Properties

Label 690.2.i.f.47.4
Level $690$
Weight $2$
Character 690.47
Analytic conductor $5.510$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.4
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.f.323.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.144577 - 1.72601i) q^{3} -1.00000i q^{4} +(1.25275 + 1.85219i) q^{5} +(1.32270 + 1.11824i) q^{6} +(-2.31531 - 2.31531i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.95819 + 0.499082i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.144577 - 1.72601i) q^{3} -1.00000i q^{4} +(1.25275 + 1.85219i) q^{5} +(1.32270 + 1.11824i) q^{6} +(-2.31531 - 2.31531i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.95819 + 0.499082i) q^{9} +(-2.19553 - 0.423868i) q^{10} -0.0826422i q^{11} +(-1.72601 + 0.144577i) q^{12} +(-2.92164 + 2.92164i) q^{13} +3.27434 q^{14} +(3.01578 - 2.43004i) q^{15} -1.00000 q^{16} +(-5.30247 + 5.30247i) q^{17} +(1.73886 - 2.44466i) q^{18} -6.47652i q^{19} +(1.85219 - 1.25275i) q^{20} +(-3.66150 + 4.33098i) q^{21} +(0.0584368 + 0.0584368i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(1.11824 - 1.32270i) q^{24} +(-1.86123 + 4.64067i) q^{25} -4.13182i q^{26} +(1.28911 + 5.03371i) q^{27} +(-2.31531 + 2.31531i) q^{28} +1.98555 q^{29} +(-0.414176 + 3.85077i) q^{30} -4.16017 q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.142641 + 0.0119482i) q^{33} -7.49883i q^{34} +(1.38789 - 7.18891i) q^{35} +(0.499082 + 2.95819i) q^{36} +(4.80467 + 4.80467i) q^{37} +(4.57959 + 4.57959i) q^{38} +(5.46517 + 4.62037i) q^{39} +(-0.423868 + 2.19553i) q^{40} -0.882958i q^{41} +(-0.473395 - 5.65154i) q^{42} +(-1.69981 + 1.69981i) q^{43} -0.0826422 q^{44} +(-4.63028 - 4.85392i) q^{45} +1.00000 q^{46} +(-7.63231 + 7.63231i) q^{47} +(0.144577 + 1.72601i) q^{48} +3.72133i q^{49} +(-1.96536 - 4.59754i) q^{50} +(9.91872 + 8.38549i) q^{51} +(2.92164 + 2.92164i) q^{52} +(-7.26221 - 7.26221i) q^{53} +(-4.47090 - 2.64783i) q^{54} +(0.153069 - 0.103530i) q^{55} -3.27434i q^{56} +(-11.1785 + 0.936357i) q^{57} +(-1.40400 + 1.40400i) q^{58} -10.0777 q^{59} +(-2.43004 - 3.01578i) q^{60} -0.876183 q^{61} +(2.94168 - 2.94168i) q^{62} +(8.00467 + 5.69361i) q^{63} +1.00000i q^{64} +(-9.07153 - 1.75135i) q^{65} +(0.0924137 - 0.109311i) q^{66} +(0.768241 + 0.768241i) q^{67} +(5.30247 + 5.30247i) q^{68} +(-1.11824 + 1.32270i) q^{69} +(4.10194 + 6.06471i) q^{70} +1.70346i q^{71} +(-2.44466 - 1.73886i) q^{72} +(-0.265720 + 0.265720i) q^{73} -6.79483 q^{74} +(8.27892 + 2.54156i) q^{75} -6.47652 q^{76} +(-0.191342 + 0.191342i) q^{77} +(-7.13155 + 0.597367i) q^{78} +16.8063i q^{79} +(-1.25275 - 1.85219i) q^{80} +(8.50183 - 2.95276i) q^{81} +(0.624346 + 0.624346i) q^{82} +(-8.84618 - 8.84618i) q^{83} +(4.33098 + 3.66150i) q^{84} +(-16.4639 - 3.17852i) q^{85} -2.40390i q^{86} +(-0.287065 - 3.42708i) q^{87} +(0.0584368 - 0.0584368i) q^{88} +5.65142 q^{89} +(6.70634 + 0.158137i) q^{90} +13.5290 q^{91} +(-0.707107 + 0.707107i) q^{92} +(0.601465 + 7.18048i) q^{93} -10.7937i q^{94} +(11.9958 - 8.11347i) q^{95} +(-1.32270 - 1.11824i) q^{96} +(-7.30890 - 7.30890i) q^{97} +(-2.63138 - 2.63138i) q^{98} +(0.0412452 + 0.244472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{3} + 12q^{6} + 8q^{7} + O(q^{10}) \) \( 32q + 4q^{3} + 12q^{6} + 8q^{7} - 4q^{12} - 12q^{15} - 32q^{16} + 8q^{18} - 40q^{22} + 32q^{25} + 4q^{27} + 8q^{28} - 20q^{30} + 8q^{31} + 8q^{33} + 20q^{36} - 16q^{37} + 8q^{40} - 8q^{42} - 80q^{43} - 4q^{45} + 32q^{46} - 4q^{48} + 36q^{51} + 12q^{57} - 16q^{58} - 4q^{60} + 8q^{61} + 44q^{63} + 52q^{66} + 64q^{67} + 64q^{70} - 8q^{72} - 56q^{73} - 68q^{75} - 8q^{76} + 60q^{78} - 44q^{81} - 48q^{85} - 60q^{87} - 40q^{88} - 64q^{90} + 40q^{91} + 92q^{93} - 12q^{96} - 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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
\(3\) −0.144577 1.72601i −0.0834716 0.996510i
\(4\) 1.00000i 0.500000i
\(5\) 1.25275 + 1.85219i 0.560247 + 0.828325i
\(6\) 1.32270 + 1.11824i 0.539991 + 0.456519i
\(7\) −2.31531 2.31531i −0.875106 0.875106i 0.117918 0.993023i \(-0.462378\pi\)
−0.993023 + 0.117918i \(0.962378\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.95819 + 0.499082i −0.986065 + 0.166361i
\(10\) −2.19553 0.423868i −0.694286 0.134039i
\(11\) 0.0826422i 0.0249176i −0.999922 0.0124588i \(-0.996034\pi\)
0.999922 0.0124588i \(-0.00396585\pi\)
\(12\) −1.72601 + 0.144577i −0.498255 + 0.0417358i
\(13\) −2.92164 + 2.92164i −0.810317 + 0.810317i −0.984681 0.174364i \(-0.944213\pi\)
0.174364 + 0.984681i \(0.444213\pi\)
\(14\) 3.27434 0.875106
\(15\) 3.01578 2.43004i 0.778670 0.627434i
\(16\) −1.00000 −0.250000
\(17\) −5.30247 + 5.30247i −1.28604 + 1.28604i −0.348866 + 0.937172i \(0.613433\pi\)
−0.937172 + 0.348866i \(0.886567\pi\)
\(18\) 1.73886 2.44466i 0.409852 0.576213i
\(19\) 6.47652i 1.48582i −0.669393 0.742908i \(-0.733446\pi\)
0.669393 0.742908i \(-0.266554\pi\)
\(20\) 1.85219 1.25275i 0.414163 0.280124i
\(21\) −3.66150 + 4.33098i −0.799005 + 0.945098i
\(22\) 0.0584368 + 0.0584368i 0.0124588 + 0.0124588i
\(23\) −0.707107 0.707107i −0.147442 0.147442i
\(24\) 1.11824 1.32270i 0.228260 0.269995i
\(25\) −1.86123 + 4.64067i −0.372246 + 0.928134i
\(26\) 4.13182i 0.810317i
\(27\) 1.28911 + 5.03371i 0.248088 + 0.968737i
\(28\) −2.31531 + 2.31531i −0.437553 + 0.437553i
\(29\) 1.98555 0.368708 0.184354 0.982860i \(-0.440981\pi\)
0.184354 + 0.982860i \(0.440981\pi\)
\(30\) −0.414176 + 3.85077i −0.0756179 + 0.703052i
\(31\) −4.16017 −0.747188 −0.373594 0.927592i \(-0.621875\pi\)
−0.373594 + 0.927592i \(0.621875\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −0.142641 + 0.0119482i −0.0248306 + 0.00207991i
\(34\) 7.49883i 1.28604i
\(35\) 1.38789 7.18891i 0.234596 1.21515i
\(36\) 0.499082 + 2.95819i 0.0831803 + 0.493032i
\(37\) 4.80467 + 4.80467i 0.789883 + 0.789883i 0.981475 0.191591i \(-0.0613649\pi\)
