Properties

Label 370.2.h.e.253.6
Level $370$
Weight $2$
Character 370.253
Analytic conductor $2.954$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.h (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: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.6
Root \(0.536506 + 0.536506i\) of defining polynomial
Character \(\chi\) \(=\) 370.253
Dual form 370.2.h.e.117.6

$q$-expansion

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

Character values

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

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.536506 0.536506i 0.309752 0.309752i −0.535061 0.844813i \(-0.679712\pi\)
0.844813 + 0.535061i \(0.179712\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.23241 + 0.127776i −0.998366 + 0.0571431i
\(6\) −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 \(0.184217\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.42432i 0.808108i
\(10\) 2.23241 0.127776i 0.705951 0.0404063i
\(11\) 4.39414i 1.32488i −0.749114 0.662442i \(-0.769520\pi\)
0.749114 0.662442i \(-0.230480\pi\)
\(12\) 0.536506 0.536506i 0.154876 0.154876i
\(13\) 6.74274 1.87010 0.935050 0.354516i \(-0.115355\pi\)
0.935050 + 0.354516i \(0.115355\pi\)
\(14\) −0.767774 + 0.767774i −0.205196 + 0.205196i
\(15\) −1.12915 + 1.26626i −0.291545 + 0.326946i
\(16\) 1.00000 0.250000
\(17\) 7.34365i 1.78110i −0.454889 0.890548i \(-0.650321\pi\)
0.454889 0.890548i \(-0.349679\pi\)
\(18\) 2.42432i 0.571419i
\(19\) −2.59760 2.59760i −0.595930 0.595930i 0.343297 0.939227i \(-0.388456\pi\)
−0.939227 + 0.343297i \(0.888456\pi\)
\(20\) −2.23241 + 0.127776i −0.499183 + 0.0285715i
\(21\) 0.823831i 0.179775i
\(22\) 4.39414i 0.936834i
\(23\) 1.20395 0.251040 0.125520 0.992091i \(-0.459940\pi\)
0.125520 + 0.992091i \(0.459940\pi\)
\(24\) −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 \(-0.802561\pi\)
0.581257 + 0.813720i \(0.302561\pi\)
\(30\) 1.12915 1.26626i 0.206154 0.231185i
\(31\) −4.14855 4.14855i −0.745101 0.745101i 0.228454 0.973555i \(-0.426633\pi\)
−0.973555 + 0.228454i \(0.926633\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.35748 2.35748i −0.410385 0.410385i
\(34\) 7.34365i 1.25943i
\(35\) −1.61589 + 1.81209i −0.273135 + 0.306300i
\(36\) 2.42432i 0.404054i
\(37\) 6.04973 0.633071i 0.994569 0.104076i
\(38\) 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 \(-0.897028\pi\)
0.948129 0.317884i \(-0.102972\pi\)
\(42\) 0.823831i 0.127120i
\(43\) −8.56098 −1.30554 −0.652769 0.757557i \(-0.726393\pi\)
−0.652769 + 0.757557i \(0.726393\pi\)
\(44\) 4.39414i 0.662442i
\(45\) −0.309770 5.41209i −0.0461778 0.806787i
\(46\) −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
\(50\) −4.96735 + 0.570497i −0.702489 + 0.0806805i
\(51\) −3.93991 3.93991i −0.551697 0.551697i
\(52\) 6.74274 0.935050
\(53\) 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
\(55\) 0.561465 + 9.80954i 0.0757079 + 1.32272i
\(56\) −0.767774 + 0.767774i −0.102598 + 0.102598i
\(57\) −2.78725 −0.369181
\(58\) 1.25185 1.25185i 0.164376 0.164376i
\(59\) 7.61323 + 7.61323i 0.991158 + 0.991158i 0.999961 0.00880307i \(-0.00280214\pi\)
−0.00880307 + 0.999961i \(0.502802\pi\)
\(60\) −1.12915 + 1.26626i −0.145773 + 0.163473i
\(61\) 1.14451 + 1.14451i 0.146539 + 0.146539i 0.776570 0.630031i \(-0.216958\pi\)
−0.630031 + 0.776570i \(0.716958\pi\)
\(62\) 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 0.977030 0.213100i \(-0.0683560\pi\)
−0.213100 + 0.977030i \(0.568356\pi\)
\(68\) 7.34365i 0.890548i
\(69\) 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 \(0.605117\pi\)
\(72\) 2.42432i 0.285709i
\(73\) −1.88159 + 1.88159i −0.220224 + 0.220224i −0.808593 0.588369i \(-0.799770\pi\)
0.588369 + 0.808593i \(0.299770\pi\)
\(74\) −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 \(-0.383905\pi\)
−0.934223 + 0.356690i \(0.883905\pi\)
