Properties

Label 546.2.o.d.307.4
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 307.4
Root \(-0.916813i\) of defining polynomial
Character \(\chi\) \(=\) 546.307
Dual form 546.2.o.d.265.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{3} +1.00000i q^{4} +(2.56510 - 2.56510i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.56510 + 0.648285i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(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} +(2.56510 + 0.648285i) 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} +(-0.648285 + 2.56510i) 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} +(-0.648285 + 2.56510i) 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} +(-2.56510 - 0.648285i) 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} +(9.30514 + 2.35172i) 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} +(-2.56510 - 0.648285i) 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} +(-3.18534 - 8.99186i) 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} +(2.00368 + 6.70711i) q^{98} +(1.64828 - 1.64828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{5} + 4q^{7} - 8q^{9} + O(q^{10}) \) \( 8q + 4q^{5} + 4q^{7} - 8q^{9} - 4q^{10} - 8q^{11} - 8q^{12} - 16q^{13} + 4q^{15} - 8q^{16} + 12q^{17} - 4q^{19} + 4q^{20} + 4q^{22} - 12q^{29} - 20q^{31} - 8q^{33} + 24q^{34} + 32q^{35} - 8q^{37} - 12q^{38} + 24q^{39} - 16q^{41} + 4q^{42} - 8q^{44} - 4q^{45} - 20q^{46} + 16q^{47} + 4q^{49} + 24q^{50} + 24q^{52} - 24q^{53} + 4q^{56} - 4q^{57} - 16q^{58} - 28q^{59} - 4q^{60} - 4q^{63} - 20q^{65} + 8q^{67} + 20q^{69} + 24q^{70} + 52q^{71} + 8q^{73} - 4q^{74} + 20q^{75} - 4q^{76} - 32q^{77} - 48q^{79} - 4q^{80} + 8q^{81} - 40q^{82} - 32q^{83} - 4q^{84} + 20q^{85} - 20q^{86} - 4q^{89} + 4q^{90} - 8q^{91} + 20q^{92} - 20q^{93} + 36q^{97} + 8q^{99} + O(q^{100}) \)

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 \(-0.448839\pi\)
0.987111 0.160035i \(-0.0511608\pi\)
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) 2.56510 + 0.648285i 0.969516 + 0.245029i
\(8\) −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 \(-0.165270\pi\)
0.868211 + 0.496195i \(0.165270\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) 2.86167 2.86167i 0.656512 0.656512i −0.298041 0.954553i \(-0.596333\pi\)
0.954553 + 0.298041i \(0.0963334\pi\)
\(20\) 2.56510 + 2.56510i 0.573573 + 0.573573i
\(21\) −0.648285 + 2.56510i −0.141467 + 0.559750i
\(22\) −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
\(28\) −0.648285 + 2.56510i −0.122514 + 0.484758i
\(29\) −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 −0.965156 0.261676i \(-0.915725\pi\)
0.261676 + 0.965156i \(0.415725\pi\)
\(32\) −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 \(0.563129\pi\)
−0.980398 + 0.197029i \(0.936871\pi\)
\(42\) −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 0.756546 0.653940i \(-0.226885\pi\)
−0.653940 + 0.756546i \(0.726885\pi\)
\(48\) 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 \(-0.837383\pi\)
−0.488942 0.872316i \(-0.662617\pi\)
\(60\) −2.56510 + 2.56510i −0.331153 + 0.331153i
\(61\) 7.15945i 0.916674i −0.888778 0.458337i \(-0.848445\pi\)
0.888778 0.458337i \(-0.151555\pi\)
\(62\) −5.53921 −0.703480
\(63\) −2.56510 0.648285i −0.323172 0.0816762i
\(64\) 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
\(70\) 9.30514 + 2.35172i 1.11218 + 0.281084i
