Properties

Label 441.2.w.a.251.3
Level $441$
Weight $2$
Character 441.251
Analytic conductor $3.521$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.w (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 251.3
Character \(\chi\) \(=\) 441.251
Dual form 441.2.w.a.188.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.64686 - 1.31333i) q^{2} +(0.542276 + 2.37587i) q^{4} +(0.0408049 + 0.0196506i) q^{5} +(0.337158 + 2.62418i) q^{7} +(0.399358 - 0.829276i) q^{8} +O(q^{10})\) \(q+(-1.64686 - 1.31333i) q^{2} +(0.542276 + 2.37587i) q^{4} +(0.0408049 + 0.0196506i) q^{5} +(0.337158 + 2.62418i) q^{7} +(0.399358 - 0.829276i) q^{8} +(-0.0413923 - 0.0859519i) q^{10} +(-3.28716 - 2.62143i) q^{11} +(-1.87621 - 1.49623i) q^{13} +(2.89115 - 4.76445i) q^{14} +(2.64446 - 1.27351i) q^{16} +(1.21091 - 5.30534i) q^{17} -3.24209i q^{19} +(-0.0245597 + 0.107603i) q^{20} +(1.97071 + 8.63423i) q^{22} +(3.85813 - 0.880593i) q^{23} +(-3.11617 - 3.90755i) q^{25} +(1.12482 + 4.92814i) q^{26} +(-6.05187 + 2.22407i) q^{28} +(-4.40425 - 1.00524i) q^{29} -5.18247i q^{31} +(-7.82228 - 1.78538i) q^{32} +(-8.96183 + 7.14682i) q^{34} +(-0.0378091 + 0.113705i) q^{35} +(0.882518 - 3.86656i) q^{37} +(-4.25792 + 5.33926i) q^{38} +(0.0325916 - 0.0259909i) q^{40} +(4.08180 + 1.96569i) q^{41} +(4.96346 - 2.39028i) q^{43} +(4.44561 - 9.23140i) q^{44} +(-7.51030 - 3.61677i) q^{46} +(-5.79967 + 7.27256i) q^{47} +(-6.77265 + 1.76953i) q^{49} +10.5277i q^{50} +(2.53741 - 5.26898i) q^{52} +(-5.38661 + 1.22946i) q^{53} +(-0.0826199 - 0.171562i) q^{55} +(2.31082 + 0.768392i) q^{56} +(5.93297 + 7.43971i) q^{58} +(3.45794 - 1.66525i) q^{59} +(-12.2316 - 2.79179i) q^{61} +(-6.80627 + 8.53479i) q^{62} +(6.87735 + 8.62392i) q^{64} +(-0.0471568 - 0.0979220i) q^{65} +3.28996 q^{67} +13.2614 q^{68} +(0.211598 - 0.137600i) q^{70} +(1.72277 - 0.393212i) q^{71} +(8.05062 - 6.42016i) q^{73} +(-6.53144 + 5.20865i) q^{74} +(7.70277 - 1.75811i) q^{76} +(5.77080 - 9.50995i) q^{77} -6.50139 q^{79} +0.132932 q^{80} +(-4.14055 - 8.59794i) q^{82} +(2.63094 + 3.29909i) q^{83} +(0.153664 - 0.192689i) q^{85} +(-11.3133 - 2.58219i) q^{86} +(-3.48664 + 1.67908i) q^{88} +(6.50763 + 8.16031i) q^{89} +(3.29379 - 5.42797i) q^{91} +(4.18434 + 8.68888i) q^{92} +(19.1025 - 4.36002i) q^{94} +(0.0637090 - 0.132293i) q^{95} +18.6558i q^{97} +(13.4776 + 5.98053i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 24 q^{4} + O(q^{10}) \) \( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{9}{14}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.64686 1.31333i −1.16450 0.928661i −0.166155 0.986100i \(-0.553135\pi\)
−0.998349 + 0.0574383i \(0.981707\pi\)
\(3\) 0 0
\(4\) 0.542276 + 2.37587i 0.271138 + 1.18793i
\(5\) 0.0408049 + 0.0196506i 0.0182485 + 0.00878802i 0.442986 0.896529i \(-0.353919\pi\)
−0.424737 + 0.905317i \(0.639634\pi\)
\(6\) 0 0
\(7\) 0.337158 + 2.62418i 0.127434 + 0.991847i
\(8\) 0.399358 0.829276i 0.141195 0.293193i
\(9\) 0 0
\(10\) −0.0413923 0.0859519i −0.0130894 0.0271804i
\(11\) −3.28716 2.62143i −0.991117 0.790390i −0.0133135 0.999911i \(-0.504238\pi\)
−0.977804 + 0.209522i \(0.932809\pi\)
\(12\) 0 0
\(13\) −1.87621 1.49623i −0.520366 0.414978i 0.327769 0.944758i \(-0.393703\pi\)
−0.848135 + 0.529780i \(0.822275\pi\)
\(14\) 2.89115 4.76445i 0.772693 1.27335i
\(15\) 0 0
\(16\) 2.64446 1.27351i 0.661116 0.318377i
\(17\) 1.21091 5.30534i 0.293688 1.28673i −0.585661 0.810556i \(-0.699165\pi\)
0.879349 0.476177i \(-0.157978\pi\)
\(18\) 0 0
\(19\) 3.24209i 0.743786i −0.928276 0.371893i \(-0.878709\pi\)
0.928276 0.371893i \(-0.121291\pi\)
\(20\) −0.0245597 + 0.107603i −0.00549171 + 0.0240608i
\(21\) 0 0
\(22\) 1.97071 + 8.63423i 0.420156 + 1.84082i
\(23\) 3.85813 0.880593i 0.804476 0.183616i 0.199539 0.979890i \(-0.436055\pi\)
0.604937 + 0.796273i \(0.293198\pi\)
\(24\) 0 0
\(25\) −3.11617 3.90755i −0.623234 0.781511i
\(26\) 1.12482 + 4.92814i 0.220595 + 0.966488i
\(27\) 0 0
\(28\) −6.05187 + 2.22407i −1.14370 + 0.420310i
\(29\) −4.40425 1.00524i −0.817849 0.186669i −0.206924 0.978357i \(-0.566345\pi\)
−0.610925 + 0.791688i \(0.709202\pi\)
\(30\) 0 0
\(31\) 5.18247i 0.930799i −0.885101 0.465399i \(-0.845911\pi\)
0.885101 0.465399i \(-0.154089\pi\)
\(32\) −7.82228 1.78538i −1.38280 0.315614i
\(33\) 0 0
\(34\) −8.96183 + 7.14682i −1.53694 + 1.22567i
\(35\) −0.0378091 + 0.113705i −0.00639090 + 0.0192196i
\(36\) 0 0
\(37\) 0.882518 3.86656i 0.145085 0.635659i −0.849124 0.528194i \(-0.822869\pi\)
0.994209 0.107465i \(-0.0342734\pi\)
\(38\) −4.25792 + 5.33926i −0.690725 + 0.866142i
\(39\) 0 0
\(40\) 0.0325916 0.0259909i 0.00515318 0.00410952i
\(41\) 4.08180 + 1.96569i 0.637470 + 0.306989i 0.724561 0.689211i \(-0.242043\pi\)
−0.0870907 + 0.996200i \(0.527757\pi\)
\(42\) 0 0
\(43\) 4.96346 2.39028i 0.756920 0.364514i −0.0152880 0.999883i \(-0.504867\pi\)
0.772208 + 0.635370i \(0.219152\pi\)
\(44\) 4.44561 9.23140i 0.670200 1.39169i
\(45\) 0 0
\(46\) −7.51030 3.61677i −1.10733 0.533264i
