Properties

Label 441.2.f.d.295.1
Level $441$
Weight $2$
Character 441.295
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.1
Root \(0.500000 + 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.d.148.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.849814 + 1.47192i) q^{2} +(-0.349814 + 1.69636i) q^{3} +(-0.444368 - 0.769668i) q^{4} +(-1.79418 - 3.10761i) q^{5} +(-2.19963 - 1.95649i) q^{6} -1.88874 q^{8} +(-2.75526 - 1.18682i) q^{9} +O(q^{10})\) \(q+(-0.849814 + 1.47192i) q^{2} +(-0.349814 + 1.69636i) q^{3} +(-0.444368 - 0.769668i) q^{4} +(-1.79418 - 3.10761i) q^{5} +(-2.19963 - 1.95649i) q^{6} -1.88874 q^{8} +(-2.75526 - 1.18682i) q^{9} +6.09888 q^{10} +(1.40545 - 2.43430i) q^{11} +(1.46108 - 0.484566i) q^{12} +(0.500000 + 0.866025i) q^{13} +(5.89926 - 1.95649i) q^{15} +(2.49381 - 4.31941i) q^{16} +4.11126 q^{17} +(4.08836 - 3.04695i) q^{18} +0.888736 q^{19} +(-1.59455 + 2.76185i) q^{20} +(2.38874 + 4.13741i) q^{22} +(-2.93818 - 5.08907i) q^{23} +(0.660706 - 3.20397i) q^{24} +(-3.93818 + 6.82112i) q^{25} -1.69963 q^{26} +(2.97710 - 4.25874i) q^{27} +(0.849814 - 1.47192i) q^{29} +(-2.13348 + 10.3459i) q^{30} +(-3.49381 - 6.05146i) q^{31} +(2.34981 + 4.07000i) q^{32} +(3.63781 + 3.23569i) q^{33} +(-3.49381 + 6.05146i) q^{34} +(0.310892 + 2.64802i) q^{36} +4.76509 q^{37} +(-0.755260 + 1.30815i) q^{38} +(-1.64400 + 0.545231i) q^{39} +(3.38874 + 5.86946i) q^{40} +(-2.70582 - 4.68661i) q^{41} +(-2.60507 + 4.51212i) q^{43} -2.49814 q^{44} +(1.25526 + 10.6917i) q^{45} +9.98762 q^{46} +(-1.33310 + 2.30900i) q^{47} +(6.45489 + 5.74138i) q^{48} +(-6.69344 - 11.5934i) q^{50} +(-1.43818 + 6.97418i) q^{51} +(0.444368 - 0.769668i) q^{52} -0.123644 q^{53} +(3.73855 + 8.00119i) q^{54} -10.0865 q^{55} +(-0.310892 + 1.50761i) q^{57} +(1.44437 + 2.50172i) q^{58} +(-4.43818 - 7.68715i) q^{59} +(-4.12729 - 3.67107i) q^{60} +(1.93818 - 3.35702i) q^{61} +11.8764 q^{62} +1.98762 q^{64} +(1.79418 - 3.10761i) q^{65} +(-7.85414 + 2.60483i) q^{66} +(-6.15452 - 10.6599i) q^{67} +(-1.82691 - 3.16431i) q^{68} +(9.66071 - 3.20397i) q^{69} -2.87636 q^{71} +(5.20396 + 2.24159i) q^{72} +10.6414 q^{73} +(-4.04944 + 7.01384i) q^{74} +(-10.1934 - 9.06668i) q^{75} +(-0.394926 - 0.684031i) q^{76} +(0.594554 - 2.88318i) q^{78} +(3.54325 - 6.13709i) q^{79} -17.8974 q^{80} +(6.18292 + 6.53999i) q^{81} +9.19777 q^{82} +(-2.05563 + 3.56046i) q^{83} +(-7.37636 - 12.7762i) q^{85} +(-4.42766 - 7.66893i) q^{86} +(2.19963 + 1.95649i) q^{87} +(-2.65452 + 4.59776i) q^{88} -9.60940 q^{89} +(-16.8040 - 7.23828i) q^{90} +(-2.61126 + 4.52284i) q^{92} +(11.4876 - 3.80987i) q^{93} +(-2.26578 - 3.92445i) q^{94} +(-1.59455 - 2.76185i) q^{95} +(-7.72617 + 2.56238i) q^{96} +(3.66071 - 6.34053i) q^{97} +(-6.76145 + 5.03913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{2} + 4q^{3} - 3q^{4} - 5q^{5} - q^{6} - 12q^{8} - 4q^{9} + O(q^{10}) \) \( 6q + q^{2} + 4q^{3} - 3q^{4} - 5q^{5} - q^{6} - 12q^{8} - 4q^{9} + 2q^{11} + 2q^{12} + 3q^{13} + 11q^{15} - 3q^{16} + 24q^{17} + 13q^{18} + 6q^{19} - 16q^{20} + 15q^{22} - 15q^{24} - 6q^{25} + 2q^{26} + 7q^{27} - q^{29} - 26q^{30} - 3q^{31} + 8q^{32} - 8q^{33} - 3q^{34} - 11q^{36} - 6q^{37} + 8q^{38} + 2q^{39} + 21q^{40} - 22q^{41} + 3q^{43} + 46q^{44} - 5q^{45} + 24q^{46} - 9q^{47} + 14q^{48} - 10q^{50} + 9q^{51} + 3q^{52} - 36q^{53} + 17q^{54} + 12q^{55} + 11q^{57} + 9q^{58} - 9q^{59} - 20q^{60} - 6q^{61} + 36q^{62} - 24q^{64} + 5q^{65} + 2q^{66} + 6q^{68} + 39q^{69} + 18q^{71} - 24q^{72} - 6q^{73} - 6q^{74} - 31q^{75} - 21q^{76} + 10q^{78} - 15q^{79} - 22q^{80} + 32q^{81} - 18q^{82} - 12q^{83} - 9q^{85} - 34q^{86} + q^{87} + 21q^{88} + 4q^{89} - 73q^{90} - 15q^{92} + 33q^{93} + 24q^{94} - 16q^{95} - 5q^{96} + 3q^{97} - 46q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.849814 + 1.47192i −0.600909 + 1.04081i 0.391774 + 0.920061i \(0.371861\pi\)
−0.992684 + 0.120744i \(0.961472\pi\)
\(3\) −0.349814 + 1.69636i −0.201965 + 0.979393i
\(4\) −0.444368 0.769668i −0.222184 0.384834i
\(5\) −1.79418 3.10761i −0.802383 1.38977i −0.918044 0.396479i \(-0.870232\pi\)
0.115661 0.993289i \(-0.463101\pi\)
\(6\) −2.19963 1.95649i −0.897994 0.798733i
\(7\) 0 0
\(8\) −1.88874 −0.667769
\(9\) −2.75526 1.18682i −0.918420 0.395607i
\(10\) 6.09888 1.92864
\(11\) 1.40545 2.43430i 0.423758 0.733970i −0.572546 0.819873i \(-0.694044\pi\)
0.996304 + 0.0859026i \(0.0273774\pi\)
\(12\) 1.46108 0.484566i 0.421777 0.139882i
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) 0 0
\(15\) 5.89926 1.95649i 1.52318 0.505163i
\(16\) 2.49381 4.31941i 0.623453 1.07985i
\(17\) 4.11126 0.997128 0.498564 0.866853i \(-0.333861\pi\)
0.498564 + 0.866853i \(0.333861\pi\)
\(18\) 4.08836 3.04695i 0.963637 0.718173i
\(19\) 0.888736 0.203890 0.101945 0.994790i \(-0.467493\pi\)
0.101945 + 0.994790i \(0.467493\pi\)
\(20\) −1.59455 + 2.76185i −0.356553 + 0.617568i
\(21\) 0 0
\(22\) 2.38874 + 4.13741i 0.509280 + 0.882099i
\(23\) −2.93818 5.08907i −0.612652 1.06115i −0.990792 0.135396i \(-0.956769\pi\)
0.378139 0.925749i \(-0.376564\pi\)
\(24\) 0.660706 3.20397i 0.134866 0.654008i
\(25\) −3.93818 + 6.82112i −0.787636 + 1.36422i
\(26\) −1.69963 −0.333325
\(27\) 2.97710 4.25874i 0.572943 0.819595i
\(28\) 0 0
\(29\) 0.849814 1.47192i 0.157807 0.273329i −0.776271 0.630399i \(-0.782891\pi\)
0.934077 + 0.357071i \(0.116224\pi\)
\(30\) −2.13348 + 10.3459i −0.389518 + 1.88889i
\(31\) −3.49381 6.05146i −0.627507 1.08687i −0.988050 0.154131i \(-0.950742\pi\)
