Properties

Label 570.2.m.b.37.2
Level $570$
Weight $2$
Character 570.37
Analytic conductor $4.551$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 108 x^{16} + 1318 x^{12} + 4652 x^{8} + 5057 x^{4} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.2
Root \(2.20512 - 2.20512i\) of defining polynomial
Character \(\chi\) \(=\) 570.37
Dual form 570.2.m.b.493.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(0.114611 - 2.23313i) q^{5} -1.00000 q^{6} +(-1.40368 - 1.40368i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(0.114611 - 2.23313i) q^{5} -1.00000 q^{6} +(-1.40368 - 1.40368i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(1.49802 + 1.66010i) q^{10} -5.29298 q^{11} +(0.707107 - 0.707107i) q^{12} +(-1.91968 - 1.91968i) q^{13} +1.98511 q^{14} +(1.66010 - 1.49802i) q^{15} -1.00000 q^{16} +(0.488117 + 0.488117i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-2.44789 - 3.60663i) q^{19} +(-2.23313 - 0.114611i) q^{20} -1.98511i q^{21} +(3.74270 - 3.74270i) q^{22} +(-3.88930 + 3.88930i) q^{23} +1.00000i q^{24} +(-4.97373 - 0.511883i) q^{25} +2.71483 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.40368 + 1.40368i) q^{28} -6.19060 q^{29} +(-0.114611 + 2.23313i) q^{30} +7.84986i q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.74270 - 3.74270i) q^{33} -0.690302 q^{34} +(-3.29548 + 2.97373i) q^{35} +1.00000 q^{36} +(5.60602 - 5.60602i) q^{37} +(4.28120 + 0.819353i) q^{38} -2.71483i q^{39} +(1.66010 - 1.49802i) q^{40} -1.90599i q^{41} +(1.40368 + 1.40368i) q^{42} +(7.12884 - 7.12884i) q^{43} +5.29298i q^{44} +(2.23313 + 0.114611i) q^{45} -5.50029i q^{46} +(-7.86994 - 7.86994i) q^{47} +(-0.707107 - 0.707107i) q^{48} -3.05934i q^{49} +(3.87891 - 3.15500i) q^{50} +0.690302i q^{51} +(-1.91968 + 1.91968i) q^{52} +(8.93991 + 8.93991i) q^{53} -1.00000i q^{54} +(-0.606635 + 11.8199i) q^{55} -1.98511i q^{56} +(0.819353 - 4.28120i) q^{57} +(4.37741 - 4.37741i) q^{58} -0.611185 q^{59} +(-1.49802 - 1.66010i) q^{60} +8.31021 q^{61} +(-5.55069 - 5.55069i) q^{62} +(1.40368 - 1.40368i) q^{63} +1.00000i q^{64} +(-4.50690 + 4.06687i) q^{65} +5.29298 q^{66} +(10.2011 - 10.2011i) q^{67} +(0.488117 - 0.488117i) q^{68} -5.50029 q^{69} +(0.227516 - 4.43300i) q^{70} +3.97022i q^{71} +(-0.707107 + 0.707107i) q^{72} +(7.72265 - 7.72265i) q^{73} +7.92810i q^{74} +(-3.15500 - 3.87891i) q^{75} +(-3.60663 + 2.44789i) q^{76} +(7.42967 + 7.42967i) q^{77} +(1.91968 + 1.91968i) q^{78} -17.1528 q^{79} +(-0.114611 + 2.23313i) q^{80} -1.00000 q^{81} +(1.34774 + 1.34774i) q^{82} +(5.43217 - 5.43217i) q^{83} -1.98511 q^{84} +(1.14597 - 1.03408i) q^{85} +10.0817i q^{86} +(-4.37741 - 4.37741i) q^{87} +(-3.74270 - 3.74270i) q^{88} +5.42118 q^{89} +(-1.66010 + 1.49802i) q^{90} +5.38924i q^{91} +(3.88930 + 3.88930i) q^{92} +(-5.55069 + 5.55069i) q^{93} +11.1298 q^{94} +(-8.33464 + 5.05310i) q^{95} +1.00000 q^{96} +(-3.10415 + 3.10415i) q^{97} +(2.16328 + 2.16328i) q^{98} -5.29298i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 12q^{5} - 20q^{6} - 4q^{7} + O(q^{10}) \) \( 20q + 12q^{5} - 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} - 12q^{17} - 4q^{23} - 28q^{25} + 24q^{26} - 4q^{28} - 12q^{30} + 4q^{35} + 20q^{36} - 12q^{38} + 4q^{42} - 12q^{43} - 44q^{47} + 64q^{55} + 12q^{57} - 8q^{58} - 24q^{62} + 4q^{63} + 8q^{66} - 12q^{68} - 4q^{73} + 4q^{76} + 88q^{77} - 12q^{80} - 20q^{81} - 8q^{82} + 76q^{83} - 12q^{85} + 8q^{87} + 4q^{92} - 24q^{93} - 24q^{95} + 20q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 0.114611 2.23313i 0.0512557 0.998686i
\(6\) −1.00000 −0.408248
\(7\) −1.40368 1.40368i −0.530543 0.530543i 0.390191 0.920734i \(-0.372409\pi\)
−0.920734 + 0.390191i \(0.872409\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 1.49802 + 1.66010i 0.473715 + 0.524971i
\(11\) −5.29298 −1.59589 −0.797947 0.602728i \(-0.794080\pi\)
−0.797947 + 0.602728i \(0.794080\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) −1.91968 1.91968i −0.532423 0.532423i 0.388870 0.921293i \(-0.372866\pi\)
−0.921293 + 0.388870i \(0.872866\pi\)
\(14\) 1.98511 0.530543
\(15\) 1.66010 1.49802i 0.428637 0.386787i
\(16\) −1.00000 −0.250000
\(17\) 0.488117 + 0.488117i 0.118386 + 0.118386i 0.763818 0.645432i \(-0.223323\pi\)
−0.645432 + 0.763818i \(0.723323\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) −2.44789 3.60663i −0.561585 0.827419i
\(20\) −2.23313 0.114611i −0.499343 0.0256278i
\(21\) 1.98511i 0.433186i
\(22\) 3.74270 3.74270i 0.797947 0.797947i
\(23\) −3.88930 + 3.88930i −0.810974 + 0.810974i −0.984780 0.173806i \(-0.944393\pi\)
0.173806 + 0.984780i \(0.444393\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −4.97373 0.511883i −0.994746 0.102377i
\(26\) 2.71483 0.532423
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) −1.40368 + 1.40368i −0.265271 + 0.265271i
\(29\) −6.19060 −1.14956 −0.574782 0.818306i \(-0.694913\pi\)
−0.574782 + 0.818306i \(0.694913\pi\)
\(30\) −0.114611 + 2.23313i −0.0209250 + 0.407712i
\(31\) 7.84986i 1.40988i 0.709268 + 0.704938i \(0.249025\pi\)
−0.709268 + 0.704938i \(0.750975\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −3.74270 3.74270i −0.651521 0.651521i
\(34\) −0.690302 −0.118386
\(35\) −3.29548 + 2.97373i −0.557039 + 0.502652i
\(36\) 1.00000 0.166667
\(37\) 5.60602 5.60602i 0.921623 0.921623i −0.0755209 0.997144i \(-0.524062\pi\)
0.997144 + 0.0755209i \(0.0240620\pi\)
\(38\) 4.28120 + 0.819353i 0.694502 + 0.132917i
\(39\) 2.71483i 0.434721i
\(40\) 1.66010 1.49802i 0.262485 0.236857i
\(41\) 1.90599i 0.297666i −0.988862 0.148833i \(-0.952448\pi\)