\(47\) −5.79967 + 7.27256i −0.845969 + 1.06081i 0.151411 + 0.988471i \(0.451618\pi\)
−0.997380 + 0.0723410i \(0.976953\pi\)
\(48\) 0 0
\(49\) −6.77265 + 1.76953i −0.967521 + 0.252790i
\(50\) 10.5277i 1.48885i
\(51\) 0 0
\(52\) 2.53741 5.26898i 0.351875 0.730677i
\(53\) −5.38661 + 1.22946i −0.739908 + 0.168879i −0.575831 0.817568i \(-0.695322\pi\)
−0.164077 + 0.986448i \(0.552464\pi\)
\(54\) 0 0
\(55\) −0.0826199 0.171562i −0.0111405 0.0231334i
\(56\) 2.31082 + 0.768392i 0.308796 + 0.102681i
\(57\) 0 0
\(58\) 5.93297 + 7.43971i 0.779037 + 0.976881i
\(59\) 3.45794 1.66525i 0.450185 0.216798i −0.195032 0.980797i \(-0.562481\pi\)
0.645217 + 0.763999i \(0.276767\pi\)
\(60\) 0 0
\(61\) −12.2316 2.79179i −1.56610 0.357452i −0.650489 0.759516i \(-0.725436\pi\)
−0.915612 + 0.402064i \(0.868293\pi\)
\(62\) −6.80627 + 8.53479i −0.864397 + 1.08392i
\(63\) 0 0
\(64\) 6.87735 + 8.62392i 0.859668 + 1.07799i
\(65\) −0.0471568 0.0979220i −0.00584907 0.0121457i
\(66\) 0 0
\(67\) 3.28996 0.401933 0.200966 0.979598i \(-0.435592\pi\)
0.200966 + 0.979598i \(0.435592\pi\)
\(68\) 13.2614 1.60818
\(69\) 0 0
\(70\) 0.211598 0.137600i 0.0252908 0.0164464i
\(71\) 1.72277 0.393212i 0.204456 0.0466657i −0.119066 0.992886i \(-0.537990\pi\)
0.323522 + 0.946221i \(0.395133\pi\)
\(72\) 0 0
\(73\) 8.05062 6.42016i 0.942254 0.751422i −0.0264478 0.999650i \(-0.508420\pi\)
0.968702 + 0.248228i \(0.0798481\pi\)
\(74\) −6.53144 + 5.20865i −0.759264 + 0.605493i
\(75\) 0 0
\(76\) 7.70277 1.75811i 0.883568 0.201669i
\(77\) 5.77080 9.50995i 0.657644 1.08376i
\(78\) 0 0
\(79\) −6.50139 −0.731464 −0.365732 0.930720i \(-0.619181\pi\)
−0.365732 + 0.930720i \(0.619181\pi\)
\(80\) 0.132932 0.0148623
\(81\) 0 0
\(82\) −4.14055 8.59794i −0.457247 0.949484i
\(83\) 2.63094 + 3.29909i 0.288783 + 0.362122i 0.904968 0.425479i \(-0.139894\pi\)
−0.616186 + 0.787601i \(0.711323\pi\)
\(84\) 0 0
\(85\) 0.153664 0.192689i 0.0166672 0.0209000i
\(86\) −11.3133 2.58219i −1.21995 0.278445i
\(87\) 0 0
\(88\) −3.48664 + 1.67908i −0.371678 + 0.178990i
\(89\) 6.50763 + 8.16031i 0.689808 + 0.864991i 0.996216 0.0869087i \(-0.0276988\pi\)
−0.306409 + 0.951900i \(0.599127\pi\)
\(90\) 0 0
\(91\) 3.29379 5.42797i 0.345283 0.569006i
\(92\) 4.18434 + 8.68888i 0.436248 + 0.905878i
\(93\) 0 0
\(94\) 19.1025 4.36002i 1.97027 0.449701i
\(95\) 0.0637090 0.132293i 0.00653641 0.0135730i
\(96\) 0 0
\(97\) 18.6558i 1.89420i 0.320932 + 0.947102i \(0.396004\pi\)
−0.320932 + 0.947102i \(0.603996\pi\)
\(98\) 13.4776 + 5.98053i 1.36144 + 0.604125i
\(99\) 0 0
\(100\) 7.59400 9.52257i 0.759400 0.952257i
\(101\) −12.5759 6.05621i −1.25134 0.602616i −0.313473 0.949597i \(-0.601492\pi\)
−0.937872 + 0.346981i \(0.887207\pi\)
\(102\) 0 0
\(103\) 3.90418 8.10711i 0.384690 0.798817i −0.615255 0.788328i \(-0.710947\pi\)
0.999945 0.0104889i \(-0.00333878\pi\)
\(104\) −1.99006 + 0.958364i −0.195142 + 0.0939754i
\(105\) 0 0
\(106\) 10.4857 + 5.04963i 1.01846 + 0.490463i
\(107\) 12.4400 9.92059i 1.20262 0.959060i 0.202826 0.979215i \(-0.434987\pi\)
0.999797 + 0.0201548i \(0.00641589\pi\)
\(108\) 0 0
\(109\) 1.72830 2.16722i 0.165541 0.207582i −0.692141 0.721762i \(-0.743332\pi\)
0.857682 + 0.514180i \(0.171904\pi\)
\(110\) −0.0892534 + 0.391045i −0.00850998 + 0.0372847i
\(111\) 0 0
\(112\) 4.23351 + 6.51017i 0.400029 + 0.615154i
\(113\) 11.3723 9.06907i 1.06981 0.853147i 0.0801810 0.996780i \(-0.474450\pi\)
0.989631 + 0.143634i \(0.0458787\pi\)
\(114\) 0 0
\(115\) 0.174735 + 0.0398821i 0.0162941 + 0.00371903i
\(116\) 11.0090i 1.02216i
\(117\) 0 0
\(118\) −7.88175 1.79896i −0.725574 0.165608i
\(119\) 14.3304 + 1.38891i 1.31367 + 0.127321i
\(120\) 0 0
\(121\) 1.48585 + 6.50991i 0.135077 + 0.591810i
\(122\) 16.4772 + 20.6618i 1.49178 + 1.87063i
\(123\) 0 0
\(124\) 12.3128 2.81033i 1.10573 0.252375i
\(125\) −0.100759 0.441455i −0.00901217 0.0394849i
\(126\) 0 0
\(127\) −0.625644 + 2.74112i −0.0555169 + 0.243235i −0.995071 0.0991651i \(-0.968383\pi\)
0.939554 + 0.342400i \(0.111240\pi\)
\(128\) 7.18767i 0.635307i
\(129\) 0 0
\(130\) −0.0509430 + 0.223196i −0.00446800 + 0.0195756i
\(131\) −1.56990 + 0.756022i −0.137162 + 0.0660539i −0.501206 0.865328i \(-0.667110\pi\)
0.364044 + 0.931382i \(0.381396\pi\)
\(132\) 0 0
\(133\) 8.50783 1.09310i 0.737722 0.0947835i
\(134\) −5.41810 4.32079i −0.468053 0.373260i
\(135\) 0 0
\(136\) −3.91600 3.12291i −0.335795 0.267787i
\(137\) −5.99435 12.4474i −0.512132 1.06345i −0.983398 0.181462i \(-0.941917\pi\)
0.471266 0.881991i \(-0.343797\pi\)
\(138\) 0 0
\(139\) 1.69915 3.52832i 0.144120 0.299268i −0.816396 0.577492i \(-0.804031\pi\)
0.960516 + 0.278224i \(0.0897457\pi\)
\(140\) −0.290650 0.0281698i −0.0245644 0.00238079i
\(141\) 0 0
\(142\) −3.35358 1.61500i −0.281426 0.135528i
\(143\) 2.24516 + 9.83668i 0.187750 + 0.822585i
\(144\) 0 0
\(145\) −0.159961 0.127565i −0.0132841 0.0105937i
\(146\) −21.6900 −1.79508
\(147\) 0 0
\(148\) 9.66500 0.794458
\(149\) −15.1661 12.0945i −1.24245 0.990824i −0.999785 0.0207145i \(-0.993406\pi\)
