Properties

Label 349.2.e.a.123.14
Level 349
Weight 2
Character 349.123
Analytic conductor 2.787
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.78677903054\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 123.14
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.14

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.327556 + 0.189114i) q^{2} +(-1.06274 + 1.84073i) q^{3} +(-0.928472 + 1.60816i) q^{4} +(-1.07891 + 1.86873i) q^{5} -0.803920i q^{6} +(-2.19494 + 1.26725i) q^{7} -1.45881i q^{8} +(-0.758847 - 1.31436i) q^{9} +O(q^{10})\) \(q+(-0.327556 + 0.189114i) q^{2} +(-1.06274 + 1.84073i) q^{3} +(-0.928472 + 1.60816i) q^{4} +(-1.07891 + 1.86873i) q^{5} -0.803920i q^{6} +(-2.19494 + 1.26725i) q^{7} -1.45881i q^{8} +(-0.758847 - 1.31436i) q^{9} -0.816152i q^{10} +1.09898i q^{11} +(-1.97345 - 3.41812i) q^{12} +(5.04525 - 2.91287i) q^{13} +(0.479309 - 0.830187i) q^{14} +(-2.29322 - 3.97197i) q^{15} +(-1.58106 - 2.73848i) q^{16} +0.593876 q^{17} +(0.497129 + 0.287018i) q^{18} +(-0.552681 + 0.957272i) q^{19} +(-2.00348 - 3.47013i) q^{20} -5.38703i q^{21} +(-0.207833 - 0.359978i) q^{22} +(1.80243 + 3.12190i) q^{23} +(2.68526 + 1.55034i) q^{24} +(0.171890 + 0.297723i) q^{25} +(-1.10173 + 1.90826i) q^{26} -3.15062 q^{27} -4.70641i q^{28} +(0.325504 - 0.563790i) q^{29} +(1.50231 + 0.867360i) q^{30} -1.48782 q^{31} +(3.56250 + 2.05681i) q^{32} +(-2.02292 - 1.16794i) q^{33} +(-0.194527 + 0.112310i) q^{34} -5.46900i q^{35} +2.81827 q^{36} -1.94389 q^{37} -0.418080i q^{38} +12.3826i q^{39} +(2.72612 + 1.57393i) q^{40} -4.81147 q^{41} +(1.01876 + 1.76455i) q^{42} +(-9.90857 - 5.72071i) q^{43} +(-1.76734 - 1.02037i) q^{44} +3.27492 q^{45} +(-1.18079 - 0.681730i) q^{46} +5.11421i q^{47} +6.72105 q^{48} +(-0.288172 + 0.499129i) q^{49} +(-0.112607 - 0.0650139i) q^{50} +(-0.631137 + 1.09316i) q^{51} +10.8181i q^{52} +1.09802i q^{53} +(1.03200 - 0.595828i) q^{54} +(-2.05370 - 1.18571i) q^{55} +(1.84867 + 3.20199i) q^{56} +(-1.17472 - 2.03467i) q^{57} +0.246230i q^{58} +(-0.459159 - 0.265095i) q^{59} +8.51675 q^{60} +3.54861i q^{61} +(0.487345 - 0.281369i) q^{62} +(3.33124 + 1.92329i) q^{63} +4.76836 q^{64} +12.5710i q^{65} +0.883494 q^{66} +9.41324 q^{67} +(-0.551397 + 0.955047i) q^{68} -7.66207 q^{69} +(1.03427 + 1.79140i) q^{70} +(-7.34903 + 4.24296i) q^{71} +(-1.91740 + 1.10701i) q^{72} +(5.47740 - 9.48714i) q^{73} +(0.636733 - 0.367618i) q^{74} -0.730702 q^{75} +(-1.02630 - 1.77760i) q^{76} +(-1.39268 - 2.41219i) q^{77} +(-2.34172 - 4.05597i) q^{78} -5.94744i q^{79} +6.82332 q^{80} +(5.62484 - 9.74251i) q^{81} +(1.57602 - 0.909917i) q^{82} +(5.88545 + 10.1939i) q^{83} +(8.66321 + 5.00171i) q^{84} +(-0.640741 + 1.10980i) q^{85} +4.32748 q^{86} +(0.691855 + 1.19833i) q^{87} +1.60320 q^{88} +(-1.27263 - 0.734755i) q^{89} +(-1.07272 + 0.619335i) q^{90} +(-7.38266 + 12.7871i) q^{91} -6.69401 q^{92} +(1.58117 - 2.73867i) q^{93} +(-0.967170 - 1.67519i) q^{94} +(-1.19259 - 2.06563i) q^{95} +(-7.57204 + 4.37172i) q^{96} +(6.45122 - 3.72462i) q^{97} -0.217990i q^{98} +(1.44446 - 0.833959i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} + O(q^{10}) \) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} - q^{12} - 3q^{13} - 10q^{14} + q^{15} - 29q^{16} - 10q^{17} + 15q^{18} - 9q^{19} - 3q^{22} - 17q^{23} - 48q^{24} - 29q^{25} - 4q^{26} + 18q^{27} - 2q^{29} + 9q^{30} + 32q^{31} + 9q^{32} - 12q^{33} - 63q^{34} + 24q^{36} - 16q^{37} + 54q^{40} - 10q^{41} - 15q^{42} - 45q^{43} + 18q^{44} - 2q^{45} + 27q^{46} + 6q^{48} + 35q^{49} + 6q^{50} - 14q^{51} + 27q^{54} + 24q^{55} + 11q^{56} - 29q^{57} - 18q^{59} + 116q^{60} - 9q^{62} - 21q^{63} - 132q^{64} + 130q^{66} + 58q^{67} + 42q^{69} + 40q^{70} - 24q^{71} + 72q^{72} - 6q^{73} + 30q^{74} - 58q^{75} + 37q^{76} - 4q^{77} - 33q^{78} - 40q^{80} - 81q^{81} + 21q^{82} + 12q^{83} + 18q^{84} - 11q^{85} - 126q^{86} - 42q^{87} - 50q^{88} + 3q^{89} - 12q^{90} - 28q^{91} - 120q^{92} + 31q^{93} + 29q^{94} + 60q^{95} - 120q^{96} - 15q^{97} + 39q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.327556 + 0.189114i −0.231617 + 0.133724i −0.611318 0.791385i \(-0.709360\pi\)
0.379701 + 0.925109i \(0.376027\pi\)
\(3\) −1.06274 + 1.84073i −0.613575 + 1.06274i 0.377058 + 0.926190i \(0.376936\pi\)
−0.990633 + 0.136554i \(0.956397\pi\)
\(4\) −0.928472 + 1.60816i −0.464236 + 0.804080i
\(5\) −1.07891 + 1.86873i −0.482505 + 0.835723i −0.999798 0.0200852i \(-0.993606\pi\)
0.517293 + 0.855808i \(0.326940\pi\)
\(6\) 0.803920i 0.328199i
\(7\) −2.19494 + 1.26725i −0.829608 + 0.478974i −0.853718 0.520735i \(-0.825658\pi\)
0.0241107 + 0.999709i \(0.492325\pi\)
\(8\) 1.45881i 0.515766i
\(9\) −0.758847 1.31436i −0.252949 0.438121i
\(10\) 0.816152i 0.258090i
\(11\) 1.09898i 0.331356i 0.986180 + 0.165678i \(0.0529812\pi\)
−0.986180 + 0.165678i \(0.947019\pi\)
\(12\) −1.97345 3.41812i −0.569687 0.986727i
\(13\) 5.04525 2.91287i 1.39930 0.807886i 0.404980 0.914325i \(-0.367278\pi\)
0.994319 + 0.106439i \(0.0339450\pi\)
\(14\) 0.479309 0.830187i 0.128101 0.221877i
\(15\) −2.29322 3.97197i −0.592106 1.02556i
\(16\) −1.58106 2.73848i −0.395265 0.684620i
\(17\) 0.593876 0.144036 0.0720180 0.997403i \(-0.477056\pi\)
0.0720180 + 0.997403i \(0.477056\pi\)
\(18\) 0.497129 + 0.287018i 0.117174 + 0.0676507i
\(19\) −0.552681 + 0.957272i −0.126794 + 0.219613i −0.922433 0.386158i \(-0.873802\pi\)
0.795639 + 0.605771i \(0.207135\pi\)
\(20\) −2.00348 3.47013i −0.447992 0.775945i
\(21\) 5.38703i 1.17555i
\(22\) −0.207833 0.359978i −0.0443102 0.0767475i
\(23\) 1.80243 + 3.12190i 0.375832 + 0.650960i 0.990451 0.137864i \(-0.0440236\pi\)
−0.614619 + 0.788824i \(0.710690\pi\)
\(24\) 2.68526 + 1.55034i 0.548127 + 0.316461i
