Properties

Label 370.2.h.e.117.1
Level $370$
Weight $2$
Character 370.117
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.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 117.1
Root \(-2.09082 + 2.09082i\) of defining polynomial
Character \(\chi\) \(=\) 370.117
Dual form 370.2.h.e.253.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-2.09082 - 2.09082i) q^{3} +1.00000 q^{4} +(-1.81614 + 1.30447i) q^{5} +(2.09082 + 2.09082i) q^{6} +(-0.643605 - 0.643605i) q^{7} -1.00000 q^{8} +5.74304i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-2.09082 - 2.09082i) q^{3} +1.00000 q^{4} +(-1.81614 + 1.30447i) q^{5} +(2.09082 + 2.09082i) q^{6} +(-0.643605 - 0.643605i) q^{7} -1.00000 q^{8} +5.74304i q^{9} +(1.81614 - 1.30447i) q^{10} +1.88405i q^{11} +(-2.09082 - 2.09082i) q^{12} -0.536082 q^{13} +(0.643605 + 0.643605i) q^{14} +(6.52462 + 1.06980i) q^{15} +1.00000 q^{16} +0.334703i q^{17} -5.74304i q^{18} +(1.08518 - 1.08518i) q^{19} +(-1.81614 + 1.30447i) q^{20} +2.69132i q^{21} -1.88405i q^{22} +4.65098 q^{23} +(2.09082 + 2.09082i) q^{24} +(1.59670 - 4.73820i) q^{25} +0.536082 q^{26} +(5.73519 - 5.73519i) q^{27} +(-0.643605 - 0.643605i) q^{28} +(3.33033 + 3.33033i) q^{29} +(-6.52462 - 1.06980i) q^{30} +(4.90948 - 4.90948i) q^{31} -1.00000 q^{32} +(3.93919 - 3.93919i) q^{33} -0.334703i q^{34} +(2.00844 + 0.329310i) q^{35} +5.74304i q^{36} +(-0.819646 + 6.02729i) q^{37} +(-1.08518 + 1.08518i) q^{38} +(1.12085 + 1.12085i) q^{39} +(1.81614 - 1.30447i) q^{40} +8.26486i q^{41} -2.69132i q^{42} +11.9117 q^{43} +1.88405i q^{44} +(-7.49163 - 10.4301i) q^{45} -4.65098 q^{46} +(-0.141535 - 0.141535i) q^{47} +(-2.09082 - 2.09082i) q^{48} -6.17154i q^{49} +(-1.59670 + 4.73820i) q^{50} +(0.699803 - 0.699803i) q^{51} -0.536082 q^{52} +(-5.03296 + 5.03296i) q^{53} +(-5.73519 + 5.73519i) q^{54} +(-2.45768 - 3.42168i) q^{55} +(0.643605 + 0.643605i) q^{56} -4.53784 q^{57} +(-3.33033 - 3.33033i) q^{58} +(-4.10789 + 4.10789i) q^{59} +(6.52462 + 1.06980i) q^{60} +(-8.90180 + 8.90180i) q^{61} +(-4.90948 + 4.90948i) q^{62} +(3.69625 - 3.69625i) q^{63} +1.00000 q^{64} +(0.973599 - 0.699305i) q^{65} +(-3.93919 + 3.93919i) q^{66} +(-3.61956 + 3.61956i) q^{67} +0.334703i q^{68} +(-9.72436 - 9.72436i) q^{69} +(-2.00844 - 0.329310i) q^{70} +15.5121 q^{71} -5.74304i q^{72} +(6.82739 + 6.82739i) q^{73} +(0.819646 - 6.02729i) q^{74} +(-13.2451 + 6.56829i) q^{75} +(1.08518 - 1.08518i) q^{76} +(1.21258 - 1.21258i) q^{77} +(-1.12085 - 1.12085i) q^{78} +(-5.73637 + 5.73637i) q^{79} +(-1.81614 + 1.30447i) q^{80} -6.75336 q^{81} -8.26486i q^{82} +(-7.90475 + 7.90475i) q^{83} +2.69132i q^{84} +(-0.436611 - 0.607866i) q^{85} -11.9117 q^{86} -13.9262i q^{87} -1.88405i q^{88} +(1.21521 + 1.21521i) q^{89} +(7.49163 + 10.4301i) q^{90} +(0.345025 + 0.345025i) q^{91} +4.65098 q^{92} -20.5297 q^{93} +(0.141535 + 0.141535i) q^{94} +(-0.555249 + 3.38643i) q^{95} +(2.09082 + 2.09082i) q^{96} -17.1767i q^{97} +6.17154i q^{98} -10.8201 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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.09082 2.09082i −1.20713 1.20713i −0.971951 0.235183i \(-0.924431\pi\)
−0.235183 0.971951i \(-0.575569\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.81614 + 1.30447i −0.812201 + 0.583378i
\(6\) 2.09082 + 2.09082i 0.853573 + 0.853573i
\(7\) −0.643605 0.643605i −0.243260 0.243260i 0.574937 0.818197i \(-0.305026\pi\)
−0.818197 + 0.574937i \(0.805026\pi\)
\(8\) −1.00000 −0.353553
\(9\) 5.74304i 1.91435i
\(10\) 1.81614 1.30447i 0.574313 0.412510i
\(11\) 1.88405i 0.568061i 0.958815 + 0.284030i \(0.0916717\pi\)
−0.958815 + 0.284030i \(0.908328\pi\)
\(12\) −2.09082 2.09082i −0.603567 0.603567i
\(13\) −0.536082 −0.148683 −0.0743413 0.997233i \(-0.523685\pi\)
−0.0743413 + 0.997233i \(0.523685\pi\)
\(14\) 0.643605 + 0.643605i 0.172011 + 0.172011i
\(15\) 6.52462 + 1.06980i 1.68465 + 0.276220i
\(16\) 1.00000 0.250000
\(17\) 0.334703i 0.0811774i 0.999176 + 0.0405887i \(0.0129233\pi\)
−0.999176 + 0.0405887i \(0.987077\pi\)
\(18\) 5.74304i 1.35365i
\(19\) 1.08518 1.08518i 0.248958 0.248958i −0.571585 0.820543i \(-0.693671\pi\)
0.820543 + 0.571585i \(0.193671\pi\)
\(20\) −1.81614 + 1.30447i −0.406101 + 0.291689i
\(21\) 2.69132i 0.587295i
\(22\) 1.88405i 0.401680i
\(23\) 4.65098 0.969797 0.484899 0.874570i \(-0.338856\pi\)
0.484899 + 0.874570i \(0.338856\pi\)
\(24\) 2.09082 + 2.09082i 0.426786 + 0.426786i
\(25\) 1.59670 4.73820i 0.319341 0.947640i
\(26\) 0.536082 0.105134
\(27\) 5.73519 5.73519i 1.10374 1.10374i
\(28\) −0.643605 0.643605i −0.121630 0.121630i
\(29\) 3.33033 + 3.33033i 0.618427 + 0.618427i 0.945128 0.326701i \(-0.105937\pi\)
−0.326701 + 0.945128i \(0.605937\pi\)
\(30\) −6.52462 1.06980i −1.19123 0.195317i
\(31\) 4.90948 4.90948i 0.881769 0.881769i −0.111945 0.993714i \(-0.535708\pi\)
0.993714 + 0.111945i \(0.0357081\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.93919 3.93919i 0.685726 0.685726i
\(34\) 0.334703i 0.0574011i
\(35\) 2.00844 + 0.329310i 0.339488 + 0.0556635i
\(36\) 5.74304i 0.957173i
\(37\) −0.819646 + 6.02729i −0.134749 + 0.990880i
\(38\) −1.08518 + 1.08518i −0.176040 + 0.176040i
\(39\) 1.12085 + 1.12085i 0.179480 + 0.179480i
\(40\) 1.81614 1.30447i 0.287156 0.206255i
\(41\) 8.26486i 1.29075i 0.763864 + 0.645377i \(0.223300\pi\)
−0.763864 + 0.645377i \(0.776700\pi\)
\(42\) 2.69132i 0.415280i
\(43\) 11.9117 1.81652 0.908259 0.418409i \(-0.137412\pi\)
0.908259 + 0.418409i \(0.137412\pi\)
\(44\) 1.88405i 0.284030i