−0.242668 0.970109i \(-0.578023\pi\)
\(150\) 0 0
\(151\) −1.50637 6.59983i −0.122586 0.537086i −0.998507 0.0546302i \(-0.982602\pi\)
0.875920 0.482456i \(-0.160255\pi\)
\(152\) −2.68859 1.29476i −0.218073 0.105019i
\(153\) 0 0
\(154\) −21.9934 + 8.08259i −1.77227 + 0.651314i
\(155\) 0.101839 0.211470i 0.00817988 0.0169857i
\(156\) 0 0
\(157\) 8.03101 + 16.6766i 0.640944 + 1.33093i 0.927842 + 0.372973i \(0.121662\pi\)
−0.286898 + 0.957961i \(0.592624\pi\)
\(158\) 10.7069 + 8.53844i 0.851793 + 0.679282i
\(159\) 0 0
\(160\) −0.284104 0.226565i −0.0224604 0.0179115i
\(161\) 3.61164 + 9.82754i 0.284637 + 0.774518i
\(162\) 0 0
\(163\) −17.2137 + 8.28967i −1.34828 + 0.649297i −0.961991 0.273081i \(-0.911957\pi\)
−0.386288 + 0.922378i \(0.626243\pi\)
\(164\) −2.45676 + 10.7638i −0.191840 + 0.840508i
\(165\) 0 0
\(166\) 8.88841i 0.689874i
\(167\) −2.33206 + 10.2174i −0.180460 + 0.790648i 0.800951 + 0.598730i \(0.204328\pi\)
−0.981411 + 0.191918i \(0.938529\pi\)
\(168\) 0 0
\(169\) −1.61131 7.05960i −0.123947 0.543046i
\(170\) −0.506126 + 0.115520i −0.0388181 + 0.00885998i
\(171\) 0 0
\(172\) 8.37053 + 10.4963i 0.638247 + 0.800337i
\(173\) −1.49929 6.56881i −0.113989 0.499418i −0.999401 0.0346106i \(-0.988981\pi\)
0.885412 0.464807i \(-0.153876\pi\)
\(174\) 0 0
\(175\) 9.20349 9.49486i 0.695718 0.717744i
\(176\) −12.0312 2.74604i −0.906885 0.206991i
\(177\) 0 0
\(178\) 21.9855i 1.64788i
\(179\) 4.03099 + 0.920048i 0.301291 + 0.0687676i 0.370494 0.928835i \(-0.379189\pi\)
−0.0692031 + 0.997603i \(0.522046\pi\)
\(180\) 0 0
\(181\) −20.0232 + 15.9680i −1.48831 + 1.18689i −0.552941 + 0.833221i \(0.686494\pi\)
−0.935371 + 0.353668i \(0.884934\pi\)
\(182\) −12.5531 + 4.61328i −0.930497 + 0.341959i
\(183\) 0 0
\(184\) 0.810522 3.55113i 0.0597525 0.261793i
\(185\) 0.111991 0.140433i 0.00823377 0.0103248i
\(186\) 0 0
\(187\) −17.8880 + 14.2652i −1.30810 + 1.04318i
\(188\) −20.4236 9.83551i −1.48955 0.717328i
\(189\) 0 0
\(190\) −0.278664 + 0.134197i −0.0202164 + 0.00973570i
\(191\) −2.54518 + 5.28512i −0.184163 + 0.382418i −0.972527 0.232791i \(-0.925214\pi\)
0.788364 + 0.615209i \(0.210928\pi\)
\(192\) 0 0
\(193\) 4.72926 + 2.27749i 0.340420 + 0.163938i 0.596281 0.802776i \(-0.296645\pi\)
−0.255861 + 0.966714i \(0.582359\pi\)
\(194\) 24.5011 30.7234i 1.75907 2.20581i
\(195\) 0 0
\(196\) −7.87680 15.1313i −0.562629 1.08081i
\(197\) 16.8005i 1.19699i 0.801127 + 0.598494i \(0.204234\pi\)
−0.801127 + 0.598494i \(0.795766\pi\)
\(198\) 0 0
\(199\) −10.2654 + 21.3164i −0.727696 + 1.51108i 0.126974 + 0.991906i \(0.459473\pi\)
−0.854671 + 0.519171i \(0.826241\pi\)
\(200\) −4.48491 + 1.02365i −0.317131 + 0.0723831i
\(201\) 0 0
\(202\) 12.7569 + 26.4899i 0.897571 + 1.86382i
\(203\) 1.15301 11.8965i 0.0809252 0.834969i
\(204\) 0 0
\(205\) 0.127930 + 0.160420i 0.00893505 + 0.0112042i
\(206\) −17.0769 + 8.22380i −1.18980 + 0.572979i
\(207\) 0 0
\(208\) −6.86701 1.56735i −0.476142 0.108676i
\(209\) −8.49890 + 10.6573i −0.587881 + 0.737180i
\(210\) 0 0
\(211\) −16.0402 20.1138i −1.10425 1.38469i −0.915334 0.402696i \(-0.868073\pi\)
−0.188919 0.981993i \(-0.560498\pi\)
\(212\) −5.84206 12.1312i −0.401234 0.833171i
\(213\) 0 0
\(214\) −33.5159 −2.29110
\(215\) 0.249504 0.0170160
\(216\) 0 0
\(217\) 13.5997 1.74731i 0.923210 0.118615i
\(218\) −5.69254 + 1.29928i −0.385547 + 0.0879986i
\(219\) 0 0
\(220\) 0.362805 0.289327i 0.0244603 0.0195065i
\(221\) −10.2099 + 8.14212i −0.686792 + 0.547698i
\(222\) 0 0
\(223\) 25.6677 5.85848i 1.71883 0.392313i 0.754354 0.656468i \(-0.227950\pi\)
0.964480 + 0.264156i \(0.0850933\pi\)
\(224\) 2.04783 21.1290i 0.136826 1.41174i
\(225\) 0 0
\(226\) −30.6391 −2.03808
\(227\) 29.1528 1.93494 0.967468 0.252993i \(-0.0814150\pi\)
0.967468 + 0.252993i \(0.0814150\pi\)
\(228\) 0 0
\(229\) −0.965738 2.00537i −0.0638177 0.132519i 0.866620 0.498968i \(-0.166288\pi\)
−0.930438 + 0.366449i \(0.880573\pi\)
\(230\) −0.235385 0.295164i −0.0155209 0.0194625i
\(231\) 0 0
\(232\) −2.59250 + 3.25089i −0.170206 + 0.213431i
\(233\) 0.564422 + 0.128826i 0.0369765 + 0.00843965i 0.240969 0.970533i \(-0.422535\pi\)
−0.203993 + 0.978972i \(0.565392\pi\)
\(234\) 0 0
\(235\) −0.379565 + 0.182789i −0.0247601 + 0.0119238i
\(236\) 5.83158 + 7.31256i 0.379603 + 0.476007i
\(237\) 0 0
\(238\) −21.7761 21.1078i −1.41153 1.36822i
\(239\) 9.11840 + 18.9346i 0.589821 + 1.22478i 0.955763 + 0.294138i \(0.0950324\pi\)
−0.365943 + 0.930637i \(0.619253\pi\)
\(240\) 0 0
\(241\) −13.0890 + 2.98747i −0.843134 + 0.192440i −0.622209 0.782851i \(-0.713765\pi\)
−0.220925 + 0.975291i \(0.570908\pi\)
\(242\) 6.10266 12.6723i 0.392294 0.814607i
\(243\) 0 0
\(244\) 30.5746i 1.95734i
\(245\) −0.311130 0.0608813i −0.0198773 0.00388956i
\(246\) 0 0
\(247\) −4.85090 + 6.08283i −0.308655 + 0.387041i
\(248\) −4.29770 2.06966i −0.272904 0.131424i
\(249\) 0 0
\(250\) −0.413838 + 0.859343i −0.0261734 + 0.0543496i
\(251\) 22.5427 10.8560i 1.42288 0.685223i 0.445222 0.895420i \(-0.353125\pi\)