\(25\) 0.171890 + 0.297723i 0.0343781 + 0.0595446i
\(26\) −1.10173 + 1.90826i −0.216068 + 0.374240i
\(27\) −3.15062 −0.606337
\(28\) 4.70641i 0.889428i
\(29\) 0.325504 0.563790i 0.0604446 0.104693i −0.834220 0.551432i \(-0.814081\pi\)
0.894664 + 0.446739i \(0.147415\pi\)
\(30\) 1.50231 + 0.867360i 0.274283 + 0.158358i
\(31\) −1.48782 −0.267221 −0.133611 0.991034i \(-0.542657\pi\)
−0.133611 + 0.991034i \(0.542657\pi\)
\(32\) 3.56250 + 2.05681i 0.629767 + 0.363596i
\(33\) −2.02292 1.16794i −0.352146 0.203312i
\(34\) −0.194527 + 0.112310i −0.0333612 + 0.0192611i
\(35\) 5.46900i 0.924430i
\(36\) 2.81827 0.469712
\(37\) −1.94389 −0.319574 −0.159787 0.987152i \(-0.551081\pi\)
−0.159787 + 0.987152i \(0.551081\pi\)
\(38\) 0.418080i 0.0678215i
\(39\) 12.3826i 1.98280i
\(40\) 2.72612 + 1.57393i 0.431037 + 0.248860i
\(41\) −4.81147 −0.751425 −0.375712 0.926736i \(-0.622602\pi\)
−0.375712 + 0.926736i \(0.622602\pi\)
\(42\) 1.01876 + 1.76455i 0.157199 + 0.272276i
\(43\) −9.90857 5.72071i −1.51104 0.872401i −0.999917 0.0128949i \(-0.995895\pi\)
−0.511126 0.859506i \(-0.670771\pi\)
\(44\) −1.76734 1.02037i −0.266436 0.153827i
\(45\) 3.27492 0.488196
\(46\) −1.18079 0.681730i −0.174098 0.100516i
\(47\) 5.11421i 0.745984i 0.927835 + 0.372992i \(0.121668\pi\)
−0.927835 + 0.372992i \(0.878332\pi\)
\(48\) 6.72105 0.970100
\(49\) −0.288172 + 0.499129i −0.0411675 + 0.0713042i
\(50\) −0.112607 0.0650139i −0.0159251 0.00919435i
\(51\) −0.631137 + 1.09316i −0.0883769 + 0.153073i
\(52\) 10.8181i 1.50020i
\(53\) 1.09802i 0.150825i 0.997152 + 0.0754126i \(0.0240274\pi\)
−0.997152 + 0.0754126i \(0.975973\pi\)
\(54\) 1.03200 0.595828i 0.140438 0.0810819i
\(55\) −2.05370 1.18571i −0.276921 0.159881i
\(56\) 1.84867 + 3.20199i 0.247039 + 0.427883i
\(57\) −1.17472 2.03467i −0.155595 0.269498i
\(58\) 0.246230i 0.0323316i
\(59\) −0.459159 0.265095i −0.0597774 0.0345125i 0.469813 0.882766i \(-0.344321\pi\)
−0.529591 + 0.848253i \(0.677655\pi\)
\(60\) 8.51675 1.09951
\(61\) 3.54861i 0.454353i 0.973854 + 0.227177i \(0.0729495\pi\)
−0.973854 + 0.227177i \(0.927051\pi\)
\(62\) 0.487345 0.281369i 0.0618929 0.0357339i
\(63\) 3.33124 + 1.92329i 0.419697 + 0.242312i
\(64\) 4.76836 0.596045
\(65\) 12.5710i 1.55924i
\(66\) 0.883494 0.108751
\(67\) 9.41324 1.15001 0.575005 0.818150i \(-0.305000\pi\)
0.575005 + 0.818150i \(0.305000\pi\)
\(68\) −0.551397 + 0.955047i −0.0668667 + 0.115816i
\(69\) −7.66207 −0.922405
\(70\) 1.03427 + 1.79140i 0.123618 + 0.214113i
\(71\) −7.34903 + 4.24296i −0.872169 + 0.503547i −0.868069 0.496444i \(-0.834639\pi\)
−0.00410080 + 0.999992i \(0.501305\pi\)
\(72\) −1.91740 + 1.10701i −0.225968 + 0.130462i
\(73\) 5.47740 9.48714i 0.641081 1.11039i −0.344111 0.938929i \(-0.611819\pi\)
0.985192 0.171456i \(-0.0548472\pi\)
\(74\) 0.636733 0.367618i 0.0740187 0.0427347i
\(75\) −0.730702 −0.0843741
\(76\) −1.02630 1.77760i −0.117724 0.203905i
\(77\) −1.39268 2.41219i −0.158711 0.274895i
\(78\) −2.34172 4.05597i −0.265147 0.459249i
\(79\) 5.94744i 0.669139i −0.942371 0.334569i \(-0.891409\pi\)
0.942371 0.334569i \(-0.108591\pi\)
\(80\) 6.82332 0.762870
\(81\) 5.62484 9.74251i 0.624983 1.08250i
\(82\) 1.57602 0.909917i 0.174043 0.100484i
\(83\) 5.88545 + 10.1939i 0.646012 + 1.11893i 0.984067 + 0.177799i \(0.0568978\pi\)
−0.338055 + 0.941126i \(0.609769\pi\)
\(84\) 8.66321 + 5.00171i 0.945233 + 0.545731i
\(85\) −0.640741 + 1.10980i −0.0694981 + 0.120374i
\(86\) 4.32748 0.466644
\(87\) 0.691855 + 1.19833i 0.0741747 + 0.128474i
\(88\) 1.60320 0.170902
\(89\) −1.27263 0.734755i −0.134899 0.0778839i 0.431032 0.902337i \(-0.358150\pi\)
−0.565931 + 0.824453i \(0.691483\pi\)
\(90\) −1.07272 + 0.619335i −0.113075 + 0.0652836i
\(91\) −7.38266 + 12.7871i −0.773913 + 1.34046i
\(92\) −6.69401 −0.697899
\(93\) 1.58117 2.73867i 0.163960 0.283987i
\(94\) −0.967170 1.67519i −0.0997560 0.172782i
\(95\) −1.19259 2.06563i −0.122357 0.211929i
\(96\) −7.57204 + 4.37172i −0.772818 + 0.446187i
\(97\) 6.45122 3.72462i 0.655023 0.378177i −0.135355 0.990797i \(-0.543218\pi\)
0.790378 + 0.612620i \(0.209884\pi\)
\(98\) 0.217990i 0.0220203i
\(99\) 1.44446 0.833959i 0.145174 0.0838160i
\(100\) −0.638381 −0.0638381
\(101\) 18.3368i 1.82458i 0.409548 + 0.912289i \(0.365686\pi\)
−0.409548 + 0.912289i \(0.634314\pi\)
\(102\) 0.477428i 0.0472725i
\(103\) 14.3486i 1.41381i −0.707307 0.706907i \(-0.750090\pi\)
0.707307 0.706907i \(-0.249910\pi\)
\(104\) −4.24932 7.36004i −0.416680 0.721711i
\(105\) 10.0669 + 5.81214i 0.982431 + 0.567207i
\(106\) −0.207652 0.359664i −0.0201690 0.0349337i
\(107\) −3.26773 + 1.88663i −0.315903 + 0.182387i −0.649565 0.760306i \(-0.725049\pi\)
0.333662 + 0.942693i \(0.391716\pi\)
\(108\) 2.92526 5.06670i 0.281484 0.487544i
\(109\) −2.73361 + 4.73476i −0.261833 + 0.453508i −0.966729 0.255803i \(-0.917660\pi\)
0.704896 + 0.709310i \(0.250994\pi\)
\(110\) 0.896937 0.0855195
\(111\) 2.06586 3.57817i 0.196083 0.339625i
\(112\) 6.94066 + 4.00719i 0.655830 + 0.378644i
\(113\) 3.58084 2.06740i 0.336857 0.194484i −0.322024 0.946731i \(-0.604363\pi\)
0.658881 + 0.752247i \(0.271030\pi\)
\(114\) 0.769570 + 0.444312i 0.0720768 + 0.0416136i
\(115\) −7.77866 −0.725364
\(116\) 0.604443 + 1.04693i 0.0561211 + 0.0972047i
\(117\) −7.65714 4.42085i −0.707903 0.408708i
\(118\) 0.200533 0.0184606
\(119\) −1.30352 + 0.752587i −0.119493 + 0.0689895i
\(120\) −5.79433 + 3.34536i −0.528948 + 0.305388i
\(121\) 9.79224 0.890204
\(122\) −0.671093 1.16237i −0.0607579 0.105236i
\(123\) 5.11335 8.85659i 0.461056 0.798572i
\(124\) 1.38140 2.39266i 0.124054 0.214867i
\(125\) −11.5310 −1.03136
\(126\) −1.45489 −0.129612
\(127\) 8.97785i 0.796655i −0.917243 0.398328i \(-0.869591\pi\)
