Properties

Label 546.2.o.d.265.3
Level $546$
Weight $2$
Character 546.265
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 265.3
Root \(-1.91681i\) of defining polynomial
Character \(\chi\) \(=\) 546.265
Dual form 546.2.o.d.307.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(-2.27220 - 2.27220i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.27220 + 1.35539i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(-2.27220 - 2.27220i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.27220 + 1.35539i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -3.21338 q^{10} +(0.355392 + 0.355392i) q^{11} -1.00000 q^{12} +(-2.00000 + 3.00000i) q^{13} +(-0.648285 + 2.56510i) q^{14} +(-2.27220 + 2.27220i) q^{15} -1.00000 q^{16} +4.32583 q^{17} +(-0.707107 + 0.707107i) q^{18} +(-5.98299 - 5.98299i) q^{19} +(-2.27220 + 2.27220i) q^{20} +(1.35539 + 2.27220i) q^{21} +0.502600 q^{22} +2.38496i q^{23} +(-0.707107 + 0.707107i) q^{24} +5.32583i q^{25} +(0.707107 + 3.53553i) q^{26} +1.00000i q^{27} +(1.35539 + 2.27220i) q^{28} +1.09574 q^{29} +3.21338i q^{30} +(-1.08319 - 1.08319i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.355392 - 0.355392i) q^{33} +(3.05882 - 3.05882i) q^{34} +(8.24264 + 2.08319i) q^{35} +1.00000i q^{36} +(-5.18902 - 5.18902i) q^{37} -8.46122 q^{38} +(3.00000 + 2.00000i) q^{39} +3.21338i q^{40} +(-3.53186 - 3.53186i) q^{41} +(2.56510 + 0.648285i) q^{42} -7.44867i q^{43} +(0.355392 - 0.355392i) q^{44} +(2.27220 + 2.27220i) q^{45} +(1.68642 + 1.68642i) q^{46} +(4.71078 - 4.71078i) q^{47} +1.00000i q^{48} +(3.32583 - 6.15945i) q^{49} +(3.76593 + 3.76593i) q^{50} -4.32583i q^{51} +(3.00000 + 2.00000i) q^{52} -11.2552 q^{53} +(0.707107 + 0.707107i) q^{54} -1.61504i q^{55} +(2.56510 + 0.648285i) q^{56} +(-5.98299 + 5.98299i) q^{57} +(0.774804 - 0.774804i) q^{58} +(-3.61504 + 3.61504i) q^{59} +(2.27220 + 2.27220i) q^{60} +4.32583i q^{61} -1.53186 q^{62} +(2.27220 - 1.35539i) q^{63} +1.00000i q^{64} +(11.3610 - 2.27220i) q^{65} -0.502600i q^{66} +(-0.531858 + 0.531858i) q^{67} -4.32583i q^{68} +2.38496 q^{69} +(7.30146 - 4.35539i) q^{70} +(6.38496 - 6.38496i) q^{71} +(0.707107 + 0.707107i) q^{72} +(5.18902 - 5.18902i) q^{73} -7.33838 q^{74} +5.32583 q^{75} +(-5.98299 + 5.98299i) q^{76} +(-1.28922 - 0.325828i) q^{77} +(3.53553 - 0.707107i) q^{78} -11.3143 q^{79} +(2.27220 + 2.27220i) q^{80} +1.00000 q^{81} -4.99480 q^{82} +(-6.71078 - 6.71078i) q^{83} +(2.27220 - 1.35539i) q^{84} +(-9.82917 - 9.82917i) q^{85} +(-5.26701 - 5.26701i) q^{86} -1.09574i q^{87} -0.502600i q^{88} +(3.75044 - 3.75044i) q^{89} +3.21338 q^{90} +(0.478235 - 9.52740i) q^{91} +2.38496 q^{92} +(-1.08319 + 1.08319i) q^{93} -6.66205i q^{94} +27.1891i q^{95} +(0.707107 + 0.707107i) q^{96} +(12.9931 + 12.9931i) q^{97} +(-2.00368 - 6.70711i) q^{98} +(-0.355392 - 0.355392i) 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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 1.00000i 0.577350i
\(4\) 1.00000i 0.500000i
\(5\) −2.27220 2.27220i −1.01616 1.01616i −0.999867 0.0162935i \(-0.994813\pi\)
−0.0162935 0.999867i \(-0.505187\pi\)
\(6\) −0.707107 0.707107i −0.288675 0.288675i
\(7\) −2.27220 + 1.35539i −0.858813 + 0.512290i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −1.00000 −0.333333
\(10\) −3.21338 −1.01616
\(11\) 0.355392 + 0.355392i 0.107155 + 0.107155i 0.758651 0.651497i \(-0.225859\pi\)
−0.651497 + 0.758651i \(0.725859\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.00000 + 3.00000i −0.554700 + 0.832050i
\(14\) −0.648285 + 2.56510i −0.173261 + 0.685551i
\(15\) −2.27220 + 2.27220i −0.586681 + 0.586681i
\(16\) −1.00000 −0.250000
\(17\) 4.32583 1.04917 0.524584 0.851359i \(-0.324221\pi\)
0.524584 + 0.851359i \(0.324221\pi\)
\(18\) −0.707107 + 0.707107i −0.166667 + 0.166667i
\(19\) −5.98299 5.98299i −1.37259 1.37259i −0.856584 0.516007i \(-0.827418\pi\)
−0.516007 0.856584i \(-0.672582\pi\)
\(20\) −2.27220 + 2.27220i −0.508080 + 0.508080i
\(21\) 1.35539 + 2.27220i 0.295771 + 0.495836i
\(22\) 0.502600 0.107155
\(23\) 2.38496i 0.497298i 0.968594 + 0.248649i \(0.0799865\pi\)
−0.968594 + 0.248649i \(0.920014\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) 5.32583i 1.06517i
\(26\) 0.707107 + 3.53553i 0.138675 + 0.693375i
\(27\) 1.00000i 0.192450i
\(28\) 1.35539 + 2.27220i 0.256145 + 0.429406i
\(29\) 1.09574 0.203474 0.101737 0.994811i \(-0.467560\pi\)
0.101737 + 0.994811i \(0.467560\pi\)
\(30\) 3.21338i 0.586681i
\(31\) −1.08319 1.08319i −0.194546 0.194546i 0.603111 0.797657i \(-0.293928\pi\)
−0.797657 + 0.603111i \(0.793928\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 0.355392 0.355392i 0.0618657 0.0618657i
\(34\) 3.05882 3.05882i 0.524584 0.524584i
\(35\) 8.24264 + 2.08319i 1.39326 + 0.352123i
\(36\) 1.00000i 0.166667i
\(37\) −5.18902 5.18902i −0.853069 0.853069i 0.137441 0.990510i \(-0.456112\pi\)
−0.990510 + 0.137441i \(0.956112\pi\)
\(38\) −8.46122 −1.37259
\(39\) 3.00000 + 2.00000i 0.480384 + 0.320256i
\(40\) 3.21338i 0.508080i
\(41\) −3.53186 3.53186i −0.551583 0.551583i 0.375314 0.926898i \(-0.377535\pi\)
−0.926898 + 0.375314i \(0.877535\pi\)
\(42\) 2.56510 + 0.648285i 0.395803 + 0.100033i
\(43\) 7.44867i 1.13591i −0.823059 0.567956i \(-0.807734\pi\)
0.823059 0.567956i \(-0.192266\pi\)
\(44\) 0.355392 0.355392i 0.0535773 0.0535773i
\(45\) 2.27220 + 2.27220i 0.338720 + 0.338720i
\(46\) 1.68642 + 1.68642i 0.248649 + 0.248649i
\(47\) 4.71078 4.71078i 0.687138 0.687138i −0.274460 0.961598i \(-0.588499\pi\)
