Properties

Label 78.2.g.a.47.4
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 47.4
Root \(-0.779723 + 1.54662i\) of defining polynomial
Character \(\chi\) \(=\) 78.47
Dual form 78.2.g.a.5.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.64497 - 0.542278i) q^{3} -1.00000i q^{4} +(2.32634 - 2.32634i) q^{5} +(-1.54662 + 0.779723i) q^{6} +(-1.76690 + 1.76690i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.41187 + 1.78406i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.64497 - 0.542278i) q^{3} -1.00000i q^{4} +(2.32634 - 2.32634i) q^{5} +(-1.54662 + 0.779723i) 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} +(-5.08829 + 2.56525i) q^{15} -1.00000 q^{16} -5.73724 q^{17} +(2.96697 - 0.443925i) q^{18} +(2.28995 + 2.28995i) q^{19} +(-2.32634 - 2.32634i) q^{20} +(3.86465 - 1.94835i) q^{21} +1.53379 q^{22} +4.65268 q^{23} +(0.779723 + 1.54662i) 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} +(-1.19593 - 2.37220i) 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} +(0.648947 - 6.21119i) 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} +(9.76118 - 1.46049i) 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} +(-5.12132 - 0.878680i) q^{54} +5.04610 q^{55} +2.49877 q^{56} +(-2.52511 - 5.00868i) q^{57} +(-3.28995 - 3.28995i) q^{58} +(-4.65268 - 4.65268i) q^{59} +(2.56525 + 5.08829i) q^{60} +3.06759 q^{61} -5.40758 q^{62} +(-7.41378 + 1.10927i) 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} +(-0.443925 - 2.96697i) 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} +(-3.93310 - 4.85085i) 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} +(-1.94835 - 3.86465i) 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} +(4.21642 + 8.36347i) q^{93} -10.8237 q^{94} +10.6544 q^{95} +(1.54662 - 0.779723i) q^{96} +(-11.5799 - 11.5799i) q^{97} +(0.534680 + 0.534680i) q^{98} +(0.680889 + 4.55072i) 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 \(-0.486875\pi\)
0.999150 0.0412220i \(-0.0131251\pi\)
\(6\) −1.54662 + 0.779723i −0.631405 + 0.318321i
\(7\) −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 0.851447 0.524441i \(-0.175726\pi\)
−0.524441 + 0.851447i \(0.675726\pi\)
\(12\) −0.542278 + 1.64497i −0.156542 + 0.474863i
\(13\) 0.766897 + 3.52305i 0.212699 + 0.977118i
\(14\) 2.49877i 0.667824i
\(15\) −5.08829 + 2.56525i −1.31379 + 0.662344i
\(16\) −1.00000 −0.250000
\(17\) −5.73724 −1.39149 −0.695743 0.718291i \(-0.744925\pi\)
−0.695743 + 0.718291i \(0.744925\pi\)
\(18\) 2.96697 0.443925i 0.699322 0.104634i
\(19\) 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
\(21\) 3.86465 1.94835i 0.843335 0.425164i
\(22\) 1.53379 0.327006
\(23\) 4.65268 0.970152 0.485076 0.874472i \(-0.338792\pi\)
0.485076 + 0.874472i \(0.338792\pi\)
\(24\) 0.779723 + 1.54662i 0.159160 + 0.315702i
\(25\) 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 \(-0.857811\pi\)
0.901878 0.431991i \(-0.142189\pi\)
\(30\) −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
\(33\) −1.19593 2.37220i −0.208185 0.412946i
\(34\) −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
\(39\) 0.648947 6.21119i 0.103915 0.994586i
\(40\) −3.28995 −0.520186