0.988862 0.148833i \(-0.0475517\pi\)
\(42\) 1.40368 + 1.40368i 0.216593 + 0.216593i
\(43\) 7.12884 7.12884i 1.08714 1.08714i 0.0913152 0.995822i \(-0.470893\pi\)
0.995822 0.0913152i \(-0.0291071\pi\)
\(44\) 5.29298i 0.797947i
\(45\) 2.23313 + 0.114611i 0.332895 + 0.0170852i
\(46\) 5.50029i 0.810974i
\(47\) −7.86994 7.86994i −1.14795 1.14795i −0.986955 0.160993i \(-0.948530\pi\)
−0.160993 0.986955i \(-0.551470\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 3.05934i 0.437049i
\(50\) 3.87891 3.15500i 0.548561 0.446185i
\(51\) 0.690302i 0.0966616i
\(52\) −1.91968 + 1.91968i −0.266211 + 0.266211i
\(53\) 8.93991 + 8.93991i 1.22799 + 1.22799i 0.964723 + 0.263268i \(0.0848003\pi\)
0.263268 + 0.964723i \(0.415200\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −0.606635 + 11.8199i −0.0817986 + 1.59380i
\(56\) 1.98511i 0.265271i
\(57\) 0.819353 4.28120i 0.108526 0.567059i
\(58\) 4.37741 4.37741i 0.574782 0.574782i
\(59\) −0.611185 −0.0795696 −0.0397848 0.999208i \(-0.512667\pi\)
−0.0397848 + 0.999208i \(0.512667\pi\)
\(60\) −1.49802 1.66010i −0.193393 0.214318i
\(61\) 8.31021 1.06401 0.532007 0.846740i \(-0.321438\pi\)
0.532007 + 0.846740i \(0.321438\pi\)
\(62\) −5.55069 5.55069i −0.704938 0.704938i
\(63\) 1.40368 1.40368i 0.176848 0.176848i
\(64\) 1.00000i 0.125000i
\(65\) −4.50690 + 4.06687i −0.559013 + 0.504433i
\(66\) 5.29298 0.651521
\(67\) 10.2011 10.2011i 1.24626 1.24626i 0.288905 0.957358i \(-0.406709\pi\)
0.957358 0.288905i \(-0.0932913\pi\)
\(68\) 0.488117 0.488117i 0.0591929 0.0591929i
\(69\) −5.50029 −0.662158
\(70\) 0.227516 4.43300i 0.0271933 0.529845i
\(71\) 3.97022i 0.471178i 0.971853 + 0.235589i \(0.0757019\pi\)
−0.971853 + 0.235589i \(0.924298\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) 7.72265 7.72265i 0.903867 0.903867i −0.0919007 0.995768i \(-0.529294\pi\)
0.995768 + 0.0919007i \(0.0292942\pi\)
\(74\) 7.92810i 0.921623i
\(75\) −3.15500 3.87891i −0.364308 0.447898i
\(76\) −3.60663 + 2.44789i −0.413709 + 0.280793i
\(77\) 7.42967 + 7.42967i 0.846689 + 0.846689i
\(78\) 1.91968 + 1.91968i 0.217361 + 0.217361i
\(79\) −17.1528 −1.92984 −0.964918 0.262550i \(-0.915437\pi\)
−0.964918 + 0.262550i \(0.915437\pi\)
\(80\) −0.114611 + 2.23313i −0.0128139 + 0.249671i
\(81\) −1.00000 −0.111111
\(82\) 1.34774 + 1.34774i 0.148833 + 0.148833i
\(83\) 5.43217 5.43217i 0.596258 0.596258i −0.343056 0.939315i \(-0.611462\pi\)
0.939315 + 0.343056i \(0.111462\pi\)
\(84\) −1.98511 −0.216593
\(85\) 1.14597 1.03408i 0.124298 0.112162i
\(86\) 10.0817i 1.08714i
\(87\) −4.37741 4.37741i −0.469308 0.469308i
\(88\) −3.74270 3.74270i −0.398973 0.398973i
\(89\) 5.42118 0.574644 0.287322 0.957834i \(-0.407235\pi\)
0.287322 + 0.957834i \(0.407235\pi\)
\(90\) −1.66010 + 1.49802i −0.174990 + 0.157905i
\(91\) 5.38924i 0.564946i
\(92\) 3.88930 + 3.88930i 0.405487 + 0.405487i
\(93\) −5.55069 + 5.55069i −0.575580 + 0.575580i
\(94\) 11.1298 1.14795
\(95\) −8.33464 + 5.05310i −0.855116 + 0.518437i
\(96\) 1.00000 0.102062
\(97\) −3.10415 + 3.10415i −0.315178 + 0.315178i −0.846912 0.531734i \(-0.821541\pi\)
0.531734 + 0.846912i \(0.321541\pi\)
\(98\) 2.16328 + 2.16328i 0.218525 + 0.218525i
\(99\) 5.29298i 0.531964i
\(100\) −0.511883 + 4.97373i −0.0511883 + 0.497373i
\(101\) −2.79454 −0.278067 −0.139034 0.990288i \(-0.544400\pi\)
−0.139034 + 0.990288i \(0.544400\pi\)
\(102\) −0.488117 0.488117i −0.0483308 0.0483308i
\(103\) −4.05319 4.05319i −0.399372 0.399372i 0.478639 0.878012i \(-0.341130\pi\)
−0.878012 + 0.478639i \(0.841130\pi\)
\(104\) 2.71483i 0.266211i
\(105\) −4.43300 0.227516i −0.432617 0.0222033i
\(106\) −12.6429 −1.22799
\(107\) −7.04015 + 7.04015i −0.680597 + 0.680597i −0.960135 0.279537i \(-0.909819\pi\)
0.279537 + 0.960135i \(0.409819\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) −8.64011 −0.827573 −0.413786 0.910374i \(-0.635794\pi\)
−0.413786 + 0.910374i \(0.635794\pi\)
\(110\) −7.92898 8.78689i −0.755998 0.837797i
\(111\) 7.92810 0.752502
\(112\) 1.40368 + 1.40368i 0.132636 + 0.132636i
\(113\) −6.47280 6.47280i −0.608910 0.608910i 0.333751 0.942661i \(-0.391685\pi\)
−0.942661 + 0.333751i \(0.891685\pi\)
\(114\) 2.44789 + 3.60663i 0.229266 + 0.337792i
\(115\) 8.23954 + 9.13105i 0.768341 + 0.851475i
\(116\) 6.19060i 0.574782i
\(117\) 1.91968 1.91968i 0.177474 0.177474i
\(118\) 0.432173 0.432173i 0.0397848 0.0397848i
\(119\) 1.37032i 0.125617i
\(120\) 2.23313 + 0.114611i 0.203856 + 0.0104625i
\(121\) 17.0156 1.54688
\(122\) −5.87621 + 5.87621i −0.532007 + 0.532007i
\(123\) 1.34774 1.34774i 0.121522 0.121522i
\(124\) 7.84986 0.704938
\(125\) −1.71315 + 11.0483i −0.153228 + 0.988191i
\(126\) 1.98511i 0.176848i
\(127\) −1.33748 + 1.33748i −0.118683 + 0.118683i −0.763954 0.645271i \(-0.776744\pi\)
0.645271 + 0.763954i \(0.276744\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 10.0817 0.887644
\(130\) 0.311150 6.06257i 0.0272897 0.531723i
\(131\) 5.33670 0.466269 0.233135 0.972444i \(-0.425102\pi\)
0.233135 + 0.972444i \(0.425102\pi\)
\(132\) −3.74270 + 3.74270i −0.325760 + 0.325760i
\(133\) −1.62650 + 8.49864i −0.141036 + 0.736926i
\(134\) 14.4265i 1.24626i
\(135\) 1.49802 + 1.66010i 0.128929 + 0.142879i
\(136\) 0.690302i 0.0591929i
\(137\) −2.97373 2.97373i −0.254063 0.254063i 0.568571 0.822634i \(-0.307496\pi\)
−0.822634 + 0.568571i \(0.807496\pi\)
\(138\) 3.88930 3.88930i 0.331079 0.331079i
\(139\) 13.8993i 1.17892i 0.807796 + 0.589462i \(0.200660\pi\)
−0.807796 + 0.589462i \(0.799340\pi\)
\(140\) 2.97373 + 3.29548i 0.251326 + 0.278519i
\(141\) 11.1298i 0.937296i
