Properties

Label 570.2.c.f.569.3
Level $570$
Weight $2$
Character 570.569
Analytic conductor $4.551$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.1499238400.2
Defining polynomial: \(x^{8} - 4 x^{7} + 16 x^{6} - 34 x^{5} + 59 x^{4} - 66 x^{3} + 54 x^{2} - 26 x + 5\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 569.3
Root \(0.500000 + 1.41267i\) of defining polynomial
Character \(\chi\) \(=\) 570.569
Dual form 570.2.c.f.569.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(0.500000 + 1.65831i) q^{3} -1.00000 q^{4} +(-1.91267 - 1.15831i) q^{5} +(1.65831 - 0.500000i) q^{6} -3.21974i q^{7} +1.00000i q^{8} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(0.500000 + 1.65831i) q^{3} -1.00000 q^{4} +(-1.91267 - 1.15831i) q^{5} +(1.65831 - 0.500000i) q^{6} -3.21974i q^{7} +1.00000i q^{8} +(-2.50000 + 1.65831i) q^{9} +(-1.15831 + 1.91267i) q^{10} +4.31662i q^{11} +(-0.500000 - 1.65831i) q^{12} -3.31662 q^{13} -3.21974 q^{14} +(0.964508 - 3.75096i) q^{15} +1.00000 q^{16} -3.21974 q^{17} +(1.65831 + 2.50000i) q^{18} +(-4.31662 - 0.605599i) q^{19} +(1.91267 + 1.15831i) q^{20} +(5.33934 - 1.60987i) q^{21} +4.31662 q^{22} -7.04509 q^{23} +(-1.65831 + 0.500000i) q^{24} +(2.31662 + 4.43094i) q^{25} +3.31662i q^{26} +(-4.00000 - 3.31662i) q^{27} +3.21974i q^{28} +8.25629 q^{29} +(-3.75096 - 0.964508i) q^{30} -2.61414i q^{31} -1.00000i q^{32} +(-7.15831 + 2.15831i) q^{33} +3.21974i q^{34} +(-3.72947 + 6.15831i) q^{35} +(2.50000 - 1.65831i) q^{36} +2.00000 q^{37} +(-0.605599 + 4.31662i) q^{38} +(-1.65831 - 5.50000i) q^{39} +(1.15831 - 1.91267i) q^{40} -11.4760 q^{41} +(-1.60987 - 5.33934i) q^{42} -3.82534i q^{43} -4.31662i q^{44} +(6.70252 - 0.276026i) q^{45} +7.04509i q^{46} -8.86188 q^{47} +(0.500000 + 1.65831i) q^{48} -3.36675 q^{49} +(4.43094 - 2.31662i) q^{50} +(-1.60987 - 5.33934i) q^{51} +3.31662 q^{52} -1.00000i q^{53} +(-3.31662 + 4.00000i) q^{54} +(5.00000 - 8.25629i) q^{55} +3.21974 q^{56} +(-1.15404 - 7.46111i) q^{57} -8.25629i q^{58} -5.64214 q^{59} +(-0.964508 + 3.75096i) q^{60} -2.31662 q^{61} -2.61414 q^{62} +(5.33934 + 8.04936i) q^{63} -1.00000 q^{64} +(6.34361 + 3.84169i) q^{65} +(2.15831 + 7.15831i) q^{66} +7.00000 q^{67} +3.21974 q^{68} +(-3.52254 - 11.6830i) q^{69} +(6.15831 + 3.72947i) q^{70} +10.2648 q^{71} +(-1.65831 - 2.50000i) q^{72} +1.81680i q^{73} -2.00000i q^{74} +(-6.18957 + 6.05716i) q^{75} +(4.31662 + 0.605599i) q^{76} +13.8984 q^{77} +(-5.50000 + 1.65831i) q^{78} +15.3014i q^{79} +(-1.91267 - 1.15831i) q^{80} +(3.50000 - 8.29156i) q^{81} +11.4760i q^{82} +6.43949 q^{83} +(-5.33934 + 1.60987i) q^{84} +(6.15831 + 3.72947i) q^{85} -3.82534 q^{86} +(4.12814 + 13.6915i) q^{87} -4.31662 q^{88} +2.61414 q^{89} +(-0.276026 - 6.70252i) q^{90} +10.6787i q^{91} +7.04509 q^{92} +(4.33507 - 1.30707i) q^{93} +8.86188i q^{94} +(7.55481 + 6.15831i) q^{95} +(1.65831 - 0.500000i) q^{96} +3.36675 q^{97} +3.36675i q^{98} +(-7.15831 - 10.7916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} - 8q^{4} - 20q^{9} + O(q^{10}) \) \( 8q + 4q^{3} - 8q^{4} - 20q^{9} + 4q^{10} - 4q^{12} + 22q^{15} + 8q^{16} - 8q^{19} + 8q^{22} - 8q^{25} - 32q^{27} + 2q^{30} - 44q^{33} + 20q^{36} + 16q^{37} - 4q^{40} + 22q^{45} + 4q^{48} - 80q^{49} + 40q^{55} - 4q^{57} - 22q^{60} + 8q^{61} - 8q^{64} + 4q^{66} + 56q^{67} + 36q^{70} - 4q^{75} + 8q^{76} - 44q^{78} + 28q^{81} + 36q^{85} - 8q^{88} - 10q^{90} + 80q^{97} - 44q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.500000 + 1.65831i 0.288675 + 0.957427i
\(4\) −1.00000 −0.500000
\(5\) −1.91267 1.15831i −0.855373 0.518013i
\(6\) 1.65831 0.500000i 0.677003 0.204124i
\(7\) 3.21974i 1.21695i −0.793574 0.608474i \(-0.791782\pi\)
0.793574 0.608474i \(-0.208218\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −2.50000 + 1.65831i −0.833333 + 0.552771i
\(10\) −1.15831 + 1.91267i −0.366291 + 0.604840i
\(11\) 4.31662i 1.30151i 0.759287 + 0.650756i \(0.225548\pi\)
−0.759287 + 0.650756i \(0.774452\pi\)
\(12\) −0.500000 1.65831i −0.144338 0.478714i
\(13\) −3.31662 −0.919866 −0.459933 0.887954i \(-0.652127\pi\)
−0.459933 + 0.887954i \(0.652127\pi\)
\(14\) −3.21974 −0.860513
\(15\) 0.964508 3.75096i 0.249035 0.968495i
\(16\) 1.00000 0.250000
\(17\) −3.21974 −0.780903 −0.390451 0.920624i \(-0.627681\pi\)
−0.390451 + 0.920624i \(0.627681\pi\)
\(18\) 1.65831 + 2.50000i 0.390868 + 0.589256i
\(19\) −4.31662 0.605599i −0.990302 0.138934i
\(20\) 1.91267 + 1.15831i 0.427686 + 0.259007i
\(21\) 5.33934 1.60987i 1.16514 0.351303i
\(22\) 4.31662 0.920307
\(23\) −7.04509 −1.46900 −0.734501 0.678608i \(-0.762584\pi\)
−0.734501 + 0.678608i \(0.762584\pi\)
\(24\) −1.65831 + 0.500000i −0.338502 + 0.102062i
\(25\) 2.31662 + 4.43094i 0.463325 + 0.886188i
\(26\) 3.31662i 0.650444i
\(27\) −4.00000 3.31662i −0.769800 0.638285i
\(28\) 3.21974i 0.608474i
\(29\) 8.25629 1.53315 0.766577 0.642153i \(-0.221958\pi\)
0.766577 + 0.642153i \(0.221958\pi\)
\(30\) −3.75096 0.964508i −0.684829 0.176094i
\(31\) 2.61414i 0.469514i −0.972054 0.234757i \(-0.924571\pi\)
0.972054 0.234757i \(-0.0754295\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −7.15831 + 2.15831i −1.24610 + 0.375714i
\(34\) 3.21974i 0.552182i
\(35\) −3.72947 + 6.15831i −0.630395 + 1.04094i
\(36\) 2.50000 1.65831i 0.416667 0.276385i
