Properties

Label 690.3.b.a.599.8
Level $690$
Weight $3$
Character 690.599
Analytic conductor $18.801$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(88\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 599.8
Character \(\chi\) \(=\) 690.599
Dual form 690.3.b.a.599.7

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +(-2.76001 + 1.17574i) q^{3} +2.00000 q^{4} +(-2.52270 + 4.31694i) q^{5} +(3.90324 - 1.66274i) q^{6} +6.80400i q^{7} -2.82843 q^{8} +(6.23528 - 6.49009i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(-2.76001 + 1.17574i) q^{3} +2.00000 q^{4} +(-2.52270 + 4.31694i) q^{5} +(3.90324 - 1.66274i) q^{6} +6.80400i q^{7} -2.82843 q^{8} +(6.23528 - 6.49009i) q^{9} +(3.56764 - 6.10507i) q^{10} -9.88220i q^{11} +(-5.52002 + 2.35147i) q^{12} +4.88365i q^{13} -9.62230i q^{14} +(1.88710 - 14.8808i) q^{15} +4.00000 q^{16} +23.8286 q^{17} +(-8.81802 + 9.17837i) q^{18} +36.4177 q^{19} +(-5.04541 + 8.63388i) q^{20} +(-7.99971 - 18.7791i) q^{21} +13.9755i q^{22} +4.79583 q^{23} +(7.80648 - 3.32549i) q^{24} +(-12.2719 - 21.7807i) q^{25} -6.90652i q^{26} +(-9.57879 + 25.2437i) q^{27} +13.6080i q^{28} -11.1656i q^{29} +(-2.66876 + 21.0447i) q^{30} +10.5765 q^{31} -5.65685 q^{32} +(11.6189 + 27.2749i) q^{33} -33.6988 q^{34} +(-29.3724 - 17.1645i) q^{35} +(12.4706 - 12.9802i) q^{36} -41.3514i q^{37} -51.5024 q^{38} +(-5.74188 - 13.4789i) q^{39} +(7.13528 - 12.2101i) q^{40} +34.4083i q^{41} +(11.3133 + 26.5576i) q^{42} -33.3830i q^{43} -19.7644i q^{44} +(12.2875 + 43.2899i) q^{45} -6.78233 q^{46} -13.0445 q^{47} +(-11.0400 + 4.70295i) q^{48} +2.70565 q^{49} +(17.3551 + 30.8026i) q^{50} +(-65.7672 + 28.0162i) q^{51} +9.76729i q^{52} +42.5227 q^{53} +(13.5465 - 35.7000i) q^{54} +(42.6608 + 24.9299i) q^{55} -19.2446i q^{56} +(-100.513 + 42.8177i) q^{57} +15.7905i q^{58} +94.4998i q^{59} +(3.77419 - 29.7616i) q^{60} +10.7373 q^{61} -14.9574 q^{62} +(44.1585 + 42.4248i) q^{63} +8.00000 q^{64} +(-21.0824 - 12.3200i) q^{65} +(-16.4316 - 38.5726i) q^{66} +17.6081i q^{67} +47.6573 q^{68} +(-13.2365 + 5.63864i) q^{69} +(41.5389 + 24.2742i) q^{70} +83.8565i q^{71} +(-17.6360 + 18.3567i) q^{72} +70.2097i q^{73} +58.4797i q^{74} +(59.4790 + 45.6864i) q^{75} +72.8355 q^{76} +67.2384 q^{77} +(8.12025 + 19.0620i) q^{78} -1.50786 q^{79} +(-10.0908 + 17.2678i) q^{80} +(-3.24248 - 80.9351i) q^{81} -48.6607i q^{82} +99.1421 q^{83} +(-15.9994 - 37.5582i) q^{84} +(-60.1126 + 102.867i) q^{85} +47.2107i q^{86} +(13.1278 + 30.8171i) q^{87} +27.9511i q^{88} -25.8390i q^{89} +(-17.3772 - 61.2212i) q^{90} -33.2283 q^{91} +9.59166 q^{92} +(-29.1912 + 12.4352i) q^{93} +18.4477 q^{94} +(-91.8711 + 157.213i) q^{95} +(15.6130 - 6.65097i) q^{96} -39.5735i q^{97} -3.82636 q^{98} +(-64.1363 - 61.6183i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88q + 176q^{4} + 8q^{9} + O(q^{10}) \) \( 88q + 176q^{4} + 8q^{9} + 32q^{10} - 12q^{15} + 352q^{16} - 16q^{19} - 176q^{21} + 72q^{25} - 72q^{30} + 32q^{31} + 160q^{34} + 16q^{36} + 144q^{39} + 64q^{40} + 92q^{45} - 360q^{49} + 48q^{51} - 144q^{54} + 16q^{55} - 24q^{60} + 208q^{61} + 704q^{64} + 512q^{66} + 304q^{70} + 536q^{75} - 32q^{76} + 448q^{79} - 24q^{81} - 352q^{84} - 96q^{85} + 32q^{90} - 64q^{91} + 160q^{94} + 296q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −2.76001 + 1.17574i −0.920003 + 0.391912i
\(4\) 2.00000 0.500000
\(5\) −2.52270 + 4.31694i −0.504541 + 0.863388i
\(6\) 3.90324 1.66274i 0.650540 0.277124i
\(7\) 6.80400i 0.971999i 0.873959 + 0.486000i \(0.161544\pi\)
−0.873959 + 0.486000i \(0.838456\pi\)
\(8\) −2.82843 −0.353553
\(9\) 6.23528 6.49009i 0.692809 0.721121i
\(10\) 3.56764 6.10507i 0.356764 0.610507i
\(11\) 9.88220i 0.898382i −0.893436 0.449191i \(-0.851712\pi\)
0.893436 0.449191i \(-0.148288\pi\)
\(12\) −5.52002 + 2.35147i −0.460001 + 0.195956i
\(13\) 4.88365i 0.375665i 0.982201 + 0.187833i \(0.0601462\pi\)
−0.982201 + 0.187833i \(0.939854\pi\)
\(14\) 9.62230i 0.687307i
\(15\) 1.88710 14.8808i 0.125806 0.992055i
\(16\) 4.00000 0.250000
\(17\) 23.8286 1.40168 0.700842 0.713316i \(-0.252808\pi\)
0.700842 + 0.713316i \(0.252808\pi\)
\(18\) −8.81802 + 9.17837i −0.489890 + 0.509909i
\(19\) 36.4177 1.91672 0.958361 0.285559i \(-0.0921792\pi\)
0.958361 + 0.285559i \(0.0921792\pi\)
\(20\) −5.04541 + 8.63388i −0.252270 + 0.431694i
\(21\) −7.99971 18.7791i −0.380939 0.894242i
\(22\) 13.9755i 0.635252i
\(23\) 4.79583 0.208514
\(24\) 7.80648 3.32549i 0.325270 0.138562i
\(25\) −12.2719 21.7807i −0.490877 0.871229i
\(26\) 6.90652i 0.265635i
\(27\) −9.57879 + 25.2437i −0.354770 + 0.934954i
\(28\) 13.6080i 0.486000i
\(29\) 11.1656i 0.385021i −0.981295 0.192510i \(-0.938337\pi\)
0.981295 0.192510i \(-0.0616629\pi\)
\(30\) −2.66876 + 21.0447i −0.0889585 + 0.701489i
\(31\) 10.5765 0.341177 0.170588 0.985342i \(-0.445433\pi\)
0.170588 + 0.985342i \(0.445433\pi\)
\(32\) −5.65685 −0.176777
\(33\) 11.6189 + 27.2749i 0.352087 + 0.826513i
\(34\) −33.6988 −0.991140
\(35\) −29.3724 17.1645i −0.839212 0.490413i
\(36\) 12.4706 12.9802i 0.346405 0.360560i
\(37\) 41.3514i 1.11761i −0.829301 0.558803i \(-0.811261\pi\)
0.829301 0.558803i \(-0.188739\pi\)
\(38\) −51.5024 −1.35533
\(39\) −5.74188 13.4789i −0.147228 0.345613i
