Properties

Label 368.2.j.e.93.6
Level $368$
Weight $2$
Character 368.93
Analytic conductor $2.938$
Analytic rank $0$
Dimension $46$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [368,2,Mod(93,368)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(368, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("368.93");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 368 = 2^{4} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 368.j (of order \(4\), degree \(2\), 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: \(2.93849479438\)
Analytic rank: \(0\)
Dimension: \(46\)
Relative dimension: \(23\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 93.6
Character \(\chi\) \(=\) 368.93
Dual form 368.2.j.e.277.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.924538 - 1.07015i) q^{2} +(0.777788 + 0.777788i) q^{3} +(-0.290458 + 1.97880i) q^{4} +(2.81868 - 2.81868i) q^{5} +(0.113258 - 1.55145i) q^{6} -2.32052i q^{7} +(2.38616 - 1.51864i) q^{8} -1.79009i q^{9} +(-5.62240 - 0.410443i) q^{10} +(-3.20492 + 3.20492i) q^{11} +(-1.76500 + 1.31317i) q^{12} +(1.79361 + 1.79361i) q^{13} +(-2.48331 + 2.14541i) q^{14} +4.38467 q^{15} +(-3.83127 - 1.14951i) q^{16} +1.66137 q^{17} +(-1.91567 + 1.65501i) q^{18} +(-3.17012 - 3.17012i) q^{19} +(4.75889 + 6.39630i) q^{20} +(1.80487 - 1.80487i) q^{21} +(6.39283 + 0.466685i) q^{22} +1.00000i q^{23} +(3.03710 + 0.674744i) q^{24} -10.8899i q^{25} +(0.261177 - 3.57769i) q^{26} +(3.72568 - 3.72568i) q^{27} +(4.59184 + 0.674013i) q^{28} +(1.82665 + 1.82665i) q^{29} +(-4.05380 - 4.69227i) q^{30} +0.296491 q^{31} +(2.31200 + 5.16281i) q^{32} -4.98550 q^{33} +(-1.53600 - 1.77792i) q^{34} +(-6.54080 - 6.54080i) q^{35} +(3.54222 + 0.519945i) q^{36} +(4.66394 - 4.66394i) q^{37} +(-0.461618 + 6.32342i) q^{38} +2.79009i q^{39} +(2.44525 - 11.0064i) q^{40} +7.17636i q^{41} +(-3.60017 - 0.262817i) q^{42} +(-2.78473 + 2.78473i) q^{43} +(-5.41099 - 7.27278i) q^{44} +(-5.04569 - 5.04569i) q^{45} +(1.07015 - 0.924538i) q^{46} +3.83110 q^{47} +(-2.08584 - 3.87399i) q^{48} +1.61518 q^{49} +(-11.6539 + 10.0681i) q^{50} +(1.29220 + 1.29220i) q^{51} +(-4.07015 + 3.02822i) q^{52} +(-9.81496 + 9.81496i) q^{53} +(-7.43158 - 0.542515i) q^{54} +18.0673i q^{55} +(-3.52403 - 5.53712i) q^{56} -4.93137i q^{57} +(0.265988 - 3.64360i) q^{58} +(3.74914 - 3.74914i) q^{59} +(-1.27356 + 8.67637i) q^{60} +(0.614784 + 0.614784i) q^{61} +(-0.274117 - 0.317291i) q^{62} -4.15394 q^{63} +(3.38747 - 7.24742i) q^{64} +10.1112 q^{65} +(4.60929 + 5.33525i) q^{66} +(9.89515 + 9.89515i) q^{67} +(-0.482558 + 3.28752i) q^{68} +(-0.777788 + 0.777788i) q^{69} +(-0.952441 + 13.0469i) q^{70} -2.83241i q^{71} +(-2.71850 - 4.27143i) q^{72} -10.7672i q^{73} +(-9.30312 - 0.679141i) q^{74} +(8.47004 - 8.47004i) q^{75} +(7.19381 - 5.35224i) q^{76} +(7.43708 + 7.43708i) q^{77} +(2.98583 - 2.57955i) q^{78} -6.74460 q^{79} +(-14.0392 + 7.55901i) q^{80} +0.425305 q^{81} +(7.67981 - 6.63482i) q^{82} +(4.88698 + 4.88698i) q^{83} +(3.04724 + 4.09572i) q^{84} +(4.68287 - 4.68287i) q^{85} +(5.55468 + 0.405499i) q^{86} +2.84149i q^{87} +(-2.78032 + 12.5146i) q^{88} +6.31401i q^{89} +(-0.734730 + 10.0646i) q^{90} +(4.16210 - 4.16210i) q^{91} +(-1.97880 - 0.290458i) q^{92} +(0.230607 + 0.230607i) q^{93} +(-3.54200 - 4.09987i) q^{94} -17.8711 q^{95} +(-2.21733 + 5.81382i) q^{96} -12.7651 q^{97} +(-1.49330 - 1.72849i) q^{98} +(5.73710 + 5.73710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46 q + 2 q^{2} + 6 q^{3} + 4 q^{5} + 2 q^{8} - 10 q^{10} + 4 q^{11} - 16 q^{12} + 2 q^{13} + 28 q^{14} - 12 q^{15} - 8 q^{16} - 16 q^{17} - 34 q^{18} + 4 q^{19} + 18 q^{20} - 28 q^{22} - 30 q^{24} + 2 q^{26}+ \cdots - 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/368\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(97\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.924538 1.07015i −0.653747 0.756713i
\(3\) 0.777788 + 0.777788i 0.449056 + 0.449056i 0.895041 0.445984i \(-0.147146\pi\)
−0.445984 + 0.895041i \(0.647146\pi\)
\(4\) −0.290458 + 1.97880i −0.145229 + 0.989398i
\(5\) 2.81868 2.81868i 1.26055 1.26055i 0.309726 0.950826i \(-0.399763\pi\)
0.950826 0.309726i \(-0.100237\pi\)
\(6\) 0.113258 1.55145i 0.0462373 0.633376i
\(7\) 2.32052i 0.877074i −0.898713 0.438537i \(-0.855497\pi\)
0.898713 0.438537i \(-0.144503\pi\)
\(8\) 2.38616 1.51864i 0.843633 0.536920i
\(9\) 1.79009i 0.596697i
\(10\) −5.62240 0.410443i −1.77796 0.129793i
\(11\) −3.20492 + 3.20492i −0.966320 + 0.966320i −0.999451 0.0331311i \(-0.989452\pi\)
0.0331311 + 0.999451i \(0.489452\pi\)
\(12\) −1.76500 + 1.31317i −0.509511 + 0.379080i
\(13\) 1.79361 + 1.79361i 0.497457 + 0.497457i 0.910646 0.413188i \(-0.135585\pi\)
−0.413188 + 0.910646i \(0.635585\pi\)
\(14\) −2.48331 + 2.14541i −0.663693 + 0.573385i
\(15\) 4.38467 1.13212
\(16\) −3.83127 1.14951i −0.957817 0.287378i
\(17\) 1.66137 0.402942 0.201471 0.979494i \(-0.435428\pi\)
0.201471 + 0.979494i \(0.435428\pi\)
\(18\) −1.91567 + 1.65501i −0.451528 + 0.390089i
\(19\) −3.17012 3.17012i −0.727276 0.727276i 0.242800 0.970076i \(-0.421934\pi\)
−0.970076 + 0.242800i \(0.921934\pi\)
\(20\) 4.75889 + 6.39630i 1.06412 + 1.43026i
\(21\) 1.80487 1.80487i 0.393856 0.393856i
\(22\) 6.39283 + 0.466685i 1.36296 + 0.0994976i
\(23\) 1.00000i 0.208514i
\(24\) 3.03710 + 0.674744i 0.619946 + 0.137732i
\(25\) 10.8899i 2.17798i
\(26\) 0.261177 3.57769i 0.0512209 0.701644i
\(27\) 3.72568 3.72568i 0.717007 0.717007i
\(28\) 4.59184 + 0.674013i 0.867776 + 0.127376i
\(29\) 1.82665 + 1.82665i 0.339200 + 0.339200i 0.856066 0.516866i \(-0.172902\pi\)
−0.516866 + 0.856066i \(0.672902\pi\)
\(30\) −4.05380 4.69227i −0.740119 0.856688i
\(31\) 0.296491 0.0532513 0.0266257 0.999645i \(-0.491524\pi\)
0.0266257 + 0.999645i \(0.491524\pi\)
\(32\) 2.31200 + 5.16281i 0.408708 + 0.912665i
\(33\) −4.98550 −0.867864
\(34\) −1.53600 1.77792i −0.263422 0.304911i
\(35\) −6.54080 6.54080i −1.10560 1.10560i
\(36\) 3.54222 + 0.519945i 0.590371 + 0.0866576i
\(37\) 4.66394 4.66394i 0.766747 0.766747i −0.210785 0.977532i \(-0.567602\pi\)
0.977532 + 0.210785i \(0.0676021\pi\)
\(38\) −0.461618 + 6.32342i −0.0748844 + 1.02579i
\(39\) 2.79009i 0.446773i
\(40\) 2.44525 11.0064i 0.386628 1.74026i
\(41\) 7.17636i 1.12076i 0.828236 + 0.560380i \(0.189345\pi\)
−0.828236 + 0.560380i \(0.810655\pi\)
\(42\) −3.60017 0.262817i −0.555518 0.0405536i
\(43\) −2.78473 + 2.78473i −0.424667 + 0.424667i −0.886807 0.462140i \(-0.847082\pi\)
0.462140 + 0.886807i \(0.347082\pi\)
\(44\) −5.41099 7.27278i −0.815738 1.09641i
\(45\) −5.04569 5.04569i −0.752167 0.752167i
\(46\) 1.07015 0.924538i 0.157786 0.136316i
\(47\) 3.83110 0.558823 0.279412 0.960171i \(-0.409861\pi\)
0.279412 + 0.960171i \(0.409861\pi\)
\(48\) −2.08584 3.87399i −0.301065 0.559163i
\(49\) 1.61518 0.230741
\(50\) −11.6539 + 10.0681i −1.64811 + 1.42385i
\(51\) 1.29220 + 1.29220i 0.180944 + 0.180944i
\(52\) −4.07015 + 3.02822i −0.564428 + 0.419938i
\(53\) −9.81496 + 9.81496i −1.34819 + 1.34819i −0.460560 + 0.887628i \(0.652351\pi\)
−0.887628 + 0.460560i \(0.847649\pi\)
\(54\) −7.43158 0.542515i −1.01131 0.0738270i
\(55\) 18.0673i 2.43619i
\(56\) −3.52403 5.53712i −0.470919 0.739929i
\(57\) 4.93137i 0.653176i
\(58\) 0.265988 3.64360i 0.0349259 0.478428i
\(59\) 3.74914 3.74914i 0.488096 0.488096i −0.419609 0.907705i \(-0.637833\pi\)
0.907705 + 0.419609i \(0.137833\pi\)