−0.191591 + 0.981475i \(0.561365\pi\)
\(38\) 4.57959 + 4.57959i 0.742908 + 0.742908i
\(39\) 5.46517 + 4.62037i 0.875128 + 0.739851i
\(40\) −0.423868 + 2.19553i −0.0670194 + 0.347143i
\(41\) 0.882958i 0.137895i −0.997620 0.0689474i \(-0.978036\pi\)
0.997620 0.0689474i \(-0.0219641\pi\)
\(42\) −0.473395 5.65154i −0.0730465 0.872052i
\(43\) −1.69981 + 1.69981i −0.259219 + 0.259219i −0.824736 0.565518i \(-0.808676\pi\)
0.565518 + 0.824736i \(0.308676\pi\)
\(44\) −0.0826422 −0.0124588
\(45\) −4.63028 4.85392i −0.690241 0.723579i
\(46\) 1.00000 0.147442
\(47\) −7.63231 + 7.63231i −1.11329 + 1.11329i −0.120584 + 0.992703i \(0.538477\pi\)
−0.992703 + 0.120584i \(0.961523\pi\)
\(48\) 0.144577 + 1.72601i 0.0208679 + 0.249128i
\(49\) 3.72133i 0.531619i
\(50\) −1.96536 4.59754i −0.277944 0.650190i
\(51\) 9.91872 + 8.38549i 1.38890 + 1.17420i
\(52\) 2.92164 + 2.92164i 0.405159 + 0.405159i
\(53\) −7.26221 7.26221i −0.997541 0.997541i 0.00245571 0.999997i \(-0.499218\pi\)
−0.999997 + 0.00245571i \(0.999218\pi\)
\(54\) −4.47090 2.64783i −0.608413 0.360324i
\(55\) 0.153069 0.103530i 0.0206398 0.0139600i
\(56\) 3.27434i 0.437553i
\(57\) −11.1785 + 0.936357i −1.48063 + 0.124023i
\(58\) −1.40400 + 1.40400i −0.184354 + 0.184354i
\(59\) −10.0777 −1.31201 −0.656003 0.754759i \(-0.727754\pi\)
−0.656003 + 0.754759i \(0.727754\pi\)
\(60\) −2.43004 3.01578i −0.313717 0.389335i
\(61\) −0.876183 −0.112184 −0.0560919 0.998426i \(-0.517864\pi\)
−0.0560919 + 0.998426i \(0.517864\pi\)
\(62\) 2.94168 2.94168i 0.373594 0.373594i
\(63\) 8.00467 + 5.69361i 1.00849 + 0.717328i
\(64\) 1.00000i 0.125000i
\(65\) −9.07153 1.75135i −1.12518 0.217228i
\(66\) 0.0924137 0.109311i 0.0113753 0.0134553i
\(67\) 0.768241 + 0.768241i 0.0938556 + 0.0938556i 0.752476 0.658620i \(-0.228860\pi\)
−0.658620 + 0.752476i \(0.728860\pi\)
\(68\) 5.30247 + 5.30247i 0.643019 + 0.643019i
\(69\) −1.11824 + 1.32270i −0.134620 + 0.159235i
\(70\) 4.10194 + 6.06471i 0.490276 + 0.724872i
\(71\) 1.70346i 0.202163i 0.994878 + 0.101082i \(0.0322303\pi\)
−0.994878 + 0.101082i \(0.967770\pi\)
\(72\) −2.44466 1.73886i −0.288106 0.204926i
\(73\) −0.265720 + 0.265720i −0.0311002 + 0.0311002i −0.722486 0.691386i \(-0.757001\pi\)
0.691386 + 0.722486i \(0.257001\pi\)
\(74\) −6.79483 −0.789883
\(75\) 8.27892 + 2.54156i 0.955967 + 0.293474i
\(76\) −6.47652 −0.742908
\(77\) −0.191342 + 0.191342i −0.0218055 + 0.0218055i
\(78\) −7.13155 + 0.597367i −0.807490 + 0.0676385i
\(79\) 16.8063i 1.89085i 0.325834 + 0.945427i \(0.394355\pi\)
−0.325834 + 0.945427i \(0.605645\pi\)
\(80\) −1.25275 1.85219i −0.140062 0.207081i
\(81\) 8.50183 2.95276i 0.944648 0.328085i
\(82\) 0.624346 + 0.624346i 0.0689474 + 0.0689474i
\(83\) −8.84618 8.84618i −0.970994 0.970994i 0.0285970 0.999591i \(-0.490896\pi\)
−0.999591 + 0.0285970i \(0.990896\pi\)
\(84\) 4.33098 + 3.66150i 0.472549 + 0.399503i
\(85\) −16.4639 3.17852i −1.78576 0.344758i
\(86\) 2.40390i 0.259219i
\(87\) −0.287065 3.42708i −0.0307766 0.367421i
\(88\) 0.0584368 0.0584368i 0.00622939 0.00622939i
\(89\) 5.65142 0.599049 0.299525 0.954089i \(-0.403172\pi\)
0.299525 + 0.954089i \(0.403172\pi\)
\(90\) 6.70634 + 0.158137i 0.706910 + 0.0166691i
\(91\) 13.5290 1.41823
\(92\) −0.707107 + 0.707107i −0.0737210 + 0.0737210i
\(93\) 0.601465 + 7.18048i 0.0623690 + 0.744581i
\(94\) 10.7937i 1.11329i
\(95\) 11.9958 8.11347i 1.23074 0.832425i
\(96\) −1.32270 1.11824i −0.134998 0.114130i
\(97\) −7.30890 7.30890i −0.742107 0.742107i 0.230876 0.972983i \(-0.425841\pi\)
−0.972983 + 0.230876i \(0.925841\pi\)
\(98\) −2.63138 2.63138i −0.265810 0.265810i
\(99\) 0.0412452 + 0.244472i 0.00414530 + 0.0245703i
\(100\) 4.64067 + 1.86123i 0.464067 + 0.186123i
\(101\) 2.99650i 0.298163i −0.988825 0.149082i \(-0.952368\pi\)
0.988825 0.149082i \(-0.0476317\pi\)
\(102\) −12.9430 + 1.08416i −1.28155 + 0.107348i
\(103\) 7.92493 7.92493i 0.780866 0.780866i −0.199111 0.979977i \(-0.563805\pi\)
0.979977 + 0.199111i \(0.0638053\pi\)
\(104\) −4.13182 −0.405159
\(105\) −12.6088 1.35616i −1.23049 0.132347i
\(106\) 10.2703 0.997541
\(107\) −5.54562 + 5.54562i −0.536115 + 0.536115i −0.922386 0.386270i \(-0.873763\pi\)
0.386270 + 0.922386i \(0.373763\pi\)
\(108\) 5.03371 1.28911i 0.484369 0.124044i
\(109\) 14.3159i 1.37121i −0.727974 0.685605i \(-0.759538\pi\)
0.727974 0.685605i \(-0.240462\pi\)
\(110\) −0.0350294 + 0.181443i −0.00333992 + 0.0172999i
\(111\) 7.59825 8.98754i 0.721194 0.853060i
\(112\) 2.31531 + 2.31531i 0.218776 + 0.218776i
\(113\) 1.54977 + 1.54977i 0.145791 + 0.145791i 0.776235 0.630444i \(-0.217127\pi\)
−0.630444 + 0.776235i \(0.717127\pi\)
\(114\) 7.24230 8.56651i 0.678304 0.802327i
\(115\) 0.423868 2.19553i 0.0395259 0.204734i
\(116\) 1.98555i 0.184354i
\(117\) 7.18465 10.1009i 0.664221 0.933831i
\(118\) 7.12601 7.12601i 0.656003 0.656003i
\(119\) 24.5538 2.25084
\(120\) 3.85077 + 0.414176i 0.351526 + 0.0378090i
\(121\) 10.9932 0.999379
\(122\) 0.619555 0.619555i 0.0560919 0.0560919i
\(123\) −1.52399 + 0.127655i −0.137414 + 0.0115103i
\(124\) 4.16017i 0.373594i
\(125\) −10.9271 + 2.36626i −0.977347 + 0.211645i
\(126\) −9.68615 + 1.63417i −0.862911 + 0.145583i
\(127\) −2.65907 2.65907i −0.235954 0.235954i 0.579218 0.815172i \(-0.303358\pi\)
−0.815172 + 0.579218i \(0.803358\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 3.17964 + 2.68813i 0.279952 + 0.236677i
\(130\) 7.65293 5.17615i 0.671206 0.453978i
\(131\) 12.0048i 1.04887i −0.851452 0.524433i \(-0.824277\pi\)
0.851452 0.524433i \(-0.175723\pi\)
\(132\) 0.0119482 + 0.142641i 0.00103995 + 0.0124153i
\(133\) −14.9952 + 14.9952i −1.30025 + 1.30025i
\(134\) −1.08646 −0.0938556
\(135\) −7.70846 + 8.69365i −0.663439 + 0.748231i
\(136\) −7.49883 −0.643019
\(137\) 4.13246 4.13246i 0.353060 0.353060i −0.508187 0.861247i \(-0.669684\pi\)
0.861247 + 0.508187i \(0.169684\pi\)