\(40\) 7.13528 12.2101i 0.178382 0.305254i
\(41\) 34.4083i 0.839227i 0.907703 + 0.419614i \(0.137834\pi\)
−0.907703 + 0.419614i \(0.862166\pi\)
\(42\) 11.3133 + 26.5576i 0.269364 + 0.632324i
\(43\) 33.3830i 0.776350i −0.921586 0.388175i \(-0.873106\pi\)
0.921586 0.388175i \(-0.126894\pi\)
\(44\) 19.7644i 0.449191i
\(45\) 12.2875 + 43.2899i 0.273056 + 0.961998i
\(46\) −6.78233 −0.147442
\(47\) −13.0445 −0.277542 −0.138771 0.990324i \(-0.544315\pi\)
−0.138771 + 0.990324i \(0.544315\pi\)
\(48\) −11.0400 + 4.70295i −0.230001 + 0.0979781i
\(49\) 2.70565 0.0552173
\(50\) 17.3551 + 30.8026i 0.347103 + 0.616052i
\(51\) −65.7672 + 28.0162i −1.28955 + 0.549337i
\(52\) 9.76729i 0.187833i
\(53\) 42.5227 0.802315 0.401157 0.916009i \(-0.368608\pi\)
0.401157 + 0.916009i \(0.368608\pi\)
\(54\) 13.5465 35.7000i 0.250860 0.661112i
\(55\) 42.6608 + 24.9299i 0.775652 + 0.453270i
\(56\) 19.2446i 0.343654i
\(57\) −100.513 + 42.8177i −1.76339 + 0.751187i
\(58\) 15.7905i 0.272251i
\(59\) 94.4998i 1.60169i 0.598871 + 0.800846i \(0.295616\pi\)
−0.598871 + 0.800846i \(0.704384\pi\)
\(60\) 3.77419 29.7616i 0.0629032 0.496027i
\(61\) 10.7373 0.176021 0.0880104 0.996120i \(-0.471949\pi\)
0.0880104 + 0.996120i \(0.471949\pi\)
\(62\) −14.9574 −0.241248
\(63\) 44.1585 + 42.4248i 0.700929 + 0.673410i
\(64\) 8.00000 0.125000
\(65\) −21.0824 12.3200i −0.324345 0.189538i
\(66\) −16.4316 38.5726i −0.248963 0.584433i
\(67\) 17.6081i 0.262808i 0.991329 + 0.131404i \(0.0419485\pi\)
−0.991329 + 0.131404i \(0.958051\pi\)
\(68\) 47.6573 0.700842
\(69\) −13.2365 + 5.63864i −0.191834 + 0.0817194i
\(70\) 41.5389 + 24.2742i 0.593413 + 0.346775i
\(71\) 83.8565i 1.18108i 0.807009 + 0.590539i \(0.201085\pi\)
−0.807009 + 0.590539i \(0.798915\pi\)
\(72\) −17.6360 + 18.3567i −0.244945 + 0.254955i
\(73\) 70.2097i 0.961777i 0.876782 + 0.480888i \(0.159686\pi\)
−0.876782 + 0.480888i \(0.840314\pi\)
\(74\) 58.4797i 0.790266i
\(75\) 59.4790 + 45.6864i 0.793054 + 0.609152i
\(76\) 72.8355 0.958361
\(77\) 67.2384 0.873226
\(78\) 8.12025 + 19.0620i 0.104106 + 0.244385i
\(79\) −1.50786 −0.0190868 −0.00954341 0.999954i \(-0.503038\pi\)
−0.00954341 + 0.999954i \(0.503038\pi\)
\(80\) −10.0908 + 17.2678i −0.126135 + 0.215847i
\(81\) −3.24248 80.9351i −0.0400306 0.999198i
\(82\) 48.6607i 0.593423i
\(83\) 99.1421 1.19448 0.597242 0.802061i \(-0.296263\pi\)
0.597242 + 0.802061i \(0.296263\pi\)
\(84\) −15.9994 37.5582i −0.190469 0.447121i
\(85\) −60.1126 + 102.867i −0.707207 + 1.21020i
\(86\) 47.2107i 0.548962i
\(87\) 13.1278 + 30.8171i 0.150894 + 0.354220i
\(88\) 27.9511i 0.317626i
\(89\) 25.8390i 0.290326i −0.989408 0.145163i \(-0.953629\pi\)
0.989408 0.145163i \(-0.0463706\pi\)
\(90\) −17.3772 61.2212i −0.193080 0.680235i
\(91\) −33.2283 −0.365146
\(92\) 9.59166 0.104257
\(93\) −29.1912 + 12.4352i −0.313883 + 0.133711i
\(94\) 18.4477 0.196252
\(95\) −91.8711 + 157.213i −0.967065 + 1.65487i
\(96\) 15.6130 6.65097i 0.162635 0.0692810i
\(97\) 39.5735i 0.407974i −0.978974 0.203987i \(-0.934610\pi\)
0.978974 0.203987i \(-0.0653901\pi\)
\(98\) −3.82636 −0.0390445
\(99\) −64.1363 61.6183i −0.647842 0.622407i
\(100\) −24.5439 43.5614i −0.245439 0.435614i
\(101\) 73.2651i 0.725397i −0.931907 0.362698i \(-0.881856\pi\)
0.931907 0.362698i \(-0.118144\pi\)
\(102\) 93.0089 39.6209i 0.911852 0.388440i
\(103\) 78.9282i 0.766293i 0.923688 + 0.383146i \(0.125160\pi\)
−0.923688 + 0.383146i \(0.874840\pi\)
\(104\) 13.8130i 0.132818i
\(105\) 101.249 + 12.8398i 0.964277 + 0.122284i
\(106\) −60.1362 −0.567322
\(107\) 28.9236 0.270314 0.135157 0.990824i \(-0.456846\pi\)
0.135157 + 0.990824i \(0.456846\pi\)
\(108\) −19.1576 + 50.4875i −0.177385 + 0.467477i
\(109\) −176.410 −1.61844 −0.809222 0.587503i \(-0.800111\pi\)
−0.809222 + 0.587503i \(0.800111\pi\)
\(110\) −60.3315 35.2561i −0.548469 0.320510i
\(111\) 48.6184 + 114.130i 0.438003 + 1.02820i
\(112\) 27.2160i 0.243000i
\(113\) −26.1909 −0.231778 −0.115889 0.993262i \(-0.536972\pi\)
−0.115889 + 0.993262i \(0.536972\pi\)
\(114\) 142.147 60.5533i 1.24690 0.531170i
\(115\) −12.0985 + 20.7033i −0.105204 + 0.180029i
\(116\) 22.3312i 0.192510i
\(117\) 31.6953 + 30.4509i 0.270900 + 0.260264i
\(118\) 133.643i 1.13257i
\(119\) 162.130i 1.36244i
\(120\) −5.33751 + 42.0893i −0.0444793 + 0.350744i
\(121\) 23.3422 0.192911
\(122\) −15.1848 −0.124466
\(123\) −40.4551 94.9672i −0.328904 0.772091i
\(124\) 21.1530 0.170588
\(125\) 124.984 + 1.96913i 0.999876 + 0.0157530i
\(126\) −62.4496 59.9978i −0.495632 0.476173i
\(127\) 183.850i 1.44764i 0.689990 + 0.723819i \(0.257615\pi\)
−0.689990 + 0.723819i \(0.742385\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 39.2497 + 92.1374i 0.304261 + 0.714244i
\(130\) 29.8150 + 17.4231i 0.229346 + 0.134024i
\(131\) 15.3027i 0.116815i 0.998293 + 0.0584073i \(0.0186022\pi\)
−0.998293 + 0.0584073i \(0.981398\pi\)
\(132\) 23.2377 + 54.5499i 0.176043 + 0.413257i
\(133\) 247.786i 1.86305i
\(134\) 24.9017i 0.185833i
\(135\) −84.8113 105.034i −0.628232 0.778026i
\(136\) −67.3975 −0.495570
\(137\) 17.9160 0.130774 0.0653870 0.997860i \(-0.479172\pi\)
0.0653870 + 0.997860i \(0.479172\pi\)
\(138\) 18.7193 7.97424i 0.135647 0.0577843i
\(139\) 21.9531 0.157936 0.0789679 0.996877i \(-0.474838\pi\)