0.917243 0.398328i \(-0.130409\pi\)
\(128\) −8.68690 + 5.01538i −0.767821 + 0.443301i
\(129\) 21.0605 12.1593i 1.85428 1.07057i
\(130\) −2.37735 4.11769i −0.208507 0.361145i
\(131\) 19.5044i 1.70411i 0.523453 + 0.852055i \(0.324644\pi\)
−0.523453 + 0.852055i \(0.675356\pi\)
\(132\) 3.75646 2.16879i 0.326957 0.188769i
\(133\) 2.80153i 0.242924i
\(134\) −3.08336 + 1.78018i −0.266362 + 0.153784i
\(135\) 3.39925 5.88767i 0.292561 0.506730i
\(136\) 0.866350i 0.0742889i
\(137\) −14.7101 8.49288i −1.25677 0.725596i −0.284323 0.958728i \(-0.591769\pi\)
−0.972445 + 0.233133i \(0.925102\pi\)
\(138\) 2.50976 1.44901i 0.213645 0.123348i
\(139\) −1.70864 −0.144925 −0.0724626 0.997371i \(-0.523086\pi\)
−0.0724626 + 0.997371i \(0.523086\pi\)
\(140\) 8.79502 + 5.07781i 0.743315 + 0.429153i
\(141\) −9.41386 5.43509i −0.792790 0.457717i
\(142\) 1.60481 2.77961i 0.134673 0.233260i
\(143\) 3.20120 + 5.54463i 0.267697 + 0.463666i
\(144\) −2.39957 + 4.15617i −0.199964 + 0.346348i
\(145\) 0.702382 + 1.21656i 0.0583297 + 0.101030i
\(146\) 4.14342i 0.342912i
\(147\) −0.612507 1.06089i −0.0505187 0.0875010i
\(148\) 1.80485 3.12609i 0.148358 0.256963i
\(149\) −13.5813 + 7.84114i −1.11262 + 0.642372i −0.939507 0.342530i \(-0.888716\pi\)
−0.173113 + 0.984902i \(0.555383\pi\)
\(150\) 0.239345 0.138186i 0.0195425 0.0112829i
\(151\) −9.60924 + 16.6437i −0.781989 + 1.35444i 0.148793 + 0.988868i \(0.452461\pi\)
−0.930782 + 0.365576i \(0.880872\pi\)
\(152\) 1.39647 + 0.806255i 0.113269 + 0.0653959i
\(153\) −0.450661 0.780567i −0.0364338 0.0631051i
\(154\) 0.912361 + 0.526752i 0.0735202 + 0.0424469i
\(155\) 1.60523 2.78035i 0.128935 0.223323i
\(156\) −19.9131 11.4968i −1.59433 0.920484i
\(157\) −1.78624 + 3.09385i −0.142557 + 0.246916i −0.928459 0.371435i \(-0.878866\pi\)
0.785902 + 0.618351i \(0.212199\pi\)
\(158\) 1.12475 + 1.94812i 0.0894799 + 0.154984i
\(159\) −2.02116 1.16692i −0.160289 0.0925426i
\(160\) −7.68726 + 4.43824i −0.607731 + 0.350874i
\(161\) −7.91243 4.56824i −0.623587 0.360028i
\(162\) 4.25495i 0.334301i
\(163\) 5.09836i 0.399335i 0.979864 + 0.199667i \(0.0639861\pi\)
−0.979864 + 0.199667i \(0.936014\pi\)
\(164\) 4.46731 7.73761i 0.348838 0.604206i
\(165\) 4.36512 2.52020i 0.339824 0.196198i
\(166\) −3.85562 2.22605i −0.299255 0.172775i
\(167\) 11.8388i 0.916114i 0.888923 + 0.458057i \(0.151455\pi\)
−0.888923 + 0.458057i \(0.848545\pi\)
\(168\) −7.85864 −0.606307
\(169\) 10.4697 18.1340i 0.805359 1.39492i
\(170\) 0.484693i 0.0371742i
\(171\) 1.67760 0.128289
\(172\) 18.3996 10.6230i 1.40296 0.809999i
\(173\) 18.7718 10.8379i 1.42719 0.823990i 0.430294 0.902689i \(-0.358410\pi\)
0.996898 + 0.0786993i \(0.0250767\pi\)
\(174\) −0.453242 0.261679i −0.0343602 0.0198379i
\(175\) −0.754577 0.435655i −0.0570406 0.0329324i
\(176\) 3.00954 1.73756i 0.226853 0.130973i
\(177\) 0.975936 0.563457i 0.0733558 0.0423520i
\(178\) 0.555811 0.0416598
\(179\) 12.8707i 0.962004i 0.876720 + 0.481002i \(0.159727\pi\)
−0.876720 + 0.481002i \(0.840273\pi\)
\(180\) −3.04067 + 5.26660i −0.226638 + 0.392549i
\(181\) −11.9279 −0.886597 −0.443299 0.896374i \(-0.646192\pi\)
−0.443299 + 0.896374i \(0.646192\pi\)
\(182\) 5.58467i 0.413963i
\(183\) −6.53202 3.77126i −0.482861 0.278780i
\(184\) 4.55424 2.62939i 0.335743 0.193841i
\(185\) 2.09729 3.63262i 0.154196 0.267075i
\(186\) 1.19609i 0.0877017i
\(187\) 0.652659i 0.0477271i
\(188\) −8.22447 4.74840i −0.599831 0.346313i
\(189\) 6.91541 3.99261i 0.503022 0.290420i
\(190\) 0.781280 + 0.451072i 0.0566800 + 0.0327242i
\(191\) −9.77636 16.9331i −0.707392 1.22524i −0.965821 0.259209i \(-0.916538\pi\)
0.258429 0.966030i \(-0.416795\pi\)
\(192\) −5.06754 + 8.77724i −0.365718 + 0.633443i
\(193\) 9.24788 + 5.33926i 0.665677 + 0.384329i 0.794437 0.607347i \(-0.207766\pi\)
−0.128760 + 0.991676i \(0.541100\pi\)
\(194\) −1.40876 + 2.44004i −0.101143 + 0.175185i
\(195\) −23.1397 13.3597i −1.65707 0.956708i
\(196\) −0.535120 0.926855i −0.0382228 0.0662039i
\(197\) −7.19151 4.15202i −0.512374 0.295819i 0.221435 0.975175i \(-0.428926\pi\)
−0.733809 + 0.679356i \(0.762259\pi\)
\(198\) −0.315427 + 0.546336i −0.0224164 + 0.0388264i
\(199\) −12.3469 + 7.12847i −0.875246 + 0.505324i −0.869088 0.494657i \(-0.835294\pi\)
−0.00615815 + 0.999981i \(0.501960\pi\)
\(200\) 0.434320 0.250755i 0.0307111 0.0177310i
\(201\) −10.0039 + 17.3272i −0.705618 + 1.22217i
\(202\) −3.46775 6.00631i −0.243990 0.422603i
\(203\) 1.64998i 0.115806i
\(204\) −1.17199 2.02994i −0.0820554 0.142124i
\(205\) 5.19116 8.99135i 0.362566 0.627983i
\(206\) 2.71353 + 4.69998i 0.189061 + 0.327463i
\(207\) 2.73553 4.73808i 0.190133 0.329320i
\(208\) −15.9537 9.21087i −1.10619 0.638659i
\(209\) −1.05202 0.607387i −0.0727701 0.0420138i
\(210\) −4.39664 −0.303397
\(211\) −13.9897 + 8.07697i −0.963093 + 0.556042i −0.897123 0.441780i \(-0.854347\pi\)
−0.0659691 + 0.997822i \(0.521014\pi\)
\(212\) −1.76580 1.01948i −0.121276 0.0700185i
\(213\) 18.0367i 1.23586i
\(214\) 0.713576 1.23595i 0.0487790 0.0844878i
\(215\) 21.3810 12.3443i 1.45817 0.841875i
\(216\) 4.59615i 0.312728i
\(217\) 3.26568 1.88544i 0.221689 0.127992i
\(218\) 2.06786i 0.140053i
\(219\) 11.6421 + 20.1648i 0.786703 + 1.36261i
\(220\) 3.81361 2.20179i 0.257114 0.148445i
\(221\) 2.99625 1.72988i 0.201549 0.116365i
\(222\) 1.56273i 0.104884i
\(223\) 11.9808 0.802297 0.401148 0.916013i \(-0.368611\pi\)
0.401148 + 0.916013i \(0.368611\pi\)
\(224\) −10.4259 −0.696612
\(225\) 0.260877 0.451852i 0.0173918 0.0301235i
\(226\) −0.781949 + 1.35437i −0.0520144 + 0.0900917i
\(227\) 12.4015 + 21.4801i 0.823119 + 1.42568i 0.903349 + 0.428907i \(0.141101\pi\)
−0.0802300 + 0.996776i \(0.525565\pi\)
