Properties

Label 700.2.k.b.43.4
Level $700$
Weight $2$
Character 700.43
Analytic conductor $5.590$
Analytic rank $0$
Dimension $36$
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] = [700,2,Mod(43,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 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("700.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.k (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: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.4
Character \(\chi\) \(=\) 700.43
Dual form 700.2.k.b.407.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.26992 - 0.622342i) q^{2} +(2.09607 - 2.09607i) q^{3} +(1.22538 + 1.58065i) q^{4} +(-3.96631 + 1.35737i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.572433 - 2.76990i) q^{8} -5.78704i q^{9} +O(q^{10})\) \(q+(-1.26992 - 0.622342i) q^{2} +(2.09607 - 2.09607i) q^{3} +(1.22538 + 1.58065i) q^{4} +(-3.96631 + 1.35737i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.572433 - 2.76990i) q^{8} -5.78704i q^{9} +0.214920i q^{11} +(5.88164 + 0.744658i) q^{12} +(-4.29923 - 4.29923i) q^{13} +(0.457905 + 1.33803i) q^{14} +(-0.996878 + 3.87379i) q^{16} +(-2.00932 + 2.00932i) q^{17} +(-3.60152 + 7.34907i) q^{18} +0.877903 q^{19} -2.96429 q^{21} +(0.133754 - 0.272931i) q^{22} +(0.0902398 - 0.0902398i) q^{23} +(-7.00576 - 4.60604i) q^{24} +(2.78408 + 8.13526i) q^{26} +(-5.84185 - 5.84185i) q^{27} +(0.251209 - 1.98416i) q^{28} -4.03098i q^{29} -8.60152i q^{31} +(3.67677 - 4.29899i) q^{32} +(0.450489 + 0.450489i) q^{33} +(3.80215 - 1.30119i) q^{34} +(9.14726 - 7.09134i) q^{36} +(1.29227 - 1.29227i) q^{37} +(-1.11487 - 0.546356i) q^{38} -18.0230 q^{39} +2.91481 q^{41} +(3.76441 + 1.84480i) q^{42} +(2.06108 - 2.06108i) q^{43} +(-0.339713 + 0.263360i) q^{44} +(-0.170757 + 0.0584371i) q^{46} +(4.88813 + 4.88813i) q^{47} +(6.03021 + 10.2093i) q^{48} +1.00000i q^{49} +8.42336i q^{51} +(1.52736 - 12.0638i) q^{52} +(2.77420 + 2.77420i) q^{53} +(3.78304 + 11.0543i) q^{54} +(-1.55384 + 2.36338i) q^{56} +(1.84015 - 1.84015i) q^{57} +(-2.50864 + 5.11901i) q^{58} +10.4920 q^{59} -8.32686 q^{61} +(-5.35309 + 10.9232i) q^{62} +(-4.09206 + 4.09206i) q^{63} +(-7.34464 + 3.17116i) q^{64} +(-0.291726 - 0.852442i) q^{66} +(0.555822 + 0.555822i) q^{67} +(-5.63820 - 0.713837i) q^{68} -0.378298i q^{69} +1.75036i q^{71} +(-16.0295 + 3.31270i) q^{72} +(-4.18728 - 4.18728i) q^{73} +(-2.44532 + 0.836846i) q^{74} +(1.07577 + 1.38765i) q^{76} +(0.151972 - 0.151972i) q^{77} +(22.8877 + 11.2165i) q^{78} +12.4127 q^{79} -7.12875 q^{81} +(-3.70157 - 1.81401i) q^{82} +(-5.30716 + 5.30716i) q^{83} +(-3.63239 - 4.68550i) q^{84} +(-3.90010 + 1.33471i) q^{86} +(-8.44922 - 8.44922i) q^{87} +(0.595307 - 0.123028i) q^{88} +12.7409i q^{89} +6.08003i q^{91} +(0.253215 + 0.0320589i) q^{92} +(-18.0294 - 18.0294i) q^{93} +(-3.16544 - 9.24961i) q^{94} +(-1.30422 - 16.7178i) q^{96} +(2.58579 - 2.58579i) q^{97} +(0.622342 - 1.26992i) q^{98} +1.24375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 8 q^{6} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} - 28 q^{18} - 4 q^{22} - 32 q^{26} - 20 q^{37} + 20 q^{42} + 16 q^{46} + 24 q^{48} - 16 q^{52} + 44 q^{53} - 24 q^{56} + 16 q^{57} + 4 q^{58} - 64 q^{61} - 40 q^{62} + 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 8 q^{76} + 76 q^{78} - 36 q^{81} - 56 q^{82} + 56 q^{86} + 40 q^{88} + 56 q^{92} - 32 q^{93} + 120 q^{96} - 20 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26992 0.622342i −0.897967 0.440062i
\(3\) 2.09607 2.09607i 1.21017 1.21017i 0.239197 0.970971i \(-0.423116\pi\)
0.970971 0.239197i \(-0.0768843\pi\)
\(4\) 1.22538 + 1.58065i 0.612691 + 0.790323i
\(5\) 0 0
\(6\) −3.96631 + 1.35737i −1.61924 + 0.554143i
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) −0.572433 2.76990i −0.202386 0.979306i
\(9\) 5.78704i 1.92901i
\(10\) 0 0
\(11\) 0.214920i 0.0648009i 0.999475 + 0.0324005i \(0.0103152\pi\)
−0.999475 + 0.0324005i \(0.989685\pi\)
\(12\) 5.88164 + 0.744658i 1.69788 + 0.214964i
\(13\) −4.29923 4.29923i −1.19239 1.19239i −0.976394 0.215999i \(-0.930699\pi\)
−0.215999 0.976394i \(-0.569301\pi\)
\(14\) 0.457905 + 1.33803i 0.122380 + 0.357603i
\(15\) 0 0
\(16\) −0.996878 + 3.87379i −0.249220 + 0.968447i
\(17\) −2.00932 + 2.00932i −0.487331 + 0.487331i −0.907463 0.420132i \(-0.861984\pi\)
0.420132 + 0.907463i \(0.361984\pi\)
\(18\) −3.60152 + 7.34907i −0.848886 + 1.73219i
\(19\) 0.877903 0.201405 0.100702 0.994917i \(-0.467891\pi\)
0.100702 + 0.994917i \(0.467891\pi\)
\(20\) 0 0
\(21\) −2.96429 −0.646862
\(22\) 0.133754 0.272931i 0.0285164 0.0581891i
\(23\) 0.0902398 0.0902398i 0.0188163 0.0188163i −0.697636 0.716452i \(-0.745765\pi\)
0.716452 + 0.697636i \(0.245765\pi\)
\(24\) −7.00576 4.60604i −1.43005 0.940204i
\(25\) 0 0
\(26\) 2.78408 + 8.13526i 0.546003 + 1.59546i
\(27\) −5.84185 5.84185i −1.12426 1.12426i
\(28\) 0.251209 1.98416i 0.0474740 0.374971i
\(29\) 4.03098i 0.748534i −0.927321 0.374267i \(-0.877894\pi\)
0.927321 0.374267i \(-0.122106\pi\)
\(30\) 0 0
\(31\) 8.60152i 1.54488i −0.635088 0.772440i \(-0.719036\pi\)
0.635088 0.772440i \(-0.280964\pi\)
\(32\) 3.67677 4.29899i 0.649968 0.759962i
\(33\) 0.450489 + 0.450489i 0.0784200 + 0.0784200i
\(34\) 3.80215 1.30119i 0.652064 0.223152i
\(35\) 0 0
\(36\) 9.14726 7.09134i 1.52454 1.18189i
\(37\) 1.29227 1.29227i 0.212448 0.212448i −0.592858 0.805307i \(-0.702001\pi\)
0.805307 + 0.592858i \(0.202001\pi\)
\(38\) −1.11487 0.546356i −0.180855 0.0886306i
\(39\) −18.0230 −2.88599
\(40\) 0 0
\(41\) 2.91481 0.455217 0.227608 0.973753i \(-0.426909\pi\)
0.227608 + 0.973753i \(0.426909\pi\)
\(42\) 3.76441 + 1.84480i 0.580861 + 0.284659i
\(43\) 2.06108 2.06108i 0.314312 0.314312i −0.532265 0.846578i \(-0.678659\pi\)
0.846578 + 0.532265i \(0.178659\pi\)
\(44\) −0.339713 + 0.263360i −0.0512136 + 0.0397030i
\(45\) 0 0
\(46\) −0.170757 + 0.0584371i −0.0251768 + 0.00861609i
\(47\) 4.88813 + 4.88813i 0.713007 + 0.713007i 0.967163 0.254156i \(-0.0817977\pi\)
−0.254156 + 0.967163i \(0.581798\pi\)
\(48\) 6.03021 + 10.2093i 0.870386 + 1.47358i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 8.42336i 1.17951i
\(52\) 1.52736 12.0638i 0.211807 1.67294i
\(53\) 2.77420 + 2.77420i 0.381066 + 0.381066i 0.871486 0.490420i \(-0.163157\pi\)
−0.490420 + 0.871486i \(0.663157\pi\)
\(54\) 3.78304 + 11.0543i 0.514807 + 1.50430i
\(55\) 0 0
\(56\) −1.55384 + 2.36338i −0.207641 + 0.315820i
\(57\) 1.84015 1.84015i 0.243734 0.243734i
\(58\) −2.50864 + 5.11901i −0.329401 + 0.672159i
\(59\) 10.4920 1.36594 0.682972 0.730445i \(-0.260687\pi\)
0.682972 + 0.730445i \(0.260687\pi\)
\(60\) 0 0
\(61\) −8.32686 −1.06615 −0.533073 0.846069i \(-0.678963\pi\)
−0.533073 + 0.846069i \(0.678963\pi\)
\(62\) −5.35309 + 10.9232i −0.679843 + 1.38725i
\(63\) −4.09206 + 4.09206i −0.515551 + 0.515551i
