Properties

Label 210.3.c.a.29.9
Level $210$
Weight $3$
Character 210.29
Analytic conductor $5.722$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 29.9
Character \(\chi\) \(=\) 210.29
Dual form 210.3.c.a.29.10

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +(2.70965 - 1.28756i) q^{3} +2.00000 q^{4} +(-3.71627 - 3.34505i) q^{5} +(-3.83202 + 1.82088i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(5.68438 - 6.97766i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(2.70965 - 1.28756i) q^{3} +2.00000 q^{4} +(-3.71627 - 3.34505i) q^{5} +(-3.83202 + 1.82088i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(5.68438 - 6.97766i) q^{9} +(5.25560 + 4.73061i) q^{10} -10.4698i q^{11} +(5.41930 - 2.57512i) q^{12} -11.9937i q^{13} -3.74166i q^{14} +(-14.3767 - 4.27898i) q^{15} +4.00000 q^{16} -29.1133 q^{17} +(-8.03893 + 9.86791i) q^{18} +20.3176 q^{19} +(-7.43254 - 6.69010i) q^{20} +(3.40656 + 7.16905i) q^{21} +14.8066i q^{22} +7.71572 q^{23} +(-7.66404 + 3.64177i) q^{24} +(2.62131 + 24.8622i) q^{25} +16.9617i q^{26} +(6.41851 - 26.2260i) q^{27} +5.29150i q^{28} -47.4046i q^{29} +(20.3318 + 6.05140i) q^{30} -35.5084 q^{31} -5.65685 q^{32} +(-13.4805 - 28.3695i) q^{33} +41.1724 q^{34} +(8.85016 - 9.83232i) q^{35} +(11.3688 - 13.9553i) q^{36} -58.0907i q^{37} -28.7334 q^{38} +(-15.4426 - 32.4988i) q^{39} +(10.5112 + 9.46122i) q^{40} +52.5850i q^{41} +(-4.81761 - 10.1386i) q^{42} +15.7629i q^{43} -20.9396i q^{44} +(-44.4653 + 6.91635i) q^{45} -10.9117 q^{46} +85.2023 q^{47} +(10.8386 - 5.15024i) q^{48} -7.00000 q^{49} +(-3.70710 - 35.1605i) q^{50} +(-78.8867 + 37.4850i) q^{51} -23.9875i q^{52} +42.7649 q^{53} +(-9.07715 + 37.0892i) q^{54} +(-35.0221 + 38.9087i) q^{55} -7.48331i q^{56} +(55.0535 - 26.1601i) q^{57} +67.0403i q^{58} +37.9769i q^{59} +(-28.7535 - 8.55797i) q^{60} +53.5108 q^{61} +50.2165 q^{62} +(18.4612 + 15.0395i) q^{63} +8.00000 q^{64} +(-40.1196 + 44.5719i) q^{65} +(19.0643 + 40.1206i) q^{66} +27.6366i q^{67} -58.2265 q^{68} +(20.9069 - 9.93444i) q^{69} +(-12.5160 + 13.9050i) q^{70} +58.0688i q^{71} +(-16.0779 + 19.7358i) q^{72} +67.8080i q^{73} +82.1526i q^{74} +(39.1144 + 63.9927i) q^{75} +40.6352 q^{76} +27.7005 q^{77} +(21.8392 + 45.9602i) q^{78} +19.2994 q^{79} +(-14.8651 - 13.3802i) q^{80} +(-16.3756 - 79.3274i) q^{81} -74.3664i q^{82} +33.6998 q^{83} +(6.81312 + 14.3381i) q^{84} +(108.193 + 97.3852i) q^{85} -22.2920i q^{86} +(-61.0363 - 128.450i) q^{87} +29.6131i q^{88} +46.8325i q^{89} +(62.8834 - 9.78120i) q^{90} +31.7324 q^{91} +15.4314 q^{92} +(-96.2153 + 45.7192i) q^{93} -120.494 q^{94} +(-75.5056 - 67.9633i) q^{95} +(-15.3281 + 7.28354i) q^{96} +65.1337i q^{97} +9.89949 q^{98} +(-73.0549 - 59.5145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 48 q^{4} + 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 48 q^{4} + 44 q^{9} + 16 q^{10} + 4 q^{15} + 96 q^{16} - 80 q^{19} - 28 q^{21} + 48 q^{25} - 56 q^{30} + 224 q^{31} + 128 q^{34} + 88 q^{36} - 92 q^{39} + 32 q^{40} - 72 q^{45} - 144 q^{46} - 168 q^{49} - 284 q^{51} - 144 q^{54} - 320 q^{55} + 8 q^{60} + 192 q^{64} + 224 q^{66} - 152 q^{69} - 56 q^{70} + 48 q^{75} - 160 q^{76} - 72 q^{79} - 212 q^{81} - 56 q^{84} - 64 q^{85} - 240 q^{90} + 168 q^{91} - 128 q^{94} - 876 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) 2.70965 1.28756i 0.903216 0.429186i
\(4\) 2.00000 0.500000
\(5\) −3.71627 3.34505i −0.743254 0.669010i
\(6\) −3.83202 + 1.82088i −0.638670 + 0.303481i
\(7\) 2.64575i 0.377964i
\(8\) −2.82843 −0.353553
\(9\) 5.68438 6.97766i 0.631598 0.775296i
\(10\) 5.25560 + 4.73061i 0.525560 + 0.473061i
\(11\) 10.4698i 0.951802i −0.879499 0.475901i \(-0.842122\pi\)
0.879499 0.475901i \(-0.157878\pi\)
\(12\) 5.41930 2.57512i 0.451608 0.214593i
\(13\) 11.9937i 0.922595i −0.887246 0.461297i \(-0.847384\pi\)
0.887246 0.461297i \(-0.152616\pi\)
\(14\) 3.74166i 0.267261i
\(15\) −14.3767 4.27898i −0.958449 0.285266i
\(16\) 4.00000 0.250000
\(17\) −29.1133 −1.71254 −0.856272 0.516525i \(-0.827225\pi\)
−0.856272 + 0.516525i \(0.827225\pi\)
\(18\) −8.03893 + 9.86791i −0.446607 + 0.548217i
\(19\) 20.3176 1.06935 0.534673 0.845059i \(-0.320435\pi\)
0.534673 + 0.845059i \(0.320435\pi\)
\(20\) −7.43254 6.69010i −0.371627 0.334505i
\(21\) 3.40656 + 7.16905i 0.162217 + 0.341384i
\(22\) 14.8066i 0.673026i
\(23\) 7.71572 0.335466 0.167733 0.985832i \(-0.446355\pi\)
0.167733 + 0.985832i \(0.446355\pi\)
\(24\) −7.66404 + 3.64177i −0.319335 + 0.151740i
\(25\) 2.62131 + 24.8622i 0.104853 + 0.994488i
\(26\) 16.9617i 0.652373i
\(27\) 6.41851 26.2260i 0.237723 0.971333i
\(28\) 5.29150i 0.188982i
\(29\) 47.4046i 1.63464i −0.576182 0.817321i \(-0.695458\pi\)
0.576182 0.817321i \(-0.304542\pi\)
\(30\) 20.3318 + 6.05140i 0.677725 + 0.201713i
\(31\) −35.5084 −1.14543 −0.572717 0.819753i \(-0.694110\pi\)
−0.572717 + 0.819753i \(0.694110\pi\)
\(32\) −5.65685 −0.176777
\(33\) −13.4805 28.3695i −0.408501 0.859683i
\(34\) 41.1724 1.21095
\(35\) 8.85016 9.83232i 0.252862 0.280924i
\(36\) 11.3688 13.9553i 0.315799 0.387648i
\(37\) 58.0907i 1.57002i −0.619485 0.785009i \(-0.712658\pi\)
0.619485 0.785009i \(-0.287342\pi\)
\(38\) −28.7334 −0.756142
\(39\) −15.4426 32.4988i −0.395965 0.833302i
