Properties

Label 756.2.ba.a.71.15
Level $756$
Weight $2$
Character 756.71
Analytic conductor $6.037$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.ba (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 71.15
Character \(\chi\) \(=\) 756.71
Dual form 756.2.ba.a.575.15

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.412980 + 1.35257i) q^{2} +(-1.65890 - 1.11717i) q^{4} +(-2.51813 - 1.45385i) q^{5} +(0.866025 - 0.500000i) q^{7} +(2.19614 - 1.78241i) q^{8} +O(q^{10})\) \(q+(-0.412980 + 1.35257i) q^{2} +(-1.65890 - 1.11717i) q^{4} +(-2.51813 - 1.45385i) q^{5} +(0.866025 - 0.500000i) q^{7} +(2.19614 - 1.78241i) q^{8} +(3.00637 - 2.80555i) q^{10} +(-1.18430 - 2.05127i) q^{11} +(-0.125913 + 0.218087i) q^{13} +(0.318634 + 1.37785i) q^{14} +(1.50387 + 3.70653i) q^{16} +7.60859i q^{17} +2.60920i q^{19} +(2.55313 + 5.22496i) q^{20} +(3.26359 - 0.754720i) q^{22} +(-4.51674 + 7.82323i) q^{23} +(1.72733 + 2.99183i) q^{25} +(-0.242979 - 0.260371i) q^{26} +(-1.99523 - 0.138049i) q^{28} +(5.53448 - 3.19533i) q^{29} +(-0.0905658 - 0.0522882i) q^{31} +(-5.63441 + 0.503365i) q^{32} +(-10.2912 - 3.14219i) q^{34} -2.90769 q^{35} -3.15261 q^{37} +(-3.52912 - 1.07755i) q^{38} +(-8.12152 + 1.29549i) q^{40} +(7.24183 + 4.18107i) q^{41} +(-7.18102 + 4.14596i) q^{43} +(-0.326984 + 4.72592i) q^{44} +(-8.71615 - 9.34005i) q^{46} +(-0.248282 - 0.430036i) q^{47} +(0.500000 - 0.866025i) q^{49} +(-4.76001 + 1.10078i) q^{50} +(0.452516 - 0.221118i) q^{52} -2.38678i q^{53} +6.88718i q^{55} +(1.01071 - 2.64168i) q^{56} +(2.03629 + 8.80538i) q^{58} +(-3.99487 + 6.91932i) q^{59} +(3.69592 + 6.40151i) q^{61} +(0.108125 - 0.100903i) q^{62} +(1.64606 - 7.82882i) q^{64} +(0.634129 - 0.366115i) q^{65} +(0.444103 + 0.256403i) q^{67} +(8.50008 - 12.6219i) q^{68} +(1.20082 - 3.93286i) q^{70} -1.45233 q^{71} +4.06828 q^{73} +(1.30196 - 4.26412i) q^{74} +(2.91491 - 4.32839i) q^{76} +(-2.05127 - 1.18430i) q^{77} +(-10.0369 + 5.79482i) q^{79} +(1.60178 - 11.5199i) q^{80} +(-8.64592 + 8.06839i) q^{82} +(0.439593 + 0.761398i) q^{83} +(11.0617 - 19.1594i) q^{85} +(-2.64209 - 11.4250i) q^{86} +(-6.25710 - 2.39398i) q^{88} +14.6787i q^{89} +0.251825i q^{91} +(16.2327 - 7.93195i) q^{92} +(0.684190 - 0.158222i) q^{94} +(3.79337 - 6.57031i) q^{95} +(2.88066 + 4.98945i) q^{97} +(0.964871 + 1.03394i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + O(q^{10}) \) \( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.412980 + 1.35257i −0.292021 + 0.956412i
\(3\) 0 0
\(4\) −1.65890 1.11717i −0.829448 0.558584i
\(5\) −2.51813 1.45385i −1.12614 0.650179i −0.183182 0.983079i \(-0.558640\pi\)
−0.942962 + 0.332900i \(0.891973\pi\)
\(6\) 0 0
\(7\) 0.866025 0.500000i 0.327327 0.188982i
\(8\) 2.19614 1.78241i 0.776453 0.630175i
\(9\) 0 0
\(10\) 3.00637 2.80555i 0.950697 0.887191i
\(11\) −1.18430 2.05127i −0.357081 0.618483i 0.630391 0.776278i \(-0.282895\pi\)
−0.987472 + 0.157795i \(0.949561\pi\)
\(12\) 0 0
\(13\) −0.125913 + 0.218087i −0.0349219 + 0.0604864i −0.882958 0.469452i \(-0.844452\pi\)
0.848036 + 0.529938i \(0.177785\pi\)
\(14\) 0.318634 + 1.37785i 0.0851586 + 0.368246i
\(15\) 0 0
\(16\) 1.50387 + 3.70653i 0.375967 + 0.926633i
\(17\) 7.60859i 1.84535i 0.385574 + 0.922677i \(0.374003\pi\)
−0.385574 + 0.922677i \(0.625997\pi\)
\(18\) 0 0
\(19\) 2.60920i 0.598591i 0.954160 + 0.299295i \(0.0967516\pi\)
−0.954160 + 0.299295i \(0.903248\pi\)
\(20\) 2.55313 + 5.22496i 0.570897 + 1.16834i
\(21\) 0 0
\(22\) 3.26359 0.754720i 0.695799 0.160907i
\(23\) −4.51674 + 7.82323i −0.941806 + 1.63126i −0.179782 + 0.983706i \(0.557539\pi\)
−0.762024 + 0.647549i \(0.775794\pi\)
\(24\) 0 0
\(25\) 1.72733 + 2.99183i 0.345467 + 0.598366i
\(26\) −0.242979 0.260371i −0.0476520 0.0510630i
\(27\) 0 0
\(28\) −1.99523 0.138049i −0.377063 0.0260888i
\(29\) 5.53448 3.19533i 1.02773 0.593358i 0.111394 0.993776i \(-0.464468\pi\)
0.916333 + 0.400418i \(0.131135\pi\)
\(30\) 0 0
\(31\) −0.0905658 0.0522882i −0.0162661 0.00939124i 0.491845 0.870683i \(-0.336323\pi\)
−0.508111 + 0.861292i \(0.669656\pi\)
\(32\) −5.63441 + 0.503365i −0.996033 + 0.0889831i
\(33\) 0 0
\(34\) −10.2912 3.14219i −1.76492 0.538882i
\(35\) −2.90769 −0.491489
\(36\) 0 0
\(37\) −3.15261 −0.518285 −0.259143 0.965839i \(-0.583440\pi\)
−0.259143 + 0.965839i \(0.583440\pi\)
\(38\) −3.52912 1.07755i −0.572499 0.174801i
\(39\) 0 0
\(40\) −8.12152 + 1.29549i −1.28412 + 0.204835i
\(41\) 7.24183 + 4.18107i 1.13098 + 0.652974i 0.944182 0.329424i \(-0.106855\pi\)
0.186801 + 0.982398i \(0.440188\pi\)
\(42\) 0 0
\(43\) −7.18102 + 4.14596i −1.09510 + 0.632254i −0.934928 0.354836i \(-0.884537\pi\)
−0.160167 + 0.987090i \(0.551203\pi\)
\(44\) −0.326984 + 4.72592i −0.0492946 + 0.712459i
\(45\) 0 0
\(46\) −8.71615 9.34005i −1.28513 1.37712i
\(47\) −0.248282 0.430036i −0.0362156 0.0627273i 0.847349 0.531036i \(-0.178197\pi\)