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −0.605599 + 4.31662i −0.0982412 + 0.700249i
\(39\) −1.65831 5.50000i −0.265543 0.880705i
\(40\) 1.15831 1.91267i 0.183145 0.302420i
\(41\) −11.4760 −1.79225 −0.896127 0.443797i \(-0.853631\pi\)
−0.896127 + 0.443797i \(0.853631\pi\)
\(42\) −1.60987 5.33934i −0.248409 0.823878i
\(43\) 3.82534i 0.583359i −0.956516 0.291680i \(-0.905786\pi\)
0.956516 0.291680i \(-0.0942141\pi\)
\(44\) 4.31662i 0.650756i
\(45\) 6.70252 0.276026i 0.999153 0.0411475i
\(46\) 7.04509i 1.03874i
\(47\) −8.86188 −1.29264 −0.646319 0.763067i \(-0.723693\pi\)
−0.646319 + 0.763067i \(0.723693\pi\)
\(48\) 0.500000 + 1.65831i 0.0721688 + 0.239357i
\(49\) −3.36675 −0.480964
\(50\) 4.43094 2.31662i 0.626630 0.327620i
\(51\) −1.60987 5.33934i −0.225427 0.747657i
\(52\) 3.31662 0.459933
\(53\) 1.00000i 0.137361i −0.997639 0.0686803i \(-0.978121\pi\)
0.997639 0.0686803i \(-0.0218788\pi\)
\(54\) −3.31662 + 4.00000i −0.451335 + 0.544331i
\(55\) 5.00000 8.25629i 0.674200 1.11328i
\(56\) 3.21974 0.430256
\(57\) −1.15404 7.46111i −0.152856 0.988248i
\(58\) 8.25629i 1.08410i
\(59\) −5.64214 −0.734544 −0.367272 0.930114i \(-0.619708\pi\)
−0.367272 + 0.930114i \(0.619708\pi\)
\(60\) −0.964508 + 3.75096i −0.124517 + 0.484247i
\(61\) −2.31662 −0.296613 −0.148307 0.988941i \(-0.547382\pi\)
−0.148307 + 0.988941i \(0.547382\pi\)
\(62\) −2.61414 −0.331997
\(63\) 5.33934 + 8.04936i 0.672694 + 1.01412i
\(64\) −1.00000 −0.125000
\(65\) 6.34361 + 3.84169i 0.786828 + 0.476503i
\(66\) 2.15831 + 7.15831i 0.265670 + 0.881127i
\(67\) 7.00000 0.855186 0.427593 0.903971i \(-0.359362\pi\)
0.427593 + 0.903971i \(0.359362\pi\)
\(68\) 3.21974 0.390451
\(69\) −3.52254 11.6830i −0.424064 1.40646i
\(70\) 6.15831 + 3.72947i 0.736059 + 0.445757i
\(71\) 10.2648 1.21821 0.609106 0.793089i \(-0.291529\pi\)
0.609106 + 0.793089i \(0.291529\pi\)
\(72\) −1.65831 2.50000i −0.195434 0.294628i
\(73\) 1.81680i 0.212640i 0.994332 + 0.106320i \(0.0339068\pi\)
−0.994332 + 0.106320i \(0.966093\pi\)
\(74\) 2.00000i 0.232495i
\(75\) −6.18957 + 6.05716i −0.714710 + 0.699420i
\(76\) 4.31662 + 0.605599i 0.495151 + 0.0694670i
\(77\) 13.8984 1.58387
\(78\) −5.50000 + 1.65831i −0.622752 + 0.187767i
\(79\) 15.3014i 1.72154i 0.508995 + 0.860769i \(0.330017\pi\)
−0.508995 + 0.860769i \(0.669983\pi\)
\(80\) −1.91267 1.15831i −0.213843 0.129503i
\(81\) 3.50000 8.29156i 0.388889 0.921285i
\(82\) 11.4760i 1.26732i
\(83\) 6.43949 0.706826 0.353413 0.935467i \(-0.385021\pi\)
0.353413 + 0.935467i \(0.385021\pi\)
\(84\) −5.33934 + 1.60987i −0.582570 + 0.175651i
\(85\) 6.15831 + 3.72947i 0.667963 + 0.404518i
\(86\) −3.82534 −0.412497
\(87\) 4.12814 + 13.6915i 0.442583 + 1.46788i
\(88\) −4.31662 −0.460154
\(89\) 2.61414 0.277099 0.138549 0.990356i \(-0.455756\pi\)
0.138549 + 0.990356i \(0.455756\pi\)
\(90\) −0.276026 6.70252i −0.0290957 0.706508i
\(91\) 10.6787i 1.11943i
\(92\) 7.04509 0.734501
\(93\) 4.33507 1.30707i 0.449526 0.135537i
\(94\) 8.86188i 0.914034i
\(95\) 7.55481 + 6.15831i 0.775107 + 0.631830i
\(96\) 1.65831 0.500000i 0.169251 0.0510310i
\(97\) 3.36675 0.341842 0.170921 0.985285i \(-0.445326\pi\)
0.170921 + 0.985285i \(0.445326\pi\)
\(98\) 3.36675i 0.340093i
\(99\) −7.15831 10.7916i −0.719437 1.08459i
\(100\) −2.31662 4.43094i −0.231662 0.443094i
\(101\) 14.3166i 1.42456i −0.701897 0.712279i \(-0.747663\pi\)
0.701897 0.712279i \(-0.252337\pi\)
\(102\) −5.33934 + 1.60987i −0.528674 + 0.159401i
\(103\) 17.5831 1.73252 0.866258 0.499596i \(-0.166518\pi\)
0.866258 + 0.499596i \(0.166518\pi\)
\(104\) 3.31662i 0.325222i
\(105\) −12.0771 3.10547i −1.17861 0.303063i
\(106\) −1.00000 −0.0971286
\(107\) 0.0501256i 0.00484583i −0.999997 0.00242291i \(-0.999229\pi\)
0.999997 0.00242291i \(-0.000771238\pi\)
\(108\) 4.00000 + 3.31662i 0.384900 + 0.319142i
\(109\) 6.85334i 0.656431i −0.944603 0.328215i \(-0.893553\pi\)
0.944603 0.328215i \(-0.106447\pi\)
\(110\) −8.25629 5.00000i −0.787206 0.476731i
\(111\) 1.00000 + 3.31662i 0.0949158 + 0.314800i
\(112\) 3.21974i 0.304237i
\(113\) 1.68338i 0.158359i −0.996860 0.0791793i \(-0.974770\pi\)
0.996860 0.0791793i \(-0.0252300\pi\)
\(114\) −7.46111 + 1.15404i −0.698797 + 0.108086i
\(115\) 13.4749 + 8.16041i 1.25654 + 0.760962i
\(116\) −8.25629 −0.766577
\(117\) 8.29156 5.50000i 0.766555 0.508475i
\(118\) 5.64214i 0.519401i
\(119\) 10.3668i 0.950318i
\(120\) 3.75096 + 0.964508i 0.342415 + 0.0880471i
\(121\) −7.63325 −0.693932
\(122\) 2.31662i 0.209737i
\(123\) −5.73801 19.0308i −0.517379 1.71595i
\(124\) 2.61414i 0.234757i
\(125\) 0.701473 11.1583i 0.0627417 0.998030i
\(126\) 8.04936 5.33934i 0.717094 0.475666i
\(127\) −16.6332 −1.47596 −0.737981 0.674821i \(-0.764221\pi\)
−0.737981 + 0.674821i \(0.764221\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 6.34361 1.91267i 0.558524 0.168401i
\(130\) 3.84169 6.34361i 0.336938 0.556372i
\(131\) 10.0000i 0.873704i −0.899533 0.436852i \(-0.856093\pi\)
0.899533 0.436852i \(-0.143907\pi\)
\(132\) 7.15831 2.15831i 0.623051 0.187857i
\(133\) −1.94987 + 13.8984i −0.169076 + 1.20515i
\(134\) 7.00000i 0.604708i
\(135\) 3.80900 + 10.9769i 0.327826 + 0.944738i
\(136\) 3.21974i 0.276091i
\(137\) −3.21974 −0.275081 −0.137541 0.990496i \(-0.543920\pi\)
−0.137541 + 0.990496i \(0.543920\pi\)