0.0789679 + 0.996877i \(0.474838\pi\)
\(140\) −58.7449 34.3289i −0.419606 0.245207i
\(141\) 36.0029 15.3369i 0.255340 0.108772i
\(142\) 118.591i 0.835148i
\(143\) 48.2611 0.337491
\(144\) 24.9411 25.9604i 0.173202 0.180280i
\(145\) 48.2012 + 28.1675i 0.332422 + 0.194259i
\(146\) 99.2915i 0.680079i
\(147\) −7.46761 + 3.18113i −0.0508001 + 0.0216404i
\(148\) 82.7028i 0.558803i
\(149\) 156.433i 1.04989i 0.851138 + 0.524943i \(0.175913\pi\)
−0.851138 + 0.524943i \(0.824087\pi\)
\(150\) −84.1160 64.6103i −0.560774 0.430735i
\(151\) −217.732 −1.44193 −0.720966 0.692970i \(-0.756302\pi\)
−0.720966 + 0.692970i \(0.756302\pi\)
\(152\) −103.005 −0.677664
\(153\) 148.578 154.650i 0.971100 1.01078i
\(154\) −95.0895 −0.617464
\(155\) −26.6813 + 45.6580i −0.172138 + 0.294568i
\(156\) −11.4838 26.9578i −0.0736139 0.172806i
\(157\) 274.821i 1.75045i −0.483714 0.875226i \(-0.660712\pi\)
0.483714 0.875226i \(-0.339288\pi\)
\(158\) 2.13243 0.0134964
\(159\) −117.363 + 49.9955i −0.738132 + 0.314437i
\(160\) 14.2706 24.4203i 0.0891911 0.152627i
\(161\) 32.6308i 0.202676i
\(162\) 4.58556 + 114.459i 0.0283059 + 0.706540i
\(163\) 181.322i 1.11240i −0.831048 0.556201i \(-0.812258\pi\)
0.831048 0.556201i \(-0.187742\pi\)
\(164\) 68.8166i 0.419614i
\(165\) −147.055 18.6486i −0.891244 0.113022i
\(166\) −140.208 −0.844627
\(167\) −186.672 −1.11780 −0.558898 0.829237i \(-0.688775\pi\)
−0.558898 + 0.829237i \(0.688775\pi\)
\(168\) 22.6266 + 53.1153i 0.134682 + 0.316162i
\(169\) 145.150 0.858876
\(170\) 85.0120 145.476i 0.500071 0.855739i
\(171\) 227.075 236.354i 1.32792 1.38219i
\(172\) 66.7661i 0.388175i
\(173\) 315.255 1.82228 0.911141 0.412095i \(-0.135203\pi\)
0.911141 + 0.412095i \(0.135203\pi\)
\(174\) −18.5655 43.5820i −0.106698 0.250471i
\(175\) 148.196 83.4982i 0.846834 0.477132i
\(176\) 39.5288i 0.224595i
\(177\) −111.107 260.820i −0.627723 1.47356i
\(178\) 36.5419i 0.205291i
\(179\) 74.2072i 0.414565i 0.978281 + 0.207283i \(0.0664620\pi\)
−0.978281 + 0.207283i \(0.933538\pi\)
\(180\) 24.5751 + 86.5798i 0.136528 + 0.480999i
\(181\) 277.209 1.53154 0.765771 0.643113i \(-0.222358\pi\)
0.765771 + 0.643113i \(0.222358\pi\)
\(182\) 46.9919 0.258197
\(183\) −29.6349 + 12.6242i −0.161940 + 0.0689847i
\(184\) −13.5647 −0.0737210
\(185\) 178.511 + 104.317i 0.964927 + 0.563877i
\(186\) 41.2825 17.5860i 0.221949 0.0945482i
\(187\) 235.479i 1.25925i
\(188\) −26.0890 −0.138771
\(189\) −171.758 65.1741i −0.908774 0.344836i
\(190\) 129.925 222.333i 0.683818 1.17017i
\(191\) 36.5558i 0.191391i 0.995411 + 0.0956957i \(0.0305076\pi\)
−0.995411 + 0.0956957i \(0.969492\pi\)
\(192\) −22.0801 + 9.40590i −0.115000 + 0.0489891i
\(193\) 132.274i 0.685357i −0.939453 0.342678i \(-0.888666\pi\)
0.939453 0.342678i \(-0.111334\pi\)
\(194\) 55.9654i 0.288481i
\(195\) 72.6727 + 9.21590i 0.372680 + 0.0472610i
\(196\) 5.41130 0.0276087
\(197\) −271.150 −1.37639 −0.688197 0.725523i \(-0.741598\pi\)
−0.688197 + 0.725523i \(0.741598\pi\)
\(198\) 90.7025 + 87.1414i 0.458093 + 0.440108i
\(199\) −178.921 −0.899100 −0.449550 0.893255i \(-0.648416\pi\)
−0.449550 + 0.893255i \(0.648416\pi\)
\(200\) 34.7103 + 61.6052i 0.173551 + 0.308026i
\(201\) −20.7025 48.5986i −0.102998 0.241784i
\(202\) 103.612i 0.512933i
\(203\) 75.9707 0.374240
\(204\) −131.534 + 56.0324i −0.644776 + 0.274669i
\(205\) −148.539 86.8020i −0.724579 0.423424i
\(206\) 111.621i 0.541851i
\(207\) 29.9034 31.1254i 0.144461 0.150364i
\(208\) 19.5346i 0.0939163i
\(209\) 359.887i 1.72195i
\(210\) −143.188 18.1582i −0.681847 0.0864676i
\(211\) 259.891 1.23171 0.615856 0.787859i \(-0.288810\pi\)
0.615856 + 0.787859i \(0.288810\pi\)
\(212\) 85.0454 0.401157
\(213\) −98.5932 231.444i −0.462879 1.08659i
\(214\) −40.9041 −0.191141
\(215\) 144.113 + 84.2155i 0.670291 + 0.391700i
\(216\) 27.0929 71.4001i 0.125430 0.330556i
\(217\) 71.9623i 0.331623i
\(218\) 249.482 1.14441
\(219\) −82.5482 193.779i −0.376932 0.884837i
\(220\) 85.3217 + 49.8597i 0.387826 + 0.226635i
\(221\) 116.371i 0.526564i
\(222\) −68.7568 161.404i −0.309715 0.727047i
\(223\) 308.191i 1.38202i 0.722843 + 0.691012i \(0.242835\pi\)
−0.722843 + 0.691012i \(0.757165\pi\)
\(224\) 38.4892i 0.171827i
\(225\) −217.878 56.1631i −0.968346 0.249614i
\(226\) 37.0396 0.163892
\(227\) 125.303 0.551997 0.275998 0.961158i \(-0.410992\pi\)
0.275998 + 0.961158i \(0.410992\pi\)
\(228\) −201.026 + 85.6354i −0.881695 + 0.375594i
\(229\) −338.928 −1.48003 −0.740017 0.672588i \(-0.765183\pi\)
−0.740017 + 0.672588i \(0.765183\pi\)
\(230\) 17.1098 29.2789i 0.0743905 0.127300i
\(231\) −185.579 + 79.0547i −0.803370 + 0.342228i
\(232\) 31.5811i 0.136125i
\(233\) 160.840 0.690301 0.345151 0.938547i \(-0.387828\pi\)
0.345151 + 0.938547i \(0.387828\pi\)
\(234\) −44.8239 43.0641i −0.191555 0.184035i
\(235\) 32.9074 56.3123i 0.140031 0.239627i
\(236\) 189.000i 0.800846i
\(237\) 4.16170 1.77285i 0.0175599 0.00748036i
\(238\) 229.286i 0.963388i
\(239\) 279.640i 1.17004i −0.811019 0.585020i \(-0.801087\pi\)
0.811019 0.585020i \(-0.198913\pi\)
\(240\) 7.54838 59.5233i 0.0314516 0.248014i
\(241\) −370.691 −1.53814 −0.769069 0.639166i \(-0.779280\pi\)
−0.769069 + 0.639166i \(0.779280\pi\)
\(242\) −33.0108 −0.136408
\(243\) 104.108 + 219.569i 0.428427 + 0.903577i
