Properties

Label 546.2.o.a.307.3
Level $546$
Weight $2$
Character 546.307
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.7442857984.4
Defining polynomial: \(x^{8} + 26 x^{6} + 205 x^{4} + 540 x^{2} + 324\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 307.3
Root \(1.91681i\) of defining polynomial
Character \(\chi\) \(=\) 546.307
Dual form 546.2.o.a.265.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(-2.56510 + 2.56510i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.648285 - 2.56510i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(-2.56510 + 2.56510i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.648285 - 2.56510i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -3.62760 q^{10} +(-1.64828 + 1.64828i) q^{11} +1.00000 q^{12} +(2.00000 + 3.00000i) q^{13} +(1.35539 - 2.27220i) q^{14} +(2.56510 + 2.56510i) q^{15} -1.00000 q^{16} -7.15945 q^{17} +(-0.707107 - 0.707107i) q^{18} +(-2.86167 + 2.86167i) q^{19} +(-2.56510 - 2.56510i) q^{20} +(-2.56510 + 0.648285i) q^{21} -2.33103 q^{22} +4.45602i q^{23} +(0.707107 + 0.707107i) q^{24} -8.15945i q^{25} +(-0.707107 + 3.53553i) q^{26} +1.00000i q^{27} +(2.56510 - 0.648285i) q^{28} -9.75259 q^{29} +3.62760i q^{30} +(3.91681 - 3.91681i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.64828 + 1.64828i) q^{33} +(-5.06250 - 5.06250i) q^{34} +(8.24264 + 4.91681i) q^{35} -1.00000i q^{36} +(2.48191 - 2.48191i) q^{37} -4.04701 q^{38} +(3.00000 - 2.00000i) q^{39} -3.62760i q^{40} +(7.53921 - 7.53921i) q^{41} +(-2.27220 - 1.35539i) q^{42} +8.62240i q^{43} +(-1.64828 - 1.64828i) q^{44} +(2.56510 - 2.56510i) q^{45} +(-3.15088 + 3.15088i) q^{46} +(-0.703431 - 0.703431i) q^{47} +1.00000i q^{48} +(-6.15945 + 3.32583i) q^{49} +(5.76961 - 5.76961i) q^{50} +7.15945i q^{51} +(-3.00000 + 2.00000i) q^{52} +2.42677 q^{53} +(-0.707107 + 0.707107i) q^{54} -8.45602i q^{55} +(2.27220 + 1.35539i) q^{56} +(2.86167 + 2.86167i) q^{57} +(-6.89612 - 6.89612i) q^{58} +(10.4560 + 10.4560i) q^{59} +(-2.56510 + 2.56510i) q^{60} +7.15945i q^{61} +5.53921 q^{62} +(0.648285 + 2.56510i) q^{63} -1.00000i q^{64} +(-12.8255 - 2.56510i) q^{65} +2.33103i q^{66} +(-4.53921 - 4.53921i) q^{67} -7.15945i q^{68} +4.45602 q^{69} +(2.35172 + 9.30514i) q^{70} +(-0.456023 - 0.456023i) q^{71} +(0.707107 - 0.707107i) q^{72} +(2.48191 + 2.48191i) q^{73} +3.50995 q^{74} -8.15945 q^{75} +(-2.86167 - 2.86167i) q^{76} +(5.29657 + 3.15945i) q^{77} +(3.53553 + 0.707107i) q^{78} +12.0422 q^{79} +(2.56510 - 2.56510i) q^{80} +1.00000 q^{81} +10.6621 q^{82} +(2.70343 - 2.70343i) q^{83} +(-0.648285 - 2.56510i) q^{84} +(18.3647 - 18.3647i) q^{85} +(-6.09696 + 6.09696i) q^{86} +9.75259i q^{87} -2.33103i q^{88} +(4.75044 + 4.75044i) q^{89} +3.62760 q^{90} +(6.39872 - 7.07505i) q^{91} -4.45602 q^{92} +(-3.91681 - 3.91681i) q^{93} -0.994801i q^{94} -14.6809i q^{95} +(-0.707107 + 0.707107i) q^{96} +(-4.49220 + 4.49220i) q^{97} +(-6.70711 - 2.00368i) q^{98} +(1.64828 - 1.64828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{5} - 8q^{9} + O(q^{10}) \) \( 8q - 4q^{5} - 8q^{9} + 4q^{10} - 8q^{11} + 8q^{12} + 16q^{13} + 4q^{15} - 8q^{16} - 12q^{17} + 4q^{19} - 4q^{20} - 4q^{21} + 4q^{22} + 4q^{28} - 12q^{29} + 20q^{31} + 8q^{33} - 24q^{34} + 32q^{35} - 8q^{37} + 12q^{38} + 24q^{39} + 16q^{41} + 4q^{42} - 8q^{44} + 4q^{45} - 20q^{46} - 16q^{47} - 4q^{49} + 24q^{50} - 24q^{52} - 24q^{53} - 4q^{56} - 4q^{57} - 16q^{58} + 28q^{59} - 4q^{60} - 20q^{65} + 8q^{67} - 20q^{69} + 24q^{70} + 52q^{71} - 8q^{73} - 4q^{74} - 20q^{75} + 4q^{76} + 32q^{77} - 48q^{79} + 4q^{80} + 8q^{81} + 40q^{82} + 32q^{83} + 20q^{85} - 20q^{86} + 4q^{89} - 4q^{90} + 12q^{91} + 20q^{92} - 20q^{93} - 36q^{97} - 48q^{98} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 1.00000i 0.577350i
\(4\) 1.00000i 0.500000i
\(5\) −2.56510 + 2.56510i −1.14715 + 1.14715i −0.160035 + 0.987111i \(0.551161\pi\)
−0.987111 + 0.160035i \(0.948839\pi\)
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) −0.648285 2.56510i −0.245029 0.969516i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −1.00000 −0.333333
\(10\) −3.62760 −1.14715
\(11\) −1.64828 + 1.64828i −0.496977 + 0.496977i −0.910496 0.413519i \(-0.864300\pi\)
0.413519 + 0.910496i \(0.364300\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.00000 + 3.00000i 0.554700 + 0.832050i
\(14\) 1.35539 2.27220i 0.362244 0.607272i
\(15\) 2.56510 + 2.56510i 0.662305 + 0.662305i
\(16\) −1.00000 −0.250000
\(17\) −7.15945 −1.73642 −0.868211 0.496195i \(-0.834730\pi\)
−0.868211 + 0.496195i \(0.834730\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) −2.86167 + 2.86167i −0.656512 + 0.656512i −0.954553 0.298041i \(-0.903667\pi\)
0.298041 + 0.954553i \(0.403667\pi\)
\(20\) −2.56510 2.56510i −0.573573 0.573573i
\(21\) −2.56510 + 0.648285i −0.559750 + 0.141467i
\(22\) −2.33103 −0.496977
\(23\) 4.45602i 0.929145i 0.885535 + 0.464573i \(0.153792\pi\)
−0.885535 + 0.464573i \(0.846208\pi\)
\(24\) 0.707107 + 0.707107i 0.144338 + 0.144338i
\(25\) 8.15945i 1.63189i
\(26\) −0.707107 + 3.53553i −0.138675 + 0.693375i
\(27\) 1.00000i 0.192450i
\(28\) 2.56510 0.648285i 0.484758 0.122514i
\(29\) −9.75259 −1.81101 −0.905506 0.424335i \(-0.860508\pi\)
−0.905506 + 0.424335i \(0.860508\pi\)
\(30\) 3.62760i 0.662305i
\(31\) 3.91681 3.91681i 0.703480 0.703480i −0.261676 0.965156i \(-0.584275\pi\)
0.965156 + 0.261676i \(0.0842750\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 1.64828 + 1.64828i 0.286930 + 0.286930i
\(34\) −5.06250 5.06250i −0.868211 0.868211i
\(35\) 8.24264 + 4.91681i 1.39326 + 0.831093i
