Properties

Label 370.2.h.e.253.1
Level $370$
Weight $2$
Character 370.253
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 253.1
Root \(-2.09082 - 2.09082i\) of defining polynomial
Character \(\chi\) \(=\) 370.253
Dual form 370.2.h.e.117.1

$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

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

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
\(3\) −2.09082 + 2.09082i −1.20713 + 1.20713i −0.235183 + 0.971951i \(0.575569\pi\)
−0.971951 + 0.235183i \(0.924431\pi\)
\(4\) 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 −0.818197 0.574937i \(-0.805026\pi\)
0.574937 + 0.818197i \(0.305026\pi\)
\(8\) −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 \(-0.908328\pi\)
0.958815 0.284030i \(-0.0916717\pi\)
\(12\) −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 \(-0.987077\pi\)
0.999176 0.0405887i \(-0.0129233\pi\)
\(18\) 5.74304i 1.35365i
\(19\) 1.08518 + 1.08518i 0.248958 + 0.248958i 0.820543 0.571585i \(-0.193671\pi\)
−0.571585 + 0.820543i \(0.693671\pi\)
\(20\) −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 −0.326701 0.945128i \(-0.605937\pi\)
0.945128 + 0.326701i \(0.105937\pi\)
\(30\) −6.52462 + 1.06980i −1.19123 + 0.195317i
\(31\) 4.90948 + 4.90948i 0.881769 + 0.881769i 0.993714 0.111945i \(-0.0357081\pi\)
−0.111945 + 0.993714i \(0.535708\pi\)
\(32\) −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 \(-0.776700\pi\)
0.763864 0.645377i \(-0.223300\pi\)
\(42\) 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 −0.717354 0.696709i \(-0.754647\pi\)
0.696709 + 0.717354i \(0.254647\pi\)
\(48\) −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 0.271194 0.962525i \(-0.412581\pi\)
−0.962525 + 0.271194i \(0.912581\pi\)
\(54\) −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 0.387195 0.921998i \(-0.373444\pi\)
−0.921998 + 0.387195i \(0.873444\pi\)
\(60\) 6.52462 1.06980i 0.842325 0.138110i
\(61\) −8.90180 8.90180i −1.13976 1.13976i −0.988493 0.151265i \(-0.951665\pi\)
−0.151265 0.988493i \(-0.548335\pi\)
\(62\) −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 0.450551 0.892751i \(-0.351227\pi\)
−0.892751 + 0.450551i \(0.851227\pi\)
\(68\) 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 −0.183866 0.982951i \(-0.558861\pi\)
0.982951 + 0.183866i \(0.0588611\pi\)
\(74\) 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 0.306484 0.951876i \(-0.400847\pi\)
−0.951876 + 0.306484i \(0.900847\pi\)
\(80\) −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 0.124554 0.992213i \(-0.460250\pi\)
−0.992213 + 0.124554i \(0.960250\pi\)
\(84\) 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 −0.639761 0.768574i \(-0.720967\pi\)
0.768574 + 0.639761i \(0.220967\pi\)
\(90\) 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 \(0.337188\pi\)
−0.489477 + 0.872016i \(0.662812\pi\)
\(98\) 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 \(0.233723\pi\)
−0.742324 + 0.670041i \(0.766277\pi\)
\(102\) −0.699803 0.699803i −0.0692908 0.0692908i
\(103\) 12.6201i 1.24350i −0.783216 0.621749i \(-0.786422\pi\)
0.783216 0.621749i \(-0.213578\pi\)
\(104\) 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 −0.782263 0.622949i \(-0.785935\pi\)
0.622949 + 0.782263i \(0.285935\pi\)
\(108\) 5.73519 + 5.73519i 0.551869 + 0.551869i
\(109\) 7.06206 + 7.06206i 0.676422 + 0.676422i 0.959189 0.282766i \(-0.0912521\pi\)
−0.282766 + 0.959189i \(0.591252\pi\)
\(110\) 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 \(-0.747089\pi\)
0.700612 0.713543i \(-0.252911\pi\)
\(114\) 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 −0.848489 0.529213i \(-0.822487\pi\)
0.529213 + 0.848489i \(0.322487\pi\)
\(128\) −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 0.957066 0.289871i \(-0.0936126\pi\)
−0.289871 + 0.957066i \(0.593613\pi\)
\(132\) 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 −0.433118 0.901337i \(-0.642587\pi\)
0.901337 + 0.433118i \(0.142587\pi\)
\(138\) 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 \(-0.687282\pi\)
0.555002 0.831849i \(-0.312718\pi\)
\(150\) 13.2451 + 6.56829i 1.08146 + 0.536299i
\(151\) 13.8362i 1.12597i −0.826466 0.562987i \(-0.809652\pi\)
0.826466 0.562987i \(-0.190348\pi\)
\(152\) −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 0.0607691 0.998152i \(-0.480645\pi\)
0.998152 0.0607691i \(-0.0193553\pi\)
\(158\) 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 \(0.0185208\pi\)
−0.998308 + 0.0581520i \(0.981479\pi\)
\(164\) 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 \(0.0581091\pi\)
−0.983383 + 0.181543i \(0.941891\pi\)
\(168\) 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 −0.768125 0.640300i \(-0.778810\pi\)
