Properties

Label 980.2.c.e.979.35
Level $980$
Weight $2$
Character 980.979
Analytic conductor $7.825$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 979.35
Character \(\chi\) \(=\) 980.979
Dual form 980.2.c.e.979.34

$q$-expansion

\(f(q)\) \(=\) \(q+(1.14730 + 0.826865i) q^{2} -1.52335i q^{3} +(0.632590 + 1.89732i) q^{4} +(0.0967363 + 2.23397i) q^{5} +(1.25961 - 1.74774i) q^{6} +(-0.843059 + 2.69986i) q^{8} +0.679393 q^{9} +O(q^{10})\) \(q+(1.14730 + 0.826865i) q^{2} -1.52335i q^{3} +(0.632590 + 1.89732i) q^{4} +(0.0967363 + 2.23397i) q^{5} +(1.25961 - 1.74774i) q^{6} +(-0.843059 + 2.69986i) q^{8} +0.679393 q^{9} +(-1.73621 + 2.64302i) q^{10} +4.56056i q^{11} +(2.89029 - 0.963658i) q^{12} -2.19514 q^{13} +(3.40313 - 0.147364i) q^{15} +(-3.19966 + 2.40045i) q^{16} -6.22202 q^{17} +(0.779467 + 0.561766i) q^{18} +3.83396 q^{19} +(-4.17737 + 1.59673i) q^{20} +(-3.77097 + 5.23233i) q^{22} +0.430261 q^{23} +(4.11284 + 1.28428i) q^{24} +(-4.98128 + 0.432213i) q^{25} +(-2.51848 - 1.81508i) q^{26} -5.60502i q^{27} -0.473706 q^{29} +(4.02626 + 2.64486i) q^{30} +7.59779 q^{31} +(-5.65582 + 0.108351i) q^{32} +6.94735 q^{33} +(-7.13851 - 5.14477i) q^{34} +(0.429777 + 1.28903i) q^{36} +8.44308i q^{37} +(4.39870 + 3.17017i) q^{38} +3.34397i q^{39} +(-6.11298 - 1.62220i) q^{40} +1.45831i q^{41} +8.58232 q^{43} +(-8.65285 + 2.88496i) q^{44} +(0.0657220 + 1.51775i) q^{45} +(0.493638 + 0.355767i) q^{46} +4.48893i q^{47} +(3.65674 + 4.87421i) q^{48} +(-6.07240 - 3.62297i) q^{50} +9.47833i q^{51} +(-1.38862 - 4.16488i) q^{52} -9.23911i q^{53} +(4.63459 - 6.43063i) q^{54} +(-10.1882 + 0.441172i) q^{55} -5.84048i q^{57} +(-0.543482 - 0.391691i) q^{58} -3.13601 q^{59} +(2.43238 + 6.36362i) q^{60} +5.71165i q^{61} +(8.71694 + 6.28235i) q^{62} +(-6.57850 - 4.55228i) q^{64} +(-0.212349 - 4.90388i) q^{65} +(7.97068 + 5.74451i) q^{66} +14.9459 q^{67} +(-3.93598 - 11.8052i) q^{68} -0.655439i q^{69} -4.57799i q^{71} +(-0.572768 + 1.83427i) q^{72} +12.2715 q^{73} +(-6.98128 + 9.68674i) q^{74} +(0.658413 + 7.58826i) q^{75} +(2.42532 + 7.27425i) q^{76} +(-2.76501 + 3.83653i) q^{78} -6.20417i q^{79} +(-5.67207 - 6.91575i) q^{80} -6.50025 q^{81} +(-1.20583 + 1.67312i) q^{82} -7.69966i q^{83} +(-0.601895 - 13.8998i) q^{85} +(9.84648 + 7.09641i) q^{86} +0.721622i q^{87} +(-12.3129 - 3.84482i) q^{88} -9.32432i q^{89} +(-1.17957 + 1.79565i) q^{90} +(0.272178 + 0.816343i) q^{92} -11.5741i q^{93} +(-3.71174 + 5.15014i) q^{94} +(0.370883 + 8.56497i) q^{95} +(0.165057 + 8.61581i) q^{96} -9.05280 q^{97} +3.09841i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 16 q^{4} - 64 q^{9} + O(q^{10}) \) \( 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.14730 + 0.826865i 0.811263 + 0.584682i
\(3\) 1.52335i 0.879509i −0.898118 0.439754i \(-0.855065\pi\)
0.898118 0.439754i \(-0.144935\pi\)
\(4\) 0.632590 + 1.89732i 0.316295 + 0.948661i
\(5\) 0.0967363 + 2.23397i 0.0432618 + 0.999064i
\(6\) 1.25961 1.74774i 0.514233 0.713513i
\(7\) 0 0
\(8\) −0.843059 + 2.69986i −0.298066 + 0.954545i
\(9\) 0.679393 0.226464
\(10\) −1.73621 + 2.64302i −0.549038 + 0.835798i
\(11\) 4.56056i 1.37506i 0.726156 + 0.687530i \(0.241305\pi\)
−0.726156 + 0.687530i \(0.758695\pi\)
\(12\) 2.89029 0.963658i 0.834356 0.278184i
\(13\) −2.19514 −0.608822 −0.304411 0.952541i \(-0.598460\pi\)
−0.304411 + 0.952541i \(0.598460\pi\)
\(14\) 0 0
\(15\) 3.40313 0.147364i 0.878685 0.0380491i
\(16\) −3.19966 + 2.40045i −0.799915 + 0.600113i
\(17\) −6.22202 −1.50906 −0.754530 0.656265i \(-0.772135\pi\)
−0.754530 + 0.656265i \(0.772135\pi\)
\(18\) 0.779467 + 0.561766i 0.183722 + 0.132410i
\(19\) 3.83396 0.879571 0.439785 0.898103i \(-0.355055\pi\)
0.439785 + 0.898103i \(0.355055\pi\)
\(20\) −4.17737 + 1.59673i −0.934089 + 0.357040i
\(21\) 0 0
\(22\) −3.77097 + 5.23233i −0.803973 + 1.11554i
\(23\) 0.430261 0.0897155 0.0448578 0.998993i \(-0.485717\pi\)
0.0448578 + 0.998993i \(0.485717\pi\)
\(24\) 4.11284 + 1.28428i 0.839531 + 0.262152i
\(25\) −4.98128 + 0.432213i −0.996257 + 0.0864426i
\(26\) −2.51848 1.81508i −0.493914 0.355967i
\(27\) 5.60502i 1.07869i
\(28\) 0 0
\(29\) −0.473706 −0.0879650 −0.0439825 0.999032i \(-0.514005\pi\)
−0.0439825 + 0.999032i \(0.514005\pi\)
\(30\) 4.02626 + 2.64486i 0.735091 + 0.482883i
\(31\) 7.59779 1.36460 0.682302 0.731070i \(-0.260979\pi\)
0.682302 + 0.731070i \(0.260979\pi\)
\(32\) −5.65582 + 0.108351i −0.999817 + 0.0191539i
\(33\) 6.94735 1.20938
\(34\) −7.13851 5.14477i −1.22424 0.882320i
\(35\) 0 0
\(36\) 0.429777 + 1.28903i 0.0716295 + 0.214838i
\(37\) 8.44308i 1.38803i 0.719959 + 0.694017i \(0.244161\pi\)
−0.719959 + 0.694017i \(0.755839\pi\)
\(38\) 4.39870 + 3.17017i 0.713563 + 0.514269i
\(39\) 3.34397i 0.535464i
\(40\) −6.11298 1.62220i −0.966546 0.256492i
\(41\) 1.45831i 0.227750i 0.993495 + 0.113875i \(0.0363264\pi\)
−0.993495 + 0.113875i \(0.963674\pi\)
\(42\) 0 0
\(43\) 8.58232 1.30879 0.654396 0.756152i \(-0.272923\pi\)
0.654396 + 0.756152i \(0.272923\pi\)
\(44\) −8.65285 + 2.88496i −1.30447 + 0.434925i
\(45\) 0.0657220 + 1.51775i 0.00979725 + 0.226252i