\(41\) −0.410044 + 0.410044i −0.0640382 + 0.0640382i −0.738401 0.674362i \(-0.764419\pi\)
0.674362 + 0.738401i \(0.264419\pi\)
\(42\) 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
\(45\) 9.76118 1.46049i 1.45511 0.217717i
\(46\) 3.28995 3.28995i 0.485076 0.485076i
\(47\) −7.65354 7.65354i −1.11638 1.11638i −0.992268 0.124116i \(-0.960391\pi\)
−0.124116 0.992268i \(-0.539609\pi\)
\(48\) 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 \(0.271560\pi\)
−0.657627 + 0.753344i \(0.728440\pi\)
\(54\) −5.12132 0.878680i −0.696923 0.119573i
\(55\) 5.04610 0.680416
\(56\) 2.49877 0.333912
\(57\) −2.52511 5.00868i −0.334459 0.663416i
\(58\) −3.28995 3.28995i −0.431991 0.431991i
\(59\) −4.65268 4.65268i −0.605728 0.605728i 0.336099 0.941827i \(-0.390892\pi\)
−0.941827 + 0.336099i \(0.890892\pi\)
\(60\) 2.56525 + 5.08829i 0.331172 + 0.656896i
\(61\) 3.06759 0.392764 0.196382 0.980527i \(-0.437081\pi\)
0.196382 + 0.980527i \(0.437081\pi\)
\(62\) −5.40758 −0.686764
\(63\) −7.41378 + 1.10927i −0.934049 + 0.139754i
\(64\) 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 −0.953205 0.302324i \(-0.902238\pi\)
0.302324 + 0.953205i \(0.402238\pi\)
\(72\) −0.443925 2.96697i −0.0523171 0.349661i
\(73\) 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
\(78\) −3.93310 4.85085i −0.445336 0.549250i
\(79\) 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 −0.626145 0.779707i \(-0.715368\pi\)
0.779707 + 0.626145i \(0.215368\pi\)
\(84\) −1.94835 3.86465i −0.212582 0.421667i
\(85\) −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 0.280275 0.959920i \(-0.409574\pi\)
−0.959920 + 0.280275i \(0.909574\pi\)
\(90\) 5.86947 7.93492i 0.618697 0.836414i
\(91\) −7.57989 4.86984i −0.794588 0.510497i
\(92\) 4.65268i 0.485076i
\(93\) 4.21642 + 8.36347i 0.437222 + 0.867252i
\(94\) −10.8237 −1.11638
\(95\) 10.6544 1.09312
\(96\) 1.54662 0.779723i 0.157851 0.0795801i
\(97\) −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
\(99\) 0.680889 + 4.55072i 0.0684320 + 0.457365i
\(100\) −5.82374 −0.582374
\(101\) 12.8235 1.27599 0.637993 0.770042i \(-0.279765\pi\)
0.637993 + 0.770042i \(0.279765\pi\)
\(102\) 8.87333 4.47346i 0.878591 0.442938i
\(103\) 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 \(-0.966564\pi\)
0.994488 0.104848i \(-0.0334356\pi\)
\(108\) −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
\(111\) 6.68608 3.37076i 0.634615 0.319939i
\(112\) 1.76690 1.76690i 0.166956 0.166956i
\(113\) 15.6215i 1.46955i −0.678310 0.734775i \(-0.737288\pi\)
0.678310 0.734775i \(-0.262712\pi\)
\(114\) −5.32720 1.75615i −0.498938 0.164479i
\(115\) 10.8237 10.8237i 1.00932 1.00932i
\(116\) −4.65268 −0.431991
\(117\) −4.43569 + 9.86533i −0.410080 + 0.912050i
\(118\) −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
\(123\) 0.896870 0.452154i 0.0808680 0.0407693i
\(124\) −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 \(0.00367761\pi\)
−0.999933 + 0.0115533i \(0.996322\pi\)
\(132\) −2.37220 + 1.19593i −0.206473 + 0.104093i
\(133\) −8.09219 −0.701682
\(134\) 0.754898 0.0652133
\(135\) −16.8489 2.89081i −1.45012 0.248801i
\(136\) 4.05684 + 4.05684i 0.347871 + 0.347871i
\(137\) 3.66371 + 3.66371i 0.313012 + 0.313012i 0.846075 0.533063i \(-0.178959\pi\)