\(64\) −7.34464 + 3.17116i −0.918080 + 0.396395i
\(65\) 0 0
\(66\) −0.291726 0.852442i −0.0359090 0.104928i
\(67\) 0.555822 + 0.555822i 0.0679045 + 0.0679045i 0.740243 0.672339i \(-0.234710\pi\)
−0.672339 + 0.740243i \(0.734710\pi\)
\(68\) −5.63820 0.713837i −0.683732 0.0865654i
\(69\) 0.378298i 0.0455418i
\(70\) 0 0
\(71\) 1.75036i 0.207729i 0.994591 + 0.103865i \(0.0331209\pi\)
−0.994591 + 0.103865i \(0.966879\pi\)
\(72\) −16.0295 + 3.31270i −1.88910 + 0.390405i
\(73\) −4.18728 4.18728i −0.490084 0.490084i 0.418249 0.908333i \(-0.362644\pi\)
−0.908333 + 0.418249i \(0.862644\pi\)
\(74\) −2.44532 + 0.836846i −0.284262 + 0.0972813i
\(75\) 0 0
\(76\) 1.07577 + 1.38765i 0.123399 + 0.159175i
\(77\) 0.151972 0.151972i 0.0173188 0.0173188i
\(78\) 22.8877 + 11.2165i 2.59153 + 1.27002i
\(79\) 12.4127 1.39654 0.698270 0.715834i \(-0.253953\pi\)
0.698270 + 0.715834i \(0.253953\pi\)
\(80\) 0 0
\(81\) −7.12875 −0.792083
\(82\) −3.70157 1.81401i −0.408770 0.200324i
\(83\) −5.30716 + 5.30716i −0.582537 + 0.582537i −0.935600 0.353063i \(-0.885140\pi\)
0.353063 + 0.935600i \(0.385140\pi\)
\(84\) −3.63239 4.68550i −0.396327 0.511230i
\(85\) 0 0
\(86\) −3.90010 + 1.33471i −0.420559 + 0.143925i
\(87\) −8.44922 8.44922i −0.905852 0.905852i
\(88\) 0.595307 0.123028i 0.0634599 0.0131148i
\(89\) 12.7409i 1.35053i 0.737576 + 0.675264i \(0.235971\pi\)
−0.737576 + 0.675264i \(0.764029\pi\)
\(90\) 0 0
\(91\) 6.08003i 0.637361i
\(92\) 0.253215 + 0.0320589i 0.0263995 + 0.00334237i
\(93\) −18.0294 18.0294i −1.86956 1.86956i
\(94\) −3.16544 9.24961i −0.326490 0.954024i
\(95\) 0 0
\(96\) −1.30422 16.7178i −0.133111 1.70625i
\(97\) 2.58579 2.58579i 0.262547 0.262547i −0.563541 0.826088i \(-0.690561\pi\)
0.826088 + 0.563541i \(0.190561\pi\)
\(98\) 0.622342 1.26992i 0.0628660 0.128281i
\(99\) 1.24375 0.125002
\(100\) 0 0
\(101\) −15.1945 −1.51190 −0.755952 0.654627i \(-0.772826\pi\)
−0.755952 + 0.654627i \(0.772826\pi\)
\(102\) 5.24221 10.6970i 0.519056 1.05916i
\(103\) 1.08907 1.08907i 0.107309 0.107309i −0.651414 0.758723i \(-0.725824\pi\)
0.758723 + 0.651414i \(0.225824\pi\)
\(104\) −9.44740 + 14.3694i −0.926394 + 1.40904i
\(105\) 0 0
\(106\) −1.79651 5.24951i −0.174492 0.509877i
\(107\) 9.68529 + 9.68529i 0.936312 + 0.936312i 0.998090 0.0617779i \(-0.0196771\pi\)
−0.0617779 + 0.998090i \(0.519677\pi\)
\(108\) 2.07539 16.3924i 0.199705 1.57736i
\(109\) 12.0416i 1.15337i −0.816966 0.576686i \(-0.804345\pi\)
0.816966 0.576686i \(-0.195655\pi\)
\(110\) 0 0
\(111\) 5.41740i 0.514197i
\(112\) 3.44408 2.03428i 0.325435 0.192222i
\(113\) 3.14409 + 3.14409i 0.295771 + 0.295771i 0.839355 0.543584i \(-0.182933\pi\)
−0.543584 + 0.839355i \(0.682933\pi\)
\(114\) −3.48204 + 1.19164i −0.326123 + 0.111607i
\(115\) 0 0
\(116\) 6.37154 4.93949i 0.591583 0.458620i
\(117\) −24.8798 + 24.8798i −2.30014 + 2.30014i
\(118\) −13.3240 6.52961i −1.22657 0.601100i
\(119\) 2.84161 0.260490
\(120\) 0 0
\(121\) 10.9538 0.995801
\(122\) 10.5744 + 5.18215i 0.957364 + 0.469170i
\(123\) 6.10965 6.10965i 0.550889 0.550889i
\(124\) 13.5960 10.5402i 1.22095 0.946534i
\(125\) 0 0
\(126\) 7.74323 2.64992i 0.689822 0.236074i
\(127\) −2.21268 2.21268i −0.196344 0.196344i 0.602087 0.798431i \(-0.294336\pi\)
−0.798431 + 0.602087i \(0.794336\pi\)
\(128\) 11.3006 + 0.543764i 0.998844 + 0.0480624i
\(129\) 8.64036i 0.760741i
\(130\) 0 0
\(131\) 3.71791i 0.324835i 0.986722 + 0.162418i \(0.0519292\pi\)
−0.986722 + 0.162418i \(0.948071\pi\)
\(132\) −0.160042 + 1.26408i −0.0139299 + 0.110024i
\(133\) −0.620772 0.620772i −0.0538277 0.0538277i
\(134\) −0.359937 1.05176i −0.0310939 0.0908582i
\(135\) 0 0
\(136\) 6.71580 + 4.41540i 0.575875 + 0.378618i
\(137\) −1.84961 + 1.84961i −0.158023 + 0.158023i −0.781690 0.623667i \(-0.785642\pi\)
0.623667 + 0.781690i \(0.285642\pi\)
\(138\) −0.235431 + 0.480408i −0.0200412 + 0.0408950i
\(139\) 10.9071 0.925130 0.462565 0.886585i \(-0.346929\pi\)
0.462565 + 0.886585i \(0.346929\pi\)
\(140\) 0 0
\(141\) 20.4918 1.72572
\(142\) 1.08932 2.22281i 0.0914137 0.186534i
\(143\) 0.923993 0.923993i 0.0772682 0.0772682i
\(144\) 22.4178 + 5.76898i 1.86815 + 0.480748i
\(145\) 0 0
\(146\) 2.71158 + 7.92342i 0.224412 + 0.655747i
\(147\) 2.09607 + 2.09607i 0.172881 + 0.172881i
\(148\) 3.62615 + 0.459097i 0.298068 + 0.0377376i
\(149\) 11.2422i 0.920997i −0.887661 0.460498i \(-0.847671\pi\)
0.887661 0.460498i \(-0.152329\pi\)
\(150\) 0 0
\(151\) 9.08107i 0.739007i −0.929229 0.369504i \(-0.879528\pi\)
0.929229 0.369504i \(-0.120472\pi\)
\(152\) −0.502541 2.43170i −0.0407615 0.197237i
\(153\) 11.6280 + 11.6280i 0.940069 + 0.940069i
\(154\) −0.287570 + 0.0984132i −0.0231730 + 0.00793036i
\(155\) 0 0
\(156\) −22.0851 28.4880i −1.76822 2.28086i
\(157\) −14.8107 + 14.8107i −1.18202 + 1.18202i −0.202799 + 0.979220i \(0.565004\pi\)
−0.979220 + 0.202799i \(0.934996\pi\)
\(158\) −15.7631 7.72495i −1.25405 0.614564i
\(159\) 11.6299 0.922307
\(160\) 0 0
\(161\) −0.127618 −0.0100577
\(162\) 9.05292 + 4.43652i 0.711265 + 0.348566i
\(163\) 11.2444 11.2444i 0.880727 0.880727i −0.112882 0.993608i \(-0.536008\pi\)
0.993608 + 0.112882i \(0.0360082\pi\)
\(164\) 3.57176 + 4.60728i 0.278907 + 0.359768i
\(165\) 0 0
\(166\) 10.0425 3.43679i 0.779452 0.266747i
\(167\) 12.0570 + 12.0570i 0.932995 + 0.932995i 0.997892 0.0648970i \(-0.0206719\pi\)
−0.0648970 + 0.997892i \(0.520672\pi\)
\(168\) 1.69686 + 8.21079i 0.130916 + 0.633476i
\(169\) 23.9668i 1.84360i
\(170\) 0 0
\(171\) 5.08047i 0.388513i
\(172\) 5.78345 + 0.732227i 0.440984 + 0.0558318i
\(173\) 0.321011 + 0.321011i 0.0244060 + 0.0244060i 0.719204 0.694798i \(-0.244506\pi\)
−0.694798 + 0.719204i \(0.744506\pi\)
\(174\) 5.47151 + 15.9881i 0.414794 + 1.21206i
\(175\) 0 0
\(176\) −0.832556 0.214249i −0.0627563 0.0161497i
\(177\) 21.9920 21.9920i 1.65302 1.65302i
\(178\) 7.92917 16.1798i 0.594316 1.21273i
\(179\) 4.85521 0.362895 0.181448 0.983401i \(-0.441922\pi\)
0.181448 + 0.983401i \(0.441922\pi\)
\(180\) 0 0
\(181\) 6.88269 0.511586 0.255793 0.966732i \(-0.417663\pi\)
0.255793 + 0.966732i \(0.417663\pi\)
\(182\) 3.78386 7.72114i 0.280478 0.572329i
\(183\) −17.4537 + 17.4537i −1.29022 + 1.29022i
\(184\) −0.301611 0.198299i −0.0222351 0.0146188i
\(185\) 0 0
\(186\) 11.6754 + 34.1163i 0.856084 + 2.50153i
\(187\) −0.431844 0.431844i −0.0315795 0.0315795i
\(188\) −1.73657 + 13.7162i −0.126653 + 1.00036i
\(189\) 8.26162i 0.600944i
\(190\) 0 0
\(191\) 17.2429i 1.24765i 0.781563 + 0.623826i \(0.214423\pi\)
−0.781563 + 0.623826i \(0.785577\pi\)
\(192\) −8.74792 + 22.0419i −0.631327 + 1.59074i
\(193\) 14.3334 + 14.3334i 1.03174 + 1.03174i 0.999480 + 0.0322597i \(0.0102704\pi\)
0.0322597 + 0.999480i \(0.489730\pi\)
\(194\) −4.89299 + 1.67450i −0.351296 + 0.120222i
\(195\) 0 0