\(80\) −2.23241 + 0.127776i −0.249591 + 0.0142858i
\(81\) −4.15032 −0.461146
\(82\) 4.07091i 0.449557i
\(83\) 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
\(87\) 1.34325i 0.144012i
\(88\) 4.39414i 0.468417i
\(89\) −7.54653 + 7.54653i −0.799931 + 0.799931i −0.983084 0.183153i \(-0.941370\pi\)
0.183153 + 0.983084i \(0.441370\pi\)
\(90\) 0.309770 + 5.41209i 0.0326526 + 0.570485i
\(91\) 5.17690 5.17690i 0.542687 0.542687i
\(92\) 1.20395 0.125520
\(93\) −4.45144 −0.461593
\(94\) −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
\(97\) 5.39443i 0.547721i 0.961769 + 0.273861i \(0.0883007\pi\)
−0.961769 + 0.273861i \(0.911699\pi\)
\(98\) 5.82104i 0.588014i
\(99\) 10.6528 1.07065
\(100\) 4.96735 0.570497i 0.496735 0.0570497i
\(101\) 14.5684i 1.44961i 0.688956 + 0.724803i \(0.258069\pi\)
−0.688956 + 0.724803i \(0.741931\pi\)
\(102\) 3.93991 + 3.93991i 0.390109 + 0.390109i
\(103\) 10.1623i 1.00132i −0.865643 0.500662i \(-0.833090\pi\)
0.865643 0.500662i \(-0.166910\pi\)
\(104\) −6.74274 −0.661180
\(105\) 0.105266 + 1.83913i 0.0102729 + 0.179481i
\(106\) −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 \(-0.355041\pi\)
−0.898084 + 0.439824i \(0.855041\pi\)
\(110\) −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
\(113\) 18.0037i 1.69365i 0.531872 + 0.846825i \(0.321489\pi\)
−0.531872 + 0.846825i \(0.678511\pi\)
\(114\) 2.78725 0.261050
\(115\) −2.68771 + 0.153835i −0.250630 + 0.0143452i
\(116\) −1.25185 + 1.25185i −0.116232 + 0.116232i
\(117\) 16.3466i 1.51124i
\(118\) −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
\(125\) −11.0163 + 1.90829i −0.985326 + 0.170683i
\(126\) −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 \(0.0538720\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.59302 + 4.59302i −0.404393 + 0.404393i
\(130\) 15.0526 0.861559i 1.32020 0.0755637i
\(131\) −1.53844 1.53844i −0.134414 0.134414i 0.636698 0.771113i \(-0.280300\pi\)
−0.771113 + 0.636698i \(0.780300\pi\)
\(132\) −2.35748 2.35748i −0.205192 0.205192i
\(133\) −3.98874 −0.345868
\(134\) −6.25304 6.25304i −0.540180 0.540180i
\(135\) −6.86858 6.12488i −0.591153 0.527145i
\(136\) 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 \(-0.407482\pi\)
0.286580 + 0.958056i \(0.407482\pi\)
\(140\) −1.61589 + 1.81209i −0.136567 + 0.153150i
\(141\) 8.24684i 0.694509i
\(142\) 5.46460 0.458579
\(143\) 29.6285i 2.47766i
\(144\) 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
\(148\) 6.04973 0.633071i 0.497285 0.0520381i
\(149\) 5.18543i 0.424807i −0.977182 0.212404i \(-0.931871\pi\)
0.977182 0.212404i \(-0.0681291\pi\)
\(150\) −2.35893 + 2.97108i −0.192606 + 0.242588i
\(151\) 12.5372i 1.02026i 0.860097 + 0.510131i \(0.170403\pi\)
−0.860097 + 0.510131i \(0.829597\pi\)
\(152\) 2.59760 + 2.59760i 0.210693 + 0.210693i
\(153\) 17.8034 1.43932
\(154\) 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
\(162\) 4.15032 0.326080
\(163\) 13.0393i 1.02132i −0.859783 0.510660i \(-0.829401\pi\)
0.859783 0.510660i \(-0.170599\pi\)
\(164\) 4.07091i 0.317884i
\(165\) 5.56410 + 4.96164i 0.433165 + 0.386264i
\(166\) −0.570350 0.570350i −0.0442678 0.0442678i
\(167\) 24.6405i 1.90674i −0.301805 0.953370i \(-0.597589\pi\)
0.301805 0.953370i \(-0.402411\pi\)
\(168\) 0.823831i 0.0635599i
\(169\) 32.4645 2.49727
\(170\) −0.938340 16.3941i −0.0719674 1.25737i
\(171\) 6.29742 6.29742i 0.481576 0.481576i
\(172\) −8.56098 −0.652769
\(173\) −5.32250 + 5.32250i −0.404662 + 0.404662i −0.879872 0.475210i \(-0.842372\pi\)
0.475210 + 0.879872i \(0.342372\pi\)
\(174\) 1.34325i 0.101832i
\(175\) 3.37579 4.25182i 0.255186 0.321407i
\(176\) 4.39414i 0.331221i
\(177\) 8.16908 0.614026
\(178\) 7.54653 7.54653i 0.565637 0.565637i
\(179\) −7.93007 + 7.93007i −0.592721 + 0.592721i −0.938366 0.345644i \(-0.887660\pi\)
0.345644 + 0.938366i \(0.387660\pi\)
\(180\) −0.309770 5.41209i −0.0230889 0.403394i