\(138\) −0.144577 1.72601i −0.0123072 0.146927i
\(139\) 0.433456i 0.0367652i 0.999831 + 0.0183826i \(0.00585170\pi\)
−0.999831 + 0.0183826i \(0.994148\pi\)
\(140\) −7.18891 1.38789i −0.607574 0.117298i
\(141\) 14.2769 + 12.0700i 1.20233 + 1.01647i
\(142\) −1.20453 1.20453i −0.101082 0.101082i
\(143\) 0.241451 + 0.241451i 0.0201911 + 0.0201911i
\(144\) 2.95819 0.499082i 0.246516 0.0415902i
\(145\) 2.48740 + 3.67762i 0.206568 + 0.305410i
\(146\) 0.375785i 0.0311002i
\(147\) 6.42305 0.538020i 0.529764 0.0443751i
\(148\) 4.80467 4.80467i 0.394942 0.394942i
\(149\) 20.0239 1.64042 0.820212 0.572059i \(-0.193855\pi\)
0.820212 + 0.572059i \(0.193855\pi\)
\(150\) −7.65123 + 4.05693i −0.624720 + 0.331247i
\(151\) −17.1989 −1.39963 −0.699814 0.714325i \(-0.746734\pi\)
−0.699814 + 0.714325i \(0.746734\pi\)
\(152\) 4.57959 4.57959i 0.371454 0.371454i
\(153\) 13.0394 18.3321i 1.05417 1.48206i
\(154\) 0.270599i 0.0218055i
\(155\) −5.21166 7.70543i −0.418610 0.618915i
\(156\) 4.62037 5.46517i 0.369926 0.437564i
\(157\) 16.4821 + 16.4821i 1.31542 + 1.31542i 0.917362 + 0.398054i \(0.130314\pi\)
0.398054 + 0.917362i \(0.369686\pi\)
\(158\) −11.8838 11.8838i −0.945427 0.945427i
\(159\) −11.4847 + 13.5846i −0.910794 + 1.07733i
\(160\) 2.19553 + 0.423868i 0.173572 + 0.0335097i
\(161\) 3.27434i 0.258055i
\(162\) −3.92379 + 8.09962i −0.308282 + 0.636367i
\(163\) 7.21629 7.21629i 0.565224 0.565224i −0.365563 0.930787i \(-0.619124\pi\)
0.930787 + 0.365563i \(0.119124\pi\)
\(164\) −0.882958 −0.0689474
\(165\) −0.200824 0.249230i −0.0156341 0.0194025i
\(166\) 12.5104 0.970994
\(167\) 11.3314 11.3314i 0.876846 0.876846i −0.116361 0.993207i \(-0.537123\pi\)
0.993207 + 0.116361i \(0.0371228\pi\)
\(168\) −5.65154 + 0.473395i −0.436026 + 0.0365232i
\(169\) 4.07197i 0.313229i
\(170\) 13.8893 9.39417i 1.06526 0.720500i
\(171\) 3.23232 + 19.1588i 0.247181 + 1.46511i
\(172\) 1.69981 + 1.69981i 0.129609 + 0.129609i
\(173\) −6.03766 6.03766i −0.459035 0.459035i 0.439304 0.898339i \(-0.355225\pi\)
−0.898339 + 0.439304i \(0.855225\pi\)
\(174\) 2.62629 + 2.22032i 0.199099 + 0.168322i
\(175\) 15.0539 6.43528i 1.13797 0.486461i
\(176\) 0.0826422i 0.00622939i
\(177\) 1.45700 + 17.3942i 0.109515 + 1.30743i
\(178\) −3.99616 + 3.99616i −0.299525 + 0.299525i
\(179\) 10.2241 0.764188 0.382094 0.924123i \(-0.375203\pi\)
0.382094 + 0.924123i \(0.375203\pi\)
\(180\) −4.85392 + 4.63028i −0.361790 + 0.345121i
\(181\) −7.86650 −0.584712 −0.292356 0.956310i \(-0.594439\pi\)
−0.292356 + 0.956310i \(0.594439\pi\)
\(182\) −9.56646 + 9.56646i −0.709113 + 0.709113i
\(183\) 0.126676 + 1.51230i 0.00936416 + 0.111792i
\(184\) 1.00000i 0.0737210i
\(185\) −2.88011 + 14.9182i −0.211750 + 1.09681i
\(186\) −5.50266 4.65206i −0.403475 0.341106i
\(187\) 0.438208 + 0.438208i 0.0320449 + 0.0320449i
\(188\) 7.63231 + 7.63231i 0.556644 + 0.556644i
\(189\) 8.66992 14.6393i 0.630644 1.06485i
\(190\) −2.74519 + 14.2194i −0.199157 + 1.03158i
\(191\) 23.2816i 1.68460i 0.539009 + 0.842300i \(0.318799\pi\)
−0.539009 + 0.842300i \(0.681201\pi\)
\(192\) 1.72601 0.144577i 0.124564 0.0104340i
\(193\) −13.3531 + 13.3531i −0.961176 + 0.961176i −0.999274 0.0380984i \(-0.987870\pi\)
0.0380984 + 0.999274i \(0.487870\pi\)
\(194\) 10.3363 0.742107
\(195\) −1.71130 + 15.9107i −0.122549 + 1.13939i
\(196\) 3.72133 0.265810
\(197\) 3.92746 3.92746i 0.279820 0.279820i −0.553217 0.833037i \(-0.686600\pi\)
0.833037 + 0.553217i \(0.186600\pi\)
\(198\) −0.202032 0.143703i −0.0143578 0.0102125i
\(199\) 14.6406i 1.03784i −0.854822 0.518921i \(-0.826334\pi\)
0.854822 0.518921i \(-0.173666\pi\)
\(200\) −4.59754 + 1.96536i −0.325095 + 0.138972i
\(201\) 1.21492 1.43706i 0.0856937 0.101362i
\(202\) 2.11885 + 2.11885i 0.149082 + 0.149082i
\(203\) −4.59717 4.59717i −0.322658 0.322658i
\(204\) 8.38549 9.91872i 0.587102 0.694449i
\(205\) 1.63541 1.10613i 0.114222 0.0772553i
\(206\) 11.2075i 0.780866i
\(207\) 2.44466 + 1.73886i 0.169916 + 0.120859i
\(208\) 2.92164 2.92164i 0.202579 0.202579i
\(209\) −0.535234 −0.0370229
\(210\) 9.87469 7.95679i 0.681418 0.549071i
\(211\) 1.39261 0.0958715 0.0479357 0.998850i \(-0.484736\pi\)
0.0479357 + 0.998850i \(0.484736\pi\)
\(212\) −7.26221 + 7.26221i −0.498771 + 0.498771i
\(213\) 2.94018 0.246281i 0.201458 0.0168749i
\(214\) 7.84269i 0.536115i
\(215\) −5.27782 1.01894i −0.359944 0.0694908i
\(216\) −2.64783 + 4.47090i −0.180162 + 0.304206i
\(217\) 9.63209 + 9.63209i 0.653869 + 0.653869i
\(218\) 10.1228 + 10.1228i 0.685605 + 0.685605i
\(219\) 0.497052 + 0.420218i 0.0335876 + 0.0283957i
\(220\) −0.103530 0.153069i −0.00698000 0.0103199i
\(221\) 30.9839i 2.08420i
\(222\) 0.982377 + 11.7279i 0.0659328 + 0.787127i
\(223\) 16.9943 16.9943i 1.13802 1.13802i 0.149216 0.988805i \(-0.452325\pi\)
0.988805 0.149216i \(-0.0476749\pi\)
\(224\) −3.27434 −0.218776
\(225\) 3.18980 14.6569i 0.212653 0.977128i
\(226\) −2.19171 −0.145791
\(227\) −6.77558 + 6.77558i −0.449711 + 0.449711i −0.895258 0.445547i \(-0.853009\pi\)
0.445547 + 0.895258i \(0.353009\pi\)
\(228\) 0.936357 + 11.1785i 0.0620117 + 0.740316i
\(229\) 11.6200i 0.767870i 0.923360 + 0.383935i \(0.125431\pi\)
−0.923360 + 0.383935i \(0.874569\pi\)
\(230\) 1.25275 + 1.85219i 0.0826040 + 0.122130i
\(231\) 0.357922 + 0.302594i 0.0235495 + 0.0199093i
\(232\) 1.40400 + 1.40400i 0.0921770 + 0.0921770i
\(233\) −12.9668 12.9668i −0.849484 0.849484i 0.140585 0.990069i \(-0.455102\pi\)
−0.990069 + 0.140585i \(0.955102\pi\)
\(234\) 2.06212 + 12.2227i 0.134805 + 0.799026i
\(235\) −23.6979 4.57512i −1.54588 0.298448i
\(236\) 10.0777i 0.656003i
\(237\) 29.0077 2.42980i 1.88426 0.157833i
\(238\) −17.3621 + 17.3621i −1.12542 + 1.12542i
\(239\) −6.05401 −0.391602 −0.195801 0.980644i \(-0.562731\pi\)
−0.195801 + 0.980644i \(0.562731\pi\)
\(240\) −3.01578 + 2.43004i −0.194667 + 0.156858i
\(241\) −17.7288 −1.14201 −0.571007 0.820945i \(-0.693447\pi\)
