Properties

Label 690.2.i.f.323.8
Level $690$
Weight $2$
Character 690.323
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 323.8
Character \(\chi\) \(=\) 690.323
Dual form 690.2.i.f.47.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(1.40373 - 1.01467i) q^{3} +1.00000i q^{4} +(2.22721 + 0.198845i) q^{5} +(-1.71006 - 0.275105i) q^{6} +(0.787190 - 0.787190i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.940895 - 2.84863i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(1.40373 - 1.01467i) q^{3} +1.00000i q^{4} +(2.22721 + 0.198845i) q^{5} +(-1.71006 - 0.275105i) q^{6} +(0.787190 - 0.787190i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.940895 - 2.84863i) q^{9} +(-1.43427 - 1.71548i) q^{10} +0.307245i q^{11} +(1.01467 + 1.40373i) q^{12} +(-4.92204 - 4.92204i) q^{13} -1.11326 q^{14} +(3.32815 - 1.98075i) q^{15} -1.00000 q^{16} +(0.790416 + 0.790416i) q^{17} +(-2.67960 + 1.34897i) q^{18} +0.691928i q^{19} +(-0.198845 + 2.22721i) q^{20} +(0.306263 - 1.90374i) q^{21} +(0.217255 - 0.217255i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(0.275105 - 1.71006i) q^{24} +(4.92092 + 0.885741i) q^{25} +6.96081i q^{26} +(-1.56966 - 4.95340i) q^{27} +(0.787190 + 0.787190i) q^{28} +6.67517 q^{29} +(-3.75397 - 0.952756i) q^{30} +4.52557 q^{31} +(0.707107 + 0.707107i) q^{32} +(0.311752 + 0.431287i) q^{33} -1.11782i q^{34} +(1.90977 - 1.59671i) q^{35} +(2.84863 + 0.940895i) q^{36} +(1.77676 - 1.77676i) q^{37} +(0.489267 - 0.489267i) q^{38} +(-11.9034 - 1.91496i) q^{39} +(1.71548 - 1.43427i) q^{40} +0.596103i q^{41} +(-1.56271 + 1.12959i) q^{42} +(-6.70489 - 6.70489i) q^{43} -0.307245 q^{44} +(2.66201 - 6.15741i) q^{45} +1.00000 q^{46} +(6.88967 + 6.88967i) q^{47} +(-1.40373 + 1.01467i) q^{48} +5.76066i q^{49} +(-2.85330 - 4.10593i) q^{50} +(1.91154 + 0.307518i) q^{51} +(4.92204 - 4.92204i) q^{52} +(-5.94467 + 5.94467i) q^{53} +(-2.39267 + 4.61250i) q^{54} +(-0.0610942 + 0.684298i) q^{55} -1.11326i q^{56} +(0.702077 + 0.971277i) q^{57} +(-4.72006 - 4.72006i) q^{58} +6.38319 q^{59} +(1.98075 + 3.32815i) q^{60} -9.95861 q^{61} +(-3.20006 - 3.20006i) q^{62} +(-1.50175 - 2.98308i) q^{63} -1.00000i q^{64} +(-9.98368 - 11.9411i) q^{65} +(0.0845247 - 0.525408i) q^{66} +(2.19342 - 2.19342i) q^{67} +(-0.790416 + 0.790416i) q^{68} +(-0.275105 + 1.71006i) q^{69} +(-2.47945 - 0.221366i) q^{70} +4.55564i q^{71} +(-1.34897 - 2.67960i) q^{72} +(-4.90914 - 4.90914i) q^{73} -2.51272 q^{74} +(7.80636 - 3.74977i) q^{75} -0.691928 q^{76} +(0.241860 + 0.241860i) q^{77} +(7.06292 + 9.77108i) q^{78} +15.7352i q^{79} +(-2.22721 - 0.198845i) q^{80} +(-7.22943 - 5.36053i) q^{81} +(0.421508 - 0.421508i) q^{82} +(6.65861 - 6.65861i) q^{83} +(1.90374 + 0.306263i) q^{84} +(1.60325 + 1.91759i) q^{85} +9.48214i q^{86} +(9.37012 - 6.77309i) q^{87} +(0.217255 + 0.217255i) q^{88} -11.5425 q^{89} +(-6.23627 + 2.47162i) q^{90} -7.74916 q^{91} +(-0.707107 - 0.707107i) q^{92} +(6.35266 - 4.59195i) q^{93} -9.74347i q^{94} +(-0.137587 + 1.54107i) q^{95} +(1.71006 + 0.275105i) q^{96} +(-12.8277 + 12.8277i) q^{97} +(4.07340 - 4.07340i) q^{98} +(0.875228 + 0.289085i) 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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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
\(3\) 1.40373 1.01467i 0.810442 0.585819i
\(4\) 1.00000i 0.500000i
\(5\) 2.22721 + 0.198845i 0.996038 + 0.0889264i
\(6\) −1.71006 0.275105i −0.698130 0.112311i
\(7\) 0.787190 0.787190i 0.297530 0.297530i −0.542516 0.840046i \(-0.682528\pi\)
0.840046 + 0.542516i \(0.182528\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0.940895 2.84863i 0.313632 0.949545i
\(10\) −1.43427 1.71548i −0.453556 0.542482i
\(11\) 0.307245i 0.0926378i 0.998927 + 0.0463189i \(0.0147490\pi\)
−0.998927 + 0.0463189i \(0.985251\pi\)
\(12\) 1.01467 + 1.40373i 0.292910 + 0.405221i
\(13\) −4.92204 4.92204i −1.36513 1.36513i −0.867243 0.497885i \(-0.834110\pi\)
−0.497885 0.867243i \(-0.665890\pi\)
\(14\) −1.11326 −0.297530
\(15\) 3.32815 1.98075i 0.859326 0.511429i
\(16\) −1.00000 −0.250000
\(17\) 0.790416 + 0.790416i 0.191704 + 0.191704i 0.796432 0.604728i \(-0.206718\pi\)
−0.604728 + 0.796432i \(0.706718\pi\)
\(18\) −2.67960 + 1.34897i −0.631588 + 0.317956i
\(19\) 0.691928i 0.158739i 0.996845 + 0.0793696i \(0.0252907\pi\)
−0.996845 + 0.0793696i \(0.974709\pi\)
\(20\) −0.198845 + 2.22721i −0.0444632 + 0.498019i
\(21\) 0.306263 1.90374i 0.0668320 0.415430i
\(22\) 0.217255 0.217255i 0.0463189 0.0463189i
\(23\) −0.707107 + 0.707107i −0.147442 + 0.147442i
\(24\) 0.275105 1.71006i 0.0561557 0.349065i
\(25\) 4.92092 + 0.885741i 0.984184 + 0.177148i
\(26\) 6.96081i 1.36513i
\(27\) −1.56966 4.95340i −0.302081 0.953282i
\(28\) 0.787190 + 0.787190i 0.148765 + 0.148765i
\(29\) 6.67517 1.23955 0.619774 0.784780i \(-0.287224\pi\)
0.619774 + 0.784780i \(0.287224\pi\)
\(30\) −3.75397 0.952756i −0.685377 0.173949i
\(31\) 4.52557 0.812817 0.406408 0.913692i \(-0.366781\pi\)
0.406408 + 0.913692i \(0.366781\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 0.311752 + 0.431287i 0.0542690 + 0.0750775i
\(34\) 1.11782i 0.191704i
\(35\) 1.90977 1.59671i 0.322810 0.269893i
\(36\) 2.84863 + 0.940895i 0.474772 + 0.156816i
\(37\) 1.77676 1.77676i 0.292098 0.292098i −0.545811 0.837909i \(-0.683778\pi\)
0.837909 + 0.545811i \(0.183778\pi\)
\(38\) 0.489267 0.489267i 0.0793696 0.0793696i
\(39\) −11.9034 1.91496i −1.90607 0.306639i
\(40\) 1.71548 1.43427i 0.271241 0.226778i
\(41\) 0.596103i 0.0930956i 0.998916 + 0.0465478i \(0.0148220\pi\)
−0.998916 + 0.0465478i \(0.985178\pi\)
\(42\) −1.56271 + 1.12959i −0.241131 + 0.174299i
\(43\) −6.70489 6.70489i −1.02249 1.02249i −0.999741 0.0227444i \(-0.992760\pi\)
−0.0227444 0.999741i \(-0.507240\pi\)
\(44\) −0.307245 −0.0463189