−0.883565 + 0.468308i \(0.844864\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −4.76001 + 1.10078i −0.673167 + 0.155673i
\(51\) 0 0
\(52\) 0.452516 0.221118i 0.0627526 0.0306635i
\(53\) 2.38678i 0.327849i −0.986473 0.163925i \(-0.947585\pi\)
0.986473 0.163925i \(-0.0524154\pi\)
\(54\) 0 0
\(55\) 6.88718i 0.928667i
\(56\) 1.01071 2.64168i 0.135062 0.353009i
\(57\) 0 0
\(58\) 2.03629 + 8.80538i 0.267377 + 1.15620i
\(59\) −3.99487 + 6.91932i −0.520088 + 0.900818i 0.479640 + 0.877466i \(0.340767\pi\)
−0.999727 + 0.0233526i \(0.992566\pi\)
\(60\) 0 0
\(61\) 3.69592 + 6.40151i 0.473214 + 0.819630i 0.999530 0.0306589i \(-0.00976058\pi\)
−0.526316 + 0.850289i \(0.676427\pi\)
\(62\) 0.108125 0.100903i 0.0137319 0.0128147i
\(63\) 0 0
\(64\) 1.64606 7.82882i 0.205758 0.978603i
\(65\) 0.634129 0.366115i 0.0786541 0.0454109i
\(66\) 0 0
\(67\) 0.444103 + 0.256403i 0.0542559 + 0.0313246i 0.526883 0.849938i \(-0.323361\pi\)
−0.472627 + 0.881263i \(0.656694\pi\)
\(68\) 8.50008 12.6219i 1.03079 1.53062i
\(69\) 0 0
\(70\) 1.20082 3.93286i 0.143525 0.470066i
\(71\) −1.45233 −0.172360 −0.0861800 0.996280i \(-0.527466\pi\)
−0.0861800 + 0.996280i \(0.527466\pi\)
\(72\) 0 0
\(73\) 4.06828 0.476157 0.238078 0.971246i \(-0.423483\pi\)
0.238078 + 0.971246i \(0.423483\pi\)
\(74\) 1.30196 4.26412i 0.151350 0.495694i
\(75\) 0 0
\(76\) 2.91491 4.32839i 0.334364 0.496500i
\(77\) −2.05127 1.18430i −0.233764 0.134964i
\(78\) 0 0
\(79\) −10.0369 + 5.79482i −1.12924 + 0.651968i −0.943744 0.330677i \(-0.892723\pi\)
−0.185498 + 0.982645i \(0.559390\pi\)
\(80\) 1.60178 11.5199i 0.179085 1.28797i
\(81\) 0 0
\(82\) −8.64592 + 8.06839i −0.954782 + 0.891004i
\(83\) 0.439593 + 0.761398i 0.0482516 + 0.0835743i 0.889142 0.457630i \(-0.151302\pi\)
−0.840891 + 0.541205i \(0.817968\pi\)
\(84\) 0 0
\(85\) 11.0617 19.1594i 1.19981 2.07813i
\(86\) −2.64209 11.4250i −0.284904 1.23199i
\(87\) 0 0
\(88\) −6.25710 2.39398i −0.667009 0.255199i
\(89\) 14.6787i 1.55594i 0.628304 + 0.777968i \(0.283749\pi\)
−0.628304 + 0.777968i \(0.716251\pi\)
\(90\) 0 0
\(91\) 0.251825i 0.0263984i
\(92\) 16.2327 7.93195i 1.69237 0.826963i
\(93\) 0 0
\(94\) 0.684190 0.158222i 0.0705688 0.0163194i
\(95\) 3.79337 6.57031i 0.389191 0.674099i
\(96\) 0 0
\(97\) 2.88066 + 4.98945i 0.292487 + 0.506602i 0.974397 0.224834i \(-0.0721839\pi\)
−0.681910 + 0.731436i \(0.738851\pi\)
\(98\) 0.964871 + 1.03394i 0.0974667 + 0.104443i
\(99\) 0 0
\(100\) 0.476913 6.89285i 0.0476913 0.689285i
\(101\) 12.4968 7.21504i 1.24348 0.717923i 0.273678 0.961821i \(-0.411760\pi\)
0.969801 + 0.243898i \(0.0784263\pi\)
\(102\) 0 0
\(103\) −10.3804 5.99314i −1.02281 0.590521i −0.107896 0.994162i \(-0.534411\pi\)
−0.914918 + 0.403641i \(0.867745\pi\)
\(104\) 0.112198 + 0.703377i 0.0110019 + 0.0689718i
\(105\) 0 0
\(106\) 3.22829 + 0.985691i 0.313559 + 0.0957388i
\(107\) −6.10346 −0.590043 −0.295022 0.955491i \(-0.595327\pi\)
−0.295022 + 0.955491i \(0.595327\pi\)
\(108\) 0 0
\(109\) 6.25509 0.599129 0.299564 0.954076i \(-0.403159\pi\)
0.299564 + 0.954076i \(0.403159\pi\)
\(110\) −9.31540 2.84427i −0.888188 0.271190i
\(111\) 0 0
\(112\) 3.15565 + 2.45802i 0.298181 + 0.232261i
\(113\) −15.8902 9.17418i −1.49482 0.863035i −0.494838 0.868985i \(-0.664772\pi\)
−0.999982 + 0.00595082i \(0.998106\pi\)
\(114\) 0 0
\(115\) 22.7475 13.1333i 2.12122 1.22469i
\(116\) −12.7508 0.882224i −1.18389 0.0819125i
\(117\) 0 0
\(118\) −7.70906 8.26088i −0.709677 0.760476i
\(119\) 3.80429 + 6.58923i 0.348739 + 0.604034i
\(120\) 0 0
\(121\) 2.69485 4.66762i 0.244986 0.424329i
\(122\) −10.1848 + 2.35529i −0.922092 + 0.213238i
\(123\) 0 0
\(124\) 0.0918245 + 0.187918i 0.00824608 + 0.0168755i
\(125\) 4.49335i 0.401898i
\(126\) 0 0
\(127\) 13.5835i 1.20534i 0.797989 + 0.602672i \(0.205897\pi\)
−0.797989 + 0.602672i \(0.794103\pi\)
\(128\) 9.90925 + 5.45956i 0.875862 + 0.482562i
\(129\) 0 0
\(130\) 0.233314 + 1.00890i 0.0204629 + 0.0884866i
\(131\) −0.740508 + 1.28260i −0.0646985 + 0.112061i −0.896560 0.442922i \(-0.853942\pi\)
0.831862 + 0.554983i \(0.187275\pi\)
\(132\) 0 0
\(133\) 1.30460 + 2.25963i 0.113123 + 0.195935i
\(134\) −0.530209 + 0.494792i −0.0458031 + 0.0427435i
\(135\) 0 0
\(136\) 13.5616 + 16.7095i 1.16290 + 1.43283i
\(137\) −15.5721 + 8.99055i −1.33041 + 0.768115i −0.985363 0.170469i \(-0.945472\pi\)
−0.345051 + 0.938584i \(0.612138\pi\)
\(138\) 0 0
\(139\) 7.21297 + 4.16441i 0.611796 + 0.353221i 0.773668 0.633591i \(-0.218420\pi\)
−0.161872 + 0.986812i \(0.551753\pi\)
\(140\) 4.82355 + 3.24838i 0.407665 + 0.274538i
\(141\) 0 0
\(142\) 0.599783 1.96438i 0.0503327 0.164847i
\(143\) 0.596475 0.0498797
\(144\) 0 0
\(145\) −18.5821 −1.54316
\(146\) −1.68012 + 5.50264i −0.139048 + 0.455402i
\(147\) 0 0
\(148\) 5.22984 + 3.52199i 0.429890 + 0.289506i
\(149\) 2.86752 + 1.65557i 0.234917 + 0.135629i 0.612838 0.790208i \(-0.290028\pi\)
−0.377921 + 0.925838i \(0.623361\pi\)
\(150\) 0 0
