Properties

Label 930.2.o.e.491.15
Level $930$
Weight $2$
Character 930.491
Analytic conductor $7.426$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [930,2,Mod(161,930)]
 
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, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.o (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: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 491.15
Character \(\chi\) \(=\) 930.491
Dual form 930.2.o.e.161.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.151443 + 1.72542i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.72542 - 0.151443i) q^{6} +(-1.64767 + 2.85385i) q^{7} -1.00000i q^{8} +(-2.95413 - 0.522605i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.151443 + 1.72542i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.72542 - 0.151443i) q^{6} +(-1.64767 + 2.85385i) q^{7} -1.00000i q^{8} +(-2.95413 - 0.522605i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.34247 - 4.05727i) q^{11} +(0.151443 - 1.72542i) q^{12} +(-3.57649 + 2.06489i) q^{13} +(-2.85385 - 1.64767i) q^{14} +(0.731555 + 1.56998i) q^{15} +1.00000 q^{16} +(3.02223 - 5.23465i) q^{17} +(0.522605 - 2.95413i) q^{18} +(-1.11458 + 1.93051i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(-4.67456 - 3.27512i) q^{21} +(4.05727 - 2.34247i) q^{22} -0.244780 q^{23} +(1.72542 + 0.151443i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.06489 - 3.57649i) q^{26} +(1.34909 - 5.01796i) q^{27} +(1.64767 - 2.85385i) q^{28} -2.05814 q^{29} +(-1.56998 + 0.731555i) q^{30} +(-5.16785 + 2.07204i) q^{31} +1.00000i q^{32} +(7.35524 - 3.42729i) q^{33} +(5.23465 + 3.02223i) q^{34} +3.29535i q^{35} +(2.95413 + 0.522605i) q^{36} +(-7.39979 - 4.27227i) q^{37} +(-1.93051 - 1.11458i) q^{38} +(-3.02115 - 6.48364i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-6.83739 + 3.94757i) q^{41} +(3.27512 - 4.67456i) q^{42} +(10.0366 + 5.79463i) q^{43} +(2.34247 + 4.05727i) q^{44} +(-2.81965 + 1.02448i) q^{45} -0.244780i q^{46} -3.99299i q^{47} +(-0.151443 + 1.72542i) q^{48} +(-1.92965 - 3.34226i) q^{49} +(0.866025 + 0.500000i) q^{50} +(8.57426 + 6.00736i) q^{51} +(3.57649 - 2.06489i) q^{52} +(-0.996554 - 1.72608i) q^{53} +(5.01796 + 1.34909i) q^{54} +(-4.05727 - 2.34247i) q^{55} +(2.85385 + 1.64767i) q^{56} +(-3.16214 - 2.21548i) q^{57} -2.05814i q^{58} +(0.641535 + 0.370390i) q^{59} +(-0.731555 - 1.56998i) q^{60} -6.30131i q^{61} +(-2.07204 - 5.16785i) q^{62} +(6.35888 - 7.56957i) q^{63} -1.00000 q^{64} +(-2.06489 + 3.57649i) q^{65} +(3.42729 + 7.35524i) q^{66} +(1.90767 + 3.30418i) q^{67} +(-3.02223 + 5.23465i) q^{68} +(0.0370703 - 0.422348i) q^{69} -3.29535 q^{70} +(-8.36971 + 4.83225i) q^{71} +(-0.522605 + 2.95413i) q^{72} +(0.290365 - 0.167642i) q^{73} +(4.27227 - 7.39979i) q^{74} +(1.41853 + 0.993862i) q^{75} +(1.11458 - 1.93051i) q^{76} +15.4385 q^{77} +(6.48364 - 