Properties

Label 210.3.l.b.43.8
Level 210
Weight 3
Character 210.43
Analytic conductor 5.722
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.8
Root \(-1.37832 + 1.37832i\) of \(x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + 1093889 x^{8} - 4595248 x^{7} + 18837632 x^{6} + 86081152 x^{5} + 178889856 x^{4} + 70149120 x^{3} + 10035200 x^{2} - 7168000 x + 2560000\)
Character \(\chi\) \(=\) 210.43
Dual form 210.3.l.b.127.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(4.26896 + 2.60306i) q^{5} -2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(4.26896 + 2.60306i) q^{5} -2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-6.87203 + 1.66590i) q^{10} +11.5847 q^{11} +(2.44949 - 2.44949i) q^{12} +(-2.01552 - 2.01552i) q^{13} +3.74166i q^{14} +(2.04030 + 8.41648i) q^{15} -4.00000 q^{16} +(7.75862 - 7.75862i) q^{17} +(-3.00000 - 3.00000i) q^{18} +21.8455i q^{19} +(5.20613 - 8.53793i) q^{20} +4.58258 q^{21} +(-11.5847 + 11.5847i) q^{22} +(-7.41192 - 7.41192i) q^{23} +4.89898i q^{24} +(11.4481 + 22.2248i) q^{25} +4.03103 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-3.74166 - 3.74166i) q^{28} +31.0146i q^{29} +(-10.4568 - 6.37618i) q^{30} -11.5743 q^{31} +(4.00000 - 4.00000i) q^{32} +(14.1883 + 14.1883i) q^{33} +15.5172i q^{34} +(12.8564 - 3.11661i) q^{35} +6.00000 q^{36} +(-32.0546 + 32.0546i) q^{37} +(-21.8455 - 21.8455i) q^{38} -4.93699i q^{39} +(3.33180 + 13.7441i) q^{40} +39.6845 q^{41} +(-4.58258 + 4.58258i) q^{42} +(-19.3751 - 19.3751i) q^{43} -23.1694i q^{44} +(-7.80919 + 12.8069i) q^{45} +14.8238 q^{46} +(21.8753 - 21.8753i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} +(-33.6729 - 10.7767i) q^{50} +19.0047 q^{51} +(-4.03103 + 4.03103i) q^{52} +(-42.4043 - 42.4043i) q^{53} -7.34847i q^{54} +(49.4547 + 30.1557i) q^{55} +7.48331 q^{56} +(-26.7552 + 26.7552i) q^{57} +(-31.0146 - 31.0146i) q^{58} -89.0234i q^{59} +(16.8330 - 4.08060i) q^{60} +7.07420 q^{61} +(11.5743 - 11.5743i) q^{62} +(5.61249 + 5.61249i) q^{63} +8.00000i q^{64} +(-3.35765 - 13.8507i) q^{65} -28.3766 q^{66} +(15.6985 - 15.6985i) q^{67} +(-15.5172 - 15.5172i) q^{68} -18.1554i q^{69} +(-9.73978 + 15.9730i) q^{70} +133.620 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-92.3644 - 92.3644i) q^{73} -64.1091i q^{74} +(-13.1987 + 41.2407i) q^{75} +43.6910 q^{76} +(21.6730 - 21.6730i) q^{77} +(4.93699 + 4.93699i) q^{78} -126.569i q^{79} +(-17.0759 - 10.4123i) q^{80} -9.00000 q^{81} +(-39.6845 + 39.6845i) q^{82} +(-30.0489 - 30.0489i) q^{83} -9.16515i q^{84} +(53.3174 - 12.9251i) q^{85} +38.7501 q^{86} +(-37.9849 + 37.9849i) q^{87} +(23.1694 + 23.1694i) q^{88} -4.93527i q^{89} +(-4.99770 - 20.6161i) q^{90} -7.54137 q^{91} +(-14.8238 + 14.8238i) q^{92} +(-14.1755 - 14.1755i) q^{93} +43.7506i q^{94} +(-56.8652 + 93.2577i) q^{95} +9.79796 q^{96} +(-30.2346 + 30.2346i) q^{97} +(7.00000 + 7.00000i) q^{98} +34.7541i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{2} - 16q^{5} + 32q^{8} + O(q^{10}) \) \( 16q - 16q^{2} - 16q^{5} + 32q^{8} + 24q^{10} + 8q^{11} - 32q^{13} - 12q^{15} - 64q^{16} + 56q^{17} - 48q^{18} - 16q^{20} - 8q^{22} + 24q^{23} + 40q^{25} + 64q^{26} - 112q^{31} + 64q^{32} + 24q^{33} + 28q^{35} + 96q^{36} - 152q^{37} - 16q^{40} + 24q^{45} - 48q^{46} + 80q^{47} - 72q^{50} - 72q^{51} - 64q^{52} + 48q^{53} - 24q^{55} + 24q^{57} + 96q^{58} + 24q^{60} + 96q^{61} + 112q^{62} + 16q^{65} - 48q^{66} - 80q^{67} - 112q^{68} + 536q^{71} - 96q^{72} - 288q^{75} - 168q^{77} - 48q^{78} + 64q^{80} - 144q^{81} - 256q^{83} + 40q^{85} - 144q^{87} + 16q^{88} + 24q^{90} + 48q^{92} + 192q^{93} + 360q^{95} + 688q^{97} + 112q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.00000i −0.500000 + 0.500000i
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 4.26896 + 2.60306i 0.853793 + 0.520613i
\(6\) −2.44949 −0.408248
\(7\) 1.87083 1.87083i 0.267261 0.267261i
\(8\) 2.00000 + 2.00000i 0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −6.87203 + 1.66590i −0.687203 + 0.166590i
\(11\) 11.5847 1.05316 0.526578 0.850127i \(-0.323475\pi\)
0.526578 + 0.850127i \(0.323475\pi\)
\(12\) 2.44949 2.44949i 0.204124 0.204124i
\(13\) −2.01552 2.01552i −0.155040 0.155040i 0.625325 0.780365i \(-0.284966\pi\)
−0.780365 + 0.625325i \(0.784966\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 2.04030 + 8.41648i 0.136020 + 0.561099i
\(16\) −4.00000 −0.250000
\(17\) 7.75862 7.75862i 0.456389 0.456389i −0.441079 0.897468i \(-0.645404\pi\)
0.897468 + 0.441079i \(0.145404\pi\)
\(18\) −3.00000 3.00000i −0.166667 0.166667i
\(19\) 21.8455i 1.14976i 0.818237 + 0.574882i \(0.194952\pi\)
−0.818237 + 0.574882i \(0.805048\pi\)
\(20\) 5.20613 8.53793i 0.260306 0.426896i
\(21\) 4.58258 0.218218
\(22\) −11.5847 + 11.5847i −0.526578 + 0.526578i
\(23\) −7.41192 7.41192i −0.322257 0.322257i 0.527375 0.849632i \(-0.323176\pi\)
−0.849632 + 0.527375i \(0.823176\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 11.4481 + 22.2248i 0.457924 + 0.888991i
\(26\) 4.03103 0.155040
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) −3.74166 3.74166i −0.133631 0.133631i
\(29\) 31.0146i 1.06947i 0.845021 + 0.534734i \(0.179588\pi\)
−0.845021 + 0.534734i \(0.820412\pi\)
\(30\) −10.4568 6.37618i −0.348559 0.212539i
\(31\) −11.5743 −0.373364 −0.186682 0.982420i \(-0.559773\pi\)
−0.186682 + 0.982420i \(0.559773\pi\)
\(32\) 4.00000 4.00000i 0.125000 0.125000i
\(33\) 14.1883 + 14.1883i 0.429949 + 0.429949i
\(34\) 15.5172i 0.456389i
\(35\) 12.8564 3.11661i 0.367325 0.0890461i
\(36\) 6.00000 0.166667