\(45\) −7.49163 10.4301i −1.11679 1.55483i
\(46\) −4.65098 −0.685750
\(47\) −0.141535 0.141535i −0.0206450 0.0206450i 0.696709 0.717354i \(-0.254647\pi\)
−0.717354 + 0.696709i \(0.754647\pi\)
\(48\) −2.09082 2.09082i −0.301784 0.301784i
\(49\) 6.17154i 0.881649i
\(50\) −1.59670 + 4.73820i −0.225808 + 0.670083i
\(51\) 0.699803 0.699803i 0.0979920 0.0979920i
\(52\) −0.536082 −0.0743413
\(53\) −5.03296 + 5.03296i −0.691330 + 0.691330i −0.962525 0.271194i \(-0.912581\pi\)
0.271194 + 0.962525i \(0.412581\pi\)
\(54\) −5.73519 + 5.73519i −0.780460 + 0.780460i
\(55\) −2.45768 3.42168i −0.331394 0.461380i
\(56\) 0.643605 + 0.643605i 0.0860054 + 0.0860054i
\(57\) −4.53784 −0.601051
\(58\) −3.33033 3.33033i −0.437294 0.437294i
\(59\) −4.10789 + 4.10789i −0.534802 + 0.534802i −0.921998 0.387195i \(-0.873444\pi\)
0.387195 + 0.921998i \(0.373444\pi\)
\(60\) 6.52462 + 1.06980i 0.842325 + 0.138110i
\(61\) −8.90180 + 8.90180i −1.13976 + 1.13976i −0.151265 + 0.988493i \(0.548335\pi\)
−0.988493 + 0.151265i \(0.951665\pi\)
\(62\) −4.90948 + 4.90948i −0.623505 + 0.623505i
\(63\) 3.69625 3.69625i 0.465683 0.465683i
\(64\) 1.00000 0.125000
\(65\) 0.973599 0.699305i 0.120760 0.0867381i
\(66\) −3.93919 + 3.93919i −0.484881 + 0.484881i
\(67\) −3.61956 + 3.61956i −0.442199 + 0.442199i −0.892751 0.450551i \(-0.851227\pi\)
0.450551 + 0.892751i \(0.351227\pi\)
\(68\) 0.334703i 0.0405887i
\(69\) −9.72436 9.72436i −1.17068 1.17068i
\(70\) −2.00844 0.329310i −0.240054 0.0393601i
\(71\) 15.5121 1.84095 0.920477 0.390798i \(-0.127801\pi\)
0.920477 + 0.390798i \(0.127801\pi\)
\(72\) 5.74304i 0.676823i
\(73\) 6.82739 + 6.82739i 0.799086 + 0.799086i 0.982951 0.183866i \(-0.0588611\pi\)
−0.183866 + 0.982951i \(0.558861\pi\)
\(74\) 0.819646 6.02729i 0.0952819 0.700658i
\(75\) −13.2451 + 6.56829i −1.52942 + 0.758441i
\(76\) 1.08518 1.08518i 0.124479 0.124479i
\(77\) 1.21258 1.21258i 0.138186 0.138186i
\(78\) −1.12085 1.12085i −0.126911 0.126911i
\(79\) −5.73637 + 5.73637i −0.645392 + 0.645392i −0.951876 0.306484i \(-0.900847\pi\)
0.306484 + 0.951876i \(0.400847\pi\)
\(80\) −1.81614 + 1.30447i −0.203050 + 0.145844i
\(81\) −6.75336 −0.750373
\(82\) 8.26486i 0.912701i
\(83\) −7.90475 + 7.90475i −0.867659 + 0.867659i −0.992213 0.124554i \(-0.960250\pi\)
0.124554 + 0.992213i \(0.460250\pi\)
\(84\) 2.69132i 0.293647i
\(85\) −0.436611 0.607866i −0.0473571 0.0659323i
\(86\) −11.9117 −1.28447
\(87\) 13.9262i 1.49305i
\(88\) 1.88405i 0.200840i
\(89\) 1.21521 + 1.21521i 0.128812 + 0.128812i 0.768574 0.639761i \(-0.220967\pi\)
−0.639761 + 0.768574i \(0.720967\pi\)
\(90\) 7.49163 + 10.4301i 0.789687 + 1.09943i
\(91\) 0.345025 + 0.345025i 0.0361685 + 0.0361685i
\(92\) 4.65098 0.484899
\(93\) −20.5297 −2.12883
\(94\) 0.141535 + 0.141535i 0.0145982 + 0.0145982i
\(95\) −0.555249 + 3.38643i −0.0569674 + 0.347440i
\(96\) 2.09082 + 2.09082i 0.213393 + 0.213393i
\(97\) 17.1767i 1.74403i −0.489477 0.872016i \(-0.662812\pi\)
0.489477 0.872016i \(-0.337188\pi\)
\(98\) 6.17154i 0.623420i
\(99\) −10.8201 −1.08746
\(100\) 1.59670 4.73820i 0.159670 0.473820i
\(101\) 13.4676i 1.34008i −0.742324 0.670041i \(-0.766277\pi\)
0.742324 0.670041i \(-0.233723\pi\)
\(102\) −0.699803 + 0.699803i −0.0692908 + 0.0692908i
\(103\) 12.6201i 1.24350i 0.783216 + 0.621749i \(0.213578\pi\)
−0.783216 + 0.621749i \(0.786422\pi\)
\(104\) 0.536082 0.0525672
\(105\) −3.51075 4.88781i −0.342615 0.477001i
\(106\) 5.03296 5.03296i 0.488844 0.488844i
\(107\) −1.64796 1.64796i −0.159314 0.159314i 0.622949 0.782263i \(-0.285935\pi\)
−0.782263 + 0.622949i \(0.785935\pi\)
\(108\) 5.73519 5.73519i 0.551869 0.551869i
\(109\) 7.06206 7.06206i 0.676422 0.676422i −0.282766 0.959189i \(-0.591252\pi\)
0.959189 + 0.282766i \(0.0912521\pi\)
\(110\) 2.45768 + 3.42168i 0.234331 + 0.326245i
\(111\) 14.3157 10.8882i 1.35878 1.03346i
\(112\) −0.643605 0.643605i −0.0608150 0.0608150i
\(113\) 15.1701i 1.42709i 0.700612 + 0.713543i \(0.252911\pi\)
−0.700612 + 0.713543i \(0.747089\pi\)
\(114\) 4.53784 0.425007
\(115\) −8.44682 + 6.06708i −0.787670 + 0.565758i
\(116\) 3.33033 + 3.33033i 0.309213 + 0.309213i
\(117\) 3.07874i 0.284630i
\(118\) 4.10789 4.10789i 0.378162 0.378162i
\(119\) 0.215416 0.215416i 0.0197472 0.0197472i
\(120\) −6.52462 1.06980i −0.595614 0.0976587i
\(121\) 7.45037 0.677307
\(122\) 8.90180 8.90180i 0.805931 0.805931i
\(123\) 17.2803 17.2803i 1.55811 1.55811i
\(124\) 4.90948 4.90948i 0.440885 0.440885i
\(125\) 3.28101 + 10.6881i 0.293463 + 0.955970i
\(126\) −3.69625 + 3.69625i −0.329288 + 0.329288i
\(127\) −3.59805 3.59805i −0.319275 0.319275i 0.529213 0.848489i \(-0.322487\pi\)
−0.848489 + 0.529213i \(0.822487\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −24.9052 24.9052i −2.19278 2.19278i
\(130\) −0.973599 + 0.699305i −0.0853903 + 0.0613331i
\(131\) 7.63639 7.63639i 0.667194 0.667194i −0.289871 0.957066i \(-0.593613\pi\)
0.957066 + 0.289871i \(0.0936126\pi\)
\(132\) 3.93919 3.93919i 0.342863 0.342863i
\(133\) −1.39686 −0.121123
\(134\) 3.61956 3.61956i 0.312682 0.312682i
\(135\) −2.93449 + 17.8973i −0.252561 + 1.54035i
\(136\) 0.334703i 0.0287005i
\(137\) 5.48037 + 5.48037i 0.468220 + 0.468220i 0.901337 0.433118i \(-0.142587\pi\)
−0.433118 + 0.901337i \(0.642587\pi\)
\(138\) 9.72436 + 9.72436i 0.827793 + 0.827793i
\(139\) 4.24414 0.359983 0.179991 0.983668i \(-0.442393\pi\)
0.179991 + 0.983668i \(0.442393\pi\)
\(140\) 2.00844 + 0.329310i 0.169744 + 0.0278318i
\(141\) 0.591849i 0.0498427i