3.02115i) q^{78} +(-11.1206 - 6.42046i) q^{79} +(0.866025 - 0.500000i) q^{80} +(8.45377 + 3.08769i) q^{81} +(-3.94757 - 6.83739i) q^{82} +(1.42255 + 2.46393i) q^{83} +(4.67456 + 3.27512i) q^{84} -6.04445i q^{85} +(-5.79463 + 10.0366i) q^{86} +(0.311692 - 3.55116i) q^{87} +(-4.05727 + 2.34247i) q^{88} +0.149606 q^{89} +(-1.02448 - 2.81965i) q^{90} -13.6090i q^{91} +0.244780 q^{92} +(-2.79250 - 9.23049i) q^{93} +3.99299 q^{94} +2.22916i q^{95} +(-1.72542 - 0.151443i) q^{96} -7.67331 q^{97} +(3.34226 - 1.92965i) q^{98} +(4.79960 + 13.2099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.151443 + 1.72542i −0.0874357 + 0.996170i
\(4\) −1.00000 −0.500000
\(5\) 0.866025 0.500000i 0.387298 0.223607i
\(6\) −1.72542 0.151443i −0.704399 0.0618264i
\(7\) −1.64767 + 2.85385i −0.622762 + 1.07866i 0.366207 + 0.930533i \(0.380656\pi\)
−0.988969 + 0.148122i \(0.952677\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −2.95413 0.522605i −0.984710 0.174202i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) −2.34247 4.05727i −0.706281 1.22331i −0.966227 0.257691i \(-0.917038\pi\)
0.259947 0.965623i \(-0.416295\pi\)
\(12\) 0.151443 1.72542i 0.0437179 0.498085i
\(13\) −3.57649 + 2.06489i −0.991939 + 0.572696i −0.905853 0.423592i \(-0.860769\pi\)
−0.0860855 + 0.996288i \(0.527436\pi\)
\(14\) −2.85385 1.64767i −0.762725 0.440359i
\(15\) 0.731555 + 1.56998i 0.188887 + 0.405366i
\(16\) 1.00000 0.250000
\(17\) 3.02223 5.23465i 0.732998 1.26959i −0.222598 0.974910i \(-0.571454\pi\)
0.955596 0.294679i \(-0.0952128\pi\)
\(18\) 0.522605 2.95413i 0.123179 0.696295i
\(19\) −1.11458 + 1.93051i −0.255702 + 0.442889i −0.965086 0.261933i \(-0.915640\pi\)
0.709384 + 0.704822i \(0.248973\pi\)
\(20\) −0.866025 + 0.500000i −0.193649 + 0.111803i
\(21\) −4.67456 3.27512i −1.02007 0.714690i
\(22\) 4.05727 2.34247i 0.865014 0.499416i
\(23\) −0.244780 −0.0510402 −0.0255201 0.999674i \(-0.508124\pi\)
−0.0255201 + 0.999674i \(0.508124\pi\)
\(24\) 1.72542 + 0.151443i 0.352199 + 0.0309132i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) −2.06489 3.57649i −0.404957 0.701407i
\(27\) 1.34909 5.01796i 0.259633 0.965707i
\(28\) 1.64767 2.85385i 0.311381 0.539328i
\(29\) −2.05814 −0.382188 −0.191094 0.981572i \(-0.561203\pi\)
−0.191094 + 0.981572i \(0.561203\pi\)
\(30\) −1.56998 + 0.731555i −0.286637 + 0.133563i
\(31\) −5.16785 + 2.07204i −0.928173 + 0.372149i
\(32\) 1.00000i 0.176777i
\(33\) 7.35524 3.42729i 1.28038 0.596614i
\(34\) 5.23465 + 3.02223i 0.897735 + 0.518308i
\(35\) 3.29535i 0.557015i
\(36\) 2.95413 + 0.522605i 0.492355 + 0.0871009i
\(37\) −7.39979 4.27227i −1.21652 0.702357i −0.252347 0.967637i \(-0.581202\pi\)
−0.964172 + 0.265280i \(0.914536\pi\)
\(38\) −1.93051 1.11458i −0.313170 0.180809i
\(39\) −3.02115 6.48364i −0.483772 1.03821i
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) −6.83739 + 3.94757i −1.06782 + 0.616507i −0.927585 0.373611i \(-0.878119\pi\)
