Properties

Label 546.2.p.c.239.6
Level $546$
Weight $2$
Character 546.239
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 239.6
Root \(1.47393 - 0.909692i\) of defining polynomial
Character \(\chi\) \(=\) 546.239
Dual form 546.2.p.c.281.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-1.68547 - 0.398975i) q^{3} +1.00000i q^{4} +(-0.559062 - 0.559062i) q^{5} +(-0.909692 - 1.47393i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.68164 + 1.34492i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-1.68547 - 0.398975i) q^{3} +1.00000i q^{4} +(-0.559062 - 0.559062i) q^{5} +(-0.909692 - 1.47393i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.68164 + 1.34492i) q^{9} -0.790633i q^{10} +(-0.347057 + 0.347057i) q^{11} +(0.398975 - 1.68547i) q^{12} +(-3.45365 + 1.03551i) q^{13} -1.00000i q^{14} +(0.719233 + 1.16534i) q^{15} -1.00000 q^{16} -4.50042 q^{17} +(0.945201 + 2.84721i) q^{18} +(-3.86509 + 3.86509i) q^{19} +(0.559062 - 0.559062i) q^{20} +(0.909692 + 1.47393i) q^{21} -0.490813 q^{22} -5.27970 q^{23} +(1.47393 - 0.909692i) q^{24} -4.37490i q^{25} +(-3.17432 - 1.70989i) q^{26} +(-3.98324 - 3.33674i) q^{27} +(0.707107 - 0.707107i) q^{28} -10.6966i q^{29} +(-0.315443 + 1.33259i) q^{30} +(-2.47731 + 2.47731i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.723423 - 0.446489i) q^{33} +(-3.18228 - 3.18228i) q^{34} +0.790633i q^{35} +(-1.34492 + 2.68164i) q^{36} +(6.92111 + 6.92111i) q^{37} -5.46606 q^{38} +(6.23418 - 0.367403i) q^{39} +0.790633 q^{40} +(-7.31477 - 7.31477i) q^{41} +(-0.398975 + 1.68547i) q^{42} +7.24514i q^{43} +(-0.347057 - 0.347057i) q^{44} +(-0.747308 - 2.25110i) q^{45} +(-3.73331 - 3.73331i) q^{46} +(-2.49319 + 2.49319i) q^{47} +(1.68547 + 0.398975i) q^{48} +1.00000i q^{49} +(3.09352 - 3.09352i) q^{50} +(7.58533 + 1.79555i) q^{51} +(-1.03551 - 3.45365i) q^{52} +12.0607i q^{53} +(-0.457147 - 5.17600i) q^{54} +0.388054 q^{55} +1.00000 q^{56} +(8.05657 - 4.97243i) q^{57} +(7.56362 - 7.56362i) q^{58} +(3.41247 - 3.41247i) q^{59} +(-1.16534 + 0.719233i) q^{60} +6.42464 q^{61} -3.50344 q^{62} +(-0.945201 - 2.84721i) q^{63} -1.00000i q^{64} +(2.50972 + 1.35189i) q^{65} +(0.827253 + 0.195822i) q^{66} +(-2.43437 + 2.43437i) q^{67} -4.50042i q^{68} +(8.89880 + 2.10647i) q^{69} +(-0.559062 + 0.559062i) q^{70} +(-8.49611 - 8.49611i) q^{71} +(-2.84721 + 0.945201i) q^{72} +(5.93236 + 5.93236i) q^{73} +9.78793i q^{74} +(-1.74547 + 7.37377i) q^{75} +(-3.86509 - 3.86509i) q^{76} +0.490813 q^{77} +(4.66802 + 4.14844i) q^{78} -13.2235 q^{79} +(0.559062 + 0.559062i) q^{80} +(5.38237 + 7.21319i) q^{81} -10.3446i q^{82} +(6.31304 + 6.31304i) q^{83} +(-1.47393 + 0.909692i) q^{84} +(2.51601 + 2.51601i) q^{85} +(-5.12309 + 5.12309i) q^{86} +(-4.26766 + 18.0288i) q^{87} -0.490813i q^{88} +(12.2569 - 12.2569i) q^{89} +(1.06334 - 2.12019i) q^{90} +(3.17432 + 1.70989i) q^{91} -5.27970i q^{92} +(5.16382 - 3.18705i) q^{93} -3.52590 q^{94} +4.32165 q^{95} +(0.909692 + 1.47393i) q^{96} +(-0.867358 + 0.867358i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-1.39745 + 0.463917i) 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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

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

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
\(3\) −1.68547 0.398975i −0.973108 0.230348i
\(4\) 1.00000i 0.500000i
\(5\) −0.559062 0.559062i −0.250020 0.250020i 0.570959 0.820979i \(-0.306572\pi\)
−0.820979 + 0.570959i \(0.806572\pi\)
\(6\) −0.909692 1.47393i −0.371380 0.601728i
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 2.68164 + 1.34492i 0.893879 + 0.448307i
\(10\) 0.790633i 0.250020i
\(11\) −0.347057 + 0.347057i −0.104642 + 0.104642i −0.757489 0.652848i \(-0.773574\pi\)
0.652848 + 0.757489i \(0.273574\pi\)
\(12\) 0.398975 1.68547i 0.115174 0.486554i
\(13\) −3.45365 + 1.03551i −0.957871 + 0.287199i
\(14\) 1.00000i 0.267261i
\(15\) 0.719233 + 1.16534i 0.185705 + 0.300888i
\(16\) −1.00000 −0.250000
\(17\) −4.50042 −1.09151 −0.545756 0.837944i \(-0.683757\pi\)
−0.545756 + 0.837944i \(0.683757\pi\)
\(18\) 0.945201 + 2.84721i 0.222786 + 0.671093i
\(19\) −3.86509 + 3.86509i −0.886712 + 0.886712i −0.994206 0.107494i \(-0.965717\pi\)
0.107494 + 0.994206i \(0.465717\pi\)
\(20\) 0.559062 0.559062i 0.125010 0.125010i
\(21\) 0.909692 + 1.47393i 0.198511 + 0.321637i
\(22\) −0.490813 −0.104642
\(23\) −5.27970 −1.10089 −0.550447 0.834870i \(-0.685543\pi\)
−0.550447 + 0.834870i \(0.685543\pi\)
\(24\) 1.47393 0.909692i 0.300864 0.185690i
\(25\) 4.37490i 0.874980i
\(26\) −3.17432 1.70989i −0.622535 0.335336i
\(27\) −3.98324 3.33674i −0.766575 0.642155i
\(28\) 0.707107 0.707107i 0.133631 0.133631i
\(29\) 10.6966i 1.98630i −0.116833 0.993152i \(-0.537274\pi\)
0.116833 0.993152i \(-0.462726\pi\)
\(30\) −0.315443 + 1.33259i −0.0575917 + 0.243297i
\(31\) −2.47731 + 2.47731i −0.444938 + 0.444938i −0.893667 0.448730i \(-0.851877\pi\)
0.448730 + 0.893667i \(0.351877\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 0.723423 0.446489i 0.125932 0.0777237i
\(34\) −3.18228 3.18228i −0.545756 0.545756i
\(35\) 0.790633i 0.133641i
\(36\) −1.34492 + 2.68164i −0.224154 + 0.446940i
\(37\) 6.92111 + 6.92111i 1.13782 + 1.13782i 0.988840 + 0.148984i \(0.0476004\pi\)
0.148984 + 0.988840i \(0.452400\pi\)
\(38\) −5.46606 −0.886712
\(39\) 6.23418 0.367403i 0.998268 0.0588315i
\(40\) 0.790633 0.125010
\(41\) −7.31477 7.31477i −1.14237 1.14237i −0.988015 0.154360i \(-0.950668\pi\)
−0.154360 0.988015i \(-0.549332\pi\)
\(42\) −0.398975 + 1.68547i −0.0615631 + 0.260074i
\(43\) 7.24514i 1.10487i 0.833555 + 0.552437i \(0.186302\pi\)
−0.833555 + 0.552437i \(0.813698\pi\)