\(151\) 5.39261 3.11343i 0.438845 0.253367i −0.264263 0.964451i \(-0.585129\pi\)
0.703107 + 0.711084i \(0.251795\pi\)
\(152\) 4.65065 + 5.73016i 0.377217 + 0.464778i
\(153\) 0 0
\(154\) 2.44899 2.28540i 0.197345 0.184163i
\(155\) 0.152038 + 0.263337i 0.0122120 + 0.0211518i
\(156\) 0 0
\(157\) 1.48912 2.57922i 0.118844 0.205844i −0.800466 0.599379i \(-0.795414\pi\)
0.919310 + 0.393534i \(0.128748\pi\)
\(158\) −3.69286 15.9688i −0.293788 1.27041i
\(159\) 0 0
\(160\) 14.9200 + 6.92403i 1.17953 + 0.547392i
\(161\) 9.03348i 0.711938i
\(162\) 0 0
\(163\) 8.29335i 0.649585i −0.945785 0.324793i \(-0.894706\pi\)
0.945785 0.324793i \(-0.105294\pi\)
\(164\) −7.34247 15.0263i −0.573351 1.17336i
\(165\) 0 0
\(166\) −1.21139 + 0.280139i −0.0940219 + 0.0217430i
\(167\) 9.34971 16.1942i 0.723503 1.25314i −0.236085 0.971732i \(-0.575864\pi\)
0.959587 0.281411i \(-0.0908023\pi\)
\(168\) 0 0
\(169\) 6.46829 + 11.2034i 0.497561 + 0.861801i
\(170\) 21.3462 + 22.8742i 1.63718 + 1.75437i
\(171\) 0 0
\(172\) 16.5443 + 1.14469i 1.26149 + 0.0872819i
\(173\) −7.58848 + 4.38121i −0.576942 + 0.333097i −0.759917 0.650020i \(-0.774760\pi\)
0.182975 + 0.983118i \(0.441427\pi\)
\(174\) 0 0
\(175\) 2.99183 + 1.72733i 0.226161 + 0.130574i
\(176\) 5.82208 7.47451i 0.438856 0.563412i
\(177\) 0 0
\(178\) −19.8539 6.06199i −1.48812 0.454365i
\(179\) 2.87709 0.215044 0.107522 0.994203i \(-0.465708\pi\)
0.107522 + 0.994203i \(0.465708\pi\)
\(180\) 0 0
\(181\) −4.82998 −0.359010 −0.179505 0.983757i \(-0.557450\pi\)
−0.179505 + 0.983757i \(0.557450\pi\)
\(182\) −0.340611 0.103999i −0.0252478 0.00770890i
\(183\) 0 0
\(184\) 4.02476 + 25.2316i 0.296709 + 1.86010i
\(185\) 7.93868 + 4.58340i 0.583664 + 0.336978i
\(186\) 0 0
\(187\) 15.6073 9.01088i 1.14132 0.658941i
\(188\) −0.0685500 + 0.990758i −0.00499952 + 0.0722584i
\(189\) 0 0
\(190\) 7.32022 + 7.84421i 0.531065 + 0.569078i
\(191\) −10.2584 17.7680i −0.742270 1.28565i −0.951459 0.307775i \(-0.900416\pi\)
0.209189 0.977875i \(-0.432918\pi\)
\(192\) 0 0
\(193\) −9.29894 + 16.1062i −0.669352 + 1.15935i 0.308733 + 0.951149i \(0.400095\pi\)
−0.978085 + 0.208204i \(0.933238\pi\)
\(194\) −7.93824 + 1.83576i −0.569932 + 0.131800i
\(195\) 0 0
\(196\) −1.79694 + 0.878061i −0.128353 + 0.0627187i
\(197\) 17.2523i 1.22917i −0.788850 0.614586i \(-0.789323\pi\)
0.788850 0.614586i \(-0.210677\pi\)
\(198\) 0 0
\(199\) 1.17220i 0.0830948i −0.999137 0.0415474i \(-0.986771\pi\)
0.999137 0.0415474i \(-0.0132288\pi\)
\(200\) 9.12612 + 3.49167i 0.645314 + 0.246898i
\(201\) 0 0
\(202\) 4.59792 + 19.8825i 0.323508 + 1.39893i
\(203\) 3.19533 5.53448i 0.224268 0.388444i
\(204\) 0 0
\(205\) −12.1573 21.0570i −0.849100 1.47068i
\(206\) 12.3930 11.5652i 0.863464 0.805786i
\(207\) 0 0
\(208\) −0.997702 0.138725i −0.0691782 0.00961885i
\(209\) 5.35218 3.09008i 0.370218 0.213745i
\(210\) 0 0
\(211\) −8.81152 5.08733i −0.606610 0.350226i 0.165028 0.986289i \(-0.447229\pi\)
−0.771637 + 0.636063i \(0.780562\pi\)
\(212\) −2.66643 + 3.95942i −0.183131 + 0.271934i
\(213\) 0 0
\(214\) 2.52060 8.25536i 0.172305 0.564325i
\(215\) 24.1104 1.64431
\(216\) 0 0
\(217\) −0.104576 −0.00709911
\(218\) −2.58322 + 8.46045i −0.174958 + 0.573014i
\(219\) 0 0
\(220\) 7.69414 11.4251i 0.518739 0.770281i
\(221\) −1.65933 0.958017i −0.111619 0.0644432i
\(222\) 0 0
\(223\) 5.28069 3.04881i 0.353621 0.204163i −0.312658 0.949866i \(-0.601219\pi\)
0.666279 + 0.745703i \(0.267886\pi\)
\(224\) −4.62786 + 3.25313i −0.309212 + 0.217359i
\(225\) 0 0
\(226\) 18.9710 17.7038i 1.26194 1.17764i
\(227\) 11.1581 + 19.3264i 0.740589 + 1.28274i 0.952228 + 0.305390i \(0.0987867\pi\)
−0.211639 + 0.977348i \(0.567880\pi\)
\(228\) 0 0
\(229\) −2.70895 + 4.69204i −0.179013 + 0.310059i −0.941543 0.336894i \(-0.890624\pi\)
0.762530 + 0.646953i \(0.223957\pi\)
\(230\) 8.36944 + 36.1914i 0.551864 + 2.38639i
\(231\) 0 0
\(232\) 6.45911 16.8821i 0.424062 1.10836i
\(233\) 6.08190i 0.398439i −0.979955 0.199219i \(-0.936159\pi\)
0.979955 0.199219i \(-0.0638406\pi\)
\(234\) 0 0
\(235\) 1.44385i 0.0941865i
\(236\) 14.3571 7.01548i 0.934568 0.456669i
\(237\) 0 0
\(238\) −10.4835 + 2.42436i −0.679544 + 0.157148i
\(239\) 4.58910 7.94855i 0.296844 0.514149i −0.678568 0.734538i \(-0.737399\pi\)
0.975412 + 0.220388i \(0.0707325\pi\)
\(240\) 0 0
\(241\) −4.60034 7.96801i −0.296334 0.513265i 0.678961 0.734175i \(-0.262431\pi\)
−0.975294 + 0.220910i \(0.929097\pi\)
\(242\) 5.20036 + 5.57260i 0.334292 + 0.358221i
\(243\) 0 0
\(244\) 1.02043 14.7484i 0.0653266 0.944170i
\(245\) −2.51813 + 1.45385i −0.160878 + 0.0928828i
\(246\) 0 0
\(247\) −0.569032 0.328531i −0.0362066 0.0209039i
\(248\) −0.292094 + 0.0465928i −0.0185480 + 0.00295864i
\(249\) 0 0
\(250\) −6.07758 1.85566i −0.384380 0.117363i
\(251\) −17.5771 −1.10946 −0.554729 0.832031i \(-0.687178\pi\)
−0.554729 + 0.832031i \(0.687178\pi\)
\(252\) 0 0
\(253\) 21.3968 1.34520