−0.140236 + 0.990118i \(0.544786\pi\)
\(42\) 3.27512 4.67456i 0.505362 0.721300i
\(43\) 10.0366 + 5.79463i 1.53057 + 0.883672i 0.999336 + 0.0364445i \(0.0116032\pi\)
0.531230 + 0.847228i \(0.321730\pi\)
\(44\) 2.34247 + 4.05727i 0.353140 + 0.611657i
\(45\) −2.81965 + 1.02448i −0.420329 + 0.152720i
\(46\) 0.244780i 0.0360909i
\(47\) 3.99299i 0.582437i −0.956656 0.291219i \(-0.905939\pi\)
0.956656 0.291219i \(-0.0940607\pi\)
\(48\) −0.151443 + 1.72542i −0.0218589 + 0.249043i
\(49\) −1.92965 3.34226i −0.275665 0.477466i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) 8.57426 + 6.00736i 1.20064 + 0.841198i
\(52\) 3.57649 2.06489i 0.495969 0.286348i
\(53\) −0.996554 1.72608i −0.136887 0.237096i 0.789430 0.613841i \(-0.210376\pi\)
−0.926317 + 0.376746i \(0.877043\pi\)
\(54\) 5.01796 + 1.34909i 0.682858 + 0.183589i
\(55\) −4.05727 2.34247i −0.547083 0.315858i
\(56\) 2.85385 + 1.64767i 0.381362 + 0.220180i
\(57\) −3.16214 2.21548i −0.418835 0.293447i
\(58\) 2.05814i 0.270247i
\(59\) 0.641535 + 0.370390i 0.0835207 + 0.0482207i 0.541179 0.840908i \(-0.317978\pi\)
−0.457658 + 0.889128i \(0.651312\pi\)
\(60\) −0.731555 1.56998i −0.0944434 0.202683i
\(61\) 6.30131i 0.806801i −0.915024 0.403400i \(-0.867828\pi\)
0.915024 0.403400i \(-0.132172\pi\)
\(62\) −2.07204 5.16785i −0.263149 0.656317i
\(63\) 6.35888 7.56957i 0.801144 0.953676i
\(64\) −1.00000 −0.125000
\(65\) −2.06489 + 3.57649i −0.256117 + 0.443608i
\(66\) 3.42729 + 7.35524i 0.421870 + 0.905367i
\(67\) 1.90767 + 3.30418i 0.233059 + 0.403669i 0.958707 0.284397i \(-0.0917933\pi\)
−0.725648 + 0.688066i \(0.758460\pi\)
\(68\) −3.02223 + 5.23465i −0.366499 + 0.634795i
\(69\) 0.0370703 0.422348i 0.00446273 0.0508447i
\(70\) −3.29535 −0.393869
\(71\) −8.36971 + 4.83225i −0.993302 + 0.573483i −0.906260 0.422722i \(-0.861075\pi\)
−0.0870422 + 0.996205i \(0.527741\pi\)
\(72\) −0.522605 + 2.95413i −0.0615896 + 0.348148i
\(73\) 0.290365 0.167642i 0.0339847 0.0196211i −0.482911 0.875669i \(-0.660421\pi\)
0.516896 + 0.856048i \(0.327087\pi\)
\(74\) 4.27227 7.39979i 0.496642 0.860208i
\(75\) 1.41853 + 0.993862i 0.163798 + 0.114761i
\(76\) 1.11458 1.93051i 0.127851 0.221444i
\(77\) 15.4385 1.75938
\(78\) 6.48364 3.02115i 0.734128 0.342078i
\(79\) −11.1206 6.42046i −1.25116 0.722358i −0.279820 0.960052i \(-0.590275\pi\)
−0.971340 + 0.237695i \(0.923608\pi\)
\(80\) 0.866025 0.500000i 0.0968246 0.0559017i
\(81\) 8.45377 + 3.08769i 0.939308 + 0.343076i
\(82\) −3.94757 6.83739i −0.435936 0.755063i
\(83\) 1.42255 + 2.46393i 0.156145 + 0.270451i 0.933475 0.358642i \(-0.116760\pi\)
−0.777330 + 0.629093i \(0.783427\pi\)
\(84\) 4.67456 + 3.27512i 0.510036 + 0.357345i
\(85\) 6.04445i 0.655613i
\(86\) −5.79463 + 10.0366i −0.624851 + 1.08227i
\(87\) 0.311692 3.55116i 0.0334168 0.380724i
\(88\) −4.05727 + 2.34247i −0.432507 + 0.249708i