0.360544 0.932742i \(-0.382591\pi\)
\(32\) 2.34981 + 4.07000i 0.415392 + 0.719481i
\(33\) 3.63781 + 3.23569i 0.633261 + 0.563262i
\(34\) −3.49381 + 6.05146i −0.599183 + 1.03782i
\(35\) 0 0
\(36\) 0.310892 + 2.64802i 0.0518154 + 0.441337i
\(37\) 4.76509 0.783376 0.391688 0.920098i \(-0.371891\pi\)
0.391688 + 0.920098i \(0.371891\pi\)
\(38\) −0.755260 + 1.30815i −0.122519 + 0.212210i
\(39\) −1.64400 + 0.545231i −0.263250 + 0.0873068i
\(40\) 3.38874 + 5.86946i 0.535806 + 0.928044i
\(41\) −2.70582 4.68661i −0.422578 0.731926i 0.573613 0.819126i \(-0.305541\pi\)
−0.996191 + 0.0872002i \(0.972208\pi\)
\(42\) 0 0
\(43\) −2.60507 + 4.51212i −0.397270 + 0.688092i −0.993388 0.114805i \(-0.963376\pi\)
0.596118 + 0.802897i \(0.296709\pi\)
\(44\) −2.49814 −0.376609
\(45\) 1.25526 + 10.6917i 0.187123 + 1.59382i
\(46\) 9.98762 1.47259
\(47\) −1.33310 + 2.30900i −0.194453 + 0.336803i −0.946721 0.322055i \(-0.895627\pi\)
0.752268 + 0.658857i \(0.228960\pi\)
\(48\) 6.45489 + 5.74138i 0.931683 + 0.828697i
\(49\) 0 0
\(50\) −6.69344 11.5934i −0.946595 1.63955i
\(51\) −1.43818 + 6.97418i −0.201385 + 0.976580i
\(52\) 0.444368 0.769668i 0.0616227 0.106734i
\(53\) −0.123644 −0.0169838 −0.00849190 0.999964i \(-0.502703\pi\)
−0.00849190 + 0.999964i \(0.502703\pi\)
\(54\) 3.73855 + 8.00119i 0.508752 + 1.08882i
\(55\) −10.0865 −1.36006
\(56\) 0 0
\(57\) −0.310892 + 1.50761i −0.0411787 + 0.199688i
\(58\) 1.44437 + 2.50172i 0.189655 + 0.328492i
\(59\) −4.43818 7.68715i −0.577802 1.00078i −0.995731 0.0923022i \(-0.970577\pi\)
0.417929 0.908479i \(-0.362756\pi\)
\(60\) −4.12729 3.67107i −0.532830 0.473933i
\(61\) 1.93818 3.35702i 0.248158 0.429823i −0.714857 0.699271i \(-0.753508\pi\)
0.963015 + 0.269448i \(0.0868414\pi\)
\(62\) 11.8764 1.50830
\(63\) 0 0
\(64\) 1.98762 0.248453
\(65\) 1.79418 3.10761i 0.222541 0.385452i
\(66\) −7.85414 + 2.60483i −0.966778 + 0.320632i
\(67\) −6.15452 10.6599i −0.751894 1.30232i −0.946904 0.321517i \(-0.895807\pi\)
0.195010 0.980801i \(-0.437526\pi\)
\(68\) −1.82691 3.16431i −0.221546 0.383729i
\(69\) 9.66071 3.20397i 1.16301 0.385713i
\(70\) 0 0
\(71\) −2.87636 −0.341361 −0.170680 0.985326i \(-0.554597\pi\)
−0.170680 + 0.985326i \(0.554597\pi\)
\(72\) 5.20396 + 2.24159i 0.613292 + 0.264174i
\(73\) 10.6414 1.24549 0.622744 0.782426i \(-0.286018\pi\)
0.622744 + 0.782426i \(0.286018\pi\)
\(74\) −4.04944 + 7.01384i −0.470738 + 0.815342i
\(75\) −10.1934 9.06668i −1.17704 1.04693i
\(76\) −0.394926 0.684031i −0.0453011 0.0784638i
\(77\) 0 0
\(78\) 0.594554 2.88318i 0.0673200 0.326456i
\(79\) 3.54325 6.13709i 0.398647 0.690477i −0.594912 0.803791i \(-0.702813\pi\)
0.993559 + 0.113314i \(0.0361465\pi\)
\(80\) −17.8974 −2.00099
\(81\) 6.18292 + 6.53999i 0.686991 + 0.726666i
\(82\) 9.19777 1.01572
\(83\) −2.05563 + 3.56046i −0.225635 + 0.390811i −0.956510 0.291700i \(-0.905779\pi\)
0.730875 + 0.682512i \(0.239112\pi\)
\(84\) 0 0
\(85\) −7.37636 12.7762i −0.800078 1.38578i
\(86\) −4.42766 7.66893i −0.477447 0.826962i
\(87\) 2.19963 + 1.95649i 0.235825 + 0.209757i
\(88\) −2.65452 + 4.59776i −0.282972 + 0.490123i
\(89\) −9.60940 −1.01859 −0.509297 0.860591i \(-0.670095\pi\)
−0.509297 + 0.860591i \(0.670095\pi\)
\(90\) −16.8040 7.23828i −1.77130 0.762981i
\(91\) 0 0
\(92\) −2.61126 + 4.52284i −0.272243 + 0.471539i
\(93\) 11.4876 3.80987i 1.19121 0.395065i
\(94\) −2.26578 3.92445i −0.233697 0.404776i
\(95\) −1.59455 2.76185i −0.163598 0.283360i
\(96\) −7.72617 + 2.56238i −0.788549 + 0.261522i
\(97\) 3.66071 6.34053i 0.371688 0.643783i −0.618137 0.786070i \(-0.712112\pi\)
0.989825 + 0.142287i \(0.0454456\pi\)
\(98\) 0 0
\(99\) −6.76145 + 5.03913i −0.679551 + 0.506452i
\(100\) 7.00000 0.700000
\(101\) 1.73236 3.00054i 0.172376 0.298564i −0.766874 0.641798i \(-0.778189\pi\)
0.939250 + 0.343233i \(0.111522\pi\)
\(102\) −9.04325 8.04364i −0.895415 0.796439i
\(103\) −7.93818 13.7493i −0.782172 1.35476i −0.930674 0.365849i \(-0.880779\pi\)
0.148502 0.988912i \(-0.452555\pi\)
\(104\) −0.944368 1.63569i −0.0926029 0.160393i
\(105\) 0 0
\(106\) 0.105074 0.181994i 0.0102057 0.0176768i
\(107\) −5.35346 −0.517538 −0.258769 0.965939i \(-0.583317\pi\)
−0.258769 + 0.965939i \(0.583317\pi\)
\(108\) −4.60074 0.398930i −0.442707 0.0383871i
\(109\) −18.8640 −1.80684 −0.903421 0.428755i \(-0.858952\pi\)
−0.903421 + 0.428755i \(0.858952\pi\)
\(110\) 8.57165 14.8465i 0.817275 1.41556i
\(111\) −1.66690 + 8.08330i −0.158215 + 0.767233i
\(112\) 0 0
\(113\) 9.27561 + 16.0658i 0.872576 + 1.51135i 0.859322 + 0.511434i \(0.170886\pi\)
0.0132538 + 0.999912i \(0.495781\pi\)
\(114\) −1.95489 1.73880i −0.183092 0.162854i
\(115\) −10.5433 + 18.2614i −0.983163 + 1.70289i
\(116\) −1.51052 −0.140248
\(117\) −0.349814 2.97954i −0.0323403 0.275458i
\(118\) 15.0865 1.38883
\(119\) 0 0
\(120\) −11.1421 + 3.69529i −1.01713 + 0.337332i
\(121\) 1.54944 + 2.68371i 0.140858 + 0.243974i
\(122\) 3.29418 + 5.70569i 0.298241 + 0.516569i
\(123\) 8.89671 2.95059i 0.802189 0.266046i
\(124\) −3.10507 + 5.37815i −0.278844 + 0.482972i
\(125\) 10.3214 0.923175
\(126\) 0 0
\(127\) 9.98762 0.886258 0.443129 0.896458i \(-0.353868\pi\)
0.443129 + 0.896458i \(0.353868\pi\)
\(128\) −6.38874 + 11.0656i −0.564690 + 0.978071i
\(129\) −6.74288 5.99754i −0.593678 0.528054i
\(130\) 3.04944 + 5.28179i 0.267454 + 0.463244i
\(131\) 8.02654 + 13.9024i 0.701282 + 1.21466i 0.968017 + 0.250886i \(0.0807220\pi\)
−0.266734 + 0.963770i \(0.585945\pi\)
\(132\) 0.873885 4.23774i 0.0760619 0.368848i
