Properties

Label 78.2.g.a.47.1
Level $78$
Weight $2$
Character 78.47
Analytic conductor $0.623$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 78.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.622833135766\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.58498535041007616.52
Defining polynomial: \( x^{12} - 12x^{9} + 72x^{6} - 324x^{3} + 729 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.1
Root \(1.54662 - 0.779723i\) of defining polynomial
Character \(\chi\) \(=\) 78.47
Dual form 78.2.g.a.5.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.64497 + 0.542278i) q^{3} -1.00000i q^{4} +(-2.32634 + 2.32634i) q^{5} +(0.779723 - 1.54662i) q^{6} +(-1.76690 + 1.76690i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.41187 - 1.78406i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.64497 + 0.542278i) q^{3} -1.00000i q^{4} +(-2.32634 + 2.32634i) q^{5} +(0.779723 - 1.54662i) q^{6} +(-1.76690 + 1.76690i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.41187 - 1.78406i) q^{9} -3.28995i q^{10} +(-1.08456 - 1.08456i) q^{11} +(0.542278 + 1.64497i) q^{12} +(0.766897 + 3.52305i) q^{13} -2.49877i q^{14} +(2.56525 - 5.08829i) q^{15} -1.00000 q^{16} +5.73724 q^{17} +(-0.443925 + 2.96697i) q^{18} +(2.28995 + 2.28995i) q^{19} +(2.32634 + 2.32634i) q^{20} +(1.94835 - 3.86465i) q^{21} +1.53379 q^{22} -4.65268 q^{23} +(-1.54662 - 0.779723i) q^{24} -5.82374i q^{25} +(-3.03345 - 1.94889i) q^{26} +(-3.00000 + 4.24264i) q^{27} +(1.76690 + 1.76690i) q^{28} +4.65268i q^{29} +(1.78406 + 5.41187i) q^{30} +(-3.82374 - 3.82374i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.37220 + 1.19593i) q^{33} +(-4.05684 + 4.05684i) q^{34} -8.22081i q^{35} +(-1.78406 - 2.41187i) q^{36} +(-3.05684 + 3.05684i) q^{37} -3.23847 q^{38} +(-3.17200 - 5.37945i) q^{39} -3.28995 q^{40} +(0.410044 - 0.410044i) q^{41} +(1.35503 + 4.11041i) q^{42} -0.222358i q^{43} +(-1.08456 + 1.08456i) q^{44} +(-1.46049 + 9.76118i) q^{45} +(3.28995 - 3.28995i) q^{46} +(7.65354 + 7.65354i) q^{47} +(1.64497 - 0.542278i) q^{48} +0.756152i q^{49} +(4.11801 + 4.11801i) q^{50} +(-9.43760 + 3.11118i) q^{51} +(3.52305 - 0.766897i) q^{52} -10.9689i q^{53} +(-0.878680 - 5.12132i) q^{54} +5.04610 q^{55} -2.49877 q^{56} +(-5.00868 - 2.52511i) q^{57} +(-3.28995 - 3.28995i) q^{58} +(4.65268 + 4.65268i) q^{59} +(-5.08829 - 2.56525i) q^{60} +3.06759 q^{61} +5.40758 q^{62} +(-1.10927 + 7.41378i) q^{63} +1.00000i q^{64} +(-9.97988 - 6.41175i) q^{65} +(-2.52305 + 0.831742i) q^{66} +(0.533794 + 0.533794i) q^{67} -5.73724i q^{68} +(7.65354 - 2.52305i) q^{69} +(5.81299 + 5.81299i) q^{70} +(5.48443 - 5.48443i) q^{71} +(2.96697 + 0.443925i) q^{72} +(2.28995 - 2.28995i) q^{73} -4.32303i q^{74} +(3.15808 + 9.57989i) q^{75} +(2.28995 - 2.28995i) q^{76} +3.83260 q^{77} +(6.04678 + 1.56090i) q^{78} +14.1137 q^{79} +(2.32634 - 2.32634i) q^{80} +(2.63423 - 8.60586i) q^{81} +0.579890i q^{82} +(-1.39902 + 1.39902i) q^{83} +(-3.86465 - 1.94835i) q^{84} +(-13.3468 + 13.3468i) q^{85} +(0.157231 + 0.157231i) q^{86} +(-2.52305 - 7.65354i) q^{87} -1.53379i q^{88} +(6.41175 + 6.41175i) q^{89} +(-5.86947 - 7.93492i) q^{90} +(-7.57989 - 4.86984i) q^{91} +4.65268i q^{92} +(8.36347 + 4.21642i) q^{93} -10.8237 q^{94} -10.6544 q^{95} +(-0.779723 + 1.54662i) q^{96} +(-11.5799 - 11.5799i) q^{97} +(-0.534680 - 0.534680i) q^{98} +(-4.55072 - 0.680889i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 12 q^{7} - 12 q^{16} - 12 q^{19} - 36 q^{27} + 12 q^{28} + 12 q^{31} + 36 q^{33} + 12 q^{37} + 36 q^{42} + 36 q^{45} + 12 q^{52} - 36 q^{54} - 36 q^{57} - 36 q^{63} - 12 q^{67} - 12 q^{73} - 12 q^{76} - 36 q^{78} + 72 q^{79} - 72 q^{85} - 12 q^{91} + 36 q^{93} - 72 q^{94} - 60 q^{97} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(67\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −1.64497 + 0.542278i −0.949725 + 0.313084i
\(4\) 1.00000i 0.500000i
\(5\) −2.32634 + 2.32634i −1.04037 + 1.04037i −0.0412220 + 0.999150i \(0.513125\pi\)
−0.999150 + 0.0412220i \(0.986875\pi\)
\(6\) 0.779723 1.54662i 0.318321 0.631405i
\(7\) −1.76690 + 1.76690i −0.667824 + 0.667824i −0.957212 0.289388i \(-0.906548\pi\)
0.289388 + 0.957212i \(0.406548\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 2.41187 1.78406i 0.803956 0.594688i
\(10\) 3.28995i 1.04037i
\(11\) −1.08456 1.08456i −0.327006 0.327006i 0.524441 0.851447i \(-0.324274\pi\)
−0.851447 + 0.524441i \(0.824274\pi\)
\(12\) 0.542278 + 1.64497i 0.156542 + 0.474863i
\(13\) 0.766897 + 3.52305i 0.212699 + 0.977118i
\(14\) 2.49877i 0.667824i
\(15\) 2.56525 5.08829i 0.662344 1.31379i
\(16\) −1.00000 −0.250000
\(17\) 5.73724 1.39149 0.695743 0.718291i \(-0.255075\pi\)
0.695743 + 0.718291i \(0.255075\pi\)
\(18\) −0.443925 + 2.96697i −0.104634 + 0.699322i
\(19\) 2.28995 + 2.28995i 0.525349 + 0.525349i 0.919182 0.393833i \(-0.128851\pi\)
−0.393833 + 0.919182i \(0.628851\pi\)
\(20\) 2.32634 + 2.32634i 0.520186 + 0.520186i
\(21\) 1.94835 3.86465i 0.425164 0.843335i
\(22\) 1.53379 0.327006
\(23\) −4.65268 −0.970152 −0.485076 0.874472i \(-0.661208\pi\)
−0.485076 + 0.874472i \(0.661208\pi\)
\(24\) −1.54662 0.779723i −0.315702 0.159160i
\(25\) 5.82374i 1.16475i
\(26\) −3.03345 1.94889i −0.594908 0.382209i
\(27\) −3.00000 + 4.24264i −0.577350 + 0.816497i
\(28\) 1.76690 + 1.76690i 0.333912 + 0.333912i
\(29\) 4.65268i 0.863982i 0.901878 + 0.431991i \(0.142189\pi\)
−0.901878 + 0.431991i \(0.857811\pi\)
\(30\) 1.78406 + 5.41187i 0.325724 + 0.988068i
\(31\) −3.82374 3.82374i −0.686764 0.686764i 0.274752 0.961515i \(-0.411404\pi\)
−0.961515 + 0.274752i \(0.911404\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 2.37220 + 1.19593i 0.412946 + 0.208185i
\(34\) −4.05684 + 4.05684i −0.695743 + 0.695743i
