Properties

Label 690.2.i.f.47.15
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 47.15
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.f.323.15

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(1.72601 + 0.144577i) q^{3} -1.00000i q^{4} +(-1.25275 - 1.85219i) q^{5} +(1.32270 - 1.11824i) q^{6} +(-2.31531 - 2.31531i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.95819 + 0.499082i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(1.72601 + 0.144577i) 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} +(0.144577 - 1.72601i) q^{12} +(-2.92164 + 2.92164i) q^{13} -3.27434 q^{14} +(-1.89447 - 3.37801i) q^{15} -1.00000 q^{16} +(5.30247 - 5.30247i) q^{17} +(2.44466 - 1.73886i) 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} +(5.03371 + 1.28911i) q^{27} +(-2.31531 + 2.31531i) q^{28} -1.98555 q^{29} +(-3.72821 - 1.04902i) q^{30} -4.16017 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.0119482 + 0.142641i) 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} +(-5.65154 - 0.473395i) q^{42} +(-1.69981 + 1.69981i) q^{43} +0.0826422 q^{44} +(-2.78149 - 6.10437i) q^{45} +1.00000 q^{46} +(7.63231 - 7.63231i) q^{47} +(-1.72601 - 0.144577i) 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} +(0.936357 - 11.1785i) q^{57} +(-1.40400 + 1.40400i) q^{58} +10.0777 q^{59} +(-3.37801 + 1.89447i) q^{60} -0.876183 q^{61} +(-2.94168 + 2.94168i) q^{62} +(-5.69361 - 8.00467i) 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} +(-1.73886 - 2.44466i) q^{72} +(-0.265720 + 0.265720i) q^{73} +6.79483 q^{74} +(-3.88342 + 7.74074i) q^{75} -6.47652 q^{76} +(0.191342 - 0.191342i) q^{77} +(-0.597367 + 7.13155i) 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} +(-3.42708 - 0.287065i) q^{87} +(0.0584368 - 0.0584368i) q^{88} -5.65142 q^{89} +(-6.28325 - 2.34963i) q^{90} +13.5290 q^{91} +(0.707107 - 0.707107i) q^{92} +(-7.18048 - 0.601465i) 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
\(3\) 1.72601 + 0.144577i 0.996510 + 0.0834716i
\(4\) 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 \(0.00396585\pi\)
−0.999922 + 0.0124588i \(0.996034\pi\)
\(12\) 0.144577 1.72601i 0.0417358 0.498255i
\(13\) −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
\(15\) −1.89447 3.37801i −0.489151 0.872199i
\(16\) −1.00000 −0.250000
\(17\) 5.30247 5.30247i 1.28604 1.28604i 0.348866 0.937172i \(-0.386567\pi\)
0.937172 0.348866i \(-0.113433\pi\)
\(18\) 2.44466 1.73886i 0.576213 0.409852i
\(19\) 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
\(27\) 5.03371 + 1.28911i 0.968737 + 0.248088i
\(28\) −2.31531 + 2.31531i −0.437553 + 0.437553i
\(29\) −1.98555 −0.368708 −0.184354 0.982860i \(-0.559019\pi\)
−0.184354 + 0.982860i \(0.559019\pi\)
\(30\) −3.72821 1.04902i −0.680675 0.191524i
\(31\) −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
\(33\) −0.0119482 + 0.142641i −0.00207991 + 0.0248306i
\(34\) 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 \(0.0219641\pi\)
−0.997620 + 0.0689474i \(0.978036\pi\)
\(42\) −5.65154 0.473395i −0.872052 0.0730465i
\(43\) −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
\(45\) −2.78149 6.10437i −0.414640 0.909986i
\(46\) 1.00000 0.147442
\(47\) 7.63231 7.63231i 1.11329 1.11329i 0.120584 0.992703i \(-0.461523\pi\)
0.992703 0.120584i \(-0.0384769\pi\)
\(48\) −1.72601 0.144577i −0.249128 0.0208679i
