Properties

Label 441.2.w.a.188.3
Level $441$
Weight $2$
Character 441.188
Analytic conductor $3.521$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(62,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([7, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.62");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.w (of order \(14\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
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 188.3
Character \(\chi\) \(=\) 441.188
Dual form 441.2.w.a.251.3

$q$-expansion

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

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{14}\right)\) \(-1\)

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 −0.998349 0.0574383i \(-0.981707\pi\)
−0.166155 + 0.986100i \(0.553135\pi\)
\(3\) 0 0
\(4\) 0.542276 2.37587i 0.271138 1.18793i
\(5\) 0.0408049 0.0196506i 0.0182485 0.00878802i −0.424737 0.905317i \(-0.639634\pi\)
0.442986 + 0.896529i \(0.353919\pi\)
\(6\) 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 −0.977804 0.209522i \(-0.932809\pi\)
−0.0133135 + 0.999911i \(0.504238\pi\)
\(12\) 0 0
\(13\) −1.87621 + 1.49623i −0.520366 + 0.414978i −0.848135 0.529780i \(-0.822275\pi\)
0.327769 + 0.944758i \(0.393703\pi\)
\(14\) 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 0.879349 + 0.476177i \(0.157978\pi\)
−0.585661 + 0.810556i \(0.699165\pi\)
\(18\) 0 0
\(19\) 3.24209i 0.743786i 0.928276 + 0.371893i \(0.121291\pi\)
−0.928276 + 0.371893i \(0.878709\pi\)
\(20\) −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 0.604937 0.796273i \(-0.293198\pi\)
0.199539 + 0.979890i \(0.436055\pi\)
\(24\) 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 −0.610925 0.791688i \(-0.709202\pi\)
−0.206924 + 0.978357i \(0.566345\pi\)
\(30\) 0 0
\(31\) 5.18247i 0.930799i 0.885101 + 0.465399i \(0.154089\pi\)
−0.885101 + 0.465399i \(0.845911\pi\)
\(32\) −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 0.994209 + 0.107465i \(0.0342734\pi\)
−0.849124 + 0.528194i \(0.822869\pi\)
\(38\) −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 −0.0870907 0.996200i \(-0.527757\pi\)
0.724561 + 0.689211i \(0.242043\pi\)
\(42\) 0 0
\(43\) 4.96346 + 2.39028i 0.756920 + 0.364514i 0.772208 0.635370i \(-0.219152\pi\)
−0.0152880 + 0.999883i \(0.504867\pi\)
\(44\) 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 −0.997380 0.0723410i \(-0.976953\pi\)
0.151411 0.988471i \(-0.451618\pi\)
\(48\) 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 −0.164077 0.986448i \(-0.552464\pi\)
−0.575831 + 0.817568i \(0.695322\pi\)
\(54\) 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 0.645217 0.763999i \(-0.276767\pi\)
−0.195032 + 0.980797i \(0.562481\pi\)
\(60\) 0 0
\(61\) −12.2316 + 2.79179i −1.56610 + 0.357452i −0.915612 0.402064i \(-0.868293\pi\)
−0.650489 + 0.759516i \(0.725436\pi\)
\(62\) −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 0.323522 0.946221i \(-0.395133\pi\)
−0.119066 + 0.992886i \(0.537990\pi\)
\(72\) 0 0
\(73\) 8.05062 + 6.42016i 0.942254 + 0.751422i 0.968702 0.248228i \(-0.0798481\pi\)
−0.0264478 + 0.999650i \(0.508420\pi\)
\(74\) −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 −0.616186 0.787601i \(-0.711323\pi\)
0.904968 + 0.425479i \(0.139894\pi\)
\(84\) 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 −0.306409 0.951900i \(-0.599127\pi\)
0.996216 + 0.0869087i \(0.0276988\pi\)
\(90\) 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 \(-0.603996\pi\)
0.320932 0.947102i \(-0.396004\pi\)
