Properties

Label 930.2.r.a.119.9
Level $930$
Weight $2$
Character 930.119
Analytic conductor $7.426$
Analytic rank $0$
Dimension $64$
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] = [930,2,Mod(119,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.119");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.r (of order \(6\), 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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 119.9
Character \(\chi\) \(=\) 930.119
Dual form 930.2.r.a.719.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-1.24050 - 1.20878i) q^{3} +1.00000 q^{4} +(-0.280722 - 2.21838i) q^{5} +(1.24050 + 1.20878i) q^{6} +(2.19151 + 1.26527i) q^{7} -1.00000 q^{8} +(0.0776784 + 2.99899i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-1.24050 - 1.20878i) q^{3} +1.00000 q^{4} +(-0.280722 - 2.21838i) q^{5} +(1.24050 + 1.20878i) q^{6} +(2.19151 + 1.26527i) q^{7} -1.00000 q^{8} +(0.0776784 + 2.99899i) q^{9} +(0.280722 + 2.21838i) q^{10} +(-0.583678 - 1.01096i) q^{11} +(-1.24050 - 1.20878i) q^{12} +(-3.18182 - 5.51107i) q^{13} +(-2.19151 - 1.26527i) q^{14} +(-2.33331 + 3.09123i) q^{15} +1.00000 q^{16} +(3.41739 + 1.97303i) q^{17} +(-0.0776784 - 2.99899i) q^{18} +(1.33594 - 2.31391i) q^{19} +(-0.280722 - 2.21838i) q^{20} +(-1.18913 - 4.21863i) q^{21} +(0.583678 + 1.01096i) q^{22} -2.97331i q^{23} +(1.24050 + 1.20878i) q^{24} +(-4.84239 + 1.24549i) q^{25} +(3.18182 + 5.51107i) q^{26} +(3.52878 - 3.81415i) q^{27} +(2.19151 + 1.26527i) q^{28} +4.97367 q^{29} +(2.33331 - 3.09123i) q^{30} +(-1.00997 - 5.47540i) q^{31} -1.00000 q^{32} +(-0.497981 + 1.95964i) q^{33} +(-3.41739 - 1.97303i) q^{34} +(2.19164 - 5.21678i) q^{35} +(0.0776784 + 2.99899i) q^{36} +(-2.60353 + 4.50944i) q^{37} +(-1.33594 + 2.31391i) q^{38} +(-2.71466 + 10.6826i) q^{39} +(0.280722 + 2.21838i) q^{40} +(-0.504431 + 0.291233i) q^{41} +(1.18913 + 4.21863i) q^{42} +(-0.106364 + 0.184228i) q^{43} +(-0.583678 - 1.01096i) q^{44} +(6.63109 - 1.01420i) q^{45} +2.97331i q^{46} -2.60049 q^{47} +(-1.24050 - 1.20878i) q^{48} +(-0.298188 - 0.516477i) q^{49} +(4.84239 - 1.24549i) q^{50} +(-1.85430 - 6.57843i) q^{51} +(-3.18182 - 5.51107i) q^{52} +(-5.05784 + 2.92015i) q^{53} +(-3.52878 + 3.81415i) q^{54} +(-2.07884 + 1.57862i) q^{55} +(-2.19151 - 1.26527i) q^{56} +(-4.45425 + 1.25555i) q^{57} -4.97367 q^{58} +(-10.0172 - 5.78341i) q^{59} +(-2.33331 + 3.09123i) q^{60} -7.81867i q^{61} +(1.00997 + 5.47540i) q^{62} +(-3.62430 + 6.67061i) q^{63} +1.00000 q^{64} +(-11.3324 + 8.60555i) q^{65} +(0.497981 - 1.95964i) q^{66} +(-2.19629 + 1.26803i) q^{67} +(3.41739 + 1.97303i) q^{68} +(-3.59410 + 3.68839i) q^{69} +(-2.19164 + 5.21678i) q^{70} +(-13.2612 + 7.65636i) q^{71} +(-0.0776784 - 2.99899i) q^{72} +(3.80528 + 6.59093i) q^{73} +(2.60353 - 4.50944i) q^{74} +(7.51252 + 4.30838i) q^{75} +(1.33594 - 2.31391i) q^{76} -2.95404i q^{77} +(2.71466 - 10.6826i) q^{78} +(-9.30890 - 5.37450i) q^{79} +(-0.280722 - 2.21838i) q^{80} +(-8.98793 + 0.465914i) q^{81} +(0.504431 - 0.291233i) q^{82} +(2.79531 - 1.61388i) q^{83} +(-1.18913 - 4.21863i) q^{84} +(3.41759 - 8.13493i) q^{85} +(0.106364 - 0.184228i) q^{86} +(-6.16983 - 6.01209i) q^{87} +(0.583678 + 1.01096i) q^{88} +12.6584 q^{89} +(-6.63109 + 1.01420i) q^{90} -16.1034i q^{91} -2.97331i q^{92} +(-5.36571 + 8.01306i) q^{93} +2.60049 q^{94} +(-5.50816 - 2.31405i) q^{95} +(1.24050 + 1.20878i) q^{96} -11.6154i q^{97} +(0.298188 + 0.516477i) q^{98} +(2.98652 - 1.82898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} - 6 q^{17} + 4 q^{18} + 4 q^{19} - 2 q^{20} + 2 q^{25} + 18 q^{31} - 64 q^{32} + 8 q^{33} + 6 q^{34} - 16 q^{35} - 4 q^{36} - 4 q^{38} - 8 q^{39} + 2 q^{40} + 5 q^{45} + 4 q^{47} + 30 q^{49} - 2 q^{50} - 8 q^{51} + 6 q^{53} - 6 q^{57} - 18 q^{62} - 12 q^{63} + 64 q^{64} - 8 q^{66} - 6 q^{68} - 10 q^{69} + 16 q^{70} + 4 q^{72} + 15 q^{75} + 4 q^{76} + 8 q^{78} - 30 q^{79} - 2 q^{80} - 12 q^{81} + 54 q^{83} + 16 q^{87} - 5 q^{90} + 18 q^{93} - 4 q^{94} + 56 q^{95} - 30 q^{98} - 102 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.24050 1.20878i −0.716203 0.697892i
\(4\) 1.00000 0.500000
\(5\) −0.280722 2.21838i −0.125543 0.992088i
\(6\) 1.24050 + 1.20878i 0.506432 + 0.493484i
\(7\) 2.19151 + 1.26527i 0.828313 + 0.478227i 0.853275 0.521462i \(-0.174613\pi\)
−0.0249617 + 0.999688i \(0.507946\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.0776784 + 2.99899i 0.0258928 + 0.999665i
\(10\) 0.280722 + 2.21838i 0.0887720 + 0.701512i
\(11\) −0.583678 1.01096i −0.175986 0.304816i 0.764516 0.644604i \(-0.222978\pi\)
−0.940502 + 0.339788i \(0.889645\pi\)
\(12\) −1.24050 1.20878i −0.358101 0.348946i
\(13\) −3.18182 5.51107i −0.882478 1.52850i −0.848577 0.529072i \(-0.822540\pi\)
−0.0339011 0.999425i \(-0.510793\pi\)
\(14\) −2.19151 1.26527i −0.585706 0.338157i
\(15\) −2.33331 + 3.09123i −0.602457 + 0.798152i
\(16\) 1.00000 0.250000
\(17\) 3.41739 + 1.97303i 0.828839 + 0.478530i 0.853455 0.521167i \(-0.174503\pi\)
−0.0246160 + 0.999697i \(0.507836\pi\)
\(18\) −0.0776784 2.99899i −0.0183090 0.706870i
\(19\) 1.33594 2.31391i 0.306485 0.530848i −0.671106 0.741362i \(-0.734180\pi\)
0.977591 + 0.210514i \(0.0675137\pi\)
\(20\) −0.280722 2.21838i −0.0627713 0.496044i
\(21\) −1.18913 4.21863i −0.259489 0.920581i
\(22\) 0.583678 + 1.01096i 0.124441 + 0.215537i
\(23\) 2.97331i 0.619979i −0.950740 0.309989i \(-0.899675\pi\)
0.950740 0.309989i \(-0.100325\pi\)
\(24\) 1.24050 + 1.20878i 0.253216 + 0.246742i
\(25\) −4.84239 + 1.24549i −0.968478 + 0.249099i
\(26\) 3.18182 + 5.51107i 0.624006 + 1.08081i
\(27\) 3.52878 3.81415i 0.679114 0.734033i
\(28\) 2.19151 + 1.26527i 0.414157 + 0.239113i
\(29\) 4.97367 0.923586 0.461793 0.886988i \(-0.347206\pi\)
0.461793 + 0.886988i \(0.347206\pi\)
\(30\) 2.33331 3.09123i 0.426001 0.564378i
\(31\) −1.00997 5.47540i −0.181395 0.983410i
\(32\) −1.00000 −0.176777
\(33\) −0.497981 + 1.95964i −0.0866873 + 0.341129i
\(34\) −3.41739 1.97303i −0.586078 0.338372i
\(35\) 2.19164 5.21678i 0.370455 0.881797i
\(36\) 0.0776784 + 2.99899i 0.0129464 + 0.499832i
\(37\) −2.60353 + 4.50944i −0.428017 + 0.741348i −0.996697 0.0812114i \(-0.974121\pi\)
0.568680 + 0.822559i \(0.307454\pi\)
\(38\) −1.33594 + 2.31391i −0.216718 + 0.375366i
\(39\) −2.71466 + 10.6826i −0.434693 + 1.71059i
\(40\) 0.280722 + 2.21838i 0.0443860 + 0.350756i
\(41\) −0.504431 + 0.291233i −0.0787789 + 0.0454830i −0.538872 0.842388i \(-0.681149\pi\)
0.460093 + 0.887871i \(0.347816\pi\)
\(42\) 1.18913 + 4.21863i 0.183487 + 0.650949i
\(43\) −0.106364 + 0.184228i −0.0162204 + 0.0280945i −0.874022 0.485887i \(-0.838497\pi\)
0.857801 + 0.513981i \(0.171830\pi\)
\(44\) −0.583678 1.01096i −0.0879928 0.152408i
\(45\) 6.63109 1.01420i 0.988505 0.151188i
\(46\) 2.97331i 0.438391i
\(47\) −2.60049 −0.379320 −0.189660 0.981850i \(-0.560739\pi\)
−0.189660 + 0.981850i \(0.560739\pi\)
\(48\) −1.24050 1.20878i −0.179051 0.174473i
\(49\) −0.298188 0.516477i −0.0425983 0.0737825i
\(50\) 4.84239 1.24549i 0.684817 0.176139i
\(51\) −1.85430 6.57843i −0.259654 0.921165i
\(52\) −3.18182 5.51107i −0.441239 0.764249i
\(53\) −5.05784 + 2.92015i −0.694748 + 0.401113i −0.805388 0.592748i \(-0.798043\pi\)
0.110640 + 0.993861i \(0.464710\pi\)
\(54\) −3.52878 + 3.81415i −0.480206 + 0.519040i
\(55\) −2.07884 + 1.57862i −0.280311 + 0.212861i
\(56\) −2.19151 1.26527i −0.292853 0.169079i
\(57\) −4.45425 + 1.25555i −0.589980 + 0.166301i
\(58\) −4.97367 −0.653074
\(59\) −10.0172 5.78341i −1.30412 0.752936i −0.323015 0.946394i \(-0.604696\pi\)
−0.981109 + 0.193458i \(0.938030\pi\)
\(60\) −2.33331 + 3.09123i −0.301228 + 0.399076i
\(61\) 7.81867i 1.00108i −0.865714 0.500539i \(-0.833135\pi\)
