Properties

Label 403.2.v.a.36.12
Level 403
Weight 2
Character 403.36
Analytic conductor 3.218
Analytic rank 0
Dimension 70
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.v (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(70\)
Relative dimension: \(35\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 36.12
Character \(\chi\) \(=\) 403.36
Dual form 403.2.v.a.56.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00051 + 0.577645i) q^{2} +2.38906 q^{3} +(-0.332651 + 0.576169i) q^{4} +(0.697454 - 0.402675i) q^{5} +(-2.39028 + 1.38003i) q^{6} +(-1.54805 + 0.893766i) q^{7} -3.07920i q^{8} +2.70761 q^{9} +O(q^{10})\) \(q+(-1.00051 + 0.577645i) q^{2} +2.38906 q^{3} +(-0.332651 + 0.576169i) q^{4} +(0.697454 - 0.402675i) q^{5} +(-2.39028 + 1.38003i) q^{6} +(-1.54805 + 0.893766i) q^{7} -3.07920i q^{8} +2.70761 q^{9} +(-0.465207 + 0.805762i) q^{10} +(3.60065 + 2.07884i) q^{11} +(-0.794725 + 1.37650i) q^{12} +(0.0454705 + 3.60526i) q^{13} +(1.03256 - 1.78845i) q^{14} +(1.66626 - 0.962015i) q^{15} +(1.11338 + 1.92844i) q^{16} +(1.64667 + 2.85211i) q^{17} +(-2.70900 + 1.56404i) q^{18} +(3.70145 - 2.13703i) q^{19} +0.535802i q^{20} +(-3.69838 + 2.13526i) q^{21} -4.80333 q^{22} +(2.71567 + 4.70367i) q^{23} -7.35640i q^{24} +(-2.17571 + 3.76843i) q^{25} +(-2.12806 - 3.58084i) q^{26} -0.698529 q^{27} -1.18925i q^{28} +(-3.67606 - 6.36712i) q^{29} +(-1.11141 + 1.92501i) q^{30} +(-0.308265 - 5.55922i) q^{31} +(3.10543 + 1.79292i) q^{32} +(8.60218 + 4.96647i) q^{33} +(-3.29502 - 1.90238i) q^{34} +(-0.719795 + 1.24672i) q^{35} +(-0.900692 + 1.56004i) q^{36} -6.89253i q^{37} +(-2.46890 + 4.27625i) q^{38} +(0.108632 + 8.61320i) q^{39} +(-1.23992 - 2.14760i) q^{40} +(-0.685743 - 0.395914i) q^{41} +(2.46685 - 4.27271i) q^{42} +(1.76226 + 3.05232i) q^{43} +(-2.39553 + 1.38306i) q^{44} +(1.88843 - 1.09029i) q^{45} +(-5.43411 - 3.13738i) q^{46} -9.48670i q^{47} +(2.65994 + 4.60715i) q^{48} +(-1.90236 + 3.29499i) q^{49} -5.02715i q^{50} +(3.93399 + 6.81387i) q^{51} +(-2.09237 - 1.17310i) q^{52} +(3.99281 + 6.91575i) q^{53} +(0.698886 - 0.403502i) q^{54} +3.34838 q^{55} +(2.75209 + 4.76675i) q^{56} +(8.84300 - 5.10551i) q^{57} +(7.35588 + 4.24692i) q^{58} +(-10.2914 + 5.94172i) q^{59} +1.28006i q^{60} +(4.65484 - 8.06242i) q^{61} +(3.51968 + 5.38400i) q^{62} +(-4.19152 + 2.41997i) q^{63} -8.59622 q^{64} +(1.48346 + 2.49619i) q^{65} -11.4754 q^{66} +(-10.5433 - 6.08719i) q^{67} -2.19106 q^{68} +(6.48789 + 11.2374i) q^{69} -1.66314i q^{70} +5.32807i q^{71} -8.33728i q^{72} +(9.95825 - 5.74940i) q^{73} +(3.98144 + 6.89606i) q^{74} +(-5.19789 + 9.00302i) q^{75} +2.84355i q^{76} -7.43198 q^{77} +(-5.08406 - 8.55485i) q^{78} +(7.63434 - 13.2231i) q^{79} +(1.55307 + 0.896663i) q^{80} -9.79167 q^{81} +0.914791 q^{82} +(1.70911 - 0.986753i) q^{83} -2.84119i q^{84} +(2.29695 + 1.32614i) q^{85} +(-3.52631 - 2.03592i) q^{86} +(-8.78233 - 15.2114i) q^{87} +(6.40116 - 11.0871i) q^{88} +(0.339979 - 0.196287i) q^{89} +(-1.25960 + 2.18169i) q^{90} +(-3.29266 - 5.54049i) q^{91} -3.61348 q^{92} +(-0.736465 - 13.2813i) q^{93} +(5.47995 + 9.49155i) q^{94} +(1.72106 - 2.98096i) q^{95} +(7.41905 + 4.28339i) q^{96} +(1.20253 + 0.694280i) q^{97} -4.39557i q^{98} +(9.74918 + 5.62869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 70q - 6q^{2} + 4q^{3} + 30q^{4} + 6q^{6} - 12q^{7} + 58q^{9} + O(q^{10}) \) \( 70q - 6q^{2} + 4q^{3} + 30q^{4} + 6q^{6} - 12q^{7} + 58q^{9} - q^{10} - 6q^{11} + 13q^{12} - 14q^{13} - 14q^{14} - 15q^{15} - 28q^{16} + 6q^{17} + 12q^{19} + 9q^{21} - 8q^{22} + 10q^{23} + 19q^{25} + 34q^{27} - 18q^{29} - 31q^{30} + 2q^{31} + 36q^{32} - 12q^{33} - 9q^{34} - 12q^{35} + 8q^{36} - 21q^{38} - 30q^{39} + 5q^{40} + 18q^{41} - 49q^{42} + 19q^{43} - 42q^{44} - 63q^{45} - 6q^{46} - 27q^{48} + 9q^{49} - 7q^{51} - 43q^{52} - 22q^{53} + 18q^{54} + 30q^{55} + 25q^{56} - 15q^{57} - 12q^{58} + 33q^{59} - 13q^{61} - 17q^{62} - 6q^{63} - 38q^{64} + 9q^{65} - 52q^{66} + 30q^{67} + 88q^{68} - 16q^{69} + 9q^{73} - 19q^{74} + 25q^{75} + 34q^{77} + 14q^{78} + 6q^{79} + 6q^{80} + 22q^{81} - 78q^{82} + 54q^{83} - 33q^{85} + 24q^{86} - 14q^{87} + 16q^{88} - 6q^{89} - 11q^{90} - 70q^{91} - 6q^{92} + 7q^{93} - 43q^{94} + 25q^{95} - 36q^{96} - 75q^{97} - 93q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00051 + 0.577645i −0.707468 + 0.408457i −0.810123 0.586260i \(-0.800600\pi\)
0.102655 + 0.994717i \(0.467266\pi\)
\(3\) 2.38906 1.37933 0.689663 0.724131i \(-0.257759\pi\)
0.689663 + 0.724131i \(0.257759\pi\)
\(4\) −0.332651 + 0.576169i −0.166326 + 0.288085i
\(5\) 0.697454 0.402675i 0.311911 0.180082i −0.335870 0.941908i \(-0.609030\pi\)
0.647781 + 0.761826i \(0.275697\pi\)
\(6\) −2.39028 + 1.38003i −0.975829 + 0.563395i
\(7\) −1.54805 + 0.893766i −0.585107 + 0.337812i −0.763161 0.646209i \(-0.776353\pi\)
0.178053 + 0.984021i \(0.443020\pi\)
\(8\) 3.07920i 1.08866i
\(9\) 2.70761 0.902538
\(10\) −0.465207 + 0.805762i −0.147111 + 0.254804i
\(11\) 3.60065 + 2.07884i 1.08564 + 0.626793i 0.932412 0.361398i \(-0.117700\pi\)
0.153226 + 0.988191i \(0.451034\pi\)
\(12\) −0.794725 + 1.37650i −0.229417 + 0.397362i
\(13\) 0.0454705 + 3.60526i 0.0126113 + 0.999920i
\(14\) 1.03256 1.78845i 0.275963 0.477983i
\(15\) 1.66626 0.962015i 0.430226 0.248391i
\(16\) 1.11338 + 1.92844i 0.278346 + 0.482109i
\(17\) 1.64667 + 2.85211i 0.399375 + 0.691738i 0.993649 0.112525i \(-0.0358937\pi\)
−0.594274 + 0.804263i \(0.702560\pi\)
\(18\) −2.70900 + 1.56404i −0.638517 + 0.368648i
\(19\) 3.70145 2.13703i 0.849172 0.490269i −0.0111997 0.999937i \(-0.503565\pi\)
0.860371 + 0.509668i \(0.170232\pi\)
\(20\) 0.535802i 0.119809i
\(21\) −3.69838 + 2.13526i −0.807053 + 0.465953i
\(22\) −4.80333 −1.02407