\(45\) 2.66201 6.15741i 0.396829 0.917893i
\(46\) 1.00000 0.147442
\(47\) 6.88967 + 6.88967i 1.00496 + 1.00496i 0.999988 + 0.00497448i \(0.00158343\pi\)
0.00497448 + 0.999988i \(0.498417\pi\)
\(48\) −1.40373 + 1.01467i −0.202610 + 0.146455i
\(49\) 5.76066i 0.822952i
\(50\) −2.85330 4.10593i −0.403518 0.580666i
\(51\) 1.91154 + 0.307518i 0.267669 + 0.0430611i
\(52\) 4.92204 4.92204i 0.682564 0.682564i
\(53\) −5.94467 + 5.94467i −0.816563 + 0.816563i −0.985608 0.169045i \(-0.945932\pi\)
0.169045 + 0.985608i \(0.445932\pi\)
\(54\) −2.39267 + 4.61250i −0.325601 + 0.627682i
\(55\) −0.0610942 + 0.684298i −0.00823794 + 0.0922707i
\(56\) 1.11326i 0.148765i
\(57\) 0.702077 + 0.971277i 0.0929924 + 0.128649i
\(58\) −4.72006 4.72006i −0.619774 0.619774i
\(59\) 6.38319 0.831021 0.415510 0.909588i \(-0.363603\pi\)
0.415510 + 0.909588i \(0.363603\pi\)
\(60\) 1.98075 + 3.32815i 0.255714 + 0.429663i
\(61\) −9.95861 −1.27507 −0.637535 0.770422i \(-0.720046\pi\)
−0.637535 + 0.770422i \(0.720046\pi\)
\(62\) −3.20006 3.20006i −0.406408 0.406408i
\(63\) −1.50175 2.98308i −0.189203 0.375833i
\(64\) 1.00000i 0.125000i
\(65\) −9.98368 11.9411i −1.23832 1.48112i
\(66\) 0.0845247 0.525408i 0.0104043 0.0646732i
\(67\) 2.19342 2.19342i 0.267969 0.267969i −0.560312 0.828281i \(-0.689319\pi\)
0.828281 + 0.560312i \(0.189319\pi\)
\(68\) −0.790416 + 0.790416i −0.0958521 + 0.0958521i
\(69\) −0.275105 + 1.71006i −0.0331188 + 0.205867i
\(70\) −2.47945 0.221366i −0.296351 0.0264583i
\(71\) 4.55564i 0.540655i 0.962768 + 0.270327i \(0.0871320\pi\)
−0.962768 + 0.270327i \(0.912868\pi\)
\(72\) −1.34897 2.67960i −0.158978 0.315794i
\(73\) −4.90914 4.90914i −0.574571 0.574571i 0.358831 0.933403i \(-0.383175\pi\)
−0.933403 + 0.358831i \(0.883175\pi\)
\(74\) −2.51272 −0.292098
\(75\) 7.80636 3.74977i 0.901401 0.432986i
\(76\) −0.691928 −0.0793696
\(77\) 0.241860 + 0.241860i 0.0275625 + 0.0275625i
\(78\) 7.06292 + 9.77108i 0.799718 + 1.10636i
\(79\) 15.7352i 1.77035i 0.465255 + 0.885177i \(0.345963\pi\)
−0.465255 + 0.885177i \(0.654037\pi\)
\(80\) −2.22721 0.198845i −0.249010 0.0222316i
\(81\) −7.22943 5.36053i −0.803270 0.595615i
\(82\) 0.421508 0.421508i 0.0465478 0.0465478i
\(83\) 6.65861 6.65861i 0.730878 0.730878i −0.239916 0.970794i \(-0.577120\pi\)
0.970794 + 0.239916i \(0.0771198\pi\)
\(84\) 1.90374 + 0.306263i 0.207715 + 0.0334160i
\(85\) 1.60325 + 1.91759i 0.173897 + 0.207992i
\(86\) 9.48214i 1.02249i
\(87\) 9.37012 6.77309i 1.00458 0.726151i
\(88\) 0.217255 + 0.217255i 0.0231594 + 0.0231594i
\(89\) −11.5425 −1.22351 −0.611753 0.791049i \(-0.709535\pi\)
−0.611753 + 0.791049i \(0.709535\pi\)
\(90\) −6.23627 + 2.47162i −0.657361 + 0.260532i
\(91\) −7.74916 −0.812333
\(92\) −0.707107 0.707107i −0.0737210 0.0737210i
\(93\) 6.35266 4.59195i 0.658740 0.476163i
\(94\) 9.74347i 1.00496i
\(95\) −0.137587 + 1.54107i −0.0141161 + 0.158110i
\(96\) 1.71006 + 0.275105i 0.174533 + 0.0280778i
\(97\) −12.8277 + 12.8277i −1.30246 + 1.30246i −0.375726 + 0.926731i \(0.622606\pi\)
−0.926731 + 0.375726i \(0.877394\pi\)
\(98\) 4.07340 4.07340i 0.411476 0.411476i
\(99\) 0.875228 + 0.289085i 0.0879637 + 0.0290541i
\(100\) −0.885741 + 4.92092i −0.0885741 + 0.492092i
\(101\) 0.435698i 0.0433536i −0.999765 0.0216768i \(-0.993100\pi\)
0.999765 0.0216768i \(-0.00690048\pi\)
\(102\) −1.13421 1.56911i −0.112304 0.155365i
\(103\) −2.47087 2.47087i −0.243463 0.243463i 0.574818 0.818281i \(-0.305073\pi\)
−0.818281 + 0.574818i \(0.805073\pi\)
\(104\) −6.96081 −0.682564
\(105\) 1.06066 4.17912i 0.103510 0.407841i
\(106\) 8.40703 0.816563
\(107\) 9.00580 + 9.00580i 0.870623 + 0.870623i 0.992540 0.121917i \(-0.0389042\pi\)
−0.121917 + 0.992540i \(0.538904\pi\)
\(108\) 4.95340 1.56966i 0.476641 0.151041i
\(109\) 4.71540i 0.451654i −0.974167 0.225827i \(-0.927492\pi\)
0.974167 0.225827i \(-0.0725084\pi\)
\(110\) 0.527072 0.440672i 0.0502543 0.0420164i
\(111\) 0.691264 4.29692i 0.0656118 0.407845i
\(112\) −0.787190 + 0.787190i −0.0743825 + 0.0743825i
\(113\) 9.74177 9.74177i 0.916428 0.916428i −0.0803391 0.996768i \(-0.525600\pi\)
0.996768 + 0.0803391i \(0.0256003\pi\)
\(114\) 0.190353 1.18324i 0.0178282 0.110821i
\(115\) −1.71548 + 1.43427i −0.159969 + 0.133746i
\(116\) 6.67517i 0.619774i
\(117\) −18.6522 + 9.38996i −1.72440 + 0.868102i
\(118\) −4.51360 4.51360i −0.415510 0.415510i
\(119\) 1.24442 0.114075
\(120\) 0.952756 3.75397i 0.0869743 0.342689i
\(121\) 10.9056 0.991418
\(122\) 7.04180 + 7.04180i 0.637535 + 0.637535i
\(123\) 0.604847 + 0.836765i 0.0545372 + 0.0754486i
\(124\) 4.52557i 0.406408i
\(125\) 10.7838 + 2.95123i 0.964532 + 0.263966i
\(126\) −1.04746 + 3.17126i −0.0933149 + 0.282518i
\(127\) 13.7618 13.7618i 1.22116 1.22116i 0.253945 0.967219i \(-0.418272\pi\)
0.967219 0.253945i \(-0.0817282\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −16.2151 2.60859i −1.42766 0.229673i
\(130\) −1.38413 + 15.5032i −0.121396 + 1.35972i
\(131\) 9.08484i 0.793746i 0.917874 + 0.396873i \(0.129905\pi\)
−0.917874 + 0.396873i \(0.870095\pi\)
\(132\) −0.431287 + 0.311752i −0.0375388 + 0.0271345i
\(133\) 0.544679 + 0.544679i 0.0472297 + 0.0472297i
\(134\) −3.10197 −0.267969
\(135\) −2.51100 11.3444i −0.216112 0.976368i
\(136\) 1.11782 0.0958521
\(137\) 6.12207 + 6.12207i 0.523044 + 0.523044i 0.918489 0.395445i \(-0.129410\pi\)
−0.395445 + 0.918489i \(0.629410\pi\)
\(138\) 1.40373 1.01467i 0.119493 0.0863743i
\(139\) 1.70991i 0.145033i 0.997367 + 0.0725164i \(0.0231030\pi\)
−0.997367 + 0.0725164i \(0.976897\pi\)
\(140\) 1.59671 + 1.90977i 0.134946 + 0.161405i
\(141\) 16.6620 + 2.68048i 1.40319 + 0.225737i
\(142\) 3.22132 3.22132i 0.270327 0.270327i
\(143\) 1.51227 1.51227i 0.126462 0.126462i
\(144\) −0.940895 + 2.84863i −0.0784080 + 0.237386i
\(145\) 14.8670 + 1.32733i 1.23464 + 0.110229i