\(196\) −1.58065 + 1.22538i −0.112903 + 0.0875273i
\(197\) 12.9394 12.9394i 0.921891 0.921891i −0.0752724 0.997163i \(-0.523983\pi\)
0.997163 + 0.0752724i \(0.0239826\pi\)
\(198\) −1.57947 0.774040i −0.112248 0.0550086i
\(199\) −21.8858 −1.55144 −0.775720 0.631077i \(-0.782613\pi\)
−0.775720 + 0.631077i \(0.782613\pi\)
\(200\) 0 0
\(201\) 2.33009 0.164352
\(202\) 19.2957 + 9.45614i 1.35764 + 0.665332i
\(203\) −2.85033 + 2.85033i −0.200054 + 0.200054i
\(204\) −13.3143 + 10.3218i −0.932190 + 0.722673i
\(205\) 0 0
\(206\) −2.06081 + 0.705257i −0.143583 + 0.0491376i
\(207\) −0.522222 0.522222i −0.0362969 0.0362969i
\(208\) 20.9401 12.3685i 1.45194 0.857602i
\(209\) 0.188679i 0.0130512i
\(210\) 0 0
\(211\) 3.39701i 0.233860i −0.993140 0.116930i \(-0.962695\pi\)
0.993140 0.116930i \(-0.0373053\pi\)
\(212\) −0.985571 + 7.78448i −0.0676893 + 0.534640i
\(213\) 3.66888 + 3.66888i 0.251387 + 0.251387i
\(214\) −6.27196 18.3271i −0.428742 1.25281i
\(215\) 0 0
\(216\) −12.8372 + 19.5254i −0.873464 + 1.32853i
\(217\) −6.08220 + 6.08220i −0.412886 + 0.412886i
\(218\) −7.49397 + 15.2918i −0.507555 + 1.03569i
\(219\) −17.5537 −1.18617
\(220\) 0 0
\(221\) 17.2771 1.16218
\(222\) −3.37147 + 6.87965i −0.226278 + 0.461732i
\(223\) 19.7618 19.7618i 1.32335 1.32335i 0.412300 0.911048i \(-0.364725\pi\)
0.911048 0.412300i \(-0.135275\pi\)
\(224\) −5.63972 + 0.439976i −0.376820 + 0.0293972i
\(225\) 0 0
\(226\) −2.03604 5.94944i −0.135435 0.395751i
\(227\) −14.7580 14.7580i −0.979521 0.979521i 0.0202733 0.999794i \(-0.493546\pi\)
−0.999794 + 0.0202733i \(0.993546\pi\)
\(228\) 5.16351 + 0.653738i 0.341962 + 0.0432948i
\(229\) 3.25813i 0.215303i −0.994189 0.107652i \(-0.965667\pi\)
0.994189 0.107652i \(-0.0343331\pi\)
\(230\) 0 0
\(231\) 0.637087i 0.0419173i
\(232\) −11.1654 + 2.30746i −0.733043 + 0.151492i
\(233\) −4.88513 4.88513i −0.320035 0.320035i 0.528745 0.848781i \(-0.322663\pi\)
−0.848781 + 0.528745i \(0.822663\pi\)
\(234\) 47.0791 16.1116i 3.07766 1.05325i
\(235\) 0 0
\(236\) 12.8567 + 16.5841i 0.836901 + 1.07954i
\(237\) 26.0180 26.0180i 1.69005 1.69005i
\(238\) −3.60861 1.76845i −0.233911 0.114632i
\(239\) 10.2770 0.664761 0.332380 0.943145i \(-0.392148\pi\)
0.332380 + 0.943145i \(0.392148\pi\)
\(240\) 0 0
\(241\) 4.78849 0.308454 0.154227 0.988035i \(-0.450711\pi\)
0.154227 + 0.988035i \(0.450711\pi\)
\(242\) −13.9104 6.81701i −0.894197 0.438214i
\(243\) 2.58317 2.58317i 0.165710 0.165710i
\(244\) −10.2036 13.1618i −0.653218 0.842599i
\(245\) 0 0
\(246\) −11.5611 + 3.95647i −0.737106 + 0.252255i
\(247\) −3.77431 3.77431i −0.240154 0.240154i
\(248\) −23.8253 + 4.92380i −1.51291 + 0.312661i
\(249\) 22.2484i 1.40994i
\(250\) 0 0
\(251\) 26.2656i 1.65787i −0.559347 0.828934i \(-0.688948\pi\)
0.559347 0.828934i \(-0.311052\pi\)
\(252\) −11.4824 1.45376i −0.723325 0.0915781i
\(253\) 0.0193944 + 0.0193944i 0.00121931 + 0.00121931i
\(254\) 1.43288 + 4.18697i 0.0899069 + 0.262714i
\(255\) 0 0
\(256\) −14.0125 7.72339i −0.875779 0.482712i
\(257\) 16.3898 16.3898i 1.02237 1.02237i 0.0226254 0.999744i \(-0.492798\pi\)
0.999744 0.0226254i \(-0.00720250\pi\)
\(258\) −5.37725 + 10.9725i −0.334773 + 0.683121i
\(259\) −1.82755 −0.113558
\(260\) 0 0
\(261\) −23.3274 −1.44393
\(262\) 2.31381 4.72144i 0.142948 0.291691i
\(263\) 4.21519 4.21519i 0.259920 0.259920i −0.565102 0.825021i \(-0.691163\pi\)
0.825021 + 0.565102i \(0.191163\pi\)
\(264\) 0.989932 1.50568i 0.0609261 0.0926683i
\(265\) 0 0
\(266\) 0.401997 + 1.17466i 0.0246480 + 0.0720231i
\(267\) 26.7058 + 26.7058i 1.63437 + 1.63437i
\(268\) −0.197463 + 1.55965i −0.0120620 + 0.0952710i
\(269\) 0.0668035i 0.00407308i −0.999998 0.00203654i \(-0.999352\pi\)
0.999998 0.00203654i \(-0.000648251\pi\)
\(270\) 0 0
\(271\) 2.78031i 0.168892i −0.996428 0.0844459i \(-0.973088\pi\)
0.996428 0.0844459i \(-0.0269120\pi\)
\(272\) −5.78063 9.78672i −0.350502 0.593407i
\(273\) 12.7442 + 12.7442i 0.771314 + 0.771314i
\(274\) 3.49994 1.19776i 0.211439 0.0723596i
\(275\) 0 0
\(276\) 0.597955 0.463560i 0.0359927 0.0279030i
\(277\) −4.05025 + 4.05025i −0.243356 + 0.243356i −0.818237 0.574881i \(-0.805048\pi\)
0.574881 + 0.818237i \(0.305048\pi\)
\(278\) −13.8511 6.78796i −0.830737 0.407115i
\(279\) −49.7774 −2.98010
\(280\) 0 0
\(281\) −22.9229 −1.36746 −0.683732 0.729734i \(-0.739644\pi\)
−0.683732 + 0.729734i \(0.739644\pi\)
\(282\) −26.0228 12.7529i −1.54964 0.759422i
\(283\) −0.402053 + 0.402053i −0.0238995 + 0.0238995i −0.718956 0.695056i \(-0.755380\pi\)
0.695056 + 0.718956i \(0.255380\pi\)
\(284\) −2.76669 + 2.14486i −0.164173 + 0.127274i
\(285\) 0 0
\(286\) −1.74843 + 0.598356i −0.103387 + 0.0353815i
\(287\) −2.06108 2.06108i −0.121662 0.121662i
\(288\) −24.8785 21.2776i −1.46598 1.25380i
\(289\) 8.92528i 0.525016i
\(290\) 0 0
\(291\) 10.8400i 0.635453i
\(292\) 1.48759 11.7496i 0.0870544 0.687594i
\(293\) 1.43269 + 1.43269i 0.0836989 + 0.0836989i 0.747717 0.664018i \(-0.231150\pi\)
−0.664018 + 0.747717i \(0.731150\pi\)
\(294\) −1.35737 3.96631i −0.0791632 0.231320i
\(295\) 0 0
\(296\) −4.31920 2.83972i −0.251049 0.165056i
\(297\) 1.25553 1.25553i 0.0728534 0.0728534i
\(298\) −6.99649 + 14.2767i −0.405296 + 0.827025i
\(299\) −0.775924 −0.0448728
\(300\) 0 0
\(301\) −2.91481 −0.168007
\(302\) −5.65153 + 11.5322i −0.325209 + 0.663604i
\(303\) −31.8487 + 31.8487i −1.82966 + 1.82966i
\(304\) −0.875163 + 3.40081i −0.0501940 + 0.195050i
\(305\) 0 0
\(306\) −7.53003 22.0032i −0.430463 1.25784i
\(307\) −1.51038 1.51038i −0.0862017 0.0862017i 0.662691 0.748893i \(-0.269414\pi\)
−0.748893 + 0.662691i \(0.769414\pi\)
\(308\) 0.426437 + 0.0539899i 0.0242985 + 0.00307636i
\(309\) 4.56555i 0.259725i
\(310\) 0 0
\(311\) 12.7459i 0.722753i 0.932420 + 0.361376i \(0.117693\pi\)
−0.932420 + 0.361376i \(0.882307\pi\)
\(312\) 10.3170 + 49.9219i 0.584083 + 2.82627i
\(313\) 14.3977 + 14.3977i 0.813804 + 0.813804i 0.985202 0.171398i \(-0.0548283\pi\)
−0.171398 + 0.985202i \(0.554828\pi\)
\(314\) 28.0256 9.59103i 1.58158 0.541253i
\(315\) 0 0
\(316\) 15.2103 + 19.6201i 0.855648 + 1.10372i
\(317\) −6.99137 + 6.99137i −0.392674 + 0.392674i −0.875640 0.482965i \(-0.839560\pi\)
0.482965 + 0.875640i \(0.339560\pi\)
\(318\) −14.7690 7.23774i −0.828202 0.405872i
\(319\) 0.866339 0.0485057
\(320\) 0 0
\(321\) 40.6021 2.26619
\(322\) 0.162065 + 0.0794222i 0.00903152 + 0.00442603i
\(323\) −1.76399 + 1.76399i −0.0981509 + 0.0981509i
\(324\) −8.73544 11.2680i −0.485302 0.626001i
\(325\) 0 0
\(326\) −21.2773 + 7.28158i −1.17844 + 0.403290i
\(327\) −25.2400 25.2400i −1.39578 1.39578i
\(328\) −1.66853 8.07372i −0.0921294 0.445797i
\(329\) 6.91286i 0.381118i
\(330\) 0 0
\(331\) 29.3504i 1.61324i −0.591069 0.806621i \(-0.701294\pi\)
0.591069 0.806621i \(-0.298706\pi\)
\(332\) −14.8920 1.88544i −0.817307 0.103477i
\(333\) −7.47844 7.47844i −0.409816 0.409816i