0.961598 + 0.274460i \(0.0884991\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 3.32583 6.15945i 0.475118 0.879922i
\(50\) 3.76593 + 3.76593i 0.532583 + 0.532583i
\(51\) 4.32583i 0.605737i
\(52\) 3.00000 + 2.00000i 0.416025 + 0.277350i
\(53\) −11.2552 −1.54602 −0.773010 0.634394i \(-0.781250\pi\)
−0.773010 + 0.634394i \(0.781250\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) 1.61504i 0.217773i
\(56\) 2.56510 + 0.648285i 0.342776 + 0.0866307i
\(57\) −5.98299 + 5.98299i −0.792466 + 0.792466i
\(58\) 0.774804 0.774804i 0.101737 0.101737i
\(59\) −3.61504 + 3.61504i −0.470639 + 0.470639i −0.902121 0.431483i \(-0.857991\pi\)
0.431483 + 0.902121i \(0.357991\pi\)
\(60\) 2.27220 + 2.27220i 0.293340 + 0.293340i
\(61\) 4.32583i 0.553865i 0.960889 + 0.276933i \(0.0893179\pi\)
−0.960889 + 0.276933i \(0.910682\pi\)
\(62\) −1.53186 −0.194546
\(63\) 2.27220 1.35539i 0.286271 0.170763i
\(64\) 1.00000i 0.125000i
\(65\) 11.3610 2.27220i 1.40916 0.281832i
\(66\) 0.502600i 0.0618657i
\(67\) −0.531858 + 0.531858i −0.0649768 + 0.0649768i −0.738848 0.673872i \(-0.764630\pi\)
0.673872 + 0.738848i \(0.264630\pi\)
\(68\) 4.32583i 0.524584i
\(69\) 2.38496 0.287115
\(70\) 7.30146 4.35539i 0.872692 0.520569i
\(71\) 6.38496 6.38496i 0.757755 0.757755i −0.218159 0.975913i \(-0.570005\pi\)
0.975913 + 0.218159i \(0.0700050\pi\)
\(72\) 0.707107 + 0.707107i 0.0833333 + 0.0833333i
\(73\) 5.18902 5.18902i 0.607329 0.607329i −0.334919 0.942247i \(-0.608709\pi\)
0.942247 + 0.334919i \(0.108709\pi\)
\(74\) −7.33838 −0.853069
\(75\) 5.32583 0.614974
\(76\) −5.98299 + 5.98299i −0.686296 + 0.686296i
\(77\) −1.28922 0.325828i −0.146920 0.0371315i
\(78\) 3.53553 0.707107i 0.400320 0.0800641i
\(79\) −11.3143 −1.27296 −0.636480 0.771293i \(-0.719610\pi\)
−0.636480 + 0.771293i \(0.719610\pi\)
\(80\) 2.27220 + 2.27220i 0.254040 + 0.254040i
\(81\) 1.00000 0.111111
\(82\) −4.99480 −0.551583
\(83\) −6.71078 6.71078i −0.736604 0.736604i 0.235315 0.971919i \(-0.424388\pi\)
−0.971919 + 0.235315i \(0.924388\pi\)
\(84\) 2.27220 1.35539i 0.247918 0.147885i
\(85\) −9.82917 9.82917i −1.06612 1.06612i
\(86\) −5.26701 5.26701i −0.567956 0.567956i
\(87\) 1.09574i 0.117475i
\(88\) 0.502600i 0.0535773i
\(89\) 3.75044 3.75044i 0.397546 0.397546i −0.479821 0.877367i \(-0.659298\pi\)
0.877367 + 0.479821i \(0.159298\pi\)
\(90\) 3.21338 0.338720
\(91\) 0.478235 9.52740i 0.0501326 0.998743i
\(92\) 2.38496 0.248649
\(93\) −1.08319 + 1.08319i −0.112321 + 0.112321i
\(94\) 6.66205i 0.687138i
\(95\) 27.1891i 2.78955i
\(96\) 0.707107 + 0.707107i 0.0721688 + 0.0721688i
\(97\) 12.9931 + 12.9931i 1.31925 + 1.31925i 0.914372 + 0.404876i \(0.132685\pi\)
0.404876 + 0.914372i \(0.367315\pi\)
\(98\) −2.00368 6.70711i −0.202402 0.677520i
\(99\) −0.355392 0.355392i −0.0357182 0.0357182i
\(100\) 5.32583 0.532583
\(101\) 19.7996 1.97013 0.985067 0.172171i \(-0.0550783\pi\)
0.985067 + 0.172171i \(0.0550783\pi\)
\(102\) −3.05882 3.05882i −0.302869 0.302869i
\(103\) −2.70386 −0.266420 −0.133210 0.991088i \(-0.542528\pi\)
−0.133210 + 0.991088i \(0.542528\pi\)
\(104\) 3.53553 0.707107i 0.346688 0.0693375i
\(105\) 2.08319 8.24264i 0.203298 0.804399i
\(106\) −7.95862 + 7.95862i −0.773010 + 0.773010i
\(107\) −11.6673 −1.12792 −0.563958 0.825804i \(-0.690722\pi\)
−0.563958 + 0.825804i \(0.690722\pi\)
\(108\) 1.00000 0.0962250
\(109\) −5.29626 + 5.29626i −0.507290 + 0.507290i −0.913694 0.406404i \(-0.866783\pi\)
0.406404 + 0.913694i \(0.366783\pi\)
\(110\) −1.14201 1.14201i −0.108886 0.108886i
\(111\) −5.18902 + 5.18902i −0.492520 + 0.492520i
\(112\) 2.27220 1.35539i 0.214703 0.128072i
\(113\) 20.3440 1.91380 0.956902 0.290412i \(-0.0937923\pi\)
0.956902 + 0.290412i \(0.0937923\pi\)
\(114\) 8.46122i 0.792466i
\(115\) 5.41911 5.41911i 0.505334 0.505334i
\(116\) 1.09574i 0.101737i
\(117\) 2.00000 3.00000i 0.184900 0.277350i
\(118\) 5.11245i 0.470639i
\(119\) −9.82917 + 5.86319i −0.901038 + 0.537478i
\(120\) 3.21338 0.293340
\(121\) 10.7474i 0.977036i
\(122\) 3.05882 + 3.05882i 0.276933 + 0.276933i
\(123\) −3.53186 + 3.53186i −0.318457 + 0.318457i
\(124\) −1.08319 + 1.08319i −0.0972731 + 0.0972731i
\(125\) 0.740347 0.740347i 0.0662186 0.0662186i
\(126\) 0.648285 2.56510i 0.0577538 0.228517i
\(127\) 7.60812i 0.675112i 0.941305 + 0.337556i \(0.109600\pi\)
−0.941305 + 0.337556i \(0.890400\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −7.44867 −0.655819
\(130\) 6.42677 9.64015i 0.563665 0.845497i
\(131\) 6.87024i 0.600255i 0.953899 + 0.300128i \(0.0970293\pi\)
−0.953899 + 0.300128i \(0.902971\pi\)
\(132\) −0.355392 0.355392i −0.0309329 0.0309329i
\(133\) 21.7039 + 5.48528i 1.88196 + 0.475634i
\(134\) 0.752160i 0.0649768i
\(135\) 2.27220 2.27220i 0.195560 0.195560i
\(136\) −3.05882 3.05882i −0.262292 0.262292i
\(137\) −0.272205 0.272205i −0.0232560 0.0232560i 0.695383 0.718639i \(-0.255235\pi\)
−0.718639 + 0.695383i \(0.755235\pi\)
\(138\) 1.68642 1.68642i 0.143557 0.143557i
\(139\) 20.3440i 1.72556i −0.505583 0.862778i \(-0.668722\pi\)
0.505583 0.862778i \(-0.331278\pi\)
\(140\) 2.08319 8.24264i 0.176061 0.696630i
\(141\) −4.71078 4.71078i −0.396720 0.396720i
\(142\) 9.02969i 0.757755i
\(143\) −1.77696 + 0.355392i −0.148597 + 0.0297193i
\(144\) 1.00000 0.0833333
\(145\) −2.48974 2.48974i −0.206762 0.206762i
\(146\) 7.33838i 0.607329i
\(147\) −6.15945 3.32583i −0.508023 0.274310i
\(148\) −5.18902 + 5.18902i −0.426535 + 0.426535i