\(146\) 6.94257i 0.574571i
\(147\) 5.84516 + 8.08639i 0.482101 + 0.666955i
\(148\) 1.77676 + 1.77676i 0.146049 + 0.146049i
\(149\) −4.44032 −0.363765 −0.181883 0.983320i \(-0.558219\pi\)
−0.181883 + 0.983320i \(0.558219\pi\)
\(150\) −8.17141 2.86845i −0.667193 0.234208i
\(151\) −18.8511 −1.53408 −0.767040 0.641599i \(-0.778271\pi\)
−0.767040 + 0.641599i \(0.778271\pi\)
\(152\) 0.489267 + 0.489267i 0.0396848 + 0.0396848i
\(153\) 2.99531 1.50791i 0.242156 0.121907i
\(154\) 0.342042i 0.0275625i
\(155\) 10.0794 + 0.899889i 0.809596 + 0.0722808i
\(156\) 1.91496 11.9034i 0.153319 0.953037i
\(157\) −9.78600 + 9.78600i −0.781007 + 0.781007i −0.980001 0.198993i \(-0.936233\pi\)
0.198993 + 0.980001i \(0.436233\pi\)
\(158\) 11.1265 11.1265i 0.885177 0.885177i
\(159\) −2.31282 + 14.3766i −0.183419 + 1.14014i
\(160\) 1.43427 + 1.71548i 0.113389 + 0.135621i
\(161\) 1.11326i 0.0877368i
\(162\) 1.32151 + 8.90245i 0.103828 + 0.699443i
\(163\) 9.24359 + 9.24359i 0.724014 + 0.724014i 0.969420 0.245406i \(-0.0789214\pi\)
−0.245406 + 0.969420i \(0.578921\pi\)
\(164\) −0.596103 −0.0465478
\(165\) 0.608576 + 1.02256i 0.0473776 + 0.0796060i
\(166\) −9.41670 −0.730878
\(167\) 7.44173 + 7.44173i 0.575858 + 0.575858i 0.933759 0.357901i \(-0.116508\pi\)
−0.357901 + 0.933759i \(0.616508\pi\)
\(168\) −1.12959 1.56271i −0.0871494 0.120565i
\(169\) 35.4529i 2.72715i
\(170\) 0.222273 2.48961i 0.0170476 0.190945i
\(171\) 1.97105 + 0.651032i 0.150730 + 0.0497856i
\(172\) 6.70489 6.70489i 0.511243 0.511243i
\(173\) −9.04703 + 9.04703i −0.687833 + 0.687833i −0.961753 0.273920i \(-0.911680\pi\)
0.273920 + 0.961753i \(0.411680\pi\)
\(174\) −11.4150 1.83638i −0.865367 0.139215i
\(175\) 4.57095 3.17646i 0.345531 0.240117i
\(176\) 0.307245i 0.0231594i
\(177\) 8.96025 6.47682i 0.673494 0.486828i
\(178\) 8.16181 + 8.16181i 0.611753 + 0.611753i
\(179\) −11.2260 −0.839068 −0.419534 0.907740i \(-0.637807\pi\)
−0.419534 + 0.907740i \(0.637807\pi\)
\(180\) 6.15741 + 2.66201i 0.458946 + 0.198414i
\(181\) −8.65815 −0.643555 −0.321778 0.946815i \(-0.604280\pi\)
−0.321778 + 0.946815i \(0.604280\pi\)
\(182\) 5.47949 + 5.47949i 0.406167 + 0.406167i
\(183\) −13.9792 + 10.1047i −1.03337 + 0.746960i
\(184\) 1.00000i 0.0737210i
\(185\) 4.31053 3.60392i 0.316916 0.264966i
\(186\) −7.73901 1.24501i −0.567452 0.0912885i
\(187\) −0.242851 + 0.242851i −0.0177590 + 0.0177590i
\(188\) −6.88967 + 6.88967i −0.502481 + 0.502481i
\(189\) −5.13489 2.66365i −0.373508 0.193752i
\(190\) 1.18699 0.992411i 0.0861132 0.0719971i
\(191\) 18.1677i 1.31457i 0.753643 + 0.657284i \(0.228295\pi\)
−0.753643 + 0.657284i \(0.771705\pi\)
\(192\) −1.01467 1.40373i −0.0732274 0.101305i
\(193\) 6.41622 + 6.41622i 0.461850 + 0.461850i 0.899261 0.437412i \(-0.144105\pi\)
−0.437412 + 0.899261i \(0.644105\pi\)
\(194\) 18.1411 1.30246
\(195\) −26.1307 6.63195i −1.87125 0.474924i
\(196\) −5.76066 −0.411476
\(197\) −14.6739 14.6739i −1.04547 1.04547i −0.998916 0.0465587i \(-0.985175\pi\)
−0.0465587 0.998916i \(-0.514825\pi\)
\(198\) −0.414465 0.823293i −0.0294548 0.0585089i
\(199\) 2.60795i 0.184873i 0.995719 + 0.0924363i \(0.0294655\pi\)
−0.995719 + 0.0924363i \(0.970535\pi\)
\(200\) 4.10593 2.85330i 0.290333 0.201759i
\(201\) 0.853368 5.30456i 0.0601919 0.374155i
\(202\) −0.308085 + 0.308085i −0.0216768 + 0.0216768i
\(203\) 5.25463 5.25463i 0.368803 0.368803i
\(204\) −0.307518 + 1.91154i −0.0215305 + 0.133834i
\(205\) −0.118532 + 1.32765i −0.00827865 + 0.0927268i
\(206\) 3.49434i 0.243463i
\(207\) 1.34897 + 2.67960i 0.0937602 + 0.186245i
\(208\) 4.92204 + 4.92204i 0.341282 + 0.341282i
\(209\) −0.212591 −0.0147052
\(210\) −3.70509 + 2.20509i −0.255675 + 0.152165i
\(211\) 24.9846 1.72001 0.860004 0.510287i \(-0.170461\pi\)
0.860004 + 0.510287i \(0.170461\pi\)
\(212\) −5.94467 5.94467i −0.408282 0.408282i
\(213\) 4.62246 + 6.39487i 0.316726 + 0.438169i
\(214\) 12.7361i 0.870623i
\(215\) −13.5999 16.2664i −0.927509 1.10936i
\(216\) −4.61250 2.39267i −0.313841 0.162800i
\(217\) 3.56249 3.56249i 0.241837 0.241837i
\(218\) −3.33429 + 3.33429i −0.225827 + 0.225827i
\(219\) −11.8722 1.90994i −0.802252 0.129062i
\(220\) −0.684298 0.0610942i −0.0461354 0.00411897i
\(221\) 7.78092i 0.523401i
\(222\) −3.52718 + 2.54958i −0.236729 + 0.171117i
\(223\) 2.06860 + 2.06860i 0.138524 + 0.138524i 0.772968 0.634444i \(-0.218771\pi\)
−0.634444 + 0.772968i \(0.718771\pi\)
\(224\) 1.11326 0.0743825
\(225\) 7.15322 13.1845i 0.476882 0.878968i
\(226\) −13.7769 −0.916428
\(227\) 14.8927 + 14.8927i 0.988463 + 0.988463i 0.999934 0.0114717i \(-0.00365163\pi\)
−0.0114717 + 0.999934i \(0.503652\pi\)
\(228\) −0.971277 + 0.702077i −0.0643244 + 0.0464962i
\(229\) 4.61161i 0.304743i −0.988323 0.152372i \(-0.951309\pi\)
0.988323 0.152372i \(-0.0486911\pi\)
\(230\) 2.22721 + 0.198845i 0.146858 + 0.0131115i
\(231\) 0.584913 + 0.0940976i 0.0384845 + 0.00619116i
\(232\) 4.72006 4.72006i 0.309887 0.309887i
\(233\) 3.47172 3.47172i 0.227440 0.227440i −0.584182 0.811622i \(-0.698585\pi\)
0.811622 + 0.584182i \(0.198585\pi\)
\(234\) 19.8288 + 6.54940i 1.29625 + 0.428148i
\(235\) 13.9748 + 16.7147i 0.911613 + 1.09035i
\(236\) 6.38319i 0.415510i
\(237\) 15.9661 + 22.0880i 1.03711 + 1.43477i
\(238\) −0.879935 0.879935i −0.0570377 0.0570377i
\(239\) −20.2807 −1.31185 −0.655924 0.754827i \(-0.727721\pi\)
−0.655924 + 0.754827i \(0.727721\pi\)
\(240\) −3.32815 + 1.98075i −0.214831 + 0.127857i
\(241\) 6.16685 0.397242 0.198621 0.980076i \(-0.436354\pi\)
0.198621 + 0.980076i \(0.436354\pi\)
\(242\) −7.71142 7.71142i −0.495709 0.495709i
\(243\) −15.5873 0.189246i −0.999926 0.0121401i
\(244\) 9.95861i 0.637535i
\(245\) −1.14548 + 12.8302i −0.0731821 + 0.819691i
\(246\) 0.163991 1.01937i 0.0104557 0.0649929i
\(247\) 3.40570 3.40570i 0.216699 0.216699i