\(37\) −32.0546 + 32.0546i −0.866340 + 0.866340i −0.992065 0.125725i \(-0.959874\pi\)
0.125725 + 0.992065i \(0.459874\pi\)
\(38\) −21.8455 21.8455i −0.574882 0.574882i
\(39\) 4.93699i 0.126589i
\(40\) 3.33180 + 13.7441i 0.0832950 + 0.343601i
\(41\) 39.6845 0.967914 0.483957 0.875092i \(-0.339199\pi\)
0.483957 + 0.875092i \(0.339199\pi\)
\(42\) −4.58258 + 4.58258i −0.109109 + 0.109109i
\(43\) −19.3751 19.3751i −0.450583 0.450583i 0.444965 0.895548i \(-0.353216\pi\)
−0.895548 + 0.444965i \(0.853216\pi\)
\(44\) 23.1694i 0.526578i
\(45\) −7.80919 + 12.8069i −0.173538 + 0.284598i
\(46\) 14.8238 0.322257
\(47\) 21.8753 21.8753i 0.465432 0.465432i −0.434999 0.900431i \(-0.643251\pi\)
0.900431 + 0.434999i \(0.143251\pi\)
\(48\) −4.89898 4.89898i −0.102062 0.102062i
\(49\) 7.00000i 0.142857i
\(50\) −33.6729 10.7767i −0.673458 0.215533i
\(51\) 19.0047 0.372640
\(52\) −4.03103 + 4.03103i −0.0775199 + 0.0775199i
\(53\) −42.4043 42.4043i −0.800081 0.800081i 0.183027 0.983108i \(-0.441410\pi\)
−0.983108 + 0.183027i \(0.941410\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 49.4547 + 30.1557i 0.899176 + 0.548286i
\(56\) 7.48331 0.133631
\(57\) −26.7552 + 26.7552i −0.469389 + 0.469389i
\(58\) −31.0146 31.0146i −0.534734 0.534734i
\(59\) 89.0234i 1.50887i −0.656374 0.754435i \(-0.727911\pi\)
0.656374 0.754435i \(-0.272089\pi\)
\(60\) 16.8330 4.08060i 0.280549 0.0680101i
\(61\) 7.07420 0.115970 0.0579852 0.998317i \(-0.481532\pi\)
0.0579852 + 0.998317i \(0.481532\pi\)
\(62\) 11.5743 11.5743i 0.186682 0.186682i
\(63\) 5.61249 + 5.61249i 0.0890871 + 0.0890871i
\(64\) 8.00000i 0.125000i
\(65\) −3.35765 13.8507i −0.0516561 0.213088i
\(66\) −28.3766 −0.429949
\(67\) 15.6985 15.6985i 0.234306 0.234306i −0.580181 0.814487i \(-0.697018\pi\)
0.814487 + 0.580181i \(0.197018\pi\)
\(68\) −15.5172 15.5172i −0.228195 0.228195i
\(69\) 18.1554i 0.263122i
\(70\) −9.73978 + 15.9730i −0.139140 + 0.228186i
\(71\) 133.620 1.88197 0.940986 0.338447i \(-0.109901\pi\)
0.940986 + 0.338447i \(0.109901\pi\)
\(72\) −6.00000 + 6.00000i −0.0833333 + 0.0833333i
\(73\) −92.3644 92.3644i −1.26527 1.26527i −0.948506 0.316760i \(-0.897405\pi\)
−0.316760 0.948506i \(-0.602595\pi\)
\(74\) 64.1091i 0.866340i
\(75\) −13.1987 + 41.2407i −0.175982 + 0.549876i
\(76\) 43.6910 0.574882
\(77\) 21.6730 21.6730i 0.281468 0.281468i
\(78\) 4.93699 + 4.93699i 0.0632947 + 0.0632947i
\(79\) 126.569i 1.60214i −0.598569 0.801071i \(-0.704264\pi\)
0.598569 0.801071i \(-0.295736\pi\)
\(80\) −17.0759 10.4123i −0.213448 0.130153i
\(81\) −9.00000 −0.111111
\(82\) −39.6845 + 39.6845i −0.483957 + 0.483957i
\(83\) −30.0489 30.0489i −0.362035 0.362035i 0.502527 0.864562i \(-0.332404\pi\)
−0.864562 + 0.502527i \(0.832404\pi\)
\(84\) 9.16515i 0.109109i
\(85\) 53.3174 12.9251i 0.627264 0.152060i
\(86\) 38.7501 0.450583
\(87\) −37.9849 + 37.9849i −0.436608 + 0.436608i
\(88\) 23.1694 + 23.1694i 0.263289 + 0.263289i
\(89\) 4.93527i 0.0554525i −0.999616 0.0277263i \(-0.991173\pi\)
0.999616 0.0277263i \(-0.00882667\pi\)
\(90\) −4.99770 20.6161i −0.0555300 0.229068i
\(91\) −7.54137 −0.0828723
\(92\) −14.8238 + 14.8238i −0.161129 + 0.161129i
\(93\) −14.1755 14.1755i −0.152425 0.152425i
\(94\) 43.7506i 0.465432i
\(95\) −56.8652 + 93.2577i −0.598582 + 0.981659i
\(96\) 9.79796 0.102062
\(97\) −30.2346 + 30.2346i −0.311697 + 0.311697i −0.845567 0.533870i \(-0.820737\pi\)
0.533870 + 0.845567i \(0.320737\pi\)
\(98\) 7.00000 + 7.00000i 0.0714286 + 0.0714286i
\(99\) 34.7541i 0.351052i
\(100\) 44.4496 22.8962i 0.444496 0.228962i
\(101\) −176.319 −1.74573 −0.872867 0.487958i \(-0.837742\pi\)
−0.872867 + 0.487958i \(0.837742\pi\)
\(102\) −19.0047 + 19.0047i −0.186320 + 0.186320i
\(103\) −61.1510 61.1510i −0.593699 0.593699i 0.344930 0.938629i \(-0.387903\pi\)
−0.938629 + 0.344930i \(0.887903\pi\)
\(104\) 8.06207i 0.0775199i
\(105\) 19.5629 + 11.9287i 0.186313 + 0.113607i
\(106\) 84.8086 0.800081
\(107\) −0.766043 + 0.766043i −0.00715928 + 0.00715928i −0.710677 0.703518i \(-0.751611\pi\)
0.703518 + 0.710677i \(0.251611\pi\)
\(108\) 7.34847 + 7.34847i 0.0680414 + 0.0680414i
\(109\) 26.6885i 0.244848i −0.992478 0.122424i \(-0.960933\pi\)
0.992478 0.122424i \(-0.0390668\pi\)
\(110\) −79.6104 + 19.2990i −0.723731 + 0.175445i
\(111\) −78.5173 −0.707363
\(112\) −7.48331 + 7.48331i −0.0668153 + 0.0668153i
\(113\) 133.108 + 133.108i 1.17795 + 1.17795i 0.980267 + 0.197680i \(0.0633406\pi\)
0.197680 + 0.980267i \(0.436659\pi\)
\(114\) 53.5103i 0.469389i
\(115\) −12.3475 50.9349i −0.107370 0.442912i
\(116\) 62.0291 0.534734
\(117\) 6.04655 6.04655i 0.0516799 0.0516799i
\(118\) 89.0234 + 89.0234i 0.754435 + 0.754435i
\(119\) 29.0301i 0.243950i
\(120\) −12.7524 + 20.9136i −0.106270 + 0.174280i
\(121\) 13.2054 0.109136
\(122\) −7.07420 + 7.07420i −0.0579852 + 0.0579852i
\(123\) 48.6034 + 48.6034i 0.395149 + 0.395149i
\(124\) 23.1486i 0.186682i
\(125\) −8.98097 + 124.677i −0.0718477 + 0.997416i
\(126\) −11.2250 −0.0890871
\(127\) 59.4171 59.4171i 0.467851 0.467851i −0.433367 0.901218i \(-0.642675\pi\)
0.901218 + 0.433367i \(0.142675\pi\)
\(128\) −8.00000 8.00000i −0.0625000 0.0625000i
\(129\) 47.4590i 0.367899i
\(130\) 17.2083 + 10.4930i 0.132372 + 0.0807157i
\(131\) 51.2605 0.391302 0.195651 0.980674i \(-0.437318\pi\)
0.195651 + 0.980674i \(0.437318\pi\)
\(132\) 28.3766 28.3766i 0.214974 0.214974i
\(133\) 40.8692 + 40.8692i 0.307287 + 0.307287i
\(134\) 31.3970i 0.234306i
\(135\) −25.2494 + 6.12091i −0.187033 + 0.0453400i
\(136\) 31.0345 0.228195
