Properties

Label 756.2.ba.a.71.1
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 71.1
Character \(\chi\) \(=\) 756.71
Dual form 756.2.ba.a.575.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.41075 + 0.0989244i) q^{2} +(1.98043 - 0.279115i) q^{4} +(-0.795659 - 0.459374i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-2.76628 + 0.589674i) q^{8} +O(q^{10})\) \(q+(-1.41075 + 0.0989244i) q^{2} +(1.98043 - 0.279115i) q^{4} +(-0.795659 - 0.459374i) q^{5} +(0.866025 - 0.500000i) q^{7} +(-2.76628 + 0.589674i) q^{8} +(1.16792 + 0.569351i) q^{10} +(-0.582708 - 1.00928i) q^{11} +(0.0273083 - 0.0472994i) q^{13} +(-1.17228 + 0.791046i) q^{14} +(3.84419 - 1.10553i) q^{16} -3.29574i q^{17} -0.455543i q^{19} +(-1.70396 - 0.687676i) q^{20} +(0.921897 + 1.36620i) q^{22} +(-1.77871 + 3.08081i) q^{23} +(-2.07795 - 3.59912i) q^{25} +(-0.0338462 + 0.0694291i) q^{26} +(1.57554 - 1.23193i) q^{28} +(7.58443 - 4.37887i) q^{29} +(-7.03218 - 4.06003i) q^{31} +(-5.31382 + 1.93992i) q^{32} +(0.326029 + 4.64947i) q^{34} -0.918747 q^{35} +1.20717 q^{37} +(0.0450644 + 0.642658i) q^{38} +(2.47189 + 0.801575i) q^{40} +(5.27252 + 3.04409i) q^{41} +(-5.64563 + 3.25951i) q^{43} +(-1.43572 - 1.83616i) q^{44} +(2.20454 - 4.52221i) q^{46} +(-2.82141 - 4.88682i) q^{47} +(0.500000 - 0.866025i) q^{49} +(3.28751 + 4.87189i) q^{50} +(0.0408802 - 0.101295i) q^{52} -10.6457i q^{53} +1.07072i q^{55} +(-2.10083 + 1.89381i) q^{56} +(-10.2666 + 6.92778i) q^{58} +(-0.744373 + 1.28929i) q^{59} +(-6.35962 - 11.0152i) q^{61} +(10.3223 + 5.03204i) q^{62} +(7.30457 - 3.26240i) q^{64} +(-0.0434562 + 0.0250895i) q^{65} +(-5.83071 - 3.36636i) q^{67} +(-0.919891 - 6.52698i) q^{68} +(1.29612 - 0.0908865i) q^{70} +2.97148 q^{71} +14.8214 q^{73} +(-1.70301 + 0.119419i) q^{74} +(-0.127149 - 0.902171i) q^{76} +(-1.00928 - 0.582708i) q^{77} +(10.9305 - 6.31075i) q^{79} +(-3.56652 - 0.886292i) q^{80} +(-7.73934 - 3.77287i) q^{82} +(-6.56004 - 11.3623i) q^{83} +(-1.51398 + 2.62229i) q^{85} +(7.64213 - 5.15684i) q^{86} +(2.20708 + 2.44834i) q^{88} -7.95018i q^{89} -0.0546167i q^{91} +(-2.66270 + 6.59779i) q^{92} +(4.46373 + 6.61498i) q^{94} +(-0.209265 + 0.362457i) q^{95} +(-4.26325 - 7.38417i) q^{97} +(-0.619704 + 1.27121i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + O(q^{10}) \) \( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41075 + 0.0989244i −0.997550 + 0.0699501i
\(3\) 0 0
\(4\) 1.98043 0.279115i 0.990214 0.139558i
\(5\) −0.795659 0.459374i −0.355829 0.205438i 0.311420 0.950272i \(-0.399195\pi\)
−0.667250 + 0.744834i \(0.732529\pi\)
\(6\) 0 0
\(7\) 0.866025 0.500000i 0.327327 0.188982i
\(8\) −2.76628 + 0.589674i −0.978026 + 0.208481i
\(9\) 0 0
\(10\) 1.16792 + 0.569351i 0.369328 + 0.180045i
\(11\) −0.582708 1.00928i −0.175693 0.304309i 0.764708 0.644377i \(-0.222883\pi\)
−0.940401 + 0.340068i \(0.889550\pi\)
\(12\) 0 0
\(13\) 0.0273083 0.0472994i 0.00757397 0.0131185i −0.862214 0.506545i \(-0.830922\pi\)
0.869788 + 0.493426i \(0.164256\pi\)
\(14\) −1.17228 + 0.791046i −0.313306 + 0.211416i
\(15\) 0 0
\(16\) 3.84419 1.10553i 0.961047 0.276384i
\(17\) 3.29574i 0.799335i −0.916660 0.399667i \(-0.869126\pi\)
0.916660 0.399667i \(-0.130874\pi\)
\(18\) 0 0
\(19\) 0.455543i 0.104509i −0.998634 0.0522544i \(-0.983359\pi\)
0.998634 0.0522544i \(-0.0166407\pi\)
\(20\) −1.70396 0.687676i −0.381018 0.153769i
\(21\) 0 0
\(22\) 0.921897 + 1.36620i 0.196549 + 0.291274i
\(23\) −1.77871 + 3.08081i −0.370886 + 0.642393i −0.989702 0.143143i \(-0.954279\pi\)
0.618816 + 0.785536i \(0.287613\pi\)
\(24\) 0 0
\(25\) −2.07795 3.59912i −0.415590 0.719824i
\(26\) −0.0338462 + 0.0694291i −0.00663778 + 0.0136162i
\(27\) 0 0
\(28\) 1.57554 1.23193i 0.297750 0.232814i
\(29\) 7.58443 4.37887i 1.40839 0.813136i 0.413160 0.910658i \(-0.364425\pi\)
0.995233 + 0.0975219i \(0.0310916\pi\)
\(30\) 0 0
\(31\) −7.03218 4.06003i −1.26302 0.729203i −0.289360 0.957220i \(-0.593443\pi\)
−0.973657 + 0.228017i \(0.926776\pi\)
\(32\) −5.31382 + 1.93992i −0.939360 + 0.342932i
\(33\) 0 0
\(34\) 0.326029 + 4.64947i 0.0559135 + 0.797377i
\(35\) −0.918747 −0.155297
\(36\) 0 0
\(37\) 1.20717 0.198458 0.0992288 0.995065i \(-0.468362\pi\)
0.0992288 + 0.995065i \(0.468362\pi\)
\(38\) 0.0450644 + 0.642658i 0.00731040 + 0.104253i
\(39\) 0 0
\(40\) 2.47189 + 0.801575i 0.390840 + 0.126740i
\(41\) 5.27252 + 3.04409i 0.823429 + 0.475407i 0.851598 0.524196i \(-0.175634\pi\)
−0.0281682 + 0.999603i \(0.508967\pi\)
\(42\) 0 0
\(43\) −5.64563 + 3.25951i −0.860951 + 0.497070i −0.864331 0.502924i \(-0.832258\pi\)
0.00337979 + 0.999994i \(0.498924\pi\)
\(44\) −1.43572 1.83616i −0.216442 0.276812i
\(45\) 0 0
\(46\) 2.20454 4.52221i 0.325042 0.666763i
\(47\) −2.82141 4.88682i −0.411545 0.712817i 0.583514 0.812103i \(-0.301677\pi\)
−0.995059 + 0.0992864i \(0.968344\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) 3.28751 + 4.87189i 0.464924 + 0.688990i