\(254\) −18.3727 5.60972i −1.15280 0.351985i
\(255\) 0 0
\(256\) −11.4768 + 11.1483i −0.717298 + 0.696767i
\(257\) 9.36418 + 5.40641i 0.584122 + 0.337243i 0.762770 0.646670i \(-0.223839\pi\)
−0.178648 + 0.983913i \(0.557172\pi\)
\(258\) 0 0
\(259\) −2.73024 + 1.57630i −0.169649 + 0.0979467i
\(260\) −1.46097 0.101083i −0.0906053 0.00626893i
\(261\) 0 0
\(262\) −1.42899 1.53128i −0.0882833 0.0946026i
\(263\) −1.23346 2.13642i −0.0760585 0.131737i 0.825488 0.564420i \(-0.190900\pi\)
−0.901546 + 0.432683i \(0.857567\pi\)
\(264\) 0 0
\(265\) −3.47001 + 6.01023i −0.213161 + 0.369205i
\(266\) −3.59508 + 0.831380i −0.220429 + 0.0509752i
\(267\) 0 0
\(268\) −0.450275 0.921484i −0.0275049 0.0562886i
\(269\) 18.6417i 1.13661i −0.822820 0.568303i \(-0.807600\pi\)
0.822820 0.568303i \(-0.192400\pi\)
\(270\) 0 0
\(271\) 11.9123i 0.723621i 0.932252 + 0.361811i \(0.117841\pi\)
−0.932252 + 0.361811i \(0.882159\pi\)
\(272\) −28.2015 + 11.4423i −1.70997 + 0.693792i
\(273\) 0 0
\(274\) −5.72940 24.7753i −0.346126 1.49673i
\(275\) 4.09137 7.08647i 0.246719 0.427330i
\(276\) 0 0
\(277\) 8.83024 + 15.2944i 0.530558 + 0.918953i 0.999364 + 0.0356520i \(0.0113508\pi\)
−0.468807 + 0.883301i \(0.655316\pi\)
\(278\) −8.61147 + 8.03624i −0.516482 + 0.481981i
\(279\) 0 0
\(280\) −6.38570 + 5.18268i −0.381618 + 0.309725i
\(281\) 16.5651 9.56389i 0.988193 0.570534i 0.0834596 0.996511i \(-0.473403\pi\)
0.904734 + 0.425977i \(0.140070\pi\)
\(282\) 0 0
\(283\) −2.81044 1.62261i −0.167063 0.0964541i 0.414137 0.910215i \(-0.364083\pi\)
−0.581200 + 0.813760i \(0.697417\pi\)
\(284\) 2.40927 + 1.62250i 0.142964 + 0.0962776i
\(285\) 0 0
\(286\) −0.246332 + 0.806775i −0.0145659 + 0.0477056i
\(287\) 8.36214 0.493602
\(288\) 0 0
\(289\) −40.8906 −2.40533
\(290\) 7.67402 25.1336i 0.450634 1.47589i
\(291\) 0 0
\(292\) −6.74886 4.54496i −0.394947 0.265974i
\(293\) −11.1294 6.42555i −0.650185 0.375385i 0.138342 0.990385i \(-0.455823\pi\)
−0.788527 + 0.615000i \(0.789156\pi\)
\(294\) 0 0
\(295\) 20.1192 11.6158i 1.17139 0.676300i
\(296\) −6.92356 + 5.61922i −0.402424 + 0.326611i
\(297\) 0 0
\(298\) −3.42350 + 3.19481i −0.198318 + 0.185071i
\(299\) −1.13743 1.97009i −0.0657792 0.113933i
\(300\) 0 0
\(301\) −4.14596 + 7.18102i −0.238969 + 0.413907i
\(302\) 1.98409 + 8.57967i 0.114172 + 0.493705i
\(303\) 0 0
\(304\) −9.67107 + 3.92389i −0.554674 + 0.225050i
\(305\) 21.4932i 1.23069i
\(306\) 0 0
\(307\) 17.7017i 1.01029i 0.863035 + 0.505144i \(0.168561\pi\)
−0.863035 + 0.505144i \(0.831439\pi\)
\(308\) 2.07978 + 4.25626i 0.118507 + 0.242523i
\(309\) 0 0
\(310\) −0.418971 + 0.0968890i −0.0237960 + 0.00550293i
\(311\) −3.30345 + 5.72174i −0.187321 + 0.324450i −0.944356 0.328924i \(-0.893314\pi\)
0.757035 + 0.653374i \(0.226647\pi\)
\(312\) 0 0
\(313\) 5.34114 + 9.25113i 0.301899 + 0.522905i 0.976566 0.215217i \(-0.0690460\pi\)
−0.674667 + 0.738122i \(0.735713\pi\)
\(314\) 2.87361 + 3.07930i 0.162167 + 0.173775i
\(315\) 0 0
\(316\) 23.1240 + 1.59994i 1.30083 + 0.0900034i
\(317\) 22.1073 12.7636i 1.24167 0.716878i 0.272235 0.962231i \(-0.412237\pi\)
0.969434 + 0.245353i \(0.0789040\pi\)
\(318\) 0 0
\(319\) −13.1090 7.56849i −0.733964 0.423754i
\(320\) −15.5269 + 17.3209i −0.867980 + 0.968268i
\(321\) 0 0
\(322\) −12.2184 3.73065i −0.680906 0.207901i
\(323\) −19.8523 −1.10461
\(324\) 0 0
\(325\) −0.869972 −0.0482573
\(326\) 11.2173 + 3.42498i 0.621271 + 0.189692i
\(327\) 0 0
\(328\) 23.3564 3.72565i 1.28964 0.205715i
\(329\) −0.430036 0.248282i −0.0237087 0.0136882i
\(330\) 0 0
\(331\) −23.0921 + 13.3322i −1.26925 + 0.732804i −0.974847 0.222876i \(-0.928456\pi\)
−0.294407 + 0.955680i \(0.595122\pi\)
\(332\) 0.121371 1.75418i 0.00666108 0.0962731i
\(333\) 0 0
\(334\) 18.0425 + 19.3340i 0.987243 + 1.05791i
\(335\) −0.745541 1.29132i −0.0407333 0.0705521i
\(336\) 0 0
\(337\) 3.17158 5.49333i 0.172767 0.299241i −0.766619 0.642102i \(-0.778063\pi\)
0.939386 + 0.342861i \(0.111396\pi\)
\(338\) −17.8247 + 4.12204i −0.969535 + 0.224209i
\(339\) 0 0
\(340\) −39.7546 + 19.4257i −2.15599 + 1.05351i
\(341\) 0.247700i 0.0134137i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −8.38074 + 21.9046i −0.451859 + 1.18102i
\(345\) 0 0
\(346\) −2.79201 12.0733i −0.150099 0.649065i
\(347\) −2.10127 + 3.63950i −0.112802 + 0.195379i −0.916899 0.399119i \(-0.869316\pi\)
0.804097 + 0.594498i \(0.202649\pi\)
\(348\) 0 0
\(349\) −17.6897 30.6395i −0.946908 1.64009i −0.751885 0.659294i \(-0.770855\pi\)
−0.195023 0.980799i \(-0.562478\pi\)
\(350\) −3.57190 + 3.33331i −0.190926 + 0.178173i
\(351\) 0 0
\(352\) 7.70540 + 10.9616i 0.410699 + 0.584255i
\(353\) −25.9389 + 14.9758i −1.38059 + 0.797082i −0.992229 0.124426i \(-0.960291\pi\)
−0.388358 + 0.921509i \(0.626958\pi\)
\(354\) 0 0
\(355\) 3.65716 + 2.11146i 0.194102 + 0.112065i
\(356\) 16.3985 24.3504i 0.869121 1.29057i
\(357\) 0 0
\(358\) −1.18818 + 3.89147i −0.0627973 + 0.205670i
