Properties

Label 370.2.g.e.43.5
Level $370$
Weight $2$
Character 370.43
Analytic conductor $2.954$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} - 7362 x^{11} + 13826 x^{10} + 4848 x^{9} + 13544 x^{8} - 44248 x^{7} + 76384 x^{6} + 24512 x^{5} + 28432 x^{4} - 61952 x^{3} + 61952 x^{2} - 5632 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.5
Root \(0.536506 - 0.536506i\) of defining polynomial
Character \(\chi\) \(=\) 370.43
Dual form 370.2.g.e.327.5

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.536506 + 0.536506i) q^{3} -1.00000 q^{4} +(-0.127776 - 2.23241i) q^{5} +(-0.536506 - 0.536506i) q^{6} +(0.767774 - 0.767774i) q^{7} -1.00000i q^{8} +2.42432i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.536506 + 0.536506i) q^{3} -1.00000 q^{4} +(-0.127776 - 2.23241i) q^{5} +(-0.536506 - 0.536506i) q^{6} +(0.767774 - 0.767774i) q^{7} -1.00000i q^{8} +2.42432i q^{9} +(2.23241 - 0.127776i) q^{10} +4.39414i q^{11} +(0.536506 - 0.536506i) q^{12} +6.74274i q^{13} +(0.767774 + 0.767774i) q^{14} +(1.26626 + 1.12915i) q^{15} +1.00000 q^{16} +7.34365 q^{17} -2.42432 q^{18} +(2.59760 - 2.59760i) q^{19} +(0.127776 + 2.23241i) q^{20} +0.823831i q^{21} -4.39414 q^{22} +1.20395i q^{23} +(0.536506 + 0.536506i) q^{24} +(-4.96735 + 0.570497i) q^{25} -6.74274 q^{26} +(-2.91018 - 2.91018i) q^{27} +(-0.767774 + 0.767774i) q^{28} +(1.25185 + 1.25185i) q^{29} +(-1.12915 + 1.26626i) q^{30} +(-4.14855 + 4.14855i) q^{31} +1.00000i q^{32} +(-2.35748 - 2.35748i) q^{33} +7.34365i q^{34} +(-1.81209 - 1.61589i) q^{35} -2.42432i q^{36} +(0.633071 - 6.04973i) q^{37} +(2.59760 + 2.59760i) q^{38} +(-3.61752 - 3.61752i) q^{39} +(-2.23241 + 0.127776i) q^{40} +4.07091i q^{41} -0.823831 q^{42} -8.56098i q^{43} -4.39414i q^{44} +(5.41209 - 0.309770i) q^{45} -1.20395 q^{46} +(7.68569 - 7.68569i) q^{47} +(-0.536506 + 0.536506i) q^{48} +5.82104i q^{49} +(-0.570497 - 4.96735i) q^{50} +(-3.93991 + 3.93991i) q^{51} -6.74274i q^{52} +(2.31983 + 2.31983i) q^{53} +(2.91018 - 2.91018i) q^{54} +(9.80954 - 0.561465i) q^{55} +(-0.767774 - 0.767774i) q^{56} +2.78725i q^{57} +(-1.25185 + 1.25185i) q^{58} +(-7.61323 + 7.61323i) q^{59} +(-1.26626 - 1.12915i) q^{60} +(1.14451 - 1.14451i) q^{61} +(-4.14855 - 4.14855i) q^{62} +(1.86133 + 1.86133i) q^{63} -1.00000 q^{64} +(15.0526 - 0.861559i) q^{65} +(2.35748 - 2.35748i) q^{66} +(-6.25304 - 6.25304i) q^{67} -7.34365 q^{68} +(-0.645925 - 0.645925i) q^{69} +(1.61589 - 1.81209i) q^{70} -5.46460 q^{71} +2.42432 q^{72} +(1.88159 - 1.88159i) q^{73} +(6.04973 + 0.633071i) q^{74} +(2.35893 - 2.97108i) q^{75} +(-2.59760 + 2.59760i) q^{76} +(3.37371 + 3.37371i) q^{77} +(3.61752 - 3.61752i) q^{78} +(5.13322 - 5.13322i) q^{79} +(-0.127776 - 2.23241i) q^{80} -4.15032 q^{81} -4.07091 q^{82} +(0.570350 + 0.570350i) q^{83} -0.823831i q^{84} +(-0.938340 - 16.3941i) q^{85} +8.56098 q^{86} -1.34325 q^{87} +4.39414 q^{88} +(7.54653 + 7.54653i) q^{89} +(0.309770 + 5.41209i) q^{90} +(5.17690 + 5.17690i) q^{91} -1.20395i q^{92} -4.45144i q^{93} +(7.68569 + 7.68569i) q^{94} +(-6.13083 - 5.46701i) q^{95} +(-0.536506 - 0.536506i) q^{96} -5.39443 q^{97} -5.82104 q^{98} -10.6528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 4q^{3} - 20q^{4} + 2q^{5} - 4q^{6} - 2q^{7} + O(q^{10}) \) \( 20q - 4q^{3} - 20q^{4} + 2q^{5} - 4q^{6} - 2q^{7} + 4q^{10} + 4q^{12} - 2q^{14} + 20q^{16} + 20q^{17} + 24q^{18} - 6q^{19} - 2q^{20} - 8q^{22} + 4q^{24} - 10q^{25} + 20q^{27} + 2q^{28} - 18q^{29} - 4q^{30} + 12q^{31} + 4q^{33} + 12q^{35} - 6q^{38} - 6q^{39} - 4q^{40} - 12q^{42} - 18q^{45} + 4q^{46} - 22q^{47} - 4q^{48} + 4q^{50} + 8q^{51} - 4q^{53} - 20q^{54} - 34q^{55} + 2q^{56} + 18q^{58} + 10q^{59} + 10q^{61} + 12q^{62} - 2q^{63} - 20q^{64} - 20q^{65} - 4q^{66} - 8q^{67} - 20q^{68} + 34q^{69} + 12q^{70} + 16q^{71} - 24q^{72} + 6q^{73} - 32q^{74} - 26q^{75} + 6q^{76} + 4q^{77} + 6q^{78} - 12q^{79} + 2q^{80} - 28q^{81} + 20q^{82} + 6q^{83} - 10q^{85} - 16q^{86} + 44q^{87} + 8q^{88} + 44q^{89} - 22q^{90} - 40q^{91} - 22q^{94} - 50q^{95} - 4q^{96} - 72q^{97} + 52q^{98} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.536506 + 0.536506i −0.309752 + 0.309752i −0.844813 0.535061i \(-0.820288\pi\)
0.535061 + 0.844813i \(0.320288\pi\)
\(4\) −1.00000 −0.500000
\(5\) −0.127776 2.23241i −0.0571431 0.998366i
\(6\) −0.536506 0.536506i −0.219027 0.219027i
\(7\) 0.767774 0.767774i 0.290191 0.290191i −0.546964 0.837156i \(-0.684217\pi\)
0.837156 + 0.546964i \(0.184217\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 2.42432i 0.808108i
\(10\) 2.23241 0.127776i 0.705951 0.0404063i
\(11\) 4.39414i 1.32488i 0.749114 + 0.662442i \(0.230480\pi\)
−0.749114 + 0.662442i \(0.769520\pi\)
\(12\) 0.536506 0.536506i 0.154876 0.154876i
\(13\) 6.74274i 1.87010i 0.354516 + 0.935050i \(0.384645\pi\)
−0.354516 + 0.935050i \(0.615355\pi\)
\(14\) 0.767774 + 0.767774i 0.205196 + 0.205196i
\(15\) 1.26626 + 1.12915i 0.326946 + 0.291545i
\(16\) 1.00000 0.250000
\(17\) 7.34365 1.78110 0.890548 0.454889i \(-0.150321\pi\)
0.890548 + 0.454889i \(0.150321\pi\)
\(18\) −2.42432 −0.571419
\(19\) 2.59760 2.59760i 0.595930 0.595930i −0.343297 0.939227i \(-0.611544\pi\)
0.939227 + 0.343297i \(0.111544\pi\)
\(20\) 0.127776 + 2.23241i 0.0285715 + 0.499183i
\(21\) 0.823831i 0.179775i
\(22\) −4.39414 −0.936834
\(23\) 1.20395i 0.251040i 0.992091 + 0.125520i \(0.0400600\pi\)
−0.992091 + 0.125520i \(0.959940\pi\)
\(24\) 0.536506 + 0.536506i 0.109514 + 0.109514i
\(25\) −4.96735 + 0.570497i −0.993469 + 0.114099i
\(26\) −6.74274 −1.32236
\(27\) −2.91018 2.91018i −0.560064 0.560064i
\(28\) −0.767774 + 0.767774i −0.145096 + 0.145096i