\(137\) −17.6526 + 17.6526i −0.128851 + 0.128851i −0.768591 0.639740i \(-0.779042\pi\)
0.639740 + 0.768591i \(0.279042\pi\)
\(138\) 18.1554 + 18.1554i 0.131561 + 0.131561i
\(139\) 206.210i 1.48353i 0.670662 + 0.741763i \(0.266010\pi\)
−0.670662 + 0.741763i \(0.733990\pi\)
\(140\) −6.23323 25.7128i −0.0445230 0.183663i
\(141\) 53.5834 0.380024
\(142\) −133.620 + 133.620i −0.940986 + 0.940986i
\(143\) −23.3492 23.3492i −0.163281 0.163281i
\(144\) 12.0000i 0.0833333i
\(145\) −80.7329 + 132.400i −0.556779 + 0.913104i
\(146\) 184.729 1.26527
\(147\) 8.57321 8.57321i 0.0583212 0.0583212i
\(148\) 64.1091 + 64.1091i 0.433170 + 0.433170i
\(149\) 256.780i 1.72336i 0.507456 + 0.861678i \(0.330586\pi\)
−0.507456 + 0.861678i \(0.669414\pi\)
\(150\) −28.0420 54.4394i −0.186947 0.362929i
\(151\) 255.541 1.69232 0.846161 0.532928i \(-0.178908\pi\)
0.846161 + 0.532928i \(0.178908\pi\)
\(152\) −43.6910 + 43.6910i −0.287441 + 0.287441i
\(153\) 23.2759 + 23.2759i 0.152130 + 0.152130i
\(154\) 43.3460i 0.281468i
\(155\) −49.4102 30.1286i −0.318776 0.194378i
\(156\) −9.87398 −0.0632947
\(157\) −69.5363 + 69.5363i −0.442906 + 0.442906i −0.892988 0.450081i \(-0.851395\pi\)
0.450081 + 0.892988i \(0.351395\pi\)
\(158\) 126.569 + 126.569i 0.801071 + 0.801071i
\(159\) 103.869i 0.653263i
\(160\) 27.4881 6.66360i 0.171801 0.0416475i
\(161\) −27.7328 −0.172254
\(162\) 9.00000 9.00000i 0.0555556 0.0555556i
\(163\) −220.179 220.179i −1.35079 1.35079i −0.884774 0.466020i \(-0.845687\pi\)
−0.466020 0.884774i \(-0.654313\pi\)
\(164\) 79.3690i 0.483957i
\(165\) 23.6363 + 97.5025i 0.143250 + 0.590924i
\(166\) 60.0978 0.362035
\(167\) 27.6262 27.6262i 0.165426 0.165426i −0.619539 0.784966i \(-0.712681\pi\)
0.784966 + 0.619539i \(0.212681\pi\)
\(168\) 9.16515 + 9.16515i 0.0545545 + 0.0545545i
\(169\) 160.875i 0.951925i
\(170\) −40.3924 + 66.2425i −0.237602 + 0.389662i
\(171\) −65.5365 −0.383254
\(172\) −38.7501 + 38.7501i −0.225291 + 0.225291i
\(173\) −128.172 128.172i −0.740876 0.740876i 0.231870 0.972747i \(-0.425516\pi\)
−0.972747 + 0.231870i \(0.925516\pi\)
\(174\) 75.9698i 0.436608i
\(175\) 62.9962 + 20.1613i 0.359978 + 0.115207i
\(176\) −46.3388 −0.263289
\(177\) 109.031 109.031i 0.615994 0.615994i
\(178\) 4.93527 + 4.93527i 0.0277263 + 0.0277263i
\(179\) 65.6591i 0.366811i −0.983037 0.183405i \(-0.941288\pi\)
0.983037 0.183405i \(-0.0587121\pi\)
\(180\) 25.6138 + 15.6184i 0.142299 + 0.0867688i
\(181\) −321.692 −1.77730 −0.888651 0.458584i \(-0.848357\pi\)
−0.888651 + 0.458584i \(0.848357\pi\)
\(182\) 7.54137 7.54137i 0.0414361 0.0414361i
\(183\) 8.66409 + 8.66409i 0.0473447 + 0.0473447i
\(184\) 29.6477i 0.161129i
\(185\) −220.280 + 53.3997i −1.19070 + 0.288647i
\(186\) 28.3511 0.152425
\(187\) 89.8813 89.8813i 0.480649 0.480649i
\(188\) −43.7506 43.7506i −0.232716 0.232716i
\(189\) 13.7477i 0.0727393i
\(190\) −36.3924 150.123i −0.191539 0.790121i
\(191\) −146.509 −0.767061 −0.383531 0.923528i \(-0.625292\pi\)
−0.383531 + 0.923528i \(0.625292\pi\)
\(192\) −9.79796 + 9.79796i −0.0510310 + 0.0510310i
\(193\) 11.1318 + 11.1318i 0.0576775 + 0.0576775i 0.735357 0.677680i \(-0.237014\pi\)
−0.677680 + 0.735357i \(0.737014\pi\)
\(194\) 60.4692i 0.311697i
\(195\) 12.8513 21.0758i 0.0659041 0.108081i
\(196\) −14.0000 −0.0714286
\(197\) 22.4067 22.4067i 0.113740 0.113740i −0.647946 0.761686i \(-0.724372\pi\)
0.761686 + 0.647946i \(0.224372\pi\)
\(198\) −34.7541 34.7541i −0.175526 0.175526i
\(199\) 163.016i 0.819177i −0.912270 0.409589i \(-0.865672\pi\)
0.912270 0.409589i \(-0.134328\pi\)
\(200\) −21.5533 + 67.3458i −0.107767 + 0.336729i
\(201\) 38.4533 0.191310
\(202\) 176.319 176.319i 0.872867 0.872867i
\(203\) 58.0229 + 58.0229i 0.285827 + 0.285827i
\(204\) 38.0093i 0.186320i
\(205\) 169.412 + 103.301i 0.826398 + 0.503909i
\(206\) 122.302 0.593699
\(207\) 22.2357 22.2357i 0.107419 0.107419i
\(208\) 8.06207 + 8.06207i 0.0387599 + 0.0387599i
\(209\) 253.074i 1.21088i
\(210\) −31.4916 + 7.63411i −0.149960 + 0.0363529i
\(211\) 266.247 1.26184 0.630918 0.775850i \(-0.282678\pi\)
0.630918 + 0.775850i \(0.282678\pi\)
\(212\) −84.8086 + 84.8086i −0.400040 + 0.400040i
\(213\) 163.650 + 163.650i 0.768312 + 0.768312i
\(214\) 1.53209i 0.00715928i
\(215\) −32.2769 133.146i −0.150125 0.619284i
\(216\) −14.6969 −0.0680414
\(217\) −21.6535 + 21.6535i −0.0997857 + 0.0997857i
\(218\) 26.6885 + 26.6885i 0.122424 + 0.122424i
\(219\) 226.246i 1.03309i
\(220\) 60.3115 98.9094i 0.274143 0.449588i
\(221\) −31.2753 −0.141517
\(222\) 78.5173 78.5173i 0.353682 0.353682i
\(223\) −313.209 313.209i −1.40453 1.40453i −0.784890 0.619635i \(-0.787281\pi\)
−0.619635 0.784890i \(-0.712719\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) −66.6743 + 34.3443i −0.296330 + 0.152641i
\(226\) −266.216 −1.17795
\(227\) 100.753 100.753i 0.443847 0.443847i −0.449455 0.893303i \(-0.648382\pi\)
0.893303 + 0.449455i \(0.148382\pi\)
\(228\) 53.5103 + 53.5103i 0.234694 + 0.234694i
\(229\) 120.710i 0.527119i 0.964643 + 0.263559i \(0.0848965\pi\)
−0.964643 + 0.263559i \(0.915104\pi\)
\(230\) 63.2824 + 38.5874i 0.275141 + 0.167771i
\(231\) 53.0878 0.229817
\(232\) −62.0291 + 62.0291i −0.267367 + 0.267367i
\(233\) 200.874 + 200.874i 0.862119 + 0.862119i 0.991584 0.129465i \(-0.0413260\pi\)
−0.129465 + 0.991584i \(0.541326\pi\)
\(234\) 12.0931i 0.0516799i
\(235\) 150.328 36.4421i 0.639693 0.155073i
\(236\) −178.047 −0.754435
\(237\) 155.015 155.015i 0.654072 0.654072i
\(238\) 29.0301 + 29.0301i 0.121975 + 0.121975i