\(51\) 0 0
\(52\) 0.0408802 0.101295i 0.00566907 0.0140471i
\(53\) 10.6457i 1.46230i −0.682218 0.731149i \(-0.738984\pi\)
0.682218 0.731149i \(-0.261016\pi\)
\(54\) 0 0
\(55\) 1.07072i 0.144376i
\(56\) −2.10083 + 1.89381i −0.280735 + 0.253071i
\(57\) 0 0
\(58\) −10.2666 + 6.92778i −1.34806 + 0.909662i
\(59\) −0.744373 + 1.28929i −0.0969092 + 0.167852i −0.910404 0.413721i \(-0.864229\pi\)
0.813495 + 0.581572i \(0.197562\pi\)
\(60\) 0 0
\(61\) −6.35962 11.0152i −0.814266 1.41035i −0.909854 0.414929i \(-0.863807\pi\)
0.0955881 0.995421i \(-0.469527\pi\)
\(62\) 10.3223 + 5.03204i 1.31093 + 0.639069i
\(63\) 0 0
\(64\) 7.30457 3.26240i 0.913071 0.407800i
\(65\) −0.0434562 + 0.0250895i −0.00539008 + 0.00311197i
\(66\) 0 0
\(67\) −5.83071 3.36636i −0.712335 0.411267i 0.0995902 0.995029i \(-0.468247\pi\)
−0.811925 + 0.583762i \(0.801580\pi\)
\(68\) −0.919891 6.52698i −0.111553 0.791512i
\(69\) 0 0
\(70\) 1.29612 0.0908865i 0.154916 0.0108630i
\(71\) 2.97148 0.352650 0.176325 0.984332i \(-0.443579\pi\)
0.176325 + 0.984332i \(0.443579\pi\)
\(72\) 0 0
\(73\) 14.8214 1.73471 0.867357 0.497686i \(-0.165817\pi\)
0.867357 + 0.497686i \(0.165817\pi\)
\(74\) −1.70301 + 0.119419i −0.197971 + 0.0138821i
\(75\) 0 0
\(76\) −0.127149 0.902171i −0.0145850 0.103486i
\(77\) −1.00928 0.582708i −0.115018 0.0664057i
\(78\) 0 0
\(79\) 10.9305 6.31075i 1.22978 0.710015i 0.262798 0.964851i \(-0.415355\pi\)
0.966984 + 0.254836i \(0.0820214\pi\)
\(80\) −3.56652 0.886292i −0.398749 0.0990904i
\(81\) 0 0
\(82\) −7.73934 3.77287i −0.854667 0.416644i
\(83\) −6.56004 11.3623i −0.720058 1.24718i −0.960976 0.276632i \(-0.910782\pi\)
0.240918 0.970546i \(-0.422552\pi\)
\(84\) 0 0
\(85\) −1.51398 + 2.62229i −0.164214 + 0.284427i
\(86\) 7.64213 5.15684i 0.824072 0.556076i
\(87\) 0 0
\(88\) 2.20708 + 2.44834i 0.235275 + 0.260994i
\(89\) 7.95018i 0.842717i −0.906894 0.421359i \(-0.861553\pi\)
0.906894 0.421359i \(-0.138447\pi\)
\(90\) 0 0
\(91\) 0.0546167i 0.00572539i
\(92\) −2.66270 + 6.59779i −0.277606 + 0.687867i
\(93\) 0 0
\(94\) 4.46373 + 6.61498i 0.460398 + 0.682283i
\(95\) −0.209265 + 0.362457i −0.0214701 + 0.0371873i
\(96\) 0 0
\(97\) −4.26325 7.38417i −0.432868 0.749749i 0.564251 0.825603i \(-0.309165\pi\)
−0.997119 + 0.0758544i \(0.975832\pi\)
\(98\) −0.619704 + 1.27121i −0.0625995 + 0.128411i
\(99\) 0 0
\(100\) −5.11980 6.54781i −0.511980 0.654781i
\(101\) −11.2424 + 6.49081i −1.11866 + 0.645860i −0.941059 0.338242i \(-0.890168\pi\)
−0.177604 + 0.984102i \(0.556834\pi\)
\(102\) 0 0
\(103\) −1.95855 1.13077i −0.192982 0.111418i 0.400396 0.916342i \(-0.368873\pi\)
−0.593378 + 0.804924i \(0.702206\pi\)
\(104\) −0.0476512 + 0.146946i −0.00467258 + 0.0144093i
\(105\) 0 0
\(106\) 1.05312 + 15.0184i 0.102288 + 1.45872i
\(107\) −4.66383 −0.450870 −0.225435 0.974258i \(-0.572380\pi\)
−0.225435 + 0.974258i \(0.572380\pi\)
\(108\) 0 0
\(109\) −11.1216 −1.06526 −0.532629 0.846349i \(-0.678796\pi\)
−0.532629 + 0.846349i \(0.678796\pi\)
\(110\) −0.105921 1.51052i −0.0100991 0.144023i
\(111\) 0 0
\(112\) 2.77640 2.87952i 0.262345 0.272089i
\(113\) 14.2992 + 8.25566i 1.34516 + 0.776627i 0.987559 0.157248i \(-0.0502621\pi\)
0.357599 + 0.933875i \(0.383595\pi\)
\(114\) 0 0
\(115\) 2.83049 1.63418i 0.263944 0.152388i
\(116\) 13.7982 10.7890i 1.28113 1.00173i
\(117\) 0 0
\(118\) 0.922582 1.89251i 0.0849305 0.174219i
\(119\) −1.64787 2.85420i −0.151060 0.261644i
\(120\) 0 0
\(121\) 4.82090 8.35005i 0.438264 0.759095i
\(122\) 10.0615 + 14.9105i 0.910925 + 1.34994i
\(123\) 0 0
\(124\) −15.0599 6.07781i −1.35242 0.545804i
\(125\) 8.41196i 0.752389i
\(126\) 0 0
\(127\) 17.6270i 1.56415i 0.623186 + 0.782073i \(0.285838\pi\)
−0.623186 + 0.782073i \(0.714162\pi\)
\(128\) −9.98219 + 5.32503i −0.882309 + 0.470671i
\(129\) 0 0
\(130\) 0.0588239 0.0396938i 0.00515920 0.00348138i
\(131\) 7.62368 13.2046i 0.666084 1.15369i −0.312906 0.949784i \(-0.601303\pi\)
0.978990 0.203907i \(-0.0653641\pi\)
\(132\) 0 0
\(133\) −0.227772 0.394512i −0.0197503 0.0342085i
\(134\) 8.55869 + 4.17229i 0.739358 + 0.360431i
\(135\) 0 0
\(136\) 1.94341 + 9.11693i 0.166646 + 0.781771i
\(137\) 5.64672 3.26013i 0.482432 0.278532i −0.238998 0.971020i \(-0.576819\pi\)
0.721429 + 0.692488i \(0.243485\pi\)
\(138\) 0 0
\(139\) 6.93543 + 4.00417i 0.588255 + 0.339629i 0.764407 0.644734i \(-0.223032\pi\)
−0.176152 + 0.984363i \(0.556365\pi\)
\(140\) −1.81951 + 0.256436i −0.153777 + 0.0216728i
\(141\) 0 0
\(142\) −4.19201 + 0.293952i −0.351786 + 0.0246679i
\(143\) −0.0636512 −0.00532278
\(144\) 0 0
\(145\) −8.04616 −0.668197
\(146\) −20.9093 + 1.46620i −1.73047 + 0.121343i
\(147\) 0 0
\(148\) 2.39071 0.336939i 0.196515 0.0276962i
\(149\) −1.41090 0.814584i −0.115585 0.0667333i 0.441093 0.897462i \(-0.354591\pi\)
−0.556678 + 0.830728i \(0.687924\pi\)
\(150\) 0 0
\(151\) 4.43451 2.56026i 0.360875 0.208351i −0.308589 0.951195i \(-0.599857\pi\)
0.669465 + 0.742844i \(0.266524\pi\)