\(133\) 0 0
\(134\) 20.9208 1.80728
\(135\) −18.5760 1.61072i −1.59877 0.138629i
\(136\) −7.76509 −0.665851
\(137\) 6.49381 11.2476i 0.554804 0.960948i −0.443115 0.896465i \(-0.646127\pi\)
0.997919 0.0644834i \(-0.0205400\pi\)
\(138\) −3.49381 + 16.9426i −0.297413 + 1.44225i
\(139\) 0.555632 + 0.962383i 0.0471281 + 0.0816283i 0.888627 0.458630i \(-0.151660\pi\)
−0.841499 + 0.540259i \(0.818326\pi\)
\(140\) 0 0
\(141\) −3.45056 3.06914i −0.290589 0.258468i
\(142\) 2.44437 4.23377i 0.205127 0.355290i
\(143\) 2.81089 0.235059
\(144\) −11.9975 + 8.94138i −0.999788 + 0.745115i
\(145\) −6.09888 −0.506485
\(146\) −9.04325 + 15.6634i −0.748425 + 1.29631i
\(147\) 0 0
\(148\) −2.11745 3.66754i −0.174054 0.301470i
\(149\) −4.21634 7.30291i −0.345416 0.598278i 0.640013 0.768364i \(-0.278929\pi\)
−0.985429 + 0.170086i \(0.945595\pi\)
\(150\) 22.0080 7.29894i 1.79694 0.595956i
\(151\) 7.42580 12.8619i 0.604303 1.04668i −0.387858 0.921719i \(-0.626785\pi\)
0.992161 0.124964i \(-0.0398816\pi\)
\(152\) −1.67859 −0.136151
\(153\) −11.3276 4.87933i −0.915782 0.394470i
\(154\) 0 0
\(155\) −12.5371 + 21.7148i −1.00700 + 1.74418i
\(156\) 1.15019 + 1.02305i 0.0920886 + 0.0819094i
\(157\) 1.44437 + 2.50172i 0.115273 + 0.199659i 0.917889 0.396837i \(-0.129892\pi\)
−0.802616 + 0.596496i \(0.796559\pi\)
\(158\) 6.02221 + 10.4308i 0.479101 + 0.829828i
\(159\) 0.0432524 0.209744i 0.00343014 0.0166338i
\(160\) 8.43199 14.6046i 0.666607 1.15460i
\(161\) 0 0
\(162\) −14.8807 + 3.54299i −1.16914 + 0.278363i
\(163\) −10.3090 −0.807466 −0.403733 0.914877i \(-0.632287\pi\)
−0.403733 + 0.914877i \(0.632287\pi\)
\(164\) −2.40476 + 4.16516i −0.187780 + 0.325245i
\(165\) 3.52840 17.1103i 0.274686 1.33204i
\(166\) −3.49381 6.05146i −0.271172 0.469684i
\(167\) 6.07598 + 10.5239i 0.470174 + 0.814365i 0.999418 0.0341045i \(-0.0108579\pi\)
−0.529244 + 0.848469i \(0.677525\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 25.0741 1.92310
\(171\) −2.44870 1.05477i −0.187257 0.0806602i
\(172\) 4.63045 0.353068
\(173\) −3.30470 + 5.72391i −0.251252 + 0.435181i −0.963871 0.266370i \(-0.914176\pi\)
0.712619 + 0.701551i \(0.247509\pi\)
\(174\) −4.74907 + 1.57503i −0.360026 + 0.119403i
\(175\) 0 0
\(176\) −7.00983 12.1414i −0.528386 0.915191i
\(177\) 14.5927 4.83967i 1.09685 0.363772i
\(178\) 8.16621 14.1443i 0.612083 1.06016i
\(179\) −3.84294 −0.287234 −0.143617 0.989633i \(-0.545873\pi\)
−0.143617 + 0.989633i \(0.545873\pi\)
\(180\) 7.67123 5.71716i 0.571779 0.426132i
\(181\) −18.5426 −1.37826 −0.689129 0.724639i \(-0.742007\pi\)
−0.689129 + 0.724639i \(0.742007\pi\)
\(182\) 0 0
\(183\) 5.01671 + 4.46218i 0.370846 + 0.329854i
\(184\) 5.54944 + 9.61192i 0.409110 + 0.708600i
\(185\) −8.54944 14.8081i −0.628567 1.08871i
\(186\) −4.15452 + 20.1466i −0.304624 + 1.47722i
\(187\) 5.77816 10.0081i 0.422541 0.731862i
\(188\) 2.36955 0.172818
\(189\) 0 0
\(190\) 5.42030 0.393230
\(191\) −2.31708 + 4.01330i −0.167658 + 0.290392i −0.937596 0.347726i \(-0.886954\pi\)
0.769938 + 0.638119i \(0.220287\pi\)
\(192\) −0.695298 + 3.37172i −0.0501788 + 0.243333i
\(193\) 12.6483 + 21.9075i 0.910446 + 1.57694i 0.813435 + 0.581656i \(0.197595\pi\)
0.0970118 + 0.995283i \(0.469072\pi\)
\(194\) 6.22184 + 10.7765i 0.446702 + 0.773711i
\(195\) 4.64400 + 4.13066i 0.332563 + 0.295803i
\(196\) 0 0
\(197\) 10.7207 0.763816 0.381908 0.924200i \(-0.375267\pi\)
0.381908 + 0.924200i \(0.375267\pi\)
\(198\) −1.67123 14.2346i −0.118769 1.01161i
\(199\) 8.76647 0.621439 0.310719 0.950502i \(-0.399430\pi\)
0.310719 + 0.950502i \(0.399430\pi\)
\(200\) 7.43818 12.8833i 0.525959 0.910987i
\(201\) 20.2360 6.71127i 1.42734 0.473376i
\(202\) 2.94437 + 5.09979i 0.207165 + 0.358820i
\(203\) 0 0
\(204\) 6.00688 1.99218i 0.420566 0.139481i
\(205\) −9.70946 + 16.8173i −0.678138 + 1.17457i
\(206\) 26.9839 1.88006
\(207\) 2.05563 + 17.5088i 0.142876 + 1.21695i
\(208\) 4.98762 0.345829
\(209\) 1.24907 2.16345i 0.0864000 0.149649i
\(210\) 0 0
\(211\) −5.26509 9.11941i −0.362464 0.627806i 0.625902 0.779902i \(-0.284731\pi\)
−0.988366 + 0.152096i \(0.951398\pi\)
\(212\) 0.0549434 + 0.0951647i 0.00377353 + 0.00653594i
\(213\) 1.00619 4.87933i 0.0689430 0.334326i
\(214\) 4.54944 7.87987i 0.310993 0.538656i
\(215\) 18.6959 1.27505
\(216\) −5.62296 + 8.04364i −0.382594 + 0.547300i
\(217\) 0 0
\(218\) 16.0309 27.7663i 1.08575 1.88057i
\(219\) −3.72253 + 18.0517i −0.251545 + 1.21982i
\(220\) 4.48212 + 7.76326i 0.302184 + 0.523399i
\(221\) 2.05563 + 3.56046i 0.138277 + 0.239502i
\(222\) −10.4814 9.32284i −0.703468 0.625708i
\(223\) −2.83379 + 4.90827i −0.189765 + 0.328682i −0.945172 0.326574i \(-0.894106\pi\)
0.755407 + 0.655256i \(0.227439\pi\)
\(224\) 0 0
\(225\) 18.9462 14.1201i 1.26308 0.941338i
\(226\) −31.5302 −2.09736
\(227\) −5.54944 + 9.61192i −0.368329 + 0.637965i −0.989304 0.145865i \(-0.953403\pi\)
0.620975 + 0.783830i \(0.286737\pi\)
\(228\) 1.29851 0.430652i 0.0859961 0.0285206i
\(229\) 9.82141 + 17.0112i 0.649017 + 1.12413i 0.983358 + 0.181679i \(0.0581530\pi\)
−0.334341 + 0.942452i \(0.608514\pi\)
\(230\) −17.9196 31.0377i −1.18158 2.04656i
\(231\) 0 0
\(232\) −1.60507 + 2.78007i −0.105378 + 0.182521i
\(233\) 8.96286 0.587177 0.293588 0.955932i \(-0.405151\pi\)
0.293588 + 0.955932i \(0.405151\pi\)
\(234\) 4.68292 + 2.01715i 0.306132 + 0.131865i
\(235\) 9.56732 0.624103
\(236\) −3.94437 + 6.83185i −0.256756 + 0.444715i
\(237\) 9.17123 + 8.15747i 0.595735 + 0.529884i
\(238\) 0 0
