Properties

Label 546.2.p.c.281.8
Level $546$
Weight $2$
Character 546.281
Analytic conductor $4.360$
Analytic rank $0$
Dimension $20$
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.p (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + 1065 x^{12} - 2080 x^{11} + 3712 x^{10} - 6240 x^{9} + 9585 x^{8} - 14364 x^{7} + 23328 x^{6} - 34020 x^{5} + 40824 x^{4} - 43740 x^{3} + 52488 x^{2} - 78732 x + 59049\)
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 281.8
Root \(-0.962473 + 1.44002i\) of defining polynomial
Character \(\chi\) \(=\) 546.281
Dual form 546.2.p.c.239.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.337674 - 1.69882i) q^{3} -1.00000i q^{4} +(-2.19168 + 2.19168i) q^{5} +(-1.44002 - 0.962473i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.77195 + 1.14729i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.337674 - 1.69882i) q^{3} -1.00000i q^{4} +(-2.19168 + 2.19168i) q^{5} +(-1.44002 - 0.962473i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.77195 + 1.14729i) q^{9} +3.09950i q^{10} +(-1.27674 - 1.27674i) q^{11} +(-1.69882 + 0.337674i) q^{12} +(-3.23661 + 1.58883i) q^{13} +1.00000i q^{14} +(4.46333 + 2.98318i) q^{15} -1.00000 q^{16} -3.68191 q^{17} +(-1.14881 + 2.77132i) q^{18} +(5.26937 + 5.26937i) q^{19} +(2.19168 + 2.19168i) q^{20} +(1.44002 + 0.962473i) q^{21} -1.80559 q^{22} -8.15820 q^{23} +(-0.962473 + 1.44002i) q^{24} -4.60689i q^{25} +(-1.16516 + 3.41210i) q^{26} +(2.88505 + 4.32163i) q^{27} +(0.707107 + 0.707107i) q^{28} -9.50505i q^{29} +(5.26548 - 1.04662i) q^{30} +(-0.125281 - 0.125281i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-1.73783 + 2.60007i) q^{33} +(-2.60350 + 2.60350i) q^{34} -3.09950i q^{35} +(1.14729 + 2.77195i) q^{36} +(-0.328266 + 0.328266i) q^{37} +7.45201 q^{38} +(3.79204 + 4.96190i) q^{39} +3.09950 q^{40} +(2.21794 - 2.21794i) q^{41} +(1.69882 - 0.337674i) q^{42} +1.43126i q^{43} +(-1.27674 + 1.27674i) q^{44} +(3.56073 - 8.58971i) q^{45} +(-5.76872 + 5.76872i) q^{46} +(0.805736 + 0.805736i) q^{47} +(0.337674 + 1.69882i) q^{48} -1.00000i q^{49} +(-3.25756 - 3.25756i) q^{50} +(1.24328 + 6.25489i) q^{51} +(1.58883 + 3.23661i) q^{52} +5.59755i q^{53} +(5.09589 + 1.01581i) q^{54} +5.59641 q^{55} +1.00000 q^{56} +(7.17236 - 10.7310i) q^{57} +(-6.72109 - 6.72109i) q^{58} +(-1.49217 - 1.49217i) q^{59} +(2.98318 - 4.46333i) q^{60} -8.14557 q^{61} -0.177174 q^{62} +(1.14881 - 2.77132i) q^{63} +1.00000i q^{64} +(3.61141 - 10.5758i) q^{65} +(0.609699 + 3.06736i) q^{66} +(-10.6436 - 10.6436i) q^{67} +3.68191i q^{68} +(2.75481 + 13.8593i) q^{69} +(-2.19168 - 2.19168i) q^{70} +(0.752235 - 0.752235i) q^{71} +(2.77132 + 1.14881i) q^{72} +(3.59354 - 3.59354i) q^{73} +0.464238i q^{74} +(-7.82626 + 1.55563i) q^{75} +(5.26937 - 5.26937i) q^{76} +1.80559 q^{77} +(6.18997 + 0.827215i) q^{78} +4.38864 q^{79} +(2.19168 - 2.19168i) q^{80} +(6.36745 - 6.36047i) q^{81} -3.13663i q^{82} +(-9.35133 + 9.35133i) q^{83} +(0.962473 - 1.44002i) q^{84} +(8.06956 - 8.06956i) q^{85} +(1.01205 + 1.01205i) q^{86} +(-16.1473 + 3.20961i) q^{87} +1.80559i q^{88} +(-3.19016 - 3.19016i) q^{89} +(-3.55603 - 8.59166i) q^{90} +(1.16516 - 3.41210i) q^{91} +8.15820i q^{92} +(-0.170525 + 0.255133i) q^{93} +1.13948 q^{94} -23.0975 q^{95} +(1.44002 + 0.962473i) q^{96} +(1.79334 + 1.79334i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(5.00386 + 2.07427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 4q^{5} - 4q^{6} - 8q^{9} + O(q^{10}) \) \( 20q - 4q^{5} - 4q^{6} - 8q^{9} - 16q^{11} - 8q^{12} + 4q^{13} - 4q^{15} - 20q^{16} + 12q^{17} - 8q^{18} + 12q^{19} + 4q^{20} + 4q^{21} - 12q^{22} - 4q^{23} + 4q^{24} + 24q^{27} + 12q^{30} - 8q^{31} - 48q^{33} - 4q^{34} + 32q^{37} - 4q^{38} - 16q^{39} - 4q^{40} + 8q^{41} + 8q^{42} - 16q^{44} + 16q^{45} - 8q^{46} + 32q^{50} - 8q^{51} - 8q^{52} + 28q^{54} + 28q^{55} + 20q^{56} + 36q^{57} - 4q^{58} + 20q^{59} - 4q^{60} - 4q^{61} + 48q^{62} + 8q^{63} + 52q^{65} - 36q^{67} + 68q^{69} - 4q^{70} - 28q^{71} - 16q^{72} - 24q^{73} - 76q^{75} + 12q^{76} + 12q^{77} + 40q^{78} - 64q^{79} + 4q^{80} + 32q^{81} - 24q^{83} - 4q^{84} + 24q^{85} + 4q^{86} + 4q^{87} - 4q^{89} - 8q^{90} - 32q^{93} - 40q^{94} - 76q^{95} + 4q^{96} + 32q^{97} - 4q^{99} + O(q^{100}) \)

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
\(3\) −0.337674 1.69882i −0.194956 0.980812i
\(4\) 1.00000i 0.500000i
\(5\) −2.19168 + 2.19168i −0.980147 + 0.980147i −0.999807 0.0196593i \(-0.993742\pi\)
0.0196593 + 0.999807i \(0.493742\pi\)
\(6\) −1.44002 0.962473i −0.587884 0.392928i
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −2.77195 + 1.14729i −0.923984 + 0.382430i
\(10\) 3.09950i 0.980147i
\(11\) −1.27674 1.27674i −0.384952 0.384952i 0.487930 0.872883i \(-0.337752\pi\)
−0.872883 + 0.487930i \(0.837752\pi\)
\(12\) −1.69882 + 0.337674i −0.490406 + 0.0974780i
\(13\) −3.23661 + 1.58883i −0.897674 + 0.440661i
\(14\) 1.00000i 0.267261i
\(15\) 4.46333 + 2.98318i 1.15243 + 0.770255i
\(16\) −1.00000 −0.250000
\(17\) −3.68191 −0.892995 −0.446497 0.894785i \(-0.647329\pi\)
−0.446497 + 0.894785i \(0.647329\pi\)
\(18\) −1.14881 + 2.77132i −0.270777 + 0.653207i
\(19\) 5.26937 + 5.26937i 1.20888 + 1.20888i 0.971391 + 0.237485i \(0.0763232\pi\)
0.237485 + 0.971391i \(0.423677\pi\)
\(20\) 2.19168 + 2.19168i 0.490074 + 0.490074i
\(21\) 1.44002 + 0.962473i 0.314237 + 0.210029i
\(22\) −1.80559 −0.384952
\(23\) −8.15820 −1.70110 −0.850551 0.525893i \(-0.823731\pi\)
−0.850551 + 0.525893i \(0.823731\pi\)
\(24\) −0.962473 + 1.44002i −0.196464 + 0.293942i
\(25\) 4.60689i 0.921378i
\(26\) −1.16516 + 3.41210i −0.228506 + 0.669167i
\(27\) 2.88505 + 4.32163i 0.555229 + 0.831698i
\(28\) 0.707107 + 0.707107i 0.133631 + 0.133631i
\(29\) 9.50505i 1.76504i −0.470272 0.882522i \(-0.655844\pi\)