\(359\) −5.48093 −0.289272 −0.144636 0.989485i \(-0.546201\pi\)
−0.144636 + 0.989485i \(0.546201\pi\)
\(360\) 0 0
\(361\) 12.1921 0.641689
\(362\) 1.99468 6.53289i 0.104838 0.343361i
\(363\) 0 0
\(364\) 0.281331 0.417752i 0.0147458 0.0218961i
\(365\) −10.2445 5.91465i −0.536221 0.309587i
\(366\) 0 0
\(367\) −14.7364 + 8.50804i −0.769232 + 0.444116i −0.832601 0.553874i \(-0.813149\pi\)
0.0633686 + 0.997990i \(0.479816\pi\)
\(368\) −35.7896 4.97635i −1.86566 0.259410i
\(369\) 0 0
\(370\) −9.47789 + 8.84478i −0.492732 + 0.459818i
\(371\) −1.19339 2.06701i −0.0619577 0.107314i
\(372\) 0 0
\(373\) −0.570268 + 0.987733i −0.0295274 + 0.0511429i −0.880411 0.474211i \(-0.842734\pi\)
0.850884 + 0.525353i \(0.176067\pi\)
\(374\) 5.74235 + 24.8313i 0.296930 + 1.28400i
\(375\) 0 0
\(376\) −1.31176 0.501882i −0.0676489 0.0258826i
\(377\) 1.60933i 0.0828847i
\(378\) 0 0
\(379\) 26.5456i 1.36356i −0.731559 0.681778i \(-0.761207\pi\)
0.731559 0.681778i \(-0.238793\pi\)
\(380\) −13.6329 + 6.66162i −0.699355 + 0.341734i
\(381\) 0 0
\(382\) 28.2690 6.53735i 1.44637 0.334480i
\(383\) −17.3272 + 30.0116i −0.885380 + 1.53352i −0.0401027 + 0.999196i \(0.512769\pi\)
−0.845277 + 0.534328i \(0.820565\pi\)
\(384\) 0 0
\(385\) 3.44359 + 5.96447i 0.175502 + 0.303978i
\(386\) −17.9446 19.2290i −0.913354 0.978732i
\(387\) 0 0
\(388\) 0.795344 11.4952i 0.0403775 0.583578i
\(389\) −10.2165 + 5.89849i −0.517996 + 0.299065i −0.736114 0.676857i \(-0.763341\pi\)
0.218118 + 0.975922i \(0.430008\pi\)
\(390\) 0 0
\(391\) −59.5237 34.3660i −3.01024 1.73796i
\(392\) −0.445538 2.79312i −0.0225031 0.141074i
\(393\) 0 0
\(394\) 23.3349 + 7.12483i 1.17559 + 0.358944i
\(395\) 33.6991 1.69558
\(396\) 0 0
\(397\) −13.5577 −0.680441 −0.340221 0.940346i \(-0.610502\pi\)
−0.340221 + 0.940346i \(0.610502\pi\)
\(398\) 1.58548 + 0.484094i 0.0794729 + 0.0242654i
\(399\) 0 0
\(400\) −8.49163 + 10.9017i −0.424581 + 0.545086i
\(401\) 5.39384 + 3.11414i 0.269356 + 0.155513i 0.628595 0.777733i \(-0.283630\pi\)
−0.359239 + 0.933246i \(0.616964\pi\)
\(402\) 0 0
\(403\) 0.0228067 0.0131675i 0.00113609 0.000655919i
\(404\) −28.7913 1.99206i −1.43242 0.0991085i
\(405\) 0 0
\(406\) 6.16617 + 6.60754i 0.306022 + 0.327927i
\(407\) 3.73364 + 6.46686i 0.185070 + 0.320550i
\(408\) 0 0
\(409\) −0.409311 + 0.708947i −0.0202391 + 0.0350552i −0.875968 0.482370i \(-0.839776\pi\)
0.855728 + 0.517425i \(0.173109\pi\)
\(410\) 33.5018 7.74744i 1.65453 0.382619i
\(411\) 0 0
\(412\) 10.5247 + 21.5387i 0.518514 + 1.06113i
\(413\) 7.98974i 0.393149i
\(414\) 0 0
\(415\) 2.55640i 0.125489i
\(416\) 0.599666 1.29217i 0.0294011 0.0633540i
\(417\) 0 0
\(418\) 1.96921 + 8.51534i 0.0963174 + 0.416499i
\(419\) −7.99122 + 13.8412i −0.390397 + 0.676187i −0.992502 0.122230i \(-0.960995\pi\)
0.602105 + 0.798417i \(0.294329\pi\)
\(420\) 0 0
\(421\) −4.02490 6.97133i −0.196161 0.339762i 0.751119 0.660167i \(-0.229514\pi\)
−0.947281 + 0.320405i \(0.896181\pi\)
\(422\) 10.5200 9.81723i 0.512103 0.477896i
\(423\) 0 0
\(424\) −4.25421 5.24170i −0.206603 0.254559i
\(425\) −22.7636 + 13.1426i −1.10420 + 0.637508i
\(426\) 0 0
\(427\) 6.40151 + 3.69592i 0.309791 + 0.178858i
\(428\) 10.1250 + 6.81859i 0.489410 + 0.329589i
\(429\) 0 0
\(430\) −9.95709 + 32.6110i −0.480174 + 1.57264i
\(431\) 32.4604 1.56356 0.781780 0.623554i \(-0.214312\pi\)
0.781780 + 0.623554i \(0.214312\pi\)
\(432\) 0 0
\(433\) −18.4266 −0.885525 −0.442762 0.896639i \(-0.646001\pi\)
−0.442762 + 0.896639i \(0.646001\pi\)
\(434\) 0.0431879 0.141447i 0.00207309 0.00678967i
\(435\) 0 0
\(436\) −10.3765 6.98799i −0.496946 0.334664i
\(437\) −20.4123 11.7851i −0.976455 0.563756i
\(438\) 0 0
\(439\) 31.5605 18.2214i 1.50630 0.869662i 0.506325 0.862343i \(-0.331004\pi\)
0.999973 0.00731896i \(-0.00232972\pi\)
\(440\) 12.2757 + 15.1252i 0.585223 + 0.721066i
\(441\) 0 0
\(442\) 1.98106 1.84872i 0.0942293 0.0879349i
\(443\) −11.3610 19.6778i −0.539776 0.934919i −0.998916 0.0465549i \(-0.985176\pi\)
0.459140 0.888364i \(-0.348158\pi\)
\(444\) 0 0
\(445\) 21.3405 36.9628i 1.01164 1.75221i
\(446\) 1.94291 + 8.40160i 0.0919994 + 0.397827i
\(447\) 0 0
\(448\) −2.48888 7.60299i −0.117589 0.359208i
\(449\) 9.26171i 0.437087i −0.975827 0.218544i \(-0.929869\pi\)
0.975827 0.218544i \(-0.0701306\pi\)
\(450\) 0 0
\(451\) 19.8066i 0.932658i
\(452\) 16.1110 + 32.9710i 0.757797 + 1.55083i
\(453\) 0 0
\(454\) −30.7484 + 7.11071i −1.44309 + 0.333722i
\(455\) 0.366115 0.634129i 0.0171637 0.0297284i
\(456\) 0 0
\(457\) 5.90082 + 10.2205i 0.276029 + 0.478096i 0.970394 0.241527i \(-0.0776482\pi\)
−0.694365 + 0.719623i \(0.744315\pi\)
\(458\) −5.22758 5.60177i −0.244269 0.261753i
\(459\) 0 0
\(460\) −52.4079 3.62607i −2.44353 0.169066i
\(461\) −2.21744 + 1.28024i −0.103276 + 0.0596266i −0.550749 0.834671i \(-0.685658\pi\)
0.447472 + 0.894298i \(0.352324\pi\)
\(462\) 0 0
