Properties

Label 120.2.d.b.109.3
Level $120$
Weight $2$
Character 120.109
Analytic conductor $0.958$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.958204824255\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.839056.1
Defining polynomial: \( x^{6} + 6x^{4} + 8x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 109.3
Root \(2.02852i\) of defining polynomial
Character \(\chi\) \(=\) 120.109
Dual form 120.2.d.b.109.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.321037 - 1.37729i) q^{2} -1.00000 q^{3} +(-1.79387 - 0.884323i) q^{4} +(-2.11491 - 0.726062i) q^{5} +(-0.321037 + 1.37729i) q^{6} -4.05705i q^{7} +(-1.79387 + 2.18678i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(0.321037 - 1.37729i) q^{2} -1.00000 q^{3} +(-1.79387 - 0.884323i) q^{4} +(-2.11491 - 0.726062i) q^{5} +(-0.321037 + 1.37729i) q^{6} -4.05705i q^{7} +(-1.79387 + 2.18678i) q^{8} +1.00000 q^{9} +(-1.67896 + 2.67975i) q^{10} -0.985939i q^{11} +(1.79387 + 0.884323i) q^{12} +4.94567 q^{13} +(-5.58774 - 1.30246i) q^{14} +(2.11491 + 0.726062i) q^{15} +(2.43594 + 3.17272i) q^{16} +4.52323i q^{17} +(0.321037 - 1.37729i) q^{18} -2.60492i q^{19} +(3.15180 + 3.17272i) q^{20} +4.05705i q^{21} +(-1.35793 - 0.316523i) q^{22} -3.53729i q^{23} +(1.79387 - 2.18678i) q^{24} +(3.94567 + 3.07111i) q^{25} +(1.58774 - 6.81163i) q^{26} -1.00000 q^{27} +(-3.58774 + 7.27782i) q^{28} -7.59434i q^{29} +(1.67896 - 2.67975i) q^{30} -3.28415 q^{31} +(5.15180 - 2.33645i) q^{32} +0.985939i q^{33} +(6.22982 + 1.45212i) q^{34} +(-2.94567 + 8.58028i) q^{35} +(-1.79387 - 0.884323i) q^{36} -0.945668 q^{37} +(-3.58774 - 0.836276i) q^{38} -4.94567 q^{39} +(5.38161 - 3.32239i) q^{40} +0.568295 q^{41} +(5.58774 + 1.30246i) q^{42} +8.45963 q^{43} +(-0.871889 + 1.76865i) q^{44} +(-2.11491 - 0.726062i) q^{45} +(-4.87189 - 1.13560i) q^{46} +2.60492i q^{47} +(-2.43594 - 3.17272i) q^{48} -9.45963 q^{49} +(5.49652 - 4.44840i) q^{50} -4.52323i q^{51} +(-8.87189 - 4.37357i) q^{52} +0.229815 q^{53} +(-0.321037 + 1.37729i) q^{54} +(-0.715853 + 2.08517i) q^{55} +(8.87189 + 7.27782i) q^{56} +2.60492i q^{57} +(-10.4596 - 2.43806i) q^{58} +9.10003i q^{59} +(-3.15180 - 3.17272i) q^{60} +11.0183i q^{61} +(-1.05433 + 4.52323i) q^{62} -4.05705i q^{63} +(-1.56406 - 7.84562i) q^{64} +(-10.4596 - 3.59086i) q^{65} +(1.35793 + 0.316523i) q^{66} -8.45963 q^{67} +(4.00000 - 8.11409i) q^{68} +3.53729i q^{69} +(10.8719 + 6.81163i) q^{70} +1.43171 q^{71} +(-1.79387 + 2.18678i) q^{72} -11.9507i q^{73} +(-0.303594 + 1.30246i) q^{74} +(-3.94567 - 3.07111i) q^{75} +(-2.30359 + 4.67289i) q^{76} -4.00000 q^{77} +(-1.58774 + 6.81163i) q^{78} +3.28415 q^{79} +(-2.84820 - 8.47866i) q^{80} +1.00000 q^{81} +(0.182443 - 0.782708i) q^{82} +9.89134 q^{83} +(3.58774 - 7.27782i) q^{84} +(3.28415 - 9.56622i) q^{85} +(2.71585 - 11.6514i) q^{86} +7.59434i q^{87} +(2.15604 + 1.76865i) q^{88} +12.3510 q^{89} +(-1.67896 + 2.67975i) q^{90} -20.0648i q^{91} +(-3.12811 + 6.34545i) q^{92} +3.28415 q^{93} +(3.58774 + 0.836276i) q^{94} +(-1.89134 + 5.50917i) q^{95} +(-5.15180 + 2.33645i) q^{96} -3.23797i q^{97} +(-3.03689 + 13.0287i) q^{98} -0.985939i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} - 6 q^{3} + q^{4} - q^{6} + q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{2} - 6 q^{3} + q^{4} - q^{6} + q^{8} + 6 q^{9} - 11 q^{10} - q^{12} + 8 q^{13} - 10 q^{14} + q^{16} + q^{18} + 9 q^{20} - 10 q^{22} - q^{24} + 2 q^{25} - 14 q^{26} - 6 q^{27} + 2 q^{28} + 11 q^{30} - 16 q^{31} + 21 q^{32} + 12 q^{34} + 4 q^{35} + q^{36} + 16 q^{37} + 2 q^{38} - 8 q^{39} - 3 q^{40} - 4 q^{41} + 10 q^{42} + 22 q^{44} - 2 q^{46} - q^{48} - 6 q^{49} - 15 q^{50} - 26 q^{52} - 24 q^{53} - q^{54} - 8 q^{55} + 26 q^{56} - 12 q^{58} - 9 q^{60} - 28 q^{62} - 23 q^{64} - 12 q^{65} + 10 q^{66} + 24 q^{68} + 38 q^{70} + 16 q^{71} + q^{72} + 18 q^{74} - 2 q^{75} + 6 q^{76} - 24 q^{77} + 14 q^{78} + 16 q^{79} - 27 q^{80} + 6 q^{81} + 50 q^{82} + 16 q^{83} - 2 q^{84} + 16 q^{85} + 20 q^{86} - 18 q^{88} - 20 q^{89} - 11 q^{90} - 46 q^{92} + 16 q^{93} - 2 q^{94} + 32 q^{95} - 21 q^{96} - 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.321037 1.37729i 0.227007 0.973893i
\(3\) −1.00000 −0.577350
\(4\) −1.79387 0.884323i −0.896935 0.442162i
\(5\) −2.11491 0.726062i −0.945815 0.324705i
\(6\) −0.321037 + 1.37729i −0.131063 + 0.562277i
\(7\) 4.05705i 1.53342i −0.641994 0.766710i \(-0.721893\pi\)
0.641994 0.766710i \(-0.278107\pi\)
\(8\) −1.79387 + 2.18678i −0.634229 + 0.773145i
\(9\) 1.00000 0.333333
\(10\) −1.67896 + 2.67975i −0.530935 + 0.847413i
\(11\) 0.985939i 0.297272i −0.988892 0.148636i \(-0.952512\pi\)
0.988892 0.148636i \(-0.0474882\pi\)
\(12\) 1.79387 + 0.884323i 0.517846 + 0.255282i
\(13\) 4.94567 1.37168 0.685841 0.727752i \(-0.259435\pi\)
0.685841 + 0.727752i \(0.259435\pi\)
\(14\) −5.58774 1.30246i −1.49339 0.348097i
\(15\) 2.11491 + 0.726062i 0.546067 + 0.187468i
\(16\) 2.43594 + 3.17272i 0.608986 + 0.793181i
\(17\) 4.52323i 1.09704i 0.836136 + 0.548522i \(0.184809\pi\)
−0.836136 + 0.548522i \(0.815191\pi\)
\(18\) 0.321037 1.37729i 0.0756691 0.324631i
\(19\) 2.60492i 0.597610i −0.954314 0.298805i \(-0.903412\pi\)
0.954314 0.298805i \(-0.0965881\pi\)
\(20\) 3.15180 + 3.17272i 0.704763 + 0.709443i
\(21\) 4.05705i 0.885320i
\(22\) −1.35793 0.316523i −0.289511 0.0674829i
\(23\) 3.53729i 0.737577i −0.929513 0.368788i \(-0.879773\pi\)
0.929513 0.368788i \(-0.120227\pi\)
\(24\) 1.79387 2.18678i 0.366172 0.446376i
\(25\) 3.94567 + 3.07111i 0.789134 + 0.614222i
\(26\) 1.58774 6.81163i 0.311382 1.33587i
\(27\) −1.00000 −0.192450