\(46\) 0.493638 + 0.355767i 0.0727829 + 0.0524550i
\(47\) 4.48893i 0.654778i 0.944890 + 0.327389i \(0.106169\pi\)
−0.944890 + 0.327389i \(0.893831\pi\)
\(48\) 3.65674 + 4.87421i 0.527805 + 0.703532i
\(49\) 0 0
\(50\) −6.07240 3.62297i −0.858768 0.512365i
\(51\) 9.47833i 1.32723i
\(52\) −1.38862 4.16488i −0.192567 0.577565i
\(53\) 9.23911i 1.26909i −0.772886 0.634544i \(-0.781188\pi\)
0.772886 0.634544i \(-0.218812\pi\)
\(54\) 4.63459 6.43063i 0.630688 0.875098i
\(55\) −10.1882 + 0.441172i −1.37377 + 0.0594876i
\(56\) 0 0
\(57\) 5.84048i 0.773590i
\(58\) −0.543482 0.391691i −0.0713627 0.0514315i
\(59\) −3.13601 −0.408273 −0.204137 0.978942i \(-0.565439\pi\)
−0.204137 + 0.978942i \(0.565439\pi\)
\(60\) 2.43238 + 6.36362i 0.314019 + 0.821540i
\(61\) 5.71165i 0.731302i 0.930752 + 0.365651i \(0.119154\pi\)
−0.930752 + 0.365651i \(0.880846\pi\)
\(62\) 8.71694 + 6.28235i 1.10705 + 0.797859i
\(63\) 0 0
\(64\) −6.57850 4.55228i −0.822313 0.569035i
\(65\) −0.212349 4.90388i −0.0263387 0.608252i
\(66\) 7.97068 + 5.74451i 0.981123 + 0.707101i
\(67\) 14.9459 1.82593 0.912967 0.408033i \(-0.133785\pi\)
0.912967 + 0.408033i \(0.133785\pi\)
\(68\) −3.93598 11.8052i −0.477308 1.43159i
\(69\) 0.655439i 0.0789056i
\(70\) 0 0
\(71\) 4.57799i 0.543308i −0.962395 0.271654i \(-0.912429\pi\)
0.962395 0.271654i \(-0.0875706\pi\)
\(72\) −0.572768 + 1.83427i −0.0675014 + 0.216170i
\(73\) 12.2715 1.43627 0.718134 0.695905i \(-0.244997\pi\)
0.718134 + 0.695905i \(0.244997\pi\)
\(74\) −6.98128 + 9.68674i −0.811558 + 1.12606i
\(75\) 0.658413 + 7.58826i 0.0760270 + 0.876217i
\(76\) 2.42532 + 7.27425i 0.278204 + 0.834414i
\(77\) 0 0
\(78\) −2.76501 + 3.83653i −0.313076 + 0.434402i
\(79\) 6.20417i 0.698024i −0.937118 0.349012i \(-0.886517\pi\)
0.937118 0.349012i \(-0.113483\pi\)
\(80\) −5.67207 6.91575i −0.634157 0.773204i
\(81\) −6.50025 −0.722250
\(82\) −1.20583 + 1.67312i −0.133161 + 0.184765i
\(83\) 7.69966i 0.845148i −0.906329 0.422574i \(-0.861127\pi\)
0.906329 0.422574i \(-0.138873\pi\)
\(84\) 0 0
\(85\) −0.601895 13.8998i −0.0652847 1.50765i
\(86\) 9.84648 + 7.09641i 1.06177 + 0.765226i
\(87\) 0.721622i 0.0773660i
\(88\) −12.3129 3.84482i −1.31256 0.409859i
\(89\) 9.32432i 0.988376i −0.869355 0.494188i \(-0.835466\pi\)
0.869355 0.494188i \(-0.164534\pi\)
\(90\) −1.17957 + 1.79565i −0.124337 + 0.189278i
\(91\) 0 0
\(92\) 0.272178 + 0.816343i 0.0283766 + 0.0851096i
\(93\) 11.5741i 1.20018i
\(94\) −3.71174 + 5.15014i −0.382836 + 0.531197i
\(95\) 0.370883 + 8.56497i 0.0380518 + 0.878747i
\(96\) 0.165057 + 8.61581i 0.0168460 + 0.879347i
\(97\) −9.05280 −0.919172 −0.459586 0.888133i \(-0.652002\pi\)
−0.459586 + 0.888133i \(0.652002\pi\)
\(98\) 0 0
\(99\) 3.09841i 0.311402i
\(100\) −3.97116 9.17769i −0.397116 0.917769i
\(101\) 7.99802i 0.795832i 0.917422 + 0.397916i \(0.130267\pi\)
−0.917422 + 0.397916i \(0.869733\pi\)
\(102\) −7.83730 + 10.8745i −0.776008 + 1.07673i
\(103\) 12.5017i 1.23183i 0.787813 + 0.615914i \(0.211213\pi\)
−0.787813 + 0.615914i \(0.788787\pi\)
\(104\) 1.85063 5.92657i 0.181469 0.581148i
\(105\) 0 0
\(106\) 7.63949 10.6000i 0.742013 1.02956i
\(107\) −14.4668 −1.39855 −0.699277 0.714851i \(-0.746495\pi\)
−0.699277 + 0.714851i \(0.746495\pi\)
\(108\) 10.6345 3.54568i 1.02331 0.341183i
\(109\) 18.2962 1.75246 0.876230 0.481892i \(-0.160050\pi\)
0.876230 + 0.481892i \(0.160050\pi\)
\(110\) −12.0537 7.91809i −1.14927 0.754960i
\(111\) 12.8618 1.22079
\(112\) 0 0
\(113\) 1.13588i 0.106854i −0.998572 0.0534272i \(-0.982986\pi\)
0.998572 0.0534272i \(-0.0170145\pi\)
\(114\) 4.82928 6.70077i 0.452304 0.627585i
\(115\) 0.0416218 + 0.961191i 0.00388126 + 0.0896315i
\(116\) −0.299662 0.898773i −0.0278229 0.0834490i
\(117\) −1.49136 −0.137876
\(118\) −3.59794 2.59305i −0.331217 0.238710i
\(119\) 0 0
\(120\) −2.47118 + 9.31223i −0.225587 + 0.850086i
\(121\) −9.79871 −0.890791
\(122\) −4.72277 + 6.55298i −0.427579 + 0.593278i
\(123\) 2.22153 0.200309
\(124\) 4.80629 + 14.4155i 0.431617 + 1.29455i
\(125\) −1.44742 11.0863i −0.129462 0.991584i
\(126\) 0 0
\(127\) 8.33473 0.739588 0.369794 0.929114i \(-0.379428\pi\)
0.369794 + 0.929114i \(0.379428\pi\)
\(128\) −3.78339 10.6624i −0.334407 0.942429i
\(129\) 13.0739i 1.15109i
\(130\) 3.81122 5.80180i 0.334266 0.508852i
\(131\) −5.68203 −0.496441 −0.248220 0.968704i \(-0.579846\pi\)
−0.248220 + 0.968704i \(0.579846\pi\)
\(132\) 4.39482 + 13.1814i 0.382520 + 1.14729i
\(133\) 0 0
\(134\) 17.1474 + 12.3583i 1.48131 + 1.06759i
\(135\) 12.5215 0.542209i 1.07768 0.0466659i
\(136\) 5.24553 16.7986i 0.449800 1.44047i
\(137\) 14.7846i 1.26313i −0.775321 0.631567i \(-0.782412\pi\)
0.775321 0.631567i \(-0.217588\pi\)
\(138\) 0.541959 0.751985i 0.0461347 0.0640132i
\(139\) −1.11362 −0.0944558 −0.0472279 0.998884i \(-0.515039\pi\)
−0.0472279 + 0.998884i \(0.515039\pi\)
\(140\) 0 0
\(141\) 6.83823 0.575883
\(142\) 3.78538 5.25233i 0.317662 0.440766i
\(143\) 10.0111i 0.837166i
\(144\) −2.17383 + 1.63085i −0.181152 + 0.135904i
\(145\) −0.0458246 1.05825i −0.00380552 0.0878826i
\(146\) 14.0790 + 10.1468i 1.16519 + 0.839759i