0.640300 + 0.768125i \(0.278810\pi\)
\(174\) 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 −0.999643 0.0267216i \(-0.991493\pi\)
0.0267216 + 0.999643i \(0.491493\pi\)
\(180\) −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 −0.937387 0.348289i \(-0.886763\pi\)
0.348289 + 0.937387i \(0.386763\pi\)
\(192\) −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 −0.567040 0.823690i \(-0.691912\pi\)
0.823690 + 0.567040i \(0.191912\pi\)
\(198\) 10.8201 0.768954
\(199\) −1.14697 + 1.14697i −0.0813064 + 0.0813064i −0.746590 0.665284i \(-0.768310\pi\)
0.665284 + 0.746590i \(0.268310\pi\)
\(200\) −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 0.419139 0.907922i \(-0.362332\pi\)
−0.907922 + 0.419139i \(0.862332\pi\)
\(224\) 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 \(0.226283\pi\)
−0.757783 + 0.652507i \(0.773717\pi\)
\(228\) −4.53784 −0.300526
\(229\) 13.4975i 0.891940i −0.895048 0.445970i \(-0.852859\pi\)
0.895048 0.445970i \(-0.147141\pi\)
\(230\) 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 −0.742507 0.669838i \(-0.766363\pi\)
0.669838 + 0.742507i \(0.266363\pi\)
\(234\) 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 0.960052 0.279822i \(-0.0902754\pi\)
−0.279822 + 0.960052i \(0.590275\pi\)
\(240\) 6.52462 1.06980i 0.421163 0.0690551i
\(241\) −18.7617 + 18.7617i −1.20855 + 1.20855i −0.237047 + 0.971498i \(0.576180\pi\)
−0.971498 + 0.237047i \(0.923820\pi\)
\(242\) −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 0.933205 0.359346i \(-0.117000\pi\)
−0.359346 + 0.933205i \(0.617000\pi\)
\(252\) 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 \(0.0207096\pi\)
−0.997884 + 0.0650151i \(0.979290\pi\)
\(258\) 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 −0.876648 0.481133i \(-0.840225\pi\)
0.481133 + 0.876648i \(0.340225\pi\)
\(264\) −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 \(0.104258\pi\)
−0.946838 + 0.321712i \(0.895742\pi\)
\(270\) 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 −0.946834 0.321723i \(-0.895738\pi\)
0.321723 + 0.946834i \(0.395738\pi\)
\(282\) 0.591849i 0.0352441i
\(283\) 26.3960i 1.56908i 0.620079 + 0.784539i \(0.287100\pi\)
−0.620079 + 0.784539i \(0.712900\pi\)
\(284\) 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 −0.918281 0.395928i \(-0.870423\pi\)
−0.395928 0.918281i \(-0.629577\pi\)
\(294\) 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 0.00487690 0.999988i \(-0.498448\pi\)
−0.999988 + 0.00487690i \(0.998448\pi\)
\(308\) 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 0.585361 0.810773i \(-0.300953\pi\)
−0.810773 + 0.585361i \(0.800953\pi\)
\(312\) −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 0.733286 0.679920i \(-0.237986\pi\)
−0.679920 + 0.733286i \(0.737986\pi\)
\(318\) −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 −0.0671177 + 0.997745i \(0.521380\pi\)
−0.997745 + 0.0671177i \(0.978620\pi\)
\(332\) −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 0.614212 0.789141i \(-0.289474\pi\)
−0.789141 + 0.614212i \(0.789474\pi\)
\(338\) 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 \(-0.806586\pi\)
0.821005 0.570921i \(-0.193414\pi\)
\(350\) 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 \(-0.897296\pi\)
0.948397 0.317086i \(-0.102704\pi\)
\(354\) −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 \(-0.770699\pi\)
0.751562 0.659662i \(-0.229301\pi\)
\(360\) 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 −0.701125 0.713039i \(-0.747318\pi\)
0.713039 + 0.701125i \(0.247318\pi\)
\(368\) 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 −0.555700 0.831383i \(-0.687550\pi\)
0.831383 + 0.555700i \(0.187550\pi\)
\(374\) 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 \(-0.937281\pi\)
0.980651 0.195764i \(-0.0627187\pi\)
\(380\) −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 0.320498 0.947249i \(-0.396150\pi\)
−0.947249 + 0.320498i \(0.896150\pi\)
\(390\) 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 0.993238 + 0.116100i \(0.0370394\pi\)
0.116100 + 0.993238i \(0.462961\pi\)
\(398\) 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 0.931039 0.364921i \(-0.118904\pi\)
−0.364921 + 0.931039i \(0.618904\pi\)
\(402\) −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 −0.913861 0.406027i \(-0.866914\pi\)
0.406027 + 0.913861i \(0.366914\pi\)
\(410\) 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 \(0.109895\pi\)
−0.940993 + 0.338427i \(0.890105\pi\)
\(420\) −3.51075 + 4.88781i −0.171307 + 0.238501i
\(421\) −25.5907 25.5907i −1.24722 1.24722i −0.956944 0.290273i \(-0.906254\pi\)
−0.290273 0.956944i \(-0.593746\pi\)
\(422\) −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 0.981681 0.190533i \(-0.0610215\pi\)