\(28\) −3.58774 + 7.27782i −0.678019 + 1.37538i
\(29\) 7.59434i 1.41023i −0.709091 0.705117i \(-0.750895\pi\)
0.709091 0.705117i \(-0.249105\pi\)
\(30\) 1.67896 2.67975i 0.306535 0.489254i
\(31\) −3.28415 −0.589850 −0.294925 0.955520i \(-0.595295\pi\)
−0.294925 + 0.955520i \(0.595295\pi\)
\(32\) 5.15180 2.33645i 0.910718 0.413029i
\(33\) 0.985939i 0.171630i
\(34\) 6.22982 + 1.45212i 1.06840 + 0.249037i
\(35\) −2.94567 + 8.58028i −0.497909 + 1.45033i
\(36\) −1.79387 0.884323i −0.298978 0.147387i
\(37\) −0.945668 −0.155467 −0.0777334 0.996974i \(-0.524768\pi\)
−0.0777334 + 0.996974i \(0.524768\pi\)
\(38\) −3.58774 0.836276i −0.582009 0.135662i
\(39\) −4.94567 −0.791941
\(40\) 5.38161 3.32239i 0.850908 0.525315i
\(41\) 0.568295 0.0887527 0.0443763 0.999015i \(-0.485870\pi\)
0.0443763 + 0.999015i \(0.485870\pi\)
\(42\) 5.58774 + 1.30246i 0.862207 + 0.200974i
\(43\) 8.45963 1.29008 0.645041 0.764148i \(-0.276840\pi\)
0.645041 + 0.764148i \(0.276840\pi\)
\(44\) −0.871889 + 1.76865i −0.131442 + 0.266634i
\(45\) −2.11491 0.726062i −0.315272 0.108235i
\(46\) −4.87189 1.13560i −0.718321 0.167435i
\(47\) 2.60492i 0.379967i 0.981787 + 0.189984i \(0.0608435\pi\)
−0.981787 + 0.189984i \(0.939157\pi\)
\(48\) −2.43594 3.17272i −0.351598 0.457943i
\(49\) −9.45963 −1.35138
\(50\) 5.49652 4.44840i 0.777325 0.629099i
\(51\) 4.52323i 0.633379i
\(52\) −8.87189 4.37357i −1.23031 0.606505i
\(53\) 0.229815 0.0315675 0.0157838 0.999875i \(-0.494976\pi\)
0.0157838 + 0.999875i \(0.494976\pi\)
\(54\) −0.321037 + 1.37729i −0.0436876 + 0.187426i
\(55\) −0.715853 + 2.08517i −0.0965256 + 0.281164i
\(56\) 8.87189 + 7.27782i 1.18556 + 0.972539i
\(57\) 2.60492i 0.345030i
\(58\) −10.4596 2.43806i −1.37342 0.320133i
\(59\) 9.10003i 1.18472i 0.805672 + 0.592362i \(0.201804\pi\)
−0.805672 + 0.592362i \(0.798196\pi\)
\(60\) −3.15180 3.17272i −0.406895 0.409597i
\(61\) 11.0183i 1.41075i 0.708832 + 0.705377i \(0.249222\pi\)
−0.708832 + 0.705377i \(0.750778\pi\)
\(62\) −1.05433 + 4.52323i −0.133900 + 0.574451i
\(63\) 4.05705i 0.511140i
\(64\) −1.56406 7.84562i −0.195507 0.980702i
\(65\) −10.4596 3.59086i −1.29736 0.445392i
\(66\) 1.35793 + 0.316523i 0.167149 + 0.0389612i
\(67\) −8.45963 −1.03351 −0.516754 0.856134i \(-0.672860\pi\)
−0.516754 + 0.856134i \(0.672860\pi\)
\(68\) 4.00000 8.11409i 0.485071 0.983978i
\(69\) 3.53729i 0.425840i
\(70\) 10.8719 + 6.81163i 1.29944 + 0.814146i
\(71\) 1.43171 0.169912 0.0849561 0.996385i \(-0.472925\pi\)
0.0849561 + 0.996385i \(0.472925\pi\)
\(72\) −1.79387 + 2.18678i −0.211410 + 0.257715i
\(73\) 11.9507i 1.39873i −0.714767 0.699363i \(-0.753467\pi\)
0.714767 0.699363i \(-0.246533\pi\)
\(74\) −0.303594 + 1.30246i −0.0352921 + 0.151408i
\(75\) −3.94567 3.07111i −0.455606 0.354621i
\(76\) −2.30359 + 4.67289i −0.264240 + 0.536018i
\(77\) −4.00000 −0.455842
\(78\) −1.58774 + 6.81163i −0.179776 + 0.771266i
\(79\) 3.28415 0.369495 0.184748 0.982786i \(-0.440853\pi\)
0.184748 + 0.982786i \(0.440853\pi\)
\(80\) −2.84820 8.47866i −0.318439 0.947943i
\(81\) 1.00000 0.111111
\(82\) 0.182443 0.782708i 0.0201475 0.0864356i
\(83\) 9.89134 1.08572 0.542858 0.839825i \(-0.317342\pi\)
0.542858 + 0.839825i \(0.317342\pi\)
\(84\) 3.58774 7.27782i 0.391455 0.794075i
\(85\) 3.28415 9.56622i 0.356216 1.03760i
\(86\) 2.71585 11.6514i 0.292858 1.25640i
\(87\) 7.59434i 0.814199i
\(88\) 2.15604 + 1.76865i 0.229834 + 0.188538i
\(89\) 12.3510 1.30920 0.654600 0.755976i \(-0.272837\pi\)
0.654600 + 0.755976i \(0.272837\pi\)
\(90\) −1.67896 + 2.67975i −0.176978 + 0.282471i
\(91\) 20.0648i 2.10336i
\(92\) −3.12811 + 6.34545i −0.326128 + 0.661559i
\(93\) 3.28415 0.340550
\(94\) 3.58774 + 0.836276i 0.370047 + 0.0862553i
\(95\) −1.89134 + 5.50917i −0.194047 + 0.565229i
\(96\) −5.15180 + 2.33645i −0.525803 + 0.238463i
\(97\) 3.23797i 0.328766i −0.986397 0.164383i \(-0.947437\pi\)
0.986397 0.164383i \(-0.0525633\pi\)
\(98\) −3.03689 + 13.0287i −0.306772 + 1.31610i
\(99\) 0.985939i 0.0990906i
\(100\) −4.36217 8.99842i −0.436217 0.899842i
\(101\) 4.35637i 0.433475i 0.976230 + 0.216738i \(0.0695416\pi\)
−0.976230 + 0.216738i \(0.930458\pi\)
\(102\) −6.22982 1.45212i −0.616844 0.143782i
\(103\) 15.0754i 1.48542i 0.669612 + 0.742711i \(0.266460\pi\)
−0.669612 + 0.742711i \(0.733540\pi\)
\(104\) −8.87189 + 10.8151i −0.869960 + 1.06051i
\(105\) 2.94567 8.58028i 0.287468 0.837350i
\(106\) 0.0737791 0.316523i 0.00716606 0.0307434i
\(107\) 4.00000 0.386695 0.193347 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 1.79387 + 0.884323i 0.172615 + 0.0850941i
\(109\) 4.17034i 0.399446i 0.979852 + 0.199723i \(0.0640042\pi\)
−0.979852 + 0.199723i \(0.935996\pi\)
\(110\) 2.64207 + 1.65535i 0.251912 + 0.157832i
\(111\) 0.945668 0.0897588
\(112\) 12.8719 9.88274i 1.21628 0.933831i
\(113\) 1.28526i 0.120907i 0.998171 + 0.0604537i \(0.0192548\pi\)
−0.998171 + 0.0604537i \(0.980745\pi\)
\(114\) 3.58774 + 0.836276i 0.336023 + 0.0783244i
\(115\) −2.56829 + 7.48105i −0.239495 + 0.697611i
\(116\) −6.71585 + 13.6233i −0.623551 + 1.26489i
\(117\) 4.94567 0.457227
\(118\) 12.5334 + 2.92145i 1.15379 + 0.268941i
\(119\) 18.3510 1.68223
\(120\) −5.38161 + 3.32239i −0.491272 + 0.303291i
\(121\) 10.0279 0.911630
\(122\) 15.1755 + 3.53729i 1.37392 + 0.320252i
\(123\) −0.568295 −0.0512414
\(124\) 5.89134 + 2.90425i 0.529058 + 0.260809i
\(125\) −6.11491 9.35991i −0.546934 0.837176i
\(126\) −5.58774 1.30246i −0.497796 0.116032i
\(127\) 1.15280i 0.102294i −0.998691 0.0511472i \(-0.983712\pi\)
0.998691 0.0511472i \(-0.0162878\pi\)
\(128\) −11.3078 0.364570i −0.999481 0.0322237i
