Properties

Label 400.2.l.g.301.1
Level $400$
Weight $2$
Character 400.301
Analytic conductor $3.194$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.19401608085\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.4767670494822400.1
Defining polynomial: \(x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 301.1
Root \(-1.41313 + 0.0554252i\) of defining polynomial
Character \(\chi\) \(=\) 400.301
Dual form 400.2.l.g.101.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.41313 + 0.0554252i) q^{2} +(0.488516 + 0.488516i) q^{3} +(1.99386 - 0.156646i) q^{4} +(-0.717411 - 0.663259i) q^{6} +4.71540i q^{7} +(-2.80889 + 0.331870i) q^{8} -2.52270i q^{9} +O(q^{10})\) \(q+(-1.41313 + 0.0554252i) q^{2} +(0.488516 + 0.488516i) q^{3} +(1.99386 - 0.156646i) q^{4} +(-0.717411 - 0.663259i) q^{6} +4.71540i q^{7} +(-2.80889 + 0.331870i) q^{8} -2.52270i q^{9} +(-3.91360 + 3.91360i) q^{11} +(1.05055 + 0.897506i) q^{12} +(0.0878822 + 0.0878822i) q^{13} +(-0.261352 - 6.66346i) q^{14} +(3.95092 - 0.624658i) q^{16} -4.67442 q^{17} +(0.139821 + 3.56490i) q^{18} +(1.81249 + 1.81249i) q^{19} +(-2.30355 + 2.30355i) q^{21} +(5.31350 - 5.74732i) q^{22} -1.63007i q^{23} +(-1.53431 - 1.21006i) q^{24} +(-0.129060 - 0.119318i) q^{26} +(2.69793 - 2.69793i) q^{27} +(0.738648 + 9.40184i) q^{28} +(3.26362 + 3.26362i) q^{29} -2.12875 q^{31} +(-5.54854 + 1.10170i) q^{32} -3.82371 q^{33} +(6.60555 - 0.259081i) q^{34} +(-0.395171 - 5.02991i) q^{36} +(-3.97797 + 3.97797i) q^{37} +(-2.66173 - 2.46082i) q^{38} +0.0858637i q^{39} +8.25504i q^{41} +(3.12753 - 3.38288i) q^{42} +(-2.27336 + 2.27336i) q^{43} +(-7.19010 + 8.41620i) q^{44} +(0.0903468 + 2.30349i) q^{46} +4.06129 q^{47} +(2.23524 + 1.62493i) q^{48} -15.2350 q^{49} +(-2.28353 - 2.28353i) q^{51} +(0.188991 + 0.161458i) q^{52} +(5.03938 - 5.03938i) q^{53} +(-3.66298 + 3.96205i) q^{54} +(-1.56490 - 13.2450i) q^{56} +1.77086i q^{57} +(-4.79280 - 4.43103i) q^{58} +(-5.16453 + 5.16453i) q^{59} +(7.12726 + 7.12726i) q^{61} +(3.00819 - 0.117986i) q^{62} +11.8956 q^{63} +(7.77972 - 1.86437i) q^{64} +(5.40339 - 0.211930i) q^{66} +(7.49920 + 7.49920i) q^{67} +(-9.32012 + 0.732228i) q^{68} +(0.796314 - 0.796314i) q^{69} -4.54072i q^{71} +(0.837210 + 7.08600i) q^{72} -8.30557i q^{73} +(5.40090 - 5.84186i) q^{74} +(3.89776 + 3.32992i) q^{76} +(-18.4542 - 18.4542i) q^{77} +(-0.00475901 - 0.121336i) q^{78} +11.5317 q^{79} -4.93215 q^{81} +(-0.457537 - 11.6654i) q^{82} +(1.16919 + 1.16919i) q^{83} +(-4.23211 + 4.95379i) q^{84} +(3.08655 - 3.33855i) q^{86} +3.18866i q^{87} +(9.69406 - 12.2917i) q^{88} -3.24572i q^{89} +(-0.414400 + 0.414400i) q^{91} +(-0.255343 - 3.25012i) q^{92} +(-1.03993 - 1.03993i) q^{93} +(-5.73912 + 0.225098i) q^{94} +(-3.24875 - 2.17235i) q^{96} +13.9581 q^{97} +(21.5290 - 0.844405i) q^{98} +(9.87285 + 9.87285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{2} + 2q^{3} + 2q^{4} + 6q^{6} - 8q^{8} + O(q^{10}) \) \( 12q + 4q^{2} + 2q^{3} + 2q^{4} + 6q^{6} - 8q^{8} - 2q^{11} + 8q^{12} - 4q^{13} + 14q^{14} + 2q^{16} - 8q^{17} + 18q^{18} - 14q^{19} - 20q^{21} + 2q^{22} - 14q^{24} - 16q^{26} - 10q^{27} + 26q^{28} - 4q^{31} - 16q^{32} + 28q^{33} - 6q^{34} + 2q^{36} + 8q^{37} + 10q^{38} + 10q^{42} - 44q^{44} - 10q^{46} + 8q^{47} - 28q^{48} + 4q^{49} + 10q^{51} - 12q^{52} - 16q^{53} + 10q^{54} + 6q^{56} - 60q^{58} + 20q^{59} + 4q^{61} - 18q^{62} - 8q^{63} + 38q^{64} + 32q^{66} + 50q^{67} - 60q^{68} - 14q^{72} + 10q^{74} + 60q^{76} - 8q^{77} + 4q^{78} + 12q^{79} - 8q^{81} + 42q^{82} - 2q^{83} + 34q^{84} + 6q^{86} + 30q^{88} - 2q^{92} - 44q^{93} + 32q^{94} - 34q^{96} + 64q^{98} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41313 + 0.0554252i −0.999232 + 0.0391915i
\(3\) 0.488516 + 0.488516i 0.282045 + 0.282045i 0.833924 0.551879i \(-0.186089\pi\)
−0.551879 + 0.833924i \(0.686089\pi\)
\(4\) 1.99386 0.156646i 0.996928 0.0783229i
\(5\) 0 0
\(6\) −0.717411 0.663259i −0.292882 0.270774i
\(7\) 4.71540i 1.78226i 0.453753 + 0.891128i \(0.350085\pi\)
−0.453753 + 0.891128i \(0.649915\pi\)
\(8\) −2.80889 + 0.331870i −0.993093 + 0.117334i
\(9\) 2.52270i 0.840901i
\(10\) 0 0
\(11\) −3.91360 + 3.91360i −1.17999 + 1.17999i −0.200249 + 0.979745i \(0.564175\pi\)
−0.979745 + 0.200249i \(0.935825\pi\)
\(12\) 1.05055 + 0.897506i 0.303269 + 0.259088i
\(13\) 0.0878822 + 0.0878822i 0.0243741 + 0.0243741i 0.719189 0.694815i \(-0.244514\pi\)
−0.694815 + 0.719189i \(0.744514\pi\)
\(14\) −0.261352 6.66346i −0.0698493 1.78089i
\(15\) 0 0
\(16\) 3.95092 0.624658i 0.987731 0.156165i
\(17\) −4.67442 −1.13371 −0.566857 0.823816i \(-0.691841\pi\)
−0.566857 + 0.823816i \(0.691841\pi\)
\(18\) 0.139821 + 3.56490i 0.0329562 + 0.840255i
\(19\) 1.81249 + 1.81249i 0.415813 + 0.415813i 0.883758 0.467945i \(-0.155005\pi\)
−0.467945 + 0.883758i \(0.655005\pi\)
\(20\) 0 0
\(21\) −2.30355 + 2.30355i −0.502676 + 0.502676i
\(22\) 5.31350 5.74732i 1.13284 1.22533i
\(23\) 1.63007i 0.339893i −0.985453 0.169946i \(-0.945641\pi\)
0.985453 0.169946i \(-0.0543594\pi\)
\(24\) −1.53431 1.21006i −0.313190 0.247003i
\(25\) 0 0
\(26\) −0.129060 0.119318i −0.0253107 0.0234002i
\(27\) 2.69793 2.69793i 0.519217 0.519217i
\(28\) 0.738648 + 9.40184i 0.139591 + 1.77678i
\(29\) 3.26362 + 3.26362i 0.606039 + 0.606039i 0.941909 0.335869i \(-0.109030\pi\)
−0.335869 + 0.941909i \(0.609030\pi\)