\(244\) 21.4745 0.0880104
\(245\) −6.82555 + 11.6801i −0.0278594 + 0.0476740i
\(246\) 57.2122 + 134.304i 0.232570 + 0.545951i
\(247\) 177.851i 0.720046i
\(248\) −29.9148 −0.120624
\(249\) −273.633 + 116.565i −1.09893 + 0.468133i
\(250\) −176.755 2.78477i −0.707019 0.0111391i
\(251\) 343.840i 1.36988i 0.728600 + 0.684939i \(0.240171\pi\)
−0.728600 + 0.684939i \(0.759829\pi\)
\(252\) 88.3171 + 84.8497i 0.350464 + 0.336705i
\(253\) 47.3934i 0.187326i
\(254\) 260.003i 1.02363i
\(255\) 44.9669 354.590i 0.176341 1.39055i
\(256\) 16.0000 0.0625000
\(257\) −226.994 −0.883247 −0.441624 0.897200i \(-0.645597\pi\)
−0.441624 + 0.897200i \(0.645597\pi\)
\(258\) −55.5074 130.302i −0.215145 0.505046i
\(259\) 281.355 1.08631
\(260\) −42.1648 24.6400i −0.162172 0.0947692i
\(261\) −72.4657 69.6207i −0.277646 0.266746i
\(262\) 21.6413i 0.0826003i
\(263\) 270.805 1.02968 0.514838 0.857288i \(-0.327852\pi\)
0.514838 + 0.857288i \(0.327852\pi\)
\(264\) −32.8631 77.1452i −0.124482 0.292217i
\(265\) −107.272 + 183.568i −0.404801 + 0.692709i
\(266\) 350.422i 1.31738i
\(267\) 30.3799 + 71.3158i 0.113782 + 0.267101i
\(268\) 35.2163i 0.131404i
\(269\) 86.0153i 0.319760i −0.987136 0.159880i \(-0.948889\pi\)
0.987136 0.159880i \(-0.0511107\pi\)
\(270\) 119.941 + 148.540i 0.444227 + 0.550148i
\(271\) 20.6816 0.0763158 0.0381579 0.999272i \(-0.487851\pi\)
0.0381579 + 0.999272i \(0.487851\pi\)
\(272\) 95.3145 0.350421
\(273\) 91.7104 39.0678i 0.335935 0.143105i
\(274\) −25.3371 −0.0924712
\(275\) −215.241 + 121.274i −0.782696 + 0.440995i
\(276\) −26.4731 + 11.2773i −0.0959169 + 0.0408597i
\(277\) 341.121i 1.23148i −0.787948 0.615741i \(-0.788857\pi\)
0.787948 0.615741i \(-0.211143\pi\)
\(278\) −31.0463 −0.111677
\(279\) 65.9473 68.6423i 0.236370 0.246030i
\(280\) 83.0778 + 48.5484i 0.296706 + 0.173387i
\(281\) 351.167i 1.24971i −0.780743 0.624853i \(-0.785159\pi\)
0.780743 0.624853i \(-0.214841\pi\)
\(282\) −50.9158 + 21.6897i −0.180552 + 0.0769137i
\(283\) 165.167i 0.583629i 0.956475 + 0.291815i \(0.0942591\pi\)
−0.956475 + 0.291815i \(0.905741\pi\)
\(284\) 167.713i 0.590539i
\(285\) 68.7237 541.926i 0.241136 1.90149i
\(286\) −68.2516 −0.238642
\(287\) −234.114 −0.815728
\(288\) −35.2721 + 36.7135i −0.122473 + 0.127477i
\(289\) 278.804 0.964718
\(290\) −68.1668 39.8349i −0.235058 0.137362i
\(291\) 46.5281 + 109.223i 0.159890 + 0.375338i
\(292\) 140.419i 0.480888i
\(293\) −42.7560 −0.145925 −0.0729624 0.997335i \(-0.523245\pi\)
−0.0729624 + 0.997335i \(0.523245\pi\)
\(294\) 10.5608 4.49880i 0.0359211 0.0153020i
\(295\) −407.950 238.395i −1.38288 0.808119i
\(296\) 116.959i 0.395133i
\(297\) 249.464 + 94.6595i 0.839945 + 0.318719i
\(298\) 221.230i 0.742381i
\(299\) 23.4211i 0.0783316i
\(300\) 118.958 + 91.3728i 0.396527 + 0.304576i
\(301\) 227.138 0.754611
\(302\) 307.919 1.01960
\(303\) 86.1405 + 202.212i 0.284292 + 0.667367i
\(304\) 145.671 0.479181
\(305\) −27.0870 + 46.3521i −0.0888097 + 0.151974i
\(306\) −210.121 + 218.708i −0.686671 + 0.714732i
\(307\) 381.120i 1.24143i −0.784035 0.620717i \(-0.786842\pi\)
0.784035 0.620717i \(-0.213158\pi\)
\(308\) 134.477 0.436613
\(309\) −92.7988 217.842i −0.300320 0.704991i
\(310\) 37.7331 64.5702i 0.121720 0.208291i
\(311\) 426.669i 1.37193i 0.727636 + 0.685963i \(0.240619\pi\)
−0.727636 + 0.685963i \(0.759381\pi\)
\(312\) 16.2405 + 38.1241i 0.0520529 + 0.122193i
\(313\) 383.577i 1.22548i 0.790283 + 0.612742i \(0.209934\pi\)
−0.790283 + 0.612742i \(0.790066\pi\)
\(314\) 388.656i 1.23776i
\(315\) −294.544 + 83.6044i −0.935061 + 0.265411i
\(316\) −3.01572 −0.00954341
\(317\) −93.7258 −0.295665 −0.147832 0.989012i \(-0.547230\pi\)
−0.147832 + 0.989012i \(0.547230\pi\)
\(318\) 165.976 70.7043i 0.521938 0.222341i
\(319\) −110.341 −0.345895
\(320\) −20.1816 + 34.5355i −0.0630676 + 0.107923i
\(321\) −79.8292 + 34.0065i −0.248689 + 0.105939i
\(322\) 46.1469i 0.143313i
\(323\) 867.784 2.68664
\(324\) −6.48495 161.870i −0.0200153 0.499599i
\(325\) 106.369 59.9318i 0.327290 0.184405i
\(326\) 256.427i 0.786587i
\(327\) 486.894 207.412i 1.48897 0.634288i
\(328\) 97.3214i 0.296712i
\(329\) 88.7547i 0.269771i
\(330\) 207.967 + 26.3732i 0.630205 + 0.0799187i
\(331\) 236.616 0.714851 0.357425 0.933942i \(-0.383655\pi\)
0.357425 + 0.933942i \(0.383655\pi\)
\(332\) 198.284 0.597242
\(333\) −268.374 257.838i −0.805929 0.774287i
\(334\) 263.994 0.790400
\(335\) −76.0132 44.4201i −0.226905 0.132597i
\(336\) −31.9988 75.1163i −0.0952347 0.223560i
\(337\) 185.435i 0.550251i −0.961408 0.275125i \(-0.911281\pi\)
0.961408 0.275125i \(-0.0887194\pi\)
\(338\) −205.273 −0.607317
\(339\) 72.2872 30.7937i 0.213236 0.0908367i
\(340\) −120.225 + 205.733i −0.353603 + 0.605099i
\(341\) 104.519i 0.306507i
\(342\) −321.132 + 334.255i −0.938983 + 0.977355i
\(343\) 351.805i 1.02567i
\(344\) 94.4215i 0.274481i
\(345\) 9.05019 71.3659i 0.0262324 0.206858i
\(346\) −445.837 −1.28855
\(347\) −556.885 −1.60486 −0.802429 0.596748i \(-0.796459\pi\)
−0.802429 + 0.596748i \(0.796459\pi\)
\(348\) 26.2556 + 61.6343i 0.0754472 + 0.177110i
\(349\) −226.627 −0.649360 −0.324680 0.945824i \(-0.605257\pi\)
−0.324680 + 0.945824i \(0.605257\pi\)
\(350\) −209.581 + 118.084i −0.598802 + 0.337383i