\(49\) 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 0.999997 0.00245571i \(-0.000781677\pi\)
−0.00245571 + 0.999997i \(0.500782\pi\)
\(54\) 4.47090 2.64783i 0.608413 0.360324i
\(55\) 0.153069 0.103530i 0.0206398 0.0139600i
\(56\) 3.27434i 0.437553i
\(57\) 0.936357 11.1785i 0.124023 1.48063i
\(58\) −1.40400 + 1.40400i −0.184354 + 0.184354i
\(59\) 10.0777 1.31201 0.656003 0.754759i \(-0.272246\pi\)
0.656003 + 0.754759i \(0.272246\pi\)
\(60\) −3.37801 + 1.89447i −0.436100 + 0.244575i
\(61\) −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
\(63\) −5.69361 8.00467i −0.717328 1.00849i
\(64\) 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 \(-0.967770\pi\)
0.994878 0.101082i \(-0.0322303\pi\)
\(72\) −1.73886 2.44466i −0.204926 0.288106i
\(73\) −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
\(75\) −3.88342 + 7.74074i −0.448419 + 0.893823i
\(76\) −6.47652 −0.742908
\(77\) 0.191342 0.191342i 0.0218055 0.0218055i
\(78\) −0.597367 + 7.13155i −0.0676385 + 0.807490i
\(79\) 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 0.999591 0.0285970i \(-0.00910394\pi\)
−0.0285970 + 0.999591i \(0.509104\pi\)
\(84\) −4.33098 + 3.66150i −0.472549 + 0.399503i
\(85\) −16.4639 3.17852i −1.78576 0.344758i
\(86\) 2.40390i 0.259219i
\(87\) −3.42708 0.287065i −0.367421 0.0307766i
\(88\) 0.0584368 0.0584368i 0.00622939 0.00622939i
\(89\) −5.65142 −0.599049 −0.299525 0.954089i \(-0.596828\pi\)
−0.299525 + 0.954089i \(0.596828\pi\)
\(90\) −6.28325 2.34963i −0.662313 0.247673i
\(91\) 13.5290 1.41823
\(92\) 0.707107 0.707107i 0.0737210 0.0737210i
\(93\) −7.18048 0.601465i −0.744581 0.0623690i
\(94\) 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 \(0.0476317\pi\)
−0.988825 + 0.149082i \(0.952368\pi\)
\(102\) 1.08416 12.9430i 0.107348 1.28155i
\(103\) 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
\(105\) −3.43486 + 12.2074i −0.335208 + 1.19132i
\(106\) 10.2703 0.997541
\(107\) 5.54562 5.54562i 0.536115 0.536115i −0.386270 0.922386i \(-0.626237\pi\)
0.922386 + 0.386270i \(0.126237\pi\)
\(108\) 1.28911 5.03371i 0.124044 0.484369i
\(109\) 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 0.630444 0.776235i \(-0.282873\pi\)
−0.776235 + 0.630444i \(0.782873\pi\)
\(114\) −7.24230 8.56651i −0.678304 0.802327i
\(115\) 0.423868 2.19553i 0.0395259 0.204734i
\(116\) 1.98555i 0.184354i
\(117\) −10.1009 + 7.18465i −0.933831 + 0.664221i
\(118\) 7.12601 7.12601i 0.656003 0.656003i
\(119\) −24.5538 −2.25084
\(120\) −1.04902 + 3.72821i −0.0957622 + 0.340337i
\(121\) 10.9932 0.999379
\(122\) −0.619555 + 0.619555i −0.0560919 + 0.0560919i
\(123\) −0.127655 + 1.52399i −0.0115103 + 0.137414i
\(124\) 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 \(0.175723\pi\)
−0.851452 + 0.524433i \(0.824277\pi\)
\(132\) 0.142641 + 0.0119482i 0.0124153 + 0.00103995i
\(133\) −14.9952 + 14.9952i −1.30025 + 1.30025i
\(134\) 1.08646 0.0938556
\(135\) −3.91831 10.9383i −0.337235 0.941421i
\(136\) −7.49883 −0.643019
\(137\) −4.13246 + 4.13246i −0.353060 + 0.353060i −0.861247 0.508187i \(-0.830316\pi\)
0.508187 + 0.861247i \(0.330316\pi\)
\(138\) 1.72601 + 0.144577i 0.146927 + 0.0123072i
\(139\) 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
\(147\) −0.538020 + 6.42305i −0.0443751 + 0.529764i
\(148\) 4.80467 4.80467i 0.394942 0.394942i