\(129\) −8.45963 −0.744829
\(130\) −8.30359 + 13.2532i −0.728273 + 1.16238i
\(131\) 3.89019i 0.339887i −0.985454 0.169944i \(-0.945641\pi\)
0.985454 0.169944i \(-0.0543586\pi\)
\(132\) 0.871889 1.76865i 0.0758882 0.153941i
\(133\) −10.5683 −0.916387
\(134\) −2.71585 + 11.6514i −0.234614 + 1.00653i
\(135\) 2.11491 + 0.726062i 0.182022 + 0.0624895i
\(136\) −9.89134 8.11409i −0.848175 0.695778i
\(137\) 17.5135i 1.49628i −0.663544 0.748138i \(-0.730948\pi\)
0.663544 0.748138i \(-0.269052\pi\)
\(138\) 4.87189 + 1.13560i 0.414723 + 0.0966688i
\(139\) 16.8612i 1.43015i 0.699047 + 0.715076i \(0.253608\pi\)
−0.699047 + 0.715076i \(0.746392\pi\)
\(140\) 12.8719 12.7870i 1.08787 1.08070i
\(141\) 2.60492i 0.219374i
\(142\) 0.459630 1.97188i 0.0385713 0.165476i
\(143\) 4.87613i 0.407762i
\(144\) 2.43594 + 3.17272i 0.202995 + 0.264394i
\(145\) −5.51396 + 16.0613i −0.457910 + 1.33382i
\(146\) −16.4596 3.83662i −1.36221 0.317521i
\(147\) 9.45963 0.780217
\(148\) 1.69641 + 0.836276i 0.139444 + 0.0687415i
\(149\) 10.4986i 0.860078i −0.902810 0.430039i \(-0.858500\pi\)
0.902810 0.430039i \(-0.141500\pi\)
\(150\) −5.49652 + 4.44840i −0.448789 + 0.363210i
\(151\) 4.71585 0.383771 0.191885 0.981417i \(-0.438540\pi\)
0.191885 + 0.981417i \(0.438540\pi\)
\(152\) 5.69641 + 4.67289i 0.462040 + 0.379022i
\(153\) 4.52323i 0.365682i
\(154\) −1.28415 + 5.50917i −0.103480 + 0.443942i
\(155\) 6.94567 + 2.38449i 0.557889 + 0.191527i
\(156\) 8.87189 + 4.37357i 0.710320 + 0.350166i
\(157\) −8.94567 −0.713942 −0.356971 0.934115i \(-0.616191\pi\)
−0.356971 + 0.934115i \(0.616191\pi\)
\(158\) 1.05433 4.52323i 0.0838782 0.359849i
\(159\) −0.229815 −0.0182255
\(160\) −12.5920 + 1.20085i −0.995483 + 0.0949352i
\(161\) −14.3510 −1.13101
\(162\) 0.321037 1.37729i 0.0252230 0.108210i
\(163\) −15.7827 −1.23619 −0.618097 0.786102i \(-0.712096\pi\)
−0.618097 + 0.786102i \(0.712096\pi\)
\(164\) −1.01945 0.502556i −0.0796054 0.0392430i
\(165\) 0.715853 2.08517i 0.0557291 0.162330i
\(166\) 3.17548 13.6233i 0.246465 1.05737i
\(167\) 5.50917i 0.426312i 0.977018 + 0.213156i \(0.0683743\pi\)
−0.977018 + 0.213156i \(0.931626\pi\)
\(168\) −8.87189 7.27782i −0.684481 0.561496i
\(169\) 11.4596 0.881510
\(170\) −12.1212 7.59434i −0.929650 0.582459i
\(171\) 2.60492i 0.199203i
\(172\) −15.1755 7.48105i −1.15712 0.570425i
\(173\) 10.3385 0.786020 0.393010 0.919534i \(-0.371434\pi\)
0.393010 + 0.919534i \(0.371434\pi\)
\(174\) 10.4596 + 2.43806i 0.792943 + 0.184829i
\(175\) 12.4596 16.0078i 0.941860 1.21007i
\(176\) 3.12811 2.40169i 0.235790 0.181034i
\(177\) 9.10003i 0.684000i
\(178\) 3.96511 17.0109i 0.297198 1.27502i
\(179\) 16.1746i 1.20895i −0.796625 0.604474i \(-0.793383\pi\)
0.796625 0.604474i \(-0.206617\pi\)
\(180\) 3.15180 + 3.17272i 0.234921 + 0.236481i
\(181\) 8.11409i 0.603116i 0.953448 + 0.301558i \(0.0975067\pi\)
−0.953448 + 0.301558i \(0.902493\pi\)
\(182\) −27.6351 6.44154i −2.04845 0.477479i
\(183\) 11.0183i 0.814499i
\(184\) 7.73530 + 6.34545i 0.570254 + 0.467793i
\(185\) 2.00000 + 0.686614i 0.147043 + 0.0504808i
\(186\) 1.05433 4.52323i 0.0773074 0.331659i
\(187\) 4.45963 0.326120
\(188\) 2.30359 4.67289i 0.168007 0.340806i
\(189\) 4.05705i 0.295107i
\(190\) 6.98055 + 4.37357i 0.506423 + 0.317292i
\(191\) −24.9193 −1.80309 −0.901547 0.432681i \(-0.857568\pi\)
−0.901547 + 0.432681i \(0.857568\pi\)
\(192\) 1.56406 + 7.84562i 0.112876 + 0.566209i
\(193\) 1.03951i 0.0748254i −0.999300 0.0374127i \(-0.988088\pi\)
0.999300 0.0374127i \(-0.0119116\pi\)
\(194\) −4.45963 1.03951i −0.320183 0.0746323i
\(195\) 10.4596 + 3.59086i 0.749030 + 0.257147i
\(196\) 16.9694 + 8.36537i 1.21210 + 0.597527i
\(197\) 9.66152 0.688355 0.344177 0.938905i \(-0.388158\pi\)
0.344177 + 0.938905i \(0.388158\pi\)
\(198\) −1.35793 0.316523i −0.0965036 0.0224943i
\(199\) −23.0668 −1.63516 −0.817582 0.575813i \(-0.804686\pi\)
−0.817582 + 0.575813i \(0.804686\pi\)
\(200\) −13.7939 + 3.11916i −0.975374 + 0.220558i
\(201\) 8.45963 0.596696
\(202\) 6.00000 + 1.39856i 0.422159 + 0.0984020i
\(203\) −30.8106 −2.16248
\(204\) −4.00000 + 8.11409i −0.280056 + 0.568100i
\(205\) −1.20189 0.412617i −0.0839437 0.0288184i
\(206\) 20.7632 + 4.83975i 1.44664 + 0.337202i
\(207\) 3.53729i 0.245859i
\(208\) 12.0474 + 15.6912i 0.835335 + 1.08799i
\(209\) −2.56829 −0.177653
\(210\) −10.8719 6.81163i −0.750232 0.470047i
\(211\) 6.44154i 0.443454i 0.975109 + 0.221727i \(0.0711694\pi\)
−0.975109 + 0.221727i \(0.928831\pi\)
\(212\) −0.412259 0.203231i −0.0283140 0.0139580i
\(213\) −1.43171 −0.0980988
\(214\) 1.28415 5.50917i 0.0877825 0.376599i
\(215\) −17.8913 6.14222i −1.22018 0.418896i
\(216\) 1.79387 2.18678i 0.122057 0.148792i
\(217\) 13.3239i 0.904488i
\(218\) 5.74378 + 1.33883i 0.389018 + 0.0906772i
\(219\) 11.9507i 0.807554i
\(220\) 3.12811 3.10748i 0.210897 0.209506i
\(221\) 22.3704i 1.50480i
\(222\) 0.303594 1.30246i 0.0203759 0.0874155i
\(223\) 17.9796i 1.20401i 0.798494 + 0.602003i \(0.205630\pi\)
−0.798494 + 0.602003i \(0.794370\pi\)
\(224\) −9.47908 20.9011i −0.633347 1.39651i
\(225\) 3.94567 + 3.07111i 0.263045 + 0.204741i
\(226\) 1.77018 + 0.412617i 0.117751 + 0.0274469i
\(227\) 7.02792 0.466460 0.233230 0.972422i \(-0.425071\pi\)
0.233230 + 0.972422i \(0.425071\pi\)
\(228\) 2.30359 4.67289i 0.152559 0.309470i
\(229\) 4.17034i 0.275584i −0.990461 0.137792i \(-0.955999\pi\)
0.990461 0.137792i \(-0.0440005\pi\)
\(230\) 9.47908 + 5.93899i 0.625032 + 0.391605i
\(231\) 4.00000 0.263181
\(232\) 16.6072 + 13.6233i 1.09032 + 0.894411i
\(233\) 23.9894i 1.57160i 0.618483 + 0.785799i \(0.287748\pi\)