\(239\) 288.534i 1.20725i 0.797267 + 0.603627i \(0.206278\pi\)
−0.797267 + 0.603627i \(0.793722\pi\)
\(240\) −8.16121 33.6659i −0.0340050 0.140275i
\(241\) −80.3054 −0.333218 −0.166609 0.986023i \(-0.553282\pi\)
−0.166609 + 0.986023i \(0.553282\pi\)
\(242\) −13.2054 + 13.2054i −0.0545679 + 0.0545679i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 14.1484i 0.0579852i
\(245\) 18.2215 29.8827i 0.0743733 0.121970i
\(246\) −97.2067 −0.395149
\(247\) 44.0300 44.0300i 0.178259 0.178259i
\(248\) −23.1486 23.1486i −0.0933410 0.0933410i
\(249\) 73.6045i 0.295600i
\(250\) −115.696 133.658i −0.462784 0.534632i
\(251\) −238.919 −0.951868 −0.475934 0.879481i \(-0.657890\pi\)
−0.475934 + 0.879481i \(0.657890\pi\)
\(252\) 11.2250 11.2250i 0.0445435 0.0445435i
\(253\) −85.8649 85.8649i −0.339387 0.339387i
\(254\) 118.834i 0.467851i
\(255\) 81.1302 + 49.4703i 0.318158 + 0.194001i
\(256\) 16.0000 0.0625000
\(257\) 357.876 357.876i 1.39251 1.39251i 0.572859 0.819654i \(-0.305834\pi\)
0.819654 0.572859i \(-0.194166\pi\)
\(258\) 47.4590 + 47.4590i 0.183950 + 0.183950i
\(259\) 119.937i 0.463078i
\(260\) −27.7014 + 6.71530i −0.106544 + 0.0258281i
\(261\) −93.0437 −0.356489
\(262\) −51.2605 + 51.2605i −0.195651 + 0.195651i
\(263\) −73.5388 73.5388i −0.279615 0.279615i 0.553340 0.832955i \(-0.313353\pi\)
−0.832955 + 0.553340i \(0.813353\pi\)
\(264\) 56.7532i 0.214974i
\(265\) −70.6413 291.403i −0.266571 1.09964i
\(266\) −81.7384 −0.307287
\(267\) 6.04445 6.04445i 0.0226384 0.0226384i
\(268\) −31.3970 31.3970i −0.117153 0.117153i
\(269\) 63.1334i 0.234697i −0.993091 0.117348i \(-0.962561\pi\)
0.993091 0.117348i \(-0.0374394\pi\)
\(270\) 19.1285 31.3704i 0.0708464 0.116186i
\(271\) −66.1173 −0.243975 −0.121988 0.992532i \(-0.538927\pi\)
−0.121988 + 0.992532i \(0.538927\pi\)
\(272\) −31.0345 + 31.0345i −0.114097 + 0.114097i
\(273\) −9.23626 9.23626i −0.0338325 0.0338325i
\(274\) 35.3053i 0.128851i
\(275\) 132.623 + 257.468i 0.482265 + 0.936246i
\(276\) −36.3108 −0.131561
\(277\) −268.807 + 268.807i −0.970423 + 0.970423i −0.999575 0.0291522i \(-0.990719\pi\)
0.0291522 + 0.999575i \(0.490719\pi\)
\(278\) −206.210 206.210i −0.741763 0.741763i
\(279\) 34.7229i 0.124455i
\(280\) 31.9460 + 19.4796i 0.114093 + 0.0695698i
\(281\) −108.591 −0.386445 −0.193222 0.981155i \(-0.561894\pi\)
−0.193222 + 0.981155i \(0.561894\pi\)
\(282\) −53.5834 + 53.5834i −0.190012 + 0.190012i
\(283\) 208.690 + 208.690i 0.737419 + 0.737419i 0.972078 0.234658i \(-0.0753972\pi\)
−0.234658 + 0.972078i \(0.575397\pi\)
\(284\) 267.240i 0.940986i
\(285\) −183.862 + 44.5714i −0.645131 + 0.156391i
\(286\) 46.6984 0.163281
\(287\) 74.2429 74.2429i 0.258686 0.258686i
\(288\) 12.0000 + 12.0000i 0.0416667 + 0.0416667i
\(289\) 168.608i 0.583418i
\(290\) −51.6671 213.133i −0.178163 0.734941i
\(291\) −74.0593 −0.254499
\(292\) −184.729 + 184.729i −0.632633 + 0.632633i
\(293\) 315.640 + 315.640i 1.07727 + 1.07727i 0.996753 + 0.0805153i \(0.0256566\pi\)
0.0805153 + 0.996753i \(0.474343\pi\)
\(294\) 17.1464i 0.0583212i
\(295\) 231.734 380.038i 0.785538 1.28826i
\(296\) −128.218 −0.433170
\(297\) −42.5649 + 42.5649i −0.143316 + 0.143316i
\(298\) −256.780 256.780i −0.861678 0.861678i
\(299\) 29.8777i 0.0999254i
\(300\) 82.4814 + 26.3973i 0.274938 + 0.0879911i
\(301\) −72.4948 −0.240847
\(302\) −255.541 + 255.541i −0.846161 + 0.846161i
\(303\) −215.946 215.946i −0.712693 0.712693i
\(304\) 87.3820i 0.287441i
\(305\) 30.1995 + 18.4146i 0.0990147 + 0.0603757i
\(306\) −46.5517 −0.152130
\(307\) 115.484 115.484i 0.376169 0.376169i −0.493549 0.869718i \(-0.664301\pi\)
0.869718 + 0.493549i \(0.164301\pi\)
\(308\) −43.3460 43.3460i −0.140734 0.140734i
\(309\) 149.789i 0.484753i
\(310\) 79.5388 19.2816i 0.256577 0.0621987i
\(311\) −489.397 −1.57362 −0.786812 0.617192i \(-0.788270\pi\)
−0.786812 + 0.617192i \(0.788270\pi\)
\(312\) 9.87398 9.87398i 0.0316474 0.0316474i
\(313\) 95.5816 + 95.5816i 0.305372 + 0.305372i 0.843111 0.537739i \(-0.180721\pi\)
−0.537739 + 0.843111i \(0.680721\pi\)
\(314\) 139.073i 0.442906i
\(315\) 9.34984 + 38.5692i 0.0296820 + 0.122442i
\(316\) −253.138 −0.801071
\(317\) 368.537 368.537i 1.16258 1.16258i 0.178668 0.983909i \(-0.442821\pi\)
0.983909 0.178668i \(-0.0571787\pi\)
\(318\) 103.869 + 103.869i 0.326632 + 0.326632i
\(319\) 359.295i 1.12632i
\(320\) −20.8245 + 34.1517i −0.0650766 + 0.106724i
\(321\) −1.87641 −0.00584553
\(322\) 27.7328 27.7328i 0.0861269 0.0861269i
\(323\) 169.491 + 169.491i 0.524740 + 0.524740i
\(324\) 18.0000i 0.0555556i
\(325\) 21.7206 67.8683i 0.0668325 0.208825i
\(326\) 440.359 1.35079
\(327\) 32.6866 32.6866i 0.0999589 0.0999589i
\(328\) 79.3690 + 79.3690i 0.241979 + 0.241979i
\(329\) 81.8499i 0.248784i
\(330\) −121.139 73.8662i −0.367087 0.223837i
\(331\) 591.256 1.78627 0.893135 0.449788i \(-0.148501\pi\)
0.893135 + 0.449788i \(0.148501\pi\)
\(332\) −60.0978 + 60.0978i −0.181017 + 0.181017i
\(333\) −96.1637 96.1637i −0.288780 0.288780i
\(334\) 55.2524i 0.165426i
\(335\) 107.881 26.1521i 0.322031 0.0780660i
\(336\) −18.3303 −0.0545545
\(337\) −148.222 + 148.222i −0.439827 + 0.439827i −0.891954 0.452127i \(-0.850666\pi\)
0.452127 + 0.891954i \(0.350666\pi\)
\(338\) 160.875 + 160.875i 0.475963 + 0.475963i
\(339\) 326.047i 0.961789i
\(340\) −25.8502 106.635i −0.0760299 0.313632i
\(341\) −134.085 −0.393210
\(342\) 65.5365 65.5365i 0.191627 0.191627i
\(343\) −13.0958 13.0958i −0.0381802 0.0381802i
\(344\) 77.5002i 0.225291i
\(345\) 47.2597 77.5048i 0.136985 0.224652i
\(346\) 256.343 0.740876