\(35\) 8.22081i 1.38957i
\(36\) −1.78406 2.41187i −0.297344 0.401978i
\(37\) −3.05684 + 3.05684i −0.502542 + 0.502542i −0.912227 0.409685i \(-0.865639\pi\)
0.409685 + 0.912227i \(0.365639\pi\)
\(38\) −3.23847 −0.525349
\(39\) −3.17200 5.37945i −0.507926 0.861401i
\(40\) −3.28995 −0.520186
\(41\) 0.410044 0.410044i 0.0640382 0.0640382i −0.674362 0.738401i \(-0.735581\pi\)
0.738401 + 0.674362i \(0.235581\pi\)
\(42\) 1.35503 + 4.11041i 0.209085 + 0.634250i
\(43\) 0.222358i 0.0339093i −0.999856 0.0169546i \(-0.994603\pi\)
0.999856 0.0169546i \(-0.00539709\pi\)
\(44\) −1.08456 + 1.08456i −0.163503 + 0.163503i
\(45\) −1.46049 + 9.76118i −0.217717 + 1.45511i
\(46\) 3.28995 3.28995i 0.485076 0.485076i
\(47\) 7.65354 + 7.65354i 1.11638 + 1.11638i 0.992268 + 0.124116i \(0.0396094\pi\)
0.124116 + 0.992268i \(0.460391\pi\)
\(48\) 1.64497 0.542278i 0.237431 0.0782711i
\(49\) 0.756152i 0.108022i
\(50\) 4.11801 + 4.11801i 0.582374 + 0.582374i
\(51\) −9.43760 + 3.11118i −1.32153 + 0.435652i
\(52\) 3.52305 0.766897i 0.488559 0.106349i
\(53\) 10.9689i 1.50669i −0.657627 0.753344i \(-0.728440\pi\)
0.657627 0.753344i \(-0.271560\pi\)
\(54\) −0.878680 5.12132i −0.119573 0.696923i
\(55\) 5.04610 0.680416
\(56\) −2.49877 −0.333912
\(57\) −5.00868 2.52511i −0.663416 0.334459i
\(58\) −3.28995 3.28995i −0.431991 0.431991i
\(59\) 4.65268 + 4.65268i 0.605728 + 0.605728i 0.941827 0.336099i \(-0.109108\pi\)
−0.336099 + 0.941827i \(0.609108\pi\)
\(60\) −5.08829 2.56525i −0.656896 0.331172i
\(61\) 3.06759 0.392764 0.196382 0.980527i \(-0.437081\pi\)
0.196382 + 0.980527i \(0.437081\pi\)
\(62\) 5.40758 0.686764
\(63\) −1.10927 + 7.41378i −0.139754 + 0.934049i
\(64\) 1.00000i 0.125000i
\(65\) −9.97988 6.41175i −1.23785 0.795280i
\(66\) −2.52305 + 0.831742i −0.310566 + 0.102380i
\(67\) 0.533794 + 0.533794i 0.0652133 + 0.0652133i 0.738961 0.673748i \(-0.235317\pi\)
−0.673748 + 0.738961i \(0.735317\pi\)
\(68\) 5.73724i 0.695743i
\(69\) 7.65354 2.52305i 0.921378 0.303739i
\(70\) 5.81299 + 5.81299i 0.694786 + 0.694786i
\(71\) 5.48443 5.48443i 0.650882 0.650882i −0.302324 0.953205i \(-0.597762\pi\)
0.953205 + 0.302324i \(0.0977623\pi\)
\(72\) 2.96697 + 0.443925i 0.349661 + 0.0523171i
\(73\) 2.28995 2.28995i 0.268018 0.268018i −0.560283 0.828301i \(-0.689308\pi\)
0.828301 + 0.560283i \(0.189308\pi\)
\(74\) 4.32303i 0.502542i
\(75\) 3.15808 + 9.57989i 0.364664 + 1.10619i
\(76\) 2.28995 2.28995i 0.262675 0.262675i
\(77\) 3.83260 0.436765
\(78\) 6.04678 + 1.56090i 0.684663 + 0.176738i
\(79\) 14.1137 1.58791 0.793957 0.607974i \(-0.208018\pi\)
0.793957 + 0.607974i \(0.208018\pi\)
\(80\) 2.32634 2.32634i 0.260093 0.260093i
\(81\) 2.63423 8.60586i 0.292692 0.956207i
\(82\) 0.579890i 0.0640382i
\(83\) −1.39902 + 1.39902i −0.153562 + 0.153562i −0.779707 0.626145i \(-0.784632\pi\)
0.626145 + 0.779707i \(0.284632\pi\)
\(84\) −3.86465 1.94835i −0.421667 0.212582i
\(85\) −13.3468 + 13.3468i −1.44766 + 1.44766i
\(86\) 0.157231 + 0.157231i 0.0169546 + 0.0169546i
\(87\) −2.52305 7.65354i −0.270499 0.820546i
\(88\) 1.53379i 0.163503i
\(89\) 6.41175 + 6.41175i 0.679644 + 0.679644i 0.959920 0.280275i \(-0.0904257\pi\)
−0.280275 + 0.959920i \(0.590426\pi\)
\(90\) −5.86947 7.93492i −0.618697 0.836414i
\(91\) −7.57989 4.86984i −0.794588 0.510497i
\(92\) 4.65268i 0.485076i
\(93\) 8.36347 + 4.21642i 0.867252 + 0.437222i
\(94\) −10.8237 −1.11638
\(95\) −10.6544 −1.09312
\(96\) −0.779723 + 1.54662i −0.0795801 + 0.157851i
\(97\) −11.5799 11.5799i −1.17576 1.17576i −0.980814 0.194946i \(-0.937547\pi\)
−0.194946 0.980814i \(-0.562453\pi\)
\(98\) −0.534680 0.534680i −0.0540108 0.0540108i
\(99\) −4.55072 0.680889i −0.457365 0.0684320i
\(100\) −5.82374 −0.582374
\(101\) −12.8235 −1.27599 −0.637993 0.770042i \(-0.720235\pi\)
−0.637993 + 0.770042i \(0.720235\pi\)
\(102\) 4.47346 8.87333i 0.442938 0.878591i
\(103\) 2.11368i 0.208267i 0.994563 + 0.104134i \(0.0332070\pi\)
−0.994563 + 0.104134i \(0.966793\pi\)
\(104\) −1.94889 + 3.03345i −0.191105 + 0.297454i
\(105\) 4.45797 + 13.5230i 0.435053 + 1.31971i
\(106\) 7.75615 + 7.75615i 0.753344 + 0.753344i
\(107\) 2.16911i 0.209696i 0.994488 + 0.104848i \(0.0334356\pi\)
−0.994488 + 0.104848i \(0.966564\pi\)
\(108\) 4.24264 + 3.00000i 0.408248 + 0.288675i
\(109\) 2.47695 + 2.47695i 0.237249 + 0.237249i 0.815710 0.578461i \(-0.196347\pi\)
−0.578461 + 0.815710i \(0.696347\pi\)
\(110\) −3.56813 + 3.56813i −0.340208 + 0.340208i
\(111\) 3.37076 6.68608i 0.319939 0.634615i
\(112\) 1.76690 1.76690i 0.166956 0.166956i
\(113\) 15.6215i 1.46955i 0.678310 + 0.734775i \(0.262712\pi\)
−0.678310 + 0.734775i \(0.737288\pi\)
\(114\) 5.32720 1.75615i 0.498938 0.164479i
\(115\) 10.8237 10.8237i 1.00932 1.00932i
\(116\) 4.65268 0.431991
\(117\) 8.13500 + 7.12894i 0.752081 + 0.659071i
\(118\) −6.57989 −0.605728
\(119\) −10.1371 + 10.1371i −0.929268 + 0.929268i
\(120\) 5.41187 1.78406i 0.494034 0.162862i
\(121\) 8.64748i 0.786134i
\(122\) −2.16911 + 2.16911i −0.196382 + 0.196382i
\(123\) −0.452154 + 0.896870i −0.0407693 + 0.0808680i
\(124\) −3.82374 + 3.82374i −0.343382 + 0.343382i
\(125\) 1.91630 + 1.91630i 0.171399 + 0.171399i
\(126\) −4.45797 6.02671i −0.397147 0.536902i
\(127\) 10.6936i 0.948901i 0.880282 + 0.474451i \(0.157353\pi\)
−0.880282 + 0.474451i \(0.842647\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 0.120580 + 0.365773i 0.0106165 + 0.0322045i
\(130\) 11.5906 2.52305i 1.01657 0.221286i
\(131\) 0.264467i 0.0231066i −0.999933 0.0115533i \(-0.996322\pi\)
0.999933 0.0115533i \(-0.00367761\pi\)
\(132\) 1.19593 2.37220i 0.104093 0.206473i
\(133\) −8.09219 −0.701682
\(134\) −0.754898 −0.0652133
\(135\) −2.89081 16.8489i −0.248801 1.45012i
\(136\) 4.05684 + 4.05684i 0.347871 + 0.347871i