\(149\) −20.0239 −1.64042 −0.820212 0.572059i \(-0.806145\pi\)
−0.820212 + 0.572059i \(0.806145\pi\)
\(150\) 2.72753 + 8.21952i 0.222702 + 0.671121i
\(151\) −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
\(153\) 18.3321 13.0394i 1.48206 1.05417i
\(154\) 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
\(162\) 8.09962 3.92379i 0.636367 0.308282i
\(163\) 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
\(165\) 0.279166 0.156563i 0.0217331 0.0121884i
\(166\) 12.5104 0.970994
\(167\) −11.3314 + 11.3314i −0.876846 + 0.876846i −0.993207 0.116361i \(-0.962877\pi\)
0.116361 + 0.993207i \(0.462877\pi\)
\(168\) −0.473395 + 5.65154i −0.0365232 + 0.436026i
\(169\) 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 0.898339 0.439304i \(-0.144775\pi\)
−0.439304 + 0.898339i \(0.644775\pi\)
\(174\) −2.62629 + 2.22032i −0.199099 + 0.168322i
\(175\) 15.0539 6.43528i 1.13797 0.486461i
\(176\) 0.0826422i 0.00622939i
\(177\) 17.3942 + 1.45700i 1.30743 + 0.109515i
\(178\) −3.99616 + 3.99616i −0.299525 + 0.299525i
\(179\) −10.2241 −0.764188 −0.382094 0.924123i \(-0.624797\pi\)
−0.382094 + 0.924123i \(0.624797\pi\)
\(180\) −6.10437 + 2.78149i −0.454993 + 0.207320i
\(181\) −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
\(183\) −1.51230 0.126676i −0.111792 0.00936416i
\(184\) 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 \(-0.681201\pi\)
0.539009 0.842300i \(-0.318799\pi\)
\(192\) −0.144577 + 1.72601i −0.0104340 + 0.124564i
\(193\) −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
\(195\) 15.4043 + 4.33437i 1.10313 + 0.310391i
\(196\) 3.72133 0.265810
\(197\) −3.92746 + 3.92746i −0.279820 + 0.279820i −0.833037 0.553217i \(-0.813400\pi\)
0.553217 + 0.833037i \(0.313400\pi\)
\(198\) 0.143703 + 0.202032i 0.0102125 + 0.0143578i
\(199\) 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
\(207\) 1.73886 + 2.44466i 0.120859 + 0.169916i
\(208\) 2.92164 2.92164i 0.202579 0.202579i
\(209\) 0.535234 0.0370229
\(210\) 6.20316 + 11.0608i 0.428058 + 0.763266i
\(211\) 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
\(213\) 0.246281 2.94018i 0.0168749 0.201458i
\(214\) 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
\(222\) 11.7279 + 0.982377i 0.787127 + 0.0659328i
\(223\) 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
\(225\) −7.82195 + 12.7991i −0.521463 + 0.853274i
\(226\) −2.19171 −0.145791
\(227\) 6.77558 6.77558i 0.449711 0.449711i −0.445547 0.895258i \(-0.646991\pi\)
0.895258 + 0.445547i \(0.146991\pi\)
\(228\) −11.1785 0.936357i −0.740316 0.0620117i
\(229\) 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 0.990069 0.140585i \(-0.0448983\pi\)
−0.140585 + 0.990069i \(0.544898\pi\)
\(234\) −2.06212 + 12.2227i −0.134805 + 0.799026i
\(235\) −23.6979 4.57512i −1.54588 0.298448i
\(236\) 10.0777i 0.656003i
\(237\) −2.42980 + 29.0077i −0.157833 + 1.88426i
\(238\) −17.3621 + 17.3621i −1.12542 + 1.12542i
\(239\) 6.05401 0.391602 0.195801 0.980644i \(-0.437269\pi\)
0.195801 + 0.980644i \(0.437269\pi\)
\(240\) 1.89447 + 3.37801i 0.122288 + 0.218050i
\(241\) −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
\(243\) 14.2473 + 6.32566i 0.913966 + 0.405791i
\(244\) 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 \(-0.751079\pi\)
0.709501 0.704705i \(-0.248921\pi\)
\(252\) −8.00467 + 5.69361i −0.504247 + 0.358664i