\(142\) −15.5121 −1.30175
\(143\) 1.01000i 0.0844607i
\(144\) 5.74304i 0.478586i
\(145\) −10.3927 1.70401i −0.863063 0.141510i
\(146\) −6.82739 6.82739i −0.565039 0.565039i
\(147\) −12.9036 + 12.9036i −1.06427 + 1.06427i
\(148\) −0.819646 + 6.02729i −0.0673745 + 0.495440i
\(149\) 20.3080i 1.66370i 0.555002 + 0.831849i \(0.312718\pi\)
−0.555002 + 0.831849i \(0.687282\pi\)
\(150\) 13.2451 6.56829i 1.08146 0.536299i
\(151\) 13.8362i 1.12597i 0.826466 + 0.562987i \(0.190348\pi\)
−0.826466 + 0.562987i \(0.809652\pi\)
\(152\) −1.08518 + 1.08518i −0.0880199 + 0.0880199i
\(153\) −1.92221 −0.155402
\(154\) −1.21258 + 1.21258i −0.0977126 + 0.0977126i
\(155\) −2.51201 + 15.3206i −0.201769 + 1.23058i
\(156\) 1.12085 + 1.12085i 0.0897399 + 0.0897399i
\(157\) 13.2682 + 13.2682i 1.05892 + 1.05892i 0.998152 + 0.0607691i \(0.0193553\pi\)
0.0607691 + 0.998152i \(0.480645\pi\)
\(158\) 5.73637 5.73637i 0.456361 0.456361i
\(159\) 21.0460 1.66906
\(160\) 1.81614 1.30447i 0.143578 0.103128i
\(161\) −2.99340 2.99340i −0.235913 0.235913i
\(162\) 6.75336 0.530594
\(163\) 1.48487i 0.116304i −0.998308 0.0581520i \(-0.981479\pi\)
0.998308 0.0581520i \(-0.0185208\pi\)
\(164\) 8.26486i 0.645377i
\(165\) −2.01555 + 12.2927i −0.156910 + 0.956984i
\(166\) 7.90475 7.90475i 0.613527 0.613527i
\(167\) 4.69210i 0.363086i −0.983383 0.181543i \(-0.941891\pi\)
0.983383 0.181543i \(-0.0581091\pi\)
\(168\) 2.69132i 0.207640i
\(169\) −12.7126 −0.977894
\(170\) 0.436611 + 0.607866i 0.0334865 + 0.0466212i
\(171\) 6.23224 + 6.23224i 0.476591 + 0.476591i
\(172\) 11.9117 0.908259
\(173\) −1.68127 1.68127i −0.127825 0.127825i 0.640300 0.768125i \(-0.278810\pi\)
−0.768125 + 0.640300i \(0.778810\pi\)
\(174\) 13.9262i 1.05574i
\(175\) −4.07718 + 2.02188i −0.308206 + 0.152840i
\(176\) 1.88405i 0.142015i
\(177\) 17.1777 1.29116
\(178\) −1.21521 1.21521i −0.0910840 0.0910840i
\(179\) −13.0168 13.0168i −0.972921 0.972921i 0.0267216 0.999643i \(-0.491493\pi\)
−0.999643 + 0.0267216i \(0.991493\pi\)
\(180\) −7.49163 10.4301i −0.558393 0.777417i
\(181\) 5.91911 0.439964 0.219982 0.975504i \(-0.429400\pi\)
0.219982 + 0.975504i \(0.429400\pi\)
\(182\) −0.345025 0.345025i −0.0255750 0.0255750i
\(183\) 37.2241 2.75168
\(184\) −4.65098 −0.342875
\(185\) −6.37384 12.0156i −0.468614 0.883403i
\(186\) 20.5297 1.50531
\(187\) −0.630595 −0.0461137
\(188\) −0.141535 0.141535i −0.0103225 0.0103225i
\(189\) −7.38239 −0.536990
\(190\) 0.555249 3.38643i 0.0402820 0.245677i
\(191\) −8.14150 8.14150i −0.589099 0.589099i 0.348289 0.937387i \(-0.386763\pi\)
−0.937387 + 0.348289i \(0.886763\pi\)
\(192\) −2.09082 2.09082i −0.150892 0.150892i
\(193\) 15.8717 1.14247 0.571235 0.820787i \(-0.306465\pi\)
0.571235 + 0.820787i \(0.306465\pi\)
\(194\) 17.1767i 1.23322i
\(195\) −3.49774 0.573499i −0.250478 0.0410691i
\(196\) 6.17154i 0.440825i
\(197\) 3.60225 + 3.60225i 0.256650 + 0.256650i 0.823690 0.567040i \(-0.191912\pi\)
−0.567040 + 0.823690i \(0.691912\pi\)
\(198\) 10.8201 0.768954
\(199\) −1.14697 1.14697i −0.0813064 0.0813064i 0.665284 0.746590i \(-0.268310\pi\)
−0.746590 + 0.665284i \(0.768310\pi\)
\(200\) −1.59670 + 4.73820i −0.112904 + 0.335041i
\(201\) 15.1357 1.06759
\(202\) 13.4676i 0.947581i
\(203\) 4.28683i 0.300877i
\(204\) 0.699803 0.699803i 0.0489960 0.0489960i
\(205\) −10.7813 15.0101i −0.752997 1.04835i
\(206\) 12.6201i 0.879286i
\(207\) 26.7108i 1.85653i
\(208\) −0.536082 −0.0371706
\(209\) 2.04453 + 2.04453i 0.141423 + 0.141423i
\(210\) 3.51075 + 4.88781i 0.242265 + 0.337291i
\(211\) 3.19579 0.220008 0.110004 0.993931i \(-0.464914\pi\)
0.110004 + 0.993931i \(0.464914\pi\)
\(212\) −5.03296 + 5.03296i −0.345665 + 0.345665i
\(213\) −32.4331 32.4331i −2.22228 2.22228i
\(214\) 1.64796 + 1.64796i 0.112652 + 0.112652i
\(215\) −21.6333 + 15.5385i −1.47538 + 1.05972i
\(216\) −5.73519 + 5.73519i −0.390230 + 0.390230i
\(217\) −6.31954 −0.428998
\(218\) −7.06206 + 7.06206i −0.478303 + 0.478303i
\(219\) 28.5497i 1.92921i
\(220\) −2.45768 3.42168i −0.165697 0.230690i
\(221\) 0.179428i 0.0120697i
\(222\) −14.3157 + 10.8882i −0.960806 + 0.730770i
\(223\) −7.29909 + 7.29909i −0.488783 + 0.488783i −0.907922 0.419139i \(-0.862332\pi\)
0.419139 + 0.907922i \(0.362332\pi\)
\(224\) 0.643605 + 0.643605i 0.0430027 + 0.0430027i
\(225\) 27.2117 + 9.16993i 1.81411 + 0.611329i
\(226\) 15.1701i 1.00910i
\(227\) 19.6620i 1.30501i −0.757783 0.652507i \(-0.773717\pi\)
0.757783 0.652507i \(-0.226283\pi\)
\(228\) −4.53784 −0.300526
\(229\) 13.4975i 0.891940i 0.895048 + 0.445970i \(0.147141\pi\)
−0.895048 + 0.445970i \(0.852859\pi\)
\(230\) 8.44682 6.06708i 0.556967 0.400051i
\(231\) −5.07057 −0.333619
\(232\) −3.33033 3.33033i −0.218647 0.218647i
\(233\) −1.10924 1.10924i −0.0726687 0.0726687i 0.669838 0.742507i \(-0.266363\pi\)
−0.742507 + 0.669838i \(0.766363\pi\)
\(234\) 3.07874i 0.201264i
\(235\) 0.441676 + 0.0724186i 0.0288118 + 0.00472407i
\(236\) −4.10789 + 4.10789i −0.267401 + 0.267401i
\(237\) 23.9874 1.55815
\(238\) −0.215416 + 0.215416i −0.0139634 + 0.0139634i
\(239\) 10.5161 10.5161i 0.680230 0.680230i −0.279822 0.960052i \(-0.590275\pi\)
0.960052 + 0.279822i \(0.0902754\pi\)
\(240\) 6.52462 + 1.06980i 0.421163 + 0.0690551i
\(241\) −18.7617 18.7617i −1.20855 1.20855i −0.971498 0.237047i \(-0.923820\pi\)
−0.237047 0.971498i \(-0.576180\pi\)
\(242\) −7.45037 −0.478928
\(243\) −3.08553 3.08553i −0.197937 0.197937i
\(244\) −8.90180 + 8.90180i −0.569879 + 0.569879i
\(245\) 8.05061 + 11.2084i 0.514334 + 0.716076i