\(152\) 0.268622 + 1.26016i 0.0217881 + 0.102212i
\(153\) 0 0
\(154\) 1.48148 + 0.722212i 0.119381 + 0.0581975i
\(155\) 3.73015 + 6.46080i 0.299612 + 0.518944i
\(156\) 0 0
\(157\) 0.242007 0.419168i 0.0193142 0.0334532i −0.856207 0.516633i \(-0.827185\pi\)
0.875521 + 0.483180i \(0.160518\pi\)
\(158\) −14.7960 + 9.98419i −1.17710 + 0.794299i
\(159\) 0 0
\(160\) 5.11914 + 0.897520i 0.404703 + 0.0709552i
\(161\) 3.55741i 0.280363i
\(162\) 0 0
\(163\) 23.8078i 1.86477i 0.361466 + 0.932385i \(0.382276\pi\)
−0.361466 + 0.932385i \(0.617724\pi\)
\(164\) 11.2915 + 4.55696i 0.881718 + 0.355839i
\(165\) 0 0
\(166\) 10.3786 + 15.3804i 0.805535 + 1.19375i
\(167\) −9.37726 + 16.2419i −0.725634 + 1.25684i 0.233078 + 0.972458i \(0.425120\pi\)
−0.958713 + 0.284377i \(0.908213\pi\)
\(168\) 0 0
\(169\) 6.49851 + 11.2557i 0.499885 + 0.865827i
\(170\) 1.87643 3.84916i 0.143916 0.295217i
\(171\) 0 0
\(172\) −10.2710 + 8.03100i −0.783156 + 0.612358i
\(173\) −15.3852 + 8.88264i −1.16971 + 0.675334i −0.953613 0.301037i \(-0.902667\pi\)
−0.216101 + 0.976371i \(0.569334\pi\)
\(174\) 0 0
\(175\) −3.59912 2.07795i −0.272068 0.157078i
\(176\) −3.35583 3.23566i −0.252955 0.243897i
\(177\) 0 0
\(178\) 0.786466 + 11.2157i 0.0589481 + 0.840653i
\(179\) 7.17934 0.536609 0.268305 0.963334i \(-0.413537\pi\)
0.268305 + 0.963334i \(0.413537\pi\)
\(180\) 0 0
\(181\) 2.79633 0.207849 0.103925 0.994585i \(-0.466860\pi\)
0.103925 + 0.994585i \(0.466860\pi\)
\(182\) 0.00540292 + 0.0770505i 0.000400491 + 0.00571136i
\(183\) 0 0
\(184\) 3.10372 9.57123i 0.228809 0.705600i
\(185\) −0.960495 0.554542i −0.0706170 0.0407708i
\(186\) 0 0
\(187\) −3.32633 + 1.92045i −0.243245 + 0.140438i
\(188\) −6.95158 8.89051i −0.506996 0.648407i
\(189\) 0 0
\(190\) 0.259364 0.532037i 0.0188163 0.0385981i
\(191\) 12.0033 + 20.7903i 0.868527 + 1.50433i 0.863502 + 0.504346i \(0.168266\pi\)
0.00502585 + 0.999987i \(0.498400\pi\)
\(192\) 0 0
\(193\) −8.57949 + 14.8601i −0.617565 + 1.06965i 0.372363 + 0.928087i \(0.378548\pi\)
−0.989929 + 0.141567i \(0.954786\pi\)
\(194\) 6.74485 + 9.99547i 0.484252 + 0.717633i
\(195\) 0 0
\(196\) 0.748493 1.85466i 0.0534638 0.132476i
\(197\) 2.40069i 0.171042i 0.996336 + 0.0855211i \(0.0272555\pi\)
−0.996336 + 0.0855211i \(0.972744\pi\)
\(198\) 0 0
\(199\) 2.50012i 0.177229i −0.996066 0.0886146i \(-0.971756\pi\)
0.996066 0.0886146i \(-0.0282439\pi\)
\(200\) 7.87049 + 8.73084i 0.556528 + 0.617364i
\(201\) 0 0
\(202\) 15.2181 10.2691i 1.07074 0.722529i
\(203\) 4.37887 7.58443i 0.307337 0.532323i
\(204\) 0 0
\(205\) −2.79675 4.84412i −0.195334 0.338328i
\(206\) 2.87489 + 1.40149i 0.200303 + 0.0976461i
\(207\) 0 0
\(208\) 0.0526873 0.212018i 0.00365321 0.0147008i
\(209\) −0.459771 + 0.265449i −0.0318030 + 0.0183615i
\(210\) 0 0
\(211\) 2.68339 + 1.54926i 0.184732 + 0.106655i 0.589514 0.807758i \(-0.299319\pi\)
−0.404782 + 0.914413i \(0.632653\pi\)
\(212\) −2.97137 21.0830i −0.204075 1.44799i
\(213\) 0 0
\(214\) 6.57950 0.461367i 0.449765 0.0315384i
\(215\) 5.98933 0.408469
\(216\) 0 0
\(217\) −8.12007 −0.551226
\(218\) 15.6898 1.10020i 1.06265 0.0745149i
\(219\) 0 0
\(220\) 0.298855 + 2.12049i 0.0201488 + 0.142963i
\(221\) −0.155887 0.0900013i −0.0104861 0.00605414i
\(222\) 0 0
\(223\) 7.33815 4.23669i 0.491399 0.283709i −0.233756 0.972295i \(-0.575102\pi\)
0.725155 + 0.688586i \(0.241768\pi\)
\(224\) −3.63195 + 4.33693i −0.242670 + 0.289773i
\(225\) 0 0
\(226\) −20.9893 10.2321i −1.39619 0.680631i
\(227\) 6.73436 + 11.6643i 0.446975 + 0.774184i 0.998187 0.0601814i \(-0.0191679\pi\)
−0.551212 + 0.834365i \(0.685835\pi\)
\(228\) 0 0
\(229\) −3.16856 + 5.48811i −0.209385 + 0.362665i −0.951521 0.307584i \(-0.900479\pi\)
0.742136 + 0.670249i \(0.233813\pi\)
\(230\) −3.83145 + 2.58543i −0.252638 + 0.170478i
\(231\) 0 0
\(232\) −18.3985 + 16.5855i −1.20792 + 1.08889i
\(233\) 3.30819i 0.216727i −0.994111 0.108363i \(-0.965439\pi\)
0.994111 0.108363i \(-0.0345610\pi\)
\(234\) 0 0
\(235\) 5.18433i 0.338188i
\(236\) −1.11432 + 2.76112i −0.0725359 + 0.179733i
\(237\) 0 0
\(238\) 2.60708 + 3.86354i 0.168992 + 0.250436i
\(239\) −9.17721 + 15.8954i −0.593624 + 1.02819i 0.400115 + 0.916465i \(0.368970\pi\)
−0.993739 + 0.111722i \(0.964363\pi\)
\(240\) 0 0
\(241\) 10.5580 + 18.2871i 0.680103 + 1.17797i 0.974949 + 0.222429i \(0.0713984\pi\)
−0.294846 + 0.955545i \(0.595268\pi\)
\(242\) −5.97506 + 12.2567i −0.384092 + 0.787893i
\(243\) 0 0
\(244\) −15.6693 20.0397i −1.00312 1.28291i
\(245\) −0.795659 + 0.459374i −0.0508328 + 0.0293483i
\(246\) 0 0
\(247\) −0.0215470 0.0124401i −0.00137100 0.000791547i
\(248\) 21.8471 + 7.08448i 1.38729 + 0.449865i
\(249\) 0 0
\(250\) −0.832148 11.8672i −0.0526297 0.750546i
\(251\) 13.9450 0.880199 0.440099 0.897949i \(-0.354943\pi\)
0.440099 + 0.897949i \(0.354943\pi\)
\(252\) 0 0
\(253\) 4.14587 0.260648
\(254\) −1.74374 24.8673i −0.109412 1.56032i
\(255\) 0 0