\(137\) −3.66371 3.66371i −0.313012 0.313012i 0.533063 0.846075i \(-0.321041\pi\)
−0.846075 + 0.533063i \(0.821041\pi\)
\(138\) −3.62780 + 7.19593i −0.308819 + 0.612559i
\(139\) 2.22236 0.188498 0.0942490 0.995549i \(-0.469955\pi\)
0.0942490 + 0.995549i \(0.469955\pi\)
\(140\) −8.22081 −0.694786
\(141\) −16.7402 8.43952i −1.40978 0.710735i
\(142\) 7.75615i 0.650882i
\(143\) 2.98920 4.65268i 0.249969 0.389077i
\(144\) −2.41187 + 1.78406i −0.200989 + 0.148672i
\(145\) −10.8237 10.8237i −0.898863 0.898863i
\(146\) 3.23847i 0.268018i
\(147\) −0.410044 1.24385i −0.0338199 0.102591i
\(148\) 3.05684 + 3.05684i 0.251271 + 0.251271i
\(149\) 6.41175 6.41175i 0.525271 0.525271i −0.393887 0.919159i \(-0.628870\pi\)
0.919159 + 0.393887i \(0.128870\pi\)
\(150\) −9.00711 4.54090i −0.735427 0.370763i
\(151\) 0.812993 0.812993i 0.0661605 0.0661605i −0.673252 0.739413i \(-0.735103\pi\)
0.739413 + 0.673252i \(0.235103\pi\)
\(152\) 3.23847i 0.262675i
\(153\) 13.8375 10.2356i 1.11869 0.827500i
\(154\) −2.71005 + 2.71005i −0.218382 + 0.218382i
\(155\) 17.7907 1.42898
\(156\) −5.37945 + 3.17200i −0.430700 + 0.253963i
\(157\) 8.09219 0.645827 0.322914 0.946428i \(-0.395338\pi\)
0.322914 + 0.946428i \(0.395338\pi\)
\(158\) −9.97988 + 9.97988i −0.793957 + 0.793957i
\(159\) 5.94817 + 18.0435i 0.471720 + 1.43094i
\(160\) 3.28995i 0.260093i
\(161\) 8.22081 8.22081i 0.647891 0.647891i
\(162\) 4.22258 + 7.94794i 0.331757 + 0.624449i
\(163\) 17.2274 17.2274i 1.34935 1.34935i 0.462986 0.886366i \(-0.346778\pi\)
0.886366 0.462986i \(-0.153222\pi\)
\(164\) −0.410044 0.410044i −0.0320191 0.0320191i
\(165\) −8.30069 + 2.73639i −0.646208 + 0.213027i
\(166\) 1.97851i 0.153562i
\(167\) −6.82180 6.82180i −0.527886 0.527886i 0.392055 0.919942i \(-0.371764\pi\)
−0.919942 + 0.392055i \(0.871764\pi\)
\(168\) 4.11041 1.35503i 0.317125 0.104543i
\(169\) −11.8237 + 5.40363i −0.909518 + 0.415664i
\(170\) 18.8752i 1.44766i
\(171\) 9.60846 + 1.43764i 0.734777 + 0.109939i
\(172\) −0.222358 −0.0169546
\(173\) 1.85465 0.141006 0.0705032 0.997512i \(-0.477539\pi\)
0.0705032 + 0.997512i \(0.477539\pi\)
\(174\) 7.19593 + 3.62780i 0.545522 + 0.275023i
\(175\) 10.2899 + 10.2899i 0.777847 + 0.777847i
\(176\) 1.08456 + 1.08456i 0.0817515 + 0.0817515i
\(177\) −10.1766 5.13049i −0.764919 0.385631i
\(178\) −9.06759 −0.679644
\(179\) −0.264467 −0.0197672 −0.00988361 0.999951i \(-0.503146\pi\)
−0.00988361 + 0.999951i \(0.503146\pi\)
\(180\) 9.76118 + 1.46049i 0.727555 + 0.108858i
\(181\) 8.11368i 0.603085i 0.953453 + 0.301543i \(0.0975016\pi\)
−0.953453 + 0.301543i \(0.902498\pi\)
\(182\) 8.80329 1.91630i 0.652543 0.142045i
\(183\) −5.04610 + 1.66348i −0.373018 + 0.122968i
\(184\) −3.28995 3.28995i −0.242538 0.242538i
\(185\) 14.2225i 1.04566i
\(186\) −8.89533 + 2.93241i −0.652237 + 0.215015i
\(187\) −6.22236 6.22236i −0.455024 0.455024i
\(188\) 7.65354 7.65354i 0.558192 0.558192i
\(189\) −2.19562 12.7970i −0.159708 0.930845i
\(190\) 7.53379 7.53379i 0.546559 0.546559i
\(191\) 16.1272i 1.16692i 0.812142 + 0.583460i \(0.198302\pi\)
−0.812142 + 0.583460i \(0.801698\pi\)
\(192\) −0.542278 1.64497i −0.0391355 0.118716i
\(193\) −2.53379 + 2.53379i −0.182386 + 0.182386i −0.792395 0.610008i \(-0.791166\pi\)
0.610008 + 0.792395i \(0.291166\pi\)
\(194\) 16.3764 1.17576
\(195\) 19.8936 + 5.13529i 1.42461 + 0.367746i
\(196\) 0.756152 0.0540108
\(197\) −4.49545 + 4.49545i −0.320288 + 0.320288i −0.848877 0.528590i \(-0.822721\pi\)
0.528590 + 0.848877i \(0.322721\pi\)
\(198\) 3.69931 2.73639i 0.262898 0.194467i
\(199\) 23.1383i 1.64023i 0.572199 + 0.820115i \(0.306091\pi\)
−0.572199 + 0.820115i \(0.693909\pi\)
\(200\) 4.11801 4.11801i 0.291187 0.291187i
\(201\) −1.16754 0.588611i −0.0823519 0.0415174i
\(202\) 9.06759 9.06759i 0.637993 0.637993i
\(203\) −8.22081 8.22081i −0.576988 0.576988i
\(204\) 3.11118 + 9.43760i 0.217826 + 0.660764i
\(205\) 1.90781i 0.133247i
\(206\) −1.49460 1.49460i −0.104134 0.104134i
\(207\) −11.2217 + 8.30069i −0.779960 + 0.576938i
\(208\) −0.766897 3.52305i −0.0531747 0.244279i
\(209\) 4.96715i 0.343585i
\(210\) −12.7145 6.40996i −0.877382 0.442329i
\(211\) 15.2899 1.05260 0.526302 0.850298i \(-0.323578\pi\)
0.526302 + 0.850298i \(0.323578\pi\)
\(212\) −10.9689 −0.753344
\(213\) −6.04765 + 11.9958i −0.414378 + 0.821940i
\(214\) −1.53379 1.53379i −0.104848 0.104848i
\(215\) 0.517281 + 0.517281i 0.0352783 + 0.0352783i
\(216\) −5.12132 + 0.878680i −0.348462 + 0.0597866i
\(217\) 13.5123 0.917275
\(218\) −3.50294 −0.237249
\(219\) −2.52511 + 5.00868i −0.170631 + 0.338455i
\(220\) 5.04610i 0.340208i
\(221\) 4.39987 + 20.2126i 0.295967 + 1.35965i
\(222\) 2.34428 + 7.11126i 0.157338 + 0.477277i
\(223\) −3.30069 3.30069i −0.221031 0.221031i 0.587902 0.808932i \(-0.299954\pi\)
−0.808932 + 0.587902i \(0.799954\pi\)
\(224\) 2.49877i 0.166956i
\(225\) −10.3899 14.0461i −0.692662 0.936406i
\(226\) −11.0461 11.0461i −0.734775 0.734775i
\(227\) −4.33822 + 4.33822i −0.287938 + 0.287938i −0.836264 0.548326i \(-0.815265\pi\)
0.548326 + 0.836264i \(0.315265\pi\)
\(228\) −2.52511 + 5.00868i −0.167230 + 0.331708i
\(229\) 2.47695 2.47695i 0.163682 0.163682i −0.620514 0.784195i \(-0.713076\pi\)
0.784195 + 0.620514i \(0.213076\pi\)
\(230\) 15.3071i 1.00932i
\(231\) −6.30452 + 2.07833i −0.414807 + 0.136744i
\(232\) −3.28995 + 3.28995i −0.215995 + 0.215995i
\(233\) −12.0534 −0.789645 −0.394823 0.918757i \(-0.629194\pi\)
−0.394823 + 0.918757i \(0.629194\pi\)
\(234\) −10.7932 + 0.711393i −0.705576 + 0.0465052i
\(235\) −35.6095 −2.32291
\(236\) 4.65268 4.65268i 0.302864 0.302864i
\(237\) −23.2166 + 7.65354i −1.50808 + 0.497151i
\(238\) 14.3360i 0.929268i
\(239\) 14.7898 14.7898i 0.956672 0.956672i −0.0424271 0.999100i \(-0.513509\pi\)
0.999100 + 0.0424271i \(0.0135090\pi\)