0.470272 0.882522i \(-0.344156\pi\)
\(30\) 5.26548 1.04662i 0.961340 0.191086i
\(31\) −0.125281 0.125281i −0.0225011 0.0225011i 0.695767 0.718268i \(-0.255065\pi\)
−0.718268 + 0.695767i \(0.755065\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −1.73783 + 2.60007i −0.302517 + 0.452614i
\(34\) −2.60350 + 2.60350i −0.446497 + 0.446497i
\(35\) 3.09950i 0.523911i
\(36\) 1.14729 + 2.77195i 0.191215 + 0.461992i
\(37\) −0.328266 + 0.328266i −0.0539666 + 0.0539666i −0.733575 0.679608i \(-0.762150\pi\)
0.679608 + 0.733575i \(0.262150\pi\)
\(38\) 7.45201 1.20888
\(39\) 3.79204 + 4.96190i 0.607212 + 0.794540i
\(40\) 3.09950 0.490074
\(41\) 2.21794 2.21794i 0.346383 0.346383i −0.512377 0.858761i \(-0.671235\pi\)
0.858761 + 0.512377i \(0.171235\pi\)
\(42\) 1.69882 0.337674i 0.262133 0.0521042i
\(43\) 1.43126i 0.218265i 0.994027 + 0.109133i \(0.0348073\pi\)
−0.994027 + 0.109133i \(0.965193\pi\)
\(44\) −1.27674 + 1.27674i −0.192476 + 0.192476i
\(45\) 3.56073 8.58971i 0.530803 1.28048i
\(46\) −5.76872 + 5.76872i −0.850551 + 0.850551i
\(47\) 0.805736 + 0.805736i 0.117529 + 0.117529i 0.763425 0.645896i \(-0.223516\pi\)
−0.645896 + 0.763425i \(0.723516\pi\)
\(48\) 0.337674 + 1.69882i 0.0487390 + 0.245203i
\(49\) 1.00000i 0.142857i
\(50\) −3.25756 3.25756i −0.460689 0.460689i
\(51\) 1.24328 + 6.25489i 0.174095 + 0.875860i
\(52\) 1.58883 + 3.23661i 0.220330 + 0.448837i
\(53\) 5.59755i 0.768882i 0.923150 + 0.384441i \(0.125606\pi\)
−0.923150 + 0.384441i \(0.874394\pi\)
\(54\) 5.09589 + 1.01581i 0.693463 + 0.138235i
\(55\) 5.59641 0.754620
\(56\) 1.00000 0.133631
\(57\) 7.17236 10.7310i 0.950003 1.42136i
\(58\) −6.72109 6.72109i −0.882522 0.882522i
\(59\) −1.49217 1.49217i −0.194264 0.194264i 0.603272 0.797536i \(-0.293864\pi\)
−0.797536 + 0.603272i \(0.793864\pi\)
\(60\) 2.98318 4.46333i 0.385127 0.576213i
\(61\) −8.14557 −1.04293 −0.521467 0.853272i \(-0.674615\pi\)
−0.521467 + 0.853272i \(0.674615\pi\)
\(62\) −0.177174 −0.0225011
\(63\) 1.14881 2.77132i 0.144736 0.349154i
\(64\) 1.00000i 0.125000i
\(65\) 3.61141 10.5758i 0.447940 1.31177i
\(66\) 0.609699 + 3.06736i 0.0750487 + 0.377566i
\(67\) −10.6436 10.6436i −1.30033 1.30033i −0.928170 0.372157i \(-0.878618\pi\)
−0.372157 0.928170i \(-0.621382\pi\)
\(68\) 3.68191i 0.446497i
\(69\) 2.75481 + 13.8593i 0.331640 + 1.66846i
\(70\) −2.19168 2.19168i −0.261955 0.261955i
\(71\) 0.752235 0.752235i 0.0892739 0.0892739i −0.661060 0.750333i \(-0.729893\pi\)
0.750333 + 0.661060i \(0.229893\pi\)
\(72\) 2.77132 + 1.14881i 0.326604 + 0.135389i
\(73\) 3.59354 3.59354i 0.420592 0.420592i −0.464815 0.885408i \(-0.653879\pi\)
0.885408 + 0.464815i \(0.153879\pi\)
\(74\) 0.464238i 0.0539666i
\(75\) −7.82626 + 1.55563i −0.903699 + 0.179628i
\(76\) 5.26937 5.26937i 0.604438 0.604438i
\(77\) 1.80559 0.205766
\(78\) 6.18997 + 0.827215i 0.700876 + 0.0936637i
\(79\) 4.38864 0.493760 0.246880 0.969046i \(-0.420595\pi\)
0.246880 + 0.969046i \(0.420595\pi\)
\(80\) 2.19168 2.19168i 0.245037 0.245037i
\(81\) 6.36745 6.36047i 0.707494 0.706719i
\(82\) 3.13663i 0.346383i
\(83\) −9.35133 + 9.35133i −1.02644 + 1.02644i −0.0268014 + 0.999641i \(0.508532\pi\)
−0.999641 + 0.0268014i \(0.991468\pi\)
\(84\) 0.962473 1.44002i 0.105014 0.157119i
\(85\) 8.06956 8.06956i 0.875266 0.875266i
\(86\) 1.01205 + 1.01205i 0.109133 + 0.109133i
\(87\) −16.1473 + 3.20961i −1.73118 + 0.344106i
\(88\) 1.80559i 0.192476i
\(89\) −3.19016 3.19016i −0.338156 0.338156i 0.517517 0.855673i \(-0.326856\pi\)
−0.855673 + 0.517517i \(0.826856\pi\)
\(90\) −3.55603 8.59166i −0.374838 0.905641i
\(91\) 1.16516 3.41210i 0.122142 0.357685i
\(92\) 8.15820i 0.850551i
\(93\) −0.170525 + 0.255133i −0.0176826 + 0.0264560i
\(94\) 1.13948 0.117529
\(95\) −23.0975 −2.36975
\(96\) 1.44002 + 0.962473i 0.146971 + 0.0982320i
\(97\) 1.79334 + 1.79334i 0.182086 + 0.182086i 0.792264 0.610178i \(-0.208902\pi\)
−0.610178 + 0.792264i \(0.708902\pi\)
\(98\) −0.707107 0.707107i −0.0714286 0.0714286i
\(99\) 5.00386 + 2.07427i 0.502907 + 0.208472i
\(100\) −4.60689 −0.460689
\(101\) −8.55213 −0.850969 −0.425484 0.904966i \(-0.639896\pi\)
−0.425484 + 0.904966i \(0.639896\pi\)
\(102\) 5.30201 + 3.54374i 0.524977 + 0.350883i
\(103\) 6.72083i 0.662223i 0.943592 + 0.331112i \(0.107424\pi\)
−0.943592 + 0.331112i \(0.892576\pi\)
\(104\) 3.41210 + 1.16516i 0.334584 + 0.114253i
\(105\) −5.26548 + 1.04662i −0.513858 + 0.102140i
\(106\) 3.95806 + 3.95806i 0.384441 + 0.384441i
\(107\) 7.64497i 0.739067i −0.929217 0.369534i \(-0.879517\pi\)
0.929217 0.369534i \(-0.120483\pi\)
\(108\) 4.32163 2.88505i 0.415849 0.277614i
\(109\) −11.0618 11.0618i −1.05953 1.05953i −0.998112 0.0614199i \(-0.980437\pi\)
−0.0614199 0.998112i \(-0.519563\pi\)
\(110\) 3.95726 3.95726i 0.377310 0.377310i
\(111\) 0.668510 + 0.446817i 0.0634522 + 0.0424100i
\(112\) 0.707107 0.707107i 0.0668153 0.0668153i
\(113\) 19.2385i 1.80980i 0.425619 + 0.904902i \(0.360056\pi\)
−0.425619 + 0.904902i \(0.639944\pi\)
\(114\) −2.51635 12.6596i −0.235678 1.18568i
\(115\) 17.8801 17.8801i 1.66733 1.66733i
\(116\) −9.50505 −0.882522
\(117\) 7.14888 8.11748i 0.660914 0.750461i
\(118\) −2.11025 −0.194264
\(119\) 2.60350 2.60350i 0.238663 0.238663i
\(120\) −1.04662 5.26548i −0.0955428 0.480670i
\(121\) 7.73986i 0.703624i
\(122\) −5.75979 + 5.75979i −0.521467 + 0.521467i
\(123\) −4.51680 3.01893i −0.407266 0.272207i
\(124\) −0.125281 + 0.125281i −0.0112505 + 0.0112505i
\(125\) −0.861568 0.861568i −0.0770610 0.0770610i
\(126\) −1.14729 2.77195i −0.102209 0.246945i
\(127\) 12.4807i 1.10749i 0.832688 + 0.553743i \(0.186801\pi\)
−0.832688 + 0.553743i \(0.813199\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 2.43145 0.483299i 0.214077 0.0425521i
\(130\) −4.92456 10.0319i −0.431913 0.879853i
\(131\) 8.33777i 0.728475i −0.931306 0.364237i \(-0.881330\pi\)
