Properties

Label 349.2.e.a.123.7
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 123.7
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.34862 + 0.778626i) q^{2} +(1.56432 - 2.70948i) q^{3} +(0.212518 - 0.368092i) q^{4} +(-1.71886 + 2.97716i) q^{5} +4.87208i q^{6} +(0.0378395 - 0.0218466i) q^{7} -2.45262i q^{8} +(-3.39418 - 5.87890i) q^{9} +O(q^{10})\) \(q+(-1.34862 + 0.778626i) q^{2} +(1.56432 - 2.70948i) q^{3} +(0.212518 - 0.368092i) q^{4} +(-1.71886 + 2.97716i) q^{5} +4.87208i q^{6} +(0.0378395 - 0.0218466i) q^{7} -2.45262i q^{8} +(-3.39418 - 5.87890i) q^{9} -5.35340i q^{10} -5.81943i q^{11} +(-0.664891 - 1.15162i) q^{12} +(0.607751 - 0.350885i) q^{13} +(-0.0340207 + 0.0589256i) q^{14} +(5.37769 + 9.31444i) q^{15} +(2.33471 + 4.04383i) q^{16} +1.42655 q^{17} +(9.15493 + 5.28560i) q^{18} +(2.16840 - 3.75578i) q^{19} +(0.730578 + 1.26540i) q^{20} -0.136700i q^{21} +(4.53116 + 7.84820i) q^{22} +(-3.24640 - 5.62292i) q^{23} +(-6.64531 - 3.83667i) q^{24} +(-3.40897 - 5.90451i) q^{25} +(-0.546417 + 0.946422i) q^{26} -11.8524 q^{27} -0.0185712i q^{28} +(0.358257 - 0.620519i) q^{29} +(-14.5049 - 8.37443i) q^{30} +8.37278 q^{31} +(-2.04921 - 1.18311i) q^{32} +(-15.7676 - 9.10344i) q^{33} +(-1.92388 + 1.11075i) q^{34} +0.150205i q^{35} -2.88530 q^{36} +0.874031 q^{37} +6.75350i q^{38} -2.19559i q^{39} +(7.30182 + 4.21571i) q^{40} -10.8746 q^{41} +(0.106438 + 0.184357i) q^{42} +(-3.09729 - 1.78822i) q^{43} +(-2.14208 - 1.23673i) q^{44} +23.3365 q^{45} +(8.75631 + 5.05546i) q^{46} +7.39390i q^{47} +14.6089 q^{48} +(-3.49905 + 6.06052i) q^{49} +(9.19482 + 5.30863i) q^{50} +(2.23158 - 3.86522i) q^{51} -0.298278i q^{52} -11.3804i q^{53} +(15.9844 - 9.22860i) q^{54} +(17.3254 + 10.0028i) q^{55} +(-0.0535814 - 0.0928057i) q^{56} +(-6.78414 - 11.7505i) q^{57} +1.11579i q^{58} +(1.98394 + 1.14543i) q^{59} +4.57142 q^{60} +10.0127i q^{61} +(-11.2917 + 6.51927i) q^{62} +(-0.256868 - 0.148303i) q^{63} -5.65402 q^{64} +2.41249i q^{65} +28.3527 q^{66} +5.82156 q^{67} +(0.303168 - 0.525103i) q^{68} -20.3136 q^{69} +(-0.116954 - 0.202570i) q^{70} +(-4.26828 + 2.46429i) q^{71} +(-14.4187 + 8.32463i) q^{72} +(5.25710 - 9.10556i) q^{73} +(-1.17874 + 0.680544i) q^{74} -21.3309 q^{75} +(-0.921648 - 1.59634i) q^{76} +(-0.127135 - 0.220204i) q^{77} +(1.70954 + 2.96101i) q^{78} -2.91976i q^{79} -16.0522 q^{80} +(-8.35840 + 14.4772i) q^{81} +(14.6657 - 8.46726i) q^{82} +(6.89131 + 11.9361i) q^{83} +(-0.0503182 - 0.0290512i) q^{84} +(-2.45205 + 4.24707i) q^{85} +5.56942 q^{86} +(-1.12086 - 1.94138i) q^{87} -14.2728 q^{88} +(10.4442 + 6.02998i) q^{89} +(-31.4721 + 18.1704i) q^{90} +(0.0153313 - 0.0265546i) q^{91} -2.75967 q^{92} +(13.0977 - 22.6859i) q^{93} +(-5.75708 - 9.97156i) q^{94} +(7.45437 + 12.9113i) q^{95} +(-6.41124 + 3.70153i) q^{96} +(9.42345 - 5.44063i) q^{97} -10.8978i q^{98} +(-34.2118 + 19.7522i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34862 + 0.778626i −0.953619 + 0.550572i −0.894203 0.447661i \(-0.852257\pi\)
−0.0594154 + 0.998233i \(0.518924\pi\)
\(3\) 1.56432 2.70948i 0.903159 1.56432i 0.0797905 0.996812i \(-0.474575\pi\)
0.823369 0.567506i \(-0.192092\pi\)
\(4\) 0.212518 0.368092i 0.106259 0.184046i
\(5\) −1.71886 + 2.97716i −0.768698 + 1.33142i 0.169571 + 0.985518i \(0.445762\pi\)
−0.938269 + 0.345907i \(0.887571\pi\)
\(6\) 4.87208i 1.98902i
\(7\) 0.0378395 0.0218466i 0.0143020 0.00825725i −0.492832 0.870125i \(-0.664038\pi\)
0.507134 + 0.861867i \(0.330705\pi\)
\(8\) 2.45262i 0.867131i
\(9\) −3.39418 5.87890i −1.13139 1.95963i
\(10\) 5.35340i 1.69290i
\(11\) 5.81943i 1.75462i −0.479920 0.877312i \(-0.659334\pi\)
0.479920 0.877312i \(-0.340666\pi\)
\(12\) −0.664891 1.15162i −0.191937 0.332445i
\(13\) 0.607751 0.350885i 0.168560 0.0973181i −0.413347 0.910574i \(-0.635640\pi\)
0.581907 + 0.813256i \(0.302307\pi\)
\(14\) −0.0340207 + 0.0589256i −0.00909242 + 0.0157485i
\(15\) 5.37769 + 9.31444i 1.38851 + 2.40498i
\(16\) 2.33471 + 4.04383i 0.583677 + 1.01096i
\(17\) 1.42655 0.345990 0.172995 0.984923i \(-0.444656\pi\)
0.172995 + 0.984923i \(0.444656\pi\)
\(18\) 9.15493 + 5.28560i 2.15784 + 1.24583i
\(19\) 2.16840 3.75578i 0.497466 0.861636i −0.502530 0.864560i \(-0.667597\pi\)
0.999996 + 0.00292405i \(0.000930756\pi\)
\(20\) 0.730578 + 1.26540i 0.163362 + 0.282951i
\(21\) 0.136700i 0.0298304i
\(22\) 4.53116 + 7.84820i 0.966047 + 1.67324i
\(23\) −3.24640 5.62292i −0.676920 1.17246i −0.975904 0.218202i \(-0.929981\pi\)
0.298983 0.954258i \(-0.403352\pi\)
\(24\) −6.64531 3.83667i −1.35647 0.783158i
\(25\) −3.40897 5.90451i −0.681795 1.18090i
\(26\) −0.546417 + 0.946422i −0.107161 + 0.185609i
\(27\) −11.8524 −2.28100
\(28\) 0.0185712i 0.00350962i
\(29\) 0.358257 0.620519i 0.0665266 0.115227i −0.830844 0.556506i \(-0.812142\pi\)
0.897370 + 0.441279i \(0.145475\pi\)
\(30\) −14.5049 8.37443i −2.64823 1.52895i
\(31\) 8.37278 1.50380 0.751898 0.659280i \(-0.229139\pi\)
0.751898 + 0.659280i \(0.229139\pi\)
\(32\) −2.04921 1.18311i −0.362253 0.209147i
\(33\) −15.7676 9.10344i −2.74479 1.58471i
\(34\) −1.92388 + 1.11075i −0.329943 + 0.190493i
\(35\) 0.150205i 0.0253893i
\(36\) −2.88530 −0.480883
\(37\) 0.874031 0.143690 0.0718449 0.997416i \(-0.477111\pi\)
0.0718449 + 0.997416i \(0.477111\pi\)
\(38\) 6.75350i 1.09556i
\(39\) 2.19559i 0.351575i
\(40\) 7.30182 + 4.21571i 1.15452 + 0.666562i
\(41\) −10.8746 −1.69833 −0.849165 0.528128i \(-0.822894\pi\)
−0.849165 + 0.528128i \(0.822894\pi\)
\(42\) 0.106438 + 0.184357i 0.0164238 + 0.0284469i