\(248\) 3.20006 3.20006i 0.203204 0.203204i
\(249\) 2.59059 16.1032i 0.164172 1.02050i
\(250\) −5.53846 9.71213i −0.350283 0.614249i
\(251\) 6.43760i 0.406338i −0.979144 0.203169i \(-0.934876\pi\)
0.979144 0.203169i \(-0.0651240\pi\)
\(252\) 2.98308 1.50175i 0.187916 0.0946016i
\(253\) −0.217255 0.217255i −0.0136587 0.0136587i
\(254\) −19.4621 −1.22116
\(255\) 4.19625 + 1.06501i 0.262779 + 0.0666933i
\(256\) 1.00000 0.0625000
\(257\) −8.53147 8.53147i −0.532178 0.532178i 0.389042 0.921220i \(-0.372806\pi\)
−0.921220 + 0.389042i \(0.872806\pi\)
\(258\) 9.62123 + 13.3103i 0.598992 + 0.828665i
\(259\) 2.79730i 0.173816i
\(260\) 11.9411 9.98368i 0.740558 0.619162i
\(261\) 6.28064 19.0151i 0.388762 1.17701i
\(262\) 6.42395 6.42395i 0.396873 0.396873i
\(263\) −4.18176 + 4.18176i −0.257858 + 0.257858i −0.824183 0.566324i \(-0.808365\pi\)
0.566324 + 0.824183i \(0.308365\pi\)
\(264\) 0.525408 + 0.0845247i 0.0323366 + 0.00520213i
\(265\) −14.4221 + 12.0580i −0.885942 + 0.740714i
\(266\) 0.770292i 0.0472297i
\(267\) −16.2026 + 11.7118i −0.991581 + 0.716754i
\(268\) 2.19342 + 2.19342i 0.133985 + 0.133985i
\(269\) 4.70169 0.286667 0.143334 0.989674i \(-0.454218\pi\)
0.143334 + 0.989674i \(0.454218\pi\)
\(270\) −6.24614 + 9.79723i −0.380128 + 0.596240i
\(271\) 2.81014 0.170704 0.0853521 0.996351i \(-0.472799\pi\)
0.0853521 + 0.996351i \(0.472799\pi\)
\(272\) −0.790416 0.790416i −0.0479260 0.0479260i
\(273\) −10.8777 + 7.86283i −0.658349 + 0.475880i
\(274\) 8.65792i 0.523044i
\(275\) −0.272139 + 1.51193i −0.0164106 + 0.0911726i
\(276\) −1.71006 0.275105i −0.102934 0.0165594i
\(277\) −7.56846 + 7.56846i −0.454744 + 0.454744i −0.896926 0.442181i \(-0.854205\pi\)
0.442181 + 0.896926i \(0.354205\pi\)
\(278\) 1.20909 1.20909i 0.0725164 0.0725164i
\(279\) 4.25809 12.8917i 0.254925 0.771806i
\(280\) 0.221366 2.47945i 0.0132291 0.148176i
\(281\) 6.92797i 0.413288i −0.978416 0.206644i \(-0.933746\pi\)
0.978416 0.206644i \(-0.0662542\pi\)
\(282\) −9.88639 13.6772i −0.588726 0.814463i
\(283\) −12.5993 12.5993i −0.748951 0.748951i 0.225331 0.974282i \(-0.427654\pi\)
−0.974282 + 0.225331i \(0.927654\pi\)
\(284\) −4.55564 −0.270327
\(285\) 1.37054 + 2.30284i 0.0811837 + 0.136409i
\(286\) −2.13867 −0.126462
\(287\) 0.469246 + 0.469246i 0.0276987 + 0.0276987i
\(288\) 2.67960 1.34897i 0.157897 0.0794891i
\(289\) 15.7505i 0.926499i
\(290\) −9.57400 11.4511i −0.562205 0.672433i
\(291\) −4.99072 + 31.0225i −0.292561 + 1.81857i
\(292\) 4.90914 4.90914i 0.287286 0.287286i
\(293\) −4.71078 + 4.71078i −0.275207 + 0.275207i −0.831192 0.555985i \(-0.812341\pi\)
0.555985 + 0.831192i \(0.312341\pi\)
\(294\) 1.58479 9.85110i 0.0924268 0.574528i
\(295\) 14.2167 + 1.26927i 0.827728 + 0.0738997i
\(296\) 2.51272i 0.146049i
\(297\) 1.52191 0.482270i 0.0883099 0.0279841i
\(298\) 3.13978 + 3.13978i 0.181883 + 0.181883i
\(299\) 6.96081 0.402554
\(300\) 3.74977 + 7.80636i 0.216493 + 0.450700i
\(301\) −10.5560 −0.608440
\(302\) 13.3297 + 13.3297i 0.767040 + 0.767040i
\(303\) −0.442089 0.611601i −0.0253974 0.0351356i
\(304\) 0.691928i 0.0396848i
\(305\) −22.1799 1.98022i −1.27002 0.113387i
\(306\) −3.18425 1.05175i −0.182032 0.0601245i
\(307\) 6.16188 6.16188i 0.351677 0.351677i −0.509056 0.860733i \(-0.670006\pi\)
0.860733 + 0.509056i \(0.170006\pi\)
\(308\) −0.241860 + 0.241860i −0.0137813 + 0.0137813i
\(309\) −5.97555 0.961313i −0.339937 0.0546872i
\(310\) −6.49089 7.76352i −0.368658 0.440939i
\(311\) 6.56745i 0.372406i 0.982511 + 0.186203i \(0.0596182\pi\)
−0.982511 + 0.186203i \(0.940382\pi\)
\(312\) −9.77108 + 7.06292i −0.553178 + 0.399859i
\(313\) 5.15434 + 5.15434i 0.291341 + 0.291341i 0.837610 0.546269i \(-0.183952\pi\)
−0.546269 + 0.837610i \(0.683952\pi\)
\(314\) 13.8395 0.781007
\(315\) −2.75155 6.94256i −0.155032 0.391169i
\(316\) −15.7352 −0.885177
\(317\) −18.9615 18.9615i −1.06498 1.06498i −0.997736 0.0672456i \(-0.978579\pi\)
−0.0672456 0.997736i \(-0.521421\pi\)
\(318\) 11.8012 8.53035i 0.661777 0.478358i
\(319\) 2.05091i 0.114829i
\(320\) 0.198845 2.22721i 0.0111158 0.124505i
\(321\) 21.7796 + 3.50378i 1.21562 + 0.195562i
\(322\) 0.787190 0.787190i 0.0438684 0.0438684i
\(323\) −0.546911 + 0.546911i −0.0304309 + 0.0304309i
\(324\) 5.36053 7.22943i 0.297807 0.401635i
\(325\) −19.8613 28.5806i −1.10171 1.58537i
\(326\) 13.0724i 0.724014i
\(327\) −4.78457 6.61914i −0.264587 0.366039i
\(328\) 0.421508 + 0.421508i 0.0232739 + 0.0232739i
\(329\) 10.8470 0.598013
\(330\) 0.292729 1.15339i 0.0161142 0.0634918i
\(331\) −0.116417 −0.00639884 −0.00319942 0.999995i \(-0.501018\pi\)
−0.00319942 + 0.999995i \(0.501018\pi\)
\(332\) 6.65861 + 6.65861i 0.365439 + 0.365439i
\(333\) −3.38960 6.73310i −0.185749 0.368971i
\(334\) 10.5242i 0.575858i
\(335\) 5.32136 4.44906i 0.290737 0.243078i
\(336\) −0.306263 + 1.90374i −0.0167080 + 0.103857i
\(337\) 8.19544 8.19544i 0.446434 0.446434i −0.447733 0.894167i \(-0.647769\pi\)
0.894167 + 0.447733i \(0.147769\pi\)
\(338\) 25.0690 25.0690i 1.36357 1.36357i
\(339\) 3.79011 23.5594i 0.205851 1.27957i
\(340\) −1.91759 + 1.60325i −0.103996 + 0.0869485i
\(341\) 1.39046i 0.0752975i
\(342\) −0.933393 1.85409i −0.0504721 0.100258i
\(343\) 10.0451 + 10.0451i 0.542383 + 0.542383i
\(344\) −9.48214 −0.511243
\(345\) −0.952756 + 3.75397i −0.0512946 + 0.202107i
\(346\) 12.7944 0.687833
\(347\) −4.19660 4.19660i −0.225285 0.225285i 0.585435 0.810720i \(-0.300924\pi\)
−0.810720 + 0.585435i \(0.800924\pi\)
\(348\) 6.77309 + 9.37012i 0.363076 + 0.502291i
\(349\) 5.51143i 0.295020i 0.989061 + 0.147510i \(0.0471259\pi\)
−0.989061 + 0.147510i \(0.952874\pi\)
\(350\) −5.47824 0.986056i −0.292824 0.0527069i
\(351\) −16.6549 + 32.1067i −0.888973 + 1.71373i
\(352\) −0.217255 + 0.217255i −0.0115797 + 0.0115797i
\(353\) 2.34200 2.34200i 0.124652 0.124652i −0.642029 0.766681i \(-0.721907\pi\)