−0.571007 + 0.820945i \(0.693447\pi\)
\(242\) −7.77335 + 7.77335i −0.499690 + 0.499690i
\(243\) −6.32566 14.2473i −0.405791 0.913966i
\(244\) 0.876183i 0.0560919i
\(245\) −6.89263 + 4.66191i −0.440354 + 0.297838i
\(246\) 0.987358 1.16789i 0.0629517 0.0744620i
\(247\) 18.9221 + 18.9221i 1.20398 + 1.20398i
\(248\) −2.94168 2.94168i −0.186797 0.186797i
\(249\) −13.9896 + 16.5475i −0.886555 + 1.04866i
\(250\) 6.05341 9.39980i 0.382851 0.594496i
\(251\) 22.3292i 1.40941i 0.709501 + 0.704705i \(0.248921\pi\)
−0.709501 + 0.704705i \(0.751079\pi\)
\(252\) 5.69361 8.00467i 0.358664 0.504247i
\(253\) −0.0584368 + 0.0584368i −0.00367389 + 0.00367389i
\(254\) 3.76049 0.235954
\(255\) −3.10584 + 28.8763i −0.194495 + 1.80830i
\(256\) 1.00000 0.0625000
\(257\) 3.75966 3.75966i 0.234521 0.234521i −0.580056 0.814577i \(-0.696969\pi\)
0.814577 + 0.580056i \(0.196969\pi\)
\(258\) −4.14914 + 0.347548i −0.258314 + 0.0216374i
\(259\) 22.2486i 1.38246i
\(260\) −1.75135 + 9.07153i −0.108614 + 0.562592i
\(261\) −5.87365 + 0.990953i −0.363570 + 0.0613385i
\(262\) 8.48869 + 8.48869i 0.524433 + 0.524433i
\(263\) −9.73597 9.73597i −0.600346 0.600346i 0.340058 0.940404i \(-0.389553\pi\)
−0.940404 + 0.340058i \(0.889553\pi\)
\(264\) −0.109311 0.0924137i −0.00672763 0.00568767i
\(265\) 4.35326 22.5487i 0.267419 1.38516i
\(266\) 21.2064i 1.30025i
\(267\) −0.817066 9.75439i −0.0500036 0.596959i
\(268\) 0.768241 0.768241i 0.0469278 0.0469278i
\(269\) −1.99991 −0.121937 −0.0609684 0.998140i \(-0.519419\pi\)
−0.0609684 + 0.998140i \(0.519419\pi\)
\(270\) −0.696637 11.5980i −0.0423960 0.705835i
\(271\) −7.75320 −0.470973 −0.235487 0.971878i \(-0.575668\pi\)
−0.235487 + 0.971878i \(0.575668\pi\)
\(272\) 5.30247 5.30247i 0.321510 0.321510i
\(273\) −1.95599 23.3512i −0.118382 1.41328i
\(274\) 5.84419i 0.353060i
\(275\) 0.383515 + 0.153816i 0.0231268 + 0.00927545i
\(276\) 1.32270 + 1.11824i 0.0796173 + 0.0673101i
\(277\) −8.36272 8.36272i −0.502467 0.502467i 0.409737 0.912204i \(-0.365621\pi\)
−0.912204 + 0.409737i \(0.865621\pi\)
\(278\) −0.306500 0.306500i −0.0183826 0.0183826i
\(279\) 12.3066 2.07627i 0.736776 0.124303i
\(280\) 6.06471 4.10194i 0.362436 0.245138i
\(281\) 10.4388i 0.622729i −0.950291 0.311365i \(-0.899214\pi\)
0.950291 0.311365i \(-0.100786\pi\)
\(282\) −18.6300 + 1.56052i −1.10940 + 0.0929279i
\(283\) 9.18213 9.18213i 0.545821 0.545821i −0.379408 0.925229i \(-0.623872\pi\)
0.925229 + 0.379408i \(0.123872\pi\)
\(284\) 1.70346 0.101082
\(285\) −15.7382 19.5317i −0.932252 1.15696i
\(286\) −0.341463 −0.0201911
\(287\) −2.04432 + 2.04432i −0.120673 + 0.120673i
\(288\) −1.73886 + 2.44466i −0.102463 + 0.144053i
\(289\) 39.2325i 2.30779i
\(290\) −4.35933 0.841612i −0.255989 0.0494212i
\(291\) −11.5585 + 13.6719i −0.677572 + 0.801462i
\(292\) 0.265720 + 0.265720i 0.0155501 + 0.0155501i
\(293\) 12.9233 + 12.9233i 0.754988 + 0.754988i 0.975406 0.220418i \(-0.0707421\pi\)
−0.220418 + 0.975406i \(0.570742\pi\)
\(294\) −4.16134 + 4.92222i −0.242694 + 0.287070i
\(295\) −12.6249 18.6658i −0.735048 1.08677i
\(296\) 6.79483i 0.394942i
\(297\) 0.415997 0.106534i 0.0241386 0.00618176i
\(298\) −14.1591 + 14.1591i −0.820212 + 0.820212i
\(299\) 4.13182 0.238950
\(300\) 2.54156 8.27892i 0.146737 0.477984i
\(301\) 7.87119 0.453688
\(302\) 12.1615 12.1615i 0.699814 0.699814i
\(303\) −5.17198 + 0.433226i −0.297123 + 0.0248882i
\(304\) 6.47652i 0.371454i
\(305\) −1.09764 1.62286i −0.0628507 0.0929246i
\(306\) 3.74253 + 22.1830i 0.213946 + 1.26812i
\(307\) −9.27023 9.27023i −0.529080 0.529080i 0.391218 0.920298i \(-0.372054\pi\)
−0.920298 + 0.391218i \(0.872054\pi\)
\(308\) 0.191342 + 0.191342i 0.0109027 + 0.0109027i
\(309\) −14.8242 12.5327i −0.843321 0.712961i
\(310\) 9.13376 + 1.76336i 0.518763 + 0.100152i
\(311\) 34.1062i 1.93399i −0.254804 0.966993i \(-0.582011\pi\)
0.254804 0.966993i \(-0.417989\pi\)
\(312\) 0.597367 + 7.13155i 0.0338193 + 0.403745i
\(313\) −21.0097 + 21.0097i −1.18754 + 1.18754i −0.209795 + 0.977745i \(0.567280\pi\)
−0.977745 + 0.209795i \(0.932720\pi\)
\(314\) −23.3092 −1.31542
\(315\) −0.517796 + 21.9589i −0.0291745 + 1.23724i
\(316\) 16.8063 0.945427
\(317\) 1.88900 1.88900i 0.106097 0.106097i −0.652066 0.758163i \(-0.726097\pi\)
0.758163 + 0.652066i \(0.226097\pi\)
\(318\) −1.48485 17.7266i −0.0832664 0.994060i
\(319\) 0.164090i 0.00918730i
\(320\) −1.85219 + 1.25275i −0.103541 + 0.0700309i
\(321\) 10.3735 + 8.77000i 0.578995 + 0.489494i
\(322\) −2.31531 2.31531i −0.129027 0.129027i
\(323\) 34.3416 + 34.3416i 1.91082 + 1.91082i
\(324\) −2.95276 8.50183i −0.164042 0.472324i
\(325\) −8.12054 18.9962i −0.450446 1.05372i
\(326\) 10.2054i 0.565224i
\(327\) −24.7092 + 2.06974i −1.36642 + 0.114457i
\(328\) 0.624346 0.624346i 0.0344737 0.0344737i
\(329\) 35.3424 1.94849
\(330\) 0.318236 + 0.0342284i 0.0175183 + 0.00188421i
\(331\) −18.4120 −1.01202 −0.506008 0.862529i \(-0.668879\pi\)
−0.506008 + 0.862529i \(0.668879\pi\)
\(332\) −8.84618 + 8.84618i −0.485497 + 0.485497i
\(333\) −16.6111 11.8152i −0.910282 0.647471i
\(334\) 16.0250i 0.876846i
\(335\) −0.460514 + 2.38534i −0.0251606 + 0.130325i
\(336\) 3.66150 4.33098i 0.199751 0.236274i
\(337\) −4.80586 4.80586i −0.261792 0.261792i 0.563990 0.825782i \(-0.309266\pi\)
−0.825782 + 0.563990i \(0.809266\pi\)
\(338\) 2.87932 + 2.87932i 0.156614 + 0.156614i
\(339\) 2.45086 2.89898i 0.133112 0.157451i
\(340\) −3.17852 + 16.4639i −0.172379 + 0.892879i
\(341\) 0.343805i 0.0186181i
\(342\) −15.8329 11.2617i −0.856146 0.608965i
\(343\) −7.59113 + 7.59113i −0.409883 + 0.409883i
\(344\) −2.40390 −0.129609
\(345\) −3.85077 0.414176i −0.207319 0.0222985i
\(346\) 8.53854 0.459035
\(347\) −17.1222 + 17.1222i −0.919167 + 0.919167i −0.996969 0.0778017i \(-0.975210\pi\)
0.0778017 + 0.996969i \(0.475210\pi\)
\(348\) −3.42708 + 0.287065i −0.183711 + 0.0153883i