\(181\) −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
\(183\) 1.22807 0.0907813
\(184\) −1.20395 −0.0887562
\(185\) −13.4246 + 2.18628i −0.986997 + 0.160739i
\(186\) 4.45144 0.326395
\(187\) −32.2690 −2.35974
\(188\) 7.68569 7.68569i 0.560537 0.560537i
\(189\) 4.46872 0.325052
\(190\) −6.13083 5.46701i −0.444777 0.396618i
\(191\) 2.08620 2.08620i 0.150952 0.150952i −0.627591 0.778543i \(-0.715959\pi\)
0.778543 + 0.627591i \(0.215959\pi\)
\(192\) 0.536506 0.536506i 0.0387190 0.0387190i
\(193\) −13.6280 −0.980961 −0.490481 0.871452i \(-0.663179\pi\)
−0.490481 + 0.871452i \(0.663179\pi\)
\(194\) 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 \(0.168080\pi\)
\(198\) −10.6528 −0.757063
\(199\) 12.1515 12.1515i 0.861395 0.861395i −0.130105 0.991500i \(-0.541531\pi\)
0.991500 + 0.130105i \(0.0415314\pi\)
\(200\) −4.96735 + 0.570497i −0.351244 + 0.0403402i
\(201\) 6.70958 0.473257
\(202\) 14.5684i 1.02503i
\(203\) 1.92228i 0.134918i
\(204\) −3.93991 3.93991i −0.275849 0.275849i
\(205\) 0.520163 + 9.08795i 0.0363298 + 0.634730i
\(206\) 10.1623i 0.708043i
\(207\) 2.91876i 0.202868i
\(208\) 6.74274 0.467525
\(209\) −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
\(217\) −6.37030 −0.432444
\(218\) 4.78437 + 4.78437i 0.324038 + 0.324038i
\(219\) 2.01897i 0.136429i
\(220\) 0.561465 + 9.80954i 0.0378539 + 0.661359i
\(221\) 49.5163i 3.33083i
\(222\) −2.90607 + 3.58536i −0.195042 + 0.240634i
\(223\) 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
\(227\) 20.1807i 1.33944i 0.742613 + 0.669721i \(0.233586\pi\)
−0.742613 + 0.669721i \(0.766414\pi\)
\(228\) −2.78725 −0.184590
\(229\) 3.02631i 0.199984i 0.994988 + 0.0999920i \(0.0318817\pi\)
−0.994988 + 0.0999920i \(0.968118\pi\)
\(230\) 2.68771 0.153835i 0.177222 0.0101436i
\(231\) −3.62003 −0.238180
\(232\) 1.25185 1.25185i 0.0821882 0.0821882i
\(233\) −4.33931 + 4.33931i −0.284278 + 0.284278i −0.834812 0.550534i \(-0.814424\pi\)
0.550534 + 0.834812i \(0.314424\pi\)
\(234\) 16.3466i 1.06861i
\(235\) −16.1756 + 18.1397i −1.05518 + 1.18330i
\(236\) 7.61323 + 7.61323i 0.495579 + 0.495579i
\(237\) −5.50801 −0.357783
\(238\) 5.63827 + 5.63827i 0.365474 + 0.365474i
\(239\) 2.92398 + 2.92398i 0.189137 + 0.189137i 0.795323 0.606186i \(-0.207301\pi\)
−0.606186 + 0.795323i \(0.707301\pi\)
\(240\) −1.12915 + 1.26626i −0.0728863 + 0.0817364i
\(241\) −14.9825 + 14.9825i −0.965105 + 0.965105i −0.999411 0.0343063i \(-0.989078\pi\)
0.0343063 + 0.999411i \(0.489078\pi\)
\(242\) 8.30847 0.534089
\(243\) −10.9572 + 10.9572i −0.702905 + 0.702905i
\(244\) 1.14451 + 1.14451i 0.0732694 + 0.0732694i
\(245\) −0.743789 12.9950i −0.0475189 0.830219i
\(246\) 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 0.936007 0.351981i \(-0.114492\pi\)
−0.351981 + 0.936007i \(0.614492\pi\)
\(252\) 1.86133 + 1.86133i 0.117253 + 0.117253i
\(253\) 5.29031i 0.332599i
\(254\) −9.21023 + 9.21023i −0.577901 + 0.577901i
\(255\) 9.29893 + 8.29208i 0.582322 + 0.519270i
\(256\) 1.00000 0.0625000
\(257\) 11.5476i 0.720317i 0.932891 + 0.360158i \(0.117277\pi\)
−0.932891 + 0.360158i \(0.882723\pi\)
\(258\) 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 −0.875602 0.483033i \(-0.839535\pi\)
0.483033 + 0.875602i \(0.339535\pi\)
\(264\) 2.35748 + 2.35748i 0.145093 + 0.145093i
\(265\) −5.47524 4.88241i −0.336342 0.299924i
\(266\) 3.98874 0.244565
\(267\) 8.09751i 0.495560i
\(268\) 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 \(0.250678\pi\)
\(272\) 7.34365i 0.445274i
\(273\) 5.55488i 0.336196i
\(274\) −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
\(277\) −12.8392 −0.771434 −0.385717 0.922617i \(-0.626046\pi\)
−0.385717 + 0.922617i \(0.626046\pi\)
\(278\) −6.75745 −0.405285
\(279\) 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 −0.0850287 0.996378i \(-0.527098\pi\)
0.996378 + 0.0850287i \(0.0270982\pi\)