\(29\) 1.25185 + 1.25185i 0.232463 + 0.232463i 0.813720 0.581257i \(-0.197439\pi\)
−0.581257 + 0.813720i \(0.697439\pi\)
\(30\) −1.12915 + 1.26626i −0.206154 + 0.231185i
\(31\) −4.14855 + 4.14855i −0.745101 + 0.745101i −0.973555 0.228454i \(-0.926633\pi\)
0.228454 + 0.973555i \(0.426633\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −2.35748 2.35748i −0.410385 0.410385i
\(34\) 7.34365i 1.25943i
\(35\) −1.81209 1.61589i −0.306300 0.273135i
\(36\) 2.42432i 0.404054i
\(37\) 0.633071 6.04973i 0.104076 0.994569i
\(38\) 2.59760 + 2.59760i 0.421386 + 0.421386i
\(39\) −3.61752 3.61752i −0.579266 0.579266i
\(40\) −2.23241 + 0.127776i −0.352976 + 0.0202031i
\(41\) 4.07091i 0.635769i 0.948129 + 0.317884i \(0.102972\pi\)
−0.948129 + 0.317884i \(0.897028\pi\)
\(42\) −0.823831 −0.127120
\(43\) 8.56098i 1.30554i −0.757557 0.652769i \(-0.773607\pi\)
0.757557 0.652769i \(-0.226393\pi\)
\(44\) 4.39414i 0.662442i
\(45\) 5.41209 0.309770i 0.806787 0.0461778i
\(46\) −1.20395 −0.177512
\(47\) 7.68569 7.68569i 1.12107 1.12107i 0.129493 0.991580i \(-0.458665\pi\)
0.991580 0.129493i \(-0.0413351\pi\)
\(48\) −0.536506 + 0.536506i −0.0774379 + 0.0774379i
\(49\) 5.82104i 0.831578i
\(50\) −0.570497 4.96735i −0.0806805 0.702489i
\(51\) −3.93991 + 3.93991i −0.551697 + 0.551697i
\(52\) 6.74274i 0.935050i
\(53\) 2.31983 + 2.31983i 0.318653 + 0.318653i 0.848250 0.529596i \(-0.177657\pi\)
−0.529596 + 0.848250i \(0.677657\pi\)
\(54\) 2.91018 2.91018i 0.396025 0.396025i
\(55\) 9.80954 0.561465i 1.32272 0.0757079i
\(56\) −0.767774 0.767774i −0.102598 0.102598i
\(57\) 2.78725i 0.369181i
\(58\) −1.25185 + 1.25185i −0.164376 + 0.164376i
\(59\) −7.61323 + 7.61323i −0.991158 + 0.991158i −0.999961 0.00880307i \(-0.997198\pi\)
0.00880307 + 0.999961i \(0.497198\pi\)
\(60\) −1.26626 1.12915i −0.163473 0.145773i
\(61\) 1.14451 1.14451i 0.146539 0.146539i −0.630031 0.776570i \(-0.716958\pi\)
0.776570 + 0.630031i \(0.216958\pi\)
\(62\) −4.14855 4.14855i −0.526866 0.526866i
\(63\) 1.86133 + 1.86133i 0.234506 + 0.234506i
\(64\) −1.00000 −0.125000
\(65\) 15.0526 0.861559i 1.86704 0.106863i
\(66\) 2.35748 2.35748i 0.290186 0.290186i
\(67\) −6.25304 6.25304i −0.763930 0.763930i 0.213100 0.977030i \(-0.431644\pi\)
−0.977030 + 0.213100i \(0.931644\pi\)
\(68\) −7.34365 −0.890548
\(69\) −0.645925 0.645925i −0.0777602 0.0777602i
\(70\) 1.61589 1.81209i 0.193136 0.216587i
\(71\) −5.46460 −0.648529 −0.324265 0.945966i \(-0.605117\pi\)
−0.324265 + 0.945966i \(0.605117\pi\)
\(72\) 2.42432 0.285709
\(73\) 1.88159 1.88159i 0.220224 0.220224i −0.588369 0.808593i \(-0.700230\pi\)
0.808593 + 0.588369i \(0.200230\pi\)
\(74\) 6.04973 + 0.633071i 0.703267 + 0.0735930i
\(75\) 2.35893 2.97108i 0.272386 0.343071i
\(76\) −2.59760 + 2.59760i −0.297965 + 0.297965i
\(77\) 3.37371 + 3.37371i 0.384470 + 0.384470i
\(78\) 3.61752 3.61752i 0.409603 0.409603i
\(79\) 5.13322 5.13322i 0.577533 0.577533i −0.356690 0.934223i \(-0.616095\pi\)
0.934223 + 0.356690i \(0.116095\pi\)
\(80\) −0.127776 2.23241i −0.0142858 0.249591i
\(81\) −4.15032 −0.461146
\(82\) −4.07091 −0.449557
\(83\) 0.570350 + 0.570350i 0.0626041 + 0.0626041i 0.737716 0.675112i \(-0.235905\pi\)
−0.675112 + 0.737716i \(0.735905\pi\)
\(84\) 0.823831i 0.0898873i
\(85\) −0.938340 16.3941i −0.101777 1.77819i
\(86\) 8.56098 0.923155
\(87\) −1.34325 −0.144012
\(88\) 4.39414 0.468417
\(89\) 7.54653 + 7.54653i 0.799931 + 0.799931i 0.983084 0.183153i \(-0.0586305\pi\)
−0.183153 + 0.983084i \(0.558630\pi\)
\(90\) 0.309770 + 5.41209i 0.0326526 + 0.570485i
\(91\) 5.17690 + 5.17690i 0.542687 + 0.542687i
\(92\) 1.20395i 0.125520i
\(93\) 4.45144i 0.461593i
\(94\) 7.68569 + 7.68569i 0.792719 + 0.792719i
\(95\) −6.13083 5.46701i −0.629009 0.560903i
\(96\) −0.536506 0.536506i −0.0547569 0.0547569i
\(97\) −5.39443 −0.547721 −0.273861 0.961769i \(-0.588301\pi\)
−0.273861 + 0.961769i \(0.588301\pi\)
\(98\) −5.82104 −0.588014
\(99\) −10.6528 −1.07065
\(100\) 4.96735 0.570497i 0.496735 0.0570497i
\(101\) 14.5684i 1.44961i −0.688956 0.724803i \(-0.741931\pi\)
0.688956 0.724803i \(-0.258069\pi\)
\(102\) −3.93991 3.93991i −0.390109 0.390109i
\(103\) −10.1623 −1.00132 −0.500662 0.865643i \(-0.666910\pi\)
−0.500662 + 0.865643i \(0.666910\pi\)
\(104\) 6.74274 0.661180
\(105\) 1.83913 0.105266i 0.179481 0.0102729i
\(106\) −2.31983 + 2.31983i −0.225322 + 0.225322i
\(107\) −13.4161 + 13.4161i −1.29698 + 1.29698i −0.366601 + 0.930378i \(0.619479\pi\)
−0.930378 + 0.366601i \(0.880521\pi\)
\(108\) 2.91018 + 2.91018i 0.280032 + 0.280032i
\(109\) 4.78437 4.78437i 0.458259 0.458259i −0.439824 0.898084i \(-0.644959\pi\)
0.898084 + 0.439824i \(0.144959\pi\)
\(110\) 0.561465 + 9.80954i 0.0535336 + 0.935303i
\(111\) 2.90607 + 3.58536i 0.275832 + 0.340307i
\(112\) 0.767774 0.767774i 0.0725479 0.0725479i
\(113\) 18.0037 1.69365 0.846825 0.531872i \(-0.178511\pi\)
0.846825 + 0.531872i \(0.178511\pi\)
\(114\) −2.78725 −0.261050
\(115\) 2.68771 0.153835i 0.250630 0.0143452i
\(116\) −1.25185 1.25185i −0.116232 0.116232i
\(117\) −16.3466 −1.51124
\(118\) −7.61323 7.61323i −0.700855 0.700855i
\(119\) 5.63827 5.63827i 0.516859 0.516859i
\(120\) 1.12915 1.26626i 0.103077 0.115593i
\(121\) −8.30847 −0.755316
\(122\) 1.14451 + 1.14451i 0.103619 + 0.103619i
\(123\) −2.18406 2.18406i −0.196930 0.196930i
\(124\) 4.14855 4.14855i 0.372551 0.372551i
\(125\) 1.90829 + 11.0163i 0.170683 + 0.985326i
\(126\) −1.86133 + 1.86133i −0.165821 + 0.165821i
\(127\) 9.21023 9.21023i 0.817275 0.817275i −0.168437 0.985712i \(-0.553872\pi\)
0.985712 + 0.168437i \(0.0538720\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 4.59302 + 4.59302i 0.404393 + 0.404393i