\(246\) −17.2803 + 17.2803i −1.10175 + 1.10175i
\(247\) −0.581747 + 0.581747i −0.0370157 + 0.0370157i
\(248\) −4.90948 + 4.90948i −0.311752 + 0.311752i
\(249\) 33.0548 2.09476
\(250\) −3.28101 10.6881i −0.207510 0.675973i
\(251\) 9.09164 9.09164i 0.573859 0.573859i −0.359346 0.933205i \(-0.617000\pi\)
0.933205 + 0.359346i \(0.117000\pi\)
\(252\) 3.69625 3.69625i 0.232842 0.232842i
\(253\) 8.76267i 0.550904i
\(254\) 3.59805 + 3.59805i 0.225762 + 0.225762i
\(255\) −0.358064 + 2.18381i −0.0224228 + 0.136756i
\(256\) 1.00000 0.0625000
\(257\) 2.08454i 0.130030i −0.997884 0.0650151i \(-0.979290\pi\)
0.997884 0.0650151i \(-0.0207096\pi\)
\(258\) 24.9052 + 24.9052i 1.55053 + 1.55053i
\(259\) 4.40672 3.35166i 0.273820 0.208262i
\(260\) 0.973599 0.699305i 0.0603800 0.0433690i
\(261\) −19.1262 + 19.1262i −1.18388 + 1.18388i
\(262\) −7.63639 + 7.63639i −0.471778 + 0.471778i
\(263\) −6.41417 6.41417i −0.395515 0.395515i 0.481133 0.876648i \(-0.340225\pi\)
−0.876648 + 0.481133i \(0.840225\pi\)
\(264\) −3.93919 + 3.93919i −0.242441 + 0.242441i
\(265\) 2.57519 15.7059i 0.158192 0.964806i
\(266\) 1.39686 0.0856469
\(267\) 5.08157i 0.310987i
\(268\) −3.61956 + 3.61956i −0.221100 + 0.221100i
\(269\) 10.5529i 0.643424i −0.946838 0.321712i \(-0.895742\pi\)
0.946838 0.321712i \(-0.104258\pi\)
\(270\) 2.93449 17.8973i 0.178588 1.08919i
\(271\) 19.2734 1.17078 0.585389 0.810753i \(-0.300942\pi\)
0.585389 + 0.810753i \(0.300942\pi\)
\(272\) 0.334703i 0.0202943i
\(273\) 1.44277i 0.0873204i
\(274\) −5.48037 5.48037i −0.331081 0.331081i
\(275\) 8.92698 + 3.00826i 0.538317 + 0.181405i
\(276\) −9.72436 9.72436i −0.585338 0.585338i
\(277\) 7.82056 0.469892 0.234946 0.972008i \(-0.424509\pi\)
0.234946 + 0.972008i \(0.424509\pi\)
\(278\) −4.24414 −0.254546
\(279\) 28.1953 + 28.1953i 1.68801 + 1.68801i
\(280\) −2.00844 0.329310i −0.120027 0.0196800i
\(281\) −10.4788 10.4788i −0.625110 0.625110i 0.321723 0.946834i \(-0.395738\pi\)
−0.946834 + 0.321723i \(0.895738\pi\)
\(282\) 0.591849i 0.0352441i
\(283\) 26.3960i 1.56908i −0.620079 0.784539i \(-0.712900\pi\)
0.620079 0.784539i \(-0.287100\pi\)
\(284\) 15.5121 0.920477
\(285\) 8.24133 5.91948i 0.488174 0.350640i
\(286\) 1.01000i 0.0597228i
\(287\) 5.31930 5.31930i 0.313989 0.313989i
\(288\) 5.74304i 0.338412i
\(289\) 16.8880 0.993410
\(290\) 10.3927 + 1.70401i 0.610278 + 0.100063i
\(291\) −35.9134 + 35.9134i −2.10528 + 2.10528i
\(292\) 6.82739 + 6.82739i 0.399543 + 0.399543i
\(293\) −22.4956 + 22.4956i −1.31421 + 1.31421i −0.395928 + 0.918281i \(0.629577\pi\)
−0.918281 + 0.395928i \(0.870423\pi\)
\(294\) 12.9036 12.9036i 0.752552 0.752552i
\(295\) 2.10186 12.8191i 0.122375 0.746359i
\(296\) 0.819646 6.02729i 0.0476410 0.350329i
\(297\) 10.8054 + 10.8054i 0.626990 + 0.626990i
\(298\) 20.3080i 1.17641i
\(299\) −2.49331 −0.144192
\(300\) −13.2451 + 6.56829i −0.764708 + 0.379221i
\(301\) −7.66643 7.66643i −0.441886 0.441886i
\(302\) 13.8362i 0.796183i
\(303\) −28.1584 + 28.1584i −1.61766 + 1.61766i
\(304\) 1.08518 1.08518i 0.0622395 0.0622395i
\(305\) 4.55473 27.7790i 0.260803 1.59062i
\(306\) 1.92221 0.109885
\(307\) −17.4358 + 17.4358i −0.995111 + 0.995111i −0.999988 0.00487690i \(-0.998448\pi\)
0.00487690 + 0.999988i \(0.498448\pi\)
\(308\) 1.21258 1.21258i 0.0690932 0.0690932i
\(309\) 26.3864 26.3864i 1.50107 1.50107i
\(310\) 2.51201 15.3206i 0.142672 0.870150i
\(311\) −3.97519 + 3.97519i −0.225412 + 0.225412i −0.810773 0.585361i \(-0.800953\pi\)
0.585361 + 0.810773i \(0.300953\pi\)
\(312\) −1.12085 1.12085i −0.0634557 0.0634557i
\(313\) 15.8472 0.895735 0.447867 0.894100i \(-0.352184\pi\)
0.447867 + 0.894100i \(0.352184\pi\)
\(314\) −13.2682 13.2682i −0.748770 0.748770i
\(315\) −1.89124 + 11.5345i −0.106559 + 0.649898i
\(316\) −5.73637 + 5.73637i −0.322696 + 0.322696i
\(317\) 0.950144 0.950144i 0.0533654 0.0533654i −0.679920 0.733286i \(-0.737986\pi\)
0.733286 + 0.679920i \(0.237986\pi\)
\(318\) −21.0460 −1.18020
\(319\) −6.27449 + 6.27449i −0.351304 + 0.351304i
\(320\) −1.81614 + 1.30447i −0.101525 + 0.0729222i
\(321\) 6.89116i 0.384627i
\(322\) 2.99340 + 2.99340i 0.166816 + 0.166816i
\(323\) 0.363214 + 0.363214i 0.0202097 + 0.0202097i
\(324\) −6.75336 −0.375186
\(325\) −0.855965 + 2.54007i −0.0474804 + 0.140897i
\(326\) 1.48487i 0.0822394i
\(327\) −29.5309 −1.63306
\(328\) 8.26486i 0.456350i
\(329\) 0.182186i 0.0100442i
\(330\) 2.01555 12.2927i 0.110952 0.676690i
\(331\) −19.3735 19.3735i −1.06486 1.06486i −0.997745 0.0671177i \(-0.978620\pi\)
−0.0671177 0.997745i \(-0.521380\pi\)
\(332\) −7.90475 + 7.90475i −0.433829 + 0.433829i
\(333\) −34.6149 4.70726i −1.89689 0.257956i
\(334\) 4.69210i 0.256740i
\(335\) 1.85200 11.2952i 0.101186 0.617124i
\(336\) 2.69132i 0.146824i
\(337\) −3.21128 + 3.21128i −0.174929 + 0.174929i −0.789141 0.614212i \(-0.789474\pi\)
0.614212 + 0.789141i \(0.289474\pi\)
\(338\) 12.7126 0.691475
\(339\) 31.7180 31.7180i 1.72268 1.72268i
\(340\) −0.436611 0.607866i −0.0236785 0.0329662i
\(341\) 9.24969 + 9.24969i 0.500899 + 0.500899i
\(342\) −6.23224 6.23224i −0.337001 0.337001i
\(343\) −8.47727 + 8.47727i −0.457730 + 0.457730i
\(344\) −11.9117 −0.642236
\(345\) 30.3459 + 4.97561i 1.63377 + 0.267878i
\(346\) 1.68127 + 1.68127i 0.0903856 + 0.0903856i
\(347\) −18.4401 −0.989915 −0.494957 0.868917i \(-0.664816\pi\)
−0.494957 + 0.868917i \(0.664816\pi\)
\(348\) 13.9262i 0.746524i
\(349\) 21.3314i 1.14184i 0.821005 + 0.570921i \(0.193414\pi\)
−0.821005 + 0.570921i \(0.806586\pi\)