\(138\) −11.6830 + 3.52254i −0.994519 + 0.299859i
\(139\) −10.0000 −0.848189 −0.424094 0.905618i \(-0.639408\pi\)
−0.424094 + 0.905618i \(0.639408\pi\)
\(140\) 3.72947 6.15831i 0.315198 0.520472i
\(141\) −4.43094 14.6958i −0.373153 1.23761i
\(142\) 10.2648i 0.861405i
\(143\) 14.3166i 1.19722i
\(144\) −2.50000 + 1.65831i −0.208333 + 0.138193i
\(145\) −15.7916 9.56336i −1.31142 0.794194i
\(146\) 1.81680 0.150359
\(147\) −1.68338 5.58312i −0.138842 0.460488i
\(148\) −2.00000 −0.164399
\(149\) 4.00000i 0.327693i 0.986486 + 0.163846i \(0.0523901\pi\)
−0.986486 + 0.163846i \(0.947610\pi\)
\(150\) 6.05716 + 6.18957i 0.494565 + 0.505377i
\(151\) 16.5126i 1.34377i 0.740654 + 0.671887i \(0.234516\pi\)
−0.740654 + 0.671887i \(0.765484\pi\)
\(152\) 0.605599 4.31662i 0.0491206 0.350125i
\(153\) 8.04936 5.33934i 0.650752 0.431660i
\(154\) 13.8984i 1.11997i
\(155\) −3.02800 + 5.00000i −0.243215 + 0.401610i
\(156\) 1.65831 + 5.50000i 0.132771 + 0.440352i
\(157\) 7.65069i 0.610591i 0.952258 + 0.305296i \(0.0987553\pi\)
−0.952258 + 0.305296i \(0.901245\pi\)
\(158\) 15.3014 1.21731
\(159\) 1.65831 0.500000i 0.131513 0.0396526i
\(160\) −1.15831 + 1.91267i −0.0915726 + 0.151210i
\(161\) 22.6834i 1.78770i
\(162\) −8.29156 3.50000i −0.651447 0.274986i
\(163\) 1.40295i 0.109887i 0.998489 + 0.0549436i \(0.0174979\pi\)
−0.998489 + 0.0549436i \(0.982502\pi\)
\(164\) 11.4760 0.896127
\(165\) 16.1915 + 4.16342i 1.26051 + 0.324122i
\(166\) 6.43949i 0.499801i
\(167\) 24.9499i 1.93068i 0.260997 + 0.965340i \(0.415949\pi\)
−0.260997 + 0.965340i \(0.584051\pi\)
\(168\) 1.60987 + 5.33934i 0.124204 + 0.411939i
\(169\) −2.00000 −0.153846
\(170\) 3.72947 6.15831i 0.286037 0.472321i
\(171\) 11.7958 5.64431i 0.902050 0.431632i
\(172\) 3.82534i 0.291680i
\(173\) 13.2665i 1.00863i −0.863519 0.504317i \(-0.831744\pi\)
0.863519 0.504317i \(-0.168256\pi\)
\(174\) 13.6915 4.12814i 1.03795 0.312954i
\(175\) 14.2665 7.45894i 1.07845 0.563843i
\(176\) 4.31662i 0.325378i
\(177\) −2.82107 9.35643i −0.212045 0.703272i
\(178\) 2.61414i 0.195938i
\(179\) −16.5126 −1.23421 −0.617104 0.786882i \(-0.711694\pi\)
−0.617104 + 0.786882i \(0.711694\pi\)
\(180\) −6.70252 + 0.276026i −0.499577 + 0.0205738i
\(181\) 16.5126i 1.22737i −0.789551 0.613685i \(-0.789687\pi\)
0.789551 0.613685i \(-0.210313\pi\)
\(182\) 10.6787 0.791557
\(183\) −1.15831 3.84169i −0.0856249 0.283986i
\(184\) 7.04509i 0.519371i
\(185\) −3.82534 2.31662i −0.281245 0.170322i
\(186\) −1.30707 4.33507i −0.0958392 0.317863i
\(187\) 13.8984i 1.01635i
\(188\) 8.86188 0.646319
\(189\) −10.6787 + 12.8790i −0.776760 + 0.936808i
\(190\) 6.15831 7.55481i 0.446771 0.548084i
\(191\) 5.00000i 0.361787i −0.983503 0.180894i \(-0.942101\pi\)
0.983503 0.180894i \(-0.0578990\pi\)
\(192\) −0.500000 1.65831i −0.0360844 0.119678i
\(193\) 6.00000 0.431889 0.215945 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) 3.36675i 0.241719i
\(195\) −3.19891 + 12.4405i −0.229079 + 0.890885i
\(196\) 3.36675 0.240482
\(197\) 5.03654 0.358839 0.179419 0.983773i \(-0.442578\pi\)
0.179419 + 0.983773i \(0.442578\pi\)
\(198\) −10.7916 + 7.15831i −0.766923 + 0.508719i
\(199\) −25.2164 −1.78754 −0.893771 0.448524i \(-0.851950\pi\)
−0.893771 + 0.448524i \(0.851950\pi\)
\(200\) −4.43094 + 2.31662i −0.313315 + 0.163810i
\(201\) 3.50000 + 11.6082i 0.246871 + 0.818778i
\(202\) −14.3166 −1.00731
\(203\) 26.5831i 1.86577i
\(204\) 1.60987 + 5.33934i 0.112714 + 0.373829i
\(205\) 21.9499 + 13.2928i 1.53305 + 0.928411i
\(206\) 17.5831i 1.22507i
\(207\) 17.6127 11.6830i 1.22417 0.812022i
\(208\) −3.31662 −0.229967
\(209\) 2.61414 18.6332i 0.180824 1.28889i
\(210\) −3.10547 + 12.0771i −0.214298 + 0.833402i
\(211\) 3.02800i 0.208456i −0.994553 0.104228i \(-0.966763\pi\)
0.994553 0.104228i \(-0.0332371\pi\)
\(212\) 1.00000i 0.0686803i
\(213\) 5.13242 + 17.0223i 0.351667 + 1.16635i
\(214\) −0.0501256 −0.00342652
\(215\) −4.43094 + 7.31662i −0.302188 + 0.498990i
\(216\) 3.31662 4.00000i 0.225668 0.272166i
\(217\) −8.41688 −0.571375
\(218\) −6.85334 −0.464167
\(219\) −3.01282 + 0.908399i −0.203587 + 0.0613839i
\(220\) −5.00000 + 8.25629i −0.337100 + 0.556639i
\(221\) 10.6787 0.718326
\(222\) 3.31662 1.00000i 0.222597 0.0671156i
\(223\) 3.26650 0.218741 0.109370 0.994001i \(-0.465117\pi\)
0.109370 + 0.994001i \(0.465117\pi\)
\(224\) −3.21974 −0.215128
\(225\) −13.1394 7.23567i −0.875963 0.482378i
\(226\) −1.68338 −0.111976
\(227\) 19.9499i 1.32412i 0.749451 + 0.662060i \(0.230318\pi\)
−0.749451 + 0.662060i \(0.769682\pi\)
\(228\) 1.15404 + 7.46111i 0.0764281 + 0.494124i
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 8.16041 13.4749i 0.538082 0.888511i
\(231\) 6.94921 + 23.0479i 0.457225 + 1.51644i
\(232\) 8.25629i 0.542052i
\(233\) −26.5857 −1.74168 −0.870842 0.491563i \(-0.836426\pi\)
−0.870842 + 0.491563i \(0.836426\pi\)
\(234\) −5.50000 8.29156i −0.359546 0.542036i
\(235\) 16.9499 + 10.2648i 1.10569 + 0.669604i
\(236\) 5.64214 0.367272
\(237\) −25.3745 + 7.65069i −1.64825 + 0.496965i
\(238\) 10.3668 0.671977
\(239\) 19.6332i 1.26997i −0.772525 0.634985i \(-0.781006\pi\)
0.772525 0.634985i \(-0.218994\pi\)
\(240\) 0.964508 3.75096i 0.0622587 0.242124i
\(241\) 5.22829i 0.336784i −0.985720 0.168392i \(-0.946143\pi\)