\(130\) 0.861559 + 15.0526i 0.0755637 + 1.32020i
\(131\) −1.53844 + 1.53844i −0.134414 + 0.134414i −0.771113 0.636698i \(-0.780300\pi\)
0.636698 + 0.771113i \(0.280300\pi\)
\(132\) 2.35748 + 2.35748i 0.205192 + 0.205192i
\(133\) 3.98874i 0.345868i
\(134\) 6.25304 6.25304i 0.540180 0.540180i
\(135\) −6.12488 + 6.86858i −0.527145 + 0.591153i
\(136\) 7.34365i 0.629713i
\(137\) 11.9150 11.9150i 1.01797 1.01797i 0.0181339 0.999836i \(-0.494227\pi\)
0.999836 0.0181339i \(-0.00577252\pi\)
\(138\) 0.645925 0.645925i 0.0549847 0.0549847i
\(139\) −6.75745 −0.573159 −0.286580 0.958056i \(-0.592518\pi\)
−0.286580 + 0.958056i \(0.592518\pi\)
\(140\) 1.81209 + 1.61589i 0.153150 + 0.136567i
\(141\) 8.24684i 0.694509i
\(142\) 5.46460i 0.458579i
\(143\) −29.6285 −2.47766
\(144\) 2.42432i 0.202027i
\(145\) 2.63470 2.95461i 0.218800 0.245367i
\(146\) 1.88159 + 1.88159i 0.155722 + 0.155722i
\(147\) −3.12302 3.12302i −0.257583 0.257583i
\(148\) −0.633071 + 6.04973i −0.0520381 + 0.497285i
\(149\) 5.18543i 0.424807i −0.977182 0.212404i \(-0.931871\pi\)
0.977182 0.212404i \(-0.0681291\pi\)
\(150\) 2.97108 + 2.35893i 0.242588 + 0.192606i
\(151\) 12.5372i 1.02026i −0.860097 0.510131i \(-0.829597\pi\)
0.860097 0.510131i \(-0.170403\pi\)
\(152\) −2.59760 2.59760i −0.210693 0.210693i
\(153\) 17.8034i 1.43932i
\(154\) −3.37371 + 3.37371i −0.271861 + 0.271861i
\(155\) 9.79136 + 8.73119i 0.786461 + 0.701306i
\(156\) 3.61752 + 3.61752i 0.289633 + 0.289633i
\(157\) −0.530292 + 0.530292i −0.0423219 + 0.0423219i −0.727951 0.685629i \(-0.759527\pi\)
0.685629 + 0.727951i \(0.259527\pi\)
\(158\) 5.13322 + 5.13322i 0.408377 + 0.408377i
\(159\) −2.48921 −0.197407
\(160\) 2.23241 0.127776i 0.176488 0.0101016i
\(161\) 0.924360 + 0.924360i 0.0728498 + 0.0728498i
\(162\) 4.15032i 0.326080i
\(163\) −13.0393 −1.02132 −0.510660 0.859783i \(-0.670599\pi\)
−0.510660 + 0.859783i \(0.670599\pi\)
\(164\) 4.07091i 0.317884i
\(165\) −4.96164 + 5.56410i −0.386264 + 0.433165i
\(166\) −0.570350 + 0.570350i −0.0442678 + 0.0442678i
\(167\) 24.6405 1.90674 0.953370 0.301805i \(-0.0975892\pi\)
0.953370 + 0.301805i \(0.0975892\pi\)
\(168\) 0.823831 0.0635599
\(169\) −32.4645 −2.49727
\(170\) 16.3941 0.938340i 1.25737 0.0719674i
\(171\) 6.29742 + 6.29742i 0.481576 + 0.481576i
\(172\) 8.56098i 0.652769i
\(173\) 5.32250 5.32250i 0.404662 0.404662i −0.475210 0.879872i \(-0.657628\pi\)
0.879872 + 0.475210i \(0.157628\pi\)
\(174\) 1.34325i 0.101832i
\(175\) −3.37579 + 4.25182i −0.255186 + 0.321407i
\(176\) 4.39414i 0.331221i
\(177\) 8.16908i 0.614026i
\(178\) −7.54653 + 7.54653i −0.565637 + 0.565637i
\(179\) 7.93007 + 7.93007i 0.592721 + 0.592721i 0.938366 0.345644i \(-0.112340\pi\)
−0.345644 + 0.938366i \(0.612340\pi\)
\(180\) −5.41209 + 0.309770i −0.403394 + 0.0230889i
\(181\) −4.29385 −0.319160 −0.159580 0.987185i \(-0.551014\pi\)
−0.159580 + 0.987185i \(0.551014\pi\)
\(182\) −5.17690 + 5.17690i −0.383738 + 0.383738i
\(183\) 1.22807i 0.0907813i
\(184\) 1.20395 0.0887562
\(185\) −13.5864 0.640267i −0.998891 0.0470734i
\(186\) 4.45144 0.326395
\(187\) 32.2690i 2.35974i
\(188\) −7.68569 + 7.68569i −0.560537 + 0.560537i
\(189\) −4.46872 −0.325052
\(190\) 5.46701 6.13083i 0.396618 0.444777i
\(191\) 2.08620 + 2.08620i 0.150952 + 0.150952i 0.778543 0.627591i \(-0.215959\pi\)
−0.627591 + 0.778543i \(0.715959\pi\)
\(192\) 0.536506 0.536506i 0.0387190 0.0387190i
\(193\) 13.6280i 0.980961i −0.871452 0.490481i \(-0.836821\pi\)
0.871452 0.490481i \(-0.163179\pi\)
\(194\) 5.39443i 0.387298i
\(195\) −7.61357 + 8.53803i −0.545219 + 0.611421i
\(196\) 5.82104i 0.415789i
\(197\) 5.05224 5.05224i 0.359957 0.359957i −0.503840 0.863797i \(-0.668080\pi\)
0.863797 + 0.503840i \(0.168080\pi\)
\(198\) 10.6528i 0.757063i
\(199\) −12.1515 12.1515i −0.861395 0.861395i 0.130105 0.991500i \(-0.458469\pi\)
−0.991500 + 0.130105i \(0.958469\pi\)
\(200\) 0.570497 + 4.96735i 0.0403402 + 0.351244i
\(201\) 6.70958 0.473257
\(202\) 14.5684 1.02503
\(203\) 1.92228 0.134918
\(204\) 3.93991 3.93991i 0.275849 0.275849i
\(205\) 9.08795 0.520163i 0.634730 0.0363298i
\(206\) 10.1623i 0.708043i
\(207\) −2.91876 −0.202868
\(208\) 6.74274i 0.467525i
\(209\) 11.4142 + 11.4142i 0.789538 + 0.789538i
\(210\) 0.105266 + 1.83913i 0.00726402 + 0.126912i
\(211\) 8.27973 0.570000 0.285000 0.958527i \(-0.408006\pi\)
0.285000 + 0.958527i \(0.408006\pi\)
\(212\) −2.31983 2.31983i −0.159327 0.159327i
\(213\) 2.93179 2.93179i 0.200883 0.200883i
\(214\) −13.4161 13.4161i −0.917103 0.917103i
\(215\) −19.1117 + 1.09389i −1.30340 + 0.0746024i
\(216\) −2.91018 + 2.91018i −0.198013 + 0.198013i
\(217\) 6.37030i 0.432444i
\(218\) 4.78437 + 4.78437i 0.324038 + 0.324038i
\(219\) 2.01897i 0.136429i
\(220\) −9.80954 + 0.561465i −0.661359 + 0.0378539i
\(221\) 49.5163i 3.33083i
\(222\) −3.58536 + 2.90607i −0.240634 + 0.195042i
\(223\) 9.35468 + 9.35468i 0.626436 + 0.626436i 0.947169 0.320733i \(-0.103929\pi\)
−0.320733 + 0.947169i \(0.603929\pi\)
\(224\) 0.767774 + 0.767774i 0.0512991 + 0.0512991i
\(225\) −1.38307 12.0425i −0.0922046 0.802830i
\(226\) 18.0037i 1.19759i
\(227\) −20.1807 −1.33944 −0.669721 0.742613i \(-0.733586\pi\)
−0.669721 + 0.742613i \(0.733586\pi\)
\(228\) 2.78725i 0.184590i
\(229\) 3.02631i 0.199984i 0.994988 + 0.0999920i \(0.0318817\pi\)
−0.994988 + 0.0999920i \(0.968118\pi\)
\(230\) 0.153835 + 2.68771i 0.0101436 + 0.177222i
\(231\) −3.62003 −0.238180
\(232\) 1.25185 1.25185i 0.0821882 0.0821882i
\(233\) 4.33931 4.33931i 0.284278 0.284278i −0.550534 0.834812i \(-0.685576\pi\)
0.834812 + 0.550534i \(0.185576\pi\)
\(234\) 16.3466i 1.06861i
\(235\) −18.1397 16.1756i −1.18330 1.05518i