\(60\) −1.27356 + 8.67637i −0.164416 + 1.12011i
\(61\) 0.614784 + 0.614784i 0.0787150 + 0.0787150i 0.745368 0.666653i \(-0.232274\pi\)
−0.666653 + 0.745368i \(0.732274\pi\)
\(62\) −0.274117 0.317291i −0.0348129 0.0402960i
\(63\) −4.15394 −0.523347
\(64\) 3.38747 7.24742i 0.423434 0.905927i
\(65\) 10.1112 1.25414
\(66\) 4.60929 + 5.33525i 0.567364 + 0.656724i
\(67\) 9.89515 + 9.89515i 1.20888 + 1.20888i 0.971388 + 0.237496i \(0.0763267\pi\)
0.237496 + 0.971388i \(0.423673\pi\)
\(68\) −0.482558 + 3.28752i −0.0585188 + 0.398670i
\(69\) −0.777788 + 0.777788i −0.0936347 + 0.0936347i
\(70\) −0.952441 + 13.0469i −0.113838 + 1.55940i
\(71\) 2.83241i 0.336145i −0.985775 0.168073i \(-0.946246\pi\)
0.985775 0.168073i \(-0.0537543\pi\)
\(72\) −2.71850 4.27143i −0.320378 0.503393i
\(73\) 10.7672i 1.26021i −0.776510 0.630105i \(-0.783012\pi\)
0.776510 0.630105i \(-0.216988\pi\)
\(74\) −9.30312 0.679141i −1.08147 0.0789485i
\(75\) 8.47004 8.47004i 0.978036 0.978036i
\(76\) 7.19381 5.35224i 0.825187 0.613944i
\(77\) 7.43708 + 7.43708i 0.847534 + 0.847534i
\(78\) 2.98583 2.57955i 0.338079 0.292076i
\(79\) −6.74460 −0.758826 −0.379413 0.925227i \(-0.623874\pi\)
−0.379413 + 0.925227i \(0.623874\pi\)
\(80\) −14.0392 + 7.55901i −1.56963 + 0.845123i
\(81\) 0.425305 0.0472561
\(82\) 7.67981 6.63482i 0.848093 0.732694i
\(83\) 4.88698 + 4.88698i 0.536416 + 0.536416i 0.922474 0.386058i \(-0.126164\pi\)
−0.386058 + 0.922474i \(0.626164\pi\)
\(84\) 3.04724 + 4.09572i 0.332481 + 0.446879i
\(85\) 4.68287 4.68287i 0.507929 0.507929i
\(86\) 5.55468 + 0.405499i 0.598976 + 0.0437261i
\(87\) 2.84149i 0.304640i
\(88\) −2.78032 + 12.5146i −0.296383 + 1.33406i
\(89\) 6.31401i 0.669284i 0.942345 + 0.334642i \(0.108615\pi\)
−0.942345 + 0.334642i \(0.891385\pi\)
\(90\) −0.734730 + 10.0646i −0.0774473 + 1.06090i
\(91\) 4.16210 4.16210i 0.436307 0.436307i
\(92\) −1.97880 0.290458i −0.206304 0.0302823i
\(93\) 0.230607 + 0.230607i 0.0239128 + 0.0239128i
\(94\) −3.54200 4.09987i −0.365329 0.422869i
\(95\) −17.8711 −1.83354
\(96\) −2.21733 + 5.81382i −0.226305 + 0.593371i
\(97\) −12.7651 −1.29610 −0.648049 0.761598i \(-0.724415\pi\)
−0.648049 + 0.761598i \(0.724415\pi\)
\(98\) −1.49330 1.72849i −0.150846 0.174604i
\(99\) 5.73710 + 5.73710i 0.576600 + 0.576600i
\(100\) 21.5489 + 3.16306i 2.15489 + 0.316306i
\(101\) 0.885037 0.885037i 0.0880645 0.0880645i −0.661702 0.749767i \(-0.730166\pi\)
0.749767 + 0.661702i \(0.230166\pi\)
\(102\) 0.188163 2.57753i 0.0186310 0.255214i
\(103\) 18.7525i 1.84774i 0.382708 + 0.923869i \(0.374991\pi\)
−0.382708 + 0.923869i \(0.625009\pi\)
\(104\) 7.00367 + 1.55598i 0.686766 + 0.152577i
\(105\) 10.1747i 0.992951i
\(106\) 19.5778 + 1.42921i 1.90157 + 0.138817i
\(107\) −8.45618 + 8.45618i −0.817489 + 0.817489i −0.985744 0.168254i \(-0.946187\pi\)
0.168254 + 0.985744i \(0.446187\pi\)
\(108\) 6.29020 + 8.45451i 0.605275 + 0.813535i
\(109\) 14.1693 + 14.1693i 1.35717 + 1.35717i 0.877382 + 0.479793i \(0.159288\pi\)
0.479793 + 0.877382i \(0.340712\pi\)
\(110\) 19.3348 16.7039i 1.84350 1.59265i
\(111\) 7.25512 0.688625
\(112\) −2.66747 + 8.89054i −0.252052 + 0.840077i
\(113\) −15.1806 −1.42807 −0.714034 0.700111i \(-0.753134\pi\)
−0.714034 + 0.700111i \(0.753134\pi\)
\(114\) −5.27732 + 4.55924i −0.494266 + 0.427012i
\(115\) 2.81868 + 2.81868i 0.262843 + 0.262843i
\(116\) −4.14513 + 3.08400i −0.384866 + 0.286342i
\(117\) 3.21072 3.21072i 0.296831 0.296831i
\(118\) −7.47838 0.545932i −0.688440 0.0502571i
\(119\) 3.85525i 0.353410i
\(120\) 10.4625 6.65873i 0.955092 0.607856i
\(121\) 9.54303i 0.867548i
\(122\) 0.0895220 1.22631i 0.00810494 0.111024i
\(123\) −5.58169 + 5.58169i −0.503284 + 0.503284i
\(124\) −0.0861180 + 0.586695i −0.00773362 + 0.0526867i
\(125\) −16.6018 16.6018i −1.48491 1.48491i
\(126\) 3.84048 + 4.44536i 0.342137 + 0.396024i
\(127\) −9.14635 −0.811608 −0.405804 0.913960i \(-0.633008\pi\)
−0.405804 + 0.913960i \(0.633008\pi\)
\(128\) −10.8877 + 3.07540i −0.962345 + 0.271829i
\(129\) −4.33186 −0.381399
\(130\) −9.34820 10.8205i −0.819891 0.949025i
\(131\) 9.87952 + 9.87952i 0.863178 + 0.863178i 0.991706 0.128528i \(-0.0410253\pi\)
−0.128528 + 0.991706i \(0.541025\pi\)
\(132\) 1.44808 9.86529i 0.126039 0.858663i
\(133\) −7.35633 + 7.35633i −0.637875 + 0.637875i
\(134\) 1.44088 19.7378i 0.124473 1.70508i
\(135\) 21.0030i 1.80765i
\(136\) 3.96429 2.52302i 0.339935 0.216348i
\(137\) 10.3676i 0.885763i −0.896580 0.442881i \(-0.853956\pi\)
0.896580 0.442881i \(-0.146044\pi\)
\(138\) 1.55145 + 0.113258i 0.132068 + 0.00964115i
\(139\) 9.13155 9.13155i 0.774528 0.774528i −0.204367 0.978894i \(-0.565513\pi\)
0.978894 + 0.204367i \(0.0655135\pi\)
\(140\) 14.8427 11.0431i 1.25444 0.933312i
\(141\) 2.97979 + 2.97979i 0.250943 + 0.250943i
\(142\) −3.03111 + 2.61867i −0.254365 + 0.219754i
\(143\) −11.4967 −0.961405
\(144\) −2.05773 + 6.85832i −0.171478 + 0.571526i
\(145\) 10.2975 0.855159
\(146\) −11.5226 + 9.95473i −0.953617 + 0.823859i
\(147\) 1.25627 + 1.25627i 0.103616 + 0.103616i
\(148\) 7.87431 + 10.5837i 0.647264 + 0.869972i
\(149\) −13.2715 + 13.2715i −1.08724 + 1.08724i −0.0914284 + 0.995812i \(0.529143\pi\)
−0.995812 + 0.0914284i \(0.970857\pi\)
\(150\) −16.8951 1.23337i −1.37948 0.100704i
\(151\) 10.6562i 0.867192i 0.901107 + 0.433596i \(0.142755\pi\)
−0.901107 + 0.433596i \(0.857245\pi\)
\(152\) −12.3787 2.75013i −1.00404 0.223065i
\(153\) 2.97401i 0.240434i
\(154\) 1.08295 14.8347i 0.0872668 1.19541i
\(155\) 0.835712 0.835712i 0.0671260 0.0671260i
\(156\) −5.52103 0.810404i −0.442036 0.0648842i
\(157\) −1.22420 1.22420i −0.0977020 0.0977020i 0.656566 0.754268i \(-0.272008\pi\)
−0.754268 + 0.656566i \(0.772008\pi\)
\(158\) 6.23564 + 7.21775i 0.496081 + 0.574214i
\(159\) −15.2679 −1.21083
\(160\) 21.0691 + 8.03553i 1.66566 + 0.635265i
\(161\) 2.32052 0.182883
\(162\) −0.393211 0.455142i −0.0308936 0.0357593i
\(163\) −3.02940 3.02940i −0.237281 0.237281i 0.578443 0.815723i \(-0.303661\pi\)
−0.815723 + 0.578443i \(0.803661\pi\)
\(164\) −14.2006 2.08443i −1.10888 0.162767i
\(165\) −14.0525 + 14.0525i −1.09399 + 1.09399i
\(166\) 0.711619 9.74802i 0.0552324 0.756593i
\(167\) 7.88807i 0.610397i −0.952289 0.305199i \(-0.901277\pi\)
0.952289 0.305199i \(-0.0987229\pi\)
\(168\) 1.56576 7.04766i 0.120801 0.543739i
\(169\) 6.56595i 0.505073i
\(170\) −9.34089 0.681898i −0.716414 0.0522992i
\(171\) −5.67481 + 5.67481i −0.433963 + 0.433963i
\(172\) −4.70157 6.31926i −0.358491 0.481839i
\(173\) 12.5070 + 12.5070i 0.950886 + 0.950886i 0.998849 0.0479627i \(-0.0152729\pi\)
−0.0479627 + 0.998849i \(0.515273\pi\)
\(174\) 3.04083 2.62707i 0.230525 0.199158i
\(175\) −25.2703 −1.91025
\(176\) 15.9630 8.59482i 1.20326 0.647859i
\(177\) 5.83207 0.438365
\(178\) 6.75696 5.83755i 0.506456 0.437543i
\(179\) −10.0110 10.0110i −0.748258 0.748258i 0.225894 0.974152i \(-0.427470\pi\)
−0.974152 + 0.225894i \(0.927470\pi\)
\(180\) 11.4500 8.51883i 0.853429 0.634956i
\(181\) 8.59528 8.59528i 0.638882 0.638882i −0.311397 0.950280i \(-0.600797\pi\)
0.950280 + 0.311397i \(0.100797\pi\)
\(182\) −8.30211 0.606066i −0.615394 0.0449246i
\(183\) 0.956344i 0.0706950i
\(184\) 1.51864 + 2.38616i 0.111956 + 0.175910i
\(185\) 26.2923i 1.93305i
\(186\) 0.0335799 0.459990i 0.00246220 0.0337281i
\(187\) −5.32457 + 5.32457i −0.389371 + 0.389371i
\(188\) −1.11277 + 7.58097i −0.0811572 + 0.552899i