0.865714 0.500539i \(-0.166865\pi\)
\(62\) 1.00997 + 5.47540i 0.128266 + 0.695376i
\(63\) −3.62430 + 6.67061i −0.456619 + 0.840418i
\(64\) 1.00000 0.125000
\(65\) −11.3324 + 8.60555i −1.40562 + 1.06739i
\(66\) 0.497981 1.95964i 0.0612972 0.241215i
\(67\) −2.19629 + 1.26803i −0.268320 + 0.154914i −0.628124 0.778113i \(-0.716177\pi\)
0.359804 + 0.933028i \(0.382844\pi\)
\(68\) 3.41739 + 1.97303i 0.414419 + 0.239265i
\(69\) −3.59410 + 3.68839i −0.432678 + 0.444030i
\(70\) −2.19164 + 5.21678i −0.261951 + 0.623525i
\(71\) −13.2612 + 7.65636i −1.57381 + 0.908642i −0.578120 + 0.815952i \(0.696213\pi\)
−0.995695 + 0.0926906i \(0.970453\pi\)
\(72\) −0.0776784 2.99899i −0.00915449 0.353435i
\(73\) 3.80528 + 6.59093i 0.445374 + 0.771410i 0.998078 0.0619672i \(-0.0197374\pi\)
−0.552704 + 0.833377i \(0.686404\pi\)
\(74\) 2.60353 4.50944i 0.302654 0.524212i
\(75\) 7.51252 + 4.30838i 0.867471 + 0.497488i
\(76\) 1.33594 2.31391i 0.153243 0.265424i
\(77\) 2.95404i 0.336644i
\(78\) 2.71466 10.6826i 0.307374 1.20957i
\(79\) −9.30890 5.37450i −1.04733 0.604678i −0.125432 0.992102i \(-0.540032\pi\)
−0.921902 + 0.387424i \(0.873365\pi\)
\(80\) −0.280722 2.21838i −0.0313856 0.248022i
\(81\) −8.98793 + 0.465914i −0.998659 + 0.0517682i
\(82\) 0.504431 0.291233i 0.0557051 0.0321613i
\(83\) 2.79531 1.61388i 0.306826 0.177146i −0.338680 0.940902i \(-0.609980\pi\)
0.645505 + 0.763756i \(0.276647\pi\)
\(84\) −1.18913 4.21863i −0.129745 0.460290i
\(85\) 3.41759 8.13493i 0.370690 0.882357i
\(86\) 0.106364 0.184228i 0.0114695 0.0198658i
\(87\) −6.16983 6.01209i −0.661475 0.644564i
\(88\) 0.583678 + 1.01096i 0.0622203 + 0.107769i
\(89\) 12.6584 1.34179 0.670894 0.741553i \(-0.265911\pi\)
0.670894 + 0.741553i \(0.265911\pi\)
\(90\) −6.63109 + 1.01420i −0.698979 + 0.106906i
\(91\) 16.1034i 1.68810i
\(92\) 2.97331i 0.309989i
\(93\) −5.36571 + 8.01306i −0.556399 + 0.830916i
\(94\) 2.60049 0.268220
\(95\) −5.50816 2.31405i −0.565125 0.237416i
\(96\) 1.24050 + 1.20878i 0.126608 + 0.123371i
\(97\) 11.6154i 1.17937i −0.807635 0.589683i \(-0.799253\pi\)
0.807635 0.589683i \(-0.200747\pi\)
\(98\) 0.298188 + 0.516477i 0.0301216 + 0.0521721i
\(99\) 2.98652 1.82898i 0.300157 0.183819i
\(100\) −4.84239 + 1.24549i −0.484239 + 0.124549i
\(101\) 2.60547i 0.259254i 0.991563 + 0.129627i \(0.0413781\pi\)
−0.991563 + 0.129627i \(0.958622\pi\)
\(102\) 1.85430 + 6.57843i 0.183603 + 0.651362i
\(103\) −11.9006 + 6.87079i −1.17260 + 0.676999i −0.954290 0.298881i \(-0.903387\pi\)
−0.218306 + 0.975880i \(0.570053\pi\)
\(104\) 3.18182 + 5.51107i 0.312003 + 0.540405i
\(105\) −9.02470 + 3.82220i −0.880720 + 0.373008i
\(106\) 5.05784 2.92015i 0.491261 0.283630i
\(107\) −1.02068 + 1.76788i −0.0986733 + 0.170907i −0.911136 0.412106i \(-0.864793\pi\)
0.812462 + 0.583014i \(0.198127\pi\)
\(108\) 3.52878 3.81415i 0.339557 0.367017i
\(109\) 5.29320 0.506997 0.253498 0.967336i \(-0.418419\pi\)
0.253498 + 0.967336i \(0.418419\pi\)
\(110\) 2.07884 1.57862i 0.198209 0.150515i
\(111\) 8.68062 2.44686i 0.823928 0.232245i
\(112\) 2.19151 + 1.26527i 0.207078 + 0.119557i
\(113\) −6.29037 10.8952i −0.591748 1.02494i −0.993997 0.109408i \(-0.965105\pi\)
0.402249 0.915531i \(-0.368229\pi\)
\(114\) 4.45425 1.25555i 0.417179 0.117593i
\(115\) −6.59593 + 0.834673i −0.615073 + 0.0778337i
\(116\) 4.97367 0.461793
\(117\) 16.2805 9.97035i 1.50513 0.921759i
\(118\) 10.0172 + 5.78341i 0.922154 + 0.532406i
\(119\) 4.99283 + 8.64784i 0.457692 + 0.792746i
\(120\) 2.33331 3.09123i 0.213001 0.282189i
\(121\) 4.81864 8.34613i 0.438058 0.758739i
\(122\) 7.81867i 0.707869i
\(123\) 0.977785 + 0.248474i 0.0881639 + 0.0224041i
\(124\) −1.00997 5.47540i −0.0906977 0.491705i
\(125\) 4.12234 + 10.3926i 0.368713 + 0.929543i
\(126\) 3.62430 6.67061i 0.322878 0.594265i
\(127\) −9.47777 + 16.4160i −0.841016 + 1.45668i 0.0480201 + 0.998846i \(0.484709\pi\)
−0.889036 + 0.457837i \(0.848624\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.354636 0.0999633i 0.0312240 0.00880128i
\(130\) 11.3324 8.60555i 0.993920 0.754757i
\(131\) 4.32442 + 2.49670i 0.377826 + 0.218138i 0.676872 0.736101i \(-0.263335\pi\)
−0.299046 + 0.954239i \(0.596668\pi\)
\(132\) −0.497981 + 1.95964i −0.0433437 + 0.170564i
\(133\) 5.85544 3.38064i 0.507731 0.293139i
\(134\) 2.19629 1.26803i 0.189731 0.109541i
\(135\) −9.45182 6.75745i −0.813483 0.581588i
\(136\) −3.41739 1.97303i −0.293039 0.169186i
\(137\) 8.59916 4.96473i 0.734676 0.424165i −0.0854546 0.996342i \(-0.527234\pi\)
0.820130 + 0.572177i \(0.193901\pi\)
\(138\) 3.59410 3.68839i 0.305950 0.313977i
\(139\) 5.27999i 0.447843i 0.974607 + 0.223921i \(0.0718859\pi\)
−0.974607 + 0.223921i \(0.928114\pi\)
\(140\) 2.19164 5.21678i 0.185227 0.440899i
\(141\) 3.22591 + 3.14343i 0.271670 + 0.264725i
\(142\) 13.2612 7.65636i 1.11286 0.642507i
\(143\) −3.71432 + 6.43339i −0.310607 + 0.537987i
\(144\) 0.0776784 + 2.99899i 0.00647320 + 0.249916i
\(145\) −1.39622 11.0335i −0.115949 0.916279i
\(146\) −3.80528 6.59093i −0.314927 0.545469i
\(147\) −0.254408 + 1.00114i −0.0209832 + 0.0825723i
\(148\) −2.60353 + 4.50944i −0.214009 + 0.370674i
\(149\) −13.6758 7.89572i −1.12036 0.646843i −0.178870 0.983873i \(-0.557244\pi\)
−0.941494 + 0.337030i \(0.890578\pi\)
\(150\) −7.51252 4.30838i −0.613394 0.351777i
\(151\) 9.89798i 0.805486i −0.915313 0.402743i \(-0.868057\pi\)
0.915313 0.402743i \(-0.131943\pi\)
\(152\) −1.33594 + 2.31391i −0.108359 + 0.187683i
\(153\) −5.65165 + 10.4020i −0.456909 + 0.840952i
\(154\) 2.95404i 0.238043i
\(155\) −11.8630 + 3.77755i −0.952857 + 0.303420i
\(156\) −2.71466 + 10.6826i −0.217346 + 0.855294i
\(157\) 4.41348i 0.352234i 0.984369 + 0.176117i \(0.0563537\pi\)
−0.984369 + 0.176117i \(0.943646\pi\)
\(158\) 9.30890 + 5.37450i 0.740577 + 0.427572i
\(159\) 9.80408 + 2.49140i 0.777514 + 0.197581i
\(160\) 0.280722 + 2.21838i 0.0221930 + 0.175378i
\(161\) 3.76204 6.51605i 0.296490 0.513536i
\(162\) 8.98793 0.465914i 0.706159 0.0366057i
\(163\) 2.35826i 0.184713i 0.995726 + 0.0923567i \(0.0294400\pi\)
−0.995726 + 0.0923567i \(0.970560\pi\)
\(164\) −0.504431 + 0.291233i −0.0393894 + 0.0227415i
\(165\) 4.48701 + 0.554596i 0.349313 + 0.0431753i
\(166\) −2.79531 + 1.61388i −0.216958 + 0.125261i
\(167\) −3.61526 2.08727i −0.279758 0.161518i 0.353556 0.935413i \(-0.384972\pi\)
−0.633314 + 0.773895i \(0.718306\pi\)
\(168\) 1.18913 + 4.21863i 0.0917433 + 0.325474i
\(169\) −13.7480 + 23.8122i −1.05754 + 1.83171i
\(170\) −3.41759 + 8.13493i −0.262117 + 0.623921i
\(171\) 7.04318 + 3.82673i 0.538606 + 0.292637i
\(172\) −0.106364 + 0.184228i −0.00811018 + 0.0140472i
\(173\) 6.74927 + 11.6901i 0.513137 + 0.888780i 0.999884 + 0.0152367i \(0.00485018\pi\)
−0.486747 + 0.873543i \(0.661816\pi\)
\(174\) 6.16983 + 6.01209i 0.467734 + 0.455775i
\(175\) −12.1880 3.39742i −0.921329 0.256821i
\(176\) −0.583678 1.01096i −0.0439964 0.0762040i
\(177\) 5.43538 + 19.2829i 0.408549 + 1.44939i
\(178\) −12.6584 −0.948787
\(179\) 7.50882 13.0057i 0.561236 0.972089i −0.436153 0.899872i \(-0.643659\pi\)
0.997389 0.0722165i \(-0.0230073\pi\)
\(180\) 6.63109 1.01420i 0.494252 0.0755942i
\(181\) 2.21896 1.28112i 0.164934 0.0952246i −0.415261 0.909702i \(-0.636310\pi\)
0.580195 + 0.814478i \(0.302976\pi\)
\(182\) 16.1034i 1.19367i
\(183\) −9.45108 + 9.69905i −0.698644 + 0.716975i
\(184\) 2.97331i 0.219196i
\(185\) 10.7345 + 4.50971i 0.789217 + 0.331560i
\(186\) 5.36571 8.01306i 0.393433 0.587546i
\(187\) 4.60646i 0.336858i
\(188\) −2.60049 −0.189660
\(189\) 12.5593 3.89389i 0.913553 0.283239i
\(190\) 5.50816 + 2.31405i 0.399604 + 0.167879i
\(191\) −6.67352 + 3.85296i −0.482879 + 0.278791i −0.721616 0.692294i \(-0.756600\pi\)
