Properties

Label 349.2.e.a.123.10
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 123.10
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.03662 + 0.598491i) q^{2} +(0.00513702 - 0.00889758i) q^{3} +(-0.283617 + 0.491238i) q^{4} +(-0.193021 + 0.334323i) q^{5} +0.0122978i q^{6} +(3.23720 - 1.86900i) q^{7} -3.07293i q^{8} +(1.49995 + 2.59798i) q^{9} +O(q^{10})\) \(q+(-1.03662 + 0.598491i) q^{2} +(0.00513702 - 0.00889758i) q^{3} +(-0.283617 + 0.491238i) q^{4} +(-0.193021 + 0.334323i) q^{5} +0.0122978i q^{6} +(3.23720 - 1.86900i) q^{7} -3.07293i q^{8} +(1.49995 + 2.59798i) q^{9} -0.462086i q^{10} -4.48490i q^{11} +(0.00291389 + 0.00504700i) q^{12} +(-1.35467 + 0.782122i) q^{13} +(-2.23716 + 3.87487i) q^{14} +(0.00198311 + 0.00343484i) q^{15} +(1.27189 + 2.20298i) q^{16} +6.40967 q^{17} +(-3.10974 - 1.79541i) q^{18} +(-2.90902 + 5.03856i) q^{19} +(-0.109488 - 0.189639i) q^{20} -0.0384043i q^{21} +(2.68417 + 4.64912i) q^{22} +(2.27143 + 3.93424i) q^{23} +(-0.0273417 - 0.0157857i) q^{24} +(2.42549 + 4.20106i) q^{25} +(0.936186 - 1.62152i) q^{26} +0.0616432 q^{27} +2.12032i q^{28} +(3.46755 - 6.00597i) q^{29} +(-0.00411145 - 0.00237375i) q^{30} -2.15649 q^{31} +(2.68555 + 1.55050i) q^{32} +(-0.0399047 - 0.0230390i) q^{33} +(-6.64438 + 3.83613i) q^{34} +1.44303i q^{35} -1.70164 q^{36} +4.45227 q^{37} -6.96408i q^{38} +0.0160711i q^{39} +(1.02735 + 0.593141i) q^{40} +5.24919 q^{41} +(0.0229847 + 0.0398106i) q^{42} +(-7.50306 - 4.33190i) q^{43} +(2.20315 + 1.27199i) q^{44} -1.15809 q^{45} +(-4.70921 - 2.71886i) q^{46} +2.22995i q^{47} +0.0261349 q^{48} +(3.48632 - 6.03848i) q^{49} +(-5.02860 - 2.90326i) q^{50} +(0.0329266 - 0.0570306i) q^{51} -0.887291i q^{52} +6.90943i q^{53} +(-0.0639003 + 0.0368929i) q^{54} +(1.49940 + 0.865681i) q^{55} +(-5.74331 - 9.94770i) q^{56} +(0.0298874 + 0.0517664i) q^{57} +8.30119i q^{58} +(-7.74318 - 4.47053i) q^{59} -0.00224977 q^{60} +4.16196i q^{61} +(2.23545 - 1.29064i) q^{62} +(9.71126 + 5.60680i) q^{63} -8.79941 q^{64} -0.603864i q^{65} +0.0551546 q^{66} +1.09453 q^{67} +(-1.81789 + 3.14868i) q^{68} +0.0466736 q^{69} +(-0.863639 - 1.49587i) q^{70} +(5.25715 - 3.03521i) q^{71} +(7.98343 - 4.60924i) q^{72} +(1.25178 - 2.16815i) q^{73} +(-4.61530 + 2.66465i) q^{74} +0.0498391 q^{75} +(-1.65009 - 2.85804i) q^{76} +(-8.38227 - 14.5185i) q^{77} +(-0.00961841 - 0.0166596i) q^{78} -7.81600i q^{79} -0.982007 q^{80} +(-4.49953 + 7.79341i) q^{81} +(-5.44140 + 3.14159i) q^{82} +(-6.53928 - 11.3264i) q^{83} +(0.0188657 + 0.0108921i) q^{84} +(-1.23720 + 2.14290i) q^{85} +10.3704 q^{86} +(-0.0356257 - 0.0617056i) q^{87} -13.7818 q^{88} +(-1.83741 - 1.06083i) q^{89} +(1.20049 - 0.693105i) q^{90} +(-2.92357 + 5.06377i) q^{91} -2.57686 q^{92} +(-0.0110779 + 0.0191875i) q^{93} +(-1.33461 - 2.31161i) q^{94} +(-1.12300 - 1.94510i) q^{95} +(0.0275914 - 0.0159299i) q^{96} +(-7.79942 + 4.50300i) q^{97} +8.34612i q^{98} +(11.6517 - 6.72711i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.03662 + 0.598491i −0.732999 + 0.423197i −0.819518 0.573053i \(-0.805759\pi\)
0.0865193 + 0.996250i \(0.472426\pi\)
\(3\) 0.00513702 0.00889758i 0.00296586 0.00513702i −0.864539 0.502566i \(-0.832389\pi\)
0.867505 + 0.497429i \(0.165723\pi\)
\(4\) −0.283617 + 0.491238i −0.141808 + 0.245619i
\(5\) −0.193021 + 0.334323i −0.0863217 + 0.149514i −0.905954 0.423377i \(-0.860845\pi\)
0.819632 + 0.572890i \(0.194178\pi\)
\(6\) 0.0122978i 0.00502057i
\(7\) 3.23720 1.86900i 1.22355 0.706415i 0.257875 0.966178i \(-0.416978\pi\)
0.965672 + 0.259763i \(0.0836444\pi\)
\(8\) 3.07293i 1.08645i
\(9\) 1.49995 + 2.59798i 0.499982 + 0.865995i
\(10\) 0.462086i 0.146124i
\(11\) 4.48490i 1.35225i −0.736788 0.676124i \(-0.763658\pi\)
0.736788 0.676124i \(-0.236342\pi\)
\(12\) 0.00291389 + 0.00504700i 0.000841167 + 0.00145694i
\(13\) −1.35467 + 0.782122i −0.375719 + 0.216921i −0.675954 0.736944i \(-0.736268\pi\)
0.300235 + 0.953865i \(0.402935\pi\)
\(14\) −2.23716 + 3.87487i −0.597906 + 1.03560i
\(15\) 0.00198311 + 0.00343484i 0.000512036 + 0.000886873i
\(16\) 1.27189 + 2.20298i 0.317973 + 0.550745i
\(17\) 6.40967 1.55457 0.777287 0.629146i \(-0.216595\pi\)
0.777287 + 0.629146i \(0.216595\pi\)
\(18\) −3.10974 1.79541i −0.732973 0.423182i
\(19\) −2.90902 + 5.03856i −0.667374 + 1.15593i 0.311262 + 0.950324i \(0.399248\pi\)
−0.978636 + 0.205602i \(0.934085\pi\)
\(20\) −0.109488 0.189639i −0.0244823 0.0424045i
\(21\) 0.0384043i 0.00838051i
\(22\) 2.68417 + 4.64912i 0.572267 + 0.991196i
\(23\) 2.27143 + 3.93424i 0.473626 + 0.820345i 0.999544 0.0301904i \(-0.00961138\pi\)
−0.525918 + 0.850535i \(0.676278\pi\)
\(24\) −0.0273417 0.0157857i −0.00558109 0.00322225i
\(25\) 2.42549 + 4.20106i 0.485097 + 0.840213i
\(26\) 0.936186 1.62152i 0.183601 0.318006i
\(27\) 0.0616432 0.0118632
\(28\) 2.12032i 0.400702i
\(29\) 3.46755 6.00597i 0.643908 1.11528i −0.340645 0.940192i \(-0.610645\pi\)
0.984553 0.175089i \(-0.0560213\pi\)
\(30\) −0.00411145 0.00237375i −0.000750644 0.000433385i
\(31\) −2.15649 −0.387317 −0.193659 0.981069i \(-0.562035\pi\)
−0.193659 + 0.981069i \(0.562035\pi\)
\(32\) 2.68555 + 1.55050i 0.474743 + 0.274093i
\(33\) −0.0399047 0.0230390i −0.00694652 0.00401058i
\(34\) −6.64438 + 3.83613i −1.13950 + 0.657891i
\(35\) 1.44303i 0.243916i
\(36\) −1.70164 −0.283607
\(37\) 4.45227 0.731949 0.365975 0.930625i \(-0.380736\pi\)
0.365975 + 0.930625i \(0.380736\pi\)
\(38\) 6.96408i 1.12972i
\(39\) 0.0160711i 0.00257343i
\(40\) 1.02735 + 0.593141i 0.162438 + 0.0937839i
\(41\) 5.24919 0.819785 0.409893 0.912134i \(-0.365566\pi\)
0.409893 + 0.912134i \(0.365566\pi\)
\(42\) 0.0229847 + 0.0398106i 0.00354661 + 0.00614291i