0.766681 + 0.642029i \(0.221907\pi\)
\(354\) −10.9157 1.75605i −0.580161 0.0933330i
\(355\) −0.905868 + 10.1464i −0.0480785 + 0.538513i
\(356\) 11.5425i 0.611753i
\(357\) 1.74682 1.26267i 0.0924515 0.0668276i
\(358\) 7.93796 + 7.93796i 0.419534 + 0.419534i
\(359\) 12.4668 0.657974 0.328987 0.944334i \(-0.393293\pi\)
0.328987 + 0.944334i \(0.393293\pi\)
\(360\) −2.47162 6.23627i −0.130266 0.328680i
\(361\) 18.5212 0.974802
\(362\) 6.12224 + 6.12224i 0.321778 + 0.321778i
\(363\) 15.3085 11.0656i 0.803487 0.580792i
\(364\) 7.74916i 0.406167i
\(365\) −9.95752 11.9098i −0.521201 0.623390i
\(366\) 17.0299 + 2.73967i 0.890165 + 0.143205i
\(367\) 3.53418 3.53418i 0.184483 0.184483i −0.608823 0.793306i \(-0.708358\pi\)
0.793306 + 0.608823i \(0.208358\pi\)
\(368\) 0.707107 0.707107i 0.0368605 0.0368605i
\(369\) 1.69808 + 0.560870i 0.0883984 + 0.0291977i
\(370\) −5.59636 0.499644i −0.290941 0.0259752i
\(371\) 9.35918i 0.485904i
\(372\) 4.59195 + 6.35266i 0.238082 + 0.329370i
\(373\) −17.4340 17.4340i −0.902700 0.902700i 0.0929686 0.995669i \(-0.470364\pi\)
−0.995669 + 0.0929686i \(0.970364\pi\)
\(374\) 0.343444 0.0177590
\(375\) 18.1320 6.79925i 0.936333 0.351112i
\(376\) 9.74347 0.502481
\(377\) −32.8555 32.8555i −1.69214 1.69214i
\(378\) 1.74743 + 5.51440i 0.0898782 + 0.283630i
\(379\) 27.9253i 1.43443i 0.696853 + 0.717214i \(0.254583\pi\)
−0.696853 + 0.717214i \(0.745417\pi\)
\(380\) −1.54107 0.137587i −0.0790551 0.00705805i
\(381\) 5.35414 33.2815i 0.274301 1.70506i
\(382\) 12.8465 12.8465i 0.657284 0.657284i
\(383\) 10.0383 10.0383i 0.512932 0.512932i −0.402492 0.915424i \(-0.631856\pi\)
0.915424 + 0.402492i \(0.131856\pi\)
\(384\) −0.275105 + 1.71006i −0.0140389 + 0.0872663i
\(385\) 0.490580 + 0.586766i 0.0250023 + 0.0299044i
\(386\) 9.07391i 0.461850i
\(387\) −25.4084 + 12.7912i −1.29158 + 0.650212i
\(388\) −12.8277 12.8277i −0.651228 0.651228i
\(389\) −20.3937 −1.03400 −0.517000 0.855985i \(-0.672951\pi\)
−0.517000 + 0.855985i \(0.672951\pi\)
\(390\) 13.7877 + 23.1667i 0.698165 + 1.17309i
\(391\) −1.11782 −0.0565305
\(392\) 4.07340 + 4.07340i 0.205738 + 0.205738i
\(393\) 9.21810 + 12.7526i 0.464992 + 0.643285i
\(394\) 20.7521i 1.04547i
\(395\) −3.12888 + 35.0457i −0.157431 + 1.76334i
\(396\) −0.289085 + 0.875228i −0.0145271 + 0.0439818i
\(397\) 11.8044 11.8044i 0.592447 0.592447i −0.345845 0.938292i \(-0.612408\pi\)
0.938292 + 0.345845i \(0.112408\pi\)
\(398\) 1.84410 1.84410i 0.0924363 0.0924363i
\(399\) 1.31725 + 0.211912i 0.0659449 + 0.0106089i
\(400\) −4.92092 0.885741i −0.246046 0.0442870i
\(401\) 8.66485i 0.432702i −0.976316 0.216351i \(-0.930584\pi\)
0.976316 0.216351i \(-0.0694156\pi\)
\(402\) −4.35431 + 3.14747i −0.217173 + 0.156981i
\(403\) −22.2750 22.2750i −1.10960 1.10960i
\(404\) 0.435698 0.0216768
\(405\) −15.0355 13.3766i −0.747122 0.664687i
\(406\) −7.43117 −0.368803
\(407\) 0.545901 + 0.545901i 0.0270593 + 0.0270593i
\(408\) 1.56911 1.13421i 0.0776825 0.0561520i
\(409\) 22.5197i 1.11353i −0.830670 0.556765i \(-0.812043\pi\)
0.830670 0.556765i \(-0.187957\pi\)
\(410\) 1.02260 0.854972i 0.0505027 0.0422241i
\(411\) 14.8056 + 2.38184i 0.730306 + 0.117488i
\(412\) 2.47087 2.47087i 0.121731 0.121731i
\(413\) 5.02479 5.02479i 0.247254 0.247254i
\(414\) 0.940895 2.84863i 0.0462425 0.140003i
\(415\) 16.1542 13.5061i 0.792977 0.662988i
\(416\) 6.96081i 0.341282i
\(417\) 1.73499 + 2.40025i 0.0849630 + 0.117541i
\(418\) 0.150325 + 0.150325i 0.00735262 + 0.00735262i
\(419\) 19.7745 0.966048 0.483024 0.875607i \(-0.339538\pi\)
0.483024 + 0.875607i \(0.339538\pi\)
\(420\) 4.17912 + 1.06066i 0.203920 + 0.0517549i
\(421\) −3.54002 −0.172530 −0.0862649 0.996272i \(-0.527493\pi\)
−0.0862649 + 0.996272i \(0.527493\pi\)
\(422\) −17.6667 17.6667i −0.860004 0.860004i
\(423\) 26.1086 13.1437i 1.26944 0.639068i
\(424\) 8.40703i 0.408282i
\(425\) 3.18947 + 4.58968i 0.154712 + 0.222632i
\(426\) 1.25328 7.79043i 0.0607217 0.377448i
\(427\) −7.83932 + 7.83932i −0.379371 + 0.379371i
\(428\) −9.00580 + 9.00580i −0.435312 + 0.435312i
\(429\) 0.588361 3.65727i 0.0284063 0.176574i
\(430\) −1.88548 + 21.1187i −0.0909260 + 1.01843i
\(431\) 6.98806i 0.336603i −0.985736 0.168302i \(-0.946172\pi\)
0.985736 0.168302i \(-0.0538282\pi\)
\(432\) 1.56966 + 4.95340i 0.0755203 + 0.238321i
\(433\) −22.0257 22.0257i −1.05849 1.05849i −0.998180 0.0603055i \(-0.980793\pi\)
−0.0603055 0.998180i \(-0.519207\pi\)
\(434\) −5.03812 −0.241837
\(435\) 22.2160 13.2219i 1.06518 0.633941i
\(436\) 4.71540 0.225827
\(437\) −0.489267 0.489267i −0.0234048 0.0234048i
\(438\) 7.04441 + 9.74547i 0.336595 + 0.465657i
\(439\) 12.4962i 0.596410i −0.954502 0.298205i \(-0.903612\pi\)
0.954502 0.298205i \(-0.0963879\pi\)
\(440\) 0.440672 + 0.527072i 0.0210082 + 0.0251272i
\(441\) 16.4100 + 5.42018i 0.781429 + 0.258104i
\(442\) −5.50194 + 5.50194i −0.261701 + 0.261701i
\(443\) 3.45517 3.45517i 0.164160 0.164160i −0.620247 0.784407i \(-0.712967\pi\)
0.784407 + 0.620247i \(0.212967\pi\)
\(444\) 4.29692 + 0.691264i 0.203923 + 0.0328059i
\(445\) −25.7076 2.29518i −1.21866 0.108802i
\(446\) 2.92545i 0.138524i
\(447\) −6.23300 + 4.50546i −0.294811 + 0.213101i
\(448\) −0.787190 0.787190i −0.0371913 0.0371913i
\(449\) 5.44836 0.257124 0.128562 0.991701i \(-0.458964\pi\)
0.128562 + 0.991701i \(0.458964\pi\)
\(450\) −14.3810 + 4.26477i −0.677925 + 0.201043i
\(451\) −0.183149 −0.00862417
\(452\) 9.74177 + 9.74177i 0.458214 + 0.458214i
\(453\) −26.4618 + 19.1276i −1.24328 + 0.898694i
\(454\) 21.0614i 0.988463i
\(455\) −17.2590 1.54089i −0.809115 0.0722378i
\(456\) 1.18324 + 0.190353i 0.0554103 + 0.00891410i
\(457\) −9.46760 + 9.46760i −0.442876 + 0.442876i −0.892977 0.450102i \(-0.851388\pi\)
0.450102 + 0.892977i \(0.351388\pi\)