0.238736 + 0.971084i \(0.423267\pi\)
\(192\) −1.24050 1.20878i −0.0895253 0.0872365i
\(193\) 7.14681 + 4.12622i 0.514439 + 0.297011i 0.734656 0.678439i \(-0.237343\pi\)
−0.220217 + 0.975451i \(0.570677\pi\)
\(194\) 11.6154i 0.833938i
\(195\) 24.4601 + 3.02329i 1.75163 + 0.216502i
\(196\) −0.298188 0.516477i −0.0212992 0.0368912i
\(197\) 22.0501 12.7306i 1.57100 0.907020i 0.574958 0.818183i \(-0.305018\pi\)
0.996046 0.0888373i \(-0.0283151\pi\)
\(198\) −2.98652 + 1.82898i −0.212243 + 0.129980i
\(199\) −15.1490 + 8.74625i −1.07388 + 0.620006i −0.929239 0.369479i \(-0.879536\pi\)
−0.144642 + 0.989484i \(0.546203\pi\)
\(200\) 4.84239 1.24549i 0.342409 0.0880696i
\(201\) 4.25727 + 1.08185i 0.300285 + 0.0763081i
\(202\) 2.60547i 0.183321i
\(203\) 10.8998 + 6.29302i 0.765019 + 0.441684i
\(204\) −1.85430 6.57843i −0.129827 0.460583i
\(205\) 0.787670 + 1.03726i 0.0550133 + 0.0724455i
\(206\) 11.9006 6.87079i 0.829151 0.478711i
\(207\) 8.91695 0.230962i 0.619771 0.0160530i
\(208\) −3.18182 5.51107i −0.220620 0.382124i
\(209\) −3.11903 −0.215748
\(210\) 9.02470 3.82220i 0.622763 0.263757i
\(211\) 11.6155 20.1187i 0.799647 1.38503i −0.120198 0.992750i \(-0.538353\pi\)
0.919846 0.392280i \(-0.128314\pi\)
\(212\) −5.05784 + 2.92015i −0.347374 + 0.200556i
\(213\) 25.7054 + 6.53223i 1.76131 + 0.447581i
\(214\) 1.02068 1.76788i 0.0697726 0.120850i
\(215\) 0.438545 + 0.184239i 0.0299085 + 0.0125650i
\(216\) −3.52878 + 3.81415i −0.240103 + 0.259520i
\(217\) 4.71450 13.2773i 0.320041 0.901320i
\(218\) −5.29320 −0.358501
\(219\) 3.24658 12.7758i 0.219383 0.863309i
\(220\) −2.07884 + 1.57862i −0.140155 + 0.106430i
\(221\) 25.1113i 1.68917i
\(222\) −8.68062 + 2.44686i −0.582605 + 0.164222i
\(223\) 12.7804 22.1364i 0.855841 1.48236i −0.0200215 0.999800i \(-0.506373\pi\)
0.875863 0.482561i \(-0.160293\pi\)
\(224\) −2.19151 1.26527i −0.146426 0.0845393i
\(225\) −4.11137 14.4256i −0.274092 0.961704i
\(226\) 6.29037 + 10.8952i 0.418429 + 0.724741i
\(227\) −9.83982 17.0431i −0.653092 1.13119i −0.982369 0.186954i \(-0.940138\pi\)
0.329277 0.944233i \(-0.393195\pi\)
\(228\) −4.45425 + 1.25555i −0.294990 + 0.0831506i
\(229\) 0.583432 + 0.336845i 0.0385543 + 0.0222593i 0.519153 0.854681i \(-0.326247\pi\)
−0.480599 + 0.876940i \(0.659581\pi\)
\(230\) 6.59593 0.834673i 0.434923 0.0550367i
\(231\) −3.57080 + 3.66448i −0.234941 + 0.241105i
\(232\) −4.97367 −0.326537
\(233\) 25.5858 1.67618 0.838090 0.545533i \(-0.183673\pi\)
0.838090 + 0.545533i \(0.183673\pi\)
\(234\) −16.2805 + 9.97035i −1.06429 + 0.651782i
\(235\) 0.730014 + 5.76886i 0.0476208 + 0.376319i
\(236\) −10.0172 5.78341i −0.652062 0.376468i
\(237\) 5.05108 + 17.9195i 0.328103 + 1.16400i
\(238\) −4.99283 8.64784i −0.323637 0.560556i
\(239\) 12.1832 + 21.1019i 0.788065 + 1.36497i 0.927151 + 0.374688i \(0.122250\pi\)
−0.139086 + 0.990280i \(0.544416\pi\)
\(240\) −2.33331 + 3.09123i −0.150614 + 0.199538i
\(241\) 22.6146 + 13.0565i 1.45673 + 0.841045i 0.998849 0.0479665i \(-0.0152741\pi\)
0.457884 + 0.889012i \(0.348607\pi\)
\(242\) −4.81864 + 8.34613i −0.309754 + 0.536510i
\(243\) 11.7127 + 10.2865i 0.751371 + 0.659880i
\(244\) 7.81867i 0.500539i
\(245\) −1.06203 + 0.806481i −0.0678508 + 0.0515242i
\(246\) −0.977785 0.248474i −0.0623413 0.0158421i
\(247\) −17.0029 −1.08187
\(248\) 1.00997 + 5.47540i 0.0641329 + 0.347688i
\(249\) −5.41841 1.37692i −0.343378 0.0872589i
\(250\) −4.12234 10.3926i −0.260719 0.657286i
\(251\) 8.56462 14.8344i 0.540594 0.936337i −0.458276 0.888810i \(-0.651533\pi\)
0.998870 0.0475266i \(-0.0151339\pi\)
\(252\) −3.62430 + 6.67061i −0.228310 + 0.420209i
\(253\) −3.00590 + 1.73546i −0.188979 + 0.109107i
\(254\) 9.47777 16.4160i 0.594688 1.03003i
\(255\) −14.0729 + 5.96025i −0.881279 + 0.373245i
\(256\) 1.00000 0.0625000
\(257\) −6.32974 10.9634i −0.394838 0.683880i 0.598242 0.801315i \(-0.295866\pi\)
−0.993081 + 0.117435i \(0.962533\pi\)
\(258\) −0.354636 + 0.0999633i −0.0220787 + 0.00622345i
\(259\) −11.4113 + 6.58833i −0.709065 + 0.409379i
\(260\) −11.3324 + 8.60555i −0.702808 + 0.533694i
\(261\) 0.386346 + 14.9160i 0.0239142 + 0.923277i
\(262\) −4.32442 2.49670i −0.267163 0.154247i
\(263\) 7.65133i 0.471801i 0.971777 + 0.235901i \(0.0758040\pi\)
−0.971777 + 0.235901i \(0.924196\pi\)
\(264\) 0.497981 1.95964i 0.0306486 0.120607i
\(265\) 7.89783 + 10.4004i 0.485160 + 0.638894i
\(266\) −5.85544 + 3.38064i −0.359020 + 0.207280i
\(267\) −15.7027 15.3013i −0.960992 0.936423i
\(268\) −2.19629 + 1.26803i −0.134160 + 0.0774572i
\(269\) 0.846925 + 1.46692i 0.0516379 + 0.0894395i 0.890689 0.454613i \(-0.150222\pi\)
−0.839051 + 0.544053i \(0.816889\pi\)
\(270\) 9.45182 + 6.75745i 0.575219 + 0.411245i
\(271\) 30.2591i 1.83811i −0.394130 0.919055i \(-0.628954\pi\)
0.394130 0.919055i \(-0.371046\pi\)
\(272\) 3.41739 + 1.97303i 0.207210 + 0.119633i
\(273\) −19.4656 + 19.9763i −1.17811 + 1.20902i
\(274\) −8.59916 + 4.96473i −0.519494 + 0.299930i
\(275\) 4.08554 + 4.16850i 0.246367 + 0.251370i
\(276\) −3.59410 + 3.68839i −0.216339 + 0.222015i
\(277\) 32.9288 1.97850 0.989250 0.146235i \(-0.0467155\pi\)
0.989250 + 0.146235i \(0.0467155\pi\)
\(278\) 5.27999i 0.316673i
\(279\) 16.3422 3.45420i 0.978384 0.206798i
\(280\) −2.19164 + 5.21678i −0.130975 + 0.311762i
\(281\) 13.9762i 0.833752i 0.908963 + 0.416876i \(0.136875\pi\)
−0.908963 + 0.416876i \(0.863125\pi\)
\(282\) −3.22591 3.14343i −0.192100 0.187189i
\(283\) 11.4141i 0.678498i −0.940697 0.339249i \(-0.889827\pi\)
0.940697 0.339249i \(-0.110173\pi\)
\(284\) −13.2612 + 7.65636i −0.786907 + 0.454321i
\(285\) 4.03568 + 9.52875i 0.239053 + 0.564435i
\(286\) 3.71432 6.43339i 0.219632 0.380414i
\(287\) −1.47395 −0.0870048
\(288\) −0.0776784 2.99899i −0.00457724 0.176717i
\(289\) −0.714295 1.23719i −0.0420173 0.0727762i
\(290\) 1.39622 + 11.0335i 0.0819886 + 0.647907i
\(291\) −14.0405 + 14.4089i −0.823071 + 0.844666i
\(292\) 3.80528 + 6.59093i 0.222687 + 0.385705i
\(293\) 2.33280 4.04052i 0.136283 0.236050i −0.789804 0.613360i \(-0.789818\pi\)
0.926087 + 0.377310i \(0.123151\pi\)
\(294\) 0.254408 1.00114i 0.0148374 0.0583874i
\(295\) −10.0177 + 23.8454i −0.583256 + 1.38833i
\(296\) 2.60353 4.50944i 0.151327 0.262106i
\(297\) −5.91562 1.34122i −0.343259 0.0778255i
\(298\) 13.6758 + 7.89572i 0.792217 + 0.457387i
\(299\) −16.3861 + 9.46055i −0.947635 + 0.547118i
\(300\) 7.51252 + 4.30838i 0.433735 + 0.248744i
\(301\) −0.466195 + 0.269158i −0.0268711 + 0.0155140i
\(302\) 9.89798i 0.569565i
\(303\) 3.14946 3.23209i 0.180932 0.185679i
\(304\) 1.33594 2.31391i 0.0766213 0.132712i
\(305\) −17.3447 + 2.19487i −0.993157 + 0.125678i
\(306\) 5.65165 10.4020i 0.323083 0.594643i
\(307\) −6.69856 3.86742i −0.382307 0.220725i 0.296514 0.955028i \(-0.404176\pi\)
−0.678822 + 0.734303i \(0.737509\pi\)
\(308\) 2.95404i 0.168322i
\(309\) 23.0679 + 5.86200i 1.31229 + 0.333478i
\(310\) 11.8630 3.77755i 0.673772 0.214550i
\(311\) 3.48291i 0.197498i 0.995112 + 0.0987489i \(0.0314840\pi\)
−0.995112 + 0.0987489i \(0.968516\pi\)
\(312\) 2.71466 10.6826i 0.153687 0.604784i
\(313\) 0.752791 1.30387i 0.0425503 0.0736993i −0.843966 0.536397i \(-0.819785\pi\)
0.886516 + 0.462698i \(0.153118\pi\)
\(314\) 4.41348i 0.249067i
\(315\) 15.8153 + 6.16748i 0.891094 + 0.347498i
\(316\) −9.30890 5.37450i −0.523667 0.302339i
\(317\) 8.17705 14.1631i 0.459269 0.795477i −0.539653 0.841887i \(-0.681445\pi\)
0.998922 + 0.0464099i \(0.0147780\pi\)
\(318\) −9.80408 2.49140i −0.549785 0.139711i
\(319\) −2.90302 5.02818i −0.162538 0.281524i
\(320\) −0.280722 2.21838i −0.0156928 0.124011i
\(321\) 3.40314 0.959263i 0.189945 0.0535409i
\(322\) −3.76204 + 6.51605i −0.209650 + 0.363125i
\(323\) 9.13085 5.27170i 0.508054 0.293325i