\(142\) −2.80737 2.80737i −0.235589 0.235589i
\(143\) 10.1608 + 10.1608i 0.849690 + 0.849690i
\(144\) 1.00000i 0.0833333i
\(145\) −0.709511 + 13.8244i −0.0589217 + 1.14805i
\(146\) 10.9215i 0.903867i
\(147\) 2.16328 2.16328i 0.178425 0.178425i
\(148\) −5.60602 5.60602i −0.460812 0.460812i
\(149\) 12.9453i 1.06052i −0.847834 0.530262i \(-0.822094\pi\)
0.847834 0.530262i \(-0.177906\pi\)
\(150\) 4.97373 + 0.511883i 0.406103 + 0.0417951i
\(151\) 21.7518i 1.77013i 0.465465 + 0.885066i \(0.345887\pi\)
−0.465465 + 0.885066i \(0.654113\pi\)
\(152\) 0.819353 4.28120i 0.0664583 0.347251i
\(153\) −0.488117 + 0.488117i −0.0394619 + 0.0394619i
\(154\) −10.5071 −0.846689
\(155\) 17.5298 + 0.899682i 1.40802 + 0.0722642i
\(156\) −2.71483 −0.217361
\(157\) 2.34642 + 2.34642i 0.187264 + 0.187264i 0.794512 0.607248i \(-0.207727\pi\)
−0.607248 + 0.794512i \(0.707727\pi\)
\(158\) 12.1288 12.1288i 0.964918 0.964918i
\(159\) 12.6429i 1.00265i
\(160\) −1.49802 1.66010i −0.118429 0.131243i
\(161\) 10.9187 0.860513
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) −14.1411 + 14.1411i −1.10761 + 1.10761i −0.114150 + 0.993464i \(0.536414\pi\)
−0.993464 + 0.114150i \(0.963586\pi\)
\(164\) −1.90599 −0.148833
\(165\) −8.78689 + 7.92898i −0.684058 + 0.617270i
\(166\) 7.68225i 0.596258i
\(167\) 9.19018 9.19018i 0.711157 0.711157i −0.255620 0.966777i \(-0.582280\pi\)
0.966777 + 0.255620i \(0.0822797\pi\)
\(168\) 1.40368 1.40368i 0.108297 0.108297i
\(169\) 5.62968i 0.433052i
\(170\) −0.0791163 + 1.54153i −0.00606794 + 0.118230i
\(171\) 3.60663 2.44789i 0.275806 0.187195i
\(172\) −7.12884 7.12884i −0.543569 0.543569i
\(173\) 2.10806 + 2.10806i 0.160273 + 0.160273i 0.782688 0.622415i \(-0.213848\pi\)
−0.622415 + 0.782688i \(0.713848\pi\)
\(174\) 6.19060 0.469308
\(175\) 6.26302 + 7.70006i 0.473440 + 0.582070i
\(176\) 5.29298 0.398973
\(177\) −0.432173 0.432173i −0.0324841 0.0324841i
\(178\) −3.83335 + 3.83335i −0.287322 + 0.287322i
\(179\) −7.93836 −0.593341 −0.296670 0.954980i \(-0.595876\pi\)
−0.296670 + 0.954980i \(0.595876\pi\)
\(180\) 0.114611 2.23313i 0.00854261 0.166448i
\(181\) 4.77157i 0.354668i −0.984151 0.177334i \(-0.943253\pi\)
0.984151 0.177334i \(-0.0567473\pi\)
\(182\) −3.81077 3.81077i −0.282473 0.282473i
\(183\) 5.87621 + 5.87621i 0.434382 + 0.434382i
\(184\) −5.50029 −0.405487
\(185\) −11.8764 13.1615i −0.873173 0.967650i
\(186\) 7.84986i 0.575580i
\(187\) −2.58359 2.58359i −0.188931 0.188931i
\(188\) −7.86994 + 7.86994i −0.573974 + 0.573974i
\(189\) 1.98511 0.144395
\(190\) 2.32039 9.46656i 0.168339 0.686776i
\(191\) −13.8711 −1.00368 −0.501840 0.864961i \(-0.667343\pi\)
−0.501840 + 0.864961i \(0.667343\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) −8.22061 8.22061i −0.591733 0.591733i 0.346367 0.938099i \(-0.387415\pi\)
−0.938099 + 0.346367i \(0.887415\pi\)
\(194\) 4.38992i 0.315178i
\(195\) −6.06257 0.311150i −0.434150 0.0222819i
\(196\) −3.05934 −0.218525
\(197\) −0.844893 0.844893i −0.0601961 0.0601961i 0.676368 0.736564i \(-0.263553\pi\)
−0.736564 + 0.676368i \(0.763553\pi\)
\(198\) 3.74270 + 3.74270i 0.265982 + 0.265982i
\(199\) 17.2265i 1.22116i −0.791956 0.610578i \(-0.790937\pi\)
0.791956 0.610578i \(-0.209063\pi\)
\(200\) −3.15500 3.87891i −0.223092 0.274281i
\(201\) 14.4265 1.01757
\(202\) 1.97604 1.97604i 0.139034 0.139034i
\(203\) 8.68964 + 8.68964i 0.609893 + 0.609893i
\(204\) 0.690302 0.0483308
\(205\) −4.25633 0.218448i −0.297275 0.0152571i
\(206\) 5.73207 0.399372
\(207\) −3.88930 3.88930i −0.270325 0.270325i
\(208\) 1.91968 + 1.91968i 0.133106 + 0.133106i
\(209\) 12.9567 + 19.0898i 0.896230 + 1.32047i
\(210\) 3.29548 2.97373i 0.227410 0.205207i
\(211\) 7.30842i 0.503132i −0.967840 0.251566i \(-0.919054\pi\)
0.967840 0.251566i \(-0.0809456\pi\)
\(212\) 8.93991 8.93991i 0.613995 0.613995i
\(213\) −2.80737 + 2.80737i −0.192358 + 0.192358i
\(214\) 9.95628i 0.680597i
\(215\) −15.1026 16.7367i −1.02999 1.14143i
\(216\) −1.00000 −0.0680414
\(217\) 11.0187 11.0187i 0.748000 0.748000i
\(218\) 6.10948 6.10948i 0.413786 0.413786i
\(219\) 10.9215 0.738005
\(220\) 11.8199 + 0.606635i 0.796898 + 0.0408993i
\(221\) 1.87405i 0.126063i
\(222\) −5.60602 + 5.60602i −0.376251 + 0.376251i
\(223\) 4.27908 + 4.27908i 0.286548 + 0.286548i 0.835714 0.549165i \(-0.185054\pi\)
−0.549165 + 0.835714i \(0.685054\pi\)
\(224\) −1.98511 −0.132636
\(225\) 0.511883 4.97373i 0.0341255 0.331582i
\(226\) 9.15392 0.608910
\(227\) 13.7190 13.7190i 0.910561 0.910561i −0.0857552 0.996316i \(-0.527330\pi\)
0.996316 + 0.0857552i \(0.0273303\pi\)
\(228\) −4.28120 0.819353i −0.283529 0.0542630i
\(229\) 25.2634i 1.66945i 0.550667 + 0.834725i \(0.314373\pi\)
−0.550667 + 0.834725i \(0.685627\pi\)
\(230\) −12.2829 0.630395i −0.809908 0.0415670i
\(231\) 10.5071i 0.691319i
\(232\) −4.37741 4.37741i −0.287391 0.287391i
\(233\) 7.73738 7.73738i 0.506892 0.506892i −0.406679 0.913571i \(-0.633313\pi\)
0.913571 + 0.406679i \(0.133313\pi\)
\(234\) 2.71483i 0.177474i
\(235\) −18.4766 + 16.6726i −1.20528 + 1.08760i
\(236\) 0.611185i 0.0397848i
\(237\) −12.1288 12.1288i −0.787853 0.787853i
\(238\) 0.968965 + 0.968965i 0.0628087 + 0.0628087i
\(239\) 11.0820i 0.716837i 0.933561 + 0.358418i \(0.116684\pi\)
−0.933561 + 0.358418i \(0.883316\pi\)
\(240\) −1.66010 + 1.49802i −0.107159 + 0.0966967i
\(241\) 14.5158i 0.935043i −0.883982 0.467522i \(-0.845147\pi\)
0.883982 0.467522i \(-0.154853\pi\)
\(242\) −12.0319 + 12.0319i −0.773438 + 0.773438i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 8.31021i 0.532007i