\(334\) −7.80779 22.8149i −0.427224 1.24837i
\(335\) 0 0
\(336\) 2.95504 11.4831i 0.161211 0.626452i
\(337\) −21.9434 + 21.9434i −1.19533 + 1.19533i −0.219784 + 0.975549i \(0.570535\pi\)
−0.975549 + 0.219784i \(0.929465\pi\)
\(338\) 14.9155 30.4359i 0.811298 1.65549i
\(339\) 13.1805 0.715866
\(340\) 0 0
\(341\) 1.84864 0.100110
\(342\) −3.16179 + 6.45177i −0.170970 + 0.348872i
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) −6.88881 4.52915i −0.371420 0.244195i
\(345\) 0 0
\(346\) −0.207879 0.607435i −0.0111756 0.0326559i
\(347\) −5.74445 5.74445i −0.308378 0.308378i 0.535902 0.844280i \(-0.319972\pi\)
−0.844280 + 0.535902i \(0.819972\pi\)
\(348\) 3.00170 23.7087i 0.160908 1.27092i
\(349\) 8.46417i 0.453076i 0.974002 + 0.226538i \(0.0727408\pi\)
−0.974002 + 0.226538i \(0.927259\pi\)
\(350\) 0 0
\(351\) 50.2309i 2.68113i
\(352\) 0.923941 + 0.790213i 0.0492462 + 0.0421185i
\(353\) −14.7063 14.7063i −0.782739 0.782739i 0.197553 0.980292i \(-0.436700\pi\)
−0.980292 + 0.197553i \(0.936700\pi\)
\(354\) −41.6146 + 14.2415i −2.21179 + 0.756928i
\(355\) 0 0
\(356\) −20.1388 + 15.6124i −1.06735 + 0.827457i
\(357\) 5.95621 5.95621i 0.315236 0.315236i
\(358\) −6.16571 3.02160i −0.325868 0.159696i
\(359\) 23.5648 1.24370 0.621851 0.783135i \(-0.286381\pi\)
0.621851 + 0.783135i \(0.286381\pi\)
\(360\) 0 0
\(361\) −18.2293 −0.959436
\(362\) −8.74045 4.28338i −0.459388 0.225130i
\(363\) 22.9600 22.9600i 1.20509 1.20509i
\(364\) −9.61038 + 7.45036i −0.503721 + 0.390505i
\(365\) 0 0
\(366\) 33.0269 11.3026i 1.72635 0.590797i
\(367\) 3.77172 + 3.77172i 0.196882 + 0.196882i 0.798662 0.601780i \(-0.205542\pi\)
−0.601780 + 0.798662i \(0.705542\pi\)
\(368\) 0.259612 + 0.439528i 0.0135332 + 0.0229120i
\(369\) 16.8681i 0.878120i
\(370\) 0 0
\(371\) 3.92331i 0.203688i
\(372\) 6.40519 50.5911i 0.332094 2.62302i
\(373\) 22.7964 + 22.7964i 1.18035 + 1.18035i 0.979653 + 0.200699i \(0.0643213\pi\)
0.200699 + 0.979653i \(0.435679\pi\)
\(374\) 0.279652 + 0.817160i 0.0144604 + 0.0422543i
\(375\) 0 0
\(376\) 10.7415 16.3377i 0.553950 0.842554i
\(377\) −17.3301 + 17.3301i −0.892546 + 0.892546i
\(378\) 5.14155 10.4916i 0.264453 0.539629i
\(379\) 3.18566 0.163637 0.0818183 0.996647i \(-0.473927\pi\)
0.0818183 + 0.996647i \(0.473927\pi\)
\(380\) 0 0
\(381\) −9.27589 −0.475218
\(382\) 10.7310 21.8971i 0.549044 1.12035i
\(383\) −19.9331 + 19.9331i −1.01853 + 1.01853i −0.0187081 + 0.999825i \(0.505955\pi\)
−0.999825 + 0.0187081i \(0.994045\pi\)
\(384\) 24.8267 22.5472i 1.26693 1.15061i
\(385\) 0 0
\(386\) −9.28195 27.1225i −0.472439 1.38050i
\(387\) −11.9276 11.9276i −0.606313 0.606313i
\(388\) 7.25580 + 0.918636i 0.368357 + 0.0466367i
\(389\) 16.3461i 0.828781i 0.910099 + 0.414391i \(0.136005\pi\)
−0.910099 + 0.414391i \(0.863995\pi\)
\(390\) 0 0
\(391\) 0.362641i 0.0183395i
\(392\) 2.76990 0.572433i 0.139901 0.0289122i
\(393\) 7.79301 + 7.79301i 0.393105 + 0.393105i
\(394\) −24.4846 + 8.37921i −1.23352 + 0.422139i
\(395\) 0 0
\(396\) 1.52407 + 1.96593i 0.0765876 + 0.0987919i
\(397\) 10.7408 10.7408i 0.539067 0.539067i −0.384188 0.923255i \(-0.625519\pi\)
0.923255 + 0.384188i \(0.125519\pi\)
\(398\) 27.7931 + 13.6204i 1.39314 + 0.682730i
\(399\) −2.60236 −0.130281
\(400\) 0 0
\(401\) 23.7605 1.18654 0.593271 0.805003i \(-0.297836\pi\)
0.593271 + 0.805003i \(0.297836\pi\)
\(402\) −2.95902 1.45011i −0.147583 0.0723250i
\(403\) −36.9800 + 36.9800i −1.84210 + 1.84210i
\(404\) −18.6190 24.0170i −0.926330 1.19489i
\(405\) 0 0
\(406\) 5.39357 1.84581i 0.267678 0.0916058i
\(407\) 0.277736 + 0.277736i 0.0137669 + 0.0137669i
\(408\) 23.3318 4.82181i 1.15510 0.238715i
\(409\) 22.5684i 1.11593i −0.829863 0.557967i \(-0.811582\pi\)
0.829863 0.557967i \(-0.188418\pi\)
\(410\) 0 0
\(411\) 7.75384i 0.382469i
\(412\) 3.05596 + 0.386907i 0.150557 + 0.0190615i
\(413\) −7.41897 7.41897i −0.365064 0.365064i
\(414\) 0.338178 + 0.988179i 0.0166206 + 0.0485663i
\(415\) 0 0
\(416\) −34.2897 + 2.67507i −1.68119 + 0.131156i
\(417\) 22.8621 22.8621i 1.11956 1.11956i
\(418\) 0.117423 0.239607i 0.00574335 0.0117196i
\(419\) −12.4351 −0.607495 −0.303748 0.952753i \(-0.598238\pi\)
−0.303748 + 0.952753i \(0.598238\pi\)
\(420\) 0 0
\(421\) −31.2799 −1.52449 −0.762244 0.647289i \(-0.775902\pi\)
−0.762244 + 0.647289i \(0.775902\pi\)
\(422\) −2.11410 + 4.31392i −0.102913 + 0.209998i
\(423\) 28.2878 28.2878i 1.37540 1.37540i
\(424\) 6.09620 9.27229i 0.296058 0.450302i
\(425\) 0 0
\(426\) −2.37588 6.94246i −0.115112 0.336364i
\(427\) 5.88798 + 5.88798i 0.284939 + 0.284939i
\(428\) −3.44083 + 27.1772i −0.166319 + 1.31366i
\(429\) 3.87351i 0.187015i
\(430\) 0 0
\(431\) 19.1288i 0.921402i 0.887556 + 0.460701i \(0.152402\pi\)
−0.887556 + 0.460701i \(0.847598\pi\)
\(432\) 28.4537 16.8065i 1.36898 0.808602i
\(433\) −4.87478 4.87478i −0.234267 0.234267i 0.580204 0.814471i \(-0.302973\pi\)
−0.814471 + 0.580204i \(0.802973\pi\)
\(434\) 11.5091 3.93869i 0.552454 0.189063i
\(435\) 0 0
\(436\) 19.0334 14.7555i 0.911536 0.706661i
\(437\) 0.0792218 0.0792218i 0.00378969 0.00378969i
\(438\) 22.2917 + 10.9244i 1.06514 + 0.521987i
\(439\) −32.7840 −1.56470 −0.782349 0.622841i \(-0.785978\pi\)
−0.782349 + 0.622841i \(0.785978\pi\)
\(440\) 0 0
\(441\) 5.78704 0.275574
\(442\) −21.9404 10.7522i −1.04360 0.511431i
\(443\) 8.51358 8.51358i 0.404493 0.404493i −0.475320 0.879813i \(-0.657668\pi\)
0.879813 + 0.475320i \(0.157668\pi\)
\(444\) 8.56299 6.63838i 0.406381 0.315044i
\(445\) 0 0
\(446\) −37.3945 + 12.7973i −1.77068 + 0.605968i
\(447\) −23.5645 23.5645i −1.11456 1.11456i
\(448\) 7.43579 + 2.95110i 0.351308 + 0.139426i
\(449\) 5.52889i 0.260925i 0.991453 + 0.130462i \(0.0416462\pi\)
−0.991453 + 0.130462i \(0.958354\pi\)
\(450\) 0 0
\(451\) 0.626452i 0.0294985i
\(452\) −1.11698 + 8.82241i −0.0525383 + 0.414971i
\(453\) −19.0346 19.0346i −0.894323 0.894323i
\(454\) 9.55691 + 27.9259i 0.448528 + 1.31063i
\(455\) 0 0
\(456\) −6.15038 4.04366i −0.288018 0.189362i
\(457\) −19.0996 + 19.0996i −0.893440 + 0.893440i −0.994845 0.101405i \(-0.967666\pi\)
0.101405 + 0.994845i \(0.467666\pi\)
\(458\) −2.02767 + 4.13755i −0.0947467 + 0.193335i
\(459\) 23.4763 1.09578
\(460\) 0 0
\(461\) −8.24886 −0.384188 −0.192094 0.981377i \(-0.561528\pi\)
−0.192094 + 0.981377i \(0.561528\pi\)
\(462\) −0.396486 + 0.809049i −0.0184462 + 0.0376403i
\(463\) −15.4884 + 15.4884i −0.719806 + 0.719806i −0.968565 0.248759i \(-0.919977\pi\)
0.248759 + 0.968565i \(0.419977\pi\)
\(464\) 15.6152 + 4.01839i 0.724915 + 0.186549i
\(465\) 0 0
\(466\) 3.16349 + 9.24392i 0.146546 + 0.428217i
\(467\) 27.7817 + 27.7817i 1.28558 + 1.28558i 0.937442 + 0.348141i \(0.113187\pi\)
0.348141 + 0.937442i \(0.386813\pi\)
\(468\) −69.8135 8.83889i −3.22713 0.408578i
\(469\) 0.786052i 0.0362965i
\(470\) 0 0