\(89\) 0.149606 0.0158582 0.00792909 0.999969i \(-0.497476\pi\)
0.00792909 + 0.999969i \(0.497476\pi\)
\(90\) −1.02448 2.81965i −0.107989 0.297218i
\(91\) 13.6090i 1.42661i
\(92\) 0.244780 0.0255201
\(93\) −2.79250 9.23049i −0.289568 0.957157i
\(94\) 3.99299 0.411845
\(95\) 2.22916i 0.228707i
\(96\) −1.72542 0.151443i −0.176100 0.0154566i
\(97\) −7.67331 −0.779107 −0.389553 0.921004i \(-0.627371\pi\)
−0.389553 + 0.921004i \(0.627371\pi\)
\(98\) 3.34226 1.92965i 0.337619 0.194925i
\(99\) 4.79960 + 13.2099i 0.482378 + 1.32764i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 5.06959i 0.504443i −0.967669 0.252222i \(-0.918839\pi\)
0.967669 0.252222i \(-0.0811612\pi\)
\(102\) −6.00736 + 8.57426i −0.594817 + 0.848978i
\(103\) 9.37875 + 16.2445i 0.924115 + 1.60061i 0.792978 + 0.609251i \(0.208530\pi\)
0.131138 + 0.991364i \(0.458137\pi\)
\(104\) 2.06489 + 3.57649i 0.202479 + 0.350703i
\(105\) −5.68585 0.499058i −0.554882 0.0487030i
\(106\) 1.72608 0.996554i 0.167652 0.0967939i
\(107\) 3.66151 + 2.11397i 0.353971 + 0.204366i 0.666433 0.745565i \(-0.267820\pi\)
−0.312462 + 0.949930i \(0.601154\pi\)
\(108\) −1.34909 + 5.01796i −0.129817 + 0.482854i
\(109\) 5.84653 0.559996 0.279998 0.960001i \(-0.409666\pi\)
0.279998 + 0.960001i \(0.409666\pi\)
\(110\) 2.34247 4.05727i 0.223346 0.386846i
\(111\) 8.49210 12.1207i 0.806034 1.15045i
\(112\) −1.64767 + 2.85385i −0.155690 + 0.269664i
\(113\) −5.58805 + 3.22626i −0.525679 + 0.303501i −0.739255 0.673425i \(-0.764822\pi\)
0.213576 + 0.976926i \(0.431489\pi\)
\(114\) 2.21548 3.16214i 0.207498 0.296161i
\(115\) −0.211986 + 0.122390i −0.0197678 + 0.0114129i
\(116\) 2.05814 0.191094
\(117\) 11.6445 4.23085i 1.07654 0.391142i
\(118\) −0.370390 + 0.641535i −0.0340972 + 0.0590580i
\(119\) 9.95929 + 17.2500i 0.912966 + 1.58130i
\(120\) 1.56998 0.731555i 0.143319 0.0667815i
\(121\) −5.47431 + 9.48178i −0.497665 + 0.861980i
\(122\) 6.30131 0.570494
\(123\) −5.77573 12.3952i −0.520780 1.11764i
\(124\) 5.16785 2.07204i 0.464086 0.186075i
\(125\) 1.00000i 0.0894427i
\(126\) 7.56957 + 6.35888i 0.674351 + 0.566494i
\(127\) 0.366646 + 0.211683i 0.0325346 + 0.0187839i 0.516179 0.856481i \(-0.327354\pi\)
−0.483644 + 0.875265i \(0.660687\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −11.5181 + 16.4397i −1.01411 + 1.44744i
\(130\) −3.57649 2.06489i −0.313679 0.181102i
\(131\) 1.79983 + 1.03913i 0.157252 + 0.0907895i 0.576561 0.817054i \(-0.304394\pi\)
−0.419309 + 0.907844i \(0.637728\pi\)
\(132\) −7.35524 + 3.42729i −0.640191 + 0.298307i
\(133\) −3.67293 6.36169i −0.318483 0.551629i
\(134\) −3.30418 + 1.90767i −0.285437 + 0.164797i
\(135\) −1.34063 5.02023i −0.115383 0.432073i
\(136\) −5.23465 3.02223i −0.448868 0.259154i
\(137\) −9.76518 16.9138i −0.834296 1.44504i −0.894602 0.446863i \(-0.852541\pi\)
0.0603063 0.998180i \(-0.480792\pi\)