\(236\) 7.61323 7.61323i 0.495579 0.495579i
\(237\) 5.50801i 0.357783i
\(238\) 5.63827 + 5.63827i 0.365474 + 0.365474i
\(239\) −2.92398 + 2.92398i −0.189137 + 0.189137i −0.795323 0.606186i \(-0.792699\pi\)
0.606186 + 0.795323i \(0.292699\pi\)
\(240\) 1.26626 + 1.12915i 0.0817364 + 0.0728863i
\(241\) −14.9825 14.9825i −0.965105 0.965105i 0.0343063 0.999411i \(-0.489078\pi\)
−0.999411 + 0.0343063i \(0.989078\pi\)
\(242\) 8.30847i 0.534089i
\(243\) 10.9572 10.9572i 0.702905 0.702905i
\(244\) −1.14451 + 1.14451i −0.0732694 + 0.0732694i
\(245\) 12.9950 0.743789i 0.830219 0.0475189i
\(246\) 2.18406 2.18406i 0.139251 0.139251i
\(247\) 17.5149 + 17.5149i 1.11445 + 1.11445i
\(248\) 4.14855 + 4.14855i 0.263433 + 0.263433i
\(249\) −0.611992 −0.0387834
\(250\) −11.0163 + 1.90829i −0.696731 + 0.120691i
\(251\) 9.25271 9.25271i 0.584026 0.584026i −0.351981 0.936007i \(-0.614492\pi\)
0.936007 + 0.351981i \(0.114492\pi\)
\(252\) −1.86133 1.86133i −0.117253 0.117253i
\(253\) −5.29031 −0.332599
\(254\) 9.21023 + 9.21023i 0.577901 + 0.577901i
\(255\) 9.29893 + 8.29208i 0.582322 + 0.519270i
\(256\) 1.00000 0.0625000
\(257\) −11.5476 −0.720317 −0.360158 0.932891i \(-0.617277\pi\)
−0.360158 + 0.932891i \(0.617277\pi\)
\(258\) −4.59302 + 4.59302i −0.285949 + 0.285949i
\(259\) −4.15877 5.13088i −0.258414 0.318818i
\(260\) −15.0526 + 0.861559i −0.933522 + 0.0534316i
\(261\) −3.03490 + 3.03490i −0.187855 + 0.187855i
\(262\) −1.53844 1.53844i −0.0950454 0.0950454i
\(263\) 6.36639 6.36639i 0.392569 0.392569i −0.483033 0.875602i \(-0.660465\pi\)
0.875602 + 0.483033i \(0.160465\pi\)
\(264\) −2.35748 + 2.35748i −0.145093 + 0.145093i
\(265\) 4.88241 5.47524i 0.299924 0.336342i
\(266\) 3.98874 0.244565
\(267\) −8.09751 −0.495560
\(268\) 6.25304 + 6.25304i 0.381965 + 0.381965i
\(269\) 3.72238i 0.226958i 0.993540 + 0.113479i \(0.0361994\pi\)
−0.993540 + 0.113479i \(0.963801\pi\)
\(270\) −6.86858 6.12488i −0.418008 0.372748i
\(271\) 23.2312 1.41120 0.705598 0.708612i \(-0.250678\pi\)
0.705598 + 0.708612i \(0.250678\pi\)
\(272\) 7.34365 0.445274
\(273\) −5.55488 −0.336196
\(274\) 11.9150 + 11.9150i 0.719813 + 0.719813i
\(275\) −2.50684 21.8272i −0.151168 1.31623i
\(276\) 0.645925 + 0.645925i 0.0388801 + 0.0388801i
\(277\) 12.8392i 0.771434i 0.922617 + 0.385717i \(0.126046\pi\)
−0.922617 + 0.385717i \(0.873954\pi\)
\(278\) 6.75745i 0.405285i
\(279\) −10.0574 10.0574i −0.602122 0.602122i
\(280\) −1.61589 + 1.81209i −0.0965678 + 0.108293i
\(281\) 15.2770 + 15.2770i 0.911350 + 0.911350i 0.996378 0.0850287i \(-0.0270982\pi\)
−0.0850287 + 0.996378i \(0.527098\pi\)
\(282\) −8.24684 −0.491092
\(283\) −20.7901 −1.23584 −0.617920 0.786241i \(-0.712025\pi\)
−0.617920 + 0.786241i \(0.712025\pi\)
\(284\) 5.46460 0.324265
\(285\) 6.22230 0.356143i 0.368577 0.0210961i
\(286\) 29.6285i 1.75197i
\(287\) 3.12554 + 3.12554i 0.184495 + 0.184495i
\(288\) −2.42432 −0.142855
\(289\) 36.9292 2.17230
\(290\) 2.95461 + 2.63470i 0.173501 + 0.154715i
\(291\) 2.89414 2.89414i 0.169658 0.169658i
\(292\) −1.88159 + 1.88159i −0.110112 + 0.110112i
\(293\) 0.449201 + 0.449201i 0.0262426 + 0.0262426i 0.720106 0.693864i \(-0.244093\pi\)
−0.693864 + 0.720106i \(0.744093\pi\)
\(294\) 3.12302 3.12302i 0.182138 0.182138i
\(295\) 17.9687 + 16.0231i 1.04618 + 0.932901i
\(296\) −6.04973 0.633071i −0.351633 0.0367965i
\(297\) 12.7877 12.7877i 0.742020 0.742020i
\(298\) 5.18543 0.300384
\(299\) −8.11790 −0.469471
\(300\) −2.35893 + 2.97108i −0.136193 + 0.171536i
\(301\) −6.57291 6.57291i −0.378856 0.378856i
\(302\) 12.5372 0.721434
\(303\) 7.81601 + 7.81601i 0.449018 + 0.449018i
\(304\) 2.59760 2.59760i 0.148982 0.148982i
\(305\) −2.70125 2.40877i −0.154673 0.137926i
\(306\) −17.8034 −1.01775
\(307\) 0.0144735 + 0.0144735i 0.000826048 + 0.000826048i 0.707520 0.706694i \(-0.249814\pi\)
−0.706694 + 0.707520i \(0.749814\pi\)
\(308\) −3.37371 3.37371i −0.192235 0.192235i
\(309\) 5.45215 5.45215i 0.310162 0.310162i
\(310\) −8.73119 + 9.79136i −0.495899 + 0.556112i
\(311\) 22.9260 22.9260i 1.30001 1.30001i 0.371635 0.928379i \(-0.378797\pi\)
0.928379 0.371635i \(-0.121203\pi\)
\(312\) −3.61752 + 3.61752i −0.204802 + 0.204802i
\(313\) 14.6520i 0.828177i 0.910237 + 0.414089i \(0.135900\pi\)
−0.910237 + 0.414089i \(0.864100\pi\)
\(314\) −0.530292 0.530292i −0.0299261 0.0299261i
\(315\) 3.91743 4.39310i 0.220722 0.247523i
\(316\) −5.13322 + 5.13322i −0.288766 + 0.288766i
\(317\) −14.2710 14.2710i −0.801537 0.801537i 0.181799 0.983336i \(-0.441808\pi\)
−0.983336 + 0.181799i \(0.941808\pi\)
\(318\) 2.48921i 0.139588i
\(319\) −5.50082 + 5.50082i −0.307987 + 0.307987i
\(320\) 0.127776 + 2.23241i 0.00714288 + 0.124796i
\(321\) 14.3956i 0.803483i
\(322\) −0.924360 + 0.924360i −0.0515126 + 0.0515126i
\(323\) 19.0758 19.0758i 1.06141 1.06141i
\(324\) 4.15032 0.230573
\(325\) −3.84671 33.4935i −0.213377 1.85789i
\(326\) 13.0393i 0.722183i
\(327\) 5.13368i 0.283893i
\(328\) 4.07091 0.224778
\(329\) 11.8018i 0.650652i
\(330\) −5.56410 4.96164i −0.306294 0.273130i
\(331\) −19.0443 19.0443i −1.04677 1.04677i −0.998851 0.0479194i \(-0.984741\pi\)
−0.0479194 0.998851i \(-0.515259\pi\)
\(332\) −0.570350 0.570350i −0.0313020 0.0313020i
\(333\) 14.6665 + 1.53477i 0.803719 + 0.0841048i
\(334\) 24.6405i 1.34827i
\(335\) −13.1604 + 14.7584i −0.719029 + 0.806336i
\(336\) 0.823831i 0.0449436i
\(337\) 11.2643 + 11.2643i 0.613604 + 0.613604i 0.943883 0.330279i \(-0.107143\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(338\) 32.4645i 1.76584i
\(339\) −9.65911 + 9.65911i −0.524611 + 0.524611i
\(340\) 0.938340 + 16.3941i 0.0508886 + 0.889093i
\(341\) −18.2293 18.2293i −0.987172 0.987172i