\(228\) 4.36276 0.288931
\(229\) 22.8858 13.2131i 1.51234 0.873149i 0.512442 0.858722i \(-0.328741\pi\)
0.999896 0.0144273i \(-0.00459252\pi\)
\(230\) 2.54794 1.47106i 0.168006 0.0969985i
\(231\) 5.92025 0.389524
\(232\) −0.822461 0.474848i −0.0539972 0.0311753i
\(233\) 2.39162 + 4.14240i 0.156680 + 0.271378i 0.933669 0.358136i \(-0.116588\pi\)
−0.776990 + 0.629514i \(0.783254\pi\)
\(234\) 3.34419 0.218616
\(235\) −9.55709 5.51779i −0.623436 0.359941i
\(236\) 0.852631 0.492267i 0.0555016 0.0320438i
\(237\) 10.9476 + 6.32060i 0.711123 + 0.410567i
\(238\) 0.284650 0.493028i 0.0184511 0.0319583i
\(239\) −10.9171 −0.706168 −0.353084 0.935592i \(-0.614867\pi\)
−0.353084 + 0.935592i \(0.614867\pi\)
\(240\) −7.25144 + 12.5599i −0.468078 + 0.810735i
\(241\) −1.88498 + 3.26488i −0.121422 + 0.210309i −0.920329 0.391146i \(-0.872079\pi\)
0.798907 + 0.601455i \(0.205412\pi\)
\(242\) −3.20750 + 1.85185i −0.206186 + 0.119042i
\(243\) 7.22960 + 12.5220i 0.463779 + 0.803289i
\(244\) −5.70674 3.29479i −0.365336 0.210927i
\(245\) −0.621826 1.07703i −0.0397270 0.0688092i
\(246\) 3.86803i 0.246617i
\(247\) 6.43956i 0.409740i
\(248\) 2.17045i 0.137824i
\(249\) −25.0189 −1.58551
\(250\) 3.77703 2.18067i 0.238880 0.137918i
\(251\) 6.96910i 0.439886i −0.975513 0.219943i \(-0.929413\pi\)
0.975513 0.219943i \(-0.0705871\pi\)
\(252\) −6.18592 + 3.57144i −0.389677 + 0.224980i
\(253\) −3.43091 + 1.98084i −0.215699 + 0.124534i
\(254\) 1.69784 + 2.94074i 0.106532 + 0.184519i
\(255\) −1.36189 2.35885i −0.0852846 0.147717i
\(256\) −2.87140 + 4.97341i −0.179462 + 0.310838i
\(257\) 17.9468 1.11949 0.559745 0.828665i \(-0.310899\pi\)
0.559745 + 0.828665i \(0.310899\pi\)
\(258\) −4.59900 + 7.96570i −0.286321 + 0.495923i
\(259\) 4.26672 2.46339i 0.265121 0.153068i
\(260\) −20.2161 11.6718i −1.25375 0.723853i
\(261\) −0.988032 −0.0611576
\(262\) −3.68857 6.38878i −0.227880 0.394700i
\(263\) 32.0228 1.97461 0.987306 0.158831i \(-0.0507725\pi\)
0.987306 + 0.158831i \(0.0507725\pi\)
\(264\) −1.70379 + 2.95105i −0.104861 + 0.181625i
\(265\) −2.05191 1.18467i −0.126048 0.0727739i
\(266\) 0.529810 + 0.917658i 0.0324847 + 0.0562652i
\(267\) 2.70496 1.56171i 0.165541 0.0955752i
\(268\) −8.73992 + 15.1380i −0.533876 + 0.924700i
\(269\) 19.7208 1.20240 0.601199 0.799100i \(-0.294690\pi\)
0.601199 + 0.799100i \(0.294690\pi\)
\(270\) 2.57139i 0.156490i
\(271\) −5.41772 9.38376i −0.329103 0.570023i 0.653231 0.757158i \(-0.273413\pi\)
−0.982334 + 0.187136i \(0.940080\pi\)
\(272\) −0.938954 1.62632i −0.0569325 0.0986099i
\(273\) −15.6917 27.1789i −0.949708 1.64494i
\(274\) 6.42450 0.388118
\(275\) −0.327192 + 0.188904i −0.0197304 + 0.0113914i
\(276\) 7.11402 12.3218i 0.428214 0.741688i
\(277\) −17.8539 + 10.3080i −1.07274 + 0.619346i −0.928928 0.370259i \(-0.879269\pi\)
−0.143810 + 0.989605i \(0.545936\pi\)
\(278\) 0.559676 0.323129i 0.0335671 0.0193800i
\(279\) 1.12903 + 1.95554i 0.0675933 + 0.117075i
\(280\) −7.97821 −0.476789
\(281\) 2.70027 4.67701i 0.161085 0.279007i −0.774173 0.632974i \(-0.781834\pi\)
0.935258 + 0.353967i \(0.115167\pi\)
\(282\) 4.11142 0.244831
\(283\) 20.5445 1.22124 0.610622 0.791922i \(-0.290919\pi\)
0.610622 + 0.791922i \(0.290919\pi\)
\(284\) 15.7579i 0.935058i
\(285\) 5.06967 0.300301
\(286\) −2.09714 1.21078i −0.124006 0.0715952i
\(287\) 10.5609 6.09731i 0.623388 0.359913i
\(288\) 6.24321i 0.367885i
\(289\) −16.6473 −0.979254
\(290\) −0.460139 0.265661i −0.0270203 0.0156002i
\(291\) 15.8332i 0.928161i
\(292\) 10.1712 + 17.6171i 0.595226 + 1.03096i
\(293\) 7.72241 + 13.3756i 0.451148 + 0.781411i 0.998458 0.0555192i \(-0.0176814\pi\)
−0.547310 + 0.836930i \(0.684348\pi\)
\(294\) 0.401260 + 0.231668i 0.0234020 + 0.0135111i
\(295\) 0.990785 0.572030i 0.0576857 0.0333049i
\(296\) 2.83576i 0.164825i
\(297\) 3.46248i 0.200913i
\(298\) 2.96575 5.13682i 0.171801 0.297568i
\(299\) 18.1874 + 10.5005i 1.05180 + 0.607259i
\(300\) 0.678436 1.17508i 0.0391695 0.0678436i
\(301\) 28.9982 1.67143
\(302\) 7.26898i 0.418283i
\(303\) −33.7530 19.4873i −1.93906 1.11952i
\(304\) 3.49529 0.200469
\(305\) −6.63141 3.82865i −0.379713 0.219228i
\(306\) 0.295233 + 0.170453i 0.0168773 + 0.00974414i
\(307\) 1.85656 + 3.21565i 0.105959 + 0.183527i 0.914130 0.405422i \(-0.132875\pi\)
−0.808170 + 0.588949i \(0.799542\pi\)
\(308\) 5.17226 0.294717
\(309\) 26.4119 + 15.2489i 1.50252 + 0.867481i
\(310\) 1.21429i 0.0689671i
\(311\) 18.5186i 1.05009i 0.851073 + 0.525047i \(0.175952\pi\)
−0.851073 + 0.525047i \(0.824048\pi\)
\(312\) 18.0637 1.02266
\(313\) 20.2166 1.14271 0.571356 0.820702i \(-0.306418\pi\)
0.571356 + 0.820702i \(0.306418\pi\)
\(314\) 1.35121i 0.0762532i
\(315\) −7.18824 + 4.15013i −0.405012 + 0.233834i
\(316\) 9.56443 + 5.52203i 0.538041 + 0.310638i
\(317\) −14.4176 8.32403i −0.809776 0.467524i 0.0371022 0.999311i \(-0.488187\pi\)
−0.846878 + 0.531787i \(0.821521\pi\)
\(318\) 0.882724 0.0495007
\(319\) 0.619595 + 0.357723i 0.0346907 + 0.0200287i
\(320\) −5.14465 + 8.91079i −0.287595 + 0.498128i
\(321\) 8.01999i 0.447632i
\(322\) 3.45568 0.192577
\(323\) −0.328224 + 0.568500i −0.0182629 + 0.0316322i
\(324\) 10.4450 + 18.0913i 0.580279 + 1.00507i
\(325\) 1.73446 + 1.00139i 0.0962105 + 0.0555471i
\(326\) −0.964174 1.67000i −0.0534006 0.0924926i
\(327\) −5.81026 10.0637i −0.321308 0.556522i
\(328\) 7.01900i 0.387559i
\(329\) −6.48096 11.2254i −0.357307 0.618874i
\(330\) −0.953213 + 1.65101i −0.0524727 + 0.0908853i
\(331\) 7.94390 + 4.58642i 0.436636 + 0.252092i 0.702170 0.712009i \(-0.252215\pi\)
−0.265533 + 0.964102i \(0.585548\pi\)
\(332\) −21.8579 −1.19961
\(333\) 1.47512 + 2.55498i 0.0808359 + 0.140012i
\(334\) −2.23889 3.87787i −0.122507 0.212187i