\(138\) 0.422348 + 0.0370703i 0.0359526 + 0.00315563i
\(139\) 22.5295i 1.91092i 0.295114 + 0.955462i \(0.404642\pi\)
−0.295114 + 0.955462i \(0.595358\pi\)
\(140\) 3.29535i 0.278508i
\(141\) 6.88957 + 0.604711i 0.580207 + 0.0509258i
\(142\) −4.83225 8.36971i −0.405514 0.702370i
\(143\) 16.7556 + 9.67385i 1.40117 + 0.808968i
\(144\) −2.95413 0.522605i −0.246177 0.0435504i
\(145\) −1.78240 + 1.02907i −0.148021 + 0.0854597i
\(146\) 0.167642 + 0.290365i 0.0138742 + 0.0240308i
\(147\) 6.05903 2.82330i 0.499740 0.232862i
\(148\) 7.39979 + 4.27227i 0.608259 + 0.351179i
\(149\) −13.4165 7.74601i −1.09912 0.634578i −0.163131 0.986604i \(-0.552159\pi\)
−0.935990 + 0.352027i \(0.885493\pi\)
\(150\) −0.993862 + 1.41853i −0.0811485 + 0.115823i
\(151\) 18.2693i 1.48673i −0.668884 0.743367i \(-0.733228\pi\)
0.668884 0.743367i \(-0.266772\pi\)
\(152\) 1.93051 + 1.11458i 0.156585 + 0.0904043i
\(153\) −11.6637 + 13.8844i −0.942955 + 1.12249i
\(154\) 15.4385i 1.24407i
\(155\) −3.43947 + 4.37836i −0.276265 + 0.351679i
\(156\) 3.02115 + 6.48364i 0.241886 + 0.519107i
\(157\) −18.3537 −1.46478 −0.732391 0.680885i \(-0.761596\pi\)
−0.732391 + 0.680885i \(0.761596\pi\)
\(158\) 6.42046 11.1206i 0.510784 0.884704i
\(159\) 3.12913 1.45807i 0.248156 0.115632i
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) 0.403318 0.698566i 0.0317859 0.0550548i
\(162\) −3.08769 + 8.45377i −0.242592 + 0.664191i
\(163\) 1.70445 0.133503 0.0667515 0.997770i \(-0.478737\pi\)
0.0667515 + 0.997770i \(0.478737\pi\)
\(164\) 6.83739 3.94757i 0.533910 0.308253i
\(165\) 4.65618 6.64574i 0.362483 0.517370i
\(166\) −2.46393 + 1.42255i −0.191238 + 0.110411i
\(167\) −6.28618 + 10.8880i −0.486439 + 0.842537i −0.999878 0.0155887i \(-0.995038\pi\)
0.513439 + 0.858126i \(0.328371\pi\)
\(168\) −3.27512 + 4.67456i −0.252681 + 0.360650i
\(169\) 2.02750 3.51174i 0.155962 0.270134i
\(170\) 6.04445 0.463588
\(171\) 4.30151 5.12049i 0.328944 0.391573i
\(172\) −10.0366 5.79463i −0.765283 0.441836i
\(173\) −2.25868 + 1.30405i −0.171724 + 0.0991450i −0.583399 0.812186i \(-0.698277\pi\)
0.411674 + 0.911331i \(0.364944\pi\)
\(174\) 3.55116 + 0.311692i 0.269212 + 0.0236293i
\(175\) 1.64767 + 2.85385i 0.124552 + 0.215731i
\(176\) −2.34247 4.05727i −0.176570 0.305828i
\(177\) −0.736234 + 1.05082i −0.0553387 + 0.0789846i
\(178\) 0.149606i 0.0112134i
\(179\) −9.49768 + 16.4505i −0.709890 + 1.22957i 0.255008 + 0.966939i \(0.417922\pi\)
−0.964898 + 0.262626i \(0.915411\pi\)
\(180\) 2.81965 1.02448i 0.210165 0.0763599i
\(181\) −14.3763 + 8.30014i −1.06858 + 0.616944i −0.927793 0.373096i \(-0.878296\pi\)
−0.140786 + 0.990040i \(0.544963\pi\)
\(182\) 13.6090 1.00877
\(183\) 10.8724 + 0.954291i 0.803711 + 0.0705432i
\(184\) 0.244780i 0.0180454i
\(185\) −8.54454 −0.628207
\(186\) 9.23049 2.79250i 0.676812 0.204756i
\(187\) −28.3179 −2.07081
\(188\) 3.99299i 0.291219i