\(342\) −6.29742 + 6.29742i −0.340525 + 0.340525i
\(343\) 9.84367 + 9.84367i 0.531508 + 0.531508i
\(344\) −8.56098 −0.461577
\(345\) −1.35944 + 1.52450i −0.0731897 + 0.0820766i
\(346\) 5.32250 + 5.32250i 0.286139 + 0.286139i
\(347\) 2.40110i 0.128898i 0.997921 + 0.0644489i \(0.0205290\pi\)
−0.997921 + 0.0644489i \(0.979471\pi\)
\(348\) 1.34325 0.0720059
\(349\) 13.3892i 0.716708i 0.933586 + 0.358354i \(0.116662\pi\)
−0.933586 + 0.358354i \(0.883338\pi\)
\(350\) −4.25182 3.37579i −0.227269 0.180444i
\(351\) 19.6226 19.6226i 1.04738 1.04738i
\(352\) −4.39414 −0.234208
\(353\) −7.34993 −0.391198 −0.195599 0.980684i \(-0.562665\pi\)
−0.195599 + 0.980684i \(0.562665\pi\)
\(354\) 8.16908 0.434182
\(355\) 0.698244 + 12.1993i 0.0370590 + 0.647470i
\(356\) −7.54653 7.54653i −0.399965 0.399965i
\(357\) 6.04992i 0.320196i
\(358\) −7.93007 + 7.93007i −0.419117 + 0.419117i
\(359\) 24.0685i 1.27029i −0.772394 0.635143i \(-0.780941\pi\)
0.772394 0.635143i \(-0.219059\pi\)
\(360\) −0.309770 5.41209i −0.0163263 0.285242i
\(361\) 5.50496i 0.289735i
\(362\) 4.29385i 0.225680i
\(363\) 4.45754 4.45754i 0.233960 0.233960i
\(364\) −5.17690 5.17690i −0.271343 0.271343i
\(365\) −4.44092 3.96007i −0.232448 0.207280i
\(366\) −1.22807 −0.0641921
\(367\) −0.833192 + 0.833192i −0.0434923 + 0.0434923i −0.728518 0.685026i \(-0.759791\pi\)
0.685026 + 0.728518i \(0.259791\pi\)
\(368\) 1.20395i 0.0627601i
\(369\) −9.86920 −0.513770
\(370\) 0.640267 13.5864i 0.0332859 0.706323i
\(371\) 3.56222 0.184941
\(372\) 4.45144i 0.230796i
\(373\) −2.09090 + 2.09090i −0.108262 + 0.108262i −0.759163 0.650901i \(-0.774391\pi\)
0.650901 + 0.759163i \(0.274391\pi\)
\(374\) −32.2690 −1.66859
\(375\) −6.93410 4.88649i −0.358076 0.252337i
\(376\) −7.68569 7.68569i −0.396359 0.396359i
\(377\) −8.44092 + 8.44092i −0.434729 + 0.434729i
\(378\) 4.46872i 0.229846i
\(379\) 4.36102i 0.224010i −0.993708 0.112005i \(-0.964273\pi\)
0.993708 0.112005i \(-0.0357273\pi\)
\(380\) 6.13083 + 5.46701i 0.314505 + 0.280451i
\(381\) 9.88267i 0.506305i
\(382\) −2.08620 + 2.08620i −0.106739 + 0.106739i
\(383\) 16.6051i 0.848480i −0.905550 0.424240i \(-0.860541\pi\)
0.905550 0.424240i \(-0.139459\pi\)
\(384\) 0.536506 + 0.536506i 0.0273784 + 0.0273784i
\(385\) 7.10044 7.96259i 0.361872 0.405811i
\(386\) 13.6280 0.693644
\(387\) 20.7546 1.05502
\(388\) 5.39443 0.273861
\(389\) −12.9306 + 12.9306i −0.655609 + 0.655609i −0.954338 0.298729i \(-0.903437\pi\)
0.298729 + 0.954338i \(0.403437\pi\)
\(390\) −8.53803 7.61357i −0.432340 0.385528i
\(391\) 8.84137i 0.447127i
\(392\) 5.82104 0.294007
\(393\) 1.65077i 0.0832702i
\(394\) 5.05224 + 5.05224i 0.254528 + 0.254528i
\(395\) −12.1154 10.8036i −0.609591 0.543587i
\(396\) 10.6528 0.535324
\(397\) 1.98404 + 1.98404i 0.0995762 + 0.0995762i 0.755140 0.655564i \(-0.227569\pi\)
−0.655564 + 0.755140i \(0.727569\pi\)
\(398\) 12.1515 12.1515i 0.609098 0.609098i
\(399\) 2.13998 + 2.13998i 0.107133 + 0.107133i
\(400\) −4.96735 + 0.570497i −0.248367 + 0.0285248i
\(401\) −14.2034 + 14.2034i −0.709283 + 0.709283i −0.966384 0.257101i \(-0.917233\pi\)
0.257101 + 0.966384i \(0.417233\pi\)
\(402\) 6.70958i 0.334644i
\(403\) −27.9726 27.9726i −1.39341 1.39341i
\(404\) 14.5684i 0.724803i
\(405\) 0.530310 + 9.26522i 0.0263513 + 0.460393i
\(406\) 1.92228i 0.0954012i
\(407\) 26.5834 + 2.78180i 1.31769 + 0.137889i
\(408\) 3.93991 + 3.93991i 0.195054 + 0.195054i
\(409\) −13.7291 13.7291i −0.678859 0.678859i 0.280883 0.959742i \(-0.409373\pi\)
−0.959742 + 0.280883i \(0.909373\pi\)
\(410\) 0.520163 + 9.08795i 0.0256890 + 0.448822i
\(411\) 12.7850i 0.630635i
\(412\) 10.1623 0.500662
\(413\) 11.6905i 0.575251i
\(414\) 2.91876i 0.143449i
\(415\) 1.20038 1.34614i 0.0589244 0.0660792i
\(416\) −6.74274 −0.330590
\(417\) 3.62541 3.62541i 0.177537 0.177537i
\(418\) −11.4142 + 11.4142i −0.558287 + 0.558287i
\(419\) 10.6476i 0.520169i −0.965586 0.260084i \(-0.916250\pi\)
0.965586 0.260084i \(-0.0837504\pi\)
\(420\) −1.83913 + 0.105266i −0.0897404 + 0.00513644i
\(421\) 21.3367 21.3367i 1.03989 1.03989i 0.0407156 0.999171i \(-0.487036\pi\)
0.999171 0.0407156i \(-0.0129638\pi\)
\(422\) 8.27973i 0.403051i
\(423\) 18.6326 + 18.6326i 0.905948 + 0.905948i
\(424\) 2.31983 2.31983i 0.112661 0.112661i
\(425\) −36.4784 + 4.18953i −1.76946 + 0.203222i
\(426\) 2.93179 + 2.93179i 0.142046 + 0.142046i
\(427\) 1.75744i 0.0850487i
\(428\) 13.4161 13.4161i 0.648490 0.648490i
\(429\) 15.8959 15.8959i 0.767460 0.767460i
\(430\) −1.09389 19.1117i −0.0527519 0.921646i
\(431\) −5.16220 + 5.16220i −0.248655 + 0.248655i −0.820418 0.571764i \(-0.806259\pi\)
0.571764 + 0.820418i \(0.306259\pi\)
\(432\) −2.91018 2.91018i −0.140016 0.140016i
\(433\) 2.75289 + 2.75289i 0.132296 + 0.132296i 0.770154 0.637858i \(-0.220179\pi\)
−0.637858 + 0.770154i \(0.720179\pi\)
\(434\) −6.37030 −0.305784
\(435\) 0.171635 + 2.99870i 0.00822927 + 0.143776i
\(436\) −4.78437 + 4.78437i −0.229130 + 0.229130i
\(437\) 3.12737 + 3.12737i 0.149602 + 0.149602i
\(438\) −2.01897 −0.0964701
\(439\) 28.9545 + 28.9545i 1.38192 + 1.38192i 0.841200 + 0.540725i \(0.181850\pi\)
0.540725 + 0.841200i \(0.318150\pi\)
\(440\) −0.561465 9.80954i −0.0267668 0.467652i
\(441\) −14.1121 −0.672005
\(442\) −49.5163 −2.35525
\(443\) 19.2383 19.2383i 0.914040 0.914040i −0.0825469 0.996587i \(-0.526305\pi\)
0.996587 + 0.0825469i \(0.0263054\pi\)
\(444\) −2.90607 3.58536i −0.137916 0.170154i
\(445\) 15.8827 17.8113i 0.752913 0.844334i
\(446\) −9.35468 + 9.35468i −0.442957 + 0.442957i
\(447\) 2.78201 + 2.78201i 0.131585 + 0.131585i
\(448\) −0.767774 + 0.767774i −0.0362739 + 0.0362739i