0.977659 + 0.210197i \(0.0674106\pi\)
\(252\) 0 0
\(253\) −14.9907 7.21915i −0.942459 0.453864i
\(254\) 4.63033 3.69257i 0.290533 0.231692i
\(255\) 0 0
\(256\) 4.31494 5.41076i 0.269684 0.338173i
\(257\) 0.0311024 0.136268i 0.00194011 0.00850019i −0.973949 0.226769i \(-0.927184\pi\)
0.975889 + 0.218269i \(0.0700409\pi\)
\(258\) 0 0
\(259\) 10.4441 + 1.01224i 0.648965 + 0.0628977i
\(260\) 0.207078 0.165139i 0.0128424 0.0102415i
\(261\) 0 0
\(262\) 3.57830 + 0.816723i 0.221068 + 0.0504573i
\(263\) 22.2556i 1.37234i −0.727441 0.686170i \(-0.759291\pi\)
0.727441 0.686170i \(-0.240709\pi\)
\(264\) 0 0
\(265\) −0.243960 0.0556822i −0.0149863 0.00342053i
\(266\) −15.4468 9.37337i −0.947103 0.574718i
\(267\) 0 0
\(268\) 1.78407 + 7.81651i 0.108979 + 0.477469i
\(269\) −4.33764 5.43923i −0.264471 0.331636i 0.631810 0.775124i \(-0.282312\pi\)
−0.896281 + 0.443488i \(0.853741\pi\)
\(270\) 0 0
\(271\) 22.9710 5.24299i 1.39539 0.318489i 0.542272 0.840203i \(-0.317564\pi\)
0.853120 + 0.521714i \(0.174707\pi\)
\(272\) −3.55418 15.5719i −0.215504 0.944183i
\(273\) 0 0
\(274\) −6.47564 + 28.3716i −0.391208 + 1.71399i
\(275\) 21.0136i 1.26717i
\(276\) 0 0
\(277\) −1.46454 + 6.41658i −0.0879958 + 0.385535i −0.999678 0.0253604i \(-0.991927\pi\)
0.911683 + 0.410895i \(0.134784\pi\)
\(278\) −7.43209 + 3.57910i −0.445747 + 0.214660i
\(279\) 0 0
\(280\) 0.0791934 + 0.0767631i 0.00473271 + 0.00458748i
\(281\) −13.7575 10.9713i −0.820706 0.654491i 0.120354 0.992731i \(-0.461597\pi\)
−0.941060 + 0.338240i \(0.890168\pi\)
\(282\) 0 0
\(283\) 14.2993 + 11.4033i 0.850006 + 0.677857i 0.948326 0.317298i \(-0.102776\pi\)
−0.0983203 + 0.995155i \(0.531347\pi\)
\(284\) 1.86844 + 3.87985i 0.110871 + 0.230227i
\(285\) 0 0
\(286\) 9.22131 19.1482i 0.545267 1.13226i
\(287\) −3.78212 + 11.3741i −0.223251 + 0.671394i
\(288\) 0 0
\(289\) −11.3638 5.47253i −0.668460 0.321914i
\(290\) 0.0958995 + 0.420163i 0.00563141 + 0.0246728i
\(291\) 0 0
\(292\) 19.6191 + 15.6457i 1.14812 + 0.915595i
\(293\) −14.1666 −0.827620 −0.413810 0.910363i \(-0.635802\pi\)
−0.413810 + 0.910363i \(0.635802\pi\)
\(294\) 0 0
\(295\) 0.173824 0.0101204
\(296\) −2.85401 2.27600i −0.165886 0.132290i
\(297\) 0 0
\(298\) 9.09231 + 39.8360i 0.526703 + 2.30764i
\(299\) −8.55622 4.12046i −0.494819 0.238292i
\(300\) 0 0
\(301\) 7.94598 + 12.2191i 0.457999 + 0.704298i
\(302\) −6.18695 + 12.8473i −0.356019 + 0.739281i
\(303\) 0 0
\(304\) −4.12882 8.57358i −0.236804 0.491729i
\(305\) −0.444250 0.354278i −0.0254377 0.0202859i
\(306\) 0 0
\(307\) 6.80391 + 5.42594i 0.388320 + 0.309675i 0.798118 0.602502i \(-0.205829\pi\)
−0.409798 + 0.912176i \(0.634401\pi\)
\(308\) 25.7237 + 8.55363i 1.46575 + 0.487389i
\(309\) 0 0
\(310\) −0.445443 + 0.214514i −0.0252995 + 0.0121836i
\(311\) 3.26111 14.2879i 0.184921 0.810191i −0.794321 0.607498i \(-0.792173\pi\)
0.979242 0.202693i \(-0.0649695\pi\)
\(312\) 0 0
\(313\) 23.9510i 1.35379i 0.736078 + 0.676896i \(0.236676\pi\)
−0.736078 + 0.676896i \(0.763324\pi\)
\(314\) 8.67582 38.0113i 0.489605 2.14510i
\(315\) 0 0
\(316\) −3.52555 15.4464i −0.198327 0.868929i
\(317\) 20.5063 4.68044i 1.15175 0.262880i 0.396323 0.918111i \(-0.370286\pi\)
0.755428 + 0.655231i \(0.227429\pi\)
\(318\) 0 0
\(319\) 11.8423 + 14.8498i 0.663043 + 0.831430i
\(320\) 0.111164 + 0.487042i 0.00621427 + 0.0272265i
\(321\) 0 0
\(322\) 6.95890 20.9278i 0.387804 1.16626i
\(323\) −17.2004 3.92587i −0.957054 0.218441i
\(324\) 0 0
\(325\) 11.9939i 0.665301i
\(326\) 39.2355 + 8.95525i 2.17305 + 0.495985i
\(327\) 0 0
\(328\) 3.26020 2.59992i 0.180015 0.143557i
\(329\) −21.0399 12.7674i −1.15997 0.703889i
\(330\) 0 0
\(331\) 5.22958 22.9123i 0.287444 1.25937i −0.600576 0.799568i \(-0.705062\pi\)
0.888020 0.459805i \(-0.152081\pi\)
\(332\) −6.41150 + 8.03977i −0.351877 + 0.441239i
\(333\) 0 0
\(334\) 17.2594 13.7639i 0.944391 0.753127i
\(335\) 0.134247 + 0.0646498i 0.00733468 + 0.00353219i
\(336\) 0 0
\(337\) 19.6874 9.48093i 1.07244 0.516459i 0.187547 0.982256i \(-0.439946\pi\)
0.884892 + 0.465796i \(0.154232\pi\)
\(338\) −6.61796 + 13.7423i −0.359970 + 0.747484i
\(339\) 0 0
\(340\) 0.541131 + 0.260595i 0.0293469 + 0.0141327i
\(341\) −13.5855 + 17.0356i −0.735694 + 0.922531i
\(342\) 0 0
\(343\) −6.92701 17.1760i −0.374024 0.927419i
\(344\) 5.07066i 0.273391i
\(345\) 0 0
\(346\) −6.15787 + 12.7870i −0.331049 + 0.687431i
\(347\) −34.5057 + 7.87571i −1.85237 + 0.422790i −0.995664 0.0930223i \(-0.970347\pi\)
−0.856701 + 0.515813i \(0.827490\pi\)
\(348\) 0 0
\(349\) 10.4131 + 21.6229i 0.557398 + 1.15745i 0.969222 + 0.246186i \(0.0791775\pi\)
−0.411824 + 0.911263i \(0.635108\pi\)
\(350\) −27.6267 + 3.54951i −1.47671 + 0.189729i
\(351\) 0 0
\(352\) 21.0329 + 26.3744i 1.12106 + 1.40576i
\(353\) −0.186806 + 0.0899609i −0.00994267 + 0.00478814i −0.438848 0.898561i \(-0.644614\pi\)
0.428906 + 0.903349i \(0.358899\pi\)
\(354\) 0 0
\(355\) 0.0780245 + 0.0178086i 0.00414111 + 0.000945181i
\(356\) −15.8589 + 19.8864i −0.840518 + 1.05398i