\(43\) −3.09729 1.78822i −0.472332 0.272701i 0.244884 0.969552i \(-0.421250\pi\)
−0.717215 + 0.696852i \(0.754584\pi\)
\(44\) −2.14208 1.23673i −0.322931 0.186444i
\(45\) 23.3365 3.47880
\(46\) 8.75631 + 5.05546i 1.29105 + 0.745387i
\(47\) 7.39390i 1.07851i 0.842142 + 0.539255i \(0.181294\pi\)
−0.842142 + 0.539255i \(0.818706\pi\)
\(48\) 14.6089 2.10861
\(49\) −3.49905 + 6.06052i −0.499864 + 0.865789i
\(50\) 9.19482 + 5.30863i 1.30034 + 0.750754i
\(51\) 2.23158 3.86522i 0.312484 0.541239i
\(52\) 0.298278i 0.0413637i
\(53\) 11.3804i 1.56322i −0.623770 0.781608i \(-0.714400\pi\)
0.623770 0.781608i \(-0.285600\pi\)
\(54\) 15.9844 9.22860i 2.17520 1.25585i
\(55\) 17.3254 + 10.0028i 2.33615 + 1.34878i
\(56\) −0.0535814 0.0928057i −0.00716012 0.0124017i
\(57\) −6.78414 11.7505i −0.898581 1.55639i
\(58\) 1.11579i 0.146511i
\(59\) 1.98394 + 1.14543i 0.258287 + 0.149122i 0.623553 0.781781i \(-0.285689\pi\)
−0.365266 + 0.930903i \(0.619022\pi\)
\(60\) 4.57142 0.590168
\(61\) 10.0127i 1.28200i 0.767541 + 0.641000i \(0.221480\pi\)
−0.767541 + 0.641000i \(0.778520\pi\)
\(62\) −11.2917 + 6.51927i −1.43405 + 0.827947i
\(63\) −0.256868 0.148303i −0.0323623 0.0186844i
\(64\) −5.65402 −0.706753
\(65\) 2.41249i 0.299233i
\(66\) 28.3527 3.48998
\(67\) 5.82156 0.711216 0.355608 0.934635i \(-0.384274\pi\)
0.355608 + 0.934635i \(0.384274\pi\)
\(68\) 0.303168 0.525103i 0.0367645 0.0636781i
\(69\) −20.3136 −2.44547
\(70\) −0.116954 0.202570i −0.0139787 0.0242117i
\(71\) −4.26828 + 2.46429i −0.506552 + 0.292458i −0.731415 0.681932i \(-0.761140\pi\)
0.224863 + 0.974390i \(0.427807\pi\)
\(72\) −14.4187 + 8.32463i −1.69926 + 0.981067i
\(73\) 5.25710 9.10556i 0.615296 1.06572i −0.375036 0.927010i \(-0.622370\pi\)
0.990332 0.138715i \(-0.0442970\pi\)
\(74\) −1.17874 + 0.680544i −0.137025 + 0.0791116i
\(75\) −21.3309 −2.46308
\(76\) −0.921648 1.59634i −0.105720 0.183113i
\(77\) −0.127135 0.220204i −0.0144884 0.0250946i
\(78\) 1.70954 + 2.96101i 0.193567 + 0.335269i
\(79\) 2.91976i 0.328499i −0.986419 0.164249i \(-0.947480\pi\)
0.986419 0.164249i \(-0.0525202\pi\)
\(80\) −16.0522 −1.79469
\(81\) −8.35840 + 14.4772i −0.928711 + 1.60857i
\(82\) 14.6657 8.46726i 1.61956 0.935053i
\(83\) 6.89131 + 11.9361i 0.756419 + 1.31016i 0.944666 + 0.328035i \(0.106386\pi\)
−0.188246 + 0.982122i \(0.560280\pi\)
\(84\) −0.0503182 0.0290512i −0.00549017 0.00316975i
\(85\) −2.45205 + 4.24707i −0.265962 + 0.460660i
\(86\) 5.56942 0.600566
\(87\) −1.12086 1.94138i −0.120168 0.208138i
\(88\) −14.2728 −1.52149
\(89\) 10.4442 + 6.02998i 1.10709 + 0.639177i 0.938073 0.346437i \(-0.112609\pi\)
0.169014 + 0.985614i \(0.445942\pi\)
\(90\) −31.4721 + 18.1704i −3.31745 + 1.91533i
\(91\) 0.0153313 0.0265546i 0.00160716 0.00278368i
\(92\) −2.75967 −0.287715
\(93\) 13.0977 22.6859i 1.35817 2.35241i
\(94\) −5.75708 9.97156i −0.593798 1.02849i
\(95\) 7.45437 + 12.9113i 0.764802 + 1.32468i
\(96\) −6.41124 + 3.70153i −0.654344 + 0.377786i
\(97\) 9.42345 5.44063i 0.956806 0.552412i 0.0616175 0.998100i \(-0.480374\pi\)
0.895189 + 0.445688i \(0.147041\pi\)
\(98\) 10.8978i 1.10084i
\(99\) −34.2118 + 19.7522i −3.43842 + 1.98517i
\(100\) −2.89787 −0.289787
\(101\) 2.62987i 0.261682i 0.991403 + 0.130841i \(0.0417678\pi\)
−0.991403 + 0.130841i \(0.958232\pi\)
\(102\) 6.95028i 0.688180i
\(103\) 10.0630i 0.991539i 0.868454 + 0.495769i \(0.165114\pi\)
−0.868454 + 0.495769i \(0.834886\pi\)
\(104\) −0.860588 1.49058i −0.0843876 0.146164i
\(105\) 0.406978 + 0.234969i 0.0397170 + 0.0229306i
\(106\) 8.86106 + 15.3478i 0.860663 + 1.49071i
\(107\) 6.88199 3.97332i 0.665307 0.384115i −0.128989 0.991646i \(-0.541173\pi\)
0.794296 + 0.607531i \(0.207840\pi\)
\(108\) −2.51885 + 4.36278i −0.242376 + 0.419808i
\(109\) 1.03360 1.79025i 0.0990009 0.171475i −0.812270 0.583281i \(-0.801769\pi\)
0.911271 + 0.411806i \(0.135102\pi\)
\(110\) −31.1538 −2.97039
\(111\) 1.36726 2.36817i 0.129775 0.224777i
\(112\) 0.176688 + 0.102011i 0.0166955 + 0.00963913i
\(113\) −2.14992 + 1.24126i −0.202247 + 0.116767i −0.597703 0.801717i \(-0.703920\pi\)
0.395456 + 0.918485i \(0.370587\pi\)
\(114\) 18.2985 + 10.5646i 1.71381 + 0.989467i
\(115\) 22.3204 2.08139
\(116\) −0.152272 0.263743i −0.0141381 0.0244879i
\(117\) −4.12564 2.38194i −0.381415 0.220210i
\(118\) −3.56745 −0.328410
\(119\) 0.0539800 0.0311654i 0.00494834 0.00285693i
\(120\) 22.8448 13.1894i 2.08543 1.20402i
\(121\) −22.8658 −2.07871
\(122\) −7.79618 13.5034i −0.705833 1.22254i
\(123\) −17.0114 + 29.4645i −1.53386 + 2.65673i
\(124\) 1.77936 3.08195i 0.159792 0.276767i
\(125\) 6.24959 0.558981
\(126\) 0.461890 0.0411484
\(127\) 11.2623i 0.999372i −0.866207 0.499686i \(-0.833449\pi\)
0.866207 0.499686i \(-0.166551\pi\)
\(128\) 11.7236 6.76860i 1.03623 0.598265i
\(129\) −9.69028 + 5.59469i −0.853181 + 0.492585i
\(130\) −1.87843 3.25354i −0.164749 0.285354i
\(131\) 18.0110i 1.57363i 0.617189 + 0.786815i \(0.288271\pi\)
−0.617189 + 0.786815i \(0.711729\pi\)
\(132\) −6.70180 + 3.86929i −0.583317 + 0.336778i
\(133\) 0.189489i 0.0164308i
\(134\) −7.85107 + 4.53282i −0.678229 + 0.391576i
\(135\) 20.3727 35.2865i 1.75340 3.03698i
\(136\) 3.49879i 0.300019i
\(137\) −9.22950 5.32865i −0.788529 0.455257i 0.0509154 0.998703i \(-0.483786\pi\)
−0.839444 + 0.543446i \(0.817119\pi\)
\(138\) 27.3953 15.8167i 2.33204 1.34641i
\(139\) −1.21603 −0.103143 −0.0515713 0.998669i \(-0.516423\pi\)
−0.0515713 + 0.998669i \(0.516423\pi\)
\(140\) 0.0552893 + 0.0319213i 0.00467280 + 0.00269784i
\(141\) 20.0336 + 11.5664i 1.68713 + 0.974067i