\(449\) −21.0464 + 21.0464i −0.993243 + 0.993243i −0.999977 0.00673470i \(-0.997856\pi\)
0.00673470 + 0.999977i \(0.497856\pi\)
\(450\) 12.0425 1.38307i 0.567687 0.0651985i
\(451\) −17.8881 −0.842320
\(452\) −18.0037 −0.846825
\(453\) 6.72627 + 6.72627i 0.316028 + 0.316028i
\(454\) 20.1807i 0.947129i
\(455\) 10.8955 12.2185i 0.510789 0.572811i
\(456\) 2.78725 0.130525
\(457\) 21.7070 1.01541 0.507705 0.861531i \(-0.330494\pi\)
0.507705 + 0.861531i \(0.330494\pi\)
\(458\) −3.02631 −0.141410
\(459\) −21.3713 21.3713i −0.997528 0.997528i
\(460\) −2.68771 + 0.153835i −0.125315 + 0.00717261i
\(461\) 1.31376 + 1.31376i 0.0611879 + 0.0611879i 0.737039 0.675851i \(-0.236224\pi\)
−0.675851 + 0.737039i \(0.736224\pi\)
\(462\) 3.62003i 0.168419i
\(463\) 8.05167i 0.374193i −0.982342 0.187096i \(-0.940092\pi\)
0.982342 0.187096i \(-0.0599077\pi\)
\(464\) 1.25185 + 1.25185i 0.0581158 + 0.0581158i
\(465\) −9.93746 + 0.568786i −0.460838 + 0.0263768i
\(466\) 4.33931 + 4.33931i 0.201015 + 0.201015i
\(467\) −5.04806 −0.233596 −0.116798 0.993156i \(-0.537263\pi\)
−0.116798 + 0.993156i \(0.537263\pi\)
\(468\) 16.3466 0.755621
\(469\) −9.60185 −0.443372
\(470\) 16.1756 18.1397i 0.746125 0.836722i
\(471\) 0.569009i 0.0262186i
\(472\) 7.61323 + 7.61323i 0.350427 + 0.350427i
\(473\) 37.6182 1.72969
\(474\) −5.50801 −0.252991
\(475\) −11.4213 + 14.3851i −0.524043 + 0.660033i
\(476\) −5.63827 + 5.63827i −0.258429 + 0.258429i
\(477\) −5.62402 + 5.62402i −0.257506 + 0.257506i
\(478\) −2.92398 2.92398i −0.133740 0.133740i
\(479\) −4.20701 + 4.20701i −0.192223 + 0.192223i −0.796656 0.604433i \(-0.793400\pi\)
0.604433 + 0.796656i \(0.293400\pi\)
\(480\) −1.12915 + 1.26626i −0.0515384 + 0.0577964i
\(481\) 40.7917 + 4.26863i 1.85994 + 0.194633i
\(482\) 14.9825 14.9825i 0.682432 0.682432i
\(483\) −0.991849 −0.0451307
\(484\) 8.30847 0.377658
\(485\) 0.689278 + 12.0426i 0.0312985 + 0.546826i
\(486\) 10.9572 + 10.9572i 0.497029 + 0.497029i
\(487\) −23.0440 −1.04422 −0.522111 0.852877i \(-0.674855\pi\)
−0.522111 + 0.852877i \(0.674855\pi\)
\(488\) −1.14451 1.14451i −0.0518093 0.0518093i
\(489\) 6.99568 6.99568i 0.316356 0.316356i
\(490\) 0.743789 + 12.9950i 0.0336009 + 0.587053i
\(491\) 17.5204 0.790684 0.395342 0.918534i \(-0.370626\pi\)
0.395342 + 0.918534i \(0.370626\pi\)
\(492\) 2.18406 + 2.18406i 0.0984652 + 0.0984652i
\(493\) 9.19317 + 9.19317i 0.414039 + 0.414039i
\(494\) −17.5149 + 17.5149i −0.788034 + 0.788034i
\(495\) 1.36117 + 23.7815i 0.0611801 + 1.06890i
\(496\) −4.14855 + 4.14855i −0.186275 + 0.186275i
\(497\) −4.19558 + 4.19558i −0.188198 + 0.188198i
\(498\) 0.611992i 0.0274240i
\(499\) 3.14878 + 3.14878i 0.140959 + 0.140959i 0.774065 0.633106i \(-0.218220\pi\)
−0.633106 + 0.774065i \(0.718220\pi\)
\(500\) −1.90829 11.0163i −0.0853414 0.492663i
\(501\) −13.2198 + 13.2198i −0.590616 + 0.590616i
\(502\) 9.25271 + 9.25271i 0.412969 + 0.412969i
\(503\) 38.5464i 1.71870i 0.511390 + 0.859349i \(0.329131\pi\)
−0.511390 + 0.859349i \(0.670869\pi\)
\(504\) 1.86133 1.86133i 0.0829104 0.0829104i
\(505\) −32.5226 + 1.86148i −1.44724 + 0.0828350i
\(506\) 5.29031i 0.235183i
\(507\) 17.4174 17.4174i 0.773534 0.773534i
\(508\) −9.21023 + 9.21023i −0.408638 + 0.408638i
\(509\) −18.2209 −0.807627 −0.403814 0.914841i \(-0.632316\pi\)
−0.403814 + 0.914841i \(0.632316\pi\)
\(510\) −8.29208 + 9.29893i −0.367180 + 0.411764i
\(511\) 2.88928i 0.127814i
\(512\) 1.00000i 0.0441942i
\(513\) −15.1190 −0.667518
\(514\) 11.5476i 0.509341i
\(515\) 1.29850 + 22.6865i 0.0572188 + 0.999688i
\(516\) −4.59302 4.59302i −0.202196 0.202196i
\(517\) 33.7720 + 33.7720i 1.48529 + 1.48529i
\(518\) 5.13088 4.15877i 0.225438 0.182726i
\(519\) 5.71110i 0.250689i
\(520\) −0.861559 15.0526i −0.0377819 0.660100i
\(521\) 8.10778i 0.355208i −0.984102 0.177604i \(-0.943165\pi\)
0.984102 0.177604i \(-0.0568347\pi\)
\(522\) −3.03490 3.03490i −0.132834 0.132834i
\(523\) 9.18819i 0.401772i 0.979615 + 0.200886i \(0.0643820\pi\)
−0.979615 + 0.200886i \(0.935618\pi\)
\(524\) 1.53844 1.53844i 0.0672072 0.0672072i
\(525\) −0.469993 4.09225i −0.0205122 0.178601i
\(526\) 6.36639 + 6.36639i 0.277588 + 0.277588i
\(527\) −30.4655 + 30.4655i −1.32710 + 1.32710i
\(528\) −2.35748 2.35748i −0.102596 0.102596i
\(529\) 21.5505 0.936979
\(530\) 5.47524 + 4.88241i 0.237829 + 0.212078i
\(531\) −18.4569 18.4569i −0.800963 0.800963i
\(532\) 3.98874i 0.172934i
\(533\) −27.4491 −1.18895
\(534\) 8.09751i 0.350414i
\(535\) 31.6644 + 28.2360i 1.36897 + 1.22075i
\(536\) −6.25304 + 6.25304i −0.270090 + 0.270090i
\(537\) −8.50905 −0.367193
\(538\) −3.72238 −0.160483
\(539\) −25.5785 −1.10174
\(540\) 6.12488 6.86858i 0.263573 0.295577i
\(541\) −14.3951 14.3951i −0.618893 0.618893i 0.326355 0.945247i \(-0.394180\pi\)
−0.945247 + 0.326355i \(0.894180\pi\)
\(542\) 23.2312i 0.997867i
\(543\) 2.30368 2.30368i 0.0988602 0.0988602i
\(544\) 7.34365i 0.314856i
\(545\) −11.2920 10.0694i −0.483697 0.431324i
\(546\) 5.55488i 0.237727i
\(547\) 3.07074i 0.131295i −0.997843 0.0656477i \(-0.979089\pi\)
0.997843 0.0656477i \(-0.0209114\pi\)
\(548\) −11.9150 + 11.9150i −0.508985 + 0.508985i
\(549\) 2.77465 + 2.77465i 0.118419 + 0.118419i
\(550\) 21.8272 2.50684i 0.930716 0.106892i
\(551\) 6.50362 0.277064
\(552\) −0.645925 + 0.645925i −0.0274924 + 0.0274924i
\(553\) 7.88232i 0.335190i
\(554\) −12.8392 −0.545486
\(555\) 7.63268 6.94567i 0.323989 0.294827i
\(556\) 6.75745 0.286580
\(557\) 33.2382i 1.40835i −0.710028 0.704173i \(-0.751318\pi\)
0.710028 0.704173i \(-0.248682\pi\)
\(558\) 10.0574 10.0574i 0.425765 0.425765i
\(559\) 57.7245 2.44149
\(560\) −1.81209 1.61589i −0.0765749 0.0682837i