\(458\) −3.26090 + 3.26090i −0.152372 + 0.152372i
\(459\) 2.67456 5.15593i 0.124838 0.240658i
\(460\) −1.43427 1.71548i −0.0668732 0.0799847i
\(461\) 29.8517i 1.39033i 0.718849 + 0.695166i \(0.244669\pi\)
−0.718849 + 0.695166i \(0.755331\pi\)
\(462\) −0.347059 0.480133i −0.0161466 0.0223378i
\(463\) −17.9865 17.9865i −0.835905 0.835905i 0.152412 0.988317i \(-0.451296\pi\)
−0.988317 + 0.152412i \(0.951296\pi\)
\(464\) −6.67517 −0.309887
\(465\) 15.0618 8.96404i 0.698474 0.415698i
\(466\) −4.90975 −0.227440
\(467\) −3.58351 3.58351i −0.165825 0.165825i 0.619317 0.785141i \(-0.287410\pi\)
−0.785141 + 0.619317i \(0.787410\pi\)
\(468\) −9.38996 18.6522i −0.434051 0.862199i
\(469\) 3.45328i 0.159458i
\(470\) 1.93744 21.7007i 0.0893677 1.00098i
\(471\) −3.80732 + 23.6664i −0.175432 + 1.09049i
\(472\) 4.51360 4.51360i 0.207755 0.207755i
\(473\) 2.06004 2.06004i 0.0947208 0.0947208i
\(474\) 4.32885 26.9083i 0.198831 1.23594i
\(475\) −0.612869 + 3.40492i −0.0281203 + 0.156229i
\(476\) 1.24442i 0.0570377i
\(477\) 11.3409 + 22.5275i 0.519263 + 1.03146i
\(478\) 14.3406 + 14.3406i 0.655924 + 0.655924i
\(479\) −39.2172 −1.79188 −0.895939 0.444177i \(-0.853496\pi\)
−0.895939 + 0.444177i \(0.853496\pi\)
\(480\) 3.75397 + 0.952756i 0.171344 + 0.0434871i
\(481\) −17.4906 −0.797503
\(482\) −4.36062 4.36062i −0.198621 0.198621i
\(483\) 1.12959 + 1.56271i 0.0513979 + 0.0711056i
\(484\) 10.9056i 0.495709i
\(485\) −31.1207 + 26.0193i −1.41312 + 1.18147i
\(486\) 10.8881 + 11.1557i 0.493893 + 0.506033i
\(487\) 18.9608 18.9608i 0.859194 0.859194i −0.132049 0.991243i \(-0.542156\pi\)
0.991243 + 0.132049i \(0.0421556\pi\)
\(488\) −7.04180 + 7.04180i −0.318767 + 0.318767i
\(489\) 22.3547 + 3.59629i 1.01091 + 0.162630i
\(490\) 9.88230 8.26234i 0.446437 0.373255i
\(491\) 14.7080i 0.663761i −0.943321 0.331880i \(-0.892317\pi\)
0.943321 0.331880i \(-0.107683\pi\)
\(492\) −0.836765 + 0.604847i −0.0377243 + 0.0272686i
\(493\) 5.27617 + 5.27617i 0.237627 + 0.237627i
\(494\) −4.81638 −0.216699
\(495\) 1.89183 + 0.817888i 0.0850315 + 0.0367613i
\(496\) −4.52557 −0.203204
\(497\) 3.58616 + 3.58616i 0.160861 + 0.160861i
\(498\) −13.2185 + 9.55483i −0.592334 + 0.428162i
\(499\) 12.6459i 0.566109i −0.959104 0.283055i \(-0.908652\pi\)
0.959104 0.283055i \(-0.0913477\pi\)
\(500\) −2.95123 + 10.7838i −0.131983 + 0.482266i
\(501\) 17.9970 + 2.89526i 0.804048 + 0.129351i
\(502\) −4.55207 + 4.55207i −0.203169 + 0.203169i
\(503\) −29.2502 + 29.2502i −1.30420 + 1.30420i −0.378668 + 0.925532i \(0.623618\pi\)
−0.925532 + 0.378668i \(0.876382\pi\)
\(504\) −3.17126 1.04746i −0.141259 0.0466574i
\(505\) 0.0866366 0.970391i 0.00385528 0.0431818i
\(506\) 0.307245i 0.0136587i
\(507\) 35.9730 + 49.7662i 1.59762 + 2.21019i
\(508\) 13.7618 + 13.7618i 0.610582 + 0.610582i
\(509\) 17.2813 0.765978 0.382989 0.923753i \(-0.374895\pi\)
0.382989 + 0.923753i \(0.374895\pi\)
\(510\) −2.21412 3.72027i −0.0980430 0.164736i
\(511\) −7.72886 −0.341904
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 3.42740 1.08609i 0.151323 0.0479521i
\(514\) 12.0653i 0.532178i
\(515\) −5.01183 5.99448i −0.220848 0.264148i
\(516\) 2.60859 16.2151i 0.114837 0.713828i
\(517\) −2.11682 + 2.11682i −0.0930974 + 0.0930974i
\(518\) −1.97799 + 1.97799i −0.0869080 + 0.0869080i
\(519\) −3.51982 + 21.8793i −0.154503 + 0.960394i
\(520\) −15.5032 1.38413i −0.679860 0.0606980i
\(521\) 34.5203i 1.51236i 0.654363 + 0.756181i \(0.272937\pi\)
−0.654363 + 0.756181i \(0.727063\pi\)
\(522\) −17.8868 + 9.00464i −0.782884 + 0.394123i
\(523\) 29.4556 + 29.4556i 1.28800 + 1.28800i 0.935998 + 0.352005i \(0.114500\pi\)
0.352005 + 0.935998i \(0.385500\pi\)
\(524\) −9.08484 −0.396873
\(525\) 3.19331 9.09687i 0.139368 0.397020i
\(526\) 5.91390 0.257858
\(527\) 3.57709 + 3.57709i 0.155820 + 0.155820i
\(528\) −0.311752 0.431287i −0.0135672 0.0187694i
\(529\) 1.00000i 0.0434783i
\(530\) 18.7242 + 1.67170i 0.813328 + 0.0726140i
\(531\) 6.00591 18.1834i 0.260634 0.789091i
\(532\) −0.544679 + 0.544679i −0.0236148 + 0.0236148i
\(533\) 2.93404 2.93404i 0.127087 0.127087i
\(534\) 19.7385 + 3.17541i 0.854167 + 0.137414i
\(535\) 18.2670 + 21.8486i 0.789753 + 0.944595i
\(536\) 3.10197i 0.133985i
\(537\) −15.7582 + 11.3906i −0.680016 + 0.491542i
\(538\) −3.32460 3.32460i −0.143334 0.143334i
\(539\) −1.76993 −0.0762364
\(540\) 11.3444 2.51100i 0.488184 0.108056i
\(541\) −22.6506 −0.973824 −0.486912 0.873451i \(-0.661877\pi\)
−0.486912 + 0.873451i \(0.661877\pi\)
\(542\) −1.98707 1.98707i −0.0853521 0.0853521i
\(543\) −12.1537 + 8.78515i −0.521564 + 0.377007i
\(544\) 1.11782i 0.0479260i
\(545\) 0.937637 10.5022i 0.0401639 0.449864i
\(546\) 13.2516 + 2.13184i 0.567114 + 0.0912342i
\(547\) 0.166563 0.166563i 0.00712170 0.00712170i −0.703537 0.710659i \(-0.748397\pi\)
0.710659 + 0.703537i \(0.248397\pi\)
\(548\) −6.12207 + 6.12207i −0.261522 + 0.261522i
\(549\) −9.37001 + 28.3684i −0.399902 + 1.21074i
\(550\) 1.26153 0.876662i 0.0537916 0.0373810i
\(551\) 4.61874i 0.196765i
\(552\) 1.01467 + 1.40373i 0.0431872 + 0.0597466i
\(553\) 12.3866 + 12.3866i 0.526733 + 0.526733i
\(554\) 10.7034 0.454744
\(555\) 2.39401 9.43268i 0.101620 0.400395i
\(556\) −1.70991 −0.0725164
\(557\) 22.4801 + 22.4801i 0.952511 + 0.952511i 0.998922 0.0464113i \(-0.0147785\pi\)
−0.0464113 + 0.998922i \(0.514778\pi\)
\(558\) −12.1267 + 6.10488i −0.513365 + 0.258440i
\(559\) 66.0034i 2.79165i
\(560\) −1.90977 + 1.59671i −0.0807024 + 0.0674732i
\(561\) −0.0944832 + 0.587310i −0.00398908 + 0.0247963i
\(562\) −4.89882 + 4.89882i −0.206644 + 0.206644i
\(563\) 24.7485 24.7485i 1.04302 1.04302i 0.0439915 0.999032i \(-0.485993\pi\)
0.999032 0.0439915i \(-0.0140075\pi\)
\(564\) −2.68048 + 16.6620i −0.112869 + 0.701595i
\(565\) 23.6341 19.7598i 0.994292 0.831303i
\(566\) 17.8181i 0.748951i