\(44\) −0.347057 0.347057i −0.0523209 0.0523209i
\(45\) −0.747308 2.25110i −0.111402 0.335574i
\(46\) −3.73331 3.73331i −0.550447 0.550447i
\(47\) −2.49319 + 2.49319i −0.363669 + 0.363669i −0.865162 0.501493i \(-0.832784\pi\)
0.501493 + 0.865162i \(0.332784\pi\)
\(48\) 1.68547 + 0.398975i 0.243277 + 0.0575870i
\(49\) 1.00000i 0.142857i
\(50\) 3.09352 3.09352i 0.437490 0.437490i
\(51\) 7.58533 + 1.79555i 1.06216 + 0.251428i
\(52\) −1.03551 3.45365i −0.143599 0.478936i
\(53\) 12.0607i 1.65667i 0.560236 + 0.828333i \(0.310710\pi\)
−0.560236 + 0.828333i \(0.689290\pi\)
\(54\) −0.457147 5.17600i −0.0622098 0.704365i
\(55\) 0.388054 0.0523251
\(56\) 1.00000 0.133631
\(57\) 8.05657 4.97243i 1.06712 0.658614i
\(58\) 7.56362 7.56362i 0.993152 0.993152i
\(59\) 3.41247 3.41247i 0.444266 0.444266i −0.449177 0.893443i \(-0.648283\pi\)
0.893443 + 0.449177i \(0.148283\pi\)
\(60\) −1.16534 + 0.719233i −0.150444 + 0.0928525i
\(61\) 6.42464 0.822591 0.411296 0.911502i \(-0.365076\pi\)
0.411296 + 0.911502i \(0.365076\pi\)
\(62\) −3.50344 −0.444938
\(63\) −0.945201 2.84721i −0.119084 0.358715i
\(64\) 1.00000i 0.125000i
\(65\) 2.50972 + 1.35189i 0.311293 + 0.167682i
\(66\) 0.827253 + 0.195822i 0.101828 + 0.0241040i
\(67\) −2.43437 + 2.43437i −0.297405 + 0.297405i −0.839997 0.542592i \(-0.817443\pi\)
0.542592 + 0.839997i \(0.317443\pi\)
\(68\) 4.50042i 0.545756i
\(69\) 8.89880 + 2.10647i 1.07129 + 0.253589i
\(70\) −0.559062 + 0.559062i −0.0668207 + 0.0668207i
\(71\) −8.49611 8.49611i −1.00830 1.00830i −0.999965 0.00833786i \(-0.997346\pi\)
−0.00833786 0.999965i \(-0.502654\pi\)
\(72\) −2.84721 + 0.945201i −0.335547 + 0.111393i
\(73\) 5.93236 + 5.93236i 0.694330 + 0.694330i 0.963182 0.268851i \(-0.0866440\pi\)
−0.268851 + 0.963182i \(0.586644\pi\)
\(74\) 9.78793i 1.13782i
\(75\) −1.74547 + 7.37377i −0.201550 + 0.851450i
\(76\) −3.86509 3.86509i −0.443356 0.443356i
\(77\) 0.490813 0.0559334
\(78\) 4.66802 + 4.14844i 0.528550 + 0.469718i
\(79\) −13.2235 −1.48776 −0.743882 0.668311i \(-0.767017\pi\)
−0.743882 + 0.668311i \(0.767017\pi\)
\(80\) 0.559062 + 0.559062i 0.0625051 + 0.0625051i
\(81\) 5.38237 + 7.21319i 0.598041 + 0.801466i
\(82\) 10.3446i 1.14237i
\(83\) 6.31304 + 6.31304i 0.692946 + 0.692946i 0.962879 0.269933i \(-0.0870016\pi\)
−0.269933 + 0.962879i \(0.587002\pi\)
\(84\) −1.47393 + 0.909692i −0.160819 + 0.0992555i
\(85\) 2.51601 + 2.51601i 0.272900 + 0.272900i
\(86\) −5.12309 + 5.12309i −0.552437 + 0.552437i
\(87\) −4.26766 + 18.0288i −0.457541 + 1.93289i
\(88\) 0.490813i 0.0523209i
\(89\) 12.2569 12.2569i 1.29923 1.29923i 0.370335 0.928898i \(-0.379243\pi\)
0.928898 0.370335i \(-0.120757\pi\)
\(90\) 1.06334 2.12019i 0.112086 0.223488i
\(91\) 3.17432 + 1.70989i 0.332759 + 0.179245i
\(92\) 5.27970i 0.550447i
\(93\) 5.16382 3.18705i 0.535463 0.330482i
\(94\) −3.52590 −0.363669
\(95\) 4.32165 0.443392
\(96\) 0.909692 + 1.47393i 0.0928450 + 0.150432i
\(97\) −0.867358 + 0.867358i −0.0880669 + 0.0880669i −0.749768 0.661701i \(-0.769835\pi\)
0.661701 + 0.749768i \(0.269835\pi\)
\(98\) −0.707107 + 0.707107i −0.0714286 + 0.0714286i
\(99\) −1.39745 + 0.463917i −0.140449 + 0.0466254i
\(100\) 4.37490 0.437490
\(101\) 3.42487 0.340787 0.170393 0.985376i \(-0.445496\pi\)
0.170393 + 0.985376i \(0.445496\pi\)
\(102\) 4.09399 + 6.63329i 0.405366 + 0.656794i
\(103\) 0.0883069i 0.00870114i −0.999991 0.00435057i \(-0.998615\pi\)
0.999991 0.00435057i \(-0.00138483\pi\)
\(104\) 1.70989 3.17432i 0.167668 0.311267i
\(105\) 0.315443 1.33259i 0.0307841 0.130048i
\(106\) −8.52821 + 8.52821i −0.828333 + 0.828333i
\(107\) 5.08715i 0.491794i 0.969296 + 0.245897i \(0.0790824\pi\)
−0.969296 + 0.245897i \(0.920918\pi\)
\(108\) 3.33674 3.98324i 0.321078 0.383287i
\(109\) 5.92580 5.92580i 0.567589 0.567589i −0.363863 0.931452i \(-0.618542\pi\)
0.931452 + 0.363863i \(0.118542\pi\)
\(110\) 0.274395 + 0.274395i 0.0261626 + 0.0261626i
\(111\) −8.90400 14.4267i −0.845130 1.36932i
\(112\) 0.707107 + 0.707107i 0.0668153 + 0.0668153i
\(113\) 2.88604i 0.271496i 0.990743 + 0.135748i \(0.0433438\pi\)
−0.990743 + 0.135748i \(0.956656\pi\)
\(114\) 9.21290 + 2.18082i 0.862867 + 0.204252i
\(115\) 2.95168 + 2.95168i 0.275246 + 0.275246i
\(116\) 10.6966 0.993152
\(117\) −10.6541 1.86803i −0.984975 0.172700i
\(118\) 4.82596 0.444266
\(119\) 3.18228 + 3.18228i 0.291719 + 0.291719i
\(120\) −1.33259 0.315443i −0.121648 0.0287959i
\(121\) 10.7591i 0.978100i
\(122\) 4.54291 + 4.54291i 0.411296 + 0.411296i
\(123\) 9.41044 + 15.2473i 0.848511 + 1.37480i
\(124\) −2.47731 2.47731i −0.222469 0.222469i
\(125\) −5.24115 + 5.24115i −0.468783 + 0.468783i
\(126\) 1.34492 2.68164i 0.119815 0.238899i
\(127\) 21.1044i 1.87271i −0.351053 0.936356i \(-0.614176\pi\)
0.351053 0.936356i \(-0.385824\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 2.89063 12.2115i 0.254506 1.07516i
\(130\) 0.818708 + 2.73057i 0.0718055 + 0.239487i
\(131\) 7.76803i 0.678696i −0.940661 0.339348i \(-0.889794\pi\)
0.940661 0.339348i \(-0.110206\pi\)
\(132\) 0.446489 + 0.723423i 0.0388619 + 0.0629659i
\(133\) 5.46606 0.473967
\(134\) −3.44271 −0.297405
\(135\) 0.361436 + 4.09232i 0.0311074 + 0.352211i
\(136\) 3.18228 3.18228i 0.272878 0.272878i
\(137\) −2.35653 + 2.35653i −0.201332 + 0.201332i −0.800570 0.599239i \(-0.795470\pi\)
0.599239 + 0.800570i \(0.295470\pi\)
\(138\) 4.80290 + 7.78190i 0.408850 + 0.662439i
\(139\) 1.53895 0.130532 0.0652659 0.997868i \(-0.479210\pi\)
0.0652659 + 0.997868i \(0.479210\pi\)
\(140\) −0.790633 −0.0668207
\(141\) 5.19692 3.20748i 0.437660 0.270119i
\(142\) 12.0153i 1.00830i
\(143\) 0.839235 1.55800i 0.0701803 0.130286i
\(144\) −2.68164 1.34492i −0.223470 0.112077i