\(471\) 62.0885i 2.86089i
\(472\) −6.00597 29.0618i −0.276447 1.33768i
\(473\) 0.442969 + 0.442969i 0.0203677 + 0.0203677i
\(474\) −49.2328 + 16.8486i −2.26134 + 0.773883i
\(475\) 0 0
\(476\) 3.48205 + 4.49157i 0.159600 + 0.205871i
\(477\) 16.0544 16.0544i 0.735082 0.735082i
\(478\) −13.0509 6.39578i −0.596934 0.292536i
\(479\) −3.86716 −0.176695 −0.0883475 0.996090i \(-0.528159\pi\)
−0.0883475 + 0.996090i \(0.528159\pi\)
\(480\) 0 0
\(481\) −11.1116 −0.506644
\(482\) −6.08099 2.98008i −0.276982 0.135739i
\(483\) −0.267497 + 0.267497i −0.0121716 + 0.0121716i
\(484\) 13.4226 + 17.3141i 0.610118 + 0.787004i
\(485\) 0 0
\(486\) −4.88803 + 1.67280i −0.221725 + 0.0758797i
\(487\) 0.314754 + 0.314754i 0.0142629 + 0.0142629i 0.714202 0.699939i \(-0.246790\pi\)
−0.699939 + 0.714202i \(0.746790\pi\)
\(488\) 4.76657 + 23.0645i 0.215773 + 1.04408i
\(489\) 47.1380i 2.13165i
\(490\) 0 0
\(491\) 40.4240i 1.82431i 0.409844 + 0.912156i \(0.365583\pi\)
−0.409844 + 0.912156i \(0.634417\pi\)
\(492\) 17.1439 + 2.17054i 0.772905 + 0.0978553i
\(493\) 8.09952 + 8.09952i 0.364784 + 0.364784i
\(494\) 2.44415 + 7.14198i 0.109968 + 0.321333i
\(495\) 0 0
\(496\) 33.3205 + 8.57467i 1.49613 + 0.385014i
\(497\) 1.23769 1.23769i 0.0555180 0.0555180i
\(498\) 13.8461 28.2536i 0.620459 1.26608i
\(499\) 31.7874 1.42300 0.711501 0.702686i \(-0.248016\pi\)
0.711501 + 0.702686i \(0.248016\pi\)
\(500\) 0 0
\(501\) 50.5445 2.25816
\(502\) −16.3461 + 33.3551i −0.729564 + 1.48871i
\(503\) −6.28613 + 6.28613i −0.280285 + 0.280285i −0.833222 0.552938i \(-0.813507\pi\)
0.552938 + 0.833222i \(0.313507\pi\)
\(504\) 13.6770 + 8.99214i 0.609222 + 0.400542i
\(505\) 0 0
\(506\) −0.0125593 0.0366992i −0.000558330 0.00163148i
\(507\) 50.2362 + 50.2362i 2.23107 + 2.23107i
\(508\) 0.786085 6.20885i 0.0348769 0.275473i
\(509\) 3.09416i 0.137146i 0.997646 + 0.0685730i \(0.0218446\pi\)
−0.997646 + 0.0685730i \(0.978155\pi\)
\(510\) 0 0
\(511\) 5.92171i 0.261961i
\(512\) 12.9881 + 18.5286i 0.573998 + 0.818857i
\(513\) −5.12858 5.12858i −0.226432 0.226432i
\(514\) −31.0138 + 10.6137i −1.36796 + 0.468149i
\(515\) 0 0
\(516\) 13.6573 10.5877i 0.601231 0.466099i
\(517\) −1.05056 + 1.05056i −0.0462035 + 0.0462035i
\(518\) 2.32084 + 1.13736i 0.101972 + 0.0499728i
\(519\) 1.34572 0.0590707
\(520\) 0 0
\(521\) 5.11386 0.224042 0.112021 0.993706i \(-0.464268\pi\)
0.112021 + 0.993706i \(0.464268\pi\)
\(522\) 29.6239 + 14.5176i 1.29660 + 0.635420i
\(523\) −17.9247 + 17.9247i −0.783791 + 0.783791i −0.980468 0.196677i \(-0.936985\pi\)
0.196677 + 0.980468i \(0.436985\pi\)
\(524\) −5.87669 + 4.55586i −0.256725 + 0.199024i
\(525\) 0 0
\(526\) −7.97623 + 2.72966i −0.347780 + 0.119019i
\(527\) 17.2832 + 17.2832i 0.752868 + 0.752868i
\(528\) −2.19418 + 1.29602i −0.0954895 + 0.0564018i
\(529\) 22.9837i 0.999292i
\(530\) 0 0
\(531\) 60.7177i 2.63493i
\(532\) 0.220537 1.74190i 0.00956150 0.0755210i
\(533\) −12.5314 12.5314i −0.542797 0.542797i
\(534\) −17.2940 50.5343i −0.748386 2.18683i
\(535\) 0 0
\(536\) 1.22140 1.85774i 0.0527564 0.0802422i
\(537\) 10.1769 10.1769i 0.439164 0.439164i
\(538\) −0.0415746 + 0.0848349i −0.00179241 + 0.00365749i
\(539\) −0.214920 −0.00925728
\(540\) 0 0
\(541\) 1.00395 0.0431633 0.0215817 0.999767i \(-0.493130\pi\)
0.0215817 + 0.999767i \(0.493130\pi\)
\(542\) −1.73030 + 3.53077i −0.0743229 + 0.151659i
\(543\) 14.4266 14.4266i 0.619105 0.619105i
\(544\) 1.25024 + 16.0259i 0.0536036 + 0.687103i
\(545\) 0 0
\(546\) −8.25284 24.1153i −0.353189 1.03204i
\(547\) −11.1953 11.1953i −0.478676 0.478676i 0.426032 0.904708i \(-0.359911\pi\)
−0.904708 + 0.426032i \(0.859911\pi\)
\(548\) −5.19006 0.657099i −0.221708 0.0280699i
\(549\) 48.1879i 2.05661i
\(550\) 0 0
\(551\) 3.53881i 0.150758i
\(552\) −1.04785 + 0.216550i −0.0445993 + 0.00921700i
\(553\) −8.77712 8.77712i −0.373241 0.373241i
\(554\) 7.66412 2.62285i 0.325617 0.111434i
\(555\) 0 0
\(556\) 13.3654 + 17.2403i 0.566819 + 0.731151i
\(557\) 7.46496 7.46496i 0.316301 0.316301i −0.531044 0.847344i \(-0.678200\pi\)
0.847344 + 0.531044i \(0.178200\pi\)
\(558\) 63.2132 + 30.9785i 2.67603 + 1.31143i
\(559\) −17.7221 −0.749567
\(560\) 0 0
\(561\) −1.81035 −0.0764331
\(562\) 29.1101 + 14.2658i 1.22794 + 0.601769i
\(563\) 5.26839 5.26839i 0.222036 0.222036i −0.587319 0.809355i \(-0.699817\pi\)
0.809355 + 0.587319i \(0.199817\pi\)
\(564\) 25.1102 + 32.3902i 1.05733 + 1.36387i
\(565\) 0 0
\(566\) 0.760788 0.260360i 0.0319783 0.0109437i
\(567\) 5.04079 + 5.04079i 0.211693 + 0.211693i
\(568\) 4.84831 1.00196i 0.203430 0.0420414i
\(569\) 27.2916i 1.14413i 0.820210 + 0.572063i \(0.193857\pi\)
−0.820210 + 0.572063i \(0.806143\pi\)
\(570\) 0 0
\(571\) 6.44056i 0.269529i −0.990878 0.134765i \(-0.956972\pi\)
0.990878 0.134765i \(-0.0430278\pi\)
\(572\) 2.59275 + 0.328261i 0.108408 + 0.0137253i
\(573\) 36.1424 + 36.1424i 1.50987 + 1.50987i
\(574\) 1.33471 + 3.90010i 0.0557096 + 0.162787i
\(575\) 0 0
\(576\) 18.3516 + 42.5038i 0.764652 + 1.77099i
\(577\) 10.4727 10.4727i 0.435984 0.435984i −0.454674 0.890658i \(-0.650244\pi\)
0.890658 + 0.454674i \(0.150244\pi\)
\(578\) 5.55457 11.3344i 0.231040 0.471448i
\(579\) 60.0876 2.49716
\(580\) 0 0
\(581\) 7.50546 0.311379
\(582\) −6.74619 + 13.7659i −0.279639 + 0.570616i
\(583\) −0.596232 + 0.596232i −0.0246934 + 0.0246934i
\(584\) −9.20139 + 13.9953i −0.380756 + 0.579128i
\(585\) 0 0
\(586\) −0.927778 2.71103i −0.0383262 0.111992i
\(587\) −15.0807 15.0807i −0.622447 0.622447i 0.323710 0.946156i \(-0.395070\pi\)
−0.946156 + 0.323710i \(0.895070\pi\)
\(588\) −0.744658 + 5.88164i −0.0307092 + 0.242555i
\(589\) 7.55131i 0.311146i
\(590\) 0 0
\(591\) 54.2436i 2.23129i
\(592\) 3.71775 + 6.29423i 0.152799 + 0.258691i
\(593\) −25.3176 25.3176i −1.03967 1.03967i −0.999180 0.0404897i \(-0.987108\pi\)
−0.0404897 0.999180i \(-0.512892\pi\)
\(594\) −2.37579 + 0.813053i −0.0974800 + 0.0333600i
\(595\) 0 0
\(596\) 17.7699 13.7760i 0.727884 0.564286i
\(597\) −45.8741 + 45.8741i −1.87750 + 1.87750i
\(598\) 0.985359 + 0.482890i 0.0402943 + 0.0197468i
\(599\) −22.3540 −0.913359 −0.456680 0.889631i \(-0.650961\pi\)
−0.456680 + 0.889631i \(0.650961\pi\)
\(600\) 0 0
\(601\) −43.6119 −1.77897 −0.889483 0.456969i \(-0.848935\pi\)
−0.889483 + 0.456969i \(0.848935\pi\)
\(602\) 3.70157 + 1.81401i 0.150865 + 0.0739334i
\(603\) 3.21657 3.21657i 0.130989 0.130989i
\(604\) 14.3540 11.1278i 0.584054 0.452783i
\(605\) 0 0
\(606\) 60.2660 20.6244i 2.44814 0.837811i
\(607\) −16.8823 16.8823i −0.685232 0.685232i 0.275943 0.961174i \(-0.411010\pi\)
−0.961174 + 0.275943i \(0.911010\pi\)
\(608\) 3.22785 3.77410i 0.130907 0.153060i
\(609\) 11.9490i 0.484198i
\(610\) 0 0
\(611\) 42.0304i 1.70037i
\(612\) −4.13101 + 32.6285i −0.166986 + 1.31893i
\(613\) 20.8003 + 20.8003i 0.840115 + 0.840115i 0.988874 0.148759i \(-0.0475278\pi\)