0.931306 0.364237i \(-0.118670\pi\)
\(132\) 2.60007 + 1.73783i 0.226307 + 0.151258i
\(133\) −7.45201 −0.646172
\(134\) −15.0524 −1.30033
\(135\) −15.7947 3.14851i −1.35939 0.270981i
\(136\) 2.60350 + 2.60350i 0.223249 + 0.223249i
\(137\) 14.2203 + 14.2203i 1.21492 + 1.21492i 0.969388 + 0.245535i \(0.0789636\pi\)
0.245535 + 0.969388i \(0.421036\pi\)
\(138\) 11.7479 + 7.85205i 1.00005 + 0.668411i
\(139\) 5.53897 0.469809 0.234905 0.972018i \(-0.424522\pi\)
0.234905 + 0.972018i \(0.424522\pi\)
\(140\) −3.09950 −0.261955
\(141\) 1.09672 1.64087i 0.0923606 0.138186i
\(142\) 1.06382i 0.0892739i
\(143\) 6.16083 + 2.10379i 0.515195 + 0.175928i
\(144\) 2.77195 1.14729i 0.230996 0.0956076i
\(145\) 20.8320 + 20.8320i 1.73000 + 1.73000i
\(146\) 5.08204i 0.420592i
\(147\) −1.69882 + 0.337674i −0.140116 + 0.0278509i
\(148\) 0.328266 + 0.328266i 0.0269833 + 0.0269833i
\(149\) 3.72237 3.72237i 0.304949 0.304949i −0.537998 0.842946i \(-0.680819\pi\)
0.842946 + 0.537998i \(0.180819\pi\)
\(150\) −4.43401 + 6.63400i −0.362035 + 0.541663i
\(151\) −15.2455 + 15.2455i −1.24066 + 1.24066i −0.280929 + 0.959729i \(0.590642\pi\)
−0.959729 + 0.280929i \(0.909358\pi\)
\(152\) 7.45201i 0.604438i
\(153\) 10.2061 4.22422i 0.825113 0.341508i
\(154\) 1.27674 1.27674i 0.102883 0.102883i
\(155\) 0.549149 0.0441087
\(156\) 4.96190 3.79204i 0.397270 0.303606i
\(157\) −10.2830 −0.820676 −0.410338 0.911934i \(-0.634589\pi\)
−0.410338 + 0.911934i \(0.634589\pi\)
\(158\) 3.10323 3.10323i 0.246880 0.246880i
\(159\) 9.50920 1.89014i 0.754129 0.149898i
\(160\) 3.09950i 0.245037i
\(161\) 5.76872 5.76872i 0.454639 0.454639i
\(162\) 0.00493109 9.00000i 0.000387423 0.707107i
\(163\) 16.4136 16.4136i 1.28561 1.28561i 0.348188 0.937425i \(-0.386797\pi\)
0.937425 0.348188i \(-0.113203\pi\)
\(164\) −2.21794 2.21794i −0.173192 0.173192i
\(165\) −1.88976 9.50727i −0.147118 0.740140i
\(166\) 13.2248i 1.02644i
\(167\) 10.1688 + 10.1688i 0.786888 + 0.786888i 0.980983 0.194095i \(-0.0621770\pi\)
−0.194095 + 0.980983i \(0.562177\pi\)
\(168\) −0.337674 1.69882i −0.0260521 0.131067i
\(169\) 7.95127 10.2848i 0.611636 0.791139i
\(170\) 11.4121i 0.875266i
\(171\) −20.6519 8.56095i −1.57929 0.654672i
\(172\) 1.43126 0.109133
\(173\) 8.72942 0.663686 0.331843 0.943335i \(-0.392330\pi\)
0.331843 + 0.943335i \(0.392330\pi\)
\(174\) −9.14836 + 13.6874i −0.693535 + 1.03764i
\(175\) 3.25756 + 3.25756i 0.246249 + 0.246249i
\(176\) 1.27674 + 1.27674i 0.0962380 + 0.0962380i
\(177\) −2.03106 + 3.03879i −0.152664 + 0.228410i
\(178\) −4.51157 −0.338156
\(179\) 21.4346 1.60210 0.801048 0.598600i \(-0.204276\pi\)
0.801048 + 0.598600i \(0.204276\pi\)
\(180\) −8.58971 3.56073i −0.640240 0.265401i
\(181\) 7.53227i 0.559869i 0.960019 + 0.279935i \(0.0903128\pi\)
−0.960019 + 0.279935i \(0.909687\pi\)
\(182\) −1.58883 3.23661i −0.117772 0.239913i
\(183\) 2.75055 + 13.8378i 0.203326 + 1.02292i
\(184\) 5.76872 + 5.76872i 0.425275 + 0.425275i
\(185\) 1.43891i 0.105790i
\(186\) 0.0598268 + 0.300985i 0.00438672 + 0.0220693i
\(187\) 4.70085 + 4.70085i 0.343760 + 0.343760i
\(188\) 0.805736 0.805736i 0.0587644 0.0587644i
\(189\) −5.09589 1.01581i −0.370672 0.0738895i
\(190\) −16.3324 + 16.3324i −1.18488 + 1.18488i
\(191\) 1.80118i 0.130329i 0.997875 + 0.0651645i \(0.0207572\pi\)
−0.997875 + 0.0651645i \(0.979243\pi\)
\(192\) 1.69882 0.337674i 0.122601 0.0243695i
\(193\) 14.4054 14.4054i 1.03692 1.03692i 0.0376326 0.999292i \(-0.488018\pi\)
0.999292 0.0376326i \(-0.0119817\pi\)
\(194\) 2.53616 0.182086
\(195\) −19.1858 2.56395i −1.37392 0.183608i
\(196\) −1.00000 −0.0714286
\(197\) −6.93319 + 6.93319i −0.493970 + 0.493970i −0.909554 0.415585i \(-0.863577\pi\)
0.415585 + 0.909554i \(0.363577\pi\)
\(198\) 5.00500 2.07153i 0.355690 0.147217i
\(199\) 10.2593i 0.727262i 0.931543 + 0.363631i \(0.118463\pi\)
−0.931543 + 0.363631i \(0.881537\pi\)
\(200\) −3.25756 + 3.25756i −0.230345 + 0.230345i
\(201\) −14.4875 + 21.6756i −1.02187 + 1.52888i
\(202\) −6.04727 + 6.04727i −0.425484 + 0.425484i
\(203\) 6.72109 + 6.72109i 0.471728 + 0.471728i
\(204\) 6.25489 1.24328i 0.437930 0.0870473i
\(205\) 9.72199i 0.679013i
\(206\) 4.75235 + 4.75235i 0.331112 + 0.331112i
\(207\) 22.6141 9.35983i 1.57179 0.650553i
\(208\) 3.23661 1.58883i 0.224418 0.110165i
\(209\) 13.4552i 0.930719i
\(210\) −2.98318 + 4.46333i −0.205859 + 0.307999i
\(211\) −19.4541 −1.33928 −0.669638 0.742687i \(-0.733551\pi\)
−0.669638 + 0.742687i \(0.733551\pi\)
\(212\) 5.59755 0.384441
\(213\) −1.53192 1.02390i −0.104965 0.0701564i
\(214\) −5.40581 5.40581i −0.369534 0.369534i
\(215\) −3.13686 3.13686i −0.213932 0.213932i
\(216\) 1.01581 5.09589i 0.0691173 0.346732i
\(217\) 0.177174 0.0120273
\(218\) −15.6438 −1.05953
\(219\) −7.31821 4.89132i −0.494519 0.330525i
\(220\) 5.59641i 0.377310i
\(221\) 11.9169 5.84991i 0.801618 0.393508i
\(222\) 0.788656 0.156761i 0.0529311 0.0105211i
\(223\) 11.9464 + 11.9464i 0.799992 + 0.799992i 0.983094 0.183102i \(-0.0586140\pi\)
−0.183102 + 0.983094i \(0.558614\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) 5.28544 + 12.7701i 0.352363 + 0.851339i
\(226\) 13.6037 + 13.6037i 0.904902 + 0.904902i
\(227\) −18.6457 + 18.6457i −1.23756 + 1.23756i −0.276560 + 0.960997i \(0.589195\pi\)
−0.960997 + 0.276560i \(0.910805\pi\)
\(228\) −10.7310 7.17236i −0.710679 0.475001i
\(229\) −1.93830 + 1.93830i −0.128087 + 0.128087i −0.768244 0.640157i \(-0.778869\pi\)
0.640157 + 0.768244i \(0.278869\pi\)
\(230\) 25.2863i 1.66733i
\(231\) −0.609699 3.06736i −0.0401152 0.201817i
\(232\) −6.72109 + 6.72109i −0.441261 + 0.441261i
\(233\) 3.76840 0.246876 0.123438 0.992352i \(-0.460608\pi\)
0.123438 + 0.992352i \(0.460608\pi\)
\(234\) −0.684903 10.7949i −0.0447735 0.705688i
\(235\) −3.53183 −0.230391
\(236\) −1.49217 + 1.49217i −0.0971321 + 0.0971321i