\(350\) 4.07718 2.02188i 0.217934 0.108074i
\(351\) −3.07453 + 3.07453i −0.164106 + 0.164106i
\(352\) 1.88405i 0.100420i
\(353\) 11.9150i 0.634173i 0.948397 + 0.317086i \(0.102704\pi\)
−0.948397 + 0.317086i \(0.897296\pi\)
\(354\) −17.1777 −0.912985
\(355\) −28.1722 + 20.2352i −1.49522 + 1.07397i
\(356\) 1.21521 + 1.21521i 0.0644061 + 0.0644061i
\(357\) −0.900793 −0.0476750
\(358\) 13.0168 + 13.0168i 0.687959 + 0.687959i
\(359\) 24.9976i 1.31932i 0.751562 + 0.659662i \(0.229301\pi\)
−0.751562 + 0.659662i \(0.770699\pi\)
\(360\) 7.49163 + 10.4301i 0.394844 + 0.549717i
\(361\) 16.6448i 0.876040i
\(362\) −5.91911 −0.311101
\(363\) −15.5774 15.5774i −0.817600 0.817600i
\(364\) 0.345025 + 0.345025i 0.0180842 + 0.0180842i
\(365\) −21.3056 3.49333i −1.11519 0.182849i
\(366\) −37.2241 −1.94573
\(367\) 0.228241 + 0.228241i 0.0119141 + 0.0119141i 0.713039 0.701125i \(-0.247318\pi\)
−0.701125 + 0.713039i \(0.747318\pi\)
\(368\) 4.65098 0.242449
\(369\) −47.4654 −2.47095
\(370\) 6.37384 + 12.0156i 0.331360 + 0.624660i
\(371\) 6.47848 0.336346
\(372\) −20.5297 −1.06441
\(373\) 5.32431 + 5.32431i 0.275682 + 0.275682i 0.831383 0.555700i \(-0.187550\pi\)
−0.555700 + 0.831383i \(0.687550\pi\)
\(374\) 0.630595 0.0326073
\(375\) 15.4868 29.2068i 0.799735 1.50823i
\(376\) 0.141535 + 0.141535i 0.00729912 + 0.00729912i
\(377\) −1.78533 1.78533i −0.0919492 0.0919492i
\(378\) 7.38239 0.379709
\(379\) 7.62224i 0.391528i 0.980651 + 0.195764i \(0.0627187\pi\)
−0.980651 + 0.195764i \(0.937281\pi\)
\(380\) −0.555249 + 3.38643i −0.0284837 + 0.173720i
\(381\) 15.0457i 0.770816i
\(382\) 8.14150 + 8.14150i 0.416556 + 0.416556i
\(383\) 9.60774 0.490933 0.245466 0.969405i \(-0.421059\pi\)
0.245466 + 0.969405i \(0.421059\pi\)
\(384\) 2.09082 + 2.09082i 0.106697 + 0.106697i
\(385\) −0.620435 + 3.78399i −0.0316203 + 0.192850i
\(386\) −15.8717 −0.807848
\(387\) 68.4093i 3.47744i
\(388\) 17.1767i 0.872016i
\(389\) −12.3615 + 12.3615i −0.626751 + 0.626751i −0.947249 0.320498i \(-0.896150\pi\)
0.320498 + 0.947249i \(0.396150\pi\)
\(390\) 3.49774 + 0.573499i 0.177115 + 0.0290403i
\(391\) 1.55670i 0.0787256i
\(392\) 6.17154i 0.311710i
\(393\) −31.9326 −1.61079
\(394\) −3.60225 3.60225i −0.181479 0.181479i
\(395\) 2.93510 17.9010i 0.147681 0.900695i
\(396\) −10.8201 −0.543732
\(397\) 22.1034 22.1034i 1.10934 1.10934i 0.116100 0.993238i \(-0.462961\pi\)
0.993238 0.116100i \(-0.0370394\pi\)
\(398\) 1.14697 + 1.14697i 0.0574923 + 0.0574923i
\(399\) 2.92058 + 2.92058i 0.146212 + 0.146212i
\(400\) 1.59670 4.73820i 0.0798352 0.236910i
\(401\) 11.3365 11.3365i 0.566118 0.566118i −0.364921 0.931039i \(-0.618904\pi\)
0.931039 + 0.364921i \(0.118904\pi\)
\(402\) −15.1357 −0.754899
\(403\) −2.63189 + 2.63189i −0.131104 + 0.131104i
\(404\) 13.4676i 0.670041i
\(405\) 12.2650 8.80956i 0.609454 0.437751i
\(406\) 4.28683i 0.212752i
\(407\) −11.3557 1.54425i −0.562880 0.0765456i
\(408\) −0.699803 + 0.699803i −0.0346454 + 0.0346454i
\(409\) −10.2703 10.2703i −0.507834 0.507834i 0.406027 0.913861i \(-0.366914\pi\)
−0.913861 + 0.406027i \(0.866914\pi\)
\(410\) 10.7813 + 15.0101i 0.532449 + 0.741297i
\(411\) 22.9169i 1.13041i
\(412\) 12.6201i 0.621749i
\(413\) 5.28772 0.260192
\(414\) 26.7108i 1.31276i
\(415\) 4.04458 24.6676i 0.198541 1.21089i
\(416\) 0.536082 0.0262836
\(417\) −8.87372 8.87372i −0.434548 0.434548i
\(418\) −2.04453 2.04453i −0.100001 0.100001i
\(419\) 13.8549i 0.676854i −0.940993 0.338427i \(-0.890105\pi\)
0.940993 0.338427i \(-0.109895\pi\)
\(420\) −3.51075 4.88781i −0.171307 0.238501i
\(421\) −25.5907 + 25.5907i −1.24722 + 1.24722i −0.290273 + 0.956944i \(0.593746\pi\)
−0.956944 + 0.290273i \(0.906254\pi\)
\(422\) −3.19579 −0.155569
\(423\) 0.812842 0.812842i 0.0395217 0.0395217i
\(424\) 5.03296 5.03296i 0.244422 0.244422i
\(425\) 1.58589 + 0.534422i 0.0769269 + 0.0259233i
\(426\) 32.4331 + 32.4331i 1.57139 + 1.57139i
\(427\) 11.4585 0.554515
\(428\) −1.64796 1.64796i −0.0796571 0.0796571i
\(429\) −2.11173 + 2.11173i −0.101955 + 0.101955i
\(430\) 21.6333 15.5385i 1.04325 0.749332i
\(431\) 16.4247 16.4247i 0.791148 0.791148i −0.190533 0.981681i \(-0.561021\pi\)
0.981681 + 0.190533i \(0.0610215\pi\)
\(432\) 5.73519 5.73519i 0.275934 0.275934i
\(433\) 7.66855 7.66855i 0.368527 0.368527i −0.498413 0.866940i \(-0.666084\pi\)
0.866940 + 0.498413i \(0.166084\pi\)
\(434\) 6.31954 0.303347
\(435\) 18.1664 + 25.2919i 0.871011 + 1.21265i
\(436\) 7.06206 7.06206i 0.338211 0.338211i
\(437\) 5.04717 5.04717i 0.241439 0.241439i
\(438\) 28.5497i 1.36416i
\(439\) 22.6564 + 22.6564i 1.08133 + 1.08133i 0.996385 + 0.0849471i \(0.0270721\pi\)
0.0849471 + 0.996385i \(0.472928\pi\)
\(440\) 2.45768 + 3.42168i 0.117166 + 0.163122i
\(441\) 35.4434 1.68778
\(442\) 0.179428i 0.00853453i
\(443\) 10.4105 + 10.4105i 0.494616 + 0.494616i 0.909757 0.415141i \(-0.136268\pi\)
−0.415141 + 0.909757i \(0.636268\pi\)
\(444\) 14.3157 10.8882i 0.679392 0.516732i
\(445\) −3.79220 0.621781i −0.179768 0.0294753i
\(446\) 7.29909 7.29909i 0.345622 0.345622i
\(447\) 42.4604 42.4604i 2.00831 2.00831i
\(448\) −0.643605 0.643605i −0.0304075 0.0304075i
\(449\) −16.6573 + 16.6573i −0.786107 + 0.786107i −0.980854 0.194746i \(-0.937612\pi\)
0.194746 + 0.980854i \(0.437612\pi\)
\(450\) −27.2117 9.16993i −1.28277 0.432275i
\(451\) −15.5714 −0.733227
\(452\) 15.1701i 0.713543i
\(453\) 28.9290 28.9290i 1.35920 1.35920i
\(454\) 19.6620i 0.922784i
\(455\) −1.07669 0.176537i −0.0504760 0.00827619i
\(456\) 4.53784 0.212504