\(147\) 0 0
\(148\) −16.0192 + 5.34101i −1.31677 + 0.439028i
\(149\) 6.87811 0.563476 0.281738 0.959491i \(-0.409089\pi\)
0.281738 + 0.959491i \(0.409089\pi\)
\(150\) −5.51907 + 9.25042i −0.450630 + 0.755294i
\(151\) 21.2380i 1.72832i −0.503215 0.864161i \(-0.667850\pi\)
0.503215 0.864161i \(-0.332150\pi\)
\(152\) −3.23225 + 10.3512i −0.262170 + 0.839590i
\(153\) −4.22720 −0.341748
\(154\) 0 0
\(155\) 0.734983 + 16.9733i 0.0590352 + 1.36333i
\(156\) −6.34459 + 2.11536i −0.507974 + 0.169364i
\(157\) −2.32742 −0.185748 −0.0928741 0.995678i \(-0.529605\pi\)
−0.0928741 + 0.995678i \(0.529605\pi\)
\(158\) 5.13001 7.11804i 0.408122 0.566281i
\(159\) −14.0744 −1.11617
\(160\) −0.789176 12.6245i −0.0623898 0.998052i
\(161\) 0 0
\(162\) −7.45773 5.37482i −0.585934 0.422286i
\(163\) 3.06683 0.240213 0.120106 0.992761i \(-0.461676\pi\)
0.120106 + 0.992761i \(0.461676\pi\)
\(164\) −2.76689 + 0.922515i −0.216058 + 0.0720363i
\(165\) 0.672061 + 15.5202i 0.0523199 + 1.20825i
\(166\) 6.36658 8.83381i 0.494142 0.685637i
\(167\) 13.0431i 1.00930i −0.863323 0.504652i \(-0.831621\pi\)
0.863323 0.504652i \(-0.168379\pi\)
\(168\) 0 0
\(169\) −8.18137 −0.629336
\(170\) 10.8027 16.4449i 0.828531 1.26127i
\(171\) 2.60477 0.199191
\(172\) 5.42909 + 16.2834i 0.413964 + 1.24160i
\(173\) 11.0602 0.840895 0.420448 0.907317i \(-0.361873\pi\)
0.420448 + 0.907317i \(0.361873\pi\)
\(174\) −0.596684 + 0.827916i −0.0452345 + 0.0627642i
\(175\) 0 0
\(176\) −10.9474 14.5922i −0.825192 1.09993i
\(177\) 4.77725i 0.359080i
\(178\) 7.70995 10.6978i 0.577885 0.801832i
\(179\) 22.0450i 1.64772i −0.566794 0.823860i \(-0.691816\pi\)
0.566794 0.823860i \(-0.308184\pi\)
\(180\) −2.83808 + 1.08481i −0.211538 + 0.0808567i
\(181\) 2.49964i 0.185797i −0.995676 0.0928984i \(-0.970387\pi\)
0.995676 0.0928984i \(-0.0296132\pi\)
\(182\) 0 0
\(183\) 8.70087 0.643187
\(184\) −0.362735 + 1.16164i −0.0267412 + 0.0856375i
\(185\) −18.8616 + 0.816752i −1.38673 + 0.0600488i
\(186\) 9.57024 13.2790i 0.701724 0.973662i
\(187\) 28.3759i 2.07505i
\(188\) −8.51694 + 2.83965i −0.621162 + 0.207103i
\(189\) 0 0
\(190\) −6.65655 + 10.1332i −0.482917 + 0.735143i
\(191\) 7.76066i 0.561542i 0.959775 + 0.280771i \(0.0905901\pi\)
−0.959775 + 0.280771i \(0.909410\pi\)
\(192\) −6.93474 + 10.0214i −0.500472 + 0.723231i
\(193\) 6.03714i 0.434563i 0.976109 + 0.217281i \(0.0697189\pi\)
−0.976109 + 0.217281i \(0.930281\pi\)
\(194\) −10.3863 7.48544i −0.745690 0.537423i
\(195\) −7.47035 + 0.323483i −0.534963 + 0.0231651i
\(196\) 0 0
\(197\) 9.74467i 0.694279i 0.937813 + 0.347140i \(0.112847\pi\)
−0.937813 + 0.347140i \(0.887153\pi\)
\(198\) −2.56197 + 3.55481i −0.182071 + 0.252629i
\(199\) −17.2535 −1.22307 −0.611535 0.791217i \(-0.709448\pi\)
−0.611535 + 0.791217i \(0.709448\pi\)
\(200\) 3.03260 13.8132i 0.214437 0.976738i
\(201\) 22.7679i 1.60593i
\(202\) −6.61328 + 9.17612i −0.465309 + 0.645629i
\(203\) 0 0
\(204\) −17.9834 + 5.99590i −1.25909 + 0.419797i
\(205\) −3.25784 + 0.141072i −0.227537 + 0.00985289i
\(206\) −10.3372 + 14.3432i −0.720227 + 0.999336i
\(207\) 0.292316 0.0203174
\(208\) 7.02369 5.26932i 0.487006 0.365362i
\(209\) 17.4850i 1.20946i
\(210\) 0 0
\(211\) 26.8147i 1.84600i −0.384796 0.923002i \(-0.625728\pi\)
0.384796 0.923002i \(-0.374272\pi\)
\(212\) 17.5296 5.84456i 1.20393 0.401406i
\(213\) −6.97391 −0.477844
\(214\) −16.5977 11.9620i −1.13459 0.817709i
\(215\) 0.830222 + 19.1727i 0.0566207 + 1.30757i
\(216\) 15.1328 + 4.72536i 1.02965 + 0.321520i
\(217\) 0 0
\(218\) 20.9912 + 15.1285i 1.42171 + 1.02463i
\(219\) 18.6938i 1.26321i
\(220\) −7.28198 19.0512i −0.490951 1.28443i
\(221\) 13.6582 0.918749
\(222\) 14.7563 + 10.6350i 0.990380 + 0.713772i
\(223\) 17.6054i 1.17894i 0.807789 + 0.589472i \(0.200664\pi\)
−0.807789 + 0.589472i \(0.799336\pi\)
\(224\) 0 0
\(225\) −3.38425 + 0.293642i −0.225617 + 0.0195762i
\(226\) 0.939217 1.30319i 0.0624758 0.0866870i
\(227\) 8.79143i 0.583508i −0.956493 0.291754i \(-0.905761\pi\)
0.956493 0.291754i \(-0.0942388\pi\)
\(228\) 11.0813 3.69463i 0.733875 0.244683i
\(229\) 17.0838i 1.12893i 0.825457 + 0.564466i \(0.190918\pi\)
−0.825457 + 0.564466i \(0.809082\pi\)
\(230\) −0.747022 + 1.13719i −0.0492572 + 0.0749840i
\(231\) 0 0
\(232\) 0.399362 1.27894i 0.0262194 0.0839666i
\(233\) 14.1823i 0.929114i 0.885543 + 0.464557i \(0.153786\pi\)
−0.885543 + 0.464557i \(0.846214\pi\)
\(234\) −1.71104 1.23315i −0.111854 0.0806138i
\(235\) −10.0282 + 0.434242i −0.654164 + 0.0283269i
\(236\) −1.98381 5.95001i −0.129135 0.387313i
\(237\) −9.45115 −0.613918
\(238\) 0 0
\(239\) 13.6734i 0.884456i 0.896903 + 0.442228i \(0.145812\pi\)
−0.896903 + 0.442228i \(0.854188\pi\)
\(240\) −10.5351 + 8.64058i −0.680040 + 0.557747i
\(241\) 3.35937i 0.216396i 0.994129 + 0.108198i \(0.0345080\pi\)
−0.994129 + 0.108198i \(0.965492\pi\)
\(242\) −11.2420 8.10220i −0.722666 0.520829i
\(243\) 6.91288i 0.443461i
\(244\) −10.8368 + 3.61313i −0.693758 + 0.231307i
\(245\) 0 0
\(246\) 2.54876 + 1.83690i 0.162503 + 0.117117i
\(247\) −8.41607 −0.535502
\(248\) −6.40539 + 20.5130i −0.406742 + 1.30258i