\(561\) −17.3125 17.3125i −0.730935 0.730935i
\(562\) −15.2770 + 15.2770i −0.644422 + 0.644422i
\(563\) 34.1847i 1.44071i 0.693605 + 0.720356i \(0.256021\pi\)
−0.693605 + 0.720356i \(0.743979\pi\)
\(564\) 8.24684i 0.347254i
\(565\) −2.30044 40.1918i −0.0967803 1.69088i
\(566\) 20.7901i 0.873871i
\(567\) −3.18651 + 3.18651i −0.133821 + 0.133821i
\(568\) 5.46460i 0.229290i
\(569\) 29.8527 + 29.8527i 1.25149 + 1.25149i 0.955052 + 0.296438i \(0.0957989\pi\)
0.296438 + 0.955052i \(0.404201\pi\)
\(570\) 0.356143 + 6.22230i 0.0149172 + 0.260624i
\(571\) −18.1250 −0.758508 −0.379254 0.925293i \(-0.623819\pi\)
−0.379254 + 0.925293i \(0.623819\pi\)
\(572\) 29.6285 1.23883
\(573\) −2.23851 −0.0935152
\(574\) −3.12554 + 3.12554i −0.130457 + 0.130457i
\(575\) −0.686848 5.98042i −0.0286436 0.249401i
\(576\) 2.42432i 0.101013i
\(577\) −14.6571 −0.610182 −0.305091 0.952323i \(-0.598687\pi\)
−0.305091 + 0.952323i \(0.598687\pi\)
\(578\) 36.9292i 1.53605i
\(579\) 7.31147 + 7.31147i 0.303854 + 0.303854i
\(580\) −2.63470 + 2.95461i −0.109400 + 0.122684i
\(581\) 0.875801 0.0363343
\(582\) 2.89414 + 2.89414i 0.119966 + 0.119966i
\(583\) −10.1937 + 10.1937i −0.422179 + 0.422179i
\(584\) −1.88159 1.88159i −0.0778609 0.0778609i
\(585\) 2.08870 + 36.4923i 0.0863570 + 1.50877i
\(586\) −0.449201 + 0.449201i −0.0185563 + 0.0185563i
\(587\) 2.78069i 0.114772i −0.998352 0.0573858i \(-0.981724\pi\)
0.998352 0.0573858i \(-0.0182765\pi\)
\(588\) 3.12302 + 3.12302i 0.128791 + 0.128791i
\(589\) 21.5525i 0.888056i
\(590\) −16.0231 + 17.9687i −0.659660 + 0.739758i
\(591\) 5.42111i 0.222995i
\(592\) 0.633071 6.04973i 0.0260190 0.248642i
\(593\) 4.64974 + 4.64974i 0.190942 + 0.190942i 0.796103 0.605161i \(-0.206891\pi\)
−0.605161 + 0.796103i \(0.706891\pi\)
\(594\) 12.7877 + 12.7877i 0.524687 + 0.524687i
\(595\) −13.3074 11.8665i −0.545549 0.486479i
\(596\) 5.18543i 0.212404i
\(597\) 13.0387 0.533637
\(598\) 8.11790i 0.331966i
\(599\) 8.57057i 0.350184i −0.984552 0.175092i \(-0.943978\pi\)
0.984552 0.175092i \(-0.0560223\pi\)
\(600\) −2.97108 2.35893i −0.121294 0.0963031i
\(601\) −4.61240 −0.188144 −0.0940719 0.995565i \(-0.529988\pi\)
−0.0940719 + 0.995565i \(0.529988\pi\)
\(602\) 6.57291 6.57291i 0.267892 0.267892i
\(603\) 15.1594 15.1594i 0.617338 0.617338i
\(604\) 12.5372i 0.510131i
\(605\) 1.06162 + 18.5480i 0.0431611 + 0.754081i
\(606\) −7.81601 + 7.81601i −0.317504 + 0.317504i
\(607\) 36.4725i 1.48037i −0.672403 0.740186i \(-0.734738\pi\)
0.672403 0.740186i \(-0.265262\pi\)
\(608\) 2.59760 + 2.59760i 0.105347 + 0.105347i
\(609\) −1.03131 + 1.03131i −0.0417910 + 0.0417910i
\(610\) 2.40877 2.70125i 0.0975282 0.109370i
\(611\) 51.8226 + 51.8226i 2.09652 + 2.09652i
\(612\) 17.8034i 0.719659i
\(613\) 3.07671 3.07671i 0.124267 0.124267i −0.642238 0.766505i \(-0.721994\pi\)
0.766505 + 0.642238i \(0.221994\pi\)
\(614\) −0.0144735 + 0.0144735i −0.000584104 + 0.000584104i
\(615\) −4.59667 + 5.15481i −0.185355 + 0.207862i
\(616\) 3.37371 3.37371i 0.135931 0.135931i
\(617\) −6.95912 6.95912i −0.280164 0.280164i 0.553011 0.833174i \(-0.313479\pi\)
−0.833174 + 0.553011i \(0.813479\pi\)
\(618\) 5.45215 + 5.45215i 0.219318 + 0.219318i
\(619\) 28.9801 1.16481 0.582405 0.812899i \(-0.302112\pi\)
0.582405 + 0.812899i \(0.302112\pi\)
\(620\) −9.79136 8.73119i −0.393231 0.350653i
\(621\) 3.50370 3.50370i 0.140599 0.140599i
\(622\) 22.9260 + 22.9260i 0.919249 + 0.919249i
\(623\) 11.5881 0.464266
\(624\) −3.61752 3.61752i −0.144817 0.144817i
\(625\) 24.3491 5.66771i 0.973963 0.226708i
\(626\) −14.6520 −0.585610
\(627\) −12.2476 −0.489121
\(628\) 0.530292 0.530292i 0.0211610 0.0211610i
\(629\) 4.64905 44.4271i 0.185370 1.77142i
\(630\) 4.39310 + 3.91743i 0.175025 + 0.156074i
\(631\) −8.58133 + 8.58133i −0.341617 + 0.341617i −0.856975 0.515358i \(-0.827659\pi\)
0.515358 + 0.856975i \(0.327659\pi\)
\(632\) −5.13322 5.13322i −0.204189 0.204189i
\(633\) −4.44212 + 4.44212i −0.176559 + 0.176559i
\(634\) 14.2710 14.2710i 0.566772 0.566772i
\(635\) −21.7379 19.3842i −0.862642 0.769238i
\(636\) 2.48921 0.0987034
\(637\) −39.2498 −1.55513
\(638\) −5.50082 5.50082i −0.217779 0.217779i
\(639\) 13.2480i 0.524082i
\(640\) −2.23241 + 0.127776i −0.0882439 + 0.00505078i
\(641\) −39.7584 −1.57036 −0.785181 0.619267i \(-0.787430\pi\)
−0.785181 + 0.619267i \(0.787430\pi\)
\(642\) 14.3956 0.568148
\(643\) 0.0494458 0.00194995 0.000974976 1.00000i \(-0.499690\pi\)
0.000974976 1.00000i \(0.499690\pi\)
\(644\) −0.924360 0.924360i −0.0364249 0.0364249i
\(645\) 9.66664 10.8404i 0.380623 0.426840i
\(646\) 19.0758 + 19.0758i 0.750529 + 0.750529i
\(647\) 20.0867i 0.789689i 0.918748 + 0.394844i \(0.129202\pi\)
−0.918748 + 0.394844i \(0.870798\pi\)
\(648\) 4.15032i 0.163040i
\(649\) −33.4536 33.4536i −1.31317 1.31317i
\(650\) 33.4935 3.84671i 1.31372 0.150880i
\(651\) −3.41770 3.41770i −0.133950 0.133950i
\(652\) 13.0393 0.510660
\(653\) 2.91044 0.113894 0.0569471 0.998377i \(-0.481863\pi\)
0.0569471 + 0.998377i \(0.481863\pi\)
\(654\) −5.13368 −0.200743
\(655\) 3.63102 + 3.23787i 0.141876 + 0.126514i
\(656\) 4.07091i 0.158942i
\(657\) 4.56159 + 4.56159i 0.177965 + 0.177965i
\(658\) 11.8018 0.460080
\(659\) 18.9341 0.737568 0.368784 0.929515i \(-0.379774\pi\)
0.368784 + 0.929515i \(0.379774\pi\)
\(660\) 4.96164 5.56410i 0.193132 0.216582i
\(661\) −14.8550 + 14.8550i −0.577792 + 0.577792i −0.934294 0.356502i \(-0.883969\pi\)
0.356502 + 0.934294i \(0.383969\pi\)
\(662\) 19.0443 19.0443i 0.740179 0.740179i
\(663\) −26.5658 26.5658i −1.03173 1.03173i
\(664\) 0.570350 0.570350i 0.0221339 0.0221339i
\(665\) −8.90452 + 0.509664i −0.345302 + 0.0197639i
\(666\) −1.53477 + 14.6665i −0.0594711 + 0.568315i