\(36\) 1.00000i 0.166667i
\(37\) 2.48191 2.48191i 0.408024 0.408024i −0.473025 0.881049i \(-0.656838\pi\)
0.881049 + 0.473025i \(0.156838\pi\)
\(38\) −4.04701 −0.656512
\(39\) 3.00000 2.00000i 0.480384 0.320256i
\(40\) 3.62760i 0.573573i
\(41\) 7.53921 7.53921i 1.17743 1.17743i 0.197029 0.980398i \(-0.436871\pi\)
0.980398 0.197029i \(-0.0631294\pi\)
\(42\) −2.27220 1.35539i −0.350609 0.209141i
\(43\) 8.62240i 1.31490i 0.753497 + 0.657452i \(0.228366\pi\)
−0.753497 + 0.657452i \(0.771634\pi\)
\(44\) −1.64828 1.64828i −0.248488 0.248488i
\(45\) 2.56510 2.56510i 0.382382 0.382382i
\(46\) −3.15088 + 3.15088i −0.464573 + 0.464573i
\(47\) −0.703431 0.703431i −0.102606 0.102606i 0.653940 0.756546i \(-0.273115\pi\)
−0.756546 + 0.653940i \(0.773115\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −6.15945 + 3.32583i −0.879922 + 0.475118i
\(50\) 5.76961 5.76961i 0.815945 0.815945i
\(51\) 7.15945i 1.00252i
\(52\) −3.00000 + 2.00000i −0.416025 + 0.277350i
\(53\) 2.42677 0.333342 0.166671 0.986013i \(-0.446698\pi\)
0.166671 + 0.986013i \(0.446698\pi\)
\(54\) −0.707107 + 0.707107i −0.0962250 + 0.0962250i
\(55\) 8.45602i 1.14021i
\(56\) 2.27220 + 1.35539i 0.303636 + 0.181122i
\(57\) 2.86167 + 2.86167i 0.379037 + 0.379037i
\(58\) −6.89612 6.89612i −0.905506 0.905506i
\(59\) 10.4560 + 10.4560i 1.36126 + 1.36126i 0.872316 + 0.488942i \(0.162617\pi\)
0.488942 + 0.872316i \(0.337383\pi\)
\(60\) −2.56510 + 2.56510i −0.331153 + 0.331153i
\(61\) 7.15945i 0.916674i 0.888778 + 0.458337i \(0.151555\pi\)
−0.888778 + 0.458337i \(0.848445\pi\)
\(62\) 5.53921 0.703480
\(63\) 0.648285 + 2.56510i 0.0816762 + 0.323172i
\(64\) 1.00000i 0.125000i
\(65\) −12.8255 2.56510i −1.59081 0.318161i
\(66\) 2.33103i 0.286930i
\(67\) −4.53921 4.53921i −0.554553 0.554553i 0.373199 0.927751i \(-0.378261\pi\)
−0.927751 + 0.373199i \(0.878261\pi\)
\(68\) 7.15945i 0.868211i
\(69\) 4.45602 0.536442
\(70\) 2.35172 + 9.30514i 0.281084 + 1.11218i
\(71\) −0.456023 0.456023i −0.0541200 0.0541200i 0.679529 0.733649i \(-0.262184\pi\)
−0.733649 + 0.679529i \(0.762184\pi\)
\(72\) 0.707107 0.707107i 0.0833333 0.0833333i
\(73\) 2.48191 + 2.48191i 0.290486 + 0.290486i 0.837272 0.546786i \(-0.184149\pi\)
−0.546786 + 0.837272i \(0.684149\pi\)
\(74\) 3.50995 0.408024
\(75\) −8.15945 −0.942173
\(76\) −2.86167 2.86167i −0.328256 0.328256i
\(77\) 5.29657 + 3.15945i 0.603600 + 0.360053i
\(78\) 3.53553 + 0.707107i 0.400320 + 0.0800641i
\(79\) 12.0422 1.35486 0.677429 0.735588i \(-0.263094\pi\)
0.677429 + 0.735588i \(0.263094\pi\)
\(80\) 2.56510 2.56510i 0.286787 0.286787i
\(81\) 1.00000 0.111111
\(82\) 10.6621 1.17743
\(83\) 2.70343 2.70343i 0.296740 0.296740i −0.542996 0.839736i \(-0.682710\pi\)
0.839736 + 0.542996i \(0.182710\pi\)
\(84\) −0.648285 2.56510i −0.0707337 0.279875i
\(85\) 18.3647 18.3647i 1.99193 1.99193i
\(86\) −6.09696 + 6.09696i −0.657452 + 0.657452i
\(87\) 9.75259i 1.04559i
\(88\) 2.33103i 0.248488i
\(89\) 4.75044 + 4.75044i 0.503546 + 0.503546i 0.912538 0.408992i \(-0.134120\pi\)
−0.408992 + 0.912538i \(0.634120\pi\)
\(90\) 3.62760 0.382382
\(91\) 6.39872 7.07505i 0.670769 0.741667i
\(92\) −4.45602 −0.464573
\(93\) −3.91681 3.91681i −0.406155 0.406155i
\(94\) 0.994801i 0.102606i
\(95\) 14.6809i 1.50623i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) −4.49220 + 4.49220i −0.456114 + 0.456114i −0.897378 0.441264i \(-0.854530\pi\)
0.441264 + 0.897378i \(0.354530\pi\)
\(98\) −6.70711 2.00368i −0.677520 0.202402i
\(99\) 1.64828 1.64828i 0.165659 0.165659i
\(100\) 8.15945 0.815945
\(101\) 3.55696 0.353931 0.176965 0.984217i \(-0.443372\pi\)
0.176965 + 0.984217i \(0.443372\pi\)
\(102\) −5.06250 + 5.06250i −0.501262 + 0.501262i
\(103\) −9.80437 −0.966053 −0.483027 0.875606i \(-0.660463\pi\)
−0.483027 + 0.875606i \(0.660463\pi\)
\(104\) −3.53553 0.707107i −0.346688 0.0693375i
\(105\) 4.91681 8.24264i 0.479832 0.804399i
\(106\) 1.71598 + 1.71598i 0.166671 + 0.166671i
\(107\) −0.332748 −0.0321679 −0.0160840 0.999871i \(-0.505120\pi\)
−0.0160840 + 0.999871i \(0.505120\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −12.9672 12.9672i −1.24203 1.24203i −0.959157 0.282875i \(-0.908712\pi\)
−0.282875 0.959157i \(-0.591288\pi\)
\(110\) 5.97931 5.97931i 0.570105 0.570105i
\(111\) −2.48191 2.48191i −0.235573 0.235573i
\(112\) 0.648285 + 2.56510i 0.0612572 + 0.242379i
\(113\) −12.6872 −1.19351 −0.596754 0.802425i \(-0.703543\pi\)
−0.596754 + 0.802425i \(0.703543\pi\)
\(114\) 4.04701i 0.379037i
\(115\) −11.4301 11.4301i −1.06587 1.06587i
\(116\) 9.75259i 0.905506i
\(117\) −2.00000 3.00000i −0.184900 0.277350i
\(118\) 14.7870i 1.36126i
\(119\) 4.64136 + 18.3647i 0.425473 + 1.68349i
\(120\) −3.62760 −0.331153
\(121\) 5.56631i 0.506029i
\(122\) −5.06250 + 5.06250i −0.458337 + 0.458337i
\(123\) −7.53921 7.53921i −0.679788 0.679788i
\(124\) 3.91681 + 3.91681i 0.351740 + 0.351740i
\(125\) 8.10431 + 8.10431i 0.724871 + 0.724871i
\(126\) −1.35539 + 2.27220i −0.120748 + 0.202424i
\(127\) 5.94822i 0.527820i −0.964547 0.263910i \(-0.914988\pi\)
0.964547 0.263910i \(-0.0850121\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 8.62240 0.759160
\(130\) −7.25519 10.8828i −0.636322 0.954484i
\(131\) 0.0292581i 0.00255629i 0.999999 + 0.00127815i \(0.000406847\pi\)
−0.999999 + 0.00127815i \(0.999593\pi\)
\(132\) −1.64828 + 1.64828i −0.143465 + 0.143465i
\(133\) 9.19563 + 5.48528i 0.797362 + 0.475634i
\(134\) 6.41941i 0.554553i
\(135\) −2.56510 2.56510i −0.220768 0.220768i
\(136\) 5.06250 5.06250i 0.434106 0.434106i