\(189\) −8.64551 8.64551i −0.628868 0.628868i
\(190\) 16.5225 + 19.1248i 1.19867 + 1.38746i
\(191\) −4.68980 −0.339342 −0.169671 0.985501i \(-0.554271\pi\)
−0.169671 + 0.985501i \(0.554271\pi\)
\(192\) 8.27169 3.00222i 0.596958 0.216666i
\(193\) −7.89668 −0.568415 −0.284208 0.958763i \(-0.591731\pi\)
−0.284208 + 0.958763i \(0.591731\pi\)
\(194\) 11.8018 + 13.6606i 0.847321 + 0.980775i
\(195\) 7.86438 + 7.86438i 0.563180 + 0.563180i
\(196\) −0.469142 + 3.19612i −0.0335102 + 0.228294i
\(197\) 7.73490 7.73490i 0.551089 0.551089i −0.375666 0.926755i \(-0.622586\pi\)
0.926755 + 0.375666i \(0.122586\pi\)
\(198\) 0.835409 11.4437i 0.0593699 0.813271i
\(199\) 13.1324i 0.930934i −0.885065 0.465467i \(-0.845886\pi\)
0.885065 0.465467i \(-0.154114\pi\)
\(200\) −16.5378 25.9850i −1.16940 1.83742i
\(201\) 15.3927i 1.08571i
\(202\) −1.76538 0.128875i −0.124211 0.00906760i
\(203\) 4.23878 4.23878i 0.297504 0.297504i
\(204\) −2.93232 + 2.18166i −0.205303 + 0.152747i
\(205\) 20.2279 + 20.2279i 1.41278 + 1.41278i
\(206\) 20.0681 17.3374i 1.39821 1.20795i
\(207\) 1.79009 0.124420
\(208\) −4.81002 8.93357i −0.333515 0.619431i
\(209\) 20.3200 1.40556
\(210\) −10.8885 + 9.40692i −0.751379 + 0.649139i
\(211\) −14.0513 14.0513i −0.967328 0.967328i 0.0321547 0.999483i \(-0.489763\pi\)
−0.999483 + 0.0321547i \(0.989763\pi\)
\(212\) −16.5710 22.2726i −1.13810 1.52969i
\(213\) 2.20302 2.20302i 0.150948 0.150948i
\(214\) 16.8675 + 1.23135i 1.15304 + 0.0841732i
\(215\) 15.6985i 1.07063i
\(216\) 3.23209 14.5480i 0.219916 0.989866i
\(217\) 0.688013i 0.0467054i
\(218\) 2.06327 28.2634i 0.139742 1.91424i
\(219\) 8.37464 8.37464i 0.565905 0.565905i
\(220\) −35.7515 5.24778i −2.41036 0.353805i
\(221\) 2.97985 + 2.97985i 0.200446 + 0.200446i
\(222\) −6.70763 7.76409i −0.450187 0.521091i
\(223\) 29.3004 1.96210 0.981048 0.193762i \(-0.0620691\pi\)
0.981048 + 0.193762i \(0.0620691\pi\)
\(224\) 11.9804 5.36504i 0.800475 0.358467i
\(225\) −19.4939 −1.29959
\(226\) 14.0350 + 16.2456i 0.933596 + 1.08064i
\(227\) 3.28456 + 3.28456i 0.218004 + 0.218004i 0.807657 0.589653i \(-0.200736\pi\)
−0.589653 + 0.807657i \(0.700736\pi\)
\(228\) 9.75817 + 1.43235i 0.646251 + 0.0948599i
\(229\) 8.81201 8.81201i 0.582314 0.582314i −0.353225 0.935539i \(-0.614915\pi\)
0.935539 + 0.353225i \(0.114915\pi\)
\(230\) 0.410443 5.62240i 0.0270638 0.370730i
\(231\) 11.5690i 0.761181i
\(232\) 7.13269 + 1.58465i 0.468284 + 0.104037i
\(233\) 21.3237i 1.39696i 0.715629 + 0.698481i \(0.246140\pi\)
−0.715629 + 0.698481i \(0.753860\pi\)
\(234\) −6.40440 0.467530i −0.418668 0.0305634i
\(235\) 10.7986 10.7986i 0.704426 0.704426i
\(236\) 6.32982 + 8.50775i 0.412036 + 0.553807i
\(237\) −5.24587 5.24587i −0.340756 0.340756i
\(238\) −4.12571 + 3.56432i −0.267430 + 0.231041i
\(239\) −3.64798 −0.235968 −0.117984 0.993015i \(-0.537643\pi\)
−0.117984 + 0.993015i \(0.537643\pi\)
\(240\) −16.7989 5.04024i −1.08436 0.325346i
\(241\) −21.7242 −1.39938 −0.699689 0.714448i \(-0.746678\pi\)
−0.699689 + 0.714448i \(0.746678\pi\)
\(242\) −10.2125 + 8.82290i −0.656485 + 0.567157i
\(243\) −10.8462 10.8462i −0.695786 0.695786i
\(244\) −1.39510 + 1.03796i −0.0893122 + 0.0664488i
\(245\) 4.55269 4.55269i 0.290860 0.290860i
\(246\) 11.1338 + 0.812779i 0.709862 + 0.0518209i
\(247\) 11.3719i 0.723577i
\(248\) 0.707473 0.450262i 0.0449246 0.0285917i
\(249\) 7.60208i 0.481762i
\(250\) −2.41747 + 33.1154i −0.152894 + 2.09440i
\(251\) 19.6363 19.6363i 1.23943 1.23943i 0.279201 0.960233i \(-0.409930\pi\)
0.960233 0.279201i \(-0.0900697\pi\)
\(252\) 1.20654 8.21980i 0.0760051 0.517799i
\(253\) −3.20492 3.20492i −0.201492 0.201492i
\(254\) 8.45616 + 9.78800i 0.530586 + 0.614154i
\(255\) 7.28457 0.456178
\(256\) 13.3572 + 8.80818i 0.834828 + 0.550512i
\(257\) 2.66315 0.166123 0.0830615 0.996544i \(-0.473530\pi\)
0.0830615 + 0.996544i \(0.473530\pi\)
\(258\) 4.00497 + 4.63576i 0.249339 + 0.288610i
\(259\) −10.8228 10.8228i −0.672494 0.672494i
\(260\) −2.93688 + 20.0080i −0.182137 + 1.24084i
\(261\) 3.26987 3.26987i 0.202400 0.202400i
\(262\) 1.43861 19.7066i 0.0888776 1.21748i
\(263\) 4.93186i 0.304112i −0.988372 0.152056i \(-0.951411\pi\)
0.988372 0.152056i \(-0.0485894\pi\)
\(264\) −11.8962 + 7.57117i −0.732159 + 0.465974i
\(265\) 55.3305i 3.39892i
\(266\) 14.6736 + 1.07119i 0.899697 + 0.0656791i
\(267\) −4.91096 + 4.91096i −0.300546 + 0.300546i
\(268\) −22.4546 + 16.7064i −1.37163 + 1.02050i
\(269\) 14.0004 + 14.0004i 0.853621 + 0.853621i 0.990577 0.136956i \(-0.0437319\pi\)
−0.136956 + 0.990577i \(0.543732\pi\)
\(270\) −22.4764 + 19.4181i −1.36787 + 1.18175i
\(271\) −0.438291 −0.0266243 −0.0133121 0.999911i \(-0.504238\pi\)
−0.0133121 + 0.999911i \(0.504238\pi\)
\(272\) −6.36516 1.90977i −0.385945 0.115797i
\(273\) 6.47447 0.391853
\(274\) −11.0949 + 9.58523i −0.670268 + 0.579065i
\(275\) 34.9013 + 34.9013i 2.10463 + 2.10463i
\(276\) −1.31317 1.76500i −0.0790436 0.106240i
\(277\) −12.2450 + 12.2450i −0.735728 + 0.735728i −0.971748 0.236020i \(-0.924157\pi\)
0.236020 + 0.971748i \(0.424157\pi\)
\(278\) −18.2146 1.32969i −1.09244 0.0797497i
\(279\) 0.530745i 0.0317749i
\(280\) −25.5405 5.67425i −1.52634 0.339102i
\(281\) 20.3210i 1.21225i 0.795371 + 0.606123i \(0.207276\pi\)
−0.795371 + 0.606123i \(0.792724\pi\)
\(282\) 0.433902 5.94375i 0.0258385 0.353945i
\(283\) 5.09281 5.09281i 0.302736 0.302736i −0.539347 0.842083i \(-0.681329\pi\)
0.842083 + 0.539347i \(0.181329\pi\)
\(284\) 5.60476 + 0.822695i 0.332582 + 0.0488180i
\(285\) −13.8999 13.8999i −0.823362 0.823362i
\(286\) 10.6292 + 12.3033i 0.628516 + 0.727508i
\(287\) 16.6529 0.982990
\(288\) 9.24191 4.13869i 0.544584 0.243875i
\(289\) −14.2398 −0.837638
\(290\) −9.52041 11.0199i −0.559058 0.647110i
\(291\) −9.92854 9.92854i −0.582021 0.582021i
\(292\) 21.3062 + 3.12743i 1.24685 + 0.183019i
\(293\) −23.7791 + 23.7791i −1.38919 + 1.38919i −0.562168 + 0.827023i \(0.690032\pi\)
−0.827023 + 0.562168i \(0.809968\pi\)
\(294\) 0.182932 2.50587i 0.0106688 0.146146i
\(295\) 21.1352i 1.23054i
\(296\) 4.04604 18.2117i 0.235172 1.05853i
\(297\) 23.8810i 1.38572i
\(298\) 26.4725 + 1.93253i 1.53351 + 0.111948i
\(299\) −1.79361 + 1.79361i −0.103727 + 0.103727i
\(300\) 14.3003 + 19.2207i 0.825628 + 1.10971i
\(301\) 6.46202 + 6.46202i 0.372465 + 0.372465i
\(302\) 11.4038 9.85210i 0.656215 0.566924i
\(303\) 1.37674 0.0790918
\(304\) 8.50149 + 15.7897i 0.487594 + 0.905601i
\(305\) 3.46576 0.198449
\(306\) −3.18264 + 2.74958i −0.181940 + 0.157183i
\(307\) −17.7076 17.7076i −1.01063 1.01063i −0.999943 0.0106845i \(-0.996599\pi\)
−0.0106845 0.999943i \(-0.503401\pi\)
\(308\) −16.8766 + 12.5563i −0.961635 + 0.715463i
\(309\) −14.5855 + 14.5855i −0.829739 + 0.829739i
\(310\) −1.66699 0.121692i −0.0946786 0.00691167i
\(311\) 9.95651i 0.564582i −0.959329 0.282291i \(-0.908906\pi\)
0.959329 0.282291i \(-0.0910943\pi\)
\(312\) 4.23714 + 6.65760i 0.239881 + 0.376912i
\(313\) 34.1218i 1.92868i −0.264671 0.964339i \(-0.585263\pi\)
0.264671 0.964339i \(-0.414737\pi\)
\(314\) −0.178263 + 2.44191i −0.0100599 + 0.137805i
\(315\) −11.7086 + 11.7086i −0.659707 + 0.659707i
\(316\) 1.95902 13.3462i 0.110203 0.750781i
\(317\) 6.89442 + 6.89442i 0.387229 + 0.387229i 0.873698 0.486469i \(-0.161715\pi\)
−0.486469 + 0.873698i \(0.661715\pi\)
\(318\) 14.1158 + 16.3390i 0.791574 + 0.916247i
\(319\) −11.7085 −0.655552
\(320\) −10.8799 29.9763i −0.608207 1.67573i