\(71\) −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 0.546786 0.837272i \(-0.315851\pi\)
−0.837272 + 0.546786i \(0.815851\pi\)
\(74\) 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 −0.839736 0.542996i \(-0.817290\pi\)
0.542996 + 0.839736i \(0.317290\pi\)
\(84\) −2.56510 0.648285i −0.279875 0.0707337i
\(85\) 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 0.408992 0.912538i \(-0.365880\pi\)
−0.912538 + 0.408992i \(0.865880\pi\)
\(90\) −3.62760 −0.382382
\(91\) −3.18534 8.99186i −0.333915 0.942603i
\(92\) −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 −0.441264 0.897378i \(-0.645470\pi\)
0.897378 + 0.441264i \(0.145470\pi\)
\(98\) 2.00368 + 6.70711i 0.202402 + 0.677520i
\(99\) 1.64828 1.64828i 0.165659 0.165659i
\(100\) 8.15945 0.815945
\(101\) −3.55696 −0.353931 −0.176965 0.984217i \(-0.556628\pi\)
−0.176965 + 0.984217i \(0.556628\pi\)
\(102\) −5.06250 + 5.06250i −0.501262 + 0.501262i
\(103\) 9.80437 0.966053 0.483027 0.875606i \(-0.339537\pi\)
0.483027 + 0.875606i \(0.339537\pi\)
\(104\) 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
\(112\) −2.56510 0.648285i −0.242379 0.0612572i
\(113\) −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
\(119\) 18.3647 + 4.64136i 1.68349 + 0.425473i
\(120\) −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 \(-0.999593\pi\)
0.999999 0.00127815i \(-0.000406847\pi\)
\(132\) 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 \(-0.819159\pi\)
0.842910 0.538055i \(-0.180841\pi\)
\(140\) 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
\(154\) −5.97931 1.51117i −0.481827 0.121773i
\(155\) 20.0940i 1.61399i
\(156\) 2.00000 + 3.00000i 0.160128 + 0.240192i
\(157\) 11.4198i 0.911403i 0.890133 + 0.455701i \(0.150612\pi\)
−0.890133 + 0.455701i \(0.849388\pi\)
\(158\) 8.51515 + 8.51515i 0.677429 + 0.677429i
\(159\) 2.42677i 0.192455i
\(160\) −3.62760 −0.286787
\(161\) −2.88877 + 11.4301i −0.227667 + 0.900821i
\(162\) 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 0.567091 0.823655i \(-0.308069\pi\)
−0.823655 + 0.567091i \(0.808069\pi\)
\(168\) −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 \(-0.426026\pi\)
0.230310 + 0.973117i \(0.426026\pi\)
\(174\) 6.89612 6.89612i 0.522794 0.522794i
\(175\) 5.28965 20.9298i 0.399860 1.58214i
\(176\) 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 \(-0.317730\pi\)
0.541835 + 0.840485i \(0.317730\pi\)
\(182\) 4.10583 8.61058i 0.304344 0.638259i
\(183\) 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
\(189\) 0.648285 2.56510i 0.0471558 0.186583i
\(190\) 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 \(-0.481509\pi\)
0.0580572 + 0.998313i \(0.481509\pi\)
\(200\) 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
\(203\) −25.0164 6.32246i −1.75580 0.443749i
\(204\) −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
\(210\) −2.35172 + 9.30514i −0.162284 + 0.642116i
\(211\) 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 \(-0.486307\pi\)
0.999075 0.0430034i \(-0.0136926\pi\)
\(224\) −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 −0.744537 0.667581i \(-0.767330\pi\)
0.667581 + 0.744537i \(0.267330\pi\)
\(228\) −2.86167 + 2.86167i −0.189519 + 0.189519i
\(229\) −4.15945 4.15945i −0.274864 0.274864i 0.556190 0.831055i \(-0.312263\pi\)
−0.831055 + 0.556190i \(0.812263\pi\)
\(230\) 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 0.586980 0.809602i \(-0.300317\pi\)
−0.809602 + 0.586980i \(0.800317\pi\)