−0.533063 + 0.846075i \(0.678959\pi\)
\(138\) −7.19593 + 3.62780i −0.612559 + 0.308819i
\(139\) 2.22236 0.188498 0.0942490 0.995549i \(-0.469955\pi\)
0.0942490 + 0.995549i \(0.469955\pi\)
\(140\) 8.22081 0.694786
\(141\) 8.43952 + 16.7402i 0.710735 + 1.40978i
\(142\) 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 −0.919159 0.393887i \(-0.871130\pi\)
0.393887 + 0.919159i \(0.371130\pi\)
\(150\) 4.54090 + 9.00711i 0.370763 + 0.735427i
\(151\) 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
\(156\) −6.21119 0.648947i −0.497293 0.0519574i
\(157\) 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
\(162\) 7.94794 + 4.22258i 0.624449 + 0.331757i
\(163\) 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 0.919942 0.392055i \(-0.128236\pi\)
−0.392055 + 0.919942i \(0.628236\pi\)
\(168\) −4.11041 1.35503i −0.317125 0.104543i
\(169\) −11.8237 + 5.40363i −0.909518 + 0.415664i
\(170\) 18.8752i 1.44766i
\(171\) 1.43764 + 9.60846i 0.109939 + 0.734777i
\(172\) −0.222358 −0.0169546
\(173\) −1.85465 −0.141006 −0.0705032 0.997512i \(-0.522461\pi\)
−0.0705032 + 0.997512i \(0.522461\pi\)
\(174\) 3.62780 + 7.19593i 0.275023 + 0.545522i
\(175\) 10.2899 + 10.2899i 0.777847 + 0.777847i
\(176\) −1.08456 1.08456i −0.0817515 0.0817515i
\(177\) 5.13049 + 10.1766i 0.385631 + 0.764919i
\(178\) −9.06759 −0.679644
\(179\) 0.264467 0.0197672 0.00988361 0.999951i \(-0.496854\pi\)
0.00988361 + 0.999951i \(0.496854\pi\)
\(180\) −1.46049 9.76118i −0.108858 0.727555i
\(181\) 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
\(189\) 12.7970 + 2.19562i 0.930845 + 0.159708i
\(190\) 7.53379 7.53379i 0.546559 0.546559i
\(191\) 16.1272i 1.16692i −0.812142 0.583460i \(-0.801698\pi\)
0.812142 0.583460i \(-0.198302\pi\)
\(192\) 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
\(195\) −12.9397 15.9590i −0.926630 1.14285i
\(196\) 0.756152 0.0540108
\(197\) 4.49545 4.49545i 0.320288 0.320288i −0.528590 0.848877i \(-0.677279\pi\)
0.848877 + 0.528590i \(0.177279\pi\)
\(198\) 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
\(201\) −0.588611 1.16754i −0.0415174 0.0823519i
\(202\) 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
\(210\) −6.40996 12.7145i −0.442329 0.877382i
\(211\) 15.2899 1.05260 0.526302 0.850298i \(-0.323578\pi\)
0.526302 + 0.850298i \(0.323578\pi\)
\(212\) 10.9689 0.753344
\(213\) 11.9958 6.04765i 0.821940 0.414378i
\(214\) −1.53379 1.53379i −0.104848 0.104848i
\(215\) −0.517281 0.517281i −0.0352783 0.0352783i
\(216\) −0.878680 + 5.12132i −0.0597866 + 0.348462i
\(217\) 13.5123 0.917275
\(218\) 3.50294 0.237249
\(219\) −5.00868 + 2.52511i −0.338455 + 0.170631i
\(220\) 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 −0.548326 0.836264i \(-0.684735\pi\)
0.836264 + 0.548326i \(0.184735\pi\)
\(228\) −5.00868 + 2.52511i −0.331708 + 0.167230i
\(229\) 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 \(-0.370806\pi\)
0.394823 + 0.918757i \(0.370806\pi\)
\(234\) 3.83933 + 10.1123i 0.250985 + 0.661065i
\(235\) −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 −0.999100 0.0424271i \(-0.986491\pi\)
0.0424271 + 0.999100i \(0.486491\pi\)
\(240\) 5.08829 2.56525i 0.328448 0.165586i