\(142\) 3.83753 6.64680i 0.322038 0.557787i
\(143\) −2.04195 3.53677i −0.170757 0.295759i
\(144\) 15.8488 27.4510i 1.32074 2.28758i
\(145\) 1.23159 + 2.13317i 0.102278 + 0.177150i
\(146\) 16.3733i 1.35506i
\(147\) 10.9472 + 18.9612i 0.902913 + 1.56389i
\(148\) 0.185747 0.321724i 0.0152683 0.0264455i
\(149\) 12.6939 7.32880i 1.03992 0.600399i 0.120110 0.992761i \(-0.461675\pi\)
0.919811 + 0.392362i \(0.128342\pi\)
\(150\) 28.7672 16.6088i 2.34884 1.35610i
\(151\) 2.11413 3.66178i 0.172045 0.297991i −0.767089 0.641540i \(-0.778296\pi\)
0.939135 + 0.343549i \(0.111629\pi\)
\(152\) −9.21150 5.31826i −0.747151 0.431368i
\(153\) −4.84199 8.38656i −0.391451 0.678014i
\(154\) 0.342913 + 0.197981i 0.0276327 + 0.0159538i
\(155\) −14.3916 + 24.9271i −1.15597 + 2.00219i
\(156\) −0.808177 0.466601i −0.0647059 0.0373580i
\(157\) −5.81909 + 10.0790i −0.464414 + 0.804388i −0.999175 0.0406150i \(-0.987068\pi\)
0.534761 + 0.845003i \(0.320402\pi\)
\(158\) 2.27340 + 3.93765i 0.180862 + 0.313263i
\(159\) −30.8349 17.8025i −2.44537 1.41183i
\(160\) 7.04462 4.06722i 0.556926 0.321542i
\(161\) −0.245684 0.141846i −0.0193626 0.0111790i
\(162\) 26.0323i 2.04529i
\(163\) 14.8061i 1.15970i −0.814722 0.579851i \(-0.803111\pi\)
0.814722 0.579851i \(-0.196889\pi\)
\(164\) −2.31105 + 4.00286i −0.180463 + 0.312571i
\(165\) 54.2047 31.2951i 4.21983 2.43632i
\(166\) −18.5875 10.7315i −1.44267 0.832926i
\(167\) 14.3496i 1.11040i −0.831715 0.555202i \(-0.812641\pi\)
0.831715 0.555202i \(-0.187359\pi\)
\(168\) −0.335273 −0.0258669
\(169\) −6.25376 + 10.8318i −0.481058 + 0.833218i
\(170\) 7.63692i 0.585725i
\(171\) −29.4398 −2.25132
\(172\) −1.31646 + 0.760057i −0.100379 + 0.0579538i
\(173\) 1.10800 0.639706i 0.0842399 0.0486359i −0.457288 0.889318i \(-0.651179\pi\)
0.541528 + 0.840683i \(0.317846\pi\)
\(174\) 3.02322 + 1.74545i 0.229189 + 0.132323i
\(175\) −0.257987 0.148949i −0.0195020 0.0112595i
\(176\) 23.5328 13.5867i 1.77385 1.02413i
\(177\) 6.20703 3.58363i 0.466549 0.269362i
\(178\) −18.7804 −1.40765
\(179\) 9.63428i 0.720100i −0.932933 0.360050i \(-0.882760\pi\)
0.932933 0.360050i \(-0.117240\pi\)
\(180\) 4.95943 8.58998i 0.369654 0.640259i
\(181\) 1.00183 0.0744652 0.0372326 0.999307i \(-0.488146\pi\)
0.0372326 + 0.999307i \(0.488146\pi\)
\(182\) 0.0477495i 0.00353943i
\(183\) 27.1293 + 15.6631i 2.00545 + 1.15785i
\(184\) −13.7909 + 7.96217i −1.01668 + 0.586979i
\(185\) −1.50234 + 2.60213i −0.110454 + 0.191312i
\(186\) 40.7928i 2.99107i
\(187\) 8.30173i 0.607083i
\(188\) 2.72163 + 1.57134i 0.198495 + 0.114601i
\(189\) −0.448489 + 0.258935i −0.0326228 + 0.0188348i
\(190\) −20.1062 11.6083i −1.45866 0.842157i
\(191\) 2.01780 + 3.49494i 0.146003 + 0.252885i 0.929747 0.368200i \(-0.120026\pi\)
−0.783744 + 0.621084i \(0.786692\pi\)
\(192\) −8.84469 + 15.3194i −0.638310 + 1.10559i
\(193\) 21.5792 + 12.4587i 1.55330 + 0.896799i 0.997870 + 0.0652368i \(0.0207803\pi\)
0.555432 + 0.831562i \(0.312553\pi\)
\(194\) −8.47243 + 14.6747i −0.608285 + 1.05358i
\(195\) 6.53660 + 3.77391i 0.468096 + 0.270255i
\(196\) 1.48722 + 2.57594i 0.106230 + 0.183996i
\(197\) 9.39165 + 5.42227i 0.669127 + 0.386321i 0.795746 0.605631i \(-0.207079\pi\)
−0.126619 + 0.991951i \(0.540412\pi\)
\(198\) 30.7592 53.2764i 2.18596 3.78619i
\(199\) −0.767218 + 0.442953i −0.0543866 + 0.0314001i −0.526947 0.849898i \(-0.676663\pi\)
0.472560 + 0.881298i \(0.343330\pi\)
\(200\) −14.4815 + 8.36091i −1.02400 + 0.591205i
\(201\) 9.10677 15.7734i 0.642342 1.11257i
\(202\) −2.04769 3.54670i −0.144075 0.249545i
\(203\) 0.0313068i 0.00219731i
\(204\) −0.948503 1.64286i −0.0664085 0.115023i
\(205\) 18.6920 32.3754i 1.30550 2.26120i
\(206\) −7.83533 13.5712i −0.545913 0.945550i
\(207\) −22.0377 + 38.1704i −1.53173 + 2.65303i
\(208\) 2.83784 + 1.63843i 0.196769 + 0.113605i
\(209\) −21.8565 12.6189i −1.51185 0.872865i
\(210\) −0.731812 −0.0504998
\(211\) 21.1357 12.2027i 1.45504 0.840069i 0.456281 0.889836i \(-0.349181\pi\)
0.998761 + 0.0497669i \(0.0158478\pi\)
\(212\) −4.18902 2.41853i −0.287703 0.166106i
\(213\) 15.4198i 1.05654i
\(214\) −6.18746 + 10.7170i −0.422966 + 0.732599i
\(215\) 10.6476 6.14740i 0.726161 0.419249i
\(216\) 29.0694i 1.97792i
\(217\) 0.316821 0.182917i 0.0215072 0.0124172i
\(218\) 3.21915i 0.218028i
\(219\) −16.4475 28.4880i −1.11142 1.92504i
\(220\) 7.36389 4.25154i 0.496473 0.286639i
\(221\) 0.866990 0.500557i 0.0583201 0.0336711i
\(222\) 4.25835i 0.285802i
\(223\) 15.5431 1.04084 0.520421 0.853910i \(-0.325775\pi\)
0.520421 + 0.853910i \(0.325775\pi\)
\(224\) −0.103388 −0.00690791
\(225\) −23.1413 + 40.0820i −1.54276 + 2.67213i
\(226\) 1.93295 3.34796i 0.128578 0.222703i
\(227\) −9.46934 16.4014i −0.628502 1.08860i −0.987852 0.155395i \(-0.950335\pi\)
0.359350 0.933203i \(-0.382998\pi\)
\(228\) −5.76700 −0.381929
\(229\) −21.3697 + 12.3378i −1.41215 + 0.815304i −0.995591 0.0938048i \(-0.970097\pi\)
−0.416558 + 0.909109i \(0.636764\pi\)
\(230\) −30.1018 + 17.3793i −1.98485 + 1.14596i
\(231\) −0.795518 −0.0523412
\(232\) −1.52190 0.878667i −0.0999174 0.0576873i
\(233\) 11.8911 + 20.5960i 0.779012 + 1.34929i 0.932512 + 0.361140i \(0.117612\pi\)
−0.153500 + 0.988149i \(0.549054\pi\)
\(234\) 7.41856 0.484966
\(235\) −22.0128 12.7091i −1.43596 0.829050i
\(236\) 0.843246 0.486848i 0.0548906 0.0316911i
\(237\) −7.91103 4.56743i −0.513877 0.296687i
\(238\) −0.0485324 + 0.0840606i −0.00314589 + 0.00544884i
\(239\) 4.69753 0.303858 0.151929 0.988391i \(-0.451452\pi\)
0.151929 + 0.988391i \(0.451452\pi\)
\(240\) −25.1107 + 43.4930i −1.62089 + 2.80746i