\(351\) −123.282 46.7794i −0.351229 0.133275i
\(352\) 55.9022i 0.158813i
\(353\) 214.562 0.607823 0.303912 0.952700i \(-0.401707\pi\)
0.303912 + 0.952700i \(0.401707\pi\)
\(354\) 157.129 + 368.855i 0.443867 + 1.04196i
\(355\) −362.003 211.545i −1.01973 0.595902i
\(356\) 51.6780i 0.145163i
\(357\) −190.622 447.480i −0.533956 1.25344i
\(358\) 104.945i 0.293142i
\(359\) 496.982i 1.38435i 0.721730 + 0.692175i \(0.243347\pi\)
−0.721730 + 0.692175i \(0.756653\pi\)
\(360\) −34.7544 122.442i −0.0965400 0.340118i
\(361\) 965.251 2.67382
\(362\) −392.033 −1.08296
\(363\) −64.4246 + 27.4443i −0.177478 + 0.0756040i
\(364\) −66.4566 −0.182573
\(365\) −303.091 177.118i −0.830387 0.485256i
\(366\) 41.9101 17.8533i 0.114509 0.0487796i
\(367\) 504.879i 1.37569i 0.725857 + 0.687846i \(0.241443\pi\)
−0.725857 + 0.687846i \(0.758557\pi\)
\(368\) 19.1833 0.0521286
\(369\) 223.313 + 214.546i 0.605184 + 0.581425i
\(370\) −252.453 147.527i −0.682306 0.398722i
\(371\) 289.324i 0.779849i
\(372\) −58.3823 + 24.8703i −0.156942 + 0.0668557i
\(373\) 316.318i 0.848038i 0.905653 + 0.424019i \(0.139381\pi\)
−0.905653 + 0.424019i \(0.860619\pi\)
\(374\) 333.018i 0.890422i
\(375\) −347.273 + 141.514i −0.926062 + 0.377371i
\(376\) 36.8954 0.0981261
\(377\) 54.5288 0.144639
\(378\) 242.903 + 92.1700i 0.642600 + 0.243836i
\(379\) 88.0235 0.232252 0.116126 0.993234i \(-0.462952\pi\)
0.116126 + 0.993234i \(0.462952\pi\)
\(380\) −183.742 + 314.426i −0.483532 + 0.827437i
\(381\) −216.159 507.427i −0.567347 1.33183i
\(382\) 51.6977i 0.135334i
\(383\) 399.427 1.04289 0.521446 0.853285i \(-0.325393\pi\)
0.521446 + 0.853285i \(0.325393\pi\)
\(384\) 31.2259 13.3019i 0.0813175 0.0346405i
\(385\) −169.623 + 290.264i −0.440578 + 0.753933i
\(386\) 187.064i 0.484620i
\(387\) −216.659 208.153i −0.559842 0.537862i
\(388\) 79.1470i 0.203987i
\(389\) 403.418i 1.03706i −0.855058 0.518532i \(-0.826479\pi\)
0.855058 0.518532i \(-0.173521\pi\)
\(390\) −102.775 13.0333i −0.263525 0.0334186i
\(391\) 114.278 0.292271
\(392\) −7.65273 −0.0195223
\(393\) −17.9920 42.2356i −0.0457811 0.107470i
\(394\) 383.464 0.973258
\(395\) 3.80388 6.50933i 0.00963008 0.0164793i
\(396\) −128.273 123.237i −0.323921 0.311204i
\(397\) 554.412i 1.39650i 0.715852 + 0.698252i \(0.246039\pi\)
−0.715852 + 0.698252i \(0.753961\pi\)
\(398\) 253.032 0.635760
\(399\) −291.331 683.891i −0.730154 1.71401i
\(400\) −49.0877 87.1229i −0.122719 0.217807i
\(401\) 427.924i 1.06714i 0.845755 + 0.533572i \(0.179150\pi\)
−0.845755 + 0.533572i \(0.820850\pi\)
\(402\) 29.2778 + 68.7288i 0.0728304 + 0.170967i
\(403\) 51.6518i 0.128168i
\(404\) 146.530i 0.362698i
\(405\) 357.572 + 190.178i 0.882893 + 0.469574i
\(406\) −107.439 −0.264627
\(407\) −408.643 −1.00404
\(408\) 186.018 79.2418i 0.455926 0.194220i
\(409\) 717.855 1.75515 0.877573 0.479442i \(-0.159161\pi\)
0.877573 + 0.479442i \(0.159161\pi\)
\(410\) 210.065 + 122.757i 0.512355 + 0.299406i
\(411\) −49.4484 + 21.0646i −0.120312 + 0.0512520i
\(412\) 157.856i 0.383146i
\(413\) −642.976 −1.55684
\(414\) −42.2898 + 44.0179i −0.102149 + 0.106323i
\(415\) −250.106 + 427.990i −0.602665 + 1.03130i
\(416\) 27.6261i 0.0664088i
\(417\) −60.5906 + 25.8110i −0.145301 + 0.0618970i
\(418\) 508.957i 1.21760i
\(419\) 7.70955i 0.0183999i 0.999958 + 0.00919994i \(0.00292847\pi\)
−0.999958 + 0.00919994i \(0.997072\pi\)
\(420\) 202.498 + 25.6796i 0.482138 + 0.0611418i
\(421\) 641.178 1.52299 0.761494 0.648171i \(-0.224466\pi\)
0.761494 + 0.648171i \(0.224466\pi\)
\(422\) −367.541 −0.870951
\(423\) −81.3361 + 84.6599i −0.192284 + 0.200142i
\(424\) −120.272 −0.283661
\(425\) −292.423 519.005i −0.688055 1.22119i
\(426\) 139.432 + 327.312i 0.327305 + 0.768338i
\(427\) 73.0563i 0.171092i
\(428\) 57.8471 0.135157
\(429\) −133.201 + 56.7424i −0.310492 + 0.132267i
\(430\) −203.806 119.099i −0.473967 0.276974i
\(431\) 731.842i 1.69801i 0.528385 + 0.849005i \(0.322798\pi\)
−0.528385 + 0.849005i \(0.677202\pi\)
\(432\) −38.3152 + 100.975i −0.0886925 + 0.233738i
\(433\) 68.2321i 0.157580i −0.996891 0.0787900i \(-0.974894\pi\)
0.996891 0.0787900i \(-0.0251057\pi\)
\(434\) 101.770i 0.234493i
\(435\) −166.153 21.0705i −0.381962 0.0484380i
\(436\) −352.821 −0.809222
\(437\) 174.653 0.399664
\(438\) 116.741 + 274.045i 0.266531 + 0.625674i
\(439\) 472.232 1.07570 0.537850 0.843041i \(-0.319237\pi\)
0.537850 + 0.843041i \(0.319237\pi\)
\(440\) −120.663 70.5123i −0.274234 0.160255i
\(441\) 16.8705 17.5599i 0.0382551 0.0398184i
\(442\) 164.573i 0.372337i
\(443\) 633.039 1.42898 0.714491 0.699644i \(-0.246658\pi\)
0.714491 + 0.699644i \(0.246658\pi\)
\(444\) 97.2368 + 228.260i 0.219002 + 0.514100i
\(445\) 111.545 + 65.1841i 0.250664 + 0.146481i
\(446\) 435.849i 0.977239i
\(447\) −183.924 431.756i −0.411463 0.965897i
\(448\) 54.4320i 0.121500i
\(449\) 664.528i 1.48002i −0.672597 0.740009i \(-0.734821\pi\)
0.672597 0.740009i \(-0.265179\pi\)
\(450\) 308.126 + 79.4266i 0.684724 + 0.176503i
\(451\) 340.030 0.753946
\(452\) −52.3819 −0.115889
\(453\) 600.942 255.995i 1.32658 0.565111i
\(454\) −177.206 −0.390321
\(455\) 83.8252 143.445i 0.184231 0.315263i
\(456\) 284.294 121.107i 0.623452 0.265585i
\(457\) 464.273i 1.01591i 0.861382 + 0.507957i \(0.169599\pi\)