\(242\) −3.93598 + 3.93598i −0.253014 + 0.253014i
\(243\) 1.00000i 0.0641500i
\(244\) 7.15945 0.458337
\(245\) 24.3307 7.26853i 1.55443 0.464369i
\(246\) 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 \(-0.443015\pi\)
0.178069 + 0.984018i \(0.443015\pi\)
\(252\) 0.648285 2.56510i 0.0408381 0.161586i
\(253\) −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 \(-0.784959\pi\)
−0.780349 + 0.625344i \(0.784959\pi\)
\(258\) −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
\(266\) 10.3810 + 2.62361i 0.636498 + 0.160864i
\(267\) 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 \(0.208081\pi\)
−0.793836 + 0.608132i \(0.791919\pi\)
\(270\) 3.62760i 0.220768i
\(271\) 8.31432 + 8.31432i 0.505059 + 0.505059i 0.913006 0.407947i \(-0.133755\pi\)
−0.407947 + 0.913006i \(0.633755\pi\)
\(272\) −7.15945 −0.434106
\(273\) 8.99186 3.18534i 0.544212 0.192786i
\(274\) 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
\(280\) −2.35172 + 9.30514i −0.140542 + 0.556088i
\(281\) −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 \(-0.561377\pi\)
−0.191627 + 0.981468i \(0.561377\pi\)
\(284\) 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 \(0.118479\pi\)
0.363677 + 0.931525i \(0.381521\pi\)
\(294\) −6.70711 + 2.00368i −0.391166 + 0.116857i
\(295\) −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
\(301\) −5.58977 + 22.1173i −0.322189 + 1.27482i
\(302\) 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 0.530900 0.847434i \(-0.321854\pi\)
−0.847434 + 0.530900i \(0.821854\pi\)
\(308\) −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 \(-0.353511\pi\)
0.444135 + 0.895960i \(0.353511\pi\)
\(312\) −0.707107 + 3.53553i −0.0400320 + 0.200160i
\(313\) 2.58640i 0.146192i −0.997325 0.0730959i \(-0.976712\pi\)
0.997325 0.0730959i \(-0.0232879\pi\)
\(314\) −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
\(336\) 0.648285 2.56510i 0.0353668 0.139938i
\(337\) 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
\(343\) 13.6435 + 12.5242i 0.736681 + 0.676241i
\(344\) −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 0.672112 0.740450i \(-0.265388\pi\)
−0.740450 + 0.672112i \(0.765388\pi\)
\(350\) 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 −0.124291 0.992246i \(-0.539665\pi\)
0.992246 + 0.124291i \(0.0396655\pi\)
\(354\) 14.7870 0.785923
\(355\) −2.33949 −0.124167
\(356\) 4.75044 4.75044i 0.251773 0.251773i
\(357\) −4.64136 + 18.3647i −0.245647 + 0.971963i
\(358\) −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
\(364\) 8.99186 3.18534i 0.471302 0.166957i
\(365\) −12.7327 −0.666459
\(366\) 5.06250 + 5.06250i 0.264621 + 0.264621i
\(367\) 2.42677i 0.126676i −0.997992 0.0633381i \(-0.979825\pi\)
0.997992 0.0633381i \(-0.0201746\pi\)
\(368\) 4.45602i 0.232286i
\(369\) 7.53921 7.53921i 0.392476 0.392476i
\(370\) 9.00337 9.00337i 0.468063 0.468063i
\(371\) 6.22489 + 1.57323i 0.323180 + 0.0816783i
\(372\) 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 −0.998856 0.0478217i \(-0.984772\pi\)
0.0478217 + 0.998856i \(0.484772\pi\)
\(384\) 0.707107 + 0.707107i 0.0360844 + 0.0360844i
\(385\) −5.48191 + 21.6905i −0.279384 + 1.10545i
\(386\) 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
\(392\) −6.70711 + 2.00368i −0.338760 + 0.101201i
\(393\) 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 0.0486486 0.998816i \(-0.484509\pi\)
−0.998816 + 0.0486486i \(0.984509\pi\)