\(457\) 39.7899i 1.86129i 0.365919 + 0.930647i \(0.380755\pi\)
−0.365919 + 0.930647i \(0.619245\pi\)
\(458\) 13.4975i 0.630697i
\(459\) 1.91958 + 1.91958i 0.0895985 + 0.0895985i
\(460\) −8.44682 + 6.06708i −0.393835 + 0.282879i
\(461\) 7.71541 + 7.71541i 0.359342 + 0.359342i 0.863570 0.504228i \(-0.168223\pi\)
−0.504228 + 0.863570i \(0.668223\pi\)
\(462\) 5.07057 0.235904
\(463\) 14.7430 0.685164 0.342582 0.939488i \(-0.388698\pi\)
0.342582 + 0.939488i \(0.388698\pi\)
\(464\) 3.33033 + 3.33033i 0.154607 + 0.154607i
\(465\) 37.2847 26.7804i 1.72904 1.24191i
\(466\) 1.10924 + 1.10924i 0.0513845 + 0.0513845i
\(467\) 28.4840i 1.31808i −0.752107 0.659041i \(-0.770962\pi\)
0.752107 0.659041i \(-0.229038\pi\)
\(468\) 3.07874i 0.142315i
\(469\) 4.65913 0.215139
\(470\) −0.441676 0.0724186i −0.0203730 0.00334042i
\(471\) 55.4829i 2.55652i
\(472\) 4.10789 4.10789i 0.189081 0.189081i
\(473\) 22.4422i 1.03189i
\(474\) −23.9874 −1.10178
\(475\) −3.40909 6.87453i −0.156420 0.315425i
\(476\) 0.215416 0.215416i 0.00987360 0.00987360i
\(477\) −28.9045 28.9045i −1.32344 1.32344i
\(478\) −10.5161 + 10.5161i −0.480995 + 0.480995i
\(479\) 2.09957 2.09957i 0.0959318 0.0959318i −0.657512 0.753444i \(-0.728391\pi\)
0.753444 + 0.657512i \(0.228391\pi\)
\(480\) −6.52462 1.06980i −0.297807 0.0488293i
\(481\) 0.439398 3.23112i 0.0200348 0.147326i
\(482\) 18.7617 + 18.7617i 0.854571 + 0.854571i
\(483\) 12.5173i 0.569557i
\(484\) 7.45037 0.338653
\(485\) 22.4066 + 31.1953i 1.01743 + 1.41651i
\(486\) 3.08553 + 3.08553i 0.139962 + 0.139962i
\(487\) 17.7878i 0.806044i 0.915190 + 0.403022i \(0.132040\pi\)
−0.915190 + 0.403022i \(0.867960\pi\)
\(488\) 8.90180 8.90180i 0.402965 0.402965i
\(489\) −3.10459 + 3.10459i −0.140395 + 0.140395i
\(490\) −8.05061 11.2084i −0.363689 0.506342i
\(491\) 11.1728 0.504221 0.252110 0.967698i \(-0.418875\pi\)
0.252110 + 0.967698i \(0.418875\pi\)
\(492\) 17.2803 17.2803i 0.779056 0.779056i
\(493\) −1.11467 + 1.11467i −0.0502022 + 0.0502022i
\(494\) 0.581747 0.581747i 0.0261740 0.0261740i
\(495\) 19.6509 14.1146i 0.883240 0.634403i
\(496\) 4.90948 4.90948i 0.220442 0.220442i
\(497\) −9.98370 9.98370i −0.447830 0.447830i
\(498\) −33.0548 −1.48122
\(499\) 9.60201 + 9.60201i 0.429845 + 0.429845i 0.888576 0.458730i \(-0.151696\pi\)
−0.458730 + 0.888576i \(0.651696\pi\)
\(500\) 3.28101 + 10.6881i 0.146731 + 0.477985i
\(501\) −9.81033 + 9.81033i −0.438293 + 0.438293i
\(502\) −9.09164 + 9.09164i −0.405780 + 0.405780i
\(503\) −14.7806 −0.659035 −0.329518 0.944149i \(-0.606886\pi\)
−0.329518 + 0.944149i \(0.606886\pi\)
\(504\) −3.69625 + 3.69625i −0.164644 + 0.164644i
\(505\) 17.5682 + 24.4591i 0.781773 + 1.08842i
\(506\) 8.76267i 0.389548i
\(507\) 26.5798 + 26.5798i 1.18045 + 1.18045i
\(508\) −3.59805 3.59805i −0.159638 0.159638i
\(509\) 4.49759 0.199352 0.0996760 0.995020i \(-0.468219\pi\)
0.0996760 + 0.995020i \(0.468219\pi\)
\(510\) 0.358064 2.18381i 0.0158553 0.0967007i
\(511\) 8.78829i 0.388771i
\(512\) −1.00000 −0.0441942
\(513\) 12.4475i 0.549568i
\(514\) 2.08454i 0.0919453i
\(515\) −16.4626 22.9199i −0.725429 1.00997i
\(516\) −24.9052 24.9052i −1.09639 1.09639i
\(517\) 0.266659 0.266659i 0.0117276 0.0117276i
\(518\) −4.40672 + 3.35166i −0.193620 + 0.147264i
\(519\) 7.03045i 0.308603i
\(520\) −0.973599 + 0.699305i −0.0426951 + 0.0306665i
\(521\) 14.5173i 0.636014i 0.948088 + 0.318007i \(0.103014\pi\)
−0.948088 + 0.318007i \(0.896986\pi\)
\(522\) 19.1262 19.1262i 0.837131 0.837131i
\(523\) 27.3756 1.19705 0.598526 0.801103i \(-0.295753\pi\)
0.598526 + 0.801103i \(0.295753\pi\)
\(524\) 7.63639 7.63639i 0.333597 0.333597i
\(525\) 12.7520 + 4.29725i 0.556544 + 0.187547i
\(526\) 6.41417 + 6.41417i 0.279671 + 0.279671i
\(527\) 1.64322 + 1.64322i 0.0715797 + 0.0715797i
\(528\) 3.93919 3.93919i 0.171431 0.171431i
\(529\) −1.36834 −0.0594930
\(530\) −2.57519 + 15.7059i −0.111859 + 0.682221i
\(531\) −23.5918 23.5918i −1.02380 1.02380i
\(532\) −1.39686 −0.0605615
\(533\) 4.43064i 0.191913i
\(534\) 5.08157i 0.219901i
\(535\) 5.14264 + 0.843202i 0.222336 + 0.0364548i
\(536\) 3.61956 3.61956i 0.156341 0.156341i
\(537\) 54.4315i 2.34889i
\(538\) 10.5529i 0.454970i
\(539\) 11.6275 0.500831
\(540\) −2.93449 + 17.8973i −0.126280 + 0.770176i
\(541\) 15.0886 + 15.0886i 0.648708 + 0.648708i 0.952681 0.303973i \(-0.0983133\pi\)
−0.303973 + 0.952681i \(0.598313\pi\)
\(542\) −19.2734 −0.827865
\(543\) −12.3758 12.3758i −0.531095 0.531095i
\(544\) 0.334703i 0.0143503i
\(545\) −3.61340 + 22.0379i −0.154781 + 0.944001i
\(546\) 1.44277i 0.0617449i
\(547\) −24.9954 −1.06873 −0.534363 0.845255i \(-0.679448\pi\)
−0.534363 + 0.845255i \(0.679448\pi\)
\(548\) 5.48037 + 5.48037i 0.234110 + 0.234110i
\(549\) −51.1233 51.1233i −2.18189 2.18189i
\(550\) −8.92698 3.00826i −0.380648 0.128273i
\(551\) 7.22803 0.307924
\(552\) 9.72436 + 9.72436i 0.413896 + 0.413896i
\(553\) 7.38391 0.313996
\(554\) −7.82056 −0.332264
\(555\) −11.7959 + 38.4489i −0.500706 + 1.63207i
\(556\) 4.24414 0.179991
\(557\) 12.4355 0.526909 0.263455 0.964672i \(-0.415138\pi\)
0.263455 + 0.964672i \(0.415138\pi\)
\(558\) −28.1953 28.1953i −1.19360 1.19360i
\(559\) −6.38565 −0.270084
\(560\) 2.00844 + 0.329310i 0.0848721 + 0.0139159i
\(561\) 1.31846 + 1.31846i 0.0556654 + 0.0556654i
\(562\) 10.4788 + 10.4788i 0.442020 + 0.442020i
\(563\) 9.73552 0.410303 0.205152 0.978730i \(-0.434231\pi\)
0.205152 + 0.978730i \(0.434231\pi\)
\(564\) 0.591849i 0.0249213i
\(565\) −19.7890 27.5510i −0.832530 1.15908i