\(137\) 4.56510 4.56510i 0.390023 0.390023i −0.484673 0.874695i \(-0.661061\pi\)
0.874695 + 0.484673i \(0.161061\pi\)
\(138\) 3.15088 + 3.15088i 0.268221 + 0.268221i
\(139\) 12.6872i 1.07611i 0.842910 + 0.538055i \(0.180841\pi\)
−0.842910 + 0.538055i \(0.819159\pi\)
\(140\) −4.91681 + 8.24264i −0.415547 + 0.696630i
\(141\) −0.703431 + 0.703431i −0.0592395 + 0.0592395i
\(142\) 0.644914i 0.0541200i
\(143\) −8.24142 1.64828i −0.689182 0.137836i
\(144\) 1.00000 0.0833333
\(145\) 25.0164 25.0164i 2.07750 2.07750i
\(146\) 3.50995i 0.290486i
\(147\) 3.32583 + 6.15945i 0.274310 + 0.508023i
\(148\) 2.48191 + 2.48191i 0.204012 + 0.204012i
\(149\) 13.4021 + 13.4021i 1.09794 + 1.09794i 0.994651 + 0.103291i \(0.0329374\pi\)
0.103291 + 0.994651i \(0.467063\pi\)
\(150\) −5.76961 5.76961i −0.471086 0.471086i
\(151\) 3.02804 3.02804i 0.246418 0.246418i −0.573081 0.819499i \(-0.694252\pi\)
0.819499 + 0.573081i \(0.194252\pi\)
\(152\) 4.04701i 0.328256i
\(153\) 7.15945 0.578808
\(154\) 1.51117 + 5.97931i 0.121773 + 0.481827i
\(155\) 20.0940i 1.61399i
\(156\) 2.00000 + 3.00000i 0.160128 + 0.240192i
\(157\) 11.4198i 0.911403i −0.890133 0.455701i \(-0.849388\pi\)
0.890133 0.455701i \(-0.150612\pi\)
\(158\) 8.51515 + 8.51515i 0.677429 + 0.677429i
\(159\) 2.42677i 0.192455i
\(160\) 3.62760 0.286787
\(161\) 11.4301 2.88877i 0.900821 0.227667i
\(162\) 0.707107 + 0.707107i 0.0555556 + 0.0555556i
\(163\) −9.07627 + 9.07627i −0.710908 + 0.710908i −0.966725 0.255817i \(-0.917656\pi\)
0.255817 + 0.966725i \(0.417656\pi\)
\(164\) 7.53921 + 7.53921i 0.588713 + 0.588713i
\(165\) −8.45602 −0.658301
\(166\) 3.82323 0.296740
\(167\) 3.31554 + 3.31554i 0.256564 + 0.256564i 0.823655 0.567091i \(-0.191931\pi\)
−0.567091 + 0.823655i \(0.691931\pi\)
\(168\) 1.35539 2.27220i 0.104571 0.175304i
\(169\) −5.00000 + 12.0000i −0.384615 + 0.923077i
\(170\) 25.9716 1.99193
\(171\) 2.86167 2.86167i 0.218837 0.218837i
\(172\) −8.62240 −0.657452
\(173\) −6.05852 −0.460620 −0.230310 0.973117i \(-0.573974\pi\)
−0.230310 + 0.973117i \(0.573974\pi\)
\(174\) −6.89612 + 6.89612i −0.522794 + 0.522794i
\(175\) −20.9298 + 5.28965i −1.58214 + 0.399860i
\(176\) 1.64828 1.64828i 0.124244 0.124244i
\(177\) 10.4560 10.4560i 0.785923 0.785923i
\(178\) 6.71814i 0.503546i
\(179\) 13.5570i 1.01329i 0.862153 + 0.506647i \(0.169115\pi\)
−0.862153 + 0.506647i \(0.830885\pi\)
\(180\) 2.56510 + 2.56510i 0.191191 + 0.191191i
\(181\) −14.5793 −1.08367 −0.541835 0.840485i \(-0.682270\pi\)
−0.541835 + 0.840485i \(0.682270\pi\)
\(182\) 9.52740 0.478235i 0.706218 0.0354491i
\(183\) 7.15945 0.529242
\(184\) −3.15088 3.15088i −0.232286 0.232286i
\(185\) 12.7327i 0.936126i
\(186\) 5.53921i 0.406155i
\(187\) 11.8008 11.8008i 0.862961 0.862961i
\(188\) 0.703431 0.703431i 0.0513029 0.0513029i
\(189\) 2.56510 0.648285i 0.186583 0.0471558i
\(190\) 10.3810 10.3810i 0.753115 0.753115i
\(191\) −26.3837 −1.90906 −0.954528 0.298123i \(-0.903640\pi\)
−0.954528 + 0.298123i \(0.903640\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 2.86288 2.86288i 0.206075 0.206075i −0.596522 0.802597i \(-0.703451\pi\)
0.802597 + 0.596522i \(0.203451\pi\)
\(194\) −6.35293 −0.456114
\(195\) −2.56510 + 12.8255i −0.183690 + 0.918452i
\(196\) −3.32583 6.15945i −0.237559 0.439961i
\(197\) −6.21338 6.21338i −0.442685 0.442685i 0.450228 0.892913i \(-0.351343\pi\)
−0.892913 + 0.450228i \(0.851343\pi\)
\(198\) 2.33103 0.165659
\(199\) −1.63799 −0.116114 −0.0580572 0.998313i \(-0.518491\pi\)
−0.0580572 + 0.998313i \(0.518491\pi\)
\(200\) 5.76961 + 5.76961i 0.407973 + 0.407973i
\(201\) −4.53921 + 4.53921i −0.320171 + 0.320171i
\(202\) 2.51515 + 2.51515i 0.176965 + 0.176965i
\(203\) 6.32246 + 25.0164i 0.443749 + 1.75580i
\(204\) −7.15945 −0.501262
\(205\) 38.6776i 2.70136i
\(206\) −6.93274 6.93274i −0.483027 0.483027i
\(207\) 4.45602i 0.309715i
\(208\) −2.00000 3.00000i −0.138675 0.208013i
\(209\) 9.43369i 0.652542i
\(210\) 9.30514 2.35172i 0.642116 0.162284i
\(211\) 0.622397 0.0428476 0.0214238 0.999770i \(-0.493180\pi\)
0.0214238 + 0.999770i \(0.493180\pi\)
\(212\) 2.42677i 0.166671i
\(213\) −0.456023 + 0.456023i −0.0312462 + 0.0312462i
\(214\) −0.235288 0.235288i −0.0160840 0.0160840i
\(215\) −22.1173 22.1173i −1.50839 1.50839i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) −12.5862 7.50780i −0.854408 0.509663i
\(218\) 18.3384i 1.24203i
\(219\) 2.48191 2.48191i 0.167712 0.167712i
\(220\) 8.45602 0.570105
\(221\) −14.3189 21.4784i −0.963194 1.44479i
\(222\) 3.50995i 0.235573i
\(223\) −15.5615 + 15.5615i −1.04208 + 1.04208i −0.0430034 + 0.999075i \(0.513693\pi\)
−0.999075 + 0.0430034i \(0.986307\pi\)
\(224\) −1.35539 + 2.27220i −0.0905609 + 0.151818i
\(225\) 8.15945i 0.543964i
\(226\) −8.97117 8.97117i −0.596754 0.596754i
\(227\) 1.15945 1.15945i 0.0769556 0.0769556i −0.667581 0.744537i \(-0.732670\pi\)
0.744537 + 0.667581i \(0.232670\pi\)
\(228\) −2.86167 + 2.86167i −0.189519 + 0.189519i
\(229\) 4.15945 + 4.15945i 0.274864 + 0.274864i 0.831055 0.556190i \(-0.187737\pi\)
−0.556190 + 0.831055i \(0.687737\pi\)
\(230\) 16.1647i 1.06587i
\(231\) 3.15945 5.29657i 0.207877 0.348489i
\(232\) 6.89612 6.89612i 0.452753 0.452753i
\(233\) 10.7974i 0.707364i −0.935366 0.353682i \(-0.884929\pi\)
0.935366 0.353682i \(-0.115071\pi\)
\(234\) 0.707107 3.53553i 0.0462250 0.231125i
\(235\) 3.60874 0.235408
\(236\) −10.4560 + 10.4560i −0.680629 + 0.680629i
\(237\) 12.0422i 0.782228i
\(238\) −9.70386 + 16.2677i −0.629008 + 1.05448i
\(239\) 16.1501 + 16.1501i 1.04466 + 1.04466i 0.998955 + 0.0457083i \(0.0145545\pi\)
0.0457083 + 0.998955i \(0.485446\pi\)