\(241\) 5.57770 9.66087i 0.359291 0.622311i −0.628551 0.777768i \(-0.716352\pi\)
0.987843 + 0.155457i \(0.0496851\pi\)
\(242\) 30.8372 17.8039i 1.98229 1.14448i
\(243\) 8.37177 + 14.5003i 0.537049 + 0.930197i
\(244\) 3.68560 + 2.12788i 0.235947 + 0.136224i
\(245\) −12.0288 20.8344i −0.768489 1.33106i
\(246\) 52.9820i 3.37801i
\(247\) 3.04344i 0.193650i
\(248\) 20.5352i 1.30399i
\(249\) 43.1208 2.73267
\(250\) −8.42833 + 4.86610i −0.533054 + 0.307759i
\(251\) 8.56674i 0.540728i 0.962758 + 0.270364i \(0.0871440\pi\)
−0.962758 + 0.270364i \(0.912856\pi\)
\(252\) −0.109178 + 0.0630340i −0.00687757 + 0.00397077i
\(253\) −32.7222 + 18.8922i −2.05723 + 1.18774i
\(254\) 8.76916 + 15.1886i 0.550226 + 0.953020i
\(255\) 7.67157 + 13.2876i 0.480412 + 0.832099i
\(256\) −4.88639 + 8.46348i −0.305399 + 0.528967i
\(257\) −11.7251 −0.731394 −0.365697 0.930734i \(-0.619169\pi\)
−0.365697 + 0.930734i \(0.619169\pi\)
\(258\) 8.71234 15.0902i 0.542406 0.939476i
\(259\) 0.0330729 0.0190946i 0.00205505 0.00118648i
\(260\) 0.888019 + 0.512698i 0.0550726 + 0.0317962i
\(261\) −4.86396 −0.301071
\(262\) −14.0238 24.2900i −0.866396 1.50064i
\(263\) −14.1949 −0.875293 −0.437647 0.899147i \(-0.644188\pi\)
−0.437647 + 0.899147i \(0.644188\pi\)
\(264\) −22.3273 + 38.6719i −1.37415 + 2.38009i
\(265\) 33.8812 + 19.5613i 2.08130 + 1.20164i
\(266\) 0.147541 + 0.255549i 0.00904633 + 0.0156687i
\(267\) 32.6762 18.8656i 1.99975 1.15456i
\(268\) 1.23718 2.14287i 0.0755731 0.130896i
\(269\) 5.70965 0.348124 0.174062 0.984735i \(-0.444311\pi\)
0.174062 + 0.984735i \(0.444311\pi\)
\(270\) 63.4508i 3.86149i
\(271\) −0.878825 1.52217i −0.0533848 0.0924652i 0.838098 0.545520i \(-0.183668\pi\)
−0.891483 + 0.453054i \(0.850334\pi\)
\(272\) 3.33059 + 5.76875i 0.201947 + 0.349782i
\(273\) −0.0479661 0.0830798i −0.00290304 0.00502822i
\(274\) 16.5961 1.00261
\(275\) −34.3609 + 19.8383i −2.07204 + 1.19629i
\(276\) −4.31700 + 7.47726i −0.259853 + 0.450078i
\(277\) −9.95977 + 5.75028i −0.598425 + 0.345501i −0.768422 0.639944i \(-0.778958\pi\)
0.169997 + 0.985445i \(0.445624\pi\)
\(278\) 1.63997 0.946836i 0.0983588 0.0567875i
\(279\) −28.4187 49.2227i −1.70139 2.94689i
\(280\) 0.368396 0.0220159
\(281\) 6.67211 11.5564i 0.398025 0.689399i −0.595457 0.803387i \(-0.703029\pi\)
0.993482 + 0.113988i \(0.0363625\pi\)
\(282\) −36.0236 −2.14518
\(283\) −14.0398 −0.834579 −0.417290 0.908774i \(-0.637020\pi\)
−0.417290 + 0.908774i \(0.637020\pi\)
\(284\) 2.09483i 0.124305i
\(285\) 46.6440 2.76295
\(286\) 5.50764 + 3.17984i 0.325674 + 0.188028i
\(287\) −0.411490 + 0.237574i −0.0242895 + 0.0140235i
\(288\) 16.0628i 0.946510i
\(289\) −14.9649 −0.880291
\(290\) −3.32189 1.91789i −0.195068 0.112623i
\(291\) 34.0435i 1.99567i
\(292\) −2.23445 3.87019i −0.130761 0.226486i
\(293\) 7.18679 + 12.4479i 0.419857 + 0.727214i 0.995925 0.0901884i \(-0.0287469\pi\)
−0.576068 + 0.817402i \(0.695414\pi\)
\(294\) −29.5273 17.0476i −1.72207 0.994237i
\(295\) −6.82024 + 3.93767i −0.397090 + 0.229260i
\(296\) 2.14366i 0.124598i
\(297\) 68.9743i 4.00229i
\(298\) −11.4128 + 19.7675i −0.661126 + 1.14510i
\(299\) −3.94600 2.27823i −0.228203 0.131753i
\(300\) −4.53319 + 7.85172i −0.261724 + 0.453319i
\(301\) −0.156266 −0.00900703
\(302\) 6.58447i 0.378894i
\(303\) 7.12559 + 4.11396i 0.409354 + 0.236341i
\(304\) 20.2503 1.16144
\(305\) −29.8095 17.2105i −1.70689 0.985471i
\(306\) 13.0600 + 7.54019i 0.746590 + 0.431044i
\(307\) −0.119591 0.207138i −0.00682543 0.0118220i 0.862593 0.505899i \(-0.168839\pi\)
−0.869418 + 0.494077i \(0.835506\pi\)
\(308\) −0.108074 −0.00615807
\(309\) 27.2655 + 15.7418i 1.55108 + 0.895518i
\(310\) 44.8229i 2.54577i
\(311\) 18.7578i 1.06366i 0.846853 + 0.531828i \(0.178495\pi\)
−0.846853 + 0.531828i \(0.821505\pi\)
\(312\) −5.38493 −0.304862
\(313\) −2.26407 −0.127973 −0.0639865 0.997951i \(-0.520381\pi\)
−0.0639865 + 0.997951i \(0.520381\pi\)
\(314\) 18.1236i 1.02277i
\(315\) 0.883041 0.509824i 0.0497537 0.0287253i
\(316\) −1.07474 0.620501i −0.0604588 0.0349059i
\(317\) 5.48913 + 3.16915i 0.308300 + 0.177997i 0.646166 0.763197i \(-0.276372\pi\)
−0.337865 + 0.941194i \(0.609705\pi\)
\(318\) 55.4461 3.10926
\(319\) −3.61107 2.08485i −0.202181 0.116729i
\(320\) 9.71848 16.8329i 0.543280 0.940988i
\(321\) 24.8621i 1.38767i
\(322\) 0.441779 0.0246194
\(323\) 3.09334 5.35783i 0.172118 0.298117i
\(324\) 3.55262 + 6.15332i 0.197368 + 0.341851i
\(325\) −4.14362 2.39232i −0.229846 0.132702i
\(326\) 11.5284 + 19.9678i 0.638499 + 1.10591i
\(327\) −3.23376 5.60103i −0.178827 0.309738i
\(328\) 26.6713i 1.47267i
\(329\) 0.161532 + 0.279781i 0.00890553 + 0.0154248i
\(330\) −48.7344 + 84.4104i −2.68274 + 4.64664i
\(331\) −19.2568 11.1179i −1.05845 0.611096i −0.133446 0.991056i \(-0.542604\pi\)
−0.925003 + 0.379960i \(0.875938\pi\)
\(332\) 5.85810 0.321505
\(333\) −2.96662 5.13834i −0.162570 0.281579i
\(334\) 11.1730 + 19.3522i 0.611358 + 1.05890i
\(335\) −10.0065 + 17.3317i −0.546711 + 0.946931i
\(336\) 0.552793 0.319155i 0.0301573 0.0174113i
\(337\) −3.87135 6.70537i −0.210886 0.365265i 0.741106 0.671388i \(-0.234301\pi\)
−0.951992 + 0.306123i \(0.900968\pi\)
\(338\) 19.4774i 1.05943i
\(339\) 7.76687i 0.421839i
\(340\) 1.04221 + 1.80516i 0.0565217 + 0.0978984i
\(341\) 48.7248i 2.63860i
\(342\) 39.7031 22.9226i 2.14690 1.23951i
\(343\) 0.611622i 0.0330245i
\(344\) −4.38582 + 7.59646i −0.236467 + 0.409573i
\(345\) 34.9162 60.4767i 1.87983 3.25596i
\(346\) −0.996183 + 1.72544i −0.0535551 + 0.0927602i