\(567\) −9.91070 + 1.47118i −0.416210 + 0.0617837i
\(568\) 3.22132 + 3.22132i 0.135164 + 0.135164i
\(569\) 41.8001 1.75235 0.876176 0.481991i \(-0.160086\pi\)
0.876176 + 0.481991i \(0.160086\pi\)
\(570\) 0.659238 2.59747i 0.0276124 0.108796i
\(571\) −6.16454 −0.257978 −0.128989 0.991646i \(-0.541173\pi\)
−0.128989 + 0.991646i \(0.541173\pi\)
\(572\) 1.51227 + 1.51227i 0.0632312 + 0.0632312i
\(573\) 18.4342 + 25.5025i 0.770099 + 1.06538i
\(574\) 0.663614i 0.0276987i
\(575\) −4.10593 + 2.85330i −0.171229 + 0.118991i
\(576\) −2.84863 0.940895i −0.118693 0.0392040i
\(577\) −32.6610 + 32.6610i −1.35970 + 1.35970i −0.485410 + 0.874287i \(0.661330\pi\)
−0.874287 + 0.485410i \(0.838670\pi\)
\(578\) −11.1373 + 11.1373i −0.463250 + 0.463250i
\(579\) 15.5170 + 2.49628i 0.644863 + 0.103742i
\(580\) −1.32733 + 14.8670i −0.0551143 + 0.617319i
\(581\) 10.4832i 0.434916i
\(582\) 25.4652 18.4072i 1.05557 0.763004i
\(583\) −1.82647 1.82647i −0.0756446 0.0756446i
\(584\) −6.94257 −0.287286
\(585\) −43.4095 + 17.2045i −1.79476 + 0.711319i
\(586\) 6.66204 0.275207
\(587\) −22.6013 22.6013i −0.932856 0.932856i 0.0650272 0.997883i \(-0.479287\pi\)
−0.997883 + 0.0650272i \(0.979287\pi\)
\(588\) −8.08639 + 5.84516i −0.333477 + 0.241050i
\(589\) 3.13137i 0.129026i
\(590\) −9.15522 10.9502i −0.376914 0.450814i
\(591\) −35.4874 5.70901i −1.45975 0.234837i
\(592\) −1.77676 + 1.77676i −0.0730245 + 0.0730245i
\(593\) −16.9395 + 16.9395i −0.695621 + 0.695621i −0.963463 0.267842i \(-0.913689\pi\)
0.267842 + 0.963463i \(0.413689\pi\)
\(594\) −1.41717 0.735134i −0.0581470 0.0301629i
\(595\) 2.77158 + 0.247447i 0.113624 + 0.0101443i
\(596\) 4.44032i 0.181883i
\(597\) 2.64620 + 3.66085i 0.108302 + 0.149828i
\(598\) −4.92204 4.92204i −0.201277 0.201277i
\(599\) 35.0050 1.43027 0.715133 0.698988i \(-0.246366\pi\)
0.715133 + 0.698988i \(0.246366\pi\)
\(600\) 2.86845 8.17141i 0.117104 0.333597i
\(601\) −2.10282 −0.0857759 −0.0428880 0.999080i \(-0.513656\pi\)
−0.0428880 + 0.999080i \(0.513656\pi\)
\(602\) 7.46425 + 7.46425i 0.304220 + 0.304220i
\(603\) −4.18447 8.31203i −0.170405 0.338492i
\(604\) 18.8511i 0.767040i
\(605\) 24.2891 + 2.16853i 0.987490 + 0.0881633i
\(606\) −0.119863 + 0.745072i −0.00486910 + 0.0302665i
\(607\) 3.54626 3.54626i 0.143938 0.143938i −0.631466 0.775404i \(-0.717546\pi\)
0.775404 + 0.631466i \(0.217546\pi\)
\(608\) −0.489267 + 0.489267i −0.0198424 + 0.0198424i
\(609\) 2.04436 12.7078i 0.0828415 0.514945i
\(610\) 14.2833 + 17.0838i 0.578315 + 0.691703i
\(611\) 67.8225i 2.74380i
\(612\) 1.50791 + 2.99531i 0.0609536 + 0.121078i
\(613\) −29.6529 29.6529i −1.19767 1.19767i −0.974862 0.222808i \(-0.928478\pi\)
−0.222808 0.974862i \(-0.571522\pi\)
\(614\) −8.71421 −0.351677
\(615\) 1.18073 + 1.98392i 0.0476117 + 0.0799994i
\(616\) 0.342042 0.0137813
\(617\) −32.2270 32.2270i −1.29741 1.29741i −0.930098 0.367311i \(-0.880279\pi\)
−0.367311 0.930098i \(-0.619721\pi\)
\(618\) 3.54560 + 4.90510i 0.142625 + 0.197312i
\(619\) 17.9166i 0.720130i 0.932927 + 0.360065i \(0.117245\pi\)
−0.932927 + 0.360065i \(0.882755\pi\)
\(620\) −0.899889 + 10.0794i −0.0361404 + 0.404798i
\(621\) 4.61250 + 2.39267i 0.185093 + 0.0960144i
\(622\) 4.64389 4.64389i 0.186203 0.186203i
\(623\) −9.08617 + 9.08617i −0.364030 + 0.364030i
\(624\) 11.9034 + 1.91496i 0.476519 + 0.0766597i
\(625\) 23.4309 + 8.71732i 0.937237 + 0.348693i
\(626\) 7.28934i 0.291341i
\(627\) −0.298420 + 0.215710i −0.0119177 + 0.00861461i
\(628\) −9.78600 9.78600i −0.390504 0.390504i
\(629\) 2.80877 0.111993
\(630\) −2.96350 + 6.85477i −0.118068 + 0.273101i
\(631\) −7.91640 −0.315147 −0.157573 0.987507i \(-0.550367\pi\)
−0.157573 + 0.987507i \(0.550367\pi\)
\(632\) 11.1265 + 11.1265i 0.442588 + 0.442588i
\(633\) 35.0715 25.3510i 1.39397 1.00761i
\(634\) 26.8156i 1.06498i
\(635\) 33.3869 27.9140i 1.32492 1.10773i
\(636\) −14.3766 2.31282i −0.570068 0.0917093i
\(637\) 28.3542 28.3542i 1.12343 1.12343i
\(638\) 1.45021 1.45021i 0.0574145 0.0574145i
\(639\) 12.9773 + 4.28638i 0.513376 + 0.169567i
\(640\) −1.71548 + 1.43427i −0.0678103 + 0.0566945i
\(641\) 27.3529i 1.08037i −0.841545 0.540187i \(-0.818354\pi\)
0.841545 0.540187i \(-0.181646\pi\)
\(642\) −12.9229 17.8780i −0.510028 0.705589i
\(643\) −9.00024 9.00024i −0.354935 0.354935i 0.507007 0.861942i \(-0.330752\pi\)
−0.861942 + 0.507007i \(0.830752\pi\)
\(644\) −1.11326 −0.0438684
\(645\) −35.5956 9.03417i −1.40158 0.355720i
\(646\) 0.773449 0.0304309
\(647\) 15.7372 + 15.7372i 0.618691 + 0.618691i 0.945196 0.326504i \(-0.105871\pi\)
−0.326504 + 0.945196i \(0.605871\pi\)
\(648\) −8.90245 + 1.32151i −0.349721 + 0.0519138i
\(649\) 1.96120i 0.0769839i
\(650\) −6.16548 + 34.2536i −0.241830 + 1.34354i
\(651\) 1.38601 8.61550i 0.0543221 0.337668i
\(652\) −9.24359 + 9.24359i −0.362007 + 0.362007i
\(653\) 9.00813 9.00813i 0.352515 0.352515i −0.508529 0.861045i \(-0.669811\pi\)
0.861045 + 0.508529i \(0.169811\pi\)
\(654\) −1.29723 + 8.06364i −0.0507258 + 0.315313i
\(655\) −1.80648 + 20.2338i −0.0705850 + 0.790601i
\(656\) 0.596103i 0.0232739i
\(657\) −18.6033 + 9.36536i −0.725785 + 0.365377i
\(658\) −7.66997 7.66997i −0.299006 0.299006i
\(659\) 0.859802 0.0334931 0.0167466 0.999860i \(-0.494669\pi\)
0.0167466 + 0.999860i \(0.494669\pi\)
\(660\) −1.02256 + 0.608576i −0.0398030 + 0.0236888i
\(661\) −2.50289 −0.0973513 −0.0486757 0.998815i \(-0.515500\pi\)
−0.0486757 + 0.998815i \(0.515500\pi\)
\(662\) 0.0823190 + 0.0823190i 0.00319942 + 0.00319942i
\(663\) −7.89505 10.9223i −0.306619 0.424186i
\(664\) 9.41670i 0.365439i
\(665\) 1.10481 + 1.32142i 0.0428426 + 0.0512425i
\(666\) −2.36421 + 7.15783i −0.0916113 + 0.277360i
\(667\) −4.72006 + 4.72006i −0.182762 + 0.182762i
\(668\) −7.44173 + 7.44173i −0.287929 + 0.287929i
\(669\) 5.00270 + 0.804807i 0.193416 + 0.0311156i