\(237\) −1.48193 7.45549i −0.0962615 0.484286i
\(238\) 3.68191i 0.238663i
\(239\) 2.94952 2.94952i 0.190789 0.190789i −0.605248 0.796037i \(-0.706926\pi\)
0.796037 + 0.605248i \(0.206926\pi\)
\(240\) −4.46333 2.98318i −0.288107 0.192564i
\(241\) 14.8333 14.8333i 0.955499 0.955499i −0.0435517 0.999051i \(-0.513867\pi\)
0.999051 + 0.0435517i \(0.0138673\pi\)
\(242\) −5.47291 5.47291i −0.351812 0.351812i
\(243\) −12.9554 8.66936i −0.831089 0.556140i
\(244\) 8.14557i 0.521467i
\(245\) 2.19168 + 2.19168i 0.140021 + 0.140021i
\(246\) −5.32857 + 1.05916i −0.339737 + 0.0675295i
\(247\) −25.4270 8.68278i −1.61788 0.552472i
\(248\) 0.177174i 0.0112505i
\(249\) 19.0439 + 12.7285i 1.20686 + 0.806636i
\(250\) −1.21844 −0.0770610
\(251\) −26.0328 −1.64318 −0.821589 0.570080i \(-0.806912\pi\)
−0.821589 + 0.570080i \(0.806912\pi\)
\(252\) −2.77132 1.14881i −0.174577 0.0723682i
\(253\) 10.4159 + 10.4159i 0.654843 + 0.654843i
\(254\) 8.82521 + 8.82521i 0.553743 + 0.553743i
\(255\) −16.4336 10.9838i −1.02911 0.687833i
\(256\) 1.00000 0.0625000
\(257\) −1.24091 −0.0774055 −0.0387028 0.999251i \(-0.512323\pi\)
−0.0387028 + 0.999251i \(0.512323\pi\)
\(258\) 1.37755 2.06104i 0.0857624 0.128315i
\(259\) 0.464238i 0.0288464i
\(260\) −10.5758 3.61141i −0.655883 0.223970i
\(261\) 10.9051 + 26.3476i 0.675006 + 1.63087i
\(262\) −5.89570 5.89570i −0.364237 0.364237i
\(263\) 11.9752i 0.738425i 0.929345 + 0.369213i \(0.120373\pi\)
−0.929345 + 0.369213i \(0.879627\pi\)
\(264\) 3.06736 0.609699i 0.188783 0.0375244i
\(265\) −12.2680 12.2680i −0.753618 0.753618i
\(266\) −5.26937 + 5.26937i −0.323086 + 0.323086i
\(267\) −4.34226 + 6.49672i −0.265742 + 0.397593i
\(268\) −10.6436 + 10.6436i −0.650163 + 0.650163i
\(269\) 7.12840i 0.434626i 0.976102 + 0.217313i \(0.0697293\pi\)
−0.976102 + 0.217313i \(0.930271\pi\)
\(270\) −13.3949 + 8.94221i −0.815187 + 0.544206i
\(271\) 9.80032 9.80032i 0.595327 0.595327i −0.343738 0.939065i \(-0.611693\pi\)
0.939065 + 0.343738i \(0.111693\pi\)
\(272\) 3.68191 0.223249
\(273\) −6.18997 0.827215i −0.374634 0.0500653i
\(274\) 20.1105 1.21492
\(275\) −5.88181 + 5.88181i −0.354686 + 0.354686i
\(276\) 13.8593 2.75481i 0.834231 0.165820i
\(277\) 1.47925i 0.0888795i 0.999012 + 0.0444397i \(0.0141503\pi\)
−0.999012 + 0.0444397i \(0.985850\pi\)
\(278\) 3.91664 3.91664i 0.234905 0.234905i
\(279\) 0.491005 + 0.203539i 0.0293957 + 0.0121855i
\(280\) −2.19168 + 2.19168i −0.130978 + 0.130978i
\(281\) 11.3699 + 11.3699i 0.678270 + 0.678270i 0.959609 0.281339i \(-0.0907784\pi\)
−0.281339 + 0.959609i \(0.590778\pi\)
\(282\) −0.384773 1.93577i −0.0229129 0.115274i
\(283\) 19.9300i 1.18471i 0.805676 + 0.592357i \(0.201802\pi\)
−0.805676 + 0.592357i \(0.798198\pi\)
\(284\) −0.752235 0.752235i −0.0446369 0.0446369i
\(285\) 7.79942 + 39.2384i 0.461998 + 2.32428i
\(286\) 5.84397 2.86876i 0.345561 0.169633i
\(287\) 3.13663i 0.185150i
\(288\) 1.14881 2.77132i 0.0676943 0.163302i
\(289\) −3.44353 −0.202561
\(290\) 29.4609 1.73000
\(291\) 2.44099 3.65211i 0.143093 0.214090i
\(292\) −3.59354 3.59354i −0.210296 0.210296i
\(293\) −10.3404 10.3404i −0.604092 0.604092i 0.337304 0.941396i \(-0.390485\pi\)
−0.941396 + 0.337304i \(0.890485\pi\)
\(294\) −0.962473 + 1.44002i −0.0561326 + 0.0839834i
\(295\) 6.54072 0.380815
\(296\) 0.464238 0.0269833
\(297\) 1.83414 9.20107i 0.106427 0.533900i
\(298\) 5.26423i 0.304949i
\(299\) 26.4049 12.9620i 1.52703 0.749609i
\(300\) 1.55563 + 7.82626i 0.0898141 + 0.451849i
\(301\) −1.01205 1.01205i −0.0583338 0.0583338i
\(302\) 21.5603i 1.24066i
\(303\) 2.88783 + 14.5285i 0.165901 + 0.834640i
\(304\) −5.26937 5.26937i −0.302219 0.302219i
\(305\) 17.8525 17.8525i 1.02223 1.02223i
\(306\) 4.22981 10.2038i 0.241802 0.583311i
\(307\) −6.10278 + 6.10278i −0.348304 + 0.348304i −0.859478 0.511174i \(-0.829211\pi\)
0.511174 + 0.859478i \(0.329211\pi\)
\(308\) 1.80559i 0.102883i
\(309\) 11.4175 2.26945i 0.649517 0.129104i
\(310\) 0.388307 0.388307i 0.0220544 0.0220544i
\(311\) −21.9647 −1.24550 −0.622752 0.782420i \(-0.713985\pi\)
−0.622752 + 0.782420i \(0.713985\pi\)
\(312\) 0.827215 6.18997i 0.0468318 0.350438i
\(313\) −4.26972 −0.241339 −0.120669 0.992693i \(-0.538504\pi\)
−0.120669 + 0.992693i \(0.538504\pi\)
\(314\) −7.27121 + 7.27121i −0.410338 + 0.410338i
\(315\) 3.55603 + 8.59166i 0.200359 + 0.484085i
\(316\) 4.38864i 0.246880i
\(317\) 17.6141 17.6141i 0.989307 0.989307i −0.0106369 0.999943i \(-0.503386\pi\)
0.999943 + 0.0106369i \(0.00338588\pi\)
\(318\) 5.38749 8.06055i 0.302115 0.452013i
\(319\) −12.1355 + 12.1355i −0.679457 + 0.679457i
\(320\) −2.19168 2.19168i −0.122518 0.122518i
\(321\) −12.9874 + 2.58150i −0.724886 + 0.144086i
\(322\) 8.15820i 0.454639i
\(323\) −19.4014 19.4014i −1.07952 1.07952i
\(324\) −6.36047 6.36745i −0.353360 0.353747i
\(325\) 7.31954 + 14.9107i 0.406015 + 0.827097i
\(326\) 23.2123i 1.28561i
\(327\) −15.0567 + 22.5273i −0.832639 + 1.24576i
\(328\) −3.13663 −0.173192
\(329\) −1.13948 −0.0628217
\(330\) −8.05892 5.38639i −0.443629 0.296511i
\(331\) −16.3963 16.3963i −0.901220 0.901220i 0.0943216 0.995542i \(-0.469932\pi\)
−0.995542 + 0.0943216i \(0.969932\pi\)
\(332\) 9.35133 + 9.35133i 0.513221 + 0.513221i
\(333\) 0.533321 1.28655i 0.0292258 0.0705028i
\(334\) 14.3809 0.786888
\(335\) 46.6548 2.54902
\(336\) −1.44002 0.962473i −0.0785593 0.0525072i
\(337\) 8.77212i 0.477848i 0.971038 + 0.238924i \(0.0767947\pi\)
−0.971038 + 0.238924i \(0.923205\pi\)
\(338\) −1.65006 12.8949i −0.0897516 0.701388i
\(339\) 32.6827 6.49633i 1.77508 0.352832i
\(340\) −8.06956 8.06956i −0.437633 0.437633i
\(341\) 0.319902i 0.0173237i
\(342\) −20.6566 + 8.54963i −1.11698 + 0.462311i
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) 1.01205 1.01205i 0.0545663 0.0545663i