\(357\) 0 0
\(358\) −5.43015 6.80919i −0.286992 0.359877i
\(359\) 11.6787 + 24.2511i 0.616380 + 1.27993i 0.942376 + 0.334555i \(0.108586\pi\)
−0.325996 + 0.945371i \(0.605700\pi\)
\(360\) 0 0
\(361\) 8.48886 0.446782
\(362\) 53.9465 2.83536
\(363\) 0 0
\(364\) 14.6823 + 4.88214i 0.769560 + 0.255894i
\(365\) 0.454665 0.103774i 0.0237983 0.00543180i
\(366\) 0 0
\(367\) 8.40395 6.70192i 0.438682 0.349838i −0.379109 0.925352i \(-0.623770\pi\)
0.817792 + 0.575514i \(0.195198\pi\)
\(368\) 9.08124 7.24205i 0.473393 0.377518i
\(369\) 0 0
\(370\) −0.368868 + 0.0841917i −0.0191765 + 0.00437692i
\(371\) −5.04246 13.7209i −0.261792 0.712355i
\(372\) 0 0
\(373\) −30.6084 −1.58484 −0.792421 0.609974i \(-0.791180\pi\)
−0.792421 + 0.609974i \(0.791180\pi\)
\(374\) 48.1939 2.49205
\(375\) 0 0
\(376\) 3.71481 + 7.71389i 0.191577 + 0.397814i
\(377\) 6.75922 + 8.47580i 0.348118 + 0.436526i
\(378\) 0 0
\(379\) 5.81241 7.28853i 0.298563 0.374387i −0.609809 0.792548i \(-0.708754\pi\)
0.908373 + 0.418162i \(0.137325\pi\)
\(380\) 0.348859 + 0.0796247i 0.0178961 + 0.00408466i
\(381\) 0 0
\(382\) 11.1326 5.36119i 0.569595 0.274302i
\(383\) −0.204649 0.256621i −0.0104571 0.0131127i 0.776575 0.630024i \(-0.216955\pi\)
−0.787033 + 0.616912i \(0.788384\pi\)
\(384\) 0 0
\(385\) 0.422353 0.274653i 0.0215251 0.0139976i
\(386\) −4.79734 9.96177i −0.244178 0.507041i
\(387\) 0 0
\(388\) −44.3235 + 10.1166i −2.25019 + 0.513591i
\(389\) 1.98108 4.11376i 0.100445 0.208576i −0.844690 0.535255i \(-0.820215\pi\)
0.945135 + 0.326679i \(0.105930\pi\)
\(390\) 0 0
\(391\) 21.5350i 1.08907i
\(392\) −1.23729 + 6.32307i −0.0624925 + 0.319363i
\(393\) 0 0
\(394\) 22.0646 27.6681i 1.11160 1.39390i
\(395\) −0.265289 0.127756i −0.0133481 0.00642812i
\(396\) 0 0
\(397\) 8.27747 17.1884i 0.415434 0.862659i −0.583295 0.812261i \(-0.698237\pi\)
0.998729 0.0503980i \(-0.0160490\pi\)
\(398\) 44.9010 21.6232i 2.25068 1.08387i
\(399\) 0 0
\(400\) −13.2169 6.36492i −0.660844 0.318246i
\(401\) 5.90604 4.70991i 0.294934 0.235202i −0.464832 0.885399i \(-0.653885\pi\)
0.759765 + 0.650197i \(0.225314\pi\)
\(402\) 0 0
\(403\) −7.75414 + 9.72338i −0.386261 + 0.484356i
\(404\) 7.56917 33.1627i 0.376580 1.64991i
\(405\) 0 0
\(406\) −17.5228 + 18.0775i −0.869641 + 0.897173i
\(407\) −13.0369 + 10.3966i −0.646215 + 0.515339i
\(408\) 0 0
\(409\) −18.6929 4.26654i −0.924307 0.210967i −0.266223 0.963912i \(-0.585776\pi\)
−0.658084 + 0.752945i \(0.728633\pi\)
\(410\) 0.432203i 0.0213450i
\(411\) 0 0
\(412\) 21.3785 + 4.87951i 1.05324 + 0.240396i
\(413\) 5.53580 + 8.51280i 0.272399 + 0.418887i
\(414\) 0 0
\(415\) 0.0425260 + 0.186319i 0.00208752 + 0.00914602i
\(416\) 12.0049 + 15.0537i 0.588588 + 0.738066i
\(417\) 0 0
\(418\) 27.9930 6.38921i 1.36918 0.312506i
\(419\) 4.45134 + 19.5026i 0.217462 + 0.952763i 0.959345 + 0.282234i \(0.0910756\pi\)
−0.741883 + 0.670529i \(0.766067\pi\)
\(420\) 0 0
\(421\) 3.64719 15.9794i 0.177753 0.778788i −0.804911 0.593395i \(-0.797787\pi\)
0.982664 0.185393i \(-0.0593557\pi\)
\(422\) 54.1905i 2.63795i
\(423\) 0 0
\(424\) −1.13163 + 4.95798i −0.0549567 + 0.240781i
\(425\) −24.5043 + 11.8006i −1.18863 + 0.572415i
\(426\) 0 0
\(427\) 3.20217 33.0393i 0.154964 1.59888i
\(428\) 30.3159 + 24.1761i 1.46538 + 1.16860i
\(429\) 0 0
\(430\) −0.410897 0.327680i −0.0198152 0.0158021i
\(431\) 4.12622 + 8.56819i 0.198753 + 0.412715i 0.976395 0.215992i \(-0.0692986\pi\)
−0.777642 + 0.628707i \(0.783584\pi\)
\(432\) 0 0
\(433\) 12.1776 25.2870i 0.585218 1.21522i −0.372640 0.927976i \(-0.621547\pi\)
0.957858 0.287242i \(-0.0927383\pi\)
\(434\) −24.6916 14.9833i −1.18524 0.719221i
\(435\) 0 0
\(436\) 6.08624 + 2.93098i 0.291478 + 0.140369i
\(437\) −2.85496 12.5084i −0.136571 0.598358i
\(438\) 0 0
\(439\) 22.4497 + 17.9030i 1.07146 + 0.854464i 0.989838 0.142199i \(-0.0454173\pi\)
0.0816258 + 0.996663i \(0.473989\pi\)
\(440\) −0.175267 −0.00835553
\(441\) 0 0
\(442\) 27.5075 1.30840
\(443\) 1.55249 + 1.23807i 0.0737612 + 0.0588226i 0.659676 0.751550i \(-0.270693\pi\)
−0.585915 + 0.810372i \(0.699265\pi\)
\(444\) 0 0
\(445\) 0.105188 + 0.460860i 0.00498640 + 0.0218469i
\(446\) −49.9651 24.0619i −2.36592 1.13936i
\(447\) 0 0
\(448\) −20.3120 + 20.9550i −0.959651 + 0.990032i
\(449\) 0.740682 1.53804i 0.0349550 0.0725847i −0.882760 0.469824i \(-0.844317\pi\)
0.917715 + 0.397239i \(0.130032\pi\)
\(450\) 0 0
\(451\) −8.26463 17.1617i −0.389166 0.808112i
\(452\) 27.7138 + 22.1010i 1.30355 + 1.03954i
\(453\) 0 0
\(454\) −48.0104 38.2871i −2.25324 1.79690i
\(455\) 0.241066 0.156763i 0.0113013 0.00734916i
\(456\) 0 0
\(457\) −33.5854 + 16.1739i −1.57106 + 0.756582i −0.998017 0.0629452i \(-0.979951\pi\)
−0.573041 + 0.819527i \(0.694236\pi\)
\(458\) −1.04328 + 4.57089i −0.0487491 + 0.213584i
\(459\) 0 0
\(460\) 0.436774i 0.0203647i
\(461\) 2.50035 10.9548i 0.116453 0.510214i −0.882733 0.469875i \(-0.844299\pi\)
0.999186 0.0403389i \(-0.0128438\pi\)
\(462\) 0 0