\(347\) 25.8460 14.9222i 1.38749 0.801067i 0.394457 0.918914i \(-0.370933\pi\)
0.993032 + 0.117847i \(0.0375994\pi\)
\(348\) −0.952807 −0.0510758
\(349\) 17.9444 + 5.19612i 0.960540 + 0.278142i
\(350\) 0.463903 0.0247966
\(351\) −7.20332 + 4.15884i −0.384485 + 0.221982i
\(352\) −6.88504 + 11.9252i −0.366974 + 0.635618i
\(353\) 16.2980 28.2289i 0.867453 1.50247i 0.00286143 0.999996i \(-0.499089\pi\)
0.864591 0.502476i \(-0.167577\pi\)
\(354\) −5.58062 + 9.66592i −0.296607 + 0.513738i
\(355\) 16.9431i 0.899248i
\(356\) 4.43917 2.56296i 0.235276 0.135836i
\(357\) 0.195010i 0.0103210i
\(358\) 7.50150 + 12.9930i 0.396467 + 0.686701i
\(359\) 12.3124i 0.649824i 0.945744 + 0.324912i \(0.105335\pi\)
−0.945744 + 0.324912i \(0.894665\pi\)
\(360\) 57.2356i 3.01658i
\(361\) 0.0960647 + 0.166389i 0.00505604 + 0.00875731i
\(362\) −1.35108 + 0.780048i −0.0710114 + 0.0409984i
\(363\) −35.7693 + 61.9543i −1.87740 + 3.25176i
\(364\) −0.00651636 0.0112867i −0.000341550 0.000591582i
\(365\) 18.0724 + 31.3024i 0.945955 + 1.63844i
\(366\) −48.7828 −2.54992
\(367\) −12.4993 7.21646i −0.652457 0.376696i 0.136940 0.990579i \(-0.456273\pi\)
−0.789397 + 0.613883i \(0.789607\pi\)
\(368\) 15.1588 26.2558i 0.790206 1.36868i
\(369\) 36.9104 + 63.9307i 1.92148 + 3.32810i
\(370\) 4.67904i 0.243252i
\(371\) −0.248623 0.430627i −0.0129079 0.0223571i
\(372\) −5.56698 9.64230i −0.288635 0.499930i
\(373\) 31.9489 + 18.4457i 1.65425 + 0.955081i 0.975297 + 0.220899i \(0.0708991\pi\)
0.678952 + 0.734182i \(0.262434\pi\)
\(374\) 6.46395 + 11.1959i 0.334243 + 0.578925i
\(375\) 9.77635 16.9331i 0.504849 0.874423i
\(376\) 18.1344 0.935210
\(377\) 0.502828i 0.0258970i
\(378\) 0.403228 0.698411i 0.0207398 0.0359224i
\(379\) 13.7436 + 7.93485i 0.705959 + 0.407586i 0.809563 0.587033i \(-0.199704\pi\)
−0.103604 + 0.994619i \(0.533037\pi\)
\(380\) 6.33674 0.325068
\(381\) −30.5151 17.6179i −1.56334 0.902592i
\(382\) −5.44250 3.14223i −0.278462 0.160770i
\(383\) 9.82887 5.67470i 0.502232 0.289964i −0.227403 0.973801i \(-0.573023\pi\)
0.729635 + 0.683837i \(0.239690\pi\)
\(384\) 42.3529i 2.16131i
\(385\) 0.874109 0.0445487
\(386\) −38.8028 −1.97501
\(387\) 24.2782i 1.23413i
\(388\) 4.62492i 0.234795i
\(389\) 2.03903 + 1.17723i 0.103383 + 0.0596881i 0.550800 0.834637i \(-0.314323\pi\)
−0.447417 + 0.894325i \(0.647656\pi\)
\(390\) −11.7539 −0.595180
\(391\) −4.63116 8.02140i −0.234208 0.405660i
\(392\) 14.8641 + 8.58182i 0.750753 + 0.433447i
\(393\) 48.8005 + 28.1750i 2.46166 + 1.42124i
\(394\) −16.8877 −0.850789
\(395\) 8.69258 + 5.01867i 0.437371 + 0.252516i
\(396\) 16.7908i 0.843769i
\(397\) 33.8893 1.70086 0.850428 0.526091i \(-0.176343\pi\)
0.850428 + 0.526091i \(0.176343\pi\)
\(398\) 0.689790 1.19475i 0.0345761 0.0598875i
\(399\) −0.513416 0.296421i −0.0257030 0.0148396i
\(400\) 15.9179 27.5706i 0.795896 1.37853i
\(401\) 3.81354i 0.190439i −0.995456 0.0952197i \(-0.969645\pi\)
0.995456 0.0952197i \(-0.0303554\pi\)
\(402\) 28.3631i 1.41462i
\(403\) 5.08857 2.93789i 0.253480 0.146347i
\(404\) 0.968035 + 0.558895i 0.0481615 + 0.0278061i
\(405\) −28.7339 49.7685i −1.42780 2.47302i
\(406\) 0.0243763 + 0.0422210i 0.00120978 + 0.00209539i
\(407\) 5.08636i 0.252122i
\(408\) −9.47990 5.47322i −0.469325 0.270965i
\(409\) −1.30971 −0.0647611 −0.0323805 0.999476i \(-0.510309\pi\)
−0.0323805 + 0.999476i \(0.510309\pi\)
\(410\) 58.2162i 2.87509i
\(411\) −28.8757 + 16.6714i −1.42433 + 0.822340i
\(412\) 3.70411 + 2.13857i 0.182489 + 0.105360i
\(413\) 0.100095 0.00492535
\(414\) 68.6366i 3.37330i
\(415\) −47.3808 −2.32583
\(416\) −1.66055 −0.0814151
\(417\) −1.90226 + 3.29482i −0.0931543 + 0.161348i
\(418\) 39.3015 1.92230
\(419\) 5.93968 + 10.2878i 0.290172 + 0.502593i 0.973850 0.227191i \(-0.0729540\pi\)
−0.683678 + 0.729784i \(0.739621\pi\)
\(420\) 0.172980 0.0998701i 0.00844057 0.00487316i
\(421\) −18.5540 + 10.7121i −0.904264 + 0.522077i −0.878581 0.477593i \(-0.841509\pi\)
−0.0256831 + 0.999670i \(0.508176\pi\)
\(422\) −19.0027 + 32.9136i −0.925037 + 1.60221i
\(423\) 43.4680 25.0962i 2.11348 1.22022i
\(424\) −27.9117 −1.35551
\(425\) −4.86308 8.42311i −0.235894 0.408581i
\(426\) −12.0062 20.7954i −0.581704 1.00754i
\(427\) 0.218744 + 0.378876i 0.0105858 + 0.0183351i
\(428\) 3.37761i 0.163263i
\(429\) −12.7771 −0.616882
\(430\) −9.57306 + 16.5810i −0.461654 + 0.799608i
\(431\) −11.7859 + 6.80461i −0.567708 + 0.327767i −0.756234 0.654302i \(-0.772963\pi\)
0.188525 + 0.982068i \(0.439629\pi\)
\(432\) −27.6719 47.9292i −1.33137 2.30599i
\(433\) −25.4331 14.6838i −1.22224 0.705659i −0.256842 0.966453i \(-0.582682\pi\)
−0.965394 + 0.260795i \(0.916015\pi\)
\(434\) −0.284848 + 0.493371i −0.0136731 + 0.0236826i
\(435\) 7.70638 0.369493
\(436\) −0.439317 0.760919i −0.0210395 0.0364414i
\(437\) −28.1580 −1.34698
\(438\) 44.3630 + 25.6130i 2.11974 + 1.22384i
\(439\) −4.74587 + 2.74003i −0.226508 + 0.130774i −0.608960 0.793201i \(-0.708413\pi\)
0.382452 + 0.923975i \(0.375080\pi\)
\(440\) 24.5330 42.4925i 1.16957 2.02575i
\(441\) 47.5056 2.26217
\(442\) −0.779494 + 1.35012i −0.0370767 + 0.0642188i
\(443\) −3.84959 6.66769i −0.182900 0.316792i 0.759967 0.649962i \(-0.225215\pi\)
−0.942867 + 0.333170i \(0.891882\pi\)
\(444\) −0.581136 1.00656i −0.0275795 0.0477691i
\(445\) −35.9044 + 20.7294i −1.70203 + 0.982668i
\(446\) −20.9617 + 12.1022i −0.992565 + 0.573058i
\(447\) 45.8583i 2.16902i
\(448\) −0.213945 + 0.123521i −0.0101080 + 0.00583583i
\(449\) −16.8192 −0.793748 −0.396874 0.917873i \(-0.629905\pi\)
−0.396874 + 0.917873i \(0.629905\pi\)