\(240\) −2.56525 + 5.08829i −0.165586 + 0.328448i
\(241\) −12.3821 + 12.3821i −0.797604 + 0.797604i −0.982717 0.185114i \(-0.940735\pi\)
0.185114 + 0.982717i \(0.440735\pi\)
\(242\) 6.11469 + 6.11469i 0.393067 + 0.393067i
\(243\) 0.333537 + 15.5849i 0.0213964 + 0.999771i
\(244\) 3.06759i 0.196382i
\(245\) −1.75907 1.75907i −0.112383 0.112383i
\(246\) −0.314462 0.953903i −0.0200493 0.0608187i
\(247\) −6.31144 + 9.82374i −0.401587 + 0.625070i
\(248\) 5.40758i 0.343382i
\(249\) 1.54269 3.06000i 0.0977639 0.193920i
\(250\) −2.71005 −0.171399
\(251\) −12.2946 −0.776026 −0.388013 0.921654i \(-0.626839\pi\)
−0.388013 + 0.921654i \(0.626839\pi\)
\(252\) 7.41378 + 1.10927i 0.467024 + 0.0698772i
\(253\) 5.04610 + 5.04610i 0.317245 + 0.317245i
\(254\) −7.56150 7.56150i −0.474451 0.474451i
\(255\) 14.7174 29.1928i 0.921641 1.82812i
\(256\) 1.00000 0.0625000
\(257\) 30.0352 1.87355 0.936773 0.349938i \(-0.113797\pi\)
0.936773 + 0.349938i \(0.113797\pi\)
\(258\) −0.343903 0.173378i −0.0214105 0.0107940i
\(259\) 10.8022i 0.671219i
\(260\) −6.41175 + 9.97988i −0.397640 + 0.618926i
\(261\) 8.30069 + 11.2217i 0.513800 + 0.694604i
\(262\) 0.187007 + 0.187007i 0.0115533 + 0.0115533i
\(263\) 18.6107i 1.14759i −0.819000 0.573794i \(-0.805471\pi\)
0.819000 0.573794i \(-0.194529\pi\)
\(264\) 0.831742 + 2.52305i 0.0511902 + 0.155283i
\(265\) 25.5173 + 25.5173i 1.56752 + 1.56752i
\(266\) 5.72204 5.72204i 0.350841 0.350841i
\(267\) −14.0241 7.07020i −0.858261 0.432690i
\(268\) 0.533794 0.533794i 0.0326066 0.0326066i
\(269\) 0.820089i 0.0500017i 0.999687 + 0.0250008i \(0.00795884\pi\)
−0.999687 + 0.0250008i \(0.992041\pi\)
\(270\) 13.9581 + 9.86984i 0.849460 + 0.600659i
\(271\) −9.85909 + 9.85909i −0.598897 + 0.598897i −0.940019 0.341122i \(-0.889193\pi\)
0.341122 + 0.940019i \(0.389193\pi\)
\(272\) −5.73724 −0.347871
\(273\) 15.1095 + 3.90034i 0.914469 + 0.236059i
\(274\) 5.18127 0.313012
\(275\) −6.31617 + 6.31617i −0.380879 + 0.380879i
\(276\) −2.52305 7.65354i −0.151870 0.460689i
\(277\) 17.3871i 1.04469i −0.852733 0.522346i \(-0.825057\pi\)
0.852733 0.522346i \(-0.174943\pi\)
\(278\) −1.57144 + 1.57144i −0.0942490 + 0.0942490i
\(279\) −16.0442 2.40056i −0.960538 0.143718i
\(280\) 5.81299 5.81299i 0.347393 0.347393i
\(281\) 13.5480 + 13.5480i 0.808207 + 0.808207i 0.984362 0.176156i \(-0.0563662\pi\)
−0.176156 + 0.984362i \(0.556366\pi\)
\(282\) 17.8048 5.86947i 1.06026 0.349522i
\(283\) 17.6475i 1.04903i −0.851400 0.524517i \(-0.824246\pi\)
0.851400 0.524517i \(-0.175754\pi\)
\(284\) −5.48443 5.48443i −0.325441 0.325441i
\(285\) 17.5262 5.77764i 1.03816 0.342238i
\(286\) 1.17626 + 5.40363i 0.0695538 + 0.319523i
\(287\) 1.44901i 0.0855325i
\(288\) 0.443925 2.96697i 0.0261585 0.174831i
\(289\) 15.9159 0.936231
\(290\) 15.3071 0.898863
\(291\) 25.3281 + 12.7691i 1.48476 + 0.748537i
\(292\) −2.28995 2.28995i −0.134009 0.134009i
\(293\) −15.4643 15.4643i −0.903435 0.903435i 0.0922970 0.995732i \(-0.470579\pi\)
−0.995732 + 0.0922970i \(0.970579\pi\)
\(294\) 1.16948 + 0.589589i 0.0682054 + 0.0343855i
\(295\) −21.6475 −1.26036
\(296\) −4.32303 −0.251271
\(297\) 7.85505 1.34771i 0.455796 0.0782023i
\(298\) 9.06759i 0.525271i
\(299\) −3.56813 16.3916i −0.206350 0.947953i
\(300\) 9.57989 3.15808i 0.553095 0.182332i
\(301\) 0.392884 + 0.392884i 0.0226454 + 0.0226454i
\(302\) 1.14975i 0.0661605i
\(303\) 21.0943 6.95390i 1.21184 0.399491i
\(304\) −2.28995 2.28995i −0.131337 0.131337i
\(305\) −7.13626 + 7.13626i −0.408621 + 0.408621i
\(306\) −2.54690 + 17.0222i −0.145597 + 0.973097i
\(307\) −20.8698 + 20.8698i −1.19110 + 1.19110i −0.214347 + 0.976758i \(0.568762\pi\)
−0.976758 + 0.214347i \(0.931238\pi\)
\(308\) 3.83260i 0.218382i
\(309\) −1.14620 3.47695i −0.0652053 0.197797i
\(310\) −12.5799 + 12.5799i −0.714490 + 0.714490i
\(311\) 15.6215 0.885816 0.442908 0.896567i \(-0.353947\pi\)
0.442908 + 0.896567i \(0.353947\pi\)
\(312\) 1.56090 6.04678i 0.0883688 0.342332i
\(313\) 17.4036 0.983711 0.491856 0.870677i \(-0.336319\pi\)
0.491856 + 0.870677i \(0.336319\pi\)
\(314\) −5.72204 + 5.72204i −0.322914 + 0.322914i
\(315\) −14.6665 19.8275i −0.826362 1.11715i
\(316\) 14.1137i 0.793957i
\(317\) 2.89362 2.89362i 0.162522 0.162522i −0.621161 0.783683i \(-0.713339\pi\)
0.783683 + 0.621161i \(0.213339\pi\)
\(318\) −16.9646 8.55267i −0.951330 0.479610i
\(319\) 5.04610 5.04610i 0.282527 0.282527i
\(320\) −2.32634 2.32634i −0.130046 0.130046i
\(321\) −1.17626 3.56813i −0.0656525 0.199154i
\(322\) 11.6260i 0.647891i
\(323\) 13.1380 + 13.1380i 0.731016 + 0.731016i
\(324\) −8.60586 2.63423i −0.478103 0.146346i
\(325\) 20.5173 4.46621i 1.13810 0.247741i
\(326\) 24.3632i 1.34935i
\(327\) −5.41771 2.73132i −0.299600 0.151042i
\(328\) 0.579890 0.0320191
\(329\) −27.0460 −1.49110
\(330\) 3.93456 7.80439i 0.216590 0.429618i
\(331\) 2.06759 + 2.06759i 0.113645 + 0.113645i 0.761642 0.647998i \(-0.224393\pi\)
−0.647998 + 0.761642i \(0.724393\pi\)
\(332\) 1.39902 + 1.39902i 0.0767811 + 0.0767811i
\(333\) −1.91910 + 12.8263i −0.105166 + 0.702877i
\(334\) 9.64748 0.527886
\(335\) −2.48357 −0.135692
\(336\) −1.94835 + 3.86465i −0.106291 + 0.210834i
\(337\) 20.5634i 1.12016i −0.828438 0.560080i \(-0.810770\pi\)
0.828438 0.560080i \(-0.189230\pi\)
\(338\) 4.53970 12.1816i 0.246927 0.662591i
\(339\) −8.47122 25.6970i −0.460093 1.39567i
\(340\) 13.3468 + 13.3468i 0.723831 + 0.723831i
\(341\) 8.29412i 0.449152i
\(342\) −7.81077 + 5.77764i −0.422358 + 0.312419i
\(343\) −13.7043 13.7043i −0.739964 0.739964i
\(344\) 0.157231 0.157231i 0.00847732 0.00847732i
\(345\) −11.9353 + 23.6742i −0.642574 + 1.27458i
\(346\) −1.31144 + 1.31144i −0.0705032 + 0.0705032i
\(347\) 2.72473i 0.146271i −0.997322 0.0731357i \(-0.976699\pi\)