\(463\) 0.757284 + 3.31788i 0.0351940 + 0.154195i 0.989472 0.144727i \(-0.0462303\pi\)
−0.954278 + 0.298922i \(0.903373\pi\)
\(464\) −12.9271 + 2.95052i −0.600124 + 0.136974i
\(465\) 0 0
\(466\) −0.760333 0.953427i −0.0352217 0.0441667i
\(467\) 7.33920 + 32.1551i 0.339618 + 1.48796i 0.799869 + 0.600174i \(0.204902\pi\)
−0.460252 + 0.887789i \(0.652241\pi\)
\(468\) 0 0
\(469\) 1.10924 + 8.63346i 0.0512198 + 0.398656i
\(470\) 0.865152 + 0.197465i 0.0399065 + 0.00910839i
\(471\) 0 0
\(472\) 3.53262i 0.162602i
\(473\) −22.5816 5.15411i −1.03830 0.236986i
\(474\) 0 0
\(475\) −12.6686 + 10.1029i −0.581277 + 0.463553i
\(476\) 4.47119 + 34.8003i 0.204937 + 1.59507i
\(477\) 0 0
\(478\) 9.85052 43.1580i 0.450553 1.97400i
\(479\) 7.54322 9.45890i 0.344658 0.432188i −0.579045 0.815295i \(-0.696575\pi\)
0.923704 + 0.383107i \(0.125146\pi\)
\(480\) 0 0
\(481\) −7.44104 + 5.93403i −0.339282 + 0.270568i
\(482\) 25.4792 + 12.2701i 1.16055 + 0.558889i
\(483\) 0 0
\(484\) −14.6609 + 7.06034i −0.666406 + 0.320924i
\(485\) −0.366597 + 0.761246i −0.0166463 + 0.0345664i
\(486\) 0 0
\(487\) 5.67643 + 2.73363i 0.257224 + 0.123872i 0.558052 0.829806i \(-0.311549\pi\)
−0.300828 + 0.953678i \(0.597263\pi\)
\(488\) −7.19997 + 9.02848i −0.325927 + 0.408700i
\(489\) 0 0
\(490\) 0.432429 + 0.508877i 0.0195352 + 0.0229887i
\(491\) 0.00191807i 8.65614e-5i 1.00000 4.32807e-5i \(1.37767e-5\pi\)
−1.00000 4.32807e-5i \(0.999986\pi\)
\(492\) 0 0
\(493\) −10.6663 + 22.1488i −0.480386 + 0.997531i
\(494\) 15.9775 3.64675i 0.718861 0.164075i
\(495\) 0 0
\(496\) −6.59990 13.7048i −0.296344 0.615365i
\(497\) 1.61271 + 4.38829i 0.0723397 + 0.196842i
\(498\) 0 0
\(499\) 4.62945 + 5.80515i 0.207243 + 0.259874i 0.874580 0.484882i \(-0.161137\pi\)
−0.667337 + 0.744756i \(0.732566\pi\)
\(500\) 0.994198 0.478780i 0.0444619 0.0214117i
\(501\) 0 0
\(502\) −51.3820 11.7276i −2.29329 0.523429i
\(503\) −7.91497 + 9.92506i −0.352911 + 0.442536i −0.926323 0.376731i \(-0.877048\pi\)
0.573412 + 0.819267i \(0.305620\pi\)
\(504\) 0 0
\(505\) −0.394149 0.494247i −0.0175394 0.0219937i
\(506\) 15.2065 + 31.5766i 0.676011 + 1.40375i
\(507\) 0 0
\(508\) −6.85181 −0.304000
\(509\) 22.8097 1.01102 0.505511 0.862820i \(-0.331304\pi\)
0.505511 + 0.862820i \(0.331304\pi\)
\(510\) 0 0
\(511\) 19.5620 + 18.9617i 0.865371 + 0.838815i
\(512\) −28.2271 + 6.44265i −1.24747 + 0.284728i
\(513\) 0 0
\(514\) −0.230186 + 0.183567i −0.0101531 + 0.00809680i
\(515\) 0.318619 0.254090i 0.0140400 0.0111966i
\(516\) 0 0
\(517\) 38.1290 8.70269i 1.67691 0.382744i
\(518\) −15.8706 15.3835i −0.697312 0.675914i
\(519\) 0 0
\(520\) −0.100037 −0.00438691
\(521\) −30.8180 −1.35016 −0.675082 0.737743i \(-0.735892\pi\)
−0.675082 + 0.737743i \(0.735892\pi\)
\(522\) 0 0
\(523\) −2.96954 6.16631i −0.129849 0.269634i 0.825901 0.563816i \(-0.190667\pi\)
−0.955750 + 0.294182i \(0.904953\pi\)
\(524\) −2.64752 3.31989i −0.115658 0.145030i
\(525\) 0 0
\(526\) −29.2289 + 36.6518i −1.27444 + 1.59810i
\(527\) −27.4947 6.27549i −1.19769 0.273365i
\(528\) 0 0
\(529\) −6.61255 + 3.18443i −0.287502 + 0.138454i
\(530\) 0.328638 + 0.412099i 0.0142751 + 0.0179005i
\(531\) 0 0
\(532\) 7.21064 + 19.6207i 0.312621 + 0.850665i
\(533\) −4.71719 9.79534i −0.204324 0.424283i
\(534\) 0 0
\(535\) 0.702560 0.160355i 0.0303743 0.00693274i
\(536\) 1.31387 2.72829i 0.0567507 0.117844i
\(537\) 0 0
\(538\) 14.6544i 0.631795i
\(539\) 26.9015 + 11.9373i 1.15873 + 0.514175i
\(540\) 0 0
\(541\) 21.5628 27.0389i 0.927058 1.16249i −0.0593590 0.998237i \(-0.518906\pi\)
0.986417 0.164258i \(-0.0525229\pi\)
\(542\) −44.7158 21.5340i −1.92071 0.924965i
\(543\) 0 0
\(544\) −18.9441 + 39.3379i −0.812223 + 1.68660i
\(545\) 0.113110 0.0544711i 0.00484512 0.00233329i
\(546\) 0 0
\(547\) −25.1721 12.1223i −1.07628 0.518311i −0.190156 0.981754i \(-0.560899\pi\)
−0.886127 + 0.463443i \(0.846614\pi\)
\(548\) 26.3228 20.9917i 1.12445 0.896721i
\(549\) 0 0
\(550\) 27.5977 34.6064i 1.17677 1.47562i
\(551\) −3.25908 + 14.2790i −0.138842 + 0.608305i
\(552\) 0 0
\(553\) −2.19200 17.0608i −0.0932132 0.725500i
\(554\) 10.8390 8.64378i 0.460503 0.367239i
\(555\) 0 0
\(556\) 9.30422 + 2.12363i 0.394587 + 0.0900618i
\(557\) 5.23531i 0.221827i 0.993830 + 0.110914i \(0.0353777\pi\)
−0.993830 + 0.110914i \(0.964622\pi\)
\(558\) 0 0
\(559\) −12.8889 2.94180i −0.545141 0.124425i
\(560\) 0.0448192 + 0.348838i 0.00189396 + 0.0147411i
\(561\) 0 0
\(562\) 8.24786 + 36.1362i 0.347915 + 1.52432i
\(563\) −16.2541 20.3820i −0.685030 0.859000i 0.310777 0.950483i \(-0.399411\pi\)
−0.995807 + 0.0914829i \(0.970839\pi\)
\(564\) 0 0
\(565\) 0.642257 0.146591i 0.0270199 0.00616713i
\(566\) −8.57266 37.5593i −0.360336 1.57873i
\(567\) 0 0
\(568\) 0.361923 1.58569i 0.0151859 0.0665340i
\(569\) 1.66695i 0.0698821i −0.999389 0.0349410i \(-0.988876\pi\)
0.999389 0.0349410i \(-0.0111243\pi\)
\(570\) 0 0
\(571\) 5.29827 23.2132i 0.221726 0.971444i −0.734453 0.678660i \(-0.762561\pi\)
0.956179 0.292784i \(-0.0945817\pi\)
\(572\) −22.1531 + 10.6684i −0.926269 + 0.446068i