\(349\) 2.01226i 0.107714i 0.998549 + 0.0538569i \(0.0171515\pi\)
−0.998549 + 0.0538569i \(0.982849\pi\)
\(350\) −6.09430 + 15.1952i −0.325754 + 0.812215i
\(351\) −18.4730 10.9404i −0.986015 0.583954i
\(352\) −0.0584368 0.0584368i −0.00311469 0.00311469i
\(353\) −23.0099 23.0099i −1.22469 1.22469i −0.965945 0.258749i \(-0.916690\pi\)
−0.258749 0.965945i \(-0.583310\pi\)
\(354\) −13.3298 11.2693i −0.708471 0.598956i
\(355\) −3.15513 + 2.13401i −0.167457 + 0.113261i
\(356\) 5.65142i 0.299525i
\(357\) −3.54991 42.3799i −0.187881 2.24298i
\(358\) −7.22956 + 7.22956i −0.382094 + 0.382094i
\(359\) 19.5535 1.03199 0.515996 0.856591i \(-0.327422\pi\)
0.515996 + 0.856591i \(0.327422\pi\)
\(360\) 0.158137 6.70634i 0.00833457 0.353455i
\(361\) −22.9454 −1.20765
\(362\) 5.56245 5.56245i 0.292356 0.292356i
\(363\) −1.58936 18.9743i −0.0834198 0.995891i
\(364\) 13.5290i 0.709113i
\(365\) −0.825046 0.159283i −0.0431849 0.00833727i
\(366\) −1.15893 0.979782i −0.0605782 0.0512140i
\(367\) 6.00838 + 6.00838i 0.313635 + 0.313635i 0.846316 0.532681i \(-0.178815\pi\)
−0.532681 + 0.846316i \(0.678815\pi\)
\(368\) 0.707107 + 0.707107i 0.0368605 + 0.0368605i
\(369\) 0.440668 + 2.61196i 0.0229403 + 0.135973i
\(370\) −8.51224 12.5853i −0.442530 0.654280i
\(371\) 33.6286i 1.74591i
\(372\) 7.18048 0.601465i 0.372290 0.0311845i
\(373\) −18.4696 + 18.4696i −0.956318 + 0.956318i −0.999085 0.0427675i \(-0.986383\pi\)
0.0427675 + 0.999085i \(0.486383\pi\)
\(374\) −0.619720 −0.0320449
\(375\) 5.66398 + 18.5181i 0.292487 + 0.956270i
\(376\) −10.7937 −0.556644
\(377\) −5.80107 + 5.80107i −0.298770 + 0.298770i
\(378\) 4.22098 + 16.4821i 0.217104 + 0.847747i
\(379\) 2.21381i 0.113716i −0.998382 0.0568579i \(-0.981892\pi\)
0.998382 0.0568579i \(-0.0181082\pi\)
\(380\) −8.11347 11.9958i −0.416212 0.615370i
\(381\) −4.20513 + 4.97401i −0.215435 + 0.254826i
\(382\) −16.4626 16.4626i −0.842300 0.842300i
\(383\) 24.0015 + 24.0015i 1.22642 + 1.22642i 0.965308 + 0.261112i \(0.0840893\pi\)
0.261112 + 0.965308i \(0.415911\pi\)
\(384\) −1.11824 + 1.32270i −0.0570649 + 0.0674989i
\(385\) −0.594107 0.114698i −0.0302785 0.00584557i
\(386\) 18.8841i 0.961176i
\(387\) 4.18003 5.87672i 0.212483 0.298730i
\(388\) −7.30890 + 7.30890i −0.371053 + 0.371053i
\(389\) 8.89237 0.450861 0.225431 0.974259i \(-0.427621\pi\)
0.225431 + 0.974259i \(0.427621\pi\)
\(390\) −10.0405 12.4607i −0.508421 0.630970i
\(391\) 7.49883 0.379232
\(392\) −2.63138 + 2.63138i −0.132905 + 0.132905i
\(393\) −20.7204 + 1.73562i −1.04521 + 0.0875505i
\(394\) 5.55427i 0.279820i
\(395\) −31.1284 + 21.0541i −1.56624 + 1.05935i
\(396\) 0.244472 0.0412452i 0.0122852 0.00207265i
\(397\) 21.4168 + 21.4168i 1.07488 + 1.07488i 0.996960 + 0.0779195i \(0.0248277\pi\)
0.0779195 + 0.996960i \(0.475172\pi\)
\(398\) 10.3524 + 10.3524i 0.518921 + 0.518921i
\(399\) 28.0497 + 23.7138i 1.40424 + 1.18717i
\(400\) 1.86123 4.64067i 0.0930614 0.232034i
\(401\) 32.8935i 1.64262i 0.570480 + 0.821312i \(0.306757\pi\)
−0.570480 + 0.821312i \(0.693243\pi\)
\(402\) 0.157077 + 1.87523i 0.00783428 + 0.0935280i
\(403\) 12.1545 12.1545i 0.605460 0.605460i
\(404\) −2.99650 −0.149082
\(405\) 16.1198 + 12.0479i 0.800998 + 0.598667i
\(406\) 6.50138 0.322658
\(407\) 0.397069 0.397069i 0.0196820 0.0196820i
\(408\) 1.08416 + 12.9430i 0.0536739 + 0.640775i
\(409\) 29.4036i 1.45392i 0.686682 + 0.726958i \(0.259066\pi\)
−0.686682 + 0.726958i \(0.740934\pi\)
\(410\) −0.374258 + 1.93856i −0.0184833 + 0.0957385i
\(411\) −7.73012 6.53520i −0.381299 0.322358i
\(412\) −7.92493 7.92493i −0.390433 0.390433i
\(413\) 23.3330 + 23.3330i 1.14814 + 1.14814i
\(414\) −2.95819 + 0.499082i −0.145387 + 0.0245285i
\(415\) 5.30275 27.4669i 0.260302 1.34830i
\(416\) 4.13182i 0.202579i
\(417\) 0.748148 0.0626678i 0.0366369 0.00306885i
\(418\) 0.378468 0.378468i 0.0185115 0.0185115i
\(419\) 4.84269 0.236581 0.118290 0.992979i \(-0.462259\pi\)
0.118290 + 0.992979i \(0.462259\pi\)
\(420\) −1.35616 + 12.6088i −0.0661736 + 0.615245i
\(421\) 19.4455 0.947714 0.473857 0.880602i \(-0.342861\pi\)
0.473857 + 0.880602i \(0.342861\pi\)
\(422\) −0.984727 + 0.984727i −0.0479357 + 0.0479357i
\(423\) 18.7687 26.3870i 0.912567 1.28298i
\(424\) 10.2703i 0.498771i
\(425\) −14.7379 34.4762i −0.714895 1.67234i
\(426\) −1.90487 + 2.25317i −0.0922913 + 0.109166i
\(427\) 2.02864 + 2.02864i 0.0981726 + 0.0981726i
\(428\) 5.54562 + 5.54562i 0.268058 + 0.268058i
\(429\) 0.381837 0.451654i 0.0184353 0.0218061i
\(430\) 4.45248 3.01148i 0.214717 0.145227i
\(431\) 23.4150i 1.12786i 0.825822 + 0.563932i \(0.190712\pi\)
−0.825822 + 0.563932i \(0.809288\pi\)
\(432\) −1.28911 5.03371i −0.0620221 0.242184i
\(433\) −18.6129 + 18.6129i −0.894478 + 0.894478i −0.994941 0.100463i \(-0.967968\pi\)
0.100463 + 0.994941i \(0.467968\pi\)
\(434\) −13.6218 −0.653869
\(435\) 5.98798 4.82497i 0.287102 0.231340i
\(436\) −14.3159 −0.685605
\(437\) −4.57959 + 4.57959i −0.219072 + 0.219072i
\(438\) −0.648607 + 0.0543299i −0.0309917 + 0.00259598i
\(439\) 2.74419i 0.130973i 0.997853 + 0.0654864i \(0.0208599\pi\)
−0.997853 + 0.0654864i \(0.979140\pi\)
\(440\) 0.181443 + 0.0350294i 0.00864996 + 0.00166996i
\(441\) −1.85725 11.0084i −0.0884405 0.524211i
\(442\) 21.9089 + 21.9089i 1.04210 + 1.04210i
\(443\) −5.24175 5.24175i −0.249043 0.249043i 0.571535 0.820578i \(-0.306348\pi\)
−0.820578 + 0.571535i \(0.806348\pi\)
\(444\) −8.98754 7.59825i −0.426530 0.360597i
\(445\) 7.07983 + 10.4675i 0.335616 + 0.496208i
\(446\) 24.0335i 1.13802i
\(447\) −2.89500 34.5614i −0.136929 1.63470i
\(448\) 2.31531 2.31531i 0.109388 0.109388i
\(449\) −4.17586 −0.197071 −0.0985356 0.995134i \(-0.531416\pi\)
−0.0985356 + 0.995134i \(0.531416\pi\)
\(450\) 8.10848 + 12.6195i 0.382237 + 0.594890i
\(451\) −0.0729696 −0.00343600
\(452\) 1.54977 1.54977i 0.0728953 0.0728953i
\(453\) 2.48657 + 29.6854i 0.116829 + 1.39474i