\(245\) −6.83191 0.350635i −0.436475 0.0224013i
\(246\) 1.90599i 0.121522i
\(247\) −2.22441 + 11.6227i −0.141536 + 0.739537i
\(248\) −5.55069 + 5.55069i −0.352469 + 0.352469i
\(249\) 7.68225 0.486843
\(250\) −6.60096 9.02371i −0.417481 0.570710i
\(251\) 6.78199 0.428075 0.214038 0.976825i \(-0.431338\pi\)
0.214038 + 0.976825i \(0.431338\pi\)
\(252\) −1.40368 1.40368i −0.0884238 0.0884238i
\(253\) 20.5860 20.5860i 1.29423 1.29423i
\(254\) 1.89149i 0.118683i
\(255\) 1.54153 + 0.0791163i 0.0965345 + 0.00495445i
\(256\) 1.00000 0.0625000
\(257\) −13.1118 + 13.1118i −0.817891 + 0.817891i −0.985802 0.167911i \(-0.946298\pi\)
0.167911 + 0.985802i \(0.446298\pi\)
\(258\) −7.12884 + 7.12884i −0.443822 + 0.443822i
\(259\) −15.7381 −0.977921
\(260\) 4.06687 + 4.50690i 0.252217 + 0.279506i
\(261\) 6.19060i 0.383188i
\(262\) −3.77362 + 3.77362i −0.233135 + 0.233135i
\(263\) 8.10698 8.10698i 0.499898 0.499898i −0.411508 0.911406i \(-0.634998\pi\)
0.911406 + 0.411508i \(0.134998\pi\)
\(264\) 5.29298i 0.325760i
\(265\) 20.9886 18.9393i 1.28932 1.16343i
\(266\) −4.85934 7.15956i −0.297945 0.438981i
\(267\) 3.83335 + 3.83335i 0.234597 + 0.234597i
\(268\) −10.2011 10.2011i −0.623132 0.623132i
\(269\) −16.5207 −1.00729 −0.503644 0.863911i \(-0.668008\pi\)
−0.503644 + 0.863911i \(0.668008\pi\)
\(270\) −2.23313 0.114611i −0.135904 0.00697501i
\(271\) −1.20001 −0.0728953 −0.0364477 0.999336i \(-0.511604\pi\)
−0.0364477 + 0.999336i \(0.511604\pi\)
\(272\) −0.488117 0.488117i −0.0295964 0.0295964i
\(273\) −3.81077 + 3.81077i −0.230638 + 0.230638i
\(274\) 4.20549 0.254063
\(275\) 26.3258 + 2.70939i 1.58751 + 0.163382i
\(276\) 5.50029i 0.331079i
\(277\) −5.15378 5.15378i −0.309661 0.309661i 0.535117 0.844778i \(-0.320268\pi\)
−0.844778 + 0.535117i \(0.820268\pi\)
\(278\) −9.82829 9.82829i −0.589462 0.589462i
\(279\) −7.84986 −0.469959
\(280\) −4.43300 0.227516i −0.264923 0.0135967i
\(281\) 21.1406i 1.26114i −0.776132 0.630570i \(-0.782821\pi\)
0.776132 0.630570i \(-0.217179\pi\)
\(282\) 7.86994 + 7.86994i 0.468648 + 0.468648i
\(283\) −15.7352 + 15.7352i −0.935358 + 0.935358i −0.998034 0.0626758i \(-0.980037\pi\)
0.0626758 + 0.998034i \(0.480037\pi\)
\(284\) 3.97022 0.235589
\(285\) −9.46656 2.32039i −0.560751 0.137448i
\(286\) −14.3696 −0.849690
\(287\) −2.67541 + 2.67541i −0.157924 + 0.157924i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 16.5235i 0.971970i
\(290\) −9.27362 10.2770i −0.544566 0.603488i
\(291\) −4.38992 −0.257342
\(292\) −7.72265 7.72265i −0.451934 0.451934i
\(293\) −11.6988 11.6988i −0.683451 0.683451i 0.277325 0.960776i \(-0.410552\pi\)
−0.960776 + 0.277325i \(0.910552\pi\)
\(294\) 3.05934i 0.178425i
\(295\) −0.0700487 + 1.36486i −0.00407839 + 0.0794650i
\(296\) 7.92810 0.460812
\(297\) 3.74270 3.74270i 0.217174 0.217174i
\(298\) 9.15374 + 9.15374i 0.530262 + 0.530262i
\(299\) 14.9324 0.863562
\(300\) −3.87891 + 3.15500i −0.223949 + 0.182154i
\(301\) −20.0133 −1.15355
\(302\) −15.3808 15.3808i −0.885066 0.885066i
\(303\) −1.97604 1.97604i −0.113521 0.113521i
\(304\) 2.44789 + 3.60663i 0.140396 + 0.206855i
\(305\) 0.952444 18.5578i 0.0545368 1.06262i
\(306\) 0.690302i 0.0394619i
\(307\) 13.8361 13.8361i 0.789668 0.789668i −0.191772 0.981440i \(-0.561423\pi\)
0.981440 + 0.191772i \(0.0614233\pi\)
\(308\) 7.42967 7.42967i 0.423345 0.423345i
\(309\) 5.73207i 0.326086i
\(310\) −13.0316 + 11.7592i −0.740144 + 0.667880i
\(311\) −0.990577 −0.0561705 −0.0280852 0.999606i \(-0.508941\pi\)
−0.0280852 + 0.999606i \(0.508941\pi\)
\(312\) 1.91968 1.91968i 0.108680 0.108680i
\(313\) 5.68394 5.68394i 0.321275 0.321275i −0.527981 0.849256i \(-0.677051\pi\)
0.849256 + 0.527981i \(0.177051\pi\)
\(314\) −3.31834 −0.187264
\(315\) −2.97373 3.29548i −0.167551 0.185680i
\(316\) 17.1528i 0.964918i
\(317\) 9.63331 9.63331i 0.541061 0.541061i −0.382779 0.923840i \(-0.625033\pi\)
0.923840 + 0.382779i \(0.125033\pi\)
\(318\) −8.93991 8.93991i −0.501325 0.501325i
\(319\) 32.7667 1.83458
\(320\) 2.23313 + 0.114611i 0.124836 + 0.00640696i
\(321\) −9.95628 −0.555705
\(322\) −7.72067 + 7.72067i −0.430256 + 0.430256i
\(323\) 0.565601 2.95532i 0.0314709 0.164438i
\(324\) 1.00000i 0.0555556i
\(325\) 8.56530 + 10.5306i 0.475118 + 0.584133i
\(326\) 19.9985i 1.10761i
\(327\) −6.10948 6.10948i −0.337855 0.337855i
\(328\) 1.34774 1.34774i 0.0744165 0.0744165i
\(329\) 22.0938i 1.21807i
\(330\) 0.606635 11.8199i 0.0333941 0.650664i
\(331\) 19.9864i 1.09855i 0.835641 + 0.549276i \(0.185096\pi\)
−0.835641 + 0.549276i \(0.814904\pi\)
\(332\) −5.43217 5.43217i −0.298129 0.298129i
\(333\) 5.60602 + 5.60602i 0.307208 + 0.307208i
\(334\) 12.9969i 0.711157i
\(335\) −21.6112 23.9495i −1.18075 1.30850i
\(336\) 1.98511i 0.108297i
\(337\) −4.18460 + 4.18460i −0.227950 + 0.227950i −0.811836 0.583886i \(-0.801532\pi\)
0.583886 + 0.811836i \(0.301532\pi\)
\(338\) 3.98078 + 3.98078i 0.216526 + 0.216526i
\(339\) 9.15392i 0.497173i
\(340\) −1.03408 1.14597i −0.0560811 0.0621490i
\(341\) 41.5492i 2.25001i
\(342\) −0.819353 + 4.28120i −0.0443055 + 0.231501i
\(343\) −14.1201 + 14.1201i −0.762416 + 0.762416i
\(344\) 10.0817 0.543569
\(345\) −0.630395 + 12.2829i −0.0339393 + 0.661287i
\(346\) −2.98124 −0.160273
\(347\) 2.65197 + 2.65197i 0.142365 + 0.142365i 0.774697 0.632332i \(-0.217902\pi\)
−0.632332 + 0.774697i \(0.717902\pi\)
\(348\) −4.37741 + 4.37741i −0.234654 + 0.234654i
\(349\) 17.8125i 0.953481i −0.879044 0.476740i \(-0.841818\pi\)
0.879044 0.476740i \(-0.158182\pi\)
\(350\) −9.87339 1.01614i −0.527755 0.0543151i
\(351\) 2.71483 0.144907