−0.861382 + 0.507957i \(0.830401\pi\)
\(458\) 479.316 1.04654
\(459\) −228.249 + 601.524i −0.497276 + 1.31051i
\(460\) −24.1969 + 41.4066i −0.0526020 + 0.0900144i
\(461\) 176.434i 0.382721i −0.981520 0.191361i \(-0.938710\pi\)
0.981520 0.191361i \(-0.0612900\pi\)
\(462\) 262.448 111.800i 0.568069 0.241992i
\(463\) 120.561i 0.260392i 0.991488 + 0.130196i \(0.0415606\pi\)
−0.991488 + 0.130196i \(0.958439\pi\)
\(464\) 44.6624i 0.0962551i
\(465\) 19.9588 157.387i 0.0429222 0.338466i
\(466\) −227.462 −0.488117
\(467\) −366.952 −0.785765 −0.392882 0.919589i \(-0.628522\pi\)
−0.392882 + 0.919589i \(0.628522\pi\)
\(468\) 63.3906 + 60.9018i 0.135450 + 0.130132i
\(469\) −119.806 −0.255449
\(470\) −46.5381 + 79.6376i −0.0990172 + 0.169442i
\(471\) 323.117 + 758.508i 0.686024 + 1.61042i
\(472\) 267.286i 0.566283i
\(473\) −329.898 −0.697458
\(474\) −5.88553 + 2.50718i −0.0124167 + 0.00528941i
\(475\) −446.916 793.204i −0.940875 1.66990i
\(476\) 324.260i 0.681218i
\(477\) 265.141 275.976i 0.555851 0.578566i
\(478\) 395.470i 0.827343i
\(479\) 790.473i 1.65026i −0.564945 0.825129i \(-0.691103\pi\)
0.564945 0.825129i \(-0.308897\pi\)
\(480\) −10.6750 + 84.1786i −0.0222396 + 0.175372i
\(481\) 201.946 0.419845
\(482\) 524.236 1.08763
\(483\) −38.3653 90.0613i −0.0794312 0.186462i
\(484\) 46.6843 0.0964553
\(485\) 170.836 + 99.8323i 0.352240 + 0.205840i
\(486\) −147.230 310.518i −0.302943 0.638925i
\(487\) 35.6013i 0.0731033i 0.999332 + 0.0365516i \(0.0116373\pi\)
−0.999332 + 0.0365516i \(0.988363\pi\)
\(488\) −30.3696 −0.0622328
\(489\) 213.187 + 500.449i 0.435964 + 1.02341i
\(490\) 9.65278 16.5182i 0.0196996 0.0337106i
\(491\) 822.108i 1.67435i −0.546932 0.837177i \(-0.684205\pi\)
0.546932 0.837177i \(-0.315795\pi\)
\(492\) −80.9103 189.934i −0.164452 0.386046i
\(493\) 266.061i 0.539677i
\(494\) 251.520i 0.509149i
\(495\) 427.799 121.428i 0.864241 0.245309i
\(496\) 42.3059 0.0852942
\(497\) −570.559 −1.14801
\(498\) 386.975 164.848i 0.777059 0.331020i
\(499\) 101.299 0.203005 0.101502 0.994835i \(-0.467635\pi\)
0.101502 + 0.994835i \(0.467635\pi\)
\(500\) 249.969 + 3.93825i 0.499938 + 0.00787651i
\(501\) 515.215 219.477i 1.02837 0.438078i
\(502\) 486.263i 0.968650i
\(503\) −198.216 −0.394067 −0.197033 0.980397i \(-0.563131\pi\)
−0.197033 + 0.980397i \(0.563131\pi\)
\(504\) −124.899 119.996i −0.247816 0.238086i
\(505\) 316.281 + 184.826i 0.626299 + 0.365992i
\(506\) 67.0243i 0.132459i
\(507\) −400.615 + 170.658i −0.790168 + 0.336604i
\(508\) 367.700i 0.723819i
\(509\) 249.428i 0.490036i 0.969519 + 0.245018i \(0.0787938\pi\)
−0.969519 + 0.245018i \(0.921206\pi\)
\(510\) −63.5928 + 501.465i −0.124692 + 0.983266i
\(511\) −477.707 −0.934847
\(512\) −22.6274 −0.0441942
\(513\) −348.838 + 919.320i −0.679996 + 1.79205i
\(514\) 321.019 0.624550
\(515\) −340.728 199.112i −0.661608 0.386626i
\(516\) 78.4993 + 184.275i 0.152131 + 0.357122i
\(517\) 128.908i 0.249339i
\(518\) −397.896 −0.768138
\(519\) −870.105 + 370.657i −1.67650 + 0.714175i
\(520\) 59.6300 + 34.8462i 0.114673 + 0.0670119i
\(521\) 451.691i 0.866969i −0.901161 0.433484i \(-0.857284\pi\)
0.901161 0.433484i \(-0.142716\pi\)
\(522\) 102.482 + 98.4585i 0.196326 + 0.188618i
\(523\) 250.044i 0.478095i 0.971008 + 0.239047i \(0.0768352\pi\)
−0.971008 + 0.239047i \(0.923165\pi\)
\(524\) 30.6054i 0.0584073i
\(525\) −310.850 + 404.695i −0.592095 + 0.770848i
\(526\) −382.976 −0.728091
\(527\) 252.023 0.478222
\(528\) 46.4755 + 109.100i 0.0880217 + 0.206628i
\(529\) 23.0000 0.0434783
\(530\) 151.706 259.604i 0.286237 0.489819i
\(531\) 613.312 + 589.233i 1.15501 + 1.10967i
\(532\) 495.572i 0.931526i
\(533\) −168.038 −0.315268
\(534\) −42.9636 100.856i −0.0804562 0.188869i
\(535\) −72.9656 + 124.861i −0.136384 + 0.233386i
\(536\) 49.8033i 0.0929166i
\(537\) −87.2482 204.812i −0.162473 0.381401i
\(538\) 121.644i 0.226104i
\(539\) 26.7378i 0.0496062i
\(540\) −169.623 210.067i −0.314116 0.389013i
\(541\) −678.246 −1.25369 −0.626845 0.779144i \(-0.715654\pi\)
−0.626845 + 0.779144i \(0.715654\pi\)
\(542\) −29.2482 −0.0539634
\(543\) −765.099 + 325.925i −1.40902 + 0.600230i
\(544\) −134.795 −0.247785
\(545\) 445.031 761.553i 0.816571 1.39735i
\(546\) −129.698 + 55.2501i −0.237542 + 0.101191i
\(547\) 703.374i 1.28587i 0.765919 + 0.642937i \(0.222284\pi\)
−0.765919 + 0.642937i \(0.777716\pi\)
\(548\) 35.8321 0.0653870
\(549\) 66.9499 69.6858i 0.121949 0.126932i
\(550\) 304.397 171.507i 0.553450 0.311831i
\(551\) 406.626i 0.737978i
\(552\) 37.4386 15.9485i 0.0678235 0.0288922i
\(553\) 10.2595i 0.0185524i
\(554\) 482.417i 0.870790i
\(555\) −615.343 78.0340i −1.10873 0.140602i
\(556\) 43.9061 0.0789679
\(557\) 611.566 1.09796 0.548982 0.835834i \(-0.315016\pi\)
0.548982 + 0.835834i \(0.315016\pi\)
\(558\) −93.2636 + 97.0748i −0.167139 + 0.173969i
\(559\) 163.031 0.291647
\(560\) −117.490 68.6579i −0.209803 0.122603i
\(561\) 276.862 + 649.924i 0.493515 + 1.15851i
\(562\) 496.625i 0.883675i
\(563\) 775.464 1.37738 0.688689 0.725057i \(-0.258187\pi\)
0.688689 + 0.725057i \(0.258187\pi\)
\(564\) 72.0058 30.6738i 0.127670 0.0543862i
\(565\) 66.0720 113.065i 0.116942 0.200114i
\(566\) 233.582i 0.412688i
\(567\) 550.682 22.0618i 0.971220 0.0389097i