0.985720 0.168392i \(-0.0538574\pi\)
\(242\) 7.63325i 0.490684i
\(243\) 15.5000 + 1.65831i 0.994325 + 0.106381i
\(244\) 2.31662 0.148307
\(245\) 6.43949 + 3.89975i 0.411404 + 0.249146i
\(246\) −19.0308 + 5.73801i −1.21336 + 0.365842i
\(247\) 14.3166 + 2.00855i 0.910945 + 0.127801i
\(248\) 2.61414 0.165998
\(249\) 3.21974 + 10.6787i 0.204043 + 0.676734i
\(250\) −11.1583 0.701473i −0.705714 0.0443651i
\(251\) 31.5831i 1.99351i 0.0805007 + 0.996755i \(0.474348\pi\)
−0.0805007 + 0.996755i \(0.525652\pi\)
\(252\) −5.33934 8.04936i −0.336347 0.507062i
\(253\) 30.4110i 1.91192i
\(254\) 16.6332i 1.04366i
\(255\) −3.10547 + 12.0771i −0.194472 + 0.756300i
\(256\) 1.00000 0.0625000
\(257\) 4.94987i 0.308765i 0.988011 + 0.154382i \(0.0493388\pi\)
−0.988011 + 0.154382i \(0.950661\pi\)
\(258\) −1.91267 6.34361i −0.119078 0.394936i
\(259\) 6.43949i 0.400130i
\(260\) −6.34361 3.84169i −0.393414 0.238251i
\(261\) −20.6407 + 13.6915i −1.27763 + 0.847483i
\(262\) −10.0000 −0.617802
\(263\) −20.5297 −1.26591 −0.632957 0.774187i \(-0.718159\pi\)
−0.632957 + 0.774187i \(0.718159\pi\)
\(264\) −2.15831 7.15831i −0.132835 0.440564i
\(265\) −1.15831 + 1.91267i −0.0711546 + 0.117494i
\(266\) 13.8984 + 1.94987i 0.852167 + 0.119554i
\(267\) 1.30707 + 4.33507i 0.0799915 + 0.265302i
\(268\) −7.00000 −0.427593
\(269\) −21.7409 −1.32556 −0.662782 0.748813i \(-0.730624\pi\)
−0.662782 + 0.748813i \(0.730624\pi\)
\(270\) 10.9769 3.80900i 0.668031 0.231808i
\(271\) 2.68338 0.163003 0.0815017 0.996673i \(-0.474028\pi\)
0.0815017 + 0.996673i \(0.474028\pi\)
\(272\) −3.21974 −0.195226
\(273\) −17.7086 + 5.33934i −1.07177 + 0.323152i
\(274\) 3.21974i 0.194512i
\(275\) −19.1267 + 10.0000i −1.15338 + 0.603023i
\(276\) 3.52254 + 11.6830i 0.212032 + 0.703231i
\(277\) 14.0902i 0.846596i −0.905990 0.423298i \(-0.860872\pi\)
0.905990 0.423298i \(-0.139128\pi\)
\(278\) 10.0000i 0.599760i
\(279\) 4.33507 + 6.53536i 0.259534 + 0.391262i
\(280\) −6.15831 3.72947i −0.368030 0.222878i
\(281\) −6.24774 −0.372709 −0.186354 0.982483i \(-0.559667\pi\)
−0.186354 + 0.982483i \(0.559667\pi\)
\(282\) −14.6958 + 4.43094i −0.875121 + 0.263859i
\(283\) 26.5857i 1.58035i 0.612879 + 0.790177i \(0.290011\pi\)
−0.612879 + 0.790177i \(0.709989\pi\)
\(284\) −10.2648 −0.609106
\(285\) −6.43500 + 15.6074i −0.381176 + 0.924502i
\(286\) −14.3166 −0.846560
\(287\) 36.9499i 2.18108i
\(288\) 1.65831 + 2.50000i 0.0977170 + 0.147314i
\(289\) −6.63325 −0.390191
\(290\) −9.56336 + 15.7916i −0.561580 + 0.927312i
\(291\) 1.68338 + 5.58312i 0.0986812 + 0.327289i
\(292\) 1.81680i 0.106320i
\(293\) 18.2665i 1.06714i −0.845756 0.533570i \(-0.820850\pi\)
0.845756 0.533570i \(-0.179150\pi\)
\(294\) −5.58312 + 1.68338i −0.325614 + 0.0981764i
\(295\) 10.7916 + 6.53536i 0.628309 + 0.380503i
\(296\) 2.00000i 0.116248i
\(297\) 14.3166 17.2665i 0.830735 1.00190i
\(298\) 4.00000 0.231714
\(299\) 23.3659 1.35129
\(300\) 6.18957 6.05716i 0.357355 0.349710i
\(301\) −12.3166 −0.709918
\(302\) 16.5126 0.950192
\(303\) 23.7414 7.15831i 1.36391 0.411234i
\(304\) −4.31662 0.605599i −0.247575 0.0347335i
\(305\) 4.43094 + 2.68338i 0.253715 + 0.153650i
\(306\) −5.33934 8.04936i −0.305230 0.460151i
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) −13.8984 −0.791936
\(309\) 8.79156 + 29.1583i 0.500134 + 1.65876i
\(310\) 5.00000 + 3.02800i 0.283981 + 0.171979i
\(311\) 20.8997i 1.18512i −0.805528 0.592558i \(-0.798118\pi\)
0.805528 0.592558i \(-0.201882\pi\)
\(312\) 5.50000 1.65831i 0.311376 0.0938835i
\(313\) 20.7518i 1.17296i −0.809964 0.586480i \(-0.800513\pi\)
0.809964 0.586480i \(-0.199487\pi\)
\(314\) 7.65069 0.431753
\(315\) −0.888733 21.5804i −0.0500744 1.21592i
\(316\) 15.3014i 0.860769i
\(317\) 17.0000i 0.954815i 0.878682 + 0.477408i \(0.158423\pi\)
−0.878682 + 0.477408i \(0.841577\pi\)
\(318\) −0.500000 1.65831i −0.0280386 0.0929935i
\(319\) 35.6393i 1.99542i
\(320\) 1.91267 + 1.15831i 0.106922 + 0.0647516i
\(321\) 0.0831240 0.0250628i 0.00463953 0.00139887i
\(322\) 22.6834 1.26410
\(323\) 13.8984 + 1.94987i 0.773329 + 0.108494i
\(324\) −3.50000 + 8.29156i −0.194444 + 0.460642i
\(325\) −7.68338 14.6958i −0.426197 0.815175i
\(326\) 1.40295 0.0777020
\(327\) 11.3650 3.42667i 0.628485 0.189495i
\(328\) 11.4760i 0.633658i
\(329\) 28.5330i 1.57308i
\(330\) 4.16342 16.1915i 0.229189 0.891313i
\(331\) 13.4846i 0.741179i 0.928797 + 0.370590i \(0.120844\pi\)
−0.928797 + 0.370590i \(0.879156\pi\)
\(332\) −6.43949 −0.353413
\(333\) −5.00000 + 3.31662i −0.273998 + 0.181750i
\(334\) 24.9499 1.36520
\(335\) −13.3887 8.10819i −0.731503 0.442998i
\(336\) 5.33934 1.60987i 0.291285 0.0878257i
\(337\) −28.2164 −1.53704 −0.768522 0.639823i \(-0.779007\pi\)
−0.768522 + 0.639823i \(0.779007\pi\)
\(338\) 2.00000i 0.108786i
\(339\) 2.79156 0.841688i 0.151617 0.0457142i
\(340\) −6.15831 3.72947i −0.333981 0.202259i
\(341\) 11.2843 0.611078
\(342\) −5.64431 11.7958i −0.305210 0.637846i
\(343\) 11.6981i 0.631640i
\(344\) 3.82534 0.206249
\(345\) −6.79504 + 26.4259i −0.365833 + 1.42272i
\(346\) −13.2665 −0.713211
\(347\) −20.1462 −1.08150 −0.540751 0.841182i \(-0.681860\pi\)
−0.540751 + 0.841182i \(0.681860\pi\)
\(348\) −4.12814 13.6915i −0.221292 0.733941i
\(349\) 8.63325 0.462127 0.231064 0.972939i \(-0.425779\pi\)
0.231064 + 0.972939i \(0.425779\pi\)