\(189\) 12.0977 + 12.1181i 0.879975 + 0.881461i
\(190\) −2.22916 −0.161720
\(191\) −14.6036 + 8.43140i −1.05668 + 0.610074i −0.924512 0.381153i \(-0.875527\pi\)
−0.132168 + 0.991227i \(0.542194\pi\)
\(192\) 0.151443 1.72542i 0.0109295 0.124521i
\(193\) −3.46345 + 5.99887i −0.249305 + 0.431808i −0.963333 0.268308i \(-0.913535\pi\)
0.714028 + 0.700117i \(0.246869\pi\)
\(194\) 7.67331i 0.550912i
\(195\) −5.85822 4.10442i −0.419516 0.293924i
\(196\) 1.92965 + 3.34226i 0.137832 + 0.238733i
\(197\) −7.40933 12.8333i −0.527893 0.914337i −0.999471 0.0325129i \(-0.989649\pi\)
0.471579 0.881824i \(-0.343684\pi\)
\(198\) −13.2099 + 4.79960i −0.938787 + 0.341093i
\(199\) −16.4647 + 9.50589i −1.16715 + 0.673855i −0.953007 0.302947i \(-0.902029\pi\)
−0.214143 + 0.976802i \(0.568696\pi\)
\(200\) −0.866025 0.500000i −0.0612372 0.0353553i
\(201\) −5.98999 + 2.79113i −0.422501 + 0.196871i
\(202\) 5.06959 0.356695
\(203\) 3.39115 5.87364i 0.238012 0.412249i
\(204\) −8.57426 6.00736i −0.600318 0.420599i
\(205\) −3.94757 + 6.83739i −0.275710 + 0.477544i
\(206\) −16.2445 + 9.37875i −1.13181 + 0.653448i
\(207\) 0.723112 + 0.127923i 0.0502598 + 0.00889129i
\(208\) −3.57649 + 2.06489i −0.247985 + 0.143174i
\(209\) 10.4435 0.722390
\(210\) 0.499058 5.68585i 0.0344382 0.392361i
\(211\) −0.159771 + 0.276731i −0.0109991 + 0.0190509i −0.871473 0.490444i \(-0.836835\pi\)
0.860473 + 0.509495i \(0.170168\pi\)
\(212\) 0.996554 + 1.72608i 0.0684436 + 0.118548i
\(213\) −7.07012 15.1731i −0.484437 1.03964i
\(214\) −2.11397 + 3.66151i −0.144508 + 0.250296i
\(215\) 11.5893 0.790381
\(216\) −5.01796 1.34909i −0.341429 0.0917943i
\(217\) 2.60163 18.1623i 0.176610 1.23294i
\(218\) 5.84653i 0.395977i
\(219\) 0.245279 + 0.526389i 0.0165744 + 0.0355701i
\(220\) 4.05727 + 2.34247i 0.273541 + 0.157929i
\(221\) 24.9622i 1.67914i
\(222\) 12.1207 + 8.49210i 0.813490 + 0.569952i
\(223\) −1.19955 0.692562i −0.0803279 0.0463774i 0.459298 0.888282i \(-0.348101\pi\)
−0.539626 + 0.841905i \(0.681434\pi\)
\(224\) −2.85385 1.64767i −0.190681 0.110090i
\(225\) −1.92965 + 2.29705i −0.128644 + 0.153137i
\(226\) −3.22626 5.58805i −0.214608 0.371711i
\(227\) −7.88419 + 4.55194i −0.523292 + 0.302123i −0.738281 0.674494i \(-0.764362\pi\)
0.214988 + 0.976617i \(0.431029\pi\)
\(228\) 3.16214 + 2.21548i 0.209418 + 0.146724i
\(229\) 6.91782 + 3.99401i 0.457143 + 0.263931i 0.710842 0.703352i \(-0.248314\pi\)
−0.253699 + 0.967283i \(0.581647\pi\)
\(230\) −0.122390 0.211986i −0.00807016 0.0139779i
\(231\) −2.33805 + 26.6378i −0.153833 + 1.75264i
\(232\) 2.05814i 0.135124i
\(233\) 15.9529i 1.04511i 0.852606 + 0.522554i \(0.175021\pi\)
−0.852606 + 0.522554i \(0.824979\pi\)
\(234\) 4.23085 + 11.6445i 0.276579 + 0.761226i
\(235\) −1.99650 3.45803i −0.130237 0.225577i
\(236\) −0.641535 0.370390i −0.0417603 0.0241103i
\(237\) 12.7621 18.2153i 0.828987 1.18321i