\(240\) −2.56510 2.56510i −0.165576 0.165576i
\(241\) 3.45602 + 3.45602i 0.222622 + 0.222622i 0.809602 0.586980i \(-0.199683\pi\)
−0.586980 + 0.809602i \(0.699683\pi\)
\(242\) −3.93598 + 3.93598i −0.253014 + 0.253014i
\(243\) 1.00000i 0.0641500i
\(244\) −7.15945 −0.458337
\(245\) 7.26853 24.3307i 0.464369 1.55443i
\(246\) 10.6621i 0.679788i
\(247\) −14.3083 2.86167i −0.910418 0.182084i
\(248\) 5.53921i 0.351740i
\(249\) −2.70343 2.70343i −0.171323 0.171323i
\(250\) 11.4612i 0.724871i
\(251\) −5.64230 −0.356139 −0.178069 0.984018i \(-0.556985\pi\)
−0.178069 + 0.984018i \(0.556985\pi\)
\(252\) −2.56510 + 0.648285i −0.161586 + 0.0408381i
\(253\) −7.34480 7.34480i −0.461763 0.461763i
\(254\) 4.20603 4.20603i 0.263910 0.263910i
\(255\) −18.3647 18.3647i −1.15004 1.15004i
\(256\) 1.00000 0.0625000
\(257\) 25.0199 1.56070 0.780349 0.625344i \(-0.215041\pi\)
0.780349 + 0.625344i \(0.215041\pi\)
\(258\) 6.09696 + 6.09696i 0.379580 + 0.379580i
\(259\) −7.97533 4.75736i −0.495563 0.295608i
\(260\) 2.56510 12.8255i 0.159081 0.795403i
\(261\) 9.75259 0.603670
\(262\) −0.0206886 + 0.0206886i −0.00127815 + 0.00127815i
\(263\) −12.1525 −0.749357 −0.374679 0.927155i \(-0.622247\pi\)
−0.374679 + 0.927155i \(0.622247\pi\)
\(264\) −2.33103 −0.143465
\(265\) −6.22489 + 6.22489i −0.382392 + 0.382392i
\(266\) 2.62361 + 10.3810i 0.160864 + 0.636498i
\(267\) 4.75044 4.75044i 0.290722 0.290722i
\(268\) 4.53921 4.53921i 0.277276 0.277276i
\(269\) 19.9482i 1.21626i −0.793836 0.608132i \(-0.791919\pi\)
0.793836 0.608132i \(-0.208081\pi\)
\(270\) 3.62760i 0.220768i
\(271\) −8.31432 8.31432i −0.505059 0.505059i 0.407947 0.913006i \(-0.366245\pi\)
−0.913006 + 0.407947i \(0.866245\pi\)
\(272\) 7.15945 0.434106
\(273\) −7.07505 6.39872i −0.428201 0.387268i
\(274\) 6.45602 0.390023
\(275\) 13.4491 + 13.4491i 0.811011 + 0.811011i
\(276\) 4.45602i 0.268221i
\(277\) 5.55696i 0.333885i 0.985967 + 0.166943i \(0.0533895\pi\)
−0.985967 + 0.166943i \(0.946611\pi\)
\(278\) −8.97117 + 8.97117i −0.538055 + 0.538055i
\(279\) −3.91681 + 3.91681i −0.234493 + 0.234493i
\(280\) −9.30514 + 2.35172i −0.556088 + 0.140542i
\(281\) −11.4807 + 11.4807i −0.684881 + 0.684881i −0.961096 0.276215i \(-0.910920\pi\)
0.276215 + 0.961096i \(0.410920\pi\)
\(282\) −0.994801 −0.0592395
\(283\) 6.44735 0.383255 0.191627 0.981468i \(-0.438623\pi\)
0.191627 + 0.981468i \(0.438623\pi\)
\(284\) 0.456023 0.456023i 0.0270600 0.0270600i
\(285\) −14.6809 −0.869622
\(286\) −4.66205 6.99308i −0.275673 0.413509i
\(287\) −24.2264 14.4513i −1.43004 0.853031i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 34.2578 2.01516
\(290\) 35.3785 2.07750
\(291\) 4.49220 + 4.49220i 0.263338 + 0.263338i
\(292\) −2.48191 + 2.48191i −0.145243 + 0.145243i
\(293\) −22.1703 22.1703i −1.29520 1.29520i −0.931525 0.363677i \(-0.881521\pi\)
−0.363677 0.931525i \(-0.618479\pi\)
\(294\) −2.00368 + 6.70711i −0.116857 + 0.391166i
\(295\) −53.6414 −3.12313
\(296\) 3.50995i 0.204012i
\(297\) −1.64828 1.64828i −0.0956432 0.0956432i
\(298\) 18.9534i 1.09794i
\(299\) −13.3681 + 8.91205i −0.773095 + 0.515397i
\(300\) 8.15945i 0.471086i
\(301\) 22.1173 5.58977i 1.27482 0.322189i
\(302\) 4.28230 0.246418
\(303\) 3.55696i 0.204342i
\(304\) 2.86167 2.86167i 0.164128 0.164128i
\(305\) −18.3647 18.3647i −1.05156 1.05156i
\(306\) 5.06250 + 5.06250i 0.289404 + 0.289404i
\(307\) 5.54613 + 5.54613i 0.316534 + 0.316534i 0.847434 0.530900i \(-0.178146\pi\)
−0.530900 + 0.847434i \(0.678146\pi\)
\(308\) −3.15945 + 5.29657i −0.180027 + 0.301800i
\(309\) 9.80437i 0.557751i
\(310\) −14.2086 + 14.2086i −0.806995 + 0.806995i
\(311\) −15.6648 −0.888270 −0.444135 0.895960i \(-0.646489\pi\)
−0.444135 + 0.895960i \(0.646489\pi\)
\(312\) −0.707107 + 3.53553i −0.0400320 + 0.200160i
\(313\) 2.58640i 0.146192i 0.997325 + 0.0730959i \(0.0232879\pi\)
−0.997325 + 0.0730959i \(0.976712\pi\)
\(314\) 8.07505 8.07505i 0.455701 0.455701i
\(315\) −8.24264 4.91681i −0.464420 0.277031i
\(316\) 12.0422i 0.677429i
\(317\) 5.33059 + 5.33059i 0.299396 + 0.299396i 0.840777 0.541381i \(-0.182098\pi\)
−0.541381 + 0.840777i \(0.682098\pi\)
\(318\) 1.71598 1.71598i 0.0962275 0.0962275i
\(319\) 16.0750 16.0750i 0.900030 0.900030i
\(320\) 2.56510 + 2.56510i 0.143393 + 0.143393i
\(321\) 0.332748i 0.0185722i
\(322\) 10.1250 + 6.03966i 0.564244 + 0.336577i
\(323\) 20.4880 20.4880i 1.13998 1.13998i
\(324\) 1.00000i 0.0555556i
\(325\) 24.4784 16.3189i 1.35782 0.905210i
\(326\) −12.8358 −0.710908
\(327\) −12.9672 + 12.9672i −0.717087 + 0.717087i
\(328\) 10.6621i 0.588713i
\(329\) −1.34834 + 2.26039i −0.0743367 + 0.124619i
\(330\) −5.97931 5.97931i −0.329150 0.329150i
\(331\) 17.3927 + 17.3927i 0.955991 + 0.955991i 0.999072 0.0430801i \(-0.0137171\pi\)
−0.0430801 + 0.999072i \(0.513717\pi\)
\(332\) 2.70343 + 2.70343i 0.148370 + 0.148370i
\(333\) −2.48191 + 2.48191i −0.136008 + 0.136008i
\(334\) 4.68888i 0.256564i
\(335\) 23.2870 1.27231
\(336\) 2.56510 0.648285i 0.139938 0.0353668i
\(337\) 9.75259i 0.531258i 0.964075 + 0.265629i \(0.0855795\pi\)
−0.964075 + 0.265629i \(0.914420\pi\)
\(338\) −12.0208 + 4.94975i −0.653846 + 0.269231i
\(339\) 12.6872i 0.689072i
\(340\) 18.3647 + 18.3647i 0.995966 + 0.995966i
\(341\) 12.9120i 0.699227i
\(342\) 4.04701 0.218837
\(343\) 12.5242 + 13.6435i 0.676241 + 0.736681i
\(344\) −6.09696 6.09696i −0.328726 0.328726i
\(345\) −11.4301 + 11.4301i −0.615378 + 0.615378i
\(346\) −4.28402 4.28402i −0.230310 0.230310i
\(347\) 2.38696 0.128139 0.0640693 0.997945i \(-0.479592\pi\)
0.0640693 + 0.997945i \(0.479592\pi\)