\(568\) 237.182i 0.417574i
\(569\) 993.400i 1.74587i 0.487836 + 0.872935i \(0.337786\pi\)
−0.487836 + 0.872935i \(0.662214\pi\)
\(570\) −97.1900 + 766.399i −0.170509 + 1.34456i
\(571\) 524.115 0.917890 0.458945 0.888465i \(-0.348228\pi\)
0.458945 + 0.888465i \(0.348228\pi\)
\(572\) 96.5223 0.168745
\(573\) −42.9800 100.894i −0.0750087 0.176081i
\(574\) 331.087 0.576807
\(575\) −58.8541 104.457i −0.102355 0.181664i
\(576\) 49.8823 51.9207i 0.0866012 0.0901401i
\(577\) 302.382i 0.524059i −0.965060 0.262029i \(-0.915608\pi\)
0.965060 0.262029i \(-0.0843918\pi\)
\(578\) −394.288 −0.682159
\(579\) 155.519 + 365.077i 0.268600 + 0.630530i
\(580\) 96.4024 + 56.3350i 0.166211 + 0.0971293i
\(581\) 674.562i 1.16104i
\(582\) −65.8006 154.465i −0.113059 0.265404i
\(583\) 420.218i 0.720785i
\(584\) 198.583i 0.340040i
\(585\) −211.413 + 60.0080i −0.361389 + 0.102578i
\(586\) 60.4661 0.103184
\(587\) −171.830 −0.292725 −0.146363 0.989231i \(-0.546757\pi\)
−0.146363 + 0.989231i \(0.546757\pi\)
\(588\) −14.9352 + 6.36226i −0.0254000 + 0.0108202i
\(589\) 385.171 0.653941
\(590\) 576.928 + 337.141i 0.977844 + 0.571426i
\(591\) 748.376 318.801i 1.26629 0.539426i
\(592\) 165.406i 0.279401i
\(593\) −1163.90 −1.96273 −0.981363 0.192161i \(-0.938450\pi\)
−0.981363 + 0.192161i \(0.938450\pi\)
\(594\) −352.795 133.869i −0.593931 0.225368i
\(595\) −699.905 409.006i −1.17631 0.687405i
\(596\) 312.866i 0.524943i
\(597\) 493.823 210.364i 0.827174 0.352368i
\(598\) 33.1225i 0.0553888i
\(599\) 1116.41i 1.86380i 0.362720 + 0.931898i \(0.381848\pi\)
−0.362720 + 0.931898i \(0.618152\pi\)
\(600\) −168.232 129.221i −0.280387 0.215368i
\(601\) −164.655 −0.273969 −0.136984 0.990573i \(-0.543741\pi\)
−0.136984 + 0.990573i \(0.543741\pi\)
\(602\) −321.222 −0.533591
\(603\) 114.278 + 109.792i 0.189516 + 0.182076i
\(604\) −435.464 −0.720966
\(605\) −58.8854 + 100.767i −0.0973312 + 0.166557i
\(606\) −121.821 285.971i −0.201025 0.471900i
\(607\) 997.201i 1.64284i 0.570327 + 0.821418i \(0.306817\pi\)
−0.570327 + 0.821418i \(0.693183\pi\)
\(608\) −206.010 −0.338832
\(609\) −209.680 + 89.3216i −0.344302 + 0.146669i
\(610\) 38.3067 65.5518i 0.0627979 0.107462i
\(611\) 63.7047i 0.104263i
\(612\) 297.157 309.300i 0.485550 0.505392i
\(613\) 368.242i 0.600721i −0.953826 0.300361i \(-0.902893\pi\)
0.953826 0.300361i \(-0.0971070\pi\)
\(614\) 538.985i 0.877826i
\(615\) 512.024 + 64.9318i 0.832560 + 0.105580i
\(616\) −190.179 −0.308732
\(617\) 6.35206 0.0102951 0.00514754 0.999987i \(-0.498361\pi\)
0.00514754 + 0.999987i \(0.498361\pi\)
\(618\) 131.237 + 308.076i 0.212358 + 0.498504i
\(619\) 601.534 0.971783 0.485892 0.874019i \(-0.338495\pi\)
0.485892 + 0.874019i \(0.338495\pi\)
\(620\) −53.3626 + 91.3160i −0.0860688 + 0.147284i
\(621\) −45.9383 + 121.065i −0.0739747 + 0.194951i
\(622\) 603.401i 0.970098i
\(623\) 175.808 0.282197
\(624\) −22.9675 53.9156i −0.0368069 0.0864032i
\(625\) −323.799 + 534.583i −0.518079 + 0.855333i
\(626\) 542.459i 0.866548i
\(627\) 423.133 + 993.291i 0.674853 + 1.58420i
\(628\) 549.642i 0.875226i
\(629\) 985.347i 1.56653i
\(630\) 416.549 118.234i 0.661188 0.187674i
\(631\) −837.199 −1.32678 −0.663391 0.748273i \(-0.730883\pi\)
−0.663391 + 0.748273i \(0.730883\pi\)
\(632\) 4.26487 0.00674821
\(633\) −717.301 + 305.564i −1.13318 + 0.482723i
\(634\) 132.548 0.209067
\(635\) −793.669 463.799i −1.24987 0.730392i
\(636\) −234.726 + 99.9910i −0.369066 + 0.157219i
\(637\) 13.2134i 0.0207432i
\(638\) 156.045 0.244585
\(639\) 544.236 + 522.869i 0.851699 + 0.818261i
\(640\) 28.5411 48.8406i 0.0445955 0.0763134i
\(641\) 1023.80i 1.59720i −0.601864 0.798599i \(-0.705575\pi\)
0.601864 0.798599i \(-0.294425\pi\)
\(642\) 112.896 48.0925i 0.175850 0.0749104i
\(643\) 567.219i 0.882144i 0.897472 + 0.441072i \(0.145402\pi\)
−0.897472 + 0.441072i \(0.854598\pi\)
\(644\) 65.2616i 0.101338i
\(645\) −496.767 62.9970i −0.770181 0.0976697i
\(646\) −1227.23 −1.89974
\(647\) −161.598 −0.249765 −0.124882 0.992172i \(-0.539855\pi\)
−0.124882 + 0.992172i \(0.539855\pi\)
\(648\) 9.17111 + 228.919i 0.0141529 + 0.353270i
\(649\) 933.866 1.43893
\(650\) −150.429 + 84.7563i −0.231429 + 0.130394i
\(651\) −84.6088 198.616i −0.129967 0.305094i
\(652\) 362.643i 0.556201i
\(653\) 61.5410 0.0942435 0.0471218 0.998889i \(-0.484995\pi\)
0.0471218 + 0.998889i \(0.484995\pi\)
\(654\) −688.572 + 293.325i −1.05286 + 0.448510i
\(655\) −66.0608 38.6042i −0.100856 0.0589377i
\(656\) 137.633i 0.209807i
\(657\) 455.667 + 437.778i 0.693557 + 0.666328i
\(658\) 125.518i 0.190757i
\(659\) 451.630i 0.685326i −0.939458 0.342663i \(-0.888671\pi\)
0.939458 0.342663i \(-0.111329\pi\)
\(660\) −294.110 37.2973i −0.445622 0.0565111i
\(661\) −11.7356 −0.0177543 −0.00887717 0.999961i \(-0.502826\pi\)
−0.00887717 + 0.999961i \(0.502826\pi\)
\(662\) −334.625 −0.505476
\(663\) −136.821 321.184i −0.206367 0.484440i
\(664\) −280.416 −0.422314
\(665\) −1069.68 625.091i −1.60854 0.939986i
\(666\) 379.538 + 364.638i 0.569878 + 0.547504i
\(667\) 53.5483i 0.0802823i
\(668\) −373.344 −0.558898
\(669\) −362.352 850.611i −0.541633 1.27147i
\(670\) 107.499 + 62.8195i 0.160446 + 0.0937605i
\(671\) 106.108i 0.158134i
\(672\) 45.2532 + 106.231i 0.0673411 + 0.158081i