\(450\) 72.0739i 3.39759i
\(451\) 63.2841i 2.97993i
\(452\) 1.05516i 0.0496303i
\(453\) −6.61434 11.4564i −0.310769 0.538268i
\(454\) 25.5411 + 14.7462i 1.19870 + 0.692072i
\(455\) 0.0527049 + 0.0912875i 0.00247084 + 0.00427962i
\(456\) −28.8194 + 16.6389i −1.34959 + 0.779188i
\(457\) 5.57187 9.65076i 0.260641 0.451443i −0.705771 0.708440i \(-0.749399\pi\)
0.966412 + 0.256996i \(0.0827328\pi\)
\(458\) 19.2131 33.2780i 0.897767 1.55498i
\(459\) −16.9081 −0.789203
\(460\) 4.74349 8.21596i 0.221166 0.383071i
\(461\) 8.73782 + 5.04478i 0.406961 + 0.234959i 0.689483 0.724302i \(-0.257838\pi\)
−0.282522 + 0.959261i \(0.591171\pi\)
\(462\) 1.07285 0.619411i 0.0499135 0.0288176i
\(463\) −9.51662 5.49442i −0.442275 0.255348i 0.262287 0.964990i \(-0.415523\pi\)
−0.704562 + 0.709642i \(0.748857\pi\)
\(464\) 3.34570 0.155320
\(465\) 45.0262 + 77.9877i 2.08804 + 3.61659i
\(466\) −32.0732 18.5175i −1.48576 0.857804i
\(467\) 27.2303 1.26007 0.630034 0.776568i \(-0.283041\pi\)
0.630034 + 0.776568i \(0.283041\pi\)
\(468\) −1.75354 + 1.01241i −0.0810576 + 0.0467986i
\(469\) 0.220285 0.127181i 0.0101718 0.00587269i
\(470\) 39.5825 1.82581
\(471\) 18.2058 + 31.5334i 0.838879 + 1.45298i
\(472\) 2.80930 4.86585i 0.129309 0.223969i
\(473\) −10.4064 + 18.0244i −0.478487 + 0.828764i
\(474\) 14.2253 0.653390
\(475\) −29.5681 −1.35668
\(476\) 0.0264928i 0.00121430i
\(477\) −66.9041 + 38.6271i −3.06333 + 1.76861i
\(478\) −6.33518 + 3.65762i −0.289764 + 0.167296i
\(479\) 3.82096 + 6.61810i 0.174584 + 0.302389i 0.940017 0.341127i \(-0.110809\pi\)
−0.765433 + 0.643516i \(0.777475\pi\)
\(480\) 25.4497i 1.16161i
\(481\) 0.531194 0.306685i 0.0242204 0.0139836i
\(482\) 17.3718i 0.791263i
\(483\) −0.768655 + 0.443783i −0.0349750 + 0.0201928i
\(484\) −4.85938 + 8.41670i −0.220881 + 0.382577i
\(485\) 37.4068i 1.69855i
\(486\) −22.5807 13.0370i −1.02428 0.591369i
\(487\) 20.4833 11.8260i 0.928186 0.535888i 0.0419485 0.999120i \(-0.486643\pi\)
0.886237 + 0.463231i \(0.153310\pi\)
\(488\) 24.5574 1.11166
\(489\) −40.1168 23.1614i −1.81414 1.04740i
\(490\) 32.4444 + 18.7318i 1.46569 + 0.846217i
\(491\) 5.29639 9.17361i 0.239023 0.413999i −0.721411 0.692507i \(-0.756506\pi\)
0.960434 + 0.278507i \(0.0898396\pi\)
\(492\) 7.23043 + 12.5235i 0.325973 + 0.564602i
\(493\) 0.511073 0.885204i 0.0230176 0.0398676i
\(494\) 2.36970 + 4.10445i 0.106618 + 0.184668i
\(495\) 135.805i 6.10399i
\(496\) 19.5480 + 33.8581i 0.877731 + 1.52027i
\(497\) −0.107673 + 0.186495i −0.00482980 + 0.00836545i
\(498\) −58.1536 + 33.5750i −2.60592 + 1.50453i
\(499\) −33.7396 + 19.4796i −1.51039 + 0.872024i −0.510464 + 0.859899i \(0.670526\pi\)
−0.999926 + 0.0121254i \(0.996140\pi\)
\(500\) 1.32815 2.30042i 0.0593967 0.102878i
\(501\) −38.8799 22.4473i −1.73703 1.00287i
\(502\) −6.67029 11.5533i −0.297710 0.515648i
\(503\) 20.6937 + 11.9475i 0.922688 + 0.532714i 0.884492 0.466556i \(-0.154505\pi\)
0.0381964 + 0.999270i \(0.487839\pi\)
\(504\) −0.363730 + 0.629999i −0.0162018 + 0.0280624i
\(505\) −7.82954 4.52039i −0.348410 0.201155i
\(506\) 29.4199 50.9567i 1.30787 2.26530i
\(507\) 19.5657 + 33.8888i 0.868945 + 1.50506i
\(508\) −4.14558 2.39345i −0.183930 0.106192i
\(509\) 14.6911 8.48193i 0.651173 0.375955i −0.137733 0.990469i \(-0.543981\pi\)
0.788905 + 0.614515i \(0.210648\pi\)
\(510\) −20.6921 11.9466i −0.916260 0.529003i
\(511\) 0.459399i 0.0203226i
\(512\) 11.8557i 0.523952i
\(513\) −25.7008 + 44.5151i −1.13472 + 1.96539i
\(514\) 15.8128 9.12950i 0.697471 0.402685i
\(515\) −29.9592 17.2969i −1.32016 0.762194i
\(516\) 4.75588i 0.209366i
\(517\) 43.0283 1.89238
\(518\) −0.0297352 + 0.0515028i −0.00130649 + 0.00226290i
\(519\) 4.00281i 0.175704i
\(520\) 5.91693 0.259474
\(521\) −16.1687 + 9.33499i −0.708363 + 0.408973i −0.810455 0.585802i \(-0.800780\pi\)
0.102092 + 0.994775i \(0.467446\pi\)
\(522\) 6.55963 3.78720i 0.287107 0.165761i
\(523\) −3.21643 1.85701i −0.140645 0.0812014i 0.428026 0.903766i \(-0.359209\pi\)
−0.568671 + 0.822565i \(0.692542\pi\)
\(524\) 6.62970 + 3.82766i 0.289620 + 0.167212i
\(525\) −0.807149 + 0.466007i −0.0352268 + 0.0203382i
\(526\) 19.1435 11.0525i 0.834696 0.481912i
\(527\) 11.9442 0.520298
\(528\) 85.0155i 3.69982i
\(529\) −9.57817 + 16.5899i −0.416442 + 0.721299i
\(530\) −60.9238 −2.64636
\(531\) 15.5512i 0.674864i
\(532\) −0.0697493 0.0402698i −0.00302402 0.00174592i
\(533\) −6.60906 + 3.81574i −0.286270 + 0.165278i
\(534\) −29.3785 + 50.8851i −1.27133 + 2.20201i
\(535\) 27.3184i 1.18108i
\(536\) 14.2780i 0.616718i
\(537\) −26.1039 15.0711i −1.12647 0.650365i
\(538\) −7.70015 + 4.44569i −0.331977 + 0.191667i
\(539\) 35.2688 + 20.3624i 1.51913 + 0.877073i
\(540\) −8.65911 14.9980i −0.372629 0.645412i
\(541\) −5.41679 + 9.38216i −0.232886 + 0.403371i −0.958656 0.284567i \(-0.908150\pi\)
0.725770 + 0.687937i \(0.241484\pi\)
\(542\) 2.37040 + 1.36855i 0.101817 + 0.0587843i
\(543\) 1.56717 2.71443i 0.0672539 0.116487i
\(544\) −2.92331 1.68777i −0.125336 0.0723627i
\(545\) 3.55323 + 6.15438i 0.152204 + 0.263624i
\(546\) 0.129376 + 0.0746954i 0.00553679 + 0.00319667i
\(547\) 4.73766 8.20586i 0.202568 0.350857i −0.746787 0.665063i \(-0.768405\pi\)
0.949355 + 0.314206i \(0.101738\pi\)
\(548\) −3.92286 + 2.26487i −0.167576 + 0.0967503i
\(549\) 58.8638 33.9850i 2.51225 1.45045i
\(550\) 30.8932 53.5086i 1.31729 2.28161i
\(551\) −1.55369 2.69107i −0.0661894 0.114643i
\(552\) 49.8214i 2.12054i
\(553\) −0.0637869 0.110482i −0.00271250 0.00469818i
\(554\) 8.95463 15.5099i 0.380446 0.658952i