−0.148759 + 0.988874i \(0.547528\pi\)
\(614\) 0.978084 + 2.85802i 0.0394722 + 0.115340i
\(615\) 0 0
\(616\) −0.507939 0.333952i −0.0204655 0.0134553i
\(617\) −12.8248 + 12.8248i −0.516307 + 0.516307i −0.916452 0.400145i \(-0.868960\pi\)
0.400145 + 0.916452i \(0.368960\pi\)
\(618\) −2.84133 + 5.79787i −0.114295 + 0.233224i
\(619\) 14.7614 0.593309 0.296655 0.954985i \(-0.404129\pi\)
0.296655 + 0.954985i \(0.404129\pi\)
\(620\) 0 0
\(621\) −1.05433 −0.0423090
\(622\) 7.93229 16.1862i 0.318056 0.649008i
\(623\) 9.00915 9.00915i 0.360944 0.360944i
\(624\) 17.9667 69.8173i 0.719245 2.79493i
\(625\) 0 0
\(626\) −9.32359 27.2441i −0.372645 1.08889i
\(627\) 0.395486 + 0.395486i 0.0157942 + 0.0157942i
\(628\) −41.5591 5.26168i −1.65839 0.209964i
\(629\) 5.19318i 0.207066i
\(630\) 0 0
\(631\) 31.4840i 1.25336i −0.779278 0.626678i \(-0.784414\pi\)
0.779278 0.626678i \(-0.215586\pi\)
\(632\) −7.10545 34.3819i −0.282640 1.36764i
\(633\) −7.12038 7.12038i −0.283010 0.283010i
\(634\) 13.2295 4.52744i 0.525410 0.179808i
\(635\) 0 0
\(636\) 14.2510 + 18.3827i 0.565089 + 0.728920i
\(637\) 4.29923 4.29923i 0.170342 0.170342i
\(638\) −1.10018 0.539159i −0.0435565 0.0213455i
\(639\) 10.1294 0.400713
\(640\) 0 0
\(641\) −22.8470 −0.902403 −0.451201 0.892422i \(-0.649004\pi\)
−0.451201 + 0.892422i \(0.649004\pi\)
\(642\) −51.5614 25.2684i −2.03496 0.997264i
\(643\) 13.3643 13.3643i 0.527038 0.527038i −0.392650 0.919688i \(-0.628442\pi\)
0.919688 + 0.392650i \(0.128442\pi\)
\(644\) −0.156381 0.201719i −0.00616228 0.00794885i
\(645\) 0 0
\(646\) 3.33792 1.14232i 0.131329 0.0449438i
\(647\) −16.5557 16.5557i −0.650872 0.650872i 0.302331 0.953203i \(-0.402235\pi\)
−0.953203 + 0.302331i \(0.902235\pi\)
\(648\) 4.08073 + 19.7459i 0.160306 + 0.775692i
\(649\) 2.25495i 0.0885144i
\(650\) 0 0
\(651\) 25.4975i 0.999324i
\(652\) 31.5520 + 3.99471i 1.23567 + 0.156445i
\(653\) −15.6135 15.6135i −0.611004 0.611004i 0.332204 0.943208i \(-0.392208\pi\)
−0.943208 + 0.332204i \(0.892208\pi\)
\(654\) 16.3448 + 47.7606i 0.639133 + 1.86759i
\(655\) 0 0
\(656\) −2.90571 + 11.2914i −0.113449 + 0.440853i
\(657\) −24.2320 + 24.2320i −0.945379 + 0.945379i
\(658\) −4.30216 + 8.77876i −0.167716 + 0.342232i
\(659\) −23.8406 −0.928696 −0.464348 0.885653i \(-0.653711\pi\)
−0.464348 + 0.885653i \(0.653711\pi\)
\(660\) 0 0
\(661\) 22.0247 0.856662 0.428331 0.903622i \(-0.359102\pi\)
0.428331 + 0.903622i \(0.359102\pi\)
\(662\) −18.2660 + 37.2725i −0.709926 + 1.44864i
\(663\) 36.2140 36.2140i 1.40643 1.40643i
\(664\) 17.7383 + 11.6623i 0.688379 + 0.452585i
\(665\) 0 0
\(666\) 4.84286 + 14.1512i 0.187657 + 0.548346i
\(667\) −0.363755 0.363755i −0.0140846 0.0140846i
\(668\) −4.28339 + 33.8321i −0.165729 + 1.30900i
\(669\) 82.8444i 3.20295i
\(670\) 0 0
\(671\) 1.78961i 0.0690872i
\(672\) −10.8990 + 12.7435i −0.420440 + 0.491591i
\(673\) −15.2135 15.2135i −0.586437 0.586437i 0.350227 0.936665i \(-0.386104\pi\)
−0.936665 + 0.350227i \(0.886104\pi\)
\(674\) 41.5226 14.2100i 1.59939 0.547349i
\(675\) 0 0
\(676\) −37.8830 + 29.3685i −1.45704 + 1.12956i
\(677\) 8.40158 8.40158i 0.322899 0.322899i −0.526979 0.849878i \(-0.676675\pi\)
0.849878 + 0.526979i \(0.176675\pi\)
\(678\) −16.7381 8.20277i −0.642825 0.315026i
\(679\) −3.65686 −0.140337
\(680\) 0 0
\(681\) −61.8676 −2.37077
\(682\) −2.34762 1.15049i −0.0898952 0.0440544i
\(683\) 25.3664 25.3664i 0.970617 0.970617i −0.0289635 0.999580i \(-0.509221\pi\)
0.999580 + 0.0289635i \(0.00922064\pi\)
\(684\) 8.03041 6.22551i 0.307051 0.238038i
\(685\) 0 0
\(686\) −1.33803 + 0.457905i −0.0510862 + 0.0174829i
\(687\) −6.82927 6.82927i −0.260553 0.260553i
\(688\) 5.92955 + 10.0388i 0.226062 + 0.382727i
\(689\) 23.8539i 0.908760i
\(690\) 0 0
\(691\) 43.8205i 1.66701i 0.552512 + 0.833505i \(0.313669\pi\)
−0.552512 + 0.833505i \(0.686331\pi\)
\(692\) −0.114043 + 0.900764i −0.00433527 + 0.0342419i
\(693\) −0.879467 0.879467i −0.0334082 0.0334082i
\(694\) 3.71997 + 10.8700i 0.141208 + 0.412619i
\(695\) 0 0
\(696\) −18.5668 + 28.2401i −0.703775 + 1.07044i
\(697\) −5.85678 + 5.85678i −0.221841 + 0.221841i
\(698\) 5.26760 10.7488i 0.199382 0.406848i
\(699\) −20.4792 −0.774593
\(700\) 0 0
\(701\) 38.4455 1.45207 0.726033 0.687660i \(-0.241362\pi\)
0.726033 + 0.687660i \(0.241362\pi\)
\(702\) 31.2608 63.7891i 1.17986 2.40757i
\(703\) 1.13449 1.13449i 0.0427882 0.0427882i
\(704\) −0.681547 1.57851i −0.0256868 0.0594925i
\(705\) 0 0
\(706\) 9.52347 + 27.8282i 0.358420 + 1.04733i
\(707\) 10.7441 + 10.7441i 0.404073 + 0.404073i
\(708\) 61.7102 + 7.81296i 2.31921 + 0.293629i
\(709\) 39.0425i 1.46627i 0.680082 + 0.733137i \(0.261944\pi\)
−0.680082 + 0.733137i \(0.738056\pi\)
\(710\) 0 0
\(711\) 71.8330i 2.69395i
\(712\) 35.2909 7.29329i 1.32258 0.273328i
\(713\) −0.776200 0.776200i −0.0290689 0.0290689i
\(714\) −11.2707 + 3.85710i −0.421795 + 0.144348i
\(715\) 0 0
\(716\) 5.94948 + 7.67436i 0.222343 + 0.286804i
\(717\) 21.5412 21.5412i 0.804473 0.804473i
\(718\) −29.9254 14.6654i −1.11680 0.547306i
\(719\) −4.65847 −0.173732 −0.0868659 0.996220i \(-0.527685\pi\)
−0.0868659 + 0.996220i \(0.527685\pi\)
\(720\) 0 0
\(721\) −1.54018 −0.0573593
\(722\) 23.1497 + 11.3448i 0.861542 + 0.422211i
\(723\) 10.0370 10.0370i 0.373281 0.373281i
\(724\) 8.43392 + 10.8791i 0.313444 + 0.404318i
\(725\) 0 0
\(726\) −43.4462 + 14.8683i −1.61244 + 0.551816i
\(727\) −8.55868 8.55868i −0.317424 0.317424i 0.530353 0.847777i \(-0.322059\pi\)
−0.847777 + 0.530353i \(0.822059\pi\)
\(728\) 16.8411 3.48041i 0.624171 0.128993i
\(729\) 32.2153i 1.19316i
\(730\) 0 0
\(731\) 8.28274i 0.306348i
\(732\) −48.9756 6.20066i −1.81019 0.229183i
\(733\) 0.785057 + 0.785057i 0.0289967 + 0.0289967i 0.721456 0.692460i \(-0.243473\pi\)
−0.692460 + 0.721456i \(0.743473\pi\)
\(734\) −2.44248 7.13708i −0.0901535 0.263434i
\(735\) 0 0
\(736\) −0.0561491 0.719731i −0.00206968 0.0265297i
\(737\) −0.119458 + 0.119458i −0.00440028 + 0.00440028i
\(738\) −10.4977 + 21.4211i −0.386427 + 0.788523i
\(739\) 4.86588 0.178994 0.0894972 0.995987i \(-0.471474\pi\)
0.0894972 + 0.995987i \(0.471474\pi\)
\(740\) 0 0
\(741\) −15.8225 −0.581253
\(742\) −2.44164 + 4.98228i −0.0896354 + 0.182905i
\(743\) 24.8474 24.8474i 0.911564 0.911564i −0.0848314 0.996395i \(-0.527035\pi\)
0.996395 + 0.0848314i \(0.0270352\pi\)
\(744\) −39.6190 + 60.2603i −1.45250 + 2.20925i
\(745\) 0 0
\(746\) −14.7624 43.1367i −0.540490 1.57935i
\(747\) 30.7128 + 30.7128i 1.12372 + 1.12372i
\(748\) 0.153418 1.21176i 0.00560952 0.0443065i
\(749\) 13.6971i 0.500480i
\(750\) 0 0
\(751\) 20.0268i 0.730789i 0.930853 + 0.365394i \(0.119066\pi\)
−0.930853 + 0.365394i \(0.880934\pi\)
\(752\) −23.8084 + 14.0627i −0.868205 + 0.512814i
\(753\) −55.0545 55.0545i −2.00630 2.00630i
\(754\) 32.7931 11.2226i 1.19425 0.408702i