−0.618483 + 0.785799i \(0.712252\pi\)
\(234\) 1.58774 6.81163i 0.103794 0.445290i
\(235\) 1.89134 5.50917i 0.123377 0.359379i
\(236\) 8.04737 16.3243i 0.523839 1.06262i
\(237\) −3.28415 −0.213328
\(238\) 5.89134 25.2747i 0.381879 1.63831i
\(239\) 8.91926 0.576939 0.288469 0.957489i \(-0.406854\pi\)
0.288469 + 0.957489i \(0.406854\pi\)
\(240\) 2.84820 + 8.47866i 0.183851 + 0.547295i
\(241\) −16.3510 −1.05326 −0.526629 0.850095i \(-0.676544\pi\)
−0.526629 + 0.850095i \(0.676544\pi\)
\(242\) 3.21933 13.8114i 0.206947 0.887830i
\(243\) −1.00000 −0.0641500
\(244\) 9.74378 19.7655i 0.623781 1.26536i
\(245\) 20.0062 + 6.86828i 1.27815 + 0.438798i
\(246\) −0.182443 + 0.782708i −0.0116322 + 0.0499036i
\(247\) 12.8831i 0.819731i
\(248\) 5.89134 7.18172i 0.374100 0.456040i
\(249\) −9.89134 −0.626838
\(250\) −14.8544 + 5.41714i −0.939478 + 0.342610i
\(251\) 4.22391i 0.266611i −0.991075 0.133305i \(-0.957441\pi\)
0.991075 0.133305i \(-0.0425591\pi\)
\(252\) −3.58774 + 7.27782i −0.226006 + 0.458459i
\(253\) −3.48755 −0.219261
\(254\) −1.58774 0.370091i −0.0996238 0.0232216i
\(255\) −3.28415 + 9.56622i −0.205661 + 0.599060i
\(256\) −4.13235 + 15.4572i −0.258272 + 0.966072i
\(257\) 24.6952i 1.54044i 0.637777 + 0.770221i \(0.279854\pi\)
−0.637777 + 0.770221i \(0.720146\pi\)
\(258\) −2.71585 + 11.6514i −0.169082 + 0.725384i
\(259\) 3.83662i 0.238396i
\(260\) 15.5877 + 15.6912i 0.966711 + 0.973129i
\(261\) 7.59434i 0.470078i
\(262\) −5.35793 1.24889i −0.331014 0.0771569i
\(263\) 14.6628i 0.904145i −0.891981 0.452073i \(-0.850685\pi\)
0.891981 0.452073i \(-0.149315\pi\)
\(264\) −2.15604 1.76865i −0.132695 0.108853i
\(265\) −0.486038 0.166860i −0.0298571 0.0102501i
\(266\) −3.39281 + 14.5556i −0.208027 + 0.892463i
\(267\) −12.3510 −0.755867
\(268\) 15.1755 + 7.48105i 0.926990 + 0.456978i
\(269\) 11.5381i 0.703490i 0.936096 + 0.351745i \(0.114412\pi\)
−0.936096 + 0.351745i \(0.885588\pi\)
\(270\) 1.67896 2.67975i 0.102178 0.163085i
\(271\) 5.63511 0.342309 0.171154 0.985244i \(-0.445250\pi\)
0.171154 + 0.985244i \(0.445250\pi\)
\(272\) −14.3510 + 11.0183i −0.870155 + 0.668085i
\(273\) 20.0648i 1.21438i
\(274\) −24.1212 5.62246i −1.45721 0.339665i
\(275\) 3.02792 3.89019i 0.182591 0.234587i
\(276\) 3.12811 6.34545i 0.188290 0.381951i
\(277\) 17.4053 1.04578 0.522892 0.852399i \(-0.324853\pi\)
0.522892 + 0.852399i \(0.324853\pi\)
\(278\) 23.2229 + 5.41308i 1.39281 + 0.324655i
\(279\) −3.28415 −0.196617
\(280\) −13.4791 21.8335i −0.805529 1.30480i
\(281\) 21.7827 1.29945 0.649723 0.760171i \(-0.274885\pi\)
0.649723 + 0.760171i \(0.274885\pi\)
\(282\) −3.58774 0.836276i −0.213647 0.0497995i
\(283\) 21.5962 1.28376 0.641881 0.766804i \(-0.278154\pi\)
0.641881 + 0.766804i \(0.278154\pi\)
\(284\) −2.56829 1.26609i −0.152400 0.0751287i
\(285\) 1.89134 5.50917i 0.112033 0.326335i
\(286\) −6.71585 1.56542i −0.397117 0.0925650i
\(287\) 2.30560i 0.136095i
\(288\) 5.15180 2.33645i 0.303573 0.137676i
\(289\) −3.45963 −0.203508
\(290\) 20.3510 + 12.7506i 1.19505 + 0.748742i
\(291\) 3.23797i 0.189813i
\(292\) −10.5683 + 21.4380i −0.618463 + 1.25457i
\(293\) −32.0125 −1.87019 −0.935095 0.354398i \(-0.884686\pi\)
−0.935095 + 0.354398i \(0.884686\pi\)
\(294\) 3.03689 13.0287i 0.177115 0.759848i
\(295\) 6.60719 19.2457i 0.384685 1.12053i
\(296\) 1.69641 2.06797i 0.0986016 0.120198i
\(297\) 0.985939i 0.0572100i
\(298\) −14.4596 3.37043i −0.837624 0.195244i
\(299\) 17.4943i 1.01172i
\(300\) 4.36217 + 8.99842i 0.251850 + 0.519524i
\(301\) 34.3211i 1.97824i
\(302\) 1.51396 6.49511i 0.0871187 0.373752i
\(303\) 4.35637i 0.250267i
\(304\) 8.26470 6.34545i 0.474013 0.363936i
\(305\) 8.00000 23.3028i 0.458079 1.33431i
\(306\) 6.22982 + 1.45212i 0.356135 + 0.0830124i
\(307\) −1.13659 −0.0648686 −0.0324343 0.999474i \(-0.510326\pi\)
−0.0324343 + 0.999474i \(0.510326\pi\)
\(308\) 7.17548 + 3.53729i 0.408861 + 0.201556i
\(309\) 15.0754i 0.857609i
\(310\) 5.51396 8.80071i 0.313172 0.499847i
\(311\) 5.13659 0.291269 0.145635 0.989338i \(-0.453478\pi\)
0.145635 + 0.989338i \(0.453478\pi\)
\(312\) 8.87189 10.8151i 0.502272 0.612285i
\(313\) 23.0762i 1.30434i −0.758071 0.652172i \(-0.773858\pi\)
0.758071 0.652172i \(-0.226142\pi\)
\(314\) −2.87189 + 12.3208i −0.162070 + 0.695303i
\(315\) −2.94567 + 8.58028i −0.165970 + 0.483444i
\(316\) −5.89134 2.90425i −0.331414 0.163377i
\(317\) 1.66152 0.0933203 0.0466601 0.998911i \(-0.485142\pi\)
0.0466601 + 0.998911i \(0.485142\pi\)
\(318\) −0.0737791 + 0.316523i −0.00413733 + 0.0177497i
\(319\) −7.48755 −0.419223
\(320\) −2.38857 + 17.7284i −0.133525 + 0.991045i
\(321\) −4.00000 −0.223258
\(322\) −4.60719 + 19.7655i −0.256749 + 1.10149i
\(323\) 11.7827 0.655605
\(324\) −1.79387 0.884323i −0.0996595 0.0491291i
\(325\) 19.5140 + 15.1887i 1.08244 + 0.842516i
\(326\) −5.06682 + 21.7374i −0.280625 + 1.20392i
\(327\) 4.17034i 0.230620i
\(328\) −1.01945 + 1.24274i −0.0562895 + 0.0686187i
\(329\) 10.5683 0.582649
\(330\) −2.64207 1.65535i −0.145441 0.0911243i
\(331\) 25.9077i 1.42402i 0.702171 + 0.712008i \(0.252214\pi\)
−0.702171 + 0.712008i \(0.747786\pi\)
\(332\) −17.7438 8.74714i −0.973816 0.480062i
\(333\) −0.945668 −0.0518223
\(334\) 7.58774 + 1.76865i 0.415183 + 0.0967760i
\(335\) 17.8913 + 6.14222i 0.977508 + 0.335585i
\(336\) −12.8719 + 9.88274i −0.702219 + 0.539148i
\(337\) 8.00696i 0.436167i 0.975930 + 0.218083i \(0.0699805\pi\)
−0.975930 + 0.218083i \(0.930020\pi\)
\(338\) 3.67896 15.7833i 0.200109 0.858496i
\(339\) 1.28526i 0.0698060i
\(340\) −14.3510 + 14.2563i −0.778290 + 0.773157i
\(341\) 3.23797i 0.175346i