\(253\) −0.0584368 + 0.0584368i −0.00367389 + 0.00367389i
\(254\) −3.76049 −0.235954
\(255\) −27.9572 7.86644i −1.75075 0.492615i
\(256\) 1.00000 0.0625000
\(257\) −3.75966 + 3.75966i −0.234521 + 0.234521i −0.814577 0.580056i \(-0.803031\pi\)
0.580056 + 0.814577i \(0.303031\pi\)
\(258\) −0.347548 + 4.14914i −0.0216374 + 0.258314i
\(259\) 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 0.940404 0.340058i \(-0.110447\pi\)
−0.340058 + 0.940404i \(0.610447\pi\)
\(264\) 0.109311 0.0924137i 0.00672763 0.00568767i
\(265\) 4.35326 22.5487i 0.267419 1.38516i
\(266\) 21.2064i 1.30025i
\(267\) −9.75439 0.817066i −0.596959 0.0500036i
\(268\) 0.768241 0.768241i 0.0469278 0.0469278i
\(269\) 1.99991 0.121937 0.0609684 0.998140i \(-0.480581\pi\)
0.0609684 + 0.998140i \(0.480581\pi\)
\(270\) −10.5052 4.96389i −0.639328 0.302093i
\(271\) −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
\(273\) 23.3512 + 1.95599i 1.41328 + 0.118382i
\(274\) 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 \(0.100786\pi\)
−0.950291 + 0.311365i \(0.899214\pi\)
\(282\) 1.56052 18.6300i 0.0929279 1.10940i
\(283\) 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
\(285\) −21.8778 + 12.2696i −1.29593 + 0.726788i
\(286\) −0.341463 −0.0201911
\(287\) 2.04432 2.04432i 0.120673 0.120673i
\(288\) −2.44466 + 1.73886i −0.144053 + 0.102463i
\(289\) 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 0.220418 0.975406i \(-0.429258\pi\)
−0.975406 + 0.220418i \(0.929258\pi\)
\(294\) 4.16134 + 4.92222i 0.242694 + 0.287070i
\(295\) −12.6249 18.6658i −0.735048 1.08677i
\(296\) 6.79483i 0.394942i
\(297\) −0.106534 + 0.415997i −0.00618176 + 0.0241386i
\(298\) −14.1591 + 14.1591i −0.820212 + 0.820212i
\(299\) −4.13182 −0.238950
\(300\) 7.74074 + 3.88342i 0.446912 + 0.224210i
\(301\) 7.87119 0.453688
\(302\) −12.1615 + 12.1615i −0.699814 + 0.699814i
\(303\) −0.433226 + 5.17198i −0.0248882 + 0.297123i
\(304\) 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 \(0.417989\pi\)
−0.254804 + 0.966993i \(0.582011\pi\)
\(312\) 7.13155 + 0.597367i 0.403745 + 0.0338193i
\(313\) −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
\(315\) −7.69351 + 20.5735i −0.433480 + 1.15919i
\(316\) 16.8063 0.945427
\(317\) −1.88900 + 1.88900i −0.106097 + 0.106097i −0.758163 0.652066i \(-0.773903\pi\)
0.652066 + 0.758163i \(0.273903\pi\)
\(318\) 17.7266 + 1.48485i 0.994060 + 0.0832664i
\(319\) 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
\(327\) 2.06974 24.7092i 0.114457 1.36642i
\(328\) 0.624346 0.624346i 0.0344737 0.0344737i
\(329\) −35.3424 −1.94849
\(330\) 0.0866935 0.308107i 0.00477232 0.0169608i
\(331\) −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
\(333\) 11.8152 + 16.6111i 0.647471 + 0.910282i
\(334\) 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
\(342\) −11.2617 15.8329i −0.608965 0.856146i
\(343\) −7.59113 + 7.59113i −0.409883 + 0.409883i
\(344\) 2.40390 0.129609
\(345\) 1.04902 3.72821i 0.0564774 0.200720i
\(346\) 8.53854 0.459035
\(347\) 17.1222 17.1222i 0.919167 0.919167i −0.0778017 0.996969i \(-0.524790\pi\)
0.996969 + 0.0778017i \(0.0247901\pi\)
\(348\) −0.287065 + 3.42708i −0.0153883 + 0.183711i
\(349\) 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 \(0.0833102\pi\)
0.258749 + 0.965945i \(0.416690\pi\)
\(354\) 13.3298 11.2693i 0.708471 0.598956i