\(98\) 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 −0.937872 0.346981i \(-0.887207\pi\)
−0.313473 + 0.949597i \(0.601492\pi\)
\(102\) 0 0
\(103\) 3.90418 + 8.10711i 0.384690 + 0.798817i 0.999945 + 0.0104889i \(0.00333878\pi\)
−0.615255 + 0.788328i \(0.710947\pi\)
\(104\) −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 0.999797 0.0201548i \(-0.00641589\pi\)
0.202826 + 0.979215i \(0.434987\pi\)
\(108\) 0 0
\(109\) 1.72830 + 2.16722i 0.165541 + 0.207582i 0.857682 0.514180i \(-0.171904\pi\)
−0.692141 + 0.721762i \(0.743332\pi\)
\(110\) −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 0.989631 0.143634i \(-0.0458787\pi\)
0.0801810 + 0.996780i \(0.474450\pi\)
\(114\) 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 0.939554 0.342400i \(-0.111240\pi\)
−0.995071 + 0.0991651i \(0.968383\pi\)
\(128\) 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 0.364044 0.931382i \(-0.381396\pi\)
−0.501206 + 0.865328i \(0.667110\pi\)
\(132\) 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 0.471266 + 0.881991i \(0.343797\pi\)
−0.983398 + 0.181462i \(0.941917\pi\)
\(138\) 0 0
\(139\) 1.69915 + 3.52832i 0.144120 + 0.299268i 0.960516 0.278224i \(-0.0897457\pi\)
−0.816396 + 0.577492i \(0.804031\pi\)
\(140\) −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 −0.242668 + 0.970109i \(0.578023\pi\)
−0.999785 + 0.0207145i \(0.993406\pi\)
\(150\) 0 0
\(151\) −1.50637 + 6.59983i −0.122586 + 0.537086i 0.875920 + 0.482456i \(0.160255\pi\)
−0.998507 + 0.0546302i \(0.982602\pi\)
\(152\) −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 −0.286898 0.957961i \(-0.592624\pi\)
0.927842 0.372973i \(-0.121662\pi\)
\(158\) 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 −0.386288 0.922378i \(-0.626243\pi\)
−0.961991 + 0.273081i \(0.911957\pi\)
\(164\) −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 −0.981411 0.191918i \(-0.938529\pi\)
0.800951 0.598730i \(-0.204328\pi\)
\(168\) 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 0.885412 + 0.464807i \(0.153876\pi\)
−0.999401 + 0.0346106i \(0.988981\pi\)
\(174\) 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 −0.0692031 0.997603i \(-0.522046\pi\)
0.370494 + 0.928835i \(0.379189\pi\)
\(180\) 0 0
\(181\) −20.0232 15.9680i −1.48831 1.18689i −0.935371 0.353668i \(-0.884934\pi\)
−0.552941 0.833221i \(-0.686494\pi\)
\(182\) −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 0.788364 0.615209i \(-0.210928\pi\)
−0.972527 + 0.232791i \(0.925214\pi\)
\(192\) 0 0
\(193\) 4.72926 2.27749i 0.340420 0.163938i −0.255861 0.966714i \(-0.582359\pi\)
0.596281 + 0.802776i \(0.296645\pi\)
\(194\) 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 \(-0.795766\pi\)
0.801127 0.598494i \(-0.204234\pi\)
\(198\) 0 0
\(199\) −10.2654 21.3164i −0.727696 1.51108i −0.854671 0.519171i \(-0.826241\pi\)
0.126974 0.991906i \(-0.459473\pi\)
\(200\) −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 −0.188919 + 0.981993i \(0.560498\pi\)
−0.915334 + 0.402696i \(0.868073\pi\)
\(212\) −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 0.964480 0.264156i \(-0.0850933\pi\)
0.754354 + 0.656468i \(0.227950\pi\)
\(224\) 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 −0.930438 0.366449i \(-0.880573\pi\)
0.866620 + 0.498968i \(0.166288\pi\)
\(230\) −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 −0.203993 0.978972i \(-0.565392\pi\)
0.240969 + 0.970533i \(0.422535\pi\)
\(234\) 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 −0.365943 0.930637i \(-0.619253\pi\)