\(241\) −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
\(249\) −3.06000 + 1.54269i −0.193920 + 0.0977639i
\(250\) −2.71005 −0.171399
\(251\) 12.2946 0.776026 0.388013 0.921654i \(-0.373161\pi\)
0.388013 + 0.921654i \(0.373161\pi\)
\(252\) 1.10927 + 7.41378i 0.0698772 + 0.467024i
\(253\) 5.04610 + 5.04610i 0.317245 + 0.317245i
\(254\) 7.56150 + 7.56150i 0.474451 + 0.474451i
\(255\) 29.1928 14.7174i 1.82812 0.921641i
\(256\) 1.00000 0.0625000
\(257\) −30.0352 −1.87355 −0.936773 0.349938i \(-0.886203\pi\)
−0.936773 + 0.349938i \(0.886203\pi\)
\(258\) 0.173378 + 0.343903i 0.0107940 + 0.0214105i
\(259\) 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 \(0.194529\pi\)
−0.819000 + 0.573794i \(0.805471\pi\)
\(264\) −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
\(267\) 7.07020 + 14.0241i 0.432690 + 0.858261i
\(268\) 0.533794 0.533794i 0.0326066 0.0326066i
\(269\) 0.820089i 0.0500017i −0.999687 0.0250008i \(-0.992041\pi\)
0.999687 0.0250008i \(-0.00795884\pi\)
\(270\) −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
\(273\) 9.82791 + 12.1212i 0.594812 + 0.733606i
\(274\) 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
\(279\) −2.40056 16.0442i −0.143718 0.960538i
\(280\) 5.81299 5.81299i 0.347393 0.347393i
\(281\) −13.5480 13.5480i −0.808207 0.808207i 0.176156 0.984362i \(-0.443634\pi\)
−0.984362 + 0.176156i \(0.943634\pi\)
\(282\) 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
\(288\) −2.96697 + 0.443925i −0.174831 + 0.0261585i
\(289\) 15.9159 0.936231
\(290\) −15.3071 −0.898863
\(291\) 12.7691 + 25.3281i 0.748537 + 1.48476i
\(292\) −2.28995 2.28995i −0.134009 0.134009i
\(293\) 15.4643 + 15.4643i 0.903435 + 0.903435i 0.995732 0.0922970i \(-0.0294209\pi\)
−0.0922970 + 0.995732i \(0.529421\pi\)
\(294\) −0.589589 1.16948i −0.0343855 0.0682054i
\(295\) −21.6475 −1.26036
\(296\) 4.32303 0.251271
\(297\) 1.34771 7.85505i 0.0782023 0.455796i
\(298\) 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
\(306\) −17.0222 + 2.54690i −0.973097 + 0.145597i
\(307\) −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 \(-0.646053\pi\)
−0.442908 + 0.896567i \(0.646053\pi\)
\(312\) −4.85085 + 3.93310i −0.274625 + 0.222668i
\(313\) 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 −0.783683 0.621161i \(-0.786661\pi\)
0.621161 + 0.783683i \(0.286661\pi\)
\(318\) −8.55267 16.9646i −0.479610 0.951330i
\(319\) 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
\(327\) −2.73132 5.41771i −0.151042 0.299600i
\(328\) 0.579890 0.0320191
\(329\) 27.0460 1.49110
\(330\) −7.80439 + 3.93456i −0.429618 + 0.216590i
\(331\) 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
\(333\) −12.8263 + 1.91910i −0.702877 + 0.105166i
\(334\) 9.64748 0.527886
\(335\) 2.48357 0.135692
\(336\) −3.86465 + 1.94835i −0.210834 + 0.106291i
\(337\) 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
\(345\) −23.6742 + 11.9353i −1.27458 + 0.642574i
\(346\) −1.31144 + 1.31144i −0.0705032 + 0.0705032i
\(347\) 2.72473i 0.146271i 0.997322 + 0.0731357i \(0.0233006\pi\)
−0.997322 + 0.0731357i \(0.976699\pi\)
\(348\) 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
\(351\) 12.6463 13.8228i 0.675012 0.737807i