\(355\) −3.15513 + 2.13401i −0.167457 + 0.113261i
\(356\) 5.65142i 0.299525i
\(357\) −42.3799 3.54991i −2.24298 0.187881i
\(358\) −7.22956 + 7.22956i −0.382094 + 0.382094i
\(359\) −19.5535 −1.03199 −0.515996 0.856591i \(-0.672578\pi\)
−0.515996 + 0.856591i \(0.672578\pi\)
\(360\) −2.34963 + 6.28325i −0.123836 + 0.331156i
\(361\) −22.9454 −1.20765
\(362\) −5.56245 + 5.56245i −0.292356 + 0.292356i
\(363\) 18.9743 + 1.58936i 0.995891 + 0.0834198i
\(364\) 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
\(372\) −0.601465 + 7.18048i −0.0311845 + 0.372290i
\(373\) −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
\(375\) 19.2023 2.50437i 0.991602 0.129325i
\(376\) −10.7937 −0.556644
\(377\) 5.80107 5.80107i 0.298770 0.298770i
\(378\) −16.4821 4.22098i −0.847747 0.217104i
\(379\) 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 \(-0.915911\pi\)
−0.261112 0.965308i \(-0.584089\pi\)
\(384\) 1.11824 + 1.32270i 0.0570649 + 0.0674989i
\(385\) −0.594107 0.114698i −0.0302785 0.00584557i
\(386\) 18.8841i 0.961176i
\(387\) −5.87672 + 4.18003i −0.298730 + 0.212483i
\(388\) −7.30890 + 7.30890i −0.371053 + 0.371053i
\(389\) −8.89237 −0.450861 −0.225431 0.974259i \(-0.572379\pi\)
−0.225431 + 0.974259i \(0.572379\pi\)
\(390\) 13.9574 7.82763i 0.706758 0.396367i
\(391\) 7.49883 0.379232
\(392\) 2.63138 2.63138i 0.132905 0.132905i
\(393\) −1.73562 + 20.7204i −0.0875505 + 1.04521i
\(394\) 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 \(-0.693243\pi\)
0.570480 0.821312i \(-0.306757\pi\)
\(402\) 1.87523 + 0.157077i 0.0935280 + 0.00783428i
\(403\) 12.1545 12.1545i 0.605460 0.605460i
\(404\) 2.99650 0.149082
\(405\) −5.18160 19.4461i −0.257476 0.966285i
\(406\) 6.50138 0.322658
\(407\) −0.397069 + 0.397069i −0.0196820 + 0.0196820i
\(408\) −12.9430 1.08416i −0.640775 0.0536739i
\(409\) 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
\(417\) −0.0626678 + 0.748148i −0.00306885 + 0.0366369i
\(418\) 0.378468 0.378468i 0.0185115 0.0185115i
\(419\) −4.84269 −0.236581 −0.118290 0.992979i \(-0.537741\pi\)
−0.118290 + 0.992979i \(0.537741\pi\)
\(420\) 12.2074 + 3.43486i 0.595662 + 0.167604i
\(421\) 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
\(423\) 26.3870 18.7687i 1.28298 0.912567i
\(424\) 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 \(-0.809288\pi\)
0.825822 0.563932i \(-0.190712\pi\)
\(432\) −5.03371 1.28911i −0.242184 0.0620221i
\(433\) −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
\(435\) 3.76157 + 6.70722i 0.180354 + 0.321587i
\(436\) −14.3159 −0.685605
\(437\) 4.57959 4.57959i 0.219072 0.219072i
\(438\) −0.0543299 + 0.648607i −0.00259598 + 0.0309917i
\(439\) 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 0.820578 0.571535i \(-0.193652\pi\)
−0.571535 + 0.820578i \(0.693652\pi\)
\(444\) 8.98754 7.59825i 0.426530 0.360597i
\(445\) 7.07983 + 10.4675i 0.335616 + 0.496208i
\(446\) 24.0335i 1.13802i
\(447\) −34.5614 2.89500i −1.63470 0.136929i
\(448\) 2.31531 2.31531i 0.109388 0.109388i
\(449\) 4.17586 0.197071 0.0985356 0.995134i \(-0.468584\pi\)
0.0985356 + 0.995134i \(0.468584\pi\)
\(450\) 3.51938 + 14.5813i 0.165905 + 0.687368i
\(451\) −0.0729696 −0.00343600
\(452\) −1.54977 + 1.54977i −0.0728953 + 0.0728953i
\(453\) −29.6854 2.48657i −1.39474 0.116829i
\(454\) 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 \(-0.914846\pi\)