\(145\) −5.98005 + 5.98005i −0.496616 + 0.496616i
\(146\) 8.38963i 0.694330i
\(147\) 0.398975 1.68547i 0.0329069 0.139015i
\(148\) −6.92111 + 6.92111i −0.568912 + 0.568912i
\(149\) 6.80987 + 6.80987i 0.557887 + 0.557887i 0.928705 0.370819i \(-0.120923\pi\)
−0.370819 + 0.928705i \(0.620923\pi\)
\(150\) −6.44828 + 3.97981i −0.526500 + 0.324950i
\(151\) 1.21937 + 1.21937i 0.0992308 + 0.0992308i 0.754979 0.655749i \(-0.227647\pi\)
−0.655749 + 0.754979i \(0.727647\pi\)
\(152\) 5.46606i 0.443356i
\(153\) −12.0685 6.05271i −0.975680 0.489333i
\(154\) 0.347057 + 0.347057i 0.0279667 + 0.0279667i
\(155\) 2.76994 0.222487
\(156\) 0.367403 + 6.23418i 0.0294158 + 0.499134i
\(157\) −5.63769 −0.449936 −0.224968 0.974366i \(-0.572228\pi\)
−0.224968 + 0.974366i \(0.572228\pi\)
\(158\) −9.35045 9.35045i −0.743882 0.743882i
\(159\) 4.81192 20.3280i 0.381610 1.61211i
\(160\) 0.790633i 0.0625051i
\(161\) 3.73331 + 3.73331i 0.294226 + 0.294226i
\(162\) −1.29459 + 8.90640i −0.101712 + 0.699753i
\(163\) 3.47849 + 3.47849i 0.272456 + 0.272456i 0.830088 0.557632i \(-0.188290\pi\)
−0.557632 + 0.830088i \(0.688290\pi\)
\(164\) 7.31477 7.31477i 0.571187 0.571187i
\(165\) −0.654054 0.154824i −0.0509180 0.0120530i
\(166\) 8.92798i 0.692946i
\(167\) 2.49027 2.49027i 0.192703 0.192703i −0.604160 0.796863i \(-0.706491\pi\)
0.796863 + 0.604160i \(0.206491\pi\)
\(168\) −1.68547 0.398975i −0.130037 0.0307816i
\(169\) 10.8554 7.15258i 0.835034 0.550199i
\(170\) 3.55818i 0.272900i
\(171\) −15.5630 + 5.16653i −1.19013 + 0.395094i
\(172\) −7.24514 −0.552437
\(173\) −13.1775 −1.00187 −0.500934 0.865486i \(-0.667010\pi\)
−0.500934 + 0.865486i \(0.667010\pi\)
\(174\) −15.7660 + 9.73058i −1.19521 + 0.737673i
\(175\) −3.09352 + 3.09352i −0.233848 + 0.233848i
\(176\) 0.347057 0.347057i 0.0261604 0.0261604i
\(177\) −7.11311 + 4.39013i −0.534654 + 0.329983i
\(178\) 17.3339 1.29923
\(179\) −13.9967 −1.04616 −0.523081 0.852283i \(-0.675217\pi\)
−0.523081 + 0.852283i \(0.675217\pi\)
\(180\) 2.25110 0.747308i 0.167787 0.0557010i
\(181\) 3.47621i 0.258385i −0.991620 0.129192i \(-0.958762\pi\)
0.991620 0.129192i \(-0.0412384\pi\)
\(182\) 1.03551 + 3.45365i 0.0767571 + 0.256002i
\(183\) −10.8286 2.56327i −0.800471 0.189482i
\(184\) 3.73331 3.73331i 0.275224 0.275224i
\(185\) 7.73867i 0.568958i
\(186\) 5.90496 + 1.39779i 0.432973 + 0.102491i
\(187\) 1.56190 1.56190i 0.114218 0.114218i
\(188\) −2.49319 2.49319i −0.181834 0.181834i
\(189\) 0.457147 + 5.17600i 0.0332525 + 0.376499i
\(190\) 3.05587 + 3.05587i 0.221696 + 0.221696i
\(191\) 26.9246i 1.94820i 0.226120 + 0.974099i \(0.427396\pi\)
−0.226120 + 0.974099i \(0.572604\pi\)
\(192\) −0.398975 + 1.68547i −0.0287935 + 0.121639i
\(193\) −15.1725 15.1725i −1.09214 1.09214i −0.995300 0.0968371i \(-0.969127\pi\)
−0.0968371 0.995300i \(-0.530873\pi\)
\(194\) −1.22663 −0.0880669
\(195\) −3.69070 3.27989i −0.264296 0.234878i
\(196\) −1.00000 −0.0714286
\(197\) −15.8927 15.8927i −1.13231 1.13231i −0.989792 0.142517i \(-0.954480\pi\)
−0.142517 0.989792i \(-0.545520\pi\)
\(198\) −1.31618 0.660106i −0.0935371 0.0469117i
\(199\) 4.30765i 0.305361i 0.988276 + 0.152681i \(0.0487905\pi\)
−0.988276 + 0.152681i \(0.951209\pi\)
\(200\) 3.09352 + 3.09352i 0.218745 + 0.218745i
\(201\) 5.07431 3.13181i 0.357914 0.220901i
\(202\) 2.42175 + 2.42175i 0.170393 + 0.170393i
\(203\) −7.56362 + 7.56362i −0.530862 + 0.530862i
\(204\) −1.79555 + 7.58533i −0.125714 + 0.531080i
\(205\) 8.17882i 0.571234i
\(206\) 0.0624424 0.0624424i 0.00435057 0.00435057i
\(207\) −14.1583 7.10079i −0.984067 0.493539i
\(208\) 3.45365 1.03551i 0.239468 0.0717997i
\(209\) 2.68282i 0.185574i
\(210\) 1.16534 0.719233i 0.0804158 0.0496318i
\(211\) 9.69453 0.667399 0.333700 0.942679i \(-0.391703\pi\)
0.333700 + 0.942679i \(0.391703\pi\)
\(212\) −12.0607 −0.828333
\(213\) 10.9302 + 17.7097i 0.748927 + 1.21345i
\(214\) −3.59716 + 3.59716i −0.245897 + 0.245897i
\(215\) 4.05049 4.05049i 0.276241 0.276241i
\(216\) 5.17600 0.457147i 0.352182 0.0311049i
\(217\) 3.50344 0.237829
\(218\) 8.38035 0.567589
\(219\) −7.63197 12.3657i −0.515721 0.835596i
\(220\) 0.388054i 0.0261626i
\(221\) 15.5429 4.66023i 1.04553 0.313481i
\(222\) 3.90514 16.4973i 0.262096 1.10723i
\(223\) −7.49728 + 7.49728i −0.502055 + 0.502055i −0.912076 0.410021i \(-0.865521\pi\)
0.410021 + 0.912076i \(0.365521\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) 5.88390 11.7319i 0.392260 0.782126i
\(226\) −2.04074 + 2.04074i −0.135748 + 0.135748i
\(227\) 17.5224 + 17.5224i 1.16300 + 1.16300i 0.983815 + 0.179185i \(0.0573459\pi\)
0.179185 + 0.983815i \(0.442654\pi\)
\(228\) 4.97243 + 8.05657i 0.329307 + 0.533560i
\(229\) −13.8742 13.8742i −0.916834 0.916834i 0.0799635 0.996798i \(-0.474520\pi\)
−0.996798 + 0.0799635i \(0.974520\pi\)
\(230\) 4.17431i 0.275246i
\(231\) −0.827253 0.195822i −0.0544292 0.0128842i
\(232\) 7.56362 + 7.56362i 0.496576 + 0.496576i
\(233\) 4.80094 0.314520 0.157260 0.987557i \(-0.449734\pi\)
0.157260 + 0.987557i \(0.449734\pi\)
\(234\) −6.21271 8.85451i −0.406137 0.578837i
\(235\) 2.78770 0.181849
\(236\) 3.41247 + 3.41247i 0.222133 + 0.222133i
\(237\) 22.2879 + 5.27585i 1.44775 + 0.342703i
\(238\) 4.50042i 0.291719i
\(239\) −8.85356 8.85356i −0.572689 0.572689i 0.360190 0.932879i \(-0.382712\pi\)
−0.932879 + 0.360190i \(0.882712\pi\)
\(240\) −0.719233 1.16534i −0.0464263 0.0752221i
\(241\) 8.79467 + 8.79467i 0.566515 + 0.566515i 0.931150 0.364636i \(-0.118806\pi\)
−0.364636 + 0.931150i \(0.618806\pi\)
\(242\) −7.60783 + 7.60783i −0.489050 + 0.489050i
\(243\) −6.19396 14.3051i −0.397343 0.917670i
\(244\) 6.42464i 0.411296i
\(245\) 0.559062 0.559062i 0.0357172 0.0357172i
\(246\) −4.12725 + 17.4356i −0.263144 + 1.11165i