\(249\) −11.7293 −0.743315
\(250\) 7.50620 13.9161i 0.474734 0.880129i
\(251\) 26.2007 1.65377 0.826887 0.562368i \(-0.190110\pi\)
0.826887 + 0.562368i \(0.190110\pi\)
\(252\) 0 0
\(253\) 1.96223i 0.123364i
\(254\) 9.56243 + 6.89170i 0.600000 + 0.432423i
\(255\) −21.1744 + 0.916899i −1.32599 + 0.0574184i
\(256\) 4.47565 15.3613i 0.279728 0.960079i
\(257\) −22.2810 −1.38985 −0.694926 0.719081i \(-0.744563\pi\)
−0.694926 + 0.719081i \(0.744563\pi\)
\(258\) 10.8104 14.9997i 0.673023 0.933839i
\(259\) 0 0
\(260\) 9.16991 3.50504i 0.568694 0.217373i
\(261\) −0.321833 −0.0199209
\(262\) −6.51898 4.69827i −0.402744 0.290260i
\(263\) −13.7838 −0.849944 −0.424972 0.905207i \(-0.639716\pi\)
−0.424972 + 0.905207i \(0.639716\pi\)
\(264\) −5.85702 + 18.7569i −0.360475 + 1.15441i
\(265\) 20.6399 0.893757i 1.26790 0.0549031i
\(266\) 0 0
\(267\) −14.2042 −0.869285
\(268\) 9.45463 + 28.3572i 0.577534 + 1.73219i
\(269\) 5.86157i 0.357386i −0.983905 0.178693i \(-0.942813\pi\)
0.983905 0.178693i \(-0.0571869\pi\)
\(270\) 14.8142 + 9.73148i 0.901563 + 0.592239i
\(271\) 17.3982 1.05687 0.528433 0.848975i \(-0.322780\pi\)
0.528433 + 0.848975i \(0.322780\pi\)
\(272\) 19.9083 14.9357i 1.20712 0.905607i
\(273\) 0 0
\(274\) 12.2249 16.9624i 0.738532 1.02473i
\(275\) −1.97113 22.7174i −0.118864 1.36991i
\(276\) 1.24358 0.414624i 0.0748547 0.0249574i
\(277\) 4.01044i 0.240964i −0.992716 0.120482i \(-0.961556\pi\)
0.992716 0.120482i \(-0.0384440\pi\)
\(278\) −1.27765 0.920811i −0.0766285 0.0552266i
\(279\) 5.16189 0.309034
\(280\) 0 0
\(281\) −11.7101 −0.698566 −0.349283 0.937017i \(-0.613575\pi\)
−0.349283 + 0.937017i \(0.613575\pi\)
\(282\) 7.84549 + 5.65429i 0.467192 + 0.336708i
\(283\) 17.6039i 1.04644i 0.852197 + 0.523221i \(0.175270\pi\)
−0.852197 + 0.523221i \(0.824730\pi\)
\(284\) 8.68593 2.89599i 0.515415 0.171846i
\(285\) 13.0475 0.564986i 0.772866 0.0334669i
\(286\) 8.27779 11.4857i 0.489476 0.679162i
\(287\) 0 0
\(288\) −3.84252 + 0.0736129i −0.226423 + 0.00433768i
\(289\) 21.7135 1.27726
\(290\) 0.822453 1.25202i 0.0482961 0.0735209i
\(291\) 13.7906i 0.808420i
\(292\) 7.76281 + 23.2829i 0.454284 + 1.36253i
\(293\) 23.5436 1.37543 0.687715 0.725980i \(-0.258614\pi\)
0.687715 + 0.725980i \(0.258614\pi\)
\(294\) 0 0
\(295\) −0.303366 7.00576i −0.0176626 0.407891i
\(296\) −22.7951 7.11801i −1.32494 0.413726i
\(297\) 25.5620 1.48326
\(298\) 7.89124 + 5.68726i 0.457127 + 0.329454i
\(299\) −0.944481 −0.0546208
\(300\) −13.9809 + 6.04948i −0.807185 + 0.349267i
\(301\) 0 0
\(302\) 17.5609 24.3663i 1.01052 1.40212i
\(303\) 12.1838 0.699941
\(304\) −12.2674 + 9.20324i −0.703582 + 0.527842i
\(305\) −12.7597 + 0.552524i −0.730618 + 0.0316375i
\(306\) −4.84986 3.49532i −0.277248 0.199814i
\(307\) 11.0383i 0.629989i −0.949093 0.314995i \(-0.897997\pi\)
0.949093 0.314995i \(-0.102003\pi\)
\(308\) 0 0
\(309\) 19.0445 1.08340
\(310\) −13.1914 + 20.0812i −0.749219 + 1.14053i
\(311\) 21.6665 1.22859 0.614297 0.789075i \(-0.289440\pi\)
0.614297 + 0.789075i \(0.289440\pi\)
\(312\) −9.02826 2.81916i −0.511124 0.159604i
\(313\) 3.82369 0.216128 0.108064 0.994144i \(-0.465535\pi\)
0.108064 + 0.994144i \(0.465535\pi\)
\(314\) −2.67025 1.92446i −0.150691 0.108604i
\(315\) 0 0
\(316\) 11.7713 3.92469i 0.662188 0.220781i
\(317\) 8.73885i 0.490823i 0.969419 + 0.245411i \(0.0789230\pi\)
−0.969419 + 0.245411i \(0.921077\pi\)
\(318\) −16.1476 11.6376i −0.905511 0.652607i
\(319\) 2.16036i 0.120957i
\(320\) 9.53331 15.1366i 0.532928 0.846161i
\(321\) 22.0380i 1.23004i
\(322\) 0 0
\(323\) −23.8550 −1.32733
\(324\) −4.11199 12.3331i −0.228444 0.685170i
\(325\) 10.9346 0.948767i 0.606543 0.0526281i
\(326\) 3.51857 + 2.53585i 0.194876 + 0.140448i
\(327\) 27.8716i 1.54130i
\(328\) −3.93725 1.22944i −0.217398 0.0678847i
\(329\) 0 0
\(330\) −12.0620 + 18.3620i −0.663994 + 1.01080i
\(331\) 9.68144i 0.532140i 0.963954 + 0.266070i \(0.0857252\pi\)
−0.963954 + 0.266070i \(0.914275\pi\)
\(332\) 14.6087 4.87073i 0.801758 0.267316i
\(333\) 5.73617i 0.314340i
\(334\) 10.7849 14.9643i 0.590121 0.818810i
\(335\) 1.44581 + 33.3888i 0.0789932 + 1.82422i
\(336\) 0 0
\(337\) 9.54187i 0.519779i 0.965638 + 0.259889i \(0.0836861\pi\)
−0.965638 + 0.259889i \(0.916314\pi\)
\(338\) −9.38648 6.76489i −0.510557 0.367961i
\(339\) −1.73034 −0.0939793
\(340\) 25.9917 9.93488i 1.40960 0.538794i
\(341\) 34.6502i 1.87641i
\(342\) 2.98844 + 2.15379i 0.161597 + 0.116464i
\(343\) 0 0
\(344\) −7.23540 + 23.1711i −0.390106 + 1.24930i
\(345\) 1.46423 0.0634048i 0.0788317 0.00341360i
\(346\) 12.6894 + 9.14533i 0.682187 + 0.491656i
\(347\) 24.1787 1.29798 0.648991 0.760796i \(-0.275191\pi\)
0.648991 + 0.760796i \(0.275191\pi\)
\(348\) −1.36915 + 0.456491i −0.0733941 + 0.0244705i
\(349\) 8.31416i 0.445047i −0.974927 0.222523i \(-0.928571\pi\)
0.974927 0.222523i \(-0.0714294\pi\)
\(350\) 0 0
\(351\) 12.3038i 0.656727i
\(352\) −0.494141 25.7937i −0.0263378 1.37481i
\(353\) −10.5285 −0.560377 −0.280189 0.959945i \(-0.590397\pi\)
−0.280189 + 0.959945i \(0.590397\pi\)
\(354\) −3.95014 + 5.48093i −0.209947 + 0.291308i