\(324\) −8.98793 + 0.465914i −0.499330 + 0.0258841i
\(325\) 22.2716 + 22.7238i 1.23541 + 1.26049i
\(326\) 2.35826i 0.130612i
\(327\) −6.56622 6.39834i −0.363113 0.353829i
\(328\) 0.504431 0.291233i 0.0278525 0.0160807i
\(329\) −5.69900 3.29032i −0.314196 0.181401i
\(330\) −4.48701 0.554596i −0.247002 0.0305295i
\(331\) 7.86876 4.54303i 0.432506 0.249707i −0.267908 0.963445i \(-0.586332\pi\)
0.700414 + 0.713737i \(0.252999\pi\)
\(332\) 2.79531 1.61388i 0.153413 0.0885729i
\(333\) −13.7260 7.45768i −0.752182 0.408678i
\(334\) 3.61526 + 2.08727i 0.197818 + 0.114211i
\(335\) 3.42951 + 4.51624i 0.187374 + 0.246748i
\(336\) −1.18913 4.21863i −0.0648723 0.230145i
\(337\) −30.3494 −1.65324 −0.826619 0.562762i \(-0.809739\pi\)
−0.826619 + 0.562762i \(0.809739\pi\)
\(338\) 13.7480 23.8122i 0.747790 1.29521i
\(339\) −5.36680 + 21.1193i −0.291485 + 1.14704i
\(340\) 3.41759 8.13493i 0.185345 0.441179i
\(341\) −4.94591 + 4.21690i −0.267836 + 0.228358i
\(342\) −7.04318 3.82673i −0.380852 0.206926i
\(343\) 19.2229i 1.03794i
\(344\) 0.106364 0.184228i 0.00573476 0.00993290i
\(345\) 9.19119 + 6.93765i 0.494837 + 0.373510i
\(346\) −6.74927 11.6901i −0.362843 0.628462i
\(347\) 8.16914 + 4.71646i 0.438542 + 0.253193i 0.702979 0.711210i \(-0.251853\pi\)
−0.264437 + 0.964403i \(0.585186\pi\)
\(348\) −6.16983 6.01209i −0.330738 0.322282i
\(349\) −5.45162 −0.291819 −0.145909 0.989298i \(-0.546611\pi\)
−0.145909 + 0.989298i \(0.546611\pi\)
\(350\) 12.1880 + 3.39742i 0.651478 + 0.181600i
\(351\) −32.2480 7.31143i −1.72127 0.390255i
\(352\) 0.583678 + 1.01096i 0.0311101 + 0.0538843i
\(353\) −20.6931 11.9472i −1.10138 0.635883i −0.164798 0.986327i \(-0.552697\pi\)
−0.936584 + 0.350444i \(0.886031\pi\)
\(354\) −5.43538 19.2829i −0.288887 1.02488i
\(355\) 20.7074 + 27.2690i 1.09903 + 1.44729i
\(356\) 12.6584 0.670894
\(357\) 4.25977 16.7629i 0.225451 0.887187i
\(358\) −7.50882 + 13.0057i −0.396854 + 0.687371i
\(359\) 7.81527 4.51215i 0.412474 0.238142i −0.279378 0.960181i \(-0.590128\pi\)
0.691852 + 0.722039i \(0.256795\pi\)
\(360\) −6.63109 + 1.01420i −0.349489 + 0.0534532i
\(361\) 5.93054 + 10.2720i 0.312134 + 0.540631i
\(362\) −2.21896 + 1.28112i −0.116626 + 0.0673339i
\(363\) −16.0662 + 4.52867i −0.843257 + 0.237694i
\(364\) 16.1034i 0.844049i
\(365\) 13.5529 10.2918i 0.709394 0.538695i
\(366\) 9.45108 9.69905i 0.494016 0.506978i
\(367\) 15.7765 + 27.3257i 0.823525 + 1.42639i 0.903041 + 0.429554i \(0.141329\pi\)
−0.0795162 + 0.996834i \(0.525338\pi\)
\(368\) 2.97331i 0.154995i
\(369\) −0.912590 1.49016i −0.0475076 0.0775748i
\(370\) −10.7345 4.50971i −0.558061 0.234449i
\(371\) −14.7791 −0.767292
\(372\) −5.36571 + 8.01306i −0.278199 + 0.415458i
\(373\) 9.79690i 0.507264i 0.967301 + 0.253632i \(0.0816253\pi\)
−0.967301 + 0.253632i \(0.918375\pi\)
\(374\) 4.60646i 0.238194i
\(375\) 7.44867 17.8750i 0.384648 0.923063i
\(376\) 2.60049 0.134110
\(377\) −15.8253 27.4102i −0.815045 1.41170i
\(378\) −12.5593 + 3.89389i −0.645980 + 0.200280i
\(379\) −10.2994 + 17.8392i −0.529047 + 0.916336i 0.470379 + 0.882464i \(0.344117\pi\)
−0.999426 + 0.0338717i \(0.989216\pi\)
\(380\) −5.50816 2.31405i −0.282563 0.118708i
\(381\) 31.6006 8.90743i 1.61895 0.456342i
\(382\) 6.67352 3.85296i 0.341447 0.197135i
\(383\) 25.4503 14.6938i 1.30045 0.750816i 0.319970 0.947428i \(-0.396327\pi\)
0.980481 + 0.196612i \(0.0629939\pi\)
\(384\) 1.24050 + 1.20878i 0.0633040 + 0.0616855i
\(385\) −6.55317 + 0.829263i −0.333980 + 0.0422631i
\(386\) −7.14681 4.12622i −0.363763 0.210019i
\(387\) −0.560760 0.304674i −0.0285050 0.0154875i
\(388\) 11.6154i 0.589683i
\(389\) 1.62322 2.81150i 0.0823006 0.142549i −0.821937 0.569578i \(-0.807107\pi\)
0.904238 + 0.427029i \(0.140440\pi\)
\(390\) −24.4601 3.02329i −1.23859 0.153090i
\(391\) 5.86644 10.1610i 0.296679 0.513862i
\(392\) 0.298188 + 0.516477i 0.0150608 + 0.0260861i
\(393\) −2.34646 8.32445i −0.118363 0.419913i
\(394\) −22.0501 + 12.7306i −1.11087 + 0.641360i
\(395\) −9.30945 + 22.1594i −0.468409 + 1.11496i
\(396\) 2.98652 1.82898i 0.150078 0.0919095i
\(397\) −23.6825 13.6731i −1.18859 0.686232i −0.230603 0.973048i \(-0.574070\pi\)
−0.957986 + 0.286816i \(0.907403\pi\)
\(398\) 15.1490 8.74625i 0.759349 0.438410i
\(399\) −11.3501 2.88429i −0.568218 0.144395i
\(400\) −4.84239 + 1.24549i −0.242120 + 0.0622746i
\(401\) −9.60608 −0.479705 −0.239852 0.970809i \(-0.577099\pi\)
−0.239852 + 0.970809i \(0.577099\pi\)
\(402\) −4.25727 1.08185i −0.212333 0.0539579i
\(403\) −26.9618 + 22.9877i −1.34306 + 1.14510i
\(404\) 2.60547i 0.129627i
\(405\) 3.55668 + 19.8078i 0.176733 + 0.984259i
\(406\) −10.8998 6.29302i −0.540950 0.312318i
\(407\) 6.07849 0.301299
\(408\) 1.85430 + 6.57843i 0.0918016 + 0.325681i
\(409\) 26.5680 + 15.3390i 1.31370 + 0.758466i 0.982707 0.185167i \(-0.0592824\pi\)
0.330995 + 0.943633i \(0.392616\pi\)
\(410\) −0.787670 1.03726i −0.0389002 0.0512267i
\(411\) −16.6685 4.23579i −0.822198 0.208936i
\(412\) −11.9006 + 6.87079i −0.586298 + 0.338499i
\(413\) −14.6351 25.3488i −0.720148 1.24733i
\(414\) −8.91695 + 0.230962i −0.438244 + 0.0113512i
\(415\) −4.36489 5.74801i −0.214264 0.282159i
\(416\) 3.18182 + 5.51107i 0.156002 + 0.270203i
\(417\) 6.38237 6.54982i 0.312546 0.320746i
\(418\) 3.11903 0.152557
\(419\) 8.50389i 0.415442i 0.978188 + 0.207721i \(0.0666047\pi\)
−0.978188 + 0.207721i \(0.933395\pi\)
\(420\) −9.02470 + 3.82220i −0.440360 + 0.186504i
\(421\) 2.12626 + 3.68278i 0.103627 + 0.179488i 0.913177 0.407564i \(-0.133622\pi\)
−0.809549 + 0.587052i \(0.800288\pi\)
\(422\) −11.6155 + 20.1187i −0.565436 + 0.979364i
\(423\) −0.202002 7.79885i −0.00982166 0.379193i
\(424\) 5.05784 2.92015i 0.245630 0.141815i
\(425\) −19.0057 5.29785i −0.921914 0.256984i
\(426\) −25.7054 6.53223i −1.24543 0.316488i
\(427\) 9.89272 17.1347i 0.478742 0.829206i
\(428\) −1.02068 + 1.76788i −0.0493367 + 0.0854536i
\(429\) 12.3842 3.49080i 0.597914 0.168538i
\(430\) −0.438545 0.184239i −0.0211485 0.00888477i
\(431\) −3.67853 2.12380i −0.177189 0.102300i 0.408782 0.912632i \(-0.365953\pi\)
−0.585971 + 0.810332i \(0.699287\pi\)
\(432\) 3.52878 3.81415i 0.169778 0.183508i
\(433\) 26.6589 1.28115 0.640573 0.767898i \(-0.278697\pi\)
0.640573 + 0.767898i \(0.278697\pi\)
\(434\) −4.71450 + 13.2773i −0.226303 + 0.637329i
\(435\) −11.6051 + 15.3747i −0.556421 + 0.737162i
\(436\) 5.29320 0.253498
\(437\) −6.87999 3.97216i −0.329114 0.190014i
\(438\) −3.24658 + 12.7758i −0.155127 + 0.610452i
\(439\) −5.46842 9.47159i −0.260994 0.452054i 0.705513 0.708697i \(-0.250717\pi\)
−0.966506 + 0.256643i \(0.917384\pi\)
\(440\) 2.07884 1.57862i 0.0991047 0.0752576i
\(441\) 1.52575 0.934384i 0.0726548 0.0444945i
\(442\) 25.1113i 1.19442i
\(443\) −17.1646 29.7300i −0.815516 1.41251i −0.908957 0.416890i \(-0.863120\pi\)
0.0934414 0.995625i \(-0.470213\pi\)
\(444\) 8.68062 2.44686i 0.411964 0.116123i
\(445\) −3.55349 28.0811i −0.168451 1.33117i
\(446\) −12.7804 + 22.1364i −0.605171 + 1.04819i
\(447\) 7.42058 + 26.3257i 0.350981 + 1.24516i
\(448\) 2.19151 + 1.26527i 0.103539 + 0.0597783i
\(449\) −20.8543 −0.984176 −0.492088 0.870546i \(-0.663766\pi\)
−0.492088 + 0.870546i \(0.663766\pi\)
\(450\) 4.11137 + 14.4256i 0.193812 + 0.680027i
\(451\) 0.588850 + 0.339973i 0.0277279 + 0.0160087i
\(452\) −6.29037 10.8952i −0.295874 0.512469i
\(453\) −11.9645 + 12.2784i −0.562143 + 0.576891i
\(454\) 9.83982 + 17.0431i 0.461805 + 0.799870i
\(455\) −35.7235 + 4.52058i −1.67474 + 0.211928i
\(456\) 4.45425 1.25555i 0.208590 0.0587963i
\(457\) −9.71757 −0.454569 −0.227284 0.973828i \(-0.572985\pi\)
−0.227284 + 0.973828i \(0.572985\pi\)
\(458\) −0.583432 0.336845i −0.0272620 0.0157397i