\(347\) −299.896 + 299.896i −0.864252 + 0.864252i −0.991829 0.127577i \(-0.959280\pi\)
0.127577 + 0.991829i \(0.459280\pi\)
\(348\) 75.9698 + 75.9698i 0.218304 + 0.218304i
\(349\) 421.152i 1.20674i 0.797462 + 0.603369i \(0.206176\pi\)
−0.797462 + 0.603369i \(0.793824\pi\)
\(350\) −83.1575 + 42.8349i −0.237593 + 0.122385i
\(351\) 14.8110 0.0421965
\(352\) 46.3388 46.3388i 0.131644 0.131644i
\(353\) 310.590 + 310.590i 0.879858 + 0.879858i 0.993519 0.113662i \(-0.0362581\pi\)
−0.113662 + 0.993519i \(0.536258\pi\)
\(354\) 218.062i 0.615994i
\(355\) 570.419 + 347.821i 1.60681 + 0.979779i
\(356\) −9.87055 −0.0277263
\(357\) 35.5545 35.5545i 0.0995923 0.0995923i
\(358\) 65.6591 + 65.6591i 0.183405 + 0.183405i
\(359\) 223.309i 0.622030i 0.950405 + 0.311015i \(0.100669\pi\)
−0.950405 + 0.311015i \(0.899331\pi\)
\(360\) −41.2322 + 9.99540i −0.114534 + 0.0277650i
\(361\) −116.226 −0.321955
\(362\) 321.692 321.692i 0.888651 0.888651i
\(363\) 16.1733 + 16.1733i 0.0445545 + 0.0445545i
\(364\) 15.0827i 0.0414361i
\(365\) −153.870 634.731i −0.421561 1.73899i
\(366\) −17.3282 −0.0473447
\(367\) −262.093 + 262.093i −0.714149 + 0.714149i −0.967401 0.253251i \(-0.918500\pi\)
0.253251 + 0.967401i \(0.418500\pi\)
\(368\) 29.6477 + 29.6477i 0.0805643 + 0.0805643i
\(369\) 119.053i 0.322638i
\(370\) 166.880 273.680i 0.451028 0.739675i
\(371\) −158.662 −0.427661
\(372\) −28.3511 + 28.3511i −0.0762126 + 0.0762126i
\(373\) 56.2361 + 56.2361i 0.150767 + 0.150767i 0.778461 0.627694i \(-0.216001\pi\)
−0.627694 + 0.778461i \(0.716001\pi\)
\(374\) 179.763i 0.480649i
\(375\) −163.697 + 141.698i −0.436525 + 0.377862i
\(376\) 87.5012 0.232716
\(377\) 62.5104 62.5104i 0.165810 0.165810i
\(378\) −13.7477 13.7477i −0.0363696 0.0363696i
\(379\) 179.724i 0.474206i 0.971485 + 0.237103i \(0.0761979\pi\)
−0.971485 + 0.237103i \(0.923802\pi\)
\(380\) 186.515 + 113.730i 0.490830 + 0.299291i
\(381\) 145.541 0.381999
\(382\) 146.509 146.509i 0.383531 0.383531i
\(383\) −285.701 285.701i −0.745956 0.745956i 0.227761 0.973717i \(-0.426859\pi\)
−0.973717 + 0.227761i \(0.926859\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 148.937 36.1050i 0.386851 0.0937793i
\(386\) −22.2635 −0.0576775
\(387\) 58.1252 58.1252i 0.150194 0.150194i
\(388\) 60.4692 + 60.4692i 0.155848 + 0.155848i
\(389\) 728.870i 1.87370i −0.349730 0.936851i \(-0.613727\pi\)
0.349730 0.936851i \(-0.386273\pi\)
\(390\) 8.22453 + 33.9271i 0.0210885 + 0.0869926i
\(391\) −115.012 −0.294149
\(392\) 14.0000 14.0000i 0.0357143 0.0357143i
\(393\) 62.7811 + 62.7811i 0.159748 + 0.159748i
\(394\) 44.8135i 0.113740i
\(395\) 329.468 540.319i 0.834096 1.36790i
\(396\) 69.5082 0.175526
\(397\) 19.6549 19.6549i 0.0495086 0.0495086i −0.681919 0.731428i \(-0.738854\pi\)
0.731428 + 0.681919i \(0.238854\pi\)
\(398\) 163.016 + 163.016i 0.409589 + 0.409589i
\(399\) 100.109i 0.250899i
\(400\) −45.7924 88.8991i −0.114481 0.222248i
\(401\) 230.054 0.573701 0.286851 0.957975i \(-0.407392\pi\)
0.286851 + 0.957975i \(0.407392\pi\)
\(402\) −38.4533 + 38.4533i −0.0956550 + 0.0956550i
\(403\) 23.3282 + 23.3282i 0.0578863 + 0.0578863i
\(404\) 352.638i 0.872867i
\(405\) −38.4207 23.4276i −0.0948659 0.0578459i
\(406\) −116.046 −0.285827
\(407\) −371.343 + 371.343i −0.912390 + 0.912390i
\(408\) 38.0093 + 38.0093i 0.0931601 + 0.0931601i
\(409\) 420.833i 1.02893i 0.857511 + 0.514466i \(0.172010\pi\)
−0.857511 + 0.514466i \(0.827990\pi\)
\(410\) −272.713 + 66.1103i −0.665153 + 0.161245i
\(411\) −43.2400 −0.105207
\(412\) −122.302 + 122.302i −0.296849 + 0.296849i
\(413\) −166.547 166.547i −0.403263 0.403263i
\(414\) 44.4715i 0.107419i
\(415\) −50.0584 206.497i −0.120623 0.497583i
\(416\) −16.1241 −0.0387599
\(417\) −252.555 + 252.555i −0.605647 + 0.605647i
\(418\) −253.074 253.074i −0.605439 0.605439i
\(419\) 196.613i 0.469243i 0.972087 + 0.234621i \(0.0753850\pi\)
−0.972087 + 0.234621i \(0.924615\pi\)
\(420\) 23.8575 39.1257i 0.0568035 0.0931564i
\(421\) −169.718 −0.403132 −0.201566 0.979475i \(-0.564603\pi\)
−0.201566 + 0.979475i \(0.564603\pi\)
\(422\) −266.247 + 266.247i −0.630918 + 0.630918i
\(423\) 65.6259 + 65.6259i 0.155144 + 0.155144i
\(424\) 169.617i 0.400040i
\(425\) 261.255 + 83.6121i 0.614718 + 0.196734i
\(426\) −327.301 −0.768312
\(427\) 13.2346 13.2346i 0.0309944 0.0309944i
\(428\) 1.53209 + 1.53209i 0.00357964 + 0.00357964i
\(429\) 57.1936i 0.133318i
\(430\) 165.423 + 100.869i 0.384704 + 0.234579i
\(431\) −279.559 −0.648628 −0.324314 0.945949i \(-0.605133\pi\)
−0.324314 + 0.945949i \(0.605133\pi\)
\(432\) 14.6969 14.6969i 0.0340207 0.0340207i
\(433\) −354.216 354.216i −0.818050 0.818050i 0.167776 0.985825i \(-0.446342\pi\)
−0.985825 + 0.167776i \(0.946342\pi\)
\(434\) 43.3070i 0.0997857i
\(435\) −261.033 + 63.2791i −0.600077 + 0.145469i
\(436\) −53.3770 −0.122424
\(437\) 161.917 161.917i 0.370519 0.370519i
\(438\) 226.246 + 226.246i 0.516543 + 0.516543i
\(439\) 506.541i 1.15385i 0.816797 + 0.576926i \(0.195748\pi\)
−0.816797 + 0.576926i \(0.804252\pi\)
\(440\) 38.5979 + 159.221i 0.0877225 + 0.361866i
\(441\) 21.0000 0.0476190
\(442\) 31.2753 31.2753i 0.0707585 0.0707585i
\(443\) 443.138 + 443.138i 1.00031 + 1.00031i 1.00000 0.000312670i \(9.95260e-5\pi\)
0.000312670 1.00000i \(0.499900\pi\)
\(444\) 157.035i 0.353682i
\(445\) 12.8468 21.0685i 0.0288693 0.0473450i
\(446\) 626.418 1.40453
\(447\) −314.490 + 314.490i −0.703557 + 0.703557i
\(448\) 14.9666 + 14.9666i 0.0334077 + 0.0334077i
\(449\) 360.679i 0.803294i −0.915795 0.401647i \(-0.868438\pi\)