\(352\) −3.74270 + 3.74270i −0.199487 + 0.199487i
\(353\) −11.6167 + 11.6167i −0.618293 + 0.618293i −0.945093 0.326801i \(-0.894029\pi\)
0.326801 + 0.945093i \(0.394029\pi\)
\(354\) 0.611185 0.0324841
\(355\) 8.86601 + 0.455031i 0.470559 + 0.0241506i
\(356\) 5.42118i 0.287322i
\(357\) 0.968965 0.968965i 0.0512831 0.0512831i
\(358\) 5.61326 5.61326i 0.296670 0.296670i
\(359\) 4.76092i 0.251272i −0.992076 0.125636i \(-0.959903\pi\)
0.992076 0.125636i \(-0.0400971\pi\)
\(360\) 1.49802 + 1.66010i 0.0789525 + 0.0874951i
\(361\) −7.01563 + 17.6573i −0.369243 + 0.929333i
\(362\) 3.37401 + 3.37401i 0.177334 + 0.177334i
\(363\) 12.0319 + 12.0319i 0.631509 + 0.631509i
\(364\) 5.38924 0.282473
\(365\) −16.3606 18.1308i −0.856351 0.949008i
\(366\) −8.31021 −0.434382
\(367\) 12.6008 + 12.6008i 0.657754 + 0.657754i 0.954848 0.297094i \(-0.0960176\pi\)
−0.297094 + 0.954848i \(0.596018\pi\)
\(368\) 3.88930 3.88930i 0.202744 0.202744i
\(369\) 1.90599 0.0992220
\(370\) 17.7045 + 0.908649i 0.920412 + 0.0472384i
\(371\) 25.0976i 1.30300i
\(372\) 5.55069 + 5.55069i 0.287790 + 0.287790i
\(373\) 6.72967 + 6.72967i 0.348449 + 0.348449i 0.859532 0.511083i \(-0.170755\pi\)
−0.511083 + 0.859532i \(0.670755\pi\)
\(374\) 3.65375 0.188931
\(375\) −9.02371 + 6.60096i −0.465982 + 0.340872i
\(376\) 11.1298i 0.573974i
\(377\) 11.8839 + 11.8839i 0.612054 + 0.612054i
\(378\) −1.40368 + 1.40368i −0.0721977 + 0.0721977i
\(379\) −10.5434 −0.541578 −0.270789 0.962639i \(-0.587285\pi\)
−0.270789 + 0.962639i \(0.587285\pi\)
\(380\) 5.05310 + 8.33464i 0.259219 + 0.427558i
\(381\) −1.89149 −0.0969039
\(382\) 9.80837 9.80837i 0.501840 0.501840i
\(383\) 8.53662 + 8.53662i 0.436201 + 0.436201i 0.890731 0.454530i \(-0.150193\pi\)
−0.454530 + 0.890731i \(0.650193\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 17.4429 15.7399i 0.888974 0.802179i
\(386\) 11.6257 0.591733
\(387\) 7.12884 + 7.12884i 0.362379 + 0.362379i
\(388\) 3.10415 + 3.10415i 0.157589 + 0.157589i
\(389\) 25.1180i 1.27353i −0.771056 0.636767i \(-0.780271\pi\)
0.771056 0.636767i \(-0.219729\pi\)
\(390\) 4.50690 4.06687i 0.228216 0.205934i
\(391\) −3.79686 −0.192016
\(392\) 2.16328 2.16328i 0.109262 0.109262i
\(393\) 3.77362 + 3.77362i 0.190354 + 0.190354i
\(394\) 1.19486 0.0601961
\(395\) −1.96590 + 38.3043i −0.0989151 + 1.92730i
\(396\) −5.29298 −0.265982
\(397\) 10.0839 + 10.0839i 0.506098 + 0.506098i 0.913326 0.407228i \(-0.133505\pi\)
−0.407228 + 0.913326i \(0.633505\pi\)
\(398\) 12.1810 + 12.1810i 0.610578 + 0.610578i
\(399\) −7.15956 + 4.85934i −0.358426 + 0.243271i
\(400\) 4.97373 + 0.511883i 0.248686 + 0.0255942i
\(401\) 1.57077i 0.0784407i −0.999231 0.0392203i \(-0.987513\pi\)
0.999231 0.0392203i \(-0.0124874\pi\)
\(402\) −10.2011 + 10.2011i −0.508785 + 0.508785i
\(403\) 15.0692 15.0692i 0.750651 0.750651i
\(404\) 2.79454i 0.139034i
\(405\) −0.114611 + 2.23313i −0.00569508 + 0.110965i
\(406\) −12.2890 −0.609893
\(407\) −29.6725 + 29.6725i −1.47081 + 1.47081i
\(408\) −0.488117 + 0.488117i −0.0241654 + 0.0241654i
\(409\) 10.9037 0.539153 0.269576 0.962979i \(-0.413116\pi\)
0.269576 + 0.962979i \(0.413116\pi\)
\(410\) 3.16414 2.85521i 0.156266 0.141009i
\(411\) 4.20549i 0.207441i
\(412\) −4.05319 + 4.05319i −0.199686 + 0.199686i
\(413\) 0.857911 + 0.857911i 0.0422150 + 0.0422150i
\(414\) 5.50029 0.270325
\(415\) −11.5082 12.7533i −0.564913 0.626036i
\(416\) −2.71483 −0.133106
\(417\) −9.82829 + 9.82829i −0.481293 + 0.481293i
\(418\) −22.6603 4.33682i −1.10835 0.212121i
\(419\) 6.93967i 0.339025i −0.985528 0.169512i \(-0.945781\pi\)
0.985528 0.169512i \(-0.0542193\pi\)
\(420\) −0.227516 + 4.43300i −0.0111016 + 0.216308i
\(421\) 17.7896i 0.867010i 0.901151 + 0.433505i \(0.142723\pi\)
−0.901151 + 0.433505i \(0.857277\pi\)
\(422\) 5.16783 + 5.16783i 0.251566 + 0.251566i
\(423\) 7.86994 7.86994i 0.382650 0.382650i
\(424\) 12.6429i 0.613995i
\(425\) −2.17790 2.67762i −0.105644 0.129884i
\(426\) 3.97022i 0.192358i
\(427\) −11.6649 11.6649i −0.564505 0.564505i
\(428\) 7.04015 + 7.04015i 0.340299 + 0.340299i
\(429\) 14.3696i 0.693769i
\(430\) 22.5137 + 1.15548i 1.08571 + 0.0557220i
\(431\) 35.0344i 1.68755i −0.536697 0.843775i \(-0.680328\pi\)
0.536697 0.843775i \(-0.319672\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) 14.6222 + 14.6222i 0.702699 + 0.702699i 0.964989 0.262290i \(-0.0844778\pi\)
−0.262290 + 0.964989i \(0.584478\pi\)
\(434\) 15.5828i 0.748000i
\(435\) −10.2770 + 9.27362i −0.492746 + 0.444636i
\(436\) 8.64011i 0.413786i
\(437\) 23.5479 + 4.50668i 1.12645 + 0.215584i
\(438\) −7.72265 + 7.72265i −0.369002 + 0.369002i
\(439\) −25.2333 −1.20432 −0.602160 0.798376i \(-0.705693\pi\)
−0.602160 + 0.798376i \(0.705693\pi\)
\(440\) −8.78689 + 7.92898i −0.418899 + 0.377999i
\(441\) 3.05934 0.145683
\(442\) 1.32516 + 1.32516i 0.0630313 + 0.0630313i
\(443\) −17.3294 + 17.3294i −0.823344 + 0.823344i −0.986586 0.163242i \(-0.947805\pi\)
0.163242 + 0.986586i \(0.447805\pi\)
\(444\) 7.92810i 0.376251i
\(445\) 0.621328 12.1062i 0.0294538 0.573888i
\(446\) −6.05153 −0.286548
\(447\) 9.15374 9.15374i 0.432957 0.432957i
\(448\) 1.40368 1.40368i 0.0663178 0.0663178i
\(449\) 20.6855 0.976211 0.488105 0.872785i \(-0.337688\pi\)
0.488105 + 0.872785i \(0.337688\pi\)
\(450\) 3.15500 + 3.87891i 0.148728 + 0.182854i
\(451\) 10.0884i 0.475043i
\(452\) −6.47280 + 6.47280i −0.304455 + 0.304455i
\(453\) −15.3808 + 15.3808i −0.722654 + 0.722654i
\(454\) 19.4016i 0.910561i
\(455\) 12.0349 + 0.617667i 0.564203 + 0.0289567i
\(456\) 3.60663 2.44789i 0.168896 0.114633i