\(30\) 0 0
\(31\) −2.12875 −0.382334 −0.191167 0.981557i \(-0.561227\pi\)
−0.191167 + 0.981557i \(0.561227\pi\)
\(32\) −5.54854 + 1.10170i −0.980852 + 0.194755i
\(33\) −3.82371 −0.665622
\(34\) 6.60555 0.259081i 1.13284 0.0444320i
\(35\) 0 0
\(36\) −0.395171 5.02991i −0.0658618 0.838318i
\(37\) −3.97797 + 3.97797i −0.653974 + 0.653974i −0.953948 0.299973i \(-0.903022\pi\)
0.299973 + 0.953948i \(0.403022\pi\)
\(38\) −2.66173 2.46082i −0.431790 0.399197i
\(39\) 0.0858637i 0.0137492i
\(40\) 0 0
\(41\) 8.25504i 1.28922i 0.764511 + 0.644611i \(0.222980\pi\)
−0.764511 + 0.644611i \(0.777020\pi\)
\(42\) 3.12753 3.38288i 0.482589 0.521990i
\(43\) −2.27336 + 2.27336i −0.346685 + 0.346685i −0.858873 0.512188i \(-0.828835\pi\)
0.512188 + 0.858873i \(0.328835\pi\)
\(44\) −7.19010 + 8.41620i −1.08395 + 1.26879i
\(45\) 0 0
\(46\) 0.0903468 + 2.30349i 0.0133209 + 0.339631i
\(47\) 4.06129 0.592400 0.296200 0.955126i \(-0.404281\pi\)
0.296200 + 0.955126i \(0.404281\pi\)
\(48\) 2.23524 + 1.62493i 0.322630 + 0.234539i
\(49\) −15.2350 −2.17643
\(50\) 0 0
\(51\) −2.28353 2.28353i −0.319758 0.319758i
\(52\) 0.188991 + 0.161458i 0.0262083 + 0.0223902i
\(53\) 5.03938 5.03938i 0.692211 0.692211i −0.270507 0.962718i \(-0.587191\pi\)
0.962718 + 0.270507i \(0.0871912\pi\)
\(54\) −3.66298 + 3.96205i −0.498469 + 0.539167i
\(55\) 0 0
\(56\) −1.56490 13.2450i −0.209119 1.76994i
\(57\) 1.77086i 0.234556i
\(58\) −4.79280 4.43103i −0.629325 0.581822i
\(59\) −5.16453 + 5.16453i −0.672365 + 0.672365i −0.958261 0.285896i \(-0.907709\pi\)
0.285896 + 0.958261i \(0.407709\pi\)
\(60\) 0 0
\(61\) 7.12726 + 7.12726i 0.912552 + 0.912552i 0.996472 0.0839206i \(-0.0267442\pi\)
−0.0839206 + 0.996472i \(0.526744\pi\)
\(62\) 3.00819 0.117986i 0.382041 0.0149843i
\(63\) 11.8956 1.49870
\(64\) 7.77972 1.86437i 0.972466 0.233047i
\(65\) 0 0
\(66\) 5.40339 0.211930i 0.665111 0.0260868i
\(67\) 7.49920 + 7.49920i 0.916173 + 0.916173i 0.996748 0.0805758i \(-0.0256759\pi\)
−0.0805758 + 0.996748i \(0.525676\pi\)
\(68\) −9.32012 + 0.732228i −1.13023 + 0.0887957i
\(69\) 0.796314 0.796314i 0.0958649 0.0958649i
\(70\) 0 0
\(71\) 4.54072i 0.538884i −0.963017 0.269442i \(-0.913161\pi\)
0.963017 0.269442i \(-0.0868393\pi\)
\(72\) 0.837210 + 7.08600i 0.0986662 + 0.835093i
\(73\) 8.30557i 0.972093i −0.873933 0.486047i \(-0.838439\pi\)
0.873933 0.486047i \(-0.161561\pi\)
\(74\) 5.40090 5.84186i 0.627842 0.679102i
\(75\) 0 0
\(76\) 3.89776 + 3.32992i 0.447104 + 0.381968i
\(77\) −18.4542 18.4542i −2.10305 2.10305i
\(78\) −0.00475901 0.121336i −0.000538852 0.0137386i
\(79\) 11.5317 1.29742 0.648709 0.761037i \(-0.275309\pi\)
0.648709 + 0.761037i \(0.275309\pi\)
\(80\) 0 0
\(81\) −4.93215 −0.548017
\(82\) −0.457537 11.6654i −0.0505266 1.28823i
\(83\) 1.16919 + 1.16919i 0.128335 + 0.128335i 0.768357 0.640022i \(-0.221075\pi\)
−0.640022 + 0.768357i \(0.721075\pi\)
\(84\) −4.23211 + 4.95379i −0.461761 + 0.540503i
\(85\) 0 0
\(86\) 3.08655 3.33855i 0.332831 0.360006i
\(87\) 3.18866i 0.341861i
\(88\) 9.69406 12.2917i 1.03339 1.31030i
\(89\) 3.24572i 0.344046i −0.985093 0.172023i \(-0.944970\pi\)
0.985093 0.172023i \(-0.0550304\pi\)
\(90\) 0 0
\(91\) −0.414400 + 0.414400i −0.0434409 + 0.0434409i
\(92\) −0.255343 3.25012i −0.0266214 0.338848i
\(93\) −1.03993 1.03993i −0.107835 0.107835i
\(94\) −5.73912 + 0.225098i −0.591945 + 0.0232171i
\(95\) 0 0
\(96\) −3.24875 2.17235i −0.331574 0.221714i
\(97\) 13.9581 1.41723 0.708613 0.705598i \(-0.249321\pi\)
0.708613 + 0.705598i \(0.249321\pi\)
\(98\) 21.5290 0.844405i 2.17476 0.0852978i
\(99\) 9.87285 + 9.87285i 0.992258 + 0.992258i
\(100\) 0 0
\(101\) 13.4088 13.4088i 1.33422 1.33422i 0.432672 0.901552i \(-0.357571\pi\)
0.901552 0.432672i \(-0.142429\pi\)
\(102\) 3.35348 + 3.10035i 0.332044 + 0.306981i
\(103\) 13.7638i 1.35618i −0.734977 0.678092i \(-0.762807\pi\)
0.734977 0.678092i \(-0.237193\pi\)
\(104\) −0.276017 0.217686i −0.0270657 0.0213459i
\(105\) 0 0
\(106\) −6.84197 + 7.40059i −0.664551 + 0.718808i
\(107\) 0.327996 0.327996i 0.0317086 0.0317086i −0.691075 0.722783i \(-0.742862\pi\)
0.722783 + 0.691075i \(0.242862\pi\)
\(108\) 4.95666 5.80190i 0.476955 0.558288i
\(109\) −0.149698 0.149698i −0.0143385 0.0143385i 0.699901 0.714240i \(-0.253227\pi\)
−0.714240 + 0.699901i \(0.753227\pi\)
\(110\) 0 0
\(111\) −3.88660 −0.368900
\(112\) 2.94551 + 18.6302i 0.278325 + 1.76039i
\(113\) −5.97999 −0.562550 −0.281275 0.959627i \(-0.590757\pi\)
−0.281275 + 0.959627i \(0.590757\pi\)
\(114\) −0.0981502 2.50245i −0.00919261 0.234376i
\(115\) 0 0
\(116\) 7.01843 + 5.99596i 0.651644 + 0.556711i
\(117\) 0.221701 0.221701i 0.0204962 0.0204962i
\(118\) 7.01189 7.58439i 0.645497 0.698199i
\(119\) 22.0418i 2.02057i
\(120\) 0 0
\(121\) 19.6325i 1.78477i
\(122\) −10.4668 9.67669i −0.947615 0.876086i
\(123\) −4.03272 + 4.03272i −0.363618 + 0.363618i
\(124\) −4.24442 + 0.333459i −0.381160 + 0.0299455i
\(125\) 0 0
\(126\) −16.8100 + 0.659314i −1.49755 + 0.0587364i
\(127\) 2.73076 0.242315 0.121158 0.992633i \(-0.461339\pi\)
0.121158 + 0.992633i \(0.461339\pi\)
\(128\) −10.8904 + 3.06579i −0.962585 + 0.270980i
\(129\) −2.22115 −0.195561
\(130\) 0 0
\(131\) −0.813555 0.813555i −0.0710806 0.0710806i 0.670673 0.741753i \(-0.266006\pi\)
−0.741753 + 0.670673i \(0.766006\pi\)
\(132\) −7.62392 + 0.598967i −0.663577 + 0.0521334i