\(667\) −1.50717 + 1.50717i −0.0583577 + 0.0583577i
\(668\) −24.6405 −0.953370
\(669\) −10.0377 −0.388079
\(670\) −14.7584 13.1604i −0.570165 0.508430i
\(671\) 5.02912 + 5.02912i 0.194147 + 0.194147i
\(672\) −0.823831 −0.0317800
\(673\) −4.39502 4.39502i −0.169416 0.169416i 0.617307 0.786722i \(-0.288224\pi\)
−0.786722 + 0.617307i \(0.788224\pi\)
\(674\) −11.2643 + 11.2643i −0.433884 + 0.433884i
\(675\) 16.1161 + 12.7956i 0.620310 + 0.492504i
\(676\) 32.4645 1.24864
\(677\) −15.6334 15.6334i −0.600841 0.600841i 0.339695 0.940536i \(-0.389676\pi\)
−0.940536 + 0.339695i \(0.889676\pi\)
\(678\) −9.65911 9.65911i −0.370956 0.370956i
\(679\) −4.14171 + 4.14171i −0.158944 + 0.158944i
\(680\) −16.3941 + 0.938340i −0.628684 + 0.0359837i
\(681\) 10.8271 10.8271i 0.414895 0.414895i
\(682\) 18.2293 18.2293i 0.698036 0.698036i
\(683\) 2.66101i 0.101821i −0.998703 0.0509104i \(-0.983788\pi\)
0.998703 0.0509104i \(-0.0162123\pi\)
\(684\) −6.29742 6.29742i −0.240788 0.240788i
\(685\) −28.1217 25.0768i −1.07448 0.958136i
\(686\) −9.84367 + 9.84367i −0.375833 + 0.375833i
\(687\) −1.62363 1.62363i −0.0619454 0.0619454i
\(688\) 8.56098i 0.326384i
\(689\) −15.6420 + 15.6420i −0.595914 + 0.595914i
\(690\) −1.52450 1.35944i −0.0580369 0.0517529i
\(691\) 6.84103i 0.260245i −0.991498 0.130123i \(-0.958463\pi\)
0.991498 0.130123i \(-0.0415371\pi\)
\(692\) −5.32250 + 5.32250i −0.202331 + 0.202331i
\(693\) −8.17896 + 8.17896i −0.310693 + 0.310693i
\(694\) −2.40110 −0.0911445
\(695\) 0.863438 + 15.0854i 0.0327521 + 0.572223i
\(696\) 1.34325i 0.0509158i
\(697\) 29.8953i 1.13237i
\(698\) −13.3892 −0.506789
\(699\) 4.65613i 0.176111i
\(700\) 3.37579 4.25182i 0.127593 0.160704i
\(701\) −15.1890 15.1890i −0.573682 0.573682i 0.359473 0.933155i \(-0.382956\pi\)
−0.933155 + 0.359473i \(0.882956\pi\)
\(702\) 19.6226 + 19.6226i 0.740607 + 0.740607i
\(703\) −14.0703 17.3592i −0.530672 0.654716i
\(704\) 4.39414i 0.165610i
\(705\) 18.4104 1.05375i 0.693374 0.0396864i
\(706\) 7.34993i 0.276618i
\(707\) −11.1852 11.1852i −0.420663 0.420663i
\(708\) 8.16908i 0.307013i
\(709\) −13.9085 + 13.9085i −0.522343 + 0.522343i −0.918278 0.395935i \(-0.870420\pi\)
0.395935 + 0.918278i \(0.370420\pi\)
\(710\) −12.1993 + 0.698244i −0.457830 + 0.0262046i
\(711\) 12.4446 + 12.4446i 0.466709 + 0.466709i
\(712\) 7.54653 7.54653i 0.282818 0.282818i
\(713\) −4.99463 4.99463i −0.187051 0.187051i
\(714\) −6.04992 −0.226413
\(715\) 3.78581 + 66.1432i 0.141581 + 2.47362i
\(716\) −7.93007 7.93007i −0.296361 0.296361i
\(717\) 3.13746i 0.117171i
\(718\) 24.0685 0.898228
\(719\) 23.7742i 0.886629i −0.896366 0.443314i \(-0.853803\pi\)
0.896366 0.443314i \(-0.146197\pi\)
\(720\) 5.41209 0.309770i 0.201697 0.0115444i
\(721\) −7.80238 + 7.80238i −0.290576 + 0.290576i
\(722\) −5.50496 −0.204874
\(723\) 16.0763 0.597886
\(724\) 4.29385 0.159580
\(725\) −6.93257 5.50421i −0.257469 0.204421i
\(726\) 4.45754 + 4.45754i 0.165435 + 0.165435i
\(727\) 0.783597i 0.0290620i 0.999894 + 0.0145310i \(0.00462552\pi\)
−0.999894 + 0.0145310i \(0.995374\pi\)
\(728\) 5.17690 5.17690i 0.191869 0.191869i
\(729\) 0.693741i 0.0256941i
\(730\) 3.96007 4.44092i 0.146569 0.164366i
\(731\) 62.8689i 2.32529i
\(732\) 1.22807i 0.0453907i
\(733\) −8.72850 + 8.72850i −0.322395 + 0.322395i −0.849685 0.527291i \(-0.823208\pi\)
0.527291 + 0.849685i \(0.323208\pi\)
\(734\) −0.833192 0.833192i −0.0307537 0.0307537i
\(735\) −6.57283 + 7.37093i −0.242443 + 0.271881i
\(736\) −1.20395 −0.0443781
\(737\) 27.4767 27.4767i 1.01212 1.01212i
\(738\) 9.86920i 0.363290i
\(739\) 11.2844 0.415102 0.207551 0.978224i \(-0.433451\pi\)
0.207551 + 0.978224i \(0.433451\pi\)
\(740\) 13.5864 + 0.640267i 0.499446 + 0.0235367i
\(741\) −18.7937 −0.690404
\(742\) 3.56222i 0.130773i
\(743\) −11.8850 + 11.8850i −0.436018 + 0.436018i −0.890669 0.454652i \(-0.849764\pi\)
0.454652 + 0.890669i \(0.349764\pi\)
\(744\) −4.45144 −0.163198
\(745\) −11.5760 + 0.662573i −0.424113 + 0.0242748i
\(746\) −2.09090 2.09090i −0.0765531 0.0765531i
\(747\) −1.38271 + 1.38271i −0.0505909 + 0.0505909i
\(748\) 32.2690i 1.17987i
\(749\) 20.6010i 0.752745i
\(750\) 4.88649 6.93410i 0.178429 0.253198i
\(751\) 18.7371i 0.683727i 0.939750 + 0.341864i \(0.111058\pi\)
−0.939750 + 0.341864i \(0.888942\pi\)
\(752\) 7.68569 7.68569i 0.280268 0.280268i
\(753\) 9.92826i 0.361806i
\(754\) −8.44092 8.44092i −0.307400 0.307400i
\(755\) −27.9882 + 1.60195i −1.01859 + 0.0583009i
\(756\) 4.46872 0.162526
\(757\) −5.00038 −0.181742 −0.0908710 0.995863i \(-0.528965\pi\)
−0.0908710 + 0.995863i \(0.528965\pi\)
\(758\) 4.36102 0.158399
\(759\) 2.83828 2.83828i 0.103023 0.103023i
\(760\) −5.46701 + 6.13083i −0.198309 + 0.222388i
\(761\) 9.44966i 0.342550i −0.985223 0.171275i \(-0.945211\pi\)
0.985223 0.171275i \(-0.0547887\pi\)
\(762\) −9.88267 −0.358012
\(763\) 7.34663i 0.265966i
\(764\) −2.08620 2.08620i −0.0754759 0.0754759i
\(765\) 39.7445 2.27484i 1.43697 0.0822470i
\(766\) 16.6051 0.599966
\(767\) −51.3340 51.3340i −1.85356 1.85356i
\(768\) −0.536506 + 0.536506i −0.0193595 + 0.0193595i
\(769\) −11.4556 11.4556i −0.413100 0.413100i 0.469717 0.882817i \(-0.344356\pi\)
−0.882817 + 0.469717i \(0.844356\pi\)
\(770\) 7.96259 + 7.10044i 0.286952 + 0.255882i
\(771\) 6.19533 6.19533i 0.223119 0.223119i
\(772\) 13.6280i 0.490481i
\(773\) 7.63579 + 7.63579i 0.274640 + 0.274640i 0.830965 0.556325i \(-0.187789\pi\)
−0.556325 + 0.830965i \(0.687789\pi\)
\(774\) 20.7546i 0.746009i
\(775\) 18.2405 22.9740i 0.655220 0.825251i
\(776\) 5.39443i 0.193649i
\(777\) 4.98395 + 0.521543i 0.178798 + 0.0187102i
\(778\) −12.9306 12.9306i −0.463