\(350\) −7.45894 14.2665i −0.398697 0.762576i
\(351\) 13.2665 + 11.0000i 0.708113 + 0.587137i
\(352\) 4.31662 0.230077
\(353\) 23.3659 1.24364 0.621821 0.783159i \(-0.286393\pi\)
0.621821 + 0.783159i \(0.286393\pi\)
\(354\) −9.35643 + 2.82107i −0.497289 + 0.149938i
\(355\) −19.6332 11.8899i −1.04202 0.631049i
\(356\) −2.61414 −0.138549
\(357\) −17.1913 + 5.18338i −0.909861 + 0.274333i
\(358\) 16.5126i 0.872716i
\(359\) 4.89975i 0.258599i 0.991606 + 0.129299i \(0.0412728\pi\)
−0.991606 + 0.129299i \(0.958727\pi\)
\(360\) 0.276026 + 6.70252i 0.0145478 + 0.353254i
\(361\) 18.2665 + 5.22829i 0.961395 + 0.275173i
\(362\) −16.5126 −0.867881
\(363\) −3.81662 12.6583i −0.200321 0.664389i
\(364\) 10.6787i 0.559715i
\(365\) 2.10442 3.47494i 0.110150 0.181887i
\(366\) −3.84169 + 1.15831i −0.200808 + 0.0605460i
\(367\) 7.65069i 0.399363i 0.979861 + 0.199681i \(0.0639907\pi\)
−0.979861 + 0.199681i \(0.936009\pi\)
\(368\) −7.04509 −0.367251
\(369\) 28.6901 19.0308i 1.49355 0.990706i
\(370\) −2.31662 + 3.82534i −0.120436 + 0.198870i
\(371\) −3.21974 −0.167161
\(372\) −4.33507 + 1.30707i −0.224763 + 0.0677685i
\(373\) −23.3166 −1.20729 −0.603645 0.797254i \(-0.706285\pi\)
−0.603645 + 0.797254i \(0.706285\pi\)
\(374\) −13.8984 −0.718671
\(375\) 18.8547 4.41589i 0.973653 0.228036i
\(376\) 8.86188i 0.457017i
\(377\) −27.3830 −1.41030
\(378\) 12.8790 + 10.6787i 0.662423 + 0.549252i
\(379\) 36.4366i 1.87162i −0.352499 0.935812i \(-0.614668\pi\)
0.352499 0.935812i \(-0.385332\pi\)
\(380\) −7.55481 6.15831i −0.387554 0.315915i
\(381\) −8.31662 27.5831i −0.426074 1.41313i
\(382\) −5.00000 −0.255822
\(383\) 7.58312i 0.387480i −0.981053 0.193740i \(-0.937938\pi\)
0.981053 0.193740i \(-0.0620617\pi\)
\(384\) −1.65831 + 0.500000i −0.0846254 + 0.0255155i
\(385\) −26.5831 16.0987i −1.35480 0.820467i
\(386\) 6.00000i 0.305392i
\(387\) 6.34361 + 9.56336i 0.322464 + 0.486133i
\(388\) −3.36675 −0.170921
\(389\) 16.2164i 0.822203i −0.911590 0.411101i \(-0.865144\pi\)
0.911590 0.411101i \(-0.134856\pi\)
\(390\) 12.4405 + 3.19891i 0.629951 + 0.161983i
\(391\) 22.6834 1.14715
\(392\) 3.36675i 0.170047i
\(393\) 16.5831 5.00000i 0.836508 0.252217i
\(394\) 5.03654i 0.253737i
\(395\) 17.7238 29.2665i 0.891780 1.47256i
\(396\) 7.15831 + 10.7916i 0.359719 + 0.542296i
\(397\) 29.3915i 1.47512i 0.675282 + 0.737560i \(0.264022\pi\)
−0.675282 + 0.737560i \(0.735978\pi\)
\(398\) 25.2164i 1.26398i
\(399\) −24.0229 + 3.71571i −1.20265 + 0.186018i
\(400\) 2.31662 + 4.43094i 0.115831 + 0.221547i
\(401\) 21.5491 1.07611 0.538056 0.842909i \(-0.319159\pi\)
0.538056 + 0.842909i \(0.319159\pi\)
\(402\) 11.6082 3.50000i 0.578964 0.174564i
\(403\) 8.67014i 0.431890i
\(404\) 14.3166i 0.712279i
\(405\) −16.2986 + 11.8049i −0.809882 + 0.586592i
\(406\) −26.5831 −1.31930
\(407\) 8.63325i 0.427934i
\(408\) 5.33934 1.60987i 0.264337 0.0797005i
\(409\) 3.82534i 0.189151i −0.995518 0.0945755i \(-0.969851\pi\)
0.995518 0.0945755i \(-0.0301494\pi\)
\(410\) 13.2928 21.9499i 0.656486 1.08403i
\(411\) −1.60987 5.33934i −0.0794091 0.263370i
\(412\) −17.5831 −0.866258
\(413\) 18.1662i 0.893903i
\(414\) −11.6830 17.6127i −0.574186 0.865618i
\(415\) −12.3166 7.45894i −0.604599 0.366145i
\(416\) 3.31662i 0.162611i
\(417\) −5.00000 16.5831i −0.244851 0.812079i
\(418\) −18.6332 2.61414i −0.911382 0.127862i
\(419\) 3.05013i 0.149008i −0.997221 0.0745042i \(-0.976263\pi\)
0.997221 0.0745042i \(-0.0237374\pi\)
\(420\) 12.0771 + 3.10547i 0.589304 + 0.151531i
\(421\) 16.0987i 0.784604i −0.919837 0.392302i \(-0.871679\pi\)
0.919837 0.392302i \(-0.128321\pi\)
\(422\) −3.02800 −0.147401
\(423\) 22.1547 14.6958i 1.07720 0.714533i
\(424\) 1.00000 0.0485643
\(425\) −7.45894 14.2665i −0.361812 0.692027i
\(426\) 17.0223 5.13242i 0.824733 0.248666i
\(427\) 7.45894i 0.360963i
\(428\) 0.0501256i 0.00242291i
\(429\) 23.7414 7.15831i 1.14625 0.345607i
\(430\) 7.31662 + 4.43094i 0.352839 + 0.213679i
\(431\) −17.5320 −0.844488 −0.422244 0.906482i \(-0.638757\pi\)
−0.422244 + 0.906482i \(0.638757\pi\)
\(432\) −4.00000 3.31662i −0.192450 0.159571i
\(433\) 1.68338 0.0808978 0.0404489 0.999182i \(-0.487121\pi\)
0.0404489 + 0.999182i \(0.487121\pi\)
\(434\) 8.41688i 0.404023i
\(435\) 7.96325 30.9690i 0.381809 1.48485i
\(436\) 6.85334i 0.328215i
\(437\) 30.4110 + 4.26650i 1.45476 + 0.204094i
\(438\) 0.908399 + 3.01282i 0.0434050 + 0.143958i
\(439\) 3.82534i 0.182574i −0.995825 0.0912868i \(-0.970902\pi\)
0.995825 0.0912868i \(-0.0290980\pi\)
\(440\) 8.25629 + 5.00000i 0.393603 + 0.238366i
\(441\) 8.41688 5.58312i 0.400804 0.265863i
\(442\) 10.6787i 0.507933i
\(443\) −12.6872 −0.602788 −0.301394 0.953500i \(-0.597452\pi\)
−0.301394 + 0.953500i \(0.597452\pi\)
\(444\) −1.00000 3.31662i −0.0474579 0.157400i
\(445\) −5.00000 3.02800i −0.237023 0.143541i
\(446\) 3.26650i 0.154673i
\(447\) −6.63325 + 2.00000i −0.313742 + 0.0945968i
\(448\) 3.21974i 0.152119i
\(449\) 26.9691 1.27275 0.636376 0.771379i \(-0.280433\pi\)
0.636376 + 0.771379i \(0.280433\pi\)
\(450\) −7.23567 + 13.1394i −0.341093 + 0.619400i
\(451\) 49.5377i 2.33264i
\(452\) 1.68338i 0.0791793i
\(453\) −27.3830 + 8.25629i −1.28657 + 0.387914i
\(454\) 19.9499 0.936294
\(455\) 12.3693 20.4248i 0.579879 0.957530i
\(456\) 7.46111 1.15404i 0.349399 0.0540429i