\(247\) 9.34634 17.3510i 0.594693 1.10402i
\(248\) 3.50344i 0.222469i
\(249\) −8.12171 13.1592i −0.514693 0.833930i
\(250\) −7.41211 −0.468783
\(251\) −13.6883 −0.863998 −0.431999 0.901874i \(-0.642192\pi\)
−0.431999 + 0.901874i \(0.642192\pi\)
\(252\) 2.84721 0.945201i 0.179357 0.0595421i
\(253\) 1.83236 1.83236i 0.115200 0.115200i
\(254\) 14.9231 14.9231i 0.936356 0.936356i
\(255\) −3.23685 5.24450i −0.202699 0.328423i
\(256\) 1.00000 0.0625000
\(257\) −18.2988 −1.14145 −0.570723 0.821142i \(-0.693337\pi\)
−0.570723 + 0.821142i \(0.693337\pi\)
\(258\) 10.6788 6.59085i 0.664834 0.410328i
\(259\) 9.78793i 0.608192i
\(260\) −1.35189 + 2.50972i −0.0838408 + 0.155646i
\(261\) 14.3861 28.6843i 0.890474 1.77552i
\(262\) 5.49282 5.49282i 0.339348 0.339348i
\(263\) 16.5203i 1.01868i −0.860564 0.509342i \(-0.829889\pi\)
0.860564 0.509342i \(-0.170111\pi\)
\(264\) −0.195822 + 0.827253i −0.0120520 + 0.0509139i
\(265\) 6.74269 6.74269i 0.414200 0.414200i
\(266\) 3.86509 + 3.86509i 0.236984 + 0.236984i
\(267\) −25.5490 + 15.7685i −1.56357 + 0.965019i
\(268\) −2.43437 2.43437i −0.148703 0.148703i
\(269\) 11.7448i 0.716091i 0.933704 + 0.358046i \(0.116557\pi\)
−0.933704 + 0.358046i \(0.883443\pi\)
\(270\) −2.63814 + 3.14928i −0.160552 + 0.191659i
\(271\) 9.75803 + 9.75803i 0.592758 + 0.592758i 0.938375 0.345618i \(-0.112331\pi\)
−0.345618 + 0.938375i \(0.612331\pi\)
\(272\) 4.50042 0.272878
\(273\) −4.66802 4.14844i −0.282522 0.251075i
\(274\) −3.33263 −0.201332
\(275\) 1.51834 + 1.51834i 0.0915594 + 0.0915594i
\(276\) −2.10647 + 8.89880i −0.126794 + 0.535645i
\(277\) 1.88463i 0.113236i −0.998396 0.0566181i \(-0.981968\pi\)
0.998396 0.0566181i \(-0.0180318\pi\)
\(278\) 1.08820 + 1.08820i 0.0652659 + 0.0652659i
\(279\) −9.97503 + 3.31146i −0.597190 + 0.198252i
\(280\) −0.559062 0.559062i −0.0334104 0.0334104i
\(281\) −2.85196 + 2.85196i −0.170134 + 0.170134i −0.787038 0.616904i \(-0.788387\pi\)
0.616904 + 0.787038i \(0.288387\pi\)
\(282\) 5.94281 + 1.40675i 0.353889 + 0.0837705i
\(283\) 15.2599i 0.907107i −0.891229 0.453553i \(-0.850156\pi\)
0.891229 0.453553i \(-0.149844\pi\)
\(284\) 8.49611 8.49611i 0.504152 0.504152i
\(285\) −7.28402 1.72423i −0.431468 0.102134i
\(286\) 1.69510 0.508242i 0.100233 0.0300530i
\(287\) 10.3446i 0.610625i
\(288\) −0.945201 2.84721i −0.0556965 0.167773i
\(289\) 3.25377 0.191398
\(290\) −8.45707 −0.496616
\(291\) 1.80796 1.11585i 0.105985 0.0654126i
\(292\) −5.93236 + 5.93236i −0.347165 + 0.347165i
\(293\) 13.4365 13.4365i 0.784968 0.784968i −0.195696 0.980665i \(-0.562697\pi\)
0.980665 + 0.195696i \(0.0626967\pi\)
\(294\) 1.47393 0.909692i 0.0859612 0.0530543i
\(295\) −3.81556 −0.222151
\(296\) −9.78793 −0.568912
\(297\) 2.54045 0.224374i 0.147412 0.0130195i
\(298\) 9.63062i 0.557887i
\(299\) 18.2343 5.46718i 1.05451 0.316175i
\(300\) −7.37377 1.74547i −0.425725 0.100775i
\(301\) 5.12309 5.12309i 0.295290 0.295290i
\(302\) 1.72445i 0.0992308i
\(303\) −5.77252 1.36644i −0.331623 0.0784997i
\(304\) 3.86509 3.86509i 0.221678 0.221678i
\(305\) −3.59178 3.59178i −0.205665 0.205665i
\(306\) −4.25380 12.8136i −0.243174 0.732506i
\(307\) 14.1492 + 14.1492i 0.807539 + 0.807539i 0.984261 0.176722i \(-0.0565493\pi\)
−0.176722 + 0.984261i \(0.556549\pi\)
\(308\) 0.490813i 0.0279667i
\(309\) −0.0352322 + 0.148839i −0.00200429 + 0.00846715i
\(310\) 1.95864 + 1.95864i 0.111243 + 0.111243i
\(311\) −33.2959 −1.88804 −0.944019 0.329890i \(-0.892988\pi\)
−0.944019 + 0.329890i \(0.892988\pi\)
\(312\) −4.14844 + 4.66802i −0.234859 + 0.264275i
\(313\) −23.5153 −1.32917 −0.664583 0.747214i \(-0.731391\pi\)
−0.664583 + 0.747214i \(0.731391\pi\)
\(314\) −3.98645 3.98645i −0.224968 0.224968i
\(315\) −1.06334 + 2.12019i −0.0599124 + 0.119459i
\(316\) 13.2235i 0.743882i
\(317\) 2.21672 + 2.21672i 0.124503 + 0.124503i 0.766613 0.642110i \(-0.221941\pi\)
−0.642110 + 0.766613i \(0.721941\pi\)
\(318\) 17.7766 10.9715i 0.996862 0.615253i
\(319\) 3.71232 + 3.71232i 0.207850 + 0.207850i
\(320\) −0.559062 + 0.559062i −0.0312525 + 0.0312525i
\(321\) 2.02965 8.57426i 0.113284 0.478568i
\(322\) 5.27970i 0.294226i
\(323\) 17.3945 17.3945i 0.967857 0.967857i
\(324\) −7.21319 + 5.38237i −0.400733 + 0.299020i
\(325\) 4.53025 + 15.1094i 0.251293 + 0.838118i
\(326\) 4.91933i 0.272456i
\(327\) −12.3520 + 7.62354i −0.683069 + 0.421583i
\(328\) 10.3446 0.571187
\(329\) 3.52590 0.194389
\(330\) −0.353009 0.571963i −0.0194325 0.0314855i
\(331\) −21.9301 + 21.9301i −1.20539 + 1.20539i −0.232882 + 0.972505i \(0.574816\pi\)
−0.972505 + 0.232882i \(0.925184\pi\)
\(332\) −6.31304 + 6.31304i −0.346473 + 0.346473i
\(333\) 9.25156 + 27.8683i 0.506983 + 1.52717i
\(334\) 3.52177 0.192703
\(335\) 2.72192 0.148715
\(336\) −0.909692 1.47393i −0.0496277 0.0804093i
\(337\) 12.0386i 0.655785i 0.944715 + 0.327892i \(0.106338\pi\)
−0.944715 + 0.327892i \(0.893662\pi\)
\(338\) 12.7336 + 2.61832i 0.692616 + 0.142418i
\(339\) 1.15146 4.86435i 0.0625387 0.264195i
\(340\) −2.51601 + 2.51601i −0.136450 + 0.136450i
\(341\) 1.71954i 0.0931181i
\(342\) −14.6580 7.35142i −0.792614 0.397519i
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) −5.12309 5.12309i −0.276219 0.276219i
\(345\) −3.79734 6.15263i −0.204442 0.331246i
\(346\) −9.31790 9.31790i −0.500934 0.500934i
\(347\) 4.91439i 0.263819i −0.991262 0.131909i \(-0.957889\pi\)
0.991262 0.131909i \(-0.0421108\pi\)
\(348\) −18.0288 4.26766i −0.966444 0.228771i
\(349\) −3.33670 3.33670i −0.178609 0.178609i 0.612140 0.790749i \(-0.290309\pi\)
−0.790749 + 0.612140i \(0.790309\pi\)
\(350\) −4.37490 −0.233848
\(351\) 17.2119 + 7.39925i 0.918706 + 0.394943i
\(352\) 0.490813 0.0261604