\(321\) −13.1542 −0.734198
\(322\) −2.14541 2.48331i −0.119559 0.138390i
\(323\) −5.26675 5.26675i −0.293050 0.293050i
\(324\) −0.123533 + 0.841592i −0.00686295 + 0.0467551i
\(325\) 19.5322 19.5322i 1.08345 1.08345i
\(326\) −0.441126 + 6.04271i −0.0244317 + 0.334675i
\(327\) 22.0415i 1.21890i
\(328\) 10.8983 + 17.1239i 0.601758 + 0.945510i
\(329\) 8.89015i 0.490130i
\(330\) 28.0305 + 2.04626i 1.54303 + 0.112643i
\(331\) 21.5926 21.5926i 1.18684 1.18684i 0.208901 0.977937i \(-0.433011\pi\)
0.977937 0.208901i \(-0.0669888\pi\)
\(332\) −11.0898 + 8.25088i −0.608632 + 0.452826i
\(333\) −8.34887 8.34887i −0.457515 0.457515i
\(334\) −8.44145 + 7.29282i −0.461895 + 0.399046i
\(335\) 55.7825 3.04772
\(336\) −8.98968 + 4.84023i −0.490427 + 0.264056i
\(337\) −16.8015 −0.915236 −0.457618 0.889149i \(-0.651297\pi\)
−0.457618 + 0.889149i \(0.651297\pi\)
\(338\) −7.02657 + 6.07047i −0.382195 + 0.330190i
\(339\) −11.8073 11.8073i −0.641283 0.641283i
\(340\) 7.90628 + 10.6266i 0.428778 + 0.576310i
\(341\) −0.950229 + 0.950229i −0.0514578 + 0.0514578i
\(342\) 11.3195 + 0.826338i 0.612088 + 0.0446833i
\(343\) 19.9917i 1.07945i
\(344\) −2.41580 + 10.8738i −0.130251 + 0.586276i
\(345\) 4.38467i 0.236063i
\(346\) 1.82120 24.9475i 0.0979085 1.34119i
\(347\) −7.83787 + 7.83787i −0.420759 + 0.420759i −0.885465 0.464706i \(-0.846160\pi\)
0.464706 + 0.885465i \(0.346160\pi\)
\(348\) −5.62273 0.825333i −0.301410 0.0442425i
\(349\) 2.37699 + 2.37699i 0.127237 + 0.127237i 0.767858 0.640621i \(-0.221323\pi\)
−0.640621 + 0.767858i \(0.721323\pi\)
\(350\) 23.3633 + 27.0431i 1.24882 + 1.44551i
\(351\) 13.3648 0.713360
\(352\) −23.9562 9.13664i −1.27687 0.486984i
\(353\) −3.52647 −0.187695 −0.0938474 0.995587i \(-0.529917\pi\)
−0.0938474 + 0.995587i \(0.529917\pi\)
\(354\) −5.39198 6.24121i −0.286580 0.331717i
\(355\) −7.98366 7.98366i −0.423729 0.423729i
\(356\) −12.4941 1.83395i −0.662188 0.0971993i
\(357\) 2.99857 2.99857i 0.158701 0.158701i
\(358\) −1.45776 + 19.9689i −0.0770448 + 1.05539i
\(359\) 6.18644i 0.326508i 0.986584 + 0.163254i \(0.0521989\pi\)
−0.986584 + 0.163254i \(0.947801\pi\)
\(360\) −19.7024 4.37722i −1.03841 0.230700i
\(361\) 1.09935i 0.0578605i
\(362\) −17.1449 1.25160i −0.901118 0.0657829i
\(363\) 7.42246 7.42246i 0.389578 0.389578i
\(364\) 7.02704 + 9.44487i 0.368317 + 0.495046i
\(365\) −30.3494 30.3494i −1.58856 1.58856i
\(366\) 1.02344 0.884177i 0.0534958 0.0462167i
\(367\) −8.92361 −0.465809 −0.232904 0.972500i \(-0.574823\pi\)
−0.232904 + 0.972500i \(0.574823\pi\)
\(368\) 1.14951 3.83127i 0.0599225 0.199719i
\(369\) 12.8463 0.668754
\(370\) −28.1368 + 24.3082i −1.46276 + 1.26373i
\(371\) 22.7758 + 22.7758i 1.18246 + 1.18246i
\(372\) −0.523306 + 0.389343i −0.0271321 + 0.0201865i
\(373\) 23.2859 23.2859i 1.20570 1.20570i 0.233290 0.972407i \(-0.425051\pi\)
0.972407 0.233290i \(-0.0749492\pi\)
\(374\) 10.6209 + 0.775338i 0.549192 + 0.0400918i
\(375\) 25.8253i 1.33361i
\(376\) 9.14160 5.81806i 0.471442 0.300043i
\(377\) 6.55258i 0.337475i
\(378\) −1.25892 + 17.2451i −0.0647518 + 0.886994i
\(379\) −8.59665 + 8.59665i −0.441580 + 0.441580i −0.892543 0.450963i \(-0.851081\pi\)
0.450963 + 0.892543i \(0.351081\pi\)
\(380\) 5.19080 35.3633i 0.266282 1.81410i
\(381\) −7.11393 7.11393i −0.364458 0.364458i
\(382\) 4.33590 + 5.01881i 0.221844 + 0.256784i
\(383\) −1.40860 −0.0719761 −0.0359880 0.999352i \(-0.511458\pi\)
−0.0359880 + 0.999352i \(0.511458\pi\)
\(384\) −10.8603 6.07632i −0.554214 0.310081i
\(385\) 41.9255 2.13672
\(386\) 7.30078 + 8.45066i 0.371600 + 0.430127i
\(387\) 4.98492 + 4.98492i 0.253398 + 0.253398i
\(388\) 3.70772 25.2595i 0.188231 1.28236i
\(389\) −0.461939 + 0.461939i −0.0234212 + 0.0234212i −0.718720 0.695299i \(-0.755272\pi\)
0.695299 + 0.718720i \(0.255272\pi\)
\(390\) 1.14517 15.6870i 0.0579881 0.794343i
\(391\) 1.66137i 0.0840192i
\(392\) 3.85408 2.45288i 0.194660 0.123889i
\(393\) 15.3684i 0.775231i
\(394\) −15.4287 1.12632i −0.777289 0.0567431i
\(395\) −19.0109 + 19.0109i −0.956540 + 0.956540i
\(396\) −13.0189 + 9.68616i −0.654226 + 0.486748i
\(397\) 14.2358 + 14.2358i 0.714473 + 0.714473i 0.967468 0.252995i \(-0.0814155\pi\)
−0.252995 + 0.967468i \(0.581416\pi\)
\(398\) −14.0537 + 12.1414i −0.704450 + 0.608596i
\(399\) −11.4433 −0.572884
\(400\) −12.5181 + 41.7222i −0.625904 + 2.08611i
\(401\) 18.5653 0.927107 0.463553 0.886069i \(-0.346574\pi\)
0.463553 + 0.886069i \(0.346574\pi\)
\(402\) 16.4725 14.2311i 0.821574 0.709783i
\(403\) 0.531788 + 0.531788i 0.0264902 + 0.0264902i
\(404\) 1.49424 + 2.00837i 0.0743413 + 0.0999203i
\(405\) 1.19880 1.19880i 0.0595688 0.0595688i
\(406\) −8.45505 0.617230i −0.419617 0.0306326i
\(407\) 29.8951i 1.48185i
\(408\) 5.04576 + 1.12100i 0.249802 + 0.0554978i
\(409\) 8.73112i 0.431726i −0.976424 0.215863i \(-0.930744\pi\)
0.976424 0.215863i \(-0.0692565\pi\)
\(410\) 2.94549 40.3484i 0.145467 1.99266i
\(411\) 8.06379 8.06379i 0.397757 0.397757i
\(412\) −37.1074 5.44681i −1.82815 0.268345i
\(413\) −8.69995 8.69995i −0.428097 0.428097i
\(414\) −1.65501 1.91567i −0.0813392 0.0941501i
\(415\) 27.5497 1.35236
\(416\) −5.11324 + 13.4069i −0.250697 + 0.657326i
\(417\) 14.2048 0.695613
\(418\) −18.7866 21.7455i −0.918883 1.06361i
\(419\) −6.27734 6.27734i −0.306668 0.306668i 0.536947 0.843616i \(-0.319577\pi\)
−0.843616 + 0.536947i \(0.819577\pi\)
\(420\) 20.1337 + 2.95533i 0.982424 + 0.144205i
\(421\) 22.3738 22.3738i 1.09043 1.09043i 0.0949502 0.995482i \(-0.469731\pi\)
0.995482 0.0949502i \(-0.0302692\pi\)
\(422\) −2.04608 + 28.0279i −0.0996015 + 1.36438i
\(423\) 6.85802i 0.333448i
\(424\) −8.51464 + 38.3254i −0.413507 + 1.86125i
\(425\) 18.0922i 0.877600i
\(426\) −4.39434 0.320793i −0.212906 0.0155425i
\(427\) 1.42662 1.42662i 0.0690390 0.0690390i
\(428\) −14.2769 19.1892i −0.690100 0.927546i
\(429\) −8.94203 8.94203i −0.431725 0.431725i
\(430\) 16.7998 14.5139i 0.810160 0.699922i
\(431\) −14.0721 −0.677828 −0.338914 0.940817i \(-0.610060\pi\)
−0.338914 + 0.940817i \(0.610060\pi\)
\(432\) −18.5568 + 9.99136i −0.892814 + 0.480709i
\(433\) −18.0306 −0.866496 −0.433248 0.901275i \(-0.642633\pi\)
−0.433248 + 0.901275i \(0.642633\pi\)
\(434\) −0.736280 + 0.636094i −0.0353425 + 0.0305335i
\(435\) 8.00926 + 8.00926i 0.384014 + 0.384014i
\(436\) −32.1538 + 23.9226i −1.53989 + 1.14569i
\(437\) 3.17012 3.17012i 0.151648 0.151648i
\(438\) −16.7048 1.21947i −0.798187 0.0582688i
\(439\) 4.35394i 0.207802i −0.994588 0.103901i \(-0.966867\pi\)
0.994588 0.103901i \(-0.0331325\pi\)
\(440\) 27.4377 + 43.1113i 1.30804 + 2.05525i
\(441\) 2.89133i 0.137682i
\(442\) 0.433911 5.94388i 0.0206391 0.282722i
\(443\) −11.7542 + 11.7542i −0.558460 + 0.558460i −0.928869 0.370409i \(-0.879218\pi\)
0.370409 + 0.928869i \(0.379218\pi\)
\(444\) −2.10730 + 14.3564i −0.100008 + 0.681324i
\(445\) 17.7972 + 17.7972i 0.843667 + 0.843667i
\(446\) −27.0893 31.3559i −1.28272 1.48474i
\(447\) −20.6448 −0.976464
\(448\) −16.8178 7.86070i −0.794565 0.371383i
\(449\) 11.0996 0.523824 0.261912 0.965092i \(-0.415647\pi\)
0.261912 + 0.965092i \(0.415647\pi\)
\(450\) 18.0229 + 20.8615i 0.849606 + 0.983420i
\(451\) −22.9997 22.9997i −1.08301 1.08301i
\(452\) 4.40931 30.0393i 0.207397 1.41293i
\(453\) −8.28830 + 8.28830i −0.389418 + 0.389418i
\(454\) 0.478281 6.55168i 0.0224469 0.307485i
\(455\) 23.4633i 1.09997i
\(456\) −7.48897 11.7670i −0.350703 0.551041i