0.915795 0.401647i \(-0.131562\pi\)
\(450\) 32.3300 101.019i 0.0718445 0.224486i
\(451\) 459.733 1.01936
\(452\) 266.216 266.216i 0.588973 0.588973i
\(453\) 312.972 + 312.972i 0.690887 + 0.690887i
\(454\) 201.507i 0.443847i
\(455\) −32.1939 19.6307i −0.0707557 0.0431444i
\(456\) −107.021 −0.234694
\(457\) 206.799 206.799i 0.452514 0.452514i −0.443674 0.896188i \(-0.646325\pi\)
0.896188 + 0.443674i \(0.146325\pi\)
\(458\) −120.710 120.710i −0.263559 0.263559i
\(459\) 57.0140i 0.124213i
\(460\) −101.870 + 24.6950i −0.221456 + 0.0536848i
\(461\) −649.704 −1.40934 −0.704668 0.709537i \(-0.748904\pi\)
−0.704668 + 0.709537i \(0.748904\pi\)
\(462\) −53.0878 + 53.0878i −0.114909 + 0.114909i
\(463\) 199.904 + 199.904i 0.431759 + 0.431759i 0.889226 0.457467i \(-0.151243\pi\)
−0.457467 + 0.889226i \(0.651243\pi\)
\(464\) 124.058i 0.267367i
\(465\) −23.6150 97.4148i −0.0507850 0.209494i
\(466\) −401.747 −0.862119
\(467\) −120.654 + 120.654i −0.258359 + 0.258359i −0.824386 0.566027i \(-0.808480\pi\)
0.566027 + 0.824386i \(0.308480\pi\)
\(468\) −12.0931 12.0931i −0.0258400 0.0258400i
\(469\) 58.7384i 0.125242i
\(470\) −113.886 + 186.770i −0.242310 + 0.397383i
\(471\) −170.328 −0.361632
\(472\) 178.047 178.047i 0.377218 0.377218i
\(473\) −224.454 224.454i −0.474534 0.474534i
\(474\) 310.030i 0.654072i
\(475\) −485.511 + 250.090i −1.02213 + 0.526505i
\(476\) −58.0602 −0.121975
\(477\) 127.213 127.213i 0.266694 0.266694i
\(478\) −288.534 288.534i −0.603627 0.603627i
\(479\) 527.483i 1.10122i −0.834764 0.550609i \(-0.814396\pi\)
0.834764 0.550609i \(-0.185604\pi\)
\(480\) 41.8271 + 25.5047i 0.0871399 + 0.0531348i
\(481\) 129.213 0.268634
\(482\) 80.3054 80.3054i 0.166609 0.166609i
\(483\) −33.9657 33.9657i −0.0703223 0.0703223i
\(484\) 26.4109i 0.0545679i
\(485\) −207.773 + 50.3678i −0.428398 + 0.103851i
\(486\) 22.0454 0.0453609
\(487\) −361.051 + 361.051i −0.741378 + 0.741378i −0.972843 0.231465i \(-0.925648\pi\)
0.231465 + 0.972843i \(0.425648\pi\)
\(488\) 14.1484 + 14.1484i 0.0289926 + 0.0289926i
\(489\) 539.327i 1.10292i
\(490\) 11.6613 + 48.1042i 0.0237986 + 0.0981718i
\(491\) 579.301 1.17984 0.589920 0.807462i \(-0.299159\pi\)
0.589920 + 0.807462i \(0.299159\pi\)
\(492\) 97.2067 97.2067i 0.197575 0.197575i
\(493\) 240.630 + 240.630i 0.488093 + 0.488093i
\(494\) 88.0600i 0.178259i
\(495\) −90.4672 + 148.364i −0.182762 + 0.299725i
\(496\) 46.2971 0.0933410
\(497\) 249.980 249.980i 0.502978 0.502978i
\(498\) 73.6045 + 73.6045i 0.147800 + 0.147800i
\(499\) 269.123i 0.539324i −0.962955 0.269662i \(-0.913088\pi\)
0.962955 0.269662i \(-0.0869120\pi\)
\(500\) 249.354 + 17.9619i 0.498708 + 0.0359239i
\(501\) 67.6701 0.135070
\(502\) 238.919 238.919i 0.475934 0.475934i
\(503\) −297.017 297.017i −0.590492 0.590492i 0.347273 0.937764i \(-0.387108\pi\)
−0.937764 + 0.347273i \(0.887108\pi\)
\(504\) 22.4499i 0.0445435i
\(505\) −752.700 458.970i −1.49050 0.908852i
\(506\) 171.730 0.339387
\(507\) 197.031 197.031i 0.388622 0.388622i
\(508\) −118.834 118.834i −0.233925 0.233925i
\(509\) 518.564i 1.01879i −0.860533 0.509395i \(-0.829869\pi\)
0.860533 0.509395i \(-0.170131\pi\)
\(510\) −130.601 + 31.6598i −0.256079 + 0.0620781i
\(511\) −345.596 −0.676313
\(512\) −16.0000 + 16.0000i −0.0312500 + 0.0312500i
\(513\) −80.2655 80.2655i −0.156463 0.156463i
\(514\) 715.752i 1.39251i
\(515\) −101.871 420.231i −0.197809 0.815983i
\(516\) −94.9180 −0.183950
\(517\) 253.419 253.419i 0.490172 0.490172i
\(518\) −119.937 119.937i −0.231539 0.231539i
\(519\) 313.955i 0.604923i
\(520\) 20.9861 34.4167i 0.0403579 0.0661859i
\(521\) 583.187 1.11936 0.559680 0.828709i \(-0.310924\pi\)
0.559680 + 0.828709i \(0.310924\pi\)
\(522\) 93.0437 93.0437i 0.178245 0.178245i
\(523\) −135.776 135.776i −0.259610 0.259610i 0.565286 0.824895i \(-0.308766\pi\)
−0.824895 + 0.565286i \(0.808766\pi\)
\(524\) 102.521i 0.195651i
\(525\) 52.4618 + 101.847i 0.0999273 + 0.193994i
\(526\) 147.078 0.279615
\(527\) −89.8004 + 89.8004i −0.170399 + 0.170399i
\(528\) −56.7532 56.7532i −0.107487 0.107487i
\(529\) 419.127i 0.792301i
\(530\) 362.045 + 220.762i 0.683103 + 0.416532i
\(531\) 267.070 0.502957
\(532\) 81.7384 81.7384i 0.153644 0.153644i
\(533\) −79.9847 79.9847i −0.150065 0.150065i
\(534\) 12.0889i 0.0226384i
\(535\) −5.26427 + 1.27615i −0.00983976 + 0.00238533i
\(536\) 62.7940 0.117153
\(537\) 80.4157 80.4157i 0.149750 0.149750i
\(538\) 63.1334 + 63.1334i 0.117348 + 0.117348i
\(539\) 81.0929i 0.150451i
\(540\) 12.2418 + 50.4989i 0.0226700 + 0.0935165i
\(541\) −631.949 −1.16811 −0.584057 0.811713i \(-0.698535\pi\)
−0.584057 + 0.811713i \(0.698535\pi\)
\(542\) 66.1173 66.1173i 0.121988 0.121988i
\(543\) −393.990 393.990i −0.725581 0.725581i
\(544\) 62.0689i 0.114097i
\(545\) 69.4718 113.932i 0.127471 0.209050i
\(546\) 18.4725 0.0338325
\(547\) −465.158 + 465.158i −0.850381 + 0.850381i −0.990180 0.139799i \(-0.955354\pi\)
0.139799 + 0.990180i \(0.455354\pi\)
\(548\) 35.3053 + 35.3053i 0.0644257 + 0.0644257i
\(549\) 21.2226i 0.0386568i
\(550\) −390.091 124.845i −0.709256 0.226990i
\(551\) −677.529 −1.22963
\(552\) 36.3108 36.3108i 0.0657805 0.0657805i
\(553\) −236.789 236.789i −0.428190 0.428190i
\(554\) 537.614i 0.970423i
\(555\) −335.188 204.386i −0.603942 0.368263i
\(556\) 412.421 0.741763
\(557\) 432.756 432.756i 0.776941 0.776941i −0.202368 0.979309i \(-0.564864\pi\)
0.979309 + 0.202368i \(0.0648639\pi\)
\(558\) 34.7229 + 34.7229i 0.0622273 + 0.0622273i
\(559\) 78.1015i 0.139717i