\(40\) 10.5112 + 9.46122i 0.262780 + 0.236531i
\(41\) 52.5850i 1.28256i 0.767307 + 0.641280i \(0.221596\pi\)
−0.767307 + 0.641280i \(0.778404\pi\)
\(42\) −4.81761 10.1386i −0.114705 0.241395i
\(43\) 15.7629i 0.366578i 0.983059 + 0.183289i \(0.0586744\pi\)
−0.983059 + 0.183289i \(0.941326\pi\)
\(44\) 20.9396i 0.475901i
\(45\) −44.4653 + 6.91635i −0.988118 + 0.153697i
\(46\) −10.9117 −0.237210
\(47\) 85.2023 1.81281 0.906407 0.422405i \(-0.138814\pi\)
0.906407 + 0.422405i \(0.138814\pi\)
\(48\) 10.8386 5.15024i 0.225804 0.107297i
\(49\) −7.00000 −0.142857
\(50\) −3.70710 35.1605i −0.0741419 0.703209i
\(51\) −78.8867 + 37.4850i −1.54680 + 0.735001i
\(52\) 23.9875i 0.461297i
\(53\) 42.7649 0.806885 0.403443 0.915005i \(-0.367813\pi\)
0.403443 + 0.915005i \(0.367813\pi\)
\(54\) −9.07715 + 37.0892i −0.168095 + 0.686836i
\(55\) −35.0221 + 38.9087i −0.636765 + 0.707431i
\(56\) 7.48331i 0.133631i
\(57\) 55.0535 26.1601i 0.965850 0.458949i
\(58\) 67.0403i 1.15587i
\(59\) 37.9769i 0.643676i 0.946795 + 0.321838i \(0.104301\pi\)
−0.946795 + 0.321838i \(0.895699\pi\)
\(60\) −28.7535 8.55797i −0.479224 0.142633i
\(61\) 53.5108 0.877226 0.438613 0.898676i \(-0.355470\pi\)
0.438613 + 0.898676i \(0.355470\pi\)
\(62\) 50.2165 0.809944
\(63\) 18.4612 + 15.0395i 0.293034 + 0.238722i
\(64\) 8.00000 0.125000
\(65\) −40.1196 + 44.5719i −0.617225 + 0.685722i
\(66\) 19.0643 + 40.1206i 0.288854 + 0.607888i
\(67\) 27.6366i 0.412487i 0.978501 + 0.206243i \(0.0661238\pi\)
−0.978501 + 0.206243i \(0.933876\pi\)
\(68\) −58.2265 −0.856272
\(69\) 20.9069 9.93444i 0.302998 0.143977i
\(70\) −12.5160 + 13.9050i −0.178800 + 0.198643i
\(71\) 58.0688i 0.817871i 0.912563 + 0.408935i \(0.134100\pi\)
−0.912563 + 0.408935i \(0.865900\pi\)
\(72\) −16.0779 + 19.7358i −0.223304 + 0.274109i
\(73\) 67.8080i 0.928877i 0.885605 + 0.464438i \(0.153744\pi\)
−0.885605 + 0.464438i \(0.846256\pi\)
\(74\) 82.1526i 1.11017i
\(75\) 39.1144 + 63.9927i 0.521525 + 0.853236i
\(76\) 40.6352 0.534673
\(77\) 27.7005 0.359747
\(78\) 21.8392 + 45.9602i 0.279990 + 0.589234i
\(79\) 19.2994 0.244296 0.122148 0.992512i \(-0.461022\pi\)
0.122148 + 0.992512i \(0.461022\pi\)
\(80\) −14.8651 13.3802i −0.185813 0.167252i
\(81\) −16.3756 79.3274i −0.202168 0.979351i
\(82\) 74.3664i 0.906907i
\(83\) 33.6998 0.406021 0.203011 0.979177i \(-0.434927\pi\)
0.203011 + 0.979177i \(0.434927\pi\)
\(84\) 6.81312 + 14.3381i 0.0811086 + 0.170692i
\(85\) 108.193 + 97.3852i 1.27286 + 1.14571i
\(86\) 22.2920i 0.259210i
\(87\) −61.0363 128.450i −0.701566 1.47643i
\(88\) 29.6131i 0.336513i
\(89\) 46.8325i 0.526208i 0.964768 + 0.263104i \(0.0847462\pi\)
−0.964768 + 0.263104i \(0.915254\pi\)
\(90\) 62.8834 9.78120i 0.698705 0.108680i
\(91\) 31.7324 0.348708
\(92\) 15.4314 0.167733
\(93\) −96.2153 + 45.7192i −1.03457 + 0.491604i
\(94\) −120.494 −1.28185
\(95\) −75.5056 67.9633i −0.794796 0.715403i
\(96\) −15.3281 + 7.28354i −0.159668 + 0.0758702i
\(97\) 65.1337i 0.671482i 0.941954 + 0.335741i \(0.108987\pi\)
−0.941954 + 0.335741i \(0.891013\pi\)
\(98\) 9.89949 0.101015
\(99\) −73.0549 59.5145i −0.737928 0.601156i
\(100\) 5.24263 + 49.7244i 0.0524263 + 0.497244i
\(101\) 171.169i 1.69474i 0.531000 + 0.847372i \(0.321816\pi\)
−0.531000 + 0.847372i \(0.678184\pi\)
\(102\) 111.563 53.0119i 1.09375 0.519724i
\(103\) 129.879i 1.26096i −0.776205 0.630481i \(-0.782858\pi\)
0.776205 0.630481i \(-0.217142\pi\)
\(104\) 33.9234i 0.326186i
\(105\) 11.3211 38.0372i 0.107820 0.362259i
\(106\) −60.4787 −0.570554
\(107\) −29.1627 −0.272549 −0.136274 0.990671i \(-0.543513\pi\)
−0.136274 + 0.990671i \(0.543513\pi\)
\(108\) 12.8370 52.4520i 0.118861 0.485667i
\(109\) 19.3296 0.177336 0.0886680 0.996061i \(-0.471739\pi\)
0.0886680 + 0.996061i \(0.471739\pi\)
\(110\) 49.5287 55.0252i 0.450261 0.500229i
\(111\) −74.7952 157.405i −0.673830 1.41807i
\(112\) 10.5830i 0.0944911i
\(113\) 28.5568 0.252715 0.126358 0.991985i \(-0.459671\pi\)
0.126358 + 0.991985i \(0.459671\pi\)
\(114\) −77.8574 + 36.9959i −0.682959 + 0.324526i
\(115\) −28.6737 25.8094i −0.249336 0.224430i
\(116\) 94.8092i 0.817321i
\(117\) −83.6882 68.1769i −0.715284 0.582709i
\(118\) 53.7074i 0.455148i
\(119\) 77.0264i 0.647281i
\(120\) 40.6635 + 12.1028i 0.338863 + 0.100857i
\(121\) 11.3828 0.0940727
\(122\) −75.6757 −0.620292
\(123\) 67.7063 + 142.487i 0.550457 + 1.15843i
\(124\) −71.0169 −0.572717
\(125\) 73.4237 101.163i 0.587390 0.809304i
\(126\) −26.1080 21.2690i −0.207207 0.168802i
\(127\) 162.116i 1.27650i −0.769828 0.638252i \(-0.779658\pi\)
0.769828 0.638252i \(-0.220342\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 20.2956 + 42.7118i 0.157330 + 0.331099i
\(130\) 56.7377 63.0342i 0.436444 0.484879i
\(131\) 49.5756i 0.378440i −0.981935 0.189220i \(-0.939404\pi\)
0.981935 0.189220i \(-0.0605959\pi\)
\(132\) −26.9610 56.7391i −0.204250 0.429841i
\(133\) 53.7553i 0.404175i
\(134\) 39.0840i 0.291672i
\(135\) −111.580 + 75.9926i −0.826519 + 0.562908i
\(136\) 82.3447 0.605476
\(137\) 212.721 1.55271 0.776354 0.630297i \(-0.217067\pi\)
0.776354 + 0.630297i \(0.217067\pi\)
\(138\) −29.5668 + 14.0494i −0.214252 + 0.101807i
\(139\) 74.1650 0.533561 0.266780 0.963757i \(-0.414040\pi\)