\(335\) −10.1561 + 17.5908i −0.554885 + 0.961090i
\(336\) −14.7523 + 8.51723i −0.804803 + 0.464653i
\(337\) 17.6040 + 30.4910i 0.958951 + 1.66095i 0.725057 + 0.688689i \(0.241813\pi\)
0.233894 + 0.972262i \(0.424853\pi\)
\(338\) 7.91986i 0.430784i
\(339\) 8.78845i 0.477323i
\(340\) −1.18982 2.06083i −0.0645270 0.111764i
\(341\) 1.63509i 0.0885452i
\(342\) −0.549508 + 0.317259i −0.0297140 + 0.0171554i
\(343\) 19.2022i 1.03682i
\(344\) −8.34542 + 14.4547i −0.449955 + 0.779344i
\(345\) 8.26672 14.3184i 0.445065 0.770875i
\(346\) −4.09920 + 7.10003i −0.220374 + 0.381700i
\(347\) −21.9862 + 12.6937i −1.18028 + 0.681436i −0.956080 0.293106i \(-0.905311\pi\)
−0.224202 + 0.974543i \(0.571978\pi\)
\(348\) −2.56947 −0.137738
\(349\) 6.58665 + 17.4819i 0.352576 + 0.935783i
\(350\) 0.329554 0.0176154
\(351\) −15.8957 + 9.17737i −0.848448 + 0.489852i
\(352\) −2.26040 + 3.91512i −0.120480 + 0.208677i
\(353\) −3.93943 + 6.82329i −0.209675 + 0.363167i −0.951612 0.307302i \(-0.900574\pi\)
0.741937 + 0.670469i \(0.233907\pi\)
\(354\) −0.213115 + 0.369127i −0.0113270 + 0.0196189i
\(355\) 18.3112i 0.971856i
\(356\) 2.36321 1.36440i 0.125250 0.0723129i
\(357\) 3.19923i 0.169321i
\(358\) −2.43404 4.21588i −0.128643 0.222816i
\(359\) 15.2300i 0.803808i 0.915682 + 0.401904i \(0.131651\pi\)
−0.915682 + 0.401904i \(0.868349\pi\)
\(360\) 4.77748i 0.251795i
\(361\) 8.88909 + 15.3964i 0.467847 + 0.810334i
\(362\) 3.90707 2.25575i 0.205351 0.118559i
\(363\) −10.4066 + 18.0248i −0.546207 + 0.946058i
\(364\) −13.7092 23.7450i −0.718556 1.24458i
\(365\) 11.8193 + 20.4716i 0.618650 + 1.07153i
\(366\) 2.85280 0.149118
\(367\) 1.20541 + 0.695947i 0.0629221 + 0.0363281i 0.531131 0.847290i \(-0.321767\pi\)
−0.468209 + 0.883618i \(0.655101\pi\)
\(368\) 5.69950 9.87182i 0.297107 0.514604i
\(369\) 3.65117 + 6.32401i 0.190072 + 0.329215i
\(370\) 1.58651i 0.0824788i
\(371\) −1.39147 2.41009i −0.0722414 0.125126i
\(372\) 2.93615 + 5.08556i 0.152232 + 0.263674i
\(373\) −22.7629 13.1422i −1.17862 0.680475i −0.222923 0.974836i \(-0.571560\pi\)
−0.955694 + 0.294361i \(0.904893\pi\)
\(374\) −0.123427 0.213782i −0.00638226 0.0110544i
\(375\) 12.2544 21.2253i 0.632817 1.09607i
\(376\) 7.46064 0.384753
\(377\) 3.79261i 0.195330i
\(378\) −1.51012 + 2.61561i −0.0776723 + 0.134532i
\(379\) 15.3747 + 8.87661i 0.789748 + 0.455961i 0.839874 0.542782i \(-0.182629\pi\)
−0.0501261 + 0.998743i \(0.515962\pi\)
\(380\) 4.42915 0.227210
\(381\) 16.5258 + 9.54115i 0.846640 + 0.488808i
\(382\) 6.40460 + 3.69770i 0.327688 + 0.189191i
\(383\) 31.9782 18.4626i 1.63401 0.943397i 0.651173 0.758930i \(-0.274277\pi\)
0.982839 0.184467i \(-0.0590559\pi\)
\(384\) 21.3203i 1.08800i
\(385\) 6.01033 0.306315
\(386\) −4.03893 −0.205576
\(387\) 17.3646i 0.882692i
\(388\) 13.8328i 0.702254i
\(389\) −25.7586 14.8717i −1.30601 0.754027i −0.324585 0.945857i \(-0.605225\pi\)
−0.981428 + 0.191830i \(0.938558\pi\)
\(390\) 10.1060 0.511740
\(391\) 1.07042 + 1.85402i 0.0541334 + 0.0937617i
\(392\) 0.728133 + 0.420388i 0.0367763 + 0.0212328i
\(393\) −35.9023 20.7282i −1.81103 1.04560i
\(394\) 3.14083 0.158233
\(395\) 11.1142 + 6.41677i 0.559215 + 0.322863i
\(396\) 3.09723i 0.155642i
\(397\) −19.1725 −0.962238 −0.481119 0.876655i \(-0.659770\pi\)
−0.481119 + 0.876655i \(0.659770\pi\)
\(398\) 2.69619 4.66994i 0.135148 0.234083i
\(399\) 5.15685 + 2.97731i 0.258166 + 0.149052i
\(400\) 0.543539 0.941437i 0.0271769 0.0470718i
\(401\) 11.0789i 0.553256i 0.960977 + 0.276628i \(0.0892170\pi\)
−0.960977 + 0.276628i \(0.910783\pi\)
\(402\) 7.56749i 0.377432i
\(403\) −7.50644 + 4.33384i −0.373922 + 0.215884i
\(404\) −29.4885 17.0252i −1.46711 0.847034i
\(405\) 12.1374 + 21.0227i 0.603114 + 1.04462i
\(406\) −0.312034 0.540459i −0.0154860 0.0268225i
\(407\) 2.13630i 0.105893i
\(408\) 1.59471 + 0.920707i 0.0789500 + 0.0455818i
\(409\) 10.1232 0.500559 0.250279 0.968174i \(-0.419478\pi\)
0.250279 + 0.968174i \(0.419478\pi\)
\(410\) 3.92689i 0.193935i
\(411\) 31.2661 18.0515i 1.54224 0.890415i
\(412\) 23.0749 + 13.3223i 1.13682 + 0.656343i
\(413\) 1.34376 0.0661223
\(414\) 2.06931i 0.101701i
\(415\) −25.3996 −1.24682
\(416\) 23.9649 1.17498
\(417\) 1.81585 3.14514i 0.0889226 0.154018i
\(418\) 0.459462 0.0224730
\(419\) −0.185964 0.322099i −0.00908493 0.0157356i 0.861447 0.507847i \(-0.169559\pi\)
−0.870532 + 0.492112i \(0.836225\pi\)
\(420\) −18.6937 + 10.7928i −0.912160 + 0.526636i
\(421\) 30.8119 17.7893i 1.50168 0.866995i 0.501682 0.865052i \(-0.332715\pi\)
0.999998 0.00194293i \(-0.000618453\pi\)
\(422\) 3.05494 5.29132i 0.148712 0.257577i
\(423\) 6.72192 3.88090i 0.326831 0.188696i
\(424\) 1.60181 0.0777905
\(425\) 0.102082 + 0.176810i 0.00495168 + 0.00857656i
\(426\) 3.41100 + 5.90803i 0.165264 + 0.286245i
\(427\) −4.49697 7.78897i −0.217623 0.376935i
\(428\) 7.00671i 0.338682i
\(429\) −13.6082 −0.657010
\(430\) −4.66897 + 8.08690i −0.225158 + 0.389985i
\(431\) 5.40726 3.12188i 0.260458 0.150376i −0.364085 0.931366i \(-0.618618\pi\)
0.624544 + 0.780990i \(0.285285\pi\)
\(432\) 4.98133 + 8.62791i 0.239664 + 0.415111i
\(433\) −33.8694 19.5545i −1.62766 0.939730i −0.984789 0.173756i \(-0.944409\pi\)
−0.642872 0.765974i \(-0.722257\pi\)
\(434\) −0.713127 + 1.23517i −0.0342312 + 0.0592902i
\(435\) −2.98581 −0.143159
\(436\) −5.07617 8.79218i −0.243104 0.421069i
\(437\) −3.98467 −0.190613
\(438\) −7.62690 4.40339i −0.364427 0.210402i
\(439\) 5.11434 2.95276i 0.244094 0.140928i −0.372963 0.927846i \(-0.621658\pi\)
0.617057 + 0.786918i \(0.288325\pi\)
\(440\) −1.72972 + 2.99596i −0.0824610 + 0.142827i
\(441\) 0.874715 0.0416531
\(442\) −0.654292 + 1.13327i −0.0311215 + 0.0539040i