\(555\) 4.70027 + 8.14111i 0.199516 + 0.345571i
\(556\) −0.258429 + 0.447612i −0.0109598 + 0.0189830i
\(557\) 28.2592 + 16.3154i 1.19738 + 0.691307i 0.959970 0.280103i \(-0.0903686\pi\)
0.237409 + 0.971410i \(0.423702\pi\)
\(558\) 76.6522 + 44.2551i 3.24494 + 1.87347i
\(559\) −2.50984 −0.106155
\(560\) −0.607405 + 0.350686i −0.0256676 + 0.0148192i
\(561\) −22.4934 12.9865i −0.949671 0.548293i
\(562\) 20.7803i 0.876565i
\(563\) −6.62463 + 11.4742i −0.279195 + 0.483579i −0.971185 0.238328i \(-0.923401\pi\)
0.691990 + 0.721907i \(0.256734\pi\)
\(564\) 8.51500 4.91614i 0.358546 0.207007i
\(565\) 8.53418i 0.359036i
\(566\) 18.9344 10.9318i 0.795870 0.459496i
\(567\) 0.730411i 0.0306744i
\(568\) 6.04397 + 10.4685i 0.253599 + 0.439247i
\(569\) 33.3751 19.2691i 1.39916 0.807804i 0.404853 0.914382i \(-0.367323\pi\)
0.994304 + 0.106578i \(0.0339892\pi\)
\(570\) −62.9051 + 36.3183i −2.63480 + 1.52120i
\(571\) 7.43867i 0.311299i 0.987812 + 0.155649i \(0.0497470\pi\)
−0.987812 + 0.155649i \(0.950253\pi\)
\(572\) −1.73581 −0.0725777
\(573\) 12.6259 0.527456
\(574\) 0.369962 0.640793i 0.0154419 0.0267462i
\(575\) −22.1337 + 38.3368i −0.923041 + 1.59875i
\(576\) 19.1908 + 33.2394i 0.799616 + 1.38498i
\(577\) −30.6578 −1.27630 −0.638151 0.769911i \(-0.720300\pi\)
−0.638151 + 0.769911i \(0.720300\pi\)
\(578\) 20.1820 11.6521i 0.839462 0.484663i
\(579\) 67.5133 38.9788i 2.80576 1.61991i
\(580\) 1.04694 0.0434717
\(581\) 0.521527 + 0.301104i 0.0216366 + 0.0124919i
\(582\) 26.5072 + 45.9118i 1.09876 + 1.90310i
\(583\) −66.2273 −2.74286
\(584\) −22.3324 12.8936i −0.924123 0.533543i
\(585\) 14.1828 8.18845i 0.586387 0.338551i
\(586\) −19.3845 11.1917i −0.800767 0.462323i
\(587\) −3.48790 + 6.04121i −0.143961 + 0.249348i −0.928985 0.370118i \(-0.879317\pi\)
0.785024 + 0.619465i \(0.212651\pi\)
\(588\) 9.30594 0.383770
\(589\) 18.1555 31.4463i 0.748086 1.29572i
\(590\) 6.13195 10.6208i 0.252448 0.437253i
\(591\) 29.3830 16.9643i 1.20866 0.697818i
\(592\) 2.04061 + 3.53444i 0.0838685 + 0.145264i
\(593\) 17.7036 + 10.2212i 0.727000 + 0.419733i 0.817324 0.576179i \(-0.195457\pi\)
−0.0903239 + 0.995912i \(0.528790\pi\)
\(594\) −53.7052 93.0201i −2.20355 3.81666i
\(595\) 0.214276i 0.00878446i
\(596\) 6.23001i 0.255191i
\(597\) 2.77168i 0.113437i
\(598\) 7.09555 0.290158
\(599\) −10.0839 + 5.82193i −0.412016 + 0.237878i −0.691656 0.722227i \(-0.743118\pi\)
0.279639 + 0.960105i \(0.409785\pi\)
\(600\) 52.3165i 2.13581i
\(601\) 21.0862 12.1741i 0.860122 0.496592i −0.00393090 0.999992i \(-0.501251\pi\)
0.864053 + 0.503400i \(0.167918\pi\)
\(602\) 0.210744 0.121673i 0.00858927 0.00495902i
\(603\) −19.7594 34.2243i −0.804666 1.39372i
\(604\) −0.898581 1.55639i −0.0365627 0.0633285i
\(605\) 39.3031 68.0749i 1.59790 2.76764i
\(606\) −12.8129 −0.520490
\(607\) 15.3544 26.5946i 0.623215 1.07944i −0.365668 0.930745i \(-0.619160\pi\)
0.988883 0.148694i \(-0.0475071\pi\)
\(608\) −8.88703 + 5.13093i −0.360417 + 0.208087i
\(609\) −0.0848251 0.0489738i −0.00343729 0.00198452i
\(610\) 53.6022 2.17029
\(611\) 2.59441 + 4.49365i 0.104959 + 0.181794i
\(612\) −4.11603 −0.166381
\(613\) 7.82342 13.5506i 0.315985 0.547302i −0.663662 0.748033i \(-0.730998\pi\)
0.979646 + 0.200731i \(0.0643318\pi\)
\(614\) 0.322566 + 0.186234i 0.0130177 + 0.00751578i
\(615\) −58.4804 101.291i −2.35816 4.08444i
\(616\) −0.540076 + 0.311813i −0.0217603 + 0.0125633i
\(617\) 8.51407 14.7468i 0.342763 0.593684i −0.642181 0.766553i \(-0.721970\pi\)
0.984945 + 0.172869i \(0.0553038\pi\)
\(618\) −49.0278 −1.97219
\(619\) 31.4907i 1.26572i 0.774268 + 0.632858i \(0.218118\pi\)
−0.774268 + 0.632858i \(0.781882\pi\)
\(620\) 6.11696 + 10.5949i 0.245663 + 0.425501i
\(621\) 38.4776 + 66.6452i 1.54405 + 2.67438i
\(622\) −14.6053 25.2971i −0.585619 1.01432i
\(623\) 0.526939 0.0211114
\(624\) 8.87858 5.12605i 0.355428 0.205206i
\(625\) 6.30268 10.9166i 0.252107 0.436662i
\(626\) 3.05337 1.76287i 0.122037 0.0704583i
\(627\) −68.3811 + 39.4798i −2.73088 + 1.57667i
\(628\) 2.47332 + 4.28392i 0.0986962 + 0.170947i
\(629\) 1.24685 0.0497153
\(630\) −0.793925 + 1.37512i −0.0316307 + 0.0547860i
\(631\) −41.5065 −1.65235 −0.826174 0.563414i \(-0.809487\pi\)
−0.826174 + 0.563414i \(0.809487\pi\)
\(632\) −7.16106 −0.284852
\(633\) 76.3556i 3.03486i
\(634\) −9.87033 −0.392001
\(635\) 33.5298 + 19.3584i 1.33059 + 0.768216i
\(636\) −13.1059 + 7.56671i −0.519684 + 0.300040i
\(637\) 4.91106i 0.194583i
\(638\) 6.49328 0.257071
\(639\) 28.9747 + 16.7285i 1.14622 + 0.661771i
\(640\) 46.5371i 1.83954i
\(641\) 15.7911 + 27.3510i 0.623712 + 1.08030i 0.988788 + 0.149323i \(0.0477094\pi\)
−0.365077 + 0.930977i \(0.618957\pi\)
\(642\) 19.3583 + 33.5296i 0.764012 + 1.32331i
\(643\) 15.3238 + 8.84719i 0.604311 + 0.348899i 0.770736 0.637155i \(-0.219889\pi\)
−0.166425 + 0.986054i \(0.553222\pi\)
\(644\) −0.104424 + 0.0602894i −0.00411490 + 0.00237574i
\(645\) 38.4660i 1.51460i
\(646\) 9.63423i 0.379054i
\(647\) 6.43149 11.1397i 0.252848 0.437945i −0.711461 0.702726i \(-0.751966\pi\)
0.964309 + 0.264780i \(0.0852994\pi\)
\(648\) 35.5070 + 20.5000i 1.39485 + 0.805314i
\(649\) 6.66575 11.5454i 0.261653 0.453197i
\(650\) 7.45089 0.292248
\(651\) 1.14456i 0.0448589i
\(652\) −5.45000 3.14656i −0.213438 0.123229i
\(653\) −24.2380 −0.948508 −0.474254 0.880388i \(-0.657282\pi\)
−0.474254 + 0.880388i \(0.657282\pi\)
\(654\) 8.72222 + 5.03578i 0.341066 + 0.196914i
\(655\) −53.6216 30.9584i −2.09517 1.20965i
\(656\) −25.3891 43.9751i −0.991276 1.71694i
\(657\) −71.3742 −2.78457