\(463\) 10.0234 + 5.78704i 0.465829 + 0.268947i 0.714492 0.699643i \(-0.246658\pi\)
−0.248663 + 0.968590i \(0.579991\pi\)
\(464\) 20.1667 + 15.7084i 0.936217 + 0.729243i
\(465\) 0 0
\(466\) 8.22620 + 2.51170i 0.381071 + 0.116352i
\(467\) −0.571766 −0.0264582 −0.0132291 0.999912i \(-0.504211\pi\)
−0.0132291 + 0.999912i \(0.504211\pi\)
\(468\) 0 0
\(469\) 0.512806 0.0236792
\(470\) −1.95291 0.596282i −0.0900811 0.0275044i
\(471\) 0 0
\(472\) 3.55973 + 22.3163i 0.163850 + 1.02719i
\(473\) 17.0090 + 9.82016i 0.782076 + 0.451532i
\(474\) 0 0
\(475\) −7.80627 + 4.50695i −0.358176 + 0.206793i
\(476\) 1.05036 15.1809i 0.0481430 0.695815i
\(477\) 0 0
\(478\) 8.85578 + 9.48967i 0.405054 + 0.434048i
\(479\) −13.9036 24.0818i −0.635273 1.10033i −0.986457 0.164019i \(-0.947554\pi\)
0.351184 0.936306i \(-0.385779\pi\)
\(480\) 0 0
\(481\) 0.396953 0.687542i 0.0180995 0.0313492i
\(482\) 12.6771 2.93165i 0.577428 0.133533i
\(483\) 0 0
\(484\) −9.68499 + 4.73248i −0.440227 + 0.215113i
\(485\) 16.7521i 0.760676i
\(486\) 0 0
\(487\) 10.3286i 0.468031i 0.972233 + 0.234016i \(0.0751867\pi\)
−0.972233 + 0.234016i \(0.924813\pi\)
\(488\) 19.5268 + 7.47100i 0.883939 + 0.338196i
\(489\) 0 0
\(490\) −0.926490 4.00636i −0.0418546 0.180989i
\(491\) 16.9157 29.2988i 0.763394 1.32224i −0.177697 0.984085i \(-0.556865\pi\)
0.941091 0.338153i \(-0.109802\pi\)
\(492\) 0 0
\(493\) 24.3120 + 42.1096i 1.09496 + 1.89652i
\(494\) 0.679360 0.633979i 0.0305658 0.0285241i
\(495\) 0 0
\(496\) 0.0576089 0.414320i 0.00258672 0.0186035i
\(497\) −1.25776 + 0.726166i −0.0564181 + 0.0325730i
\(498\) 0 0
\(499\) −5.27446 3.04521i −0.236117 0.136322i 0.377274 0.926102i \(-0.376862\pi\)
−0.613391 + 0.789779i \(0.710195\pi\)
\(500\) 5.01984 7.45400i 0.224494 0.333353i
\(501\) 0 0
\(502\) 7.25900 23.7743i 0.323985 1.06110i
\(503\) −21.4710 −0.957345 −0.478673 0.877993i \(-0.658882\pi\)
−0.478673 + 0.877993i \(0.658882\pi\)
\(504\) 0 0
\(505\) −41.9582 −1.86712
\(506\) −8.83644 + 28.9407i −0.392828 + 1.28657i
\(507\) 0 0
\(508\) 15.1751 22.5337i 0.673286 0.999769i
\(509\) 18.4897 + 10.6750i 0.819540 + 0.473161i 0.850258 0.526367i \(-0.176446\pi\)
−0.0307180 + 0.999528i \(0.509779\pi\)
\(510\) 0 0
\(511\) 3.52324 2.03414i 0.155859 0.0899851i
\(512\) −10.3392 20.1271i −0.456930 0.889503i
\(513\) 0 0
\(514\) −11.1798 + 10.4330i −0.493119 + 0.460179i
\(515\) 17.4262 + 30.1830i 0.767890 + 1.33002i
\(516\) 0 0
\(517\) −0.588082 + 1.01859i −0.0258638 + 0.0447974i
\(518\) −1.00453 4.34382i −0.0441365 0.190856i
\(519\) 0 0
\(520\) 0.740072 1.93431i 0.0324543 0.0848253i
\(521\) 30.4799i 1.33535i 0.744453 + 0.667675i \(0.232710\pi\)
−0.744453 + 0.667675i \(0.767290\pi\)
\(522\) 0 0
\(523\) 28.4494i 1.24401i −0.783014 0.622004i \(-0.786319\pi\)
0.783014 0.622004i \(-0.213681\pi\)
\(524\) 2.66130 1.30042i 0.116260 0.0568092i
\(525\) 0 0
\(526\) 3.39905 0.786046i 0.148206 0.0342733i
\(527\) 0.397839 0.689078i 0.0173302 0.0300167i
\(528\) 0 0
\(529\) −29.3019 50.7524i −1.27400 2.20663i
\(530\) −6.69622 7.17553i −0.290865 0.311685i
\(531\) 0 0
\(532\) 0.360197 5.20595i 0.0156165 0.225706i
\(533\) −1.82367 + 1.05290i −0.0789921 + 0.0456061i
\(534\) 0 0
\(535\) 15.3693 + 8.87348i 0.664474 + 0.383634i
\(536\) 1.43233 0.228475i 0.0618671 0.00986861i
\(537\) 0 0
\(538\) 25.2142 + 7.69865i 1.08706 + 0.331912i
\(539\) −2.36861 −0.102023
\(540\) 0 0
\(541\) 28.9747 1.24572 0.622861 0.782333i \(-0.285970\pi\)
0.622861 + 0.782333i \(0.285970\pi\)
\(542\) −16.1122 4.91954i −0.692080 0.211312i
\(543\) 0 0
\(544\) −3.82989 42.8699i −0.164205 1.83803i
\(545\) −15.7512 9.09393i −0.674705 0.389541i
\(546\) 0 0
\(547\) −32.0274 + 18.4910i −1.36939 + 0.790619i −0.990850 0.134966i \(-0.956908\pi\)
−0.378541 + 0.925584i \(0.623574\pi\)
\(548\) 35.8764 + 2.48227i 1.53257 + 0.106037i
\(549\) 0 0
\(550\) 7.89529 + 8.46044i 0.336656 + 0.360754i
\(551\) 8.33725 + 14.4405i 0.355179 + 0.615188i
\(552\) 0 0
\(553\) −5.79482 + 10.0369i −0.246421 + 0.426813i
\(554\) −24.3335 + 5.62724i −1.03383 + 0.239078i
\(555\) 0 0
\(556\) −7.31321 14.9664i −0.310149 0.634718i
\(557\) 4.29428i 0.181955i 0.995853 + 0.0909773i \(0.0289991\pi\)
−0.995853 + 0.0909773i \(0.971001\pi\)
\(558\) 0 0
\(559\) 2.08812i 0.0883179i
\(560\) −4.37278 10.7774i −0.184784 0.455430i
\(561\) 0 0
\(562\) 6.09477 + 26.3552i 0.257092 + 1.11173i
\(563\) −2.78657 + 4.82649i −0.117440 + 0.203412i −0.918753 0.394834i \(-0.870802\pi\)
0.801312 + 0.598246i \(0.204135\pi\)
\(564\) 0 0
\(565\) 26.6757 + 46.2037i 1.12225 + 1.94380i
\(566\) 3.35535 3.13122i 0.141036 0.131615i
\(567\) 0 0
\(568\) −3.18952 + 2.58864i −0.133829 + 0.108617i
\(569\) 5.72734 3.30668i 0.240103 0.138623i −0.375121 0.926976i \(-0.622399\pi\)
0.615224 + 0.788352i \(0.289066\pi\)
\(570\) 0 0
\(571\) 28.7640 + 16.6069i 1.20374 + 0.694978i 0.961384 0.275211i \(-0.0887476\pi\)
0.242353 + 0.970188i \(0.422081\pi\)
\(572\) −0.989489 0.666363i −0.0413726 0.0278620i