\(457\) 27.1913i 1.27195i 0.771708 + 0.635977i \(0.219403\pi\)
−0.771708 + 0.635977i \(0.780597\pi\)
\(458\) 0 0
\(459\) 12.8790 + 10.6787i 0.601139 + 0.498438i
\(460\) −13.4749 8.16041i −0.628272 0.380481i
\(461\) 21.5831i 1.00523i 0.864511 + 0.502613i \(0.167628\pi\)
−0.864511 + 0.502613i \(0.832372\pi\)
\(462\) 23.0479 6.94921i 1.07229 0.323307i
\(463\) 15.3014i 0.711115i 0.934654 + 0.355558i \(0.115709\pi\)
−0.934654 + 0.355558i \(0.884291\pi\)
\(464\) 8.25629 0.383288
\(465\) −9.80556 2.52136i −0.454722 0.116925i
\(466\) 26.5857i 1.23156i
\(467\) 26.7774 1.23911 0.619555 0.784953i \(-0.287313\pi\)
0.619555 + 0.784953i \(0.287313\pi\)
\(468\) −8.29156 + 5.50000i −0.383278 + 0.254238i
\(469\) 22.5382i 1.04072i
\(470\) 10.2648 16.9499i 0.473481 0.781839i
\(471\) −12.6872 + 3.82534i −0.584597 + 0.176263i
\(472\) 5.64214i 0.259701i
\(473\) 16.5126 0.759249
\(474\) 7.65069 + 25.3745i 0.351408 + 1.16549i
\(475\) −7.31662 20.5297i −0.335710 0.941965i
\(476\) 10.3668i 0.475159i
\(477\) 1.65831 + 2.50000i 0.0759289 + 0.114467i
\(478\) −19.6332 −0.898004
\(479\) 14.0000i 0.639676i 0.947472 + 0.319838i \(0.103629\pi\)
−0.947472 + 0.319838i \(0.896371\pi\)
\(480\) −3.75096 0.964508i −0.171207 0.0440236i
\(481\) −6.63325 −0.302450
\(482\) −5.22829 −0.238142
\(483\) −37.6161 + 11.3417i −1.71159 + 0.516065i
\(484\) 7.63325 0.346966
\(485\) −6.43949 3.89975i −0.292402 0.177078i
\(486\) 1.65831 15.5000i 0.0752226 0.703094i
\(487\) 36.5330 1.65547 0.827734 0.561121i \(-0.189630\pi\)
0.827734 + 0.561121i \(0.189630\pi\)
\(488\) 2.31662i 0.104869i
\(489\) −2.32652 + 0.701473i −0.105209 + 0.0317217i
\(490\) 3.89975 6.43949i 0.176173 0.290906i
\(491\) 8.41688i 0.379848i 0.981799 + 0.189924i \(0.0608242\pi\)
−0.981799 + 0.189924i \(0.939176\pi\)
\(492\) 5.73801 + 19.0308i 0.258690 + 0.857977i
\(493\) −26.5831 −1.19724
\(494\) 2.00855 14.3166i 0.0903687 0.644135i
\(495\) 1.19150 + 28.9323i 0.0535540 + 1.30041i
\(496\) 2.61414i 0.117379i
\(497\) 33.0501i 1.48250i
\(498\) 10.6787 3.21974i 0.478523 0.144280i
\(499\) 8.41688 0.376791 0.188396 0.982093i \(-0.439671\pi\)
0.188396 + 0.982093i \(0.439671\pi\)
\(500\) −0.701473 + 11.1583i −0.0313708 + 0.499015i
\(501\) −41.3747 + 12.4749i −1.84848 + 0.557339i
\(502\) 31.5831 1.40962
\(503\) −18.3294 −0.817266 −0.408633 0.912699i \(-0.633994\pi\)
−0.408633 + 0.912699i \(0.633994\pi\)
\(504\) −8.04936 + 5.33934i −0.358547 + 0.237833i
\(505\) −16.5831 + 27.3830i −0.737939 + 1.21853i
\(506\) −30.4110 −1.35193
\(507\) −1.00000 3.31662i −0.0444116 0.147296i
\(508\) 16.6332 0.737981
\(509\) −5.22829 −0.231740 −0.115870 0.993264i \(-0.536966\pi\)
−0.115870 + 0.993264i \(0.536966\pi\)
\(510\) 12.0771 + 3.10547i 0.534785 + 0.137512i
\(511\) 5.84962 0.258772
\(512\) 1.00000i 0.0441942i
\(513\) 15.2580 + 16.7390i 0.673655 + 0.739046i
\(514\) 4.94987 0.218330
\(515\) −33.6307 20.3668i −1.48195 0.897466i
\(516\) −6.34361 + 1.91267i −0.279262 + 0.0842007i
\(517\) 38.2534i 1.68238i
\(518\) −6.43949 −0.282935
\(519\) 22.0000 6.63325i 0.965693 0.291167i
\(520\) −3.84169 + 6.34361i −0.168469 + 0.278186i
\(521\) −14.9179 −0.653564 −0.326782 0.945100i \(-0.605964\pi\)
−0.326782 + 0.945100i \(0.605964\pi\)
\(522\) 13.6915 + 20.6407i 0.599261 + 0.903419i
\(523\) −29.0000 −1.26808 −0.634041 0.773300i \(-0.718605\pi\)
−0.634041 + 0.773300i \(0.718605\pi\)
\(524\) 10.0000i 0.436852i
\(525\) 19.5025 + 19.9288i 0.851159 + 0.869766i
\(526\) 20.5297i 0.895136i
\(527\) 8.41688i 0.366645i
\(528\) −7.15831 + 2.15831i −0.311526 + 0.0939285i
\(529\) 26.6332 1.15797
\(530\) 1.91267 + 1.15831i 0.0830811 + 0.0503139i
\(531\) 14.1054 9.35643i 0.612120 0.406035i
\(532\) 1.94987 13.8984i 0.0845378 0.602573i
\(533\) 38.0617 1.64863
\(534\) 4.33507 1.30707i 0.187597 0.0565626i
\(535\) −0.0580611 + 0.0958739i −0.00251020 + 0.00414499i
\(536\) 7.00000i 0.302354i
\(537\) −8.25629 27.3830i −0.356285 1.18166i
\(538\) 21.7409i 0.937315i
\(539\) 14.5330i 0.625981i
\(540\) −3.80900 10.9769i −0.163913 0.472369i
\(541\) 30.8496 1.32633 0.663164 0.748474i \(-0.269213\pi\)
0.663164 + 0.748474i \(0.269213\pi\)
\(542\) 2.68338i 0.115261i
\(543\) 27.3830 8.25629i 1.17512 0.354311i
\(544\) 3.21974i 0.138045i
\(545\) −7.93831 + 13.1082i −0.340040 + 0.561493i
\(546\) 5.33934 + 17.7086i 0.228503 + 0.757858i
\(547\) 12.0000 0.513083 0.256541 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) 3.21974 0.137541
\(549\) 5.79156 3.84169i 0.247178 0.163959i
\(550\) 10.0000 + 19.1267i 0.426401 + 0.815566i
\(551\) −35.6393 5.00000i −1.51828 0.213007i
\(552\) 11.6830 3.52254i 0.497260 0.149929i
\(553\) 49.2665 2.09502
\(554\) −14.0902 −0.598634
\(555\) 1.92902 7.50193i 0.0818822 0.318439i
\(556\) 10.0000 0.424094
\(557\) 13.7067 0.580771 0.290385 0.956910i \(-0.406217\pi\)
0.290385 + 0.956910i \(0.406217\pi\)
\(558\) 6.53536 4.33507i 0.276664 0.183518i
\(559\) 12.6872i 0.536613i
\(560\) −3.72947 + 6.15831i −0.157599 + 0.260236i
\(561\) 23.0479 6.94921i 0.973084 0.293396i
\(562\) 6.24774i 0.263545i
\(563\) 29.8997i 1.26012i 0.776545 + 0.630062i \(0.216971\pi\)
−0.776545 + 0.630062i \(0.783029\pi\)
\(564\) 4.43094 + 14.6958i 0.186576 + 0.618804i
\(565\) −1.94987 + 3.21974i −0.0820318 + 0.135456i
\(566\) 26.5857 1.11748