\(755\) 0 0
\(756\) −13.0587 + 10.1236i −0.474940 + 0.368193i
\(757\) −10.7543 + 10.7543i −0.390871 + 0.390871i −0.874998 0.484127i \(-0.839137\pi\)
0.484127 + 0.874998i \(0.339137\pi\)
\(758\) −4.04553 1.98257i −0.146940 0.0720102i
\(759\) 0.0813040 0.00295115
\(760\) 0 0
\(761\) 20.6034 0.746874 0.373437 0.927655i \(-0.378179\pi\)
0.373437 + 0.927655i \(0.378179\pi\)
\(762\) 11.7796 + 5.77277i 0.426730 + 0.209125i
\(763\) −8.51467 + 8.51467i −0.308252 + 0.308252i
\(764\) −27.2549 + 21.1291i −0.986048 + 0.764426i
\(765\) 0 0
\(766\) 37.7186 12.9082i 1.36283 0.466392i
\(767\) −45.1076 45.1076i −1.62874 1.62874i
\(768\) −45.5599 + 13.1824i −1.64400 + 0.475678i
\(769\) 9.33534i 0.336641i −0.985732 0.168320i \(-0.946166\pi\)
0.985732 0.168320i \(-0.0538343\pi\)
\(770\) 0 0
\(771\) 68.7086i 2.47448i
\(772\) −5.09212 + 40.2199i −0.183269 + 1.44754i
\(773\) 10.3739 + 10.3739i 0.373125 + 0.373125i 0.868614 0.495489i \(-0.165011\pi\)
−0.495489 + 0.868614i \(0.665011\pi\)
\(774\) 7.72401 + 22.5701i 0.277634 + 0.811264i
\(775\) 0 0
\(776\) −8.64256 5.68218i −0.310250 0.203978i
\(777\) −3.83068 + 3.83068i −0.137425 + 0.137425i
\(778\) 10.1729 20.7582i 0.364715 0.744218i
\(779\) 2.55892 0.0916829
\(780\) 0 0
\(781\) −0.376187 −0.0134610
\(782\) 0.225687 0.460524i 0.00807053 0.0164683i
\(783\) −23.5484 + 23.5484i −0.841550 + 0.841550i
\(784\) −3.87379 0.996878i −0.138350 0.0356028i
\(785\) 0 0
\(786\) −5.04657 14.7464i −0.180005 0.525986i
\(787\) −20.1167 20.1167i −0.717081 0.717081i 0.250925 0.968007i \(-0.419265\pi\)
−0.968007 + 0.250925i \(0.919265\pi\)
\(788\) 36.3082 + 4.59688i 1.29342 + 0.163757i
\(789\) 17.6707i 0.629093i
\(790\) 0 0
\(791\) 4.44642i 0.158096i
\(792\) −0.711966 3.44507i −0.0252986 0.122415i
\(793\) 35.7991 + 35.7991i 1.27126 + 1.27126i
\(794\) −20.3244 + 6.95551i −0.721287 + 0.246842i
\(795\) 0 0
\(796\) −26.8184 34.5936i −0.950553 1.22614i
\(797\) 4.43257 4.43257i 0.157010 0.157010i −0.624231 0.781240i \(-0.714587\pi\)
0.781240 + 0.624231i \(0.214587\pi\)
\(798\) 3.30479 + 1.61956i 0.116988 + 0.0573318i
\(799\) −19.6436 −0.694941
\(800\) 0 0
\(801\) 73.7319 2.60519
\(802\) −30.1739 14.7871i −1.06548 0.522152i
\(803\) 0.899932 0.899932i 0.0317579 0.0317579i
\(804\) 2.85525 + 3.68304i 0.100697 + 0.129891i
\(805\) 0 0
\(806\) 69.9757 23.9473i 2.46479 0.843509i
\(807\) −0.140025 0.140025i −0.00492911 0.00492911i
\(808\) 8.69781 + 42.0870i 0.305988 + 1.48062i
\(809\) 2.61396i 0.0919020i −0.998944 0.0459510i \(-0.985368\pi\)
0.998944 0.0459510i \(-0.0146318\pi\)
\(810\) 0 0
\(811\) 20.5143i 0.720354i 0.932884 + 0.360177i \(0.117284\pi\)
−0.932884 + 0.360177i \(0.882716\pi\)
\(812\) −7.99811 1.01262i −0.280679 0.0355359i
\(813\) −5.82774 5.82774i −0.204388 0.204388i
\(814\) −0.179855 0.525548i −0.00630392 0.0184205i
\(815\) 0 0
\(816\) −32.6303 8.39706i −1.14229 0.293956i
\(817\) 1.80943 1.80943i 0.0633040 0.0633040i
\(818\) −14.0452 + 28.6600i −0.491080 + 1.00207i
\(819\) 35.1854 1.22948
\(820\) 0 0
\(821\) −7.11902 −0.248456 −0.124228 0.992254i \(-0.539645\pi\)
−0.124228 + 0.992254i \(0.539645\pi\)
\(822\) 4.82554 9.84674i 0.168310 0.343444i
\(823\) 15.9450 15.9450i 0.555807 0.555807i −0.372304 0.928111i \(-0.621432\pi\)
0.928111 + 0.372304i \(0.121432\pi\)
\(824\) −3.64003 2.39319i −0.126807 0.0833708i
\(825\) 0 0
\(826\) 4.80435 + 14.0386i 0.167165 + 0.488466i
\(827\) −27.0197 27.0197i −0.939566 0.939566i 0.0587089 0.998275i \(-0.481302\pi\)
−0.998275 + 0.0587089i \(0.981302\pi\)
\(828\) 0.185526 1.46537i 0.00644748 0.0509251i
\(829\) 22.0054i 0.764278i −0.924105 0.382139i \(-0.875188\pi\)
0.924105 0.382139i \(-0.124812\pi\)
\(830\) 0 0
\(831\) 16.9792i 0.589003i
\(832\) 45.2099 + 17.9428i 1.56737 + 0.622054i
\(833\) −2.00932 2.00932i −0.0696188 0.0696188i
\(834\) −43.2611 + 14.8050i −1.49801 + 0.512654i
\(835\) 0 0
\(836\) −0.298235 + 0.231204i −0.0103147 + 0.00799637i
\(837\) −50.2488 + 50.2488i −1.73685 + 1.73685i
\(838\) 15.7916 + 7.73889i 0.545511 + 0.267335i
\(839\) 47.2741 1.63208 0.816041 0.577994i \(-0.196164\pi\)
0.816041 + 0.577994i \(0.196164\pi\)
\(840\) 0 0
\(841\) 12.7512 0.439697
\(842\) 39.7229 + 19.4668i 1.36894 + 0.670869i
\(843\) −48.0480 + 48.0480i −1.65486 + 1.65486i
\(844\) 5.36947 4.16263i 0.184825 0.143284i
\(845\) 0 0
\(846\) −53.5279 + 18.3185i −1.84033 + 0.629804i
\(847\) −7.74551 7.74551i −0.266139 0.266139i
\(848\) −13.5122 + 7.98113i −0.464011 + 0.274073i
\(849\) 1.68546i 0.0578449i
\(850\) 0 0
\(851\) 0.233229i 0.00799499i
\(852\) −1.30342 + 10.2950i −0.0446543 + 0.352700i
\(853\) −11.2255 11.2255i −0.384355 0.384355i 0.488313 0.872668i \(-0.337612\pi\)
−0.872668 + 0.488313i \(0.837612\pi\)
\(854\) −3.81292 11.1416i −0.130475 0.381257i
\(855\) 0 0
\(856\) 21.2831 32.3714i 0.727440 1.10643i
\(857\) −3.34445 + 3.34445i −0.114244 + 0.114244i −0.761918 0.647674i \(-0.775742\pi\)
0.647674 + 0.761918i \(0.275742\pi\)
\(858\) −2.41065 + 4.91904i −0.0822982 + 0.167933i
\(859\) −5.60701 −0.191309 −0.0956543 0.995415i \(-0.530494\pi\)
−0.0956543 + 0.995415i \(0.530494\pi\)
\(860\) 0 0
\(861\) −8.64036 −0.294463
\(862\) 11.9046 24.2920i 0.405474 0.827389i
\(863\) −35.2995 + 35.2995i −1.20161 + 1.20161i −0.227931 + 0.973677i \(0.573196\pi\)
−0.973677 + 0.227931i \(0.926804\pi\)
\(864\) −46.5932 + 3.63492i −1.58513 + 0.123662i
\(865\) 0 0
\(866\) 3.15679 + 9.22435i 0.107272 + 0.313456i
\(867\) 18.7080 + 18.7080i 0.635358 + 0.635358i
\(868\) −17.0668 2.16078i −0.579285 0.0733417i
\(869\) 2.66775i 0.0904971i
\(870\) 0 0
\(871\) 4.77922i 0.161938i
\(872\) −33.3539 + 6.89299i −1.12950 + 0.233426i
\(873\) −14.9641 14.9641i −0.506458 0.506458i
\(874\) −0.149908 + 0.0513022i −0.00507072 + 0.00173532i
\(875\) 0 0
\(876\) −21.5100 27.7461i −0.726754 0.937455i
\(877\) −19.6457 + 19.6457i −0.663389 + 0.663389i −0.956177 0.292789i \(-0.905417\pi\)
0.292789 + 0.956177i \(0.405417\pi\)
\(878\) 41.6330 + 20.4029i 1.40505 + 0.688564i
\(879\) 6.00606 0.202579
\(880\) 0 0
\(881\) −3.05077 −0.102783 −0.0513915 0.998679i \(-0.516366\pi\)
−0.0513915 + 0.998679i \(0.516366\pi\)
\(882\) −7.34907 3.60152i −0.247456 0.121269i
\(883\) −15.9128 + 15.9128i −0.535509 + 0.535509i −0.922207 0.386697i \(-0.873616\pi\)
0.386697 + 0.922207i \(0.373616\pi\)
\(884\) 21.1710 + 27.3089i 0.712058 + 0.918498i
\(885\) 0 0
\(886\) −16.1099 + 5.51319i −0.541223 + 0.185219i
\(887\) 27.6148 + 27.6148i 0.927215 + 0.927215i 0.997525 0.0703102i \(-0.0223989\pi\)
−0.0703102 + 0.997525i \(0.522399\pi\)
\(888\) −15.0056 + 3.10110i −0.503556 + 0.104066i
\(889\) 3.12921i 0.104950i
\(890\) 0 0
\(891\) 1.53211i 0.0513277i
\(892\) 55.4522 + 7.02064i 1.85668 + 0.235068i
\(893\) 4.29131 + 4.29131i 0.143603 + 0.143603i
\(894\) 15.2598 + 44.5901i 0.510364 + 1.49132i
\(895\) 0 0
\(896\) −7.60626 8.37525i −0.254107 0.279798i