\(573\) 0 0
\(574\) −3.45340 + 11.3104i −0.144142 + 0.472087i
\(575\) −31.2077 −1.30145
\(576\) 0 0
\(577\) 27.6524 1.15119 0.575593 0.817736i \(-0.304771\pi\)
0.575593 + 0.817736i \(0.304771\pi\)
\(578\) 16.8870 55.3074i 0.702406 2.30049i
\(579\) 0 0
\(580\) 30.8257 + 20.7593i 1.27997 + 0.861984i
\(581\) 0.761398 + 0.439593i 0.0315881 + 0.0182374i
\(582\) 0 0
\(583\) −4.89594 + 2.82667i −0.202769 + 0.117069i
\(584\) 8.93452 7.25133i 0.369713 0.300062i
\(585\) 0 0
\(586\) 13.2872 12.3996i 0.548890 0.512225i
\(587\) 12.0238 + 20.8258i 0.496274 + 0.859571i 0.999991 0.00429733i \(-0.00136789\pi\)
−0.503717 + 0.863869i \(0.668035\pi\)
\(588\) 0 0
\(589\) 0.136430 0.236304i 0.00562151 0.00973674i
\(590\) 7.40241 + 32.0098i 0.304753 + 1.31782i
\(591\) 0 0
\(592\) −4.74110 11.6852i −0.194858 0.480260i
\(593\) 7.02971i 0.288675i 0.989528 + 0.144338i \(0.0461052\pi\)
−0.989528 + 0.144338i \(0.953895\pi\)
\(594\) 0 0
\(595\) 22.1234i 0.906972i
\(596\) −2.90738 5.94992i −0.119091 0.243718i
\(597\) 0 0
\(598\) 3.13441 0.724848i 0.128176 0.0296412i
\(599\) −14.7689 + 25.5804i −0.603439 + 1.04519i 0.388857 + 0.921298i \(0.372870\pi\)
−0.992296 + 0.123889i \(0.960463\pi\)
\(600\) 0 0
\(601\) −11.2326 19.4555i −0.458188 0.793605i 0.540677 0.841230i \(-0.318168\pi\)
−0.998865 + 0.0476250i \(0.984835\pi\)
\(602\) −8.00064 8.57333i −0.326082 0.349423i
\(603\) 0 0
\(604\) −12.4240 0.859610i −0.505526 0.0349770i
\(605\) −13.5720 + 7.83579i −0.551780 + 0.318570i
\(606\) 0 0
\(607\) 31.5236 + 18.2002i 1.27950 + 0.738722i 0.976757 0.214348i \(-0.0687628\pi\)
0.302748 + 0.953071i \(0.402096\pi\)
\(608\) −1.31338 14.7013i −0.0532645 0.596216i
\(609\) 0 0
\(610\) 29.0710 + 8.87624i 1.17705 + 0.359388i
\(611\) 0.125047 0.00505886
\(612\) 0 0
\(613\) 12.8571 0.519293 0.259646 0.965704i \(-0.416394\pi\)
0.259646 + 0.965704i \(0.416394\pi\)
\(614\) −23.9428 7.31043i −0.966251 0.295025i
\(615\) 0 0
\(616\) −6.61580 + 1.05531i −0.266558 + 0.0425195i
\(617\) 37.5894 + 21.7022i 1.51329 + 0.873699i 0.999879 + 0.0155564i \(0.00495195\pi\)
0.513412 + 0.858142i \(0.328381\pi\)
\(618\) 0 0
\(619\) −0.893596 + 0.515918i −0.0359167 + 0.0207365i −0.517851 0.855471i \(-0.673268\pi\)
0.481934 + 0.876207i \(0.339934\pi\)
\(620\) 0.0419773 0.606701i 0.00168585 0.0243657i
\(621\) 0 0
\(622\) −6.37480 6.83111i −0.255606 0.273903i
\(623\) 7.33933 + 12.7121i 0.294044 + 0.509299i
\(624\) 0 0
\(625\) 15.1693 26.2740i 0.606772 1.05096i
\(626\) −14.7186 + 3.40374i −0.588274 + 0.136041i
\(627\) 0 0
\(628\) −5.35172 + 2.61507i −0.213557 + 0.104353i
\(629\) 23.9869i 0.956420i
\(630\) 0 0
\(631\) 25.4447i 1.01294i 0.862258 + 0.506469i \(0.169049\pi\)
−0.862258 + 0.506469i \(0.830951\pi\)
\(632\) −11.7138 + 30.6161i −0.465949 + 1.21784i
\(633\) 0 0
\(634\) 8.13387 + 35.1728i 0.323037 + 1.39689i
\(635\) 19.7483 34.2051i 0.783689 1.35739i
\(636\) 0 0
\(637\) 0.125913 + 0.218087i 0.00498884 + 0.00864092i
\(638\) 15.6507 14.6052i 0.619616 0.578227i
\(639\) 0 0
\(640\) −17.0155 28.1544i −0.672595 1.11290i
\(641\) 24.3065 14.0334i 0.960049 0.554284i 0.0638607 0.997959i \(-0.479659\pi\)
0.896188 + 0.443674i \(0.146325\pi\)
\(642\) 0 0
\(643\) 11.1062 + 6.41216i 0.437985 + 0.252871i 0.702743 0.711444i \(-0.251959\pi\)
−0.264757 + 0.964315i \(0.585292\pi\)
\(644\) 10.0919 14.9856i 0.397678 0.590516i
\(645\) 0 0
\(646\) 8.19860 26.8516i 0.322570 1.05646i
\(647\) 39.1711 1.53998 0.769988 0.638058i \(-0.220262\pi\)
0.769988 + 0.638058i \(0.220262\pi\)
\(648\) 0 0
\(649\) 18.9246 0.742854
\(650\) 0.359281 1.17670i 0.0140921 0.0461539i
\(651\) 0 0
\(652\) −9.26507 + 13.7578i −0.362848 + 0.538797i
\(653\) −5.09574 2.94203i −0.199412 0.115130i 0.396969 0.917832i \(-0.370062\pi\)
−0.596381 + 0.802701i \(0.703395\pi\)
\(654\) 0 0
\(655\) 3.72940 2.15317i 0.145720 0.0841313i
\(656\) −4.60652 + 33.1298i −0.179855 + 1.29350i
\(657\) 0 0
\(658\) 0.513415 0.479119i 0.0200150 0.0186780i
\(659\) 12.9730 + 22.4699i 0.505357 + 0.875304i 0.999981 + 0.00619658i \(0.00197245\pi\)
−0.494624 + 0.869107i \(0.664694\pi\)
\(660\) 0 0
\(661\) −19.8403 + 34.3644i −0.771699 + 1.33662i 0.164933 + 0.986305i \(0.447259\pi\)
−0.936631 + 0.350316i \(0.886074\pi\)
\(662\) −8.49620 36.7396i −0.330214 1.42792i
\(663\) 0 0
\(664\) 2.32253 + 0.888603i 0.0901316 + 0.0344845i
\(665\) 7.58674i 0.294201i
\(666\) 0 0
\(667\) 57.7300i 2.23531i
\(668\) −33.6018 + 16.4192i −1.30009 + 0.635279i
\(669\) 0 0
\(670\) 2.05449 0.475110i 0.0793718 0.0183551i
\(671\) 8.75417 15.1627i 0.337951 0.585349i
\(672\) 0 0
\(673\) 5.16943 + 8.95371i 0.199267 + 0.345140i 0.948291 0.317403i \(-0.102811\pi\)
−0.749024 + 0.662543i \(0.769477\pi\)
\(674\) 6.12032 + 6.55842i 0.235746 + 0.252621i
\(675\) 0 0
\(676\) 1.78588 25.8115i 0.0686877 0.992748i
\(677\) 4.67459 2.69887i 0.179659 0.103726i −0.407473 0.913217i \(-0.633590\pi\)
0.587132 + 0.809491i \(0.300257\pi\)