\(23\) 2.71567 + 4.70367i 0.566255 + 0.980783i 0.996932 + 0.0782765i \(0.0249417\pi\)
−0.430676 + 0.902506i \(0.641725\pi\)
\(24\) 7.35640i 1.50162i
\(25\) −2.17571 + 3.76843i −0.435141 + 0.753687i
\(26\) −2.12806 3.58084i −0.417347 0.702261i
\(27\) −0.698529 −0.134432
\(28\) 1.18925i 0.224747i
\(29\) −3.67606 6.36712i −0.682627 1.18235i −0.974176 0.225789i \(-0.927504\pi\)
0.291549 0.956556i \(-0.405829\pi\)
\(30\) −1.11141 + 1.92501i −0.202914 + 0.351458i
\(31\) −0.308265 5.55922i −0.0553661 0.998466i
\(32\) 3.10543 + 1.79292i 0.548967 + 0.316946i
\(33\) 8.60218 + 4.96647i 1.49745 + 0.864552i
\(34\) −3.29502 1.90238i −0.565091 0.326255i
\(35\) −0.719795 + 1.24672i −0.121668 + 0.210734i
\(36\) −0.900692 + 1.56004i −0.150115 + 0.260007i
\(37\) 6.89253i 1.13313i −0.824019 0.566563i \(-0.808273\pi\)
0.824019 0.566563i \(-0.191727\pi\)
\(38\) −2.46890 + 4.27625i −0.400508 + 0.693700i
\(39\) 0.108632 + 8.61320i 0.0173950 + 1.37922i
\(40\) −1.23992 2.14760i −0.196048 0.339565i
\(41\) −0.685743 0.395914i −0.107095 0.0618313i 0.445496 0.895284i \(-0.353027\pi\)
−0.552591 + 0.833453i \(0.686361\pi\)
\(42\) 2.46685 4.27271i 0.380643 0.659293i
\(43\) 1.76226 + 3.05232i 0.268741 + 0.465474i 0.968537 0.248869i \(-0.0800589\pi\)
−0.699796 + 0.714343i \(0.746726\pi\)
\(44\) −2.39553 + 1.38306i −0.361139 + 0.208504i
\(45\) 1.88843 1.09029i 0.281511 0.162531i
\(46\) −5.43411 3.13738i −0.801215 0.462582i
\(47\) 9.48670i 1.38378i −0.722004 0.691889i \(-0.756779\pi\)
0.722004 0.691889i \(-0.243221\pi\)
\(48\) 2.65994 + 4.60715i 0.383929 + 0.664985i
\(49\) −1.90236 + 3.29499i −0.271766 + 0.470713i
\(50\) 5.02715i 0.710946i
\(51\) 3.93399 + 6.81387i 0.550868 + 0.954132i
\(52\) −2.09237 1.17310i −0.290159 0.162679i
\(53\) 3.99281 + 6.91575i 0.548454 + 0.949951i 0.998381 + 0.0568851i \(0.0181169\pi\)
−0.449926 + 0.893066i \(0.648550\pi\)
\(54\) 0.698886 0.403502i 0.0951063 0.0549097i
\(55\) 3.34838 0.451496
\(56\) 2.75209 + 4.76675i 0.367763 + 0.636984i
\(57\) 8.84300 5.10551i 1.17128 0.676241i
\(58\) 7.35588 + 4.24692i 0.965874 + 0.557648i
\(59\) −10.2914 + 5.94172i −1.33982 + 0.773547i −0.986781 0.162061i \(-0.948186\pi\)
−0.353041 + 0.935608i \(0.614852\pi\)
\(60\) 1.28006i 0.165255i
\(61\) 4.65484 8.06242i 0.595991 1.03229i −0.397415 0.917639i \(-0.630093\pi\)
0.993406 0.114648i \(-0.0365739\pi\)
\(62\) 3.51968 + 5.38400i 0.447000 + 0.683768i
\(63\) −4.19152 + 2.41997i −0.528082 + 0.304888i
\(64\) −8.59622 −1.07453
\(65\) 1.48346 + 2.49619i 0.184001 + 0.309615i
\(66\) −11.4754 −1.41253
\(67\) −10.5433 6.08719i −1.28807 0.743668i −0.309761 0.950815i \(-0.600249\pi\)
−0.978310 + 0.207146i \(0.933582\pi\)
\(68\) −2.19106 −0.265706
\(69\) 6.48789 + 11.2374i 0.781050 + 1.35282i
\(70\) 1.66314i 0.198784i
\(71\) 5.32807i 0.632326i 0.948705 + 0.316163i \(0.102395\pi\)
−0.948705 + 0.316163i \(0.897605\pi\)
\(72\) 8.33728i 0.982558i
\(73\) 9.95825 5.74940i 1.16552 0.672916i 0.212903 0.977073i \(-0.431708\pi\)
0.952622 + 0.304157i \(0.0983748\pi\)
\(74\) 3.98144 + 6.89606i 0.462833 + 0.801650i
\(75\) −5.19789 + 9.00302i −0.600201 + 1.03958i
\(76\) 2.84355i 0.326178i
\(77\) −7.43198 −0.846953
\(78\) −5.08406 8.55485i −0.575657 0.968646i
\(79\) 7.63434 13.2231i 0.858930 1.48771i −0.0140206 0.999902i \(-0.504463\pi\)
0.872951 0.487809i \(-0.162204\pi\)
\(80\) 1.55307 + 0.896663i 0.173638 + 0.100250i
\(81\) −9.79167 −1.08796
\(82\) 0.914791 0.101022
\(83\) 1.70911 0.986753i 0.187599 0.108310i −0.403259 0.915086i \(-0.632123\pi\)
0.590858 + 0.806776i \(0.298789\pi\)
\(84\) 2.84119i 0.310000i
\(85\) 2.29695 + 1.32614i 0.249139 + 0.143840i
\(86\) −3.52631 2.03592i −0.380252 0.219539i
\(87\) −8.78233 15.2114i −0.941565 1.63084i
\(88\) 6.40116 11.0871i 0.682366 1.18189i
\(89\) 0.339979 0.196287i 0.0360377 0.0208064i −0.481873 0.876241i \(-0.660043\pi\)
0.517911 + 0.855435i \(0.326710\pi\)
\(90\) −1.25960 + 2.18169i −0.132774 + 0.229970i
\(91\) −3.29266 5.54049i −0.345164 0.580801i
\(92\) −3.61348 −0.376731
\(93\) −0.736465 13.2813i −0.0763679 1.37721i
\(94\) 5.47995 + 9.49155i 0.565214 + 0.978979i
\(95\) 1.72106 2.98096i 0.176577 0.305841i
\(96\) 7.41905 + 4.28339i 0.757204 + 0.437172i
\(97\) 1.20253 + 0.694280i 0.122098 + 0.0704935i 0.559805 0.828624i \(-0.310876\pi\)
−0.437707 + 0.899118i \(0.644209\pi\)
\(98\) 4.39557i 0.444019i
\(99\) 9.74918 + 5.62869i 0.979829 + 0.565705i
\(100\) −1.44750 2.50715i −0.144750 0.250715i
\(101\) −5.32157 9.21723i −0.529516 0.917149i −0.999407 0.0344246i \(-0.989040\pi\)
0.469891 0.882724i \(-0.344293\pi\)
\(102\) −7.87200 4.54490i −0.779444 0.450012i
\(103\) −6.24750 10.8210i −0.615585 1.06622i −0.990282 0.139077i \(-0.955587\pi\)
0.374697 0.927147i \(-0.377747\pi\)
\(104\) 11.1013 0.140013i 1.08858 0.0137294i
\(105\) −1.71963 + 2.97849i −0.167819 + 0.290671i
\(106\) −7.98970 4.61285i −0.776028 0.448040i
\(107\) 18.0338 1.74339 0.871695 0.490049i \(-0.163021\pi\)
0.871695 + 0.490049i \(0.163021\pi\)
\(108\) 0.232367 0.402471i 0.0223595 0.0387278i
\(109\) 17.6586i 1.69139i −0.533670 0.845693i \(-0.679188\pi\)
0.533670 0.845693i \(-0.320812\pi\)
\(110\) −3.35010 + 1.93418i −0.319419 + 0.184417i
\(111\) 16.4667i 1.56295i
\(112\) −3.44714 1.99021i −0.325724 0.188057i
\(113\) −2.66640 −0.250834 −0.125417 0.992104i \(-0.540027\pi\)
−0.125417 + 0.992104i \(0.540027\pi\)
\(114\) −5.89835 + 10.2162i −0.552431 + 0.956838i
\(115\) 3.78810 + 2.18706i 0.353242 + 0.203944i
\(116\) 4.89139 0.454154
\(117\) 0.123117 + 9.76166i 0.0113821 + 0.902466i
\(118\) 6.86442 11.8895i 0.631921 1.09452i
\(119\) −5.09824 2.94347i −0.467355 0.269827i
\(120\) −2.96224 5.13075i −0.270414 0.468371i
\(121\) 3.14314 + 5.44408i 0.285740 + 0.494916i
\(122\) 10.7554i 0.973747i
\(123\) −1.63828 0.945862i −0.147719 0.0852855i