\(443\) −2.14584 3.71670i −0.101952 0.176586i 0.810537 0.585688i \(-0.199175\pi\)
−0.912489 + 0.409102i \(0.865842\pi\)
\(444\) 3.83618 + 6.64446i 0.182057 + 0.315332i
\(445\) 2.74612 1.58547i 0.130179 0.0751587i
\(446\) −3.92439 + 2.26575i −0.185825 + 0.107286i
\(447\) 33.3325i 1.57657i
\(448\) −10.4662 + 6.04269i −0.494483 + 0.285490i
\(449\) 13.5220 0.638144 0.319072 0.947731i \(-0.396629\pi\)
0.319072 + 0.947731i \(0.396629\pi\)
\(450\) 0.197342i 0.00930281i
\(451\) 5.28772i 0.248989i
\(452\) 7.67808i 0.361146i
\(453\) −20.4243 35.3759i −0.959618 1.66211i
\(454\) −8.12438 4.69062i −0.381296 0.220141i
\(455\) −15.9305 27.5924i −0.746834 1.29355i
\(456\) −2.96819 + 1.71368i −0.138998 + 0.0802506i
\(457\) 0.0974515 0.168791i 0.00455859 0.00789571i −0.863737 0.503943i \(-0.831882\pi\)
0.868296 + 0.496047i \(0.165216\pi\)
\(458\) −4.99759 + 8.65608i −0.233522 + 0.404472i
\(459\) −1.87108 −0.0873344
\(460\) 7.22226 12.5093i 0.336740 0.583250i
\(461\) 2.28870 + 1.32138i 0.106595 + 0.0615428i 0.552350 0.833612i \(-0.313731\pi\)
−0.445755 + 0.895155i \(0.647065\pi\)
\(462\) −1.93921 + 1.11960i −0.0902203 + 0.0520887i
\(463\) −26.9780 15.5758i −1.25377 0.723867i −0.281918 0.959439i \(-0.590971\pi\)
−0.971857 + 0.235571i \(0.924304\pi\)
\(464\) −2.05857 −0.0955667
\(465\) 3.41190 + 5.90959i 0.158223 + 0.274051i
\(466\) −1.56677 0.904578i −0.0725794 0.0419038i
\(467\) 21.1407 0.978273 0.489137 0.872207i \(-0.337312\pi\)
0.489137 + 0.872207i \(0.337312\pi\)
\(468\) 14.2189 8.20927i 0.657268 0.379474i
\(469\) −20.6614 + 11.9289i −0.954057 + 0.550825i
\(470\) 4.17397 0.192531
\(471\) −3.79662 6.57594i −0.174939 0.303003i
\(472\) −0.386723 + 0.669824i −0.0178004 + 0.0308311i
\(473\) 6.28696 10.8893i 0.289075 0.500692i
\(474\) −4.78126 −0.219611
\(475\) −0.380002 −0.0174357
\(476\) 2.79502i 0.128110i
\(477\) 1.44320 0.833232i 0.0660796 0.0381511i
\(478\) 3.57596 2.06458i 0.163560 0.0944316i
\(479\) 2.81941 + 4.88335i 0.128822 + 0.223126i 0.923220 0.384271i \(-0.125547\pi\)
−0.794398 + 0.607397i \(0.792214\pi\)
\(480\) 18.8668i 0.861149i
\(481\) −9.80741 + 5.66231i −0.447180 + 0.258179i
\(482\) 1.42591i 0.0649483i
\(483\) 16.8178 9.70974i 0.765234 0.441808i
\(484\) −9.09181 + 15.7475i −0.413264 + 0.715795i
\(485\) 16.0742i 0.729890i
\(486\) −4.73619 2.73444i −0.214838 0.124037i
\(487\) −12.5906 + 7.26916i −0.570532 + 0.329397i −0.757362 0.652995i \(-0.773512\pi\)
0.186830 + 0.982392i \(0.440179\pi\)
\(488\) 5.17674 0.234340
\(489\) −9.38469 5.41825i −0.424390 0.245022i
\(490\) 0.407365 + 0.235193i 0.0184029 + 0.0106249i
\(491\) 12.6173 21.8538i 0.569412 0.986250i −0.427212 0.904151i \(-0.640504\pi\)
0.996624 0.0820990i \(-0.0261624\pi\)
\(492\) 9.49521 + 16.4462i 0.428077 + 0.741451i
\(493\) 0.193309 0.334821i 0.00870620 0.0150796i
\(494\) −1.21781 2.10932i −0.0547920 0.0949026i
\(495\) 3.59908i 0.161767i
\(496\) 2.35234 + 4.07437i 0.105623 + 0.182945i
\(497\) 10.7538 18.6261i 0.482372 0.835493i
\(498\) 8.19508 4.73143i 0.367230 0.212021i
\(499\) −6.03269 + 3.48298i −0.270060 + 0.155919i −0.628915 0.777474i \(-0.716501\pi\)
0.358855 + 0.933393i \(0.383167\pi\)
\(500\) 10.7062 18.5436i 0.478794 0.829296i
\(501\) −21.7920 12.5816i −0.973595 0.562105i
\(502\) 1.31796 + 2.28277i 0.0588233 + 0.101885i
\(503\) −29.9983 17.3195i −1.33756 0.772240i −0.351113 0.936333i \(-0.614197\pi\)
−0.986445 + 0.164093i \(0.947530\pi\)
\(504\) 2.80571 4.85963i 0.124976 0.216465i
\(505\) −34.2665 19.7838i −1.52484 0.880367i
\(506\) 0.749209 1.29767i 0.0333064 0.0576884i
\(507\) 22.2531 + 38.5436i 0.988297 + 1.71178i
\(508\) 14.4378 + 8.33567i 0.640574 + 0.369836i
\(509\) −27.2981 + 15.7606i −1.20997 + 0.698575i −0.962752 0.270386i \(-0.912849\pi\)
−0.247215 + 0.968961i \(0.579515\pi\)
\(510\) 0.892187 + 0.515104i 0.0395067 + 0.0228092i
\(511\) 27.7649i 1.22825i
\(512\) 22.2336i 0.982597i
\(513\) 1.74129 3.01600i 0.0768798 0.133160i
\(514\) −5.87857 + 3.39399i −0.259292 + 0.149703i
\(515\) 26.8138 + 15.4809i 1.18156 + 0.682172i
\(516\) 45.1583i 1.98798i
\(517\) −5.62042 −0.247186
\(518\) −0.931725 + 1.61379i −0.0409376 + 0.0709061i
\(519\) 46.0716i 2.02232i
\(520\) 18.3386 0.804201
\(521\) 21.8631 12.6226i 0.957838 0.553008i 0.0623308 0.998056i \(-0.480147\pi\)
0.895507 + 0.445048i \(0.146813\pi\)
\(522\) 0.323635 0.186851i 0.0141651 0.00817825i
\(523\) 14.6624 + 8.46534i 0.641142 + 0.370164i 0.785054 0.619427i \(-0.212635\pi\)
−0.143912 + 0.989590i \(0.545968\pi\)
\(524\) −31.3662 18.1093i −1.37024 0.791108i
\(525\) 1.60384 0.925979i 0.0699974 0.0404130i
\(526\) −10.4893 + 6.05597i −0.457353 + 0.264053i
\(527\) −0.883582 −0.0384894
\(528\) 7.38632i 0.321448i
\(529\) 5.00251 8.66460i 0.217500 0.376722i
\(530\) 0.896155 0.0389265
\(531\) 0.804667i 0.0349196i
\(532\) 4.50531 + 2.60114i 0.195330 + 0.112774i
\(533\) −24.2750 + 14.0152i −1.05147 + 0.607066i
\(534\) −0.590684 + 1.02309i −0.0255614 + 0.0442736i
\(535\) 8.14202i 0.352010i
\(536\) 13.7321i 0.593136i
\(537\) −23.6915 13.6783i −1.02236 0.590262i
\(538\) −6.45965 + 3.72948i −0.278495 + 0.160789i
\(539\) −0.548534 0.316696i −0.0236270 0.0136411i
\(540\) 6.31221 + 10.9331i 0.271634 + 0.470485i
\(541\) −14.4995 + 25.1139i −0.623384 + 1.07973i 0.365467 + 0.930824i \(0.380909\pi\)
−0.988851 + 0.148909i \(0.952424\pi\)
\(542\) 3.54921 + 2.04914i 0.152452 + 0.0880179i
\(543\) 12.6763 21.9561i 0.543994 0.942225i
\(544\) 2.11568 + 1.22149i 0.0907091 + 0.0523709i
\(545\) −5.89867 10.2168i −0.252671 0.437639i
\(546\) 10.2798 + 5.93507i 0.439936 + 0.253997i
\(547\) 18.5364 32.1059i 0.792557 1.37275i −0.131822 0.991273i \(-0.542083\pi\)
0.924379 0.381476i \(-0.124584\pi\)
\(548\) 27.3158 15.7708i 1.16687 0.673695i