\(133\) −8.54661 + 8.54661i −0.741085 + 0.741085i
\(134\) −11.0130 10.1817i −0.951375 0.879563i
\(135\) 0 0
\(136\) 13.1299 1.55130i 1.12588 0.133023i
\(137\) 0.199812i 0.0170711i 0.999964 + 0.00853557i \(0.00271699\pi\)
−0.999964 + 0.00853557i \(0.997283\pi\)
\(138\) −1.08116 + 1.16943i −0.0920342 + 0.0995484i
\(139\) −11.6301 + 11.6301i −0.986448 + 0.986448i −0.999909 0.0134610i \(-0.995715\pi\)
0.0134610 + 0.999909i \(0.495715\pi\)
\(140\) 0 0
\(141\) 1.98400 + 1.98400i 0.167083 + 0.167083i
\(142\) 0.251670 + 6.41661i 0.0211197 + 0.538470i
\(143\) −0.687871 −0.0575227
\(144\) −1.57583 9.96701i −0.131319 0.830585i
\(145\) 0 0
\(146\) 0.460338 + 11.7368i 0.0380978 + 0.971346i
\(147\) −7.44256 7.44256i −0.613852 0.613852i
\(148\) −7.30837 + 8.55463i −0.600744 + 0.703186i
\(149\) −1.13384 + 1.13384i −0.0928880 + 0.0928880i −0.752024 0.659136i \(-0.770922\pi\)
0.659136 + 0.752024i \(0.270922\pi\)
\(150\) 0 0
\(151\) 7.12216i 0.579593i −0.957088 0.289797i \(-0.906412\pi\)
0.957088 0.289797i \(-0.0935877\pi\)
\(152\) −5.69259 4.48957i −0.461730 0.364152i
\(153\) 11.7922i 0.953341i
\(154\) 27.1009 + 25.0553i 2.18386 + 2.01901i
\(155\) 0 0
\(156\) 0.0134502 + 0.171200i 0.00107688 + 0.0137070i
\(157\) 5.32145 + 5.32145i 0.424698 + 0.424698i 0.886818 0.462120i \(-0.152911\pi\)
−0.462120 + 0.886818i \(0.652911\pi\)
\(158\) −16.2957 + 0.639147i −1.29642 + 0.0508478i
\(159\) 4.92363 0.390469
\(160\) 0 0
\(161\) 7.68643 0.605775
\(162\) 6.96976 0.273365i 0.547596 0.0214776i
\(163\) 12.3010 + 12.3010i 0.963488 + 0.963488i 0.999357 0.0358685i \(-0.0114197\pi\)
−0.0358685 + 0.999357i \(0.511420\pi\)
\(164\) 1.29312 + 16.4594i 0.100975 + 1.28526i
\(165\) 0 0
\(166\) −1.71702 1.58741i −0.133266 0.123207i
\(167\) 9.86820i 0.763624i 0.924240 + 0.381812i \(0.124700\pi\)
−0.924240 + 0.381812i \(0.875300\pi\)
\(168\) 5.70594 7.23490i 0.440223 0.558184i
\(169\) 12.9846i 0.998812i
\(170\) 0 0
\(171\) 4.57237 4.57237i 0.349658 0.349658i
\(172\) −4.17665 + 4.88887i −0.318466 + 0.372773i
\(173\) 13.4089 + 13.4089i 1.01946 + 1.01946i 0.999807 + 0.0196525i \(0.00625599\pi\)
0.0196525 + 0.999807i \(0.493744\pi\)
\(174\) −0.176732 4.50599i −0.0133980 0.341598i
\(175\) 0 0
\(176\) −13.0177 + 17.9070i −0.981243 + 1.34979i
\(177\) −5.04591 −0.379274
\(178\) 0.179895 + 4.58662i 0.0134837 + 0.343782i
\(179\) 0.419587 + 0.419587i 0.0313614 + 0.0313614i 0.722614 0.691252i \(-0.242941\pi\)
−0.691252 + 0.722614i \(0.742941\pi\)
\(180\) 0 0
\(181\) −14.2605 + 14.2605i −1.05998 + 1.05998i −0.0618956 + 0.998083i \(0.519715\pi\)
−0.998083 + 0.0618956i \(0.980285\pi\)
\(182\) 0.562632 0.608568i 0.0417050 0.0451101i
\(183\) 6.96356i 0.514761i
\(184\) 0.540971 + 4.57868i 0.0398809 + 0.337545i
\(185\) 0 0
\(186\) 1.52719 + 1.41191i 0.111979 + 0.103526i
\(187\) 18.2938 18.2938i 1.33777 1.33777i
\(188\) 8.09762 0.636183i 0.590580 0.0463984i
\(189\) 12.7218 + 12.7218i 0.925377 + 0.925377i
\(190\) 0 0
\(191\) 17.3304 1.25399 0.626993 0.779025i \(-0.284285\pi\)
0.626993 + 0.779025i \(0.284285\pi\)
\(192\) 4.71130 + 2.88974i 0.340008 + 0.208549i
\(193\) −16.8667 −1.21409 −0.607045 0.794667i \(-0.707645\pi\)
−0.607045 + 0.794667i \(0.707645\pi\)
\(194\) −19.7245 + 0.773628i −1.41614 + 0.0555432i
\(195\) 0 0
\(196\) −30.3765 + 2.38650i −2.16975 + 0.170464i
\(197\) 3.58908 3.58908i 0.255712 0.255712i −0.567596 0.823307i \(-0.692126\pi\)
0.823307 + 0.567596i \(0.192126\pi\)
\(198\) −14.4988 13.4044i −1.03038 0.952608i
\(199\) 6.64501i 0.471052i −0.971868 0.235526i \(-0.924319\pi\)
0.971868 0.235526i \(-0.0756813\pi\)
\(200\) 0 0
\(201\) 7.32695i 0.516803i
\(202\) −18.2051 + 19.6915i −1.28091 + 1.38549i
\(203\) −15.3893 + 15.3893i −1.08012 + 1.08012i
\(204\) −4.91073 4.19532i −0.343820 0.293731i
\(205\) 0 0
\(206\) 0.762860 + 19.4500i 0.0531510 + 1.35514i
\(207\) −4.11218 −0.285816
\(208\) 0.402112 + 0.292320i 0.0278815 + 0.0202687i
\(209\) −14.1867 −0.981314
\(210\) 0 0
\(211\) 1.90906 + 1.90906i 0.131425 + 0.131425i 0.769759 0.638334i \(-0.220376\pi\)
−0.638334 + 0.769759i \(0.720376\pi\)
\(212\) 9.25839 10.8372i 0.635869 0.744301i
\(213\) 2.21821 2.21821i 0.151989 0.151989i
\(214\) −0.445321 + 0.481680i −0.0304415 + 0.0329270i
\(215\) 0 0
\(216\) −6.68282 + 8.47355i −0.454709 + 0.576552i
\(217\) 10.0379i 0.681418i
\(218\) 0.219839 + 0.203245i 0.0148894 + 0.0137655i
\(219\) 4.05740 4.05740i 0.274174 0.274174i
\(220\) 0 0
\(221\) −0.410798 0.410798i −0.0276333 0.0276333i
\(222\) 5.49226 0.215416i 0.368617 0.0144578i
\(223\) −24.1071 −1.61433 −0.807165 0.590326i \(-0.798999\pi\)
−0.807165 + 0.590326i \(0.798999\pi\)
\(224\) −5.19497 26.1636i −0.347103 1.74813i
\(225\) 0 0
\(226\) 8.45048 0.331442i 0.562118 0.0220472i
\(227\) −6.67411 6.67411i −0.442977 0.442977i 0.450035 0.893011i \(-0.351412\pi\)
−0.893011 + 0.450035i \(0.851412\pi\)
\(228\) 0.277397 + 3.53084i 0.0183711 + 0.233835i
\(229\) 16.0807 16.0807i 1.06264 1.06264i 0.0647388 0.997902i \(-0.479379\pi\)
0.997902 0.0647388i \(-0.0206214\pi\)
\(230\) 0 0
\(231\) 18.0303i 1.18631i
\(232\) −10.2503 8.08406i −0.672962 0.530744i
\(233\) 16.4976i 1.08079i −0.841411 0.540396i \(-0.818274\pi\)
0.841411 0.540396i \(-0.181726\pi\)
\(234\) −0.301004 + 0.325579i −0.0196772 + 0.0212838i
\(235\) 0 0
\(236\) −9.48833 + 11.1063i −0.617638 + 0.722961i