\(345\) −36.4127 24.3374i −1.96039 1.31028i
\(346\) 6.17263 6.17263i 0.331843 0.331843i
\(347\) 8.56153i 0.459607i −0.973237 0.229803i \(-0.926192\pi\)
0.973237 0.229803i \(-0.0738083\pi\)
\(348\) 3.20961 + 16.1473i 0.172053 + 0.865588i
\(349\) −0.0314225 + 0.0314225i −0.00168201 + 0.00168201i −0.707947 0.706265i \(-0.750379\pi\)
0.706265 + 0.707947i \(0.250379\pi\)
\(350\) 4.60689 0.246249
\(351\) −16.2041 9.40358i −0.864911 0.501926i
\(352\) 1.80559 0.0962380
\(353\) −1.70236 + 1.70236i −0.0906076 + 0.0906076i −0.750958 0.660350i \(-0.770408\pi\)
0.660350 + 0.750958i \(0.270408\pi\)
\(354\) 0.712576 + 3.58493i 0.0378730 + 0.190537i
\(355\) 3.29731i 0.175003i
\(356\) −3.19016 + 3.19016i −0.169078 + 0.169078i
\(357\) −5.30201 3.54374i −0.280612 0.187555i
\(358\) 15.1565 15.1565i 0.801048 0.801048i
\(359\) 19.7911 + 19.7911i 1.04453 + 1.04453i 0.998961 + 0.0455713i \(0.0145108\pi\)
0.0455713 + 0.998961i \(0.485489\pi\)
\(360\) −8.59166 + 3.55603i −0.452820 + 0.187419i
\(361\) 36.5325i 1.92276i
\(362\) 5.32612 + 5.32612i 0.279935 + 0.279935i
\(363\) −13.1486 + 2.61355i −0.690123 + 0.137176i
\(364\) −3.41210 1.16516i −0.178842 0.0610709i
\(365\) 15.7518i 0.824485i
\(366\) 11.7298 + 7.83989i 0.613124 + 0.409798i
\(367\) −18.1422 −0.947016 −0.473508 0.880790i \(-0.657012\pi\)
−0.473508 + 0.880790i \(0.657012\pi\)
\(368\) 8.15820 0.425275
\(369\) −3.60340 + 8.69263i −0.187585 + 0.452520i
\(370\) −1.01746 1.01746i −0.0528952 0.0528952i
\(371\) −3.95806 3.95806i −0.205492 0.205492i
\(372\) 0.255133 + 0.170525i 0.0132280 + 0.00884130i
\(373\) −27.3139 −1.41426 −0.707130 0.707083i \(-0.750011\pi\)
−0.707130 + 0.707083i \(0.750011\pi\)
\(374\) 6.64800 0.343760
\(375\) −1.17272 + 1.75457i −0.0605588 + 0.0906058i
\(376\) 1.13948i 0.0587644i
\(377\) 15.1019 + 30.7641i 0.777786 + 1.58443i
\(378\) −4.32163 + 2.88505i −0.222281 + 0.148391i
\(379\) 11.0481 + 11.0481i 0.567502 + 0.567502i 0.931428 0.363926i \(-0.118564\pi\)
−0.363926 + 0.931428i \(0.618564\pi\)
\(380\) 23.0975i 1.18488i
\(381\) 21.2025 4.21441i 1.08624 0.215911i
\(382\) 1.27363 + 1.27363i 0.0651645 + 0.0651645i
\(383\) −18.4315 + 18.4315i −0.941808 + 0.941808i −0.998398 0.0565899i \(-0.981977\pi\)
0.0565899 + 0.998398i \(0.481977\pi\)
\(384\) 0.962473 1.44002i 0.0491160 0.0734855i
\(385\) −3.95726 + 3.95726i −0.201681 + 0.201681i
\(386\) 20.3723i 1.03692i
\(387\) −1.64207 3.96738i −0.0834712 0.201673i
\(388\) 1.79334 1.79334i 0.0910428 0.0910428i
\(389\) −13.3245 −0.675579 −0.337790 0.941222i \(-0.609679\pi\)
−0.337790 + 0.941222i \(0.609679\pi\)
\(390\) −15.3794 + 11.7534i −0.778766 + 0.595158i
\(391\) 30.0378 1.51907
\(392\) −0.707107 + 0.707107i −0.0357143 + 0.0357143i
\(393\) −14.1643 + 2.81545i −0.714497 + 0.142020i
\(394\) 9.80502i 0.493970i
\(395\) −9.61847 + 9.61847i −0.483958 + 0.483958i
\(396\) 2.07427 5.00386i 0.104236 0.251454i
\(397\) −16.7117 + 16.7117i −0.838738 + 0.838738i −0.988693 0.149955i \(-0.952087\pi\)
0.149955 + 0.988693i \(0.452087\pi\)
\(398\) 7.25442 + 7.25442i 0.363631 + 0.363631i
\(399\) 2.51635 + 12.6596i 0.125975 + 0.633773i
\(400\) 4.60689i 0.230345i
\(401\) 0.352145 + 0.352145i 0.0175853 + 0.0175853i 0.715845 0.698259i \(-0.246042\pi\)
−0.698259 + 0.715845i \(0.746042\pi\)
\(402\) 5.08279 + 25.5712i 0.253506 + 1.27538i
\(403\) 0.604533 + 0.206435i 0.0301140 + 0.0102833i
\(404\) 8.55213i 0.425484i
\(405\) −0.0152839 + 27.8955i −0.000759463 + 1.38614i
\(406\) 9.50505 0.471728
\(407\) 0.838222 0.0415491
\(408\) 3.54374 5.30201i 0.175441 0.262489i
\(409\) −23.1842 23.1842i −1.14638 1.14638i −0.987258 0.159126i \(-0.949132\pi\)
−0.159126 0.987258i \(-0.550868\pi\)
\(410\) 6.87449 + 6.87449i 0.339507 + 0.339507i
\(411\) 19.3559 28.9595i 0.954754 1.42847i
\(412\) 6.72083 0.331112
\(413\) 2.11025 0.103839
\(414\) 9.37222 22.6090i 0.460619 1.11117i
\(415\) 40.9902i 2.01213i
\(416\) 1.16516 3.41210i 0.0571266 0.167292i
\(417\) −1.87036 9.40969i −0.0915921 0.460795i
\(418\) −9.51430 9.51430i −0.465360 0.465360i
\(419\) 9.60922i 0.469441i −0.972063 0.234721i \(-0.924582\pi\)
0.972063 0.234721i \(-0.0754175\pi\)
\(420\) 1.04662 + 5.26548i 0.0510698 + 0.256929i
\(421\) −10.1653 10.1653i −0.495425 0.495425i 0.414586 0.910010i \(-0.363927\pi\)
−0.910010 + 0.414586i \(0.863927\pi\)
\(422\) −13.7561 + 13.7561i −0.669638 + 0.669638i
\(423\) −3.15788 1.30905i −0.153541 0.0636481i
\(424\) 3.95806 3.95806i 0.192220 0.192220i
\(425\) 16.9622i 0.822786i
\(426\) −1.80724 + 0.359224i −0.0875609 + 0.0174045i
\(427\) 5.75979 5.75979i 0.278736 0.278736i
\(428\) −7.64497 −0.369534
\(429\) 1.49361 11.1765i 0.0721120 0.539607i
\(430\) −4.43619 −0.213932
\(431\) −6.40858 + 6.40858i −0.308690 + 0.308690i −0.844401 0.535711i \(-0.820044\pi\)
0.535711 + 0.844401i \(0.320044\pi\)
\(432\) −2.88505 4.32163i −0.138807 0.207924i
\(433\) 33.5644i 1.61300i −0.591232 0.806502i \(-0.701358\pi\)
0.591232 0.806502i \(-0.298642\pi\)
\(434\) 0.125281 0.125281i 0.00601366 0.00601366i
\(435\) 28.3553 42.4241i 1.35953 2.03408i
\(436\) −11.0618 + 11.0618i −0.529766 + 0.529766i
\(437\) −42.9886 42.9886i −2.05642 2.05642i
\(438\) −8.63345 + 1.71607i −0.412522 + 0.0819970i
\(439\) 7.08017i 0.337918i −0.985623 0.168959i \(-0.945959\pi\)
0.985623 0.168959i \(-0.0540405\pi\)
\(440\) −3.95726 3.95726i −0.188655 0.188655i
\(441\) 1.14729 + 2.77195i 0.0546329 + 0.131998i
\(442\) 4.29001 12.5630i 0.204055 0.597563i
\(443\) 6.61082i 0.314089i 0.987591 + 0.157045i \(0.0501967\pi\)
−0.987591 + 0.157045i \(0.949803\pi\)
\(444\) 0.446817 0.668510i 0.0212050 0.0317261i
\(445\) 13.9836 0.662886
\(446\) 16.8948 0.799992
\(447\) −7.58057 5.06668i −0.358549 0.239646i
\(448\) −0.707107 0.707107i −0.0334077 0.0334077i
\(449\) 15.0860 + 15.0860i 0.711951 + 0.711951i 0.966943 0.254992i \(-0.0820728\pi\)
−0.254992 + 0.966943i \(0.582073\pi\)