\(342\) −3.58774 0.836276i −0.194003 0.0452206i
\(343\) 9.97884i 0.538806i
\(344\) −15.1755 + 18.4994i −0.818207 + 0.997420i
\(345\) 2.56829 7.48105i 0.138272 0.402766i
\(346\) 3.31903 14.2391i 0.178432 0.765499i
\(347\) −23.0279 −1.23620 −0.618102 0.786098i \(-0.712098\pi\)
−0.618102 + 0.786098i \(0.712098\pi\)
\(348\) 6.71585 13.6233i 0.360007 0.730284i
\(349\) 21.4380i 1.14755i −0.819012 0.573776i \(-0.805478\pi\)
0.819012 0.573776i \(-0.194522\pi\)
\(350\) −18.0474 22.2996i −0.964673 1.19197i
\(351\) −4.94567 −0.263980
\(352\) −2.30359 5.07936i −0.122782 0.270731i
\(353\) 4.52323i 0.240747i 0.992729 + 0.120374i \(0.0384093\pi\)
−0.992729 + 0.120374i \(0.961591\pi\)
\(354\) −12.5334 2.92145i −0.666143 0.155273i
\(355\) −3.02792 1.03951i −0.160706 0.0551713i
\(356\) −22.1560 10.9222i −1.17427 0.578878i
\(357\) −18.3510 −0.971236
\(358\) −22.2772 5.19265i −1.17739 0.274440i
\(359\) −10.3510 −0.546303 −0.273152 0.961971i \(-0.588066\pi\)
−0.273152 + 0.961971i \(0.588066\pi\)
\(360\) 5.38161 3.32239i 0.283636 0.175105i
\(361\) 12.2144 0.642862
\(362\) 11.1755 + 2.60492i 0.587370 + 0.136912i
\(363\) −10.0279 −0.526330
\(364\) −17.7438 + 35.9937i −0.930027 + 1.88658i
\(365\) −8.67696 + 25.2747i −0.454173 + 1.32294i
\(366\) −15.1755 3.53729i −0.793235 0.184897i
\(367\) 0.485359i 0.0253355i −0.999920 0.0126678i \(-0.995968\pi\)
0.999920 0.0126678i \(-0.00403238\pi\)
\(368\) 11.2229 8.61665i 0.585032 0.449174i
\(369\) 0.568295 0.0295842
\(370\) 1.58774 2.53416i 0.0825427 0.131745i
\(371\) 0.932371i 0.0484063i
\(372\) −5.89134 2.90425i −0.305452 0.150578i
\(373\) −30.0823 −1.55760 −0.778800 0.627272i \(-0.784171\pi\)
−0.778800 + 0.627272i \(0.784171\pi\)
\(374\) 1.43171 6.14222i 0.0740317 0.317606i
\(375\) 6.11491 + 9.35991i 0.315772 + 0.483344i
\(376\) −5.69641 4.67289i −0.293770 0.240986i
\(377\) 37.5591i 1.93439i
\(378\) 5.58774 + 1.30246i 0.287402 + 0.0669914i
\(379\) 33.6881i 1.73044i −0.501392 0.865220i \(-0.667179\pi\)
0.501392 0.865220i \(-0.332821\pi\)
\(380\) 8.26470 8.21019i 0.423970 0.421174i
\(381\) 1.15280i 0.0590597i
\(382\) −8.00000 + 34.3211i −0.409316 + 1.75602i
\(383\) 5.17545i 0.264453i 0.991220 + 0.132227i \(0.0422127\pi\)
−0.991220 + 0.132227i \(0.957787\pi\)
\(384\) 11.3078 + 0.364570i 0.577050 + 0.0186044i
\(385\) 8.45963 + 2.90425i 0.431143 + 0.148014i
\(386\) −1.43171 0.333720i −0.0728719 0.0169859i
\(387\) 8.45963 0.430027
\(388\) −2.86341 + 5.80850i −0.145368 + 0.294882i
\(389\) 16.6408i 0.843722i 0.906660 + 0.421861i \(0.138623\pi\)
−0.906660 + 0.421861i \(0.861377\pi\)
\(390\) 8.30359 13.2532i 0.420469 0.671101i
\(391\) 16.0000 0.809155
\(392\) 16.9694 20.6862i 0.857082 1.04481i
\(393\) 3.89019i 0.196234i
\(394\) 3.10170 13.3067i 0.156262 0.670384i
\(395\) −6.94567 2.38449i −0.349474 0.119977i
\(396\) −0.871889 + 1.76865i −0.0438141 + 0.0888778i
\(397\) 20.4332 1.02551 0.512757 0.858534i \(-0.328624\pi\)
0.512757 + 0.858534i \(0.328624\pi\)
\(398\) −7.40530 + 31.7698i −0.371194 + 1.59247i
\(399\) 10.5683 0.529076
\(400\) −0.132350 + 19.9996i −0.00661751 + 0.999978i
\(401\) −4.56829 −0.228130 −0.114065 0.993473i \(-0.536387\pi\)
−0.114065 + 0.993473i \(0.536387\pi\)
\(402\) 2.71585 11.6514i 0.135454 0.581118i
\(403\) −16.2423 −0.809087
\(404\) 3.85244 7.81477i 0.191666 0.388799i
\(405\) −2.11491 0.726062i −0.105091 0.0360783i
\(406\) −9.89134 + 42.4352i −0.490899 + 2.10602i
\(407\) 0.932371i 0.0462159i
\(408\) 9.89134 + 8.11409i 0.489694 + 0.401708i
\(409\) −19.8913 −0.983563 −0.491782 0.870719i \(-0.663654\pi\)
−0.491782 + 0.870719i \(0.663654\pi\)
\(410\) −0.954146 + 1.52289i −0.0471219 + 0.0752102i
\(411\) 17.5135i 0.863875i
\(412\) 13.3315 27.0433i 0.656797 1.33233i
\(413\) 36.9193 1.81668
\(414\) −4.87189 1.13560i −0.239440 0.0558118i
\(415\) −20.9193 7.18172i −1.02689 0.352537i
\(416\) 25.4791 11.5553i 1.24921 0.566545i
\(417\) 16.8612i 0.825698i
\(418\) −0.824517 + 3.53729i −0.0403284 + 0.173015i
\(419\) 0.387288i 0.0189203i 0.999955 + 0.00946013i \(0.00301130\pi\)
−0.999955 + 0.00946013i \(0.996989\pi\)
\(420\) −12.8719 + 12.7870i −0.628084 + 0.623941i
\(421\) 12.0578i 0.587664i −0.955857 0.293832i \(-0.905069\pi\)
0.955857 0.293832i \(-0.0949306\pi\)
\(422\) 8.87189 + 2.06797i 0.431877 + 0.100667i
\(423\) 2.60492i 0.126656i
\(424\) −0.412259 + 0.502556i −0.0200210 + 0.0244063i
\(425\) −13.8913 + 17.8472i −0.673829 + 0.865715i
\(426\) −0.459630 + 1.97188i −0.0222692 + 0.0955378i
\(427\) 44.7019 2.16328
\(428\) −7.17548 3.53729i −0.346840 0.170982i
\(429\) 4.87613i 0.235422i
\(430\) −14.2034 + 22.6697i −0.684949 + 1.09323i
\(431\) 40.4068 1.94633 0.973164 0.230113i \(-0.0739096\pi\)
0.973164 + 0.230113i \(0.0739096\pi\)
\(432\) −2.43594 3.17272i −0.117199 0.152648i
\(433\) 36.1859i 1.73898i −0.493949 0.869491i \(-0.664447\pi\)
0.493949 0.869491i \(-0.335553\pi\)
\(434\) 18.3510 + 4.27748i 0.880875 + 0.205325i
\(435\) 5.51396 16.0613i 0.264374 0.770082i
\(436\) 3.68793 7.48105i 0.176620 0.358277i
\(437\) −9.21438 −0.440783
\(438\) 16.4596 + 3.83662i 0.786472 + 0.183321i
\(439\) 25.4178 1.21312 0.606562 0.795036i \(-0.292548\pi\)
0.606562 + 0.795036i \(0.292548\pi\)
\(440\) −3.27567 5.30594i −0.156161 0.252951i
\(441\) −9.45963 −0.450459
\(442\) 30.8106 + 7.18172i 1.46551 + 0.341600i
\(443\) −7.02792 −0.333907 −0.166953 0.985965i \(-0.553393\pi\)
−0.166953 + 0.985965i \(0.553393\pi\)
\(444\) −1.69641 0.836276i −0.0805079 0.0396879i
\(445\) −26.1212 8.96757i −1.23826 0.425103i
\(446\) 24.7632 + 5.77213i 1.17257 + 0.273318i
\(447\) 10.4986i 0.496566i