0.955763 0.294138i \(-0.0950324\pi\)
\(240\) 0 0
\(241\) −13.0890 2.98747i −0.843134 0.192440i −0.220925 0.975291i \(-0.570908\pi\)
−0.622209 + 0.782851i \(0.713765\pi\)
\(242\) 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 0.977659 0.210197i \(-0.0674106\pi\)
0.445222 + 0.895420i \(0.353125\pi\)
\(252\) 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 0.975889 0.218269i \(-0.0700409\pi\)
−0.973949 + 0.226769i \(0.927184\pi\)
\(258\) 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 \(0.240709\pi\)
−0.727441 + 0.686170i \(0.759291\pi\)
\(264\) 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 −0.896281 0.443488i \(-0.853741\pi\)
0.631810 + 0.775124i \(0.282312\pi\)
\(270\) 0 0
\(271\) 22.9710 + 5.24299i 1.39539 + 0.318489i 0.853120 0.521714i \(-0.174707\pi\)
0.542272 + 0.840203i \(0.317564\pi\)
\(272\) −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 0.911683 0.410895i \(-0.134784\pi\)
−0.999678 + 0.0253604i \(0.991927\pi\)
\(278\) −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 −0.941060 0.338240i \(-0.890168\pi\)
0.120354 + 0.992731i \(0.461597\pi\)
\(282\) 0 0
\(283\) 14.2993 11.4033i 0.850006 0.677857i −0.0983203 0.995155i \(-0.531347\pi\)
0.948326 + 0.317298i \(0.102776\pi\)
\(284\) 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 −0.409798 0.912176i \(-0.634401\pi\)
0.798118 + 0.602502i \(0.205829\pi\)
\(308\) 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 0.979242 + 0.202693i \(0.0649695\pi\)
−0.794321 + 0.607498i \(0.792173\pi\)
\(312\) 0 0
\(313\) 23.9510i 1.35379i −0.736078 0.676896i \(-0.763324\pi\)
0.736078 0.676896i \(-0.236676\pi\)
\(314\) 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 0.755428 0.655231i \(-0.227429\pi\)
0.396323 + 0.918111i \(0.370286\pi\)
\(318\) 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 0.888020 + 0.459805i \(0.152081\pi\)
−0.600576 + 0.799568i \(0.705062\pi\)
\(332\) −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 0.884892 0.465796i \(-0.154232\pi\)
0.187547 + 0.982256i \(0.439946\pi\)
\(338\) −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 −0.856701 0.515813i \(-0.827490\pi\)
−0.995664 + 0.0930223i \(0.970347\pi\)
\(348\) 0 0
\(349\) 10.4131 21.6229i 0.557398 1.15745i −0.411824 0.911263i \(-0.635108\pi\)
0.969222 0.246186i \(-0.0791775\pi\)
\(350\) −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 0.428906 0.903349i \(-0.358899\pi\)
−0.438848 + 0.898561i \(0.644614\pi\)
\(354\) 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 −0.325996 0.945371i \(-0.605700\pi\)
0.942376 0.334555i \(-0.108586\pi\)
\(360\) 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 0.817792 0.575514i \(-0.195198\pi\)
−0.379109 + 0.925352i \(0.623770\pi\)
\(368\) 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 0.908373 0.418162i \(-0.137325\pi\)
−0.609809 + 0.792548i \(0.708754\pi\)
\(380\) 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 −0.787033 0.616912i \(-0.788384\pi\)
0.776575 + 0.630024i \(0.216955\pi\)
\(384\) 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 0.945135 0.326679i \(-0.105930\pi\)
−0.844690 + 0.535255i \(0.820215\pi\)
\(390\) 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 0.998729 + 0.0503980i \(0.0160490\pi\)
−0.583295 + 0.812261i \(0.698237\pi\)
\(398\) 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 0.759765 0.650197i \(-0.225314\pi\)
−0.464832 + 0.885399i \(0.653885\pi\)
\(402\) 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 −0.658084 0.752945i \(-0.728633\pi\)