\(450\) 12.7672 + 5.29244i 0.601851 + 0.249488i
\(451\) −5.66346 −0.266682
\(452\) 19.2385 0.904902
\(453\) 31.0472 + 20.7512i 1.45873 + 0.974978i
\(454\) 26.3690i 1.23756i
\(455\) 4.92456 + 10.0319i 0.230867 + 0.470301i
\(456\) −12.6596 + 2.51635i −0.592840 + 0.117839i
\(457\) −18.4880 18.4880i −0.864831 0.864831i 0.127063 0.991895i \(-0.459445\pi\)
−0.991895 + 0.127063i \(0.959445\pi\)
\(458\) 2.74117i 0.128087i
\(459\) −10.6225 15.9119i −0.495816 0.742702i
\(460\) −17.8801 17.8801i −0.833665 0.833665i
\(461\) 11.9307 11.9307i 0.555668 0.555668i −0.372403 0.928071i \(-0.621466\pi\)
0.928071 + 0.372403i \(0.121466\pi\)
\(462\) −2.60007 1.73783i −0.120966 0.0808511i
\(463\) 2.01800 2.01800i 0.0937846 0.0937846i −0.658658 0.752443i \(-0.728876\pi\)
0.752443 + 0.658658i \(0.228876\pi\)
\(464\) 9.50505i 0.441261i
\(465\) −0.185433 0.932903i −0.00859926 0.0432624i
\(466\) 2.66466 2.66466i 0.123438 0.123438i
\(467\) 11.3847 0.526823 0.263411 0.964684i \(-0.415152\pi\)
0.263411 + 0.964684i \(0.415152\pi\)
\(468\) −8.11748 7.14888i −0.375231 0.330457i
\(469\) 15.0524 0.695054
\(470\) −2.49738 + 2.49738i −0.115195 + 0.115195i
\(471\) 3.47231 + 17.4690i 0.159996 + 0.804929i
\(472\) 2.11025i 0.0971321i
\(473\) 1.82735 1.82735i 0.0840216 0.0840216i
\(474\) −6.31970 4.22394i −0.290274 0.194012i
\(475\) 24.2754 24.2754i 1.11383 1.11383i
\(476\) −2.60350 2.60350i −0.119331 0.119331i
\(477\) −6.42201 15.5161i −0.294044 0.710435i
\(478\) 4.17126i 0.190789i
\(479\) 21.9770 + 21.9770i 1.00415 + 1.00415i 0.999991 + 0.00416246i \(0.00132496\pi\)
0.00416246 + 0.999991i \(0.498675\pi\)
\(480\) −5.26548 + 1.04662i −0.240335 + 0.0477714i
\(481\) 0.540911 1.58403i 0.0246634 0.0722254i
\(482\) 20.9775i 0.955499i
\(483\) −11.7479 7.85205i −0.534550 0.357281i
\(484\) −7.73986 −0.351812
\(485\) −7.86082 −0.356942
\(486\) −15.2910 + 3.03069i −0.693614 + 0.137475i
\(487\) −21.7649 21.7649i −0.986263 0.986263i 0.0136436 0.999907i \(-0.495657\pi\)
−0.999907 + 0.0136436i \(0.995657\pi\)
\(488\) 5.75979 + 5.75979i 0.260733 + 0.260733i
\(489\) −33.4261 22.3413i −1.51158 1.01031i
\(490\) 3.09950 0.140021
\(491\) −24.6630 −1.11303 −0.556513 0.830839i \(-0.687861\pi\)
−0.556513 + 0.830839i \(0.687861\pi\)
\(492\) −3.01893 + 4.51680i −0.136104 + 0.203633i
\(493\) 34.9968i 1.57617i
\(494\) −24.1193 + 11.8400i −1.08518 + 0.532705i
\(495\) −15.5130 + 6.42071i −0.697257 + 0.288589i
\(496\) 0.125281 + 0.125281i 0.00562527 + 0.00562527i
\(497\) 1.06382i 0.0477189i
\(498\) 22.4665 4.46566i 1.00675 0.200111i
\(499\) 30.6363 + 30.6363i 1.37147 + 1.37147i 0.858268 + 0.513202i \(0.171541\pi\)
0.513202 + 0.858268i \(0.328459\pi\)
\(500\) −0.861568 + 0.861568i −0.0385305 + 0.0385305i
\(501\) 13.8412 20.7087i 0.618380 0.925197i
\(502\) −18.4080 + 18.4080i −0.821589 + 0.821589i
\(503\) 34.2723i 1.52813i −0.645141 0.764064i \(-0.723201\pi\)
0.645141 0.764064i \(-0.276799\pi\)
\(504\) −2.77195 + 1.14729i −0.123473 + 0.0511044i
\(505\) 18.7435 18.7435i 0.834075 0.834075i
\(506\) 14.7303 0.654843
\(507\) −20.1569 10.0348i −0.895201 0.445663i
\(508\) 12.4807 0.553743
\(509\) −3.24519 + 3.24519i −0.143840 + 0.143840i −0.775360 0.631520i \(-0.782432\pi\)
0.631520 + 0.775360i \(0.282432\pi\)
\(510\) −19.3870 + 3.85356i −0.858472 + 0.170638i
\(511\) 5.08204i 0.224816i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −7.56985 + 37.9747i −0.334217 + 1.67662i
\(514\) −0.877452 + 0.877452i −0.0387028 + 0.0387028i
\(515\) −14.7299 14.7299i −0.649077 0.649077i
\(516\) −0.483299 2.43145i −0.0212760 0.107038i
\(517\) 2.05743i 0.0904858i
\(518\) −0.328266 0.328266i −0.0144232 0.0144232i
\(519\) −2.94770 14.8297i −0.129389 0.650951i
\(520\) −10.0319 + 4.92456i −0.439926 + 0.215956i
\(521\) 44.5505i 1.95179i −0.218238 0.975896i \(-0.570031\pi\)
0.218238 0.975896i \(-0.429969\pi\)
\(522\) 26.3416 + 10.9195i 1.15294 + 0.477933i
\(523\) 16.3414 0.714560 0.357280 0.933997i \(-0.383704\pi\)
0.357280 + 0.933997i \(0.383704\pi\)
\(524\) −8.33777 −0.364237
\(525\) 4.43401 6.63400i 0.193516 0.289531i
\(526\) 8.46778 + 8.46778i 0.369213 + 0.369213i
\(527\) 0.461272 + 0.461272i 0.0200933 + 0.0200933i
\(528\) 1.73783 2.60007i 0.0756292 0.113154i
\(529\) 43.5562 1.89375
\(530\) −17.3496 −0.753618
\(531\) 5.84819 + 2.42428i 0.253790 + 0.105205i
\(532\) 7.45201i 0.323086i
\(533\) −3.65468 + 10.7025i −0.158302 + 0.463577i
\(534\) 1.52344 + 7.66432i 0.0659256 + 0.331668i
\(535\) 16.7553 + 16.7553i 0.724395 + 0.724395i
\(536\) 15.0524i 0.650163i
\(537\) −7.23789 36.4134i −0.312338 1.57135i
\(538\) 5.04054 + 5.04054i 0.217313 + 0.217313i
\(539\) −1.27674 + 1.27674i −0.0549932 + 0.0549932i
\(540\) −3.14851 + 15.7947i −0.135490 + 0.679696i
\(541\) 14.6761 14.6761i 0.630977 0.630977i −0.317336 0.948313i \(-0.602788\pi\)
0.948313 + 0.317336i \(0.102788\pi\)
\(542\) 13.8597i 0.595327i
\(543\) 12.7959 2.54345i 0.549127 0.109150i
\(544\) 2.60350 2.60350i 0.111624 0.111624i
\(545\) 48.4879 2.07699
\(546\) −4.96190 + 3.79204i −0.212350 + 0.162284i
\(547\) 3.25656 0.139240 0.0696202 0.997574i \(-0.477821\pi\)
0.0696202 + 0.997574i \(0.477821\pi\)
\(548\) 14.2203 14.2203i 0.607461 0.607461i
\(549\) 22.5791 9.34534i 0.963654 0.398849i
\(550\) 8.31814i 0.354686i
\(551\) 50.0856 50.0856i 2.13372 2.13372i
\(552\) 7.85205 11.7479i 0.334205 0.500025i
\(553\) −3.10323 + 3.10323i −0.131963 + 0.131963i
\(554\) 1.04599 + 1.04599i 0.0444397 + 0.0444397i
\(555\) −2.44444 + 0.485881i −0.103761 + 0.0206245i
\(556\) 5.53897i 0.234905i
\(557\) −3.70450 3.70450i −0.156965 0.156965i 0.624255 0.781220i \(-0.285402\pi\)
−0.781220 + 0.624255i \(0.785402\pi\)
\(558\) 0.491117 0.203270i 0.0207906 0.00860509i
\(559\) −2.27402 4.63243i −0.0961809 0.195931i
\(560\) 3.09950i 0.130978i
\(561\) 6.39853 9.57323i 0.270146 0.404182i