\(282\) 8.24684i 0.491092i
\(283\) 20.7901i 1.23584i −0.786241 0.617920i \(-0.787975\pi\)
0.786241 0.617920i \(-0.212025\pi\)
\(284\) −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
\(288\) 2.42432i 0.142855i
\(289\) −36.9292 −2.17230
\(290\) −2.63470 + 2.95461i −0.154715 + 0.173501i
\(291\) 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
\(298\) 5.18543i 0.300384i
\(299\) 8.11790 0.469471
\(300\) 2.35893 2.97108i 0.136193 0.171536i
\(301\) −6.57291 + 6.57291i −0.378856 + 0.378856i
\(302\) 12.5372i 0.721434i
\(303\) 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 0.706694 0.707520i \(-0.250186\pi\)
−0.707520 + 0.706694i \(0.750186\pi\)
\(308\) −3.37371 3.37371i −0.192235 0.192235i
\(309\) −5.45215 5.45215i −0.310162 0.310162i
\(310\) −9.79136 8.73119i −0.556112 0.495899i
\(311\) 22.9260 + 22.9260i 1.30001 + 1.30001i 0.928379 + 0.371635i \(0.121203\pi\)
0.371635 + 0.928379i \(0.378797\pi\)
\(312\) −3.61752 + 3.61752i −0.204802 + 0.204802i
\(313\) 14.6520 0.828177 0.414089 0.910237i \(-0.364100\pi\)
0.414089 + 0.910237i \(0.364100\pi\)
\(314\) 0.530292 0.530292i 0.0299261 0.0299261i
\(315\) −4.39310 3.91743i −0.247523 0.220722i
\(316\) −5.13322 5.13322i −0.288766 0.288766i
\(317\) 14.2710 + 14.2710i 0.801537 + 0.801537i 0.983336 0.181799i \(-0.0581919\pi\)
−0.181799 + 0.983336i \(0.558192\pi\)
\(318\) −2.48921 −0.139588
\(319\) 5.50082 + 5.50082i 0.307987 + 0.307987i
\(320\) −2.23241 + 0.127776i −0.124796 + 0.00714288i
\(321\) 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
\(325\) 33.4935 3.84671i 1.85789 0.213377i
\(326\) 13.0393i 0.722183i
\(327\) −5.13368 −0.283893
\(328\) 4.07091i 0.224778i
\(329\) 11.8018i 0.650652i
\(330\) −5.56410 4.96164i −0.306294 0.273130i
\(331\) −19.0443 + 19.0443i −1.04677 + 1.04677i −0.0479194 + 0.998851i \(0.515259\pi\)
−0.998851 + 0.0479194i \(0.984741\pi\)
\(332\) 0.570350 + 0.570350i 0.0313020 + 0.0313020i
\(333\) 1.53477 + 14.6665i 0.0841048 + 0.803719i
\(334\) 24.6405i 1.34827i
\(335\) −14.7584 13.1604i −0.806336 0.719029i
\(336\) 0.823831i 0.0449436i
\(337\) −11.2643 11.2643i −0.613604 0.613604i 0.330279 0.943883i \(-0.392857\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(338\) −32.4645 −1.76584
\(339\) 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
\(347\) −2.40110 −0.128898 −0.0644489 0.997921i \(-0.520529\pi\)
−0.0644489 + 0.997921i \(0.520529\pi\)
\(348\) 1.34325i 0.0720059i
\(349\) 13.3892i 0.716708i 0.933586 + 0.358354i \(0.116662\pi\)
−0.933586 + 0.358354i \(0.883338\pi\)
\(350\) −3.37579 + 4.25182i −0.180444 + 0.227269i
\(351\) 19.6226 + 19.6226i 1.04738 + 1.04738i
\(352\) 4.39414i 0.234208i
\(353\) 7.34993i 0.391198i −0.980684 0.195599i \(-0.937335\pi\)
0.980684 0.195599i \(-0.0626650\pi\)
\(354\) −8.16908 −0.434182
\(355\) 12.1993 0.698244i 0.647470 0.0370590i
\(356\) −7.54653 + 7.54653i −0.399965 + 0.399965i
\(357\) −6.04992 −0.320196
\(358\) 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
\(362\) 4.29385 0.225680
\(363\) −4.45754 + 4.45754i −0.233960 + 0.233960i
\(364\) 5.17690 5.17690i 0.271343 0.271343i
\(365\) 3.96007 4.44092i 0.207280 0.232448i
\(366\) −1.22807 −0.0641921
\(367\) −0.833192 + 0.833192i −0.0434923 + 0.0434923i −0.728518 0.685026i \(-0.759791\pi\)
0.685026 + 0.728518i \(0.259791\pi\)
\(368\) 1.20395 0.0627601
\(369\) 9.86920 0.513770
\(370\) 13.4246 2.18628i 0.697912 0.113660i
\(371\) 3.56222 0.184941
\(372\) −4.45144 −0.230796
\(373\) 2.09090 2.09090i 0.108262 0.108262i −0.650901 0.759163i \(-0.725609\pi\)
0.759163 + 0.650901i \(0.225609\pi\)
\(374\) 32.2690 1.66859
\(375\) −4.88649 + 6.93410i −0.252337 + 0.358076i
\(376\) −7.68569 + 7.68569i −0.396359 + 0.396359i
\(377\) −8.44092 + 8.44092i −0.434729 + 0.434729i
\(378\) −4.46872 −0.229846
\(379\) 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