\(567\) −26.6967 11.2691i −1.12116 0.473258i
\(568\) 10.2648i 0.430703i
\(569\) −5.22829 −0.219181 −0.109591 0.993977i \(-0.534954\pi\)
−0.109591 + 0.993977i \(0.534954\pi\)
\(570\) 15.6074 + 6.43500i 0.653722 + 0.269532i
\(571\) −32.3166 −1.35241 −0.676204 0.736714i \(-0.736376\pi\)
−0.676204 + 0.736714i \(0.736376\pi\)
\(572\) 14.3166i 0.598608i
\(573\) 8.29156 2.50000i 0.346385 0.104439i
\(574\) 36.9499 1.54226
\(575\) −16.3208 31.2164i −0.680625 1.30181i
\(576\) 2.50000 1.65831i 0.104167 0.0690963i
\(577\) 17.1182i 0.712639i −0.934364 0.356319i \(-0.884032\pi\)
0.934364 0.356319i \(-0.115968\pi\)
\(578\) 6.63325i 0.275907i
\(579\) 3.00000 + 9.94987i 0.124676 + 0.413503i
\(580\) 15.7916 + 9.56336i 0.655709 + 0.397097i
\(581\) 20.7335i 0.860171i
\(582\) 5.58312 1.68338i 0.231428 0.0697781i
\(583\) 4.31662 0.178776
\(584\) −1.81680 −0.0751796
\(585\) −22.2298 + 0.915474i −0.919087 + 0.0378502i
\(586\) −18.2665 −0.754582
\(587\) 16.3208 0.673632 0.336816 0.941570i \(-0.390650\pi\)
0.336816 + 0.941570i \(0.390650\pi\)
\(588\) 1.68338 + 5.58312i 0.0694212 + 0.230244i
\(589\) −1.58312 + 11.2843i −0.0652315 + 0.464961i
\(590\) 6.53536 10.7916i 0.269057 0.444282i
\(591\) 2.51827 + 8.35216i 0.103588 + 0.343562i
\(592\) 2.00000 0.0821995
\(593\) −20.5297 −0.843052 −0.421526 0.906816i \(-0.638505\pi\)
−0.421526 + 0.906816i \(0.638505\pi\)
\(594\) −17.2665 14.3166i −0.708453 0.587418i
\(595\) 12.0079 19.8282i 0.492277 0.812876i
\(596\) 4.00000i 0.163846i
\(597\) −12.6082 41.8166i −0.516019 1.71144i
\(598\) 23.3659i 0.955503i
\(599\) −19.9544 −0.815315 −0.407658 0.913135i \(-0.633654\pi\)
−0.407658 + 0.913135i \(0.633654\pi\)
\(600\) −6.05716 6.18957i −0.247282 0.252688i
\(601\) 24.3550i 0.993461i 0.867905 + 0.496731i \(0.165466\pi\)
−0.867905 + 0.496731i \(0.834534\pi\)
\(602\) 12.3166i 0.501988i
\(603\) −17.5000 + 11.6082i −0.712655 + 0.472722i
\(604\) 16.5126i 0.671887i
\(605\) 14.5999 + 8.84169i 0.593570 + 0.359466i
\(606\) −7.15831 23.7414i −0.290787 0.964430i
\(607\) −36.6332 −1.48690 −0.743449 0.668793i \(-0.766811\pi\)
−0.743449 + 0.668793i \(0.766811\pi\)
\(608\) −0.605599 + 4.31662i −0.0245603 + 0.175062i
\(609\) 44.0831 13.2916i 1.78634 0.538601i
\(610\) 2.68338 4.43094i 0.108647 0.179404i
\(611\) 29.3915 1.18905
\(612\) −8.04936 + 5.33934i −0.325376 + 0.215830i
\(613\) 17.9155i 0.723601i 0.932256 + 0.361800i \(0.117838\pi\)
−0.932256 + 0.361800i \(0.882162\pi\)
\(614\) 2.00000i 0.0807134i
\(615\) −11.0687 + 43.0462i −0.446334 + 1.73579i
\(616\) 13.8984i 0.559984i
\(617\) 18.9350 0.762293 0.381147 0.924515i \(-0.375529\pi\)
0.381147 + 0.924515i \(0.375529\pi\)
\(618\) 29.1583 8.79156i 1.17292 0.353648i
\(619\) 1.58312 0.0636311 0.0318156 0.999494i \(-0.489871\pi\)
0.0318156 + 0.999494i \(0.489871\pi\)
\(620\) 3.02800 5.00000i 0.121607 0.200805i
\(621\) 28.1803 + 23.3659i 1.13084 + 0.937642i
\(622\) −20.8997 −0.838004
\(623\) 8.41688i 0.337215i
\(624\) −1.65831 5.50000i −0.0663856 0.220176i
\(625\) −14.2665 + 20.5297i −0.570660 + 0.821186i
\(626\) −20.7518 −0.829407
\(627\) 32.2068 4.98156i 1.28622 0.198944i
\(628\) 7.65069i 0.305296i
\(629\) −6.43949 −0.256759
\(630\) −21.5804 + 0.888733i −0.859784 + 0.0354080i
\(631\) −23.8997 −0.951434 −0.475717 0.879598i \(-0.657811\pi\)
−0.475717 + 0.879598i \(0.657811\pi\)
\(632\) −15.3014 −0.608656
\(633\) 5.02136 1.51400i 0.199581 0.0601760i
\(634\) 17.0000 0.675156
\(635\) 31.8139 + 19.2665i 1.26250 + 0.764568i
\(636\) −1.65831 + 0.500000i −0.0657564 + 0.0198263i
\(637\) 11.1662 0.442423
\(638\) 35.6393 1.41097
\(639\) −25.6621 + 17.0223i −1.01518 + 0.673392i
\(640\) 1.15831 1.91267i 0.0457863 0.0756050i
\(641\) −0.191748 −0.00757358 −0.00378679 0.999993i \(-0.501205\pi\)
−0.00378679 + 0.999993i \(0.501205\pi\)
\(642\) −0.0250628 0.0831240i −0.000989150 0.00328064i
\(643\) 0.383495i 0.0151236i −0.999971 0.00756179i \(-0.997593\pi\)
0.999971 0.00756179i \(-0.00240702\pi\)
\(644\) 22.6834i 0.893850i
\(645\) −14.3487 3.68957i −0.564980 0.145277i
\(646\) 1.94987 13.8984i 0.0767168 0.546826i
\(647\) −0.605599 −0.0238086 −0.0119043 0.999929i \(-0.503789\pi\)
−0.0119043 + 0.999929i \(0.503789\pi\)
\(648\) 8.29156 + 3.50000i 0.325723 + 0.137493i
\(649\) 24.3550i 0.956018i
\(650\) −14.6958 + 7.68338i −0.576416 + 0.301367i
\(651\) −4.20844 13.9578i −0.164942 0.547050i
\(652\) 1.40295i 0.0549436i
\(653\) 11.6678 0.456595 0.228298 0.973591i \(-0.426684\pi\)
0.228298 + 0.973591i \(0.426684\pi\)
\(654\) −3.42667 11.3650i −0.133993 0.444406i
\(655\) −11.5831 + 19.1267i −0.452590 + 0.747343i
\(656\) −11.4760 −0.448064
\(657\) −3.01282 4.54199i −0.117541 0.177200i
\(658\) 28.5330 1.11233
\(659\) 22.1547 0.863025 0.431513 0.902107i \(-0.357980\pi\)
0.431513 + 0.902107i \(0.357980\pi\)
\(660\) −16.1915 4.16342i −0.630253 0.162061i
\(661\) 32.6113i 1.26843i 0.773156 + 0.634216i \(0.218677\pi\)
−0.773156 + 0.634216i \(0.781323\pi\)
\(662\) 13.4846 0.524093
\(663\) 5.33934 + 17.7086i 0.207363 + 0.687745i
\(664\) 6.43949i 0.249901i
\(665\) 19.8282 24.3246i 0.768904 0.943266i
\(666\) 3.31662 + 5.00000i 0.128517 + 0.193746i
\(667\) −58.1662 −2.25221
\(668\) 24.9499i 0.965340i
\(669\) 1.63325 + 5.41688i 0.0631451 + 0.209429i
\(670\) −8.10819 + 13.3887i −0.313247 + 0.517251i
\(671\) 10.0000i 0.386046i