\(560\) −51.4256 + 12.4665i −0.0918313 + 0.0222615i
\(561\) 220.163 0.392448
\(562\) 108.591 108.591i 0.193222 0.193222i
\(563\) 382.111 + 382.111i 0.678706 + 0.678706i 0.959707 0.281002i \(-0.0906666\pi\)
−0.281002 + 0.959707i \(0.590667\pi\)
\(564\) 107.167i 0.190012i
\(565\) 221.744 + 914.722i 0.392468 + 1.61898i
\(566\) −417.379 −0.737419
\(567\) −16.8375 + 16.8375i −0.0296957 + 0.0296957i
\(568\) 267.240 + 267.240i 0.470493 + 0.470493i
\(569\) 298.102i 0.523905i 0.965081 + 0.261952i \(0.0843663\pi\)
−0.965081 + 0.261952i \(0.915634\pi\)
\(570\) 139.291 228.434i 0.244370 0.400761i
\(571\) 769.585 1.34778 0.673892 0.738830i \(-0.264621\pi\)
0.673892 + 0.738830i \(0.264621\pi\)
\(572\) −46.6984 + 46.6984i −0.0816405 + 0.0816405i
\(573\) −179.436 179.436i −0.313151 0.313151i
\(574\) 148.486i 0.258686i
\(575\) 79.8758 249.581i 0.138914 0.434053i
\(576\) −24.0000 −0.0416667
\(577\) −357.027 + 357.027i −0.618765 + 0.618765i −0.945215 0.326450i \(-0.894148\pi\)
0.326450 + 0.945215i \(0.394148\pi\)
\(578\) −168.608 168.608i −0.291709 0.291709i
\(579\) 27.2671i 0.0470935i
\(580\) 264.800 + 161.466i 0.456552 + 0.278389i
\(581\) −112.433 −0.193516
\(582\) 74.0593 74.0593i 0.127250 0.127250i
\(583\) −491.241 491.241i −0.842609 0.842609i
\(584\) 369.458i 0.632633i
\(585\) 41.5521 10.0729i 0.0710292 0.0172187i
\(586\) −631.279 −1.07727
\(587\) −107.406 + 107.406i −0.182974 + 0.182974i −0.792650 0.609677i \(-0.791299\pi\)
0.609677 + 0.792650i \(0.291299\pi\)
\(588\) −17.1464 17.1464i −0.0291606 0.0291606i
\(589\) 252.846i 0.429280i
\(590\) 148.304 + 611.771i 0.251363 + 1.03690i
\(591\) 54.8851 0.0928682
\(592\) 128.218 128.218i 0.216585 0.216585i
\(593\) 108.955 + 108.955i 0.183735 + 0.183735i 0.792981 0.609246i \(-0.208528\pi\)
−0.609246 + 0.792981i \(0.708528\pi\)
\(594\) 85.1299i 0.143316i
\(595\) 75.5672 123.928i 0.127004 0.208283i
\(596\) 513.560 0.861678
\(597\) 199.653 199.653i 0.334428 0.334428i
\(598\) −29.8777 29.8777i −0.0499627 0.0499627i
\(599\) 641.351i 1.07070i −0.844629 0.535352i \(-0.820179\pi\)
0.844629 0.535352i \(-0.179821\pi\)
\(600\) −108.879 + 56.0841i −0.181465 + 0.0934734i
\(601\) 52.4826 0.0873255 0.0436627 0.999046i \(-0.486097\pi\)
0.0436627 + 0.999046i \(0.486097\pi\)
\(602\) 72.4948 72.4948i 0.120423 0.120423i
\(603\) 47.0955 + 47.0955i 0.0781020 + 0.0781020i
\(604\) 511.081i 0.846161i
\(605\) 56.3735 + 34.3746i 0.0931794 + 0.0568175i
\(606\) 431.892 0.712693
\(607\) 318.678 318.678i 0.525005 0.525005i −0.394074 0.919079i \(-0.628935\pi\)
0.919079 + 0.394074i \(0.128935\pi\)
\(608\) 87.3820 + 87.3820i 0.143720 + 0.143720i
\(609\) 142.127i 0.233377i
\(610\) −48.6141 + 11.7849i −0.0796952 + 0.0193195i
\(611\) −88.1801 −0.144321
\(612\) 46.5517 46.5517i 0.0760649 0.0760649i
\(613\) 102.852 + 102.852i 0.167784 + 0.167784i 0.786005 0.618220i \(-0.212146\pi\)
−0.618220 + 0.786005i \(0.712146\pi\)
\(614\) 230.968i 0.376169i
\(615\) 80.9683 + 334.004i 0.131656 + 0.543095i
\(616\) 86.6920 0.140734
\(617\) −433.993 + 433.993i −0.703392 + 0.703392i −0.965137 0.261745i \(-0.915702\pi\)
0.261745 + 0.965137i \(0.415702\pi\)
\(618\) 149.789 + 149.789i 0.242377 + 0.242377i
\(619\) 642.310i 1.03766i −0.854878 0.518828i \(-0.826368\pi\)
0.854878 0.518828i \(-0.173632\pi\)
\(620\) −60.2572 + 98.8204i −0.0971891 + 0.159388i
\(621\) 54.4662 0.0877073
\(622\) 489.397 489.397i 0.786812 0.786812i
\(623\) −9.23305 9.23305i −0.0148203 0.0148203i
\(624\) 19.7480i 0.0316474i
\(625\) −362.882 + 508.863i −0.580611 + 0.814181i
\(626\) −191.163 −0.305372
\(627\) −309.951 + 309.951i −0.494339 + 0.494339i
\(628\) 139.073 + 139.073i 0.221453 + 0.221453i
\(629\) 497.398i 0.790776i
\(630\) −47.9190 29.2193i −0.0760619 0.0463799i
\(631\) −571.788 −0.906162 −0.453081 0.891469i \(-0.649675\pi\)
−0.453081 + 0.891469i \(0.649675\pi\)
\(632\) 253.138 253.138i 0.400535 0.400535i
\(633\) 326.085 + 326.085i 0.515142 + 0.515142i
\(634\) 737.074i 1.16258i
\(635\) 408.316 98.9828i 0.643017 0.155878i
\(636\) −207.738 −0.326632
\(637\) −14.1086 + 14.1086i −0.0221485 + 0.0221485i
\(638\) −359.295 359.295i −0.563158 0.563158i
\(639\) 400.860i 0.627324i
\(640\) −13.3272 54.9762i −0.0208237 0.0859004i
\(641\) −530.212 −0.827164 −0.413582 0.910467i \(-0.635722\pi\)
−0.413582 + 0.910467i \(0.635722\pi\)
\(642\) 1.87641 1.87641i 0.00292276 0.00292276i
\(643\) 314.561 + 314.561i 0.489208 + 0.489208i 0.908056 0.418848i \(-0.137566\pi\)
−0.418848 + 0.908056i \(0.637566\pi\)
\(644\) 55.4657i 0.0861269i
\(645\) 123.539 202.601i 0.191533 0.314110i
\(646\) −338.982 −0.524740
\(647\) −62.4615 + 62.4615i −0.0965401 + 0.0965401i −0.753727 0.657187i \(-0.771746\pi\)
0.657187 + 0.753727i \(0.271746\pi\)
\(648\) −18.0000 18.0000i −0.0277778 0.0277778i
\(649\) 1031.31i 1.58907i
\(650\) 46.1477 + 89.5888i 0.0709965 + 0.137829i
\(651\) −53.0400 −0.0814747
\(652\) −440.359 + 440.359i −0.675397 + 0.675397i
\(653\) 666.847 + 666.847i 1.02121 + 1.02121i 0.999770 + 0.0214354i \(0.00682362\pi\)
0.0214354 + 0.999770i \(0.493176\pi\)
\(654\) 65.3731i 0.0999589i
\(655\) 218.829 + 133.435i 0.334091 + 0.203717i
\(656\) −158.738 −0.241979
\(657\) 277.093 277.093i 0.421755 0.421755i
\(658\) 81.8499 + 81.8499i 0.124392 + 0.124392i
\(659\) 594.414i 0.901994i 0.892525 + 0.450997i \(0.148932\pi\)
−0.892525 + 0.450997i \(0.851068\pi\)
\(660\) 195.005 47.2726i 0.295462 0.0716252i
\(661\) 1114.18 1.68560 0.842799 0.538228i \(-0.180906\pi\)
0.842799 + 0.538228i \(0.180906\pi\)
\(662\) −591.256 + 591.256i −0.893135 + 0.893135i