\(457\) 23.9218i 1.11901i 0.828825 + 0.559507i \(0.189010\pi\)
−0.828825 + 0.559507i \(0.810990\pi\)
\(458\) −17.5772 1.28316i −0.821331 0.0599583i
\(459\) 6.18973 6.18973i 0.288912 0.288912i
\(460\) −6.39630 + 4.75889i −0.298229 + 0.221884i
\(461\) 19.7026 + 19.7026i 0.917641 + 0.917641i 0.996857 0.0792160i \(-0.0252417\pi\)
−0.0792160 + 0.996857i \(0.525242\pi\)
\(462\) 12.3806 10.6959i 0.575996 0.497620i
\(463\) −22.7966 −1.05945 −0.529725 0.848170i \(-0.677705\pi\)
−0.529725 + 0.848170i \(0.677705\pi\)
\(464\) −4.89863 9.09814i −0.227413 0.422370i
\(465\) 1.30001 0.0602867
\(466\) 22.8196 19.7146i 1.05710 0.913260i
\(467\) −17.4792 17.4792i −0.808841 0.808841i 0.175617 0.984458i \(-0.443808\pi\)
−0.984458 + 0.175617i \(0.943808\pi\)
\(468\) 5.42078 + 7.28594i 0.250576 + 0.336793i
\(469\) 22.9619 22.9619i 1.06028 1.06028i
\(470\) −21.5400 1.57245i −0.993565 0.0725316i
\(471\) 1.90434i 0.0877474i
\(472\) 3.25244 14.6396i 0.149706 0.673843i
\(473\) 17.8497i 0.820729i
\(474\) −0.763878 + 10.4639i −0.0350861 + 0.480622i
\(475\) −34.5223 + 34.5223i −1.58399 + 1.58399i
\(476\) 7.62875 + 1.11979i 0.349663 + 0.0513253i
\(477\) 17.5697 + 17.5697i 0.804460 + 0.804460i
\(478\) 3.37270 + 3.90390i 0.154264 + 0.178560i
\(479\) 27.0802 1.23732 0.618662 0.785657i \(-0.287675\pi\)
0.618662 + 0.785657i \(0.287675\pi\)
\(480\) 10.1374 + 22.6373i 0.462705 + 1.03324i
\(481\) 16.7305 0.762847
\(482\) 20.0848 + 23.2482i 0.914840 + 1.05893i
\(483\) 1.80487 + 1.80487i 0.0821246 + 0.0821246i
\(484\) 18.8837 + 2.77185i 0.858351 + 0.125993i
\(485\) −35.9807 + 35.9807i −1.63380 + 1.63380i
\(486\) −1.57938 + 21.6349i −0.0716420 + 0.981379i
\(487\) 9.09947i 0.412336i 0.978517 + 0.206168i \(0.0660994\pi\)
−0.978517 + 0.206168i \(0.933901\pi\)
\(488\) 2.40061 + 0.533335i 0.108670 + 0.0241430i
\(489\) 4.71246i 0.213105i
\(490\) −9.08120 0.662940i −0.410247 0.0299486i
\(491\) 15.5622 15.5622i 0.702312 0.702312i −0.262595 0.964906i \(-0.584578\pi\)
0.964906 + 0.262595i \(0.0845782\pi\)
\(492\) −9.42379 12.6663i −0.424857 0.571040i
\(493\) 3.03474 + 3.03474i 0.136678 + 0.136678i
\(494\) −12.1697 + 10.5138i −0.547540 + 0.473037i
\(495\) 32.3421 1.45367
\(496\) −1.13594 0.340820i −0.0510050 0.0153033i
\(497\) −6.57267 −0.294824
\(498\) 8.13539 7.02841i 0.364555 0.314951i
\(499\) −16.7323 16.7323i −0.749042 0.749042i 0.225257 0.974299i \(-0.427678\pi\)
−0.974299 + 0.225257i \(0.927678\pi\)
\(500\) 37.6736 28.0294i 1.68481 1.25351i
\(501\) 6.13525 6.13525i 0.274103 0.274103i
\(502\) −39.1684 2.85935i −1.74817 0.127619i
\(503\) 20.5829i 0.917747i −0.888502 0.458873i \(-0.848253\pi\)
0.888502 0.458873i \(-0.151747\pi\)
\(504\) −9.91195 + 6.30834i −0.441513 + 0.280996i
\(505\) 4.98927i 0.222020i
\(506\) −0.466685 + 6.39283i −0.0207467 + 0.284196i
\(507\) 5.10692 5.10692i 0.226806 0.226806i
\(508\) 2.65663 18.0988i 0.117869 0.803003i
\(509\) −10.7325 10.7325i −0.475711 0.475711i 0.428046 0.903757i \(-0.359202\pi\)
−0.903757 + 0.428046i \(0.859202\pi\)
\(510\) −6.73487 7.79561i −0.298225 0.345195i
\(511\) −24.9856 −1.10530
\(512\) −2.92317 22.4378i −0.129187 0.991620i
\(513\) −23.6217 −1.04292
\(514\) −2.46219 2.84998i −0.108602 0.125707i
\(515\) 52.8573 + 52.8573i 2.32917 + 2.32917i
\(516\) 1.25822 8.57187i 0.0553901 0.377355i
\(517\) −12.2784 + 12.2784i −0.540002 + 0.540002i
\(518\) −1.57596 + 21.5881i −0.0692437 + 0.948526i
\(519\) 19.4555i 0.854003i
\(520\) 24.1269 15.3553i 1.05803 0.673373i
\(521\) 7.16480i 0.313895i −0.987607 0.156948i \(-0.949835\pi\)
0.987607 0.156948i \(-0.0501654\pi\)
\(522\) −6.52238 0.476142i −0.285477 0.0208402i
\(523\) 15.0278 15.0278i 0.657118 0.657118i −0.297579 0.954697i \(-0.596179\pi\)
0.954697 + 0.297579i \(0.0961792\pi\)
\(524\) −22.4191 + 16.6800i −0.979385 + 0.728668i
\(525\) −19.6549 19.6549i −0.857811 0.857811i
\(526\) −5.27785 + 4.55970i −0.230125 + 0.198812i
\(527\) 0.492581 0.0214572
\(528\) 19.1008 + 5.73090i 0.831255 + 0.249405i
\(529\) −1.00000 −0.0434783
\(530\) 59.2121 51.1551i 2.57201 2.22204i
\(531\) −6.71130 6.71130i −0.291245 0.291245i
\(532\) −12.4200 16.6934i −0.538475 0.723750i
\(533\) −12.8716 + 12.8716i −0.557530 + 0.557530i
\(534\) 9.79586 + 0.715111i 0.423908 + 0.0309459i
\(535\) 47.6705i 2.06098i
\(536\) 38.6385 + 8.58420i 1.66893 + 0.370781i
\(537\) 15.5729i 0.672020i
\(538\) 2.03868 27.9265i 0.0878936 1.20400i
\(539\) −5.17654 + 5.17654i −0.222969 + 0.222969i
\(540\) 41.5606 + 6.10047i 1.78848 + 0.262523i
\(541\) −18.7869 18.7869i −0.807711 0.807711i 0.176576 0.984287i \(-0.443498\pi\)
−0.984287 + 0.176576i \(0.943498\pi\)
\(542\) 0.405217 + 0.469038i 0.0174055 + 0.0201469i
\(543\) 13.3706 0.573788
\(544\) 3.84109 + 8.57736i 0.164685 + 0.367751i
\(545\) 79.8775 3.42158
\(546\) −5.98590 6.92868i −0.256173 0.296520i
\(547\) 27.6019 + 27.6019i 1.18017 + 1.18017i 0.979699 + 0.200473i \(0.0642480\pi\)
0.200473 + 0.979699i \(0.435752\pi\)
\(548\) 20.5153 + 3.01134i 0.876372 + 0.128638i
\(549\) 1.10052 1.10052i 0.0469690 0.0469690i
\(550\) 5.08216 69.6173i 0.216704 2.96849i
\(551\) 11.5814i 0.493384i
\(552\) −0.674744 + 3.03710i −0.0287190 + 0.129268i
\(553\) 15.6510i 0.665547i
\(554\) 24.4249 + 1.78305i 1.03772 + 0.0757546i
\(555\) 20.4498 20.4498i 0.868048 0.868048i
\(556\) 15.4171 + 20.7218i 0.653833 + 0.878800i
\(557\) −7.86100 7.86100i −0.333081 0.333081i 0.520674 0.853755i \(-0.325681\pi\)
−0.853755 + 0.520674i \(0.825681\pi\)
\(558\) −0.567979 + 0.490694i −0.0240445 + 0.0207727i
\(559\) −9.98942 −0.422507
\(560\) 17.5408 + 32.5783i 0.741236 + 1.37669i
\(561\) −8.28277 −0.349699
\(562\) 21.7466 18.7875i 0.917323 0.792503i
\(563\) 0.388934 + 0.388934i 0.0163916 + 0.0163916i 0.715255 0.698863i \(-0.246311\pi\)
−0.698863 + 0.715255i \(0.746311\pi\)
\(564\) −6.76189 + 5.03089i −0.284727 + 0.211839i
\(565\) −42.7892 + 42.7892i −1.80015 + 1.80015i
\(566\) −10.1586 0.741591i −0.426997 0.0311714i
\(567\) 0.986929i 0.0414471i
\(568\) −4.30141 6.75857i −0.180483 0.283583i
\(569\) 25.6806i 1.07659i −0.842758 0.538293i \(-0.819069\pi\)
0.842758 0.538293i \(-0.180931\pi\)
\(570\) −2.02404 + 27.7261i −0.0847779 + 1.16132i
\(571\) −18.7104 + 18.7104i −0.783006 + 0.783006i −0.980337 0.197331i \(-0.936773\pi\)
0.197331 + 0.980337i \(0.436773\pi\)
\(572\) 3.33931 22.7497i 0.139624 0.951213i
\(573\) −3.64767 3.64767i −0.152384 0.152384i
\(574\) −15.3962 17.8212i −0.642627 0.743841i
\(575\) 10.8899 0.454141
\(576\) −12.9735 6.06388i −0.540564 0.252662i
\(577\) 3.03487 0.126343 0.0631716 0.998003i \(-0.479878\pi\)
0.0631716 + 0.998003i \(0.479878\pi\)
\(578\) 13.1653 + 15.2388i 0.547604 + 0.633851i
\(579\) −6.14194 6.14194i −0.255251 0.255251i
\(580\) −2.99098 + 20.3766i −0.124194 + 0.846092i
\(581\) 11.3403 11.3403i 0.470477 0.470477i
\(582\) −1.44575 + 19.8044i −0.0599281 + 0.820918i
\(583\) 62.9123i 2.60556i
\(584\) −16.3516 25.6923i −0.676632 1.06316i
\(585\) 18.1000i 0.748342i
\(586\) 47.4320 + 3.46260i 1.95940 + 0.143039i
\(587\) −27.2234 + 27.2234i −1.12363 + 1.12363i −0.132438 + 0.991191i \(0.542281\pi\)
−0.991191 + 0.132438i \(0.957719\pi\)
\(588\) −2.85080 + 2.12101i −0.117565 + 0.0874690i
\(589\) −0.939912 0.939912i −0.0387284 0.0387284i
\(590\) −22.6180 + 19.5403i −0.931166 + 0.804463i
\(591\) 12.0322 0.494940
\(592\) −23.2301 + 12.5075i −0.954750 + 0.514057i
\(593\) −32.1885 −1.32182 −0.660912 0.750464i \(-0.729830\pi\)