\(237\) 5.63342 + 5.63342i 0.365930 + 0.365930i
\(238\) 1.22167 + 31.1478i 0.0791891 + 2.01901i
\(239\) 5.25917 0.340188 0.170094 0.985428i \(-0.445593\pi\)
0.170094 + 0.985428i \(0.445593\pi\)
\(240\) 0 0
\(241\) −14.1126 −0.909075 −0.454538 0.890728i \(-0.650196\pi\)
−0.454538 + 0.890728i \(0.650196\pi\)
\(242\) 1.08813 + 27.7432i 0.0699479 + 1.78340i
\(243\) −10.5032 10.5032i −0.673782 0.673782i
\(244\) 15.3272 + 13.0943i 0.981222 + 0.838275i
\(245\) 0 0
\(246\) 5.47523 5.92226i 0.349088 0.377589i
\(247\) 0.318571i 0.0202702i
\(248\) 5.97942 0.706468i 0.379693 0.0448608i
\(249\) 1.14234i 0.0723927i
\(250\) 0 0
\(251\) −9.98825 + 9.98825i −0.630453 + 0.630453i −0.948182 0.317729i \(-0.897080\pi\)
0.317729 + 0.948182i \(0.397080\pi\)
\(252\) 23.7181 1.86339i 1.49410 0.117383i
\(253\) 6.37943 + 6.37943i 0.401071 + 0.401071i
\(254\) −3.85890 + 0.151353i −0.242129 + 0.00949671i
\(255\) 0 0
\(256\) 15.2196 4.93595i 0.951225 0.308497i
\(257\) 8.44760 0.526947 0.263474 0.964667i \(-0.415132\pi\)
0.263474 + 0.964667i \(0.415132\pi\)
\(258\) 3.13877 0.123108i 0.195411 0.00766435i
\(259\) −18.7577 18.7577i −1.16555 1.16555i
\(260\) 0 0
\(261\) 8.23315 8.23315i 0.509619 0.509619i
\(262\) 1.19475 + 1.10457i 0.0738118 + 0.0682403i
\(263\) 18.3064i 1.12882i 0.825494 + 0.564410i \(0.190896\pi\)
−0.825494 + 0.564410i \(0.809104\pi\)
\(264\) 10.7404 1.26897i 0.661024 0.0781000i
\(265\) 0 0
\(266\) 11.6037 12.5511i 0.711472 0.769560i
\(267\) 1.58559 1.58559i 0.0970364 0.0970364i
\(268\) 16.1270 + 13.7776i 0.985115 + 0.841601i
\(269\) 13.5631 + 13.5631i 0.826955 + 0.826955i 0.987094 0.160140i \(-0.0511945\pi\)
−0.160140 + 0.987094i \(0.551194\pi\)
\(270\) 0 0
\(271\) −2.24520 −0.136386 −0.0681930 0.997672i \(-0.521723\pi\)
−0.0681930 + 0.997672i \(0.521723\pi\)
\(272\) −18.4683 + 2.91991i −1.11980 + 0.177046i
\(273\) −0.404882 −0.0245046
\(274\) −0.0110746 0.282360i −0.000669044 0.0170580i
\(275\) 0 0
\(276\) 1.46300 1.71247i 0.0880620 0.103079i
\(277\) −7.28255 + 7.28255i −0.437566 + 0.437566i −0.891192 0.453626i \(-0.850130\pi\)
0.453626 + 0.891192i \(0.350130\pi\)
\(278\) 15.7901 17.0793i 0.947030 1.02435i
\(279\) 5.37020i 0.321506i
\(280\) 0 0
\(281\) 6.04084i 0.360367i −0.983633 0.180183i \(-0.942331\pi\)
0.983633 0.180183i \(-0.0576691\pi\)
\(282\) −2.91361 2.69369i −0.173503 0.160407i
\(283\) 15.1350 15.1350i 0.899682 0.899682i −0.0957259 0.995408i \(-0.530517\pi\)
0.995408 + 0.0957259i \(0.0305172\pi\)
\(284\) −0.711284 9.05354i −0.0422070 0.537229i
\(285\) 0 0
\(286\) 0.972049 0.0381254i 0.0574785 0.00225440i
\(287\) −38.9259 −2.29772
\(288\) 2.77927 + 13.9973i 0.163770 + 0.824800i
\(289\) 4.85021 0.285306
\(290\) 0 0
\(291\) 6.81873 + 6.81873i 0.399721 + 0.399721i
\(292\) −1.30103 16.5601i −0.0761371 0.969107i
\(293\) 10.7777 10.7777i 0.629637 0.629637i −0.318339 0.947977i \(-0.603125\pi\)
0.947977 + 0.318339i \(0.103125\pi\)
\(294\) 10.9298 + 10.1048i 0.637438 + 0.589322i
\(295\) 0 0
\(296\) 9.85351 12.4939i 0.572724 0.726190i
\(297\) 21.1172i 1.22534i
\(298\) 1.53942 1.66511i 0.0891762 0.0964571i
\(299\) 0.143254 0.143254i 0.00828459 0.00828459i
\(300\) 0 0
\(301\) −10.7198 10.7198i −0.617881 0.617881i
\(302\) 0.394747 + 10.0645i 0.0227152 + 0.579148i
\(303\) 13.1008 0.752621
\(304\) 8.29319 + 6.02882i 0.475647 + 0.345776i
\(305\) 0 0
\(306\) −0.653584 16.6639i −0.0373629 0.952609i
\(307\) −7.94378 7.94378i −0.453376 0.453376i 0.443098 0.896473i \(-0.353880\pi\)
−0.896473 + 0.443098i \(0.853880\pi\)
\(308\) −39.6858 33.9042i −2.26131 1.93187i
\(309\) 6.72382 6.72382i 0.382505 0.382505i
\(310\) 0 0
\(311\) 31.1649i 1.76720i 0.468244 + 0.883599i \(0.344887\pi\)
−0.468244 + 0.883599i \(0.655113\pi\)
\(312\) −0.0284956 0.241182i −0.00161325 0.0136542i
\(313\) 5.35842i 0.302876i 0.988467 + 0.151438i \(0.0483903\pi\)
−0.988467 + 0.151438i \(0.951610\pi\)
\(314\) −7.81482 7.22494i −0.441016 0.407727i
\(315\) 0 0
\(316\) 22.9925 1.80639i 1.29343 0.101617i
\(317\) 8.88165 + 8.88165i 0.498843 + 0.498843i 0.911078 0.412235i \(-0.135252\pi\)
−0.412235 + 0.911078i \(0.635252\pi\)
\(318\) −6.95771 + 0.272893i −0.390169 + 0.0153031i
\(319\) −25.5450 −1.43025
\(320\) 0 0
\(321\) 0.320463 0.0178865
\(322\) −10.8619 + 0.426022i −0.605310 + 0.0237413i
\(323\) −8.47233 8.47233i −0.471413 0.471413i
\(324\) −9.83400 + 0.772600i −0.546333 + 0.0429222i
\(325\) 0 0
\(326\) −18.0646 16.7011i −1.00051 0.924987i
\(327\) 0.146260i 0.00808817i
\(328\) −2.73960 23.1875i −0.151269 1.28032i
\(329\) 19.1506i 1.05581i
\(330\) 0 0
\(331\) 6.07281 6.07281i 0.333792 0.333792i −0.520233 0.854025i \(-0.674155\pi\)
0.854025 + 0.520233i \(0.174155\pi\)
\(332\) 2.51435 + 2.14805i 0.137993 + 0.117890i
\(333\) 10.0352 + 10.0352i 0.549928 + 0.549928i
\(334\) −0.546947 13.9450i −0.0299276 0.763038i
\(335\) 0 0
\(336\) −7.66222 + 10.5401i −0.418008 + 0.575009i
\(337\) 22.0227 1.19965 0.599827 0.800130i \(-0.295236\pi\)
0.599827 + 0.800130i \(0.295236\pi\)
\(338\) 0.719672 + 18.3488i 0.0391450 + 0.998044i
\(339\) −2.92132 2.92132i −0.158664 0.158664i
\(340\) 0 0
\(341\) 8.33106 8.33106i 0.451152 0.451152i
\(342\) −6.20792 + 6.71477i −0.335686 + 0.363093i
\(343\) 38.8315i 2.09670i
\(344\) 5.63117 7.14009i 0.303612 0.384968i
\(345\) 0 0
\(346\) −19.6917 18.2053i −1.05863 0.978722i
