 0.741839 0.370919 0.928665i \(-0.379043\pi\)
0.370919 + 0.928665i \(0.379043\pi\)
\(758\) 490.476i 0.647066i
\(759\) −259.459 + 77.3925i −0.341843 + 0.101966i
\(760\) 53.7268 0.0706932
\(761\) 1338.92i 1.75943i −0.475505 0.879713i \(-0.657735\pi\)
0.475505 0.879713i \(-0.342265\pi\)
\(762\) 244.959 + 821.225i 0.321468 + 1.07772i
\(763\) −118.485 −0.155288
\(764\) 171.446i 0.224406i
\(765\) 320.860 210.109i 0.419425 0.274653i
\(766\) 480.885 0.627787
\(767\) 191.504i 0.249679i
\(768\) −45.9973 + 13.7203i −0.0598923 + 0.0178650i
\(769\) 0.701536 0.000912271 0.000456135 1.00000i \(-0.499855\pi\)
0.000456135 1.00000i \(0.499855\pi\)
\(770\) 301.370i 0.391389i
\(771\) 249.999 + 838.121i 0.324252 + 1.08706i
\(772\) −394.633 −0.511182
\(773\) 835.888i 1.08136i 0.841230 + 0.540678i \(0.181832\pi\)
−0.841230 + 0.540678i \(0.818168\pi\)
\(774\) −66.2410 101.157i −0.0855827 0.130694i
\(775\) 38.3798 0.0495223
\(776\) 118.432i 0.152619i
\(777\) −83.5925 + 24.9344i −0.107584 + 0.0320906i
\(778\) −258.620 −0.332417
\(779\) 414.189i 0.531693i
\(780\) −12.4563 41.7599i −0.0159697 0.0535384i
\(781\) 307.322 0.393498
\(782\) 129.257i 0.165290i
\(783\) 373.469 + 315.303i 0.476972 + 0.402686i
\(784\) −93.4168 −0.119154
\(785\) 221.799i 0.282546i
\(786\) 535.910 159.854i 0.681819 0.203376i