−0.660912 + 0.750464i \(0.729830\pi\)
\(594\) 25.5563 22.0789i 1.04859 0.905908i
\(595\) −10.8667 10.8667i −0.445492 0.445492i
\(596\) −22.4067 30.1163i −0.917815 1.23361i
\(597\) 10.2143 10.2143i 0.418042 0.418042i
\(598\) 3.57769 + 0.261177i 0.146303 + 0.0106803i
\(599\) 12.9914i 0.530813i −0.964137 0.265407i \(-0.914494\pi\)
0.964137 0.265407i \(-0.0855062\pi\)
\(600\) 7.34790 33.0738i 0.299977 1.35023i
\(601\) 2.11593i 0.0863107i 0.999068 + 0.0431553i \(0.0137410\pi\)
−0.999068 + 0.0431553i \(0.986259\pi\)
\(602\) 0.940969 12.8897i 0.0383510 0.525347i
\(603\) 17.7132 17.7132i 0.721338 0.721338i
\(604\) −21.0865 3.09518i −0.857998 0.125941i
\(605\) −26.8987 26.8987i −1.09359 1.09359i
\(606\) −1.27285 1.47333i −0.0517061 0.0598498i
\(607\) −35.6668 −1.44767 −0.723835 0.689973i \(-0.757622\pi\)
−0.723835 + 0.689973i \(0.757622\pi\)
\(608\) 9.03743 23.6961i 0.366516 0.961003i
\(609\) 6.59374 0.267192
\(610\) −3.20423 3.70889i −0.129735 0.150169i
\(611\) 6.87149 + 6.87149i 0.277991 + 0.277991i
\(612\) 5.88495 + 0.863823i 0.237885 + 0.0349180i
\(613\) −19.2450 + 19.2450i −0.777296 + 0.777296i −0.979370 0.202074i \(-0.935232\pi\)
0.202074 + 0.979370i \(0.435232\pi\)
\(614\) −2.57850 + 35.3213i −0.104060 + 1.42545i
\(615\) 31.4660i 1.26883i
\(616\) 29.0403 + 6.45179i 1.17007 + 0.259950i
\(617\) 10.6772i 0.429849i −0.976631 0.214924i \(-0.931049\pi\)
0.976631 0.214924i \(-0.0689505\pi\)
\(618\) 29.0935 + 2.12387i 1.17031 + 0.0854345i
\(619\) −18.8984 + 18.8984i −0.759590 + 0.759590i −0.976248 0.216658i \(-0.930484\pi\)
0.216658 + 0.976248i \(0.430484\pi\)
\(620\) 1.41097 + 1.89644i 0.0566657 + 0.0761630i
\(621\) 3.72568 + 3.72568i 0.149506 + 0.149506i
\(622\) −10.6550 + 9.20518i −0.427226 + 0.369094i
\(623\) 14.6518 0.587012
\(624\) 3.20725 10.6896i 0.128393 0.427926i
\(625\) −39.1405 −1.56562
\(626\) −36.5156 + 31.5469i −1.45946 + 1.26087i
\(627\) 15.8046 + 15.8046i 0.631177 + 0.631177i
\(628\) 2.77803 2.06687i 0.110855 0.0824770i
\(629\) 7.74854 7.74854i 0.308954 0.308954i
\(630\) 23.3551 + 1.70496i 0.930490 + 0.0679270i
\(631\) 9.44357i 0.375942i 0.982175 + 0.187971i \(0.0601912\pi\)
−0.982175 + 0.187971i \(0.939809\pi\)
\(632\) −16.0937 + 10.2426i −0.640171 + 0.407429i
\(633\) 21.8578i 0.868770i
\(634\) 1.00393 13.7522i 0.0398712 0.546171i
\(635\) −25.7806 + 25.7806i −1.02307 + 1.02307i
\(636\) 4.43469 30.2121i 0.175847 1.19799i
\(637\) 2.89701 + 2.89701i 0.114784 + 0.114784i
\(638\) 10.8250 + 12.5299i 0.428565 + 0.496064i
\(639\) −5.07027 −0.200577
\(640\) −22.0204 + 39.3575i −0.870431 + 1.55574i
\(641\) 11.7909 0.465712 0.232856 0.972511i \(-0.425193\pi\)
0.232856 + 0.972511i \(0.425193\pi\)
\(642\) 12.1616 + 14.0770i 0.479980 + 0.555577i
\(643\) 6.74700 + 6.74700i 0.266076 + 0.266076i 0.827517 0.561441i \(-0.189753\pi\)
−0.561441 + 0.827517i \(0.689753\pi\)
\(644\) −0.674013 + 4.59184i −0.0265598 + 0.180944i
\(645\) −12.2101 + 12.2101i −0.480773 + 0.480773i
\(646\) −0.766919 + 10.5055i −0.0301740 + 0.413335i
\(647\) 17.1200i 0.673057i −0.941673 0.336528i \(-0.890747\pi\)
0.941673 0.336528i \(-0.109253\pi\)
\(648\) 1.01484 0.645885i 0.0398668 0.0253727i
\(649\) 24.0314i 0.943314i
\(650\) −38.9608 2.84419i −1.52817 0.111558i
\(651\) 0.535128 0.535128i 0.0209733 0.0209733i
\(652\) 6.87447 5.11465i 0.269225 0.200305i
\(653\) −3.21167 3.21167i −0.125682 0.125682i 0.641468 0.767150i \(-0.278326\pi\)
−0.767150 + 0.641468i \(0.778326\pi\)
\(654\) 23.5878 20.3782i 0.922354 0.796850i
\(655\) 55.6944 2.17616
\(656\) 8.24932 27.4946i 0.322082 1.07348i
\(657\) −19.2743 −0.751963
\(658\) −9.51382 + 8.21928i −0.370887 + 0.320421i
\(659\) −19.7196 19.7196i −0.768166 0.768166i 0.209617 0.977783i \(-0.432778\pi\)
−0.977783 + 0.209617i \(0.932778\pi\)
\(660\) −23.7254 31.8887i −0.923511 1.24127i
\(661\) 9.76300 9.76300i 0.379737 0.379737i −0.491271 0.871007i \(-0.663467\pi\)
0.871007 + 0.491271i \(0.163467\pi\)
\(662\) −43.0706 3.14422i −1.67399 0.122203i
\(663\) 4.63538i 0.180023i
\(664\) 19.0827 + 4.23954i 0.740551 + 0.164526i
\(665\) 41.4703i 1.60815i
\(666\) −1.21572 + 16.6534i −0.0471083 + 0.645307i
\(667\) −1.82665 + 1.82665i −0.0707281 + 0.0707281i
\(668\) 15.6089 + 2.29115i 0.603926 + 0.0886473i
\(669\) 22.7895 + 22.7895i 0.881092 + 0.881092i
\(670\) −51.5731 59.6958i −1.99244 2.30625i
\(671\) −3.94067 −0.152128
\(672\) 13.4911 + 5.14536i 0.520430 + 0.198487i
\(673\) 11.8278 0.455929 0.227964 0.973669i \(-0.426793\pi\)
0.227964 + 0.973669i \(0.426793\pi\)
\(674\) 15.5336 + 17.9802i 0.598333 + 0.692571i
\(675\) −40.5723 40.5723i −1.56163 1.56163i
\(676\) 12.9927 + 1.90713i 0.499718 + 0.0733511i
\(677\) 1.09692 1.09692i 0.0421579 0.0421579i −0.685714 0.727871i \(-0.740510\pi\)
0.727871 + 0.685714i \(0.240510\pi\)
\(678\) −1.71932 + 23.5519i −0.0660301 + 0.904505i
\(679\) 29.6217i 1.13678i
\(680\) 4.06247 18.2857i 0.155789 0.701223i
\(681\) 5.10938i 0.195792i
\(682\) 1.89541 + 0.138368i 0.0725792 + 0.00529838i
\(683\) −15.5037 + 15.5037i −0.593233 + 0.593233i −0.938503 0.345270i \(-0.887787\pi\)
0.345270 + 0.938503i \(0.387787\pi\)
\(684\) −9.58099 12.8776i −0.366338 0.492386i
\(685\) −29.2229 29.2229i −1.11655 1.11655i
\(686\) −21.3942 + 18.4831i −0.816834 + 0.705688i
\(687\) 13.7078 0.522984
\(688\) 13.8701 7.46796i 0.528794 0.284713i
\(689\) −35.2084 −1.34133
\(690\) 4.69227 4.05380i 0.178632 0.154325i
\(691\) 3.79449 + 3.79449i 0.144349 + 0.144349i 0.775588 0.631239i \(-0.217453\pi\)
−0.631239 + 0.775588i \(0.717453\pi\)
\(692\) −28.3815 + 21.1160i −1.07890 + 0.802709i
\(693\) 13.3131 13.3131i 0.505721 0.505721i
\(694\) 15.6341 + 1.14131i 0.593464 + 0.0433237i
\(695\) 51.4778i 1.95266i
\(696\) 4.31520 + 6.78024i 0.163567 + 0.257004i
\(697\) 11.9226i 0.451601i
\(698\) 0.346125 4.74135i 0.0131010 0.179463i
\(699\) −16.5853 + 16.5853i −0.627314 + 0.627314i
\(700\) 7.33994 50.0047i 0.277424 1.89000i
\(701\) −28.1860 28.1860i −1.06457 1.06457i −0.997766 0.0668041i \(-0.978720\pi\)
−0.0668041 0.997766i \(-0.521280\pi\)
\(702\) −12.3563 14.3024i −0.466357 0.539809i
\(703\) −29.5705 −1.11527
\(704\) 12.3708 + 34.0840i 0.466242 + 1.28459i
\(705\) 16.7981 0.632654
\(706\) 3.26035 + 3.77386i 0.122705 + 0.142031i
\(707\) −2.05375 2.05375i −0.0772391 0.0772391i
\(708\) −1.69397 + 11.5405i −0.0636633 + 0.433718i
\(709\) −15.7363 + 15.7363i −0.590991 + 0.590991i −0.937899 0.346908i \(-0.887231\pi\)
0.346908 + 0.937899i \(0.387231\pi\)
\(710\) −1.16254 + 15.9249i −0.0436294 + 0.597652i
\(711\) 12.0734i 0.452789i
\(712\) 9.58870 + 15.0662i 0.359352 + 0.564630i
\(713\) 0.296491i 0.0111037i
\(714\) −5.98122 0.436637i −0.223841 0.0163407i
\(715\) −32.4056 + 32.4056i −1.21190 + 1.21190i
\(716\) 22.7175 16.9020i 0.848993 0.631656i
\(717\) −2.83736 2.83736i −0.105963 0.105963i
\(718\) 6.62044 5.71960i 0.247073 0.213453i
\(719\) −10.9219 −0.407318 −0.203659 0.979042i \(-0.565283\pi\)
−0.203659 + 0.979042i \(0.565283\pi\)
\(720\) 13.5313 + 25.1315i 0.504282 + 0.936595i
\(721\) 43.5156 1.62060
\(722\) 1.17647 1.01639i 0.0437838 0.0378261i
\(723\) −16.8968 16.8968i −0.628400 0.628400i
\(724\) 14.5117 + 19.5049i 0.539325 + 0.724893i
\(725\) 19.8920 19.8920i 0.738772 0.738772i
\(726\) −14.8055 1.08082i −0.549484 0.0401131i
\(727\) 15.7550i 0.584320i 0.956370 + 0.292160i \(0.0943739\pi\)
−0.956370 + 0.292160i \(0.905626\pi\)
\(728\) 3.61069 16.2522i 0.133821 0.602345i
\(729\) 18.1481i 0.672150i