\(239\) −5.61126 9.71899i −0.362963 0.628670i 0.625484 0.780237i \(-0.284901\pi\)
−0.988447 + 0.151567i \(0.951568\pi\)
\(240\) 6.26076 30.3604i 0.404130 1.95975i
\(241\) −3.49312 + 6.05026i −0.225012 + 0.389732i −0.956323 0.292312i \(-0.905575\pi\)
0.731311 + 0.682044i \(0.238909\pi\)
\(242\) −5.26695 −0.338572
\(243\) −13.2570 + 8.20066i −0.850440 + 0.526073i
\(244\) −3.44506 −0.220547
\(245\) 0 0
\(246\) −3.21751 + 15.6027i −0.205141 + 0.994792i
\(247\) 0.444368 + 0.769668i 0.0282745 + 0.0489728i
\(248\) 6.59888 + 11.4296i 0.419030 + 0.725781i
\(249\) −5.32072 4.73259i −0.337187 0.299915i
\(250\) −8.77128 + 15.1923i −0.554745 + 0.960846i
\(251\) −4.62041 −0.291638 −0.145819 0.989311i \(-0.546582\pi\)
−0.145819 + 0.989311i \(0.546582\pi\)
\(252\) 0 0
\(253\) −16.5178 −1.03847
\(254\) −8.48762 + 14.7010i −0.532561 + 0.922422i
\(255\) 24.2534 8.04364i 1.51881 0.503712i
\(256\) −8.87085 15.3648i −0.554428 0.960298i
\(257\) −0.712008 1.23323i −0.0444138 0.0769270i 0.842964 0.537970i \(-0.180809\pi\)
−0.887378 + 0.461043i \(0.847475\pi\)
\(258\) 14.5581 4.82819i 0.906348 0.300590i
\(259\) 0 0
\(260\) −3.18911 −0.197780
\(261\) −4.08836 + 3.04695i −0.253063 + 0.188601i
\(262\) −27.2843 −1.68563
\(263\) −8.13162 + 14.0844i −0.501417 + 0.868480i 0.498582 + 0.866843i \(0.333854\pi\)
−0.999999 + 0.00163692i \(0.999479\pi\)
\(264\) −6.87085 6.11137i −0.422872 0.376129i
\(265\) 0.221840 + 0.384237i 0.0136275 + 0.0236035i
\(266\) 0 0
\(267\) 3.36151 16.3010i 0.205721 0.997604i
\(268\) −5.46974 + 9.47387i −0.334118 + 0.578709i
\(269\) 18.6538 1.13734 0.568672 0.822564i \(-0.307457\pi\)
0.568672 + 0.822564i \(0.307457\pi\)
\(270\) 18.1570 25.9736i 1.10500 1.58070i
\(271\) −3.96286 −0.240727 −0.120363 0.992730i \(-0.538406\pi\)
−0.120363 + 0.992730i \(0.538406\pi\)
\(272\) 10.2527 17.7582i 0.621662 1.07675i
\(273\) 0 0
\(274\) 11.0371 + 19.1168i 0.666773 + 1.15489i
\(275\) 11.0698 + 19.1734i 0.667534 + 1.15620i
\(276\) −6.75890 6.01179i −0.406838 0.361867i
\(277\) 1.16690 2.02112i 0.0701120 0.121438i −0.828838 0.559488i \(-0.810998\pi\)
0.898950 + 0.438051i \(0.144331\pi\)
\(278\) −1.88874 −0.113279
\(279\) 2.44437 + 20.8199i 0.146340 + 1.24645i
\(280\) 0 0
\(281\) −13.9975 + 24.2443i −0.835018 + 1.44629i 0.0589978 + 0.998258i \(0.481210\pi\)
−0.894016 + 0.448035i \(0.852124\pi\)
\(282\) 7.44987 2.47075i 0.443633 0.147131i
\(283\) 5.16002 + 8.93741i 0.306731 + 0.531274i 0.977645 0.210261i \(-0.0674314\pi\)
−0.670914 + 0.741535i \(0.734098\pi\)
\(284\) 1.27816 + 2.21384i 0.0758449 + 0.131367i
\(285\) 5.24288 1.73880i 0.310561 0.102998i
\(286\) −2.38874 + 4.13741i −0.141249 + 0.244650i
\(287\) 0 0
\(288\) −1.64400 14.0027i −0.0968734 0.825117i
\(289\) −0.0975070 −0.00573571
\(290\) 5.18292 8.97708i 0.304351 0.527152i
\(291\) 9.47524 + 8.42787i 0.555448 + 0.494051i
\(292\) −4.72872 8.19038i −0.276727 0.479306i
\(293\) −15.3480 26.5834i −0.896637 1.55302i −0.831765 0.555127i \(-0.812670\pi\)
−0.0648718 0.997894i \(-0.520664\pi\)
\(294\) 0 0
\(295\) −15.9258 + 27.5843i −0.927236 + 1.60602i
\(296\) −9.00000 −0.523114
\(297\) −6.18292 13.2326i −0.358769 0.767833i
\(298\) 14.3324 0.830255
\(299\) 2.93818 5.08907i 0.169919 0.294309i
\(300\) −2.44870 + 11.8745i −0.141376 + 0.685575i
\(301\) 0 0
\(302\) 12.6211 + 21.8604i 0.726262 + 1.25792i
\(303\) 4.48398 + 3.98833i 0.257598 + 0.229124i
\(304\) 2.21634 3.83881i 0.127116 0.220171i
\(305\) −13.9098 −0.796471
\(306\) 16.8083 12.5268i 0.960869 0.716110i
\(307\) 11.4437 0.653125 0.326563 0.945176i \(-0.394110\pi\)
0.326563 + 0.945176i \(0.394110\pi\)
\(308\) 0 0
\(309\) 26.1007 8.65628i 1.48482 0.492439i
\(310\) −21.3083 36.9071i −1.21023 2.09618i
\(311\) 5.98143 + 10.3601i 0.339176 + 0.587470i 0.984278 0.176627i \(-0.0565185\pi\)
−0.645102 + 0.764096i \(0.723185\pi\)
\(312\) 3.10507 1.02980i 0.175790 0.0583008i
\(313\) −6.77197 + 11.7294i −0.382774 + 0.662985i −0.991458 0.130429i \(-0.958365\pi\)
0.608683 + 0.793413i \(0.291698\pi\)
\(314\) −4.90978 −0.277075
\(315\) 0 0
\(316\) −6.29803 −0.354292
\(317\) 14.9814 25.9486i 0.841441 1.45742i −0.0472355 0.998884i \(-0.515041\pi\)
0.888676 0.458535i \(-0.151626\pi\)
\(318\) 0.271971 + 0.241908i 0.0152514 + 0.0135655i
\(319\) −2.38874 4.13741i −0.133744 0.231651i
\(320\) −3.56615 6.17676i −0.199354 0.345291i
\(321\) 1.87271 9.08138i 0.104525 0.506873i
\(322\) 0 0
\(323\) 3.65383 0.203304
\(324\) 2.28613 7.66496i 0.127007 0.425831i
\(325\) −7.87636 −0.436902
\(326\) 8.76076 15.1741i 0.485214 0.840415i
\(327\) 6.59888 32.0001i 0.364919 1.76961i
\(328\) 5.11058 + 8.85178i 0.282184 + 0.488758i
\(329\) 0 0
\(330\) 22.1866 + 19.7341i 1.22133 + 1.08633i
\(331\) −1.04325 + 1.80697i −0.0573423 + 0.0993198i −0.893272 0.449517i \(-0.851596\pi\)
0.835929 + 0.548837i \(0.184929\pi\)
\(332\) 3.65383 0.200530
\(333\) −13.1291 5.65531i −0.719469 0.309909i
\(334\) −20.6538 −1.13013
\(335\) −22.0846 + 38.2517i −1.20661 + 2.08992i
\(336\) 0 0
\(337\) 8.10439 + 14.0372i 0.441474 + 0.764655i 0.997799 0.0663093i \(-0.0211224\pi\)
−0.556325 + 0.830965i \(0.687789\pi\)
\(338\) 10.1978 + 17.6631i 0.554686 + 0.960743i
\(339\) −30.4981 + 10.1147i −1.65643 + 0.549355i
\(340\) −6.55563 + 11.3547i −0.355529 + 0.615794i
\(341\) −19.6414 −1.06364
\(342\) 3.63348 2.70793i 0.196476 0.146428i
\(343\) 0 0
\(344\) 4.92030 8.52220i 0.265285 0.459486i
\(345\) −27.2898 24.2732i −1.46923 1.30683i
\(346\) −5.61677 9.72852i −0.301959 0.523009i
\(347\) −5.63348 9.75747i −0.302421 0.523808i 0.674263 0.738491i \(-0.264461\pi\)