\(459\) 19.5846 6.07204i 0.914133 0.283419i
\(460\) −6.59593 + 0.834673i −0.307537 + 0.0389168i
\(461\) −28.0073 −1.30443 −0.652214 0.758035i \(-0.726160\pi\)
−0.652214 + 0.758035i \(0.726160\pi\)
\(462\) 3.57080 3.66448i 0.166129 0.170487i
\(463\) 6.55196 0.304496 0.152248 0.988342i \(-0.451349\pi\)
0.152248 + 0.988342i \(0.451349\pi\)
\(464\) 4.97367 0.230897
\(465\) 19.2823 + 9.65373i 0.894193 + 0.447681i
\(466\) −25.5858 −1.18524
\(467\) 6.66673 0.308499 0.154250 0.988032i \(-0.450704\pi\)
0.154250 + 0.988032i \(0.450704\pi\)
\(468\) 16.2805 9.97035i 0.752567 0.460880i
\(469\) −6.41759 −0.296337
\(470\) −0.730014 5.76886i −0.0336730 0.266098i
\(471\) 5.33495 5.47492i 0.245821 0.252271i
\(472\) 10.0172 + 5.78341i 0.461077 + 0.266203i
\(473\) 0.248329 0.0114182
\(474\) −5.05108 17.9195i −0.232004 0.823071i
\(475\) −3.58717 + 12.8688i −0.164591 + 0.590460i
\(476\) 4.99283 + 8.64784i 0.228846 + 0.396373i
\(477\) −9.15038 14.9416i −0.418967 0.684129i
\(478\) −12.1832 21.1019i −0.557246 0.965178i
\(479\) 35.9059 + 20.7303i 1.64058 + 0.947190i 0.980627 + 0.195883i \(0.0627574\pi\)
0.659954 + 0.751306i \(0.270576\pi\)
\(480\) 2.33331 3.09123i 0.106500 0.141095i
\(481\) 33.1358 1.51086
\(482\) −22.6146 13.0565i −1.03007 0.594709i
\(483\) −12.5433 + 3.53565i −0.570740 + 0.160878i
\(484\) 4.81864 8.34613i 0.219029 0.379370i
\(485\) −25.7674 + 3.26070i −1.17004 + 0.148061i
\(486\) −11.7127 10.2865i −0.531300 0.466606i
\(487\) −7.67498 13.2935i −0.347787 0.602384i 0.638069 0.769979i \(-0.279733\pi\)
−0.985856 + 0.167595i \(0.946400\pi\)
\(488\) 7.81867i 0.353934i
\(489\) 2.85063 2.92542i 0.128910 0.132292i
\(490\) 1.06203 0.806481i 0.0479778 0.0364331i
\(491\) −8.51286 14.7447i −0.384180 0.665419i 0.607475 0.794339i \(-0.292182\pi\)
−0.991655 + 0.128920i \(0.958849\pi\)
\(492\) 0.977785 + 0.248474i 0.0440819 + 0.0112021i
\(493\) 16.9970 + 9.81320i 0.765504 + 0.441964i
\(494\) 17.0029 0.764995
\(495\) −4.89574 6.11180i −0.220047 0.274705i
\(496\) −1.00997 5.47540i −0.0453488 0.245853i
\(497\) −38.7494 −1.73815
\(498\) 5.41841 + 1.37692i 0.242805 + 0.0617013i
\(499\) 9.32152 + 5.38178i 0.417289 + 0.240922i 0.693917 0.720055i \(-0.255884\pi\)
−0.276628 + 0.960977i \(0.589217\pi\)
\(500\) 4.12234 + 10.3926i 0.184356 + 0.464772i
\(501\) 1.96167 + 6.95934i 0.0876409 + 0.310920i
\(502\) −8.56462 + 14.8344i −0.382258 + 0.662090i
\(503\) 9.45987 16.3850i 0.421795 0.730570i −0.574321 0.818631i \(-0.694734\pi\)
0.996115 + 0.0880609i \(0.0280670\pi\)
\(504\) 3.62430 6.67061i 0.161439 0.297133i
\(505\) 5.77992 0.731413i 0.257203 0.0325475i
\(506\) 3.00590 1.73546i 0.133629 0.0771505i
\(507\) 45.8381 12.9207i 2.03574 0.573826i
\(508\) −9.47777 + 16.4160i −0.420508 + 0.728341i
\(509\) −14.0362 24.3114i −0.622144 1.07758i −0.989086 0.147341i \(-0.952929\pi\)
0.366942 0.930244i \(-0.380405\pi\)
\(510\) 14.0729 5.96025i 0.623159 0.263924i
\(511\) 19.2588i 0.851959i
\(512\) −1.00000 −0.0441942
\(513\) −4.11137 13.2608i −0.181522 0.585476i
\(514\) 6.32974 + 10.9634i 0.279193 + 0.483576i
\(515\) 18.5827 + 24.4711i 0.818853 + 1.07833i
\(516\) 0.354636 0.0999633i 0.0156120 0.00440064i
\(517\) 1.51785 + 2.62899i 0.0667549 + 0.115623i
\(518\) 11.4113 6.58833i 0.501384 0.289474i
\(519\) 5.75832 22.6599i 0.252762 0.994661i
\(520\) 11.3324 8.60555i 0.496960 0.377379i
\(521\) 34.9512 + 20.1791i 1.53124 + 0.884062i 0.999305 + 0.0372764i \(0.0118682\pi\)
0.531935 + 0.846785i \(0.321465\pi\)
\(522\) −0.386346 14.9160i −0.0169099 0.652855i
\(523\) −22.2396 −0.972468 −0.486234 0.873829i \(-0.661630\pi\)
−0.486234 + 0.873829i \(0.661630\pi\)
\(524\) 4.32442 + 2.49670i 0.188913 + 0.109069i
\(525\) 11.0125 + 18.9472i 0.480625 + 0.826924i
\(526\) 7.65133i 0.333614i
\(527\) 7.35168 20.7043i 0.320244 0.901892i
\(528\) −0.497981 + 1.95964i −0.0216718 + 0.0852822i
\(529\) 14.1594 0.615627
\(530\) −7.89783 10.4004i −0.343060 0.451767i
\(531\) 16.5663 30.4907i 0.718916 1.32318i
\(532\) 5.85544 3.38064i 0.253866 0.146569i
\(533\) 3.21002 + 1.85330i 0.139041 + 0.0802755i
\(534\) 15.7027 + 15.3013i 0.679524 + 0.662151i
\(535\) 4.20835 + 1.76798i 0.181943 + 0.0764365i
\(536\) 2.19629 1.26803i 0.0948653 0.0547705i
\(537\) −25.0357 + 7.05697i −1.08037 + 0.304531i
\(538\) −0.846925 1.46692i −0.0365135 0.0632433i
\(539\) −0.348092 + 0.602913i −0.0149934 + 0.0259693i
\(540\) −9.45182 6.75745i −0.406742 0.290794i
\(541\) −21.8294 + 37.8096i −0.938518 + 1.62556i −0.170280 + 0.985396i \(0.554467\pi\)
−0.768238 + 0.640165i \(0.778866\pi\)
\(542\) 30.2591i 1.29974i
\(543\) −4.30121 1.09302i −0.184583 0.0469059i
\(544\) −3.41739 1.97303i −0.146519 0.0845930i
\(545\) −1.48592 11.7423i −0.0636497 0.502986i
\(546\) 19.4656 19.9763i 0.833050 0.854907i
\(547\) 0.00396456 0.00228894i 0.000169512 9.78679e-5i −0.499915 0.866074i \(-0.666636\pi\)
0.500085 + 0.865976i \(0.333302\pi\)
\(548\) 8.59916 4.96473i 0.367338 0.212083i
\(549\) 23.4481 0.607341i 1.00074 0.0259207i
\(550\) −4.08554 4.16850i −0.174208 0.177745i
\(551\) 6.64451 11.5086i 0.283066 0.490284i
\(552\) 3.59410 3.68839i 0.152975 0.156988i
\(553\) −13.6004 23.5565i −0.578347 1.00173i
\(554\) −32.9288 −1.39901
\(555\) −7.86489 18.5700i −0.333846 0.788253i
\(556\) 5.27999i 0.223921i
\(557\) 7.40927i 0.313941i −0.987603 0.156970i \(-0.949827\pi\)
0.987603 0.156970i \(-0.0501728\pi\)
\(558\) −16.3422 + 3.45420i −0.691822 + 0.146228i
\(559\) 1.35372 0.0572564
\(560\) 2.19164 5.21678i 0.0926137 0.220449i
\(561\) −5.56822 + 5.71431i −0.235090 + 0.241258i
\(562\) 13.9762i 0.589552i
\(563\) −8.14483 14.1073i −0.343264 0.594550i 0.641773 0.766895i \(-0.278199\pi\)
−0.985037 + 0.172344i \(0.944866\pi\)
\(564\) 3.22591 + 3.14343i 0.135835 + 0.132362i
\(565\) −22.4039 + 17.0129i −0.942540 + 0.715740i
\(566\) 11.4141i 0.479771i
\(567\) −20.2867 10.3511i −0.851959 0.434705i
\(568\) 13.2612 7.65636i 0.556428 0.321254i
\(569\) −5.77803 10.0078i −0.242228 0.419551i 0.719121 0.694885i \(-0.244545\pi\)
−0.961349 + 0.275334i \(0.911211\pi\)
\(570\) −4.03568 9.52875i −0.169036 0.399116i
\(571\) −2.86065 + 1.65160i −0.119715 + 0.0691173i −0.558662 0.829396i \(-0.688685\pi\)
0.438947 + 0.898513i \(0.355352\pi\)
\(572\) −3.71432 + 6.43339i −0.155303 + 0.268993i
\(573\) 12.9359 + 3.28726i 0.540405 + 0.137327i
\(574\) 1.47395 0.0615217
\(575\) 3.70324 + 14.3979i 0.154436 + 0.600436i
\(576\) 0.0776784 + 2.99899i 0.00323660 + 0.124958i
\(577\) 33.1201 + 19.1219i 1.37881 + 0.796054i 0.992016 0.126114i \(-0.0402505\pi\)
0.386790 + 0.922168i \(0.373584\pi\)
\(578\) 0.714295 + 1.23719i 0.0297107 + 0.0514605i
\(579\) −3.87791 13.7575i −0.161161 0.571743i
\(580\) −1.39622 11.0335i −0.0579747 0.458140i
\(581\) 8.16795 0.338864
\(582\) 14.0405 14.4089i 0.581999 0.597269i
\(583\) 5.90430 + 3.40885i 0.244531 + 0.141180i
\(584\) −3.80528 6.59093i −0.157463 0.272735i
\(585\) −26.6883 33.3174i −1.10343 1.37751i
\(586\) −2.33280 + 4.04052i −0.0963669 + 0.166912i
\(587\) 28.9143i 1.19342i 0.802457 + 0.596710i \(0.203526\pi\)
−0.802457 + 0.596710i \(0.796474\pi\)
\(588\) −0.254408 + 1.00114i −0.0104916 + 0.0412861i
\(589\) −14.0188 4.97782i −0.577636 0.205107i
\(590\) 10.0177 23.8454i 0.412424 0.981698i
\(591\) −42.7417 10.8615i −1.75816 0.446782i
\(592\) −2.60353 + 4.50944i −0.107004 + 0.185337i
\(593\) 10.9026 0.447718 0.223859 0.974622i \(-0.428135\pi\)
0.223859 + 0.974622i \(0.428135\pi\)
\(594\) 5.91562 + 1.34122i 0.242721 + 0.0550309i
\(595\) 17.7826 13.5036i 0.729014 0.553594i
\(596\) −13.6758 7.89572i −0.560182 0.323421i
\(597\) 29.3646 + 7.46211i 1.20181 + 0.305404i
\(598\) 16.3861 9.46055i 0.670079 0.386871i
\(599\) −39.3112 + 22.6963i −1.60621 + 0.927348i −0.616006 + 0.787741i \(0.711250\pi\)