\(124\) 3.30560 + 1.67167i 0.296852 + 0.150120i
\(125\) 7.53116i 0.673607i
\(126\) 2.79577 4.84242i 0.249067 0.431397i
\(127\) −9.62617 −0.854185 −0.427092 0.904208i \(-0.640462\pi\)
−0.427092 + 0.904208i \(0.640462\pi\)
\(128\) 2.38976 1.37973i 0.211227 0.121952i
\(129\) 4.21014 + 7.29217i 0.370682 + 0.642040i
\(130\) −2.92614 1.64055i −0.256639 0.143886i
\(131\) −7.42072 + 12.8531i −0.648352 + 1.12298i 0.335165 + 0.942159i \(0.391208\pi\)
−0.983516 + 0.180818i \(0.942125\pi\)
\(132\) −5.72306 + 3.30421i −0.498128 + 0.287594i
\(133\) −3.82002 + 6.61647i −0.331238 + 0.573721i
\(134\) 14.0649 1.21503
\(135\) −0.487191 + 0.281280i −0.0419308 + 0.0242087i
\(136\) 8.78222 5.07042i 0.753069 0.434785i
\(137\) 6.15250i 0.525644i −0.964844 0.262822i \(-0.915347\pi\)
0.964844 0.262822i \(-0.0846531\pi\)
\(138\) −12.9824 7.49540i −1.10514 0.638051i
\(139\) −0.366141 + 0.634174i −0.0310557 + 0.0537900i −0.881136 0.472864i \(-0.843220\pi\)
0.850080 + 0.526654i \(0.176554\pi\)
\(140\) −0.478882 0.829447i −0.0404729 0.0701011i
\(141\) 22.6643i 1.90868i
\(142\) −3.07774 5.33080i −0.258278 0.447351i
\(143\) −7.33104 + 13.0758i −0.613052 + 1.09346i
\(144\) 3.01461 + 5.22146i 0.251218 + 0.435122i
\(145\) −5.12776 2.96052i −0.425838 0.245857i
\(146\) −6.64223 + 11.5047i −0.549715 + 0.952134i
\(147\) −4.54486 + 7.87193i −0.374854 + 0.649266i
\(148\) 3.97127 + 2.29281i 0.326436 + 0.188468i
\(149\) −10.0524 + 5.80375i −0.823524 + 0.475462i −0.851630 0.524143i \(-0.824386\pi\)
0.0281063 + 0.999605i \(0.491052\pi\)
\(150\) 12.0102i 0.980625i
\(151\) 4.75455i 0.386920i 0.981108 + 0.193460i \(0.0619710\pi\)
−0.981108 + 0.193460i \(0.938029\pi\)
\(152\) −6.58036 11.3975i −0.533738 0.924460i
\(153\) 4.45854 + 7.72241i 0.360451 + 0.624320i
\(154\) 7.43578 4.29305i 0.599193 0.345944i
\(155\) −2.45356 3.75317i −0.197075 0.301462i
\(156\) −4.99880 2.80260i −0.400224 0.224388i
\(157\) −5.47895 −0.437268 −0.218634 0.975807i \(-0.570160\pi\)
−0.218634 + 0.975807i \(0.570160\pi\)
\(158\) 17.6398i 1.40334i
\(159\) 9.53906 + 16.5221i 0.756497 + 1.31029i
\(160\) 2.88785 0.228305
\(161\) −8.40796 4.85434i −0.662640 0.382576i
\(162\) 9.79668 5.65611i 0.769699 0.444386i
\(163\) 6.30388 + 3.63955i 0.493758 + 0.285072i 0.726132 0.687555i \(-0.241316\pi\)
−0.232374 + 0.972627i \(0.574649\pi\)
\(164\) 0.456227 0.263403i 0.0356253 0.0205683i
\(165\) 7.99950 0.622760
\(166\) −1.13999 + 1.97452i −0.0884801 + 0.153252i
\(167\) 7.10722i 0.549973i −0.961448 0.274987i \(-0.911327\pi\)
0.961448 0.274987i \(-0.0886735\pi\)
\(168\) 6.57490 + 11.3881i 0.507265 + 0.878608i
\(169\) −12.9959 + 0.327867i −0.999682 + 0.0252205i
\(170\) −3.06416 −0.235010
\(171\) 10.0221 5.78626i 0.766409 0.442487i
\(172\) −2.34487 −0.178794
\(173\) 19.9847 1.51940 0.759702 0.650271i \(-0.225345\pi\)
0.759702 + 0.650271i \(0.225345\pi\)
\(174\) 17.5736 + 10.1462i 1.33225 + 0.769178i
\(175\) 7.77829i 0.587984i
\(176\) 9.25817i 0.697861i
\(177\) −24.5867 + 14.1951i −1.84805 + 1.06697i
\(178\) −0.226768 + 0.392774i −0.0169970 + 0.0294397i
\(179\) 1.38736 0.103696 0.0518482 0.998655i \(-0.483489\pi\)
0.0518482 + 0.998655i \(0.483489\pi\)
\(180\) 1.45074i 0.108132i
\(181\) 6.89201 + 11.9373i 0.512279 + 0.887293i 0.999899 + 0.0142371i \(0.00453197\pi\)
−0.487620 + 0.873056i \(0.662135\pi\)
\(182\) 6.49477 + 3.64133i 0.481425 + 0.269913i
\(183\) 11.1207 19.2616i 0.822065 1.42386i
\(184\) 14.4835 8.36208i 1.06774 0.616460i
\(185\) −2.77545 4.80722i −0.204055 0.353434i
\(186\) 8.40874 + 12.8627i 0.616559 + 0.943139i
\(187\) 13.6926i 1.00130i
\(188\) 5.46595 + 3.15577i 0.398645 + 0.230158i
\(189\) 1.08136 0.624322i 0.0786571 0.0454127i
\(190\) 3.97665i 0.288497i
\(191\) 5.58195 0.403896 0.201948 0.979396i \(-0.435273\pi\)
0.201948 + 0.979396i \(0.435273\pi\)
\(192\) −20.5369 −1.48212
\(193\) 5.82353i 0.419187i 0.977789 + 0.209594i \(0.0672141\pi\)
−0.977789 + 0.209594i \(0.932786\pi\)
\(194\) −1.60419 −0.115174
\(195\) 3.54408 + 5.96356i 0.253797 + 0.427060i
\(196\) −1.26565 2.19217i −0.0904034 0.156583i
\(197\) −1.70033 0.981685i −0.121143 0.0699422i 0.438204 0.898876i \(-0.355615\pi\)
−0.559347 + 0.828933i \(0.688948\pi\)
\(198\) −13.0056 −0.924264
\(199\) −13.4086 −0.950511 −0.475255 0.879848i \(-0.657644\pi\)
−0.475255 + 0.879848i \(0.657644\pi\)
\(200\) 11.6038 + 6.69943i 0.820510 + 0.473721i
\(201\) −25.1886 14.5427i −1.77667 1.02576i
\(202\) 10.6486 + 6.14796i 0.749232 + 0.432569i
\(203\) 11.3814 + 6.57108i 0.798821 + 0.461199i
\(204\) −5.23459 −0.366494
\(205\) −0.637698 −0.0445388
\(206\) 12.5014 + 7.21768i 0.871013 + 0.502880i
\(207\) 7.35297 + 12.7357i 0.511067 + 0.885194i
\(208\) −6.90190 + 4.10173i −0.478560 + 0.284404i
\(209\) 17.7702 1.22919
\(210\) 3.97335i 0.274188i
\(211\) −6.33208 −0.435918 −0.217959 0.975958i \(-0.569940\pi\)
−0.217959 + 0.975958i \(0.569940\pi\)
\(212\) −5.31285 −0.364888
\(213\) 12.7291i 0.872183i
\(214\) −18.0430 + 10.4171i −1.23339 + 0.712100i
\(215\) 2.45818 + 1.41923i 0.167647 + 0.0967908i
\(216\) 2.15091i 0.146351i
\(217\) 5.44586 + 8.33043i 0.369689 + 0.565507i
\(218\) 10.2004 + 17.6676i 0.690858 + 1.19660i
\(219\) 23.7909 13.7357i 1.60764 0.928170i
\(220\) −1.11385 + 1.92924i −0.0750954 + 0.130069i
\(221\) −10.2077 + 6.06635i −0.686647 + 0.408067i
\(222\) 9.51190 + 16.4751i 0.638397 + 1.10574i
\(223\) 5.31440i 0.355878i 0.984042 + 0.177939i \(0.0569430\pi\)
−0.984042 + 0.177939i \(0.943057\pi\)
\(224\) −6.40980 −0.428273
\(225\) −5.89097 + 10.2035i −0.392731 + 0.680231i
\(226\) 2.66776 1.54023i 0.177457 0.102455i
\(227\) 10.1666i 0.674778i 0.941365 + 0.337389i \(0.109544\pi\)
−0.941365 + 0.337389i \(0.890456\pi\)
\(228\) 6.79342i 0.449905i
\(229\) 13.1834 + 7.61147i 0.871187 + 0.502980i 0.867742 0.497014i \(-0.165570\pi\)