\(562\) 16.0794 0.678270
\(563\) −15.3860 −0.648443 −0.324221 0.945981i \(-0.605102\pi\)
−0.324221 + 0.945981i \(0.605102\pi\)
\(564\) −1.64087 1.09672i −0.0690932 0.0461803i
\(565\) −42.1645 42.1645i −1.77388 1.77388i
\(566\) 14.0926 + 14.0926i 0.592357 + 0.592357i
\(567\) −0.00493109 + 9.00000i −0.000207086 + 0.377964i
\(568\) −1.06382 −0.0446369
\(569\) −33.4793 −1.40353 −0.701763 0.712410i \(-0.747603\pi\)
−0.701763 + 0.712410i \(0.747603\pi\)
\(570\) 33.2608 + 22.2307i 1.39314 + 0.931143i
\(571\) 1.76074i 0.0736845i 0.999321 + 0.0368423i \(0.0117299\pi\)
−0.999321 + 0.0368423i \(0.988270\pi\)
\(572\) 2.10379 6.16083i 0.0879640 0.257597i
\(573\) 3.05988 0.608212i 0.127828 0.0254084i
\(574\) 2.21794 + 2.21794i 0.0925748 + 0.0925748i
\(575\) 37.5839i 1.56736i
\(576\) −1.14729 2.77195i −0.0478038 0.115498i
\(577\) −25.8072 25.8072i −1.07437 1.07437i −0.997003 0.0773650i \(-0.975349\pi\)
−0.0773650 0.997003i \(-0.524651\pi\)
\(578\) −2.43494 + 2.43494i −0.101280 + 0.101280i
\(579\) −29.3365 19.6078i −1.21918 0.814873i
\(580\) 20.8320 20.8320i 0.865002 0.865002i
\(581\) 13.2248i 0.548656i
\(582\) −0.856394 4.30847i −0.0354987 0.178592i
\(583\) 7.14662 7.14662i 0.295983 0.295983i
\(584\) −5.08204 −0.210296
\(585\) 2.12286 + 33.4589i 0.0877693 + 1.38336i
\(586\) −14.6235 −0.604092
\(587\) 4.03302 4.03302i 0.166460 0.166460i −0.618961 0.785422i \(-0.712446\pi\)
0.785422 + 0.618961i \(0.212446\pi\)
\(588\) 0.337674 + 1.69882i 0.0139254 + 0.0700580i
\(589\) 1.32030i 0.0544020i
\(590\) 4.62499 4.62499i 0.190408 0.190408i
\(591\) 14.1194 + 9.43707i 0.580794 + 0.388189i
\(592\) 0.328266 0.328266i 0.0134917 0.0134917i
\(593\) −1.35646 1.35646i −0.0557030 0.0557030i 0.678707 0.734410i \(-0.262541\pi\)
−0.734410 + 0.678707i \(0.762541\pi\)
\(594\) −5.20921 7.80307i −0.213736 0.320164i
\(595\) 11.4121i 0.467850i
\(596\) −3.72237 3.72237i −0.152474 0.152474i
\(597\) 17.4287 3.46429i 0.713307 0.141784i
\(598\) 9.50560 27.8366i 0.388713 1.13832i
\(599\) 19.3845i 0.792029i 0.918244 + 0.396014i \(0.129607\pi\)
−0.918244 + 0.396014i \(0.870393\pi\)
\(600\) 6.63400 + 4.43401i 0.270832 + 0.181018i
\(601\) −37.2292 −1.51861 −0.759306 0.650734i \(-0.774461\pi\)
−0.759306 + 0.650734i \(0.774461\pi\)
\(602\) −1.43126 −0.0583338
\(603\) 41.7150 + 17.2923i 1.69877 + 0.704197i
\(604\) 15.2455 + 15.2455i 0.620329 + 0.620329i
\(605\) 16.9633 + 16.9633i 0.689655 + 0.689655i
\(606\) 12.3152 + 8.23120i 0.500271 + 0.334370i
\(607\) −15.3314 −0.622284 −0.311142 0.950363i \(-0.600711\pi\)
−0.311142 + 0.950363i \(0.600711\pi\)
\(608\) −7.45201 −0.302219
\(609\) 9.14836 13.6874i 0.370710 0.554642i
\(610\) 25.2472i 1.02223i
\(611\) −3.88803 1.32768i −0.157293 0.0537121i
\(612\) −4.22422 10.2061i −0.170754 0.412557i
\(613\) −12.6416 12.6416i −0.510591 0.510591i 0.404116 0.914708i \(-0.367579\pi\)
−0.914708 + 0.404116i \(0.867579\pi\)
\(614\) 8.63063i 0.348304i
\(615\) 16.5159 3.28286i 0.665985 0.132378i
\(616\) −1.27674 1.27674i −0.0514414 0.0514414i
\(617\) 0.724231 0.724231i 0.0291564 0.0291564i −0.692378 0.721535i \(-0.743437\pi\)
0.721535 + 0.692378i \(0.243437\pi\)
\(618\) 6.46862 9.67811i 0.260206 0.389311i
\(619\) −4.40767 + 4.40767i −0.177159 + 0.177159i −0.790116 0.612957i \(-0.789980\pi\)
0.612957 + 0.790116i \(0.289980\pi\)
\(620\) 0.549149i 0.0220544i
\(621\) −23.5368 35.2567i −0.944500 1.41480i
\(622\) −15.5314 + 15.5314i −0.622752 + 0.622752i
\(623\) 4.51157 0.180752
\(624\) −3.79204 4.96190i −0.151803 0.198635i
\(625\) 26.8110 1.07244
\(626\) −3.01915 + 3.01915i −0.120669 + 0.120669i
\(627\) −22.8580 + 4.54348i −0.912860 + 0.181449i
\(628\) 10.2830i 0.410338i
\(629\) 1.20865 1.20865i 0.0481919 0.0481919i
\(630\) 8.58971 + 3.56073i 0.342222 + 0.141863i
\(631\) −9.93188 + 9.93188i −0.395382 + 0.395382i −0.876601 0.481219i \(-0.840194\pi\)
0.481219 + 0.876601i \(0.340194\pi\)
\(632\) −3.10323 3.10323i −0.123440 0.123440i
\(633\) 6.56914 + 33.0490i 0.261100 + 1.31358i
\(634\) 24.9101i 0.989307i
\(635\) −27.3537 27.3537i −1.08550 1.08550i
\(636\) −1.89014 9.50920i −0.0749491 0.377064i
\(637\) 1.58883 + 3.23661i 0.0629516 + 0.128239i
\(638\) 17.1622i 0.679457i
\(639\) −1.22213 + 2.94819i −0.0483466 + 0.116629i
\(640\) −3.09950 −0.122518
\(641\) −12.1939 −0.481630 −0.240815 0.970571i \(-0.577415\pi\)
−0.240815 + 0.970571i \(0.577415\pi\)
\(642\) −7.35808 + 11.0089i −0.290400 + 0.434486i
\(643\) 28.6315 + 28.6315i 1.12912 + 1.12912i 0.990321 + 0.138797i \(0.0443234\pi\)
0.138797 + 0.990321i \(0.455677\pi\)
\(644\) −5.76872 5.76872i −0.227319 0.227319i
\(645\) −4.26971 + 6.38818i −0.168120 + 0.251534i
\(646\) −27.4377 −1.07952
\(647\) 18.5157 0.727925 0.363963 0.931414i \(-0.381424\pi\)
0.363963 + 0.931414i \(0.381424\pi\)
\(648\) −9.00000 0.00493109i −0.353553 0.000193711i
\(649\) 3.81024i 0.149565i
\(650\) 15.7192 + 5.36776i 0.616556 + 0.210541i
\(651\) −0.0598268 0.300985i −0.00234480 0.0117965i
\(652\) −16.4136 16.4136i −0.642806 0.642806i
\(653\) 42.5130i 1.66366i −0.555028 0.831831i \(-0.687293\pi\)
0.555028 0.831831i \(-0.312707\pi\)
\(654\) 5.28250 + 26.5759i 0.206562 + 1.03920i
\(655\) 18.2737 + 18.2737i 0.714012 + 0.714012i
\(656\) −2.21794 + 2.21794i −0.0865958 + 0.0865958i
\(657\) −5.83829 + 14.0840i −0.227774 + 0.549468i
\(658\) −0.805736 + 0.805736i −0.0314109 + 0.0314109i
\(659\) 26.7078i 1.04039i 0.854049 + 0.520193i \(0.174140\pi\)
−0.854049 + 0.520193i \(0.825860\pi\)
\(660\) −9.50727 + 1.88976i −0.370070 + 0.0735588i
\(661\) −17.9757 + 17.9757i −0.699175 + 0.699175i −0.964233 0.265057i \(-0.914609\pi\)
0.265057 + 0.964233i \(0.414609\pi\)
\(662\) −23.1878 −0.901220
\(663\) −13.9620 18.2693i −0.542237 0.709520i
\(664\) 13.2248 0.513221
\(665\) 16.3324 16.3324i 0.633344 0.633344i
\(666\) −0.532616 1.28685i −0.0206385 0.0498643i