−0.266223 + 0.963912i \(0.585776\pi\)
\(410\) 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 −0.741883 0.670529i \(-0.766067\pi\)
0.959345 0.282234i \(-0.0910756\pi\)
\(420\) 0 0
\(421\) 3.64719 + 15.9794i 0.177753 + 0.778788i 0.982664 + 0.185393i \(0.0593557\pi\)
−0.804911 + 0.593395i \(0.797787\pi\)
\(422\) 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 −0.777642 0.628707i \(-0.783584\pi\)
0.976395 + 0.215992i \(0.0692986\pi\)
\(432\) 0 0
\(433\) 12.1776 + 25.2870i 0.585218 + 1.21522i 0.957858 + 0.287242i \(0.0927383\pi\)
−0.372640 + 0.927976i \(0.621547\pi\)
\(434\) −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 0.0816258 0.996663i \(-0.473989\pi\)
0.989838 + 0.142199i \(0.0454173\pi\)
\(440\) −0.175267 −0.00835553
\(441\) 0 0
\(442\) 27.5075 1.30840
\(443\) 1.55249 1.23807i 0.0737612 0.0588226i −0.585915 0.810372i \(-0.699265\pi\)
0.659676 + 0.751550i \(0.270693\pi\)
\(444\) 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 0.917715 0.397239i \(-0.130032\pi\)
−0.882760 + 0.469824i \(0.844317\pi\)
\(450\) 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 −0.573041 0.819527i \(-0.694236\pi\)
−0.998017 + 0.0629452i \(0.979951\pi\)
\(458\) −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 0.999186 + 0.0403389i \(0.0128438\pi\)
−0.882733 + 0.469875i \(0.844299\pi\)
\(462\) 0 0
\(463\) 0.757284 3.31788i 0.0351940 0.154195i −0.954278 0.298922i \(-0.903373\pi\)
0.989472 + 0.144727i \(0.0462303\pi\)
\(464\) −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 −0.460252 0.887789i \(-0.652241\pi\)
0.799869 0.600174i \(-0.204902\pi\)
\(468\) 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 0.923704 0.383107i \(-0.125146\pi\)
−0.579045 + 0.815295i \(0.696575\pi\)
\(480\) 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 −0.300828 0.953678i \(-0.597263\pi\)
0.558052 + 0.829806i \(0.311549\pi\)
\(488\) −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 \(-0.999986\pi\)
1.00000 4.32807e-5i \(-1.37767e-5\pi\)
\(492\) 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 −0.667337 0.744756i \(-0.732566\pi\)
0.874580 + 0.484882i \(0.161137\pi\)
\(500\) 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 0.573412 0.819267i \(-0.305620\pi\)
−0.926323 + 0.376731i \(0.877048\pi\)
\(504\) 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 −0.955750 0.294182i \(-0.904953\pi\)
0.825901 + 0.563816i \(0.190667\pi\)
\(524\) −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 0.986417 + 0.164258i \(0.0525229\pi\)
−0.0593590 + 0.998237i \(0.518906\pi\)
\(542\) −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 −0.886127 0.463443i \(-0.846614\pi\)
−0.190156 + 0.981754i \(0.560899\pi\)
\(548\) 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 \(-0.964622\pi\)
0.993830 0.110914i \(-0.0353777\pi\)
\(558\) 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 −0.995807 0.0914829i \(-0.970839\pi\)
0.310777 + 0.950483i \(0.399411\pi\)
\(564\) 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 \(0.0111243\pi\)
−0.999389 + 0.0349410i \(0.988876\pi\)
\(570\) 0 0
\(571\) 5.29827 + 23.2132i 0.221726 + 0.971444i 0.956179 + 0.292784i \(0.0945817\pi\)
−0.734453 + 0.678660i \(0.762561\pi\)
\(572\) −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 −0.400187 0.916434i \(-0.631055\pi\)
0.804407 + 0.594079i \(0.202483\pi\)
\(578\) 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 −0.971299 0.237861i \(-0.923554\pi\)
−0.419628 + 0.907696i \(0.637839\pi\)