\(355\) 10.2271 0.442858i 0.542799 0.0235045i
\(356\) 17.6912 5.89847i 0.937633 0.312618i
\(357\) 0 0
\(358\) 18.2282 25.2922i 0.963391 1.33673i
\(359\) 11.1046i 0.586080i 0.956100 + 0.293040i \(0.0946669\pi\)
−0.956100 + 0.293040i \(0.905333\pi\)
\(360\) −4.15311 1.10211i −0.218888 0.0580863i
\(361\) −4.30076 −0.226356
\(362\) 2.06686 2.86783i 0.108632 0.150730i
\(363\) 14.9269i 0.783459i
\(364\) 0 0
\(365\) 1.18710 + 27.4142i 0.0621355 + 1.43492i
\(366\) 9.98250 + 7.19444i 0.521794 + 0.376060i
\(367\) 23.3837i 1.22062i 0.792164 + 0.610309i \(0.208955\pi\)
−0.792164 + 0.610309i \(0.791045\pi\)
\(368\) −1.37669 + 1.03282i −0.0717648 + 0.0538395i
\(369\) 0.990769i 0.0515774i
\(370\) −22.3153 14.6590i −1.16012 0.762083i
\(371\) 0 0
\(372\) 21.9598 7.32168i 1.13857 0.379611i
\(373\) 8.59223i 0.444889i −0.974945 0.222444i \(-0.928596\pi\)
0.974945 0.222444i \(-0.0714035\pi\)
\(374\) 23.4630 32.5556i 1.21324 1.68341i
\(375\) −16.8883 + 2.20494i −0.872107 + 0.113863i
\(376\) −12.1195 3.78443i −0.625015 0.195167i
\(377\) 1.03985 0.0535550
\(378\) 0 0
\(379\) 5.57279i 0.286255i −0.989704 0.143128i \(-0.954284\pi\)
0.989704 0.143128i \(-0.0457159\pi\)
\(380\) −16.0159 + 6.12180i −0.821597 + 0.314041i
\(381\) 12.6967i 0.650474i
\(382\) −6.41701 + 8.90380i −0.328323 + 0.455558i
\(383\) 12.2341i 0.625135i 0.949896 + 0.312567i \(0.101189\pi\)
−0.949896 + 0.312567i \(0.898811\pi\)
\(384\) −16.2426 + 5.76344i −0.828874 + 0.294114i
\(385\) 0 0
\(386\) −4.99190 + 6.92640i −0.254081 + 0.352545i
\(387\) 5.83077 0.296395
\(388\) −5.72671 17.1761i −0.290730 0.871983i
\(389\) −3.98430 −0.202012 −0.101006 0.994886i \(-0.532206\pi\)
−0.101006 + 0.994886i \(0.532206\pi\)
\(390\) −8.83820 5.80583i −0.447539 0.293990i
\(391\) −2.67709 −0.135386
\(392\) 0 0
\(393\) 8.65574i 0.436624i
\(394\) −8.05753 + 11.1801i −0.405932 + 0.563243i
\(395\) 13.8600 0.600168i 0.697370 0.0301978i
\(396\) −5.87869 + 1.96002i −0.295415 + 0.0984949i
\(397\) −39.7805 −1.99653 −0.998263 0.0589121i \(-0.981237\pi\)
−0.998263 + 0.0589121i \(0.981237\pi\)
\(398\) −19.7950 14.2663i −0.992231 0.715107i
\(399\) 0 0
\(400\) 14.9009 13.3403i 0.745046 0.667014i
\(401\) 0.431925 0.0215693 0.0107847 0.999942i \(-0.496567\pi\)
0.0107847 + 0.999942i \(0.496567\pi\)
\(402\) 18.8260 26.1216i 0.938955 1.30283i
\(403\) −16.6782 −0.830800
\(404\) −15.1748 + 5.05946i −0.754975 + 0.251718i
\(405\) −0.628810 14.5214i −0.0312458 0.721573i
\(406\) 0 0
\(407\) −38.5052 −1.90863
\(408\) −25.5902 7.99079i −1.26690 0.395603i
\(409\) 18.3685i 0.908263i 0.890935 + 0.454132i \(0.150050\pi\)
−0.890935 + 0.454132i \(0.849950\pi\)
\(410\) −3.85436 2.53194i −0.190353 0.125044i
\(411\) −22.5222 −1.11094
\(412\) −23.7197 + 7.90844i −1.16859 + 0.389621i
\(413\) 0 0
\(414\) 0.335374 + 0.241706i 0.0164827 + 0.0118792i
\(415\) 17.2008 0.744837i 0.844356 0.0365626i
\(416\) 12.4153 0.237845i 0.608710 0.0116613i
\(417\) 1.69643i 0.0830747i
\(418\) −14.4577 + 20.0605i −0.707151 + 0.981192i
\(419\) −23.3512 −1.14078 −0.570389 0.821375i \(-0.693208\pi\)
−0.570389 + 0.821375i \(0.693208\pi\)
\(420\) 0 0
\(421\) 35.7600 1.74283 0.871417 0.490543i \(-0.163201\pi\)
0.871417 + 0.490543i \(0.163201\pi\)
\(422\) 22.1722 30.7645i 1.07932 1.49759i
\(423\) 3.04975i 0.148284i
\(424\) 24.9443 + 7.78911i 1.21140 + 0.378273i
\(425\) 30.9936 2.68924i 1.50341 0.130447i
\(426\) −8.00116 5.76648i −0.387657 0.279387i
\(427\) 0 0
\(428\) −9.15152 27.4481i −0.442355 1.32675i
\(429\) −15.2504 −0.736295
\(430\) −14.9007 + 22.6833i −0.718575 + 1.09388i
\(431\) 14.6244i 0.704430i 0.935919 + 0.352215i \(0.114571\pi\)
−0.935919 + 0.352215i \(0.885429\pi\)
\(432\) 13.4546 + 17.9342i 0.647334 + 0.862857i
\(433\) 2.12837 0.102283 0.0511414 0.998691i \(-0.483714\pi\)
0.0511414 + 0.998691i \(0.483714\pi\)
\(434\) 0 0
\(435\) −1.61208 + 0.0698070i −0.0772936 + 0.00334699i
\(436\) 11.5740 + 34.7138i 0.554294 + 1.66249i
\(437\) 1.64960 0.0789111
\(438\) 15.4572 21.4474i 0.738575 1.02480i
\(439\) 24.6770 1.17777 0.588884 0.808217i \(-0.299567\pi\)
0.588884 + 0.808217i \(0.299567\pi\)
\(440\) 7.39813 27.8786i 0.352692 1.32906i
\(441\) 0 0
\(442\) 15.6700 + 11.2935i 0.745347 + 0.537175i
\(443\) −16.1404 −0.766855 −0.383427 0.923571i \(-0.625256\pi\)
−0.383427 + 0.923571i \(0.625256\pi\)
\(444\) 8.13624 + 24.4030i 0.386129 + 1.15811i
\(445\) 20.8303 0.902000i 0.987450 0.0427589i
\(446\) −14.5573 + 20.1987i −0.689307 + 0.956434i
\(447\) 10.4778i 0.495582i
\(448\) 0 0
\(449\) −28.5162 −1.34576 −0.672882 0.739750i \(-0.734944\pi\)
−0.672882 + 0.739750i \(0.734944\pi\)
\(450\) −4.12555 2.46142i −0.194480 0.116032i
\(451\) −6.65073 −0.313171
\(452\) 2.15512 0.718544i 0.101369 0.0337975i
\(453\) −32.3530 −1.52007
\(454\) 7.26932 10.0864i 0.341166 0.473378i
\(455\) 0 0
\(456\) 15.7685 + 4.92386i 0.738427 + 0.230581i
\(457\) 23.3827i 1.09380i −0.837199 0.546899i \(-0.815808\pi\)
0.837199 0.546899i \(-0.184192\pi\)
\(458\) −14.1260 + 19.6003i −0.660065 + 0.915860i
\(459\) 34.8745i 1.62780i
\(460\) −1.79736 + 0.687010i −0.0838023 + 0.0320320i