\(730\) −4.41934 + 60.5377i −0.163567 + 2.24060i
\(731\) −4.62647 + 4.62647i −0.171116 + 0.171116i
\(732\) −1.89241 0.277777i −0.0699455 0.0102669i
\(733\) 8.54725 + 8.54725i 0.315700 + 0.315700i 0.847113 0.531413i \(-0.178339\pi\)
−0.531413 + 0.847113i \(0.678339\pi\)
\(734\) 8.25022 + 9.54963i 0.304521 + 0.352483i
\(735\) 7.08205 0.261225
\(736\) −5.16281 + 2.31200i −0.190304 + 0.0852214i
\(737\) −63.4263 −2.33634
\(738\) −11.8769 13.7476i −0.437196 0.506055i
\(739\) −2.27367 2.27367i −0.0836383 0.0836383i 0.664050 0.747688i \(-0.268836\pi\)
−0.747688 + 0.664050i \(0.768836\pi\)
\(740\) 52.0271 + 7.63680i 1.91255 + 0.280734i
\(741\) 8.84494 8.84494i 0.324927 0.324927i
\(742\) 3.31651 45.4308i 0.121753 1.66782i
\(743\) 16.2979i 0.597911i 0.954267 + 0.298955i \(0.0966381\pi\)
−0.954267 + 0.298955i \(0.903362\pi\)
\(744\) 0.900473 + 0.200055i 0.0330129 + 0.00733439i
\(745\) 74.8160i 2.74104i
\(746\) −46.4482 3.39078i −1.70059 0.124145i
\(747\) 8.74814 8.74814i 0.320078 0.320078i
\(748\) −8.98967 12.0828i −0.328695 0.441791i
\(749\) 19.6227 + 19.6227i 0.716999 + 0.716999i
\(750\) −27.6370 + 23.8765i −1.00916 + 0.871846i
\(751\) 33.5084 1.22274 0.611369 0.791345i \(-0.290619\pi\)
0.611369 + 0.791345i \(0.290619\pi\)
\(752\) −14.6780 4.40390i −0.535251 0.160594i
\(753\) 30.5458 1.11315
\(754\) 7.01227 6.05811i 0.255372 0.220623i
\(755\) 30.0365 + 30.0365i 1.09314 + 1.09314i
\(756\) 19.6189 14.5965i 0.713531 0.530871i
\(757\) 26.9343 26.9343i 0.978942 0.978942i −0.0208406 0.999783i \(-0.506634\pi\)
0.999783 + 0.0208406i \(0.00663424\pi\)
\(758\) 17.1477 + 1.25180i 0.622831 + 0.0454675i
\(759\) 4.98550i 0.180962i
\(760\) −42.6433 + 27.1398i −1.54683 + 0.984463i
\(761\) 3.45256i 0.125155i 0.998040 + 0.0625776i \(0.0199321\pi\)
−0.998040 + 0.0625776i \(0.980068\pi\)
\(762\) −1.03590 + 14.1901i −0.0375266 + 0.514053i
\(763\) 32.8802 32.8802i 1.19034 1.19034i
\(764\) 1.36219 9.28016i 0.0492822 0.335744i
\(765\) −8.38277 8.38277i −0.303080 0.303080i
\(766\) 1.30230 + 1.50742i 0.0470542 + 0.0544652i
\(767\) 13.4490 0.485614
\(768\) 3.53820 + 17.2400i 0.127674 + 0.622095i
\(769\) 6.44819 0.232528 0.116264 0.993218i \(-0.462908\pi\)
0.116264 + 0.993218i \(0.462908\pi\)
\(770\) −38.7617 44.8667i −1.39688 1.61689i
\(771\) 2.07137 + 2.07137i 0.0745986 + 0.0745986i
\(772\) 2.29365 15.6259i 0.0825503 0.562389i
\(773\) 5.71870 5.71870i 0.205687 0.205687i −0.596744 0.802432i \(-0.703539\pi\)
0.802432 + 0.596744i \(0.203539\pi\)
\(774\) 0.725880 9.94337i 0.0260912 0.357407i
\(775\) 3.22876i 0.115980i
\(776\) −30.4595 + 19.3856i −1.09343 + 0.695901i
\(777\) 16.8356i 0.603975i
\(778\) 0.921426 + 0.0672654i 0.0330347 + 0.00241158i
\(779\) 22.7499 22.7499i 0.815101 0.815101i
\(780\) −17.8463 + 13.2777i −0.638999 + 0.475419i
\(781\) 9.07765 + 9.07765i 0.324824 + 0.324824i
\(782\) 1.77792 1.53600i 0.0635784 0.0549273i
\(783\) 13.6110 0.486418
\(784\) −6.18820 1.85667i −0.221007 0.0663098i
\(785\) −6.90127 −0.246317
\(786\) 16.4465 14.2086i 0.586627 0.506805i
\(787\) −30.3767 30.3767i −1.08281 1.08281i −0.996246 0.0865664i \(-0.972411\pi\)
−0.0865664 0.996246i \(-0.527589\pi\)
\(788\) 13.0591 + 17.5524i 0.465212 + 0.625280i
\(789\) 3.83595 3.83595i 0.136563 0.136563i
\(790\) 37.9208 + 2.76827i 1.34916 + 0.0984906i
\(791\) 35.2268i 1.25252i
\(792\) 22.4022 + 4.97703i 0.796027 + 0.176851i
\(793\) 2.20536i 0.0783147i
\(794\) 2.07295 28.3960i 0.0735661 1.00774i
\(795\) −43.0354 + 43.0354i −1.52631 + 1.52631i
\(796\) 25.9864 + 3.81442i 0.921064 + 0.135198i
\(797\) 17.8450 + 17.8450i 0.632102 + 0.632102i 0.948595 0.316493i \(-0.102505\pi\)
−0.316493 + 0.948595i \(0.602505\pi\)
\(798\) 10.5798 + 12.2461i 0.374521 + 0.433508i
\(799\) 6.36488 0.225173
\(800\) 56.2226 25.1775i 1.98777 0.890158i
\(801\) 11.3027 0.399360
\(802\) −17.1643 19.8677i −0.606094 0.701554i
\(803\) 34.5082 + 34.5082i 1.21777 + 1.21777i
\(804\) −30.4589 4.47092i −1.07420 0.157677i
\(805\) 6.54080 6.54080i 0.230533 0.230533i
\(806\) 0.0774364 1.06075i 0.00272758 0.0373634i
\(807\) 21.7787i 0.766648i
\(808\) 0.767784 3.45589i 0.0270105 0.121578i
\(809\) 33.9324i 1.19300i −0.802613 0.596500i \(-0.796558\pi\)
0.802613 0.596500i \(-0.203442\pi\)
\(810\) −2.39123 0.174563i −0.0840194 0.00613353i
\(811\) −20.4080 + 20.4080i −0.716622 + 0.716622i −0.967912 0.251290i \(-0.919145\pi\)
0.251290 + 0.967912i \(0.419145\pi\)
\(812\) 7.15649 + 9.61886i 0.251144 + 0.337556i
\(813\) −0.340897 0.340897i −0.0119558 0.0119558i
\(814\) 31.9924 27.6392i 1.12133 0.968753i
\(815\) −17.0778 −0.598209
\(816\) −3.46535 6.43615i −0.121312 0.225310i
\(817\) 17.6559 0.617700
\(818\) −9.34364 + 8.07226i −0.326693 + 0.282240i
\(819\) −7.45054 7.45054i −0.260343 0.260343i
\(820\) −45.9022 + 34.1515i −1.60297 + 1.19262i
\(821\) 2.39536 2.39536i 0.0835987 0.0835987i −0.664071 0.747670i \(-0.731173\pi\)
0.747670 + 0.664071i \(0.231173\pi\)
\(822\) −16.0848 1.17421i −0.561021 0.0409553i
\(823\) 14.7963i 0.515768i −0.966176 0.257884i \(-0.916975\pi\)
0.966176 0.257884i \(-0.0830252\pi\)
\(824\) 28.4783 + 44.7464i 0.992088 + 1.55881i
\(825\) 54.2916i 1.89019i
\(826\) −1.26685 + 17.3537i −0.0440792 + 0.603813i
\(827\) 11.9039 11.9039i 0.413939 0.413939i −0.469169 0.883108i \(-0.655447\pi\)
0.883108 + 0.469169i \(0.155447\pi\)
\(828\) −0.519945 + 3.54222i −0.0180694 + 0.123101i
\(829\) −12.3214 12.3214i −0.427940 0.427940i 0.459986 0.887926i \(-0.347854\pi\)
−0.887926 + 0.459986i \(0.847854\pi\)
\(830\) −25.4707 29.4824i −0.884102 1.02335i
\(831\) −19.0480 −0.660767
\(832\) 19.0748 6.92322i 0.661300 0.240020i
\(833\) 2.68342 0.0929750
\(834\) −13.1329 15.2013i −0.454755 0.526379i
\(835\) −22.2339 22.2339i −0.769437 0.769437i
\(836\) −5.90209 + 40.2091i −0.204128 + 1.39066i
\(837\) 1.10463 1.10463i 0.0381816 0.0381816i
\(838\) −0.914077 + 12.5214i −0.0315763 + 0.432544i
\(839\) 0.397877i 0.0137362i 0.999976 + 0.00686812i \(0.00218621\pi\)
−0.999976 + 0.00686812i \(0.997814\pi\)
\(840\) −15.4517 24.2785i −0.533135 0.837687i
\(841\) 22.3267i 0.769887i
\(842\) −44.6288 3.25797i −1.53801 0.112277i
\(843\) −15.8054 + 15.8054i −0.544367 + 0.544367i
\(844\) 31.8859 23.7233i 1.09756 0.816589i
\(845\) −18.5073 18.5073i −0.636670 0.636670i
\(846\) −7.33913 + 6.34050i −0.252324 + 0.217991i
\(847\) −22.1448 −0.760904
\(848\) 48.8862 26.3213i 1.67876 0.903878i
\(849\) 7.92226 0.271891
\(850\) −19.3614 + 16.7269i −0.664091 + 0.573729i
\(851\) 4.66394 + 4.66394i 0.159878 + 0.159878i
\(852\) 3.71944 + 4.99920i 0.127426 + 0.171270i
\(853\) 15.2062 15.2062i 0.520649 0.520649i −0.397118 0.917767i \(-0.629990\pi\)
0.917767 + 0.397118i \(0.129990\pi\)
\(854\) −2.84567 0.207738i −0.0973767 0.00710863i
\(855\) 31.9909i 1.09407i
\(856\) −7.33587 + 33.0196i −0.250735 + 1.12859i
\(857\) 53.7293i 1.83536i 0.397324 + 0.917679i \(0.369939\pi\)
−0.397324 + 0.917679i \(0.630061\pi\)
\(858\) −1.30210 + 17.8366i −0.0444528 + 0.608931i
\(859\) −36.3370 + 36.3370i −1.23980 + 1.23980i −0.279721 + 0.960081i \(0.590242\pi\)
−0.960081 + 0.279721i \(0.909758\pi\)
\(860\) −31.0642 4.55975i −1.05928 0.155486i
\(861\) 12.9524 + 12.9524i 0.441418 + 0.441418i
\(862\) 13.0102 + 15.0593i 0.443128 + 0.512921i
\(863\) 29.8492 1.01608 0.508040 0.861334i \(-0.330370\pi\)
0.508040 + 0.861334i \(0.330370\pi\)
\(864\) 27.8487 + 10.6212i 0.947433 + 0.361341i
\(865\) 70.5062 2.39728
\(866\) 16.6700 + 19.2955i 0.566469 + 0.655689i