\(457\) −7.86170 7.86170i −0.367755 0.367755i 0.498903 0.866658i \(-0.333736\pi\)
−0.866658 + 0.498903i \(0.833736\pi\)
\(458\) −17.8639 17.8639i −0.834725 0.834725i
\(459\) −0.690302 −0.0322205
\(460\) 9.13105 8.23954i 0.425738 0.384171i
\(461\) 23.8664 1.11157 0.555784 0.831327i \(-0.312418\pi\)
0.555784 + 0.831327i \(0.312418\pi\)
\(462\) −7.42967 7.42967i −0.345659 0.345659i
\(463\) 22.3224 22.3224i 1.03741 1.03741i 0.0381357 0.999273i \(-0.487858\pi\)
0.999273 0.0381357i \(-0.0121419\pi\)
\(464\) 6.19060 0.287391
\(465\) 11.7592 + 13.0316i 0.545322 + 0.604325i
\(466\) 10.9423i 0.506892i
\(467\) 20.6661 + 20.6661i 0.956312 + 0.956312i 0.999085 0.0427727i \(-0.0136191\pi\)
−0.0427727 + 0.999085i \(0.513619\pi\)
\(468\) −1.91968 1.91968i −0.0887371 0.0887371i
\(469\) −28.6382 −1.32239
\(470\) 1.27560 24.8542i 0.0588389 1.14644i
\(471\) 3.31834i 0.152901i
\(472\) −0.432173 0.432173i −0.0198924 0.0198924i
\(473\) −37.7328 + 37.7328i −1.73495 + 1.73495i
\(474\) 17.1528 0.787853
\(475\) 10.3290 + 19.1915i 0.473926 + 0.880564i
\(476\) −1.37032 −0.0628087
\(477\) −8.93991 + 8.93991i −0.409330 + 0.409330i
\(478\) −7.83618 7.83618i −0.358418 0.358418i
\(479\) 15.9212i 0.727459i −0.931505 0.363730i \(-0.881503\pi\)
0.931505 0.363730i \(-0.118497\pi\)
\(480\) 0.114611 2.23313i 0.00523126 0.101928i
\(481\) −21.5235 −0.981386
\(482\) 10.2642 + 10.2642i 0.467522 + 0.467522i
\(483\) 7.72067 + 7.72067i 0.351303 + 0.351303i
\(484\) 17.0156i 0.773438i
\(485\) 6.57619 + 7.28773i 0.298609 + 0.330919i
\(486\) 1.00000 0.0453609
\(487\) −10.4874 + 10.4874i −0.475228 + 0.475228i −0.903602 0.428374i \(-0.859087\pi\)
0.428374 + 0.903602i \(0.359087\pi\)
\(488\) 5.87621 + 5.87621i 0.266003 + 0.266003i
\(489\) −19.9985 −0.904363
\(490\) 5.07883 4.58295i 0.229438 0.207037i
\(491\) 15.8352 0.714633 0.357317 0.933983i \(-0.383692\pi\)
0.357317 + 0.933983i \(0.383692\pi\)
\(492\) −1.34774 1.34774i −0.0607608 0.0607608i
\(493\) −3.02173 3.02173i −0.136092 0.136092i
\(494\) −6.64563 9.79141i −0.299001 0.440537i
\(495\) −11.8199 0.606635i −0.531265 0.0272662i
\(496\) 7.84986i 0.352469i
\(497\) 5.57293 5.57293i 0.249980 0.249980i
\(498\) −5.43217 + 5.43217i −0.243422 + 0.243422i
\(499\) 21.1108i 0.945050i −0.881317 0.472525i \(-0.843343\pi\)
0.881317 0.472525i \(-0.156657\pi\)
\(500\) 11.0483 + 1.71315i 0.494095 + 0.0766142i
\(501\) 12.9969 0.580657
\(502\) −4.79559 + 4.79559i −0.214038 + 0.214038i
\(503\) 11.3484 11.3484i 0.506001 0.506001i −0.407295 0.913297i \(-0.633528\pi\)
0.913297 + 0.407295i \(0.133528\pi\)
\(504\) 1.98511 0.0884238
\(505\) −0.320286 + 6.24058i −0.0142525 + 0.277702i
\(506\) 29.1129i 1.29423i
\(507\) 3.98078 3.98078i 0.176793 0.176793i
\(508\) 1.33748 + 1.33748i 0.0593413 + 0.0593413i
\(509\) −36.8026 −1.63125 −0.815624 0.578582i \(-0.803606\pi\)
−0.815624 + 0.578582i \(0.803606\pi\)
\(510\) −1.14597 + 1.03408i −0.0507445 + 0.0457900i
\(511\) −21.6803 −0.959080
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 4.28120 + 0.819353i 0.189020 + 0.0361753i
\(514\) 18.5429i 0.817891i
\(515\) −9.51583 + 8.58674i −0.419317 + 0.378377i
\(516\) 10.0817i 0.443822i
\(517\) 41.6554 + 41.6554i 1.83200 + 1.83200i
\(518\) 11.1285 11.1285i 0.488960 0.488960i
\(519\) 2.98124i 0.130862i
\(520\) −6.06257 0.311150i −0.265861 0.0136448i
\(521\) 6.00142i 0.262927i 0.991321 + 0.131463i \(0.0419676\pi\)
−0.991321 + 0.131463i \(0.958032\pi\)
\(522\) 4.37741 + 4.37741i 0.191594 + 0.191594i
\(523\) −19.4311 19.4311i −0.849664 0.849664i 0.140427 0.990091i \(-0.455152\pi\)
−0.990091 + 0.140427i \(0.955152\pi\)
\(524\) 5.33670i 0.233135i
\(525\) −1.01614 + 9.87339i −0.0443481 + 0.430910i
\(526\) 11.4650i 0.499898i
\(527\) −3.83165 + 3.83165i −0.166909 + 0.166909i
\(528\) 3.74270 + 3.74270i 0.162880 + 0.162880i
\(529\) 7.25324i 0.315358i
\(530\) −1.44902 + 28.2333i −0.0629415 + 1.22638i
\(531\) 0.611185i 0.0265232i
\(532\) 8.49864 + 1.62650i 0.368463 + 0.0705179i
\(533\) −3.65889 + 3.65889i −0.158484 + 0.158484i
\(534\) −5.42118 −0.234597
\(535\) 14.9147 + 16.5285i 0.644818 + 0.714587i
\(536\) 14.4265 0.623132
\(537\) −5.61326 5.61326i −0.242230 0.242230i
\(538\) 11.6819 11.6819i 0.503644 0.503644i
\(539\) 16.1930i 0.697484i
\(540\) 1.66010 1.49802i 0.0714395 0.0644644i
\(541\) 19.3859 0.833467 0.416734 0.909029i \(-0.363175\pi\)
0.416734 + 0.909029i \(0.363175\pi\)
\(542\) 0.848534 0.848534i 0.0364477 0.0364477i
\(543\) 3.37401 3.37401i 0.144793 0.144793i
\(544\) 0.690302 0.0295964
\(545\) −0.990253 + 19.2945i −0.0424178 + 0.826485i
\(546\) 5.38924i 0.230638i
\(547\) 6.28887 6.28887i 0.268893 0.268893i −0.559761 0.828654i \(-0.689107\pi\)
0.828654 + 0.559761i \(0.189107\pi\)
\(548\) −2.97373 + 2.97373i −0.127031 + 0.127031i
\(549\) 8.31021i 0.354671i
\(550\) −20.5310 + 16.6994i −0.875445 + 0.712063i
\(551\) 15.1539 + 22.3272i 0.645579 + 0.951171i
\(552\) −3.88930 3.88930i −0.165539 0.165539i
\(553\) 24.0771 + 24.0771i 1.02386 + 1.02386i
\(554\) 7.28855 0.309661
\(555\) 0.908649 17.7045i 0.0385700 0.751513i
\(556\) 13.8993 0.589462
\(557\) 9.88148 + 9.88148i 0.418692 + 0.418692i 0.884753 0.466061i \(-0.154327\pi\)
−0.466061 + 0.884753i \(0.654327\pi\)
\(558\) 5.55069 5.55069i 0.234979 0.234979i
\(559\) −27.3701 −1.15763
\(560\) 3.29548 2.97373i 0.139260 0.125663i
\(561\) 3.65375i 0.154262i
\(562\) 14.9486 + 14.9486i 0.630570 + 0.630570i
\(563\) −16.7009 16.7009i −0.703858 0.703858i 0.261379 0.965236i \(-0.415823\pi\)
−0.965236 + 0.261379i \(0.915823\pi\)
\(564\) −11.1298 −0.468648
\(565\) −15.1965 + 13.7127i −0.639320 + 0.576900i