\(461\) 9.92550i 0.462277i −0.972921 0.231138i \(-0.925755\pi\)
0.972921 0.231138i \(-0.0742450\pi\)
\(462\) 0 0
\(463\) −16.8887 −0.784887 −0.392443 0.919776i \(-0.628370\pi\)
−0.392443 + 0.919776i \(0.628370\pi\)
\(464\) 1.51570 1.13711i 0.0703645 0.0527890i
\(465\) 25.8563 1.11964i 1.19906 0.0519220i
\(466\) −11.7269 + 16.2714i −0.543236 + 0.753756i
\(467\) 30.7573i 1.42328i −0.702546 0.711638i \(-0.747954\pi\)
0.702546 0.711638i \(-0.252046\pi\)
\(468\) −0.943420 2.82959i −0.0436096 0.130798i
\(469\) 0 0
\(470\) −11.8643 7.79372i −0.547262 0.359497i
\(471\) 3.54548i 0.163367i
\(472\) 2.64384 8.46678i 0.121692 0.389715i
\(473\) 39.1402i 1.79967i
\(474\) −10.8433 7.81482i −0.498049 0.358946i
\(475\) −19.0980 + 1.65709i −0.876278 + 0.0760324i
\(476\) 0 0
\(477\) 6.27698i 0.287403i
\(478\) −11.3060 + 15.6874i −0.517125 + 0.717526i
\(479\) 15.7534 0.719792 0.359896 0.932992i \(-0.382812\pi\)
0.359896 + 0.932992i \(0.382812\pi\)
\(480\) −19.2315 + 1.20219i −0.877795 + 0.0548724i
\(481\) 18.5337i 0.845065i
\(482\) −2.77774 + 3.85420i −0.126523 + 0.175554i
\(483\) 0 0
\(484\) −6.19856 18.5913i −0.281753 0.845059i
\(485\) −0.875734 20.2237i −0.0397650 0.918312i
\(486\) 5.71601 7.93114i 0.259284 0.359764i
\(487\) −13.5048 −0.611963 −0.305981 0.952038i \(-0.598985\pi\)
−0.305981 + 0.952038i \(0.598985\pi\)
\(488\) −15.4207 4.81526i −0.698061 0.217977i
\(489\) 4.67187i 0.211269i
\(490\) 0 0
\(491\) 3.87067i 0.174681i −0.996179 0.0873404i \(-0.972163\pi\)
0.996179 0.0873404i \(-0.0278368\pi\)
\(492\) 1.40532 + 4.21496i 0.0633566 + 0.190025i
\(493\) 2.94741 0.132745
\(494\) −9.65574 6.95895i −0.434432 0.313098i
\(495\) −6.92178 + 0.299729i −0.311111 + 0.0134718i
\(496\) −24.3104 + 18.2381i −1.09157 + 0.818917i
\(497\) 0 0
\(498\) −13.4570 9.69855i −0.603024 0.434602i
\(499\) 24.3694i 1.09092i 0.838136 + 0.545462i \(0.183646\pi\)
−0.838136 + 0.545462i \(0.816354\pi\)
\(500\) 20.1186 9.75928i 0.899729 0.436448i
\(501\) −19.8692 −0.887691
\(502\) 30.0600 + 21.6644i 1.34165 + 0.966931i
\(503\) 11.2245i 0.500475i 0.968184 + 0.250238i \(0.0805087\pi\)
−0.968184 + 0.250238i \(0.919491\pi\)
\(504\) 0 0
\(505\) −17.8674 + 0.773699i −0.795087 + 0.0344291i
\(506\) −1.62250 + 2.25126i −0.0721288 + 0.100081i
\(507\) 12.4631i 0.553507i
\(508\) 5.27247 + 15.8137i 0.233928 + 0.701618i
\(509\) 14.3783i 0.637308i −0.947871 0.318654i \(-0.896769\pi\)
0.947871 0.318654i \(-0.103231\pi\)
\(510\) −25.0515 16.4564i −1.10930 0.728700i
\(511\) 0 0
\(512\) 17.8366 13.9232i 0.788274 0.615325i
\(513\) 21.4894i 0.948781i
\(514\) −25.5630 18.4234i −1.12754 0.812621i
\(515\) −27.9284 + 1.20937i −1.23067 + 0.0532911i
\(516\) 24.8054 8.27042i 1.09200 0.364085i
\(517\) −20.4720 −0.900359
\(518\) 0 0
\(519\) 16.8487i 0.739575i
\(520\) 13.4188 + 3.56095i 0.588454 + 0.156158i
\(521\) 25.8122i 1.13085i 0.824799 + 0.565426i \(0.191288\pi\)
−0.824799 + 0.565426i \(0.808712\pi\)
\(522\) −0.369238 0.266112i −0.0161611 0.0116474i
\(523\) 4.42548i 0.193513i 0.995308 + 0.0967563i \(0.0308468\pi\)
−0.995308 + 0.0967563i \(0.969153\pi\)
\(524\) −3.59439 10.7806i −0.157022 0.470954i
\(525\) 0 0
\(526\) −15.8141 11.3973i −0.689528 0.496946i
\(527\) −47.2736 −2.05927
\(528\) −22.2291 + 16.6768i −0.967400 + 0.725764i
\(529\) −22.8149 −0.991951
\(530\) 24.4192 + 16.0410i 1.06070 + 0.696777i
\(531\) −2.13058 −0.0924593
\(532\) 0 0
\(533\) 3.20120i 0.138659i
\(534\) −16.2965 11.7450i −0.705219 0.508255i
\(535\) −1.39946 32.3184i −0.0605039 1.39724i
\(536\) −12.6003 + 40.3519i −0.544249 + 1.74294i
\(537\) −33.5823 −1.44918
\(538\) 4.84672 6.72497i 0.208957 0.289934i
\(539\) 0 0
\(540\) 8.94970 + 23.4143i 0.385134 + 1.00759i
\(541\) 4.10160 0.176342 0.0881708 0.996105i \(-0.471898\pi\)
0.0881708 + 0.996105i \(0.471898\pi\)
\(542\) 19.9610 + 14.3860i 0.857396 + 0.617930i
\(543\) −3.80784 −0.163410
\(544\) 35.1906 0.674161i 1.50878 0.0289044i
\(545\) 1.76991 + 40.8733i 0.0758146 + 1.75082i
\(546\) 0 0
\(547\) −4.16833 −0.178225 −0.0891125 0.996022i \(-0.528403\pi\)
−0.0891125 + 0.996022i \(0.528403\pi\)
\(548\) 28.0512 9.35259i 1.19829 0.399523i
\(549\) 3.88046i 0.165614i
\(550\) 16.5228 27.6936i 0.704533 1.18086i
\(551\) −1.81617 −0.0773714
\(552\) 1.76959 + 0.552574i 0.0753190 + 0.0235191i
\(553\) 0 0
\(554\) 3.31609 4.60117i 0.140887 0.195485i
\(555\) 1.24420 + 28.7329i 0.0528135 + 1.21964i
\(556\) −0.704463 2.11289i −0.0298759 0.0896065i
\(557\) 12.1574i 0.515124i −0.966262 0.257562i \(-0.917081\pi\)
0.966262 0.257562i \(-0.0829192\pi\)
\(558\) 5.92223 + 4.26818i 0.250708 + 0.180687i
\(559\) −18.8394 −0.796820
\(560\) 0 0
\(561\) −43.2265 −1.82502
\(562\) −13.4350 9.68267i −0.566721 0.408439i
\(563\) 24.9027i 1.04952i −0.851249 0.524762i \(-0.824154\pi\)
0.851249 0.524762i \(-0.175846\pi\)
\(564\) 4.32579 + 12.9743i 0.182149 + 0.546317i
\(565\) 2.53752 0.109881i 0.106754 0.00462271i
\(566\) −14.5560 + 20.1969i −0.611835 + 0.848939i
\(567\) 0 0
\(568\) 12.3600 + 3.85952i 0.518612 + 0.161942i
\(569\) −29.5875 −1.24037 −0.620187 0.784454i \(-0.712943\pi\)
−0.620187 + 0.784454i \(0.712943\pi\)