−0.190533 + 0.981681i \(0.561021\pi\)
\(432\) 5.73519 + 5.73519i 0.275934 + 0.275934i
\(433\) 7.66855 + 7.66855i 0.368527 + 0.368527i 0.866940 0.498413i \(-0.166084\pi\)
−0.498413 + 0.866940i \(0.666084\pi\)
\(434\) 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 0.0849471 0.996385i \(-0.472928\pi\)
0.996385 0.0849471i \(-0.0270721\pi\)
\(440\) 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 −0.415141 0.909757i \(-0.636268\pi\)
0.909757 + 0.415141i \(0.136268\pi\)
\(444\) 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 0.194746 0.980854i \(-0.437612\pi\)
−0.980854 + 0.194746i \(0.937612\pi\)
\(450\) −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 \(-0.619245\pi\)
0.365919 0.930647i \(-0.380755\pi\)
\(458\) 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 −0.504228 0.863570i \(-0.668223\pi\)
0.863570 + 0.504228i \(0.168223\pi\)
\(462\) 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 \(0.229038\pi\)
−0.752107 + 0.659041i \(0.770962\pi\)
\(468\) 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 0.753444 0.657512i \(-0.228391\pi\)
−0.657512 + 0.753444i \(0.728391\pi\)
\(480\) −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 \(-0.867960\pi\)
0.915190 0.403022i \(-0.132040\pi\)
\(488\) 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 −0.458730 0.888576i \(-0.651696\pi\)
0.888576 + 0.458730i \(0.151696\pi\)
\(500\) 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 \(-0.896986\pi\)
0.948088 0.318007i \(-0.103014\pi\)
\(522\) 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 −0.303973 0.952681i \(-0.598313\pi\)
0.952681 + 0.303973i \(0.0983133\pi\)
\(542\) −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 −0.892893 0.450269i \(-0.851328\pi\)
0.450269 + 0.892893i \(0.351328\pi\)
\(570\) −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 \(0.0315956\pi\)
−0.995078 + 0.0990977i \(0.968404\pi\)
\(578\) −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 0.730140 0.683298i \(-0.239455\pi\)
−0.683298 + 0.730140i \(0.739455\pi\)
\(594\) −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 \(0.304671\pi\)
−0.575851 + 0.817555i \(0.695329\pi\)
\(600\) 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 −0.230178 0.973149i \(-0.573931\pi\)
0.973149 + 0.230178i \(0.0739308\pi\)
\(614\) 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 0.951250 + 0.308421i \(0.0998006\pi\)
0.308421 + 0.951250i \(0.400199\pi\)
\(618\) −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 −0.981020 0.193907i \(-0.937884\pi\)
−0.193907 0.981020i \(-0.562116\pi\)
\(632\) 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 \(-0.746318\pi\)
0.698880 0.715239i \(-0.253682\pi\)
\(644\) −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 \(0.345800\pi\)
−0.465706 + 0.884939i \(0.654200\pi\)
\(654\) 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 0.714068 0.700076i \(-0.246851\pi\)
−0.700076 + 0.714068i \(0.746851\pi\)
\(662\) 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 0.903532 0.428521i \(-0.140965\pi\)
−0.428521 + 0.903532i \(0.640965\pi\)
\(674\) 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 0.915926 0.401347i \(-0.131458\pi\)
−0.401347 + 0.915926i \(0.631458\pi\)
\(678\) −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 \(0.0507178\pi\)
−0.987333 + 0.158661i \(0.949282\pi\)
\(692\) −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 −0.363165 0.931725i \(-0.618304\pi\)
0.931725 + 0.363165i \(0.118304\pi\)
\(702\) 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 0.999989 0.00460560i \(-0.00146601\pi\)
−0.00460560 + 0.999989i \(0.501466\pi\)
\(710\) 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 \(0.103240\pi\)
−0.947862 + 0.318682i \(0.896760\pi\)
\(720\) −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 −0.525444 0.850828i \(-0.676101\pi\)
0.850828 + 0.525444i \(0.176101\pi\)
\(734\) −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 −0.946201 0.323579i \(-0.895114\pi\)
0.323579 + 0.946201i \(0.395114\pi\)
\(744\) 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 \(-0.940391\pi\)
0.982517 0.186175i \(-0.0596091\pi\)
\(752\) −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 \(-0.961066\pi\)
0.992529 0.122010i \(-0.0389340\pi\)
\(758\) 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 \(-0.992325\pi\)
0.999709 0.0241109i \(-0.00767549\pi\)
\(762\) 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 −0.299080 0.954228i \(-0.596680\pi\)
0.954228 + 0.299080i \(0.0966797\pi\)
\(770\) 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 0.968084 0.250626i \(-0.0806365\pi\)
−0.250626 + 0.968084i \(0.580637\pi\)
\(774\) 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 +