\(352\) −1.53379 −0.0817515
\(353\) 1.49460 1.49460i 0.0795495 0.0795495i −0.666212 0.745762i \(-0.732086\pi\)
0.745762 + 0.666212i \(0.232086\pi\)
\(354\) 10.8237 + 3.56813i 0.575275 + 0.189644i
\(355\) 25.5173i 1.35432i
\(356\) −6.41175 + 6.41175i −0.339822 + 0.339822i
\(357\) −22.1724 + 11.1781i −1.17349 + 0.591610i
\(358\) 0.187007 0.187007i 0.00988361 0.00988361i
\(359\) −0.314462 0.314462i −0.0165967 0.0165967i 0.698760 0.715356i \(-0.253736\pi\)
−0.715356 + 0.698760i \(0.753736\pi\)
\(360\) −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
\(366\) −4.74439 + 2.39187i −0.247993 + 0.125025i
\(367\) 21.0461 1.09860 0.549299 0.835626i \(-0.314895\pi\)
0.549299 + 0.835626i \(0.314895\pi\)
\(368\) −4.65268 −0.242538
\(369\) −1.72052 + 0.257428i −0.0895666 + 0.0134012i
\(370\) 10.0568 + 10.0568i 0.522830 + 0.522830i
\(371\) −19.3808 19.3808i −1.00620 1.00620i
\(372\) 8.36347 4.21642i 0.433626 0.218611i
\(373\) −4.22737 −0.218885 −0.109442 0.993993i \(-0.534907\pi\)
−0.109442 + 0.993993i \(0.534907\pi\)
\(374\) −8.79974 −0.455024
\(375\) 2.11309 + 4.19142i 0.109120 + 0.216444i
\(376\) 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 −0.00651435 0.999979i \(-0.502074\pi\)
0.999979 + 0.00651435i \(0.00207360\pi\)
\(384\) −0.779723 1.54662i −0.0397901 0.0789256i
\(385\) −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 \(-0.517512\pi\)
−0.0549892 + 0.998487i \(0.517512\pi\)
\(390\) −20.4345 2.13500i −1.03474 0.108110i
\(391\) −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
\(396\) 4.55072 0.680889i 0.228683 0.0342160i
\(397\) 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 0.546307 0.837585i \(-0.316033\pi\)
−0.837585 + 0.546307i \(0.816033\pi\)
\(402\) −1.24179 0.409365i −0.0619347 0.0204172i
\(403\) 10.5388 16.4036i 0.524975 0.817123i
\(404\) 12.8235i 0.637993i
\(405\) 26.1483 + 13.8921i 1.29932 + 0.690302i
\(406\) 11.6260 0.576988
\(407\) −6.63063 −0.328668
\(408\) −4.47346 8.87333i −0.221469 0.439295i
\(409\) −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
\(411\) −4.03996 8.01346i −0.199276 0.395275i
\(412\) 2.11368 0.104134
\(413\) 16.4416 0.809040
\(414\) 13.8044 2.06544i 0.678449 0.101511i
\(415\) 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 \(-0.934126\pi\)
0.978662 0.205476i \(-0.0658743\pi\)
\(420\) −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
\(423\) −4.80493 32.1137i −0.233624 1.56142i
\(424\) 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
\(429\) 7.44020 6.03256i 0.359216 0.291255i
\(430\) −0.731545 −0.0352783
\(431\) −25.4442 + 25.4442i −1.22560 + 1.22560i −0.259993 + 0.965610i \(0.583720\pi\)
−0.965610 + 0.259993i \(0.916280\pi\)
\(432\) 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
\(435\) 11.9353 + 23.6742i 0.572253 + 1.13509i
\(436\) 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 \(0.274773\pi\)
−0.649991 + 0.759942i \(0.725227\pi\)
\(444\) −3.37076 6.68608i −0.159969 0.317307i
\(445\) −29.8319 −1.41417
\(446\) −4.66788 −0.221031
\(447\) 14.0241 7.07020i 0.663318 0.334409i
\(448\) −1.76690 1.76690i −0.0834780 0.0834780i
\(449\) −5.95612 5.95612i −0.281087 0.281087i 0.552456 0.833542i \(-0.313691\pi\)