−0.976684 + 0.214683i \(0.931128\pi\)
\(348\) 0.528401 2.56238i 0.0283253 0.137358i
\(349\) −0.0988844 + 0.171273i −0.00529316 + 0.00916803i −0.868660 0.495409i \(-0.835018\pi\)
0.863367 + 0.504577i \(0.168352\pi\)
\(350\) 0 0
\(351\) 5.17673 + 0.448873i 0.276313 + 0.0239591i
\(352\) 13.2101 0.704103
\(353\) −6.25093 + 10.8269i −0.332703 + 0.576259i −0.983041 0.183386i \(-0.941294\pi\)
0.650338 + 0.759645i \(0.274627\pi\)
\(354\) −5.27747 + 25.5921i −0.280494 + 1.36021i
\(355\) 5.16071 + 8.93861i 0.273902 + 0.474412i
\(356\) 4.27011 + 7.39605i 0.226315 + 0.391990i
\(357\) 0 0
\(358\) 3.26578 5.65650i 0.172602 0.298955i
\(359\) 20.0197 1.05660 0.528299 0.849059i \(-0.322830\pi\)
0.528299 + 0.849059i \(0.322830\pi\)
\(360\) −2.37085 20.1937i −0.124955 1.06430i
\(361\) −18.2101 −0.958429
\(362\) 15.7577 27.2932i 0.828208 1.43450i
\(363\) −5.09455 + 1.68961i −0.267395 + 0.0886814i
\(364\) 0 0
\(365\) −19.0927 33.0695i −0.999357 1.73094i
\(366\) −10.8312 + 3.59218i −0.566158 + 0.187766i
\(367\) 15.0364 26.0438i 0.784892 1.35947i −0.144171 0.989553i \(-0.546052\pi\)
0.929063 0.369921i \(-0.120615\pi\)
\(368\) −29.3090 −1.52784
\(369\) 1.89307 + 16.1242i 0.0985491 + 0.839390i
\(370\) 29.0617 1.51085
\(371\) 0 0
\(372\) −8.03706 7.14867i −0.416702 0.370641i
\(373\) −3.50619 6.07290i −0.181544 0.314443i 0.760863 0.648913i \(-0.224776\pi\)
−0.942406 + 0.334470i \(0.891443\pi\)
\(374\) 9.82072 + 17.0100i 0.507818 + 0.879566i
\(375\) −3.61058 + 17.5088i −0.186449 + 0.904151i
\(376\) 2.51788 4.36110i 0.129850 0.224906i
\(377\) 1.69963 0.0875353
\(378\) 0 0
\(379\) −19.0741 −0.979772 −0.489886 0.871787i \(-0.662962\pi\)
−0.489886 + 0.871787i \(0.662962\pi\)
\(380\) −1.41714 + 2.45455i −0.0726976 + 0.125916i
\(381\) −3.49381 + 16.9426i −0.178993 + 0.867995i
\(382\) −3.93818 6.82112i −0.201495 0.348999i
\(383\) 1.60507 + 2.78007i 0.0820155 + 0.142055i 0.904116 0.427288i \(-0.140531\pi\)
−0.822100 + 0.569343i \(0.807198\pi\)
\(384\) −16.5364 14.7085i −0.843868 0.750590i
\(385\) 0 0
\(386\) −42.9949 −2.18838
\(387\) 12.5327 9.34031i 0.637075 0.474795i
\(388\) −6.50680 −0.330333
\(389\) −2.56801 + 4.44793i −0.130203 + 0.225519i −0.923755 0.382984i \(-0.874896\pi\)
0.793552 + 0.608503i \(0.208230\pi\)
\(390\) −10.0265 + 3.32530i −0.507714 + 0.168383i
\(391\) −12.0796 20.9225i −0.610893 1.05810i
\(392\) 0 0
\(393\) −26.3912 + 8.75264i −1.33126 + 0.441512i
\(394\) −9.11058 + 15.7800i −0.458984 + 0.794984i
\(395\) −25.4290 −1.27947
\(396\) 6.88303 + 2.96484i 0.345885 + 0.148989i
\(397\) −22.9381 −1.15123 −0.575615 0.817721i \(-0.695237\pi\)
−0.575615 + 0.817721i \(0.695237\pi\)
\(398\) −7.44987 + 12.9036i −0.373428 + 0.646797i
\(399\) 0 0
\(400\) 19.6421 + 34.0212i 0.982107 + 1.70106i
\(401\) 9.10507 + 15.7705i 0.454686 + 0.787539i 0.998670 0.0515566i \(-0.0164183\pi\)
−0.543984 + 0.839095i \(0.683085\pi\)
\(402\) −7.31838 + 35.4891i −0.365008 + 1.77004i
\(403\) 3.49381 6.05146i 0.174039 0.301445i
\(404\) −3.07922 −0.153197
\(405\) 9.23050 30.9481i 0.458667 1.53782i
\(406\) 0 0
\(407\) 6.69708 11.5997i 0.331962 0.574975i
\(408\) 2.71634 13.1724i 0.134479 0.652130i
\(409\) −7.66621 13.2783i −0.379070 0.656568i 0.611858 0.790968i \(-0.290423\pi\)
−0.990927 + 0.134400i \(0.957089\pi\)
\(410\) −16.5025 28.5831i −0.814999 1.41162i
\(411\) 16.8083 + 14.9504i 0.829094 + 0.737449i
\(412\) −7.05494 + 12.2195i −0.347572 + 0.602013i
\(413\) 0 0
\(414\) −27.5185 11.8535i −1.35246 0.582568i
\(415\) 14.7527 0.724182
\(416\) −2.34981 + 4.07000i −0.115209 + 0.199548i
\(417\) −1.82691 + 0.605896i −0.0894644 + 0.0296708i
\(418\) 2.12296 + 3.67707i 0.103837 + 0.179851i
\(419\) 5.28435 + 9.15276i 0.258157 + 0.447142i 0.965748 0.259481i \(-0.0835513\pi\)
−0.707591 + 0.706622i \(0.750218\pi\)
\(420\) 0 0
\(421\) 18.0858 31.3256i 0.881449 1.52671i 0.0317181 0.999497i \(-0.489902\pi\)
0.849731 0.527217i \(-0.176765\pi\)
\(422\) 17.8974 0.871232
\(423\) 6.41342 4.77975i 0.311831 0.232399i
\(424\) 0.233531 0.0113412
\(425\) −16.1909 + 28.0434i −0.785374 + 1.36031i
\(426\) 6.32691 + 5.62755i 0.306540 + 0.272656i
\(427\) 0 0
\(428\) 2.37890 + 4.12038i 0.114989 + 0.199166i
\(429\) −0.983290 + 4.76828i −0.0474737 + 0.230215i
\(430\) −15.8880 + 27.5189i −0.766190 + 1.32708i
\(431\) 35.0989 1.69065 0.845327 0.534249i \(-0.179406\pi\)
0.845327 + 0.534249i \(0.179406\pi\)
\(432\) −10.9709 23.4798i −0.527838 1.12967i
\(433\) 41.1730 1.97865 0.989324 0.145731i \(-0.0465533\pi\)
0.989324 + 0.145731i \(0.0465533\pi\)
\(434\) 0 0
\(435\) 2.13348 10.3459i 0.102292 0.496047i
\(436\) 8.38255 + 14.5190i 0.401451 + 0.695334i
\(437\) −2.61126 4.52284i −0.124914 0.216357i
\(438\) −23.4072 20.8199i −1.11844 0.994811i
\(439\) −2.33929 + 4.05178i −0.111648 + 0.193381i −0.916435 0.400184i \(-0.868946\pi\)
0.804787 + 0.593564i \(0.202280\pi\)
\(440\) 19.0507 0.908209
\(441\) 0 0
\(442\) −6.98762 −0.332367
\(443\) −15.0865 + 26.1306i −0.716781 + 1.24150i 0.245487 + 0.969400i \(0.421052\pi\)
−0.962268 + 0.272102i \(0.912281\pi\)
\(444\) 6.96217 2.30900i 0.330410 0.109580i
\(445\) 17.2410 + 29.8623i 0.817303 + 1.41561i
\(446\) −4.81639 8.34224i −0.228063 0.395016i
\(447\) 13.8633 4.59776i 0.655711 0.217466i
\(448\) 0 0
\(449\) 0.333792 0.0157526 0.00787632 0.999969i \(-0.497493\pi\)
0.00787632 + 0.999969i \(0.497493\pi\)
\(450\) 4.68292 + 39.8867i 0.220755 + 1.88028i
\(451\) −15.2115 −0.716283
\(452\) 8.24357 14.2783i 0.387745 0.671594i