0.997322 0.0731357i \(-0.0233006\pi\)
\(348\) −7.65354 + 2.52305i −0.410273 + 0.135250i
\(349\) 21.6367 21.6367i 1.15819 1.15819i 0.173323 0.984865i \(-0.444550\pi\)
0.984865 0.173323i \(-0.0554503\pi\)
\(350\) −14.5522 −0.777847
\(351\) −17.2477 7.31548i −0.920615 0.390471i
\(352\) −1.53379 −0.0817515
\(353\) −1.49460 + 1.49460i −0.0795495 + 0.0795495i −0.745762 0.666212i \(-0.767914\pi\)
0.666212 + 0.745762i \(0.267914\pi\)
\(354\) 10.8237 3.56813i 0.575275 0.189644i
\(355\) 25.5173i 1.35432i
\(356\) 6.41175 6.41175i 0.339822 0.339822i
\(357\) 11.1781 22.1724i 0.591610 1.17349i
\(358\) 0.187007 0.187007i 0.00988361 0.00988361i
\(359\) 0.314462 + 0.314462i 0.0165967 + 0.0165967i 0.715356 0.698760i \(-0.246264\pi\)
−0.698760 + 0.715356i \(0.746264\pi\)
\(360\) −7.93492 + 5.86947i −0.418207 + 0.309348i
\(361\) 8.51230i 0.448016i
\(362\) −5.73724 5.73724i −0.301543 0.301543i
\(363\) 4.68934 + 14.2249i 0.246126 + 0.746612i
\(364\) −4.86984 + 7.57989i −0.255249 + 0.397294i
\(365\) 10.6544i 0.557676i
\(366\) 2.39187 4.74439i 0.125025 0.247993i
\(367\) 21.0461 1.09860 0.549299 0.835626i \(-0.314895\pi\)
0.549299 + 0.835626i \(0.314895\pi\)
\(368\) 4.65268 0.242538
\(369\) 0.257428 1.72052i 0.0134012 0.0895666i
\(370\) 10.0568 + 10.0568i 0.522830 + 0.522830i
\(371\) 19.3808 + 19.3808i 1.00620 + 1.00620i
\(372\) 4.21642 8.36347i 0.218611 0.433626i
\(373\) −4.22737 −0.218885 −0.109442 0.993993i \(-0.534907\pi\)
−0.109442 + 0.993993i \(0.534907\pi\)
\(374\) 8.79974 0.455024
\(375\) −4.19142 2.11309i −0.216444 0.109120i
\(376\) 10.8237i 0.558192i
\(377\) −16.3916 + 3.56813i −0.844212 + 0.183768i
\(378\) 10.6014 + 7.49631i 0.545276 + 0.385568i
\(379\) −18.1598 18.1598i −0.932805 0.932805i 0.0650751 0.997880i \(-0.479271\pi\)
−0.997880 + 0.0650751i \(0.979271\pi\)
\(380\) 10.6544i 0.546559i
\(381\) −5.79889 17.5906i −0.297086 0.901196i
\(382\) −11.4036 11.4036i −0.583460 0.583460i
\(383\) −19.4425 + 19.4425i −0.993464 + 0.993464i −0.999979 0.00651435i \(-0.997926\pi\)
0.00651435 + 0.999979i \(0.497926\pi\)
\(384\) 1.54662 + 0.779723i 0.0789256 + 0.0397901i
\(385\) −8.91593 + 8.91593i −0.454398 + 0.454398i
\(386\) 3.58333i 0.182386i
\(387\) −0.396701 0.536298i −0.0201654 0.0272616i
\(388\) −11.5799 + 11.5799i −0.587880 + 0.587880i
\(389\) 2.16911 0.109978 0.0549892 0.998487i \(-0.482488\pi\)
0.0549892 + 0.998487i \(0.482488\pi\)
\(390\) −17.6981 + 10.4357i −0.896177 + 0.528432i
\(391\) −26.6936 −1.34995
\(392\) −0.534680 + 0.534680i −0.0270054 + 0.0270054i
\(393\) 0.143415 + 0.435041i 0.00723432 + 0.0219449i
\(394\) 6.35753i 0.320288i
\(395\) −32.8333 + 32.8333i −1.65202 + 1.65202i
\(396\) −0.680889 + 4.55072i −0.0342160 + 0.228683i
\(397\) 10.2685 10.2685i 0.515359 0.515359i −0.400805 0.916164i \(-0.631269\pi\)
0.916164 + 0.400805i \(0.131269\pi\)
\(398\) −16.3612 16.3612i −0.820115 0.820115i
\(399\) 13.3114 4.38822i 0.666405 0.219686i
\(400\) 5.82374i 0.291187i
\(401\) 5.83282 + 5.83282i 0.291277 + 0.291277i 0.837585 0.546307i \(-0.183967\pi\)
−0.546307 + 0.837585i \(0.683967\pi\)
\(402\) 1.24179 0.409365i 0.0619347 0.0204172i
\(403\) 10.5388 16.4036i 0.524975 0.817123i
\(404\) 12.8235i 0.637993i
\(405\) 13.8921 + 26.1483i 0.690302 + 1.29932i
\(406\) 11.6260 0.576988
\(407\) 6.63063 0.328668
\(408\) −8.87333 4.47346i −0.439295 0.221469i
\(409\) −6.62599 6.62599i −0.327634 0.327634i 0.524052 0.851686i \(-0.324420\pi\)
−0.851686 + 0.524052i \(0.824420\pi\)
\(410\) −1.34902 1.34902i −0.0666235 0.0666235i
\(411\) 8.01346 + 4.03996i 0.395275 + 0.199276i
\(412\) 2.11368 0.104134
\(413\) −16.4416 −0.809040
\(414\) 2.06544 13.8044i 0.101511 0.678449i
\(415\) 6.50919i 0.319523i
\(416\) 3.03345 + 1.94889i 0.148727 + 0.0955524i
\(417\) −3.65572 + 1.20514i −0.179021 + 0.0590157i
\(418\) 3.51230 + 3.51230i 0.171792 + 0.171792i
\(419\) 8.41198i 0.410952i 0.978662 + 0.205476i \(0.0658743\pi\)
−0.978662 + 0.205476i \(0.934126\pi\)
\(420\) 13.5230 4.45797i 0.659855 0.217526i
\(421\) −0.964649 0.964649i −0.0470141 0.0470141i 0.683209 0.730223i \(-0.260584\pi\)
−0.730223 + 0.683209i \(0.760584\pi\)
\(422\) −10.8116 + 10.8116i −0.526302 + 0.526302i
\(423\) 32.1137 + 4.80493i 1.56142 + 0.233624i
\(424\) 7.75615 7.75615i 0.376672 0.376672i
\(425\) 33.4122i 1.62073i
\(426\) −4.20599 12.7587i −0.203781 0.618159i
\(427\) −5.42011 + 5.42011i −0.262297 + 0.262297i
\(428\) 2.16911 0.104848
\(429\) −2.39410 + 9.27452i −0.115588 + 0.447778i
\(430\) −0.731545 −0.0352783
\(431\) 25.4442 25.4442i 1.22560 1.22560i 0.259993 0.965610i \(-0.416280\pi\)
0.965610 0.259993i \(-0.0837203\pi\)
\(432\) 3.00000 4.24264i 0.144338 0.204124i
\(433\) 39.6740i 1.90661i 0.302010 + 0.953305i \(0.402342\pi\)
−0.302010 + 0.953305i \(0.597658\pi\)
\(434\) −9.55464 + 9.55464i −0.458637 + 0.458637i
\(435\) 23.6742 + 11.9353i 1.13509 + 0.572253i
\(436\) 2.47695 2.47695i 0.118624 0.118624i
\(437\) −10.6544 10.6544i −0.509669 0.509669i
\(438\) −1.75615 5.32720i −0.0839122 0.254543i
\(439\) 18.0000i 0.859093i 0.903045 + 0.429547i \(0.141327\pi\)
−0.903045 + 0.429547i \(0.858673\pi\)
\(440\) 3.56813 + 3.56813i 0.170104 + 0.170104i
\(441\) 1.34902 + 1.82374i 0.0642392 + 0.0868447i
\(442\) −17.4036 11.1813i −0.827806 0.531839i
\(443\) 31.9899i 1.51988i −0.649991 0.759942i \(-0.725227\pi\)
0.649991 0.759942i \(-0.274773\pi\)
\(444\) −6.68608 3.37076i −0.317307 0.159969i
\(445\) −29.8319 −1.41417
\(446\) 4.66788 0.221031
\(447\) −7.07020 + 14.0241i −0.334409 + 0.663318i
\(448\) −1.76690 1.76690i −0.0834780 0.0834780i
\(449\) 5.95612 + 5.95612i 0.281087 + 0.281087i 0.833542 0.552456i \(-0.186309\pi\)
−0.552456 + 0.833542i \(0.686309\pi\)
\(450\) 17.2789 + 2.58530i 0.814534 + 0.121872i
\(451\) −0.889432 −0.0418817
\(452\) 15.6215 0.734775