\(897\) −1.62639 + 1.62639i −0.0543037 + 0.0543037i
\(898\) 3.44086 7.02124i 0.114823 0.234302i
\(899\) −34.6725 −1.15639
\(900\) 0 0
\(901\) −11.1485 −0.371411
\(902\) 0.389867 0.795543i 0.0129812 0.0264887i
\(903\) −6.10965 + 6.10965i −0.203317 + 0.203317i
\(904\) 6.90903 10.5086i 0.229791 0.349511i
\(905\) 0 0
\(906\) 12.3263 + 36.0184i 0.409516 + 1.19663i
\(907\) 34.9739 + 34.9739i 1.16129 + 1.16129i 0.984193 + 0.177098i \(0.0566708\pi\)
0.177098 + 0.984193i \(0.443329\pi\)
\(908\) 5.24297 41.4113i 0.173994 1.37428i
\(909\) 87.9310i 2.91649i
\(910\) 0 0
\(911\) 29.9032i 0.990736i 0.868683 + 0.495368i \(0.164967\pi\)
−0.868683 + 0.495368i \(0.835033\pi\)
\(912\) 5.29395 + 8.96276i 0.175300 + 0.296786i
\(913\) −1.14062 1.14062i −0.0377489 0.0377489i
\(914\) 36.1413 12.3684i 1.19545 0.409111i
\(915\) 0 0
\(916\) 5.14994 3.99245i 0.170159 0.131914i
\(917\) 2.62896 2.62896i 0.0868159 0.0868159i
\(918\) −29.8129 14.6103i −0.983973 0.482210i
\(919\) −46.1221 −1.52143 −0.760714 0.649087i \(-0.775151\pi\)
−0.760714 + 0.649087i \(0.775151\pi\)
\(920\) 0 0
\(921\) −6.33172 −0.208637
\(922\) 10.4754 + 5.13361i 0.344988 + 0.169066i
\(923\) 7.52519 7.52519i 0.247695 0.247695i
\(924\) 1.00701 0.780675i 0.0331282 0.0256823i
\(925\) 0 0
\(926\) 29.3080 10.0299i 0.963122 0.329603i
\(927\) −6.30250 6.30250i −0.207001 0.207001i
\(928\) −17.3291 14.8210i −0.568857 0.486523i
\(929\) 36.7649i 1.20622i −0.797659 0.603108i \(-0.793929\pi\)
0.797659 0.603108i \(-0.206071\pi\)
\(930\) 0 0
\(931\) 0.877903i 0.0287721i
\(932\) 1.73551 13.7078i 0.0568484 0.449014i
\(933\) 26.7163 + 26.7163i 0.874652 + 0.874652i
\(934\) −17.9908 52.5701i −0.588675 1.72015i
\(935\) 0 0
\(936\) 83.1566 + 54.6725i 2.71806 + 1.78703i
\(937\) −25.1593 + 25.1593i −0.821917 + 0.821917i −0.986383 0.164465i \(-0.947410\pi\)
0.164465 + 0.986383i \(0.447410\pi\)
\(938\) −0.489193 + 0.998221i −0.0159727 + 0.0325931i
\(939\) 60.3571 1.96968
\(940\) 0 0
\(941\) −25.6403 −0.835851 −0.417926 0.908481i \(-0.637243\pi\)
−0.417926 + 0.908481i \(0.637243\pi\)
\(942\) 38.6402 78.8472i 1.25897 2.56898i
\(943\) 0.263032 0.263032i 0.00856550 0.00856550i
\(944\) −10.4593 + 40.6438i −0.340420 + 1.32284i
\(945\) 0 0
\(946\) −0.286856 0.838211i −0.00932649 0.0272526i
\(947\) 2.04606 + 2.04606i 0.0664879 + 0.0664879i 0.739569 0.673081i \(-0.235029\pi\)
−0.673081 + 0.739569i \(0.735029\pi\)
\(948\) 73.0071 + 9.24323i 2.37116 + 0.300206i
\(949\) 36.0042i 1.16874i
\(950\) 0 0
\(951\) 29.3088i 0.950404i
\(952\) −1.62663 7.87095i −0.0527193 0.255099i
\(953\) 29.4048 + 29.4048i 0.952513 + 0.952513i 0.998923 0.0464091i \(-0.0147778\pi\)
−0.0464091 + 0.998923i \(0.514778\pi\)
\(954\) −30.3791 + 10.3965i −0.983561 + 0.336598i
\(955\) 0 0
\(956\) 12.5932 + 16.2442i 0.407293 + 0.525376i
\(957\) 1.81591 1.81591i 0.0587000 0.0587000i
\(958\) 4.91097 + 2.40669i 0.158666 + 0.0777567i
\(959\) 2.61574 0.0844668
\(960\) 0 0
\(961\) −42.9862 −1.38665
\(962\) 14.1108 + 6.91519i 0.454950 + 0.222955i
\(963\) 56.0492 56.0492i 1.80616 1.80616i
\(964\) 5.86774 + 7.56891i 0.188987 + 0.243778i
\(965\) 0 0
\(966\) 0.506174 0.173225i 0.0162859 0.00557342i
\(967\) 33.9934 + 33.9934i 1.09315 + 1.09315i 0.995190 + 0.0979625i \(0.0312325\pi\)
0.0979625 + 0.995190i \(0.468767\pi\)
\(968\) −6.27032 30.3409i −0.201536 0.975194i
\(969\) 7.39489i 0.237558i
\(970\) 0 0
\(971\) 13.5798i 0.435796i 0.975972 + 0.217898i \(0.0699200\pi\)
−0.975972 + 0.217898i \(0.930080\pi\)
\(972\) 7.24844 + 0.917705i 0.232494 + 0.0294354i
\(973\) −7.71250 7.71250i −0.247251 0.247251i
\(974\) −0.203827 0.595596i −0.00653104 0.0190841i
\(975\) 0 0
\(976\) 8.30087 32.2565i 0.265704 1.03251i
\(977\) 29.3429 29.3429i 0.938764 0.938764i −0.0594666 0.998230i \(-0.518940\pi\)
0.998230 + 0.0594666i \(0.0189400\pi\)
\(978\) −29.3359 + 59.8614i −0.938060 + 1.91416i
\(979\) −2.73827 −0.0875155
\(980\) 0 0
\(981\) −69.6851 −2.22487
\(982\) 25.1576 51.3352i 0.802810 1.63817i
\(983\) 1.45861 1.45861i 0.0465225 0.0465225i −0.683463 0.729985i \(-0.739527\pi\)
0.729985 + 0.683463i \(0.239527\pi\)
\(984\) −20.4205 13.4257i −0.650981 0.427997i
\(985\) 0 0
\(986\) −5.24505 15.3264i −0.167037 0.488092i
\(987\) −14.4899 14.4899i −0.461217 0.461217i
\(988\) 1.34087 10.5908i 0.0426589 0.336939i
\(989\) 0.371983i 0.0118284i
\(990\) 0 0
\(991\) 29.9628i 0.951798i 0.879500 + 0.475899i \(0.157877\pi\)
−0.879500 + 0.475899i \(0.842123\pi\)
\(992\) −36.9779 31.6258i −1.17405 1.00412i
\(993\) −61.5205 61.5205i −1.95229 1.95229i
\(994\) −2.34203 + 0.801498i −0.0742846 + 0.0254220i
\(995\) 0 0
\(996\) −35.1668 + 27.2628i −1.11430 + 0.863855i
\(997\) 41.4242 41.4242i 1.31192 1.31192i 0.391919 0.920000i \(-0.371811\pi\)
0.920000 0.391919i \(-0.128189\pi\)
\(998\) −40.3674 19.7826i −1.27781 0.626209i
\(999\) −15.0985 −0.477696
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 700.2.k.b.43.4 36
4.3 odd 2 inner 700.2.k.b.43.12 36
5.2 odd 4 inner 700.2.k.b.407.12 36
5.3 odd 4 140.2.k.a.127.7 yes 36
5.4 even 2 140.2.k.a.43.15 yes 36
20.3 even 4 140.2.k.a.127.15 yes 36
20.7 even 4 inner 700.2.k.b.407.4 36
20.19 odd 2 140.2.k.a.43.7 36
35.3 even 12 980.2.x.l.667.6 72
35.4 even 6 980.2.x.k.863.4 72
35.9 even 6 980.2.x.k.263.10 72
35.13 even 4 980.2.k.l.687.7 36
35.18 odd 12 980.2.x.k.667.6 72
35.19 odd 6 980.2.x.l.263.10 72
35.23 odd 12 980.2.x.k.67.18 72
35.24 odd 6 980.2.x.l.863.4 72
35.33 even 12 980.2.x.l.67.18 72
35.34 odd 2 980.2.k.l.883.15 36
140.3 odd 12 980.2.x.l.667.10 72
140.19 even 6 980.2.x.l.263.6 72
140.23 even 12 980.2.x.k.67.4 72
140.39 odd 6 980.2.x.k.863.18 72
140.59 even 6 980.2.x.l.863.18 72
140.79 odd 6 980.2.x.k.263.6 72
140.83 odd 4 980.2.k.l.687.15 36
140.103 odd 12 980.2.x.l.67.4 72
140.123 even 12 980.2.x.k.667.10 72
140.139 even 2 980.2.k.l.883.7 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.k.a.43.7 36 20.19 odd 2
140.2.k.a.43.15 yes 36 5.4 even 2
140.2.k.a.127.7 yes 36 5.3 odd 4
140.2.k.a.127.15 yes 36 20.3 even 4
700.2.k.b.43.4 36 1.1 even 1 trivial
700.2.k.b.43.12 36 4.3 odd 2 inner
700.2.k.b.407.4 36 20.7 even 4 inner
700.2.k.b.407.12 36 5.2 odd 4 inner
980.2.k.l.687.7 36 35.13 even 4
980.2.k.l.687.15 36 140.83 odd 4
980.2.k.l.883.7 36 140.139 even 2
980.2.k.l.883.15 36 35.34 odd 2
980.2.x.k.67.4 72 140.23 even 12
980.2.x.k.67.18 72 35.23 odd 12
980.2.x.k.263.6 72 140.79 odd 6
980.2.x.k.263.10 72 35.9 even 6
980.2.x.k.667.6 72 35.18 odd 12
980.2.x.k.667.10 72 140.123 even 12
980.2.x.k.863.4 72 35.4 even 6
980.2.x.k.863.18 72 140.39 odd 6
980.2.x.l.67.4 72 140.103 odd 12
980.2.x.l.67.18 72 35.33 even 12
980.2.x.l.263.6 72 140.19 even 6
980.2.x.l.263.10 72 35.19 odd 6
980.2.x.l.667.6 72 35.3 even 12
980.2.x.l.667.10 72 140.3 odd 12
980.2.x.l.863.4 72 35.24 odd 6
980.2.x.l.863.18 72 140.59 even 6