\(256\) 13.5556 8.49977i 0.847224 0.531235i
\(257\) −9.32528 5.38395i −0.581695 0.335842i 0.180112 0.983646i \(-0.442354\pi\)
−0.761807 + 0.647804i \(0.775687\pi\)
\(258\) 0 0
\(259\) 1.04544 0.603585i 0.0649605 0.0375049i
\(260\) −0.0790591 + 0.0618172i −0.00490304 + 0.00383374i
\(261\) 0 0
\(262\) −9.44884 + 19.3825i −0.583751 + 1.19746i
\(263\) −8.12745 14.0772i −0.501160 0.868034i −0.999999 0.00133978i \(-0.999574\pi\)
0.498839 0.866695i \(-0.333760\pi\)
\(264\) 0 0
\(265\) −4.89035 + 8.47033i −0.300412 + 0.520329i
\(266\) 0.360356 + 0.534026i 0.0220948 + 0.0327432i
\(267\) 0 0
\(268\) −12.4869 5.03940i −0.762759 0.307830i
\(269\) 9.10913i 0.555393i 0.960669 + 0.277697i \(0.0895710\pi\)
−0.960669 + 0.277697i \(0.910429\pi\)
\(270\) 0 0
\(271\) 31.7070i 1.92606i −0.269385 0.963032i \(-0.586820\pi\)
0.269385 0.963032i \(-0.413180\pi\)
\(272\) −3.64356 12.6695i −0.220923 0.768199i
\(273\) 0 0
\(274\) −7.64360 + 5.15783i −0.461767 + 0.311596i
\(275\) −2.42168 + 4.19447i −0.146033 + 0.252936i
\(276\) 0 0
\(277\) −0.801334 1.38795i −0.0481475 0.0833939i 0.840947 0.541117i \(-0.181998\pi\)
−0.889095 + 0.457723i \(0.848665\pi\)
\(278\) −10.1803 4.96280i −0.610571 0.297649i
\(279\) 0 0
\(280\) 2.54151 0.541761i 0.151884 0.0323764i
\(281\) 19.1083 11.0322i 1.13991 0.658126i 0.193500 0.981100i \(-0.438016\pi\)
0.946408 + 0.322974i \(0.104683\pi\)
\(282\) 0 0
\(283\) −18.0711 10.4334i −1.07422 0.620200i −0.144887 0.989448i \(-0.546282\pi\)
−0.929331 + 0.369249i \(0.879615\pi\)
\(284\) 5.88480 0.829384i 0.349199 0.0492149i
\(285\) 0 0
\(286\) 0.0897958 0.00629665i 0.00530974 0.000372329i
\(287\) 6.08818 0.359374
\(288\) 0 0
\(289\) 6.13809 0.361064
\(290\) 11.3511 0.795961i 0.666560 0.0467405i
\(291\) 0 0
\(292\) 29.3527 4.13688i 1.71774 0.242092i
\(293\) −16.0686 9.27721i −0.938737 0.541980i −0.0491729 0.998790i \(-0.515659\pi\)
−0.889564 + 0.456810i \(0.848992\pi\)
\(294\) 0 0
\(295\) 1.18453 0.683891i 0.0689662 0.0398177i
\(296\) −3.33937 + 0.711837i −0.194097 + 0.0413747i
\(297\) 0 0
\(298\) 2.07101 + 1.00960i 0.119970 + 0.0584846i
\(299\) 0.0971471 + 0.168264i 0.00561816 + 0.00973094i
\(300\) 0 0
\(301\) −3.25951 + 5.64563i −0.187875 + 0.325409i
\(302\) −6.00271 + 4.05057i −0.345417 + 0.233084i
\(303\) 0 0
\(304\) −0.503619 1.75120i −0.0288845 0.100438i
\(305\) 11.6858i 0.669125i
\(306\) 0 0
\(307\) 3.11806i 0.177957i 0.996034 + 0.0889786i \(0.0283603\pi\)
−0.996034 + 0.0889786i \(0.971640\pi\)
\(308\) −2.16145 0.872306i −0.123160 0.0497042i
\(309\) 0 0
\(310\) −5.90143 8.74557i −0.335179 0.496715i
\(311\) 10.5991 18.3581i 0.601018 1.04099i −0.391649 0.920115i \(-0.628095\pi\)
0.992667 0.120879i \(-0.0385713\pi\)
\(312\) 0 0
\(313\) 11.7962 + 20.4317i 0.666762 + 1.15487i 0.978804 + 0.204798i \(0.0656536\pi\)
−0.312042 + 0.950068i \(0.601013\pi\)
\(314\) −0.299945 + 0.615281i −0.0169269 + 0.0347223i
\(315\) 0 0
\(316\) 19.8857 15.5489i 1.11866 0.874692i
\(317\) −15.8115 + 9.12879i −0.888064 + 0.512724i −0.873309 0.487167i \(-0.838030\pi\)
−0.0147552 + 0.999891i \(0.504697\pi\)
\(318\) 0 0
\(319\) −8.83902 5.10321i −0.494890 0.285725i
\(320\) −7.31061 0.759769i −0.408675 0.0424724i
\(321\) 0 0
\(322\) −0.351915 5.01862i −0.0196115 0.279677i
\(323\) −1.50135 −0.0835375
\(324\) 0 0
\(325\) −0.226982 −0.0125907
\(326\) −2.35517 33.5868i −0.130441 1.86020i
\(327\) 0 0
\(328\) −16.3803 5.31173i −0.904449 0.293291i
\(329\) −4.88682 2.82141i −0.269419 0.155549i
\(330\) 0 0
\(331\) 19.6152 11.3248i 1.07815 0.622468i 0.147751 0.989025i \(-0.452797\pi\)
0.930396 + 0.366557i \(0.119463\pi\)
\(332\) −16.1631 20.6713i −0.887065 1.13448i
\(333\) 0 0
\(334\) 11.6222 23.8409i 0.635941 1.30451i
\(335\) 3.09284 + 5.35695i 0.168980 + 0.292681i
\(336\) 0 0
\(337\) 2.63847 4.56997i 0.143727 0.248942i −0.785170 0.619280i \(-0.787425\pi\)
0.928897 + 0.370338i \(0.120758\pi\)
\(338\) −10.2812 15.2362i −0.559225 0.828739i
\(339\) 0 0
\(340\) −2.26640 + 5.61582i −0.122913 + 0.304561i
\(341\) 9.46325i 0.512464i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 13.6953 12.3458i 0.738403 0.665640i
\(345\) 0 0
\(346\) 20.8259 14.0531i 1.11961 0.755502i
\(347\) 3.73945 6.47693i 0.200744 0.347700i −0.748024 0.663672i \(-0.768997\pi\)
0.948769 + 0.315972i \(0.102331\pi\)
\(348\) 0 0
\(349\) −9.00083 15.5899i −0.481803 0.834508i 0.517979 0.855393i \(-0.326685\pi\)
−0.999782 + 0.0208860i \(0.993351\pi\)
\(350\) 5.28301 + 2.57543i 0.282389 + 0.137662i
\(351\) 0 0
\(352\) 5.05432 + 4.23273i 0.269396 + 0.225605i
\(353\) 3.79516 2.19114i 0.201996 0.116622i −0.395590 0.918427i \(-0.629460\pi\)
0.597586 + 0.801805i \(0.296127\pi\)
\(354\) 0 0
\(355\) −2.36428 1.36502i −0.125483 0.0724477i
\(356\) −2.21901 15.7448i −0.117608 0.834470i
\(357\) 0 0
\(358\) −10.1283 + 0.710212i −0.535295 + 0.0375359i
\(359\) −27.6893 −1.46138 −0.730692 0.682707i \(-0.760803\pi\)
−0.730692 + 0.682707i \(0.760803\pi\)
\(360\) 0 0