\(238\) −17.2500 + 9.95929i −1.11815 + 0.645565i
\(239\) −4.52292 7.83393i −0.292564 0.506735i 0.681852 0.731491i \(-0.261175\pi\)
−0.974415 + 0.224756i \(0.927842\pi\)
\(240\) 0.731555 + 1.56998i 0.0472217 + 0.101342i
\(241\) 13.3621 + 7.71462i 0.860730 + 0.496943i 0.864257 0.503051i \(-0.167789\pi\)
−0.00352685 + 0.999994i \(0.501123\pi\)
\(242\) −9.48178 5.47431i −0.609512 0.351902i
\(243\) −6.60781 + 14.1187i −0.423891 + 0.905713i
\(244\) 6.30131i 0.403400i
\(245\) −3.34226 1.92965i −0.213529 0.123281i
\(246\) 12.3952 5.77573i 0.790288 0.368247i
\(247\) 9.20591i 0.585758i
\(248\) 2.07204 + 5.16785i 0.131575 + 0.328159i
\(249\) −4.46673 + 2.08134i −0.283068 + 0.131900i
\(250\) 1.00000 0.0632456
\(251\) 1.89792 3.28729i 0.119795 0.207492i −0.799891 0.600145i \(-0.795109\pi\)
0.919687 + 0.392653i \(0.128443\pi\)
\(252\) −6.35888 + 7.56957i −0.400572 + 0.476838i
\(253\) 0.573389 + 0.993140i 0.0360487 + 0.0624382i
\(254\) −0.211683 + 0.366646i −0.0132822 + 0.0230054i
\(255\) 10.4292 + 0.915391i 0.653102 + 0.0573240i
\(256\) 1.00000 0.0625000
\(257\) 26.8650 15.5105i 1.67579 0.967518i 0.711495 0.702691i \(-0.248018\pi\)
0.964296 0.264828i \(-0.0853150\pi\)
\(258\) −16.4397 11.5181i −1.02349 0.717087i
\(259\) 24.3849 14.0786i 1.51520 0.874803i
\(260\) 2.06489 3.57649i 0.128059 0.221804i
\(261\) 6.08002 + 1.07560i 0.376344 + 0.0665777i
\(262\) −1.03913 + 1.79983i −0.0641979 + 0.111194i
\(263\) 21.5086 1.32627 0.663137 0.748498i \(-0.269225\pi\)
0.663137 + 0.748498i \(0.269225\pi\)
\(264\) −3.42729 7.35524i −0.210935 0.452684i
\(265\) −1.72608 0.996554i −0.106032 0.0612178i
\(266\) 6.36169 3.67293i 0.390060 0.225202i
\(267\) −0.0226568 + 0.258132i −0.00138657 + 0.0157975i
\(268\) −1.90767 3.30418i −0.116529 0.201835i
\(269\) 13.5212 + 23.4194i 0.824401 + 1.42791i 0.902376 + 0.430950i \(0.141821\pi\)
−0.0779746 + 0.996955i \(0.524845\pi\)
\(270\) 5.02023 1.34063i 0.305521 0.0815882i
\(271\) 16.9825i 1.03162i −0.856704 0.515808i \(-0.827492\pi\)
0.856704 0.515808i \(-0.172508\pi\)
\(272\) 3.02223 5.23465i 0.183249 0.317397i
\(273\) 23.4812 + 2.06099i 1.42115 + 0.124737i
\(274\) 16.9138 9.76518i 1.02180 0.589936i
\(275\) −4.68494 −0.282512
\(276\) −0.0370703 + 0.422348i −0.00223137 + 0.0254223i
\(277\) 23.1214i 1.38923i 0.719381 + 0.694616i \(0.244426\pi\)
−0.719381 + 0.694616i \(0.755574\pi\)
\(278\) −22.5295 −1.35123
\(279\) 16.3494 3.42033i 0.978810 0.204770i
\(280\) 3.29535 0.196935
\(281\) 26.0722i 1.55534i −0.628674 0.777669i \(-0.716402\pi\)
0.628674 0.777669i \(-0.283598\pi\)
\(282\) −0.604711 + 6.88957i −0.0360100 + 0.410268i
\(283\) 14.5905 0.867315 0.433657 0.901078i \(-0.357223\pi\)
0.433657 + 0.901078i \(0.357223\pi\)
\(284\) 8.36971 4.83225i 0.496651 0.286742i
\(285\) −3.84623 0.337591i −0.227831 0.0199972i
\(286\) −9.67385 + 16.7556i −0.572027 + 0.990780i
\(287\) 26.0172i 1.53575i
\(288\) 0.522605 2.95413i 0.0307948 0.174074i