\(347\) −11.8920 + 11.8920i −0.638395 + 0.638395i −0.950159 0.311765i \(-0.899080\pi\)
0.311765 + 0.950159i \(0.399080\pi\)
\(348\) 0.499490 + 6.35773i 0.0267755 + 0.340810i
\(349\) −8.65696 8.65696i −0.463396 0.463396i 0.436371 0.899767i \(-0.356264\pi\)
−0.899767 + 0.436371i \(0.856264\pi\)
\(350\) 0 0
\(351\) 0.474200 0.0253109
\(352\) 17.4031 26.0263i 0.927589 1.38721i
\(353\) 26.6153 1.41659 0.708296 0.705916i \(-0.249464\pi\)
0.708296 + 0.705916i \(0.249464\pi\)
\(354\) 7.13051 0.279671i 0.378983 0.0148643i
\(355\) 0 0
\(356\) −0.508429 6.47151i −0.0269467 0.342989i
\(357\) 10.7678 10.7678i 0.569890 0.569890i
\(358\) −0.616185 0.569674i −0.0325664 0.0301082i
\(359\) 4.85032i 0.255990i 0.991775 + 0.127995i \(0.0408542\pi\)
−0.991775 + 0.127995i \(0.959146\pi\)
\(360\) 0 0
\(361\) 12.4298i 0.654199i
\(362\) 19.3616 20.9424i 1.01762 1.10071i
\(363\) 9.59078 9.59078i 0.503385 0.503385i
\(364\) −0.761340 + 0.891168i −0.0399051 + 0.0467099i
\(365\) 0 0
\(366\) −0.385957 9.84039i −0.0201743 0.514365i
\(367\) 15.6741 0.818182 0.409091 0.912494i \(-0.365846\pi\)
0.409091 + 0.912494i \(0.365846\pi\)
\(368\) −1.01823 6.44027i −0.0530792 0.335722i
\(369\) 20.8250 1.08411
\(370\) 0 0
\(371\) 23.7627 + 23.7627i 1.23370 + 1.23370i
\(372\) −2.23637 1.91057i −0.115950 0.0990582i
\(373\) −5.44481 + 5.44481i −0.281922 + 0.281922i −0.833875 0.551953i \(-0.813883\pi\)
0.551953 + 0.833875i \(0.313883\pi\)
\(374\) −24.8375 + 26.8654i −1.28432 + 1.38918i
\(375\) 0 0
\(376\) −11.4077 + 1.34782i −0.588308 + 0.0695085i
\(377\) 0.573629i 0.0295434i
\(378\) −18.6827 17.2724i −0.960933 0.888399i
\(379\) −17.4103 + 17.4103i −0.894309 + 0.894309i −0.994925 0.100616i \(-0.967919\pi\)
0.100616 + 0.994925i \(0.467919\pi\)
\(380\) 0 0
\(381\) 1.33402 + 1.33402i 0.0683438 + 0.0683438i
\(382\) −24.4901 + 0.960543i −1.25302 + 0.0491457i
\(383\) 9.04928 0.462396 0.231198 0.972907i \(-0.425735\pi\)
0.231198 + 0.972907i \(0.425735\pi\)
\(384\) −6.81782 3.82245i −0.347921 0.195064i
\(385\) 0 0
\(386\) 23.8348 0.934839i 1.21316 0.0475821i
\(387\) 5.73503 + 5.73503i 0.291528 + 0.291528i
\(388\) 27.8303 2.18647i 1.41287 0.111001i
\(389\) −15.3617 + 15.3617i −0.778871 + 0.778871i −0.979639 0.200768i \(-0.935656\pi\)
0.200768 + 0.979639i \(0.435656\pi\)
\(390\) 0 0
\(391\) 7.61962i 0.385341i
\(392\) 42.7935 5.05605i 2.16140 0.255369i
\(393\) 0.794869i 0.0400959i
\(394\) −4.87291 + 5.27076i −0.245493 + 0.265537i
\(395\) 0 0
\(396\) 21.2316 + 18.1385i 1.06693 + 0.911494i
\(397\) 9.44519 + 9.44519i 0.474041 + 0.474041i 0.903220 0.429179i \(-0.141197\pi\)
−0.429179 + 0.903220i \(0.641197\pi\)
\(398\) 0.368301 + 9.39024i 0.0184613 + 0.470690i
\(399\) −8.35031 −0.418038
\(400\) 0 0
\(401\) −21.5765 −1.07748 −0.538739 0.842473i \(-0.681099\pi\)
−0.538739 + 0.842473i \(0.681099\pi\)
\(402\) −0.406098 10.3539i −0.0202543 0.516406i
\(403\) −0.187079 0.187079i −0.00931907 0.00931907i
\(404\) 24.6347 28.8356i 1.22562 1.43462i
\(405\) 0 0
\(406\) 20.8941 22.6000i 1.03696 1.12162i
\(407\) 31.1363i 1.54337i
\(408\) 7.17202 + 5.65635i 0.355068 + 0.280031i
\(409\) 4.17336i 0.206359i 0.994663 + 0.103180i \(0.0329017\pi\)
−0.994663 + 0.103180i \(0.967098\pi\)
\(410\) 0 0
\(411\) −0.0976116 + 0.0976116i −0.00481482 + 0.00481482i
\(412\) −2.15604 27.4430i −0.106220 1.35202i
\(413\) −24.3529 24.3529i −1.19833 1.19833i
\(414\) 5.81103 0.227918i 0.285597 0.0112016i
\(415\) 0 0
\(416\) −0.584438 0.390798i −0.0286544 0.0191604i
\(417\) −11.3629 −0.556445
\(418\) 20.0476 0.786300i 0.980560 0.0384592i
\(419\) 27.1191 + 27.1191i 1.32485 + 1.32485i 0.909794 + 0.415060i \(0.136239\pi\)
0.415060 + 0.909794i \(0.363761\pi\)
\(420\) 0 0
\(421\) −26.9594 + 26.9594i −1.31392 + 1.31392i −0.395421 + 0.918500i \(0.629401\pi\)
−0.918500 + 0.395421i \(0.870599\pi\)
\(422\) −2.80355 2.59193i −0.136475 0.126173i
\(423\) 10.2454i 0.498150i
\(424\) −12.4826 + 15.8275i −0.606210 + 0.768650i
\(425\) 0 0
\(426\) −3.01167 + 3.25756i −0.145916 + 0.157829i
\(427\) −33.6079 + 33.6079i −1.62640 + 1.62640i
\(428\) 0.602598 0.705357i 0.0291277 0.0340947i
\(429\) −0.336036 0.336036i −0.0162240 0.0162240i
\(430\) 0 0
\(431\) −22.4059 −1.07925 −0.539626 0.841905i \(-0.681434\pi\)
−0.539626 + 0.841905i \(0.681434\pi\)
\(432\) 8.97403 12.3446i 0.431763 0.593930i
\(433\) 16.8061 0.807649 0.403824 0.914837i \(-0.367681\pi\)
0.403824 + 0.914837i \(0.367681\pi\)
\(434\) 0.556353 + 14.1848i 0.0267058 + 0.680894i
\(435\) 0 0
\(436\) −0.321925 0.275026i −0.0154174 0.0131714i
\(437\) 2.95448 2.95448i 0.141332 0.141332i
\(438\) −5.50874 + 5.95851i −0.263218 + 0.284708i
\(439\) 9.08322i 0.433519i −0.976225 0.216759i \(-0.930451\pi\)
0.976225 0.216759i \(-0.0695487\pi\)
\(440\) 0 0
\(441\) 38.4335i 1.83017i
\(442\) 0.603279 + 0.557742i 0.0286951 + 0.0265291i
\(443\) −12.5397 + 12.5397i −0.595781 + 0.595781i −0.939187 0.343406i \(-0.888419\pi\)
0.343406 + 0.939187i \(0.388419\pi\)
\(444\) −7.74933 + 0.608820i −0.367767 + 0.0288933i
\(445\) 0 0
\(446\) 34.0664 1.33614i 1.61309 0.0632681i
\(447\) −1.10780 −0.0523972
\(448\) 8.79127 + 36.6845i 0.415349 + 1.73318i
\(449\) 18.0707 0.852811 0.426406 0.904532i \(-0.359780\pi\)
0.426406 + 0.904532i \(0.359780\pi\)
\(450\) 0 0
\(451\) −32.3069 32.3069i −1.52127 1.52127i
\(452\) −11.9232 + 0.936740i −0.560822 + 0.0440605i