\(453\) −0.896483 + 1.77822i −0.0421205 + 0.0835481i
\(454\) 6.13517i 0.287938i
\(455\) 28.9623 6.30452i 1.35777 0.295560i
\(456\) −1.75615 5.32720i −0.0822393 0.249469i
\(457\) 10.4251 + 10.4251i 0.487667 + 0.487667i 0.907569 0.419903i \(-0.137936\pi\)
−0.419903 + 0.907569i \(0.637936\pi\)
\(458\) 3.50294i 0.163682i
\(459\) −17.2117 + 24.3411i −0.803374 + 1.13614i
\(460\) −10.8237 10.8237i −0.504659 0.504659i
\(461\) 27.4444 27.4444i 1.27821 1.27821i 0.336547 0.941667i \(-0.390741\pi\)
0.941667 0.336547i \(-0.109259\pi\)
\(462\) 2.98836 5.92757i 0.139031 0.275775i
\(463\) 8.89133 8.89133i 0.413215 0.413215i −0.469642 0.882857i \(-0.655617\pi\)
0.882857 + 0.469642i \(0.155617\pi\)
\(464\) 4.65268i 0.215995i
\(465\) −29.2651 + 9.64748i −1.35714 + 0.447391i
\(466\) 8.52305 8.52305i 0.394823 0.394823i
\(467\) −36.9303 −1.70893 −0.854466 0.519508i \(-0.826115\pi\)
−0.854466 + 0.519508i \(0.826115\pi\)
\(468\) 7.12894 8.13500i 0.329535 0.376041i
\(469\) −1.88632 −0.0871020
\(470\) 25.1797 25.1797i 1.16145 1.16145i
\(471\) −13.3114 + 4.38822i −0.613359 + 0.202198i
\(472\) 6.57989i 0.302864i
\(473\) −0.241160 + 0.241160i −0.0110885 + 0.0110885i
\(474\) 11.0048 21.8285i 0.505465 1.00262i
\(475\) 13.3360 13.3360i 0.611900 0.611900i
\(476\) 10.1371 + 10.1371i 0.464634 + 0.464634i
\(477\) −19.5691 26.4554i −0.896010 1.21131i
\(478\) 20.9159i 0.956672i
\(479\) −3.62978 3.62978i −0.165849 0.165849i 0.619303 0.785152i \(-0.287415\pi\)
−0.785152 + 0.619303i \(0.787415\pi\)
\(480\) −1.78406 5.41187i −0.0814310 0.247017i
\(481\) −13.1137 8.42512i −0.597933 0.384152i
\(482\) 17.5110i 0.797604i
\(483\) −9.06505 + 17.9810i −0.412474 + 0.818163i
\(484\) −8.64748 −0.393067
\(485\) 53.8776 2.44645
\(486\) −11.2560 10.7843i −0.510584 0.489187i
\(487\) 9.33604 + 9.33604i 0.423056 + 0.423056i 0.886255 0.463198i \(-0.153298\pi\)
−0.463198 + 0.886255i \(0.653298\pi\)
\(488\) 2.16911 + 2.16911i 0.0981911 + 0.0981911i
\(489\) −18.9965 + 37.6806i −0.859053 + 1.70397i
\(490\) 2.48770 0.112383
\(491\) 9.37867 0.423254 0.211627 0.977351i \(-0.432124\pi\)
0.211627 + 0.977351i \(0.432124\pi\)
\(492\) 0.896870 + 0.452154i 0.0404340 + 0.0203847i
\(493\) 26.6936i 1.20222i
\(494\) −2.48357 11.4093i −0.111741 0.513328i
\(495\) 12.1705 9.00256i 0.547024 0.404635i
\(496\) 3.82374 + 3.82374i 0.171691 + 0.171691i
\(497\) 19.3808i 0.869349i
\(498\) 1.07290 + 3.25459i 0.0480779 + 0.145842i
\(499\) −0.176261 0.176261i −0.00789054 0.00789054i 0.703151 0.711041i \(-0.251776\pi\)
−0.711041 + 0.703151i \(0.751776\pi\)
\(500\) 1.91630 1.91630i 0.0856995 0.0856995i
\(501\) 14.9210 + 7.52236i 0.666620 + 0.336074i
\(502\) 8.69357 8.69357i 0.388013 0.388013i
\(503\) 14.1725i 0.631922i −0.948772 0.315961i \(-0.897673\pi\)
0.948772 0.315961i \(-0.102327\pi\)
\(504\) −6.02671 + 4.45797i −0.268451 + 0.198574i
\(505\) 29.8319 29.8319i 1.32750 1.32750i
\(506\) −7.13626 −0.317245
\(507\) 16.5195 15.3006i 0.733655 0.679522i
\(508\) 10.6936 0.474451
\(509\) 0.724506 0.724506i 0.0321132 0.0321132i −0.690868 0.722981i \(-0.742771\pi\)
0.722981 + 0.690868i \(0.242771\pi\)
\(510\) 10.2356 + 31.0492i 0.453240 + 1.37488i
\(511\) 8.09219i 0.357978i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −16.5852 + 2.84558i −0.732257 + 0.125635i
\(514\) −21.2381 + 21.2381i −0.936773 + 0.936773i
\(515\) −4.91715 4.91715i −0.216676 0.216676i
\(516\) 0.365773 0.120580i 0.0161022 0.00530823i
\(517\) 16.6014i 0.730128i
\(518\) 7.63834 + 7.63834i 0.335610 + 0.335610i
\(519\) −3.05085 + 1.00574i −0.133917 + 0.0441469i
\(520\) −2.52305 11.5906i −0.110643 0.508283i
\(521\) 23.5279i 1.03078i 0.856957 + 0.515388i \(0.172352\pi\)
−0.856957 + 0.515388i \(0.827648\pi\)
\(522\) −13.8044 2.06544i −0.604202 0.0904020i
\(523\) −6.09219 −0.266393 −0.133197 0.991090i \(-0.542524\pi\)
−0.133197 + 0.991090i \(0.542524\pi\)
\(524\) −0.264467 −0.0115533
\(525\) −22.5067 11.3467i −0.982272 0.495209i
\(526\) 13.1598 + 13.1598i 0.573794 + 0.573794i
\(527\) −21.9377 21.9377i −0.955622 0.955622i
\(528\) −2.37220 1.19593i −0.103237 0.0520463i
\(529\) −1.35252 −0.0588053
\(530\) −36.0869 −1.56752
\(531\) 19.5224 + 2.92098i 0.847198 + 0.126760i
\(532\) 8.09219i 0.350841i
\(533\) 1.75907 + 1.13014i 0.0761937 + 0.0489520i
\(534\) 14.9159 4.91715i 0.645475 0.212786i
\(535\) −5.04610 5.04610i −0.218162 0.218162i
\(536\) 0.754898i 0.0326066i
\(537\) 0.435041 0.143415i 0.0187734 0.00618880i
\(538\) −0.579890 0.579890i −0.0250008 0.0250008i
\(539\) 0.820089 0.820089i 0.0353237 0.0353237i
\(540\) −16.8489 + 2.89081i −0.725060 + 0.124401i
\(541\) 14.5477 14.5477i 0.625453 0.625453i −0.321468 0.946920i \(-0.604176\pi\)
0.946920 + 0.321468i \(0.104176\pi\)
\(542\) 13.9429i 0.598897i
\(543\) −4.39987 13.3468i −0.188817 0.572765i
\(544\) 4.05684 4.05684i 0.173936 0.173936i
\(545\) −11.5245 −0.493654
\(546\) −13.4420 + 7.92609i −0.575264 + 0.339205i
\(547\) 16.1302 0.689676 0.344838 0.938662i \(-0.387934\pi\)
0.344838 + 0.938662i \(0.387934\pi\)
\(548\) −3.66371 + 3.66371i −0.156506 + 0.156506i
\(549\) 7.39862 5.47277i 0.315765 0.233572i
\(550\) 8.93241i 0.380879i
\(551\) −10.6544 + 10.6544i −0.453892 + 0.453892i
\(552\) 7.19593 + 3.62780i 0.306279 + 0.154410i
\(553\) −24.9374 + 24.9374i −1.06045 + 1.06045i
\(554\) 12.2946 + 12.2946i 0.522346 + 0.522346i
\(555\) 7.71256 + 23.3957i 0.327380 + 0.993090i
\(556\) 2.22236i 0.0942490i
\(557\) −6.66457 6.66457i −0.282387 0.282387i 0.551673 0.834060i \(-0.313989\pi\)
−0.834060 + 0.551673i \(0.813989\pi\)
\(558\) 13.0424 9.64748i 0.552128 0.408410i
\(559\) 0.783378 0.170526i 0.0331334 0.00721246i
\(560\) 8.22081i 0.347393i
\(561\) 13.6099 + 6.86136i 0.574609 + 0.289687i
\(562\) −19.1598 −0.808207
\(563\) 41.2952 1.74039 0.870193 0.492710i \(-0.163994\pi\)