\(549\) 4.66416 2.69285i 0.199061 0.114928i
\(550\) 0.0714491 0.123753i 0.00304660 0.00527686i
\(551\) 0.359800 + 0.623192i 0.0153280 + 0.0265489i
\(552\) 11.1775i 0.475745i
\(553\) 7.53687 + 13.0542i 0.320500 + 0.555123i
\(554\) 3.89877 6.75287i 0.165643 0.286902i
\(555\) 4.45777 + 7.72108i 0.189222 + 0.327741i
\(556\) 1.58643 2.74777i 0.0672795 0.116532i
\(557\) −21.1429 12.2069i −0.895855 0.517222i −0.0200022 0.999800i \(-0.506367\pi\)
−0.875853 + 0.482578i \(0.839701\pi\)
\(558\) −0.739641 0.427032i −0.0313115 0.0180777i
\(559\) −66.6549 −2.81920
\(560\) −14.9767 + 8.64683i −0.632883 + 0.365395i
\(561\) −1.20137 0.693609i −0.0507217 0.0292842i
\(562\) 2.04264i 0.0861636i
\(563\) 5.54504 9.60429i 0.233695 0.404772i −0.725197 0.688541i \(-0.758251\pi\)
0.958893 + 0.283769i \(0.0915848\pi\)
\(564\) 17.4810 10.0927i 0.736083 0.424978i
\(565\) 8.92217i 0.375359i
\(566\) −6.72947 + 3.88526i −0.282861 + 0.163310i
\(567\) 28.5123i 1.19740i
\(568\) 6.18966 + 10.7208i 0.259713 + 0.449835i
\(569\) −2.19732 + 1.26862i −0.0921165 + 0.0531835i −0.545351 0.838208i \(-0.683603\pi\)
0.453234 + 0.891392i \(0.350270\pi\)
\(570\) −1.66060 + 0.958748i −0.0695549 + 0.0401575i
\(571\) 2.74801i 0.115001i 0.998345 + 0.0575004i \(0.0183130\pi\)
−0.998345 + 0.0575004i \(0.981687\pi\)
\(572\) −11.8889 −0.497099
\(573\) 41.5590 1.73615
\(574\) −2.30618 + 3.99442i −0.0962581 + 0.166724i
\(575\) −0.619640 + 1.07325i −0.0258408 + 0.0447575i
\(576\) −3.61845 6.26735i −0.150769 0.261139i
\(577\) −45.5786 −1.89746 −0.948732 0.316082i \(-0.897633\pi\)
−0.948732 + 0.316082i \(0.897633\pi\)
\(578\) 5.45292 3.14825i 0.226812 0.130950i
\(579\) −19.6562 + 11.3485i −0.816885 + 0.471629i
\(580\) −2.60857 −0.108315
\(581\) −25.8364 14.9166i −1.07187 0.618846i
\(582\) −2.99429 5.18627i −0.124117 0.214978i
\(583\) −1.20671 −0.0499768
\(584\) −13.8399 7.99047i −0.572699 0.330648i
\(585\) 16.5228 9.53943i 0.683133 0.394407i
\(586\) −5.05903 2.92084i −0.208987 0.120659i
\(587\) −6.23491 + 10.7992i −0.257342 + 0.445730i −0.965529 0.260295i \(-0.916180\pi\)
0.708187 + 0.706025i \(0.249513\pi\)
\(588\) 2.27478 0.0938103
\(589\) 0.822292 1.42425i 0.0338820 0.0586853i
\(590\) −0.216358 + 0.374743i −0.00890732 + 0.0154279i
\(591\) 15.2855 8.82506i 0.628760 0.363015i
\(592\) 3.07341 + 5.32331i 0.126317 + 0.218787i
\(593\) 0.933305 + 0.538844i 0.0383262 + 0.0221277i 0.519041 0.854750i \(-0.326289\pi\)
−0.480714 + 0.876877i \(0.659623\pi\)
\(594\) 0.654804 + 1.13415i 0.0268669 + 0.0465349i
\(595\) 3.24790i 0.133151i
\(596\) 29.1211i 1.19285i
\(597\) 30.3029i 1.24022i
\(598\) −7.94317 −0.324821
\(599\) 32.8178 18.9474i 1.34090 0.774169i 0.353960 0.935261i \(-0.384835\pi\)
0.986939 + 0.161092i \(0.0515016\pi\)
\(600\) 1.06595i 0.0435173i
\(601\) 10.8359 6.25610i 0.442005 0.255192i −0.262443 0.964948i \(-0.584528\pi\)
0.704448 + 0.709756i \(0.251195\pi\)
\(602\) −9.49853 + 5.48398i −0.387131 + 0.223510i
\(603\) −7.14321 12.3724i −0.290894 0.503843i
\(604\) −17.8438 30.9064i −0.726054 1.25756i
\(605\) −10.5650 + 18.2991i −0.429528 + 0.743964i
\(606\) 14.7413 0.598824
\(607\) −15.9832 + 27.6838i −0.648740 + 1.12365i 0.334684 + 0.942330i \(0.391370\pi\)
−0.983424 + 0.181320i \(0.941963\pi\)
\(608\) −3.93785 + 2.27352i −0.159701 + 0.0922034i
\(609\) −3.03716 1.75350i −0.123072 0.0710555i
\(610\) 2.89621 0.117264
\(611\) 14.8970 + 25.8024i 0.602670 + 1.04386i
\(612\) 1.67370 0.0676554
\(613\) −12.1327 + 21.0144i −0.490034 + 0.848764i −0.999934 0.0114698i \(-0.996349\pi\)
0.509900 + 0.860234i \(0.329682\pi\)
\(614\) −1.21625 0.702202i −0.0490839 0.0283386i
\(615\) 11.0337 + 19.1110i 0.444923 + 0.770630i
\(616\) −3.51892 + 2.03165i −0.141782 + 0.0818576i
\(617\) 3.30576 5.72574i 0.133085 0.230510i −0.791779 0.610807i \(-0.790845\pi\)
0.924864 + 0.380297i \(0.124178\pi\)
\(618\) −11.5352 −0.464012
\(619\) 20.8463i 0.837882i 0.908013 + 0.418941i \(0.137599\pi\)
−0.908013 + 0.418941i \(0.862401\pi\)
\(620\) 2.98083 + 5.16294i 0.119713 + 0.207349i
\(621\) −5.67877 9.83592i −0.227881 0.394702i
\(622\) −3.50214 6.06588i −0.140423 0.243219i
\(623\) 3.72446 0.149217
\(624\) 33.9094 19.5776i 1.35746 0.783730i
\(625\) 11.5815 20.0597i 0.463258 0.802387i
\(626\) −6.62208 + 3.82326i −0.264671 + 0.152808i
\(627\) 2.23606 1.29099i 0.0892998 0.0515573i
\(628\) −3.31694 5.74510i −0.132360 0.229255i
\(629\) −1.15443 −0.0460301
\(630\) 1.56970 2.71880i 0.0625383 0.108320i
\(631\) −6.96451 −0.277253 −0.138626 0.990345i \(-0.544269\pi\)
−0.138626 + 0.990345i \(0.544269\pi\)
\(632\) −8.67616 −0.345119
\(633\) 34.3350i 1.36469i
\(634\) 6.29678 0.250077
\(635\) 16.7772 + 9.68632i 0.665783 + 0.384390i
\(636\) 3.75318 2.16690i 0.148823 0.0859232i
\(637\) 3.35764i 0.133035i
\(638\) −0.270603 −0.0107133
\(639\) 11.1536 + 6.43952i 0.441229 + 0.254744i
\(640\) 21.6447i 0.855581i
\(641\) 12.5322 + 21.7064i 0.494992 + 0.857351i 0.999983 0.00577358i \(-0.00183780\pi\)
−0.504992 + 0.863124i \(0.668504\pi\)
\(642\) 1.51670 + 2.62699i 0.0598592 + 0.103679i
\(643\) 21.3450 + 12.3235i 0.841763 + 0.485992i 0.857863 0.513878i \(-0.171792\pi\)
−0.0161002 + 0.999870i \(0.505125\pi\)
\(644\) 14.6929 8.48296i 0.578982 0.334276i
\(645\) 52.4754i 2.06622i
\(646\) 0.248287i 0.00976874i
\(647\) 21.6296 37.4635i 0.850347 1.47284i −0.0305489 0.999533i \(-0.509726\pi\)
0.880896 0.473310i \(-0.156941\pi\)
\(648\) −14.2124 8.20556i −0.558317 0.322345i
\(649\) 0.291335 0.504607i 0.0114359 0.0198076i
\(650\) −0.757509 −0.0297119
\(651\) 8.01495i 0.314131i
\(652\) −8.19898 4.73369i −0.321097 0.185385i
\(653\) 35.4673 1.38794 0.693972 0.720002i \(-0.255859\pi\)
0.693972 + 0.720002i \(0.255859\pi\)