\(453\) 3.47929 3.47929i 0.163471 0.163471i
\(454\) 9.80129 + 9.06146i 0.459997 + 0.425275i
\(455\) 0 0
\(456\) −0.587695 4.97415i −0.0275213 0.232936i
\(457\) 18.6637i 0.873052i 0.899692 + 0.436526i \(0.143791\pi\)
−0.899692 + 0.436526i \(0.856209\pi\)
\(458\) −21.8328 + 23.6153i −1.02018 + 1.10347i
\(459\) −12.6113 + 12.6113i −0.588643 + 0.588643i
\(460\) 0 0
\(461\) −0.831229 0.831229i −0.0387142 0.0387142i 0.687485 0.726199i \(-0.258715\pi\)
−0.726199 + 0.687485i \(0.758715\pi\)
\(462\) 0.999335 + 25.4791i 0.0464933 + 1.18540i
\(463\) −7.82533 −0.363674 −0.181837 0.983329i \(-0.558204\pi\)
−0.181837 + 0.983329i \(0.558204\pi\)
\(464\) 14.9330 + 10.8557i 0.693246 + 0.503962i
\(465\) 0 0
\(466\) 0.914382 + 23.3132i 0.0423579 + 1.07996i
\(467\) −8.75068 8.75068i −0.404933 0.404933i 0.475034 0.879967i \(-0.342436\pi\)
−0.879967 + 0.475034i \(0.842436\pi\)
\(468\) 0.407311 0.476768i 0.0188280 0.0220386i
\(469\) −35.3617 + 35.3617i −1.63285 + 1.63285i
\(470\) 0 0
\(471\) 5.19922i 0.239568i
\(472\) 12.7926 16.2206i 0.588829 0.746612i
\(473\) 17.7941i 0.818172i
\(474\) −8.27297 7.64850i −0.379990 0.351307i
\(475\) 0 0
\(476\) −3.45275 43.9481i −0.158257 2.01436i
\(477\) −12.7129 12.7129i −0.582082 0.582082i
\(478\) −7.43188 + 0.291491i −0.339926 + 0.0133325i
\(479\) 2.10417 0.0961421 0.0480710 0.998844i \(-0.484693\pi\)
0.0480710 + 0.998844i \(0.484693\pi\)
\(480\) 0 0
\(481\) −0.699186 −0.0318801
\(482\) 19.9430 0.782196i 0.908377 0.0356281i
\(483\) 3.75494 + 3.75494i 0.170856 + 0.170856i
\(484\) −3.07534 39.1443i −0.139788 1.77929i
\(485\) 0 0
\(486\) 15.4245 + 14.2602i 0.699671 + 0.646858i
\(487\) 4.87183i 0.220764i 0.993889 + 0.110382i \(0.0352074\pi\)
−0.993889 + 0.110382i \(0.964793\pi\)
\(488\) −22.3850 17.6544i −1.01332 0.799175i
\(489\) 12.0185i 0.543494i
\(490\) 0 0
\(491\) 14.3582 14.3582i 0.647975 0.647975i −0.304528 0.952503i \(-0.598499\pi\)
0.952503 + 0.304528i \(0.0984987\pi\)
\(492\) −7.40895 + 8.67237i −0.334021 + 0.390981i
\(493\) −15.2555 15.2555i −0.687075 0.687075i
\(494\) −0.0176569 0.450181i −0.000794419 0.0202546i
\(495\) 0 0
\(496\) −8.41052 + 1.32974i −0.377644 + 0.0597071i
\(497\) 21.4113 0.960429
\(498\) −0.0633143 1.61427i −0.00283718 0.0723370i
\(499\) −25.1060 25.1060i −1.12390 1.12390i −0.991150 0.132748i \(-0.957620\pi\)
−0.132748 0.991150i \(-0.542380\pi\)
\(500\) 0 0
\(501\) −4.82077 + 4.82077i −0.215376 + 0.215376i
\(502\) 13.5611 14.6683i 0.605260 0.654677i
\(503\) 18.8868i 0.842120i 0.907033 + 0.421060i \(0.138342\pi\)
−0.907033 + 0.421060i \(0.861658\pi\)
\(504\) −33.4133 + 3.94778i −1.48835 + 0.175848i
\(505\) 0 0
\(506\) −9.36852 8.66136i −0.416482 0.385044i
\(507\) 6.34316 6.34316i 0.281710 0.281710i
\(508\) 5.44473 0.427761i 0.241571 0.0189788i
\(509\) −22.9756 22.9756i −1.01837 1.01837i −0.999828 0.0185459i \(-0.994096\pi\)
−0.0185459 0.999828i \(-0.505904\pi\)
\(510\) 0 0
\(511\) 39.1641 1.73252
\(512\) −21.2337 + 7.81868i −0.938404 + 0.345540i
\(513\) 9.77993 0.431794
\(514\) −11.9375 + 0.468210i −0.526542 + 0.0206519i
\(515\) 0 0
\(516\) −4.42865 + 0.347933i −0.194961 + 0.0153169i
\(517\) −15.8942 + 15.8942i −0.699028 + 0.699028i
\(518\) 27.5467 + 25.4674i 1.21033 + 1.11897i
\(519\) 13.1009i 0.575066i
\(520\) 0 0
\(521\) 20.2089i 0.885367i −0.896678 0.442683i \(-0.854027\pi\)
0.896678 0.442683i \(-0.145973\pi\)
\(522\) −11.1782 + 12.0908i −0.489255 + 0.529201i
\(523\) 3.93445 3.93445i 0.172042 0.172042i −0.615834 0.787876i \(-0.711181\pi\)
0.787876 + 0.615834i \(0.211181\pi\)
\(524\) −1.74955 1.49467i −0.0764295 0.0652951i
\(525\) 0 0
\(526\) −1.01464 25.8693i −0.0442402 1.12795i
\(527\) 9.95066 0.433458
\(528\) −15.1072 + 2.38851i −0.657456 + 0.103947i
\(529\) 20.3429 0.884473
\(530\) 0 0
\(531\) 13.0286 + 13.0286i 0.565393 + 0.565393i
\(532\) −15.7019 + 18.3795i −0.680765 + 0.796853i
\(533\) −0.725471 + 0.725471i −0.0314237 + 0.0314237i
\(534\) −2.15276 + 2.32852i −0.0931589 + 0.100765i
\(535\) 0 0
\(536\) −23.5532 18.5757i −1.01734 0.802346i
\(537\) 0.409950i 0.0176906i
\(538\) −19.9181 18.4146i −0.858729 0.793910i
\(539\) 59.6238 59.6238i 2.56818 2.56818i
\(540\) 0 0
\(541\) −3.17895 3.17895i −0.136674 0.136674i 0.635460 0.772134i \(-0.280811\pi\)
−0.772134 + 0.635460i \(0.780811\pi\)
\(542\) 3.17275 0.124440i 0.136281 0.00534518i
\(543\) −13.9330 −0.597923
\(544\) 25.9362 5.14982i 1.11201 0.220797i
\(545\) 0 0
\(546\) 0.572150 0.0224407i 0.0244857 0.000960372i
\(547\) 1.32918 + 1.32918i 0.0568317 + 0.0568317i 0.734951 0.678120i \(-0.237205\pi\)
−0.678120 + 0.734951i \(0.737205\pi\)
\(548\) 0.0312998 + 0.398397i 0.00133706 + 0.0170187i
\(549\) 17.9800 17.9800i 0.767366 0.767366i
\(550\) 0 0
\(551\) 11.8306i 0.503998i
\(552\) −1.97249 + 2.50103i −0.0839545 + 0.106451i
\(553\) 54.3766i 2.31233i
\(554\) 9.88754 10.6948i 0.420081 0.454379i
\(555\) 0 0
\(556\) −21.3669 + 25.0105i −0.906157 + 1.06068i
\(557\) 24.9082 + 24.9082i 1.05539 + 1.05539i 0.998373 + 0.0570196i \(0.0181598\pi\)
0.0570196 + 0.998373i \(0.481840\pi\)
\(558\) −0.297645 7.58878i −0.0126003 0.321259i
\(559\) −0.399576 −0.0169003
\(560\) 0 0
\(561\) 17.8736 0.754625
\(562\) 0.334815 + 8.53648i 0.0141233 + 0.360090i
\(563\) 3.80804 + 3.80804i 0.160490 + 0.160490i 0.782784 0.622294i \(-0.213799\pi\)
−0.622294 + 0.782784i \(0.713799\pi\)
\(564\) 4.26660 + 3.64503i 0.179656 + 0.153484i