\(566\) 26.3960i 1.10951i
\(567\) 4.34649 + 4.34649i 0.182536 + 0.182536i
\(568\) −15.5121 −0.650875
\(569\) −10.5582 10.5582i −0.442624 0.442624i 0.450269 0.892893i \(-0.351328\pi\)
−0.892893 + 0.450269i \(0.851328\pi\)
\(570\) −8.24133 + 5.91948i −0.345191 + 0.247940i
\(571\) 13.3170 0.557301 0.278650 0.960393i \(-0.410113\pi\)
0.278650 + 0.960393i \(0.410113\pi\)
\(572\) 1.01000i 0.0422304i
\(573\) 34.0448i 1.42224i
\(574\) −5.31930 + 5.31930i −0.222023 + 0.222023i
\(575\) 7.42625 22.0373i 0.309696 0.919019i
\(576\) 5.74304i 0.239293i
\(577\) 4.76082i 0.198195i −0.995078 0.0990977i \(-0.968404\pi\)
0.995078 0.0990977i \(-0.0315956\pi\)
\(578\) −16.8880 −0.702447
\(579\) −33.1848 33.1848i −1.37911 1.37911i
\(580\) −10.3927 1.70401i −0.431532 0.0707552i
\(581\) 10.1751 0.422133
\(582\) 35.9134 35.9134i 1.48866 1.48866i
\(583\) −9.48232 9.48232i −0.392718 0.392718i
\(584\) −6.82739 6.82739i −0.282519 0.282519i
\(585\) 4.01613 + 5.59141i 0.166047 + 0.231177i
\(586\) 22.4956 22.4956i 0.929287 0.929287i
\(587\) −2.41574 −0.0997081 −0.0498540 0.998757i \(-0.515876\pi\)
−0.0498540 + 0.998757i \(0.515876\pi\)
\(588\) −12.9036 + 12.9036i −0.532134 + 0.532134i
\(589\) 10.6554i 0.439047i
\(590\) −2.10186 + 12.8191i −0.0865324 + 0.527755i
\(591\) 15.0633i 0.619621i
\(592\) −0.819646 + 6.02729i −0.0336872 + 0.247720i
\(593\) 1.14068 1.14068i 0.0468420 0.0468420i −0.683298 0.730140i \(-0.739455\pi\)
0.730140 + 0.683298i \(0.239455\pi\)
\(594\) −10.8054 10.8054i −0.443349 0.443349i
\(595\) −0.110221 + 0.672231i −0.00451862 + 0.0275588i
\(596\) 20.3080i 0.831849i
\(597\) 4.79620i 0.196295i
\(598\) 2.49331 0.101959
\(599\) 40.0185i 1.63511i −0.575851 0.817555i \(-0.695329\pi\)
0.575851 0.817555i \(-0.304671\pi\)
\(600\) 13.2451 6.56829i 0.540730 0.268149i
\(601\) −11.7034 −0.477393 −0.238696 0.971094i \(-0.576720\pi\)
−0.238696 + 0.971094i \(0.576720\pi\)
\(602\) 7.66643 + 7.66643i 0.312460 + 0.312460i
\(603\) −20.7873 20.7873i −0.846522 0.846522i
\(604\) 13.8362i 0.562987i
\(605\) −13.5309 + 9.71881i −0.550109 + 0.395126i
\(606\) 28.1584 28.1584i 1.14386 1.14386i
\(607\) 24.3851 0.989761 0.494881 0.868961i \(-0.335212\pi\)
0.494881 + 0.868961i \(0.335212\pi\)
\(608\) −1.08518 + 1.08518i −0.0440100 + 0.0440100i
\(609\) −8.96299 + 8.96299i −0.363199 + 0.363199i
\(610\) −4.55473 + 27.7790i −0.184416 + 1.12474i
\(611\) 0.0758746 + 0.0758746i 0.00306956 + 0.00306956i
\(612\) −1.92221 −0.0777008
\(613\) 18.3951 + 18.3951i 0.742971 + 0.742971i 0.973149 0.230178i \(-0.0739308\pi\)
−0.230178 + 0.973149i \(0.573931\pi\)
\(614\) 17.4358 17.4358i 0.703650 0.703650i
\(615\) −8.84172 + 53.9251i −0.356533 + 2.17447i
\(616\) −1.21258 + 1.21258i −0.0488563 + 0.0488563i
\(617\) 31.2896 31.2896i 1.25967 1.25967i 0.308421 0.951250i \(-0.400199\pi\)
0.951250 0.308421i \(-0.0998006\pi\)
\(618\) −26.3864 + 26.3864i −1.06142 + 1.06142i
\(619\) −39.6915 −1.59534 −0.797669 0.603096i \(-0.793934\pi\)
−0.797669 + 0.603096i \(0.793934\pi\)
\(620\) −2.51201 + 15.3206i −0.100885 + 0.615289i
\(621\) 26.6743 26.6743i 1.07040 1.07040i
\(622\) 3.97519 3.97519i 0.159391 0.159391i
\(623\) 1.56423i 0.0626697i
\(624\) 1.12085 + 1.12085i 0.0448699 + 0.0448699i
\(625\) −19.9011 15.1310i −0.796043 0.605240i
\(626\) −15.8472 −0.633380
\(627\) 8.54949i 0.341434i
\(628\) 13.2682 + 13.2682i 0.529460 + 0.529460i
\(629\) −2.01735 0.274338i −0.0804370 0.0109386i
\(630\) 1.89124 11.5345i 0.0753488 0.459547i
\(631\) −29.5138 + 29.5138i −1.17493 + 1.17493i −0.193907 + 0.981020i \(0.562116\pi\)
−0.981020 + 0.193907i \(0.937884\pi\)
\(632\) 5.73637 5.73637i 0.228181 0.228181i
\(633\) −6.68182 6.68182i −0.265579 0.265579i
\(634\) −0.950144 + 0.950144i −0.0377350 + 0.0377350i
\(635\) 11.2281 + 1.84099i 0.445574 + 0.0730576i
\(636\) 21.0460 0.834528
\(637\) 3.30846i 0.131086i
\(638\) 6.27449 6.27449i 0.248409 0.248409i
\(639\) 89.0868i 3.52422i
\(640\) 1.81614 1.30447i 0.0717891 0.0515638i
\(641\) −36.0367 −1.42336 −0.711681 0.702503i \(-0.752066\pi\)
−0.711681 + 0.702503i \(0.752066\pi\)
\(642\) 6.89116i 0.271973i
\(643\) 36.2733i 1.43048i 0.698880 + 0.715239i \(0.253682\pi\)
−0.698880 + 0.715239i \(0.746318\pi\)
\(644\) −2.99340 2.99340i −0.117956 0.117956i
\(645\) 77.7194 + 12.7431i 3.06020 + 0.501759i
\(646\) −0.363214 0.363214i −0.0142905 0.0142905i
\(647\) 20.1761 0.793203 0.396602 0.917991i \(-0.370189\pi\)
0.396602 + 0.917991i \(0.370189\pi\)
\(648\) 6.75336 0.265297
\(649\) −7.73946 7.73946i −0.303800 0.303800i
\(650\) 0.855965 2.54007i 0.0335737 0.0996296i
\(651\) 13.2130 + 13.2130i 0.517858 + 0.517858i
\(652\) 1.48487i 0.0581520i
\(653\) 45.2272i 1.76988i −0.465706 0.884939i \(-0.654200\pi\)
0.465706 0.884939i \(-0.345800\pi\)
\(654\) 29.5309 1.15475
\(655\) −3.90727 + 23.8302i −0.152670 + 0.931122i
\(656\) 8.26486i 0.322688i
\(657\) −39.2100 + 39.2100i −1.52973 + 1.52973i
\(658\) 0.182186i 0.00710234i
\(659\) −3.64301 −0.141911 −0.0709557 0.997479i \(-0.522605\pi\)
−0.0709557 + 0.997479i \(0.522605\pi\)
\(660\) −2.01555 + 12.2927i −0.0784550 + 0.478492i
\(661\) 0.359733 0.359733i 0.0139920 0.0139920i −0.700076 0.714068i \(-0.746851\pi\)
0.714068 + 0.700076i \(0.246851\pi\)
\(662\) 19.3735 + 19.3735i 0.752972 + 0.752972i
\(663\) −0.375152 + 0.375152i −0.0145697 + 0.0145697i
\(664\) 7.90475 7.90475i 0.306764 0.306764i
\(665\) 2.53689 1.82216i 0.0983762 0.0706604i
\(666\) 34.6149 + 4.70726i 1.34130 + 0.182402i
\(667\) 15.4893 + 15.4893i 0.599749 + 0.599749i