\(453\) 19.2207 + 17.0961i 0.903066 + 0.803244i
\(454\) −9.43199 16.3367i −0.442665 0.766719i
\(455\) 0 0
\(456\) 0.587193 2.84748i 0.0274979 0.133346i
\(457\) 9.65452 16.7221i 0.451619 0.782227i −0.546868 0.837219i \(-0.684180\pi\)
0.998487 + 0.0549917i \(0.0175132\pi\)
\(458\) −33.3855 −1.56000
\(459\) 12.2396 17.5088i 0.571298 0.817241i
\(460\) 18.7403 0.873773
\(461\) 19.5538 33.8681i 0.910710 1.57740i 0.0976463 0.995221i \(-0.468869\pi\)
0.813064 0.582175i \(-0.197798\pi\)
\(462\) 0 0
\(463\) −10.9382 18.9455i −0.508340 0.880471i −0.999953 0.00965741i \(-0.996926\pi\)
0.491613 0.870814i \(-0.336407\pi\)
\(464\) −4.23855 7.34138i −0.196770 0.340815i
\(465\) −32.4505 28.8635i −1.50486 1.33851i
\(466\) −7.61677 + 13.1926i −0.352840 + 0.611137i
\(467\) 12.3200 0.570103 0.285052 0.958512i \(-0.407989\pi\)
0.285052 + 0.958512i \(0.407989\pi\)
\(468\) −2.13781 + 1.59325i −0.0988201 + 0.0736480i
\(469\) 0 0
\(470\) −8.13045 + 14.0823i −0.375029 + 0.649570i
\(471\) −4.74907 + 1.57503i −0.218826 + 0.0725735i
\(472\) 8.38255 + 14.5190i 0.385838 + 0.668291i
\(473\) 7.32258 + 12.6831i 0.336693 + 0.583169i
\(474\) −19.8010 + 6.56699i −0.909489 + 0.301632i
\(475\) −3.50000 + 6.06218i −0.160591 + 0.278152i
\(476\) 0 0
\(477\) 0.340671 + 0.146743i 0.0155983 + 0.00671890i
\(478\) 19.0741 0.872430
\(479\) 6.74474 11.6822i 0.308175 0.533775i −0.669788 0.742552i \(-0.733615\pi\)
0.977963 + 0.208777i \(0.0669484\pi\)
\(480\) 21.8251 + 19.4126i 0.996173 + 0.886059i
\(481\) 2.38255 + 4.12669i 0.108635 + 0.188161i
\(482\) −5.93701 10.2832i −0.270423 0.468387i
\(483\) 0 0
\(484\) 1.37704 2.38511i 0.0625929 0.108414i
\(485\) −26.2719 −1.19295
\(486\) −0.804702 26.4824i −0.0365020 1.20126i
\(487\) 7.54394 0.341849 0.170924 0.985284i \(-0.445325\pi\)
0.170924 + 0.985284i \(0.445325\pi\)
\(488\) −3.66071 + 6.34053i −0.165712 + 0.287022i
\(489\) 3.60624 17.4878i 0.163080 0.790826i
\(490\) 0 0
\(491\) 8.06979 + 13.9773i 0.364185 + 0.630786i 0.988645 0.150270i \(-0.0480143\pi\)
−0.624460 + 0.781057i \(0.714681\pi\)
\(492\) −6.22439 5.53636i −0.280617 0.249598i
\(493\) 3.49381 6.05146i 0.157353 0.272544i
\(494\) −1.51052 −0.0679615
\(495\) 27.7909 + 11.9709i 1.24911 + 0.538050i
\(496\) −34.8516 −1.56488
\(497\) 0 0
\(498\) 11.4876 3.80987i 0.514773 0.170724i
\(499\) 15.4327 + 26.7302i 0.690862 + 1.19661i 0.971556 + 0.236810i \(0.0761019\pi\)
−0.280694 + 0.959797i \(0.590565\pi\)
\(500\) −4.58650 7.94406i −0.205115 0.355269i
\(501\) −19.9778 + 6.62563i −0.892542 + 0.296011i
\(502\) 3.92649 6.80088i 0.175248 0.303538i
\(503\) −24.6304 −1.09822 −0.549109 0.835751i \(-0.685033\pi\)
−0.549109 + 0.835751i \(0.685033\pi\)
\(504\) 0 0
\(505\) −12.4327 −0.553247
\(506\) 14.0371 24.3129i 0.624024 1.08084i
\(507\) 15.5302 + 13.8135i 0.689720 + 0.613480i
\(508\) −4.43818 7.68715i −0.196912 0.341062i
\(509\) 6.79487 + 11.7691i 0.301177 + 0.521654i 0.976403 0.215957i \(-0.0692870\pi\)
−0.675226 + 0.737611i \(0.735954\pi\)
\(510\) −8.77128 + 42.5347i −0.388399 + 1.88347i
\(511\) 0 0
\(512\) 4.59937 0.203265
\(513\) 2.64586 3.78490i 0.116817 0.167107i
\(514\) 2.42030 0.106755
\(515\) −28.4851 + 49.3376i −1.25520 + 2.17407i
\(516\) −1.61980 + 7.85489i −0.0713075 + 0.345792i
\(517\) 3.74721 + 6.49036i 0.164802 + 0.285446i
\(518\) 0 0
\(519\) −8.55377 7.60826i −0.375469 0.333966i
\(520\) −3.38874 + 5.86946i −0.148606 + 0.257393i
\(521\) 39.1730 1.71620 0.858100 0.513482i \(-0.171645\pi\)
0.858100 + 0.513482i \(0.171645\pi\)
\(522\) −1.01052 8.60709i −0.0442293 0.376722i
\(523\) −19.1236 −0.836219 −0.418109 0.908397i \(-0.637307\pi\)
−0.418109 + 0.908397i \(0.637307\pi\)
\(524\) 7.13348 12.3555i 0.311627 0.539754i
\(525\) 0 0
\(526\) −13.8207 23.9382i −0.602612 1.04375i
\(527\) −14.3640 24.8791i −0.625705 1.08375i
\(528\) 23.0483 7.64396i 1.00305 0.332660i
\(529\) −5.76578 + 9.98663i −0.250686 + 0.434201i
\(530\) −0.754090 −0.0327556
\(531\) 3.10507 + 26.4474i 0.134749 + 1.14772i
\(532\) 0 0
\(533\) 2.70582 4.68661i 0.117202 0.203000i
\(534\) 21.1371 + 18.8007i 0.914693 + 0.813585i
\(535\) 9.60507 + 16.6365i 0.415264 + 0.719258i
\(536\) 11.6243 + 20.1338i 0.502091 + 0.869648i
\(537\) 1.34431 6.51899i 0.0580114 0.281315i
\(538\) −15.8523 + 27.4570i −0.683441 + 1.18375i
\(539\) 0 0
\(540\) 7.01485 + 15.0131i 0.301871 + 0.646061i
\(541\) 2.53018 0.108781 0.0543906 0.998520i \(-0.482678\pi\)
0.0543906 + 0.998520i \(0.482678\pi\)
\(542\) 3.36769 5.83302i 0.144655 0.250550i
\(543\) 6.48645 31.4548i 0.278360 1.34986i
\(544\) 9.66071 + 16.7328i 0.414199 + 0.717414i
\(545\) 33.8454 + 58.6220i 1.44978 + 2.51109i
\(546\) 0 0
\(547\) −8.92580 + 15.4599i −0.381640 + 0.661019i −0.991297 0.131646i \(-0.957974\pi\)
0.609657 + 0.792665i \(0.291307\pi\)
\(548\) −11.5426 −0.493074
\(549\) −9.32437 + 6.94920i −0.397954 + 0.296585i
\(550\) −37.6291 −1.60451
\(551\) 0.755260 1.30815i 0.0321752 0.0557290i
\(552\) −18.2465 + 6.05146i −0.776624 + 0.257567i
\(553\) 0 0
\(554\) 1.98329 + 3.43516i 0.0842619 + 0.145946i
\(555\) 28.1105 9.32284i 1.19322 0.395733i
\(556\) 0.493810 0.855304i 0.0209422 0.0362730i
\(557\) 41.3607 1.75251 0.876255 0.481847i \(-0.160034\pi\)
0.876255 + 0.481847i \(0.160034\pi\)
\(558\) −32.7225 14.0951i −1.38525 0.596693i
\(559\) −5.21015 −0.220366
\(560\) 0 0
\(561\) 14.9560 + 13.3028i 0.631442 + 0.561644i
\(562\) −23.7905 41.2063i −1.00354 1.73818i
\(563\) −10.3683 17.9584i −0.436972 0.756858i 0.560482 0.828166i \(-0.310616\pi\)
−0.997454 + 0.0713087i \(0.977282\pi\)