0.870193 + 0.492710i \(0.163994\pi\)
\(564\) −8.43952 + 16.7402i −0.355368 + 0.704890i
\(565\) −36.3411 36.3411i −1.52888 1.52888i
\(566\) 12.4787 + 12.4787i 0.524517 + 0.524517i
\(567\) 10.5513 + 19.8601i 0.443111 + 0.834045i
\(568\) 7.75615 0.325441
\(569\) −9.35536 −0.392197 −0.196099 0.980584i \(-0.562827\pi\)
−0.196099 + 0.980584i \(0.562827\pi\)
\(570\) −8.30747 + 16.4783i −0.347962 + 0.690200i
\(571\) 9.96203i 0.416898i 0.978033 + 0.208449i \(0.0668415\pi\)
−0.978033 + 0.208449i \(0.933158\pi\)
\(572\) −4.65268 2.98920i −0.194539 0.124985i
\(573\) −8.74541 26.5287i −0.365345 1.10825i
\(574\) −1.02461 1.02461i −0.0427662 0.0427662i
\(575\) 27.0960i 1.12998i
\(576\) 1.78406 + 2.41187i 0.0743360 + 0.100495i
\(577\) 25.8022 + 25.8022i 1.07416 + 1.07416i 0.997020 + 0.0771415i \(0.0245793\pi\)
0.0771415 + 0.997020i \(0.475421\pi\)
\(578\) −11.2543 + 11.2543i −0.468116 + 0.468116i
\(579\) 2.79400 5.54204i 0.116115 0.230319i
\(580\) −10.8237 + 10.8237i −0.449431 + 0.449431i
\(581\) 4.94384i 0.205105i
\(582\) −26.9388 + 8.88058i −1.11665 + 0.368112i
\(583\) −11.8963 + 11.8963i −0.492696 + 0.492696i
\(584\) 3.23847 0.134009
\(585\) −35.5092 + 2.34044i −1.46812 + 0.0967655i
\(586\) 21.8698 0.903435
\(587\) 20.5387 20.5387i 0.847723 0.847723i −0.142126 0.989849i \(-0.545394\pi\)
0.989849 + 0.142126i \(0.0453938\pi\)
\(588\) −1.24385 + 0.410044i −0.0512954 + 0.0169099i
\(589\) 17.5123i 0.721582i
\(590\) 15.3071 15.3071i 0.630182 0.630182i
\(591\) 4.95711 9.83268i 0.203908 0.404463i
\(592\) 3.05684 3.05684i 0.125635 0.125635i
\(593\) −23.9379 23.9379i −0.983013 0.983013i 0.0168449 0.999858i \(-0.494638\pi\)
−0.999858 + 0.0168449i \(0.994638\pi\)
\(594\) −4.60138 + 6.50733i −0.188797 + 0.266999i
\(595\) 47.1648i 1.93357i
\(596\) −6.41175 6.41175i −0.262636 0.262636i
\(597\) −12.5474 38.0619i −0.513530 1.55777i
\(598\) 14.1137 + 9.06759i 0.577151 + 0.370801i
\(599\) 41.0774i 1.67838i 0.543841 + 0.839188i \(0.316969\pi\)
−0.543841 + 0.839188i \(0.683031\pi\)
\(600\) −4.54090 + 9.00711i −0.185382 + 0.367714i
\(601\) −32.0265 −1.30639 −0.653194 0.757191i \(-0.726571\pi\)
−0.653194 + 0.757191i \(0.726571\pi\)
\(602\) −0.555621 −0.0226454
\(603\) 2.23976 + 0.335118i 0.0912102 + 0.0136471i
\(604\) −0.812993 0.812993i −0.0330802 0.0330802i
\(605\) 20.1170 + 20.1170i 0.817872 + 0.817872i
\(606\) −9.99878 + 19.8331i −0.406173 + 0.805664i
\(607\) 32.9424 1.33709 0.668546 0.743671i \(-0.266917\pi\)
0.668546 + 0.743671i \(0.266917\pi\)
\(608\) 3.23847 0.131337
\(609\) 17.9810 + 9.06505i 0.728626 + 0.367334i
\(610\) 10.0922i 0.408621i
\(611\) −21.0943 + 32.8333i −0.853385 + 1.32829i
\(612\) −10.2356 13.8375i −0.413750 0.559347i
\(613\) 18.0296 + 18.0296i 0.728209 + 0.728209i 0.970263 0.242054i \(-0.0778210\pi\)
−0.242054 + 0.970263i \(0.577821\pi\)
\(614\) 29.5144i 1.19110i
\(615\) −1.03456 3.13829i −0.0417175 0.126548i
\(616\) 2.71005 + 2.71005i 0.109191 + 0.109191i
\(617\) −3.10809 + 3.10809i −0.125127 + 0.125127i −0.766897 0.641770i \(-0.778200\pi\)
0.641770 + 0.766897i \(0.278200\pi\)
\(618\) 3.26906 + 1.64809i 0.131501 + 0.0662958i
\(619\) −14.3114 + 14.3114i −0.575225 + 0.575225i −0.933584 0.358359i \(-0.883336\pi\)
0.358359 + 0.933584i \(0.383336\pi\)
\(620\) 17.7907i 0.714490i
\(621\) 13.9581 19.7397i 0.560117 0.792126i
\(622\) −11.0461 + 11.0461i −0.442908 + 0.442908i
\(623\) −22.6578 −0.907766
\(624\) 3.17200 + 5.37945i 0.126981 + 0.215350i
\(625\) 20.2028 0.808110
\(626\) −12.3062 + 12.3062i −0.491856 + 0.491856i
\(627\) 2.69357 + 8.17082i 0.107571 + 0.326311i
\(628\) 8.09219i 0.322914i
\(629\) −17.5378 + 17.5378i −0.699279 + 0.699279i
\(630\) 24.3909 + 3.64942i 0.971758 + 0.145397i
\(631\) −12.8130 + 12.8130i −0.510077 + 0.510077i −0.914550 0.404473i \(-0.867455\pi\)
0.404473 + 0.914550i \(0.367455\pi\)
\(632\) 9.97988 + 9.97988i 0.396978 + 0.396978i
\(633\) −25.1515 + 8.29140i −0.999684 + 0.329554i
\(634\) 4.09219i 0.162522i
\(635\) −24.8769 24.8769i −0.987210 0.987210i
\(636\) 18.0435 5.94817i 0.715470 0.235860i
\(637\) −2.66396 + 0.579890i −0.105550 + 0.0229761i
\(638\) 7.13626i 0.282527i
\(639\) 3.44315 23.0123i 0.136209 0.910352i
\(640\) 3.28995 0.130046
\(641\) −13.1147 −0.517998 −0.258999 0.965878i \(-0.583393\pi\)
−0.258999 + 0.965878i \(0.583393\pi\)
\(642\) 3.35479 + 1.69131i 0.132403 + 0.0667505i
\(643\) −5.60138 5.60138i −0.220897 0.220897i 0.587979 0.808876i \(-0.299924\pi\)
−0.808876 + 0.587979i \(0.799924\pi\)
\(644\) −8.22081 8.22081i −0.323945 0.323945i
\(645\) −1.13142 0.570403i −0.0445497 0.0224596i
\(646\) −18.5799 −0.731016
\(647\) 11.4745 0.451108 0.225554 0.974231i \(-0.427581\pi\)
0.225554 + 0.974231i \(0.427581\pi\)
\(648\) 7.94794 4.22258i 0.312225 0.165879i
\(649\) 10.0922i 0.396153i
\(650\) −11.3498 + 17.6660i −0.445178 + 0.692918i
\(651\) −22.2274 + 7.32742i −0.871159 + 0.287184i
\(652\) −17.2274 17.2274i −0.674676 0.674676i
\(653\) 12.1946i 0.477211i −0.971117 0.238605i \(-0.923310\pi\)
0.971117 0.238605i \(-0.0766903\pi\)
\(654\) 5.76224 1.89957i 0.225321 0.0742789i
\(655\) 0.615242 + 0.615242i 0.0240395 + 0.0240395i
\(656\) −0.410044 + 0.410044i −0.0160095 + 0.0160095i
\(657\) 1.43764 9.60846i 0.0560876 0.374862i
\(658\) 19.1244 19.1244i 0.745548 0.745548i
\(659\) 31.9632i 1.24511i −0.782577 0.622554i \(-0.786095\pi\)
0.782577 0.622554i \(-0.213905\pi\)
\(660\) 2.73639 + 8.30069i 0.106514 + 0.323104i
\(661\) −12.2470 + 12.2470i −0.476352 + 0.476352i −0.903963 0.427611i \(-0.859355\pi\)
0.427611 + 0.903963i \(0.359355\pi\)
\(662\) −2.92401 −0.113645
\(663\) −18.1985 30.8632i −0.706771 1.19863i
\(664\) −1.97851 −0.0767811
\(665\) 18.8252 18.8252i 0.730010 0.730010i
\(666\) −7.71256 10.4266i −0.298856 0.404022i