\(566\) 22.2529i 0.935358i
\(567\) 1.40368 + 1.40368i 0.0589492 + 0.0589492i
\(568\) −2.80737 + 2.80737i −0.117795 + 0.117795i
\(569\) 1.12910 0.0473344 0.0236672 0.999720i \(-0.492466\pi\)
0.0236672 + 0.999720i \(0.492466\pi\)
\(570\) 8.33464 5.05310i 0.349099 0.211651i
\(571\) −7.89992 −0.330602 −0.165301 0.986243i \(-0.552859\pi\)
−0.165301 + 0.986243i \(0.552859\pi\)
\(572\) 10.1608 10.1608i 0.424845 0.424845i
\(573\) −9.80837 9.80837i −0.409750 0.409750i
\(574\) 3.78360i 0.157924i
\(575\) 21.3352 17.3534i 0.889738 0.723688i
\(576\) −1.00000 −0.0416667
\(577\) −31.1021 31.1021i −1.29480 1.29480i −0.931785 0.363011i \(-0.881749\pi\)
−0.363011 0.931785i \(-0.618251\pi\)
\(578\) 11.6839 + 11.6839i 0.485985 + 0.485985i
\(579\) 11.6257i 0.483148i
\(580\) 13.8244 + 0.709511i 0.574027 + 0.0294609i
\(581\) −15.2501 −0.632681
\(582\) 3.10415 3.10415i 0.128671 0.128671i
\(583\) −47.3187 47.3187i −1.95974 1.95974i
\(584\) 10.9215 0.451934
\(585\) −4.06687 4.50690i −0.168144 0.186338i
\(586\) 16.5446 0.683451
\(587\) −6.49465 6.49465i −0.268063 0.268063i 0.560256 0.828319i \(-0.310703\pi\)
−0.828319 + 0.560256i \(0.810703\pi\)
\(588\) −2.16328 2.16328i −0.0892123 0.0892123i
\(589\) 28.3116 19.2156i 1.16656 0.791766i
\(590\) −0.915567 1.01463i −0.0376933 0.0417717i
\(591\) 1.19486i 0.0491499i
\(592\) −5.60602 + 5.60602i −0.230406 + 0.230406i
\(593\) 16.2871 16.2871i 0.668830 0.668830i −0.288615 0.957445i \(-0.593195\pi\)
0.957445 + 0.288615i \(0.0931948\pi\)
\(594\) 5.29298i 0.217174i
\(595\) −3.06011 0.157054i −0.125452 0.00643860i
\(596\) −12.9453 −0.530262
\(597\) 12.1810 12.1810i 0.498535 0.498535i
\(598\) −10.5588 + 10.5588i −0.431781 + 0.431781i
\(599\) −45.2347 −1.84824 −0.924119 0.382104i \(-0.875200\pi\)
−0.924119 + 0.382104i \(0.875200\pi\)
\(600\) 0.511883 4.97373i 0.0208975 0.203052i
\(601\) 18.3122i 0.746972i −0.927636 0.373486i \(-0.878162\pi\)
0.927636 0.373486i \(-0.121838\pi\)
\(602\) 14.1515 14.1515i 0.576773 0.576773i
\(603\) 10.2011 + 10.2011i 0.415421 + 0.415421i
\(604\) 21.7518 0.885066
\(605\) 1.95018 37.9981i 0.0792861 1.54484i
\(606\) 2.79454 0.113521
\(607\) −17.5130 + 17.5130i −0.710829 + 0.710829i −0.966709 0.255879i \(-0.917635\pi\)
0.255879 + 0.966709i \(0.417635\pi\)
\(608\) −4.28120 0.819353i −0.173626 0.0332292i
\(609\) 12.2890i 0.497976i
\(610\) 12.4489 + 13.7958i 0.504039 + 0.558576i
\(611\) 30.2155i 1.22239i
\(612\) 0.488117 + 0.488117i 0.0197310 + 0.0197310i
\(613\) 2.65427 2.65427i 0.107205 0.107205i −0.651470 0.758675i \(-0.725847\pi\)
0.758675 + 0.651470i \(0.225847\pi\)
\(614\) 19.5672i 0.789668i
\(615\) −2.85521 3.16414i −0.115133 0.127591i
\(616\) 10.5071i 0.423345i
\(617\) 6.67261 + 6.67261i 0.268629 + 0.268629i 0.828548 0.559919i \(-0.189168\pi\)
−0.559919 + 0.828548i \(0.689168\pi\)
\(618\) 4.05319 + 4.05319i 0.163043 + 0.163043i
\(619\) 21.6368i 0.869657i 0.900513 + 0.434829i \(0.143191\pi\)
−0.900513 + 0.434829i \(0.856809\pi\)
\(620\) 0.899682 17.5298i 0.0361321 0.704012i
\(621\) 5.50029i 0.220719i
\(622\) 0.700444 0.700444i 0.0280852 0.0280852i
\(623\) −7.60962 7.60962i −0.304873 0.304873i
\(624\) 2.71483i 0.108680i
\(625\) 24.4760 + 5.09193i 0.979038 + 0.203677i
\(626\) 8.03830i 0.321275i
\(627\) −4.33682 + 22.6603i −0.173196 + 0.904965i
\(628\) 2.34642 2.34642i 0.0936322 0.0936322i
\(629\) 5.47278 0.218214
\(630\) 4.43300 + 0.227516i 0.176615 + 0.00906444i
\(631\) −0.652184 −0.0259631 −0.0129815 0.999916i \(-0.504132\pi\)
−0.0129815 + 0.999916i \(0.504132\pi\)
\(632\) −12.1288 12.1288i −0.482459 0.482459i
\(633\) 5.16783 5.16783i 0.205403 0.205403i
\(634\) 13.6236i 0.541061i
\(635\) 2.83349 + 3.14007i 0.112443 + 0.124610i
\(636\) 12.6429 0.501325
\(637\) −5.87295 + 5.87295i −0.232695 + 0.232695i
\(638\) −23.1696 + 23.1696i −0.917291 + 0.917291i
\(639\) −3.97022 −0.157059
\(640\) −1.66010 + 1.49802i −0.0656213 + 0.0592144i
\(641\) 6.00938i 0.237356i −0.992933 0.118678i \(-0.962134\pi\)
0.992933 0.118678i \(-0.0378657\pi\)
\(642\) 7.04015 7.04015i 0.277853 0.277853i
\(643\) −7.37061 + 7.37061i −0.290669 + 0.290669i −0.837344 0.546676i \(-0.815893\pi\)
0.546676 + 0.837344i \(0.315893\pi\)
\(644\) 10.9187i 0.430256i
\(645\) 1.15548 22.5137i 0.0454968 0.886477i
\(646\) 1.68979 + 2.48967i 0.0664837 + 0.0979546i
\(647\) 6.73802 + 6.73802i 0.264899 + 0.264899i 0.827041 0.562142i \(-0.190023\pi\)
−0.562142 + 0.827041i \(0.690023\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) 3.23499 0.126985
\(650\) −13.5028 1.38968i −0.529625 0.0545076i
\(651\) 15.5828 0.610739
\(652\) 14.1411 + 14.1411i 0.553807 + 0.553807i
\(653\) −4.47188 + 4.47188i −0.174998 + 0.174998i −0.789171 0.614173i \(-0.789490\pi\)
0.614173 + 0.789171i \(0.289490\pi\)
\(654\) 8.64011 0.337855
\(655\) 0.611645 11.9175i 0.0238990 0.465657i
\(656\) 1.90599i 0.0744165i
\(657\) 7.72265 + 7.72265i 0.301289 + 0.301289i
\(658\) −15.6227 15.6227i −0.609036 0.609036i
\(659\) 29.4239 1.14619 0.573096 0.819489i \(-0.305742\pi\)
0.573096 + 0.819489i \(0.305742\pi\)
\(660\) 7.92898 + 8.78689i 0.308635 + 0.342029i
\(661\) 18.0453i 0.701881i 0.936398 + 0.350941i \(0.114138\pi\)
−0.936398 + 0.350941i \(0.885862\pi\)
\(662\) −14.1325 14.1325i −0.549276 0.549276i
\(663\) 1.32516 1.32516i 0.0514648 0.0514648i
\(664\) 7.68225 0.298129
\(665\) 18.7921 + 4.60623i 0.728728 + 0.178622i
\(666\) −7.92810 −0.307208
\(667\) 24.0771 24.0771i 0.932267 0.932267i
\(668\) −9.19018 9.19018i −0.355579 0.355579i
\(669\) 6.05153i 0.233966i
\(670\) 32.2163 + 1.65344i 1.24462 + 0.0638781i
\(671\) −43.9858 −1.69805