\(43\) −7.50306 4.33190i −1.14421 0.660608i −0.196738 0.980456i \(-0.563035\pi\)
−0.947469 + 0.319848i \(0.896368\pi\)
\(44\) 2.20315 + 1.27199i 0.332138 + 0.191760i
\(45\) −1.15809 −0.172637
\(46\) −4.70921 2.71886i −0.694335 0.400875i
\(47\) 2.22995i 0.325272i 0.986686 + 0.162636i \(0.0519996\pi\)
−0.986686 + 0.162636i \(0.948000\pi\)
\(48\) 0.0261349 0.00377225
\(49\) 3.48632 6.03848i 0.498045 0.862640i
\(50\) −5.02860 2.90326i −0.711151 0.410583i
\(51\) 0.0329266 0.0570306i 0.00461065 0.00798588i
\(52\) 0.887291i 0.123045i
\(53\) 6.90943i 0.949083i 0.880233 + 0.474542i \(0.157386\pi\)
−0.880233 + 0.474542i \(0.842614\pi\)
\(54\) −0.0639003 + 0.0368929i −0.00869574 + 0.00502049i
\(55\) 1.49940 + 0.865681i 0.202179 + 0.116728i
\(56\) −5.74331 9.94770i −0.767482 1.32932i
\(57\) 0.0298874 + 0.0517664i 0.00395868 + 0.00685663i
\(58\) 8.30119i 1.09000i
\(59\) −7.74318 4.47053i −1.00808 0.582013i −0.0974488 0.995241i \(-0.531068\pi\)
−0.910628 + 0.413227i \(0.864402\pi\)
\(60\) −0.00224977 −0.000290444
\(61\) 4.16196i 0.532884i 0.963851 + 0.266442i \(0.0858481\pi\)
−0.963851 + 0.266442i \(0.914152\pi\)
\(62\) 2.23545 1.29064i 0.283903 0.163911i
\(63\) 9.71126 + 5.60680i 1.22350 + 0.706390i
\(64\) −8.79941 −1.09993
\(65\) 0.603864i 0.0749002i
\(66\) 0.0551546 0.00678906
\(67\) 1.09453 0.133718 0.0668591 0.997762i \(-0.478702\pi\)
0.0668591 + 0.997762i \(0.478702\pi\)
\(68\) −1.81789 + 3.14868i −0.220451 + 0.381833i
\(69\) 0.0466736 0.00561884
\(70\) −0.863639 1.49587i −0.103225 0.178790i
\(71\) 5.25715 3.03521i 0.623908 0.360214i −0.154481 0.987996i \(-0.549370\pi\)
0.778389 + 0.627782i \(0.216037\pi\)
\(72\) 7.98343 4.60924i 0.940857 0.543204i
\(73\) 1.25178 2.16815i 0.146510 0.253763i −0.783425 0.621486i \(-0.786529\pi\)
0.929935 + 0.367723i \(0.119863\pi\)
\(74\) −4.61530 + 2.66465i −0.536518 + 0.309759i
\(75\) 0.0498391 0.00575492
\(76\) −1.65009 2.85804i −0.189278 0.327840i
\(77\) −8.38227 14.5185i −0.955248 1.65454i
\(78\) −0.00961841 0.0166596i −0.00108907 0.00188633i
\(79\) 7.81600i 0.879369i −0.898152 0.439685i \(-0.855090\pi\)
0.898152 0.439685i \(-0.144910\pi\)
\(80\) −0.982007 −0.109792
\(81\) −4.49953 + 7.79341i −0.499947 + 0.865934i
\(82\) −5.44140 + 3.14159i −0.600902 + 0.346931i
\(83\) −6.53928 11.3264i −0.717779 1.24323i −0.961878 0.273480i \(-0.911825\pi\)
0.244098 0.969750i \(-0.421508\pi\)
\(84\) 0.0188657 + 0.0108921i 0.00205842 + 0.00118843i
\(85\) −1.23720 + 2.14290i −0.134194 + 0.232430i
\(86\) 10.3704 1.11827
\(87\) −0.0356257 0.0617056i −0.00381948 0.00661553i
\(88\) −13.7818 −1.46914
\(89\) −1.83741 1.06083i −0.194765 0.112448i 0.399446 0.916757i \(-0.369202\pi\)
−0.594212 + 0.804309i \(0.702536\pi\)
\(90\) 1.20049 0.693105i 0.126543 0.0730597i
\(91\) −2.92357 + 5.06377i −0.306473 + 0.530827i
\(92\) −2.57686 −0.268657
\(93\) −0.0110779 + 0.0191875i −0.00114873 + 0.00198966i
\(94\) −1.33461 2.31161i −0.137654 0.238424i
\(95\) −1.12300 1.94510i −0.115218 0.199563i
\(96\) 0.0275914 0.0159299i 0.00281604 0.00162584i
\(97\) −7.79942 + 4.50300i −0.791911 + 0.457210i −0.840635 0.541602i \(-0.817818\pi\)
0.0487239 + 0.998812i \(0.484485\pi\)
\(98\) 8.34612i 0.843085i
\(99\) 11.6517 6.72711i 1.17104 0.676100i
\(100\) −2.75163 −0.275163
\(101\) 5.16963i 0.514397i −0.966359 0.257199i \(-0.917201\pi\)
0.966359 0.257199i \(-0.0827995\pi\)
\(102\) 0.0788252i 0.00780485i
\(103\) 9.73136i 0.958860i −0.877580 0.479430i \(-0.840843\pi\)
0.877580 0.479430i \(-0.159157\pi\)
\(104\) 2.40341 + 4.16282i 0.235673 + 0.408198i
\(105\) 0.0128394 + 0.00741286i 0.00125300 + 0.000723421i
\(106\) −4.13523 7.16244i −0.401649 0.695677i
\(107\) 3.62358 2.09207i 0.350305 0.202248i −0.314515 0.949253i \(-0.601842\pi\)
0.664819 + 0.747004i \(0.268508\pi\)
\(108\) −0.0174830 + 0.0302815i −0.00168230 + 0.00291384i
\(109\) 8.25160 14.2922i 0.790360 1.36894i −0.135385 0.990793i \(-0.543227\pi\)
0.925744 0.378150i \(-0.123440\pi\)
\(110\) −2.07241 −0.197596
\(111\) 0.0228714 0.0396145i 0.00217086 0.00376004i
\(112\) 8.23473 + 4.75432i 0.778109 + 0.449241i
\(113\) −2.42839 + 1.40203i −0.228444 + 0.131892i −0.609854 0.792514i \(-0.708772\pi\)
0.381410 + 0.924406i \(0.375439\pi\)
\(114\) −0.0619635 0.0357746i −0.00580341 0.00335060i
\(115\) −1.75374 −0.163537
\(116\) 1.96691 + 3.40679i 0.182623 + 0.316312i
\(117\) −4.06388 2.34628i −0.375706 0.216914i
\(118\) 10.7023 0.985226
\(119\) 20.7494 11.9797i 1.90209 1.09817i
\(120\) 0.0105550 0.00609396i 0.000963539 0.000556300i
\(121\) −9.11430 −0.828573
\(122\) −2.49090 4.31436i −0.225515 0.390604i
\(123\) 0.0269652 0.0467051i 0.00243137 0.00421125i
\(124\) 0.611616 1.05935i 0.0549248 0.0951325i
\(125\) −3.80289 −0.340141
\(126\) −13.4225 −1.19577
\(127\) 15.5408i 1.37902i 0.724276 + 0.689510i \(0.242174\pi\)
−0.724276 + 0.689510i \(0.757826\pi\)
\(128\) 3.75052 2.16536i 0.331502 0.191393i
\(129\) −0.0770868 + 0.0445061i −0.00678711 + 0.00391854i
\(130\) 0.361408 + 0.625976i 0.0316975 + 0.0549017i
\(131\) 6.38883i 0.558194i 0.960263 + 0.279097i \(0.0900352\pi\)
−0.960263 + 0.279097i \(0.909965\pi\)
\(132\) 0.0226353 0.0130685i 0.00197015 0.00113747i
\(133\) 21.7478i 1.88577i
\(134\) −1.13461 + 0.655066i −0.0980152 + 0.0565891i
\(135\) −0.0118984 + 0.0206087i −0.00102405 + 0.00177371i
\(136\) 19.6965i 1.68896i
\(137\) −11.2718 6.50781i −0.963019 0.555999i −0.0659181 0.997825i \(-0.520998\pi\)
−0.897101 + 0.441826i \(0.854331\pi\)
\(138\) −0.0483826 + 0.0279337i −0.00411860 + 0.00237788i
\(139\) 12.6754 1.07511 0.537556 0.843228i \(-0.319348\pi\)
0.537556 + 0.843228i \(0.319348\pi\)
\(140\) −0.708870 0.409266i −0.0599104 0.0345893i
\(141\) 0.0198412 + 0.0114553i 0.00167093 + 0.000964711i