0.266780 + 0.963757i \(0.414040\pi\)
\(140\) 17.7003 19.6646i 0.126431 0.140462i
\(141\) 230.868 109.703i 1.63736 0.778036i
\(142\) 82.1217i 0.578322i
\(143\) −125.572 −0.878128
\(144\) 22.7375 27.9107i 0.157899 0.193824i
\(145\) −158.571 + 176.168i −1.09359 + 1.21495i
\(146\) 95.8950i 0.656815i
\(147\) −18.9675 + 9.01292i −0.129031 + 0.0613124i
\(148\) 116.181i 0.785009i
\(149\) 23.1598i 0.155435i 0.996975 + 0.0777176i \(0.0247632\pi\)
−0.996975 + 0.0777176i \(0.975237\pi\)
\(150\) −55.3161 90.4993i −0.368774 0.603329i
\(151\) 75.1469 0.497661 0.248831 0.968547i \(-0.419954\pi\)
0.248831 + 0.968547i \(0.419954\pi\)
\(152\) −57.4668 −0.378071
\(153\) −165.491 + 203.143i −1.08164 + 1.32773i
\(154\) −39.1745 −0.254380
\(155\) 131.959 + 118.777i 0.851348 + 0.766306i
\(156\) −30.8853 64.9976i −0.197983 0.416651i
\(157\) 66.6968i 0.424820i −0.977181 0.212410i \(-0.931869\pi\)
0.977181 0.212410i \(-0.0681313\pi\)
\(158\) −27.2934 −0.172743
\(159\) 115.878 55.0624i 0.728792 0.346304i
\(160\) 21.0224 + 18.9224i 0.131390 + 0.118265i
\(161\) 20.4139i 0.126794i
\(162\) 23.1586 + 112.186i 0.142954 + 0.692506i
\(163\) 248.817i 1.52648i −0.646114 0.763241i \(-0.723607\pi\)
0.646114 0.763241i \(-0.276393\pi\)
\(164\) 105.170i 0.641280i
\(165\) −44.8002 + 150.522i −0.271516 + 0.912253i
\(166\) −47.6587 −0.287100
\(167\) −92.0222 −0.551031 −0.275516 0.961297i \(-0.588849\pi\)
−0.275516 + 0.961297i \(0.588849\pi\)
\(168\) −9.63521 20.2771i −0.0573525 0.120697i
\(169\) 25.1504 0.148819
\(170\) −153.008 137.724i −0.900045 0.810138i
\(171\) 115.493 141.769i 0.675397 0.829060i
\(172\) 31.5257i 0.183289i
\(173\) −233.473 −1.34956 −0.674778 0.738021i \(-0.735761\pi\)
−0.674778 + 0.738021i \(0.735761\pi\)
\(174\) 86.3183 + 181.655i 0.496082 + 1.04400i
\(175\) −65.7792 + 6.93534i −0.375881 + 0.0396305i
\(176\) 41.8793i 0.237951i
\(177\) 48.8975 + 102.904i 0.276257 + 0.581379i
\(178\) 66.2311i 0.372085i
\(179\) 185.252i 1.03493i −0.855705 0.517465i \(-0.826876\pi\)
0.855705 0.517465i \(-0.173124\pi\)
\(180\) −88.9306 + 13.8327i −0.494059 + 0.0768484i
\(181\) −146.372 −0.808684 −0.404342 0.914608i \(-0.632499\pi\)
−0.404342 + 0.914608i \(0.632499\pi\)
\(182\) −44.8764 −0.246574
\(183\) 144.995 68.8983i 0.792324 0.376493i
\(184\) −21.8233 −0.118605
\(185\) −194.316 + 215.881i −1.05036 + 1.16692i
\(186\) 136.069 64.6567i 0.731554 0.347617i
\(187\) 304.811i 1.63000i
\(188\) 170.405 0.906407
\(189\) 69.3875 + 16.9818i 0.367129 + 0.0898507i
\(190\) 106.781 + 96.1146i 0.562005 + 0.505866i
\(191\) 83.4780i 0.437057i 0.975831 + 0.218529i \(0.0701257\pi\)
−0.975831 + 0.218529i \(0.929874\pi\)
\(192\) 21.6772 10.3005i 0.112902 0.0536483i
\(193\) 88.5046i 0.458573i 0.973359 + 0.229287i \(0.0736393\pi\)
−0.973359 + 0.229287i \(0.926361\pi\)
\(194\) 92.1130i 0.474809i
\(195\) −51.3210 + 172.431i −0.263184 + 0.884259i
\(196\) −14.0000 −0.0714286
\(197\) −36.9343 −0.187484 −0.0937419 0.995597i \(-0.529883\pi\)
−0.0937419 + 0.995597i \(0.529883\pi\)
\(198\) 103.315 + 84.1662i 0.521794 + 0.425082i
\(199\) −205.101 −1.03066 −0.515330 0.856992i \(-0.672331\pi\)
−0.515330 + 0.856992i \(0.672331\pi\)
\(200\) −7.41419 70.3209i −0.0370710 0.351605i
\(201\) 35.5838 + 74.8854i 0.177034 + 0.372564i
\(202\) 242.070i 1.19836i
\(203\) 125.421 0.617837
\(204\) −157.773 + 74.9701i −0.773399 + 0.367500i
\(205\) 175.899 195.420i 0.858045 0.953268i
\(206\) 183.677i 0.891634i
\(207\) 43.8591 53.8377i 0.211880 0.260085i
\(208\) 47.9749i 0.230649i
\(209\) 212.721i 1.01781i
\(210\) −16.0105 + 53.7928i −0.0762404 + 0.256156i
\(211\) 49.4829 0.234516 0.117258 0.993101i \(-0.462590\pi\)
0.117258 + 0.993101i \(0.462590\pi\)
\(212\) 85.5298 0.403443
\(213\) 74.7670 + 157.346i 0.351019 + 0.738714i
\(214\) 41.2423 0.192721
\(215\) 52.7275 58.5790i 0.245244 0.272461i
\(216\) −18.1543 + 74.1783i −0.0840477 + 0.343418i
\(217\) 93.9465i 0.432933i
\(218\) −27.3362 −0.125395
\(219\) 87.3069 + 183.736i 0.398661 + 0.838976i
\(220\) −70.0441 + 77.8174i −0.318382 + 0.353715i
\(221\) 349.177i 1.57998i
\(222\) 105.776 + 222.605i 0.476470 + 1.00272i
\(223\) 1.69928i 0.00762011i −0.999993 0.00381005i \(-0.998787\pi\)
0.999993 0.00381005i \(-0.00121278\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 188.381 + 123.036i 0.837247 + 0.546825i
\(226\) −40.3855 −0.178697
\(227\) −206.970 −0.911762 −0.455881 0.890041i \(-0.650676\pi\)
−0.455881 + 0.890041i \(0.650676\pi\)
\(228\) 110.107 52.3202i 0.482925 0.229474i
\(229\) −7.02543 −0.0306787 −0.0153394 0.999882i \(-0.504883\pi\)
−0.0153394 + 0.999882i \(0.504883\pi\)
\(230\) 40.5507 + 36.5001i 0.176307 + 0.158696i
\(231\) 75.0587 35.6661i 0.324930 0.154399i
\(232\) 134.081i 0.577933i
\(233\) 116.672 0.500738 0.250369 0.968151i \(-0.419448\pi\)
0.250369 + 0.968151i \(0.419448\pi\)
\(234\) 118.353 + 96.4168i 0.505782 + 0.412037i
\(235\) −316.635 285.006i −1.34738 1.21279i
\(236\) 75.9538i 0.321838i
\(237\) 52.2945 24.8491i 0.220652 0.104848i
\(238\) 108.932i 0.457697i
\(239\) 157.119i 0.657400i −0.944434 0.328700i \(-0.893389\pi\)
0.944434 0.328700i \(-0.106611\pi\)
\(240\) −57.5069 17.1159i −0.239612 0.0713164i
\(241\) −287.032 −1.19101 −0.595503 0.803353i \(-0.703047\pi\)