\(361\) 18.7925 0.989078
\(362\) −3.94492 + 0.276625i −0.207340 + 0.0145391i
\(363\) 0 0
\(364\) −0.0152443 0.108164i −0.000799021 0.00566936i
\(365\) −11.7928 6.80856i −0.617262 0.356377i
\(366\) 0 0
\(367\) −5.23819 + 3.02427i −0.273431 + 0.157866i −0.630446 0.776233i \(-0.717128\pi\)
0.357015 + 0.934099i \(0.383795\pi\)
\(368\) −3.43174 + 13.8096i −0.178892 + 0.719877i
\(369\) 0 0
\(370\) 1.40988 + 0.687304i 0.0732960 + 0.0357312i
\(371\) −5.32284 9.21944i −0.276348 0.478649i
\(372\) 0 0
\(373\) 15.9639 27.6503i 0.826579 1.43168i −0.0741274 0.997249i \(-0.523617\pi\)
0.900706 0.434428i \(-0.143050\pi\)
\(374\) 4.50263 3.03834i 0.232826 0.157109i
\(375\) 0 0
\(376\) 10.6864 + 11.8546i 0.551111 + 0.611354i
\(377\) 0.478319i 0.0246347i
\(378\) 0 0
\(379\) 4.79709i 0.246410i −0.992381 0.123205i \(-0.960683\pi\)
0.992381 0.123205i \(-0.0393172\pi\)
\(380\) −0.313266 + 0.776229i −0.0160702 + 0.0398197i
\(381\) 0 0
\(382\) −18.9903 28.1425i −0.971628 1.43990i
\(383\) 4.80699 8.32595i 0.245626 0.425436i −0.716682 0.697401i \(-0.754340\pi\)
0.962307 + 0.271964i \(0.0876732\pi\)
\(384\) 0 0
\(385\) 0.535361 + 0.927273i 0.0272845 + 0.0472582i
\(386\) 10.6335 21.8126i 0.541230 1.11023i
\(387\) 0 0
\(388\) −10.5041 13.4339i −0.533265 0.682002i
\(389\) −2.41372 + 1.39356i −0.122381 + 0.0706565i −0.559941 0.828533i \(-0.689176\pi\)
0.437560 + 0.899189i \(0.355843\pi\)
\(390\) 0 0
\(391\) 10.1536 + 5.86216i 0.513487 + 0.296462i
\(392\) −0.872466 + 2.69050i −0.0440662 + 0.135891i
\(393\) 0 0
\(394\) −0.237487 3.38678i −0.0119644 0.170623i
\(395\) −11.5960 −0.583457
\(396\) 0 0
\(397\) −1.09041 −0.0547262 −0.0273631 0.999626i \(-0.508711\pi\)
−0.0273631 + 0.999626i \(0.508711\pi\)
\(398\) 0.247323 + 3.52705i 0.0123972 + 0.176795i
\(399\) 0 0
\(400\) −11.9670 11.5384i −0.598349 0.576922i
\(401\) 16.1356 + 9.31590i 0.805774 + 0.465214i 0.845486 0.533997i \(-0.179311\pi\)
−0.0397119 + 0.999211i \(0.512644\pi\)
\(402\) 0 0
\(403\) −0.384075 + 0.221746i −0.0191321 + 0.0110459i
\(404\) −20.4531 + 15.9925i −1.01758 + 0.795658i
\(405\) 0 0
\(406\) −5.42721 + 11.1329i −0.269348 + 0.552517i
\(407\) −0.703427 1.21837i −0.0348676 0.0603925i
\(408\) 0 0
\(409\) −14.9066 + 25.8189i −0.737082 + 1.27666i 0.216722 + 0.976233i \(0.430463\pi\)
−0.953804 + 0.300430i \(0.902870\pi\)
\(410\) 4.42472 + 6.55717i 0.218521 + 0.323835i
\(411\) 0 0
\(412\) −4.19439 1.69275i −0.206643 0.0833957i
\(413\) 1.48875i 0.0732564i
\(414\) 0 0
\(415\) 12.0540i 0.591710i
\(416\) −0.0533548 + 0.304317i −0.00261593 + 0.0149204i
\(417\) 0 0
\(418\) 0.622362 0.419964i 0.0304407 0.0205411i
\(419\) 1.72249 2.98343i 0.0841490 0.145750i −0.820879 0.571102i \(-0.806516\pi\)
0.905028 + 0.425351i \(0.139850\pi\)
\(420\) 0 0
\(421\) 7.39756 + 12.8130i 0.360535 + 0.624465i 0.988049 0.154140i \(-0.0492607\pi\)
−0.627514 + 0.778605i \(0.715927\pi\)
\(422\) −3.93885 1.92016i −0.191740 0.0934720i
\(423\) 0 0
\(424\) 6.27749 + 29.4489i 0.304862 + 1.43017i
\(425\) −11.8618 + 6.84839i −0.575380 + 0.332196i
\(426\) 0 0
\(427\) −11.0152 6.35962i −0.533062 0.307764i
\(428\) −9.23638 + 1.30175i −0.446457 + 0.0629222i
\(429\) 0 0
\(430\) −8.44944 + 0.592491i −0.407468 + 0.0285724i
\(431\) 16.9467 0.816293 0.408146 0.912917i \(-0.366175\pi\)
0.408146 + 0.912917i \(0.366175\pi\)
\(432\) 0 0
\(433\) 32.7900 1.57579 0.787894 0.615811i \(-0.211171\pi\)
0.787894 + 0.615811i \(0.211171\pi\)
\(434\) 11.4554 0.803273i 0.549876 0.0385583i
\(435\) 0 0
\(436\) −22.0256 + 3.10421i −1.05483 + 0.148665i
\(437\) 1.40344 + 0.810278i 0.0671358 + 0.0387609i
\(438\) 0 0
\(439\) 13.3048 7.68154i 0.635004 0.366620i −0.147683 0.989035i \(-0.547182\pi\)
0.782687 + 0.622415i \(0.213848\pi\)
\(440\) −0.631377 2.96191i −0.0300997 0.141204i
\(441\) 0 0
\(442\) 0.228820 + 0.111548i 0.0108839 + 0.00530581i
\(443\) 8.16517 + 14.1425i 0.387939 + 0.671930i 0.992172 0.124878i \(-0.0398538\pi\)
−0.604233 + 0.796807i \(0.706520\pi\)
\(444\) 0 0
\(445\) −3.65210 + 6.32563i −0.173126 + 0.299863i
\(446\) −9.93319 + 6.70282i −0.470350 + 0.317388i
\(447\) 0 0
\(448\) 4.69474 6.47761i 0.221806 0.306038i
\(449\) 12.7313i 0.600828i 0.953809 + 0.300414i \(0.0971248\pi\)
−0.953809 + 0.300414i \(0.902875\pi\)
\(450\) 0 0
\(451\) 7.09526i 0.334103i
\(452\) 30.6229 + 12.3586i 1.44038 + 0.581300i
\(453\) 0 0
\(454\) −10.6544 15.7891i −0.500034 0.741021i
\(455\) −0.0250895 + 0.0434562i −0.00117621 + 0.00203726i
\(456\) 0 0
\(457\) 8.98114 + 15.5558i 0.420120 + 0.727669i 0.995951 0.0898997i \(-0.0286546\pi\)
−0.575831 + 0.817569i \(0.695321\pi\)
\(458\) 3.92714 8.05580i 0.183503 0.376423i
\(459\) 0 0
\(460\) 5.14945 4.02641i 0.240094 0.187732i
\(461\) 1.90455 1.09959i 0.0887038 0.0512132i −0.454992 0.890496i \(-0.650358\pi\)
0.543696 + 0.839282i \(0.317025\pi\)
\(462\) 0 0
\(463\) 0.0470644 + 0.0271726i 0.00218727 + 0.00126282i 0.501093 0.865393i \(-0.332931\pi\)
−0.498906 + 0.866656i \(0.666265\pi\)