\(565\) 0 0
\(566\) −20.5488 + 22.2265i −0.863731 + 0.934251i
\(567\) 23.2571i 0.976706i
\(568\) 1.50693 + 12.7544i 0.0632293 + 0.535162i
\(569\) 8.43971i 0.353811i 0.984228 + 0.176905i \(0.0566087\pi\)
−0.984228 + 0.176905i \(0.943391\pi\)
\(570\) 0 0
\(571\) −21.2821 + 21.2821i −0.890629 + 0.890629i −0.994582 0.103953i \(-0.966851\pi\)
0.103953 + 0.994582i \(0.466851\pi\)
\(572\) −1.37152 + 0.107752i −0.0573460 + 0.00450534i
\(573\) 8.46619 + 8.46619i 0.353680 + 0.353680i
\(574\) 55.0072 2.15747i 2.29596 0.0900512i
\(575\) 0 0
\(576\) −4.70326 19.6259i −0.195969 0.817748i
\(577\) −36.3491 −1.51323 −0.756615 0.653860i \(-0.773148\pi\)
−0.756615 + 0.653860i \(0.773148\pi\)
\(578\) −6.85396 + 0.268824i −0.285087 + 0.0111816i
\(579\) −8.23964 8.23964i −0.342428 0.342428i
\(580\) 0 0
\(581\) −5.51321 + 5.51321i −0.228726 + 0.228726i
\(582\) −10.0137 9.25780i −0.415080 0.383748i
\(583\) 39.4442i 1.63361i
\(584\) 2.75637 + 23.3294i 0.114059 + 0.965379i
\(585\) 0 0
\(586\) −14.6328 + 15.8275i −0.604477 + 0.653830i
\(587\) −6.55994 + 6.55994i −0.270758 + 0.270758i −0.829405 0.558647i \(-0.811321\pi\)
0.558647 + 0.829405i \(0.311321\pi\)
\(588\) −16.0052 13.6735i −0.660044 0.563887i
\(589\) −3.85833 3.85833i −0.158980 0.158980i
\(590\) 0 0
\(591\) 3.50665 0.144244
\(592\) −13.2318 + 18.2015i −0.543823 + 0.748078i
\(593\) −1.40974 −0.0578911 −0.0289455 0.999581i \(-0.509215\pi\)
−0.0289455 + 0.999581i \(0.509215\pi\)
\(594\) −1.17043 29.8413i −0.0480231 1.22440i
\(595\) 0 0
\(596\) −2.08311 + 2.43833i −0.0853274 + 0.0998779i
\(597\) 3.24619 3.24619i 0.132858 0.132858i
\(598\) −0.194496 + 0.210376i −0.00795354 + 0.00860291i
\(599\) 23.3593i 0.954435i 0.878785 + 0.477218i \(0.158355\pi\)
−0.878785 + 0.477218i \(0.841645\pi\)
\(600\) 0 0
\(601\) 20.4138i 0.832695i 0.909206 + 0.416347i \(0.136690\pi\)
−0.909206 + 0.416347i \(0.863310\pi\)
\(602\) 15.7426 + 14.5543i 0.641622 + 0.593190i
\(603\) 18.9183 18.9183i 0.770411 0.770411i
\(604\) −1.11566 14.2006i −0.0453954 0.577813i
\(605\) 0 0
\(606\) −18.5131 + 0.726115i −0.752043 + 0.0294964i
\(607\) 0.758240 0.0307760 0.0153880 0.999882i \(-0.495102\pi\)
0.0153880 + 0.999882i \(0.495102\pi\)
\(608\) −12.0535 8.05983i −0.488833 0.326869i
\(609\) −15.0358 −0.609283
\(610\) 0 0
\(611\) 0.356915 + 0.356915i 0.0144392 + 0.0144392i
\(612\) 1.84719 + 23.5119i 0.0746684 + 0.950413i
\(613\) 12.0341 12.0341i 0.486052 0.486052i −0.421006 0.907058i \(-0.638323\pi\)
0.907058 + 0.421006i \(0.138323\pi\)
\(614\) 11.6659 + 10.7853i 0.470796 + 0.435259i
\(615\) 0 0
\(616\) 57.9602 + 45.7114i 2.33528 + 1.84176i
\(617\) 32.6899i 1.31605i −0.752998 0.658023i \(-0.771393\pi\)
0.752998 0.658023i \(-0.228607\pi\)
\(618\) −9.12894 + 9.87428i −0.367220 + 0.397202i
\(619\) 26.3836 26.3836i 1.06045 1.06045i 0.0623934 0.998052i \(-0.480127\pi\)
0.998052 0.0623934i \(-0.0198733\pi\)
\(620\) 0 0
\(621\) −4.39781 4.39781i −0.176478 0.176478i
\(622\) −1.72732 44.0399i −0.0692592 1.76584i
\(623\) 15.3049 0.613178
\(624\) 0.0536355 + 0.339241i 0.00214714 + 0.0135805i
\(625\) 0 0
\(626\) −0.296991 7.57213i −0.0118702 0.302643i
\(627\) −6.93042 6.93042i −0.276774 0.276774i
\(628\) 11.4438 + 9.77662i 0.456657 + 0.390130i
\(629\) 18.5947 18.5947i 0.741420 0.741420i
\(630\) 0 0
\(631\) 6.08765i 0.242345i 0.992631 + 0.121173i \(0.0386655\pi\)
−0.992631 + 0.121173i \(0.961335\pi\)
\(632\) −32.3913 + 3.82703i −1.28846 + 0.152231i
\(633\) 1.86521i 0.0741354i
\(634\) −13.0432 12.0586i −0.518010 0.478909i
\(635\) 0 0
\(636\) 9.81701 0.771266i 0.389270 0.0305827i
\(637\) −1.33889 1.33889i −0.0530487 0.0530487i
\(638\) 36.0983 1.41584i 1.42915 0.0560535i
\(639\) −11.4549 −0.453149
\(640\) 0 0
\(641\) 11.1680 0.441111 0.220555 0.975374i \(-0.429213\pi\)
0.220555 + 0.975374i \(0.429213\pi\)
\(642\) −0.452855 + 0.0177617i −0.0178728 + 0.000700999i
\(643\) −21.9585 21.9585i −0.865957 0.865957i 0.126065 0.992022i \(-0.459765\pi\)
−0.992022 + 0.126065i \(0.959765\pi\)
\(644\) 15.3256 1.20405i 0.603914 0.0474460i
\(645\) 0 0
\(646\) 12.4421 + 11.5029i 0.489526 + 0.452575i
\(647\) 36.9848i 1.45402i 0.686625 + 0.727011i \(0.259091\pi\)
−0.686625 + 0.727011i \(0.740909\pi\)
\(648\) 13.8539 1.63683i 0.544231 0.0643009i
\(649\) 40.4238i 1.58677i
\(650\) 0 0
\(651\) 4.90368 4.90368i 0.192190 0.192190i
\(652\) 26.4533 + 22.5995i 1.03599 + 0.885065i
\(653\) −18.4157 18.4157i −0.720663 0.720663i 0.248077 0.968740i \(-0.420201\pi\)
−0.968740 + 0.248077i \(0.920201\pi\)
\(654\) 0.00810646 + 0.206683i 0.000316988 + 0.00808196i
\(655\) 0 0
\(656\) 5.15658 + 32.6150i 0.201331 + 1.27340i
\(657\) −20.9525 −0.817435
\(658\) −1.06143 27.0622i −0.0413787 1.05500i
\(659\) −15.5421 15.5421i −0.605434 0.605434i 0.336316 0.941749i \(-0.390819\pi\)
−0.941749 + 0.336316i \(0.890819\pi\)
\(660\) 0 0
\(661\) 29.6677 29.6677i 1.15394 1.15394i 0.168185 0.985755i \(-0.446209\pi\)
0.985755 0.168185i \(-0.0537906\pi\)
\(662\) −8.24507 + 8.91825i −0.320454 + 0.346617i
\(663\) 0.401363i 0.0155877i
\(664\) −3.67215 2.89611i −0.142507 0.112391i
\(665\) 0 0
\(666\) −14.7373 13.6249i −0.571058 0.527953i
\(667\) 5.31992 5.31992i 0.205988 0.205988i
\(668\) 1.54581 + 19.6758i 0.0598092 + 0.761278i
\(669\) −11.7767 11.7767i −0.455313 0.455313i
\(670\) 0 0
\(671\) −55.7864 −2.15361