\(149\) 10.5685 10.5685i 0.865803 0.865803i −0.126202 0.992005i \(-0.540279\pi\)
0.992005 + 0.126202i \(0.0402787\pi\)
\(150\) 3.76593 3.76593i 0.307487 0.307487i
\(151\) −0.149362 0.149362i −0.0121549 0.0121549i 0.701003 0.713158i \(-0.252736\pi\)
−0.713158 + 0.701003i \(0.752736\pi\)
\(152\) 8.46122i 0.686296i
\(153\) −4.32583 −0.349722
\(154\) −1.14201 + 0.681219i −0.0920257 + 0.0548942i
\(155\) 4.92244i 0.395380i
\(156\) 2.00000 3.00000i 0.160128 0.240192i
\(157\) 10.7630i 0.858980i 0.903072 + 0.429490i \(0.141307\pi\)
−0.903072 + 0.429490i \(0.858693\pi\)
\(158\) −8.00043 + 8.00043i −0.636480 + 0.636480i
\(159\) 11.2552i 0.892595i
\(160\) 3.21338 0.254040
\(161\) −3.23255 5.41911i −0.254761 0.427085i
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) −3.40901 3.40901i −0.267015 0.267015i 0.560881 0.827896i \(-0.310462\pi\)
−0.827896 + 0.560881i \(0.810462\pi\)
\(164\) −3.53186 + 3.53186i −0.275792 + 0.275792i
\(165\) −1.61504 −0.125731
\(166\) −9.49048 −0.736604
\(167\) 10.0226 10.0226i 0.775575 0.775575i −0.203500 0.979075i \(-0.565232\pi\)
0.979075 + 0.203500i \(0.0652316\pi\)
\(168\) 0.648285 2.56510i 0.0500163 0.197902i
\(169\) −5.00000 12.0000i −0.384615 0.923077i
\(170\) −13.9005 −1.06612
\(171\) 5.98299 + 5.98299i 0.457531 + 0.457531i
\(172\) −7.44867 −0.567956
\(173\) 19.7405 1.50084 0.750420 0.660961i \(-0.229851\pi\)
0.750420 + 0.660961i \(0.229851\pi\)
\(174\) −0.774804 0.774804i −0.0587377 0.0587377i
\(175\) −7.21858 12.1014i −0.545673 0.914778i
\(176\) −0.355392 0.355392i −0.0267886 0.0267886i
\(177\) 3.61504 + 3.61504i 0.271723 + 0.271723i
\(178\) 5.30392i 0.397546i
\(179\) 9.79960i 0.732457i 0.930525 + 0.366228i \(0.119351\pi\)
−0.930525 + 0.366228i \(0.880649\pi\)
\(180\) 2.27220 2.27220i 0.169360 0.169360i
\(181\) −10.4372 −0.775788 −0.387894 0.921704i \(-0.626797\pi\)
−0.387894 + 0.921704i \(0.626797\pi\)
\(182\) −6.39872 7.07505i −0.474305 0.524438i
\(183\) 4.32583 0.319774
\(184\) 1.68642 1.68642i 0.124324 0.124324i
\(185\) 23.5810i 1.73371i
\(186\) 1.53186i 0.112321i
\(187\) 1.53736 + 1.53736i 0.112423 + 0.112423i
\(188\) −4.71078 4.71078i −0.343569 0.343569i
\(189\) −1.35539 2.27220i −0.0985902 0.165279i
\(190\) 19.2256 + 19.2256i 1.39477 + 1.39477i
\(191\) 11.1410 0.806136 0.403068 0.915170i \(-0.367944\pi\)
0.403068 + 0.915170i \(0.367944\pi\)
\(192\) 1.00000 0.0721688
\(193\) 4.03661 + 4.03661i 0.290562 + 0.290562i 0.837302 0.546741i \(-0.184132\pi\)
−0.546741 + 0.837302i \(0.684132\pi\)
\(194\) 18.3750 1.31925
\(195\) −2.27220 11.3610i −0.162716 0.813580i
\(196\) −6.15945 3.32583i −0.439961 0.237559i
\(197\) 0.627596 0.627596i 0.0447144 0.0447144i −0.684396 0.729110i \(-0.739934\pi\)
0.729110 + 0.684396i \(0.239934\pi\)
\(198\) −0.502600 −0.0357182
\(199\) −16.5375 −1.17231 −0.586156 0.810198i \(-0.699359\pi\)
−0.586156 + 0.810198i \(0.699359\pi\)
\(200\) 3.76593 3.76593i 0.266291 0.266291i
\(201\) 0.531858 + 0.531858i 0.0375143 + 0.0375143i
\(202\) 14.0004 14.0004i 0.985067 0.985067i
\(203\) −2.48974 + 1.48515i −0.174746 + 0.104237i
\(204\) −4.32583 −0.302869
\(205\) 16.0502i 1.12100i
\(206\) −1.91192 + 1.91192i −0.133210 + 0.133210i
\(207\) 2.38496i 0.165766i
\(208\) 2.00000 3.00000i 0.138675 0.208013i
\(209\) 4.25261i 0.294159i
\(210\) −4.35539 7.30146i −0.300551 0.503849i
\(211\) −0.551329 −0.0379551 −0.0189775 0.999820i \(-0.506041\pi\)
−0.0189775 + 0.999820i \(0.506041\pi\)
\(212\) 11.2552i 0.773010i
\(213\) −6.38496 6.38496i −0.437490 0.437490i
\(214\) −8.24999 + 8.24999i −0.563958 + 0.563958i
\(215\) −16.9249 + 16.9249i −1.15427 + 1.15427i
\(216\) 0.707107 0.707107i 0.0481125 0.0481125i
\(217\) 3.92936 + 0.993080i 0.266743 + 0.0674147i
\(218\) 7.49005i 0.507290i
\(219\) −5.18902 5.18902i −0.350641 0.350641i
\(220\) −1.61504 −0.108886
\(221\) −8.65166 + 12.9775i −0.581973 + 0.872960i
\(222\) 7.33838i 0.492520i
\(223\) 9.89430 + 9.89430i 0.662571 + 0.662571i 0.955985 0.293414i \(-0.0947915\pi\)
−0.293414 + 0.955985i \(0.594792\pi\)
\(224\) 0.648285 2.56510i 0.0433153 0.171388i
\(225\) 5.32583i 0.355055i
\(226\) 14.3854 14.3854i 0.956902 0.956902i
\(227\) 1.67417 + 1.67417i 0.111119 + 0.111119i 0.760480 0.649361i \(-0.224964\pi\)
−0.649361 + 0.760480i \(0.724964\pi\)
\(228\) 5.98299 + 5.98299i 0.396233 + 0.396233i
\(229\) −1.32583 + 1.32583i −0.0876132 + 0.0876132i −0.749555 0.661942i \(-0.769733\pi\)
0.661942 + 0.749555i \(0.269733\pi\)
\(230\) 7.66377i 0.505334i
\(231\) −0.325828 + 1.28922i −0.0214379 + 0.0848242i
\(232\) −0.774804 0.774804i −0.0508684 0.0508684i
\(233\) 10.2117i 0.668988i −0.942398 0.334494i \(-0.891435\pi\)
0.942398 0.334494i \(-0.108565\pi\)
\(234\) −0.707107 3.53553i −0.0462250 0.231125i
\(235\) −21.4077 −1.39649
\(236\) 3.61504 + 3.61504i 0.235319 + 0.235319i
\(237\) 11.3143i 0.734944i
\(238\) −2.80437 + 11.0962i −0.181780 + 0.719258i
\(239\) −15.2212 + 15.2212i −0.984575 + 0.984575i −0.999883 0.0153074i \(-0.995127\pi\)
0.0153074 + 0.999883i \(0.495127\pi\)
\(240\) 2.27220 2.27220i 0.146670 0.146670i
\(241\) 3.38496 3.38496i 0.218044 0.218044i −0.589630 0.807674i \(-0.700726\pi\)
0.807674 + 0.589630i \(0.200726\pi\)
\(242\) −7.59955 7.59955i −0.488518 0.488518i
\(243\) 1.00000i 0.0641500i
\(244\) 4.32583 0.276933
\(245\) −21.5525 + 6.43858i −1.37694 + 0.411346i
\(246\) 4.99480i 0.318457i
\(247\) 29.9149 5.98299i 1.90344 0.380688i
\(248\) 1.53186i 0.0972731i
\(249\) −6.71078 + 6.71078i −0.425279 + 0.425279i
\(250\) 1.04701i 0.0662186i