\(670\) −6.90873 0.616812i −0.266907 0.0238295i
\(671\) 3.05973i 0.118120i
\(672\) 1.56271 1.12959i 0.0602827 0.0435747i
\(673\) −22.4457 22.4457i −0.865220 0.865220i 0.126719 0.991939i \(-0.459555\pi\)
−0.991939 + 0.126719i \(0.959555\pi\)
\(674\) −11.5901 −0.446434
\(675\) −3.33674 25.7656i −0.128431 0.991718i
\(676\) −35.4529 −1.36357
\(677\) −28.5893 28.5893i −1.09878 1.09878i −0.994554 0.104222i \(-0.966765\pi\)
−0.104222 0.994554i \(-0.533235\pi\)
\(678\) −19.3391 + 13.9790i −0.742712 + 0.536861i
\(679\) 20.1957i 0.775040i
\(680\) 2.48961 + 0.222273i 0.0954723 + 0.00852378i
\(681\) 36.0164 + 5.79412i 1.38015 + 0.222031i
\(682\) 0.983202 0.983202i 0.0376488 0.0376488i
\(683\) −14.6754 + 14.6754i −0.561537 + 0.561537i −0.929744 0.368207i \(-0.879972\pi\)
0.368207 + 0.929744i \(0.379972\pi\)
\(684\) −0.651032 + 1.97105i −0.0248928 + 0.0753650i
\(685\) 12.4178 + 14.8525i 0.474459 + 0.567484i
\(686\) 14.2059i 0.542383i
\(687\) −4.67925 6.47343i −0.178525 0.246977i
\(688\) 6.70489 + 6.70489i 0.255621 + 0.255621i
\(689\) 58.5198 2.22943
\(690\) 3.32815 1.98075i 0.126701 0.0754060i
\(691\) 41.2032 1.56744 0.783721 0.621113i \(-0.213319\pi\)
0.783721 + 0.621113i \(0.213319\pi\)
\(692\) −9.04703 9.04703i −0.343916 0.343916i
\(693\) 0.916536 0.461406i 0.0348163 0.0175274i
\(694\) 5.93489i 0.225285i
\(695\) −0.340008 + 3.80833i −0.0128972 + 0.144458i
\(696\) 1.83638 11.4150i 0.0696077 0.432683i
\(697\) −0.471169 + 0.471169i −0.0178468 + 0.0178468i
\(698\) 3.89717 3.89717i 0.147510 0.147510i
\(699\) 1.35070 8.39599i 0.0510882 0.317566i
\(700\) 3.17646 + 4.57095i 0.120059 + 0.172766i
\(701\) 15.0725i 0.569281i −0.958634 0.284641i \(-0.908126\pi\)
0.958634 0.284641i \(-0.0918743\pi\)
\(702\) 34.4797 10.9261i 1.30135 0.412379i
\(703\) 1.22939 + 1.22939i 0.0463674 + 0.0463674i
\(704\) 0.307245 0.0115797
\(705\) 36.5766 + 9.28315i 1.37756 + 0.349623i
\(706\) −3.31208 −0.124652
\(707\) −0.342978 0.342978i −0.0128990 0.0128990i
\(708\) 6.47682 + 8.96025i 0.243414 + 0.336747i
\(709\) 18.9496i 0.711666i 0.934550 + 0.355833i \(0.115803\pi\)
−0.934550 + 0.355833i \(0.884197\pi\)
\(710\) 7.81511 6.53402i 0.293296 0.245217i
\(711\) 44.8240 + 14.8052i 1.68103 + 0.555239i
\(712\) −8.16181 + 8.16181i −0.305877 + 0.305877i
\(713\) −3.20006 + 3.20006i −0.119843 + 0.119843i
\(714\) −2.12803 0.342346i −0.0796396 0.0128120i
\(715\) 3.66885 3.06743i 0.137207 0.114716i
\(716\) 11.2260i 0.419534i
\(717\) −28.4685 + 20.5782i −1.06318 + 0.768506i
\(718\) −8.81537 8.81537i −0.328987 0.328987i
\(719\) 32.0644 1.19580 0.597900 0.801571i \(-0.296002\pi\)
0.597900 + 0.801571i \(0.296002\pi\)
\(720\) −2.66201 + 6.15741i −0.0992072 + 0.229473i
\(721\) −3.89010 −0.144875
\(722\) −13.0965 13.0965i −0.487401 0.487401i
\(723\) 8.65657 6.25731i 0.321941 0.232712i
\(724\) 8.65815i 0.321778i
\(725\) 32.8480 + 5.91248i 1.21994 + 0.219584i
\(726\) −18.6493 3.00019i −0.692139 0.111347i
\(727\) −24.2721 + 24.2721i −0.900201 + 0.900201i −0.995453 0.0952521i \(-0.969634\pi\)
0.0952521 + 0.995453i \(0.469634\pi\)
\(728\) −5.47949 + 5.47949i −0.203083 + 0.203083i
\(729\) −22.0723 + 15.5503i −0.817494 + 0.575937i
\(730\) −1.38050 + 15.4626i −0.0510946 + 0.572295i
\(731\) 10.5993i 0.392029i
\(732\) −10.1047 13.9792i −0.373480 0.516685i
\(733\) 26.6081 + 26.6081i 0.982793 + 0.982793i 0.999854 0.0170616i \(-0.00543113\pi\)
−0.0170616 + 0.999854i \(0.505431\pi\)
\(734\) −4.99809 −0.184483
\(735\) 11.4105 + 19.1724i 0.420881 + 0.707184i
\(736\) −1.00000 −0.0368605
\(737\) 0.673917 + 0.673917i 0.0248240 + 0.0248240i
\(738\) −0.804127 1.59732i −0.0296003 0.0587981i
\(739\) 38.0885i 1.40111i −0.713599 0.700554i \(-0.752936\pi\)
0.713599 0.700554i \(-0.247064\pi\)
\(740\) 3.60392 + 4.31053i 0.132483 + 0.158458i
\(741\) 1.32501 8.23632i 0.0486756 0.302569i
\(742\) 6.61794 6.61794i 0.242952 0.242952i
\(743\) −27.8032 + 27.8032i −1.02000 + 1.02000i −0.0202029 + 0.999796i \(0.506431\pi\)
−0.999796 + 0.0202029i \(0.993569\pi\)
\(744\) 1.24501 7.73901i 0.0456442 0.283726i
\(745\) −9.88953 0.882938i −0.362324 0.0323484i
\(746\) 24.6555i 0.902700i
\(747\) −12.7029 25.2330i −0.464775 0.923228i
\(748\) −0.242851 0.242851i −0.00887952 0.00887952i
\(749\) 14.1786 0.518073
\(750\) −17.6291 8.01348i −0.643723 0.292611i
\(751\) 11.8305 0.431701 0.215850 0.976426i \(-0.430748\pi\)
0.215850 + 0.976426i \(0.430748\pi\)
\(752\) −6.88967 6.88967i −0.251241 0.251241i
\(753\) −6.53203 9.03663i −0.238040 0.329313i
\(754\) 46.4646i 1.69214i
\(755\) −41.9853 3.74846i −1.52800 0.136420i
\(756\) 2.66365 5.13489i 0.0968759 0.186754i
\(757\) −9.09388 + 9.09388i −0.330523 + 0.330523i −0.852785 0.522262i \(-0.825088\pi\)
0.522262 + 0.852785i \(0.325088\pi\)
\(758\) 19.7462 19.7462i 0.717214 0.717214i
\(759\) −0.525408 0.0845247i −0.0190711 0.00306805i
\(760\) 0.992411 + 1.18699i 0.0359985 + 0.0430566i
\(761\) 41.4873i 1.50391i −0.659213 0.751956i \(-0.729111\pi\)
0.659213 0.751956i \(-0.270889\pi\)
\(762\) −27.3195 + 19.7476i −0.989682 + 0.715381i
\(763\) −3.71192 3.71192i −0.134381 0.134381i
\(764\) −18.1677 −0.657284
\(765\) 6.97101 2.76282i 0.252038 0.0998901i
\(766\) −14.1963 −0.512932
\(767\) −31.4183 31.4183i −1.13445 1.13445i
\(768\) 1.40373 1.01467i 0.0506526 0.0366137i
\(769\) 45.6787i 1.64722i −0.567159 0.823608i \(-0.691958\pi\)
0.567159 0.823608i \(-0.308042\pi\)
\(770\) 0.0680135 0.761799i 0.00245104 0.0274533i
\(771\) −20.6325 3.31923i −0.743060 0.119539i
\(772\) −6.41622 + 6.41622i −0.230925 + 0.230925i
\(773\) 29.1634 29.1634i 1.04894 1.04894i 0.0501962 0.998739i \(-0.484015\pi\)
0.998739 0.0501962i \(-0.0159847\pi\)
\(774\) 27.0112 + 8.92170i 0.970896 + 0.320684i
\(775\) 22.2700 + 4.00848i 0.799961 + 0.143989i
\(776\) 18.1411i 0.651228i
\(777\) −2.83833 3.92665i −0.101825