\(142\) −3.63310 + 6.29271i −0.304883 + 0.528073i
\(143\) 3.50773 + 6.07558i 0.293332 + 0.508065i
\(144\) −3.81554 + 6.60870i −0.317961 + 0.550725i
\(145\) 1.33862 + 2.31856i 0.111166 + 0.192546i
\(146\) 2.99672i 0.248011i
\(147\) −0.0358186 0.0620396i −0.00295426 0.00511694i
\(148\) −1.26274 + 2.18713i −0.103797 + 0.179781i
\(149\) −11.0183 + 6.36139i −0.902650 + 0.521145i −0.878059 0.478552i \(-0.841162\pi\)
−0.0245913 + 0.999698i \(0.507828\pi\)
\(150\) −0.0516640 + 0.0298282i −0.00421835 + 0.00243547i
\(151\) 0.00348899 0.00604311i 0.000283930 0.000491781i −0.865883 0.500246i \(-0.833243\pi\)
0.866167 + 0.499754i \(0.166576\pi\)
\(152\) 15.4832 + 8.93921i 1.25585 + 0.725066i
\(153\) 9.61417 + 16.6522i 0.777260 + 1.34625i
\(154\) 17.3784 + 10.0334i 1.40039 + 0.808517i
\(155\) 0.416248 0.720963i 0.0334339 0.0579092i
\(156\) −0.00789474 0.00455803i −0.000632085 0.000364934i
\(157\) −9.64158 + 16.6997i −0.769482 + 1.33278i 0.168362 + 0.985725i \(0.446152\pi\)
−0.937844 + 0.347057i \(0.887181\pi\)
\(158\) 4.67781 + 8.10220i 0.372147 + 0.644577i
\(159\) 0.0614772 + 0.0354939i 0.00487546 + 0.00281485i
\(160\) −1.03674 + 0.598560i −0.0819612 + 0.0473203i
\(161\) 14.7062 + 8.49061i 1.15901 + 0.669154i
\(162\) 10.7717i 0.846305i
\(163\) 19.0217i 1.48989i 0.667125 + 0.744945i \(0.267524\pi\)
−0.667125 + 0.744945i \(0.732476\pi\)
\(164\) −1.48876 + 2.57860i −0.116252 + 0.201355i
\(165\) 0.0154049 0.00889404i 0.00119927 0.000692400i
\(166\) 13.5575 + 7.82740i 1.05226 + 0.607524i
\(167\) 20.4590i 1.58317i −0.611062 0.791583i \(-0.709258\pi\)
0.611062 0.791583i \(-0.290742\pi\)
\(168\) −0.118014 −0.00910498
\(169\) −5.27657 + 9.13929i −0.405890 + 0.703022i
\(170\) 2.96182i 0.227161i
\(171\) −17.4535 −1.33470
\(172\) 4.25599 2.45720i 0.324516 0.187359i
\(173\) −11.9421 + 6.89475i −0.907938 + 0.524198i −0.879767 0.475405i \(-0.842302\pi\)
−0.0281708 + 0.999603i \(0.508968\pi\)
\(174\) 0.0738605 + 0.0426434i 0.00559935 + 0.00323279i
\(175\) 15.7036 + 9.06646i 1.18708 + 0.685360i
\(176\) 9.88013 5.70430i 0.744743 0.429977i
\(177\) −0.0795538 + 0.0459304i −0.00597963 + 0.00345234i
\(178\) 2.53959 0.190350
\(179\) 22.2533i 1.66329i −0.555306 0.831646i \(-0.687399\pi\)
0.555306 0.831646i \(-0.312601\pi\)
\(180\) 0.328453 0.568897i 0.0244814 0.0424031i
\(181\) 0.730722 0.0543141 0.0271571 0.999631i \(-0.491355\pi\)
0.0271571 + 0.999631i \(0.491355\pi\)
\(182\) 6.99892i 0.518795i
\(183\) 0.0370314 + 0.0213801i 0.00273744 + 0.00158046i
\(184\) 12.0896 6.97996i 0.891260 0.514569i
\(185\) −0.859384 + 1.48850i −0.0631831 + 0.109436i
\(186\) 0.0265202i 0.00194455i
\(187\) 28.7467i 2.10217i
\(188\) −1.09544 0.632451i −0.0798930 0.0461262i
\(189\) 0.199551 0.115211i 0.0145152 0.00838037i
\(190\) 2.32825 + 1.34422i 0.168909 + 0.0975197i
\(191\) 7.60086 + 13.1651i 0.549979 + 0.952591i 0.998275 + 0.0587061i \(0.0186975\pi\)
−0.448297 + 0.893885i \(0.647969\pi\)
\(192\) −0.0452027 + 0.0782934i −0.00326223 + 0.00565034i
\(193\) 4.21991 + 2.43637i 0.303756 + 0.175374i 0.644129 0.764917i \(-0.277220\pi\)
−0.340373 + 0.940291i \(0.610553\pi\)
\(194\) 5.39001 9.33577i 0.386980 0.670269i
\(195\) −0.00537293 0.00310206i −0.000384764 0.000222143i
\(196\) 1.97755 + 3.42523i 0.141254 + 0.244659i
\(197\) −14.5646 8.40887i −1.03768 0.599107i −0.118507 0.992953i \(-0.537811\pi\)
−0.919176 + 0.393846i \(0.871144\pi\)
\(198\) −8.05223 + 13.9469i −0.572247 + 0.991161i
\(199\) −15.6891 + 9.05809i −1.11217 + 0.642111i −0.939390 0.342850i \(-0.888608\pi\)
−0.172778 + 0.984961i \(0.555274\pi\)
\(200\) 12.9096 7.45335i 0.912846 0.527032i
\(201\) 0.00562262 0.00973867i 0.000396589 0.000686913i
\(202\) 3.09398 + 5.35893i 0.217692 + 0.377053i
\(203\) 25.9234i 1.81947i
\(204\) 0.0186771 + 0.0323496i 0.00130766 + 0.00226493i
\(205\) −1.01320 + 1.75492i −0.0707653 + 0.122569i
\(206\) 5.82414 + 10.0877i 0.405787 + 0.702843i
\(207\) −6.81406 + 11.8023i −0.473610 + 0.820316i
\(208\) −3.44599 1.98955i −0.238937 0.137950i
\(209\) 22.5974 + 13.0466i 1.56310 + 0.902455i
\(210\) −0.0177461 −0.00122460
\(211\) 6.90557 3.98693i 0.475399 0.274472i −0.243098 0.970002i \(-0.578164\pi\)
0.718497 + 0.695530i \(0.244830\pi\)
\(212\) −3.39418 1.95963i −0.233113 0.134588i
\(213\) 0.0623678i 0.00427337i
\(214\) −2.50418 + 4.33736i −0.171182 + 0.296496i
\(215\) 2.89650 1.67230i 0.197540 0.114050i
\(216\) 0.189425i 0.0128888i
\(217\) −6.98099 + 4.03048i −0.473901 + 0.273607i
\(218\) 19.7540i 1.33791i
\(219\) −0.0128609 0.0222757i −0.000869056 0.00150525i
\(220\) −0.850511 + 0.491043i −0.0573414 + 0.0331061i
\(221\) −8.68302 + 5.01314i −0.584083 + 0.337221i
\(222\) 0.0547534i 0.00367481i
\(223\) 0.0439219 0.00294123 0.00147062 0.999999i \(-0.499532\pi\)
0.00147062 + 0.999999i \(0.499532\pi\)
\(224\) 11.5916 0.774493
\(225\) −7.27620 + 12.6027i −0.485080 + 0.840183i
\(226\) 1.67821 2.90675i 0.111633 0.193354i
\(227\) 3.00631 + 5.20708i 0.199536 + 0.345606i 0.948378 0.317142i \(-0.102723\pi\)
−0.748842 + 0.662748i \(0.769390\pi\)
\(228\) −0.0339062 −0.00224549
\(229\) 6.55402 3.78397i 0.433102 0.250052i −0.267565 0.963540i \(-0.586219\pi\)
0.700667 + 0.713488i \(0.252886\pi\)
\(230\) 1.81796 1.04960i 0.119872 0.0692084i
\(231\) −0.172240 −0.0113325
\(232\) −18.4559 10.6555i −1.21169 0.699571i
\(233\) −5.94303 10.2936i −0.389341 0.674358i 0.603020 0.797726i \(-0.293964\pi\)
−0.992361 + 0.123368i \(0.960630\pi\)
\(234\) 5.61692 0.367189
\(235\) −0.745523 0.430428i −0.0486326 0.0280780i
\(236\) 4.39219 2.53583i 0.285907 0.165069i
\(237\) −0.0695435 0.0401510i −0.00451734 0.00260809i
\(238\) −14.3395 + 24.8367i −0.929489 + 1.60992i
\(239\) −25.4355 −1.64528 −0.822642 0.568560i \(-0.807501\pi\)