0.00344441 + 0.999994i \(0.498904\pi\)
\(230\) −5.05338 −0.333210
\(231\) −17.7555 −1.16822
\(232\) −19.6056 + 11.3193i −1.28717 + 0.743150i
\(233\) 1.97505 0.129390 0.0646948 0.997905i \(-0.479393\pi\)
0.0646948 + 0.997905i \(0.479393\pi\)
\(234\) −5.76196 9.69554i −0.376671 0.633817i
\(235\) −3.82006 6.61653i −0.249193 0.431615i
\(236\) 7.90609i 0.514643i
\(237\) 18.2389 31.5907i 1.18474 2.05204i
\(238\) 6.80113 0.440852
\(239\) 2.34584 1.35437i 0.151740 0.0876069i −0.422208 0.906499i \(-0.638745\pi\)
0.573947 + 0.818892i \(0.305411\pi\)
\(240\) 3.71037 + 2.14218i 0.239503 + 0.138277i
\(241\) −1.49017 + 0.860351i −0.0959904 + 0.0554201i −0.547227 0.836984i \(-0.684316\pi\)
0.451236 + 0.892404i \(0.350983\pi\)
\(242\) −6.28949 3.63124i −0.404304 0.233425i
\(243\) −21.2973 −1.36622
\(244\) 3.09688 + 5.36395i 0.198257 + 0.343392i
\(245\) 3.06414i 0.195760i
\(246\) 2.18549 0.139342
\(247\) 7.87288 + 13.2475i 0.500940 + 0.842921i
\(248\) −17.1180 + 0.949211i −1.08699 + 0.0602750i
\(249\) 4.08316 2.35741i 0.258760 0.149395i
\(250\) −4.35034 7.53501i −0.275140 0.476556i
\(251\) 5.21789 + 9.03766i 0.329351 + 0.570452i 0.982383 0.186878i \(-0.0598369\pi\)
−0.653033 + 0.757330i \(0.726504\pi\)
\(252\) 3.22003i 0.202843i
\(253\) 22.5817i 1.41970i
\(254\) 9.63109 5.56051i 0.604308 0.348898i
\(255\) 5.48755 + 3.16824i 0.343643 + 0.198403i
\(256\) 7.00223 12.1282i 0.437639 0.758014i
\(257\) 1.61064 2.78971i 0.100469 0.174017i −0.811409 0.584479i \(-0.801299\pi\)
0.911878 + 0.410461i \(0.134632\pi\)
\(258\) −8.42458 4.86393i −0.524491 0.302815i
\(259\) 6.16031 + 10.6700i 0.382783 + 0.663000i
\(260\) −1.93171 + 0.0243632i −0.119799 + 0.00151094i
\(261\) −9.95335 17.2397i −0.616097 1.06711i
\(262\) 17.1462i 1.05930i
\(263\) 7.91526 + 13.7096i 0.488076 + 0.845372i 0.999906 0.0137144i \(-0.00436558\pi\)
−0.511830 + 0.859087i \(0.671032\pi\)
\(264\) 15.2928 26.4878i 0.941204 1.63021i
\(265\) 5.56960 + 3.21561i 0.342138 + 0.197533i
\(266\) 8.82647i 0.541186i
\(267\) 0.812230 0.468941i 0.0497077 0.0286987i
\(268\) 7.01450 4.04982i 0.428479 0.247382i
\(269\) −9.43931 −0.575525 −0.287763 0.957702i \(-0.592911\pi\)
−0.287763 + 0.957702i \(0.592911\pi\)
\(270\) 0.324960 0.562848i 0.0197765 0.0342538i
\(271\) −18.0783 + 10.4375i −1.09818 + 0.634034i −0.935742 0.352685i \(-0.885269\pi\)
−0.162437 + 0.986719i \(0.551935\pi\)
\(272\) −3.66674 + 6.35098i −0.222329 + 0.385085i
\(273\) −7.86635 13.2366i −0.476093 0.801113i
\(274\) 3.55396 + 6.15565i 0.214703 + 0.371876i
\(275\) −15.6679 + 9.04588i −0.944812 + 0.545487i
\(276\) −8.63283 −0.519635
\(277\) 4.42197 7.65907i 0.265690 0.460189i −0.702054 0.712124i \(-0.747734\pi\)
0.967744 + 0.251935i \(0.0810669\pi\)
\(278\) 0.845998i 0.0507396i
\(279\) −0.834664 15.0522i −0.0499700 0.901154i
\(280\) 3.83890 + 2.21639i 0.229418 + 0.132455i
\(281\) 12.6673i 0.755665i −0.925874 0.377833i \(-0.876669\pi\)
0.925874 0.377833i \(-0.123331\pi\)
\(282\) 13.0919 + 22.6759i 0.779614 + 1.35033i
\(283\) −5.29330 9.16827i −0.314654 0.544997i 0.664710 0.747102i \(-0.268555\pi\)
−0.979364 + 0.202105i \(0.935222\pi\)
\(284\) −3.06987 1.77239i −0.182163 0.105172i
\(285\) 4.11172 7.12171i 0.243557 0.421854i
\(286\) −0.218410 17.3173i −0.0129148 1.02399i
\(287\) 1.41542 0.0835495
\(288\) 8.40830 + 4.85453i 0.495464 + 0.286056i
\(289\) 3.07698 5.32949i 0.180999 0.313499i
\(290\) 6.84051 0.401689
\(291\) 2.87291 + 1.65868i 0.168413 + 0.0972334i
\(292\) 7.65018i 0.447693i
\(293\) 18.3190 10.5765i 1.07021 0.617886i 0.141971 0.989871i \(-0.454656\pi\)
0.928239 + 0.371985i \(0.121323\pi\)
\(294\) 10.5013i 0.612447i
\(295\) −4.78517 + 8.28815i −0.278603 + 0.482555i
\(296\) −21.2235 −1.23359
\(297\) −2.51516 1.45213i −0.145944 0.0842610i
\(298\) 6.70502 11.6134i 0.388411 0.672748i
\(299\) −16.8345 + 10.0046i −0.973564 + 0.578579i
\(300\) −3.45817 5.98973i −0.199658 0.345817i
\(301\) −5.45612 3.15009i −0.314485 0.181568i
\(302\) −2.74645 4.75698i −0.158040 0.273734i
\(303\) −12.7136 22.0205i −0.730375 1.26505i
\(304\) 8.24227 + 4.75868i 0.472727 + 0.272929i
\(305\) 7.49755i 0.429308i
\(306\) −8.92163 5.15091i −0.510016 0.294458i
\(307\) −14.6341 8.44898i −0.835210 0.482209i 0.0204233 0.999791i \(-0.493499\pi\)
−0.855633 + 0.517583i \(0.826832\pi\)
\(308\) 2.47226 4.28208i 0.140870 0.243994i
\(309\) −14.9257 25.8520i −0.849091 1.47067i
\(310\) 4.62282 + 2.33780i 0.262558 + 0.132778i
\(311\) −18.1949 −1.03174 −0.515870 0.856667i \(-0.672531\pi\)
−0.515870 + 0.856667i \(0.672531\pi\)
\(312\) 26.5218 0.334499i 1.50150 0.0189373i
\(313\) 11.7235 20.3056i 0.662649 1.14774i −0.317268 0.948336i \(-0.602765\pi\)
0.979917 0.199406i \(-0.0639013\pi\)
\(314\) 5.48175 3.16489i 0.309353 0.178605i
\(315\) −1.94893 + 3.37564i −0.109810 + 0.190196i
\(316\) 5.07915 + 8.79734i 0.285724 + 0.494889i
\(317\) 21.2080 + 12.2445i 1.19116 + 0.687718i 0.958570 0.284857i \(-0.0919461\pi\)
0.232592 + 0.972574i \(0.425279\pi\)
\(318\) −19.0879 11.0204i −1.07040 0.617993i
\(319\) 30.5677i 1.71147i
\(320\) −5.99546 + 3.46148i −0.335157 + 0.193503i
\(321\) 43.0838 2.40470
\(322\) 11.2164 0.625063
\(323\) 12.1901 + 7.03797i 0.678276 + 0.391603i
\(324\) 3.25721 5.64166i 0.180956 0.313426i
\(325\) −13.6851 7.67264i −0.759114 0.425602i
\(326\) −8.40948 −0.465758
\(327\) 42.1874i 2.33297i
\(328\) −1.21910 + 2.11154i −0.0673134 + 0.116590i
\(329\) 8.47890 + 14.6859i 0.467457 + 0.809659i
\(330\) −8.00359 + 4.62087i −0.440583 + 0.254371i
\(331\) 0.683248i 0.0375547i −0.999824 0.0187773i \(-0.994023\pi\)
0.999824 0.0187773i \(-0.00597737\pi\)
\(332\) 1.31298i 0.0720591i
\(333\) 18.6623i 1.02269i
\(334\) 4.10545 + 7.11086i 0.224640 + 0.389089i
\(335\) −9.80463 −0.535684
\(336\) −8.23543 4.75473i −0.449280 0.259392i