−0.990207 + 0.139606i \(0.955416\pi\)
\(600\) −7.51252 4.30838i −0.306697 0.175889i
\(601\) 10.1555 + 5.86329i 0.414252 + 0.239169i 0.692615 0.721307i \(-0.256458\pi\)
−0.278363 + 0.960476i \(0.589792\pi\)
\(602\) 0.466195 0.269158i 0.0190007 0.0109701i
\(603\) −3.97342 6.48816i −0.161810 0.264218i
\(604\) 9.89798i 0.402743i
\(605\) −19.8676 8.34662i −0.807731 0.339338i
\(606\) −3.14946 + 3.23209i −0.127938 + 0.131295i
\(607\) 30.2803 17.4824i 1.22904 0.709587i 0.262212 0.965010i \(-0.415548\pi\)
0.966829 + 0.255423i \(0.0822147\pi\)
\(608\) −1.33594 + 2.31391i −0.0541794 + 0.0938416i
\(609\) −5.91433 20.9821i −0.239661 0.850236i
\(610\) 17.3447 2.19487i 0.702268 0.0888676i
\(611\) 8.27429 + 14.3315i 0.334742 + 0.579790i
\(612\) −5.65165 + 10.4020i −0.228454 + 0.420476i
\(613\) −13.2279 + 22.9115i −0.534271 + 0.925385i 0.464927 + 0.885349i \(0.346081\pi\)
−0.999198 + 0.0400358i \(0.987253\pi\)
\(614\) 6.69856 + 3.86742i 0.270332 + 0.156076i
\(615\) 0.276723 2.23885i 0.0111585 0.0902790i
\(616\) 2.95404i 0.119022i
\(617\) 12.1881 21.1104i 0.490674 0.849873i −0.509268 0.860608i \(-0.670084\pi\)
0.999942 + 0.0107352i \(0.00341717\pi\)
\(618\) −23.0679 5.86200i −0.927929 0.235804i
\(619\) 42.7518i 1.71834i 0.511690 + 0.859170i \(0.329020\pi\)
−0.511690 + 0.859170i \(0.670980\pi\)
\(620\) −11.8630 + 3.77755i −0.476428 + 0.151710i
\(621\) −11.3407 10.4922i −0.455085 0.421036i
\(622\) 3.48291i 0.139652i
\(623\) 27.7410 + 16.0163i 1.11142 + 0.641679i
\(624\) −2.71466 + 10.6826i −0.108673 + 0.427647i
\(625\) 21.8975 12.0623i 0.875900 0.482493i
\(626\) −0.752791 + 1.30387i −0.0300876 + 0.0521132i
\(627\) 3.86916 + 3.77024i 0.154519 + 0.150569i
\(628\) 4.41348i 0.176117i
\(629\) −17.7945 + 10.2737i −0.709515 + 0.409639i
\(630\) −15.8153 6.16748i −0.630099 0.245718i
\(631\) −4.38109 + 2.52942i −0.174408 + 0.100695i −0.584663 0.811276i \(-0.698773\pi\)
0.410254 + 0.911971i \(0.365440\pi\)
\(632\) 9.30890 + 5.37450i 0.370288 + 0.213786i
\(633\) −38.7283 + 10.9166i −1.53931 + 0.433895i
\(634\) −8.17705 + 14.1631i −0.324752 + 0.562487i
\(635\) 39.0775 + 16.4169i 1.55074 + 0.651487i
\(636\) 9.80408 + 2.49140i 0.388757 + 0.0987905i
\(637\) −1.89756 + 3.28668i −0.0751842 + 0.130223i
\(638\) 2.90302 + 5.02818i 0.114932 + 0.199067i
\(639\) −23.9915 39.1755i −0.949088 1.54976i
\(640\) 0.280722 + 2.21838i 0.0110965 + 0.0876890i
\(641\) 22.9201 + 39.6989i 0.905291 + 1.56801i 0.820526 + 0.571609i \(0.193681\pi\)
0.0847654 + 0.996401i \(0.472986\pi\)
\(642\) −3.40314 + 0.959263i −0.134311 + 0.0378591i
\(643\) 4.82979 0.190468 0.0952341 0.995455i \(-0.469640\pi\)
0.0952341 + 0.995455i \(0.469640\pi\)
\(644\) 3.76204 6.51605i 0.148245 0.256768i
\(645\) −0.321310 0.758655i −0.0126516 0.0298720i
\(646\) −9.13085 + 5.27170i −0.359248 + 0.207412i
\(647\) 14.0203i 0.551194i 0.961273 + 0.275597i \(0.0888756\pi\)
−0.961273 + 0.275597i \(0.911124\pi\)
\(648\) 8.98793 0.465914i 0.353079 0.0183028i
\(649\) 13.5026i 0.530023i
\(650\) −22.2716 22.7238i −0.873565 0.891302i
\(651\) −21.8977 + 10.7716i −0.858238 + 0.422173i
\(652\) 2.35826i 0.0923567i
\(653\) 32.7400 1.28121 0.640607 0.767869i \(-0.278683\pi\)
0.640607 + 0.767869i \(0.278683\pi\)
\(654\) 6.56622 + 6.39834i 0.256759 + 0.250195i
\(655\) 4.32467 10.2941i 0.168979 0.402222i
\(656\) −0.504431 + 0.291233i −0.0196947 + 0.0113708i
\(657\) −19.4706 + 11.9240i −0.759620 + 0.465199i
\(658\) 5.69900 + 3.29032i 0.222170 + 0.128270i
\(659\) 38.8028i 1.51154i −0.654836 0.755771i \(-0.727262\pi\)
0.654836 0.755771i \(-0.272738\pi\)
\(660\) 4.48701 + 0.554596i 0.174656 + 0.0215876i
\(661\) 19.1710 + 33.2052i 0.745667 + 1.29153i 0.949883 + 0.312607i \(0.101202\pi\)
−0.204216 + 0.978926i \(0.565464\pi\)
\(662\) −7.86876 + 4.54303i −0.305828 + 0.176570i
\(663\) −30.3542 + 31.1506i −1.17886 + 1.20979i
\(664\) −2.79531 + 1.61388i −0.108479 + 0.0626305i
\(665\) −9.14329 12.0406i −0.354562 0.466913i
\(666\) 13.7260 + 7.45768i 0.531873 + 0.288979i
\(667\) 14.7883i 0.572604i
\(668\) −3.61526 2.08727i −0.139879 0.0807591i
\(669\) −42.6122 + 12.0113i −1.64748 + 0.464386i
\(670\) −3.42951 4.51624i −0.132494 0.174477i
\(671\) −7.90436 + 4.56358i −0.305144 + 0.176175i
\(672\) 1.18913 + 4.21863i 0.0458717 + 0.162737i
\(673\) 14.8730 + 25.7608i 0.573312 + 0.993006i 0.996223 + 0.0868347i \(0.0276752\pi\)
−0.422910 + 0.906172i \(0.638991\pi\)
\(674\) 30.3494 1.16902
\(675\) −12.3372 + 22.8647i −0.474860 + 0.880061i
\(676\) −13.7480 + 23.8122i −0.528768 + 0.915853i
\(677\) −38.9582 + 22.4925i −1.49729 + 0.864459i −0.999995 0.00312507i \(-0.999005\pi\)
−0.497291 + 0.867584i \(0.665672\pi\)
\(678\) 5.36680 21.1193i 0.206111 0.811080i
\(679\) 14.6966 25.4553i 0.564005 0.976885i
\(680\) −3.41759 + 8.13493i −0.131059 + 0.311960i
\(681\) −8.39511 + 33.0361i −0.321701 + 1.26595i
\(682\) 4.94591 4.21690i 0.189389 0.161474i
\(683\) 19.9161 0.762068 0.381034 0.924561i \(-0.375568\pi\)
0.381034 + 0.924561i \(0.375568\pi\)
\(684\) 7.04318 + 3.82673i 0.269303 + 0.146319i
\(685\) −13.4276 17.6825i −0.513042 0.675612i
\(686\) 19.2229i 0.733935i
\(687\) −0.316574 1.12310i −0.0120781 0.0428489i
\(688\) −0.106364 + 0.184228i −0.00405509 + 0.00702362i
\(689\) 32.1863 + 18.5828i 1.22620 + 0.707947i
\(690\) −9.19119 6.93765i −0.349902 0.264112i
\(691\) 3.01668 + 5.22504i 0.114760 + 0.198770i 0.917684 0.397312i \(-0.130057\pi\)
−0.802924 + 0.596082i \(0.796723\pi\)
\(692\) 6.74927 + 11.6901i 0.256569 + 0.444390i
\(693\) 8.85914 0.229465i 0.336531 0.00871665i
\(694\) −8.16914 4.71646i −0.310096 0.179034i
\(695\) 11.7130 1.48221i 0.444299 0.0562233i
\(696\) 6.16983 + 6.01209i 0.233867 + 0.227888i
\(697\) −2.29845 −0.0870600
\(698\) 5.45162 0.206347
\(699\) −31.7391 30.9277i −1.20048 1.16979i
\(700\) −12.1880 3.39742i −0.460664 0.128410i
\(701\) 13.1260 + 7.57832i 0.495764 + 0.286229i 0.726962 0.686677i \(-0.240931\pi\)
−0.231199 + 0.972907i \(0.574265\pi\)
\(702\) 32.2480 + 7.31143i 1.21712 + 0.275952i
\(703\) 6.95630 + 12.0487i 0.262362 + 0.454424i
\(704\) −0.583678 1.01096i −0.0219982 0.0381020i
\(705\) 6.06773 8.03870i 0.228524 0.302755i
\(706\) 20.6931 + 11.9472i 0.778795 + 0.449637i
\(707\) −3.29663 + 5.70992i −0.123982 + 0.214744i
\(708\) 5.43538 + 19.2829i 0.204274 + 0.724696i
\(709\) 46.2342i 1.73636i −0.496247 0.868181i \(-0.665289\pi\)
0.496247 0.868181i \(-0.334711\pi\)
\(710\) −20.7074 27.2690i −0.777135 1.02339i
\(711\) 15.3950 28.3348i 0.577357 1.06264i
\(712\) −12.6584 −0.474394
\(713\) −16.2801 + 3.00295i −0.609693 + 0.112461i
\(714\) −4.25977 + 16.7629i −0.159418 + 0.627336i
\(715\) 15.3144 + 6.43376i 0.572725 + 0.240609i
\(716\) 7.50882 13.0057i 0.280618 0.486044i
\(717\) 10.3944 40.9038i 0.388187 1.52758i
\(718\) −7.81527 + 4.51215i −0.291663 + 0.168392i
\(719\) 0.850396 1.47293i 0.0317144 0.0549310i −0.849733 0.527214i \(-0.823237\pi\)
0.881447 + 0.472283i \(0.156570\pi\)
\(720\) 6.63109 1.01420i 0.247126 0.0377971i
\(721\) −34.7736 −1.29504
\(722\) −5.93054 10.2720i −0.220712 0.382284i
\(723\) −12.2708 43.5328i −0.456357 1.61900i
\(724\) 2.21896 1.28112i 0.0824669 0.0476123i
\(725\) −24.0844 + 6.19466i −0.894473 + 0.230064i
\(726\) 16.0662 4.52867i 0.596272 0.168075i
\(727\) −16.7604 9.67663i −0.621609 0.358886i 0.155886 0.987775i \(-0.450177\pi\)
−0.777495 + 0.628889i \(0.783510\pi\)
\(728\) 16.1034i 0.596833i
\(729\) −2.09544 26.9186i −0.0776089 0.996984i
\(730\) −13.5529 + 10.2918i −0.501617 + 0.380915i
\(731\) −0.726974 + 0.419719i −0.0268881 + 0.0155239i
\(732\) −9.45108 + 9.69905i −0.349322 + 0.358487i
\(733\) 7.87334 4.54568i 0.290808 0.167898i −0.347498 0.937681i \(-0.612969\pi\)
0.638306 + 0.769782i \(0.279635\pi\)