−0.822642 + 0.568560i \(0.807501\pi\)
\(240\) −0.00504459 + 0.00873749i −0.000325627 + 0.000564002i
\(241\) −0.919176 + 1.59206i −0.0592093 + 0.102554i −0.894111 0.447846i \(-0.852191\pi\)
0.834901 + 0.550400i \(0.185525\pi\)
\(242\) 9.44804 5.45483i 0.607343 0.350650i
\(243\) 0.138693 + 0.240223i 0.00889716 + 0.0154103i
\(244\) −2.04451 1.18040i −0.130887 0.0755674i
\(245\) 1.34587 + 2.33111i 0.0859843 + 0.148929i
\(246\) 0.0645537i 0.00411579i
\(247\) 9.10082i 0.579071i
\(248\) 6.62675i 0.420799i
\(249\) −0.134370 −0.00851533
\(250\) 3.94214 2.27600i 0.249323 0.143947i
\(251\) 1.24886i 0.0788271i −0.999223 0.0394135i \(-0.987451\pi\)
0.999223 0.0394135i \(-0.0125490\pi\)
\(252\) −5.50855 + 3.18036i −0.347006 + 0.200344i
\(253\) 17.6446 10.1871i 1.10931 0.640460i
\(254\) −9.30101 16.1098i −0.583597 1.01082i
\(255\) 0.0127111 + 0.0220162i 0.000795998 + 0.00137871i
\(256\) 6.20751 10.7517i 0.387969 0.671982i
\(257\) −18.9213 −1.18028 −0.590140 0.807301i \(-0.700928\pi\)
−0.590140 + 0.807301i \(0.700928\pi\)
\(258\) 0.0532730 0.0922715i 0.00331663 0.00574457i
\(259\) 14.4129 8.32130i 0.895575 0.517060i
\(260\) 0.296641 + 0.171266i 0.0183969 + 0.0106215i
\(261\) 20.8046 1.28777
\(262\) −3.82366 6.62277i −0.236226 0.409156i
\(263\) −20.7894 −1.28193 −0.640966 0.767569i \(-0.721466\pi\)
−0.640966 + 0.767569i \(0.721466\pi\)
\(264\) −0.0707973 + 0.122625i −0.00435727 + 0.00754702i
\(265\) −2.30998 1.33367i −0.141901 0.0819265i
\(266\) −13.0159 22.5441i −0.798054 1.38227i
\(267\) −0.0188777 + 0.0108990i −0.00115529 + 0.000667009i
\(268\) −0.310427 + 0.537675i −0.0189623 + 0.0328437i
\(269\) −12.8324 −0.782406 −0.391203 0.920304i \(-0.627941\pi\)
−0.391203 + 0.920304i \(0.627941\pi\)
\(270\) 0.0284844i 0.00173351i
\(271\) −8.80236 15.2461i −0.534706 0.926137i −0.999178 0.0405493i \(-0.987089\pi\)
0.464472 0.885588i \(-0.346244\pi\)
\(272\) 8.15240 + 14.1204i 0.494312 + 0.856173i
\(273\) 0.0300369 + 0.0520254i 0.00181791 + 0.00314872i
\(274\) 15.5795 0.941189
\(275\) 18.8413 10.8781i 1.13618 0.655971i
\(276\) −0.0132374 + 0.0229278i −0.000796798 + 0.00138009i
\(277\) 13.9067 8.02903i 0.835572 0.482418i −0.0201844 0.999796i \(-0.506425\pi\)
0.855757 + 0.517378i \(0.173092\pi\)
\(278\) −13.1395 + 7.58611i −0.788056 + 0.454984i
\(279\) −3.23462 5.60253i −0.193652 0.335415i
\(280\) 4.43432 0.265002
\(281\) 14.0882 24.4015i 0.840431 1.45567i −0.0490990 0.998794i \(-0.515635\pi\)
0.889530 0.456876i \(-0.151032\pi\)
\(282\) −0.0274236 −0.00163305
\(283\) −31.8724 −1.89462 −0.947308 0.320325i \(-0.896208\pi\)
−0.947308 + 0.320325i \(0.896208\pi\)
\(284\) 3.44335i 0.204325i
\(285\) −0.0230756 −0.00136688
\(286\) −7.27236 4.19870i −0.430023 0.248274i
\(287\) 16.9927 9.81073i 1.00305 0.579109i
\(288\) 9.30269i 0.548166i
\(289\) 24.0839 1.41670
\(290\) −2.77528 1.60231i −0.162970 0.0940907i
\(291\) 0.0925279i 0.00542408i
\(292\) 0.710053 + 1.22985i 0.0415527 + 0.0719714i
\(293\) 12.9482 + 22.4270i 0.756442 + 1.31020i 0.944654 + 0.328068i \(0.106398\pi\)
−0.188212 + 0.982128i \(0.560269\pi\)
\(294\) 0.0742603 + 0.0428742i 0.00433095 + 0.00250047i
\(295\) 2.98920 1.72581i 0.174038 0.100481i
\(296\) 13.6815i 0.795223i
\(297\) 0.276463i 0.0160420i
\(298\) 7.61447 13.1887i 0.441095 0.763998i
\(299\) −6.15410 3.55307i −0.355901 0.205479i
\(300\) −0.0141352 + 0.0244829i −0.000816095 + 0.00141352i
\(301\) −32.3852 −1.86665
\(302\) 0.00835252i 0.000480633i
\(303\) −0.0459972 0.0265565i −0.00264247 0.00152563i
\(304\) −14.7998 −0.848827
\(305\) −1.39144 0.803347i −0.0796735 0.0459995i
\(306\) −19.9324 11.5080i −1.13946 0.657868i
\(307\) 12.3017 + 21.3072i 0.702097 + 1.21607i 0.967729 + 0.251994i \(0.0810862\pi\)
−0.265632 + 0.964075i \(0.585580\pi\)
\(308\) 9.50940 0.541849
\(309\) −0.0865856 0.0499902i −0.00492568 0.00284384i
\(310\) 0.996484i 0.0565965i
\(311\) 13.7005i 0.776882i 0.921474 + 0.388441i \(0.126986\pi\)
−0.921474 + 0.388441i \(0.873014\pi\)
\(312\) 0.0493854 0.00279590
\(313\) −26.3292 −1.48822 −0.744108 0.668059i \(-0.767125\pi\)
−0.744108 + 0.668059i \(0.767125\pi\)
\(314\) 23.0816i 1.30257i
\(315\) −3.74896 + 2.16446i −0.211230 + 0.121954i
\(316\) 3.83952 + 2.21675i 0.215990 + 0.124702i
\(317\) 15.9446 + 9.20559i 0.895535 + 0.517037i 0.875749 0.482767i \(-0.160368\pi\)
0.0197862 + 0.999804i \(0.493701\pi\)
\(318\) −0.0849711 −0.00476494
\(319\) −26.9362 15.5516i −1.50814 0.870722i
\(320\) 1.69847 2.94184i 0.0949475 0.164454i
\(321\) 0.0429881i 0.00239936i
\(322\) −20.3262 −1.13274
\(323\) −18.6458 + 32.2956i −1.03748 + 1.79697i
\(324\) −2.55228 4.42068i −0.141793 0.245593i
\(325\) −6.57149 3.79405i −0.364520 0.210456i
\(326\) −11.3843 19.7182i −0.630518 1.09209i
\(327\) −0.0847772 0.146838i −0.00468819 0.00812019i
\(328\) 16.1304i 0.890652i
\(329\) 4.16778 + 7.21880i 0.229777 + 0.397985i
\(330\) −0.0106460 + 0.0184394i −0.000586043 + 0.00101506i
\(331\) −12.1878 7.03665i −0.669904 0.386770i 0.126136 0.992013i \(-0.459742\pi\)
−0.796040 + 0.605243i \(0.793076\pi\)
\(332\) 7.41860 0.407148
\(333\) 6.67818 + 11.5669i 0.365962 + 0.633865i
\(334\) 12.2445 + 21.2082i 0.669991 + 1.16046i
\(335\) −0.211268 + 0.365926i −0.0115428 + 0.0199927i
\(336\) 0.0846039 0.0488461i 0.00461552 0.00266477i
\(337\) −1.85401 3.21123i −0.100994 0.174927i 0.811100 0.584907i \(-0.198869\pi\)
−0.912095 + 0.409980i \(0.865536\pi\)
\(338\) 12.6319i 0.687086i
\(339\) 0.0288091i 0.00156470i
\(340\) −0.701783 1.21552i −0.0380595 0.0659210i
\(341\) 9.67164i 0.523748i
\(342\) 18.0926 10.4458i 0.978335 0.564842i
\(343\) 0.102295i 0.00552342i
\(344\) −13.3116 + 23.0564i −0.717715 + 1.24312i
\(345\) −0.00900899 + 0.0156040i −0.000485028 + 0.000840093i