\(448\) −31.8300 + 6.34545i −1.50383 + 0.299794i
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 5.49652 4.44840i 0.259108 0.209700i
\(451\) 0.560304i 0.0263837i
\(452\) 1.13659 2.30560i 0.0534607 0.108446i
\(453\) −4.71585 −0.221570
\(454\) 2.25622 9.67951i 0.105890 0.454282i
\(455\) −14.5683 + 42.4352i −0.682972 + 1.98939i
\(456\) −5.69641 4.67289i −0.266759 0.218828i
\(457\) 25.2747i 1.18230i 0.806562 + 0.591149i \(0.201326\pi\)
−0.806562 + 0.591149i \(0.798674\pi\)
\(458\) −5.74378 1.33883i −0.268389 0.0625595i
\(459\) 4.52323i 0.211126i
\(460\) 11.2229 11.1488i 0.523268 0.519817i
\(461\) 41.0902i 1.91376i −0.290479 0.956881i \(-0.593815\pi\)
0.290479 0.956881i \(-0.406185\pi\)
\(462\) 1.28415 5.50917i 0.0597439 0.256310i
\(463\) 13.2106i 0.613951i 0.951717 + 0.306975i \(0.0993169\pi\)
−0.951717 + 0.306975i \(0.900683\pi\)
\(464\) 24.0947 18.4994i 1.11857 0.858813i
\(465\) −6.94567 2.38449i −0.322098 0.110578i
\(466\) 33.0404 + 7.70148i 1.53057 + 0.356764i
\(467\) −1.89134 −0.0875206 −0.0437603 0.999042i \(-0.513934\pi\)
−0.0437603 + 0.999042i \(0.513934\pi\)
\(468\) −8.87189 4.37357i −0.410103 0.202168i
\(469\) 34.3211i 1.58480i
\(470\) −6.98055 4.37357i −0.321989 0.201738i
\(471\) 8.94567 0.412195
\(472\) −19.8998 16.3243i −0.915963 0.751386i
\(473\) 8.34068i 0.383505i
\(474\) −1.05433 + 4.52323i −0.0484271 + 0.207759i
\(475\) 8.00000 10.2782i 0.367065 0.471594i
\(476\) −32.9193 16.2282i −1.50885 0.743818i
\(477\) 0.229815 0.0105225
\(478\) 2.86341 12.2844i 0.130969 0.561877i
\(479\) −31.4876 −1.43870 −0.719352 0.694646i \(-0.755561\pi\)
−0.719352 + 0.694646i \(0.755561\pi\)
\(480\) 12.5920 1.20085i 0.574743 0.0548109i
\(481\) −4.67696 −0.213251
\(482\) −5.24926 + 22.5201i −0.239097 + 1.02576i
\(483\) 14.3510 0.652992
\(484\) −17.9888 8.86793i −0.817673 0.403088i
\(485\) −2.35097 + 6.84800i −0.106752 + 0.310952i
\(486\) −0.321037 + 1.37729i −0.0145625 + 0.0624753i
\(487\) 12.9964i 0.588922i 0.955664 + 0.294461i \(0.0951401\pi\)
−0.955664 + 0.294461i \(0.904860\pi\)
\(488\) −24.0947 19.7655i −1.09072 0.894741i
\(489\) 15.7827 0.713717
\(490\) 15.8824 25.3495i 0.717492 1.14517i
\(491\) 14.9085i 0.672812i 0.941717 + 0.336406i \(0.109212\pi\)
−0.941717 + 0.336406i \(0.890788\pi\)
\(492\) 1.01945 + 0.502556i 0.0459602 + 0.0226570i
\(493\) 34.3510 1.54709
\(494\) −17.7438 4.13594i −0.798330 0.186085i
\(495\) −0.715853 + 2.08517i −0.0321752 + 0.0937214i
\(496\) −8.00000 10.4197i −0.359211 0.467858i
\(497\) 5.80850i 0.260547i
\(498\) −3.17548 + 13.6233i −0.142297 + 0.610473i
\(499\) 35.6599i 1.59636i 0.602420 + 0.798179i \(0.294203\pi\)
−0.602420 + 0.798179i \(0.705797\pi\)
\(500\) 2.69217 + 22.1980i 0.120397 + 0.992726i
\(501\) 5.50917i 0.246132i
\(502\) −5.81756 1.35603i −0.259650 0.0605226i
\(503\) 25.3090i 1.12847i 0.825613 + 0.564237i \(0.190830\pi\)
−0.825613 + 0.564237i \(0.809170\pi\)
\(504\) 8.87189 + 7.27782i 0.395185 + 0.324180i
\(505\) 3.16300 9.21332i 0.140751 0.409988i
\(506\) −1.11963 + 4.80338i −0.0497738 + 0.213536i
\(507\) −11.4596 −0.508940
\(508\) −1.01945 + 2.06797i −0.0452306 + 0.0917514i
\(509\) 13.7366i 0.608862i 0.952534 + 0.304431i \(0.0984663\pi\)
−0.952534 + 0.304431i \(0.901534\pi\)
\(510\) 12.1212 + 7.59434i 0.536734 + 0.336283i
\(511\) −48.4846 −2.14483
\(512\) 19.9624 + 10.6538i 0.882221 + 0.470835i
\(513\) 2.60492i 0.115010i
\(514\) 34.0125 + 7.92806i 1.50023 + 0.349692i
\(515\) 10.9457 31.8831i 0.482324 1.40494i
\(516\) 15.1755 + 7.48105i 0.668063 + 0.329335i
\(517\) 2.56829 0.112953
\(518\) 5.28415 + 1.23170i 0.232172 + 0.0541176i
\(519\) −10.3385 −0.453809
\(520\) 26.6157 16.4314i 1.16717 0.720565i
\(521\) −30.9193 −1.35460 −0.677299 0.735708i \(-0.736850\pi\)
−0.677299 + 0.735708i \(0.736850\pi\)
\(522\) −10.4596 2.43806i −0.457806 0.106711i
\(523\) 21.8385 0.954932 0.477466 0.878650i \(-0.341555\pi\)
0.477466 + 0.878650i \(0.341555\pi\)
\(524\) −3.44018 + 6.97849i −0.150285 + 0.304857i
\(525\) −12.4596 + 16.0078i −0.543783 + 0.698636i
\(526\) −20.1949 4.70729i −0.880541 0.205248i
\(527\) 14.8550i 0.647092i
\(528\) −3.12811 + 2.40169i −0.136134 + 0.104520i
\(529\) 10.4876 0.455981
\(530\) −0.385851 + 0.615848i −0.0167603 + 0.0267507i
\(531\) 9.10003i 0.394908i
\(532\) 18.9582 + 9.34579i 0.821940 + 0.405191i
\(533\) 2.81060 0.121740
\(534\) −3.96511 + 17.0109i −0.171587 + 0.736133i
\(535\) −8.45963 2.90425i −0.365742 0.125562i
\(536\) 15.1755 18.4994i 0.655481 0.799052i
\(537\) 16.1746i 0.697986i
\(538\) 15.8913 + 3.70415i 0.685124 + 0.159697i
\(539\) 9.32662i 0.401726i
\(540\) −3.15180 3.17272i −0.135632 0.136532i
\(541\) 24.3423i 1.04656i 0.852162 + 0.523278i \(0.175291\pi\)
−0.852162 + 0.523278i \(0.824709\pi\)
\(542\) 1.80908 7.76120i 0.0777066 0.333372i
\(543\) 8.11409i 0.348209i
\(544\) 10.5683 + 23.3028i 0.453112 + 0.999098i
\(545\) 3.02792 8.81988i 0.129702 0.377802i
\(546\) 27.6351 + 6.44154i 1.18267 + 0.275673i
\(547\) −33.3789 −1.42718 −0.713589 0.700564i \(-0.752932\pi\)
−0.713589 + 0.700564i \(0.752932\pi\)
\(548\) −15.4876 + 31.4169i −0.661596 + 1.34206i
\(549\) 11.0183i 0.470251i
\(550\) −4.38585 5.41923i −0.187013 0.231077i
\(551\) −19.7827 −0.842770
\(552\) −7.73530 6.34545i −0.329236 0.270080i
\(553\) 13.3239i 0.566592i
\(554\) 5.58774 23.9722i 0.237400 1.01848i
\(555\) −2.00000 0.686614i −0.0848953 0.0291451i
\(556\) 14.9108 30.2469i 0.632358 1.28275i
\(557\) −30.5808 −1.29575 −0.647875 0.761747i \(-0.724342\pi\)
−0.647875 + 0.761747i \(0.724342\pi\)
\(558\) −1.05433 + 4.52323i −0.0446334 + 0.191484i
\(559\) 41.8385 1.76958
\(560\) −34.3983 + 11.5553i −1.45360 + 0.488300i