\(654\) 3.80637 + 2.19761i 0.148841 + 0.0859332i
\(655\) −36.4486 21.0436i −1.42416 0.822241i
\(656\) 7.60723 + 13.1761i 0.297012 + 0.514440i
\(657\) −16.6260 −0.648643
\(658\) 4.24575 + 2.45129i 0.165517 + 0.0955611i
\(659\) 29.8965i 1.16460i −0.812973 0.582302i \(-0.802152\pi\)
0.812973 0.582302i \(-0.197848\pi\)
\(660\) 9.35975i 0.364328i
\(661\) 9.25200 0.359861 0.179931 0.983679i \(-0.442413\pi\)
0.179931 + 0.983679i \(0.442413\pi\)
\(662\) −3.46943 −0.134843
\(663\) 7.35370i 0.285594i
\(664\) 14.8709 8.58573i 0.577104 0.333191i
\(665\) 5.23532 + 3.02261i 0.203017 + 0.117212i
\(666\) −0.966365 0.557931i −0.0374459 0.0216194i
\(667\) 2.34679 0.0908682
\(668\) −19.0387 10.9920i −0.736629 0.425293i
\(669\) −12.7326 + 22.0534i −0.492269 + 0.852635i
\(670\) 7.68263i 0.296806i
\(671\) −3.89986 −0.150552
\(672\) 11.0801 19.1913i 0.427424 0.740320i
\(673\) 22.9185 + 39.6960i 0.883443 + 1.53017i 0.847488 + 0.530815i \(0.178114\pi\)
0.0359553 + 0.999353i \(0.488553\pi\)
\(674\) −11.5326 6.65833i −0.444218 0.256469i
\(675\) −0.541562 0.938012i −0.0208447 0.0361041i
\(676\) 19.4416 + 33.6738i 0.747753 + 1.29515i
\(677\) 11.6413i 0.447413i 0.974657 + 0.223707i \(0.0718158\pi\)
−0.974657 + 0.223707i \(0.928184\pi\)
\(678\) −1.66202 2.87871i −0.0638296 0.110556i
\(679\) −9.44001 + 16.3506i −0.362274 + 0.627478i
\(680\) 1.61898 + 0.934716i 0.0620849 + 0.0358447i
\(681\) −52.7186 −2.02018
\(682\) 0.309219 + 0.535583i 0.0118406 + 0.0205085i
\(683\) −7.23862 12.5377i −0.276978 0.479740i 0.693654 0.720308i \(-0.256000\pi\)
−0.970632 + 0.240568i \(0.922666\pi\)
\(684\) −1.55761 + 2.69785i −0.0595565 + 0.103155i
\(685\) 31.7418 18.3262i 1.21279 0.700207i
\(686\) 3.63141 + 6.28979i 0.138648 + 0.240145i
\(687\) 56.1687i 2.14297i
\(688\) 36.1792i 1.37932i
\(689\) 3.19841 + 5.53980i 0.121850 + 0.211050i
\(690\) 6.25342i 0.238064i
\(691\) 17.5518 10.1335i 0.667701 0.385497i −0.127504 0.991838i \(-0.540697\pi\)
0.795205 + 0.606341i \(0.207363\pi\)
\(692\) 40.2507i 1.53010i
\(693\) −2.11366 + 3.66097i −0.0802914 + 0.139069i
\(694\) 4.80114 8.31582i 0.182249 0.315664i
\(695\) 1.84348 3.19300i 0.0699272 0.121117i
\(696\) 1.74813 1.00928i 0.0662627 0.0382568i
\(697\) −2.85741 −0.108232
\(698\) −5.46357 4.48066i −0.206799 0.169595i
\(699\) −10.1667 −0.384540
\(700\) 1.40121 0.808987i 0.0529606 0.0305768i
\(701\) −1.43242 + 2.48103i −0.0541018 + 0.0937071i −0.891808 0.452414i \(-0.850563\pi\)
0.837706 + 0.546121i \(0.183896\pi\)
\(702\) 3.47114 6.01220i 0.131010 0.226916i
\(703\) 1.07435 1.86083i 0.0405200 0.0701826i
\(704\) 5.24034i 0.197503i
\(705\) 20.3135 11.7280i 0.765050 0.441702i
\(706\) 2.98001i 0.112154i
\(707\) −23.2372 40.2480i −0.873925 1.51368i
\(708\) 2.09261i 0.0786452i
\(709\) 48.1191i 1.80715i 0.428429 + 0.903576i \(0.359067\pi\)
−0.428429 + 0.903576i \(0.640933\pi\)
\(710\) 3.46290 + 5.99793i 0.129960 + 0.225098i
\(711\) −7.81708 + 4.51319i −0.293163 + 0.169258i
\(712\) −1.07187 + 1.85652i −0.0401698 + 0.0695762i
\(713\) −2.68169 4.64483i −0.100430 0.173950i
\(714\) 0.605020 + 1.04792i 0.0226423 + 0.0392176i
\(715\) −13.8153 −0.516661
\(716\) −20.6982 11.9501i −0.773528 0.446596i
\(717\) 11.6021 20.0954i 0.433287 0.750475i
\(718\) −2.88021 4.98867i −0.107488 0.186175i
\(719\) 15.8375i 0.590638i 0.955399 + 0.295319i \(0.0954260\pi\)
−0.955399 + 0.295319i \(0.904574\pi\)
\(720\) −5.17785 8.96831i −0.192967 0.334229i
\(721\) 18.1833 + 31.4943i 0.677180 + 1.17291i
\(722\) −5.82334 3.36211i −0.216722 0.125125i
\(723\) −4.00650 6.93946i −0.149003 0.258081i
\(724\) 11.0748 19.1820i 0.411590 0.712895i
\(725\) 0.223804 0.00831188
\(726\) 7.87218i 0.292164i
\(727\) 10.2472 17.7487i 0.380049 0.658264i −0.611020 0.791615i \(-0.709241\pi\)
0.991069 + 0.133351i \(0.0425739\pi\)
\(728\) 18.6540 + 10.7699i 0.691362 + 0.399158i
\(729\) 3.01623 0.111712
\(730\) −7.74295 4.47039i −0.286579 0.165457i
\(731\) −5.88446 3.39739i −0.217645 0.125657i
\(732\) 12.1296 7.00302i 0.448323 0.258839i
\(733\) 1.97988i 0.0731286i −0.999331 0.0365643i \(-0.988359\pi\)
0.999331 0.0365643i \(-0.0116414\pi\)
\(734\) −0.526454 −0.0194318
\(735\) 2.64337 0.0975021
\(736\) 14.8290i 0.546604i
\(737\) 10.3450i 0.381062i
\(738\) −2.39192 1.38098i −0.0880478 0.0508344i
\(739\) −12.1490 −0.446909 −0.223454 0.974714i \(-0.571733\pi\)
−0.223454 + 0.974714i \(0.571733\pi\)
\(740\) 3.89455 + 6.74556i 0.143167 + 0.247972i
\(741\) −11.8535 6.84360i −0.435448 0.251406i
\(742\) 0.911566 + 0.526293i 0.0334646 + 0.0193208i
\(743\) 28.5142 1.04608 0.523041 0.852307i \(-0.324797\pi\)
0.523041 + 0.852307i \(0.324797\pi\)
\(744\) −3.99520 2.30663i −0.146471 0.0845651i
\(745\) 33.8397i 1.23979i
\(746\) 9.94148 0.363983
\(747\) 8.93231 15.4712i 0.326816 0.566062i
\(748\) −1.04958 0.605975i −0.0383764 0.0221566i
\(749\) 4.78164 8.28204i 0.174717 0.302619i
\(750\) 9.26997i 0.338491i
\(751\) 36.7696i 1.34174i −0.741574 0.670872i \(-0.765920\pi\)
0.741574 0.670872i \(-0.234080\pi\)
\(752\) 14.0052 8.08588i 0.510716 0.294862i
\(753\) 12.8282 + 7.40637i 0.467486 + 0.269903i
\(754\) 0.717238 + 1.24229i 0.0261203 + 0.0452416i
\(755\) −20.7351 35.9142i −0.754627 1.30705i
\(756\) 14.8281i 0.539293i
\(757\) 11.0293 + 6.36779i 0.400868 + 0.231441i 0.686858 0.726791i \(-0.258989\pi\)
−0.285991 + 0.958232i \(0.592323\pi\)
\(758\) −6.71478 −0.243892
\(759\) 8.42048i 0.305644i
\(760\) −3.01335 + 1.73976i −0.109306 + 0.0631077i
\(761\) 15.3568 + 8.86626i 0.556684 + 0.321402i 0.751814 0.659376i \(-0.229179\pi\)
−0.195129 + 0.980777i \(0.562513\pi\)
\(762\) −7.21747 −0.261461
\(763\) 13.8567i 0.501645i
\(764\) 36.3083 1.31359
\(765\) 1.94490 0.0703179
\(766\) −6.98310 + 12.0951i −0.252310 + 0.437013i