\(570\) 15.4365 + 10.1403i 0.646565 + 0.424730i
\(571\) 24.5175i 1.02603i −0.858381 0.513013i \(-0.828529\pi\)
0.858381 0.513013i \(-0.171471\pi\)
\(572\) 18.9942 6.33289i 0.794187 0.264791i
\(573\) 11.8222 0.493881
\(574\) 0 0
\(575\) −2.14325 + 0.185964i −0.0893797 + 0.00775524i
\(576\) −4.46939 3.09279i −0.186225 0.128866i
\(577\) −13.5476 −0.563993 −0.281997 0.959415i \(-0.590997\pi\)
−0.281997 + 0.959415i \(0.590997\pi\)
\(578\) 24.9119 + 17.9541i 1.03620 + 0.746793i
\(579\) 9.19670 0.382202
\(580\) 1.97885 0.756380i 0.0821672 0.0314070i
\(581\) 0 0
\(582\) −11.4030 + 15.8220i −0.472668 + 0.655841i
\(583\) 42.1355 1.74507
\(584\) −10.3456 + 33.1313i −0.428103 + 1.37098i
\(585\) −0.144269 3.33166i −0.00596478 0.137747i
\(586\) 27.0115 + 19.4674i 1.11584 + 0.804189i
\(587\) 26.8772i 1.10934i 0.832070 + 0.554671i \(0.187156\pi\)
−0.832070 + 0.554671i \(0.812844\pi\)
\(588\) 0 0
\(589\) 29.1296 1.20027
\(590\) 5.44476 8.28854i 0.224157 0.341234i
\(591\) 14.8446 0.610625
\(592\) −20.2672 27.0150i −0.832977 1.11031i
\(593\) −0.947148 −0.0388947 −0.0194473 0.999811i \(-0.506191\pi\)
−0.0194473 + 0.999811i \(0.506191\pi\)
\(594\) 29.3273 + 21.1363i 1.20331 + 0.867234i
\(595\) 0 0
\(596\) 4.35102 + 13.0500i 0.178225 + 0.534548i
\(597\) 26.2832i 1.07570i
\(598\) −1.08360 0.780958i −0.0443118 0.0319357i
\(599\) 22.0707i 0.901786i 0.892578 + 0.450893i \(0.148894\pi\)
−0.892578 + 0.450893i \(0.851106\pi\)
\(600\) −21.0423 4.61972i −0.859049 0.188599i
\(601\) 20.5283i 0.837367i −0.908132 0.418684i \(-0.862492\pi\)
0.908132 0.418684i \(-0.137508\pi\)
\(602\) 0 0
\(603\) 10.1542 0.413509
\(604\) 40.2953 13.4349i 1.63959 0.546660i
\(605\) −0.947891 21.8901i −0.0385372 0.889957i
\(606\) 13.9785 + 10.0744i 0.567837 + 0.409243i
\(607\) 25.0474i 1.01664i −0.861168 0.508321i \(-0.830266\pi\)
0.861168 0.508321i \(-0.169734\pi\)
\(608\) −21.6842 + 0.415413i −0.879409 + 0.0168472i
\(609\) 0 0
\(610\) −15.0960 9.91663i −0.611221 0.401512i
\(611\) 9.85381i 0.398643i
\(612\) −2.67408 8.02035i −0.108093 0.324203i
\(613\) 23.4199i 0.945921i 0.881084 + 0.472961i \(0.156815\pi\)
−0.881084 + 0.472961i \(0.843185\pi\)
\(614\) 9.12718 12.6642i 0.368343 0.511087i
\(615\) 0.214903 + 4.96284i 0.00866571 + 0.200121i
\(616\) 0 0
\(617\) 16.7405i 0.673948i 0.941514 + 0.336974i \(0.109403\pi\)
−0.941514 + 0.336974i \(0.890597\pi\)
\(618\) 21.8497 + 15.7472i 0.878925 + 0.633446i
\(619\) 27.3839 1.10065 0.550326 0.834950i \(-0.314504\pi\)
0.550326 + 0.834950i \(0.314504\pi\)
\(620\) −31.7388 + 12.1316i −1.27466 + 0.487218i
\(621\) 2.41162i 0.0967749i
\(622\) 24.8579 + 17.9153i 0.996712 + 0.718336i
\(623\) 0 0
\(624\) −8.02704 10.6996i −0.321339 0.428326i
\(625\) 24.6264 4.30595i 0.985055 0.172238i
\(626\) 4.38691 + 3.16167i 0.175336 + 0.126366i
\(627\) 26.6358 1.06373
\(628\) −1.47230 4.41586i −0.0587512 0.176212i
\(629\) 52.5330i 2.09463i
\(630\) 0 0
\(631\) 3.77099i 0.150121i 0.997179 + 0.0750604i \(0.0239150\pi\)
−0.997179 + 0.0750604i \(0.976085\pi\)
\(632\) 16.7504 + 5.23048i 0.666295 + 0.208057i
\(633\) −40.8483 −1.62358
\(634\) −7.22585 + 10.0261i −0.286975 + 0.398186i
\(635\) 0.806271 + 18.6196i 0.0319959 + 0.738896i
\(636\) −8.90334 26.7037i −0.353040 1.05887i
\(637\) 0 0
\(638\) 1.78633 2.47858i 0.0707214 0.0981281i
\(639\) 3.11026i 0.123040i
\(640\) 23.4535 9.48343i 0.927079 0.374866i
\(641\) 25.1167 0.992051 0.496026 0.868308i \(-0.334792\pi\)
0.496026 + 0.868308i \(0.334792\pi\)
\(642\) −18.2224 + 25.2842i −0.719182 + 0.997886i
\(643\) 12.8390i 0.506319i −0.967424 0.253160i \(-0.918530\pi\)
0.967424 0.253160i \(-0.0814698\pi\)
\(644\) 0 0
\(645\) 29.2068 1.26472i 1.15002 0.0497984i
\(646\) −27.3688 19.7248i −1.07681 0.776063i
\(647\) 4.44061i 0.174578i −0.996183 0.0872892i \(-0.972180\pi\)
0.996183 0.0872892i \(-0.0278204\pi\)
\(648\) 5.48009 17.5498i 0.215278 0.689420i
\(649\) 14.3019i 0.561400i
\(650\) 13.3298 + 7.95292i 0.522836 + 0.311939i
\(651\) 0 0
\(652\) 1.94005 + 5.81877i 0.0759781 + 0.227880i
\(653\) 37.9879i 1.48658i 0.668968 + 0.743291i \(0.266736\pi\)
−0.668968 + 0.743291i \(0.733264\pi\)
\(654\) 23.0461 31.9771i 0.901172 1.25040i
\(655\) −0.549658 12.6935i −0.0214769 0.495976i
\(656\) −3.50061 4.66611i −0.136676 0.182181i
\(657\) 8.33715 0.325263
\(658\) 0 0
\(659\) 19.5420i 0.761248i 0.924730 + 0.380624i \(0.124291\pi\)
−0.924730 + 0.380624i \(0.875709\pi\)
\(660\) −29.0217 + 11.0930i −1.12967 + 0.431796i
\(661\) 22.8705i 0.889560i −0.895640 0.444780i \(-0.853282\pi\)
0.895640 0.444780i \(-0.146718\pi\)
\(662\) −8.00524 + 11.1075i −0.311132 + 0.431705i
\(663\) 20.8062i 0.808048i
\(664\) 20.7880 + 6.49127i 0.806731 + 0.251910i
\(665\) 0 0
\(666\) −4.74304 + 6.58110i −0.183789 + 0.255013i
\(667\) −0.203817 −0.00789183
\(668\) 24.7469 8.25092i 0.957487 0.319238i
\(669\) 26.8193 1.03689
\(670\) −25.9492 + 39.5024i −1.00251 + 1.52611i
\(671\) −26.0483 −1.00559
\(672\) 0 0
\(673\) 23.0022i 0.886670i −0.896356 0.443335i \(-0.853795\pi\)
0.896356 0.443335i \(-0.146205\pi\)
\(674\) −7.88983 + 10.9474i −0.303905 + 0.421677i
\(675\) 2.42256 + 27.9202i 0.0932444 + 1.07465i