\(348\) −9.75259 −0.522794
\(349\) 1.27667 + 1.27667i 0.0683383 + 0.0683383i 0.740450 0.672112i \(-0.234612\pi\)
−0.672112 + 0.740450i \(0.734612\pi\)
\(350\) −18.5399 11.0593i −0.991002 0.591142i
\(351\) −3.00000 + 2.00000i −0.160128 + 0.106752i
\(352\) 2.33103 0.124244
\(353\) −16.3074 + 16.3074i −0.867955 + 0.867955i −0.992246 0.124291i \(-0.960335\pi\)
0.124291 + 0.992246i \(0.460335\pi\)
\(354\) 14.7870 0.785923
\(355\) 2.33949 0.124167
\(356\) −4.75044 + 4.75044i −0.251773 + 0.251773i
\(357\) 18.3647 4.64136i 0.971963 0.245647i
\(358\) −9.58622 + 9.58622i −0.506647 + 0.506647i
\(359\) 16.0130 16.0130i 0.845133 0.845133i −0.144388 0.989521i \(-0.546121\pi\)
0.989521 + 0.144388i \(0.0461214\pi\)
\(360\) 3.62760i 0.191191i
\(361\) 2.62172i 0.137985i
\(362\) −10.3091 10.3091i −0.541835 0.541835i
\(363\) 5.56631 0.292156
\(364\) 7.07505 + 6.39872i 0.370833 + 0.335384i
\(365\) −12.7327 −0.666459
\(366\) 5.06250 + 5.06250i 0.264621 + 0.264621i
\(367\) 2.42677i 0.126676i 0.997992 + 0.0633381i \(0.0201746\pi\)
−0.997992 + 0.0633381i \(0.979825\pi\)
\(368\) 4.45602i 0.232286i
\(369\) −7.53921 + 7.53921i −0.392476 + 0.392476i
\(370\) −9.00337 + 9.00337i −0.468063 + 0.468063i
\(371\) −1.57323 6.22489i −0.0816783 0.323180i
\(372\) 3.91681 3.91681i 0.203077 0.203077i
\(373\) −11.8759 −0.614909 −0.307455 0.951563i \(-0.599477\pi\)
−0.307455 + 0.951563i \(0.599477\pi\)
\(374\) 16.6889 0.862961
\(375\) 8.10431 8.10431i 0.418505 0.418505i
\(376\) 0.994801 0.0513029
\(377\) −19.5052 29.2578i −1.00457 1.50685i
\(378\) 2.27220 + 1.35539i 0.116870 + 0.0697138i
\(379\) 14.4021 + 14.4021i 0.739786 + 0.739786i 0.972536 0.232751i \(-0.0747726\pi\)
−0.232751 + 0.972536i \(0.574773\pi\)
\(380\) 14.6809 0.753115
\(381\) −5.94822 −0.304737
\(382\) −18.6561 18.6561i −0.954528 0.954528i
\(383\) 18.6121 18.6121i 0.951034 0.951034i −0.0478217 0.998856i \(-0.515228\pi\)
0.998856 + 0.0478217i \(0.0152279\pi\)
\(384\) −0.707107 0.707107i −0.0360844 0.0360844i
\(385\) −21.6905 + 5.48191i −1.10545 + 0.279384i
\(386\) 4.04873 0.206075
\(387\) 8.62240i 0.438301i
\(388\) −4.49220 4.49220i −0.228057 0.228057i
\(389\) 0.107858i 0.00546860i −0.999996 0.00273430i \(-0.999130\pi\)
0.999996 0.00273430i \(-0.000870356\pi\)
\(390\) −10.8828 + 7.25519i −0.551071 + 0.367381i
\(391\) 31.9027i 1.61339i
\(392\) 2.00368 6.70711i 0.101201 0.338760i
\(393\) 0.0292581 0.00147588
\(394\) 8.78705i 0.442685i
\(395\) −30.8895 + 30.8895i −1.55422 + 1.55422i
\(396\) 1.64828 + 1.64828i 0.0828294 + 0.0828294i
\(397\) 18.9320 + 18.9320i 0.950167 + 0.950167i 0.998816 0.0486486i \(-0.0154914\pi\)
−0.0486486 + 0.998816i \(0.515491\pi\)
\(398\) −1.15824 1.15824i −0.0580572 0.0580572i
\(399\) 5.48528 9.19563i 0.274608 0.460357i
\(400\) 8.15945i 0.407973i
\(401\) 1.33059 1.33059i 0.0664467 0.0664467i −0.673103 0.739549i \(-0.735039\pi\)
0.739549 + 0.673103i \(0.235039\pi\)
\(402\) −6.41941 −0.320171
\(403\) 19.5841 + 3.91681i 0.975552 + 0.195110i
\(404\) 3.55696i 0.176965i
\(405\) −2.56510 + 2.56510i −0.127461 + 0.127461i
\(406\) −13.2186 + 22.1599i −0.656027 + 1.09978i
\(407\) 8.18179i 0.405556i
\(408\) −5.06250 5.06250i −0.250631 0.250631i
\(409\) −21.6543 + 21.6543i −1.07074 + 1.07074i −0.0734389 + 0.997300i \(0.523397\pi\)
−0.997300 + 0.0734389i \(0.976603\pi\)
\(410\) −27.3492 + 27.3492i −1.35068 + 1.35068i
\(411\) −4.56510 4.56510i −0.225180 0.225180i
\(412\) 9.80437i 0.483027i
\(413\) 20.0422 33.5992i 0.986214 1.65331i
\(414\) 3.15088 3.15088i 0.154858 0.154858i
\(415\) 13.8691i 0.680809i
\(416\) 0.707107 3.53553i 0.0346688 0.173344i
\(417\) 12.6872 0.621293
\(418\) 6.67062 6.67062i 0.326271 0.326271i
\(419\) 3.41741i 0.166951i 0.996510 + 0.0834757i \(0.0266021\pi\)
−0.996510 + 0.0834757i \(0.973398\pi\)
\(420\) 8.24264 + 4.91681i 0.402200 + 0.239916i
\(421\) −1.36201 1.36201i −0.0663801 0.0663801i 0.673137 0.739517i \(-0.264946\pi\)
−0.739517 + 0.673137i \(0.764946\pi\)
\(422\) 0.440101 + 0.440101i 0.0214238 + 0.0214238i
\(423\) 0.703431 + 0.703431i 0.0342020 + 0.0342020i
\(424\) −1.71598 + 1.71598i −0.0833355 + 0.0833355i
\(425\) 58.4172i 2.83365i
\(426\) −0.644914 −0.0312462
\(427\) 18.3647 4.64136i 0.888730 0.224611i
\(428\) 0.332748i 0.0160840i
\(429\) −1.64828 + 8.24142i −0.0795799 + 0.397900i
\(430\) 31.2786i 1.50839i
\(431\) 11.1302 + 11.1302i 0.536123 + 0.536123i 0.922388 0.386265i \(-0.126235\pi\)
−0.386265 + 0.922388i \(0.626235\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −19.7843 −0.950772 −0.475386 0.879777i \(-0.657692\pi\)
−0.475386 + 0.879777i \(0.657692\pi\)
\(434\) −3.59099 14.2086i −0.172373 0.682035i
\(435\) −25.0164 25.0164i −1.19944 1.19944i
\(436\) 12.9672 12.9672i 0.621016 0.621016i
\(437\) −12.7517 12.7517i −0.609994 0.609994i
\(438\) 3.50995 0.167712
\(439\) 26.7749 1.27790 0.638949 0.769249i \(-0.279370\pi\)
0.638949 + 0.769249i \(0.279370\pi\)
\(440\) 5.97931 + 5.97931i 0.285052 + 0.285052i
\(441\) 6.15945 3.32583i 0.293307 0.158373i
\(442\) 5.06250 25.3125i 0.240798 1.20399i
\(443\) 28.3587 1.34736 0.673682 0.739022i \(-0.264712\pi\)
0.673682 + 0.739022i \(0.264712\pi\)
\(444\) 2.48191 2.48191i 0.117786 0.117786i
\(445\) −24.3707 −1.15528
\(446\) −22.0074 −1.04208
\(447\) 13.4021 13.4021i 0.633897 0.633897i
\(448\) −2.56510 + 0.648285i −0.121189 + 0.0306286i
\(449\) 2.28843 2.28843i 0.107998 0.107998i −0.651043 0.759041i \(-0.725668\pi\)
0.759041 + 0.651043i \(0.225668\pi\)
\(450\) −5.76961 + 5.76961i −0.271982 + 0.271982i
\(451\) 24.8535i 1.17031i
\(452\) 12.6872i 0.596754i
\(453\) −3.02804 3.02804i −0.142270 0.142270i