−0.595503 + 0.803353i \(0.703047\pi\)
\(242\) −16.0977 −0.0665194
\(243\) −146.511 193.865i −0.602926 0.797797i
\(244\) 107.022 0.438613
\(245\) 26.0139 + 23.4153i 0.106179 + 0.0955728i
\(246\) −95.7511 201.507i −0.389232 0.819133i
\(247\) 243.684i 0.986573i
\(248\) 100.433 0.404972
\(249\) 91.3145 43.3905i 0.366725 0.174259i
\(250\) −103.837 + 143.066i −0.415347 + 0.572264i
\(251\) 161.056i 0.641658i −0.947137 0.320829i \(-0.896039\pi\)
0.947137 0.320829i \(-0.103961\pi\)
\(252\) 36.9223 + 30.0789i 0.146517 + 0.119361i
\(253\) 80.7822i 0.319297i
\(254\) 229.267i 0.902625i
\(255\) 418.553 + 124.575i 1.64139 + 0.488530i
\(256\) 16.0000 0.0625000
\(257\) 356.900 1.38871 0.694357 0.719630i \(-0.255689\pi\)
0.694357 + 0.719630i \(0.255689\pi\)
\(258\) −28.7023 60.4036i −0.111249 0.234122i
\(259\) 153.693 0.593411
\(260\) −80.2392 + 89.1439i −0.308612 + 0.342861i
\(261\) −330.774 269.466i −1.26733 1.03244i
\(262\) 70.1105i 0.267597i
\(263\) 126.259 0.480071 0.240036 0.970764i \(-0.422841\pi\)
0.240036 + 0.970764i \(0.422841\pi\)
\(264\) 38.1287 + 80.2412i 0.144427 + 0.303944i
\(265\) −158.926 143.051i −0.599721 0.539814i
\(266\) 76.0214i 0.285795i
\(267\) 60.2996 + 126.900i 0.225841 + 0.475279i
\(268\) 55.2732i 0.206243i
\(269\) 356.319i 1.32461i −0.749236 0.662304i \(-0.769579\pi\)
0.749236 0.662304i \(-0.230421\pi\)
\(270\) 157.798 107.470i 0.584437 0.398036i
\(271\) −422.588 −1.55937 −0.779683 0.626175i \(-0.784620\pi\)
−0.779683 + 0.626175i \(0.784620\pi\)
\(272\) −116.453 −0.428136
\(273\) 85.9837 40.8574i 0.314959 0.149661i
\(274\) −300.833 −1.09793
\(275\) 260.303 27.4447i 0.946556 0.0997989i
\(276\) 41.8137 19.8689i 0.151499 0.0719887i
\(277\) 267.379i 0.965266i 0.875823 + 0.482633i \(0.160320\pi\)
−0.875823 + 0.482633i \(0.839680\pi\)
\(278\) −104.885 −0.377284
\(279\) −201.843 + 247.766i −0.723453 + 0.888050i
\(280\) −25.0320 + 27.8100i −0.0894002 + 0.0993215i
\(281\) 417.470i 1.48566i 0.669480 + 0.742830i \(0.266517\pi\)
−0.669480 + 0.742830i \(0.733483\pi\)
\(282\) −326.497 + 155.143i −1.15779 + 0.550154i
\(283\) 56.1781i 0.198509i −0.995062 0.0992546i \(-0.968354\pi\)
0.995062 0.0992546i \(-0.0316458\pi\)
\(284\) 116.138i 0.408935i
\(285\) −292.100 86.9386i −1.02491 0.305048i
\(286\) 177.586 0.620930
\(287\) −139.127 −0.484762
\(288\) −32.1557 + 39.4716i −0.111652 + 0.137054i
\(289\) 558.582 1.93281
\(290\) 224.253 249.140i 0.773286 0.859102i
\(291\) 83.8635 + 176.489i 0.288191 + 0.606493i
\(292\) 135.616i 0.464438i
\(293\) 35.8668 0.122412 0.0612062 0.998125i \(-0.480505\pi\)
0.0612062 + 0.998125i \(0.480505\pi\)
\(294\) 26.8241 12.7462i 0.0912386 0.0433544i
\(295\) 127.035 141.132i 0.430625 0.478415i
\(296\) 164.305i 0.555085i
\(297\) −274.582 67.2007i −0.924517 0.226265i
\(298\) 32.7530i 0.109909i
\(299\) 92.5402i 0.309499i
\(300\) 78.2288 + 127.985i 0.260763 + 0.426618i
\(301\) −41.7046 −0.138553
\(302\) −106.274 −0.351900
\(303\) 220.390 + 463.808i 0.727361 + 1.53072i
\(304\) 81.2703 0.267337
\(305\) −198.860 178.996i −0.652001 0.586872i
\(306\) 234.039 287.287i 0.764835 0.938846i
\(307\) 496.572i 1.61750i 0.588154 + 0.808749i \(0.299855\pi\)
−0.588154 + 0.808749i \(0.700145\pi\)
\(308\) 55.4011 0.179874
\(309\) −167.227 351.926i −0.541188 1.13892i
\(310\) −186.618 167.977i −0.601994 0.541860i
\(311\) 49.5016i 0.159169i −0.996828 0.0795846i \(-0.974641\pi\)
0.996828 0.0795846i \(-0.0253594\pi\)
\(312\) 43.6784 + 91.9204i 0.139995 + 0.294617i
\(313\) 219.172i 0.700229i −0.936707 0.350114i \(-0.886143\pi\)
0.936707 0.350114i \(-0.113857\pi\)
\(314\) 94.3235i 0.300393i
\(315\) −18.2990 117.644i −0.0580919 0.373474i
\(316\) 38.5987 0.122148
\(317\) 96.3016 0.303791 0.151895 0.988397i \(-0.451462\pi\)
0.151895 + 0.988397i \(0.451462\pi\)
\(318\) −163.876 + 77.8700i −0.515333 + 0.244874i
\(319\) −496.318 −1.55586
\(320\) −29.7302 26.7604i −0.0929067 0.0836262i
\(321\) −79.0206 + 37.5487i −0.246170 + 0.116974i
\(322\) 28.8696i 0.0896570i
\(323\) −591.511 −1.83130
\(324\) −32.7512 158.655i −0.101084 0.489675i
\(325\) 298.190 31.4393i 0.917509 0.0967364i
\(326\) 351.880i 1.07939i
\(327\) 52.3764 24.8880i 0.160173 0.0761102i
\(328\) 148.733i 0.453453i
\(329\) 225.424i 0.685180i
\(330\) 63.3570 212.870i 0.191991 0.645061i
\(331\) 538.706 1.62751 0.813755 0.581208i \(-0.197420\pi\)
0.813755 + 0.581208i \(0.197420\pi\)
\(332\) 67.3995 0.203011
\(333\) −405.337 330.209i −1.21723 0.991620i
\(334\) 130.139 0.389638
\(335\) 92.4457 102.705i 0.275957 0.306582i
\(336\) 13.6262 + 28.6762i 0.0405543 + 0.0853459i
\(337\) 202.735i 0.601589i 0.953689 + 0.300794i \(0.0972518\pi\)
−0.953689 + 0.300794i \(0.902748\pi\)
\(338\) −35.5681 −0.105231
\(339\) 77.3790 36.7686i 0.228257 0.108462i
\(340\) 216.385 + 194.770i 0.636428 + 0.572854i
\(341\) 371.767i 1.09023i
\(342\) −163.332 + 200.492i −0.477578 + 0.586234i
\(343\) 18.5203i 0.0539949i
\(344\) 44.5841i 0.129605i
\(345\) −110.927 33.0154i −0.321527 0.0956969i
\(346\) 330.181 0.954280
\(347\) −139.011 −0.400607 −0.200304 0.979734i \(-0.564193\pi\)
−0.200304 + 0.979734i \(0.564193\pi\)
\(348\) −122.073 256.900i −0.350783 0.738217i
\(349\) 452.984 1.29795 0.648974 0.760811i \(-0.275199\pi\)
0.648974 + 0.760811i \(0.275199\pi\)