\(337\) 11.4119 0.621646 0.310823 0.950468i \(-0.399395\pi\)
0.310823 + 0.950468i \(0.399395\pi\)
\(338\) 12.8131 7.83504i 0.696942 0.426170i
\(339\) −6.37019 −0.345981
\(340\) −1.52817 + 0.882287i −0.0828764 + 0.0478487i
\(341\) 10.4468 20.6577i 0.565724 1.11868i
\(342\) −6.68482 + 11.5784i −0.361474 + 0.626091i
\(343\) 19.3138i 1.04285i
\(344\) 9.39869 5.42634i 0.506744 0.292569i
\(345\) 9.05000 + 5.22502i 0.487236 + 0.281306i
\(346\) −19.9949 + 11.5440i −1.07493 + 0.620612i
\(347\) 10.0091 + 17.3363i 0.537318 + 0.930662i 0.999047 + 0.0436414i \(0.0138959\pi\)
−0.461729 + 0.887021i \(0.652771\pi\)
\(348\) 11.6858 0.626426
\(349\) −30.5312 + 17.6272i −1.63430 + 0.943563i −0.651553 + 0.758604i \(0.725882\pi\)
−0.982746 + 0.184959i \(0.940785\pi\)
\(350\) 4.49309 + 7.78227i 0.240166 + 0.415980i
\(351\) −0.0317625 2.51838i −0.00169536 0.134421i
\(352\) 7.45438 + 12.9114i 0.397320 + 0.688178i
\(353\) 20.0649i 1.06795i −0.845501 0.533974i \(-0.820698\pi\)
0.845501 0.533974i \(-0.179302\pi\)
\(354\) 16.3995 28.4048i 0.871625 1.50970i
\(355\) 2.14548 + 3.71608i 0.113870 + 0.197229i
\(356\) 0.261180i 0.0138425i
\(357\) −12.1800 7.03213i −0.644634 0.372180i
\(358\) −1.38807 + 0.801403i −0.0733619 + 0.0423555i
\(359\) −31.2079 + 18.0179i −1.64709 + 0.950949i −0.668872 + 0.743378i \(0.733222\pi\)
−0.978220 + 0.207571i \(0.933444\pi\)
\(360\) −3.35722 5.81487i −0.176941 0.306470i
\(361\) −0.366165 + 0.634216i −0.0192718 + 0.0333798i
\(362\) −13.7911 7.96228i −0.724842 0.418488i
\(363\) 7.50915 + 13.0062i 0.394128 + 0.682650i
\(364\) 4.28756 0.0540759i 0.224729 0.00283435i
\(365\) 4.63028 8.01987i 0.242360 0.419779i
\(366\) 25.6953i 1.34311i
\(367\) −6.80910 + 11.7937i −0.355432 + 0.615626i −0.987192 0.159538i \(-0.949000\pi\)
0.631760 + 0.775164i \(0.282333\pi\)
\(368\) −6.04715 + 10.4740i −0.315230 + 0.545994i
\(369\) −1.85673 1.07198i −0.0966573 0.0558051i
\(370\) 5.55374 + 3.20645i 0.288725 + 0.166696i
\(371\) −12.3621 7.13728i −0.641809 0.370549i
\(372\) 7.89728 + 3.99372i 0.409455 + 0.207065i
\(373\) −15.6690 + 27.1395i −0.811310 + 1.40523i 0.100638 + 0.994923i \(0.467912\pi\)
−0.911948 + 0.410306i \(0.865422\pi\)
\(374\) −7.90948 13.6996i −0.408989 0.708390i
\(375\) 17.9924i 0.929124i
\(376\) −29.2115 −1.50647
\(377\) 22.7880 13.5427i 1.17364 0.697484i
\(378\) −0.721273 + 1.24928i −0.0370983 + 0.0642561i
\(379\) 28.0709i 1.44191i 0.692983 + 0.720953i \(0.256296\pi\)
−0.692983 + 0.720953i \(0.743704\pi\)
\(380\) 1.14503 + 1.98324i 0.0587386 + 0.101738i
\(381\) −22.9975 −1.17820
\(382\) −5.58480 + 3.22439i −0.285743 + 0.164974i
\(383\) 19.8794i 1.01579i 0.861419 + 0.507895i \(0.169576\pi\)
−0.861419 + 0.507895i \(0.830424\pi\)
\(384\) 5.70928 3.29625i 0.291351 0.168211i
\(385\) −5.18346 + 2.99267i −0.264174 + 0.152521i
\(386\) −3.36394 5.82651i −0.171220 0.296562i
\(387\) 4.77151 + 8.26449i 0.242549 + 0.420108i
\(388\) −0.800046 + 0.461907i −0.0406162 + 0.0234498i
\(389\) 1.16249 2.01349i 0.0589404 0.102088i −0.835050 0.550175i \(-0.814561\pi\)
0.893990 + 0.448087i \(0.147894\pi\)
\(390\) −6.99072 3.91939i −0.353989 0.198466i
\(391\) −8.94359 + 15.4908i −0.452297 + 0.783401i
\(392\) 10.1459 + 5.85776i 0.512447 + 0.295861i
\(393\) −17.7286 + 30.7068i −0.894288 + 1.54895i
\(394\) 2.26826 0.114274
\(395\) 12.2966i 0.618710i
\(396\) −6.48616 + 3.74479i −0.325942 + 0.188183i
\(397\) −11.6960 + 6.75266i −0.587003 + 0.338906i −0.763912 0.645321i \(-0.776724\pi\)
0.176909 + 0.984227i \(0.443390\pi\)
\(398\) 13.4155 7.74542i 0.672456 0.388243i
\(399\) −9.12626 + 15.8071i −0.456885 + 0.791347i
\(400\) −9.68957 −0.484479
\(401\) 13.3316 7.69701i 0.665749 0.384371i −0.128715 0.991682i \(-0.541085\pi\)
0.794464 + 0.607311i \(0.207752\pi\)
\(402\) 33.6020 1.67592
\(403\) 20.0285 1.36416i 0.997688 0.0679536i
\(404\) 7.08092 0.352289
\(405\) −6.82923 + 3.94286i −0.339347 + 0.195922i
\(406\) −15.1830 −0.753520
\(407\) 14.3285 24.8176i 0.710235 1.23016i
\(408\) 20.9813 12.1135i 1.03873 0.599709i
\(409\) 3.55953 2.05510i 0.176008 0.101618i −0.409408 0.912351i \(-0.634265\pi\)
0.585416 + 0.810733i \(0.300931\pi\)
\(410\) 0.638024 0.368363i 0.0315098 0.0181922i
\(411\) 14.6987i 0.725033i
\(412\) 8.31296 0.409550
\(413\) 10.6210 18.3962i 0.522627 0.905216i
\(414\) −14.7135 8.49482i −0.723127 0.417498i
\(415\) 0.794682 1.37643i 0.0390094 0.0675662i
\(416\) −6.32274 + 11.2774i −0.309998 + 0.552921i
\(417\) −0.874733 + 1.51508i −0.0428358 + 0.0741939i
\(418\) −17.7793 + 10.2649i −0.869613 + 0.502071i
\(419\) 17.0906 + 29.6017i 0.834928 + 1.44614i 0.894089 + 0.447889i \(0.147824\pi\)
−0.0591608 + 0.998248i \(0.518842\pi\)
\(420\) −1.14408 1.98160i −0.0558253 0.0966922i
\(421\) 5.71395 3.29895i 0.278481 0.160781i −0.354255 0.935149i \(-0.615265\pi\)
0.632735 + 0.774368i \(0.281932\pi\)
\(422\) 6.33531 3.65770i 0.308398 0.178054i
\(423\) 25.6863i 1.24891i
\(424\) 21.2950 12.2947i 1.03417 0.597081i
\(425\) −14.3306 −0.695138
\(426\) −7.35290 12.7356i −0.356249 0.617042i
\(427\) 16.6414i 0.805332i
\(428\) −5.99896 + 10.3905i −0.289971 + 0.502244i
\(429\) −17.5143 + 31.2390i −0.845598 + 1.50823i
\(430\) −3.27925 −0.158140
\(431\) 3.52881i 0.169977i 0.996382 + 0.0849883i \(0.0270853\pi\)
−0.996382 + 0.0849883i \(0.972915\pi\)
\(432\) −0.777730 1.34707i −0.0374186 0.0648108i
\(433\) 5.87116 10.1691i 0.282150 0.488698i −0.689764 0.724034i \(-0.742286\pi\)
0.971914 + 0.235336i \(0.0756191\pi\)
\(434\) −10.2607 5.18892i −0.492528 0.249076i
\(435\) −12.2505 7.07285i −0.587368 0.339117i
\(436\) 10.1743 + 5.87416i 0.487262 + 0.281321i
\(437\) 20.1038 + 11.6069i 0.961696 + 0.555235i
\(438\) −15.8687 + 27.4854i −0.758235 + 1.31330i
\(439\) 11.3616 19.6789i 0.542262 0.939225i −0.456512 0.889717i \(-0.650902\pi\)