\(353\) 4.61015 + 4.61015i 0.245374 + 0.245374i 0.819069 0.573695i \(-0.194491\pi\)
−0.573695 + 0.819069i \(0.694491\pi\)
\(354\) −8.13402 1.92544i −0.432318 0.102336i
\(355\) 9.49971i 0.504192i
\(356\) 12.2569 + 12.2569i 0.649617 + 0.649617i
\(357\) −4.09399 6.63329i −0.216677 0.351071i
\(358\) −9.89715 9.89715i −0.523081 0.523081i
\(359\) 8.91675 8.91675i 0.470608 0.470608i −0.431503 0.902111i \(-0.642017\pi\)
0.902111 + 0.431503i \(0.142017\pi\)
\(360\) 2.12019 + 1.06334i 0.111744 + 0.0560430i
\(361\) 10.8778i 0.572516i
\(362\) 2.45805 2.45805i 0.129192 0.129192i
\(363\) 4.29261 18.1342i 0.225304 0.951797i
\(364\) −1.70989 + 3.17432i −0.0896224 + 0.166379i
\(365\) 6.63312i 0.347193i
\(366\) −5.84445 9.46946i −0.305494 0.494976i
\(367\) −25.6357 −1.33817 −0.669087 0.743184i \(-0.733315\pi\)
−0.669087 + 0.743184i \(0.733315\pi\)
\(368\) 5.27970 0.275224
\(369\) −9.77777 29.4534i −0.509010 1.53328i
\(370\) 5.47206 5.47206i 0.284479 0.284479i
\(371\) 8.52821 8.52821i 0.442762 0.442762i
\(372\) 3.18705 + 5.16382i 0.165241 + 0.267732i
\(373\) −27.6030 −1.42923 −0.714614 0.699519i \(-0.753398\pi\)
−0.714614 + 0.699519i \(0.753398\pi\)
\(374\) 2.20887 0.114218
\(375\) 10.9249 6.74273i 0.564160 0.348193i
\(376\) 3.52590i 0.181834i
\(377\) 11.0764 + 36.9422i 0.570464 + 1.90262i
\(378\) −3.33674 + 3.98324i −0.171623 + 0.204876i
\(379\) −15.2188 + 15.2188i −0.781739 + 0.781739i −0.980124 0.198385i \(-0.936430\pi\)
0.198385 + 0.980124i \(0.436430\pi\)
\(380\) 4.32165i 0.221696i
\(381\) −8.42012 + 35.5709i −0.431376 + 1.82235i
\(382\) −19.0386 + 19.0386i −0.974099 + 0.974099i
\(383\) 7.48783 + 7.48783i 0.382610 + 0.382610i 0.872042 0.489431i \(-0.162796\pi\)
−0.489431 + 0.872042i \(0.662796\pi\)
\(384\) −1.47393 + 0.909692i −0.0752160 + 0.0464225i
\(385\) −0.274395 0.274395i −0.0139845 0.0139845i
\(386\) 21.4571i 1.09214i
\(387\) −9.74415 + 19.4289i −0.495323 + 0.987624i
\(388\) −0.867358 0.867358i −0.0440334 0.0440334i
\(389\) −7.00656 −0.355247 −0.177623 0.984099i \(-0.556841\pi\)
−0.177623 + 0.984099i \(0.556841\pi\)
\(390\) −0.290481 4.92895i −0.0147091 0.249587i
\(391\) 23.7609 1.20164
\(392\) −0.707107 0.707107i −0.0357143 0.0357143i
\(393\) −3.09925 + 13.0928i −0.156336 + 0.660444i
\(394\) 22.4757i 1.13231i
\(395\) 7.39278 + 7.39278i 0.371971 + 0.371971i
\(396\) −0.463917 1.39745i −0.0233127 0.0702244i
\(397\) −5.42804 5.42804i −0.272425 0.272425i 0.557650 0.830076i \(-0.311703\pi\)
−0.830076 + 0.557650i \(0.811703\pi\)
\(398\) −3.04597 + 3.04597i −0.152681 + 0.152681i
\(399\) −9.21290 2.18082i −0.461222 0.109178i
\(400\) 4.37490i 0.218745i
\(401\) −22.7703 + 22.7703i −1.13709 + 1.13709i −0.148126 + 0.988969i \(0.547324\pi\)
−0.988969 + 0.148126i \(0.952676\pi\)
\(402\) 5.80260 + 1.37356i 0.289407 + 0.0685067i
\(403\) 5.99049 11.1210i 0.298407 0.553978i
\(404\) 3.42487i 0.170393i
\(405\) 1.02354 7.04170i 0.0508603 0.349905i
\(406\) −10.6966 −0.530862
\(407\) −4.80405 −0.238128
\(408\) −6.63329 + 4.09399i −0.328397 + 0.202683i
\(409\) 5.64482 5.64482i 0.279118 0.279118i −0.553639 0.832757i \(-0.686761\pi\)
0.832757 + 0.553639i \(0.186761\pi\)
\(410\) −5.78330 + 5.78330i −0.285617 + 0.285617i
\(411\) 4.91206 3.03167i 0.242294 0.149541i
\(412\) 0.0883069 0.00435057
\(413\) −4.82596 −0.237470
\(414\) −4.99038 15.0324i −0.245264 0.738803i
\(415\) 7.05876i 0.346501i
\(416\) 3.17432 + 1.70989i 0.155634 + 0.0838341i
\(417\) −2.59385 0.614001i −0.127022 0.0300678i
\(418\) 1.89704 1.89704i 0.0927871 0.0927871i
\(419\) 9.00273i 0.439812i 0.975521 + 0.219906i \(0.0705751\pi\)
−0.975521 + 0.219906i \(0.929425\pi\)
\(420\) 1.33259 + 0.315443i 0.0650238 + 0.0153920i
\(421\) −1.90886 + 1.90886i −0.0930321 + 0.0930321i −0.752091 0.659059i \(-0.770955\pi\)
0.659059 + 0.752091i \(0.270955\pi\)
\(422\) 6.85507 + 6.85507i 0.333700 + 0.333700i
\(423\) −10.0390 + 3.33269i −0.488112 + 0.162041i
\(424\) −8.52821 8.52821i −0.414166 0.414166i
\(425\) 19.6889i 0.955051i
\(426\) −4.79381 + 20.2515i −0.232261 + 0.981188i
\(427\) −4.54291 4.54291i −0.219847 0.219847i
\(428\) −5.08715 −0.245897
\(429\) −2.03611 + 2.29113i −0.0983043 + 0.110617i
\(430\) 5.72825 0.276241
\(431\) 11.7362 + 11.7362i 0.565312 + 0.565312i 0.930811 0.365500i \(-0.119102\pi\)
−0.365500 + 0.930811i \(0.619102\pi\)
\(432\) 3.98324 + 3.33674i 0.191644 + 0.160539i
\(433\) 13.9122i 0.668577i 0.942471 + 0.334289i \(0.108496\pi\)
−0.942471 + 0.334289i \(0.891504\pi\)
\(434\) 2.47731 + 2.47731i 0.118915 + 0.118915i
\(435\) 12.4651 7.69332i 0.597656 0.368867i
\(436\) 5.92580 + 5.92580i 0.283795 + 0.283795i
\(437\) 20.4065 20.4065i 0.976176 0.976176i
\(438\) 3.34725 14.1405i 0.159938 0.675659i
\(439\) 8.24651i 0.393584i −0.980445 0.196792i \(-0.936948\pi\)
0.980445 0.196792i \(-0.0630524\pi\)
\(440\) −0.274395 + 0.274395i −0.0130813 + 0.0130813i
\(441\) −1.34492 + 2.68164i −0.0640439 + 0.127697i
\(442\) 14.2858 + 7.69520i 0.679504 + 0.366023i
\(443\) 9.44990i 0.448978i −0.974477 0.224489i \(-0.927929\pi\)
0.974477 0.224489i \(-0.0720713\pi\)
\(444\) 14.4267 8.90400i 0.684661 0.422565i
\(445\) −13.7048 −0.649669
\(446\) −10.6028 −0.502055
\(447\) −8.76089 14.1948i −0.414376 0.671392i
\(448\) −0.707107 + 0.707107i −0.0334077 + 0.0334077i
\(449\) 22.9219 22.9219i 1.08175 1.08175i 0.0854053 0.996346i \(-0.472781\pi\)
0.996346 0.0854053i \(-0.0272185\pi\)
\(450\) 12.4562 4.13516i 0.587193 0.194933i
\(451\) 5.07729 0.239080
\(452\) −2.88604 −0.135748
\(453\) −1.56872 2.54171i −0.0737047 0.119420i
\(454\) 24.7804i 1.16300i
\(455\) −0.818708 2.73057i −0.0383816 0.128011i
\(456\) −2.18082 + 9.21290i −0.102126 + 0.431433i
\(457\) −2.72508 + 2.72508i −0.127474 + 0.127474i −0.767965 0.640492i \(-0.778731\pi\)