\(464\) 24.3150 25.2181i 1.12880 1.17072i
\(465\) 0 0
\(466\) 0.327260 + 4.66702i 0.0151600 + 0.216196i
\(467\) −32.8935 −1.52213 −0.761065 0.648676i \(-0.775323\pi\)
−0.761065 + 0.648676i \(0.775323\pi\)
\(468\) 0 0
\(469\) −6.73273 −0.310888
\(470\) −0.512856 7.31378i −0.0236563 0.337360i
\(471\) 0 0
\(472\) 1.29888 4.00548i 0.0597858 0.184367i
\(473\) 6.57951 + 3.79868i 0.302526 + 0.174664i
\(474\) 0 0
\(475\) −1.63955 + 0.946597i −0.0752279 + 0.0434329i
\(476\) −4.06014 5.19258i −0.186096 0.238002i
\(477\) 0 0
\(478\) 11.3743 23.3323i 0.520248 1.06719i
\(479\) −8.02688 13.9030i −0.366758 0.635243i 0.622299 0.782780i \(-0.286199\pi\)
−0.989057 + 0.147537i \(0.952865\pi\)
\(480\) 0 0
\(481\) 0.0329658 0.0570985i 0.00150311 0.00260347i
\(482\) −16.7038 24.7540i −0.760837 1.12751i
\(483\) 0 0
\(484\) 7.21683 17.8823i 0.328038 0.812830i
\(485\) 7.83370i 0.355710i
\(486\) 0 0
\(487\) 18.2339i 0.826258i 0.910673 + 0.413129i \(0.135564\pi\)
−0.910673 + 0.413129i \(0.864436\pi\)
\(488\) 24.0878 + 26.7209i 1.09040 + 1.20960i
\(489\) 0 0
\(490\) 1.07703 0.726771i 0.0486553 0.0328322i
\(491\) −14.8772 + 25.7680i −0.671398 + 1.16289i 0.306110 + 0.951996i \(0.400972\pi\)
−0.977508 + 0.210899i \(0.932361\pi\)
\(492\) 0 0
\(493\) −14.4316 24.9963i −0.649968 1.12578i
\(494\) 0.0316280 + 0.0154184i 0.00142301 + 0.000693707i
\(495\) 0 0
\(496\) −31.5216 7.83322i −1.41536 0.351722i
\(497\) 2.57338 1.48574i 0.115432 0.0666445i
\(498\) 0 0
\(499\) 37.1029 + 21.4213i 1.66095 + 0.958951i 0.972262 + 0.233895i \(0.0751473\pi\)
0.688690 + 0.725056i \(0.258186\pi\)
\(500\) 2.34791 + 16.6593i 0.105002 + 0.745026i
\(501\) 0 0
\(502\) −19.6729 + 1.37950i −0.878043 + 0.0615700i
\(503\) −14.2832 −0.636855 −0.318427 0.947947i \(-0.603155\pi\)
−0.318427 + 0.947947i \(0.603155\pi\)
\(504\) 0 0
\(505\) 11.9268 0.530737
\(506\) −5.84878 + 0.410127i −0.260010 + 0.0182324i
\(507\) 0 0
\(508\) 4.91997 + 34.9091i 0.218288 + 1.54884i
\(509\) −18.9344 10.9318i −0.839254 0.484543i 0.0177568 0.999842i \(-0.494348\pi\)
−0.857010 + 0.515299i \(0.827681\pi\)
\(510\) 0 0
\(511\) 12.8357 7.41070i 0.567819 0.327830i
\(512\) −18.2827 + 13.3320i −0.807989 + 0.589198i
\(513\) 0 0
\(514\) 13.6882 + 6.67291i 0.603762 + 0.294330i
\(515\) 1.03889 + 1.79941i 0.0457791 + 0.0792917i
\(516\) 0 0
\(517\) −3.28812 + 5.69518i −0.144611 + 0.250474i
\(518\) −1.41514 + 0.954927i −0.0621779 + 0.0419571i
\(519\) 0 0
\(520\) 0.105417 0.0950294i 0.00462286 0.00416732i
\(521\) 39.6382i 1.73658i −0.496055 0.868291i \(-0.665219\pi\)
0.496055 0.868291i \(-0.334781\pi\)
\(522\) 0 0
\(523\) 16.0515i 0.701885i −0.936397 0.350943i \(-0.885861\pi\)
0.936397 0.350943i \(-0.114139\pi\)
\(524\) 11.4125 28.2786i 0.498559 1.23536i
\(525\) 0 0
\(526\) 12.8584 + 19.0553i 0.560651 + 0.830852i
\(527\) −13.3808 + 23.1763i −0.582878 + 1.00957i
\(528\) 0 0
\(529\) 5.17240 + 8.95887i 0.224887 + 0.389516i
\(530\) 6.06114 12.4333i 0.263279 0.540068i
\(531\) 0 0
\(532\) −0.561200 0.717728i −0.0243311 0.0311175i
\(533\) 0.287968 0.166258i 0.0124733 0.00720144i
\(534\) 0 0
\(535\) 3.71082 + 2.14244i 0.160433 + 0.0926258i
\(536\) 18.1144 + 5.87407i 0.782424 + 0.253721i
\(537\) 0 0
\(538\) −0.901115 12.8507i −0.0388498 0.554033i
\(539\) −1.16542 −0.0501980
\(540\) 0 0
\(541\) −22.6938 −0.975681 −0.487841 0.872933i \(-0.662215\pi\)
−0.487841 + 0.872933i \(0.662215\pi\)
\(542\) 3.13660 + 44.7307i 0.134728 + 1.92135i
\(543\) 0 0
\(544\) 6.39346 + 17.5130i 0.274117 + 0.750863i
\(545\) 8.84901 + 5.10898i 0.379050 + 0.218845i
\(546\) 0 0
\(547\) 6.24436 3.60518i 0.266990 0.154147i −0.360529 0.932748i \(-0.617404\pi\)
0.627519 + 0.778601i \(0.284071\pi\)
\(548\) 10.2730 8.03254i 0.438839 0.343133i
\(549\) 0 0
\(550\) 3.00144 6.15691i 0.127982 0.262531i
\(551\) −1.99477 3.45504i −0.0849799 0.147190i
\(552\) 0 0
\(553\) 6.31075 10.9305i 0.268361 0.464814i
\(554\) 1.26778 + 1.87878i 0.0538629 + 0.0798217i
\(555\) 0 0
\(556\) 14.8527 + 5.99419i 0.629896 + 0.254210i
\(557\) 20.7466i 0.879063i 0.898227 + 0.439531i \(0.144855\pi\)
−0.898227 + 0.439531i \(0.855145\pi\)
\(558\) 0 0
\(559\) 0.356047i 0.0150592i
\(560\) −3.53184 + 1.01571i −0.149247 + 0.0429214i
\(561\) 0 0
\(562\) −25.8657 + 17.4540i −1.09108 + 0.736251i
\(563\) 23.5052 40.7122i 0.990625 1.71581i 0.377006 0.926211i \(-0.376954\pi\)
0.613619 0.789602i \(-0.289713\pi\)
\(564\) 0 0
\(565\) −7.58487 13.1374i −0.319098 0.552694i
\(566\) 26.5260 + 12.9312i 1.11497 + 0.543539i
\(567\) 0 0
\(568\) −8.21993 + 1.75220i −0.344901 + 0.0735208i
\(569\) 27.5683 15.9166i 1.15572 0.667258i 0.205449 0.978668i \(-0.434135\pi\)
0.950276 + 0.311410i \(0.100801\pi\)
\(570\) 0 0
\(571\) −21.1494 12.2106i −0.885077 0.510999i −0.0127478 0.999919i \(-0.504058\pi\)
−0.872329 + 0.488919i \(0.837391\pi\)
\(572\) −0.126057 + 0.0177660i −0.00527069 + 0.000742834i
\(573\) 0 0
\(574\) −8.58890 + 0.602270i −0.358494 + 0.0251383i