\(672\) −1.40368 1.40368i −0.0541483 0.0541483i
\(673\) −8.20956 8.20956i −0.316455 0.316455i 0.530949 0.847404i \(-0.321836\pi\)
−0.847404 + 0.530949i \(0.821836\pi\)
\(674\) 5.91793i 0.227950i
\(675\) 3.87891 3.15500i 0.149299 0.121436i
\(676\) −5.62968 −0.216526
\(677\) −24.0239 + 24.0239i −0.923313 + 0.923313i −0.997262 0.0739493i \(-0.976440\pi\)
0.0739493 + 0.997262i \(0.476440\pi\)
\(678\) 6.47280 + 6.47280i 0.248586 + 0.248586i
\(679\) 8.71448 0.334431
\(680\) 1.54153 + 0.0791163i 0.0591151 + 0.00303397i
\(681\) 19.4016 0.743470
\(682\) 29.3797 + 29.3797i 1.12501 + 1.12501i
\(683\) −14.5663 14.5663i −0.557363 0.557363i 0.371192 0.928556i \(-0.378949\pi\)
−0.928556 + 0.371192i \(0.878949\pi\)
\(684\) −2.44789 3.60663i −0.0935976 0.137903i
\(685\) −6.98154 + 6.29990i −0.266751 + 0.240707i
\(686\) 19.9689i 0.762416i
\(687\) −17.8639 + 17.8639i −0.681550 + 0.681550i
\(688\) −7.12884 + 7.12884i −0.271784 + 0.271784i
\(689\) 34.3235i 1.30762i
\(690\) −8.23954 9.13105i −0.313674 0.347613i
\(691\) −39.3797 −1.49807 −0.749037 0.662528i \(-0.769483\pi\)
−0.749037 + 0.662528i \(0.769483\pi\)
\(692\) 2.10806 2.10806i 0.0801363 0.0801363i
\(693\) −7.42967 + 7.42967i −0.282230 + 0.282230i
\(694\) −3.75046 −0.142365
\(695\) 31.0389 + 1.59302i 1.17737 + 0.0604265i
\(696\) 6.19060i 0.234654i
\(697\) 0.930347 0.930347i 0.0352394 0.0352394i
\(698\) 12.5953 + 12.5953i 0.476740 + 0.476740i
\(699\) 10.9423 0.413876
\(700\) 7.70006 6.26302i 0.291035 0.236720i
\(701\) 5.40623 0.204190 0.102095 0.994775i \(-0.467445\pi\)
0.102095 + 0.994775i \(0.467445\pi\)
\(702\) −1.91968 + 1.91968i −0.0724536 + 0.0724536i
\(703\) −33.9418 6.49592i −1.28014 0.244998i
\(704\) 5.29298i 0.199487i
\(705\) −24.8542 1.27560i −0.936064 0.0480418i
\(706\) 16.4284i 0.618293i
\(707\) 3.92266 + 3.92266i 0.147527 + 0.147527i
\(708\) −0.432173 + 0.432173i −0.0162421 + 0.0162421i
\(709\) 10.1007i 0.379340i 0.981848 + 0.189670i \(0.0607418\pi\)
−0.981848 + 0.189670i \(0.939258\pi\)
\(710\) −6.59097 + 5.94746i −0.247355 + 0.223204i
\(711\) 17.1528i 0.643279i
\(712\) 3.83335 + 3.83335i 0.143661 + 0.143661i
\(713\) −30.5304 30.5304i −1.14337 1.14337i
\(714\) 1.37032i 0.0512831i
\(715\) 23.8549 21.5259i 0.892124 0.805022i
\(716\) 7.93836i 0.296670i
\(717\) −7.83618 + 7.83618i −0.292647 + 0.292647i
\(718\) 3.36648 + 3.36648i 0.125636 + 0.125636i
\(719\) 41.4079i 1.54425i −0.635469 0.772126i \(-0.719193\pi\)
0.635469 0.772126i \(-0.280807\pi\)
\(720\) −2.23313 0.114611i −0.0832238 0.00427131i
\(721\) 11.3788i 0.423768i
\(722\) −7.52482 17.4464i −0.280045 0.649288i
\(723\) 10.2642 10.2642i 0.381730 0.381730i
\(724\) −4.77157 −0.177334
\(725\) 30.7903 + 3.16886i 1.14352 + 0.117689i
\(726\) −17.0156 −0.631509
\(727\) 16.2887 + 16.2887i 0.604113 + 0.604113i 0.941401 0.337288i \(-0.109510\pi\)
−0.337288 + 0.941401i \(0.609510\pi\)
\(728\) −3.81077 + 3.81077i −0.141236 + 0.141236i
\(729\) 1.00000i 0.0370370i
\(730\) 24.3891 + 1.25172i 0.902679 + 0.0463283i
\(731\) 6.95941 0.257403
\(732\) 5.87621 5.87621i 0.217191 0.217191i
\(733\) −8.03197 + 8.03197i −0.296667 + 0.296667i −0.839707 0.543040i \(-0.817273\pi\)
0.543040 + 0.839707i \(0.317273\pi\)
\(734\) −17.8202 −0.657754
\(735\) −4.58295 5.07883i −0.169045 0.187335i
\(736\) 5.50029i 0.202744i
\(737\) −53.9942 + 53.9942i −1.98890 + 1.98890i
\(738\) −1.34774 + 1.34774i −0.0496110 + 0.0496110i
\(739\) 2.95079i 0.108546i 0.998526 + 0.0542732i \(0.0172842\pi\)
−0.998526 + 0.0542732i \(0.982716\pi\)
\(740\) −13.1615 + 11.8764i −0.483825 + 0.436587i
\(741\) −9.79141 + 6.64563i −0.359697 + 0.244133i
\(742\) 17.7467 + 17.7467i 0.651501 + 0.651501i
\(743\) 15.8575 + 15.8575i 0.581756 + 0.581756i 0.935386 0.353630i \(-0.115053\pi\)
−0.353630 + 0.935386i \(0.615053\pi\)
\(744\) −7.84986 −0.287790
\(745\) −28.9086 1.48368i −1.05913 0.0543579i
\(746\) −9.51719 −0.348449
\(747\) 5.43217 + 5.43217i 0.198753 + 0.198753i
\(748\) −2.58359 + 2.58359i −0.0944655 + 0.0944655i
\(749\) 19.7643 0.722172
\(750\) 1.71315 11.0483i 0.0625552 0.403427i
\(751\) 42.3190i 1.54424i −0.635475 0.772121i \(-0.719196\pi\)
0.635475 0.772121i \(-0.280804\pi\)
\(752\) 7.86994 + 7.86994i 0.286987 + 0.286987i
\(753\) 4.79559 + 4.79559i 0.174761 + 0.174761i
\(754\) −16.8064 −0.612054
\(755\) 48.5745 + 2.49299i 1.76781 + 0.0907294i
\(756\) 1.98511i 0.0721977i
\(757\) 6.14572 + 6.14572i 0.223370 + 0.223370i 0.809916 0.586546i \(-0.199513\pi\)
−0.586546 + 0.809916i \(0.699513\pi\)
\(758\) 7.45532 7.45532i 0.270789 0.270789i
\(759\) 29.1129 1.05673
\(760\) −9.46656 2.32039i −0.343388 0.0841695i
\(761\) −32.5422 −1.17966 −0.589828 0.807529i \(-0.700804\pi\)
−0.589828 + 0.807529i \(0.700804\pi\)
\(762\) 1.33748 1.33748i 0.0484520 0.0484520i
\(763\) 12.1280 + 12.1280i 0.439063 + 0.439063i
\(764\) 13.8711i 0.501840i
\(765\) 1.03408 + 1.14597i 0.0373874 + 0.0414327i
\(766\) −12.0726 −0.436201
\(767\) 1.17328 + 1.17328i 0.0423646 + 0.0423646i
\(768\) 0.707107 + 0.707107i 0.0255155 + 0.0255155i
\(769\) 7.15156i 0.257892i −0.991652 0.128946i \(-0.958841\pi\)
0.991652 0.128946i \(-0.0411594\pi\)
\(770\) −1.20424 + 23.4638i −0.0433976 + 0.845576i
\(771\) −18.5429 −0.667805
\(772\) −8.22061 + 8.22061i −0.295866 + 0.295866i
\(773\) 28.5163 + 28.5163i 1.02566 + 1.02566i 0.999662 + 0.0259998i \(0.00827692\pi\)
0.0259998 + 0.999662i \(0.491723\pi\)
\(774\) −10.0817 −0.362379
\(775\) 4.01821 39.0431i 0.144338 1.40247i
\(776\) −4.38992 −0.157589
\(777\) −11.1285 11.1285i −0.399234 0.399234i
\(778\) 17.7611 + 17.7611i 0.636767 + 0.636767i
\(779\)