\(667\) 77.5441i 3.00252i
\(668\) 10.1688 10.1688i 0.393444 0.393444i
\(669\) 16.2608 24.3288i 0.628678 0.940604i
\(670\) 32.9899 32.9899i 1.27451 1.27451i
\(671\) 10.3998 + 10.3998i 0.401480 + 0.401480i
\(672\) −1.69882 + 0.337674i −0.0655333 + 0.0130260i
\(673\) 17.8573i 0.688350i 0.938906 + 0.344175i \(0.111841\pi\)
−0.938906 + 0.344175i \(0.888159\pi\)
\(674\) 6.20283 + 6.20283i 0.238924 + 0.238924i
\(675\) 19.9093 13.2911i 0.766308 0.511575i
\(676\) −10.2848 7.95127i −0.395570 0.305818i
\(677\) 7.00399i 0.269185i 0.990901 + 0.134593i \(0.0429726\pi\)
−0.990901 + 0.134593i \(0.957027\pi\)
\(678\) 18.5165 27.7037i 0.711123 1.06396i
\(679\) −2.53616 −0.0973289
\(680\) −11.4121 −0.437633
\(681\) 37.9717 + 25.3794i 1.45508 + 0.972542i
\(682\) 0.226205 + 0.226205i 0.00866183 + 0.00866183i
\(683\) 2.50202 + 2.50202i 0.0957372 + 0.0957372i 0.753353 0.657616i \(-0.228435\pi\)
−0.657616 + 0.753353i \(0.728435\pi\)
\(684\) −8.56095 + 20.6519i −0.327336 + 0.789647i
\(685\) −62.3326 −2.38161
\(686\) 1.00000 0.0381802
\(687\) 3.94733 + 2.63830i 0.150600 + 0.100658i
\(688\) 1.43126i 0.0545663i
\(689\) −8.89352 18.1171i −0.338816 0.690205i
\(690\) −42.9568 + 8.53853i −1.63534 + 0.325056i
\(691\) −16.1198 16.1198i −0.613227 0.613227i 0.330558 0.943786i \(-0.392763\pi\)
−0.943786 + 0.330558i \(0.892763\pi\)
\(692\) 8.72942i 0.331843i
\(693\) −5.00500 + 2.07153i −0.190124 + 0.0786910i
\(694\) −6.05391 6.05391i −0.229803 0.229803i
\(695\) −12.1396 + 12.1396i −0.460482 + 0.460482i
\(696\) 13.6874 + 9.14836i 0.518820 + 0.346768i
\(697\) −8.16624 + 8.16624i −0.309318 + 0.309318i
\(698\) 0.0444381i 0.00168201i
\(699\) −1.27249 6.40182i −0.0481300 0.242139i
\(700\) 3.25756 3.25756i 0.123124 0.123124i
\(701\) −44.4648 −1.67941 −0.839706 0.543041i \(-0.817273\pi\)
−0.839706 + 0.543041i \(0.817273\pi\)
\(702\) −18.1074 + 4.80869i −0.683418 + 0.181492i
\(703\) −3.45951 −0.130478
\(704\) 1.27674 1.27674i 0.0481190 0.0481190i
\(705\) 1.19260 + 5.99992i 0.0449161 + 0.225970i
\(706\) 2.40751i 0.0906076i
\(707\) 6.04727 6.04727i 0.227431 0.227431i
\(708\) 3.03879 + 2.03106i 0.114205 + 0.0763319i
\(709\) 17.0295 17.0295i 0.639557 0.639557i −0.310890 0.950446i \(-0.600627\pi\)
0.950446 + 0.310890i \(0.100627\pi\)
\(710\) 2.33155 + 2.33155i 0.0875016 + 0.0875016i
\(711\) −12.1651 + 5.03504i −0.456227 + 0.188829i
\(712\) 4.51157i 0.169078i
\(713\) 1.02206 + 1.02206i 0.0382766 + 0.0382766i
\(714\) −6.25489 + 1.24328i −0.234083 + 0.0465287i
\(715\) −18.1134 + 8.89172i −0.677402 + 0.332531i
\(716\) 21.4346i 0.801048i
\(717\) −6.00667 4.01472i −0.224323 0.149933i
\(718\) 27.9888 1.04453
\(719\) −6.18328 −0.230598 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(720\) −3.56073 + 8.58971i −0.132701 + 0.320120i
\(721\) −4.75235 4.75235i −0.176987 0.176987i
\(722\) 25.8324 + 25.8324i 0.961382 + 0.961382i
\(723\) −30.2079 20.1903i −1.12345 0.750885i
\(724\) 7.53227 0.279935
\(725\) −43.7887 −1.62627
\(726\) −7.44941 + 11.1455i −0.276473 + 0.413649i
\(727\) 38.6481i 1.43338i −0.697392 0.716690i \(-0.745656\pi\)
0.697392 0.716690i \(-0.254344\pi\)
\(728\) −3.23661 + 1.58883i −0.119957 + 0.0588858i
\(729\) −10.3529 + 24.9362i −0.383443 + 0.923565i
\(730\) 11.1382 + 11.1382i 0.412243 + 0.412243i
\(731\) 5.26977i 0.194909i
\(732\) 13.8378 2.75055i 0.511461 0.101663i
\(733\) −11.6899 11.6899i −0.431776 0.431776i 0.457456 0.889232i \(-0.348761\pi\)
−0.889232 + 0.457456i \(0.848761\pi\)
\(734\) −12.8285 + 12.8285i −0.473508 + 0.473508i
\(735\) 2.98318 4.46333i 0.110036 0.164632i
\(736\) 5.76872 5.76872i 0.212638 0.212638i
\(737\) 27.1783i 1.00113i
\(738\) 3.59863 + 8.69460i 0.132467 + 0.320053i
\(739\) −3.88750 + 3.88750i −0.143004 + 0.143004i −0.774984 0.631980i \(-0.782242\pi\)
0.631980 + 0.774984i \(0.282242\pi\)
\(740\) −1.43891 −0.0528952
\(741\) −6.16442 + 46.1277i −0.226456 + 1.69454i
\(742\) −5.59755 −0.205492
\(743\) 1.32188 1.32188i 0.0484952 0.0484952i −0.682443 0.730939i \(-0.739083\pi\)
0.730939 + 0.682443i \(0.239083\pi\)
\(744\) 0.300985 0.0598268i 0.0110347 0.00219336i
\(745\) 16.3165i 0.597789i
\(746\) −19.3138 + 19.3138i −0.707130 + 0.707130i
\(747\) 15.1928 36.6502i 0.555874 1.34096i
\(748\) 4.70085 4.70085i 0.171880 0.171880i
\(749\) 5.40581 + 5.40581i 0.197524 + 0.197524i
\(750\) 0.411436 + 2.06991i 0.0150235 + 0.0755823i
\(751\) 14.9686i 0.546210i 0.961984 + 0.273105i \(0.0880507\pi\)
−0.961984 + 0.273105i \(0.911949\pi\)
\(752\) −0.805736 0.805736i −0.0293822 0.0293822i
\(753\) 8.79060 + 44.2250i 0.320347 + 1.61165i
\(754\) 32.4322 + 11.0749i 1.18111 + 0.403324i
\(755\) 66.8262i 2.43205i
\(756\) −1.01581 + 5.09589i −0.0369448 + 0.185336i
\(757\) 16.6501 0.605159 0.302579 0.953124i \(-0.402152\pi\)
0.302579 + 0.953124i \(0.402152\pi\)
\(758\) 15.6243 0.567502
\(759\) 14.1775 21.2119i 0.514612 0.769943i
\(760\) 16.3324 + 16.3324i 0.592439 + 0.592439i
\(761\) 0.381043 + 0.381043i 0.0138128 + 0.0138128i 0.713979 0.700167i \(-0.246891\pi\)
−0.700167 + 0.713979i \(0.746891\pi\)
\(762\) 12.0124 17.9725i 0.435162 0.651073i
\(763\) 15.6438 0.566344
\(764\) 1.80118 0.0651645
\(765\) −13.1103 + 31.6266i −0.474004 + 1.14346i
\(766\) 26.0661i 0.941808i
\(767\) 7.20038 + 2.45878i 0.259991 + 0.0887813i
\(768\) −0.337674 1.69882i −0.0121847 0.0613007i
\(769\) 29.7844 + 29.7844i 1.07405 + 1.07405i 0.997029 + 0.0770249i \(0.0245421\pi\)
0.0770249 + 0.997029i \(0.475458\pi\)
\(770\) 5.59641i 0.201681i
\(771\) 0.419021 + 2.10807i 0.0150907 + 0.0759203i
\(772\) −14.4054 14.4054i −0.518462 0.518462i
\(773\) −22.5034 + 22.5034i −0.809390 + 0.809390i −0.984541 0.175151i \(-0.943958\pi\)
0.175151 + 0.984541i \(0.443958\pi\)
\(774\) −3.96648 1.64424i −0.142572 0.0591011i
\(775\) −0.577154 + 0.577154i −0.0207320 + 0.0207320i
\(776\) 2.53616i 0.0910428i