\(672\) 10.2435 15.3192i 0.395152 0.590949i
\(673\) −29.2198 −1.12634 −0.563171 0.826340i \(-0.690419\pi\)
−0.563171 + 0.826340i \(0.690419\pi\)
\(674\) −31.1209 + 1.22061i −1.19873 + 0.0470163i
\(675\) 0 0
\(676\) −2.03397 25.8893i −0.0782298 0.995743i
\(677\) 17.2591 17.2591i 0.663320 0.663320i −0.292841 0.956161i \(-0.594601\pi\)
0.956161 + 0.292841i \(0.0946006\pi\)
\(678\) 4.29011 + 3.96628i 0.164761 + 0.152324i
\(679\) 65.8179i 2.52586i
\(680\) 0 0
\(681\) 6.52082i 0.249878i
\(682\) −11.3111 + 12.2346i −0.433124 + 0.468487i
\(683\) 1.10407 1.10407i 0.0422459 0.0422459i −0.685668 0.727914i \(-0.740490\pi\)
0.727914 + 0.685668i \(0.240490\pi\)
\(684\) 8.40041 9.83289i 0.321198 0.375970i
\(685\) 0 0
\(686\) 2.15224 + 54.8738i 0.0821731 + 2.09509i
\(687\) 15.7113 0.599425
\(688\) −7.56181 + 10.4020i −0.288291 + 0.396571i
\(689\) 0.885743 0.0337441
\(690\) 0 0
\(691\) −28.4233 28.4233i −1.08127 1.08127i −0.996391 0.0848830i \(-0.972948\pi\)
−0.0848830 0.996391i \(-0.527052\pi\)
\(692\) 28.8359 + 24.6350i 1.09617 + 0.936481i
\(693\) −46.5545 + 46.5545i −1.76846 + 1.76846i
\(694\) 16.1458 17.4640i 0.612885 0.662924i
\(695\) 0 0
\(696\) −1.05822 8.95660i −0.0401118 0.339499i
\(697\) 38.5875i 1.46161i
\(698\) 12.7132 + 11.7536i 0.481201 + 0.444879i
\(699\) 8.05933 8.05933i 0.304832 0.304832i
\(700\) 0 0
\(701\) −23.7991 23.7991i −0.898880 0.898880i 0.0964573 0.995337i \(-0.469249\pi\)
−0.995337 + 0.0964573i \(0.969249\pi\)
\(702\) −0.670105 + 0.0262826i −0.0252915 + 0.000991974i
\(703\) −14.4200 −0.543862
\(704\) −23.1503 + 37.7431i −0.872510 + 1.42250i
\(705\) 0 0
\(706\) −37.6109 + 1.47516i −1.41550 + 0.0555184i
\(707\) 63.2278 + 63.2278i 2.37793 + 2.37793i
\(708\) −10.0608 + 0.790421i −0.378109 + 0.0297058i
\(709\) 1.49921 1.49921i 0.0563039 0.0563039i −0.678394 0.734698i \(-0.737324\pi\)
0.734698 + 0.678394i \(0.237324\pi\)
\(710\) 0 0
\(711\) 29.0911i 1.09100i
\(712\) 1.07716 + 9.11688i 0.0403682 + 0.341670i
\(713\) 3.47000i 0.129953i
\(714\) −14.6194 + 15.8130i −0.547118 + 0.591787i
\(715\) 0 0
\(716\) 0.902323 + 0.770870i 0.0337214 + 0.0288088i
\(717\) 2.56919 + 2.56919i 0.0959482 + 0.0959482i
\(718\) −0.268830 6.85412i −0.0100327 0.255794i
\(719\) 7.37612 0.275083 0.137541 0.990496i \(-0.456080\pi\)
0.137541 + 0.990496i \(0.456080\pi\)
\(720\) 0 0
\(721\) 64.9017 2.41707
\(722\) 0.688923 + 17.5649i 0.0256391 + 0.653696i
\(723\) −6.89425 6.89425i −0.256400 0.256400i
\(724\) −26.1996 + 30.6673i −0.973702 + 1.13974i
\(725\) 0 0
\(726\) −13.0214 + 14.0846i −0.483270 + 0.522727i
\(727\) 30.1470i 1.11809i −0.829137 0.559045i \(-0.811168\pi\)
0.829137 0.559045i \(-0.188832\pi\)
\(728\) 1.02648 1.30153i 0.0380438 0.0482380i
\(729\) 4.53447i 0.167943i
\(730\) 0 0
\(731\) 10.6267 10.6267i 0.393041 0.393041i
\(732\) 1.09081 + 13.8843i 0.0403176 + 0.513180i
\(733\) −1.43297 1.43297i −0.0529279 0.0529279i 0.680147 0.733075i \(-0.261916\pi\)
−0.733075 + 0.680147i \(0.761916\pi\)
\(734\) −22.1495 + 0.868740i −0.817553 + 0.0320658i
\(735\) 0 0
\(736\) 1.79585 + 9.04449i 0.0661959 + 0.333384i
\(737\) −58.6977 −2.16216
\(738\) −29.4284 + 1.15423i −1.08328 + 0.0424879i
\(739\) 31.0001 + 31.0001i 1.14036 + 1.14036i 0.988385 + 0.151973i \(0.0485626\pi\)
0.151973 + 0.988385i \(0.451437\pi\)
\(740\) 0 0
\(741\) −0.155627 + 0.155627i −0.00571710 + 0.00571710i
\(742\) −34.8968 32.2626i −1.28110 1.18440i
\(743\) 38.5395i 1.41388i 0.707276 + 0.706938i \(0.249924\pi\)
−0.707276 + 0.706938i \(0.750076\pi\)
\(744\) 3.26616 + 2.57592i 0.119743 + 0.0944378i
\(745\) 0 0
\(746\) 7.39243 7.99599i 0.270656 0.292754i
\(747\) 2.94952 2.94952i 0.107917 0.107917i
\(748\) 33.6096 39.3408i 1.22889 1.43844i
\(749\) 1.54664 + 1.54664i 0.0565128 + 0.0565128i
\(750\) 0 0
\(751\) 26.9523 0.983503 0.491751 0.870736i \(-0.336357\pi\)
0.491751 + 0.870736i \(0.336357\pi\)
\(752\) 16.0458 2.53692i 0.585132 0.0925118i
\(753\) −9.75884 −0.355632
\(754\) −0.0317935 0.810610i −0.00115785 0.0295207i
\(755\) 0 0
\(756\) 27.3583 + 23.3727i 0.995012 + 0.850056i
\(757\) 17.0688 17.0688i 0.620377 0.620377i −0.325251 0.945628i \(-0.605449\pi\)
0.945628 + 0.325251i \(0.105449\pi\)
\(758\) 23.6380 25.5680i 0.858573 0.928671i
\(759\) 6.23290i 0.226240i
\(760\) 0 0
\(761\) 6.89608i 0.249983i 0.992158 + 0.124991i \(0.0398903\pi\)
−0.992158 + 0.124991i \(0.960110\pi\)
\(762\) −1.95907 1.81120i −0.0709698 0.0656128i
\(763\) 0.705886 0.705886i 0.0255548 0.0255548i
\(764\) 34.5544 2.71474i 1.25013 0.0982158i
\(765\) 0 0
\(766\) −12.7878 + 0.501558i −0.462041 + 0.0181220i
\(767\) −0.907741 −0.0327766
\(768\) 9.84631 + 5.02373i 0.355298 + 0.181278i
\(769\) 11.8443 0.427117 0.213558 0.976930i \(-0.431495\pi\)
0.213558 + 0.976930i \(0.431495\pi\)
\(770\) 0 0
\(771\) 4.12679 + 4.12679i 0.148623 + 0.148623i
\(772\) −33.6297 + 2.64209i −1.21036 + 0.0950910i
\(773\) −3.58865 + 3.58865i −0.129075 + 0.129075i −0.768693 0.639618i \(-0.779093\pi\)
0.639618 + 0.768693i \(0.279093\pi\)
\(774\) −8.42219 7.78646i −0.302729 0.279878i
\(775\) 0 0
\(776\) −39.2066 + 4.63226i −1.40744 + 0.166288i
\(777\) 18.3269i 0.657474i
\(778\) 20.8567 22.5595i 0.747748 0.808798i
\(779\) −14.9622 + 14.9622i −0.536075 + 0.536075i
\(780\) 0 0
\(781\) 17.7705 + 17.7705i 0.635880 + 0.635880i
\(782\) −0.422319 10.7675i −0.0151021 0.385045i
\(783\) 17.6100 0.629332 <