\(454\) 1.63972 0.0769556
\(455\) 1.73484 + 34.5615i 0.0813307 + 1.62027i
\(456\) −4.04701 −0.189519
\(457\) −5.68091 5.68091i −0.265742 0.265742i 0.561640 0.827382i \(-0.310171\pi\)
−0.827382 + 0.561640i \(0.810171\pi\)
\(458\) 5.88236i 0.274864i
\(459\) 7.15945i 0.334175i
\(460\) 11.4301 11.4301i 0.532933 0.532933i
\(461\) −15.6953 + 15.6953i −0.731003 + 0.731003i −0.970818 0.239816i \(-0.922913\pi\)
0.239816 + 0.970818i \(0.422913\pi\)
\(462\) 5.97931 1.51117i 0.278183 0.0703059i
\(463\) −11.2324 + 11.2324i −0.522012 + 0.522012i −0.918179 0.396167i \(-0.870340\pi\)
0.396167 + 0.918179i \(0.370340\pi\)
\(464\) 9.75259 0.452753
\(465\) 20.0940 0.931838
\(466\) 7.63495 7.63495i 0.353682 0.353682i
\(467\) 2.81997 0.130492 0.0652462 0.997869i \(-0.479217\pi\)
0.0652462 + 0.997869i \(0.479217\pi\)
\(468\) 3.00000 2.00000i 0.138675 0.0924500i
\(469\) −8.70082 + 14.5862i −0.401766 + 0.673529i
\(470\) 2.55176 + 2.55176i 0.117704 + 0.117704i
\(471\) −11.4198 −0.526199
\(472\) −14.7870 −0.680629
\(473\) −14.2122 14.2122i −0.653476 0.653476i
\(474\) 8.51515 8.51515i 0.391114 0.391114i
\(475\) 23.3496 + 23.3496i 1.07136 + 1.07136i
\(476\) −18.3647 + 4.64136i −0.841745 + 0.212737i
\(477\) −2.42677 −0.111114
\(478\) 22.8397i 1.04466i
\(479\) −23.0456 23.0456i −1.05298 1.05298i −0.998516 0.0544653i \(-0.982655\pi\)
−0.0544653 0.998516i \(-0.517345\pi\)
\(480\) 3.62760i 0.165576i
\(481\) 12.4096 + 2.48191i 0.565827 + 0.113165i
\(482\) 4.88755i 0.222622i
\(483\) −2.88877 11.4301i −0.131444 0.520089i
\(484\) −5.56631 −0.253014
\(485\) 23.0459i 1.04646i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) 26.3503 + 26.3503i 1.19405 + 1.19405i 0.975921 + 0.218126i \(0.0699945\pi\)
0.218126 + 0.975921i \(0.430005\pi\)
\(488\) −5.06250 5.06250i −0.229169 0.229169i
\(489\) 9.07627 + 9.07627i 0.410443 + 0.410443i
\(490\) 22.3440 12.0648i 1.00940 0.545030i
\(491\) 11.7819i 0.531707i 0.964013 + 0.265854i \(0.0856538\pi\)
−0.964013 + 0.265854i \(0.914346\pi\)
\(492\) 7.53921 7.53921i 0.339894 0.339894i
\(493\) 69.8232 3.14468
\(494\) −8.09402 12.1410i −0.364167 0.546251i
\(495\) 8.45602i 0.380070i
\(496\) −3.91681 + 3.91681i −0.175870 + 0.175870i
\(497\) −0.874111 + 1.46538i −0.0392093 + 0.0657312i
\(498\) 3.82323i 0.171323i
\(499\) −25.6014 25.6014i −1.14607 1.14607i −0.987318 0.158756i \(-0.949252\pi\)
−0.158756 0.987318i \(-0.550748\pi\)
\(500\) −8.10431 + 8.10431i −0.362436 + 0.362436i
\(501\) 3.31554 3.31554i 0.148127 0.148127i
\(502\) −3.98971 3.98971i −0.178069 0.178069i
\(503\) 12.0000i 0.535054i −0.963550 0.267527i \(-0.913794\pi\)
0.963550 0.267527i \(-0.0862064\pi\)
\(504\) −2.27220 1.35539i −0.101212 0.0603739i
\(505\) −9.12395 + 9.12395i −0.406011 + 0.406011i
\(506\) 10.3871i 0.461763i
\(507\) 12.0000 + 5.00000i 0.532939 + 0.222058i
\(508\) 5.94822 0.263910
\(509\) −24.4927 + 24.4927i −1.08562 + 1.08562i −0.0896482 + 0.995973i \(0.528574\pi\)
−0.995973 + 0.0896482i \(0.971426\pi\)
\(510\) 25.9716i 1.15004i
\(511\) 4.75736 7.97533i 0.210453 0.352808i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −2.86167 2.86167i −0.126346 0.126346i
\(514\) 17.6917 + 17.6917i 0.780349 + 0.780349i
\(515\) 25.1492 25.1492i 1.10820 1.10820i
\(516\) 8.62240i 0.379580i
\(517\) 2.31891 0.101985
\(518\) −2.27545 9.00337i −0.0999775 0.395585i
\(519\) 6.05852i 0.265939i
\(520\) 10.8828 7.25519i 0.477242 0.318161i
\(521\) 24.7188i 1.08295i 0.840716 + 0.541476i \(0.182134\pi\)
−0.840716 + 0.541476i \(0.817866\pi\)
\(522\) 6.89612 + 6.89612i 0.301835 + 0.301835i
\(523\) 8.22489i 0.359649i −0.983699 0.179825i \(-0.942447\pi\)
0.983699 0.179825i \(-0.0575530\pi\)
\(524\) −0.0292581 −0.00127815
\(525\) 5.28965 + 20.9298i 0.230859 + 0.913451i
\(526\) −8.59314 8.59314i −0.374679 0.374679i
\(527\) −28.0422 + 28.0422i −1.22154 + 1.22154i
\(528\) −1.64828 1.64828i −0.0717324 0.0717324i
\(529\) 3.14386 0.136689
\(530\) −8.80332 −0.382392
\(531\) −10.4560 10.4560i −0.453753 0.453753i
\(532\) −5.48528 + 9.19563i −0.237817 + 0.398681i
\(533\) 37.6961 + 7.53921i 1.63280 + 0.326559i
\(534\) 6.71814 0.290722
\(535\) 0.853530 0.853530i 0.0369013 0.0369013i
\(536\) 6.41941 0.277276
\(537\) 13.5570 0.585026
\(538\) 14.1055 14.1055i 0.608132 0.608132i
\(539\) 4.67062 15.6344i 0.201178 0.673423i
\(540\) 2.56510 2.56510i 0.110384 0.110384i
\(541\) 15.1691 15.1691i 0.652169 0.652169i −0.301346 0.953515i \(-0.597436\pi\)
0.953515 + 0.301346i \(0.0974358\pi\)
\(542\) 11.7582i 0.505059i
\(543\) 14.5793i 0.625658i
\(544\) 5.06250 + 5.06250i 0.217053 + 0.217053i
\(545\) 66.5242 2.84959
\(546\) −0.478235 9.52740i −0.0204666 0.407735i
\(547\) −15.2261 −0.651020 −0.325510 0.945539i \(-0.605536\pi\)
−0.325510 + 0.945539i \(0.605536\pi\)
\(548\) 4.56510 + 4.56510i 0.195011 + 0.195011i
\(549\) 7.15945i 0.305558i
\(550\) 19.0199i 0.811011i
\(551\) 27.9087 27.9087i 1.18895 1.18895i
\(552\) −3.15088 + 3.15088i −0.134111 + 0.134111i
\(553\) −7.80680 30.8895i −0.331979 1.31356i
\(554\) −3.92936 + 3.92936i −0.166943 + 0.166943i
\(555\) 12.7327 0.540473
\(556\) −12.6872 −0.538055
\(557\) 24.0893 24.0893i 1.02069 1.02069i 0.0209130 0.999781i \(-0.493343\pi\)
0.999781 0.0209130i \(-0.00665731\pi\)
\(558\) −5.53921 −0.234493
\(559\) −25.8672 + 17.2448i −1.09407 + 0.729377i
\(560\) −8.24264 4.91681i −0.348315 0.207773i
\(561\) −11.8008 11.8008i −0.498231 0.498231i
\(562\) −16.2362 −0.684881
\(563\) 31.8346 1.34167 0.670835 0.741607i \(-0.265936\pi\)
0.670835 + 0.741607i \(0.265936\pi\)
\(564\) −0.703431 0.703431i −0.0296198 0.0296198i