\(346\) 8.25290 14.2944i 0.443678 0.768474i
\(347\) −15.6017 + 9.00766i −0.837545 + 0.483557i −0.856429 0.516265i \(-0.827322\pi\)
0.0188843 + 0.999822i \(0.493989\pi\)
\(348\) 0.0404162 0.00216654
\(349\) −5.77011 17.7681i −0.308867 0.951105i
\(350\) −21.7048 −1.16017
\(351\) −0.0835064 + 0.0482124i −0.00445724 + 0.00257339i
\(352\) 6.95385 12.0444i 0.370641 0.641969i
\(353\) −12.9162 + 22.3715i −0.687460 + 1.19072i 0.285197 + 0.958469i \(0.407941\pi\)
−0.972657 + 0.232247i \(0.925392\pi\)
\(354\) 0.0549779 0.0952245i 0.00292204 0.00506112i
\(355\) 2.34344i 0.124377i
\(356\) 1.04224 0.601738i 0.0552387 0.0318921i
\(357\) 0.246159i 0.0130281i
\(358\) 13.3184 + 23.0682i 0.703900 + 1.21919i
\(359\) 18.0925i 0.954883i −0.878663 0.477442i \(-0.841564\pi\)
0.878663 0.477442i \(-0.158436\pi\)
\(360\) 3.55872i 0.187561i
\(361\) −7.42476 12.8601i −0.390777 0.676845i
\(362\) −0.757479 + 0.437330i −0.0398122 + 0.0229856i
\(363\) −0.0468204 + 0.0810952i −0.00245743 + 0.00425640i
\(364\) −1.65835 2.87234i −0.0869209 0.150551i
\(365\) 0.483241 + 0.836998i 0.0252940 + 0.0438105i
\(366\) −0.0511831 −0.00267538
\(367\) 20.5388 + 11.8581i 1.07212 + 0.618987i 0.928759 0.370684i \(-0.120877\pi\)
0.143358 + 0.989671i \(0.454210\pi\)
\(368\) −5.77802 + 10.0078i −0.301200 + 0.521694i
\(369\) 7.87350 + 13.6373i 0.409878 + 0.709930i
\(370\) 2.05733i 0.106956i
\(371\) 12.9137 + 22.3672i 0.670447 + 1.16125i
\(372\) −0.00628377 0.0108838i −0.000325798 0.000564299i
\(373\) 14.7945 + 8.54161i 0.766031 + 0.442268i 0.831457 0.555589i \(-0.187507\pi\)
−0.0654261 + 0.997857i \(0.520841\pi\)
\(374\) 17.2047 + 29.7993i 0.889632 + 1.54089i
\(375\) −0.0195355 + 0.0338365i −0.00100881 + 0.00174731i
\(376\) 6.85249 0.353390
\(377\) 10.8482i 0.558710i
\(378\) −0.137906 + 0.238859i −0.00709310 + 0.0122856i
\(379\) −21.5009 12.4135i −1.10443 0.637641i −0.167046 0.985949i \(-0.553423\pi\)
−0.937380 + 0.348308i \(0.886756\pi\)
\(380\) 1.27401 0.0653554
\(381\) 0.138275 + 0.0798332i 0.00708405 + 0.00408998i
\(382\) −15.7584 9.09809i −0.806268 0.465499i
\(383\) 25.9973 15.0096i 1.32840 0.766953i 0.343349 0.939208i \(-0.388439\pi\)
0.985052 + 0.172255i \(0.0551053\pi\)
\(384\) 0.0444940i 0.00227058i
\(385\) 6.47183 0.329835
\(386\) −5.83258 −0.296871
\(387\) 25.9905i 1.32117i
\(388\) 5.10850i 0.259345i
\(389\) −1.67396 0.966464i −0.0848733 0.0490016i 0.456963 0.889486i \(-0.348937\pi\)
−0.541836 + 0.840484i \(0.682271\pi\)
\(390\) 0.00742623 0.000376042
\(391\) 14.5591 + 25.2172i 0.736287 + 1.27529i
\(392\) −18.5558 10.7132i −0.937211 0.541099i
\(393\) 0.0568451 + 0.0328195i 0.00286746 + 0.00165553i
\(394\) 20.1305 1.01416
\(395\) 2.61307 + 1.50866i 0.131478 + 0.0759087i
\(396\) 7.63168i 0.383506i
\(397\) 26.9666 1.35341 0.676706 0.736253i \(-0.263407\pi\)
0.676706 + 0.736253i \(0.263407\pi\)
\(398\) 10.8424 18.7795i 0.543479 0.941333i
\(399\) 0.193503 + 0.111719i 0.00968726 + 0.00559294i
\(400\) −6.16990 + 10.6866i −0.308495 + 0.534329i
\(401\) 30.0144i 1.49885i −0.662092 0.749423i \(-0.730331\pi\)
0.662092 0.749423i \(-0.269669\pi\)
\(402\) 0.0134604i 0.000671342i
\(403\) 2.92134 1.68664i 0.145522 0.0840174i
\(404\) 2.53952 + 1.46619i 0.126346 + 0.0729458i
\(405\) −1.73701 3.00859i −0.0863126 0.149498i
\(406\) 15.5149 + 26.8726i 0.769992 + 1.33367i
\(407\) 19.9680i 0.989777i
\(408\) −0.175251 0.101181i −0.00867622 0.00500922i
\(409\) −31.4182 −1.55353 −0.776766 0.629789i \(-0.783141\pi\)
−0.776766 + 0.629789i \(0.783141\pi\)
\(410\) 2.42558i 0.119791i
\(411\) −0.115807 + 0.0668614i −0.00571236 + 0.00329803i
\(412\) 4.78042 + 2.75998i 0.235514 + 0.135974i
\(413\) −33.4217 −1.64457
\(414\) 16.3126i 0.801721i
\(415\) 5.04888 0.247840
\(416\) −4.85073 −0.237826
\(417\) 0.0651137 0.112780i 0.00318863 0.00552287i
\(418\) −31.2332 −1.52767
\(419\) −1.10991 1.92242i −0.0542227 0.0939165i 0.837640 0.546223i \(-0.183935\pi\)
−0.891863 + 0.452306i \(0.850601\pi\)
\(420\) −0.00728296 + 0.00420482i −0.000355372 + 0.000205174i
\(421\) 31.0765 17.9421i 1.51458 0.874442i 0.514724 0.857356i \(-0.327894\pi\)
0.999854 0.0170864i \(-0.00543902\pi\)
\(422\) −4.77229 + 8.26584i −0.232311 + 0.402375i
\(423\) −5.79338 + 3.34481i −0.281684 + 0.162630i
\(424\) 21.2322 1.03113
\(425\) 15.5466 + 26.9274i 0.754119 + 1.30617i
\(426\) 0.0373266 + 0.0646516i 0.00180848 + 0.00313238i
\(427\) 7.77870 + 13.4731i 0.376438 + 0.652009i
\(428\) 2.37339i 0.114722i
\(429\) 0.0720772 0.00347992
\(430\) −2.00171 + 3.46706i −0.0965310 + 0.167197i
\(431\) −28.0274 + 16.1816i −1.35003 + 0.779441i −0.988253 0.152824i \(-0.951163\pi\)
−0.361778 + 0.932264i \(0.617830\pi\)
\(432\) 0.0784033 + 0.135799i 0.00377218 + 0.00653361i
\(433\) −19.9728 11.5313i −0.959834 0.554160i −0.0637118 0.997968i \(-0.520294\pi\)
−0.896122 + 0.443808i \(0.853627\pi\)
\(434\) 4.82441 8.35613i 0.231579 0.401107i
\(435\) 0.0275061 0.00131882
\(436\) 4.68058 + 8.10700i 0.224159 + 0.388255i
\(437\) −26.4305 −1.26434
\(438\) 0.0266636 + 0.0153942i 0.00127403 + 0.000735564i
\(439\) 21.4683 12.3947i 1.02462 0.591567i 0.109184 0.994022i \(-0.465176\pi\)
0.915440 + 0.402454i \(0.131843\pi\)
\(440\) 2.66018 4.60756i 0.126819 0.219657i
\(441\) 20.9172 0.996055
\(442\) 6.00064 10.3934i 0.285422 0.494365i
\(443\) 10.8643 + 18.8175i 0.516179 + 0.894048i 0.999824 + 0.0187834i \(0.00597929\pi\)
−0.483645 + 0.875264i \(0.660687\pi\)
\(444\) 0.0129734 + 0.0224706i 0.000615692 + 0.00106641i
\(445\) 0.709320 0.409526i 0.0336250 0.0194134i
\(446\) −0.0455302 + 0.0262869i −0.00215592 + 0.00124472i
\(447\) 0.130714i 0.00618258i
\(448\) −28.4855 + 16.4461i −1.34581 + 0.777005i
\(449\) −24.1741 −1.14085 −0.570423 0.821351i \(-0.693221\pi\)