\(383\) −16.6051 −0.848480 −0.424240 0.905550i \(-0.639459\pi\)
−0.424240 + 0.905550i \(0.639459\pi\)
\(384\) −0.536506 + 0.536506i −0.0273784 + 0.0273784i
\(385\) 7.96259 + 7.10044i 0.405811 + 0.361872i
\(386\) 13.6280 0.693644
\(387\) 20.7546i 1.05502i
\(388\) 5.39443i 0.273861i
\(389\) 12.9306 + 12.9306i 0.655609 + 0.655609i 0.954338 0.298729i \(-0.0965627\pi\)
−0.298729 + 0.954338i \(0.596563\pi\)
\(390\) 7.61357 8.53803i 0.385528 0.432340i
\(391\) 8.84137i 0.447127i
\(392\) 5.82104i 0.294007i
\(393\) −1.65077 −0.0832702
\(394\) −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 0.655564 0.755140i \(-0.272431\pi\)
−0.755140 + 0.655564i \(0.772431\pi\)
\(398\) −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 0.257101 0.966384i \(-0.417233\pi\)
−0.966384 + 0.257101i \(0.917233\pi\)
\(402\) −6.70958 −0.334644
\(403\) −27.9726 27.9726i −1.39341 1.39341i
\(404\) 14.5684i 0.724803i
\(405\) 9.26522 0.530310i 0.460393 0.0263513i
\(406\) 1.92228i 0.0954012i
\(407\) −2.78180 26.5834i −0.137889 1.31769i
\(408\) 3.93991 + 3.93991i 0.195054 + 0.195054i
\(409\) 13.7291 13.7291i 0.678859 0.678859i −0.280883 0.959742i \(-0.590627\pi\)
0.959742 + 0.280883i \(0.0906273\pi\)
\(410\) −0.520163 9.08795i −0.0256890 0.448822i
\(411\) 12.7850i 0.630635i
\(412\) 10.1623i 0.500662i
\(413\) 11.6905 0.575251
\(414\) 2.91876i 0.143449i
\(415\) −1.34614 1.20038i −0.0660792 0.0589244i
\(416\) −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 \(-0.0837504\pi\)
\(420\) 0.105266 + 1.83913i 0.00513644 + 0.0897404i
\(421\) 21.3367 + 21.3367i 1.03989 + 1.03989i 0.999171 + 0.0407156i \(0.0129638\pi\)
0.0407156 + 0.999171i \(0.487036\pi\)
\(422\) −8.27973 −0.403051
\(423\) 18.6326 + 18.6326i 0.905948 + 0.905948i
\(424\) −2.31983 2.31983i −0.112661 0.112661i
\(425\) −4.18953 36.4784i −0.203222 1.76946i
\(426\) 2.93179 2.93179i 0.142046 0.142046i
\(427\) 1.75744 0.0850487
\(428\) −13.4161 + 13.4161i −0.648490 + 0.648490i
\(429\) −15.8959 15.8959i −0.767460 0.767460i
\(430\) −19.1117 + 1.09389i −0.921646 + 0.0527519i
\(431\) −5.16220 5.16220i −0.248655 0.248655i 0.571764 0.820418i \(-0.306259\pi\)
−0.820418 + 0.571764i \(0.806259\pi\)
\(432\) 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
\(438\) 2.01897i 0.0964701i
\(439\) −28.9545 + 28.9545i −1.38192 + 1.38192i −0.540725 + 0.841200i \(0.681850\pi\)
−0.841200 + 0.540725i \(0.818150\pi\)
\(440\) −0.561465 9.80954i −0.0267668 0.467652i
\(441\) −14.1121 −0.672005
\(442\) 49.5163i 2.35525i
\(443\) −19.2383 + 19.2383i −0.914040 + 0.914040i −0.996587 0.0825469i \(-0.973695\pi\)
0.0825469 + 0.996587i \(0.473695\pi\)
\(444\) 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 \(-0.00214374\pi\)
−0.00673470 + 0.999977i \(0.502144\pi\)
\(450\) −1.38307 12.0425i −0.0651985 0.567687i
\(451\) −17.8881 −0.842320
\(452\) 18.0037i 0.846825i
\(453\) 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
\(457\) 21.7070i 1.01541i −0.861531 0.507705i \(-0.830494\pi\)
0.861531 0.507705i \(-0.169506\pi\)
\(458\) 3.02631i 0.141410i
\(459\) 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 −0.675851 0.737039i \(-0.736224\pi\)
0.737039 + 0.675851i \(0.236224\pi\)
\(462\) 3.62003 0.168419
\(463\) −8.05167 −0.374193 −0.187096 0.982342i \(-0.559908\pi\)
−0.187096 + 0.982342i \(0.559908\pi\)
\(464\) −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
\(467\) 5.04806i 0.233596i 0.993156 + 0.116798i \(0.0372631\pi\)
−0.993156 + 0.116798i \(0.962737\pi\)
\(468\) 16.3466i 0.755621i
\(469\) 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
\(473\) 37.6182i 1.72969i
\(474\) 5.50801 0.252991
\(475\) −14.3851 11.4213i −0.660033 0.524043i
\(476\) −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 \(-0.206600\pi\)
−0.604433 + 0.796656i \(0.706600\pi\)
\(480\) 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
\(483\) 0.991849i 0.0451307i
\(484\) −8.30847 −0.377658