\(573\) 0 0
\(574\) 21.1665 13.7644i 0.883474 0.574516i
\(575\) −15.4636 12.3318i −0.644875 0.514271i
\(576\) 0 0
\(577\) 9.70970 + 7.74322i 0.404220 + 0.322355i 0.804407 0.594079i \(-0.202483\pi\)
−0.400187 + 0.916434i \(0.631055\pi\)
\(578\) 11.5274 + 23.9369i 0.479476 + 0.995643i
\(579\) 0 0
\(580\) 0.216334 0.449222i 0.00898278 0.0186529i
\(581\) −7.77037 + 8.01637i −0.322369 + 0.332575i
\(582\) 0 0
\(583\) 20.9296 + 10.0792i 0.866816 + 0.417437i
\(584\) −2.10900 9.24013i −0.0872711 0.382359i
\(585\) 0 0
\(586\) 23.3303 + 18.6053i 0.963767 + 0.768579i
\(587\) 21.4652 0.885965 0.442983 0.896530i \(-0.353920\pi\)
0.442983 + 0.896530i \(0.353920\pi\)
\(588\) 0 0
\(589\) −16.8020 −0.692315
\(590\) −0.286264 0.228288i −0.0117853 0.00939845i
\(591\) 0 0
\(592\) −2.59031 11.3489i −0.106461 0.466436i
\(593\) −33.8713 16.3116i −1.39093 0.669835i −0.419628 0.907696i \(-0.637839\pi\)
−0.971299 + 0.237861i \(0.923554\pi\)
\(594\) 0 0
\(595\) 0.557459 + 0.338276i 0.0228536 + 0.0138680i
\(596\) 20.5108 42.5911i 0.840156 1.74460i
\(597\) 0 0
\(598\) 8.67938 + 18.0229i 0.354926 + 0.737012i
\(599\) 7.75286 + 6.18270i 0.316773 + 0.252618i 0.768948 0.639311i \(-0.220780\pi\)
−0.452175 + 0.891929i \(0.649352\pi\)
\(600\) 0 0
\(601\) −8.01715 6.39346i −0.327026 0.260795i 0.446188 0.894939i \(-0.352781\pi\)
−0.773215 + 0.634144i \(0.781353\pi\)
\(602\) 2.96176 30.5588i 0.120712 1.24548i
\(603\) 0 0
\(604\) 14.8634 7.15785i 0.604784 0.291249i
\(605\) −0.0672940 + 0.294834i −0.00273589 + 0.0119867i
\(606\) 0 0
\(607\) 16.9849i 0.689396i −0.938714 0.344698i \(-0.887981\pi\)
0.938714 0.344698i \(-0.112019\pi\)
\(608\) −5.78838 + 25.3605i −0.234750 + 1.02851i
\(609\) 0 0
\(610\) 0.266335 + 1.16689i 0.0107836 + 0.0472460i
\(611\) 21.7628 4.96721i 0.880428 0.200952i
\(612\) 0 0
\(613\) 5.39283 + 6.76240i 0.217814 + 0.273131i 0.878719 0.477339i \(-0.158399\pi\)
−0.660905 + 0.750470i \(0.729827\pi\)
\(614\) −4.07905 17.8715i −0.164617 0.721235i
\(615\) 0 0
\(616\) −5.58176 8.58347i −0.224895 0.345838i
\(617\) 43.4997 + 9.92853i 1.75123 + 0.399707i 0.973463 0.228843i \(-0.0734941\pi\)
0.777769 + 0.628550i \(0.216351\pi\)
\(618\) 0 0
\(619\) 5.47735i 0.220153i −0.993923 0.110077i \(-0.964890\pi\)
0.993923 0.110077i \(-0.0351096\pi\)
\(620\) 0.557649 + 0.127280i 0.0223957 + 0.00511168i
\(621\) 0 0
\(622\) −24.1352 + 19.2472i −0.967734 + 0.771742i
\(623\) −19.2200 + 19.8285i −0.770034 + 0.794413i
\(624\) 0 0
\(625\) −5.55618 + 24.3432i −0.222247 + 0.973728i
\(626\) 31.4555 39.4440i 1.25722 1.57650i
\(627\) 0 0
\(628\) −35.2662 + 28.1239i −1.40728 + 1.12227i
\(629\) −19.4448 9.36411i −0.775314 0.373371i
\(630\) 0 0
\(631\) −1.28289 + 0.617808i −0.0510711 + 0.0245946i −0.459245 0.888310i \(-0.651880\pi\)
0.408174 + 0.912904i \(0.366166\pi\)
\(632\) −2.59639 + 5.39145i −0.103279 + 0.214460i
\(633\) 0 0
\(634\) −39.9180 19.2235i −1.58535 0.763462i
\(635\) −0.0793941 + 0.0995571i −0.00315066 + 0.00395080i
\(636\) 0 0
\(637\) 15.3545 + 6.81341i 0.608368 + 0.269957i
\(638\) 40.0084i 1.58395i
\(639\) 0 0
\(640\) 0.141242 0.293292i 0.00558309 0.0115934i
\(641\) 3.57882 0.816841i 0.141355 0.0322633i −0.151258 0.988494i \(-0.548332\pi\)
0.292613 + 0.956231i \(0.405475\pi\)
\(642\) 0 0
\(643\) 16.1942 + 33.6276i 0.638636 + 1.32614i 0.929303 + 0.369317i \(0.120408\pi\)
−0.290667 + 0.956824i \(0.593877\pi\)
\(644\) −21.3904 + 13.9100i −0.842900 + 0.548131i
\(645\) 0 0
\(646\) 23.1706 + 29.0550i 0.911636 + 1.14316i
\(647\) −13.8884 + 6.68832i −0.546011 + 0.262945i −0.686491 0.727139i \(-0.740850\pi\)
0.140480 + 0.990084i \(0.455135\pi\)
\(648\) 0 0
\(649\) −15.7321 3.59076i −0.617541 0.140950i
\(650\) 15.7519 19.7522i 0.617839 0.774745i
\(651\) 0 0
\(652\) −29.0297 36.4021i −1.13689 1.42562i
\(653\) −20.8604 43.3171i −0.816331 1.69513i −0.713745 0.700405i \(-0.753003\pi\)
−0.102586 0.994724i \(-0.532712\pi\)
\(654\) 0 0
\(655\) −0.0789157 −0.00308349
\(656\) 13.2975 0.519180
\(657\) 0 0
\(658\) 17.8820 + 48.6583i 0.697114 + 1.89690i
\(659\) 40.3489 9.20937i 1.57177 0.358746i 0.654200 0.756322i \(-0.273006\pi\)
0.917569 + 0.397576i \(0.130149\pi\)
\(660\) 0 0
\(661\) 9.63413 7.68296i 0.374724 0.298832i −0.417960 0.908466i \(-0.637255\pi\)
0.792684 + 0.609633i \(0.208683\pi\)
\(662\) −38.7037 + 30.8651i −1.50426 + 1.19961i
\(663\) 0 0
\(664\) 3.78654 0.864254i 0.146946 0.0335396i
\(665\) 0.368641 + 0.122580i 0.0142953 + 0.00475346i
\(666\) 0 0
\(667\) −17.8774 −0.692215
\(668\) −25.5398 −0.988166
\(669\) 0 0
\(670\) −0.136179 0.282779i −0.00526105 0.0109247i
\(671\) 32.8889 + 41.2414i 1.26966 + 1.59211i
\(672\) 0 0
\(673\) 12.0699 15.1352i 0.465262 0.583420i −0.492742 0.870175i \(-0.664005\pi\)
0.958004 + 0.286756i \(0.0925768\pi\)
\(674\) −44.8738 10.2422i −1.72848 0.394513i
\(675\) 0 0
\(676\) 15.8989 7.65650i 0.611496 0.294481i
\(677\) −9.63191 12.0780i −0.370184 0.464196i 0.561494 0.827481i \(-0.310227\pi\)
−0.931678 + 0.363284i \(0.881655\pi\)
\(678\) 0 0