\(678\) 0 0
\(679\) 4.98945 + 2.88066i 0.191478 + 0.110550i
\(680\) −9.85683 61.7933i −0.377992 2.36966i
\(681\) 0 0
\(682\) −0.335032 0.102295i −0.0128291 0.00391709i
\(683\) −39.2840 −1.50316 −0.751581 0.659641i \(-0.770708\pi\)
−0.751581 + 0.659641i \(0.770708\pi\)
\(684\) 0 0
\(685\) 52.2835 1.99765
\(686\) 1.35257 + 0.412980i 0.0516414 + 0.0157676i
\(687\) 0 0
\(688\) −26.1665 20.3817i −0.997587 0.777045i
\(689\) 0.520525 + 0.300525i 0.0198304 + 0.0114491i
\(690\) 0 0
\(691\) −15.8640 + 9.15909i −0.603495 + 0.348428i −0.770415 0.637542i \(-0.779951\pi\)
0.166920 + 0.985970i \(0.446618\pi\)
\(692\) 17.4831 + 1.20964i 0.664606 + 0.0459837i
\(693\) 0 0
\(694\) −4.05490 4.34515i −0.153922 0.164940i
\(695\) −12.1088 20.9731i −0.459314 0.795555i
\(696\) 0 0
\(697\) −31.8120 + 55.1001i −1.20497 + 2.08706i
\(698\) 48.7475 11.2731i 1.84512 0.426693i
\(699\) 0 0
\(700\) −3.03341 6.20784i −0.114652 0.234634i
\(701\) 14.7290i 0.556306i 0.960537 + 0.278153i \(0.0897222\pi\)
−0.960537 + 0.278153i \(0.910278\pi\)
\(702\) 0 0
\(703\) 8.22577i 0.310241i
\(704\) −18.0085 + 5.89518i −0.678721 + 0.222183i
\(705\) 0 0
\(706\) −9.54362 41.2689i −0.359179 1.55317i
\(707\) 7.21504 12.4968i 0.271349 0.469991i
\(708\) 0 0
\(709\) −0.246081 0.426224i −0.00924175 0.0160072i 0.861368 0.507982i \(-0.169608\pi\)
−0.870609 + 0.491975i \(0.836275\pi\)
\(710\) −4.36624 + 4.07458i −0.163862 + 0.152916i
\(711\) 0 0
\(712\) 26.1633 + 32.2364i 0.980512 + 1.20811i
\(713\) 0.818125 0.472345i 0.0306390 0.0176894i
\(714\) 0 0
\(715\) −1.50200 0.867182i −0.0561718 0.0324308i
\(716\) −4.77279 3.21419i −0.178368 0.120120i
\(717\) 0 0
\(718\) 2.26351 7.41334i 0.0844736 0.276664i
\(719\) 7.89549 0.294452 0.147226 0.989103i \(-0.452966\pi\)
0.147226 + 0.989103i \(0.452966\pi\)
\(720\) 0 0
\(721\) −11.9863 −0.446392
\(722\) −5.03509 + 16.4907i −0.187387 + 0.613719i
\(723\) 0 0
\(724\) 8.01243 + 5.39590i 0.297780 + 0.200537i
\(725\) 19.1198 + 11.0388i 0.710091 + 0.409971i
\(726\) 0 0
\(727\) 9.22490 5.32600i 0.342133 0.197530i −0.319082 0.947727i \(-0.603375\pi\)
0.661215 + 0.750197i \(0.270041\pi\)
\(728\) 0.448854 + 0.553043i 0.0166357 + 0.0204971i
\(729\) 0 0
\(730\) 12.2308 11.4138i 0.452681 0.422442i
\(731\) −31.5449 54.6374i −1.16673 2.02084i
\(732\) 0 0
\(733\) 26.0962 45.1999i 0.963885 1.66950i 0.251304 0.967908i \(-0.419141\pi\)
0.712581 0.701590i \(-0.247526\pi\)
\(734\) −5.42191 23.4456i −0.200126 0.865394i
\(735\) 0 0
\(736\) 21.5113 46.3529i 0.792916 1.70859i
\(737\) 1.21464i 0.0447417i
\(738\) 0 0
\(739\) 34.1328i 1.25560i −0.778376 0.627798i \(-0.783956\pi\)
0.778376 0.627798i \(-0.216044\pi\)
\(740\) −8.04901 16.4722i −0.295888 0.605531i
\(741\) 0 0
\(742\) 3.28862 0.760510i 0.120729 0.0279192i
\(743\) −7.11347 + 12.3209i −0.260968 + 0.452009i −0.966499 0.256669i \(-0.917375\pi\)
0.705532 + 0.708678i \(0.250708\pi\)
\(744\) 0 0
\(745\) −4.81387 8.33787i −0.176367 0.305476i
\(746\) −1.10047 1.17924i −0.0402911 0.0431751i
\(747\) 0 0
\(748\) −35.9576 2.48788i −1.31474 0.0909660i
\(749\) −5.28575 + 3.05173i −0.193137 + 0.111508i
\(750\) 0 0
\(751\) 27.8733 + 16.0926i 1.01711 + 0.587228i 0.913265 0.407365i \(-0.133552\pi\)
0.103844 + 0.994594i \(0.466886\pi\)
\(752\) 1.22056 1.56698i 0.0445093 0.0571419i
\(753\) 0 0
\(754\) −2.17673 0.664621i −0.0792719 0.0242041i
\(755\) −18.1058 −0.658936
\(756\) 0 0
\(757\) −33.8024 −1.22857 −0.614284 0.789085i \(-0.710555\pi\)
−0.614284 + 0.789085i \(0.710555\pi\)
\(758\) 35.9048 + 10.9628i 1.30412 + 0.398187i
\(759\) 0 0
\(760\) −3.38018 21.1906i −0.122612 0.768665i
\(761\) −7.39633 4.27027i −0.268117 0.154797i 0.359915 0.932985i \(-0.382806\pi\)
−0.628031 + 0.778188i \(0.716139\pi\)
\(762\) 0 0
\(763\) 5.41707 3.12754i 0.196111 0.113225i
\(764\) −2.83232 + 40.9357i −0.102470 + 1.48100i
\(765\) 0 0
\(766\) −33.4371 35.8305i −1.20813 1.29461i
\(767\) −1.00601 1.74246i −0.0363249 0.0629165i
\(768\) 0 0
\(769\) −13.0938 + 22.6792i −0.472176 + 0.817833i −0.999493 0.0318354i \(-0.989865\pi\)
0.527317 + 0.849669i \(0.323198\pi\)
\(770\) −9.48950 + 2.19449i −0.341978 + 0.0790840i
\(771\) 0 0
\(772\) 33.4194 16.3301i 1.20279 0.587732i
\(773\) 3.16655i 0.113893i 0.998377 + 0.0569464i \(0.0181364\pi\)
−0.998377 + 0.0569464i \(0.981864\pi\)
\(774\) 0 0
\(775\) 0.361277i 0.0129774i
\(776\) 15.2196 + 5.82303i 0.546350 + 0.209035i
\(777\) 0 0
\(778\) −3.75892 16.2545i −0.134764 0.582751i
\(779\) −10.9092 + 18.8954i −0.390864 + 0.676996i
\(780\) 0 0
\(781\) 1.72000 + 2.97913i 0.0615465 + 0.106602i
\(782\) 71.0646 66.3176i 2.54126 2.37151i
\(783\) 0 0
\(784\) 3.96189 + 0.550878i 0.141496 + 0.0196742i
\(785\) −7.49959 + 4.32989i −0.267672 + 0.154540i
\(786\) 0 0
\(787\) 6.34026 + 3.66055i 0.226006 + 0.130485i 0.608728 0.793379i \(-0.291680\pi\)
−0.382722 + 0.923863i \(0.625013\pi\)
\(788\) −19.2737 + 28.6197i −0.686596 + 1.01953i
\(789\) 0 0
\(790\)