0.998774 0.0495074i \(-0.0157651\pi\)
\(440\) 10.3103i 0.491527i
\(441\) −5.15086 + 8.92156i −0.245279 + 0.424836i
\(442\) 6.70875 11.9659i 0.319103 0.569160i
\(443\) −6.37722 11.0457i −0.302991 0.524796i 0.673821 0.738895i \(-0.264652\pi\)
−0.976812 + 0.214099i \(0.931319\pi\)
\(444\) 9.48760 + 5.47767i 0.450261 + 0.259959i
\(445\) 0.158080 0.273802i 0.00749369 0.0129795i
\(446\) −3.06984 5.31711i −0.145361 0.251773i
\(447\) −24.0158 + 13.8655i −1.13591 + 0.655816i
\(448\) 13.3074 7.68301i 0.628714 0.362988i
\(449\) 27.7328 + 16.0115i 1.30879 + 0.755631i 0.981894 0.189429i \(-0.0606638\pi\)
0.326896 + 0.945060i \(0.393997\pi\)
\(450\) 13.6116i 0.641656i
\(451\) −1.64608 2.85110i −0.0775110 0.134253i
\(452\) 0.886982 1.53630i 0.0417201 0.0722614i
\(453\) 11.3589i 0.533688i
\(454\) −5.87266 10.1717i −0.275618 0.477384i
\(455\) −4.52749 2.53836i −0.212252 0.119000i
\(456\) −15.7209 27.2294i −0.736198 1.27513i
\(457\) 32.0699 18.5155i 1.50016 0.866121i 0.500165 0.865930i \(-0.333273\pi\)
1.00000 0.000190303i \(-6.05752e-5\pi\)
\(458\) −17.5869 −0.821783
\(459\) −1.15024 1.99228i −0.0536888 0.0929917i
\(460\) −2.52023 + 1.45506i −0.117507 + 0.0678424i
\(461\) −11.8564 6.84531i −0.552209 0.318818i 0.197803 0.980242i \(-0.436619\pi\)
−0.750012 + 0.661424i \(0.769953\pi\)
\(462\) 17.7645 10.2564i 0.826481 0.477169i
\(463\) 32.7120i 1.52025i 0.649774 + 0.760127i \(0.274863\pi\)
−0.649774 + 0.760127i \(0.725137\pi\)
\(464\) 8.18573 14.1781i 0.380013 0.658202i
\(465\) −5.86171 8.96655i −0.271830 0.415814i
\(466\) −1.97606 + 1.14088i −0.0915390 + 0.0528501i
\(467\) −29.9363 −1.38529 −0.692643 0.721281i \(-0.743554\pi\)
−0.692643 + 0.721281i \(0.743554\pi\)
\(468\) −5.66533 3.17630i −0.261880 0.146824i
\(469\) 21.7621 1.00488
\(470\) 7.64402 + 4.41328i 0.352592 + 0.203569i
\(471\) −13.0895 −0.603134
\(472\) 18.2958 + 31.6892i 0.842131 + 1.45861i
\(473\) 14.6538i 0.673781i
\(474\) 42.1425i 1.93567i
\(475\) 18.5982i 0.853346i
\(476\) 3.39187 1.95830i 0.155466 0.0897585i
\(477\) 10.8110 + 18.7252i 0.495001 + 0.857367i
\(478\) −1.56469 + 2.71012i −0.0715673 + 0.123958i
\(479\) 32.2896i 1.47535i −0.675156 0.737675i \(-0.735924\pi\)
0.675156 0.737675i \(-0.264076\pi\)
\(480\) 6.89926 0.314907
\(481\) 24.8494 0.313407i 1.13304 0.0142901i
\(482\) 0.993955 1.72158i 0.0452734 0.0784159i
\(483\) −20.0871 11.5973i −0.913997 0.527696i
\(484\) −4.18228 −0.190104
\(485\) 1.11828 0.0507783
\(486\) 21.3082 12.3023i 0.966560 0.558043i
\(487\) 42.2743i 1.91563i 0.287387 + 0.957815i \(0.407214\pi\)
−0.287387 + 0.957815i \(0.592786\pi\)
\(488\) −24.8258 14.3332i −1.12381 0.648833i
\(489\) 15.0604 + 8.69511i 0.681053 + 0.393206i
\(490\) −1.76998 3.06570i −0.0799597 0.138494i
\(491\) −5.34037 + 9.24978i −0.241007 + 0.417437i −0.961001 0.276543i \(-0.910811\pi\)
0.719994 + 0.693980i \(0.244144\pi\)
\(492\) 1.08995 0.629285i 0.0491389 0.0283704i
\(493\) 12.1065 20.9691i 0.545249 0.944399i
\(494\) −15.5293 8.70658i −0.698696 0.391728i
\(495\) 9.06613 0.407492
\(496\) 10.3774 6.78402i 0.465959 0.304611i
\(497\) −4.76205 8.24812i −0.213607 0.369979i
\(498\) −2.72350 + 4.71724i −0.122043 + 0.211384i
\(499\) −26.6187 15.3683i −1.19162 0.687981i −0.232944 0.972490i \(-0.574836\pi\)
−0.958673 + 0.284510i \(0.908169\pi\)
\(500\) −4.33922 2.50525i −0.194056 0.112038i
\(501\) 16.9796i 0.758592i
\(502\) −10.4411 6.02819i −0.466010 0.269051i
\(503\) 11.6064 + 20.1028i 0.517502 + 0.896340i 0.999793 + 0.0203288i \(0.00647132\pi\)
−0.482291 + 0.876011i \(0.660195\pi\)
\(504\) 7.45159 + 12.9065i 0.331920 + 0.574902i
\(505\) −7.42310 4.28573i −0.330324 0.190712i
\(506\) −13.0442 22.5933i −0.579887 1.00439i
\(507\) −31.0479 + 0.783293i −1.37889 + 0.0347873i
\(508\) 3.20216 5.54630i 0.142073 0.246077i
\(509\) −20.9206 12.0785i −0.927291 0.535372i −0.0413372 0.999145i \(-0.513162\pi\)
−0.885954 + 0.463774i \(0.846495\pi\)
\(510\) −7.32047 −0.324156
\(511\) −10.2772 + 17.8007i −0.454638 + 0.787456i
\(512\) 21.6981i 0.958931i
\(513\) −2.58557 + 1.49278i −0.114156 + 0.0659079i
\(514\) 3.72151i 0.164149i
\(515\) −8.71468 5.03143i −0.384015 0.221711i
\(516\) −5.60203 −0.246616
\(517\) 19.7213 34.1583i 0.867343 1.50228i
\(518\) −12.3269 7.11696i −0.541614 0.312701i
\(519\) 47.7446 2.09575
\(520\) 7.68628 4.56788i 0.337066 0.200315i
\(521\) 22.3223 38.6633i 0.977957 1.69387i 0.308145 0.951339i \(-0.400292\pi\)
0.669811 0.742531i \(-0.266375\pi\)
\(522\) 19.9169 + 11.4990i 0.871738 + 0.503298i
\(523\) −17.3496 30.0503i −0.758643 1.31401i −0.943543 0.331251i \(-0.892529\pi\)
0.184899 0.982757i \(-0.440804\pi\)
\(524\) −4.93703 8.55119i −0.215675 0.373560i
\(525\) 18.5828i 0.811021i
\(526\) −15.8386 9.14443i −0.690596 0.398716i
\(527\) 15.3479 10.0334i 0.668565 0.437062i
\(528\) 22.1183i 0.962577i
\(529\) −3.24967 + 5.62860i −0.141290 + 0.244722i
\(530\) −7.42992 −0.322735
\(531\) −27.8651 + 16.0879i −1.20924 + 0.698155i
\(532\) −2.54147 4.40196i −0.110187 0.190849i
\(533\) 1.39619 2.49029i 0.0604758 0.107866i
\(534\) −0.541764 + 0.938362i −0.0234444 + 0.0406069i
\(535\) 12.5777 7.26175i 0.543782 0.313953i
\(536\) −18.7437 + 32.4650i −0.809603 + 1.40227i
\(537\) 3.31449 0.143031
\(538\) 9.44414 5.45258i 0.407166 0.235077i
\(539\) −13.6995 + 7.90941i −0.590079 + 0.340682i
\(540\) 0.374273i 0.0161061i
\(541\) −32.8108 18.9433i −1.41065 0.814437i −0.415197 0.909731i \(-0.636287\pi\)
−0.995449 + 0.0952944i \(0.969621\pi\)
\(542\) 12.0584 20.8857i 0.517951 0.897118i
\(543\) 16.4654 + 28.5190i 0.706599 + 1.22387i
\(544\) 11.8094i 0.506322i
\(545\) −7.11067 12.3160i −0.304588 0.527561i
\(546\) 15.5164 + 8.69936i 0.664041 + 0.372298i
\(547\) 16.1204 + 27.9213i 0.689258 + 1.19383i 0.972078 + 0.234657i \(0.0753968\pi\)
−0.282820 + 0.959173i \(0.591270\pi\)