−0.570423 + 0.821351i \(0.693221\pi\)
\(450\) 17.4190i 0.821138i
\(451\) 23.5421i 1.10855i
\(452\) 1.59056i 0.0748137i
\(453\) −3.58460e−5 0 6.20871e-5i −1.68419e−6 0 2.91711e-6i
\(454\) −6.23278 3.59850i −0.292519 0.168886i
\(455\) −1.12862 1.95483i −0.0529106 0.0916439i
\(456\) 0.159075 0.0918418i 0.00744936 0.00430089i
\(457\) −2.95967 + 5.12630i −0.138448 + 0.239798i −0.926909 0.375286i \(-0.877545\pi\)
0.788462 + 0.615084i \(0.210878\pi\)
\(458\) −4.52934 + 7.84505i −0.211642 + 0.366575i
\(459\) 0.395112 0.0184423
\(460\) 0.497390 0.861504i 0.0231909 0.0401678i
\(461\) 30.8723 + 17.8241i 1.43787 + 0.830152i 0.997701 0.0677652i \(-0.0215869\pi\)
0.440164 + 0.897917i \(0.354920\pi\)
\(462\) 0.178546 0.103084i 0.00830673 0.00479589i
\(463\) −3.52986 2.03797i −0.164047 0.0947124i 0.415729 0.909489i \(-0.363526\pi\)
−0.579776 + 0.814776i \(0.696860\pi\)
\(464\) 17.6414 0.818980
\(465\) −0.00427655 0.00740721i −0.000198320 0.000343501i
\(466\) 12.3213 + 7.11370i 0.570773 + 0.329536i
\(467\) −14.6924 −0.679884 −0.339942 0.940446i \(-0.610407\pi\)
−0.339942 + 0.940446i \(0.610407\pi\)
\(468\) 2.30517 1.33089i 0.106556 0.0615204i
\(469\) 3.54321 2.04568i 0.163610 0.0944605i
\(470\) 1.03043 0.0475302
\(471\) 0.0990580 + 0.171574i 0.00456435 + 0.00790569i
\(472\) −13.7376 + 23.7943i −0.632326 + 1.09522i
\(473\) −19.4281 + 33.6505i −0.893305 + 1.54725i
\(474\) 0.0961200 0.00441494
\(475\) −28.2231 −1.29497
\(476\) 13.5905i 0.622921i
\(477\) −17.9506 + 10.3638i −0.821901 + 0.474525i
\(478\) 26.3668 15.2229i 1.20599 0.696279i
\(479\) 3.42434 + 5.93112i 0.156462 + 0.271000i 0.933590 0.358342i \(-0.116658\pi\)
−0.777128 + 0.629342i \(0.783324\pi\)
\(480\) 0.0122993i 0.000561382i
\(481\) −6.03138 + 3.48222i −0.275007 + 0.158776i
\(482\) 2.20047i 0.100229i
\(483\) 0.151092 0.0872329i 0.00687491 0.00396923i
\(484\) 2.58497 4.47730i 0.117499 0.203513i
\(485\) 3.47670i 0.157869i
\(486\) −0.287543 0.166013i −0.0130432 0.00753051i
\(487\) 16.6995 9.64144i 0.756725 0.436896i −0.0713935 0.997448i \(-0.522745\pi\)
0.828119 + 0.560553i \(0.189411\pi\)
\(488\) 12.7894 0.578950
\(489\) 0.169247 + 0.0977146i 0.00765360 + 0.00441881i
\(490\) −2.79030 1.61098i −0.126053 0.0727766i
\(491\) 1.74217 3.01753i 0.0786231 0.136179i −0.824033 0.566542i \(-0.808281\pi\)
0.902656 + 0.430363i \(0.141614\pi\)
\(492\) 0.0152955 + 0.0264927i 0.000689576 + 0.00119438i
\(493\) 22.2259 38.4963i 1.00100 1.73379i
\(494\) 5.44676 + 9.43407i 0.245061 + 0.424459i
\(495\) 5.19390i 0.233448i
\(496\) −2.74282 4.75070i −0.123156 0.213313i
\(497\) 11.3456 19.6512i 0.508921 0.881477i
\(498\) 0.139290 0.0804191i 0.00624173 0.00360366i
\(499\) 31.5288 18.2032i 1.41142 0.814886i 0.415901 0.909410i \(-0.363466\pi\)
0.995523 + 0.0945245i \(0.0301331\pi\)
\(500\) 1.07856 1.86813i 0.0482348 0.0835452i
\(501\) −0.182036 0.105098i −0.00813275 0.00469545i
\(502\) 0.747429 + 1.29459i 0.0333594 + 0.0577802i
\(503\) 19.5961 + 11.3138i 0.873749 + 0.504459i 0.868592 0.495527i \(-0.165025\pi\)
0.00515674 + 0.999987i \(0.498359\pi\)
\(504\) 17.2293 29.8421i 0.767455 1.32927i
\(505\) 1.72832 + 0.997849i 0.0769094 + 0.0444037i
\(506\) −12.1938 + 21.1203i −0.542082 + 0.938913i
\(507\) 0.0542117 + 0.0938974i 0.00240763 + 0.00417013i
\(508\) −7.63422 4.40762i −0.338714 0.195556i
\(509\) −19.9810 + 11.5360i −0.885641 + 0.511325i −0.872514 0.488589i \(-0.837512\pi\)
−0.0131265 + 0.999914i \(0.504178\pi\)
\(510\) −0.0263530 0.0152149i −0.00116693 0.000673728i
\(511\) 9.35832i 0.413988i
\(512\) 23.5220i 1.03954i
\(513\) −0.179321 + 0.310593i −0.00791721 + 0.0137130i
\(514\) 19.6142 11.3243i 0.865145 0.499491i
\(515\) 3.25342 + 1.87836i 0.143363 + 0.0827704i
\(516\) 0.0504906i 0.00222273i
\(517\) 10.0011 0.439848
\(518\) −9.96045 + 17.2520i −0.437637 + 0.758009i
\(519\) 0.141674i 0.00621879i
\(520\) −1.85563 −0.0813750
\(521\) 13.4284 7.75290i 0.588309 0.339661i −0.176119 0.984369i \(-0.556354\pi\)
0.764429 + 0.644708i \(0.223021\pi\)
\(522\) −21.5664 + 12.4513i −0.943934 + 0.544981i
\(523\) 32.0015 + 18.4761i 1.39933 + 0.807902i 0.994322 0.106412i \(-0.0339362\pi\)
0.405006 + 0.914314i \(0.367269\pi\)
\(524\) −3.13844 1.81198i −0.137103 0.0791566i
\(525\) 0.161339 0.0931492i 0.00704142 0.00406536i
\(526\) 21.5507 12.4423i 0.939655 0.542510i
\(527\) −13.8224 −0.602113
\(528\) 0.117212i 0.00510101i
\(529\) 1.18119 2.04588i 0.0513561 0.0889513i
\(530\) 3.19275 0.138684
\(531\) 26.8222i 1.16399i
\(532\) −10.6834 6.16804i −0.463182 0.267418i
\(533\) −7.11094 + 4.10550i −0.308009 + 0.177829i
\(534\) 0.0130459 0.0225962i 0.000564553 0.000977834i
\(535\) 1.61526i 0.0698338i
\(536\) 3.36342i 0.145277i
\(537\) −0.198001 0.114316i −0.00854436 0.00493309i
\(538\) 13.3023 7.68009i 0.573503 0.331112i
\(539\) −27.0820 15.6358i −1.16650 0.673480i
\(540\) −0.00674919 0.0116899i −0.000290439 0.000503055i
\(541\) −8.69714 + 15.0639i −0.373919 + 0.647647i −0.990165 0.139907i \(-0.955320\pi\)
0.616245 + 0.787554i \(0.288653\pi\)
\(542\) 18.2494 + 10.5363i 0.783877 + 0.452572i
\(543\) 0.00375373 0.00650165i 0.000161088 0.000279013i
\(544\) 17.2135 + 9.93822i 0.738023 + 0.426098i
\(545\) 3.18547 + 5.51739i 0.136450 + 0.236339i
\(546\) −0.0622735 0.0359536i −0.00266506 0.00153867i
\(547\) −3.21255 + 5.56430i −0.137359 + 0.237912i −0.926496 0.376305i \(-0.877195\pi\)
0.789137 + 0.614217i \(0.210528\pi\)
\(548\) 6.39377 3.69144i 0.273128 0.157691i
\(549\) −10.8127 + 6.24272i −0.461475 + 0.266433i
\(550\) −13.0208 + 22.5528i −0.555210 + 0.961653i
\(551\) 20.1743 + 34.9429i 0.859455 + 1.48862i
\(552\) 0.143425i 0.00610456i
\(553\) −14.6081 25.3020i −0.621200 1.07595i
\(554\) −9.61061 + 16.6461i −0.408316 + 0.707224i