\(350\) 93.0258 9.80806i 0.265788 0.0280230i
\(351\) −314.547 76.9819i −0.896147 0.219322i
\(352\) 59.2263i 0.168256i
\(353\) 453.499 1.28470 0.642349 0.766412i \(-0.277960\pi\)
0.642349 + 0.766412i \(0.277960\pi\)
\(354\) −69.1515 145.528i −0.195343 0.411097i
\(355\) 194.243 215.799i 0.547163 0.607885i
\(356\) 93.6650i 0.263104i
\(357\) −99.1761 208.715i −0.277804 0.584635i
\(358\) 261.986i 0.731806i
\(359\) 150.308i 0.418686i −0.977842 0.209343i \(-0.932868\pi\)
0.977842 0.209343i \(-0.0671324\pi\)
\(360\) 125.767 19.5624i 0.349352 0.0543400i
\(361\) 51.8039 0.143501
\(362\) 207.001 0.571826
\(363\) 30.8434 14.6560i 0.0849680 0.0403747i
\(364\) 63.4649 0.174354
\(365\) 226.821 251.993i 0.621428 0.690391i
\(366\) −205.054 + 97.4369i −0.560258 + 0.266221i
\(367\) 382.992i 1.04357i 0.853076 + 0.521787i \(0.174735\pi\)
−0.853076 + 0.521787i \(0.825265\pi\)
\(368\) 30.8629 0.0838665
\(369\) 366.920 + 298.913i 0.994364 + 0.810062i
\(370\) 274.804 305.301i 0.742714 0.825138i
\(371\) 113.145i 0.304974i
\(372\) −192.431 + 91.4384i −0.517287 + 0.245802i
\(373\) 80.3409i 0.215391i −0.994184 0.107696i \(-0.965653\pi\)
0.994184 0.107696i \(-0.0343472\pi\)
\(374\) 431.067i 1.15259i
\(375\) 68.6990 368.654i 0.183197 0.983076i
\(376\) −240.988 −0.640927
\(377\) −568.558 −1.50811
\(378\) −98.1287 24.0159i −0.259600 0.0635341i
\(379\) −636.088 −1.67833 −0.839166 0.543875i \(-0.816956\pi\)
−0.839166 + 0.543875i \(0.816956\pi\)
\(380\) −151.011 135.927i −0.397398 0.357701i
\(381\) −208.734 439.277i −0.547858 1.15296i
\(382\) 118.056i 0.309046i
\(383\) 343.675 0.897323 0.448661 0.893702i \(-0.351901\pi\)
0.448661 + 0.893702i \(0.351901\pi\)
\(384\) −30.6562 + 14.5671i −0.0798338 + 0.0379351i
\(385\) −102.943 92.6597i −0.267384 0.240674i
\(386\) 125.164i 0.324260i
\(387\) 109.988 + 89.6021i 0.284207 + 0.231530i
\(388\) 130.267i 0.335741i
\(389\) 520.410i 1.33782i −0.743345 0.668908i \(-0.766762\pi\)
0.743345 0.668908i \(-0.233238\pi\)
\(390\) 72.5788 243.854i 0.186100 0.625266i
\(391\) −224.630 −0.574500
\(392\) 19.7990 0.0505076
\(393\) −63.8316 134.333i −0.162421 0.341813i
\(394\) 52.2330 0.132571
\(395\) −71.7216 64.5573i −0.181574 0.163436i
\(396\) −146.110 119.029i −0.368964 0.300578i
\(397\) 184.320i 0.464281i 0.972682 + 0.232140i \(0.0745729\pi\)
−0.972682 + 0.232140i \(0.925427\pi\)
\(398\) 290.057 0.728787
\(399\) 69.2131 + 145.658i 0.173466 + 0.365057i
\(400\) 10.4853 + 99.4488i 0.0262131 + 0.248622i
\(401\) 10.1322i 0.0252674i 0.999920 + 0.0126337i \(0.00402154\pi\)
−0.999920 + 0.0126337i \(0.995978\pi\)
\(402\) −50.3230 105.904i −0.125182 0.263443i
\(403\) 425.879i 1.05677i
\(404\) 342.338i 0.847372i
\(405\) −204.498 + 349.579i −0.504933 + 0.863159i
\(406\) −177.372 −0.436876
\(407\) −608.199 −1.49435
\(408\) 223.125 106.024i 0.546876 0.259862i
\(409\) −802.483 −1.96206 −0.981031 0.193853i \(-0.937901\pi\)
−0.981031 + 0.193853i \(0.937901\pi\)
\(410\) −248.759 + 276.365i −0.606729 + 0.674062i
\(411\) 576.399 273.891i 1.40243 0.666402i
\(412\) 259.758i 0.630481i
\(413\) −100.477 −0.243287
\(414\) −62.0261 + 76.1380i −0.149822 + 0.183908i
\(415\) −125.237 112.727i −0.301777 0.271632i
\(416\) 67.8468i 0.163093i
\(417\) 200.961 95.4918i 0.481921 0.228997i
\(418\) 300.834i 0.719697i
\(419\) 27.2524i 0.0650414i 0.999471 + 0.0325207i \(0.0103535\pi\)
−0.999471 + 0.0325207i \(0.989647\pi\)
\(420\) 22.6423 76.0745i 0.0539101 0.181130i
\(421\) 792.513 1.88245 0.941227 0.337775i \(-0.109674\pi\)
0.941227 + 0.337775i \(0.109674\pi\)
\(422\) −69.9793 −0.165828
\(423\) 484.322 594.513i 1.14497 1.40547i
\(424\) −120.957 −0.285277
\(425\) −76.3150 723.819i −0.179565 1.70310i
\(426\) −105.737 222.521i −0.248208 0.522349i
\(427\) 141.576i 0.331560i
\(428\) −58.3254 −0.136274
\(429\) −340.257 + 161.682i −0.793139 + 0.376880i
\(430\) −74.5680 + 82.8433i −0.173414 + 0.192659i
\(431\) 483.889i 1.12271i −0.827574 0.561357i \(-0.810280\pi\)
0.827574 0.561357i \(-0.189720\pi\)
\(432\) 25.6741 104.904i 0.0594307 0.242833i
\(433\) 567.937i 1.31163i −0.754920 0.655816i \(-0.772325\pi\)
0.754920 0.655816i \(-0.227675\pi\)
\(434\) 132.860i 0.306130i
\(435\) −202.844 + 681.523i −0.466307 + 1.56672i
\(436\) 38.6592 0.0886680
\(437\) 156.765 0.358729
\(438\) −123.471 259.842i −0.281896 0.593246i
\(439\) 834.645 1.90124 0.950621 0.310355i \(-0.100448\pi\)
0.950621 + 0.310355i \(0.100448\pi\)
\(440\) 99.0573 110.050i 0.225130 0.250114i
\(441\) −39.7907 + 48.8437i −0.0902283 + 0.110757i
\(442\) 493.810i 1.11722i
\(443\) −543.969 −1.22792 −0.613960 0.789337i \(-0.710424\pi\)
−0.613960 + 0.789337i \(0.710424\pi\)
\(444\) −149.590 314.810i −0.336915 0.709033i
\(445\) 156.657 174.042i 0.352038 0.391106i
\(446\) 2.40315i 0.00538823i
\(447\) 29.8197 + 62.7550i 0.0667107 + 0.140392i
\(448\) 21.1660i 0.0472456i
\(449\) 308.306i 0.686649i 0.939217 + 0.343325i \(0.111553\pi\)
−0.939217 + 0.343325i \(0.888447\pi\)
\(450\) −266.410 173.999i −0.592023 0.386663i
\(451\) 550.555 1.22074
\(452\) 57.1137 0.126358
\(453\) 203.622 96.7560i 0.449496 0.213589i
\(454\) 292.700 0.644713
\(455\) −117.926 106.146i −0.259179 0.233289i
\(456\) −155.715 + 73.9919i −0.341480 + 0.162263i