\(251\) −17.2281 −1.08743 −0.543714 0.839271i \(-0.682982\pi\)
−0.543714 + 0.839271i \(0.682982\pi\)
\(252\) −1.35539 2.27220i −0.0853816 0.143135i
\(253\) −0.847593 + 0.847593i −0.0532877 + 0.0532877i
\(254\) 5.37976 + 5.37976i 0.337556 + 0.337556i
\(255\) −9.82917 + 9.82917i −0.615526 + 0.615526i
\(256\) 1.00000 0.0625000
\(257\) −3.32324 −0.207298 −0.103649 0.994614i \(-0.533052\pi\)
−0.103649 + 0.994614i \(0.533052\pi\)
\(258\) −5.26701 + 5.26701i −0.327909 + 0.327909i
\(259\) 18.8237 + 4.75736i 1.16965 + 0.295608i
\(260\) −2.27220 11.3610i −0.140916 0.704581i
\(261\) −1.09574 −0.0678245
\(262\) 4.85799 + 4.85799i 0.300128 + 0.300128i
\(263\) −0.818029 −0.0504418 −0.0252209 0.999682i \(-0.508029\pi\)
−0.0252209 + 0.999682i \(0.508029\pi\)
\(264\) −0.502600 −0.0309329
\(265\) 25.5741 + 25.5741i 1.57100 + 1.57100i
\(266\) 19.2256 11.4683i 1.17880 0.703165i
\(267\) −3.75044 3.75044i −0.229523 0.229523i
\(268\) 0.531858 + 0.531858i 0.0324884 + 0.0324884i
\(269\) 21.6081i 1.31747i −0.752375 0.658735i \(-0.771092\pi\)
0.752375 0.658735i \(-0.228908\pi\)
\(270\) 3.21338i 0.195560i
\(271\) −15.0422 + 15.0422i −0.913751 + 0.913751i −0.996565 0.0828139i \(-0.973609\pi\)
0.0828139 + 0.996565i \(0.473609\pi\)
\(272\) −4.32583 −0.262292
\(273\) −9.52740 0.478235i −0.576624 0.0289441i
\(274\) −0.384955 −0.0232560
\(275\) −1.89275 + 1.89275i −0.114137 + 0.114137i
\(276\) 2.38496i 0.143557i
\(277\) 17.7996i 1.06947i 0.845018 + 0.534737i \(0.179589\pi\)
−0.845018 + 0.534737i \(0.820411\pi\)
\(278\) −14.3854 14.3854i −0.862778 0.862778i
\(279\) 1.08319 + 1.08319i 0.0648487 + 0.0648487i
\(280\) −4.35539 7.30146i −0.260284 0.436346i
\(281\) 6.20862 + 6.20862i 0.370375 + 0.370375i 0.867614 0.497239i \(-0.165653\pi\)
−0.497239 + 0.867614i \(0.665653\pi\)
\(282\) −6.66205 −0.396720
\(283\) −25.1090 −1.49258 −0.746288 0.665624i \(-0.768166\pi\)
−0.746288 + 0.665624i \(0.768166\pi\)
\(284\) −6.38496 6.38496i −0.378877 0.378877i
\(285\) 27.1891 1.61055
\(286\) −1.00520 + 1.50780i −0.0594387 + 0.0891580i
\(287\) 12.8122 + 3.23805i 0.756277 + 0.191136i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) 1.71278 0.100752
\(290\) −3.52103 −0.206762
\(291\) 12.9931 12.9931i 0.761668 0.761668i
\(292\) −5.18902 5.18902i −0.303664 0.303664i
\(293\) −8.51343 + 8.51343i −0.497360 + 0.497360i −0.910615 0.413255i \(-0.864392\pi\)
0.413255 + 0.910615i \(0.364392\pi\)
\(294\) −6.70711 + 2.00368i −0.391166 + 0.116857i
\(295\) 16.4282 0.956489
\(296\) 7.33838i 0.426535i
\(297\) −0.355392 + 0.355392i −0.0206219 + 0.0206219i
\(298\) 14.9461i 0.865803i
\(299\) −7.15487 4.76991i −0.413777 0.275851i
\(300\) 5.32583i 0.307487i
\(301\) 10.0959 + 16.9249i 0.581916 + 0.975535i
\(302\) −0.211229 −0.0121549
\(303\) 19.7996i 1.13746i
\(304\) 5.98299 + 5.98299i 0.343148 + 0.343148i
\(305\) 9.82917 9.82917i 0.562816 0.562816i
\(306\) −3.05882 + 3.05882i −0.174861 + 0.174861i
\(307\) −10.0397 + 10.0397i −0.572993 + 0.572993i −0.932964 0.359970i \(-0.882787\pi\)
0.359970 + 0.932964i \(0.382787\pi\)
\(308\) −0.325828 + 1.28922i −0.0185658 + 0.0734600i
\(309\) 2.70386i 0.153817i
\(310\) 3.48069 + 3.48069i 0.197690 + 0.197690i
\(311\) −15.7064 −0.890631 −0.445316 0.895374i \(-0.646908\pi\)
−0.445316 + 0.895374i \(0.646908\pi\)
\(312\) −0.707107 3.53553i −0.0400320 0.200160i
\(313\) 20.7702i 1.17400i −0.809587 0.587000i \(-0.800309\pi\)
0.809587 0.587000i \(-0.199691\pi\)
\(314\) 7.61058 + 7.61058i 0.429490 + 0.429490i
\(315\) −8.24264 2.08319i −0.464420 0.117374i
\(316\) 11.3143i 0.636480i
\(317\) 19.0126 19.0126i 1.06785 1.06785i 0.0703273 0.997524i \(-0.477596\pi\)
0.997524 0.0703273i \(-0.0224044\pi\)
\(318\) 7.95862 + 7.95862i 0.446297 + 0.446297i
\(319\) 0.389416 + 0.389416i 0.0218031 + 0.0218031i
\(320\) 2.27220 2.27220i 0.127020 0.127020i
\(321\) 11.6673i 0.651203i
\(322\) −6.11764 1.54613i −0.340923 0.0861625i
\(323\) −25.8814 25.8814i −1.44008 1.44008i
\(324\) 1.00000i 0.0555556i
\(325\) −15.9775 10.6517i −0.886271 0.590848i
\(326\) −4.82107 −0.267015
\(327\) 5.29626 + 5.29626i 0.292884 + 0.292884i
\(328\) 4.99480i 0.275792i
\(329\) −4.31891 + 17.0888i −0.238109 + 0.942137i
\(330\) −1.14201 + 1.14201i −0.0628655 + 0.0628655i
\(331\) −13.9785 + 13.9785i −0.768329 + 0.768329i −0.977812 0.209483i \(-0.932822\pi\)
0.209483 + 0.977812i \(0.432822\pi\)
\(332\) −6.71078 + 6.71078i −0.368302 + 0.368302i
\(333\) 5.18902 + 5.18902i 0.284356 + 0.284356i
\(334\) 14.1742i 0.775575i
\(335\) 2.41698 0.132054
\(336\) −1.35539 2.27220i −0.0739427 0.123959i
\(337\) 1.09574i 0.0596887i 0.999555 + 0.0298443i \(0.00950116\pi\)
−0.999555 + 0.0298443i \(0.990499\pi\)
\(338\) −12.0208 4.94975i −0.653846 0.269231i
\(339\) 20.3440i 1.10493i
\(340\) −9.82917 + 9.82917i −0.533061 + 0.533061i
\(341\) 0.769911i 0.0416930i
\(342\) 8.46122 0.457531
\(343\) 0.791511 + 18.5033i 0.0427376 + 0.999086i
\(344\) −5.26701 + 5.26701i −0.283978 + 0.283978i
\(345\) −5.41911 5.41911i −0.291755 0.291755i
\(346\) 13.9586 13.9586i 0.750420 0.750420i
\(347\) 32.0983 1.72313 0.861564 0.507649i \(-0.169485\pi\)
0.861564 + 0.507649i \(0.169485\pi\)
\(348\) −1.09574 −0.0587377
\(349\) −18.9660 + 18.9660i −1.01523 + 1.01523i −0.0153431 + 0.999882i \(0.504884\pi\)
−0.999882 + 0.0153431i \(0.995116\pi\)
\(350\) −13.6613 3.45265i −0.730226 0.184552i
\(351\) −3.00000 2.00000i −0.160128 0.106752i
\(352\) −0.502600 −0.0267886
\(353\) −15.5500 15.5500i −0.827645 0.827645i 0.159545 0.987191i \(-0.448997\pi\)