\(594\) 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 −0.452175 0.891929i \(-0.649352\pi\)
0.768948 + 0.639311i \(0.220780\pi\)
\(600\) 0 0
\(601\) −8.01715 + 6.39346i −0.327026 + 0.260795i −0.773215 0.634144i \(-0.781353\pi\)
0.446188 + 0.894939i \(0.352781\pi\)
\(602\) 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 \(0.112019\pi\)
−0.938714 + 0.344698i \(0.887981\pi\)
\(608\) −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 −0.660905 0.750470i \(-0.729827\pi\)
0.878719 + 0.477339i \(0.158399\pi\)
\(614\) −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 0.777769 0.628550i \(-0.216351\pi\)
0.973463 + 0.228843i \(0.0734941\pi\)
\(618\) 0 0
\(619\) 5.47735i 0.220153i 0.993923 + 0.110077i \(0.0351096\pi\)
−0.993923 + 0.110077i \(0.964890\pi\)
\(620\) 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 0.408174 0.912904i \(-0.366166\pi\)
−0.459245 + 0.888310i \(0.651880\pi\)
\(632\) −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 0.292613 0.956231i \(-0.405475\pi\)
−0.151258 + 0.988494i \(0.548332\pi\)
\(642\) 0 0
\(643\) 16.1942 33.6276i 0.638636 1.32614i −0.290667 0.956824i \(-0.593877\pi\)
0.929303 0.369317i \(-0.120408\pi\)
\(644\) −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 0.140480 0.990084i \(-0.455135\pi\)
−0.686491 + 0.727139i \(0.740850\pi\)
\(648\) 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 −0.102586 + 0.994724i \(0.532712\pi\)
−0.713745 + 0.700405i \(0.753003\pi\)
\(654\) 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 0.917569 0.397576i \(-0.130149\pi\)
0.654200 + 0.756322i \(0.273006\pi\)
\(660\) 0 0
\(661\) 9.63413 + 7.68296i 0.374724 + 0.298832i 0.792684 0.609633i \(-0.208683\pi\)
−0.417960 + 0.908466i \(0.637255\pi\)
\(662\) −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 0.958004 0.286756i \(-0.0925768\pi\)
−0.492742 + 0.870175i \(0.664005\pi\)
\(674\) −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 −0.931678 0.363284i \(-0.881655\pi\)
0.561494 + 0.827481i \(0.310227\pi\)
\(678\) 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 0.995698 + 0.0926603i \(0.0295371\pi\)
−0.548363 + 0.836241i \(0.684749\pi\)
\(684\) 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 0.668807 0.743436i \(-0.266805\pi\)
−0.998236 + 0.0593693i \(0.981091\pi\)
\(692\) 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 0.991728 0.128359i \(-0.0409708\pi\)
0.0955398 + 0.995426i \(0.469542\pi\)
\(702\) 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 −0.919983 0.391959i \(-0.871797\pi\)
0.998940 + 0.0460223i \(0.0146545\pi\)
\(710\) −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 0.191541 0.981485i \(-0.438651\pi\)
−0.647931 + 0.761699i \(0.724366\pi\)
\(720\) 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 0.654631 0.755948i \(-0.272824\pi\)
−0.999180 + 0.0404853i \(0.987110\pi\)
\(728\) −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 −0.830711 0.556703i \(-0.812066\pi\)
0.357895 + 0.933762i \(0.383495\pi\)
\(734\) −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 −0.937507 0.347967i \(-0.886872\pi\)
0.995642 + 0.0932615i \(0.0297293\pi\)
\(740\) 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 0.999847 0.0174797i \(-0.00556424\pi\)
−0.637061 + 0.770814i \(0.719850\pi\)
\(744\) 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 0.999941 + 0.0109022i \(0.00347033\pi\)
0.631976 + 0.774988i \(0.282244\pi\)
\(752\) −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 −0.894704 0.446659i \(-0.852614\pi\)