−0.833542 + 0.552456i \(0.813691\pi\)
\(450\) −2.58530 17.2789i −0.121872 0.814534i
\(451\) −0.889432 −0.0418817
\(452\) −15.6215 −0.734775
\(453\) −1.77822 + 0.896483i −0.0835481 + 0.0421205i
\(454\) 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 \(0.609259\pi\)
−0.941667 + 0.336547i \(0.890741\pi\)
\(462\) 5.92757 2.98836i 0.275775 0.139031i
\(463\) 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 \(-0.173885\pi\)
0.854466 + 0.519508i \(0.173885\pi\)
\(468\) 9.86533 + 4.43569i 0.456025 + 0.205040i
\(469\) −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
\(474\) −21.8285 + 11.0048i −1.00262 + 0.505465i
\(475\) 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 0.785152 0.619303i \(-0.212585\pi\)
−0.619303 + 0.785152i \(0.712585\pi\)
\(480\) 1.78406 5.41187i 0.0814310 0.247017i
\(481\) −13.1137 8.42512i −0.597933 0.384152i
\(482\) 17.5110i 0.797604i
\(483\) 17.9810 9.06505i 0.818163 0.412474i
\(484\) −8.64748 −0.393067
\(485\) −53.8776 −2.44645
\(486\) −10.7843 11.2560i −0.489187 0.510584i
\(487\) 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
\(489\) −37.6806 + 18.9965i −1.70397 + 0.859053i
\(490\) 2.48770 0.112383
\(491\) −9.37867 −0.423254 −0.211627 0.977351i \(-0.567876\pi\)
−0.211627 + 0.977351i \(0.567876\pi\)
\(492\) −0.452154 0.896870i −0.0203847 0.0404340i
\(493\) 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
\(501\) −7.52236 14.9210i −0.336074 0.666620i
\(502\) 8.69357 8.69357i 0.388013 0.388013i
\(503\) 14.1725i 0.631922i 0.948772 + 0.315961i \(0.102327\pi\)
−0.948772 + 0.315961i \(0.897673\pi\)
\(504\) 6.02671 + 4.45797i 0.268451 + 0.198574i
\(505\) 29.8319 29.8319i 1.32750 1.32750i
\(506\) 7.13626 0.317245
\(507\) 22.3800 2.47707i 0.993930 0.110010i
\(508\) 10.6936 0.474451
\(509\) −0.724506 + 0.724506i −0.0321132 + 0.0321132i −0.722981 0.690868i \(-0.757229\pi\)
0.690868 + 0.722981i \(0.257229\pi\)
\(510\) 10.2356 31.0492i 0.453240 1.37488i
\(511\) 8.09219i 0.357978i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 2.84558 16.5852i 0.125635 0.732257i
\(514\) −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 \(-0.827648\pi\)
0.856957 0.515388i \(-0.172352\pi\)
\(522\) −2.06544 13.8044i −0.0904020 0.604202i
\(523\) −6.09219 −0.266393 −0.133197 0.991090i \(-0.542524\pi\)
−0.133197 + 0.991090i \(0.542524\pi\)
\(524\) 0.264467 0.0115533
\(525\) −11.3467 22.5067i −0.495209 0.982272i
\(526\) 13.1598 + 13.1598i 0.573794 + 0.573794i
\(527\) 21.9377 + 21.9377i 0.955622 + 0.955622i
\(528\) 1.19593 + 2.37220i 0.0520463 + 0.103237i
\(529\) −1.35252 −0.0588053
\(530\) 36.0869 1.56752
\(531\) −2.92098 19.5224i −0.126760 0.847198i
\(532\) 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
\(540\) −2.89081 + 16.8489i −0.124401 + 0.725060i
\(541\) 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
\(546\) 15.5203 + 1.62157i 0.664209 + 0.0693968i
\(547\) 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
\(552\) 3.62780 + 7.19593i 0.154410 + 0.306279i
\(553\) −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 0.834060 0.551673i \(-0.186011\pi\)
−0.551673 + 0.834060i \(0.686011\pi\)
\(558\) −13.0424 9.64748i −0.552128 0.408410i
\(559\) 0.783378 0.170526i 0.0331334 0.00721246i