\(564\) −0.828903 + 4.01961i −0.0349031 + 0.169256i
\(565\) 33.2843 57.6501i 1.40028 2.42536i
\(566\) −17.5402 −0.737271
\(567\) 0 0
\(568\) 5.43268 0.227950
\(569\) 0.134164 0.232379i 0.00562446 0.00974185i −0.863199 0.504863i \(-0.831543\pi\)
0.868824 + 0.495121i \(0.164876\pi\)
\(570\) −1.89610 + 9.19476i −0.0794187 + 0.385126i
\(571\) −17.9684 31.1221i −0.751953 1.30242i −0.946875 0.321601i \(-0.895779\pi\)
0.194923 0.980819i \(-0.437554\pi\)
\(572\) −1.24907 2.16345i −0.0522263 0.0904585i
\(573\) −5.99745 5.33451i −0.250547 0.222852i
\(574\) 0 0
\(575\) 46.2843 1.93019
\(576\) −5.47641 2.35895i −0.228184 0.0982895i
\(577\) −5.43130 −0.226108 −0.113054 0.993589i \(-0.536063\pi\)
−0.113054 + 0.993589i \(0.536063\pi\)
\(578\) 0.0828628 0.143523i 0.00344664 0.00596976i
\(579\) −41.5876 + 13.7925i −1.72832 + 0.573198i
\(580\) 2.71015 + 4.69412i 0.112533 + 0.194913i
\(581\) 0 0
\(582\) −20.4574 + 6.78468i −0.847985 + 0.281234i
\(583\) −0.173775 + 0.300987i −0.00719702 + 0.0124656i
\(584\) −20.0989 −0.831698
\(585\) −8.63162 + 6.43292i −0.356873 + 0.265968i
\(586\) 52.1716 2.15519
\(587\) 17.5822 30.4532i 0.725694 1.25694i −0.232994 0.972478i \(-0.574852\pi\)
0.958688 0.284461i \(-0.0918145\pi\)
\(588\) 0 0
\(589\) −3.10507 5.37815i −0.127942 0.221603i
\(590\) −27.0679 46.8830i −1.11437 1.93014i
\(591\) −3.75024 + 18.1861i −0.154264 + 0.748076i
\(592\) 11.8832 20.5824i 0.488398 0.845930i
\(593\) 33.5068 1.37596 0.687980 0.725730i \(-0.258498\pi\)
0.687980 + 0.725730i \(0.258498\pi\)
\(594\) 24.7317 + 2.14448i 1.01475 + 0.0879891i
\(595\) 0 0
\(596\) −3.74721 + 6.49036i −0.153492 + 0.265856i
\(597\) −3.06663 + 14.8711i −0.125509 + 0.608632i
\(598\) 4.99381 + 8.64953i 0.204212 + 0.353706i
\(599\) −3.12364 5.41031i −0.127629 0.221059i 0.795129 0.606441i \(-0.207403\pi\)
−0.922757 + 0.385381i \(0.874070\pi\)
\(600\) 19.2527 + 17.1246i 0.785989 + 0.699108i
\(601\) 11.2040 19.4058i 0.457019 0.791580i −0.541783 0.840519i \(-0.682250\pi\)
0.998802 + 0.0489384i \(0.0155838\pi\)
\(602\) 0 0
\(603\) 4.30587 + 36.6752i 0.175349 + 1.49353i
\(604\) −13.1991 −0.537066
\(605\) 5.55996 9.63014i 0.226045 0.391521i
\(606\) −9.68106 + 3.21072i −0.393266 + 0.130427i
\(607\) 7.47524 + 12.9475i 0.303411 + 0.525523i 0.976906 0.213669i \(-0.0685413\pi\)
−0.673496 + 0.739191i \(0.735208\pi\)
\(608\) 2.08836 + 3.61715i 0.0846943 + 0.146695i
\(609\) 0 0
\(610\) 11.8207 20.4741i 0.478607 0.828972i
\(611\) −2.66621 −0.107863
\(612\) 1.27816 + 10.8867i 0.0516666 + 0.440069i
\(613\) 35.1978 1.42162 0.710812 0.703382i \(-0.248328\pi\)
0.710812 + 0.703382i \(0.248328\pi\)
\(614\) −9.72500 + 16.8442i −0.392469 + 0.679776i
\(615\) −25.1316 22.3536i −1.01340 0.901386i
\(616\) 0 0
\(617\) 1.00619 + 1.74277i 0.0405077 + 0.0701614i 0.885568 0.464509i \(-0.153769\pi\)
−0.845061 + 0.534670i \(0.820436\pi\)
\(618\) −9.43935 + 45.7744i −0.379706 + 1.84131i
\(619\) 19.6909 34.1056i 0.791444 1.37082i −0.133629 0.991031i \(-0.542663\pi\)
0.925073 0.379789i \(-0.124004\pi\)
\(620\) 22.2843 0.894958
\(621\) −30.4203 2.63774i −1.22072 0.105849i
\(622\) −20.3324 −0.815256
\(623\) 0 0
\(624\) −1.74474 + 8.46079i −0.0698455 + 0.338703i
\(625\) 1.17240 + 2.03065i 0.0468959 + 0.0812261i
\(626\) −11.5098 19.9356i −0.460025 0.796787i
\(627\) 3.23305 + 2.87568i 0.129116 + 0.114843i
\(628\) 1.28366 2.22337i 0.0512237 0.0887220i
\(629\) 19.5906 0.781126
\(630\) 0 0
\(631\) 44.3832 1.76687 0.883433 0.468558i \(-0.155226\pi\)
0.883433 + 0.468558i \(0.155226\pi\)
\(632\) −6.69227 + 11.5913i −0.266204 + 0.461079i
\(633\) 17.3116 5.74138i 0.688074 0.228200i
\(634\) 25.4629 + 44.1030i 1.01126 + 1.75155i
\(635\) −17.9196 31.0377i −0.711118 1.23169i
\(636\) −0.180653 + 0.0599137i −0.00716337 + 0.00237573i
\(637\) 0 0
\(638\) 8.11993 0.321471
\(639\) 7.92511 + 3.41372i 0.313512 + 0.135045i
\(640\) 45.8502 1.81239
\(641\) 7.49312 12.9785i 0.295961 0.512619i −0.679247 0.733909i \(-0.737694\pi\)
0.975208 + 0.221291i \(0.0710270\pi\)
\(642\) 11.7756 + 10.4740i 0.464746 + 0.413375i
\(643\) −5.32691 9.22649i −0.210073 0.363857i 0.741664 0.670771i \(-0.234037\pi\)
−0.951737 + 0.306914i \(0.900703\pi\)
\(644\) 0 0
\(645\) −6.54009 + 31.7150i −0.257516 + 1.24878i
\(646\) −3.10507 + 5.37815i −0.122168 + 0.211600i
\(647\) −2.12955 −0.0837213 −0.0418606 0.999123i \(-0.513329\pi\)
−0.0418606 + 0.999123i \(0.513329\pi\)
\(648\) −11.6779 12.3523i −0.458751 0.485245i
\(649\) −24.9505 −0.979392
\(650\) 6.69344 11.5934i 0.262538 0.454730i
\(651\) 0 0
\(652\) 4.58100 + 7.93453i 0.179406 + 0.310740i
\(653\) −5.58582 9.67492i −0.218590 0.378609i 0.735787 0.677213i \(-0.236812\pi\)
−0.954377 + 0.298604i \(0.903479\pi\)
\(654\) 41.4937 + 36.9071i 1.62253 + 1.44318i
\(655\) 28.8022 49.8868i 1.12539 1.94924i
\(656\) −26.9912 −1.05383
\(657\) −29.3200 12.6295i −1.14388 0.492723i
\(658\) 0 0
\(659\) 5.65452 9.79391i 0.220269 0.381517i −0.734621 0.678478i \(-0.762640\pi\)
0.954890 + 0.296961i \(0.0959733\pi\)
\(660\) −14.7372 + 4.88758i −0.573644 + 0.190249i
\(661\) 16.1785 + 28.0220i 0.629271 + 1.08993i 0.987698 + 0.156372i \(0.0499798\pi\)
−0.358427 + 0.933558i \(0.616687\pi\)
\(662\) −1.77314 3.07117i −0.0689151 0.119364i
\(663\) −6.75890 + 2.24159i −0.262494 + 0.0870561i
\(664\) 3.88255 6.72477i 0.150672 0.260972i
\(665\) 0 0
\(666\) 19.4814 14.5190i 0.754890 0.562600i
\(667\) −9.98762 −0.386722
\(668\) 5.39995 9.35298i 0.208930 0.361878i
\(669\) −7.33489 6.52411i −0.283583 0.252237i