\(457\) 475.765i 1.04106i 0.853843 + 0.520530i \(0.174266\pi\)
−0.853843 + 0.520530i \(0.825734\pi\)
\(458\) 9.93545 0.0216931
\(459\) −186.864 + 763.524i −0.407111 + 1.66345i
\(460\) −57.3474 51.6189i −0.124668 0.112215i
\(461\) 764.494i 1.65834i 0.558998 + 0.829169i \(0.311186\pi\)
−0.558998 + 0.829169i \(0.688814\pi\)
\(462\) −106.149 + 50.4395i −0.229760 + 0.109176i
\(463\) 558.506i 1.20628i −0.797637 0.603138i \(-0.793917\pi\)
0.797637 0.603138i \(-0.206083\pi\)
\(464\) 189.618i 0.408661i
\(465\) 510.495 + 151.940i 1.09784 + 0.326753i
\(466\) −164.999 −0.354075
\(467\) −251.321 −0.538160 −0.269080 0.963118i \(-0.586720\pi\)
−0.269080 + 0.963118i \(0.586720\pi\)
\(468\) −167.376 136.354i −0.357642 0.291354i
\(469\) −73.1196 −0.155905
\(470\) 447.789 + 403.059i 0.952743 + 0.857572i
\(471\) −85.8761 180.725i −0.182327 0.383705i
\(472\) 107.415i 0.227574i
\(473\) 165.034 0.348910
\(474\) −73.9556 + 35.1419i −0.156024 + 0.0741391i
\(475\) 53.2587 + 505.140i 0.112124 + 1.06345i
\(476\) 154.053i 0.323641i
\(477\) 243.092 298.399i 0.509627 0.625575i
\(478\) 222.199i 0.464852i
\(479\) 343.617i 0.717363i 0.933460 + 0.358681i \(0.116774\pi\)
−0.933460 + 0.358681i \(0.883226\pi\)
\(480\) 81.3271 + 24.2056i 0.169431 + 0.0504283i
\(481\) −696.724 −1.44849
\(482\) 405.925 0.842169
\(483\) 26.2841 + 55.3144i 0.0544184 + 0.114523i
\(484\) 22.7656 0.0470363
\(485\) 217.875 242.054i 0.449228 0.499081i
\(486\) 207.198 + 274.166i 0.426333 + 0.564128i
\(487\) 909.858i 1.86829i 0.356892 + 0.934146i \(0.383837\pi\)
−0.356892 + 0.934146i \(0.616163\pi\)
\(488\) −151.351 −0.310146
\(489\) −320.366 674.206i −0.655146 1.37874i
\(490\) −36.7892 33.1143i −0.0750800 0.0675802i
\(491\) 584.882i 1.19121i 0.803279 + 0.595603i \(0.203087\pi\)
−0.803279 + 0.595603i \(0.796913\pi\)
\(492\) 135.413 + 284.973i 0.275229 + 0.579214i
\(493\) 1380.10i 2.79940i
\(494\) 344.621i 0.697612i
\(495\) 72.4130 + 465.544i 0.146289 + 0.940493i
\(496\) −142.034 −0.286358
\(497\) −153.636 −0.309126
\(498\) −129.138 + 61.3634i −0.259314 + 0.123220i
\(499\) 903.199 1.81002 0.905009 0.425392i \(-0.139864\pi\)
0.905009 + 0.425392i \(0.139864\pi\)
\(500\) 146.847 202.326i 0.293695 0.404652i
\(501\) −249.348 + 118.484i −0.497700 + 0.236495i
\(502\) 227.768i 0.453720i
\(503\) −188.576 −0.374903 −0.187452 0.982274i \(-0.560023\pi\)
−0.187452 + 0.982274i \(0.560023\pi\)
\(504\) −52.2161 42.5380i −0.103603 0.0844008i
\(505\) 572.569 636.111i 1.13380 1.25962i
\(506\) 114.243i 0.225777i
\(507\) 68.1488 32.3827i 0.134416 0.0638711i
\(508\) 324.232i 0.638252i
\(509\) 526.061i 1.03352i 0.856131 + 0.516759i \(0.172862\pi\)
−0.856131 + 0.516759i \(0.827138\pi\)
\(510\) −591.924 176.176i −1.16064 0.345443i
\(511\) −179.403 −0.351083
\(512\) −22.6274 −0.0441942
\(513\) 130.409 532.849i 0.254208 1.03869i
\(514\) −504.732 −0.981970
\(515\) −434.451 + 482.665i −0.843595 + 0.937214i
\(516\) 40.5912 + 85.4236i 0.0786652 + 0.165550i
\(517\) 892.053i 1.72544i
\(518\) −217.355 −0.419605
\(519\) −632.630 + 300.611i −1.21894 + 0.579211i
\(520\) 113.475 126.068i 0.218222 0.242439i
\(521\) 636.046i 1.22082i −0.792087 0.610408i \(-0.791005\pi\)
0.792087 0.610408i \(-0.208995\pi\)
\(522\) 467.784 + 381.082i 0.896139 + 0.730043i
\(523\) 662.926i 1.26755i 0.773519 + 0.633773i \(0.218494\pi\)
−0.773519 + 0.633773i \(0.781506\pi\)
\(524\) 99.1513i 0.189220i
\(525\) −169.309 + 103.487i −0.322493 + 0.197118i
\(526\) −178.557 −0.339461
\(527\) 1033.77 1.96161
\(528\) −53.9221 113.478i −0.102125 0.214921i
\(529\) −469.468 −0.887463
\(530\) 224.755 + 202.304i 0.424066 + 0.381706i
\(531\) 264.990 + 215.875i 0.499040 + 0.406545i
\(532\) 107.511i 0.202087i
\(533\) 630.690 1.18328
\(534\) −85.2765 179.463i −0.159694 0.336073i
\(535\) 108.376 + 97.5506i 0.202573 + 0.182338i
\(536\) 78.1681i 0.145836i
\(537\) −238.523 501.969i −0.444178 0.934765i
\(538\) 503.912i 0.936639i
\(539\) 73.2888i 0.135972i
\(540\) −223.160 + 151.985i −0.413260 + 0.281454i
\(541\) −299.602 −0.553793 −0.276897 0.960900i \(-0.589306\pi\)
−0.276897 + 0.960900i \(0.589306\pi\)
\(542\) 597.630 1.10264
\(543\) −396.616 + 188.462i −0.730416 + 0.347076i
\(544\) 164.689 0.302738
\(545\) −71.8340 64.6585i −0.131806 0.118639i
\(546\) −121.599 + 57.7811i −0.222709 + 0.105826i
\(547\) 177.699i 0.324862i 0.986720 + 0.162431i \(0.0519334\pi\)
−0.986720 + 0.162431i \(0.948067\pi\)
\(548\) 425.442 0.776354
\(549\) 304.176 373.380i 0.554054 0.680110i
\(550\) −368.124 + 38.8126i −0.669316 + 0.0705685i
\(551\) 963.147i 1.74800i
\(552\) −59.1336 + 28.0989i −0.107126 + 0.0509037i
\(553\) 51.0613i 0.0923351i
\(554\) 378.131i 0.682546i
\(555\) −248.569 + 835.154i −0.447872 + 1.50478i
\(556\) 148.330 0.266780
\(557\) 227.747 0.408882 0.204441 0.978879i \(-0.434462\pi\)
0.204441 + 0.978879i \(0.434462\pi\)
\(558\) 285.450 350.394i 0.511559 0.627946i
\(559\) 189.055 0.338203
\(560\) 35.4007 39.3293i 0.0632155 0.0702309i
\(561\) 392.462 + 825.930i 0.699575 + 1.47225i
\(562\) 590.392i 1.05052i
\(563\) 271.221 0.481742 0.240871 0.970557i \(-0.422567\pi\)
0.240871 + 0.970557i \(0.422567\pi\)
\(564\) 461.736 219.406i 0.818682 0.389018i
\(565\) −106.125 95.5240i −0.187832 0.169069i
\(566\) 79.4479i 0.140367i