\(734\) −15.7765 27.3257i −0.582320 1.00861i
\(735\) 2.29231 + 0.283331i 0.0845533 + 0.0104508i
\(736\) 2.97331i 0.109598i
\(737\) 2.56385 + 1.48024i 0.0944407 + 0.0545254i
\(738\) 0.912590 + 1.49016i 0.0335929 + 0.0548537i
\(739\) −22.7174 + 13.1159i −0.835674 + 0.482477i −0.855791 0.517321i \(-0.826929\pi\)
0.0201174 + 0.999798i \(0.493596\pi\)
\(740\) 10.7345 + 4.50971i 0.394608 + 0.165780i
\(741\) 21.0920 + 20.5528i 0.774836 + 0.755026i
\(742\) 14.7791 0.542557
\(743\) 16.6662i 0.611425i −0.952124 0.305713i \(-0.901105\pi\)
0.952124 0.305713i \(-0.0988947\pi\)
\(744\) 5.36571 8.01306i 0.196717 0.293773i
\(745\) −13.6766 + 32.5545i −0.501071 + 1.19271i
\(746\) 9.79690i 0.358690i
\(747\) 5.05714 + 8.25777i 0.185031 + 0.302136i
\(748\) 4.60646i 0.168429i
\(749\) −4.47368 + 2.58288i −0.163465 + 0.0943764i
\(750\) −7.44867 + 17.8750i −0.271987 + 0.652704i
\(751\) −14.3994 + 24.9405i −0.525441 + 0.910090i 0.474120 + 0.880460i \(0.342766\pi\)
−0.999561 + 0.0296299i \(0.990567\pi\)
\(752\) −2.60049 −0.0948301
\(753\) −28.5560 + 8.04923i −1.04064 + 0.293330i
\(754\) 15.8253 + 27.4102i 0.576324 + 0.998222i
\(755\) −21.9574 + 2.77858i −0.799113 + 0.101123i
\(756\) 12.5593 3.89389i 0.456777 0.141619i
\(757\) 6.97726 + 12.0850i 0.253593 + 0.439235i 0.964512 0.264038i \(-0.0850544\pi\)
−0.710920 + 0.703273i \(0.751721\pi\)
\(758\) 10.2994 17.8392i 0.374093 0.647947i
\(759\) 5.82661 + 1.48065i 0.211493 + 0.0537443i
\(760\) 5.50816 + 2.31405i 0.199802 + 0.0839394i
\(761\) 5.28189 9.14850i 0.191468 0.331633i −0.754269 0.656566i \(-0.772008\pi\)
0.945737 + 0.324933i \(0.105342\pi\)
\(762\) −31.6006 + 8.90743i −1.14477 + 0.322682i
\(763\) 11.6001 + 6.69733i 0.419952 + 0.242460i
\(764\) −6.67352 + 3.85296i −0.241440 + 0.139395i
\(765\) 24.6621 + 9.61743i 0.891660 + 0.347719i
\(766\) −25.4503 + 14.6938i −0.919558 + 0.530907i
\(767\) 73.6071i 2.65780i
\(768\) −1.24050 1.20878i −0.0447627 0.0436183i
\(769\) 14.8007 25.6356i 0.533728 0.924445i −0.465495 0.885050i \(-0.654124\pi\)
0.999224 0.0393944i \(-0.0125429\pi\)
\(770\) 6.55317 0.829263i 0.236160 0.0298846i
\(771\) −5.40039 + 21.2514i −0.194490 + 0.765351i
\(772\) 7.14681 + 4.12622i 0.257219 + 0.148506i
\(773\) 19.0137i 0.683875i 0.939723 + 0.341938i \(0.111083\pi\)
−0.939723 + 0.341938i \(0.888917\pi\)
\(774\) 0.560760 + 0.304674i 0.0201561 + 0.0109513i
\(775\) 11.7102 + 25.2561i 0.420643 + 0.907226i
\(776\) 11.6154i 0.416969i
\(777\) 22.1196 + 5.62101i 0.793536 + 0.201653i
\(778\) −1.62322 + 2.81150i −0.0581953 + 0.100797i
\(779\) 1.55628i 0.0557595i
\(780\) 24.4601 + 3.02329i 0.875814 + 0.108251i
\(781\) 15.4805 + 8.93769i 0.553937 + 0.319816i
\(782\) −5.86644 + 10.1610i −0.209783 + 0.363356i
\(783\) 17.5510 18.9703i 0.627220 0.677943i
\(784\) −0.298188 0.516477i −0.0106496 0.0184456i
\(785\) 9.79076 1.23896i 0.349447 0.0442204i
\(786\) 2.34646 + 8.32445i 0.0836955 + 0.296923i
\(787\) 16.8350 29.1591i 0.600103 1.03941i −0.392701 0.919666i \(-0.628459\pi\)
0.992805 0.119744i \(-0.0382073\pi\)
\(788\) 22.0501 12.7306i 0.785502 0.453510i
\(789\) 9.24881 9.49147i 0.329266 0.337905i
\(790\) 9.30945 22.1594i 0.331215 0.788396i
\(791\) 31.8361i 1.13196i
\(792\) −2.98652 + 1.82898i −0.106121 + 0.0649898i
\(793\) −43.0892 + 24.8776i −1.53014 + 0.883429i
\(794\) 23.6825 + 13.6731i 0.840459 + 0.485239i
\(795\) 2.77465 22.4485i 0.0984067 0.796167i
\(796\) −15.1490 + 8.74625i −0.536941 + 0.310003i
\(797\) 11.8837 6.86104i 0.420941 0.243030i −0.274539 0.961576i \(-0.588525\pi\)
0.695480 + 0.718546i \(0.255192\pi\)
\(798\) 11.3501 + 2.88429i 0.401791 + 0.102103i
\(799\) −8.88689 5.13085i −0.314395 0.181516i
\(800\) 4.84239 1.24549i 0.171204 0.0440348i
\(801\) 0.983284 + 37.9625i 0.0347426 + 1.34134i
\(802\) 9.60608 0.339203
\(803\) 4.44211 7.69396i 0.156759 0.271514i
\(804\) 4.25727 + 1.08185i 0.150142 + 0.0381540i
\(805\) −15.5111 6.51643i −0.546696 0.229674i
\(806\) 26.9618 22.9877i 0.949688 0.809708i
\(807\) 0.722577 2.84346i 0.0254359 0.100095i
\(808\) 2.60547i 0.0916603i
\(809\) 3.82153 6.61908i 0.134358 0.232714i −0.790994 0.611824i \(-0.790436\pi\)
0.925352 + 0.379109i \(0.123770\pi\)
\(810\) −3.55668 19.8078i −0.124969 0.695976i
\(811\) 1.11093 + 1.92419i 0.0390101 + 0.0675675i 0.884871 0.465836i \(-0.154246\pi\)
−0.845861 + 0.533403i \(0.820913\pi\)
\(812\) 10.8998 + 6.29302i 0.382509 + 0.220842i
\(813\) −36.5767 + 37.5364i −1.28280 + 1.31646i
\(814\) −6.07849 −0.213051
\(815\) 5.23152 0.662016i 0.183252 0.0231894i
\(816\) −1.85430 6.57843i −0.0649135 0.230291i
\(817\) 0.284191 + 0.492234i 0.00994260 + 0.0172211i
\(818\) −26.5680 15.3390i −0.928927 0.536317i
\(819\) 48.2941 1.25089i 1.68753 0.0437096i
\(820\) 0.787670 + 1.03726i 0.0275066 + 0.0362228i
\(821\) 33.9218 1.18388 0.591939 0.805983i \(-0.298363\pi\)
0.591939 + 0.805983i \(0.298363\pi\)
\(822\) 16.6685 + 4.23579i 0.581382 + 0.147740i
\(823\) 4.08313 7.07218i 0.142329 0.246521i −0.786044 0.618170i \(-0.787874\pi\)
0.928373 + 0.371649i \(0.121208\pi\)
\(824\) 11.9006 6.87079i 0.414575 0.239355i
\(825\) −0.0292959 10.1096i −0.00101995 0.351970i
\(826\) 14.6351 + 25.3488i 0.509222 + 0.881998i
\(827\) −8.07627 + 4.66284i −0.280839 + 0.162143i −0.633803 0.773494i \(-0.718507\pi\)
0.352964 + 0.935637i \(0.385174\pi\)
\(828\) 8.91695 0.230962i 0.309885 0.00802649i
\(829\) 31.8726i 1.10698i 0.832855 + 0.553491i \(0.186705\pi\)
−0.832855 + 0.553491i \(0.813295\pi\)
\(830\) 4.36489 + 5.74801i 0.151507 + 0.199516i
\(831\) −40.8482 39.8038i −1.41701 1.38078i
\(832\) −3.18182 5.51107i −0.110310 0.191062i
\(833\) 2.35334i 0.0815384i
\(834\) −6.38237 + 6.54982i −0.221003 + 0.226802i
\(835\) −3.61548 + 8.60596i −0.125119 + 0.297822i
\(836\) −3.11903 −0.107874
\(837\) −24.4479 15.4693i −0.845044 0.534697i
\(838\) 8.50389i 0.293762i
\(839\) 5.17690i 0.178726i −0.995999 0.0893631i \(-0.971517\pi\)
0.995999 0.0893631i \(-0.0284832\pi\)
\(840\) 9.02470 3.82220i 0.311382 0.131878i
\(841\) −4.26265 −0.146988
\(842\) −2.12626 3.68278i −0.0732756 0.126917i
\(843\) 16.8943 17.3375i 0.581869 0.597136i
\(844\) 11.6155 20.1187i 0.399824 0.692515i
\(845\) 56.6837 + 23.8136i 1.94998 + 0.819212i
\(846\) 0.202002 + 7.79885i 0.00694496 + 0.268130i
\(847\) 21.1202 12.1938i 0.725699 0.418982i
\(848\) −5.05784 + 2.92015i −0.173687 + 0.100278i
\(849\) −13.7972 + 14.1592i −0.473519 + 0.485942i
\(850\) 19.0057 + 5.29785i 0.651891 + 0.181715i
\(851\) 13.4080 + 7.74110i 0.459620 + 0.265362i
\(852\) 25.7054 + 6.53223i 0.880653 + 0.223790i
\(853\) 50.2504i 1.72054i −0.509838 0.860270i \(-0.670295\pi\)
0.509838 0.860270i \(-0.329705\pi\)
\(854\) −9.89272 + 17.1347i −0.338522 + 0.586337i
\(855\) 6.51195 16.6987i 0.222704 0.571083i
\(856\) 1.02068 1.76788i 0.0348863 0.0604248i
\(857\) 20.7236 + 35.8943i 0.707904 + 1.22613i 0.965633 + 0.259908i \(0.0836923\pi\)
−0.257730 + 0.966217i \(0.582974\pi\)
\(858\) −12.3842 + 3.49080i −0.422789 + 0.119174i
\(859\) 30.9828 17.8879i 1.05712 0.610328i 0.132485 0.991185i \(-0.457704\pi\)
0.924634 + 0.380857i \(0.124371\pi\)
\(860\) 0.438545 + 0.184239i 0.0149543 + 0.00628248i
\(861\) 1.82844 + 1.78169i 0.0623130 + 0.0607199i
\(862\) 3.67853 + 2.12380i 0.125291 + 0.0723370i
\(863\) 35.0518 20.2372i 1.19318 0.688882i 0.234152 0.972200i \(-0.424769\pi\)
0.959026 + 0.283318i \(0.0914352\pi\)
\(864\) −3.52878 + 3.81415i −0.120051 + 0.129760i
\(865\) 24.0383 18.2541i 0.817328 0.620657i
\(866\) −26.6589 −0.905906
\(867\) −0.609420 + 2.39817i −0.0206970 + 0.0814461i
\(868\) 4.71450 13.2773i 0.160020 0.450660i
\(869\) 12.5479i 0.425659i
\(870\) 11.6051 15.3747i 0.393449 0.521252i
\(871\) 13.9764 + 8.06928i 0.473572 + 0.273417i
\(872\) −5.29320 −0.179250