0.640492 + 0.767965i \(0.278731\pi\)
\(458\) 19.6211i 0.916834i
\(459\) 17.9262 + 15.0167i 0.836725 + 0.700920i
\(460\) −2.95168 + 2.95168i −0.137623 + 0.137623i
\(461\) 17.0514 + 17.0514i 0.794161 + 0.794161i 0.982168 0.188007i \(-0.0602026\pi\)
−0.188007 + 0.982168i \(0.560203\pi\)
\(462\) −0.446489 0.723423i −0.0207725 0.0336567i
\(463\) −7.20273 7.20273i −0.334739 0.334739i 0.519644 0.854383i \(-0.326065\pi\)
−0.854383 + 0.519644i \(0.826065\pi\)
\(464\) 10.6966i 0.496576i
\(465\) −4.66866 1.10514i −0.216504 0.0512494i
\(466\) 3.39478 + 3.39478i 0.157260 + 0.157260i
\(467\) −19.1716 −0.887156 −0.443578 0.896236i \(-0.646291\pi\)
−0.443578 + 0.896236i \(0.646291\pi\)
\(468\) 1.86803 10.6541i 0.0863499 0.492487i
\(469\) 3.44271 0.158970
\(470\) 1.97120 + 1.97120i 0.0909246 + 0.0909246i
\(471\) 9.50217 + 2.24929i 0.437837 + 0.103642i
\(472\) 4.82596i 0.222133i
\(473\) −2.51448 2.51448i −0.115616 0.115616i
\(474\) 12.0293 + 19.4905i 0.552526 + 0.895229i
\(475\) 16.9094 + 16.9094i 0.775855 + 0.775855i
\(476\) −3.18228 + 3.18228i −0.145859 + 0.145859i
\(477\) −16.2207 + 32.3425i −0.742695 + 1.48086i
\(478\) 12.5208i 0.572689i
\(479\) 21.3865 21.3865i 0.977174 0.977174i −0.0225708 0.999745i \(-0.507185\pi\)
0.999745 + 0.0225708i \(0.00718511\pi\)
\(480\) 0.315443 1.33259i 0.0143979 0.0608242i
\(481\) −31.0700 16.7362i −1.41667 0.763107i
\(482\) 12.4375i 0.566515i
\(483\) −4.80290 7.78190i −0.218540 0.354089i
\(484\) −10.7591 −0.489050
\(485\) 0.969814 0.0440370
\(486\) 5.73542 14.4950i 0.260164 0.657506i
\(487\) 24.0755 24.0755i 1.09096 1.09096i 0.0955392 0.995426i \(-0.469542\pi\)
0.995426 0.0955392i \(-0.0304575\pi\)
\(488\) −4.54291 + 4.54291i −0.205648 + 0.205648i
\(489\) −4.47507 7.25073i −0.202370 0.327889i
\(490\) 0.790633 0.0357172
\(491\) −10.3827 −0.468565 −0.234283 0.972169i \(-0.575274\pi\)
−0.234283 + 0.972169i \(0.575274\pi\)
\(492\) −15.2473 + 9.41044i −0.687399 + 0.424255i
\(493\) 48.1390i 2.16807i
\(494\) 18.8779 5.66016i 0.849356 0.254662i
\(495\) 1.04062 + 0.521902i 0.0467724 + 0.0234577i
\(496\) 2.47731 2.47731i 0.111234 0.111234i
\(497\) 12.0153i 0.538961i
\(498\) 3.56204 15.0479i 0.159619 0.674311i
\(499\) 3.48978 3.48978i 0.156224 0.156224i −0.624667 0.780891i \(-0.714765\pi\)
0.780891 + 0.624667i \(0.214765\pi\)
\(500\) −5.24115 5.24115i −0.234391 0.234391i
\(501\) −5.19084 + 3.20373i −0.231910 + 0.143132i
\(502\) −9.67910 9.67910i −0.431999 0.431999i
\(503\) 0.584892i 0.0260790i 0.999915 + 0.0130395i \(0.00415073\pi\)
−0.999915 + 0.0130395i \(0.995849\pi\)
\(504\) 2.68164 + 1.34492i 0.119450 + 0.0599076i
\(505\) −1.91471 1.91471i −0.0852037 0.0852037i
\(506\) 2.59135 0.115200
\(507\) −21.1503 + 7.72444i −0.939316 + 0.343054i
\(508\) 21.1044 0.936356
\(509\) 14.6995 + 14.6995i 0.651544 + 0.651544i 0.953365 0.301821i \(-0.0975944\pi\)
−0.301821 + 0.953365i \(0.597594\pi\)
\(510\) 1.41962 5.99722i 0.0628620 0.265561i
\(511\) 8.38963i 0.371135i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 28.2923 2.49879i 1.24914 0.110324i
\(514\) −12.9392 12.9392i −0.570723 0.570723i
\(515\) −0.0493691 + 0.0493691i −0.00217546 + 0.00217546i
\(516\) 12.2115 + 2.89063i 0.537581 + 0.127253i
\(517\) 1.73056i 0.0761099i
\(518\) 6.92111 6.92111i 0.304096 0.304096i
\(519\) 22.2103 + 5.25749i 0.974925 + 0.230778i
\(520\) −2.73057 + 0.818708i −0.119744 + 0.0359027i
\(521\) 2.40567i 0.105394i 0.998611 + 0.0526972i \(0.0167818\pi\)
−0.998611 + 0.0526972i \(0.983218\pi\)
\(522\) 30.4554 10.1104i 1.33299 0.442521i
\(523\) 30.2590 1.32313 0.661567 0.749886i \(-0.269892\pi\)
0.661567 + 0.749886i \(0.269892\pi\)
\(524\) 7.76803 0.339348
\(525\) 6.44828 3.97981i 0.281426 0.173693i
\(526\) 11.6816 11.6816i 0.509342 0.509342i
\(527\) 11.1489 11.1489i 0.485655 0.485655i
\(528\) −0.723423 + 0.446489i −0.0314830 + 0.0194309i
\(529\) 4.87527 0.211968
\(530\) 9.53560 0.414200
\(531\) 13.7405 4.56150i 0.596287 0.197952i
\(532\) 5.46606i 0.236984i
\(533\) 32.8372 + 17.6882i 1.42234 + 0.766159i
\(534\) −29.2159 6.91580i −1.26429 0.299276i
\(535\) 2.84404 2.84404i 0.122958 0.122958i
\(536\) 3.44271i 0.148703i
\(537\) 23.5910 + 5.58432i 1.01803 + 0.240981i
\(538\) −8.30481 + 8.30481i −0.358046 + 0.358046i
\(539\) −0.347057 0.347057i −0.0149488 0.0149488i
\(540\) −4.09232 + 0.361436i −0.176105 + 0.0155537i
\(541\) −11.6253 11.6253i −0.499812 0.499812i 0.411567 0.911379i \(-0.364981\pi\)
−0.911379 + 0.411567i \(0.864981\pi\)
\(542\) 13.7999i 0.592758i
\(543\) −1.38692 + 5.85906i −0.0595184 + 0.251436i
\(544\) 3.18228 + 3.18228i 0.136439 + 0.136439i
\(545\) −6.62579 −0.283818
\(546\) −0.367403 6.23418i −0.0157234 0.266798i
\(547\) 16.5437 0.707359 0.353680 0.935367i \(-0.384930\pi\)
0.353680 + 0.935367i \(0.384930\pi\)
\(548\) −2.35653 2.35653i −0.100666 0.100666i
\(549\) 17.2286 + 8.64065i 0.735298 + 0.368774i
\(550\) 2.14726i 0.0915594i
\(551\) 41.3432 + 41.3432i 1.76128 + 1.76128i
\(552\) −7.78190 + 4.80290i −0.331220 + 0.204425i
\(553\) 9.35045 + 9.35045i 0.397621 + 0.397621i
\(554\) 1.33263 1.33263i 0.0566181 0.0566181i
\(555\) −3.08753 + 13.0433i −0.131058 + 0.553658i
\(556\) 1.53895i 0.0652659i
\(557\) 3.77844 3.77844i 0.160098 0.160098i −0.622512 0.782610i \(-0.713888\pi\)
0.782610 + 0.622512i \(0.213888\pi\)
\(558\) −9.39497 4.71186i −0.397721 0.199469i
\(559\) −7.50241 25.0222i −0.317318 1.05833i
\(560\) 0.790633i 0.0334104i
\(561\) −3.25571 + 2.00939i −0.137456 + 0.0848364i
\(562\) −4.03328 −0.170134
\(563\) −37.3621 −1.57462 −0.787312 0.616555i \(-0.788528\pi\)
−0.787312 + 0.616555i \(0.788528\pi\)
\(564\) 3.20748 + 5.19692i 0.135059 + 0.218830i
\(565\) 1.61348 1.61348i 0.0678796 0.0678796i