\(679\) −48.9561 + 6.28994i −1.87876 + 0.241386i
\(680\) −0.0984251 0.204382i −0.00377443 0.00783769i
\(681\) 0 0
\(682\) 44.7466 10.2131i 1.71344 0.391081i
\(683\) 11.6908 24.2761i 0.447335 0.928901i −0.548363 0.836241i \(-0.684749\pi\)
0.995698 0.0926603i \(-0.0295371\pi\)
\(684\) 0 0
\(685\) 0.625708i 0.0239071i
\(686\) −11.1499 + 37.3839i −0.425706 + 1.42732i
\(687\) 0 0
\(688\) 10.0816 12.6420i 0.384359 0.481971i
\(689\) 11.9459 + 5.75287i 0.455104 + 0.219167i
\(690\) 0 0
\(691\) −8.65967 + 17.9820i −0.329429 + 0.684067i −0.998236 0.0593693i \(-0.981091\pi\)
0.668807 + 0.743436i \(0.266805\pi\)
\(692\) 14.7936 7.12421i 0.562368 0.270822i
\(693\) 0 0
\(694\) 67.1694 + 32.3471i 2.54972 + 1.22788i
\(695\) 0.138667 0.110583i 0.00525995 0.00419467i
\(696\) 0 0
\(697\) 15.3713 19.2750i 0.582231 0.730094i
\(698\) 11.2491 49.2857i 0.425786 1.86549i
\(699\) 0 0
\(700\) 27.5493 + 16.7174i 1.04127 + 0.631859i
\(701\) 28.7869 22.9568i 1.08727 0.867067i 0.0955398 0.995426i \(-0.469542\pi\)
0.991728 + 0.128359i \(0.0409708\pi\)
\(702\) 0 0
\(703\) −12.5357 2.86120i −0.472794 0.107912i
\(704\) 46.3767i 1.74789i
\(705\) 0 0
\(706\) 0.425790 + 0.0971839i 0.0160248 + 0.00365756i
\(707\) 11.6525 35.0432i 0.438239 1.31794i
\(708\) 0 0
\(709\) 2.10242 + 9.21128i 0.0789579 + 0.345937i 0.998940 0.0460223i \(-0.0146545\pi\)
−0.919983 + 0.391959i \(0.871797\pi\)
\(710\) −0.105107 0.131800i −0.00394459 0.00494636i
\(711\) 0 0
\(712\) 9.36603 2.13774i 0.351007 0.0801150i
\(713\) −4.56365 19.9946i −0.170910 0.748805i
\(714\) 0 0
\(715\) −0.101683 + 0.445504i −0.00380274 + 0.0166609i
\(716\) 10.0760i 0.376558i
\(717\) 0 0
\(718\) 12.6164 55.2762i 0.470841 2.06289i
\(719\) −12.2377 + 5.89337i −0.456390 + 0.219786i −0.647931 0.761699i \(-0.724366\pi\)
0.191541 + 0.981485i \(0.438651\pi\)
\(720\) 0 0
\(721\) 22.5908 + 7.51189i 0.841327 + 0.279757i
\(722\) −13.9799 11.1486i −0.520280 0.414909i
\(723\) 0 0
\(724\) −48.7958 38.9133i −1.81348 1.44620i
\(725\) 9.79636 + 20.3424i 0.363828 + 0.755496i
\(726\) 0 0
\(727\) −9.29005 + 19.2910i −0.344549 + 0.715463i −0.999180 0.0404853i \(-0.987110\pi\)
0.654631 + 0.755948i \(0.272824\pi\)
\(728\) −3.18589 4.89917i −0.118077 0.181575i
\(729\) 0 0
\(730\) −0.885058 0.426221i −0.0327575 0.0157752i
\(731\) −6.67092 29.2272i −0.246733 1.08101i
\(732\) 0 0
\(733\) −12.8010 10.2085i −0.472817 0.377059i 0.357895 0.933762i \(-0.383495\pi\)
−0.830711 + 0.556703i \(0.812066\pi\)
\(734\) −22.6419 −0.835728
\(735\) 0 0
\(736\) −31.7516 −1.17038
\(737\) −10.8146 8.62440i −0.398363 0.317684i
\(738\) 0 0
\(739\) 1.58037 + 6.92405i 0.0581349 + 0.254705i 0.995642 0.0932615i \(-0.0297293\pi\)
−0.937507 + 0.347967i \(0.886872\pi\)
\(740\) 0.394379 + 0.189923i 0.0144977 + 0.00698171i
\(741\) 0 0
\(742\) −9.71581 + 29.2188i −0.356679 + 1.07266i
\(743\) 9.88884 20.5344i 0.362787 0.753334i −0.637061 0.770814i \(-0.719850\pi\)
0.999847 + 0.0174797i \(0.00556424\pi\)
\(744\) 0 0
\(745\) −0.381185 0.791540i −0.0139656 0.0289998i
\(746\) 50.4077 + 40.1988i 1.84556 + 1.47178i
\(747\) 0 0
\(748\) −43.5924 34.7638i −1.59390 1.27109i
\(749\) 30.2277 + 29.3001i 1.10450 + 1.07060i
\(750\) 0 0
\(751\) 44.7217 21.5368i 1.63192 0.785890i 0.631976 0.774988i \(-0.282244\pi\)
0.999941 0.0109022i \(-0.00347033\pi\)
\(752\) −6.07537 + 26.6179i −0.221546 + 0.970656i
\(753\) 0 0
\(754\) 22.8355i 0.831619i
\(755\) 0.0682234 0.298906i 0.00248290 0.0108783i
\(756\) 0 0
\(757\) 2.89429 + 12.6807i 0.105195 + 0.460888i 0.999899 + 0.0142286i \(0.00452926\pi\)
−0.894704 + 0.446659i \(0.852614\pi\)
\(758\) −19.1444 + 4.36959i −0.695357 + 0.158711i
\(759\) 0 0
\(760\) −0.0842649 0.105665i −0.00305661 0.00383287i
\(761\) −2.16066 9.46649i −0.0783240 0.343160i 0.920549 0.390628i \(-0.127742\pi\)
−0.998873 + 0.0474677i \(0.984885\pi\)
\(762\) 0 0
\(763\) 6.26989 + 3.80468i 0.226985 + 0.137739i
\(764\) −13.9369 3.18101i −0.504220 0.115085i
\(765\) 0 0
\(766\) 0.691389i 0.0249809i
\(767\) −8.97940 2.04949i −0.324227 0.0740028i
\(768\) 0 0
\(769\) −35.1612 + 28.0401i −1.26795 + 1.01115i −0.269100 + 0.963112i \(0.586726\pi\)
−0.998845 + 0.0480409i \(0.984702\pi\)
\(770\) −1.05626 0.102373i −0.0380651 0.00368927i
\(771\) 0 0
\(772\) −2.84645 + 12.4711i −0.102446 + 0.448845i
\(773\) 6.28500 7.88115i 0.226056 0.283465i −0.655849 0.754892i \(-0.727689\pi\)
0.881905 + 0.471427i \(0.156261\pi\)
\(774\) 0 0
\(775\) −20.2508 + 16.1494i −0.727429 + 0.580105i
\(776\) 15.4708 + 7.45033i 0.555368 + 0.267451i
\(777\) 0 0
\(778\) −8.66527 + 4.17298i −0.310665 + 0.149608i
\(779\) 6.37294 13.2336i 0.228334 0.474141i
\(780\) 0 0
\(781\) −6.69382 3.22357i −0.239524 0.115348i
\(782\) −28.2825 + 35.4651i −1.01138 + 1.26823i
\(783\) 0 0
\(784\) −15.6565 + 13.3045i −0.559161 + 0.475159i
\(785\) 0.838300i 0.0299202i
\(786\) 0 0
\(787\) 6.29386 13.0693i 0.224352 0.465872i −0.758161 0.652068i \(-0.773902\pi\)
0.982513 + 0.186196i \(0.0596160\pi\)
\(788\) −39.9158 + 9.11052i −1.42194 + 0.324549i
\(789\)