\(548\) 3.54488 + 2.04664i 0.151430 + 0.0874281i
\(549\) 12.6035 21.8299i 0.537904 0.931678i
\(550\) 10.4506 18.1010i 0.445616 0.771830i
\(551\) −27.2135 15.7117i −1.15934 0.669343i
\(552\) 34.6021 19.9775i 1.47276 0.850299i
\(553\) 27.2933i 1.16063i
\(554\) 10.2173i 0.434092i
\(555\) −6.63072 11.4847i −0.281458 0.487500i
\(556\) −0.243595 0.421918i −0.0103307 0.0178933i
\(557\) 17.6225 10.1743i 0.746688 0.431101i −0.0778079 0.996968i \(-0.524792\pi\)
0.824496 + 0.565868i \(0.191459\pi\)
\(558\) 9.52994 + 14.5778i 0.403435 + 0.617127i
\(559\) −10.9243 + 6.49219i −0.462048 + 0.274590i
\(560\) −3.20563 −0.135463
\(561\) 32.7125i 1.38112i
\(562\) 7.31718 + 12.6737i 0.308657 + 0.534609i
\(563\) 7.89128 0.332578 0.166289 0.986077i \(-0.446822\pi\)
0.166289 + 0.986077i \(0.446822\pi\)
\(564\) 13.0585 + 7.53932i 0.549861 + 0.317463i
\(565\) −1.85969 + 1.07369i −0.0782377 + 0.0451706i
\(566\) 10.5920 + 6.11531i 0.445216 + 0.257046i
\(567\) 15.1580 8.75147i 0.636575 0.367527i
\(568\) 16.4062 0.688389
\(569\) −2.23039 + 3.86315i −0.0935030 + 0.161952i −0.908983 0.416834i \(-0.863140\pi\)
0.815480 + 0.578785i \(0.196473\pi\)
\(570\) 9.50046i 0.397931i
\(571\) 8.59401 + 14.8853i 0.359648 + 0.622929i 0.987902 0.155079i \(-0.0495634\pi\)
−0.628254 + 0.778008i \(0.716230\pi\)
\(572\) −5.09521 8.57362i −0.213042 0.358481i
\(573\) 13.3356 0.557104
\(574\) −1.41614 + 0.817610i −0.0591086 + 0.0341264i
\(575\) −23.6340 −0.985604
\(576\) −23.2752 −0.969802
\(577\) −20.8834 12.0570i −0.869387 0.501941i −0.00224257 0.999997i \(-0.500714\pi\)
−0.867145 + 0.498057i \(0.834047\pi\)
\(578\) 7.10961i 0.295721i
\(579\) 13.9128i 0.578195i
\(580\) 3.41152 1.96964i 0.141655 0.0817848i
\(581\) −1.76385 + 3.05508i −0.0731770 + 0.126746i
\(582\) −3.83251 −0.158863
\(583\) 33.2016i 1.37507i
\(584\) −17.7035 30.6634i −0.732578 1.26886i
\(585\) 4.01665 + 6.75873i 0.166068 + 0.279439i
\(586\) −12.2189 + 21.1638i −0.504760 + 0.874269i
\(587\) −15.3518 + 8.86338i −0.633638 + 0.365831i −0.782159 0.623078i \(-0.785882\pi\)
0.148522 + 0.988909i \(0.452548\pi\)
\(588\) −3.02371 5.23722i −0.124696 0.215979i
\(589\) −13.0213 19.9184i −0.536533 0.820725i
\(590\) 11.0565i 0.455190i
\(591\) −4.06219 2.34531i −0.167096 0.0964730i
\(592\) 13.2918 7.67403i 0.546290 0.315401i
\(593\) 16.5476i 0.679529i 0.940511 + 0.339764i \(0.110347\pi\)
−0.940511 + 0.339764i \(0.889653\pi\)
\(594\) 3.35526 0.137668
\(595\) −4.74105 −0.194364
\(596\) 7.72250i 0.316326i
\(597\) −32.0340 −1.31106
\(598\) 11.0640 19.7341i 0.452441 0.806985i
\(599\) −7.60083 13.1650i −0.310561 0.537908i 0.667923 0.744231i \(-0.267184\pi\)
−0.978484 + 0.206323i \(0.933850\pi\)
\(600\) 27.7221 + 16.0054i 1.13175 + 0.653416i
\(601\) −13.1324 −0.535683 −0.267842 0.963463i \(-0.586310\pi\)
−0.267842 + 0.963463i \(0.586310\pi\)
\(602\) 7.27854 0.296651
\(603\) −28.5472 16.4817i −1.16253 0.671189i
\(604\) −2.73943 1.58161i −0.111466 0.0643548i
\(605\) 4.38439 + 2.53133i 0.178251 + 0.102913i
\(606\) 25.4401 + 14.6879i 1.03343 + 0.596654i
\(607\) 12.0633 0.489632 0.244816 0.969570i \(-0.421272\pi\)
0.244816 + 0.969570i \(0.421272\pi\)
\(608\) 15.3261 0.621556
\(609\) 27.1910 + 15.6987i 1.10183 + 0.636144i
\(610\) 4.33092 + 7.50138i 0.175354 + 0.303722i
\(611\) 34.2021 0.431365i 1.38367 0.0174512i
\(612\) −5.93256 −0.239809
\(613\) 7.10312i 0.286892i −0.989658 0.143446i \(-0.954182\pi\)
0.989658 0.143446i \(-0.0458184\pi\)
\(614\) 19.5221 0.787846
\(615\) −1.52350 −0.0614335
\(616\) 22.8846i 0.922046i
\(617\) −10.8131 + 6.24292i −0.435317 + 0.251330i −0.701609 0.712562i \(-0.747535\pi\)
0.266292 + 0.963892i \(0.414201\pi\)
\(618\) 29.8666 + 17.2435i 1.20141 + 0.693635i
\(619\) 2.47009i 0.0992814i −0.998767 0.0496407i \(-0.984192\pi\)
0.998767 0.0496407i \(-0.0158076\pi\)
\(620\) 2.97864 0.165169i 0.119625 0.00663335i
\(621\) −1.89697 3.28565i −0.0761228 0.131849i
\(622\) 18.2042 10.5102i 0.729923 0.421421i
\(623\) −0.350869 + 0.607723i −0.0140573 + 0.0243479i
\(624\) −16.4891 + 9.79928i −0.660090 + 0.392285i
\(625\) −7.84592 13.5895i −0.313837 0.543581i
\(626\) 27.0880i 1.08265i
\(627\) 42.4541 1.69545
\(628\) 1.82258 3.15680i 0.0727289 0.125970i
\(629\) 19.6583 11.3497i 0.783826 0.452542i
\(630\) 4.50315i 0.179410i
\(631\) 17.2677i 0.687417i −0.939076 0.343709i \(-0.888317\pi\)
0.939076 0.343709i \(-0.111683\pi\)
\(632\) −40.7164 23.5077i −1.61961 0.935084i
\(633\) −15.1277 −0.601273
\(634\) −28.2918 −1.12361
\(635\) −6.71381 + 3.87622i −0.266429 + 0.153823i
\(636\) −12.6927 −0.503300
\(637\) −11.9658 6.70870i −0.474103 0.265808i
\(638\) 17.6573 + 30.5834i 0.699060 + 1.21081i
\(639\) 14.4264i 0.570698i
\(640\) 1.11116 1.92459i 0.0439226 0.0760762i
\(641\) 1.29550 0.0511691 0.0255845 0.999673i \(-0.491855\pi\)
0.0255845 + 0.999673i \(0.491855\pi\)
\(642\) −43.1058 + 24.8871i −1.70125 + 0.982217i
\(643\) 29.7065 + 17.1511i 1.17151 + 0.676372i 0.954036 0.299693i \(-0.0968844\pi\)
0.217476 + 0.976066i \(0.430218\pi\)
\(644\) 5.59384 3.22961i 0.220428 0.127264i
\(645\) 5.87275 + 3.39063i 0.231239 + 0.133506i
\(646\) −16.2618 −0.639812
\(647\) 15.7672 + 27.3096i 0.619874 + 1.07365i 0.989508 + 0.144476i \(0.0461496\pi\)
−0.369634 + 0.929177i \(0.620517\pi\)
\(648\) 30.1505i 1.18442i
\(649\) −49.4075 −1.93942
\(650\) 18.1242 0.228587i 0.710889 0.00896592i
\(651\) 13.0105 + 19.9019i 0.509921 + 0.780018i
\(652\) −4.19399 + 2.42140i −0.164249 + 0.0948295i
\(653\) 14.7589 + 25.5632i 0.577562 + 1.00037i 0.995758 + 0.0920103i \(0.0293293\pi\)
−0.418196 + 0.908357i \(0.637337\pi\)
\(654\) 24.3694 + 42.2090i 0.952918 + 1.65050i
\(655\) 11.9526i 0.467025i
\(656\) 1.76321i 0.0688420i
\(657\) 26.9631 15.5671i 1.05193 0.607332i
\(658\) −16.9665 9.79559i −0.661422 0.381872i