\(560\) 8.22081i 0.347393i
\(561\) 6.86136 + 13.6099i 0.289687 + 0.574609i
\(562\) −19.1598 −0.808207
\(563\) −41.2952 −1.74039 −0.870193 0.492710i \(-0.836006\pi\)
−0.870193 + 0.492710i \(0.836006\pi\)
\(564\) 16.7402 8.43952i 0.704890 0.355368i
\(565\) −36.3411 36.3411i −1.52888 1.52888i
\(566\) −12.4787 12.4787i −0.524517 0.524517i
\(567\) −19.8601 10.5513i −0.834045 0.443111i
\(568\) 7.75615 0.325441
\(569\) 9.35536 0.392197 0.196099 0.980584i \(-0.437173\pi\)
0.196099 + 0.980584i \(0.437173\pi\)
\(570\) −16.4783 + 8.30747i −0.690200 + 0.347962i
\(571\) 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
\(579\) 5.54204 2.79400i 0.230319 0.116115i
\(580\) −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
\(585\) 12.6312 + 33.2691i 0.522235 + 1.37551i
\(586\) 21.8698 0.903435
\(587\) −20.5387 + 20.5387i −0.847723 + 0.847723i −0.989849 0.142126i \(-0.954606\pi\)
0.142126 + 0.989849i \(0.454606\pi\)
\(588\) −1.24385 0.410044i −0.0512954 0.0169099i
\(589\) 17.5123i 0.721582i
\(590\) −15.3071 + 15.3071i −0.630182 + 0.630182i
\(591\) −9.83268 + 4.95711i −0.404463 + 0.203908i
\(592\) 3.05684 3.05684i 0.125635 0.125635i
\(593\) 23.9379 + 23.9379i 0.983013 + 0.983013i 0.999858 0.0168449i \(-0.00536215\pi\)
−0.0168449 + 0.999858i \(0.505362\pi\)
\(594\) −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 \(-0.683031\pi\)
0.543841 0.839188i \(-0.316969\pi\)
\(600\) 9.00711 4.54090i 0.367714 0.185382i
\(601\) −32.0265 −1.30639 −0.653194 0.757191i \(-0.726571\pi\)
−0.653194 + 0.757191i \(0.726571\pi\)
\(602\) 0.555621 0.0226454
\(603\) 0.335118 + 2.23976i 0.0136471 + 0.0912102i
\(604\) −0.812993 0.812993i −0.0330802 0.0330802i
\(605\) −20.1170 20.1170i −0.817872 0.817872i
\(606\) −19.8331 + 9.99878i −0.805664 + 0.406173i
\(607\) 32.9424 1.33709 0.668546 0.743671i \(-0.266917\pi\)
0.668546 + 0.743671i \(0.266917\pi\)
\(608\) −3.23847 −0.131337
\(609\) −9.06505 17.9810i −0.367334 0.728626i
\(610\) 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 −0.641770 0.766897i \(-0.721800\pi\)
0.766897 + 0.641770i \(0.221800\pi\)
\(618\) −1.64809 3.26906i −0.0662958 0.131501i
\(619\) −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
\(624\) −0.648947 + 6.21119i −0.0259787 + 0.248647i
\(625\) 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
\(630\) 3.64942 + 24.3909i 0.145397 + 0.971758i
\(631\) −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
\(639\) −23.0123 + 3.44315i −0.910352 + 0.136209i
\(640\) 3.28995 0.130046
\(641\) 13.1147 0.517998 0.258999 0.965878i \(-0.416607\pi\)
0.258999 + 0.965878i \(0.416607\pi\)
\(642\) 1.69131 + 3.35479i 0.0667505 + 0.132403i
\(643\) −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
\(645\) 0.570403 + 1.13142i 0.0224596 + 0.0445497i
\(646\) −18.5799 −0.731016
\(647\) −11.4745 −0.451108 −0.225554 0.974231i \(-0.572419\pi\)
−0.225554 + 0.974231i \(0.572419\pi\)
\(648\) 4.22258 7.94794i 0.165879 0.312225i
\(649\) 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 \(0.0766903\pi\)
−0.971117 + 0.238605i \(0.923310\pi\)
\(654\) −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
\(657\) 9.60846 1.43764i 0.374862 0.0560876i
\(658\) 19.1244 19.1244i 0.745548 0.745548i