\(873\) 34.8346 0.902267i 1.17897 0.0305371i
\(874\) 6.87999 + 3.97216i 0.232719 + 0.134360i
\(875\) −4.11531 + 27.9914i −0.139123 + 0.946281i
\(876\) 3.24658 12.7758i 0.109692 0.431655i
\(877\) −46.9146 + 27.0862i −1.58419 + 0.914635i −0.589956 + 0.807435i \(0.700855\pi\)
−0.994238 + 0.107199i \(0.965812\pi\)
\(878\) 5.46842 + 9.47159i 0.184550 + 0.319651i
\(879\) −7.77795 + 2.19242i −0.262344 + 0.0739484i
\(880\) −2.07884 + 1.57862i −0.0700776 + 0.0532151i
\(881\) −18.4587 31.9714i −0.621889 1.07714i −0.989134 0.147020i \(-0.953032\pi\)
0.367244 0.930125i \(-0.380301\pi\)
\(882\) −1.52575 + 0.934384i −0.0513747 + 0.0314624i
\(883\) 27.6274 0.929736 0.464868 0.885380i \(-0.346102\pi\)
0.464868 + 0.885380i \(0.346102\pi\)
\(884\) 25.1113i 0.844585i
\(885\) 41.2509 17.4709i 1.38663 0.587277i
\(886\) 17.1646 + 29.7300i 0.576657 + 0.998799i
\(887\) −25.5426 + 44.2411i −0.857637 + 1.48547i 0.0165390 + 0.999863i \(0.494735\pi\)
−0.874176 + 0.485608i \(0.838598\pi\)
\(888\) −8.68062 + 2.44686i −0.291303 + 0.0821111i
\(889\) −41.5413 + 23.9839i −1.39325 + 0.804393i
\(890\) 3.55349 + 28.0811i 0.119113 + 0.941281i
\(891\) 5.71708 + 8.81449i 0.191529 + 0.295297i
\(892\) 12.7804 22.1364i 0.427921 0.741180i
\(893\) −3.47409 + 6.01730i −0.116256 + 0.201361i
\(894\) −7.42058 26.3257i −0.248181 0.880464i
\(895\) −30.9594 13.0064i −1.03486 0.434757i
\(896\) −2.19151 1.26527i −0.0732132 0.0422697i
\(897\) 31.7628 + 8.07152i 1.06053 + 0.269500i
\(898\) 20.8543 0.695917
\(899\) −5.02323 27.2328i −0.167534 0.908264i
\(900\) −4.11137 14.4256i −0.137046 0.480852i
\(901\) −23.0462 −0.767779
\(902\) −0.588850 0.339973i −0.0196066 0.0113199i
\(903\) 0.903669 + 0.229640i 0.0300722 + 0.00764192i
\(904\) 6.29037 + 10.8952i 0.209215 + 0.362370i
\(905\) −3.46491 4.56285i −0.115177 0.151674i
\(906\) 11.9645 12.2784i 0.397495 0.407924i
\(907\) 27.1776i 0.902418i −0.892418 0.451209i \(-0.850993\pi\)
0.892418 0.451209i \(-0.149007\pi\)
\(908\) −9.83982 17.0431i −0.326546 0.565594i
\(909\) −7.81380 + 0.202389i −0.259168 + 0.00671282i
\(910\) 35.7235 4.52058i 1.18422 0.149856i
\(911\) 23.1209 40.0465i 0.766028 1.32680i −0.173673 0.984803i \(-0.555564\pi\)
0.939701 0.341996i \(-0.111103\pi\)
\(912\) −4.45425 + 1.25555i −0.147495 + 0.0415753i
\(913\) −3.26313 1.88397i −0.107994 0.0623502i
\(914\) 9.71757 0.321429
\(915\) 24.1693 + 18.2433i 0.799012 + 0.603106i
\(916\) 0.583432 + 0.336845i 0.0192771 + 0.0111297i
\(917\) 6.31800 + 10.9431i 0.208639 + 0.361373i
\(918\) −19.5846 + 6.07204i −0.646390 + 0.200407i
\(919\) −23.3930 40.5179i −0.771664 1.33656i −0.936650 0.350265i \(-0.886091\pi\)
0.164986 0.986296i \(-0.447242\pi\)
\(920\) 6.59593 0.834673i 0.217461 0.0275184i
\(921\) 3.63469 + 12.8947i 0.119767 + 0.424893i
\(922\) 28.0073 0.922371
\(923\) 84.3895 + 48.7223i 2.77771 + 1.60371i
\(924\) −3.57080 + 3.66448i −0.117471 + 0.120553i
\(925\) 6.99082 25.0792i 0.229857 0.824598i
\(926\) −6.55196 −0.215311
\(927\) −21.5299 35.1560i −0.707134 1.15467i
\(928\) −4.97367 −0.163269
\(929\) −4.99976 −0.164037 −0.0820184 0.996631i \(-0.526137\pi\)
−0.0820184 + 0.996631i \(0.526137\pi\)
\(930\) −19.2823 9.65373i −0.632290 0.316558i
\(931\) −1.59345 −0.0522231
\(932\) 25.5858 0.838090
\(933\) 4.21009 4.32055i 0.137832 0.141448i
\(934\) −6.66673 −0.218142
\(935\) −10.2189 + 1.29313i −0.334193 + 0.0422900i
\(936\) −16.2805 + 9.97035i −0.532145 + 0.325891i
\(937\) 30.5656 + 17.6471i 0.998536 + 0.576505i 0.907815 0.419371i \(-0.137749\pi\)
0.0907212 + 0.995876i \(0.471083\pi\)
\(938\) 6.41759 0.209542
\(939\) −2.50994 + 0.707491i −0.0819088 + 0.0230881i
\(940\) 0.730014 + 5.76886i 0.0238104 + 0.188160i
\(941\) −22.7805 39.4570i −0.742624 1.28626i −0.951297 0.308277i \(-0.900248\pi\)
0.208673 0.977985i \(-0.433086\pi\)
\(942\) −5.33495 + 5.47492i −0.173822 + 0.178383i
\(943\) 0.865928 + 1.49983i 0.0281985 + 0.0488412i
\(944\) −10.0172 5.78341i −0.326031 0.188234i
\(945\) −12.1638 26.7681i −0.395688 0.870767i
\(946\) −0.248329 −0.00807388
\(947\) 30.2955 + 17.4911i 0.984473 + 0.568386i 0.903618 0.428340i \(-0.140901\pi\)
0.0808554 + 0.996726i \(0.474235\pi\)
\(948\) 5.05108 + 17.9195i 0.164051 + 0.581999i
\(949\) 24.2154 41.9423i 0.786066 1.36151i
\(950\) 3.58717 12.8688i 0.116383 0.417518i
\(951\) −27.2637 + 7.68499i −0.884087 + 0.249203i
\(952\) −4.99283 8.64784i −0.161819 0.280278i
\(953\) 6.87324i 0.222646i 0.993784 + 0.111323i \(0.0355088\pi\)
−0.993784 + 0.111323i \(0.964491\pi\)
\(954\) 9.15038 + 14.9416i 0.296255 + 0.483752i
\(955\) 10.4207 + 13.7228i 0.337207 + 0.444059i
\(956\) 12.1832 + 21.1019i 0.394032 + 0.682484i
\(957\) −2.47679 + 9.74658i −0.0800632 + 0.315062i
\(958\) −35.9059 20.7303i −1.16007 0.669764i
\(959\) 25.1269 0.811389
\(960\) −2.33331 + 3.09123i −0.0753071 + 0.0997689i
\(961\) −28.9599 + 11.0599i −0.934191 + 0.356772i
\(962\) −33.1358 −1.06834
\(963\) −5.38114 2.92370i −0.173405 0.0942150i
\(964\) 22.6146 + 13.0565i 0.728367 + 0.420523i
\(965\) 7.14723 17.0126i 0.230078 0.547656i
\(966\) 12.5433 3.53565i 0.403574 0.113758i
\(967\) 4.20935 7.29080i 0.135363 0.234456i −0.790373 0.612626i \(-0.790113\pi\)
0.925736 + 0.378170i \(0.123446\pi\)
\(968\) −4.81864 + 8.34613i −0.154877 + 0.268255i
\(969\) −17.6992 4.49769i −0.568579 0.144487i
\(970\) 25.7674 3.26070i 0.827340 0.104695i
\(971\) 18.3274 10.5813i 0.588153 0.339570i −0.176214 0.984352i \(-0.556385\pi\)
0.764367 + 0.644782i \(0.223052\pi\)
\(972\) 11.7127 + 10.2865i 0.375686 + 0.329940i
\(973\) −6.68060 + 11.5711i −0.214170 + 0.370954i
\(974\) 7.67498 + 13.2935i 0.245922 + 0.425950i
\(975\) −0.159702 55.1105i −0.00511454 1.76495i
\(976\) 7.81867i 0.250269i
\(977\) 37.4454 1.19799 0.598993 0.800754i \(-0.295568\pi\)
0.598993 + 0.800754i \(0.295568\pi\)
\(978\) −2.85063 + 2.92542i −0.0911532 + 0.0935448i
\(979\) −7.38843 12.7971i −0.236135 0.408998i
\(980\) −1.06203 + 0.806481i −0.0339254 + 0.0257621i
\(981\) 0.411168 + 15.8743i 0.0131276 + 0.506827i
\(982\) 8.51286 + 14.7447i 0.271656 + 0.470522i
\(983\) −33.1751 + 19.1537i −1.05812 + 0.610907i −0.924912 0.380180i \(-0.875862\pi\)
−0.133210 + 0.991088i \(0.542529\pi\)
\(984\) −0.977785 0.248474i −0.0311706 0.00792105i
\(985\) −34.4313 45.3417i −1.09707 1.44471i
\(986\) −16.9970 9.81320i −0.541293 0.312516i
\(987\) 3.09232 + 10.9705i 0.0984296 + 0.349195i
\(988\) −17.0029 −0.540933
\(989\) 0.547767 + 0.316253i 0.0174180 + 0.0100563i
\(990\) 4.89574 + 6.11180i 0.155597 + 0.194246i
\(991\) 38.8224i 1.23323i −0.787263 0.616617i \(-0.788503\pi\)
0.787263 0.616617i \(-0.211497\pi\)
\(992\) 1.00997 + 5.47540i 0.0320665 + 0.173844i
\(993\) −15.2527 3.87601i −0.484031 0.123001i
\(994\) 38.7494 1.22906
\(995\) 23.6551 + 31.1508i 0.749918 + 0.987548i
\(996\) −5.41841 1.37692i −0.171689 0.0436294i
\(997\) −19.4945 + 11.2552i −0.617398 + 0.356455i −0.775855 0.630911i \(-0.782681\pi\)
0.158457 + 0.987366i \(0.449348\pi\)
\(998\) −9.32152 5.38178i −0.295068 0.170357i
\(999\) 8.01240 + 25.8431i 0.253501 + 0.817638i
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 930.2.r.a.119.9 yes 64
3.2 odd 2 930.2.r.b.119.30 yes 64
5.4 even 2 930.2.r.b.119.24 yes 64
15.14 odd 2 inner 930.2.r.a.119.3 64
31.6 odd 6 inner 930.2.r.a.719.3 yes 64
93.68 even 6 930.2.r.b.719.24 yes 64
155.99 odd 6 930.2.r.b.719.30 yes 64
465.254 even 6 inner 930.2.r.a.719.9 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.r.a.119.3 64 15.14 odd 2 inner
930.2.r.a.119.9 yes 64 1.1 even 1 trivial
930.2.r.a.719.3 yes 64 31.6 odd 6 inner
930.2.r.a.719.9 yes 64 465.254 even 6 inner
930.2.r.b.119.24 yes 64 5.4 even 2
930.2.r.b.119.30 yes 64 3.2 odd 2
930.2.r.b.719.24 yes 64 93.68 even 6
930.2.r.b.719.30 yes 64 155.99 odd 6