\(566\) 10.7904 10.7904i 0.453553 0.453553i
\(567\) 1.29459 8.90640i 0.0543675 0.374034i
\(568\) 12.0153 0.504152
\(569\) 2.27928 0.0955524 0.0477762 0.998858i \(-0.484787\pi\)
0.0477762 + 0.998858i \(0.484787\pi\)
\(570\) −3.93137 6.36980i −0.164667 0.266801i
\(571\) 8.84959i 0.370344i 0.982706 + 0.185172i \(0.0592842\pi\)
−0.982706 + 0.185172i \(0.940716\pi\)
\(572\) 1.55800 + 0.839235i 0.0651431 + 0.0350902i
\(573\) 10.7423 45.3808i 0.448764 1.89581i
\(574\) −7.31477 + 7.31477i −0.305313 + 0.305313i
\(575\) 23.0982i 0.963260i
\(576\) 1.34492 2.68164i 0.0560384 0.111735i
\(577\) 19.6466 19.6466i 0.817899 0.817899i −0.167904 0.985803i \(-0.553700\pi\)
0.985803 + 0.167904i \(0.0536999\pi\)
\(578\) 2.30076 + 2.30076i 0.0956991 + 0.0956991i
\(579\) 19.5193 + 31.6262i 0.811196 + 1.31434i
\(580\) −5.98005 5.98005i −0.248308 0.248308i
\(581\) 8.92798i 0.370395i
\(582\) 2.06745 + 0.489394i 0.0856986 + 0.0202860i
\(583\) −4.18576 4.18576i −0.173356 0.173356i
\(584\) −8.38963 −0.347165
\(585\) 4.91197 + 7.00067i 0.203085 + 0.289442i
\(586\) 19.0021 0.784968
\(587\) 11.1009 + 11.1009i 0.458182 + 0.458182i 0.898058 0.439877i \(-0.144978\pi\)
−0.439877 + 0.898058i \(0.644978\pi\)
\(588\) 1.68547 + 0.398975i 0.0695077 + 0.0164534i
\(589\) 19.1500i 0.789063i
\(590\) −2.69801 2.69801i −0.111075 0.111075i
\(591\) 20.4460 + 33.1275i 0.841034 + 1.36269i
\(592\) −6.92111 6.92111i −0.284456 0.284456i
\(593\) −7.19619 + 7.19619i −0.295512 + 0.295512i −0.839253 0.543741i \(-0.817007\pi\)
0.543741 + 0.839253i \(0.317007\pi\)
\(594\) 1.95503 + 1.63771i 0.0802157 + 0.0671962i
\(595\) 3.55818i 0.145871i
\(596\) −6.80987 + 6.80987i −0.278943 + 0.278943i
\(597\) 1.71864 7.26042i 0.0703394 0.297149i
\(598\) 16.7595 + 9.02769i 0.685345 + 0.369170i
\(599\) 3.19761i 0.130651i 0.997864 + 0.0653253i \(0.0208085\pi\)
−0.997864 + 0.0653253i \(0.979191\pi\)
\(600\) −3.97981 6.44828i −0.162475 0.263250i
\(601\) −2.82987 −0.115433 −0.0577165 0.998333i \(-0.518382\pi\)
−0.0577165 + 0.998333i \(0.518382\pi\)
\(602\) 7.24514 0.295290
\(603\) −9.80212 + 3.25406i −0.399173 + 0.132515i
\(604\) −1.21937 + 1.21937i −0.0496154 + 0.0496154i
\(605\) 6.01501 6.01501i 0.244545 0.244545i
\(606\) −3.11557 5.04800i −0.126561 0.205061i
\(607\) 31.5745 1.28157 0.640784 0.767721i \(-0.278609\pi\)
0.640784 + 0.767721i \(0.278609\pi\)
\(608\) 5.46606 0.221678
\(609\) 15.7660 9.73058i 0.638869 0.394303i
\(610\) 5.07954i 0.205665i
\(611\) 6.02889 11.1923i 0.243903 0.452793i
\(612\) 6.05271 12.0685i 0.244666 0.487840i
\(613\) −9.86043 + 9.86043i −0.398259 + 0.398259i −0.877619 0.479360i \(-0.840869\pi\)
0.479360 + 0.877619i \(0.340869\pi\)
\(614\) 20.0100i 0.807539i
\(615\) 3.26314 13.7852i 0.131583 0.555872i
\(616\) −0.347057 + 0.347057i −0.0139833 + 0.0139833i
\(617\) −23.5386 23.5386i −0.947630 0.947630i 0.0510654 0.998695i \(-0.483738\pi\)
−0.998695 + 0.0510654i \(0.983738\pi\)
\(618\) −0.130158 + 0.0803321i −0.00523572 + 0.00323143i
\(619\) −6.25762 6.25762i −0.251515 0.251515i 0.570077 0.821592i \(-0.306914\pi\)
−0.821592 + 0.570077i \(0.806914\pi\)
\(620\) 2.76994i 0.111243i
\(621\) 21.0303 + 17.6170i 0.843918 + 0.706945i
\(622\) −23.5438 23.5438i −0.944019 0.944019i
\(623\) −17.3339 −0.694469
\(624\) −6.23418 + 0.367403i −0.249567 + 0.0147079i
\(625\) −16.0142 −0.640569
\(626\) −16.6279 16.6279i −0.664583 0.664583i
\(627\) −1.07038 + 4.52181i −0.0427467 + 0.180584i
\(628\) 5.63769i 0.224968i
\(629\) −31.1479 31.1479i −1.24195 1.24195i
\(630\) −2.25110 + 0.747308i −0.0896859 + 0.0297734i
\(631\) −1.59821 1.59821i −0.0636237 0.0636237i 0.674579 0.738203i \(-0.264325\pi\)
−0.738203 + 0.674579i \(0.764325\pi\)
\(632\) 9.35045 9.35045i 0.371941 0.371941i
\(633\) −16.3399 3.86787i −0.649452 0.153734i
\(634\) 3.13491i 0.124503i
\(635\) −11.7987 + 11.7987i −0.468216 + 0.468216i
\(636\) 20.3280 + 4.81192i 0.806057 + 0.190805i
\(637\) −1.03551 3.45365i −0.0410284 0.136839i
\(638\) 5.25002i 0.207850i
\(639\) −11.3569 34.2101i −0.449272 1.35333i
\(640\) −0.790633 −0.0312525
\(641\) 22.4925 0.888400 0.444200 0.895928i \(-0.353488\pi\)
0.444200 + 0.895928i \(0.353488\pi\)
\(642\) 7.49809 4.62774i 0.295926 0.182642i
\(643\) −12.9119 + 12.9119i −0.509196 + 0.509196i −0.914280 0.405083i \(-0.867242\pi\)
0.405083 + 0.914280i \(0.367242\pi\)
\(644\) −3.73331 + 3.73331i −0.147113 + 0.147113i
\(645\) −8.44303 + 5.21094i −0.332444 + 0.205181i
\(646\) 24.5996 0.967857
\(647\) −4.76406 −0.187295 −0.0936473 0.995605i \(-0.529853\pi\)
−0.0936473 + 0.995605i \(0.529853\pi\)
\(648\) −8.90640 1.29459i −0.349877 0.0508561i
\(649\) 2.36865i 0.0929775i
\(650\) −7.48058 + 13.8873i −0.293412 + 0.544705i
\(651\) −5.90496 1.39779i −0.231434 0.0547835i
\(652\) −3.47849 + 3.47849i −0.136228 + 0.136228i
\(653\) 13.9182i 0.544660i 0.962204 + 0.272330i \(0.0877942\pi\)
−0.962204 + 0.272330i \(0.912206\pi\)
\(654\) −14.1249 3.34355i −0.552326 0.130743i
\(655\) −4.34281 + 4.34281i −0.169688 + 0.169688i
\(656\) 7.31477 + 7.31477i 0.285594 + 0.285594i
\(657\) 7.92988 + 23.8870i 0.309374 + 0.931921i
\(658\) 2.49319 + 2.49319i 0.0971946 + 0.0971946i
\(659\) 22.7816i 0.887447i −0.896164 0.443724i \(-0.853657\pi\)
0.896164 0.443724i \(-0.146343\pi\)
\(660\) 0.154824 0.654054i 0.00602650 0.0254590i
\(661\) −3.75702 3.75702i −0.146131 0.146131i 0.630256 0.776387i \(-0.282950\pi\)
−0.776387 + 0.630256i \(0.782950\pi\)
\(662\) −31.0138 −1.20539
\(663\) −28.0564 + 1.65347i −1.08962 + 0.0642153i
\(664\) −8.92798 −0.346473
\(665\) −3.05587 3.05587i −0.118501 0.118501i
\(666\) −13.1640 + 26.2477i −0.510095 + 1.01708i
\(667\) 56.4747i 2.18671i
\(668\) 2.49027 + 2.49027i 0.0963515 + 0.0963515i
\(669\) 15.6277 9.64523i 0.604201 0.372906i