\(454\) 9.58212i 0.449711i
\(455\) 16.9485 + 25.0583i 0.794558 + 1.17475i
\(456\) −8.56651 7.24230i −0.401164 0.339152i
\(457\) 3.72841 + 3.72841i 0.174408 + 0.174408i 0.788913 0.614505i \(-0.210644\pi\)
−0.614505 + 0.788913i \(0.710644\pi\)
\(458\) −8.21656 8.21656i −0.383935 0.383935i
\(459\) −33.5266 19.8557i −1.56489 0.926783i
\(460\) −2.19553 0.423868i −0.102367 0.0197630i
\(461\) 11.3512i 0.528680i 0.964430 + 0.264340i \(0.0851541\pi\)
−0.964430 + 0.264340i \(0.914846\pi\)
\(462\) −0.467056 + 0.0391224i −0.0217294 + 0.00182014i
\(463\) 15.3561 15.3561i 0.713657 0.713657i −0.253641 0.967298i \(-0.581628\pi\)
0.967298 + 0.253641i \(0.0816282\pi\)
\(464\) −1.98555 −0.0921770
\(465\) −12.5461 + 10.1094i −0.581813 + 0.468811i
\(466\) 18.3378 0.849484
\(467\) 5.99931 5.99931i 0.277615 0.277615i −0.554541 0.832156i \(-0.687106\pi\)
0.832156 + 0.554541i \(0.187106\pi\)
\(468\) −10.1009 7.18465i −0.466915 0.332110i
\(469\) 3.55743i 0.164267i
\(470\) 19.9920 13.5219i 0.922164 0.623717i
\(471\) 26.0653 30.8312i 1.20103 1.42063i
\(472\) −7.12601 7.12601i −0.328001 0.328001i
\(473\) 0.140476 + 0.140476i 0.00645910 + 0.00645910i
\(474\) −18.7934 + 22.2297i −0.863211 + 1.02104i
\(475\) 30.0554 + 12.0543i 1.37904 + 0.553088i
\(476\) 24.5538i 1.12542i
\(477\) 25.1075 + 17.8586i 1.14959 + 0.817689i
\(478\) 4.28083 4.28083i 0.195801 0.195801i
\(479\) −31.7615 −1.45122 −0.725611 0.688105i \(-0.758443\pi\)
−0.725611 + 0.688105i \(0.758443\pi\)
\(480\) 0.414176 3.85077i 0.0189045 0.175763i
\(481\) −28.0751 −1.28011
\(482\) 12.5362 12.5362i 0.571007 0.571007i
\(483\) 5.65154 0.473395i 0.257154 0.0215402i
\(484\) 10.9932i 0.499690i
\(485\) 4.38125 22.6937i 0.198942 1.03047i
\(486\) 14.5473 + 5.60146i 0.659878 + 0.254087i
\(487\) 8.53395 + 8.53395i 0.386710 + 0.386710i 0.873512 0.486802i \(-0.161837\pi\)
−0.486802 + 0.873512i \(0.661837\pi\)
\(488\) −0.619555 0.619555i −0.0280459 0.0280459i
\(489\) −13.4987 11.4121i −0.610431 0.516071i
\(490\) 1.57736 8.17029i 0.0712577 0.369096i
\(491\) 15.5734i 0.702820i 0.936222 + 0.351410i \(0.114298\pi\)
−0.936222 + 0.351410i \(0.885702\pi\)
\(492\) 0.127655 + 1.52399i 0.00575515 + 0.0687068i
\(493\) −10.5283 + 10.5283i −0.474173 + 0.474173i
\(494\) −26.7599 −1.20398
\(495\) −0.401138 + 0.382656i −0.0180298 + 0.0171991i
\(496\) 4.16017 0.186797
\(497\) 3.94403 3.94403i 0.176914 0.176914i
\(498\) −1.80871 21.5930i −0.0810504 0.967605i
\(499\) 29.9183i 1.33933i 0.742664 + 0.669664i \(0.233562\pi\)
−0.742664 + 0.669664i \(0.766438\pi\)
\(500\) 2.36626 + 10.9271i 0.105822 + 0.488673i
\(501\) −21.1962 17.9197i −0.946978 0.800595i
\(502\) −15.7892 15.7892i −0.704705 0.704705i
\(503\) −3.60669 3.60669i −0.160814 0.160814i 0.622113 0.782927i \(-0.286274\pi\)
−0.782927 + 0.622113i \(0.786274\pi\)
\(504\) 1.63417 + 9.68615i 0.0727915 + 0.431455i
\(505\) 5.55010 3.75387i 0.246976 0.167045i
\(506\) 0.0826422i 0.00367389i
\(507\) −7.02825 + 0.588714i −0.312136 + 0.0261457i
\(508\) −2.65907 + 2.65907i −0.117977 + 0.117977i
\(509\) −28.7783 −1.27558 −0.637789 0.770211i \(-0.720151\pi\)
−0.637789 + 0.770211i \(0.720151\pi\)
\(510\) −18.2225 22.6148i −0.806904 1.00140i
\(511\) 1.23045 0.0544319
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 32.6009 8.34892i 1.43937 0.368614i
\(514\) 5.31696i 0.234521i
\(515\) 24.6065 + 4.75052i 1.08429 + 0.209333i
\(516\) 2.68813 3.17964i 0.118338 0.139976i
\(517\) 0.630751 + 0.630751i 0.0277404 + 0.0277404i
\(518\) 15.7322 + 15.7322i 0.691231 + 0.691231i
\(519\) −9.54813 + 11.2939i −0.419116 + 0.495749i
\(520\) −5.17615 7.65293i −0.226989 0.335603i
\(521\) 10.8265i 0.474319i 0.971471 + 0.237159i \(0.0762164\pi\)
−0.971471 + 0.237159i \(0.923784\pi\)
\(522\) 3.45259 4.85401i 0.151116 0.212454i
\(523\) 0.723443 0.723443i 0.0316339 0.0316339i −0.691113 0.722747i \(-0.742879\pi\)
0.722747 + 0.691113i \(0.242879\pi\)
\(524\) −12.0048 −0.524433
\(525\) −13.2838 25.0528i −0.579752 1.09339i
\(526\) 13.7687 0.600346
\(527\) 22.0592 22.0592i 0.960913 0.960913i
\(528\) 0.142641 0.0119482i 0.00620765 0.000519977i
\(529\) 1.00000i 0.0434783i
\(530\) 12.8662 + 19.0226i 0.558870 + 0.826289i
\(531\) 29.8118 5.02960i 1.29372 0.218266i
\(532\) 14.9952 + 14.9952i 0.650123 + 0.650123i
\(533\) 2.57969 + 2.57969i 0.111739 + 0.111739i
\(534\) 7.47515 + 6.31964i 0.323481 + 0.273478i
\(535\) −17.2188 3.32427i −0.744435 0.143721i
\(536\) 1.08646i 0.0469278i
\(537\) −1.47818 17.6469i −0.0637880 0.761521i
\(538\) 1.41415 1.41415i 0.0609684 0.0609684i
\(539\) 0.307539 0.0132467
\(540\) 8.69365 + 7.70846i 0.374115 + 0.331719i
\(541\) −1.29260 −0.0555732 −0.0277866 0.999614i \(-0.508846\pi\)
−0.0277866 + 0.999614i \(0.508846\pi\)
\(542\) 5.48234 5.48234i 0.235487 0.235487i
\(543\) 1.13732 + 13.5776i 0.0488069 + 0.582672i
\(544\) 7.49883i 0.321510i
\(545\) 26.5157 17.9342i 1.13581 0.768217i
\(546\) 17.8949 + 15.1287i 0.765829 + 0.647448i
\(547\) 2.94655 + 2.94655i 0.125985 + 0.125985i 0.767288 0.641303i \(-0.221606\pi\)
−0.641303 + 0.767288i \(0.721606\pi\)
\(548\) −4.13246 4.13246i −0.176530 0.176530i
\(549\) 2.59192 0.437287i 0.110620 0.0186630i
\(550\) −0.379950 + 0.162422i −0.0162011 + 0.00692570i
\(551\) 12.8595i 0.547832i
\(552\) −1.72601 + 0.144577i −0.0734637 + 0.00615361i
\(553\) 38.9118 38.9118i 1.65470 1.65470i
\(554\) 11.8267 0.502467
\(555\) 26.1654 + 2.81426i 1.11066 + 0.119459i
\(556\) 0.433456 0.0183826
\(557\) 1.34754 1.34754i 0.0570969 0.0570969i −0.677982 0.735079i \(-0.737145\pi\)
0.735079 + 0.677982i \(0.237145\pi\)
\(558\) −7.23393 + 10.1702i −0.306237 + 0.430540i
\(559\) 9.93248i 0.420099i
\(560\) −1.38789 + 7.18891i −0.0586491 + 0.303787i
\(561\) 0.692995 0.819705i 0.0292583 0.0346080i
\(562\) 7.38138 + 7.38138i 0.311365 + 0.311365i
\(563\) 6.51282 + 6.51282i 0.274483 + 0.274483i 0.830902 0.556419i \(-0.187825\pi\)