0.999899 0.0142286i \(-0.00452926\pi\)
\(758\) −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 −0.998873 0.0474677i \(-0.984885\pi\)
0.920549 + 0.390628i \(0.127742\pi\)
\(762\) 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 −0.998845 0.0480409i \(-0.984702\pi\)
−0.269100 0.963112i \(-0.586726\pi\)
\(770\) −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 0.881905 0.471427i \(-0.156261\pi\)
−0.655849 + 0.754892i \(0.727689\pi\)
\(774\) 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 0.982513 0.186196i \(-0.0596160\pi\)
−0.758161 + 0.652068i \(0.773902\pi\)
\(788\) −39.9158 9.11052i −1.42194 0.324549i
\(789\) 0 0
\(790\) 0.269107 0.558807i 0.00957440 0.0198815i
\(791\) 27.6331 26.7851i 0.982521 0.952370i
\(792\) 0 0
\(793\) 18.7719 23.5393i 0.666611 0.835904i
\(794\) −36.2057 17.4358i −1.28489 0.618772i
\(795\) 0 0
\(796\) −56.2115 + 12.8299i −1.99236 + 0.454744i
\(797\) −5.19665 6.51640i −0.184075 0.230823i 0.681229 0.732071i \(-0.261446\pi\)
−0.865304 + 0.501248i \(0.832874\pi\)
\(798\) 0 0
\(799\) 31.5605 39.5756i 1.11653 1.40008i
\(800\) 17.3991 36.1296i 0.615150 1.27737i
\(801\) 0 0
\(802\) −15.9121 −0.561875
\(803\) −43.2937 −1.52780
\(804\) 0 0
\(805\) −0.0457446 0.471983i −0.00161228 0.0166352i
\(806\) 25.5399 + 5.82932i 0.899606 + 0.205329i
\(807\) 0 0
\(808\) −10.0446 8.01026i −0.353366 0.281800i
\(809\) −0.771178 0.614994i −0.0271132 0.0216220i 0.609839 0.792525i \(-0.291234\pi\)
−0.636953 + 0.770903i \(0.719805\pi\)
\(810\) 0 0
\(811\) 1.45346 + 0.331743i 0.0510379 + 0.0116491i 0.247964 0.968769i \(-0.420239\pi\)
−0.196926 + 0.980418i \(0.563096\pi\)
\(812\) 28.8897 + 3.71178i 1.01383 + 0.130258i
\(813\) 0 0
\(814\) 35.1240 1.23110
\(815\) −0.865300 −0.0303101
\(816\) 0 0
\(817\) −7.74949 + 16.0920i −0.271120 + 0.562987i
\(818\) 25.1813 31.5763i 0.880442 1.10404i
\(819\) 0 0
\(820\) −0.311762 0.390937i −0.0108872 0.0136521i
\(821\) 44.4855 10.1535i 1.55256 0.354361i 0.641657 0.766992i \(-0.278247\pi\)
0.910898 + 0.412631i \(0.135390\pi\)
\(822\) 0 0
\(823\) −24.8710 11.9773i −0.866949 0.417501i −0.0531086 0.998589i \(-0.516913\pi\)
−0.813841 + 0.581088i \(0.802627\pi\)
\(824\) −5.16387 + 6.47528i −0.179892 + 0.225577i
\(825\) 0 0
\(826\) 2.06340 + 21.2897i 0.0717947 + 0.740763i
\(827\) −16.4862 + 34.2340i −0.573283 + 1.19043i 0.389718 + 0.920934i \(0.372573\pi\)
−0.963001 + 0.269499i \(0.913142\pi\)
\(828\) 0 0
\(829\) −24.4801 5.58742i −0.850228 0.194059i −0.224862 0.974391i \(-0.572193\pi\)
−0.625366 + 0.780332i \(0.715050\pi\)
\(830\) 0.174663 + 0.362691i 0.00606263 + 0.0125892i
\(831\) 0 0
\(832\) 26.4703i 0.917694i
\(833\) 1.18688 38.0739i 0.0411230 1.31918i
\(834\) 0 0
\(835\) −0.295938 0.371095i −0.0102414 0.0128423i
\(836\) −29.9290 + 14.4131i −1.03512 + 0.498486i
\(837\) 0 0
\(838\) 18.2825 + 37.9640i 0.631559 + 1.31145i
\(839\) −45.6772 21.9970i −1.57695 0.759419i −0.578533 0.815659i \(-0.696375\pi\)
−0.998417 + 0.0562396i \(0.982089\pi\)
\(840\) 0 0
\(841\) −7.74118 + 3.72796i −0.266937 + 0.128550i
\(842\) −26.9926 21.5258i −0.930225 0.741830i
\(843\) 0 0
\(844\) 39.0894 + 49.0165i 1.34551 + 1.68722i
\(845\) 0.0729762 + 0.319730i 0.00251046 + 0.0109990i
\(846\) 0 0
\(847\) −16.5822 6.09400i −0.569772 0.209392i
\(848\) −12.6790 10.1111i −0.435398 0.347218i
\(849\) 0 0
\(850\) 55.8532 12.7481i 1.91575 0.437257i
\(851\) 15.6948i 0.538012i
\(852\) 0 0
\(853\) −11.5084 + 2.62671i −0.394040 + 0.0899370i −0.414950 0.909844i \(-0.636201\pi\)
0.0209100 + 0.999781i \(0.493344\pi\)