−0.987191 + 0.159545i \(0.948997\pi\)
\(354\) 5.11245 0.271723
\(355\) −29.0159 −1.54000
\(356\) −3.75044 3.75044i −0.198773 0.198773i
\(357\) 5.86319 + 9.82917i 0.310313 + 0.520215i
\(358\) 6.92936 + 6.92936i 0.366228 + 0.366228i
\(359\) −14.1846 14.1846i −0.748632 0.748632i 0.225590 0.974222i \(-0.427569\pi\)
−0.974222 + 0.225590i \(0.927569\pi\)
\(360\) 3.21338i 0.169360i
\(361\) 52.5923i 2.76801i
\(362\) −7.38019 + 7.38019i −0.387894 + 0.387894i
\(363\) −10.7474 −0.564092
\(364\) −9.52740 0.478235i −0.499371 0.0250663i
\(365\) −23.5810 −1.23429
\(366\) 3.05882 3.05882i 0.159887 0.159887i
\(367\) 11.2552i 0.587516i −0.955880 0.293758i \(-0.905094\pi\)
0.955880 0.293758i \(-0.0949060\pi\)
\(368\) 2.38496i 0.124324i
\(369\) 3.53186 + 3.53186i 0.183861 + 0.183861i
\(370\) 16.6743 + 16.6743i 0.866856 + 0.866856i
\(371\) 25.5741 15.2552i 1.32774 0.792010i
\(372\) 1.08319 + 1.08319i 0.0561606 + 0.0561606i
\(373\) 17.1479 0.887887 0.443944 0.896055i \(-0.353579\pi\)
0.443944 + 0.896055i \(0.353579\pi\)
\(374\) 2.17416 0.112423
\(375\) −0.740347 0.740347i −0.0382314 0.0382314i
\(376\) −6.66205 −0.343569
\(377\) −2.19148 + 3.28722i −0.112867 + 0.169300i
\(378\) −2.56510 0.648285i −0.131934 0.0333442i
\(379\) 11.5685 11.5685i 0.594232 0.594232i −0.344540 0.938772i \(-0.611965\pi\)
0.938772 + 0.344540i \(0.111965\pi\)
\(380\) 27.1891 1.39477
\(381\) 7.60812 0.389776
\(382\) 7.87790 7.87790i 0.403068 0.403068i
\(383\) −1.26657 1.26657i −0.0647189 0.0647189i 0.674007 0.738725i \(-0.264572\pi\)
−0.738725 + 0.674007i \(0.764572\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) 2.18902 + 3.66971i 0.111563 + 0.187026i
\(386\) 5.70863 0.290562
\(387\) 7.44867i 0.378637i
\(388\) 12.9931 12.9931i 0.659624 0.659624i
\(389\) 7.90685i 0.400893i −0.979705 0.200447i \(-0.935761\pi\)
0.979705 0.200447i \(-0.0642393\pi\)
\(390\) −9.64015 6.42677i −0.488148 0.325432i
\(391\) 10.3169i 0.521748i
\(392\) −6.70711 + 2.00368i −0.338760 + 0.101201i
\(393\) 6.87024 0.346558
\(394\) 0.887555i 0.0447144i
\(395\) 25.7085 + 25.7085i 1.29353 + 1.29353i
\(396\) −0.355392 + 0.355392i −0.0178591 + 0.0178591i
\(397\) 16.4467 16.4467i 0.825435 0.825435i −0.161447 0.986881i \(-0.551616\pi\)
0.986881 + 0.161447i \(0.0516160\pi\)
\(398\) −11.6938 + 11.6938i −0.586156 + 0.586156i
\(399\) 5.48528 21.7039i 0.274608 1.08655i
\(400\) 5.32583i 0.266291i
\(401\) 15.0126 + 15.0126i 0.749691 + 0.749691i 0.974421 0.224730i \(-0.0721500\pi\)
−0.224730 + 0.974421i \(0.572150\pi\)
\(402\) 0.752160 0.0375143
\(403\) 5.41593 1.08319i 0.269787 0.0539574i
\(404\) 19.7996i 0.985067i
\(405\) −2.27220 2.27220i −0.112907 0.112907i
\(406\) −0.710351 + 2.81068i −0.0352541 + 0.139492i
\(407\) 3.68827i 0.182821i
\(408\) −3.05882 + 3.05882i −0.151434 + 0.151434i
\(409\) −19.0477 19.0477i −0.941850 0.941850i 0.0565493 0.998400i \(-0.481990\pi\)
−0.998400 + 0.0565493i \(0.981990\pi\)
\(410\) 11.3492 + 11.3492i 0.560498 + 0.560498i
\(411\) −0.272205 + 0.272205i −0.0134269 + 0.0134269i
\(412\) 2.70386i 0.133210i
\(413\) 3.31432 13.1139i 0.163087 0.645294i
\(414\) −1.68642 1.68642i −0.0828829 0.0828829i
\(415\) 30.4965i 1.49702i
\(416\) −0.707107 3.53553i −0.0346688 0.173344i
\(417\) −20.3440 −0.996250
\(418\) −3.00705 3.00705i −0.147079 0.147079i
\(419\) 38.8022i 1.89561i −0.318849 0.947805i \(-0.603296\pi\)
0.318849 0.947805i \(-0.396704\pi\)
\(420\) −8.24264 2.08319i −0.402200 0.101649i
\(421\) −19.5375 + 19.5375i −0.952199 + 0.952199i −0.998909 0.0467096i \(-0.985126\pi\)
0.0467096 + 0.998909i \(0.485126\pi\)
\(422\) −0.389849 + 0.389849i −0.0189775 + 0.0189775i
\(423\) −4.71078 + 4.71078i −0.229046 + 0.229046i
\(424\) 7.95862 + 7.95862i 0.386505 + 0.386505i
\(425\) 23.0386i 1.11754i
\(426\) −9.02969 −0.437490
\(427\) −5.86319 9.82917i −0.283740 0.475667i
\(428\) 11.6673i 0.563958i
\(429\) 0.355392 + 1.77696i 0.0171585 + 0.0857923i
\(430\) 23.9354i 1.15427i
\(431\) 1.45559 1.45559i 0.0701133 0.0701133i −0.671181 0.741294i \(-0.734212\pi\)
0.741294 + 0.671181i \(0.234212\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 35.8137 1.72110 0.860548 0.509369i \(-0.170121\pi\)
0.860548 + 0.509369i \(0.170121\pi\)
\(434\) 3.48069 2.07627i 0.167079 0.0996640i
\(435\) −2.48974 + 2.48974i −0.119374 + 0.119374i
\(436\) 5.29626 + 5.29626i 0.253645 + 0.253645i
\(437\) 14.2692 14.2692i 0.682586 0.682586i
\(438\) −7.33838 −0.350641
\(439\) −14.2667 −0.680912 −0.340456 0.940260i \(-0.610582\pi\)
−0.340456 + 0.940260i \(0.610582\pi\)
\(440\) −1.14201 + 1.14201i −0.0544431 + 0.0544431i
\(441\) −3.32583 + 6.15945i −0.158373 + 0.293307i
\(442\) 3.05882 + 15.2941i 0.145493 + 0.727467i
\(443\) −20.7019 −0.983575 −0.491788 0.870715i \(-0.663656\pi\)
−0.491788 + 0.870715i \(0.663656\pi\)
\(444\) 5.18902 + 5.18902i 0.246260 + 0.246260i
\(445\) −17.0435 −0.807941
\(446\) 13.9926 0.662571
\(447\) −10.5685 10.5685i −0.499871 0.499871i
\(448\) −1.35539 2.27220i −0.0640362 0.107352i
\(449\) −20.2382 20.2382i −0.955099 0.955099i 0.0439356 0.999034i \(-0.486010\pi\)
−0.999034 + 0.0439356i \(0.986010\pi\)
\(450\) −3.76593 3.76593i −0.177528 0.177528i
\(451\) 2.51038i 0.118209i
\(452\) 20.3440i 0.956902i
\(453\) −0.149362 + 0.149362i −0.00701762 + 0.00701762i
\(454\) 2.36764 0.111119
\(455\) −22.7348 + 20.5615i −1.06583 + 0.963940i
\(456\) 8.46122 0.396233
\(457\) −18.1891 + 18.1891i −0.850852 + 0.850852i −0.990238 0.139386i \(-0.955487\pi\)
0.139386 + 0.990238i \(0.455487\pi\)
\(458\) 1.87500i 0.0876132i