\(485\) −0.689278 12.0426i −0.0312985 0.546826i
\(486\) 10.9572 10.9572i 0.497029 0.497029i
\(487\) 23.0440i 1.04422i 0.852877 + 0.522111i \(0.174855\pi\)
−0.852877 + 0.522111i \(0.825145\pi\)
\(488\) −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
\(495\) −23.7815 + 1.36117i −1.06890 + 0.0611801i
\(496\) −4.14855 4.14855i −0.186275 0.186275i
\(497\) −4.19558 + 4.19558i −0.188198 + 0.188198i
\(498\) −0.611992 −0.0274240
\(499\) −3.14878 + 3.14878i −0.140959 + 0.140959i −0.774065 0.633106i \(-0.781780\pi\)
0.633106 + 0.774065i \(0.281780\pi\)
\(500\) −11.0163 + 1.90829i −0.492663 + 0.0853414i
\(501\) −13.2198 13.2198i −0.590616 0.590616i
\(502\) −9.25271 9.25271i −0.412969 0.412969i
\(503\) 38.5464 1.71870 0.859349 0.511390i \(-0.170869\pi\)
0.859349 + 0.511390i \(0.170869\pi\)
\(504\) −1.86133 1.86133i −0.0829104 0.0829104i
\(505\) −1.86148 32.5226i −0.0828350 1.44724i
\(506\) 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 \(-0.367684\pi\)
0.403814 + 0.914841i \(0.367684\pi\)
\(510\) −9.29893 8.29208i −0.411764 0.367180i
\(511\) 2.88928i 0.127814i
\(512\) −1.00000 −0.0441942
\(513\) 15.1190i 0.667518i
\(514\) 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
\(518\) −4.15877 + 5.13088i −0.182726 + 0.225438i
\(519\) 5.71110i 0.250689i
\(520\) 15.0526 0.861559i 0.660100 0.0377819i
\(521\) 8.10778i 0.355208i 0.984102 + 0.177604i \(0.0568347\pi\)
−0.984102 + 0.177604i \(0.943165\pi\)
\(522\) 3.03490 + 3.03490i 0.132834 + 0.132834i
\(523\) 9.18819 0.401772 0.200886 0.979615i \(-0.435618\pi\)
0.200886 + 0.979615i \(0.435618\pi\)
\(524\) −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
\(532\) −3.98874 −0.172934
\(533\) 27.4491i 1.18895i
\(534\) 8.09751i 0.350414i
\(535\) 28.2360 31.6644i 1.22075 1.36897i
\(536\) −6.25304 6.25304i −0.270090 0.270090i
\(537\) 8.50905i 0.367193i
\(538\) 3.72238i 0.160483i
\(539\) 25.5785 1.10174
\(540\) −6.86858 6.12488i −0.295577 0.263573i
\(541\) −14.3951 + 14.3951i −0.618893 + 0.618893i −0.945247 0.326355i \(-0.894180\pi\)
0.326355 + 0.945247i \(0.394180\pi\)
\(542\) −23.2312 −0.997867
\(543\) −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
\(547\) 3.07074 0.131295 0.0656477 0.997843i \(-0.479089\pi\)
0.0656477 + 0.997843i \(0.479089\pi\)
\(548\) 11.9150 11.9150i 0.508985 0.508985i
\(549\) −2.77465 + 2.77465i −0.118419 + 0.118419i
\(550\) 2.50684 + 21.8272i 0.106892 + 0.930716i
\(551\) 6.50362 0.277064
\(552\) −0.645925 + 0.645925i −0.0274924 + 0.0274924i
\(553\) −7.88232 −0.335190
\(554\) 12.8392 0.545486
\(555\) −6.02942 + 8.37533i −0.255935 + 0.355513i
\(556\) 6.75745 0.286580
\(557\) 33.2382 1.40835 0.704173 0.710028i \(-0.251318\pi\)
0.704173 + 0.710028i \(0.251318\pi\)
\(558\) −10.0574 + 10.0574i −0.425765 + 0.425765i
\(559\) −57.7245 −2.44149
\(560\) −1.61589 + 1.81209i −0.0682837 + 0.0765749i
\(561\) −17.3125 + 17.3125i −0.730935 + 0.730935i
\(562\) −15.2770 + 15.2770i −0.644422 + 0.644422i
\(563\) 34.1847 1.44071 0.720356 0.693605i \(-0.243979\pi\)
0.720356 + 0.693605i \(0.243979\pi\)
\(564\) 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
\(568\) 5.46460 0.229290
\(569\) −29.8527 + 29.8527i −1.25149 + 1.25149i −0.296438 + 0.955052i \(0.595799\pi\)
−0.955052 + 0.296438i \(0.904201\pi\)
\(570\) −6.22230 + 0.356143i −0.260624 + 0.0149172i
\(571\) −18.1250 −0.758508 −0.379254 0.925293i \(-0.623819\pi\)
−0.379254 + 0.925293i \(0.623819\pi\)
\(572\) 29.6285i 1.23883i
\(573\) 2.23851i 0.0935152i
\(574\) 3.12554 + 3.12554i 0.130457 + 0.130457i
\(575\) 5.98042 0.686848i 0.249401 0.0286436i
\(576\) 2.42432i 0.101013i
\(577\) 14.6571i 0.610182i 0.952323 + 0.305091i \(0.0986868\pi\)
−0.952323 + 0.305091i \(0.901313\pi\)
\(578\) 36.9292 1.53605
\(579\) −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
\(587\) 2.78069 0.114772 0.0573858 0.998352i \(-0.481724\pi\)