\(659\) 31.9632i 1.24511i 0.782577 + 0.622554i \(0.213905\pi\)
−0.782577 + 0.622554i \(0.786095\pi\)
\(660\) −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
\(663\) −3.72317 + 35.6351i −0.144596 + 1.38395i
\(664\) −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
\(669\) 3.63965 + 7.21944i 0.140717 + 0.279120i
\(670\) 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 \(-0.900931\pi\)
0.951956 0.306235i \(-0.0990694\pi\)
\(678\) 12.1805 + 24.1606i 0.467788 + 0.927881i
\(679\) 40.9209 1.57040
\(680\) 18.8752 0.723831
\(681\) −9.48878 + 4.78374i −0.363611 + 0.183313i
\(682\) −5.86483 5.86483i −0.224576 0.224576i
\(683\) −23.5279 23.5279i −0.900270 0.900270i 0.0951894 0.995459i \(-0.469654\pi\)
−0.995459 + 0.0951894i \(0.969654\pi\)
\(684\) 9.60846 1.43764i 0.367389 0.0549695i
\(685\) 17.0461 0.651298
\(686\) −19.3808 −0.739964
\(687\) −5.41771 + 2.73132i −0.206699 + 0.104206i
\(688\) 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
\(696\) 7.19593 3.62780i 0.272761 0.137512i
\(697\) 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 \(-0.357163\pi\)
0.433825 + 0.900997i \(0.357163\pi\)
\(702\) −0.831893 18.7165i −0.0313978 0.706409i
\(703\) −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
\(708\) 10.1766 5.13049i 0.382460 0.192816i
\(709\) −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
\(717\) 32.3490 16.3086i 1.20810 0.609057i
\(718\) −0.444716 −0.0165967
\(719\) 8.46197 0.315578 0.157789 0.987473i \(-0.449563\pi\)
0.157789 + 0.987473i \(0.449563\pi\)
\(720\) −9.76118 + 1.46049i −0.363778 + 0.0544292i
\(721\) −3.73466 3.73466i −0.139086 0.139086i
\(722\) −6.01911 6.01911i −0.224008 0.224008i
\(723\) 27.0828 13.6537i 1.00722 0.507787i
\(724\) 8.11368 0.301543
\(725\) −27.0960 −1.00632
\(726\) 6.74264 + 13.3744i 0.250243 + 0.496369i
\(727\) 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
\(735\) −1.93971 3.84752i −0.0715474 0.141918i
\(736\) −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
\(741\) 15.7093 12.7372i 0.577097 0.467914i
\(742\) −27.4086 −1.00620
\(743\) 12.3062 12.3062i 0.451472 0.451472i −0.444371 0.895843i \(-0.646573\pi\)
0.895843 + 0.444371i \(0.146573\pi\)
\(744\) 2.93241 8.89533i 0.107507 0.326118i
\(745\) 29.8319i 1.09295i
\(746\) −2.98920 + 2.98920i −0.109442 + 0.109442i
\(747\) 5.87018 0.878310i 0.214779 0.0321357i
\(748\) −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
\(756\) 2.19562 12.7970i 0.0798538 0.465422i
\(757\) −35.1813 −1.27869 −0.639343 0.768922i \(-0.720793\pi\)
−0.639343 + 0.768922i \(0.720793\pi\)
\(758\) −25.6818 −0.932805
\(759\) −5.56430 11.0371i −0.201971 0.400621i
\(760\) −7.53379 7.53379i −0.273279 0.273279i
\(761\) 25.5514 + 25.5514i 0.926238 + 0.926238i 0.997460 0.0712220i \(-0.0226899\pi\)
−0.0712220 + 0.997460i \(0.522690\pi\)
\(762\) −8.33802 16.5389i −0.302055 0.599141i
\(763\) −8.75304 −0.316881
\(764\) −16.1272 −0.583460
\(765\) −56.0022 + 8.37918i −2.02477 + 0.302950i
\(766\) 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 \(-0.446010\pi\)
0.985650 0.168803i \(-0.0539901\pi\)
\(774\) −0.0987103 0.659730i −0.00354807 0.0237135i
\(775\) −22.2685 + 22.2685i −0.799907 + 0.799907i