\(672\) −1.60987 5.33934i −0.0621022 0.205970i
\(673\) 13.2665 0.511386 0.255693 0.966758i \(-0.417696\pi\)
0.255693 + 0.966758i \(0.417696\pi\)
\(674\) 28.2164i 1.08685i
\(675\) 5.42927 25.4071i 0.208973 0.977921i
\(676\) 2.00000 0.0769231
\(677\) 46.1662i 1.77431i −0.461469 0.887157i \(-0.652677\pi\)
0.461469 0.887157i \(-0.347323\pi\)
\(678\) −0.841688 2.79156i −0.0323248 0.107209i
\(679\) 10.8401i 0.416004i
\(680\) −3.72947 + 6.15831i −0.143019 + 0.236160i
\(681\) −33.0831 + 9.97494i −1.26775 + 0.382240i
\(682\) 11.2843i 0.432097i
\(683\) 24.0000i 0.918334i 0.888350 + 0.459167i \(0.151852\pi\)
−0.888350 + 0.459167i \(0.848148\pi\)
\(684\) −11.7958 + 5.64431i −0.451025 + 0.215816i
\(685\) 6.15831 + 3.72947i 0.235297 + 0.142496i
\(686\) −11.6981 −0.446637
\(687\) 0 0
\(688\) 3.82534i 0.145840i
\(689\) 3.31662i 0.126353i
\(690\) 26.4259 + 6.79504i 1.00602 + 0.258683i
\(691\) −13.8997 −0.528771 −0.264386 0.964417i \(-0.585169\pi\)
−0.264386 + 0.964417i \(0.585169\pi\)
\(692\) 13.2665i 0.504317i
\(693\) −34.7461 + 23.0479i −1.31989 + 0.875519i
\(694\) 20.1462i 0.764738i
\(695\) 19.1267 + 11.5831i 0.725518 + 0.439373i
\(696\) −13.6915 + 4.12814i −0.518975 + 0.156477i
\(697\) 36.9499 1.39958
\(698\) 8.63325i 0.326773i
\(699\) −13.2928 44.0873i −0.502781 1.66754i
\(700\) −14.2665 + 7.45894i −0.539223 + 0.281921i
\(701\) 37.2665i 1.40754i −0.710430 0.703768i \(-0.751499\pi\)
0.710430 0.703768i \(-0.248501\pi\)
\(702\) 11.0000 13.2665i 0.415168 0.500712i
\(703\) −8.63325 1.21120i −0.325609 0.0456812i
\(704\) 4.31662i 0.162689i
\(705\) −8.54736 + 33.2406i −0.321912 + 1.25191i
\(706\) 23.3659i 0.879388i
\(707\) −46.0959 −1.73361
\(708\) 2.82107 + 9.35643i 0.106022 + 0.351636i
\(709\) 28.6332 1.07534 0.537672 0.843154i \(-0.319304\pi\)
0.537672 + 0.843154i \(0.319304\pi\)
\(710\) −11.8899 + 19.6332i −0.446219 + 0.736823i
\(711\) −25.3745 38.2534i −0.951616 1.43462i
\(712\) 2.61414i 0.0979692i
\(713\) 18.4169i 0.689717i
\(714\) 5.18338 + 17.1913i 0.193983 + 0.643369i
\(715\) −16.5831 + 27.3830i −0.620174 + 1.02407i
\(716\) 16.5126 0.617104
\(717\) 32.5581 9.81662i 1.21590 0.366609i
\(718\) 4.89975 0.182857
\(719\) 34.8997i 1.30154i 0.759274 + 0.650771i \(0.225554\pi\)
−0.759274 + 0.650771i \(0.774446\pi\)
\(720\) 6.70252 0.276026i 0.249788 0.0102869i
\(721\) 56.6132i 2.10838i
\(722\) 5.22829 18.2665i 0.194577 0.679809i
\(723\) 8.67014 2.61414i 0.322446 0.0972211i
\(724\) 16.5126i 0.613685i
\(725\) 19.1267 + 36.5831i 0.710348 + 1.35866i
\(726\) −12.6583 + 3.81662i −0.469794 + 0.141648i
\(727\) 13.2928i 0.493004i 0.969142 + 0.246502i \(0.0792811\pi\)
−0.969142 + 0.246502i \(0.920719\pi\)
\(728\) −10.6787 −0.395778
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) −3.47494 2.10442i −0.128613 0.0778881i
\(731\) 12.3166i 0.455547i
\(732\) 1.15831 + 3.84169i 0.0428125 + 0.141993i
\(733\) 6.43949i 0.237848i −0.992903 0.118924i \(-0.962056\pi\)
0.992903 0.118924i \(-0.0379445\pi\)
\(734\) 7.65069 0.282392
\(735\) −3.24726 + 12.6286i −0.119777 + 0.465811i
\(736\) 7.04509i 0.259685i
\(737\) 30.2164i 1.11303i
\(738\) −19.0308 28.6901i −0.700535 1.05610i
\(739\) −10.2164 −0.375815 −0.187908 0.982187i \(-0.560171\pi\)
−0.187908 + 0.982187i \(0.560171\pi\)
\(740\) 3.82534 + 2.31662i 0.140622 + 0.0851608i
\(741\) 3.82752 + 24.7457i 0.140607 + 0.909056i
\(742\) 3.21974i 0.118201i
\(743\) 44.8496i 1.64537i −0.568495 0.822687i \(-0.692474\pi\)
0.568495 0.822687i \(-0.307526\pi\)
\(744\) 1.30707 + 4.33507i 0.0479196 + 0.158931i
\(745\) 4.63325 7.65069i 0.169749 0.280299i
\(746\) 23.3166i 0.853682i
\(747\) −16.0987 + 10.6787i −0.589021 + 0.390713i
\(748\) 13.8984i 0.508177i
\(749\) −0.161392 −0.00589712
\(750\) −4.41589 18.8547i −0.161246 0.688476i
\(751\) 24.3550i 0.888727i 0.895847 + 0.444363i \(0.146570\pi\)
−0.895847 + 0.444363i \(0.853430\pi\)
\(752\) −8.86188 −0.323160
\(753\) −52.3747 + 15.7916i −1.90864 + 0.575477i
\(754\) 27.3830i 0.997230i
\(755\) 19.1267 31.5831i 0.696092 1.14943i
\(756\) 10.6787 12.8790i 0.388380 0.468404i
\(757\) 12.8790i 0.468094i 0.972225 + 0.234047i \(0.0751970\pi\)
−0.972225 + 0.234047i \(0.924803\pi\)
\(758\) −36.4366 −1.32344
\(759\) 50.4309 15.2055i 1.83053 0.551925i
\(760\) −6.15831 + 7.55481i −0.223385 + 0.274042i
\(761\) 10.6834i 0.387272i −0.981073 0.193636i \(-0.937972\pi\)
0.981073 0.193636i \(-0.0620281\pi\)
\(762\) −27.5831 + 8.31662i −0.999231 + 0.301280i
\(763\) −22.0660 −0.798843
\(764\) 5.00000i 0.180894i
\(765\) −21.5804 + 0.888733i −0.780241 + 0.0321322i
\(766\) −7.58312 −0.273989
\(767\) 18.7129 0.675682
\(768\) 0.500000 + 1.65831i 0.0180422 + 0.0598392i
\(769\) −48.1662 −1.73692 −0.868460 0.495760i \(-0.834890\pi\)
−0.868460 + 0.495760i \(0.834890\pi\)
\(770\) −16.0987 + 26.5831i −0.580158 + 0.957989i
\(771\) −8.20844 + 2.47494i −0.295620 + 0.0891327i
\(772\) −6.00000 −0.215945
\(773\) 24.1662i 0.869200i −0.900624 0.434600i \(-0.856890\pi\)
0.900624 0.434600i \(-0.143110\pi\)
\(774\) 9.56336 6.34361i 0.343748 0.228016i
\(775\) 11.5831 6.05599i 0.416078 0.217538i
\(776\) 3.36675i 0.120859i
\(777\) 10.6787 3.21974i 0.383096 0.115508i
\(778\) −16.2164 −0.581385
\(779\) 49.5377 + 6.94987i 1.77487 + 0.249005i
\(780\) 3.19891 12.4405i 0.114539 0.445443i
\(781\) 44.3094i 1.58552i