\(658\) −0.435690 0.251546i −0.0169850 0.00980627i
\(659\) 4.27989i 0.166721i 0.996519 + 0.0833605i \(0.0265653\pi\)
−0.996519 + 0.0833605i \(0.973435\pi\)
\(660\) 26.6031i 1.03552i
\(661\) −41.4254 −1.61126 −0.805630 0.592419i \(-0.798173\pi\)
−0.805630 + 0.592419i \(0.798173\pi\)
\(662\) 34.6268 1.34581
\(663\) 3.13212i 0.121642i
\(664\) 29.2747 16.9017i 1.13608 0.655915i
\(665\) 0.564138 + 0.325705i 0.0218764 + 0.0126303i
\(666\) 8.00169 + 4.61978i 0.310059 + 0.179013i
\(667\) −4.65217 −0.180133
\(668\) −5.28197 3.04954i −0.204365 0.117990i
\(669\) 24.3143 42.1136i 0.940046 1.62821i
\(670\) 31.1651i 1.20401i
\(671\) 58.2684 2.24943
\(672\) −0.161732 + 0.280128i −0.00623894 + 0.0108062i
\(673\) −18.6307 32.2693i −0.718160 1.24389i −0.961728 0.274006i \(-0.911651\pi\)
0.243568 0.969884i \(-0.421682\pi\)
\(674\) 10.4420 + 6.02867i 0.402209 + 0.232216i
\(675\) 40.4046 + 69.9827i 1.55517 + 2.69364i
\(676\) 2.65807 + 4.60391i 0.102233 + 0.177074i
\(677\) 23.5317i 0.904397i 0.891917 + 0.452198i \(0.149360\pi\)
−0.891917 + 0.452198i \(0.850640\pi\)
\(678\) −6.04749 10.4746i −0.232252 0.402273i
\(679\) 0.237719 0.411741i 0.00912281 0.0158012i
\(680\) 10.4164 + 6.01394i 0.399453 + 0.230624i
\(681\) −59.2523 −2.27055
\(682\) 37.9384 + 65.7112i 1.45274 + 2.51621i
\(683\) 19.5119 + 33.7956i 0.746602 + 1.29315i 0.949443 + 0.313941i \(0.101649\pi\)
−0.202840 + 0.979212i \(0.565017\pi\)
\(684\) −6.25648 + 10.8365i −0.239223 + 0.414346i
\(685\) 31.7285 18.3184i 1.21228 0.699911i
\(686\) −0.476225 0.824846i −0.0181824 0.0314928i
\(687\) 77.2009i 2.94540i
\(688\) 16.6999i 0.636677i
\(689\) −3.99321 6.91644i −0.152129 0.263495i
\(690\) 108.747i 4.13992i
\(691\) 18.3808 10.6121i 0.699238 0.403705i −0.107826 0.994170i \(-0.534389\pi\)
0.807063 + 0.590465i \(0.201056\pi\)
\(692\) 0.543795i 0.0206720i
\(693\) −0.863038 + 1.49483i −0.0327841 + 0.0567837i
\(694\) −23.2377 + 40.2488i −0.882090 + 1.52782i
\(695\) 2.09019 3.62032i 0.0792856 0.137327i
\(696\) −4.76146 + 2.74903i −0.180483 + 0.104202i
\(697\) −15.5132 −0.587605
\(698\) −28.2460 + 6.96437i −1.06913 + 0.263605i
\(699\) 74.4059 2.81429
\(700\) −0.109654 + 0.0633087i −0.00414452 + 0.00239284i
\(701\) 0.747795 1.29522i 0.0282438 0.0489197i −0.851558 0.524260i \(-0.824342\pi\)
0.879802 + 0.475341i \(0.157675\pi\)
\(702\) 6.47636 11.2174i 0.244435 0.423373i
\(703\) 1.89525 3.28267i 0.0714808 0.123808i
\(704\) 32.9032i 1.24009i
\(705\) −68.8700 + 39.7621i −2.59379 + 1.49753i
\(706\) 50.7601i 1.91038i
\(707\) 0.0574538 + 0.0995130i 0.00216077 + 0.00374257i
\(708\) 3.04634i 0.114489i
\(709\) 1.06987i 0.0401797i 0.999798 + 0.0200898i \(0.00639522\pi\)
−0.999798 + 0.0200898i \(0.993605\pi\)
\(710\) 13.1924 + 22.8498i 0.495101 + 0.857540i
\(711\) −17.1650 + 9.91020i −0.643737 + 0.371662i
\(712\) 14.7892 25.6157i 0.554250 0.959989i
\(713\) −27.1813 47.0795i −1.01795 1.76314i
\(714\) 0.151840 + 0.262995i 0.00568248 + 0.00984234i
\(715\) 14.0393 0.525042
\(716\) −3.54630 2.04746i −0.132531 0.0765170i
\(717\) 7.34843 12.7278i 0.274432 0.475330i
\(718\) −9.58676 16.6048i −0.357775 0.619684i
\(719\) 41.5884i 1.55099i 0.631355 + 0.775494i \(0.282499\pi\)
−0.631355 + 0.775494i \(0.717501\pi\)
\(720\) 54.4840 + 94.3690i 2.03050 + 3.51692i
\(721\) 0.219843 + 0.380779i 0.00818738 + 0.0141810i
\(722\) −0.259110 0.149597i −0.00964306 0.00556742i
\(723\) −17.4506 30.2253i −0.648995 1.12409i
\(724\) 0.212906 0.368764i 0.00791259 0.0137050i
\(725\) −4.88515 −0.181430
\(726\) 111.404i 4.13458i
\(727\) 22.7763 39.4498i 0.844727 1.46311i −0.0411303 0.999154i \(-0.513096\pi\)
0.885858 0.463957i \(-0.153571\pi\)
\(728\) −0.0651283 0.0376019i −0.00241382 0.00139362i
\(729\) 2.23406 0.0827428
\(730\) −48.7457 28.1434i −1.80416 1.04163i
\(731\) −4.41845 2.55099i −0.163422 0.0943518i
\(732\) 11.5309 6.65738i 0.426195 0.246064i
\(733\) 6.32061i 0.233457i −0.993164 0.116729i \(-0.962759\pi\)
0.993164 0.116729i \(-0.0372408\pi\)
\(734\) 22.4757 0.829594
\(735\) −75.2672 −2.77627
\(736\) 15.3634i 0.566303i
\(737\) 33.8781i 1.24792i
\(738\) −99.5563 57.4789i −3.66472 2.11583i
\(739\) 25.9736 0.955453 0.477727 0.878509i \(-0.341461\pi\)
0.477727 + 0.878509i \(0.341461\pi\)
\(740\) 0.638548 + 1.10600i 0.0234735 + 0.0406573i
\(741\) −8.24614 4.76091i −0.302930 0.174897i
\(742\) 0.670596 + 0.387169i 0.0246183 + 0.0142134i
\(743\) −10.8889 −0.399475 −0.199737 0.979849i \(-0.564009\pi\)
−0.199737 + 0.979849i \(0.564009\pi\)
\(744\) −55.6397 32.1236i −2.03985 1.17771i
\(745\) 50.3888i 1.84610i
\(746\) −57.4492 −2.10336
\(747\) 46.7807 81.0266i 1.71162 2.96461i
\(748\) −3.05580 1.76427i −0.111731 0.0645080i
\(749\) 0.173607 0.300697i 0.00634347 0.0109872i
\(750\) 30.4485i 1.11182i
\(751\) 12.1204i 0.442281i 0.975242 + 0.221141i \(0.0709780\pi\)
−0.975242 + 0.221141i \(0.929022\pi\)
\(752\) −29.8997 + 17.2626i −1.09033 + 0.629502i
\(753\) 23.2114 + 13.4011i 0.845870 + 0.488363i
\(754\) 0.391515 + 0.678125i 0.0142582 + 0.0246958i
\(755\) 7.26779 + 12.5882i 0.264502 + 0.458131i
\(756\) 0.220113i 0.00800545i
\(757\) 14.5089 + 8.37672i 0.527335 + 0.304457i 0.739931 0.672683i \(-0.234858\pi\)
−0.212595 + 0.977140i \(0.568192\pi\)
\(758\) −24.7131 −0.897621
\(759\) 118.213i 4.29088i
\(760\) 31.6666 18.2827i 1.14867 0.663184i
\(761\) 18.4767 + 10.6675i 0.669779 + 0.386697i 0.795993 0.605306i \(-0.206949\pi\)
−0.126214 + 0.992003i \(0.540283\pi\)
\(762\) 54.8710 1.98777
\(763\) 0.0903226i 0.00326990i
\(764\) 1.71528 0.0620565
\(765\) 33.2908 1.20363
\(766\) −8.83695 + 15.3060i −0.319292 + 0.553030i