\(565\) 32.5438 32.5438i 1.36913 1.36913i
\(566\) 4.55896 + 4.55896i 0.191627 + 0.191627i
\(567\) −0.648285 2.56510i −0.0272254 0.107724i
\(568\) 0.644914 0.0270600
\(569\) 15.2218i 0.638130i 0.947733 + 0.319065i \(0.103369\pi\)
−0.947733 + 0.319065i \(0.896631\pi\)
\(570\) −10.3810 10.3810i −0.434811 0.434811i
\(571\) 2.53462i 0.106071i 0.998593 + 0.0530353i \(0.0168896\pi\)
−0.998593 + 0.0530353i \(0.983110\pi\)
\(572\) 1.64828 8.24142i 0.0689182 0.344591i
\(573\) 26.3837i 1.10219i
\(574\) −6.91205 27.3492i −0.288503 1.14153i
\(575\) 36.3587 1.51626
\(576\) 1.00000i 0.0416667i
\(577\) 14.6380 14.6380i 0.609388 0.609388i −0.333398 0.942786i \(-0.608195\pi\)
0.942786 + 0.333398i \(0.108195\pi\)
\(578\) 24.2239 + 24.2239i 1.00758 + 1.00758i
\(579\) −2.86288 2.86288i −0.118977 0.118977i
\(580\) 25.0164 + 25.0164i 1.03875 + 1.03875i
\(581\) −8.68716 5.18197i −0.360404 0.214984i
\(582\) 6.35293i 0.263338i
\(583\) −4.00000 + 4.00000i −0.165663 + 0.165663i
\(584\) −3.50995 −0.145243
\(585\) 12.8255 + 2.56510i 0.530269 + 0.106054i
\(586\) 31.3535i 1.29520i
\(587\) 21.2017 21.2017i 0.875088 0.875088i −0.117934 0.993021i \(-0.537627\pi\)
0.993021 + 0.117934i \(0.0376271\pi\)
\(588\) −6.15945 + 3.32583i −0.254012 + 0.137155i
\(589\) 22.4172i 0.923686i
\(590\) −37.9302 37.9302i −1.56156 1.56156i
\(591\) −6.21338 + 6.21338i −0.255584 + 0.255584i
\(592\) −2.48191 + 2.48191i −0.102006 + 0.102006i
\(593\) −13.9952 13.9952i −0.574715 0.574715i 0.358727 0.933442i \(-0.383211\pi\)
−0.933442 + 0.358727i \(0.883211\pi\)
\(594\) 2.33103i 0.0956432i
\(595\) −59.0128 35.2017i −2.41929 1.44313i
\(596\) −13.4021 + 13.4021i −0.548971 + 0.548971i
\(597\) 1.63799i 0.0670386i
\(598\) −15.7544 3.15088i −0.644246 0.128849i
\(599\) 26.4603 1.08114 0.540570 0.841299i \(-0.318209\pi\)
0.540570 + 0.841299i \(0.318209\pi\)
\(600\) 5.76961 5.76961i 0.235543 0.235543i
\(601\) 8.65166i 0.352908i −0.984309 0.176454i \(-0.943537\pi\)
0.984309 0.176454i \(-0.0564627\pi\)
\(602\) 19.5919 + 11.6867i 0.798504 + 0.476315i
\(603\) 4.53921 + 4.53921i 0.184851 + 0.184851i
\(604\) 3.02804 + 3.02804i 0.123209 + 0.123209i
\(605\) −14.2781 14.2781i −0.580489 0.580489i
\(606\) 2.51515 2.51515i 0.102171 0.102171i
\(607\) 2.46556i 0.100074i 0.998747 + 0.0500369i \(0.0159339\pi\)
−0.998747 + 0.0500369i \(0.984066\pi\)
\(608\) 4.04701 0.164128
\(609\) 25.0164 6.32246i 1.01371 0.256199i
\(610\) 25.9716i 1.05156i
\(611\) 0.703431 3.51715i 0.0284578 0.142289i
\(612\) 7.15945i 0.289404i
\(613\) −6.36488 6.36488i −0.257075 0.257075i 0.566788 0.823863i \(-0.308186\pi\)
−0.823863 + 0.566788i \(0.808186\pi\)
\(614\) 7.84341i 0.316534i
\(615\) 38.6776 1.55963
\(616\) −5.97931 + 1.51117i −0.240913 + 0.0608867i
\(617\) −21.1065 21.1065i −0.849714 0.849714i 0.140383 0.990097i \(-0.455167\pi\)
−0.990097 + 0.140383i \(0.955167\pi\)
\(618\) −6.93274 + 6.93274i −0.278876 + 0.278876i
\(619\) 20.3108 + 20.3108i 0.816359 + 0.816359i 0.985578 0.169220i \(-0.0541247\pi\)
−0.169220 + 0.985578i \(0.554125\pi\)
\(620\) −20.0940 −0.806995
\(621\) −4.45602 −0.178814
\(622\) −11.0767 11.0767i −0.444135 0.444135i
\(623\) 9.10570 15.2650i 0.364812 0.611578i
\(624\) −3.00000 + 2.00000i −0.120096 + 0.0800641i
\(625\) −0.779417 −0.0311767
\(626\) −1.82886 + 1.82886i −0.0730959 + 0.0730959i
\(627\) −9.43369 −0.376745
\(628\) 11.4198 0.455701
\(629\) −17.7691 + 17.7691i −0.708501 + 0.708501i
\(630\) −2.35172 9.30514i −0.0936946 0.370726i
\(631\) −10.3788 + 10.3788i −0.413174 + 0.413174i −0.882843 0.469669i \(-0.844373\pi\)
0.469669 + 0.882843i \(0.344373\pi\)
\(632\) −8.51515 + 8.51515i −0.338715 + 0.338715i
\(633\) 0.622397i 0.0247381i
\(634\) 7.53860i 0.299396i
\(635\) 15.2578 + 15.2578i 0.605486 + 0.605486i
\(636\) 2.42677 0.0962275
\(637\) −22.2964 11.8267i −0.883415 0.468591i
\(638\) 22.7336 0.900030
\(639\) 0.456023 + 0.456023i 0.0180400 + 0.0180400i
\(640\) 3.62760i 0.143393i
\(641\) 0.168808i 0.00666750i 0.999994 + 0.00333375i \(0.00106117\pi\)
−0.999994 + 0.00333375i \(0.998939\pi\)
\(642\) −0.235288 + 0.235288i −0.00928608 + 0.00928608i
\(643\) −23.4995 + 23.4995i −0.926729 + 0.926729i −0.997493 0.0707640i \(-0.977456\pi\)
0.0707640 + 0.997493i \(0.477456\pi\)
\(644\) 2.88877 + 11.4301i 0.113834 + 0.450410i
\(645\) −22.1173 + 22.1173i −0.870868 + 0.870868i
\(646\) 28.9744 1.13998
\(647\) −7.68783 −0.302240 −0.151120 0.988515i \(-0.548288\pi\)
−0.151120 + 0.988515i \(0.548288\pi\)
\(648\) −0.707107 + 0.707107i −0.0277778 + 0.0277778i
\(649\) −34.4690 −1.35303
\(650\) 28.8480 + 5.76961i 1.13151 + 0.226303i
\(651\) −7.50780 + 12.5862i −0.294254 + 0.493293i
\(652\) −9.07627 9.07627i −0.355454 0.355454i
\(653\) 15.9545 0.624347 0.312173 0.950025i \(-0.398943\pi\)
0.312173 + 0.950025i \(0.398943\pi\)
\(654\) −18.3384 −0.717087
\(655\) −0.0750499 0.0750499i −0.00293244 0.00293244i
\(656\) −7.53921 + 7.53921i −0.294357 + 0.294357i
\(657\) −2.48191 2.48191i −0.0968286 0.0968286i
\(658\) −2.55176 + 0.644914i −0.0994780 + 0.0251414i
\(659\) −24.5438 −0.956091 −0.478045 0.878335i \(-0.658655\pi\)
−0.478045 + 0.878335i \(0.658655\pi\)
\(660\) 8.45602i 0.329150i
\(661\) −3.34817 3.34817i −0.130229 0.130229i 0.638988 0.769217i \(-0.279353\pi\)
−0.769217 + 0.638988i \(0.779353\pi\)
\(662\) 24.5970i 0.955991i
\(663\) −21.4784 + 14.3189i −0.834150 + 0.556100i
\(664\) 3.82323i 0.148370i
\(665\) −37.6580 + 9.51741i −1.46031 + 0.369069i
\(666\) −3.50995 −0.136008
\(667\) 43.4578i 1.68269i
\(668\) −3.31554 + 3.31554i −0.128282 + 0.128282i
\(669\) 15.5615 + 15.5615i 0.601644 + 0.601644i