\(561\) −4.45963 −0.188286
\(562\) 6.99304 30.0011i 0.294984 1.26552i
\(563\) 7.02792 0.296192 0.148096 0.988973i \(-0.452686\pi\)
0.148096 + 0.988973i \(0.452686\pi\)
\(564\) −2.30359 + 4.67289i −0.0969988 + 0.196764i
\(565\) 0.933181 2.71821i 0.0392592 0.114356i
\(566\) 6.93318 29.7443i 0.291423 1.25025i
\(567\) 4.05705i 0.170380i
\(568\) −2.56829 + 3.13083i −0.107763 + 0.131367i
\(569\) −24.3510 −1.02085 −0.510423 0.859924i \(-0.670511\pi\)
−0.510423 + 0.859924i \(0.670511\pi\)
\(570\) −6.98055 4.37357i −0.292383 0.183189i
\(571\) 20.0992i 0.841125i 0.907263 + 0.420563i \(0.138167\pi\)
−0.907263 + 0.420563i \(0.861833\pi\)
\(572\) −4.31207 + 8.74714i −0.180297 + 0.365736i
\(573\) 24.9193 1.04102
\(574\) −3.17548 0.740182i −0.132542 0.0308946i
\(575\) 10.8634 13.9570i 0.453036 0.582047i
\(576\) −1.56406 7.84562i −0.0651690 0.326901i
\(577\) 4.76899i 0.198536i −0.995061 0.0992678i \(-0.968350\pi\)
0.995061 0.0992678i \(-0.0316501\pi\)
\(578\) −1.11067 + 4.76492i −0.0461977 + 0.198195i
\(579\) 1.03951i 0.0432004i
\(580\) 24.0947 23.9358i 1.00048 0.993881i
\(581\) 40.1296i 1.66486i
\(582\) 4.45963 + 1.03951i 0.184858 + 0.0430890i
\(583\) 0.226584i 0.00938413i
\(584\) 26.1336 + 21.4380i 1.08142 + 0.887112i
\(585\) −10.4596 3.59086i −0.432452 0.148464i
\(586\) −10.2772 + 44.0906i −0.424547 + 1.82136i
\(587\) 8.21733 0.339165 0.169583 0.985516i \(-0.445758\pi\)
0.169583 + 0.985516i \(0.445758\pi\)
\(588\) −16.9694 8.36537i −0.699804 0.344982i
\(589\) 8.55495i 0.352501i
\(590\) −24.3859 15.2786i −1.00395 0.629011i
\(591\) −9.66152 −0.397422
\(592\) −2.30359 3.00034i −0.0946771 0.123313i
\(593\) 7.76120i 0.318714i 0.987221 + 0.159357i \(0.0509421\pi\)
−0.987221 + 0.159357i \(0.949058\pi\)
\(594\) 1.35793 + 0.316523i 0.0557164 + 0.0129871i
\(595\) −38.8106 13.3239i −1.59108 0.546228i
\(596\) −9.28415 + 18.8331i −0.380293 + 0.771434i
\(597\) 23.0668 0.944062
\(598\) −24.0947 5.61631i −0.985307 0.229668i
\(599\) 5.64903 0.230813 0.115407 0.993318i \(-0.463183\pi\)
0.115407 + 0.993318i \(0.463183\pi\)
\(600\) 13.7939 3.11916i 0.563132 0.127339i
\(601\) −37.7299 −1.53903 −0.769516 0.638627i \(-0.779503\pi\)
−0.769516 + 0.638627i \(0.779503\pi\)
\(602\) −47.2702 11.0183i −1.92659 0.449074i
\(603\) −8.45963 −0.344503
\(604\) −8.45963 4.17034i −0.344217 0.169689i
\(605\) −21.2081 7.28090i −0.862233 0.296010i
\(606\) −6.00000 1.39856i −0.243733 0.0568124i
\(607\) 0.113292i 0.00459837i −0.999997 0.00229919i \(-0.999268\pi\)
0.999997 0.00229919i \(-0.000731854\pi\)
\(608\) −6.08627 13.4200i −0.246831 0.544254i
\(609\) 30.8106 1.24851
\(610\) −29.5264 18.4994i −1.19549 0.749018i
\(611\) 12.8831i 0.521194i
\(612\) 4.00000 8.11409i 0.161690 0.327993i
\(613\) −0.703366 −0.0284087 −0.0142044 0.999899i \(-0.504522\pi\)
−0.0142044 + 0.999899i \(0.504522\pi\)
\(614\) −0.364887 + 1.56542i −0.0147256 + 0.0631750i
\(615\) 1.20189 + 0.412617i 0.0484649 + 0.0166383i
\(616\) 7.17548 8.74714i 0.289108 0.352432i
\(617\) 24.4809i 0.985564i 0.870153 + 0.492782i \(0.164020\pi\)
−0.870153 + 0.492782i \(0.835980\pi\)
\(618\) −20.7632 4.83975i −0.835219 0.194683i
\(619\) 39.4966i 1.58750i −0.608243 0.793751i \(-0.708126\pi\)
0.608243 0.793751i \(-0.291874\pi\)
\(620\) −10.3510 10.4197i −0.415705 0.418465i
\(621\) 3.53729i 0.141947i
\(622\) 1.64903 7.07459i 0.0661202 0.283665i
\(623\) 50.1084i 2.00755i
\(624\) −12.0474 15.6912i −0.482281 0.628152i
\(625\) 6.13659 + 24.2351i 0.245464 + 0.969406i
\(626\) −31.7827 7.40831i −1.27029 0.296095i
\(627\) 2.56829 0.102568
\(628\) 16.0474 + 7.91086i 0.640360 + 0.315678i
\(629\) 4.27748i 0.170554i
\(630\) 10.8719 + 6.81163i 0.433146 + 0.271382i
\(631\) 17.3400 0.690294 0.345147 0.938549i \(-0.387829\pi\)
0.345147 + 0.938549i \(0.387829\pi\)
\(632\) −5.89134 + 7.18172i −0.234345 + 0.285674i
\(633\) 6.44154i 0.256028i
\(634\) 0.533409 2.28840i 0.0211844 0.0908840i
\(635\) −0.837003 + 2.43806i −0.0332155 + 0.0967516i
\(636\) 0.412259 + 0.203231i 0.0163471 + 0.00805863i
\(637\) −46.7842 −1.85366
\(638\) −2.40378 + 10.3126i −0.0951666 + 0.408278i
\(639\) 1.43171 0.0566374
\(640\) 23.6503 + 8.98122i 0.934861 + 0.355014i
\(641\) 38.7019 1.52863 0.764317 0.644840i \(-0.223076\pi\)
0.764317 + 0.644840i \(0.223076\pi\)
\(642\) −1.28415 + 5.50917i −0.0506812 + 0.217430i
\(643\) −1.13659 −0.0448227 −0.0224113 0.999749i \(-0.507134\pi\)
−0.0224113 + 0.999749i \(0.507134\pi\)
\(644\) 25.7438 + 12.6909i 1.01445 + 0.500091i
\(645\) 17.8913 + 6.14222i 0.704471 + 0.241850i
\(646\) 3.78267 16.2282i 0.148827 0.638490i
\(647\) 6.54868i 0.257455i 0.991680 + 0.128728i \(0.0410893\pi\)
−0.991680 + 0.128728i \(0.958911\pi\)
\(648\) −1.79387 + 2.18678i −0.0704699 + 0.0859050i
\(649\) 8.97208 0.352185
\(650\) 27.1840 22.0003i 1.06624 0.862923i
\(651\) 13.3239i 0.522206i
\(652\) 28.3121 + 13.9570i 1.10879 + 0.546598i
\(653\) 8.74226 0.342111 0.171056 0.985261i \(-0.445282\pi\)
0.171056 + 0.985261i \(0.445282\pi\)
\(654\) −5.74378 1.33883i −0.224599 0.0523525i
\(655\) −2.82452 + 8.22739i −0.110363 + 0.321471i
\(656\) 1.38433 + 1.80304i 0.0540492 + 0.0703969i
\(657\) 11.9507i 0.466242i
\(658\) 3.39281 14.5556i 0.132266 0.567438i
\(659\) 35.5336i 1.38419i 0.721804 + 0.692097i \(0.243313\pi\)
−0.721804 + 0.692097i \(0.756687\pi\)
\(660\) −3.12811 + 3.10748i −0.121762 + 0.120958i
\(661\) 23.3028i 0.906373i −0.891416 0.453186i \(-0.850287\pi\)
0.891416 0.453186i \(-0.149713\pi\)
\(662\) 35.6825 + 8.31732i 1.38684 + 0.323262i
\(663\) 22.3704i 0.868795i
\(664\) −17.7438 + 21.6302i −0.688592 + 0.839415i
\(665\) 22.3510 + 7.67324i 0.866733 + 0.297555i