\(567\) 209.881 43.3258i 0.370160 0.0764123i
\(568\) 164.243i 0.289161i
\(569\) 63.1031i 0.110902i −0.998461 0.0554509i \(-0.982340\pi\)
0.998461 0.0554509i \(-0.0176596\pi\)
\(570\) 413.092 + 122.950i 0.724723 + 0.215701i
\(571\) 130.175 0.227977 0.113988 0.993482i \(-0.463637\pi\)
0.113988 + 0.993482i \(0.463637\pi\)
\(572\) −251.144 −0.439064
\(573\) 107.483 + 226.196i 0.187579 + 0.394757i
\(574\) 196.755 0.342779
\(575\) 20.2253 + 191.830i 0.0351745 + 0.333617i
\(576\) 45.4751 55.8213i 0.0789497 0.0969120i
\(577\) 371.832i 0.644424i 0.946668 + 0.322212i \(0.104426\pi\)
−0.946668 + 0.322212i \(0.895574\pi\)
\(578\) −789.954 −1.36670
\(579\) 113.955 + 239.816i 0.196813 + 0.414190i
\(580\) −317.141 + 352.337i −0.546796 + 0.607477i
\(581\) 89.1612i 0.153462i
\(582\) −118.601 249.594i −0.203782 0.428855i
\(583\) 447.741i 0.767995i
\(584\) 191.790i 0.328408i
\(585\) 82.9529 + 533.305i 0.141800 + 0.911632i
\(586\) −50.7233 −0.0865586
\(587\) −824.490 −1.40458 −0.702291 0.711890i \(-0.747840\pi\)
−0.702291 + 0.711890i \(0.747840\pi\)
\(588\) −37.9351 + 18.0258i −0.0645154 + 0.0306562i
\(589\) −721.445 −1.22486
\(590\) −179.654 + 199.591i −0.304498 + 0.338290i
\(591\) −100.079 + 47.5551i −0.169338 + 0.0804655i
\(592\) 232.363i 0.392504i
\(593\) 148.957 0.251192 0.125596 0.992081i \(-0.459916\pi\)
0.125596 + 0.992081i \(0.459916\pi\)
\(594\) 388.317 + 95.0361i 0.653732 + 0.159994i
\(595\) −257.657 + 286.251i −0.433037 + 0.481094i
\(596\) 46.3197i 0.0777176i
\(597\) −555.752 + 264.080i −0.930909 + 0.442345i
\(598\) 130.872i 0.218849i
\(599\) 98.6062i 0.164618i 0.996607 + 0.0823090i \(0.0262294\pi\)
−0.996607 + 0.0823090i \(0.973771\pi\)
\(600\) −110.632 180.999i −0.184387 0.301664i
\(601\) 244.192 0.406310 0.203155 0.979147i \(-0.434880\pi\)
0.203155 + 0.979147i \(0.434880\pi\)
\(602\) 58.9792 0.0979721
\(603\) 192.839 + 157.097i 0.319799 + 0.260526i
\(604\) 150.294 0.248831
\(605\) −42.3015 38.0760i −0.0699199 0.0629355i
\(606\) −311.679 655.924i −0.514322 1.08238i
\(607\) 504.707i 0.831478i −0.909484 0.415739i \(-0.863523\pi\)
0.909484 0.415739i \(-0.136477\pi\)
\(608\) −114.934 −0.189035
\(609\) 339.846 161.487i 0.558040 0.265167i
\(610\) 281.231 + 253.139i 0.461035 + 0.414981i
\(611\) 1021.89i 1.67249i
\(612\) −330.982 + 406.285i −0.540820 + 0.663865i
\(613\) 416.536i 0.679503i −0.940515 0.339752i \(-0.889657\pi\)
0.940515 0.339752i \(-0.110343\pi\)
\(614\) 702.259i 1.14374i
\(615\) 225.010 756.000i 0.365870 1.22927i
\(616\) −78.3490 −0.127190
\(617\) −132.241 −0.214330 −0.107165 0.994241i \(-0.534177\pi\)
−0.107165 + 0.994241i \(0.534177\pi\)
\(618\) 236.495 + 497.699i 0.382677 + 0.805338i
\(619\) 669.449 1.08150 0.540751 0.841183i \(-0.318140\pi\)
0.540751 + 0.841183i \(0.318140\pi\)
\(620\) 263.918 + 237.555i 0.425674 + 0.383153i
\(621\) 49.5234 202.352i 0.0797479 0.325849i
\(622\) 70.0059i 0.112550i
\(623\) −123.907 −0.198888
\(624\) −61.7706 129.995i −0.0989913 0.208326i
\(625\) −611.257 + 130.343i −0.978012 + 0.208549i
\(626\) 309.955i 0.495137i
\(627\) −273.891 576.400i −0.436829 0.919299i
\(628\) 133.394i 0.212410i
\(629\) 1691.21i 2.68873i
\(630\) 25.8786 + 166.374i 0.0410772 + 0.264086i
\(631\) 590.546 0.935889 0.467944 0.883758i \(-0.344995\pi\)
0.467944 + 0.883758i \(0.344995\pi\)
\(632\) −54.5869 −0.0863716
\(633\) 134.081 63.7121i 0.211819 0.100651i
\(634\) −136.191 −0.214812
\(635\) −542.286 + 602.467i −0.853993 + 0.948766i
\(636\) 231.756 110.125i 0.364396 0.173152i
\(637\) 83.9561i 0.131799i
\(638\) 701.900 1.10016
\(639\) 405.185 + 330.085i 0.634092 + 0.516565i
\(640\) 42.0448 + 37.8449i 0.0656950 + 0.0591326i
\(641\) 542.271i 0.845977i 0.906135 + 0.422989i \(0.139019\pi\)
−0.906135 + 0.422989i \(0.860981\pi\)
\(642\) 111.752 53.1019i 0.174069 0.0827132i
\(643\) 546.024i 0.849181i 0.905385 + 0.424591i \(0.139582\pi\)
−0.905385 + 0.424591i \(0.860418\pi\)
\(644\) 40.8277i 0.0633971i
\(645\) 67.4490 226.618i 0.104572 0.351346i
\(646\) 836.523 1.29493
\(647\) 801.011 1.23804 0.619020 0.785376i \(-0.287530\pi\)
0.619020 + 0.785376i \(0.287530\pi\)
\(648\) 46.3172 + 224.372i 0.0714772 + 0.346253i
\(649\) 397.611 0.612652
\(650\) −421.705 + 44.4619i −0.648777 + 0.0684030i
\(651\) −120.962 254.562i −0.185809 0.391032i
\(652\) 497.633i 0.763241i
\(653\) −1193.82 −1.82821 −0.914103 0.405482i \(-0.867104\pi\)
−0.914103 + 0.405482i \(0.867104\pi\)
\(654\) −74.0715 + 35.1970i −0.113259 + 0.0538180i
\(655\) −165.833 + 184.236i −0.253180 + 0.281277i
\(656\) 210.340i 0.320640i
\(657\) 473.142 + 385.447i 0.720155 + 0.586677i
\(658\) 318.798i 0.484495i
\(659\) 1234.84i 1.87381i −0.349579 0.936907i \(-0.613675\pi\)
0.349579 0.936907i \(-0.386325\pi\)
\(660\) −89.6004 + 301.044i −0.135758 + 0.456127i
\(661\) −660.309 −0.998954 −0.499477 0.866327i \(-0.666475\pi\)
−0.499477 + 0.866327i \(0.666475\pi\)
\(662\) −761.845 −1.15082
\(663\) 449.586 + 946.146i 0.678108 + 1.42707i
\(664\) −95.3174 −0.143550
\(665\) 179.814 199.769i 0.270397 0.300405i
\(666\) 573.233 + 466.987i 0.860711 + 0.701181i
\(667\) 365.761i 0.548367i
\(668\) −184.044 −0.275516
\(669\) −2.18793 4.60446i −0.00327045 0.00688260i
\(670\) −130.738 + 145.247i −0.195131 + 0.216786i
\(671\) 560.248i 0.834945i