\(555\) 0.00882934 + 0.0152929i 0.000374785 + 0.000649146i
\(556\) −3.59495 + 6.22664i −0.152460 + 0.264068i
\(557\) 6.68880 + 3.86178i 0.283414 + 0.163629i 0.634968 0.772539i \(-0.281013\pi\)
−0.351554 + 0.936168i \(0.614347\pi\)
\(558\) 6.70613 + 3.87178i 0.283893 + 0.163906i
\(559\) 13.5523 0.573200
\(560\) −3.17896 + 1.83537i −0.134335 + 0.0775586i
\(561\) −0.255776 0.147672i −0.0107989 0.00623474i
\(562\) 33.7266i 1.42267i
\(563\) 6.74649 11.6853i 0.284331 0.492475i −0.688116 0.725601i \(-0.741562\pi\)
0.972447 + 0.233126i \(0.0748953\pi\)
\(564\) −0.0112546 + 0.00649783i −0.000473903 + 0.000273608i
\(565\) 1.08249i 0.0455407i
\(566\) 33.0394 19.0753i 1.38875 0.801796i
\(567\) 33.6384i 1.41268i
\(568\) −9.32701 16.1549i −0.391353 0.677843i
\(569\) 27.4730 15.8615i 1.15173 0.664950i 0.202420 0.979299i \(-0.435119\pi\)
0.949308 + 0.314349i \(0.101786\pi\)
\(570\) 0.0239205 0.0138105i 0.00100192 0.000578459i
\(571\) 28.5921i 1.19654i −0.801293 0.598272i \(-0.795854\pi\)
0.801293 0.598272i \(-0.204146\pi\)
\(572\) −3.97941 −0.166387
\(573\) 0.156183 0.00652464
\(574\) −11.7433 + 20.3399i −0.490155 + 0.848973i
\(575\) −11.0187 + 19.0849i −0.459510 + 0.795894i
\(576\) −13.1986 22.8607i −0.549944 0.952531i
\(577\) 38.1470 1.58808 0.794041 0.607864i \(-0.207974\pi\)
0.794041 + 0.607864i \(0.207974\pi\)
\(578\) −24.9658 + 14.4140i −1.03844 + 0.599544i
\(579\) 0.0433556 0.0250313i 0.00180180 0.00104027i
\(580\) −1.51862 −0.0630573
\(581\) −42.3379 24.4438i −1.75647 1.01410i
\(582\) −0.0553771 0.0959160i −0.00229546 0.00397585i
\(583\) 30.9881 1.28340
\(584\) −6.66258 3.84664i −0.275700 0.159175i
\(585\) 1.56883 0.905765i 0.0648632 0.0374488i
\(586\) −26.8447 15.4988i −1.10894 0.640249i
\(587\) 10.4336 18.0715i 0.430640 0.745891i −0.566288 0.824207i \(-0.691621\pi\)
0.996929 + 0.0783166i \(0.0249545\pi\)
\(588\) 0.0406349 0.00167576
\(589\) 6.27327 10.8656i 0.258485 0.447710i
\(590\) −2.06577 + 3.57802i −0.0850464 + 0.147305i
\(591\) −0.149637 + 0.0863930i −0.00615525 + 0.00355373i
\(592\) 5.66280 + 9.80826i 0.232740 + 0.403117i
\(593\) −0.680726 0.393017i −0.0279540 0.0161393i 0.485958 0.873982i \(-0.338471\pi\)
−0.513912 + 0.857843i \(0.671804\pi\)
\(594\) 0.165461 + 0.286586i 0.00678894 + 0.0117588i
\(595\) 9.24933i 0.379185i
\(596\) 7.21678i 0.295611i
\(597\) 0.186126i 0.00761764i
\(598\) 8.50593 0.347833
\(599\) −23.4092 + 13.5153i −0.956473 + 0.552220i −0.895086 0.445894i \(-0.852886\pi\)
−0.0613871 + 0.998114i \(0.519552\pi\)
\(600\) 0.153152i 0.00625241i
\(601\) −23.6632 + 13.6619i −0.965241 + 0.557282i −0.897782 0.440440i \(-0.854822\pi\)
−0.0674587 + 0.997722i \(0.521489\pi\)
\(602\) 33.5711 19.3823i 1.36826 0.789963i
\(603\) 1.64174 + 2.84357i 0.0668567 + 0.115799i
\(604\) 0.00197907 + 0.00342785i 8.05272e−5 + 0.000139477i
\(605\) 1.75925 3.04712i 0.0715239 0.123883i
\(606\) 0.0635753 0.00258257
\(607\) 10.7731 18.6596i 0.437268 0.757371i −0.560209 0.828351i \(-0.689279\pi\)
0.997478 + 0.0709800i \(0.0226126\pi\)
\(608\) −15.6246 + 9.02088i −0.633662 + 0.365845i
\(609\) −0.230655 0.133169i −0.00934663 0.00539628i
\(610\) 1.92318 0.0778674
\(611\) −1.74409 3.02086i −0.0705584 0.122211i
\(612\) −10.9070 −0.440887
\(613\) −11.1478 + 19.3086i −0.450257 + 0.779869i −0.998402 0.0565151i \(-0.982001\pi\)
0.548144 + 0.836384i \(0.315334\pi\)
\(614\) −25.5044 14.7250i −1.02927 0.594251i
\(615\) 0.0104097 + 0.0180301i 0.000419760 + 0.000727045i
\(616\) −44.6144 + 25.7582i −1.79757 + 1.03783i
\(617\) 20.8234 36.0673i 0.838320 1.45201i −0.0529779 0.998596i \(-0.516871\pi\)
0.891298 0.453418i \(-0.149795\pi\)
\(618\) 0.119675 0.00481403
\(619\) 28.1954i 1.13327i 0.823970 + 0.566634i \(0.191755\pi\)
−0.823970 + 0.566634i \(0.808245\pi\)
\(620\) 0.236110 + 0.408954i 0.00948240 + 0.0164240i
\(621\) 0.140018 + 0.242519i 0.00561874 + 0.00973194i
\(622\) −8.19960 14.2021i −0.328774 0.569453i
\(623\) −7.93077 −0.317740
\(624\) −0.0354043 + 0.0204407i −0.00141731 + 0.000818282i
\(625\) −11.3934 + 19.7339i −0.455736 + 0.789357i
\(626\) 27.2933 15.7578i 1.09086 0.629809i
\(627\) 0.232167 0.134042i 0.00927186 0.00535311i
\(628\) −5.46903 9.47263i −0.218238 0.377999i
\(629\) 28.5376 1.13787
\(630\) 2.59082 4.48744i 0.103221 0.178784i
\(631\) −2.26897 −0.0903263 −0.0451632 0.998980i \(-0.514381\pi\)
−0.0451632 + 0.998980i \(0.514381\pi\)
\(632\) −24.0181 −0.955387
\(633\) 0.0819238i 0.00325618i
\(634\) −22.0379 −0.875235
\(635\) −5.19563 2.99970i −0.206182 0.119039i
\(636\) −0.0348719 + 0.0201333i −0.00138276 + 0.000798338i
\(637\) 10.9069i 0.432147i
\(638\) 37.2300 1.47395
\(639\) 15.7709 + 9.10532i 0.623886 + 0.360201i
\(640\) 1.67184i 0.0660855i
\(641\) 8.55626 + 14.8199i 0.337952 + 0.585350i 0.984047 0.177907i \(-0.0569325\pi\)
−0.646095 + 0.763257i \(0.723599\pi\)
\(642\) 0.0257280 + 0.0445622i 0.00101540 + 0.00175873i
\(643\) −21.9744 12.6870i −0.866588 0.500325i −0.000374786 1.00000i \(-0.500119\pi\)
−0.866213 + 0.499675i \(0.833453\pi\)
\(644\) −8.34183 + 4.81616i −0.328714 + 0.189783i
\(645\) 0.0343625i 0.00135302i
\(646\) 44.6375i 1.75624i
\(647\) −6.32499 + 10.9552i −0.248661 + 0.430694i −0.963155 0.268948i \(-0.913324\pi\)
0.714493 + 0.699642i \(0.246657\pi\)
\(648\) 23.9486 + 13.8267i 0.940790 + 0.543166i
\(649\) −20.0499 + 34.7274i −0.787026 + 1.36317i
\(650\) 9.08282 0.356258
\(651\) 0.0828186i 0.00324592i
\(652\) −9.34417 5.39486i −0.365946 0.211279i
\(653\) 28.6343 1.12055 0.560274 0.828308i \(-0.310696\pi\)
0.560274 + 0.828308i \(0.310696\pi\)
\(654\) 0.175763 + 0.101477i 0.00687288 + 0.00396806i
\(655\) −2.13593 1.23318i −0.0834577 0.0481843i
\(656\) 6.67639 + 11.5638i 0.260669 + 0.451492i
\(657\) 7.51043 0.293010