0.964430 0.264340i \(-0.0851541\pi\)
\(462\) 0.0391224 0.467056i 0.00182014 0.0217294i
\(463\) 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
\(465\) 7.88133 + 14.0531i 0.365488 + 0.651697i
\(466\) 18.3378 0.849484
\(467\) −5.99931 + 5.99931i −0.277615 + 0.277615i −0.832156 0.554541i \(-0.812894\pi\)
0.554541 + 0.832156i \(0.312894\pi\)
\(468\) 7.18465 + 10.1009i 0.332110 + 0.466915i
\(469\) 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
\(477\) 17.8586 + 25.1075i 0.817689 + 1.14959i
\(478\) 4.28083 4.28083i 0.195801 0.195801i
\(479\) 31.7615 1.45122 0.725611 0.688105i \(-0.241557\pi\)
0.725611 + 0.688105i \(0.241557\pi\)
\(480\) 3.72821 + 1.04902i 0.170169 + 0.0478811i
\(481\) −28.0751 −1.28011
\(482\) −12.5362 + 12.5362i −0.571007 + 0.571007i
\(483\) 0.473395 5.65154i 0.0215402 0.257154i
\(484\) 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 \(-0.885702\pi\)
0.936222 0.351410i \(-0.114298\pi\)
\(492\) 1.52399 + 0.127655i 0.0687068 + 0.00575515i
\(493\) −10.5283 + 10.5283i −0.474173 + 0.474173i
\(494\) 26.7599 1.20398
\(495\) 0.504478 0.229868i 0.0226746 0.0103318i
\(496\) 4.16017 0.186797
\(497\) −3.94403 + 3.94403i −0.176914 + 0.176914i
\(498\) 21.5930 + 1.80871i 0.967605 + 0.0810504i
\(499\) 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 0.782927 0.622113i \(-0.213726\pi\)
−0.622113 + 0.782927i \(0.713726\pi\)
\(504\) −1.63417 + 9.68615i −0.0727915 + 0.431455i
\(505\) 5.55010 3.75387i 0.246976 0.167045i
\(506\) 0.0826422i 0.00367389i
\(507\) 0.588714 7.02825i 0.0261457 0.312136i
\(508\) −2.65907 + 2.65907i −0.117977 + 0.117977i
\(509\) 28.7783 1.27558 0.637789 0.770211i \(-0.279849\pi\)
0.637789 + 0.770211i \(0.279849\pi\)
\(510\) −25.3312 + 14.2063i −1.12168 + 0.629067i
\(511\) 1.23045 0.0544319
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 8.34892 32.6009i 0.368614 1.43937i
\(514\) 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 \(-0.923784\pi\)
0.971471 0.237159i \(-0.0762164\pi\)
\(522\) −4.85401 + 3.45259i −0.212454 + 0.151116i
\(523\) 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
\(525\) 26.9136 8.93088i 1.17460 0.389776i
\(526\) 13.7687 0.600346
\(527\) −22.0592 + 22.0592i −0.960913 + 0.960913i
\(528\) 0.0119482 0.142641i 0.000519977 0.00620765i
\(529\) 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
\(537\) −17.6469 1.47818i −0.761521 0.0637880i
\(538\) 1.41415 1.41415i 0.0609684 0.0609684i
\(539\) −0.307539 −0.0132467
\(540\) −10.9383 + 3.91831i −0.470710 + 0.168617i
\(541\) −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
\(543\) −13.5776 1.13732i −0.582672 0.0488069i
\(544\) 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
\(552\) 0.144577 1.72601i 0.00615361 0.0734637i
\(553\) 38.9118 38.9118i 1.65470 1.65470i
\(554\) −11.8267 −0.502467
\(555\) 7.12793 25.3326i 0.302564 1.07531i
\(556\) 0.433456 0.0183826
\(557\) −1.34754 + 1.34754i −0.0570969 + 0.0570969i −0.735079 0.677982i \(-0.762855\pi\)
0.677982 + 0.735079i \(0.262855\pi\)
\(558\) −10.1702 + 7.23393i −0.430540 + 0.306237i
\(559\) 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 0.556419 0.830902i \(-0.312175\pi\)
−0.830902 + 0.556419i \(0.812175\pi\)
\(564\) −12.0700 14.2769i −0.508237 0.601165i
\(565\) −0.928997 + 4.81196i −0.0390832 + 0.202441i
\(566\) 12.9855i 0.545821i
\(567\) −12.8478 26.5210i −0.539558 1.11378i