\(398\) 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 \(-0.476603\pi\)
0.997300 0.0734389i \(-0.0233974\pi\)
\(410\) −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 \(-0.973398\pi\)
0.996510 0.0834757i \(-0.0266021\pi\)
\(420\) −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
\(427\) 4.64136 18.3647i 0.224611 0.888730i
\(428\) 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 \(-0.342308\pi\)
0.475386 + 0.879777i \(0.342308\pi\)
\(434\) −14.2086 3.59099i −0.682035 0.172373i
\(435\) −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 \(-0.720630\pi\)
−0.638949 + 0.769249i \(0.720630\pi\)
\(440\) −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
\(448\) 0.648285 2.56510i 0.0306286 0.121189i
\(449\) 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
\(455\) −31.2357 14.8943i −1.46435 0.698255i
\(456\) −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 −0.239816 0.970818i \(-0.577087\pi\)
0.970818 + 0.239816i \(0.0770870\pi\)
\(462\) 1.51117 5.97931i 0.0703059 0.278183i
\(463\) −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 \(-0.520783\pi\)
−0.0652462 + 0.997869i \(0.520783\pi\)
\(468\) −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
\(476\) −4.64136 + 18.3647i −0.212737 + 0.841745i
\(477\) −2.42677 −0.111114
\(478\) 22.8397i 1.04466i
\(479\) 23.0456 + 23.0456i 1.05298 + 1.05298i 0.998516 + 0.0544653i \(0.0173454\pi\)
0.0544653 + 0.998516i \(0.482655\pi\)
\(480\) 3.62760i 0.165576i
\(481\) −12.4096 2.48191i −0.565827 0.113165i
\(482\) 4.88755i 0.222622i
\(483\) −11.4301 2.88877i −0.520089 0.131444i
\(484\) −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 \(0.0862064\pi\)
−0.963550 + 0.267527i \(0.913794\pi\)
\(504\) 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 \(-0.471426\pi\)
0.995973 0.0896482i \(-0.0285743\pi\)
\(510\) 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
\(518\) 9.00337 + 2.27545i 0.395585 + 0.0999775i
\(519\) 6.05852i 0.265939i
\(520\) 10.8828 7.25519i 0.477242 0.318161i
\(521\) 24.7188i 1.08295i −0.840716 0.541476i \(-0.817866\pi\)
0.840716 0.541476i \(-0.182134\pi\)
\(522\) 6.89612 + 6.89612i 0.301835 + 0.301835i
\(523\) 8.22489i 0.359649i 0.983699 + 0.179825i \(0.0575530\pi\)
−0.983699 + 0.179825i \(0.942447\pi\)
\(524\) 0.0292581 0.00127815
\(525\) 20.9298 + 5.28965i 0.913451 + 0.230859i
\(526\) −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
\(539\) −15.6344 + 4.67062i −0.673423 + 0.201178i
\(540\) 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
\(546\) 8.61058 + 4.10583i 0.368499 + 0.175713i
\(547\) −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
\(553\) 30.8895 + 7.80680i 1.31356 + 0.331979i
\(554\) −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 \(-0.734064\pi\)
−0.670835 + 0.741607i \(0.734064\pi\)
\(564\) −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
\(567\) 2.56510 + 0.648285i 0.107724 + 0.0272254i
\(568\) 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
\(574\) −27.3492 6.91205i −1.14153 0.288503i
\(575\) 36.3587 1.51626
\(576\) 1.00000i 0.0416667i
\(577\) −14.6380 + 14.6380i −0.609388 + 0.609388i −0.942786 0.333398i \(-0.891805\pi\)
0.333398 + 0.942786i \(0.391805\pi\)
\(578\) 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 −0.993021 0.117934i \(-0.962373\pi\)
0.117934 + 0.993021i \(0.462373\pi\)
\(588\) −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 0.933442 0.358727i \(-0.116789\pi\)