\(670\) 16.4664 + 16.4664i 0.636153 + 0.636153i
\(671\) −11.8008 11.8008i −0.455566 0.455566i
\(672\) 2.27220 + 1.35539i 0.0876522 + 0.0522854i
\(673\) 11.5369i 0.444714i −0.974965 0.222357i \(-0.928625\pi\)
0.974965 0.222357i \(-0.0713750\pi\)
\(674\) −6.89612 + 6.89612i −0.265629 + 0.265629i
\(675\) 8.15945 0.314058
\(676\) −12.0000 5.00000i −0.461538 0.192308i
\(677\) 12.8958i 0.495625i −0.968808 0.247812i \(-0.920288\pi\)
0.968808 0.247812i \(-0.0797117\pi\)
\(678\) −8.97117 + 8.97117i −0.344536 + 0.344536i
\(679\) 14.4352 + 8.61071i 0.553971 + 0.330449i
\(680\) 25.9716i 0.995966i
\(681\) −1.15945 1.15945i −0.0444304 0.0444304i
\(682\) −9.13020 + 9.13020i −0.349613 + 0.349613i
\(683\) 14.7785 14.7785i 0.565483 0.565483i −0.365377 0.930860i \(-0.619060\pi\)
0.930860 + 0.365377i \(0.119060\pi\)
\(684\) 2.86167 + 2.86167i 0.109419 + 0.109419i
\(685\) 23.4198i 0.894826i
\(686\) −0.791511 + 18.5033i −0.0302200 + 0.706461i
\(687\) 4.15945 4.15945i 0.158693 0.158693i
\(688\) 8.62240i 0.328726i
\(689\) 4.85353 + 7.28030i 0.184905 + 0.277357i
\(690\) −16.1647 −0.615378
\(691\) 13.4220 13.4220i 0.510597 0.510597i −0.404112 0.914709i \(-0.632420\pi\)
0.914709 + 0.404112i \(0.132420\pi\)
\(692\) 6.05852i 0.230310i
\(693\) −5.29657 3.15945i −0.201200 0.120018i
\(694\) 1.68783 + 1.68783i 0.0640693 + 0.0640693i
\(695\) −32.5438 32.5438i −1.23446 1.23446i
\(696\) −6.89612 6.89612i −0.261397 0.261397i
\(697\) −53.9766 + 53.9766i −2.04451 + 2.04451i
\(698\) 1.80548i 0.0683383i
\(699\) −10.7974 −0.408397
\(700\) −5.28965 20.9298i −0.199930 0.791072i
\(701\) 19.5009i 0.736538i −0.929719 0.368269i \(-0.879951\pi\)
0.929719 0.368269i \(-0.120049\pi\)
\(702\) −3.53553 0.707107i −0.133440 0.0266880i
\(703\) 14.2048i 0.535744i
\(704\) 1.64828 + 1.64828i 0.0621221 + 0.0621221i
\(705\) 3.60874i 0.135913i
\(706\) −23.0621 −0.867955
\(707\) −2.30592 9.12395i −0.0867232 0.343142i
\(708\) 10.4560 + 10.4560i 0.392961 + 0.392961i
\(709\) 36.2084 36.2084i 1.35984 1.35984i 0.485724 0.874112i \(-0.338556\pi\)
0.874112 0.485724i \(-0.161444\pi\)
\(710\) 1.65427 + 1.65427i 0.0620836 + 0.0620836i
\(711\) −12.0422 −0.451619
\(712\) −6.71814 −0.251773
\(713\) 17.4534 + 17.4534i 0.653635 + 0.653635i
\(714\) 16.2677 + 9.70386i 0.608805 + 0.363158i
\(715\) 25.3681 16.9120i 0.948712 0.632475i
\(716\) −13.5570 −0.506647
\(717\) 16.1501 16.1501i 0.603137 0.603137i
\(718\) 22.6458 0.845133
\(719\) 31.8404 1.18745 0.593723 0.804670i \(-0.297658\pi\)
0.593723 + 0.804670i \(0.297658\pi\)
\(720\) −2.56510 + 2.56510i −0.0955956 + 0.0955956i
\(721\) 6.35602 + 25.1492i 0.236711 + 0.936604i
\(722\) −1.85384 + 1.85384i −0.0689926 + 0.0689926i
\(723\) 3.45602 3.45602i 0.128531 0.128531i
\(724\) 14.5793i 0.541835i
\(725\) 79.5758i 2.95537i
\(726\) 3.93598 + 3.93598i 0.146078 + 0.146078i
\(727\) 0.263681 0.00977940 0.00488970 0.999988i \(-0.498444\pi\)
0.00488970 + 0.999988i \(0.498444\pi\)
\(728\) 0.478235 + 9.52740i 0.0177246 + 0.353109i
\(729\) −1.00000 −0.0370370
\(730\) −9.00337 9.00337i −0.333230 0.333230i
\(731\) 61.7317i 2.28323i
\(732\) 7.15945i 0.264621i
\(733\) 14.4266 14.4266i 0.532858 0.532858i −0.388564 0.921422i \(-0.627029\pi\)
0.921422 + 0.388564i \(0.127029\pi\)
\(734\) −1.71598 + 1.71598i −0.0633381 + 0.0633381i
\(735\) −24.3307 7.26853i −0.897450 0.268104i
\(736\) 3.15088 3.15088i 0.116143 0.116143i
\(737\) 14.9638 0.551199
\(738\) −10.6621 −0.392476
\(739\) 6.59099 6.59099i 0.242453 0.242453i −0.575411 0.817864i \(-0.695158\pi\)
0.817864 + 0.575411i \(0.195158\pi\)
\(740\) −12.7327 −0.468063
\(741\) −2.86167 + 14.3083i −0.105126 + 0.525630i
\(742\) 3.28922 5.51411i 0.120751 0.202429i
\(743\) 18.2311 + 18.2311i 0.668835 + 0.668835i 0.957446 0.288611i \(-0.0931934\pi\)
−0.288611 + 0.957446i \(0.593193\pi\)
\(744\) 5.53921 0.203077
\(745\) −68.7554 −2.51900
\(746\) −8.39751 8.39751i −0.307455 0.307455i
\(747\) −2.70343 + 2.70343i −0.0989133 + 0.0989133i
\(748\) 11.8008 + 11.8008i 0.431481 + 0.431481i
\(749\) 0.215715 + 0.853530i 0.00788206 + 0.0311873i
\(750\) 11.4612 0.418505
\(751\) 17.5282i 0.639613i 0.947483 + 0.319807i \(0.103618\pi\)
−0.947483 + 0.319807i \(0.896382\pi\)
\(752\) 0.703431 + 0.703431i 0.0256515 + 0.0256515i
\(753\) 5.64230i 0.205617i
\(754\) 6.89612 34.4806i 0.251142 1.25571i
\(755\) 15.5344i 0.565356i
\(756\) 0.648285 + 2.56510i 0.0235779 + 0.0932917i
\(757\) 31.7843 1.15522 0.577610 0.816313i \(-0.303986\pi\)
0.577610 + 0.816313i \(0.303986\pi\)
\(758\) 20.3676i 0.739786i
\(759\) −7.34480 + 7.34480i −0.266599 + 0.266599i
\(760\) 10.3810 + 10.3810i 0.376557 + 0.376557i
\(761\) −1.82886 1.82886i −0.0662961 0.0662961i 0.673181 0.739477i \(-0.264927\pi\)
−0.739477 + 0.673181i \(0.764927\pi\)
\(762\) −4.20603 4.20603i −0.152368 0.152368i
\(763\) −24.8557 + 41.6685i −0.899836 + 1.50850i
\(764\) 26.3837i 0.954528i
\(765\) −18.3647 + 18.3647i −0.663977 + 0.663977i
\(766\) 26.3215 0.951034
\(767\) −10.4560 + 52.2801i −0.377545 + 1.88773i
\(768\) 1.00000i 0.0360844i
\(769\) 1.20162 1.20162i 0.0433314 0.0433314i −0.685109 0.728440i \(-0.740245\pi\)
0.728440 + 0.685109i \(0.240245\pi\)
\(770\) −19.2138 11.4612i −0.692418 0.413034i
\(771\) 25.0199i 0.901070i
\(772\) 2.86288 + 2.86288i 0.103037 + 0.103037i
\(773\) 2.61687 2.61687i 0.0941224 0.0941224i −0.658478 0.752600i \(-0.728799\pi\)
0.752600 + 0.658478i \(0.228799\pi\)
\(774\) 6.09696 6.09696i 0.219151 0.219151i
\(775\) −31.9591 31.9591i −1.14800 1.14800i
\(776\) 6.35293i 0.228057i
\(777\) −4.75736 + 7.97533i −0.170669 + 0.286113i
\(778\) 0.0762669 0.0762669i 0.00273430 0.00273430i