\(575\) 14.7843 0.616547
\(576\) 0 0
\(577\) −35.7568 −1.48858 −0.744288 0.667859i \(-0.767211\pi\)
−0.744288 + 0.667859i \(0.767211\pi\)
\(578\) −8.65930 + 0.607206i −0.360179 + 0.0252565i
\(579\) 0 0
\(580\) −15.9348 + 2.24580i −0.661658 + 0.0932519i
\(581\) −11.3623 6.56004i −0.471389 0.272156i
\(582\) 0 0
\(583\) −10.7445 + 6.20333i −0.444991 + 0.256916i
\(584\) −41.0001 + 8.73980i −1.69660 + 0.361655i
\(585\) 0 0
\(586\) 23.5865 + 11.4982i 0.974349 + 0.474988i
\(587\) 12.1011 + 20.9597i 0.499466 + 0.865100i 1.00000 0.000616829i \(-0.000196343\pi\)
−0.500534 + 0.865717i \(0.666863\pi\)
\(588\) 0 0
\(589\) −1.84952 + 3.20347i −0.0762082 + 0.131996i
\(590\) −1.60343 + 1.08198i −0.0660121 + 0.0445443i
\(591\) 0 0
\(592\) 4.64059 1.33457i 0.190727 0.0548504i
\(593\) 4.63066i 0.190159i 0.995470 + 0.0950793i \(0.0303105\pi\)
−0.995470 + 0.0950793i \(0.969690\pi\)
\(594\) 0 0
\(595\) 3.02795i 0.124134i
\(596\) −3.02155 1.21942i −0.123767 0.0499494i
\(597\) 0 0
\(598\) −0.153696 0.227768i −0.00628508 0.00931411i
\(599\) −1.31442 + 2.27665i −0.0537059 + 0.0930213i −0.891628 0.452768i \(-0.850437\pi\)
0.837923 + 0.545789i \(0.183770\pi\)
\(600\) 0 0
\(601\) −16.4497 28.4918i −0.670998 1.16220i −0.977621 0.210372i \(-0.932533\pi\)
0.306623 0.951831i \(-0.400801\pi\)
\(602\) 4.03986 8.28702i 0.164652 0.337754i
\(603\) 0 0
\(604\) 8.06762 6.30816i 0.328267 0.256675i
\(605\) −7.67159 + 4.42919i −0.311894 + 0.180072i
\(606\) 0 0
\(607\) −6.79813 3.92490i −0.275928 0.159307i 0.355651 0.934619i \(-0.384259\pi\)
−0.631578 + 0.775312i \(0.717593\pi\)
\(608\) 0.883716 + 2.42068i 0.0358394 + 0.0981714i
\(609\) 0 0
\(610\) −1.15601 16.4857i −0.0468054 0.667486i
\(611\) −0.308192 −0.0124681
\(612\) 0 0
\(613\) 22.6778 0.915950 0.457975 0.888965i \(-0.348575\pi\)
0.457975 + 0.888965i \(0.348575\pi\)
\(614\) −0.308452 4.39880i −0.0124481 0.177521i
\(615\) 0 0
\(616\) 3.13555 + 1.01679i 0.126335 + 0.0409674i
\(617\) −16.7478 9.66936i −0.674242 0.389274i 0.123440 0.992352i \(-0.460607\pi\)
−0.797682 + 0.603078i \(0.793941\pi\)
\(618\) 0 0
\(619\) −10.3351 + 5.96696i −0.415402 + 0.239832i −0.693108 0.720834i \(-0.743759\pi\)
0.277706 + 0.960666i \(0.410426\pi\)
\(620\) 9.19059 + 11.7540i 0.369103 + 0.472052i
\(621\) 0 0
\(622\) −13.1366 + 26.9472i −0.526728 + 1.08049i
\(623\) −3.97509 6.88506i −0.159259 0.275844i
\(624\) 0 0
\(625\) −6.52552 + 11.3025i −0.261021 + 0.452102i
\(626\) −18.6627 27.6570i −0.745912 1.10540i
\(627\) 0 0
\(628\) 0.362281 0.897680i 0.0144566 0.0358213i
\(629\) 3.97852i 0.158634i
\(630\) 0 0
\(631\) 4.63442i 0.184493i −0.995736 0.0922467i \(-0.970595\pi\)
0.995736 0.0922467i \(-0.0294048\pi\)
\(632\) −26.5156 + 23.9027i −1.05473 + 0.950800i
\(633\) 0 0
\(634\) 21.4030 14.4426i 0.850023 0.573588i
\(635\) 8.09740 14.0251i 0.321335 0.556569i
\(636\) 0 0
\(637\) −0.0273083 0.0472994i −0.00108200 0.00187407i
\(638\) 12.9745 + 6.32495i 0.513664 + 0.250407i
\(639\) 0 0
\(640\) 10.3886 + 0.348646i 0.410645 + 0.0137814i
\(641\) −7.36518 + 4.25229i −0.290907 + 0.167955i −0.638351 0.769746i \(-0.720383\pi\)
0.347444 + 0.937701i \(0.387050\pi\)
\(642\) 0 0
\(643\) 42.3444 + 24.4476i 1.66990 + 0.964118i 0.967688 + 0.252150i \(0.0811376\pi\)
0.702212 + 0.711968i \(0.252196\pi\)
\(644\) 0.992928 + 7.04520i 0.0391268 + 0.277620i
\(645\) 0 0
\(646\) 2.11803 0.148520i 0.0833329 0.00584346i
\(647\) 19.0364 0.748397 0.374198 0.927349i \(-0.377918\pi\)
0.374198 + 0.927349i \(0.377918\pi\)
\(648\) 0 0
\(649\) 1.73501 0.0681051
\(650\) 0.320214 0.0224540i 0.0125598 0.000880719i
\(651\) 0 0
\(652\) 6.64511 + 47.1496i 0.260243 + 1.84652i
\(653\) 38.4290 + 22.1870i 1.50384 + 0.868244i 0.999990 + 0.00445434i \(0.00141786\pi\)
0.503853 + 0.863790i \(0.331915\pi\)
\(654\) 0 0
\(655\) −12.1317 + 7.00424i −0.474024 + 0.273678i
\(656\) 23.6339 + 5.87311i 0.922749 + 0.229306i
\(657\) 0 0
\(658\) 7.17319 + 3.49688i 0.279640 + 0.136322i
\(659\) 8.10116 + 14.0316i 0.315577 + 0.546595i 0.979560 0.201153i \(-0.0644688\pi\)
−0.663983 + 0.747747i \(0.731135\pi\)
\(660\) 0 0
\(661\) 5.05531 8.75605i 0.196629 0.340571i −0.750805 0.660524i \(-0.770334\pi\)
0.947433 + 0.319954i \(0.103667\pi\)
\(662\) −26.5518 + 17.9169i −1.03196 + 0.696360i
\(663\) 0 0
\(664\) 24.8470 + 27.5630i 0.964249 + 1.06965i
\(665\) 0.418529i 0.0162299i
\(666\) 0 0
\(667\) 31.1549i 1.20632i
\(668\) −14.0376 + 34.7832i −0.543132 + 1.34580i
\(669\) 0 0
\(670\) −4.89315 7.25136i −0.189039 0.280144i
\(671\) −7.41160 + 12.8373i −0.286122 + 0.495577i
\(672\) 0 0
\(673\) −6.81031 11.7958i −0.262518 0.454694i 0.704392 0.709811i \(-0.251220\pi\)
−0.966910 + 0.255116i \(0.917886\pi\)
\(674\) −3.27014 + 6.70809i −0.125961 + 0.258386i
\(675\) 0 0
\(676\) 16.0115 + 20.4774i 0.615826 + 0.787591i
\(677\) 18.1315 10.4682i 0.696851 0.402327i −0.109322 0.994006i \(-0.534868\pi\)
0.806174 + 0.591679i \(0.201535\pi\)
\(678\) 0 0