0.0573858 + 0.998352i \(0.481724\pi\)
\(588\) 3.12302 + 3.12302i 0.128791 + 0.128791i
\(589\) 21.5525i 0.888056i
\(590\) 17.9687 + 16.0231i 0.739758 + 0.659660i
\(591\) 5.42111i 0.222995i
\(592\) 6.04973 0.633071i 0.248642 0.0260190i
\(593\) 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
\(597\) 13.0387i 0.533637i
\(598\) −8.11790 −0.331966
\(599\) 8.57057i 0.350184i −0.984552 0.175092i \(-0.943978\pi\)
0.984552 0.175092i \(-0.0560223\pi\)
\(600\) −2.35893 + 2.97108i −0.0963031 + 0.121294i
\(601\) −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
\(605\) 18.5480 1.06162i 0.754081 0.0431611i
\(606\) −7.81601 7.81601i −0.317504 0.317504i
\(607\) 36.4725 1.48037 0.740186 0.672403i \(-0.234738\pi\)
0.740186 + 0.672403i \(0.234738\pi\)
\(608\) 2.59760 + 2.59760i 0.105347 + 0.105347i
\(609\) 1.03131 + 1.03131i 0.0417910 + 0.0417910i
\(610\) 2.70125 + 2.40877i 0.109370 + 0.0975282i
\(611\) 51.8226 51.8226i 2.09652 2.09652i
\(612\) 17.8034 0.719659
\(613\) −3.07671 + 3.07671i −0.124267 + 0.124267i −0.766505 0.642238i \(-0.778006\pi\)
0.642238 + 0.766505i \(0.278006\pi\)
\(614\) 0.0144735 + 0.0144735i 0.000584104 + 0.000584104i
\(615\) 5.15481 + 4.59667i 0.207862 + 0.185355i
\(616\) 3.37371 + 3.37371i 0.135931 + 0.135931i
\(617\) 6.95912 + 6.95912i 0.280164 + 0.280164i 0.833174 0.553011i \(-0.186521\pi\)
−0.553011 + 0.833174i \(0.686521\pi\)
\(618\) 5.45215 + 5.45215i 0.219318 + 0.219318i
\(619\) −28.9801 −1.16481 −0.582405 0.812899i \(-0.697888\pi\)
−0.582405 + 0.812899i \(0.697888\pi\)
\(620\) 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
\(623\) 11.5881i 0.464266i
\(624\) 3.61752 3.61752i 0.144817 0.144817i
\(625\) 24.3491 5.66771i 0.973963 0.226708i
\(626\) −14.6520 −0.585610
\(627\) 12.2476i 0.489121i
\(628\) −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 0.515358 0.856975i \(-0.327659\pi\)
−0.856975 + 0.515358i \(0.827659\pi\)
\(632\) 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
\(635\) −19.3842 + 21.7379i −0.769238 + 0.862642i
\(636\) 2.48921 0.0987034
\(637\) 39.2498i 1.55513i
\(638\) −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 \(0.787430\pi\)
\(642\) 14.3956i 0.568148i
\(643\) 0.0494458i 0.00194995i 1.00000 0.000974976i \(0.000310345\pi\)
−1.00000 0.000974976i \(0.999690\pi\)
\(644\) 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
\(647\) −20.0867 −0.789689 −0.394844 0.918748i \(-0.629202\pi\)
−0.394844 + 0.918748i \(0.629202\pi\)
\(648\) 4.15032 0.163040
\(649\) 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
\(652\) 13.0393i 0.510660i
\(653\) 2.91044i 0.113894i 0.998377 + 0.0569471i \(0.0181366\pi\)
−0.998377 + 0.0569471i \(0.981863\pi\)
\(654\) 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
\(658\) 11.8018i 0.460080i
\(659\) −18.9341 −0.737568 −0.368784 0.929515i \(-0.620226\pi\)
−0.368784 + 0.929515i \(0.620226\pi\)
\(660\) 5.56410 + 4.96164i 0.216582 + 0.193132i
\(661\) −14.8550 14.8550i −0.577792 0.577792i 0.356502 0.934294i \(-0.383969\pi\)
−0.934294 + 0.356502i \(0.883969\pi\)
\(662\) 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
\(668\) 24.6405i 0.953370i
\(669\) 10.0377 0.388079
\(670\) 14.7584 + 13.1604i 0.570165 + 0.508430i
\(671\) 5.02912 5.02912i 0.194147 0.194147i
\(672\) 0.823831i 0.0317800i
\(673\) −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 0.940536 0.339695i \(-0.110324\pi\)
−0.339695 + 0.940536i \(0.610324\pi\)
\(678\) −9.65911 9.65911i −0.370956 0.370956i
\(679\) 4.14171 + 4.14171i 0.158944 + 0.158944i
\(680\) −0.938340 16.3941i −0.0359837 0.628684i
\(681\) 10.8271 + 10.8271i 0.414895 + 0.414895i
\(682\) 18.2293 18.2293i 0.698036 0.698036i
\(683\) −2.66101 −0.101821 −0.0509104 0.998703i \(-0.516212\pi\)
−0.0509104 + 0.998703i \(0.516212\pi\)
\(684\) 6.29742 6.29742i 0.240788 0.240788i
\(685\) −25.0768 + 28.1217i −0.958136 + 1.07448i