\(670\) 1.92469 + 1.92469i 0.0743573 + 0.0743573i
\(671\) −2.22972 + 2.22972i −0.0860774 + 0.0860774i
\(672\) 0.398975 1.68547i 0.0153908 0.0650185i
\(673\) 17.2981i 0.666792i 0.942787 + 0.333396i \(0.108195\pi\)
−0.942787 + 0.333396i \(0.891805\pi\)
\(674\) −8.51258 + 8.51258i −0.327892 + 0.327892i
\(675\) −14.5979 + 17.4263i −0.561873 + 0.670737i
\(676\) 7.15258 + 10.8554i 0.275099 + 0.417517i
\(677\) 38.4320i 1.47706i 0.674219 + 0.738531i \(0.264480\pi\)
−0.674219 + 0.738531i \(0.735520\pi\)
\(678\) 4.25382 2.62541i 0.163367 0.100828i
\(679\) 1.22663 0.0470737
\(680\) −3.55818 −0.136450
\(681\) −22.5425 36.5244i −0.863830 1.39962i
\(682\) 1.21590 1.21590i 0.0465591 0.0465591i
\(683\) 3.33543 3.33543i 0.127627 0.127627i −0.640408 0.768035i \(-0.721235\pi\)
0.768035 + 0.640408i \(0.221235\pi\)
\(684\) −5.16653 15.5630i −0.197547 0.595067i
\(685\) 2.63489 0.100674
\(686\) 1.00000 0.0381802
\(687\) 17.8492 + 28.9201i 0.680988 + 1.10337i
\(688\) 7.24514i 0.276219i
\(689\) −12.4890 41.6535i −0.475792 1.58687i
\(690\) 1.66544 7.03569i 0.0634024 0.267844i
\(691\) 11.0166 11.0166i 0.419092 0.419092i −0.465799 0.884891i \(-0.654233\pi\)
0.884891 + 0.465799i \(0.154233\pi\)
\(692\) 13.1775i 0.500934i
\(693\) 1.31618 + 0.660106i 0.0499977 + 0.0250753i
\(694\) 3.47500 3.47500i 0.131909 0.131909i
\(695\) −0.860367 0.860367i −0.0326356 0.0326356i
\(696\) −9.73058 15.7660i −0.368837 0.597607i
\(697\) 32.9195 + 32.9195i 1.24692 + 1.24692i
\(698\) 4.71881i 0.178609i
\(699\) −8.09186 1.91545i −0.306062 0.0724491i
\(700\) −3.09352 3.09352i −0.116924 0.116924i
\(701\) −11.4796 −0.433579 −0.216790 0.976218i \(-0.569559\pi\)
−0.216790 + 0.976218i \(0.569559\pi\)
\(702\) 6.93863 + 17.4027i 0.261882 + 0.656824i
\(703\) −53.5014 −2.01784
\(704\) 0.347057 + 0.347057i 0.0130802 + 0.0130802i
\(705\) −4.69859 1.11222i −0.176959 0.0418886i
\(706\) 6.51974i 0.245374i
\(707\) −2.42175 2.42175i −0.0910792 0.0910792i
\(708\) −4.39013 7.11311i −0.164991 0.267327i
\(709\) 18.4081 + 18.4081i 0.691331 + 0.691331i 0.962525 0.271193i \(-0.0874183\pi\)
−0.271193 + 0.962525i \(0.587418\pi\)
\(710\) −6.71731 + 6.71731i −0.252096 + 0.252096i
\(711\) −35.4607 17.7846i −1.32988 0.666975i
\(712\) 17.3339i 0.649617i
\(713\) 13.0795 13.0795i 0.489829 0.489829i
\(714\) 1.79555 7.58533i 0.0671969 0.283874i
\(715\) −1.34020 + 0.401833i −0.0501207 + 0.0150277i
\(716\) 13.9967i 0.523081i
\(717\) 11.3901 + 18.4548i 0.425371 + 0.689207i
\(718\) 12.6102 0.470608
\(719\) −4.45696 −0.166217 −0.0831084 0.996541i \(-0.526485\pi\)
−0.0831084 + 0.996541i \(0.526485\pi\)
\(720\) 0.747308 + 2.25110i 0.0278505 + 0.0838935i
\(721\) −0.0624424 + 0.0624424i −0.00232548 + 0.00232548i
\(722\) 7.69177 7.69177i 0.286258 0.286258i
\(723\) −11.3143 18.3320i −0.420784 0.681776i
\(724\) 3.47621 0.129192
\(725\) −46.7964 −1.73797
\(726\) 15.8581 9.78747i 0.588550 0.363247i
\(727\) 48.0910i 1.78360i −0.452432 0.891799i \(-0.649443\pi\)
0.452432 0.891799i \(-0.350557\pi\)
\(728\) −3.45365 + 1.03551i −0.128001 + 0.0383785i
\(729\) 4.73239 + 26.5820i 0.175274 + 0.984520i
\(730\) 4.69032 4.69032i 0.173597 0.173597i
\(731\) 32.6062i 1.20598i
\(732\) 2.56327 10.8286i 0.0947412 0.400235i
\(733\) 12.2239 12.2239i 0.451499 0.451499i −0.444353 0.895852i \(-0.646566\pi\)
0.895852 + 0.444353i \(0.146566\pi\)
\(734\) −18.1272 18.1272i −0.669087 0.669087i
\(735\) −1.16534 + 0.719233i −0.0429841 + 0.0265293i
\(736\) 3.73331 + 3.73331i 0.137612 + 0.137612i
\(737\) 1.68973i 0.0622420i
\(738\) 13.9127 27.7406i 0.512135 1.02115i
\(739\) −0.378213 0.378213i −0.0139128 0.0139128i 0.700116 0.714029i \(-0.253132\pi\)
−0.714029 + 0.700116i \(0.753132\pi\)
\(740\) 7.73867 0.284479
\(741\) −22.6756 + 25.5157i −0.833009 + 0.937343i
\(742\) 12.0607 0.442762
\(743\) −13.1510 13.1510i −0.482465 0.482465i 0.423453 0.905918i \(-0.360818\pi\)
−0.905918 + 0.423453i \(0.860818\pi\)
\(744\) −1.39779 + 5.90496i −0.0512453 + 0.216486i
\(745\) 7.61429i 0.278966i
\(746\) −19.5183 19.5183i −0.714614 0.714614i
\(747\) 8.43874 + 25.4198i 0.308757 + 0.930063i
\(748\) 1.56190 + 1.56190i 0.0571089 + 0.0571089i
\(749\) 3.59716 3.59716i 0.131437 0.131437i
\(750\) 12.4929 + 2.95724i 0.456177 + 0.107983i
\(751\) 21.7792i 0.794735i −0.917660 0.397367i \(-0.869924\pi\)
0.917660 0.397367i \(-0.130076\pi\)
\(752\) 2.49319 2.49319i 0.0909172 0.0909172i
\(753\) 23.0713 + 5.46129i 0.840764 + 0.199020i
\(754\) −18.2899 + 33.9543i −0.666079 + 1.23654i
\(755\) 1.36341i 0.0496194i
\(756\) −5.17600 + 0.457147i −0.188249 + 0.0166263i
\(757\) −7.96654 −0.289549 −0.144774 0.989465i \(-0.546246\pi\)
−0.144774 + 0.989465i \(0.546246\pi\)
\(758\) −21.5227 −0.781739
\(759\) −3.81946 + 2.35733i −0.138638 + 0.0855656i
\(760\) −3.05587 + 3.05587i −0.110848 + 0.110848i
\(761\) −26.2245 + 26.2245i −0.950637 + 0.950637i −0.998838 0.0482010i \(-0.984651\pi\)
0.0482010 + 0.998838i \(0.484651\pi\)
\(762\) −31.1063 + 19.1985i −1.12686 + 0.695488i
\(763\) −8.38035 −0.303389
\(764\) −26.9246 −0.974099
\(765\) 3.36320 + 10.1309i 0.121597 + 0.366283i
\(766\) 10.5894i 0.382610i
\(767\) −8.25184 + 15.3191i −0.297957 + 0.553142i
\(768\) −1.68547 0.398975i −0.0608193 0.0143968i
\(769\) 4.82224 4.82224i 0.173894 0.173894i −0.614794 0.788688i \(-0.710761\pi\)
0.788688 + 0.614794i \(0.210761\pi\)
\(770\) 0.388054i 0.0139845i
\(771\) 30.8421 + 7.30075i 1.11075 + 0.262930i
\(772\) 15.1725 15.1725i 0.546069 0.546069i
\(773\) −25.9691 25.9691i −0.934044 0.934044i 0.0639117 0.997956i \(-0.479642\pi\)
−0.997956 + 0.0639117i \(0.979642\pi\)
\(774\) −20.6284 + 6.84812i −0.741474 + 0.246151i
\(775\) 10.8380 + 10.8380i 0.389311 + 0.389311i
\(776\) 1.22663i 0.0440334i