\(568\) −1.20453 + 1.20453i −0.0505408 + 0.0505408i
\(569\) 11.6625 0.488917 0.244458 0.969660i \(-0.421390\pi\)
0.244458 + 0.969660i \(0.421390\pi\)
\(570\) −6.79401 + 24.1458i −0.284570 + 1.01136i
\(571\) −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
\(573\) 3.36599 40.1842i 0.140616 1.67872i
\(574\) 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
\(582\) −17.8406 1.49440i −0.739517 0.0619448i
\(583\) −0.600165 + 0.600165i −0.0248563 + 0.0248563i
\(584\) 0.375785 0.0155501
\(585\) 25.9613 + 9.70827i 1.07337 + 0.401387i
\(586\) −18.2763 −0.754988
\(587\) 22.4198 22.4198i 0.925363 0.925363i −0.0720385 0.997402i \(-0.522950\pi\)
0.997402 + 0.0720385i \(0.0229504\pi\)
\(588\) 6.42305 + 0.538020i 0.264882 + 0.0221876i
\(589\) 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 0.743414 0.668831i \(-0.233205\pi\)
−0.668831 + 0.743414i \(0.733205\pi\)
\(594\) 0.218823 + 0.369485i 0.00897840 + 0.0151602i
\(595\) 30.7598 + 45.4783i 1.26103 + 1.86443i
\(596\) 20.0239i 0.820212i
\(597\) 2.11669 25.2697i 0.0866304 1.03422i
\(598\) −2.92164 + 2.92164i −0.119475 + 0.119475i
\(599\) −8.91093 −0.364091 −0.182045 0.983290i \(-0.558272\pi\)
−0.182045 + 0.983290i \(0.558272\pi\)
\(600\) 8.21952 2.72753i 0.335561 0.111351i
\(601\) −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
\(603\) 1.88919 + 2.65602i 0.0769338 + 0.108162i
\(604\) 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
\(612\) −13.0394 18.3321i −0.527086 0.741032i
\(613\) 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
\(615\) 2.98264 1.67274i 0.120272 0.0674514i
\(616\) −0.270599 −0.0109027
\(617\) −15.8956 + 15.8956i −0.639931 + 0.639931i −0.950538 0.310607i \(-0.899468\pi\)
0.310607 + 0.950538i \(0.399468\pi\)
\(618\) 1.62035 19.3443i 0.0651802 0.778141i
\(619\) 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
\(627\) 0.923817 + 0.0773826i 0.0368937 + 0.00309036i
\(628\) 16.4821 16.4821i 0.657708 0.657708i
\(629\) 50.9533 2.03164
\(630\) 9.10755 + 19.9878i 0.362854 + 0.796333i
\(631\) −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
\(633\) 2.40366 + 0.201340i 0.0955369 + 0.00800255i
\(634\) 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 \(0.301251\pi\)
−0.584600 + 0.811322i \(0.698749\pi\)
\(642\) 1.13387 13.5365i 0.0447504 0.534244i
\(643\) −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
\(645\) 8.96223 + 2.52174i 0.352887 + 0.0992934i
\(646\) −48.5664 −1.91082
\(647\) 19.7653 19.7653i 0.777052 0.777052i −0.202276 0.979329i \(-0.564834\pi\)
0.979329 + 0.202276i \(0.0648338\pi\)
\(648\) −3.92379 8.09962i −0.154141 0.318183i
\(649\) 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 0.669975 0.742384i \(-0.266305\pi\)
−0.742384 + 0.669975i \(0.766305\pi\)
\(654\) −16.0085 18.9356i −0.625984 0.740441i
\(655\) 22.2352 15.0391i 0.868802 0.587624i
\(656\) 0.882958i 0.0344737i
\(657\) −0.918668 + 0.653436i −0.0358406 + 0.0254930i
\(658\) −24.9908 + 24.9908i −0.974244 + 0.974244i
\(659\) 28.7705 1.12074 0.560370 0.828243i \(-0.310659\pi\)
0.560370 + 0.828243i \(0.310659\pi\)
\(660\) −0.156563 0.279166i −0.00609422 0.0108665i
\(661\) −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
\(663\) −4.47956 + 53.4783i −0.173972 + 2.07693i
\(664\) 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