\(676\) −5.17545 15.5227i −0.199056 0.597027i
\(677\) 40.7663 1.56678 0.783388 0.621533i \(-0.213490\pi\)
0.783388 + 0.621533i \(0.213490\pi\)
\(678\) −1.98522 1.43076i −0.0762419 0.0549480i
\(679\) 0 0
\(680\) 38.0350 + 10.0933i 1.45858 + 0.387062i
\(681\) −13.3925 −0.513200
\(682\) −28.6510 + 39.7541i −1.09710 + 1.52226i
\(683\) −10.9004 −0.417092 −0.208546 0.978013i \(-0.566873\pi\)
−0.208546 + 0.978013i \(0.566873\pi\)
\(684\) 1.64775 + 4.94208i 0.0630032 + 0.188965i
\(685\) 33.0284 1.43021i 1.26195 0.0546455i
\(686\) 0 0
\(687\) 26.0247 0.992905
\(688\) −27.4605 + 20.6014i −1.04692 + 0.785423i
\(689\) 20.2811i 0.772649i
\(690\) 1.73234 + 1.13798i 0.0659491 + 0.0433221i
\(691\) 16.0135 0.609183 0.304591 0.952483i \(-0.401480\pi\)
0.304591 + 0.952483i \(0.401480\pi\)
\(692\) 6.99660 + 20.9849i 0.265971 + 0.797724i
\(693\) 0 0
\(694\) 27.7402 + 19.9925i 1.05301 + 0.758907i
\(695\) −0.107727 2.48779i −0.00408633 0.0943674i
\(696\) −1.94828 0.608370i −0.0738493 0.0230602i
\(697\) 9.07366i 0.343689i
\(698\) 6.87468 9.53882i 0.260211 0.361050i
\(699\) 21.6047 0.817164
\(700\) 0 0
\(701\) 22.0640 0.833346 0.416673 0.909057i \(-0.363196\pi\)
0.416673 + 0.909057i \(0.363196\pi\)
\(702\) −10.1736 + 14.1161i −0.383976 + 0.532779i
\(703\) 32.3704i 1.22087i
\(704\) 20.7610 30.0017i 0.782458 1.13073i
\(705\) 0.661505 + 15.2764i 0.0249137 + 0.575343i
\(706\) −12.0794 8.70567i −0.454613 0.327642i
\(707\) 0 0
\(708\) −9.06398 + 3.02204i −0.340645 + 0.113575i
\(709\) −37.1908 −1.39673 −0.698364 0.715743i \(-0.746088\pi\)
−0.698364 + 0.715743i \(0.746088\pi\)
\(710\) 12.0998 + 7.94836i 0.454096 + 0.298296i
\(711\) 4.21507i 0.158077i
\(712\) 25.1744 + 7.86095i 0.943449 + 0.294601i
\(713\) 3.26903 0.122426
\(714\) 0 0
\(715\) 22.3644 0.968433i 0.836383 0.0362173i
\(716\) 41.8264 13.9454i 1.56313 0.521165i
\(717\) 20.8294 0.777887
\(718\) −9.18203 + 12.7403i −0.342670 + 0.475465i
\(719\) −36.3717 −1.35644 −0.678218 0.734861i \(-0.737247\pi\)
−0.678218 + 0.734861i \(0.737247\pi\)
\(720\) −3.85357 4.69851i −0.143614 0.175103i
\(721\) 0 0
\(722\) −4.93425 3.55614i −0.183634 0.132346i
\(723\) 5.11751 0.190322
\(724\) 4.74262 1.58125i 0.176258 0.0587666i
\(725\) 2.35966 0.204742i 0.0876357 0.00760392i
\(726\) −12.3425 + 17.1256i −0.458074 + 0.635591i
\(727\) 34.1872i 1.26793i −0.773360 0.633967i \(-0.781425\pi\)
0.773360 0.633967i \(-0.218575\pi\)
\(728\) 0 0
\(729\) −30.0315 −1.11228
\(730\) −21.3058 + 32.4338i −0.788565 + 1.20043i
\(731\) −53.3993 −1.97505
\(732\) 5.50408 + 16.5084i 0.203437 + 0.610166i
\(733\) 22.5349 0.832345 0.416172 0.909286i \(-0.363371\pi\)
0.416172 + 0.909286i \(0.363371\pi\)
\(734\) −19.3351 + 26.8281i −0.713673 + 0.990242i
\(735\) 0 0
\(736\) −2.43348 + 0.0466191i −0.0896991 + 0.00171840i
\(737\) 68.1618i 2.51077i
\(738\) −0.819232 + 1.13671i −0.0301563 + 0.0418428i
\(739\) 7.02861i 0.258552i 0.991609 + 0.129276i \(0.0412652\pi\)
−0.991609 + 0.129276i \(0.958735\pi\)
\(740\) −13.4813 35.2699i −0.495583 1.29655i
\(741\) 12.8206i 0.470978i
\(742\) 0 0
\(743\) −0.0257779 −0.000945701 −0.000472850 1.00000i \(-0.500151\pi\)
−0.000472850 1.00000i \(0.500151\pi\)
\(744\) 31.2485 + 9.75767i 1.14563 + 0.357734i
\(745\) 0.665363 + 15.3655i 0.0243770 + 0.562949i
\(746\) 7.10461 9.85785i 0.260118 0.360922i
\(747\) 5.23110i 0.191396i
\(748\) 53.8382 17.9503i 1.96852 0.656328i
\(749\) 0 0
\(750\) −21.1991 11.4346i −0.774082 0.417533i
\(751\) 10.3551i 0.377865i −0.981990 0.188932i \(-0.939497\pi\)
0.981990 0.188932i \(-0.0605027\pi\)
\(752\) −10.7755 14.3630i −0.392941 0.523766i
\(753\) 39.9129i 1.45451i
\(754\) 1.19302 + 0.859815i 0.0434472 + 0.0313126i
\(755\) 47.4451 2.05448i 1.72670 0.0747703i
\(756\) 0 0
\(757\) 36.2159i 1.31629i 0.752892 + 0.658145i \(0.228658\pi\)
−0.752892 + 0.658145i \(0.771342\pi\)
\(758\) 4.60795 6.39366i 0.167368 0.232228i
\(759\) 2.98917 0.108500
\(760\) −23.4369 6.21944i −0.850146 0.225603i
\(761\) 25.8142i 0.935765i −0.883791 0.467883i \(-0.845017\pi\)
0.883791 0.467883i \(-0.154983\pi\)
\(762\) 10.4985 14.5670i 0.380320 0.527706i
\(763\) 0 0
\(764\) −14.7245 + 4.90931i −0.532713 + 0.177613i
\(765\) −0.408923 9.44345i −0.0147847 0.341429i
\(766\) −10.1160 + 14.0362i −0.365505 + 0.507149i
\(767\) 6.88396 0.248566
\(768\) −23.4006 6.81800i −0.844398 0.246023i
\(769\) 17.9643i 0.647810i 0.946090 + 0.323905i \(0.104996\pi\)
−0.946090 + 0.323905i \(0.895004\pi\)
\(770\) 0 0
\(771\) 33.9419i 1.22239i
\(772\) −11.4544 + 3.81903i −0.412253 + 0.137450i
\(773\) −4.26473 −0.153392 −0.0766958 0.997055i \(-0.524437\pi\)
−0.0766958 + 0.997055i \(0.524437\pi\)
\(774\) 6.68963 + 4.82125i 0.240454 + 0.173296i
\(775\) −37.8468 + 3.28386i −1.35950 + 0.117960i
\(776\) 7.63204 24.4413i 0.273974 0.877392i
\(777\) 0 0
\(778\) −4.57118 3.29448i −0.163885 0.118113i
\(779\) 5.59112i 0.200323i
\(780\) −5.33942 13.9690i −0.191182 0.500171i
\(781\) 20.8782 0.747081
\(782\) −3.07142 2.21359i −0.109834 0.0791578i
\(783\) 2.65513i 0.0948866i
\(784\) 0 0
\(785\) −0.225146 5.19939i −0.00803580 0.185574i
\(786\) −7.15712