\(666\) −0.303594 + 1.30246i −0.0117640 + 0.0504694i
\(667\) −26.8634 −1.04016
\(668\) 4.87189 9.88274i 0.188499 0.382375i
\(669\) 17.9796i 0.695133i
\(670\) 14.2034 22.6697i 0.548726 0.875808i
\(671\) 10.8634 0.419377
\(672\) 9.47908 + 20.9011i 0.365663 + 0.806277i
\(673\) 14.3634i 0.553670i 0.960917 + 0.276835i \(0.0892856\pi\)
−0.960917 + 0.276835i \(0.910714\pi\)
\(674\) 11.0279 + 2.57053i 0.424780 + 0.0990130i
\(675\) −3.94567 3.07111i −0.151869 0.118207i
\(676\) −20.5571 10.1340i −0.790658 0.389770i
\(677\) 24.3076 0.934217 0.467109 0.884200i \(-0.345296\pi\)
0.467109 + 0.884200i \(0.345296\pi\)
\(678\) −1.77018 0.412617i −0.0679835 0.0158465i
\(679\) −13.1366 −0.504136
\(680\) 15.0279 + 24.3423i 0.576295 + 0.933484i
\(681\) −7.02792 −0.269311
\(682\) 4.45963 + 1.03951i 0.170768 + 0.0398048i
\(683\) 38.5933 1.47673 0.738365 0.674401i \(-0.235598\pi\)
0.738365 + 0.674401i \(0.235598\pi\)
\(684\) −2.30359 + 4.67289i −0.0880801 + 0.178673i
\(685\) −12.7159 + 37.0393i −0.485848 + 1.41520i
\(686\) 13.7438 + 3.20357i 0.524740 + 0.122313i
\(687\) 4.17034i 0.159108i
\(688\) 20.6072 + 26.8401i 0.785642 + 1.02327i
\(689\) 1.13659 0.0433006
\(690\) −9.47908 5.93899i −0.360862 0.226093i
\(691\) 13.4090i 0.510102i 0.966928 + 0.255051i \(0.0820923\pi\)
−0.966928 + 0.255051i \(0.917908\pi\)
\(692\) −18.5459 9.14256i −0.705009 0.347548i
\(693\) −4.00000 −0.151947
\(694\) −7.39281 + 31.7162i −0.280627 + 1.20393i
\(695\) 12.2423 35.6599i 0.464377 1.35266i
\(696\) −16.6072 13.6233i −0.629494 0.516389i
\(697\) 2.57053i 0.0973657i
\(698\) −29.5264 6.88240i −1.11759 0.260503i
\(699\) 23.9894i 0.907362i
\(700\) −36.5070 + 17.6975i −1.37983 + 0.668903i
\(701\) 15.6013i 0.589253i −0.955613 0.294626i \(-0.904805\pi\)
0.955613 0.294626i \(-0.0951952\pi\)
\(702\) −1.58774 + 6.81163i −0.0599254 + 0.257089i
\(703\) 2.46339i 0.0929086i
\(704\) −7.73530 + 1.54206i −0.291535 + 0.0581187i
\(705\) −1.89134 + 5.50917i −0.0712318 + 0.207487i
\(706\) 6.22982 + 1.45212i 0.234462 + 0.0546514i
\(707\) 17.6740 0.664699
\(708\) −8.04737 + 16.3243i −0.302439 + 0.613504i
\(709\) 15.7873i 0.592906i −0.955047 0.296453i \(-0.904196\pi\)
0.955047 0.296453i \(-0.0958038\pi\)
\(710\) −2.40378 + 3.83662i −0.0902123 + 0.143986i
\(711\) 3.28415 0.123165
\(712\) −22.1560 + 27.0089i −0.830333 + 1.01220i
\(713\) 11.6170i 0.435060i
\(714\) −5.89134 + 25.2747i −0.220478 + 0.945880i
\(715\) −3.54037 + 10.3126i −0.132402 + 0.385668i
\(716\) −14.3036 + 29.0152i −0.534550 + 1.08435i
\(717\) −8.91926 −0.333096
\(718\) −3.32304 + 14.2563i −0.124015 + 0.532041i
\(719\) −22.5683 −0.841655 −0.420828 0.907141i \(-0.638260\pi\)
−0.420828 + 0.907141i \(0.638260\pi\)
\(720\) −2.84820 8.47866i −0.106146 0.315981i
\(721\) 61.1616 2.27778
\(722\) 3.92126 16.8228i 0.145934 0.626079i
\(723\) 16.3510 0.608099
\(724\) 7.17548 14.5556i 0.266675 0.540956i
\(725\) 23.3230 29.9647i 0.866196 1.11286i
\(726\) −3.21933 + 13.8114i −0.119481 + 0.512589i
\(727\) 2.79096i 0.103511i 0.998660 + 0.0517554i \(0.0164816\pi\)
−0.998660 + 0.0517554i \(0.983518\pi\)
\(728\) 43.8774 + 35.9937i 1.62621 + 1.33401i
\(729\) 1.00000 0.0370370
\(730\) 32.0250 + 20.0648i 1.18530 + 0.742632i
\(731\) 38.2649i 1.41528i
\(732\) −9.74378 + 19.7655i −0.360140 + 0.730553i
\(733\) 16.4860 0.608926 0.304463 0.952524i \(-0.401523\pi\)
0.304463 + 0.952524i \(0.401523\pi\)
\(734\) −0.668481 0.155818i −0.0246741 0.00575135i
\(735\) −20.0062 6.86828i −0.737941 0.253340i
\(736\) −8.26470 18.2234i −0.304641 0.671724i
\(737\) 8.34068i 0.307233i
\(738\) 0.182443 0.782708i 0.00671584 0.0288119i
\(739\) 14.8894i 0.547714i −0.961770 0.273857i \(-0.911701\pi\)
0.961770 0.273857i \(-0.0882995\pi\)
\(740\) −2.98055 3.00034i −0.109567 0.110295i
\(741\) 12.8831i 0.473272i
\(742\) −1.28415 0.299325i −0.0471425 0.0109886i
\(743\) 41.4301i 1.51992i −0.649968 0.759961i \(-0.725218\pi\)
0.649968 0.759961i \(-0.274782\pi\)
\(744\) −5.89134 + 7.18172i −0.215987 + 0.263295i
\(745\) −7.62263 + 22.2035i −0.279271 + 0.813475i
\(746\) −9.65751 + 41.4321i −0.353587 + 1.51694i
\(747\) 9.89134 0.361905
\(748\) −8.00000 3.94376i −0.292509 0.144198i
\(749\) 16.2282i 0.592965i
\(750\) 14.8544 5.41714i 0.542408 0.197806i
\(751\) 30.5544 1.11494 0.557472 0.830195i \(-0.311771\pi\)
0.557472 + 0.830195i \(0.311771\pi\)
\(752\) −8.26470 + 6.34545i −0.301383 + 0.231395i
\(753\) 4.22391i 0.153928i
\(754\) −51.7299 12.0578i −1.88389 0.439121i
\(755\) −9.97359 3.42400i −0.362976 0.124612i
\(756\) 3.58774 7.27782i 0.130485 0.264692i
\(757\) −0.433223 −0.0157457 −0.00787287 0.999969i \(-0.502506\pi\)
−0.00787287 + 0.999969i \(0.502506\pi\)
\(758\) −46.3983 10.8151i −1.68526 0.392823i
\(759\) 3.48755 0.126590
\(760\) −8.65456 14.0187i −0.313934 0.508511i
\(761\) −14.9193 −0.540823 −0.270411 0.962745i \(-0.587160\pi\)
−0.270411 + 0.962745i \(0.587160\pi\)
\(762\) 1.58774 + 0.370091i 0.0575178 + 0.0134070i
\(763\) 16.9193 0.612518
\(764\) 44.7019 + 22.0367i 1.61726 + 0.797259i
\(765\) 3.28415 9.56622i 0.118739 0.345867i
\(766\) 7.12811 + 1.66151i 0.257549 + 0.0600328i
\(767\) 45.0057i 1.62506i
\(768\) 4.13235 15.4572i 0.149113 0.557762i
\(769\) 31.3789 1.13155 0.565776 0.824559i \(-0.308577\pi\)
0.565776 + 0.824559i \(0.308577\pi\)
\(770\) 6.71585 10.7190i 0.242023 0.386287i
\(771\) 24.6952i 0.889375i
\(772\) −0.919260 + 1.86474i −0.0330849 + 0.0671135i
\(773\) −13.4192 −0.482656 −0.241328 0.970444i \(-0.577583\pi\)
−0.241328 + 0.970444i \(0.577583\pi\)
\(774\) 2.71585 11.6514i 0.0976193 0.418800i
\(775\) −12.9582 10.0860i −0.465471 0.362299