\(854\) −48.6649 50.2055i −1.66528 1.71800i
\(855\) 0 0
\(856\) −3.25888 + 14.2781i −0.111386 + 0.488015i
\(857\) −0.143121 + 0.179468i −0.00488892 + 0.00613051i −0.784270 0.620420i \(-0.786962\pi\)
0.779381 + 0.626550i \(0.215534\pi\)
\(858\) 0 0
\(859\) −15.2180 3.47341i −0.519231 0.118511i −0.0451292 0.998981i \(-0.514370\pi\)
−0.474102 + 0.880470i \(0.657227\pi\)
\(860\) 0.135300 0.592788i 0.00461369 0.0202139i
\(861\) 0 0
\(862\) 4.45752 + 19.5297i 0.151824 + 0.665183i
\(863\) 6.78962i 0.231121i 0.993300 + 0.115561i \(0.0368665\pi\)
−0.993300 + 0.115561i \(0.963134\pi\)
\(864\) 0 0
\(865\) 0.0679028 + 0.297502i 0.00230877 + 0.0101154i
\(866\) −53.2649 25.6510i −1.81001 0.871657i
\(867\) 0 0
\(868\) 11.5262 31.3636i 0.391224 1.06455i
\(869\) 21.3711 17.0429i 0.724966 0.578141i
\(870\) 0 0
\(871\) −6.17265 + 4.92253i −0.209152 + 0.166793i
\(872\) −1.10701 + 2.29874i −0.0374882 + 0.0778451i
\(873\) 0 0
\(874\) −11.7259 24.3491i −0.396634 0.823619i
\(875\) 1.12449 + 0.413250i 0.0380145 + 0.0139704i
\(876\) 0 0
\(877\) −32.0655 + 15.4419i −1.08277 + 0.521436i −0.888203 0.459452i \(-0.848046\pi\)
−0.194571 + 0.980888i \(0.562332\pi\)
\(878\) −13.4589 + 58.9674i −0.454217 + 1.99005i
\(879\) 0 0
\(880\) −0.436970 + 0.348472i −0.0147303 + 0.0117470i
\(881\) 45.8866 1.54596 0.772979 0.634432i \(-0.218766\pi\)
0.772979 + 0.634432i \(0.218766\pi\)
\(882\) 0 0
\(883\) −10.9038 −0.366941 −0.183470 0.983025i \(-0.558733\pi\)
−0.183470 + 0.983025i \(0.558733\pi\)
\(884\) −24.8812 + 19.8421i −0.836844 + 0.667361i
\(885\) 0 0
\(886\) −0.930745 + 4.07786i −0.0312690 + 0.136998i
\(887\) 11.0313 5.31239i 0.370395 0.178373i −0.239421 0.970916i \(-0.576958\pi\)
0.609816 + 0.792543i \(0.291243\pi\)
\(888\) 0 0
\(889\) −7.40415 + 0.717610i −0.248327 + 0.0240679i
\(890\) 0.432029 + 0.897117i 0.0144816 + 0.0300714i
\(891\) 0 0
\(892\) 27.8379 57.8060i 0.932082 1.93549i
\(893\) 23.5783 18.8031i 0.789017 0.629220i
\(894\) 0 0
\(895\) 0.146405 0.116754i 0.00489377 0.00390265i
\(896\) 18.8618 + 2.42338i 0.630127 + 0.0809595i
\(897\) 0 0
\(898\) −3.23975 1.56018i −0.108112 0.0520639i
\(899\) −5.20963 22.8249i −0.173751 0.761253i
\(900\) 0 0
\(901\) 30.0665i 1.00166i
\(902\) −8.92820 39.1170i −0.297277 1.30245i
\(903\) 0 0
\(904\) −2.97916 + 13.0526i −0.0990854 + 0.434122i
\(905\) −1.13082 0.258103i −0.0375899 0.00857964i
\(906\) 0 0
\(907\) −15.9653 + 20.0198i −0.530118 + 0.664748i −0.972723 0.231969i \(-0.925483\pi\)
0.442605 + 0.896717i \(0.354055\pi\)
\(908\) 15.8088 69.2630i 0.524634 2.29857i
\(909\) 0 0
\(910\) −0.602882 + 0.0584313i −0.0199853 + 0.00193698i
\(911\) 23.6692 5.40234i 0.784195 0.178987i 0.188366 0.982099i \(-0.439681\pi\)
0.595829 + 0.803112i \(0.296824\pi\)
\(912\) 0 0
\(913\) 17.7415i 0.587157i
\(914\) 76.5519 17.4725i 2.53211 0.577938i
\(915\) 0 0
\(916\) 4.24080 + 3.38193i 0.140120 + 0.111742i
\(917\) −2.51324 + 3.86479i −0.0829945 + 0.127627i
\(918\) 0 0
\(919\) 12.0616 + 52.8454i 0.397876 + 1.74321i 0.635732 + 0.771910i \(0.280698\pi\)
−0.237856 + 0.971301i \(0.576444\pi\)
\(920\) 0.102855 + 0.128976i 0.00339104 + 0.00425222i
\(921\) 0 0
\(922\) −18.5049 14.7571i −0.609426 0.486001i
\(923\) −3.82061 + 1.83991i −0.125757 + 0.0605614i
\(924\) 0 0
\(925\) −17.8589 8.60038i −0.587196 0.282779i
\(926\) 3.11031 + 6.45864i 0.102211 + 0.212244i
\(927\) 0 0
\(928\) 32.6566 15.7266i 1.07200 0.516250i
\(929\) 25.7657 + 32.3091i 0.845345 + 1.06003i 0.997429 + 0.0716612i \(0.0228300\pi\)
−0.152084 + 0.988368i \(0.548599\pi\)