\(670\) −37.5357 65.0137i −1.45013 2.51170i
\(671\) −5.44801 9.43623i −0.210318 0.364282i
\(672\) 0 0
\(673\) 12.0803 20.9237i 0.465662 0.806550i −0.533569 0.845756i \(-0.679150\pi\)
0.999231 + 0.0392063i \(0.0124830\pi\)
\(674\) −27.5489 −1.06114
\(675\) 17.3251 + 37.0788i 0.666842 + 1.42717i
\(676\) −10.6648 −0.410186
\(677\) 12.5371 21.7148i 0.481838 0.834569i −0.517944 0.855414i \(-0.673303\pi\)
0.999783 + 0.0208457i \(0.00663587\pi\)
\(678\) 11.0297 53.4865i 0.423593 2.05414i
\(679\) 0 0
\(680\) 13.9320 + 24.1309i 0.534267 + 0.925378i
\(681\) −14.3640 12.7762i −0.550429 0.489586i
\(682\) 16.6916 28.9107i 0.639154 1.10705i
\(683\) −47.6784 −1.82436 −0.912182 0.409785i \(-0.865604\pi\)
−0.912182 + 0.409785i \(0.865604\pi\)
\(684\) 0.276301 + 2.35339i 0.0105646 + 0.0899841i
\(685\) −46.6043 −1.78066
\(686\) 0 0
\(687\) −32.2927 + 10.7099i −1.23204 + 0.408607i
\(688\) 12.9931 + 22.5047i 0.495358 + 0.857985i
\(689\) −0.0618219 0.107079i −0.00235523 0.00407937i
\(690\) 58.9195 19.5407i 2.24303 0.743900i
\(691\) −12.3400 + 21.3735i −0.469435 + 0.813085i −0.999389 0.0349408i \(-0.988876\pi\)
0.529954 + 0.848026i \(0.322209\pi\)
\(692\) 5.87402 0.223297
\(693\) 0 0
\(694\) 19.1496 0.726910
\(695\) 1.99381 3.45338i 0.0756295 0.130994i
\(696\) −4.15452 3.69529i −0.157477 0.140070i
\(697\) −11.1243 19.2679i −0.421364 0.729824i
\(698\) −0.168067 0.291100i −0.00636142 0.0110183i
\(699\) −3.13533 + 15.2042i −0.118589 + 0.575076i
\(700\) 0 0
\(701\) −29.6784 −1.12094 −0.560469 0.828175i \(-0.689379\pi\)
−0.560469 + 0.828175i \(0.689379\pi\)
\(702\) −5.05996 + 7.23828i −0.190976 + 0.273191i
\(703\) 4.23491 0.159723
\(704\) 2.79349 4.83847i 0.105284 0.182357i
\(705\) −3.34678 + 16.2296i −0.126047 + 0.611242i
\(706\) −10.6243 18.4018i −0.399849 0.692559i
\(707\) 0 0
\(708\) −10.2095 9.08094i −0.383695 0.341282i
\(709\) 14.6291 25.3383i 0.549406 0.951599i −0.448909 0.893577i \(-0.648187\pi\)
0.998315 0.0580220i \(-0.0184794\pi\)
\(710\) −17.5426 −0.658361
\(711\) −17.0462 + 12.7041i −0.639283 + 0.476440i
\(712\) 18.1496 0.680186
\(713\) −20.5309 + 35.5605i −0.768887 + 1.33175i
\(714\) 0 0
\(715\) −5.04325 8.73517i −0.188607 0.326677i
\(716\) 1.70768 + 2.95778i 0.0638189 + 0.110538i
\(717\) 18.4498 6.11887i 0.689020 0.228513i
\(718\) −17.0130 + 29.4674i −0.634919 + 1.09971i
\(719\) −1.07413 −0.0400581 −0.0200291 0.999799i \(-0.506376\pi\)
−0.0200291 + 0.999799i \(0.506376\pi\)
\(720\) 49.3120 + 21.2410i 1.83775 + 0.791605i
\(721\) 0 0
\(722\) 15.4752 26.8039i 0.575929 0.997538i
\(723\) −9.04147 8.04205i −0.336256 0.299087i
\(724\) 8.23972 + 14.2716i 0.306227 + 0.530400i
\(725\) 6.69344 + 11.5934i 0.248588 + 0.430567i
\(726\) 1.84245 8.93463i 0.0683799 0.331595i
\(727\) 12.7163 22.0253i 0.471623 0.816875i −0.527850 0.849338i \(-0.677002\pi\)
0.999473 + 0.0324628i \(0.0103350\pi\)
\(728\) 0 0
\(729\) −9.27375 25.3574i −0.343472 0.939163i
\(730\) 64.9010 2.40209
\(731\) −10.7101 + 18.5505i −0.396129 + 0.686116i
\(732\) 1.20513 5.84405i 0.0445429 0.216002i
\(733\) −5.69777 9.86883i −0.210452 0.364513i 0.741404 0.671059i \(-0.234160\pi\)
−0.951856 + 0.306545i \(0.900827\pi\)
\(734\) 25.5562 + 44.2647i 0.943298 + 1.63384i
\(735\) 0 0
\(736\) 13.8083 23.9168i 0.508982 0.881583i
\(737\) −34.5994 −1.27448
\(738\) −25.3422 10.9161i −0.932861 0.401827i
\(739\) −29.9395 −1.10134 −0.550671 0.834723i \(-0.685628\pi\)
−0.550671 + 0.834723i \(0.685628\pi\)
\(740\) −7.59820 + 13.1605i −0.279315 + 0.483788i
\(741\) −1.46108 + 0.484566i −0.0536740 + 0.0178010i
\(742\) 0 0
\(743\) 9.50069 + 16.4557i 0.348546 + 0.603700i 0.985991 0.166796i \(-0.0533420\pi\)
−0.637445 + 0.770496i \(0.720009\pi\)
\(744\) −21.6971 + 7.19583i −0.795454 + 0.263812i
\(745\) −15.1298 + 26.2055i −0.554311 + 0.960096i
\(746\) 11.9184 0.436365
\(747\) 9.88942 7.37033i 0.361835 0.269666i
\(748\) −10.2705 −0.375527
\(749\) 0 0
\(750\) −22.7033 20.1937i −0.829006 0.737370i
\(751\) −0.0130684 0.0226352i −0.000476873 0.000825969i 0.865787 0.500413i \(-0.166818\pi\)
−0.866264 + 0.499587i \(0.833485\pi\)
\(752\) 6.64902 + 11.5164i 0.242465 + 0.419961i
\(753\) 1.61628 7.83786i 0.0589006 0.285628i
\(754\) −1.44437 + 2.50172i −0.0526008 + 0.0911072i
\(755\) −53.2929 −1.93953
\(756\) 0 0
\(757\) −13.6910 −0.497607 −0.248803 0.968554i \(-0.580037\pi\)
−0.248803 + 0.968554i \(0.580037\pi\)
\(758\) 16.2095 28.0756i 0.588754 1.01975i
\(759\) 5.77816 28.0201i 0.209734 1.01707i
\(760\) 3.01169 + 5.21640i 0.109246 + 0.189219i
\(761\) −7.32141 12.6811i −0.265401 0.459688i 0.702268 0.711913i \(-0.252171\pi\)
−0.967669 + 0.252225i \(0.918838\pi\)
\(762\) −21.9691 19.5407i −0.795855 0.707883i
\(763\) 0 0
\(764\) 4.11855 0.149004
\(765\) 5.16071 + 43.9562i 0.186586 + 1.58924i
\(766\) −5.45606 −0.197135
\(767\) 4.43818 7.68715i 0.160253 0.277567i
\(768\) 29.1673 9.67333i 1.05248 0.349056i
\(769\) 24.5672 + 42.5517i 0.885918 + 1.53445i 0.844658 + 0.535306i \(0.179804\pi\)
0.0412592 + 0.999148i \(0.486863\pi\)
\(770\) 0 0
\(771\) 2.34108 0.776418i 0.0843118 0.0279620i
\(772\) 11.2410 19.4700i 0.404573 0.700741i
\(773\) −12.4413 −0.447484 −0.223742 0.974648i \(-0.571827\pi\)
−0.223742 + 0.974648i \(0.571827\pi\)
\(774\) 3.09771 + 26.3847i 0.111345 + 0.948379i
\(775\) 55.0370 1.97699
\(776\) −6.91411 + 11.9756i −0.248202 + 0.429898i
\(777\) 0 0
\(778\) −4.36467 7.55982i −0.156481 0.271033i
\(779\) −2.40476 4.16516i −0.0861594 0.149232i
\(780\) 1.11559 5.40987i 0.0399447 0.193704i
\(781\) −4.04256