−0.556419 + 0.830902i \(0.687825\pi\)
\(564\) 12.0700 14.2769i 0.508237 0.601165i
\(565\) −0.928997 + 4.81196i −0.0390832 + 0.202441i
\(566\) 12.9855i 0.545821i
\(567\) −26.5210 12.8478i −1.11378 0.539558i
\(568\) −1.20453 + 1.20453i −0.0505408 + 0.0505408i
\(569\) −11.6625 −0.488917 −0.244458 0.969660i \(-0.578610\pi\)
−0.244458 + 0.969660i \(0.578610\pi\)
\(570\) 24.9396 + 2.68242i 1.04461 + 0.112354i
\(571\) −30.0173 −1.25619 −0.628093 0.778138i \(-0.716164\pi\)
−0.628093 + 0.778138i \(0.716164\pi\)
\(572\) 0.241451 0.241451i 0.0100956 0.0100956i
\(573\) 40.1842 3.36599i 1.67872 0.140616i
\(574\) 2.89111i 0.120673i
\(575\) 4.59754 1.96536i 0.191731 0.0819613i
\(576\) −0.499082 2.95819i −0.0207951 0.123258i
\(577\) 30.9222 + 30.9222i 1.28731 + 1.28731i 0.936415 + 0.350894i \(0.114122\pi\)
0.350894 + 0.936415i \(0.385878\pi\)
\(578\) 27.7415 + 27.7415i 1.15390 + 1.15390i
\(579\) 24.9780 + 21.1169i 1.03805 + 0.877590i
\(580\) 3.67762 2.48740i 0.152705 0.103284i
\(581\) 40.9633i 1.69944i
\(582\) −1.49440 17.8406i −0.0619448 0.739517i
\(583\) −0.600165 + 0.600165i −0.0248563 + 0.0248563i
\(584\) −0.375785 −0.0155501
\(585\) 27.7094 + 0.653396i 1.14564 + 0.0270146i
\(586\) −18.2763 −0.754988
\(587\) −22.4198 + 22.4198i −0.925363 + 0.925363i −0.997402 0.0720385i \(-0.977050\pi\)
0.0720385 + 0.997402i \(0.477050\pi\)
\(588\) −0.538020 6.42305i −0.0221876 0.264882i
\(589\) 26.9434i 1.11018i
\(590\) 22.1259 + 4.27162i 0.910907 + 0.175860i
\(591\) −7.34664 6.21100i −0.302201 0.255486i
\(592\) −4.80467 4.80467i −0.197471 0.197471i
\(593\) −1.81620 1.81620i −0.0745825 0.0745825i 0.668831 0.743414i \(-0.266795\pi\)
−0.743414 + 0.668831i \(0.766795\pi\)
\(594\) −0.218823 + 0.369485i −0.00897840 + 0.0151602i
\(595\) 30.7598 + 45.4783i 1.26103 + 1.86443i
\(596\) 20.0239i 0.820212i
\(597\) −25.2697 + 2.11669i −1.03422 + 0.0866304i
\(598\) −2.92164 + 2.92164i −0.119475 + 0.119475i
\(599\) 8.91093 0.364091 0.182045 0.983290i \(-0.441728\pi\)
0.182045 + 0.983290i \(0.441728\pi\)
\(600\) 4.05693 + 7.65123i 0.165623 + 0.312360i
\(601\) −45.6488 −1.86205 −0.931027 0.364951i \(-0.881086\pi\)
−0.931027 + 0.364951i \(0.881086\pi\)
\(602\) −5.56577 + 5.56577i −0.226844 + 0.226844i
\(603\) −2.65602 1.88919i −0.108162 0.0769338i
\(604\) 17.1989i 0.699814i
\(605\) 13.7717 + 20.3615i 0.559900 + 0.827811i
\(606\) 3.35081 3.96348i 0.136117 0.161005i
\(607\) −14.6214 14.6214i −0.593463 0.593463i 0.345102 0.938565i \(-0.387844\pi\)
−0.938565 + 0.345102i \(0.887844\pi\)
\(608\) −4.57959 4.57959i −0.185727 0.185727i
\(609\) −7.27010 + 8.59939i −0.294599 + 0.348465i
\(610\) 1.92368 + 0.371386i 0.0778877 + 0.0150370i
\(611\) 44.5978i 1.80423i
\(612\) −18.3321 13.0394i −0.741032 0.527086i
\(613\) 25.3682 25.3682i 1.02461 1.02461i 0.0249223 0.999689i \(-0.492066\pi\)
0.999689 0.0249223i \(-0.00793383\pi\)
\(614\) 13.1101 0.529080
\(615\) −2.14562 2.66280i −0.0865199 0.107375i
\(616\) −0.270599 −0.0109027
\(617\) 15.8956 15.8956i 0.639931 0.639931i −0.310607 0.950538i \(-0.600532\pi\)
0.950538 + 0.310607i \(0.100532\pi\)
\(618\) 19.3443 1.62035i 0.778141 0.0651802i
\(619\) 40.8815i 1.64317i 0.570088 + 0.821584i \(0.306909\pi\)
−0.570088 + 0.821584i \(0.693091\pi\)
\(620\) −7.70543 + 5.21166i −0.309458 + 0.209305i
\(621\) 2.64783 4.47090i 0.106254 0.179411i
\(622\) 24.1167 + 24.1167i 0.966993 + 0.966993i
\(623\) −13.0848 13.0848i −0.524231 0.524231i
\(624\) −5.46517 4.62037i −0.218782 0.184963i
\(625\) −18.0717 17.2747i −0.722867 0.690988i
\(626\) 29.7123i 1.18754i
\(627\) 0.0773826 + 0.923817i 0.00309036 + 0.0368937i
\(628\) 16.4821 16.4821i 0.657708 0.657708i
\(629\) −50.9533 −2.03164
\(630\) −15.1611 15.8934i −0.604034 0.633208i
\(631\) −0.512624 −0.0204072 −0.0102036 0.999948i \(-0.503248\pi\)
−0.0102036 + 0.999948i \(0.503248\pi\)
\(632\) −11.8838 + 11.8838i −0.472714 + 0.472714i
\(633\) −0.201340 2.40366i −0.00800255 0.0955369i
\(634\) 2.67145i 0.106097i
\(635\) 1.59395 8.25625i 0.0632540 0.327639i
\(636\) 13.5846 + 11.4847i 0.538663 + 0.455397i
\(637\) −10.8724 10.8724i −0.430780 0.430780i
\(638\) 0.116029 + 0.116029i 0.00459365 + 0.00459365i
\(639\) −0.850164 5.03916i −0.0336320 0.199346i
\(640\) 0.423868 2.19553i 0.0167549 0.0867858i
\(641\) 41.0820i 1.62264i −0.584600 0.811322i \(-0.698749\pi\)
0.584600 0.811322i \(-0.301251\pi\)
\(642\) −13.5365 + 1.13387i −0.534244 + 0.0447504i
\(643\) −11.1338 + 11.1338i −0.439076 + 0.439076i −0.891701 0.452625i \(-0.850488\pi\)
0.452625 + 0.891701i \(0.350488\pi\)
\(644\) 3.27434 0.129027
\(645\) −0.995637 + 9.25686i −0.0392032 + 0.364489i
\(646\) −48.5664 −1.91082
\(647\) −19.7653 + 19.7653i −0.777052 + 0.777052i −0.979329 0.202276i \(-0.935166\pi\)
0.202276 + 0.979329i \(0.435166\pi\)
\(648\) 8.09962 + 3.92379i 0.318183 + 0.154141i
\(649\) 0.832843i 0.0326920i
\(650\) 19.1744 + 7.69027i 0.752083 + 0.301637i
\(651\) 15.2325 18.0176i 0.597007 0.706166i
\(652\) −7.21629 7.21629i −0.282612 0.282612i
\(653\) 1.85033 + 1.85033i 0.0724089 + 0.0724089i 0.742384 0.669975i \(-0.233695\pi\)
−0.669975 + 0.742384i \(0.733695\pi\)
\(654\) 16.0085 18.9356i 0.625984 0.740441i
\(655\) 22.2352 15.0391i 0.868802 0.587624i
\(656\) 0.882958i 0.0344737i
\(657\) 0.653436 0.918668i 0.0254930 0.0358406i
\(658\) −24.9908 + 24.9908i −0.974244 + 0.974244i
\(659\) −28.7705 −1.12074 −0.560370 0.828243i \(-0.689341\pi\)
−0.560370 + 0.828243i \(0.689341\pi\)
\(660\) −0.249230 + 0.200824i −0.00970127 + 0.00781706i
\(661\) −10.2697 −0.399445 −0.199722 0.979853i \(-0.564004\pi\)
−0.199722 + 0.979853i \(0.564004\pi\)
\(662\) 13.0193 13.0193i 0.506008 0.506008i
\(663\) −53.4783 + 4.47956i −2.07693 + 0.173972i
\(664\) 12.5104i 0.485497i
\(665\) −46.5591 8.98871i −1.80549 0.348567i
\(666\) 20.1004 3.39118i 0.778876 0.131405i
\(667\) −1.40400 1.40400i −0.0543630 0.0543630i
\(668\) −11.3314 11.3314i −0.438423 0.438423i