\(459\) 4.32583i 0.201912i
\(460\) −5.41911 5.41911i −0.252667 0.252667i
\(461\) 1.18339 + 1.18339i 0.0551158 + 0.0551158i 0.734127 0.679012i \(-0.237591\pi\)
−0.679012 + 0.734127i \(0.737591\pi\)
\(462\) 0.681219 + 1.14201i 0.0316932 + 0.0531311i
\(463\) 4.93946 + 4.93946i 0.229556 + 0.229556i 0.812507 0.582951i \(-0.198102\pi\)
−0.582951 + 0.812507i \(0.698102\pi\)
\(464\) −1.09574 −0.0508684
\(465\) 4.92244 0.228273
\(466\) −7.22074 7.22074i −0.334494 0.334494i
\(467\) 26.6900 1.23507 0.617533 0.786545i \(-0.288132\pi\)
0.617533 + 0.786545i \(0.288132\pi\)
\(468\) −3.00000 2.00000i −0.138675 0.0924500i
\(469\) 0.487614 1.92936i 0.0225159 0.0890898i
\(470\) −15.1375 + 15.1375i −0.698243 + 0.698243i
\(471\) 10.7630 0.495932
\(472\) 5.11245 0.235319
\(473\) 2.64719 2.64719i 0.121718 0.121718i
\(474\) 8.00043 + 8.00043i 0.367472 + 0.367472i
\(475\) 31.8644 31.8644i 1.46204 1.46204i
\(476\) 5.86319 + 9.82917i 0.268739 + 0.450519i
\(477\) 11.2552 0.515340
\(478\) 21.5260i 0.984575i
\(479\) 7.35998 7.35998i 0.336286 0.336286i −0.518682 0.854968i \(-0.673577\pi\)
0.854968 + 0.518682i \(0.173577\pi\)
\(480\) 3.21338i 0.146670i
\(481\) 25.9451 5.18902i 1.18299 0.236599i
\(482\) 4.78705i 0.218044i
\(483\) −5.41911 + 3.23255i −0.246578 + 0.147086i
\(484\) −10.7474 −0.488518
\(485\) 59.0459i 2.68113i
\(486\) −0.707107 0.707107i −0.0320750 0.0320750i
\(487\) 25.1766 25.1766i 1.14086 1.14086i 0.152567 0.988293i \(-0.451246\pi\)
0.988293 0.152567i \(-0.0487541\pi\)
\(488\) 3.05882 3.05882i 0.138466 0.138466i
\(489\) −3.40901 + 3.40901i −0.154161 + 0.154161i
\(490\) −10.6872 + 19.7927i −0.482797 + 0.894142i
\(491\) 7.77450i 0.350858i −0.984492 0.175429i \(-0.943869\pi\)
0.984492 0.175429i \(-0.0561313\pi\)
\(492\) 3.53186 + 3.53186i 0.159228 + 0.159228i
\(493\) 4.73998 0.213478
\(494\) 16.9224 25.3837i 0.761377 1.14207i
\(495\) 1.61504i 0.0725909i
\(496\) 1.08319 + 1.08319i 0.0486365 + 0.0486365i
\(497\) −5.85381 + 23.1620i −0.262579 + 1.03896i
\(498\) 9.49048i 0.425279i
\(499\) 23.4592 23.4592i 1.05018 1.05018i 0.0515063 0.998673i \(-0.483598\pi\)
0.998673 0.0515063i \(-0.0164022\pi\)
\(500\) −0.740347 0.740347i −0.0331093 0.0331093i
\(501\) −10.0226 10.0226i −0.447779 0.447779i
\(502\) −12.1821 + 12.1821i −0.543714 + 0.543714i
\(503\) 12.0000i 0.535054i −0.963550 0.267527i \(-0.913794\pi\)
0.963550 0.267527i \(-0.0862064\pi\)
\(504\) −2.56510 0.648285i −0.114259 0.0288769i
\(505\) −44.9887 44.9887i −2.00197 2.00197i
\(506\) 1.19868i 0.0532877i
\(507\) −12.0000 + 5.00000i −0.532939 + 0.222058i
\(508\) 7.60812 0.337556
\(509\) −11.0283 11.0283i −0.488820 0.488820i 0.419114 0.907934i \(-0.362341\pi\)
−0.907934 + 0.419114i \(0.862341\pi\)
\(510\) 13.9005i 0.615526i
\(511\) −4.75736 + 18.8237i −0.210453 + 0.832710i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 5.98299 5.98299i 0.264155 0.264155i
\(514\) −2.34989 + 2.34989i −0.103649 + 0.103649i
\(515\) 6.14373 + 6.14373i 0.270725 + 0.270725i
\(516\) 7.44867i 0.327909i
\(517\) 3.34834 0.147260
\(518\) 16.6743 9.94638i 0.732627 0.437019i
\(519\) 19.7405i 0.866511i
\(520\) −9.64015 6.42677i −0.422748 0.281832i
\(521\) 18.5654i 0.813366i 0.913569 + 0.406683i \(0.133315\pi\)
−0.913569 + 0.406683i \(0.866685\pi\)
\(522\) −0.774804 + 0.774804i −0.0339123 + 0.0339123i
\(523\) 27.5741i 1.20573i −0.797843 0.602866i \(-0.794026\pi\)
0.797843 0.602866i \(-0.205974\pi\)
\(524\) 6.87024 0.300128
\(525\) −12.1014 + 7.21858i −0.528147 + 0.315045i
\(526\) −0.578434 + 0.578434i −0.0252209 + 0.0252209i
\(527\) −4.68568 4.68568i −0.204111 0.204111i
\(528\) −0.355392 + 0.355392i −0.0154664 + 0.0154664i
\(529\) 17.3120 0.752695
\(530\) 36.1672 1.57100
\(531\) 3.61504 3.61504i 0.156880 0.156880i
\(532\) 5.48528 21.7039i 0.237817 0.940982i
\(533\) 17.6593 3.53186i 0.764909 0.152982i
\(534\) −5.30392 −0.229523
\(535\) 26.5104 + 26.5104i 1.14614 + 1.14614i
\(536\) 0.752160 0.0324884
\(537\) 9.79960 0.422884
\(538\) −15.2793 15.2793i −0.658735 0.658735i
\(539\) 3.37099 1.00705i 0.145199 0.0433766i
\(540\) −2.27220 2.27220i −0.0977801 0.0977801i
\(541\) −25.5330 25.5330i −1.09775 1.09775i −0.994673 0.103077i \(-0.967131\pi\)
−0.103077 0.994673i \(-0.532869\pi\)
\(542\) 21.2729i 0.913751i
\(543\) 10.4372i 0.447902i
\(544\) −3.05882 + 3.05882i −0.131146 + 0.131146i
\(545\) 24.0684 1.03098
\(546\) −7.07505 + 6.39872i −0.302784 + 0.273840i
\(547\) 44.1966 1.88971 0.944856 0.327486i \(-0.106201\pi\)
0.944856 + 0.327486i \(0.106201\pi\)
\(548\) −0.272205 + 0.272205i −0.0116280 + 0.0116280i
\(549\) 4.32583i 0.184622i
\(550\) 2.67676i 0.114137i
\(551\) −6.55579 6.55579i −0.279286 0.279286i
\(552\) −1.68642 1.68642i −0.0717787 0.0717787i
\(553\) 25.7085 15.3353i 1.09323 0.652125i
\(554\) 12.5862 + 12.5862i 0.534737 + 0.534737i
\(555\) 23.5810 1.00096
\(556\) −20.3440 −0.862778
\(557\) −11.7755 11.7755i −0.498946 0.498946i 0.412164 0.911110i \(-0.364773\pi\)
−0.911110 + 0.412164i \(0.864773\pi\)
\(558\) 1.53186 0.0648487
\(559\) 22.3460 + 14.8973i 0.945136 + 0.630090i
\(560\) −8.24264 2.08319i −0.348315 0.0880307i
\(561\) 1.53736 1.53736i 0.0649075 0.0649075i
\(562\) 8.78031 0.370375
\(563\) 45.7636 1.92870 0.964352 0.264621i \(-0.0852470\pi\)
0.964352 + 0.264621i \(0.0852470\pi\)
\(564\) −4.71078 + 4.71078i −0.198360 + 0.198360i
\(565\) −46.2258 46.2258i −1.94473 1.94473i
\(566\) −17.7547 + 17.7547i −0.746288 + 0.746288i
\(567\) −2.27220 + 1.35539i −0.0954236 + 0.0569211i
\(568\) −9.02969 −0.378877