\(686\) −9.84367 9.84367i −0.375833 0.375833i
\(687\) 1.62363 + 1.62363i 0.0619454 + 0.0619454i
\(688\) −8.56098 −0.326384
\(689\) 15.6420 + 15.6420i 0.595914 + 0.595914i
\(690\) 1.35944 1.52450i 0.0517529 0.0580369i
\(691\) 6.84103i 0.260245i 0.991498 + 0.130123i \(0.0415371\pi\)
−0.991498 + 0.130123i \(0.958463\pi\)
\(692\) −5.32250 + 5.32250i −0.202331 + 0.202331i
\(693\) 8.17896 8.17896i 0.310693 0.310693i
\(694\) 2.40110 0.0911445
\(695\) −15.0854 + 0.863438i −0.572223 + 0.0327521i
\(696\) 1.34325i 0.0509158i
\(697\) −29.8953 −1.13237
\(698\) 13.3892i 0.506789i
\(699\) 4.65613i 0.176111i
\(700\) 3.37579 4.25182i 0.127593 0.160704i
\(701\) −15.1890 + 15.1890i −0.573682 + 0.573682i −0.933155 0.359473i \(-0.882956\pi\)
0.359473 + 0.933155i \(0.382956\pi\)
\(702\) −19.6226 19.6226i −0.740607 0.740607i
\(703\) −17.3592 14.0703i −0.654716 0.530672i
\(704\) 4.39414i 0.165610i
\(705\) 1.05375 + 18.4104i 0.0396864 + 0.693374i
\(706\) 7.34993i 0.276618i
\(707\) 11.1852 + 11.1852i 0.420663 + 0.420663i
\(708\) 8.16908 0.307013
\(709\) 13.9085 + 13.9085i 0.522343 + 0.522343i 0.918278 0.395935i \(-0.129580\pi\)
−0.395935 + 0.918278i \(0.629580\pi\)
\(710\) −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
\(717\) 3.13746 0.117171
\(718\) 24.0685i 0.898228i
\(719\) 23.7742i 0.886629i −0.896366 0.443314i \(-0.853803\pi\)
0.896366 0.443314i \(-0.146197\pi\)
\(720\) −0.309770 5.41209i −0.0115444 0.201697i
\(721\) −7.80238 7.80238i −0.290576 0.290576i
\(722\) 5.50496i 0.204874i
\(723\) 16.0763i 0.597886i
\(724\) −4.29385 −0.159580
\(725\) −5.50421 + 6.93257i −0.204421 + 0.257469i
\(726\) 4.45754 4.45754i 0.165435 0.165435i
\(727\) −0.783597 −0.0290620 −0.0145310 0.999894i \(-0.504626\pi\)
−0.0145310 + 0.999894i \(0.504626\pi\)
\(728\) −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
\(732\) 1.22807 0.0453907
\(733\) 8.72850 8.72850i 0.322395 0.322395i −0.527291 0.849685i \(-0.676792\pi\)
0.849685 + 0.527291i \(0.176792\pi\)
\(734\) 0.833192 0.833192i 0.0307537 0.0307537i
\(735\) −7.37093 6.57283i −0.271881 0.242443i
\(736\) −1.20395 −0.0443781
\(737\) 27.4767 27.4767i 1.01212 1.01212i
\(738\) −9.86920 −0.363290
\(739\) −11.2844 −0.415102 −0.207551 0.978224i \(-0.566549\pi\)
−0.207551 + 0.978224i \(0.566549\pi\)
\(740\) −13.4246 + 2.18628i −0.493498 + 0.0803694i
\(741\) −18.7937 −0.690404
\(742\) −3.56222 −0.130773
\(743\) 11.8850 11.8850i 0.436018 0.436018i −0.454652 0.890669i \(-0.650236\pi\)
0.890669 + 0.454652i \(0.150236\pi\)
\(744\) 4.45144 0.163198
\(745\) 0.662573 + 11.5760i 0.0242748 + 0.424113i
\(746\) −2.09090 + 2.09090i −0.0765531 + 0.0765531i
\(747\) −1.38271 + 1.38271i −0.0505909 + 0.0505909i
\(748\) −32.2690 −1.17987
\(749\) 20.6010i 0.752745i
\(750\) 4.88649 6.93410i 0.178429 0.253198i
\(751\) 18.7371i 0.683727i −0.939750 0.341864i \(-0.888942\pi\)
0.939750 0.341864i \(-0.111058\pi\)
\(752\) 7.68569 7.68569i 0.280268 0.280268i
\(753\) 9.92826 0.361806
\(754\) 8.44092 8.44092i 0.307400 0.307400i
\(755\) −1.60195 27.9882i −0.0583009 1.01859i
\(756\) 4.46872 0.162526
\(757\) 5.00038i 0.181742i 0.995863 + 0.0908710i \(0.0289651\pi\)
−0.995863 + 0.0908710i \(0.971035\pi\)
\(758\) 4.36102i 0.158399i
\(759\) −2.83828 2.83828i −0.103023 0.103023i
\(760\) −6.13083 5.46701i −0.222388 0.198309i
\(761\) 9.44966i 0.342550i 0.985223 + 0.171275i \(0.0547887\pi\)
−0.985223 + 0.171275i \(0.945211\pi\)
\(762\) 9.88267i 0.358012i
\(763\) −7.34663 −0.265966
\(764\) 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 \(-0.655644\pi\)
0.882817 + 0.469717i \(0.155644\pi\)
\(770\) −7.96259 7.10044i −0.286952 0.255882i
\(771\) 6.19533 + 6.19533i 0.223119 + 0.223119i
\(772\) −13.6280 −0.490481
\(773\) 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
\(775\) −22.9740 18.2405i −0.825251 0.655220i
\(776\) 5.39443i 0.193649i
\(777\) −0.521543 4.98395i −0.0187102 0.178798i