\(658\) −8.64078 4.98876i −0.336853 0.194482i
\(659\) 22.4849i 0.875887i 0.899002 + 0.437944i \(0.144293\pi\)
−0.899002 + 0.437944i \(0.855707\pi\)
\(660\) 0.0100900i 0.000392752i
\(661\) 11.9641 0.465349 0.232675 0.972555i \(-0.425252\pi\)
0.232675 + 0.972555i \(0.425252\pi\)
\(662\) 16.8455 0.654719
\(663\) 0.103010i 0.00400059i
\(664\) −34.8052 + 20.0948i −1.35070 + 0.779828i
\(665\) −7.27078 4.19779i −0.281949 0.162783i
\(666\) −13.8454 7.99366i −0.536499 0.309748i
\(667\) 31.5052 1.21989
\(668\) 10.0502 + 5.80251i 0.388856 + 0.224506i
\(669\) 0.000225628 0 0.000390799i 8.72328e−6 0 1.51092e-5i
\(670\) 0.505767i 0.0195395i
\(671\) 18.6660 0.720591
\(672\) 0.0595460 0.103137i 0.00229704 0.00397859i
\(673\) 3.36883 + 5.83499i 0.129859 + 0.224922i 0.923622 0.383305i \(-0.125214\pi\)
−0.793763 + 0.608227i \(0.791881\pi\)
\(674\) 3.84379 + 2.21921i 0.148057 + 0.0854809i
\(675\) 0.149515 + 0.258967i 0.00575482 + 0.00996764i
\(676\) −2.99305 5.18411i −0.115117 0.199389i
\(677\) 2.38709i 0.0917434i 0.998947 + 0.0458717i \(0.0146065\pi\)
−0.998947 + 0.0458717i \(0.985393\pi\)
\(678\) −0.0172420 0.0298640i −0.000662175 0.00114692i
\(679\) −16.8322 + 29.1542i −0.645960 + 1.11884i
\(680\) 6.58498 + 3.80184i 0.252523 + 0.145794i
\(681\) 0.0617739 0.00236718
\(682\) −5.78839 10.0258i −0.221649 0.383907i
\(683\) −17.3319 30.0197i −0.663186 1.14867i −0.979774 0.200109i \(-0.935871\pi\)
0.316588 0.948563i \(-0.397463\pi\)
\(684\) 4.95010 8.57382i 0.189272 0.327828i
\(685\) 4.35141 2.51229i 0.166259 0.0959897i
\(686\) −0.0612227 0.106041i −0.00233749 0.00404866i
\(687\) 0.0777532i 0.00296647i
\(688\) 22.0388i 0.840221i
\(689\) −5.40402 9.36003i −0.205877 0.356589i
\(690\) 0.0215672i 0.000821050i
\(691\) −16.7177 + 9.65196i −0.635971 + 0.367178i −0.783061 0.621945i \(-0.786343\pi\)
0.147090 + 0.989123i \(0.453009\pi\)
\(692\) 7.82186i 0.297343i
\(693\) 25.1459 43.5540i 0.955215 1.65448i
\(694\) 10.7820 18.6750i 0.409280 0.708893i
\(695\) −2.44662 + 4.23767i −0.0928055 + 0.160744i
\(696\) −0.189617 + 0.109475i −0.00718742 + 0.00414966i
\(697\) 33.6456 1.27442
\(698\) 16.6155 + 14.9654i 0.628904 + 0.566448i
\(699\) −0.122118 −0.00461892
\(700\) −8.90759 + 5.14280i −0.336675 + 0.194380i
\(701\) −2.97024 + 5.14460i −0.112184 + 0.194309i −0.916651 0.399689i \(-0.869118\pi\)
0.804466 + 0.593998i \(0.202451\pi\)
\(702\) 0.0577094 0.0999557i 0.00217810 0.00377258i
\(703\) −12.9517 + 22.4331i −0.488484 + 0.846079i
\(704\) 39.4644i 1.48737i
\(705\) −0.00765953 + 0.00442223i −0.000288475 + 0.000166551i
\(706\) 30.9209i 1.16372i
\(707\) −9.66204 16.7351i −0.363378 0.629390i
\(708\) 0.0521065i 0.00195828i
\(709\) 21.9809i 0.825508i 0.910842 + 0.412754i \(0.135433\pi\)
−0.910842 + 0.412754i \(0.864567\pi\)
\(710\) −1.40253 2.42925i −0.0526360 0.0911683i
\(711\) 20.3059 11.7236i 0.761529 0.439669i
\(712\) −3.25986 + 5.64625i −0.122168 + 0.211602i
\(713\) −4.89832 8.48414i −0.183444 0.317734i
\(714\) 0.147324 + 0.255173i 0.00551347 + 0.00954961i
\(715\) −2.70827 −0.101284
\(716\) 10.9317 + 6.31141i 0.408536 + 0.235869i
\(717\) −0.130663 + 0.226314i −0.00487968 + 0.00845186i
\(718\) 10.8282 + 18.7550i 0.404104 + 0.699929i
\(719\) 23.5988i 0.880087i 0.897977 + 0.440043i \(0.145037\pi\)
−0.897977 + 0.440043i \(0.854963\pi\)
\(720\) −1.47296 2.55124i −0.0548939 0.0950791i
\(721\) −18.1879 31.5024i −0.677353 1.17321i
\(722\) 15.3933 + 8.88730i 0.572878 + 0.330751i
\(723\) 0.00944365 + 0.0163569i 0.000351213 + 0.000608319i
\(724\) −0.207245 + 0.358958i −0.00770219 + 0.0133406i
\(725\) 33.6420 1.24943
\(726\) 0.112086i 0.00415991i
\(727\) −2.72134 + 4.71350i −0.100929 + 0.174814i −0.912068 0.410040i \(-0.865515\pi\)
0.811139 + 0.584854i \(0.198848\pi\)
\(728\) 15.5606 + 8.98393i 0.576715 + 0.332967i
\(729\) −26.9943 −0.999789
\(730\) −1.00187 0.578431i −0.0370810 0.0214087i
\(731\) −48.0922 27.7660i −1.77875 1.02696i
\(732\) −0.0210054 + 0.0121275i −0.000776382 + 0.000448245i
\(733\) 39.5799i 1.46192i 0.682423 + 0.730958i \(0.260926\pi\)
−0.682423 + 0.730958i \(0.739074\pi\)
\(734\) −28.3878 −1.04781
\(735\) 0.0276550 0.00102007
\(736\) 14.0875i 0.519270i
\(737\) 4.90885i 0.180820i
\(738\) −16.3236 9.42445i −0.600881 0.346919i
\(739\) −17.0571 −0.627457 −0.313728 0.949513i \(-0.601578\pi\)
−0.313728 + 0.949513i \(0.601578\pi\)
\(740\) −0.487471 0.844325i −0.0179198 0.0310380i
\(741\) −0.0809753 0.0467511i −0.00297470 0.00171744i
\(742\) −26.7732 15.4575i −0.982874 0.567463i
\(743\) −19.8934 −0.729818 −0.364909 0.931043i \(-0.618900\pi\)
−0.364909 + 0.931043i \(0.618900\pi\)
\(744\) 0.0589620 + 0.0340417i 0.00216165 + 0.00124803i
\(745\) 4.91154i 0.179945i
\(746\) −20.4483 −0.748666
\(747\) 19.6172 33.9779i 0.717754 1.24319i
\(748\) 14.1215 + 8.15305i 0.516333 + 0.298105i
\(749\) 7.82017 13.5449i 0.285743 0.494921i
\(750\) 0.0467674i 0.00170770i
\(751\) 8.00054i 0.291944i 0.989289 + 0.145972i \(0.0466309\pi\)
−0.989289 + 0.145972i \(0.953369\pi\)
\(752\) −4.91253 + 2.83625i −0.179142 + 0.103427i
\(753\) −0.0111118 0.00641540i −0.000404936 0.000233790i
\(754\) −6.49254 11.2454i −0.236444 0.409534i
\(755\) 0.00134690 + 0.00233290i 4.90186e−5 + 8.49028e-5i
\(756\) 0.130703i 0.00475362i
\(757\) −26.5533 15.3306i −0.965097 0.557199i −0.0673588 0.997729i \(-0.521457\pi\)
−0.897738 + 0.440530i \(0.854791\pi\)
\(758\) 29.7176 1.07939
\(759\) 0.209326i 0.00759806i
\(760\) −5.97716 + 3.45092i −0.216814 + 0.125178i
\(761\) −40.2958 23.2648i −1.46072 0.843348i −0.461678 0.887048i \(-0.652752\pi\)
−0.999045 + 0.0436993i \(0.986086\pi\)
\(762\) −0.191118 −0.00692347
\(763\) 61.6889i 2.23329i
\(764\) −8.62292 −0.311966
\(765\) −7.42296 −0.268378