\(569\) 39.5061i 1.65618i 0.560595 + 0.828090i \(0.310572\pi\)
−0.560595 + 0.828090i \(0.689428\pi\)
\(570\) 19.2256 19.2256i 0.805273 0.805273i
\(571\) 19.1620i 0.801906i 0.916099 + 0.400953i \(0.131321\pi\)
−0.916099 + 0.400953i \(0.868679\pi\)
\(572\) 0.355392 + 1.77696i 0.0148597 + 0.0742983i
\(573\) 11.1410i 0.465423i
\(574\) 11.3492 6.76991i 0.473707 0.282571i
\(575\) −12.7019 −0.529704
\(576\) 1.00000i 0.0416667i
\(577\) 3.53749 + 3.53749i 0.147268 + 0.147268i 0.776896 0.629629i \(-0.216793\pi\)
−0.629629 + 0.776896i \(0.716793\pi\)
\(578\) 1.21112 1.21112i 0.0503760 0.0503760i
\(579\) 4.03661 4.03661i 0.167756 0.167756i
\(580\) −2.48974 + 2.48974i −0.103381 + 0.103381i
\(581\) 24.3440 + 6.15253i 1.00996 + 0.255250i
\(582\) 18.3750i 0.761668i
\(583\) −4.00000 4.00000i −0.165663 0.165663i
\(584\) −7.33838 −0.303664
\(585\) −11.3610 + 2.27220i −0.469720 + 0.0939441i
\(586\) 12.0398i 0.497360i
\(587\) 4.98849 + 4.98849i 0.205897 + 0.205897i 0.802521 0.596624i \(-0.203492\pi\)
−0.596624 + 0.802521i \(0.703492\pi\)
\(588\) −3.32583 + 6.15945i −0.137155 + 0.254012i
\(589\) 12.9614i 0.534065i
\(590\) 11.6165 11.6165i 0.478245 0.478245i
\(591\) −0.627596 0.627596i −0.0258159 0.0258159i
\(592\) 5.18902 + 5.18902i 0.213267 + 0.213267i
\(593\) 3.14690 3.14690i 0.129228 0.129228i −0.639535 0.768762i \(-0.720873\pi\)
0.768762 + 0.639535i \(0.220873\pi\)
\(594\) 0.502600i 0.0206219i
\(595\) 35.6562 + 9.01151i 1.46176 + 0.369436i
\(596\) −10.5685 10.5685i −0.432901 0.432901i
\(597\) 16.5375i 0.676834i
\(598\) −8.43209 + 1.68642i −0.344814 + 0.0689628i
\(599\) 14.9244 0.609796 0.304898 0.952385i \(-0.401378\pi\)
0.304898 + 0.952385i \(0.401378\pi\)
\(600\) −3.76593 3.76593i −0.153743 0.153743i
\(601\) 14.3189i 0.584080i −0.956406 0.292040i \(-0.905666\pi\)
0.956406 0.292040i \(-0.0943341\pi\)
\(602\) 19.1066 + 4.82886i 0.778726 + 0.196810i
\(603\) 0.531858 0.531858i 0.0216589 0.0216589i
\(604\) −0.149362 + 0.149362i −0.00607743 + 0.00607743i
\(605\) −24.4203 + 24.4203i −0.992825 + 0.992825i
\(606\) −14.0004 14.0004i −0.568729 0.568729i
\(607\) 17.3212i 0.703047i 0.936179 + 0.351524i \(0.114336\pi\)
−0.936179 + 0.351524i \(0.885664\pi\)
\(608\) 8.46122 0.343148
\(609\) 1.48515 + 2.48974i 0.0601815 + 0.100889i
\(610\) 13.9005i 0.562816i
\(611\) 4.71078 + 23.5539i 0.190578 + 0.952889i
\(612\) 4.32583i 0.174861i
\(613\) 28.6700 28.6700i 1.15797 1.15797i 0.173057 0.984912i \(-0.444635\pi\)
0.984912 0.173057i \(-0.0553646\pi\)
\(614\) 14.1982i 0.572993i
\(615\) 16.0502 0.647207
\(616\) 0.681219 + 1.14201i 0.0274471 + 0.0460129i
\(617\) −9.91435 + 9.91435i −0.399137 + 0.399137i −0.877929 0.478792i \(-0.841075\pi\)
0.478792 + 0.877929i \(0.341075\pi\)
\(618\) 1.91192 + 1.91192i 0.0769087 + 0.0769087i
\(619\) 3.87574 3.87574i 0.155779 0.155779i −0.624914 0.780693i \(-0.714866\pi\)
0.780693 + 0.624914i \(0.214866\pi\)
\(620\) 4.92244 0.197690
\(621\) −2.38496 −0.0957050
\(622\) −11.1061 + 11.1061i −0.445316 + 0.445316i
\(623\) −3.43845 + 13.6051i −0.137759 + 0.545076i
\(624\) −3.00000 2.00000i −0.120096 0.0800641i
\(625\) 23.2647 0.930588
\(626\) −14.6867 14.6867i −0.587000 0.587000i
\(627\) −4.25261 −0.169833
\(628\) 10.7630 0.429490
\(629\) −22.4468 22.4468i −0.895012 0.895012i
\(630\) −7.30146 + 4.35539i −0.290897 + 0.173523i
\(631\) −21.5709 21.5709i −0.858725 0.858725i 0.132463 0.991188i \(-0.457711\pi\)
−0.991188 + 0.132463i \(0.957711\pi\)
\(632\) 8.00043 + 8.00043i 0.318240 + 0.318240i
\(633\) 0.551329i 0.0219134i
\(634\) 26.8878i 1.06785i
\(635\) 17.2872 17.2872i 0.686022 0.686022i
\(636\) 11.2552 0.446297
\(637\) 11.8267 + 22.2964i 0.468591 + 0.883415i
\(638\) 0.550718 0.0218031
\(639\) −6.38496 + 6.38496i −0.252585 + 0.252585i
\(640\) 3.21338i 0.127020i
\(641\) 25.8728i 1.02192i −0.859606 0.510958i \(-0.829291\pi\)
0.859606 0.510958i \(-0.170709\pi\)
\(642\) 8.24999 + 8.24999i 0.325601 + 0.325601i
\(643\) 3.32032 + 3.32032i 0.130941 + 0.130941i 0.769540 0.638599i \(-0.220486\pi\)
−0.638599 + 0.769540i \(0.720486\pi\)
\(644\) −5.41911 + 3.23255i −0.213543 + 0.127380i
\(645\) 16.9249 + 16.9249i 0.666417 + 0.666417i
\(646\) −36.6018 −1.44008
\(647\) 28.6969 1.12819 0.564097 0.825709i \(-0.309225\pi\)
0.564097 + 0.825709i \(0.309225\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) −2.56951 −0.100862
\(650\) −18.8296 + 3.76593i −0.738559 + 0.147712i
\(651\) 0.993080 3.92936i 0.0389219 0.154004i
\(652\) −3.40901 + 3.40901i −0.133507 + 0.133507i
\(653\) −27.9250 −1.09279 −0.546395 0.837527i \(-0.684000\pi\)
−0.546395 + 0.837527i \(0.684000\pi\)
\(654\) 7.49005 0.292884
\(655\) 15.6106 15.6106i 0.609956 0.609956i
\(656\) 3.53186 + 3.53186i 0.137896 + 0.137896i
\(657\) −5.18902 + 5.18902i −0.202443 + 0.202443i
\(658\) 9.02969 + 15.1375i 0.352014 + 0.590123i
\(659\) −38.2258 −1.48906 −0.744532 0.667587i \(-0.767327\pi\)
−0.744532 + 0.667587i \(0.767327\pi\)
\(660\) 1.61504i 0.0628655i
\(661\) 4.52189 4.52189i 0.175881 0.175881i −0.613676 0.789558i \(-0.710310\pi\)
0.789558 + 0.613676i \(0.210310\pi\)
\(662\) 19.7686i 0.768329i
\(663\) 12.9775 + 8.65166i 0.504004 + 0.336002i
\(664\) 9.49048i 0.368302i
\(665\) −36.8519 61.7793i −1.42906 2.39570i
\(666\) 7.33838 0.284356
\(667\) 2.61329i 0.101187i
\(668\) −10.0226 10.0226i −0.387788 0.387788i
\(669\) 9.89430 9.89430i 0.382536 0.382536i
\(670\) 1.70906 1.70906i 0.0660268 0.0660268i
\(671\) −1.53736 + 1.53736i −0.0593492 + 0.0593492i