\(659\) 1.09747 1.90088i 0.0427515 0.0740478i −0.843858 0.536567i \(-0.819721\pi\)
0.886609 + 0.462519i \(0.153054\pi\)
\(660\) −2.66104 + 4.60906i −0.103581 + 0.179408i
\(661\) 12.4248 + 7.17343i 0.483267 + 0.279014i 0.721777 0.692126i \(-0.243326\pi\)
−0.238510 + 0.971140i \(0.576659\pi\)
\(662\) 0.394675 + 0.683597i 0.0153395 + 0.0265687i
\(663\) −24.3869 + 14.4929i −0.947109 + 0.562857i
\(664\) −3.03841 5.26268i −0.117913 0.204232i
\(665\) 6.15291i 0.238599i
\(666\) 10.7802 + 18.6719i 0.417724 + 0.723520i
\(667\) 19.9659 34.5820i 0.773083 1.33902i
\(668\) 4.09496 + 2.36423i 0.158439 + 0.0914747i
\(669\) 12.6964i 0.490872i
\(670\) 9.80964 5.66360i 0.378979 0.218804i
\(671\) 33.5209 19.3533i 1.29406 0.747126i
\(672\) −15.3134 −0.590728
\(673\) 21.2738 36.8474i 0.820047 1.42036i −0.0856002 0.996330i \(-0.527281\pi\)
0.905647 0.424033i \(-0.139386\pi\)
\(674\) −11.4177 + 6.59203i −0.439795 + 0.253915i
\(675\) 1.51979 2.63236i 0.0584969 0.101320i
\(676\) 4.13419 7.59688i 0.159007 0.292188i
\(677\) 11.5537 + 20.0117i 0.444046 + 0.769111i 0.997985 0.0634465i \(-0.0202092\pi\)
−0.553939 + 0.832557i \(0.686876\pi\)
\(678\) 6.37345 3.67971i 0.244771 0.141319i
\(679\) −2.48210 −0.0952542
\(680\) 4.08346 7.07276i 0.156593 0.271228i
\(681\) 24.2885i 0.930738i
\(682\) 1.48070 + 26.7028i 0.0566989 + 1.02250i
\(683\) −27.5003 15.8773i −1.05227 0.607527i −0.128985 0.991647i \(-0.541172\pi\)
−0.923283 + 0.384119i \(0.874505\pi\)
\(684\) 7.69924i 0.294388i
\(685\) −2.47746 4.29108i −0.0946588 0.163954i
\(686\) 11.1565 + 19.3237i 0.425958 + 0.737781i
\(687\) 31.4961 + 18.1843i 1.20165 + 0.693773i
\(688\) −3.92413 + 6.79679i −0.149606 + 0.259125i
\(689\) −24.7515 + 14.7096i −0.942958 + 0.560391i
\(690\) −12.0728 −0.459605
\(691\) 1.27578 + 0.736574i 0.0485331 + 0.0280206i 0.524070 0.851675i \(-0.324413\pi\)
−0.475537 + 0.879696i \(0.657746\pi\)
\(692\) −6.64792 + 11.5145i −0.252716 + 0.437717i
\(693\) −20.1229 −0.764407
\(694\) −20.0285 11.5635i −0.760271 0.438943i
\(695\) 0.589743i 0.0223702i
\(696\) −46.8391 + 27.0426i −1.77543 + 1.02505i
\(697\) 2.60775i 0.0987756i
\(698\) 20.3646 35.2724i 0.770810 1.33508i
\(699\) 4.71851 0.178470
\(700\) 4.48161 + 2.58746i 0.169389 + 0.0977968i
\(701\) 25.5957 44.3331i 0.966737 1.67444i 0.261862 0.965105i \(-0.415663\pi\)
0.704874 0.709332i \(-0.251003\pi\)
\(702\) 1.48651 + 2.50132i 0.0561047 + 0.0944063i
\(703\) −14.7296 25.5124i −0.555537 0.962218i
\(704\) −30.9520 17.8701i −1.16655 0.673507i
\(705\) −9.12635 15.8073i −0.343718 0.595338i
\(706\) 11.5904 + 20.0752i 0.436211 + 0.755539i
\(707\) 16.4761 + 9.51249i 0.619648 + 0.357754i
\(708\) 18.8881i 0.709860i
\(709\) −12.3780 7.14643i −0.464865 0.268390i 0.249223 0.968446i \(-0.419825\pi\)
−0.714088 + 0.700056i \(0.753158\pi\)
\(710\) −4.29316 2.47866i −0.161119 0.0930223i
\(711\) 20.6708 35.8029i 0.775217 1.34272i
\(712\) −0.604407 1.04686i −0.0226511 0.0392328i
\(713\) 25.3116 16.5470i 0.947927 0.619689i
\(714\) 16.2483 0.608078
\(715\) 0.152253 + 12.0718i 0.00569393 + 0.451460i
\(716\) −0.461508 + 0.799355i −0.0172474 + 0.0298733i
\(717\) 5.60435 3.23567i 0.209298 0.120838i
\(718\) 20.8159 36.0542i 0.776843 1.34553i
\(719\) −17.9401 31.0732i −0.669054 1.15884i −0.978169 0.207811i \(-0.933366\pi\)
0.309115 0.951025i \(-0.399967\pi\)
\(720\) 4.20510 + 2.42782i 0.156715 + 0.0904794i
\(721\) 19.3429 + 11.1676i 0.720366 + 0.415904i
\(722\) 0.846054i 0.0314869i
\(723\) −3.56011 + 2.05543i −0.132402 + 0.0764423i
\(724\) −9.17055 −0.340821
\(725\) 31.9921 1.18816
\(726\) −15.0260 8.67525i −0.557666 0.321969i
\(727\) 1.13943 1.97355i 0.0422590 0.0731948i −0.844122 0.536151i \(-0.819878\pi\)
0.886381 + 0.462956i \(0.153211\pi\)
\(728\) −17.0603 + 10.1387i −0.632295 + 0.375767i
\(729\) −21.5056 −0.796503
\(730\) 10.6986i 0.395974i
\(731\) −5.80369 + 10.0523i −0.214657 + 0.371797i
\(732\) 7.39863 + 12.8148i 0.273461 + 0.473649i
\(733\) −14.2618 + 8.23405i −0.526771 + 0.304131i −0.739701 0.672936i \(-0.765033\pi\)
0.212929 + 0.977068i \(0.431700\pi\)
\(734\) 15.7330i 0.580715i
\(735\) 7.32041i 0.270017i
\(736\) 19.4759i 0.717890i
\(737\) −25.3085 43.8357i −0.932252 1.61471i
\(738\) 2.47690 0.0911760
\(739\) −23.8471 13.7681i −0.877228 0.506468i −0.00748489 0.999972i \(-0.502383\pi\)
−0.869744 + 0.493504i \(0.835716\pi\)
\(740\) 3.69303 0.135759
\(741\) 18.8088 + 31.6492i 0.690958 + 1.16266i
\(742\) 16.4913 0.605413
\(743\) −9.02622 + 5.21129i −0.331140 + 0.191184i −0.656347 0.754459i \(-0.727899\pi\)
0.325207 + 0.945643i \(0.394566\pi\)
\(744\) −40.8959 + 2.26772i −1.49932 + 0.0831388i
\(745\) −4.67405 + 8.09569i −0.171244 + 0.296603i
\(746\) 36.2045i 1.32554i
\(747\) 4.62760 2.67175i 0.169315 0.0977541i
\(748\) −7.88926 4.55487i −0.288460 0.166542i
\(749\) −27.9172 + 16.1180i −1.02007 + 0.588938i
\(750\) −10.3932 18.0016i −0.379507 0.657325i
\(751\) −13.7549 −0.501922 −0.250961 0.967997i \(-0.580747\pi\)
−0.250961 + 0.967997i \(0.580747\pi\)
\(752\) 18.2945 10.5623i 0.667132 0.385169i
\(753\) 12.4659 + 21.5915i 0.454281 + 0.786839i
\(754\) −14.9768 + 26.7130i −0.545423 + 0.972830i
\(755\) 1.91454 + 3.31608i 0.0696772 + 0.120684i
\(756\) 0.830726i 0.0302132i
\(757\) 10.6776 18.4941i 0.388084 0.672180i −0.604108 0.796902i \(-0.706471\pi\)
0.992192 + 0.124722i \(0.0398039\pi\)
\(758\) −16.2150 28.0853i −0.588957 1.02010i
\(759\) 53.9491i 1.95823i
\(760\) −9.17899 5.29949i −0.332957 0.192233i
\(761\) −19.5839 + 11.3068i −0.709916 + 0.409870i −0.811030 0.585005i \(-0.801093\pi\)
0.101114 + 0.994875i \(0.467759\pi\)
\(762\) 23.0093 13.2844i 0.833538 0.481243i
\(763\) 15.7827 + 27.3364i 0.571370 + 0.989643i
\(764\) −1.85684 + 3.21615i −0.0671783 + 0.116356i
\(765\) 6.21924 + 3.59068i 0.224857 + 0.129821i