\(669\) −31.7892 26.8752i −1.22904 1.03906i
\(670\) −1.36106 2.01233i −0.0525823 0.0777429i
\(671\) 0.0724097i 0.00279535i
\(672\) 0.473395 + 5.65154i 0.0182616 + 0.218013i
\(673\) 6.49107 6.49107i 0.250212 0.250212i −0.570845 0.821058i \(-0.693384\pi\)
0.821058 + 0.570845i \(0.193384\pi\)
\(674\) 6.79651 0.261792
\(675\) −25.7591 3.38656i −0.991468 0.130349i
\(676\) −4.07197 −0.156614
\(677\) 11.6214 11.6214i 0.446646 0.446646i −0.447592 0.894238i \(-0.647718\pi\)
0.894238 + 0.447592i \(0.147718\pi\)
\(678\) 0.316871 + 3.78291i 0.0121694 + 0.145282i
\(679\) 33.8448i 1.29884i
\(680\) −9.39417 13.8893i −0.360250 0.532629i
\(681\) 12.6743 + 10.7151i 0.485680 + 0.410604i
\(682\) −0.243107 0.243107i −0.00930906 0.00930906i
\(683\) −13.1189 13.1189i −0.501983 0.501983i 0.410071 0.912054i \(-0.365504\pi\)
−0.912054 + 0.410071i \(0.865504\pi\)
\(684\) 19.1588 3.23232i 0.732556 0.123591i
\(685\) 12.8311 + 2.47716i 0.490250 + 0.0946476i
\(686\) 10.7355i 0.409883i
\(687\) 20.0561 1.67998i 0.765190 0.0640953i
\(688\) 1.69981 1.69981i 0.0648047 0.0648047i
\(689\) 42.4351 1.61665
\(690\) 3.01578 2.43004i 0.114809 0.0925101i
\(691\) 26.0545 0.991159 0.495580 0.868563i \(-0.334956\pi\)
0.495580 + 0.868563i \(0.334956\pi\)
\(692\) −6.03766 + 6.03766i −0.229517 + 0.229517i
\(693\) 0.470533 0.661524i 0.0178741 0.0251292i
\(694\) 24.2144i 0.919167i
\(695\) −0.802843 + 0.543012i −0.0304536 + 0.0205976i
\(696\) 2.22032 2.62629i 0.0841611 0.0995494i
\(697\) 4.68186 + 4.68186i 0.177338 + 0.177338i
\(698\) −1.42288 1.42288i −0.0538569 0.0538569i
\(699\) −20.5061 + 24.2555i −0.775611 + 0.917427i
\(700\) −6.43528 15.0539i −0.243231 0.568985i
\(701\) 39.5869i 1.49518i 0.664162 + 0.747588i \(0.268788\pi\)
−0.664162 + 0.747588i \(0.731212\pi\)
\(702\) 20.7984 5.32636i 0.784985 0.201030i
\(703\) 31.1176 31.1176i 1.17362 1.17362i
\(704\) 0.0826422 0.00311469
\(705\) −4.47050 + 41.5642i −0.168369 + 1.56540i
\(706\) 32.5409 1.22469
\(707\) −6.93784 + 6.93784i −0.260924 + 0.260924i
\(708\) 17.3942 1.45700i 0.653713 0.0547576i
\(709\) 0.0916175i 0.00344077i 0.999999 + 0.00172038i \(0.000547616\pi\)
−0.999999 + 0.00172038i \(0.999452\pi\)
\(710\) 0.722041 3.73998i 0.0270977 0.140359i
\(711\) −8.38771 49.7162i −0.314564 1.86450i
\(712\) 3.99616 + 3.99616i 0.149762 + 0.149762i
\(713\) 2.94168 + 2.94168i 0.110167 + 0.110167i
\(714\) 32.4773 + 27.4570i 1.21543 + 1.02755i
\(715\) −0.144735 + 0.749691i −0.00541279 + 0.0280369i
\(716\) 10.2241i 0.382094i
\(717\) 0.875272 + 10.4493i 0.0326876 + 0.390235i
\(718\) −13.8264 + 13.8264i −0.515996 + 0.515996i
\(719\) 9.47790 0.353466 0.176733 0.984259i \(-0.443447\pi\)
0.176733 + 0.984259i \(0.443447\pi\)
\(720\) 4.63028 + 4.85392i 0.172560 + 0.180895i
\(721\) −36.6974 −1.36668
\(722\) 16.2248 16.2248i 0.603825 0.603825i
\(723\) 2.56318 + 30.6001i 0.0953258 + 1.13803i
\(724\) 7.86650i 0.292356i
\(725\) −3.69556 + 9.21430i −0.137250 + 0.342210i
\(726\) 14.5407 + 12.2930i 0.539656 + 0.456236i
\(727\) −16.4918 16.4918i −0.611648 0.611648i 0.331727 0.943375i \(-0.392369\pi\)
−0.943375 + 0.331727i \(0.892369\pi\)
\(728\) 9.56646 + 9.56646i 0.354557 + 0.354557i
\(729\) −23.6764 + 12.9780i −0.876904 + 0.480665i
\(730\) 0.696026 0.470765i 0.0257611 0.0174238i
\(731\) 18.0264i 0.666731i
\(732\) 1.51230 0.126676i 0.0558961 0.00468208i
\(733\) 14.5823 14.5823i 0.538610 0.538610i −0.384510 0.923121i \(-0.625630\pi\)
0.923121 + 0.384510i \(0.125630\pi\)
\(734\) −8.49714 −0.313635
\(735\) 9.04300 + 11.2227i 0.333556 + 0.413956i
\(736\) −1.00000 −0.0368605
\(737\) 0.0634891 0.0634891i 0.00233865 0.00233865i
\(738\) −2.15854 1.53534i −0.0794568 0.0565165i
\(739\) 8.04723i 0.296022i 0.988986 + 0.148011i \(0.0472871\pi\)
−0.988986 + 0.148011i \(0.952713\pi\)
\(740\) 14.9182 + 2.88011i 0.548405 + 0.105875i
\(741\) 29.9239 35.3953i 1.09928 1.30028i
\(742\) −23.7790 23.7790i −0.872954 0.872954i
\(743\) −3.40804 3.40804i −0.125029 0.125029i 0.641823 0.766852i \(-0.278178\pi\)
−0.766852 + 0.641823i \(0.778178\pi\)
\(744\) −4.65206 + 5.50266i −0.170553 + 0.201737i
\(745\) 25.0850 + 37.0882i 0.919044 + 1.35881i
\(746\) 26.1199i 0.956318i
\(747\) 30.5837 + 21.7537i 1.11900 + 0.795928i
\(748\) 0.438208 0.438208i 0.0160225 0.0160225i
\(749\) 25.6797 0.938315
\(750\) −17.0993 9.08922i −0.624378 0.331891i
\(751\) 40.5910 1.48119 0.740594 0.671953i \(-0.234544\pi\)
0.740594 + 0.671953i \(0.234544\pi\)
\(752\) 7.63231 7.63231i 0.278322 0.278322i
\(753\) 38.5404 3.22830i 1.40449 0.117646i
\(754\) 8.20395i 0.298770i
\(755\) −21.5460 31.8557i −0.784138 1.15935i
\(756\) −14.6393 8.66992i −0.532426 0.315322i
\(757\) 34.6920 + 34.6920i 1.26090 + 1.26090i 0.950657 + 0.310243i \(0.100411\pi\)
0.310243 + 0.950657i \(0.399589\pi\)
\(758\) 1.56540 + 1.56540i 0.0568579 + 0.0568579i
\(759\) 0.109311 + 0.0924137i 0.00396774 + 0.00335441i
\(760\) 14.2194 + 2.74519i 0.515791 + 0.0995786i
\(761\) 50.5466i 1.83231i −0.400823 0.916156i \(-0.631276\pi\)
0.400823 0.916156i \(-0.368724\pi\)
\(762\) −0.543680 6.49063i −0.0196955 0.235131i
\(763\) −33.1457 + 33.1457i −1.19995 + 1.19995i
\(764\) 23.2816 0.842300
\(765\) 50.2897 + 1.18585i 1.81823 + 0.0428743i
\(766\) −33.9433 −1.22642
\(767\) 29.4434 29.4434i 1.06314 1.06314i
\(768\) −0.144577 1.72601i −0.00521698 0.0622819i
\(769\) 52.5084i 1.89350i −0.321969 0.946750i \(-0.604345\pi\)
0.321969 0.946750i \(-0.395655\pi\)
\(770\) 0.501201 0.338993i 0.0180620 0.0122165i
\(771\) −7.03275 5.94563i −0.253278 0.214127i
\(772\) 13.3531 + 13.3531i 0.480588 + 0.480588i
\(773\) −20.1139 20.1139i −0.723445 0.723445i 0.245860 0.969305i \(-0.420930\pi\)
−0.969305 + 0.245860i \(0.920930\pi\)
\(774\) 1.19974 + 7.11119i 0.0431238 + 0.255607i
\(775\) 7.74302 19.3060i 0.278138 0.693491i
\(776\) 10.3363i 0.371053i
\(777\) −38.4013 + 3.21664i −1.37764 + 0.115396i
\(778\) −6.28786 +