\(672\) −2.56510 0.648285i −0.0989508 0.0250081i
\(673\) 16.7180i 0.644430i 0.946667 + 0.322215i \(0.104427\pi\)
−0.946667 + 0.322215i \(0.895573\pi\)
\(674\) 0.774804 + 0.774804i 0.0298443 + 0.0298443i
\(675\) −5.32583 −0.204991
\(676\) −12.0000 + 5.00000i −0.461538 + 0.192308i
\(677\) 37.8247i 1.45372i 0.686785 + 0.726861i \(0.259021\pi\)
−0.686785 + 0.726861i \(0.740979\pi\)
\(678\) −14.3854 14.3854i −0.552467 0.552467i
\(679\) −47.1336 11.9122i −1.80882 0.457149i
\(680\) 13.9005i 0.533061i
\(681\) 1.67417 1.67417i 0.0641544 0.0641544i
\(682\) −0.544409 0.544409i −0.0208465 0.0208465i
\(683\) 3.10020 + 3.10020i 0.118626 + 0.118626i 0.763928 0.645302i \(-0.223268\pi\)
−0.645302 + 0.763928i \(0.723268\pi\)
\(684\) 5.98299 5.98299i 0.228765 0.228765i
\(685\) 1.23701i 0.0472637i
\(686\) 13.6435 + 12.5242i 0.520912 + 0.478174i
\(687\) 1.32583 + 1.32583i 0.0505835 + 0.0505835i
\(688\) 7.44867i 0.283978i
\(689\) 22.5104 33.7656i 0.857577 1.28637i
\(690\) −7.66377 −0.291755
\(691\) 11.1083 + 11.1083i 0.422579 + 0.422579i 0.886091 0.463512i \(-0.153411\pi\)
−0.463512 + 0.886091i \(0.653411\pi\)
\(692\) 19.7405i 0.750420i
\(693\) 1.28922 + 0.325828i 0.0489733 + 0.0123772i
\(694\) 22.6969 22.6969i 0.861564 0.861564i
\(695\) −46.2258 + 46.2258i −1.75344 + 1.75344i
\(696\) −0.774804 + 0.774804i −0.0293689 + 0.0293689i
\(697\) −15.2782 15.2782i −0.578703 0.578703i
\(698\) 26.8219i 1.01523i
\(699\) −10.2117 −0.386241
\(700\) −12.1014 + 7.21858i −0.457389 + 0.272837i
\(701\) 2.49912i 0.0943905i 0.998886 + 0.0471953i \(0.0150283\pi\)
−0.998886 + 0.0471953i \(0.984972\pi\)
\(702\) −3.53553 + 0.707107i −0.133440 + 0.0266880i
\(703\) 62.0917i 2.34183i
\(704\) −0.355392 + 0.355392i −0.0133943 + 0.0133943i
\(705\) 21.4077i 0.806262i
\(706\) −21.9911 −0.827645
\(707\) −44.9887 + 26.8362i −1.69198 + 1.00928i
\(708\) 3.61504 3.61504i 0.135862 0.135862i
\(709\) 25.3601 + 25.3601i 0.952419 + 0.952419i 0.998918 0.0464996i \(-0.0148066\pi\)
−0.0464996 + 0.998918i \(0.514807\pi\)
\(710\) −20.5173 + 20.5173i −0.770001 + 0.770001i
\(711\) 11.3143 0.424320
\(712\) −5.30392 −0.198773
\(713\) 2.58335 2.58335i 0.0967473 0.0967473i
\(714\) 11.0962 + 2.80437i 0.415264 + 0.104951i
\(715\) 4.84513 + 3.23009i 0.181198 + 0.120798i
\(716\) 9.79960 0.366228
\(717\) 15.2212 + 15.2212i 0.568445 + 0.568445i
\(718\) −20.0600 −0.748632
\(719\) −41.5150 −1.54825 −0.774124 0.633034i \(-0.781809\pi\)
−0.774124 + 0.633034i \(0.781809\pi\)
\(720\) −2.27220 2.27220i −0.0846801 0.0846801i
\(721\) 6.14373 3.66479i 0.228804 0.136484i
\(722\) 37.1884 + 37.1884i 1.38401 + 1.38401i
\(723\) −3.38496 3.38496i −0.125888 0.125888i
\(724\) 10.4372i 0.387894i
\(725\) 5.83571i 0.216733i
\(726\) −7.59955 + 7.59955i −0.282046 + 0.282046i
\(727\) −48.1505 −1.78580 −0.892902 0.450251i \(-0.851335\pi\)
−0.892902 + 0.450251i \(0.851335\pi\)
\(728\) −7.07505 + 6.39872i −0.262219 + 0.237152i
\(729\) −1.00000 −0.0370370
\(730\) −16.6743 + 16.6743i −0.617143 + 0.617143i
\(731\) 32.2217i 1.19176i
\(732\) 4.32583i 0.159887i
\(733\) −7.58561 7.58561i −0.280181 0.280181i 0.553000 0.833181i \(-0.313483\pi\)
−0.833181 + 0.553000i \(0.813483\pi\)
\(734\) −7.95862 7.95862i −0.293758 0.293758i
\(735\) 6.43858 + 21.5525i 0.237491 + 0.794976i
\(736\) −1.68642 1.68642i −0.0621622 0.0621622i
\(737\) −0.378035 −0.0139251
\(738\) 4.99480 0.183861
\(739\) 0.923733 + 0.923733i 0.0339801 + 0.0339801i 0.723893 0.689913i \(-0.242351\pi\)
−0.689913 + 0.723893i \(0.742351\pi\)
\(740\) 23.5810 0.866856
\(741\) −5.98299 29.9149i −0.219791 1.09895i
\(742\) 7.29657 28.8707i 0.267865 1.05988i
\(743\) −7.95906 + 7.95906i −0.291989 + 0.291989i −0.837866 0.545876i \(-0.816197\pi\)
0.545876 + 0.837866i \(0.316197\pi\)
\(744\) 1.53186 0.0561606
\(745\) −48.0274 −1.75959
\(746\) 12.1254 12.1254i 0.443944 0.443944i
\(747\) 6.71078 + 6.71078i 0.245535 + 0.245535i
\(748\) 1.53736 1.53736i 0.0562115 0.0562115i
\(749\) 26.5104 15.8137i 0.968668 0.577820i
\(750\) −1.04701 −0.0382314
\(751\) 48.2119i 1.75928i −0.475642 0.879639i \(-0.657784\pi\)
0.475642 0.879639i \(-0.342216\pi\)
\(752\) −4.71078 + 4.71078i −0.171785 + 0.171785i
\(753\) 17.2281i 0.627826i
\(754\) 0.774804 + 3.87402i 0.0282167 + 0.141084i
\(755\) 0.678760i 0.0247026i
\(756\) −2.27220 + 1.35539i −0.0826393 + 0.0492951i
\(757\) 47.8137 1.73782 0.868909 0.494972i \(-0.164822\pi\)
0.868909 + 0.494972i \(0.164822\pi\)
\(758\) 16.3603i 0.594232i
\(759\) 0.847593 + 0.847593i 0.0307657 + 0.0307657i
\(760\) 19.2256 19.2256i 0.697387 0.697387i
\(761\) −14.6867 + 14.6867i −0.532393 + 0.532393i −0.921284 0.388891i \(-0.872858\pi\)
0.388891 + 0.921284i \(0.372858\pi\)
\(762\) 5.37976 5.37976i 0.194888 0.194888i
\(763\) 4.85568 19.2127i 0.175788 0.695547i
\(764\) 11.1410i 0.403068i
\(765\) 9.82917 + 9.82917i 0.355374 + 0.355374i
\(766\) −1.79120 −0.0647189
\(767\) −3.61504 18.0752i −0.130532 0.652658i
\(768\) 1.00000i 0.0360844i
\(769\) −34.5766 34.5766i −1.24686 1.24686i −0.957098 0.289765i \(-0.906423\pi\)
−0.289765 0.957098i \(-0.593577\pi\)
\(770\) 4.14275 + 1.04701i 0.149294 + 0.0377316i
\(771\) 3.32324i 0.119684i
\(772\) 4.03661 4.03661i 0.145281 0.145281i
\(773\) 3.88033 + 3.88033i 0.139566 + 0.139566i 0.773438 0.633872i \(-0.218535\pi\)
−0.633872 + 0.773438i \(0.718535\pi\)
\(774\) 5.26701 + 5.26701i 0.189319 + 0.189319i
\(775\) 5.76887 5.76887i 0.207224 0.207224i
\(776\) 18.3750i 0.659624i
\(777\) 4.75736 18.8237i 0.170669 0.675295i
\(778\) −5.59099 5.59099i −0.200447