\(667\) 21.6475i 0.838194i
\(668\) −6.82180 + 6.82180i −0.263943 + 0.263943i
\(669\) 7.21944 + 3.63965i 0.279120 + 0.140717i
\(670\) 1.75615 1.75615i 0.0678461 0.0678461i
\(671\) −3.32697 3.32697i −0.128436 0.128436i
\(672\) −1.35503 4.11041i −0.0522713 0.158562i
\(673\) 41.8483i 1.61314i 0.591142 + 0.806568i \(0.298677\pi\)
−0.591142 + 0.806568i \(0.701323\pi\)
\(674\) 14.5405 + 14.5405i 0.560080 + 0.560080i
\(675\) 24.7080 + 17.4712i 0.951013 + 0.672467i
\(676\) 5.40363 + 11.8237i 0.207832 + 0.454759i
\(677\) 15.9360i 0.612470i 0.951956 + 0.306235i \(0.0990694\pi\)
−0.951956 + 0.306235i \(0.900931\pi\)
\(678\) 24.1606 + 12.1805i 0.927881 + 0.467788i
\(679\) 40.9209 1.57040
\(680\) −18.8752 −0.723831
\(681\) 4.78374 9.48878i 0.183313 0.363611i
\(682\) −5.86483 5.86483i −0.224576 0.224576i
\(683\) 23.5279 + 23.5279i 0.900270 + 0.900270i 0.995459 0.0951894i \(-0.0303457\pi\)
−0.0951894 + 0.995459i \(0.530346\pi\)
\(684\) 1.43764 9.60846i 0.0549695 0.367389i
\(685\) 17.0461 0.651298
\(686\) 19.3808 0.739964
\(687\) −2.73132 + 5.41771i −0.104206 + 0.206699i
\(688\) 0.222358i 0.00847732i
\(689\) 38.6438 8.41198i 1.47221 0.320471i
\(690\) −8.30069 25.1797i −0.316002 0.958576i
\(691\) 14.1763 + 14.1763i 0.539290 + 0.539290i 0.923321 0.384030i \(-0.125464\pi\)
−0.384030 + 0.923321i \(0.625464\pi\)
\(692\) 1.85465i 0.0705032i
\(693\) 9.24372 6.83760i 0.351140 0.259739i
\(694\) 1.92668 + 1.92668i 0.0731357 + 0.0731357i
\(695\) −5.16997 + 5.16997i −0.196108 + 0.196108i
\(696\) 3.62780 7.19593i 0.137512 0.272761i
\(697\) 2.35252 2.35252i 0.0891082 0.0891082i
\(698\) 30.5990i 1.15819i
\(699\) 19.8275 6.53630i 0.749946 0.247226i
\(700\) 10.2899 10.2899i 0.388923 0.388923i
\(701\) −22.9723 −0.867651 −0.433825 0.900997i \(-0.642837\pi\)
−0.433825 + 0.900997i \(0.642837\pi\)
\(702\) 17.3688 7.02315i 0.655543 0.265072i
\(703\) −14.0000 −0.528020
\(704\) 1.08456 1.08456i 0.0408757 0.0408757i
\(705\) 58.5767 19.3102i 2.20612 0.727266i
\(706\) 2.11368i 0.0795495i
\(707\) 22.6578 22.6578i 0.852135 0.852135i
\(708\) −5.13049 + 10.1766i −0.192816 + 0.382460i
\(709\) −3.10867 + 3.10867i −0.116749 + 0.116749i −0.763068 0.646319i \(-0.776308\pi\)
0.646319 + 0.763068i \(0.276308\pi\)
\(710\) −18.0435 18.0435i −0.677159 0.677159i
\(711\) 34.0404 25.1797i 1.27661 0.944313i
\(712\) 9.06759i 0.339822i
\(713\) 17.7907 + 17.7907i 0.666265 + 0.666265i
\(714\) 7.77412 + 23.5824i 0.290939 + 0.882549i
\(715\) 3.86984 + 17.7776i 0.144724 + 0.664846i
\(716\) 0.264467i 0.00988361i
\(717\) −16.3086 + 32.3490i −0.609057 + 1.20810i
\(718\) −0.444716 −0.0165967
\(719\) −8.46197 −0.315578 −0.157789 0.987473i \(-0.550437\pi\)
−0.157789 + 0.987473i \(0.550437\pi\)
\(720\) 1.46049 9.76118i 0.0544292 0.363778i
\(721\) −3.73466 3.73466i −0.139086 0.139086i
\(722\) 6.01911 + 6.01911i 0.224008 + 0.224008i
\(723\) 13.6537 27.0828i 0.507787 1.00722i
\(724\) 8.11368 0.301543
\(725\) 27.0960 1.00632
\(726\) −13.3744 6.74264i −0.496369 0.250243i
\(727\) 13.0461i 0.483853i −0.970295 0.241926i \(-0.922221\pi\)
0.970295 0.241926i \(-0.0777793\pi\)
\(728\) −1.91630 8.80329i −0.0710227 0.326271i
\(729\) −9.00000 25.4558i −0.333333 0.942809i
\(730\) −7.53379 7.53379i −0.278838 0.278838i
\(731\) 1.27572i 0.0471842i
\(732\) 1.66348 + 5.04610i 0.0614842 + 0.186509i
\(733\) −14.8180 14.8180i −0.547315 0.547315i 0.378348 0.925663i \(-0.376492\pi\)
−0.925663 + 0.378348i \(0.876492\pi\)
\(734\) −14.8818 + 14.8818i −0.549299 + 0.549299i
\(735\) 3.84752 + 1.93971i 0.141918 + 0.0715474i
\(736\) −3.28995 + 3.28995i −0.121269 + 0.121269i
\(737\) 1.15786i 0.0426502i
\(738\) 1.03456 + 1.39862i 0.0380827 + 0.0514839i
\(739\) −15.9159 + 15.9159i −0.585477 + 0.585477i −0.936403 0.350926i \(-0.885867\pi\)
0.350926 + 0.936403i \(0.385867\pi\)
\(740\) −14.2225 −0.522830
\(741\) 5.05494 19.5823i 0.185698 0.719375i
\(742\) −27.4086 −1.00620
\(743\) −12.3062 + 12.3062i −0.451472 + 0.451472i −0.895843 0.444371i \(-0.853427\pi\)
0.444371 + 0.895843i \(0.353427\pi\)
\(744\) 2.93241 + 8.89533i 0.107507 + 0.326118i
\(745\) 29.8319i 1.09295i
\(746\) 2.98920 2.98920i 0.109442 0.109442i
\(747\) −0.878310 + 5.87018i −0.0321357 + 0.214779i
\(748\) −6.22236 + 6.22236i −0.227512 + 0.227512i
\(749\) −3.83260 3.83260i −0.140040 0.140040i
\(750\) 4.45797 1.46960i 0.162782 0.0536623i
\(751\) 6.71506i 0.245036i 0.992466 + 0.122518i \(0.0390970\pi\)
−0.992466 + 0.122518i \(0.960903\pi\)
\(752\) −7.65354 7.65354i −0.279096 0.279096i
\(753\) 20.2242 6.66707i 0.737012 0.242962i
\(754\) 9.06759 14.1137i 0.330222 0.513990i
\(755\) 3.78260i 0.137663i
\(756\) −12.7970 + 2.19562i −0.465422 + 0.0798538i
\(757\) −35.1813 −1.27869 −0.639343 0.768922i \(-0.720793\pi\)
−0.639343 + 0.768922i \(0.720793\pi\)
\(758\) 25.6818 0.932805
\(759\) −11.0371 5.56430i −0.400621 0.201971i
\(760\) −7.53379 7.53379i −0.273279 0.273279i
\(761\) −25.5514 25.5514i −0.926238 0.926238i 0.0712220 0.997460i \(-0.477310\pi\)
−0.997460 + 0.0712220i \(0.977310\pi\)
\(762\) 16.5389 + 8.33802i 0.599141 + 0.302055i
\(763\) −8.75304 −0.316881
\(764\) 16.1272 0.583460
\(765\) −8.37918 + 56.0022i −0.302950 + 2.02477i
\(766\) 27.4958i 0.993464i
\(767\) −12.8235 + 19.9598i −0.463030 + 0.720705i
\(768\) −1.64497 + 0.542278i −0.0593578 + 0.0195678i
\(769\) −36.1433 36.1433i −1.30336 1.30336i −0.926112 0.377249i \(-0.876870\pi\)
−0.377249 0.926112i \(-0.623130\pi\)
\(770\) 12.6090i 0.454398i
\(771\) −49.4071 + 16.2874i −1.77935 + 0.586578i
\(772\) 2.53379 + 2.53379i 0.0911932 + 0.0911932i
\(773\) −32.0971 + 32.0971i −1.15445 + 1.15445i −0.168803 + 0.985650i \(0.553990\pi\)
−0.985650 + 0.168803i \(0.946010\pi\)
\(774\) 0.659730 + 0.0987103i 0.0237135 + 0.00354807i
\(775\) −22.2685 + 22.2685i −0.799907 + 0.799907i