\(867\) −11.0756 11.0756i −0.376147 0.376147i
\(868\) 1.36144 + 0.199839i 0.0462102 + 0.00678296i
\(869\) 21.6159 21.6159i 0.733269 0.733269i
\(870\) 1.16627 15.9760i 0.0395402 0.541637i
\(871\) 35.4960i 1.20274i
\(872\) 55.3283 + 12.2921i 1.87365 + 0.416264i
\(873\) 22.8507i 0.773378i
\(874\) −6.32342 0.461618i −0.213893 0.0156145i
\(875\) −38.5247 + 38.5247i −1.30237 + 1.30237i
\(876\) 14.1392 + 19.0042i 0.477720 + 0.642092i
\(877\) −10.5028 10.5028i −0.354656 0.354656i 0.507183 0.861839i \(-0.330687\pi\)
−0.861839 + 0.507183i \(0.830687\pi\)
\(878\) −4.65938 + 4.02538i −0.157247 + 0.135850i
\(879\) −36.9902 −1.24765
\(880\) 20.7686 69.2206i 0.700109 2.33343i
\(881\) −43.7619 −1.47438 −0.737188 0.675687i \(-0.763847\pi\)
−0.737188 + 0.675687i \(0.763847\pi\)
\(882\) −3.09416 + 2.67314i −0.104186 + 0.0900093i
\(883\) 39.4328 + 39.4328i 1.32702 + 1.32702i 0.907957 + 0.419064i \(0.137642\pi\)
0.419064 + 0.907957i \(0.362358\pi\)
\(884\) −6.76203 + 5.03099i −0.227432 + 0.169211i
\(885\) 16.4387 16.4387i 0.552582 0.552582i
\(886\) 23.4461 + 1.71159i 0.787686 + 0.0575021i
\(887\) 44.0403i 1.47873i −0.673306 0.739364i \(-0.735126\pi\)
0.673306 0.739364i \(-0.264874\pi\)
\(888\) 17.3118 11.0179i 0.580947 0.369737i
\(889\) 21.2243i 0.711840i
\(890\) 2.59154 35.4999i 0.0868686 1.18996i
\(891\) −1.36307 + 1.36307i −0.0456645 + 0.0456645i
\(892\) −8.51051 + 57.9794i −0.284953 + 1.94129i
\(893\) −12.1451 12.1451i −0.406419 0.406419i
\(894\) 19.0869 + 22.0931i 0.638361 + 0.738903i
\(895\) −56.4356 −1.88644
\(896\) 7.13652 + 25.2651i 0.238415 + 0.844049i
\(897\) −2.79009 −0.0931585
\(898\) −10.2620 11.8783i −0.342449 0.396385i
\(899\) 0.541584 + 0.541584i 0.0180629 + 0.0180629i
\(900\) 5.66216 38.5745i 0.188739 1.28582i
\(901\) −16.3063 + 16.3063i −0.543242 + 0.543242i
\(902\) −3.34910 + 45.8773i −0.111513 + 1.52755i
\(903\) 10.0522i 0.334515i
\(904\) −36.2232 + 23.0538i −1.20477 + 0.766758i
\(905\) 48.4547i 1.61069i
\(906\) 16.5326 + 1.20690i 0.549259 + 0.0400966i
\(907\) 4.11192 4.11192i 0.136534 0.136534i −0.635537 0.772071i \(-0.719221\pi\)
0.772071 + 0.635537i \(0.219221\pi\)
\(908\) −7.45349 + 5.54544i −0.247353 + 0.184032i
\(909\) −1.58430 1.58430i −0.0525478 0.0525478i
\(910\) −25.1093 + 21.6927i −0.832365 + 0.719106i
\(911\) −39.5813 −1.31139 −0.655694 0.755027i \(-0.727624\pi\)
−0.655694 + 0.755027i \(0.727624\pi\)
\(912\) −5.66867 + 18.8934i −0.187708 + 0.625623i
\(913\) −31.3248 −1.03670
\(914\) 25.6000 22.1166i 0.846773 0.731553i
\(915\) 2.69563 + 2.69563i 0.0891147 + 0.0891147i
\(916\) 14.8777 + 19.9967i 0.491572 + 0.660709i
\(917\) 22.9256 22.9256i 0.757071 0.757071i
\(918\) −12.3466 0.901320i −0.407499 0.0297480i
\(919\) 20.5604i 0.678226i −0.940746 0.339113i \(-0.889873\pi\)
0.940746 0.339113i \(-0.110127\pi\)
\(920\) 11.0064 + 2.44525i 0.362869 + 0.0806175i
\(921\) 27.5456i 0.907657i
\(922\) 2.86900 39.3006i 0.0944854 1.29430i
\(923\) 5.08023 5.08023i 0.167218 0.167218i
\(924\) −22.8926 3.36029i −0.753111 0.110545i
\(925\) −50.7899 50.7899i −1.66996 1.66996i
\(926\) 21.0764 + 24.3959i 0.692612 + 0.801699i
\(927\) 33.5687 1.10254
\(928\) −5.20744 + 13.6539i −0.170943 + 0.448210i
\(929\) 8.07522 0.264939 0.132470 0.991187i \(-0.457709\pi\)
0.132470 + 0.991187i \(0.457709\pi\)
\(930\) −1.20191 1.39122i −0.0394123 0.0456198i
\(931\) −5.12033 5.12033i −0.167812 0.167812i
\(932\) −42.1952 6.19363i −1.38215 0.202879i
\(933\) 7.74406 7.74406i 0.253529 0.253529i
\(934\) −2.54524 + 34.8656i −0.0832828 + 1.14084i
\(935\) 30.0165i 0.981644i
\(936\) 2.78535 12.5372i 0.0910421 0.409791i
\(937\) 26.3040i 0.859313i 0.902992 + 0.429657i \(0.141365\pi\)
−0.902992 + 0.429657i \(0.858635\pi\)
\(938\) −45.8019 3.34360i −1.49549 0.109172i
\(939\) 26.5395 26.5395i 0.866085 0.866085i
\(940\) 18.2318 + 24.5049i 0.594655 + 0.799260i
\(941\) 17.7772 + 17.7772i 0.579521 + 0.579521i 0.934771 0.355250i \(-0.115604\pi\)
−0.355250 + 0.934771i \(0.615604\pi\)
\(942\) −2.03794 + 1.76064i −0.0663996 + 0.0573646i
\(943\) −7.17636 −0.233695
\(944\) −18.6736 + 10.0543i −0.607775 + 0.327239i
\(945\) −48.7378 −1.58544
\(946\) −19.1019 + 16.5027i −0.621056 + 0.536549i
\(947\) 21.2907 + 21.2907i 0.691854 + 0.691854i 0.962640 0.270786i \(-0.0872834\pi\)
−0.270786 + 0.962640i \(0.587283\pi\)
\(948\) 11.9042 8.85680i 0.386631 0.287656i
\(949\) 19.3122 19.3122i 0.626901 0.626901i
\(950\) 68.8614 + 5.02698i 2.23416 + 0.163097i
\(951\) 10.7248i 0.347775i
\(952\) −5.85473 9.19922i −0.189753 0.298148i
\(953\) 10.8181i 0.350434i 0.984530 + 0.175217i \(0.0560627\pi\)
−0.984530 + 0.175217i \(0.943937\pi\)
\(954\) 2.55841 35.0461i 0.0828316 1.13466i
\(955\) −13.2190 + 13.2190i −0.427758 + 0.427758i
\(956\) 1.05958 7.21861i 0.0342694 0.233467i
\(957\) −9.10676 9.10676i −0.294380 0.294380i
\(958\) −25.0367 28.9800i −0.808898 0.936300i
\(959\) −24.0582 −0.776880
\(960\) 14.8530 31.7775i 0.479377 1.02562i
\(961\) −30.9121 −0.997164
\(962\) −15.4680 17.9043i −0.498709 0.577256i
\(963\) 15.1373 + 15.1373i 0.487793 + 0.487793i
\(964\) 6.30995 42.9877i 0.203230 1.38454i
\(965\) −22.2582 + 22.2582i −0.716517 + 0.716517i
\(966\) 0.262817 3.60017i 0.00845600 0.115834i
\(967\) 14.4928i 0.466057i 0.972470 + 0.233029i \(0.0748636\pi\)
−0.972470 + 0.233029i \(0.925136\pi\)
\(968\) −14.4924 22.7712i −0.465804 0.731893i
\(969\) 8.19284i 0.263192i
\(970\) 71.7704 + 5.23934i 2.30441 + 0.168225i
\(971\) 6.22476 6.22476i 0.199762 0.199762i −0.600136 0.799898i \(-0.704887\pi\)
0.799898 + 0.600136i \(0.204887\pi\)
\(972\) 24.6129 18.3121i 0.789458 0.587361i
\(973\) −21.1899 21.1899i −0.679318 0.679318i
\(974\) 9.73783 8.41281i 0.312020 0.269564i
\(975\) 30.3839 0.973062
\(976\) −1.64870 3.06211i −0.0527736 0.0980156i
\(977\) 19.4237 0.621421 0.310710 0.950505i \(-0.399433\pi\)
0.310710 + 0.950505i \(0.399433\pi\)
\(978\) −5.04305 + 4.35685i −0.161259 + 0.139317i
\(979\) −20.2359 20.2359i −0.646742 0.646742i
\(980\) 7.68647 + 10.3312i 0.245535 + 0.330018i
\(981\) 25.3644 25.3644i 0.809822 0.809822i
\(982\) −31.0418 2.26609i −0.990583 0.0723139i
\(983\) 9.44802i 0.301345i −0.988584 0.150672i \(-0.951856\pi\)
0.988584 0.150672i \(-0.0481439\pi\)
\(984\) −4.84221 + 21.7954i −0.154364 + 0.694811i
\(985\) 43.6044i 1.38935i
\(986\) 0.441905 6.05338i 0.0140731 0.192779i
\(987\) 6.91465 6.91465i 0.220096 0.220096i
\(988\) 22.5027 + 3.30306i 0.715906 + 0.105084i
\(989\) −2.78473 2.78473i −0.0885492 0.0885492i
\(990\) −29.9015 34.6110i −0.950332 1.10001i
\(991\) 31.3840 0.996947 0.498474 0.866905i \(-0.333894\pi\)
0.498474 + 0.866905i \(0.333894\pi\)
\(992\) 0.685487 + 1.53073i 0.0217642 + 0.0486006i
\(993\) 33.5890 1.06591
\(994\) 6.07668 + 7.03376i 0.192741 + 0.223097i
\(995\) −37.0161 37.0161i −1.17349 1.17349i
\(996\) −15.0430 2.20808i −0.476654 0.0699657i
\(997\) −24.3815 + 24.3815i −0.772169 + 0.772169i −0.978485 0.206317i \(-0.933852\pi\)
0.206317 + 0.978485i \(0.433852\pi\)
\(998\) −2.43648 + 33.3758i −0.0771255 + 1.05649i
\(999\) 34.7527i 1.09953i
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 368.2.j.e.93.6 46
4.3 odd 2 1472.2.j.e.1105.9 46
16.5 even 4 inner 368.2.j.e.277.6 yes 46
16.11 odd 4 1472.2.j.e.369.9 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
368.2.j.e.93.6 46 1.1 even 1 trivial
368.2.j.e.277.6 yes 46 16.5 even 4 inner
1472.2.j.e.369.9 46 16.11 odd 4
1472.2.j.e.1105.9 46 4.3 odd 2