\(679\) −7.38417 4.26325i −0.283378 0.163609i
\(680\) 2.64179 8.14672i 0.101308 0.312412i
\(681\) 0 0
\(682\) −0.936146 13.3503i −0.0358469 0.511209i
\(683\) −16.0167 −0.612864 −0.306432 0.951893i \(-0.599135\pi\)
−0.306432 + 0.951893i \(0.599135\pi\)
\(684\) 0 0
\(685\) −5.99048 −0.228884
\(686\) 0.0989244 + 1.41075i 0.00377695 + 0.0538627i
\(687\) 0 0
\(688\) −18.0994 + 18.7716i −0.690032 + 0.715661i
\(689\) −0.503535 0.290716i −0.0191832 0.0110754i
\(690\) 0 0
\(691\) −35.2063 + 20.3264i −1.33931 + 0.773251i −0.986705 0.162521i \(-0.948037\pi\)
−0.352605 + 0.935772i \(0.614704\pi\)
\(692\) −27.9900 + 21.8857i −1.06402 + 0.831968i
\(693\) 0 0
\(694\) −4.63471 + 9.50724i −0.175931 + 0.360890i
\(695\) −3.67882 6.37190i −0.139546 0.241700i
\(696\) 0 0
\(697\) 10.0325 17.3769i 0.380010 0.658196i
\(698\) 14.2401 + 21.1030i 0.538997 + 0.798761i
\(699\) 0 0
\(700\) −7.70778 3.11067i −0.291327 0.117572i
\(701\) 5.64269i 0.213122i −0.994306 0.106561i \(-0.966016\pi\)
0.994306 0.106561i \(-0.0339839\pi\)
\(702\) 0 0
\(703\) 0.549918i 0.0207406i
\(704\) −7.54911 5.47133i −0.284518 0.206208i
\(705\) 0 0
\(706\) −5.13726 + 3.46658i −0.193343 + 0.130466i
\(707\) −6.49081 + 11.2424i −0.244112 + 0.422815i
\(708\) 0 0
\(709\) −2.58052 4.46959i −0.0969134 0.167859i 0.813492 0.581576i \(-0.197564\pi\)
−0.910406 + 0.413717i \(0.864230\pi\)
\(710\) 3.47044 + 1.69182i 0.130243 + 0.0634927i
\(711\) 0 0
\(712\) 4.68801 + 21.9924i 0.175691 + 0.824200i
\(713\) 25.0164 14.4432i 0.936871 0.540903i
\(714\) 0 0
\(715\) 0.0506446 + 0.0292397i 0.00189400 + 0.00109350i
\(716\) 14.2182 2.00386i 0.531358 0.0748879i
\(717\) 0 0
\(718\) 39.0626 2.73915i 1.45780 0.102224i
\(719\) 28.4079 1.05944 0.529718 0.848174i \(-0.322298\pi\)
0.529718 + 0.848174i \(0.322298\pi\)
\(720\) 0 0
\(721\) −2.26154 −0.0842242
\(722\) −26.5115 + 1.85903i −0.986655 + 0.0691861i
\(723\) 0 0
\(724\) 5.53792 0.780497i 0.205815 0.0290069i
\(725\) −31.5202 18.1982i −1.17063 0.675863i
\(726\) 0 0
\(727\) −31.9367 + 18.4386i −1.18447 + 0.683852i −0.957043 0.289945i \(-0.906363\pi\)
−0.227422 + 0.973796i \(0.573030\pi\)
\(728\) 0.0322060 + 0.151085i 0.00119364 + 0.00559958i
\(729\) 0 0
\(730\) 17.3102 + 8.43859i 0.640679 + 0.312326i
\(731\) 10.7425 + 18.6065i 0.397325 + 0.688188i
\(732\) 0 0
\(733\) 4.51056 7.81251i 0.166601 0.288562i −0.770622 0.637293i \(-0.780054\pi\)
0.937223 + 0.348731i \(0.113387\pi\)
\(734\) 7.09060 4.78467i 0.261719 0.176606i
\(735\) 0 0
\(736\) 3.47522 19.8214i 0.128098 0.730627i
\(737\) 7.84642i 0.289027i
\(738\) 0 0
\(739\) 43.2538i 1.59112i −0.605876 0.795559i \(-0.707177\pi\)
0.605876 0.795559i \(-0.292823\pi\)
\(740\) −2.05697 0.830142i −0.0756158 0.0305166i
\(741\) 0 0
\(742\) 8.42123 + 12.4798i 0.309153 + 0.458146i
\(743\) 14.3410 24.8394i 0.526121 0.911268i −0.473416 0.880839i \(-0.656979\pi\)
0.999537 0.0304290i \(-0.00968733\pi\)
\(744\) 0 0
\(745\) 0.748397 + 1.29626i 0.0274191 + 0.0474913i
\(746\) −19.7858 + 40.5868i −0.724408 + 1.48599i
\(747\) 0 0
\(748\) −6.05152 + 4.73175i −0.221265 + 0.173010i
\(749\) −4.03900 + 2.33192i −0.147582 + 0.0852063i
\(750\) 0 0
\(751\) −5.83084 3.36644i −0.212771 0.122843i 0.389828 0.920888i \(-0.372535\pi\)
−0.602598 + 0.798045i \(0.705868\pi\)
\(752\) −16.2486 15.6667i −0.592525 0.571306i
\(753\) 0 0
\(754\) 0.0473174 + 0.674789i 0.00172320 + 0.0245744i
\(755\) −4.70447 −0.171213
\(756\) 0 0
\(757\) −29.3645 −1.06727 −0.533636 0.845714i \(-0.679175\pi\)
−0.533636 + 0.845714i \(0.679175\pi\)
\(758\) 0.474549 + 6.76749i 0.0172364 + 0.245806i
\(759\) 0 0
\(760\) 0.365152 1.12605i 0.0132455 0.0408463i
\(761\) 37.4743 + 21.6358i 1.35844 + 0.784297i 0.989414 0.145121i \(-0.0463571\pi\)
0.369029 + 0.929418i \(0.379690\pi\)
\(762\) 0 0
\(763\) −9.63160 + 5.56081i −0.348687 + 0.201315i
\(764\) 29.5745 + 37.8234i 1.06997 + 1.36840i
\(765\) 0 0
\(766\) −5.95782 + 12.2214i −0.215265 + 0.441576i
\(767\) 0.0406552 + 0.0704169i 0.00146797 + 0.00254261i
\(768\) 0 0
\(769\) −7.23929 + 12.5388i −0.261055 + 0.452161i −0.966523 0.256581i \(-0.917404\pi\)
0.705467 + 0.708743i \(0.250737\pi\)
\(770\) −0.846991 1.25519i −0.0305234 0.0452339i
\(771\) 0 0
\(772\) −12.8434 + 31.8241i −0.462243 + 1.14537i
\(773\) 14.1120i 0.507575i −0.967260 0.253787i \(-0.918324\pi\)
0.967260 0.253787i \(-0.0816764\pi\)
\(774\) 0 0
\(775\) 33.7462i 1.21220i
\(776\) 16.1476 + 17.9127i 0.579664 + 0.643029i
\(777\) 0 0
\(778\) 3.26730 2.20475i 0.117138 0.0790440i
\(779\) 1.38672 2.40186i 0.0496843 0.0860556i
\(780\) 0 0
\(781\) −1.73150 2.99905i −0.0619581 0.107315i
\(782\) −14.9040 7.26560i −0.532967 0.259817i
\(783\) 0 0
\(784\) 0.964674 3.88193i 0.0344526 0.138640i
\(785\) −0.385110 + 0.222343i −0.0137451 + 0.00793577i
\(786\) 0 0
\(787\) −27.4914 15.8722i −0.979962 0.565781i −0.0777033 0.996977i \(-0.524759\pi\)
−0.902259 + 0.431195i \(0.858092\pi\)
\(788\) 0.670069 + 4.75440i 0.0238702 + 0.169368i
\(789\) 0 0