\(663\) −38.3042 38.3042i −0.0577741 0.0577741i
\(664\) 120.196i 0.181017i
\(665\) 68.0840 + 280.854i 0.102382 + 0.422337i
\(666\) 192.327 0.288780
\(667\) 229.877 229.877i 0.344644 0.344644i
\(668\) −55.2524 55.2524i −0.0827132 0.0827132i
\(669\) 767.202i 1.14679i
\(670\) −81.7284 + 134.033i −0.121983 + 0.200049i
\(671\) 81.9525 0.122135
\(672\) 18.3303 18.3303i 0.0272772 0.0272772i
\(673\) 171.862 + 171.862i 0.255367 + 0.255367i 0.823167 0.567800i \(-0.192205\pi\)
−0.567800 + 0.823167i \(0.692205\pi\)
\(674\) 296.444i 0.439827i
\(675\) −123.722 39.5960i −0.183292 0.0586608i
\(676\) −321.751 −0.475963
\(677\) −920.701 + 920.701i −1.35997 + 1.35997i −0.486029 + 0.873943i \(0.661555\pi\)
−0.873943 + 0.486029i \(0.838445\pi\)
\(678\) −326.047 326.047i −0.480895 0.480895i
\(679\) 113.127i 0.166609i
\(680\) 132.485 + 80.7847i 0.194831 + 0.118801i
\(681\) 246.794 0.362400
\(682\) 134.085 134.085i 0.196605 0.196605i
\(683\) 272.628 + 272.628i 0.399162 + 0.399162i 0.877937 0.478775i \(-0.158919\pi\)
−0.478775 + 0.877937i \(0.658919\pi\)
\(684\) 131.073i 0.191627i
\(685\) −121.309 + 29.4075i −0.177094 + 0.0429307i
\(686\) 26.1916 0.0381802
\(687\) −147.839 + 147.839i −0.215195 + 0.215195i
\(688\) 77.5002 + 77.5002i 0.112646 + 0.112646i
\(689\) 170.933i 0.248089i
\(690\) 30.2451 + 124.764i 0.0438335 + 0.180818i
\(691\) 418.117 0.605090 0.302545 0.953135i \(-0.402164\pi\)
0.302545 + 0.953135i \(0.402164\pi\)
\(692\) −256.343 + 256.343i −0.370438 + 0.370438i
\(693\) 65.0190 + 65.0190i 0.0938225 + 0.0938225i
\(694\) 599.791i 0.864252i
\(695\) −536.779 + 880.304i −0.772343 + 1.26662i
\(696\) −151.940 −0.218304
\(697\) 307.897 307.897i 0.441746 0.441746i
\(698\) −421.152 421.152i −0.603369 0.603369i
\(699\) 492.038i 0.703917i
\(700\) 40.3226 125.992i 0.0576037 0.179989i
\(701\) 1093.07 1.55930 0.779651 0.626214i \(-0.215396\pi\)
0.779651 + 0.626214i \(0.215396\pi\)
\(702\) −14.8110 + 14.8110i −0.0210982 + 0.0210982i
\(703\) −700.248 700.248i −0.996085 0.996085i
\(704\) 92.6777i 0.131644i
\(705\) 228.745 + 139.481i 0.324462 + 0.197845i
\(706\) −621.179 −0.879858
\(707\) −329.863 + 329.863i −0.466567 + 0.466567i
\(708\) −218.062 218.062i −0.307997 0.307997i
\(709\) 80.7065i 0.113831i −0.998379 0.0569157i \(-0.981873\pi\)
0.998379 0.0569157i \(-0.0181266\pi\)
\(710\) −918.240 + 222.597i −1.29330 + 0.313518i
\(711\) 379.708 0.534047
\(712\) 9.87055 9.87055i 0.0138631 0.0138631i
\(713\) 85.7876 + 85.7876i 0.120319 + 0.120319i
\(714\) 71.1089i 0.0995923i
\(715\) −38.8974 160.456i −0.0544019 0.224414i
\(716\) −131.318 −0.183405
\(717\) −353.380 + 353.380i −0.492860 + 0.492860i
\(718\) −223.309 223.309i −0.311015 0.311015i
\(719\) 266.201i 0.370238i 0.982716 + 0.185119i \(0.0592670\pi\)
−0.982716 + 0.185119i \(0.940733\pi\)
\(720\) 31.2368 51.2276i 0.0433844 0.0711494i
\(721\) −228.806 −0.317345
\(722\) 116.226 116.226i 0.160978 0.160978i
\(723\) −98.3537 98.3537i −0.136035 0.136035i
\(724\) 643.383i 0.888651i
\(725\) −689.292 + 355.058i −0.950747 + 0.489735i
\(726\) −32.3466 −0.0445545
\(727\) 551.246 551.246i 0.758248 0.758248i −0.217756 0.976003i \(-0.569874\pi\)
0.976003 + 0.217756i \(0.0698736\pi\)
\(728\) −15.0827 15.0827i −0.0207181 0.0207181i
\(729\) 27.0000i 0.0370370i
\(730\) 788.601 + 480.861i 1.08028 + 0.658714i
\(731\) −300.647 −0.411282
\(732\) 17.3282 17.3282i 0.0236724 0.0236724i
\(733\) 439.355 + 439.355i 0.599393 + 0.599393i 0.940151 0.340758i \(-0.110684\pi\)
−0.340758 + 0.940151i \(0.610684\pi\)
\(734\) 524.186i 0.714149i
\(735\) 58.9154 14.2821i 0.0801570 0.0194314i
\(736\) −59.2953 −0.0805643
\(737\) 181.862 181.862i 0.246761 0.246761i
\(738\) −119.053 119.053i −0.161319 0.161319i
\(739\) 1138.45i 1.54053i 0.637722 + 0.770267i \(0.279877\pi\)
−0.637722 + 0.770267i \(0.720123\pi\)
\(740\) 106.799 + 440.560i 0.144323 + 0.595351i
\(741\) 107.851 0.145548
\(742\) 158.662 158.662i 0.213831 0.213831i
\(743\) 334.460 + 334.460i 0.450148 + 0.450148i 0.895404 0.445256i \(-0.146887\pi\)
−0.445256 + 0.895404i \(0.646887\pi\)
\(744\) 56.7022i 0.0762126i
\(745\) −668.415 + 1096.18i −0.897201 + 1.47139i
\(746\) −112.472 −0.150767
\(747\) 90.1467 90.1467i 0.120678 0.120678i
\(748\) −179.763 179.763i −0.240324 0.240324i
\(749\) 2.86627i 0.00382680i
\(750\) 21.9988 305.395i 0.0293317 0.407193i
\(751\) 1204.09 1.60331 0.801656 0.597785i \(-0.203953\pi\)
0.801656 + 0.597785i \(0.203953\pi\)
\(752\) −87.5012 + 87.5012i −0.116358 + 0.116358i
\(753\) −292.615 292.615i −0.388599 0.388599i
\(754\) 125.021i 0.165810i
\(755\) 1090.89 + 665.189i 1.44489 + 0.881045i
\(756\) 27.4955 0.0363696
\(757\) −343.214 + 343.214i −0.453387 + 0.453387i −0.896477 0.443090i \(-0.853882\pi\)
0.443090 + 0.896477i \(0.353882\pi\)
\(758\) −179.724 179.724i −0.237103 0.237103i
\(759\) 210.325i 0.277108i
\(760\) −300.246 + 72.7848i −0.395060 + 0.0957695i
\(761\) −210.154 −0.276155 −0.138078 0.990421i \(-0.544092\pi\)
−0.138078 + 0.990421i \(0.544092\pi\)
\(762\) −145.541 + 145.541i −0.190999 + 0.190999i
\(763\) −49.9296 49.9296i −0.0654385 0.0654385i
\(764\) 293.017i 0.383531i
\(765\) 38.7752 + 159.952i 0.0506866 + 0.209088i
\(766\) 571.402 0.745956
\(767\) −179.428 + 179.428i −0.233935 + 0.233935i
\(768\) 19.5959 + 19.5959i 0.0255155 + 0.0255155i
\(769\) 1250.27i 1.62583i −0.582381 0.812916i \(-0.697879\pi\)
0.582381 0.812916i \(-0.302121\pi\)
\(770\) −112.832 + 185.043i −0.146536 + 0.240315i
\(771\) 876.613 1.13698
\(772\) 22.2635 22.2635i 0.0288388 0.0288388i
\(773\) 734.887 + 734.887i </