\(673\) 312.344i 0.464107i 0.972703 + 0.232053i \(0.0745444\pi\)
−0.972703 + 0.232053i \(0.925456\pi\)
\(674\) 262.244i 0.389086i
\(675\) 667.377 101.157i 0.988707 0.149862i
\(676\) 290.300 0.429438
\(677\) −1009.66 −1.49137 −0.745686 0.666298i \(-0.767878\pi\)
−0.745686 + 0.666298i \(0.767878\pi\)
\(678\) −102.229 + 43.5488i −0.150781 + 0.0642313i
\(679\) 269.258 0.396551
\(680\) 170.024 290.951i 0.250035 0.427869i
\(681\) −345.838 + 147.324i −0.507838 + 0.216334i
\(682\) 147.812i 0.216733i
\(683\) −1040.36 −1.52323 −0.761613 0.648033i \(-0.775592\pi\)
−0.761613 + 0.648033i \(0.775592\pi\)
\(684\) 454.150 472.708i 0.663962 0.691094i
\(685\) −45.1969 + 77.3425i −0.0659808 + 0.112909i
\(686\) 497.527i 0.725259i
\(687\) 935.443 398.490i 1.36163 0.580044i
\(688\) 133.532i 0.194087i
\(689\) 207.666i 0.301402i
\(690\) −12.7989 + 100.927i −0.0185491 + 0.146271i
\(691\) −974.664 −1.41051 −0.705256 0.708953i \(-0.749168\pi\)
−0.705256 + 0.708953i \(0.749168\pi\)
\(692\) 630.509 0.911141
\(693\) 419.251 436.383i 0.604979 0.629702i
\(694\) 787.555 1.13481
\(695\) −55.3811 + 94.7701i −0.0796850 + 0.136360i
\(696\) −37.1311 87.1640i −0.0533492 0.125236i
\(697\) 819.903i 1.17633i
\(698\) 320.498 0.459167
\(699\) −443.920 + 189.106i −0.635079 + 0.270538i
\(700\) 296.392 166.996i 0.423417 0.238566i
\(701\) 954.417i 1.36151i −0.732512 0.680754i \(-0.761652\pi\)
0.732512 0.680754i \(-0.238348\pi\)
\(702\) 174.346 + 66.1561i 0.248357 + 0.0942394i
\(703\) 1505.92i 2.14214i
\(704\) 79.0576i 0.112298i
\(705\) −24.6162 + 194.113i −0.0349166 + 0.275337i
\(706\) −303.436 −0.429796
\(707\) 498.495 0.705085
\(708\) −222.214 521.640i −0.313861 0.736780i
\(709\) 833.880 1.17614 0.588068 0.808812i \(-0.299889\pi\)
0.588068 + 0.808812i \(0.299889\pi\)
\(710\) 511.950 + 299.170i 0.721056 + 0.421366i
\(711\) −9.40192 + 9.78613i −0.0132235 + 0.0137639i
\(712\) 73.0837i 0.102646i
\(713\) 50.7230 0.0711402
\(714\) 269.580 + 632.832i 0.377564 + 0.886319i
\(715\) −121.749 + 208.340i −0.170278 + 0.291385i
\(716\) 148.414i 0.207283i
\(717\) 328.783 + 771.807i 0.458553 + 1.07644i
\(718\) 702.838i 0.978883i
\(719\) 118.872i 0.165330i −0.996577 0.0826651i \(-0.973657\pi\)
0.996577 0.0826651i \(-0.0263432\pi\)
\(720\) 49.1502 + 173.160i 0.0682641 + 0.240500i
\(721\) −537.027 −0.744836
\(722\) −1365.07 −1.89068
\(723\) 1023.11 435.835i 1.41509 0.602815i
\(724\) 554.418 0.765771
\(725\) −243.195 + 137.023i −0.335441 + 0.188998i
\(726\) 91.1101 38.8121i 0.125496 0.0534601i
\(727\) 1270.03i 1.74694i −0.486878 0.873470i \(-0.661864\pi\)
0.486878 0.873470i \(-0.338136\pi\)
\(728\) 93.9838 0.129099
\(729\) −545.494 483.609i −0.748276 0.663387i
\(730\) 428.636 + 250.483i 0.587172 + 0.343128i
\(731\) 795.472i 1.08820i
\(732\) −59.2699 + 25.2484i −0.0809698 + 0.0344924i
\(733\) 814.568i 1.11128i −0.831423 0.555640i \(-0.812473\pi\)
0.831423 0.555640i \(-0.187527\pi\)
\(734\) 714.006i 0.972761i
\(735\) 5.10582 40.2623i 0.00694669 0.0547786i
\(736\) −27.1293 −0.0368605
\(737\) 174.007 0.236102
\(738\) −315.812 303.413i −0.427930 0.411129i
\(739\) 62.6723 0.0848069 0.0424035 0.999101i \(-0.486499\pi\)
0.0424035 + 0.999101i \(0.486499\pi\)
\(740\) 357.023 + 208.635i 0.482463 + 0.281939i
\(741\) −209.106 490.871i −0.282195 0.662444i
\(742\) 409.166i 0.551437i
\(743\) 867.681 1.16781 0.583904 0.811823i \(-0.301525\pi\)
0.583904 + 0.811823i \(0.301525\pi\)
\(744\) 82.5651 35.1719i 0.110975 0.0472741i
\(745\) −675.311 394.634i −0.906458 0.529710i
\(746\) 447.341i 0.599653i
\(747\) 618.179 643.441i 0.827549 0.861367i
\(748\) 470.958i 0.629624i
\(749\) 196.796i 0.262745i
\(750\) 491.119 200.131i 0.654825 0.266842i
\(751\) −437.191 −0.582145 −0.291073 0.956701i \(-0.594012\pi\)
−0.291073 + 0.956701i \(0.594012\pi\)
\(752\) −52.1780 −0.0693856
\(753\) −404.265 949.000i −0.536872 1.26029i
\(754\) −77.1154 −0.102275
\(755\) 549.273 939.935i 0.727514 1.24495i
\(756\) −343.517 130.348i −0.454387 0.172418i
\(757\) 447.984i 0.591789i 0.955221 + 0.295894i \(0.0956177\pi\)
−0.955221 + 0.295894i \(0.904382\pi\)
\(758\) −124.484 −0.164227
\(759\) 55.7221 + 130.806i 0.0734152 + 0.172340i
\(760\) 259.851 444.666i 0.341909 0.585087i
\(761\) 178.177i 0.234135i 0.993124 + 0.117067i \(0.0373494\pi\)
−0.993124 + 0.117067i \(0.962651\pi\)
\(762\) 305.695 + 717.611i 0.401175 + 0.941746i
\(763\) 1200.30i 1.57313i
\(764\) 73.1115i 0.0956957i
\(765\) 292.795 + 1031.54i 0.382739 + 1.34842i
\(766\) −564.876 −0.737435
\(767\) −461.503 −0.601699
\(768\) −44.1601 + 18.8118i −0.0575002 + 0.0244945i
\(769\) 5.08745 0.00661567 0.00330784 0.999995i \(-0.498947\pi\)
0.00330784 + 0.999995i \(0.498947\pi\)
\(770\) 239.883 410.496i 0.311536 0.533111i
\(771\) 626.507 266.886i 0.812590 0.346156i
\(772\) 264.548i 0.342678i
\(773\) 144.982 0.187558 0.0937791 0.995593i \(-0.470105\pi\)
0.0937791 + 0.995593i \(0.470105\pi\)
\(774\) 306.402 + 294.372i 0.395868 + 0.380326i
\(775\) −129.794 230.363i −0.167476 0.297243i
\(776\) 111.931i 0.144241i
\(777\) −776.541 + 330.799i −0.999409 + 0.425739i
\(778\) 570.519i 0.733315i
\(779\) 1253.07i 1.60857i
\(780\) 145.345 + 18.4318i 0.186340 + 0.0236305i
\(781\) 828.686 1.06106
\(782\) −161.614 −0.206667
\(783\) 281.862 + 106.953i