−0.358727 + 0.933442i \(0.616789\pi\)
\(594\) 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 \(0.0564627\pi\)
−0.984309 + 0.176454i \(0.943537\pi\)
\(602\) −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 \(-0.984066\pi\)
0.998747 0.0500369i \(-0.0159339\pi\)
\(608\) −4.04701 −0.164128
\(609\) 6.32246 25.0164i 0.256199 1.01371i
\(610\) 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
\(616\) 1.51117 5.97931i 0.0608867 0.240913i
\(617\) −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 0.169220 0.985578i \(-0.445875\pi\)
−0.985578 + 0.169220i \(0.945875\pi\)
\(620\) −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
\(630\) −9.30514 2.35172i −0.370726 0.0936946i
\(631\) −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
\(637\) −2.34142 25.1300i −0.0927706 0.995688i
\(638\) 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 −0.0707640 0.997493i \(-0.522544\pi\)
0.997493 + 0.0707640i \(0.0225437\pi\)
\(644\) −11.4301 2.88877i −0.450410 0.113834i
\(645\) −22.1173 + 22.1173i −0.870868 + 0.870868i
\(646\) 28.9744 1.13998
\(647\) 7.68783 0.302240 0.151120 0.988515i \(-0.451712\pi\)
0.151120 + 0.988515i \(0.451712\pi\)
\(648\) −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
\(658\) −0.644914 + 2.55176i −0.0251414 + 0.0994780i
\(659\) −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 0.769217 0.638988i \(-0.220647\pi\)
−0.638988 + 0.769217i \(0.720647\pi\)
\(662\) 24.5970i 0.955991i
\(663\) 21.4784 14.3189i 0.834150 0.556100i
\(664\) 3.82323i 0.148370i
\(665\) 9.51741 37.6580i 0.369069 1.46031i
\(666\) −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 \(0.0797117\pi\)
−0.968808 + 0.247812i \(0.920288\pi\)
\(678\) 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 −0.914709 0.404112i \(-0.867580\pi\)
0.404112 + 0.914709i \(0.367580\pi\)
\(692\) 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
\(700\) 20.9298 + 5.28965i 0.791072 + 0.199930i
\(701\) 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
\(707\) −9.12395 2.30592i −0.343142 0.0867232i
\(708\) 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 \(-0.702342\pi\)
−0.593723 + 0.804670i \(0.702342\pi\)
\(720\) 2.56510 2.56510i 0.0955956 0.0955956i
\(721\) 25.1492 + 6.35602i 0.936604 + 0.236711i
\(722\) −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 \(-0.501556\pi\)
−0.00488970 + 0.999988i \(0.501556\pi\)
\(728\) 8.61058 + 4.10583i 0.319129 + 0.152172i
\(729\) −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 −0.921422 0.388564i \(-0.872971\pi\)
0.388564 + 0.921422i \(0.372971\pi\)
\(734\) 1.71598 1.71598i 0.0633381 0.0633381i
\(735\) 7.26853 + 24.3307i 0.268104 + 0.897450i
\(736\) 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
\(749\) −0.853530 0.215715i −0.0311873 0.00788206i
\(750\) 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
\(756\) 2.56510 + 0.648285i 0.0932917 + 0.0235779i
\(757\) 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 0.739477 0.673181i \(-0.235073\pi\)
−0.673181 + 0.739477i \(0.735073\pi\)
\(762\) 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 −0.728440 0.685109i \(-0.759755\pi\)
0.685109 + 0.728440i \(0.259755\pi\)
\(770\) −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 −0.752600 0.658478i \(-0.771201\pi\)
0.658478 + 0.752600i \(0.271201\pi\)
\(774\) 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