\(930\) 0 0
\(931\) 5.73697 21.9575i 0.188021 0.719629i
\(932\) 1.41085i 0.0462139i
\(933\) 0 0
\(934\) 30.1435 + 62.5937i 0.986327 + 2.04813i
\(935\) −1.01024 0.230580i −0.0330383 0.00754078i
\(936\) 0 0
\(937\) −6.25761 + 12.9941i −0.204427 + 0.424497i −0.977825 0.209424i \(-0.932841\pi\)
0.773398 + 0.633921i \(0.218556\pi\)
\(938\) 9.51178 + 15.6749i 0.310571 + 0.511803i
\(939\) 0 0
\(940\) −0.640111 + 0.802674i −0.0208781 + 0.0261803i
\(941\) −37.2078 17.9183i −1.21294 0.584120i −0.285602 0.958348i \(-0.592193\pi\)
−0.927337 + 0.374228i \(0.877908\pi\)
\(942\) 0 0
\(943\) 17.4791 3.98949i 0.569198 0.129916i
\(944\) 7.02367 + 8.80741i 0.228601 + 0.286657i
\(945\) 0 0
\(946\) 30.4197 38.1451i 0.989030 1.24020i
\(947\) 1.38334 2.87254i 0.0449525 0.0933449i −0.877283 0.479974i \(-0.840646\pi\)
0.922235 + 0.386629i \(0.126361\pi\)
\(948\) 0 0
\(949\) −24.7106 −0.802141
\(950\) 34.1318 1.10738
\(951\) 0 0
\(952\) 6.87476 + 11.3292i 0.222812 + 0.367182i
\(953\) 39.8186 + 9.08833i 1.28985 + 0.294400i 0.811802 0.583933i \(-0.198487\pi\)
0.478049 + 0.878333i \(0.341344\pi\)
\(954\) 0 0
\(955\) −0.207712 0.165644i −0.00672139 0.00536013i
\(956\) −40.0413 31.9319i −1.29503 1.03275i
\(957\) 0 0
\(958\) −24.8452 5.67076i −0.802713 0.183214i
\(959\) 30.6432 + 19.9270i 0.989520 + 0.643477i
\(960\) 0 0
\(961\) 4.14204 0.133614
\(962\) 20.0476 0.646362
\(963\) 0 0
\(964\) −14.1957 + 29.4776i −0.457211 + 0.949409i
\(965\) 0.148223 0.185866i 0.00477147 0.00598323i
\(966\) 0 0
\(967\) 25.8538 + 32.4196i 0.831401 + 1.04254i 0.998398 + 0.0565869i \(0.0180218\pi\)
−0.166996 + 0.985958i \(0.553407\pi\)
\(968\) 5.99190 1.36761i 0.192587 0.0439567i
\(969\) 0 0
\(970\) 1.60350 + 0.772204i 0.0514852 + 0.0247940i
\(971\) 8.63760 10.8312i 0.277194 0.347590i −0.623673 0.781685i \(-0.714360\pi\)
0.900867 + 0.434095i \(0.142932\pi\)
\(972\) 0 0
\(973\) 9.83183 3.26927i 0.315194 0.104808i
\(974\) −5.75814 + 11.9569i −0.184503 + 0.383124i
\(975\) 0 0
\(976\) −35.9015 8.19427i −1.14918 0.262292i
\(977\) −15.3577 31.8906i −0.491336 1.02027i −0.988303 0.152500i \(-0.951268\pi\)
0.496968 0.867769i \(-0.334447\pi\)
\(978\) 0 0
\(979\) 43.8836i 1.40253i
\(980\) −0.0240724 + 0.772217i −0.000768963 + 0.0246676i
\(981\) 0 0
\(982\) 0.00251905 + 0.00315879i 8.03862e−5 + 0.000100801i
\(983\) 14.0392 6.76090i 0.447780 0.215639i −0.196384 0.980527i \(-0.562920\pi\)
0.644164 + 0.764888i \(0.277206\pi\)
\(984\) 0 0
\(985\) −0.330141 0.685544i −0.0105192 0.0218432i
\(986\) 46.6544 + 22.4676i 1.48578 + 0.715514i
\(987\) 0 0
\(988\) −17.0825 + 8.22650i −0.543467 + 0.261720i
\(989\) 17.0448 + 13.5928i 0.541994 + 0.432225i
\(990\) 0 0
\(991\) −11.1124 13.9345i −0.352997 0.442644i 0.573353 0.819309i \(-0.305642\pi\)
−0.926350 + 0.376664i \(0.877071\pi\)
\(992\) −9.25270 40.5387i −0.293773 1.28711i
\(993\) 0 0
\(994\) 3.10736 + 9.34491i 0.0985595 + 0.296402i
\(995\) −0.837759 0.668091i −0.0265587 0.0211799i
\(996\) 0 0
\(997\) 39.3968 8.99207i 1.24771 0.284782i 0.452857 0.891583i \(-0.350405\pi\)
0.794853 + 0.606802i \(0.207548\pi\)
\(998\) 15.6402i 0.495083i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 441.2.w.a.188.3 120
3.2 odd 2 inner 441.2.w.a.188.18 yes 120
49.6 odd 14 inner 441.2.w.a.251.18 yes 120
147.104 even 14 inner 441.2.w.a.251.3 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.w.a.188.3 120 1.1 even 1 trivial
441.2.w.a.188.18 yes 120 3.2 odd 2 inner
441.2.w.a.251.3 yes 120 147.104 even 14 inner
441.2.w.a.251.18 yes 120 49.6 odd 14 inner