\(668\) 4.69210i 0.181543i
\(669\) 30.5221 1.18005
\(670\) −1.85200 + 11.2952i −0.0715490 + 0.436373i
\(671\) −16.7714 16.7714i −0.647452 0.647452i
\(672\) 2.69132i 0.103820i
\(673\) 12.3228 12.3228i 0.475011 0.475011i −0.428521 0.903532i \(-0.640965\pi\)
0.903532 + 0.428521i \(0.140965\pi\)
\(674\) 3.21128 3.21128i 0.123694 0.123694i
\(675\) −18.0171 36.3319i −0.693477 1.39841i
\(676\) −12.7126 −0.488947
\(677\) 13.3890 13.3890i 0.514579 0.514579i −0.401347 0.915926i \(-0.631458\pi\)
0.915926 + 0.401347i \(0.131458\pi\)
\(678\) −31.7180 + 31.7180i −1.21812 + 1.21812i
\(679\) −11.0550 + 11.0550i −0.424253 + 0.424253i
\(680\) 0.436611 + 0.607866i 0.0167433 + 0.0233106i
\(681\) −41.1097 + 41.1097i −1.57533 + 1.57533i
\(682\) −9.24969 9.24969i −0.354189 0.354189i
\(683\) 26.4505 1.01210 0.506050 0.862504i \(-0.331105\pi\)
0.506050 + 0.862504i \(0.331105\pi\)
\(684\) 6.23224 + 6.23224i 0.238296 + 0.238296i
\(685\) −17.1021 2.80411i −0.653437 0.107140i
\(686\) 8.47727 8.47727i 0.323664 0.323664i
\(687\) 28.2208 28.2208i 1.07669 1.07669i
\(688\) 11.9117 0.454129
\(689\) 2.69808 2.69808i 0.102789 0.102789i
\(690\) −30.3459 4.97561i −1.15525 0.189418i
\(691\) 8.34143i 0.317323i −0.987333 0.158661i \(-0.949282\pi\)
0.987333 0.158661i \(-0.0507178\pi\)
\(692\) −1.68127 1.68127i −0.0639123 0.0639123i
\(693\) 6.96390 + 6.96390i 0.264537 + 0.264537i
\(694\) 18.4401 0.699976
\(695\) −7.70793 + 5.53636i −0.292379 + 0.210006i
\(696\) 13.9262i 0.527872i
\(697\) −2.76627 −0.104780
\(698\) 21.3314i 0.807405i
\(699\) 4.63843i 0.175442i
\(700\) −4.07718 + 2.02188i −0.154103 + 0.0764200i
\(701\) 15.0534 + 15.0534i 0.568560 + 0.568560i 0.931725 0.363165i \(-0.118304\pi\)
−0.363165 + 0.931725i \(0.618304\pi\)
\(702\) 3.07453 3.07453i 0.116041 0.116041i
\(703\) 5.65124 + 7.43017i 0.213141 + 0.280234i
\(704\) 1.88405i 0.0710076i
\(705\) −0.772050 1.07488i −0.0290771 0.0404823i
\(706\) 11.9150i 0.448428i
\(707\) −8.66785 + 8.66785i −0.325988 + 0.325988i
\(708\) 17.1777 0.645578
\(709\) 26.5041 26.5041i 0.995384 0.995384i −0.00460560 0.999989i \(-0.501466\pi\)
0.999989 + 0.00460560i \(0.00146601\pi\)
\(710\) 28.1722 20.2352i 1.05728 0.759412i
\(711\) −32.9442 32.9442i −1.23550 1.23550i
\(712\) −1.21521 1.21521i −0.0455420 0.0455420i
\(713\) 22.8339 22.8339i 0.855137 0.855137i
\(714\) 0.900793 0.0337113
\(715\) 1.31752 + 1.83430i 0.0492725 + 0.0685991i
\(716\) −13.0168 13.0168i −0.486461 0.486461i
\(717\) −43.9745 −1.64226
\(718\) 24.9976i 0.932903i
\(719\) 17.0904i 0.637364i −0.947862 0.318682i \(-0.896760\pi\)
0.947862 0.318682i \(-0.103240\pi\)
\(720\) −7.49163 10.4301i −0.279197 0.388708i
\(721\) 8.12238 8.12238i 0.302493 0.302493i
\(722\) 16.6448i 0.619454i
\(723\) 78.4545i 2.91775i
\(724\) 5.91911 0.219982
\(725\) 21.0973 10.4622i 0.783535 0.388557i
\(726\) 15.5774 + 15.5774i 0.578131 + 0.578131i
\(727\) −49.5068 −1.83611 −0.918053 0.396457i \(-0.870240\pi\)
−0.918053 + 0.396457i \(0.870240\pi\)
\(728\) −0.345025 0.345025i −0.0127875 0.0127875i
\(729\) 33.1626i 1.22825i
\(730\) 21.3056 + 3.49333i 0.788556 + 0.129294i
\(731\) 3.98688i 0.147460i
\(732\) 37.2241 1.37584
\(733\) 8.80945 + 8.80945i 0.325385 + 0.325385i 0.850828 0.525444i \(-0.176101\pi\)
−0.525444 + 0.850828i \(0.676101\pi\)
\(734\) −0.228241 0.228241i −0.00842451 0.00842451i
\(735\) 6.60230 40.2670i 0.243530 1.48527i
\(736\) −4.65098 −0.171438
\(737\) −6.81941 6.81941i −0.251196 0.251196i
\(738\) 47.4654 1.74722
\(739\) −44.3001 −1.62961 −0.814803 0.579738i \(-0.803155\pi\)
−0.814803 + 0.579738i \(0.803155\pi\)
\(740\) −6.37384 12.0156i −0.234307 0.441702i
\(741\) 2.43265 0.0893658
\(742\) −6.47848 −0.237832
\(743\) −16.9715 16.9715i −0.622623 0.622623i 0.323579 0.946201i \(-0.395114\pi\)
−0.946201 + 0.323579i \(0.895114\pi\)
\(744\) 20.5297 0.752654
\(745\) −26.4913 36.8822i −0.970564 1.35126i
\(746\) −5.32431 5.32431i −0.194937 0.194937i
\(747\) −45.3972 45.3972i −1.66100 1.66100i
\(748\) −0.630595 −0.0230568
\(749\) 2.12127i 0.0775095i
\(750\) −15.4868 + 29.2068i −0.565498 + 1.06648i
\(751\) 10.2040i 0.372350i 0.982517 + 0.186175i \(0.0596091\pi\)
−0.982517 + 0.186175i \(0.940391\pi\)
\(752\) −0.141535 0.141535i −0.00516126 0.00516126i
\(753\) −38.0179 −1.38545
\(754\) 1.78533 + 1.78533i 0.0650179 + 0.0650179i
\(755\) −18.0489 25.1284i −0.656868 0.914517i
\(756\) −7.38239 −0.268495
\(757\) 6.71387i 0.244020i 0.992529 + 0.122010i \(0.0389340\pi\)
−0.992529 + 0.122010i \(0.961066\pi\)
\(758\) 7.62224i 0.276852i
\(759\) 18.3211 18.3211i 0.665015 0.665015i
\(760\) 0.555249 3.38643i 0.0201410 0.122839i
\(761\) 1.33026i 0.0482218i 0.999709 + 0.0241109i \(0.00767549\pi\)
−0.999709 + 0.0241109i \(0.992325\pi\)
\(762\) 15.0457i 0.545049i
\(763\) −9.09035 −0.329093
\(764\) −8.14150 8.14150i −0.294549 0.294549i
\(765\) 3.49100 2.50747i 0.126217 0.0906578i
\(766\) −9.60774 −0.347142
\(767\) 2.20217 2.20217i 0.0795157 0.0795157i
\(768\) −2.09082 2.09082i −0.0754459 0.0754459i
\(769\) 18.1678 + 18.1678i 0.655148 + 0.655148i 0.954228 0.299080i \(-0.0966797\pi\)
−0.299080 + 0.954228i \(0.596680\pi\)
\(770\) 0.620435 3.78399i 0.0223589 0.136366i
\(771\) −4.35840 + 4.35840i −0.156964 + 0.156964i
\(772\) 15.8717 0.571235
\(773\) 19.9474 19.9474i 0.717458 0.717458i −0.250626 0.968084i \(-0.580637\pi\)
0.968084 + 0.250626i \(0.0806365\pi\)
\(774\) 68.4093i 2.45892i
\(775\) −15.4231 31.1011i −0.554015 1.11718i
\(776\) 17.1767i 0.616609i
\(777\) −16.2214 2.20593i −0.581938 0.0791373i
\(778\) 12.3615