\(672\) 5.65154 + 0.473395i 0.218013 + 0.0182616i
\(673\) 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
\(675\) −15.3512 + 20.9605i −0.590868 + 0.806769i
\(676\) −4.07197 −0.156614
\(677\) −11.6214 + 11.6214i −0.446646 + 0.446646i −0.894238 0.447592i \(-0.852282\pi\)
0.447592 + 0.894238i \(0.352282\pi\)
\(678\) −3.78291 0.316871i −0.145282 0.0121694i
\(679\) 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 0.912054 0.410071i \(-0.134496\pi\)
−0.410071 + 0.912054i \(0.634496\pi\)
\(684\) −19.1588 3.23232i −0.732556 0.123591i
\(685\) 12.8311 + 2.47716i 0.490250 + 0.0946476i
\(686\) 10.7355i 0.409883i
\(687\) −1.67998 + 20.0561i −0.0640953 + 0.765190i
\(688\) 1.69981 1.69981i 0.0648047 0.0648047i
\(689\) −42.4351 −1.61665
\(690\) −1.89447 3.37801i −0.0721213 0.128599i
\(691\) 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
\(693\) 0.661524 0.470533i 0.0251292 0.0178741i
\(694\) 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 \(-0.731212\pi\)
0.664162 0.747588i \(-0.268788\pi\)
\(702\) −5.32636 + 20.7984i −0.201030 + 0.784985i
\(703\) 31.1176 31.1176i 1.17362 1.17362i
\(704\) −0.0826422 −0.00311469
\(705\) −40.2413 11.3229i −1.51557 0.426443i
\(706\) 32.5409 1.22469
\(707\) 6.93784 6.93784i 0.260924 0.260924i
\(708\) 1.45700 17.3942i 0.0547576 0.653713i
\(709\) 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
\(717\) 10.4493 + 0.875272i 0.390235 + 0.0326876i
\(718\) −13.8264 + 13.8264i −0.515996 + 0.515996i
\(719\) −9.47790 −0.353466 −0.176733 0.984259i \(-0.556553\pi\)
−0.176733 + 0.984259i \(0.556553\pi\)
\(720\) 2.78149 + 6.10437i 0.103660 + 0.227496i
\(721\) −36.6974 −1.36668
\(722\) −16.2248 + 16.2248i −0.603825 + 0.603825i
\(723\) −30.6001 2.56318i −1.13803 0.0953258i
\(724\) 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
\(732\) −0.126676 + 1.51230i −0.00468208 + 0.0558961i
\(733\) 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
\(735\) 12.5707 7.04997i 0.463678 0.260042i
\(736\) −1.00000 −0.0368605
\(737\) −0.0634891 + 0.0634891i −0.00233865 + 0.00233865i
\(738\) 1.53534 + 2.15854i 0.0565165 + 0.0794568i
\(739\) 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 0.766852 0.641823i \(-0.221822\pi\)
−0.641823 + 0.766852i \(0.721822\pi\)
\(744\) 4.65206 + 5.50266i 0.170553 + 0.201737i
\(745\) 25.0850 + 37.0882i 0.919044 + 1.35881i
\(746\) 26.1199i 0.956318i
\(747\) 21.7537 + 30.5837i 0.795928 + 1.11900i
\(748\) 0.438208 0.438208i 0.0160225 0.0160225i
\(749\) −25.6797 −0.938315
\(750\) 11.8072 15.3489i 0.431138 0.560464i
\(751\) 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
\(753\) 3.22830 38.5404i 0.117646 1.40449i
\(754\) 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 \(0.368724\pi\)
−0.400823 + 0.916156i \(0.631276\pi\)
\(762\) −6.49063 0.543680i −0.235131 0.0196955i
\(763\) −33.1457 + 33.1457i −1.19995 + 1.19995i
\(764\) −23.2816 −0.842300
\(765\) −47.1170 17.6195i −1.70352 0.637034i
\(766\) −33.9433 −1.22642
\(767\) −29.4434 + 29.4434i −1.06314 + 1.06314i
\(768\) 1.72601 + 0.144577i 0.0622819 + 0.00521698i
\(769\) 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 0.969305 0.245860i \(-0.0790704\pi\)
−0.245860 + 0.969305i \(0.579070\pi\)
\(774\) −1.19974 + 7.11119i −0.0431238 + 0.255607i
\(775\) 7.74302 19.3060i 0.278138 0.693491i
\(776\) 10.3363i 0.371053i
\(777\) 3.21664 38.4013i 0.115396 1.37764i