\(672\) −19.2704 40.5543i −0.0286762 0.0603487i
\(673\) 372.706i 0.553798i 0.960899 + 0.276899i \(0.0893067\pi\)
−0.960899 + 0.276899i \(0.910693\pi\)
\(674\) 286.711i 0.425387i
\(675\) 668.861 + 90.8318i 0.990905 + 0.134566i
\(676\) 50.3009 0.0744096
\(677\) 762.928 1.12693 0.563463 0.826142i \(-0.309469\pi\)
0.563463 + 0.826142i \(0.309469\pi\)
\(678\) −109.430 + 51.9987i −0.161402 + 0.0766942i
\(679\) −172.328 −0.253796
\(680\) −306.015 275.447i −0.450022 0.405069i
\(681\) −560.816 + 266.486i −0.823518 + 0.391316i
\(682\) 525.758i 0.770906i
\(683\) 28.2779 0.0414024 0.0207012 0.999786i \(-0.493410\pi\)
0.0207012 + 0.999786i \(0.493410\pi\)
\(684\) 230.986 283.538i 0.337698 0.414530i
\(685\) −790.529 711.562i −1.15406 1.03878i
\(686\) 26.1916i 0.0381802i
\(687\) −19.0364 + 9.04565i −0.0277095 + 0.0131669i
\(688\) 63.0514i 0.0916445i
\(689\) 512.911i 0.744428i
\(690\) 156.874 + 46.6909i 0.227354 + 0.0676679i
\(691\) −587.034 −0.849543 −0.424771 0.905301i \(-0.639645\pi\)
−0.424771 + 0.905301i \(0.639645\pi\)
\(692\) −466.946 −0.674778
\(693\) 157.460 193.285i 0.227216 0.278911i
\(694\) 196.591 0.283272
\(695\) −275.617 248.085i −0.396571 0.356957i
\(696\) 172.637 + 363.311i 0.248041 + 0.521999i
\(697\) 1530.92i 2.19644i
\(698\) −640.616 −0.917787
\(699\) 316.140 150.222i 0.452274 0.214910i
\(700\) −131.558 + 13.8707i −0.187941 + 0.0198153i
\(701\) 221.461i 0.315922i −0.987445 0.157961i \(-0.949508\pi\)
0.987445 0.157961i \(-0.0504920\pi\)
\(702\) 444.837 + 108.869i 0.633671 + 0.155084i
\(703\) 1180.26i 1.67889i
\(704\) 83.7586i 0.118975i
\(705\) −1224.93 364.579i −1.73749 0.517134i
\(706\) −641.344 −0.908419
\(707\) −452.871 −0.640553
\(708\) 97.7950 + 205.808i 0.138129 + 0.290689i
\(709\) −1187.65 −1.67511 −0.837553 0.546356i \(-0.816014\pi\)
−0.837553 + 0.546356i \(0.816014\pi\)
\(710\) −274.701 + 305.186i −0.386903 + 0.429840i
\(711\) 109.705 134.665i 0.154297 0.189402i
\(712\) 132.462i 0.186043i
\(713\) −273.973 −0.384254
\(714\) 140.256 + 295.167i 0.196437 + 0.413399i
\(715\) 466.660 + 420.045i 0.652672 + 0.587476i
\(716\) 370.505i 0.517465i
\(717\) −202.300 425.736i −0.282147 0.593774i
\(718\) 212.568i 0.296055i
\(719\) 611.937i 0.851095i 0.904936 + 0.425547i \(0.139918\pi\)
−0.904936 + 0.425547i \(0.860082\pi\)
\(720\) −177.861 + 27.6654i −0.247030 + 0.0384242i
\(721\) 343.628 0.476599
\(722\) −73.2618 −0.101471
\(723\) −777.757 + 369.571i −1.07574 + 0.511164i
\(724\) −292.744 −0.404342
\(725\) 1178.58 124.262i 1.62563 0.171396i
\(726\) −43.6191 + 20.7268i −0.0600814 + 0.0285492i
\(727\) 1136.33i 1.56304i −0.623881 0.781520i \(-0.714445\pi\)
0.623881 0.781520i \(-0.285555\pi\)
\(728\) −89.7529 −0.123287
\(729\) −646.605 336.664i −0.886976 0.461816i
\(730\) −320.773 + 356.372i −0.439416 + 0.488180i
\(731\) 458.908i 0.627781i
\(732\) 289.991 137.797i 0.396162 0.188247i
\(733\) 401.450i 0.547681i 0.961775 + 0.273840i \(0.0882940\pi\)
−0.961775 + 0.273840i \(0.911706\pi\)
\(734\) 541.632i 0.737919i
\(735\) 100.637 + 29.9529i 0.136921 + 0.0407522i
\(736\) −43.6467 −0.0593026
\(737\) 289.350 0.392606
\(738\) −518.904 422.727i −0.703121 0.572801i
\(739\) −75.9398 −0.102760 −0.0513801 0.998679i \(-0.516362\pi\)
−0.0513801 + 0.998679i \(0.516362\pi\)
\(740\) −388.632 + 431.761i −0.525178 + 0.583461i
\(741\) −313.757 660.297i −0.423424 0.891088i
\(742\) 160.012i 0.215649i
\(743\) −308.906 −0.415755 −0.207877 0.978155i \(-0.566655\pi\)
−0.207877 + 0.978155i \(0.566655\pi\)
\(744\) 272.138 129.313i 0.365777 0.173808i
\(745\) 77.4708 86.0682i 0.103988 0.115528i
\(746\) 113.619i 0.152305i
\(747\) 191.562 235.146i 0.256442 0.314787i
\(748\) 609.621i 0.815002i
\(749\) 77.1572i 0.103014i
\(750\) −97.1551 + 521.355i −0.129540 + 0.695140i
\(751\) 629.294 0.837941 0.418971 0.908000i \(-0.362391\pi\)
0.418971 + 0.908000i \(0.362391\pi\)
\(752\) 340.809 0.453204
\(753\) −207.369 436.405i −0.275391 0.579555i
\(754\) 804.063 1.06640
\(755\) −279.266 251.370i −0.369889 0.332940i
\(756\) 138.775 + 33.9636i 0.183565 + 0.0449254i
\(757\) 526.381i 0.695351i −0.937615 0.347676i \(-0.886971\pi\)
0.937615 0.347676i \(-0.113029\pi\)
\(758\) 899.564 1.18676
\(759\) −104.012 218.891i −0.137038 0.288394i
\(760\) 213.562 + 192.229i 0.281003 + 0.252933i
\(761\) 955.908i 1.25612i −0.778164 0.628061i \(-0.783849\pi\)
0.778164 0.628061i \(-0.216151\pi\)
\(762\) 295.194 + 621.232i 0.387394 + 0.815265i
\(763\) 51.1414i 0.0670267i
\(764\) 166.956i 0.218529i
\(765\) 1294.53 201.358i 1.69220 0.263213i
\(766\) −486.029 −0.634503
\(767\) 455.485 0.593852
\(768\) 43.3544 20.6010i 0.0564510 0.0268242i
\(769\) 1062.16 1.38123 0.690613 0.723225i \(-0.257341\pi\)
0.690613 + 0.723225i \(0.257341\pi\)
\(770\) 145.583 + 131.041i 0.189069 + 0.170183i
\(771\) 967.072 459.530i 1.25431 0.596018i
\(772\) 177.009i 0.229287i
\(773\) −548.202 −0.709188 −0.354594 0.935020i \(-0.615381\pi\)
−0.354594 + 0.935020i \(0.615381\pi\)
\(774\) −155.546 126.717i −0.200964 0.163716i
\(775\) −93.0787 882.818i −0.120102 1.13912i
\(776\) 184.226i 0.237405i
\(777\) 416.455 197.889i 0.535978 0.254684i
\(778\) 735.971i 0.945979i
\(779\) 1068.40i 1.37150i
\(780\) −102.642 + 344.861i −0.131592 + 0.442130i