\(289\) −9.76772 16.9182i −0.574571 0.995187i
\(290\) −1.02907 1.78240i −0.0604292 0.104666i
\(291\) 1.16207 13.2397i 0.0681218 0.776123i
\(292\) −0.290365 + 0.167642i −0.0169923 + 0.00981053i
\(293\) −24.7303 14.2780i −1.44476 0.834132i −0.446598 0.894735i \(-0.647364\pi\)
−0.998162 + 0.0606026i \(0.980698\pi\)
\(294\) 2.82330 + 6.05903i 0.164658 + 0.353370i
\(295\) 0.740780 0.0431299
\(296\) −4.27227 + 7.39979i −0.248321 + 0.430104i
\(297\) −23.5195 + 6.28077i −1.36474 + 0.364447i
\(298\) 7.74601 13.4165i 0.448714 0.777196i
\(299\) 0.875452 0.505443i 0.0506287 0.0292305i
\(300\) −1.41853 0.993862i −0.0818991 0.0573807i
\(301\) −33.0740 + 19.0953i −1.90636 + 1.10064i
\(302\) 18.2693 1.05128
\(303\) 8.74716 + 0.767755i 0.502511 + 0.0441064i
\(304\) −1.11458 + 1.93051i −0.0639255 + 0.110722i
\(305\) −3.15066 5.45710i −0.180406 0.312473i
\(306\) −13.8844 11.6637i −0.793719 0.666770i
\(307\) 4.69037 8.12397i 0.267694 0.463659i −0.700572 0.713582i \(-0.747072\pi\)
0.968266 + 0.249922i \(0.0804051\pi\)
\(308\) −15.4385 −0.879689
\(309\) −29.4488 + 13.7221i −1.67529 + 0.780625i
\(310\) −4.37836 3.43947i −0.248674 0.195349i
\(311\) 1.63457i 0.0926879i 0.998926 + 0.0463440i \(0.0147570\pi\)
−0.998926 + 0.0463440i \(0.985243\pi\)
\(312\) −6.48364 + 3.02115i −0.367064 + 0.171039i
\(313\) 10.6934 + 6.17384i 0.604427 + 0.348966i 0.770781 0.637100i \(-0.219866\pi\)
−0.166354 + 0.986066i \(0.553200\pi\)
\(314\) 18.3537i 1.03576i
\(315\) 1.72217 9.73488i 0.0970330 0.548498i
\(316\) 11.1206 + 6.42046i 0.625580 + 0.361179i
\(317\) 29.5244 + 17.0459i 1.65825 + 0.957393i 0.973521 + 0.228598i \(0.0734141\pi\)
0.684732 + 0.728795i \(0.259919\pi\)
\(318\) 1.45807 + 3.12913i 0.0817644 + 0.175473i
\(319\) 4.82113 + 8.35045i 0.269932 + 0.467535i
\(320\) −0.866025 + 0.500000i −0.0484123 + 0.0279508i
\(321\) −4.20200 + 5.99748i −0.234533 + 0.334747i
\(322\) 0.698566 + 0.403318i 0.0389296 + 0.0224760i
\(323\) 6.73702 + 11.6689i 0.374858 + 0.649273i
\(324\) −8.45377 3.08769i −0.469654 0.171538i
\(325\) 4.12977i 0.229078i
\(326\) 1.70445i 0.0944009i
\(327\) −0.885417 + 10.0877i −0.0489636 + 0.557851i
\(328\) 3.94757 + 6.83739i 0.217968 + 0.377532i
\(329\) 11.3954 + 6.57914i 0.628249 + 0.362720i
\(330\) 6.64574 + 4.65618i 0.365836 + 0.256314i
\(331\) 19.1972 11.0835i 1.05517 0.609205i 0.131080 0.991372i \(-0.458155\pi\)
0.924093 + 0.382167i \(0.124822\pi\)
\(332\) −1.42255 2.46393i −0.0780725 0.135225i
\(333\) 19.6272 + 16.4880i 1.07557 + 0.903538i
\(334\) −10.8880 6.28618i −0.595764 0.343964i
\(335\) 3.30418 + 1.90767i 0.180526 + 0.104227i
\(336\) −4.67456 3.27512i −0.255018 0.178672i
\(337\) 24.0073i 1.30776i −0.756597 0.653881i \(-0.773140\pi\)
0.756597 0.653881i \(-0.226860\pi\)
\(338\) 3.51174 + 2.02750i 0.191013 + 0.110282i
\(339\) −4.72038 10.1303i −0.256376 0.550203i
\(340\) 6.04445i 0.327807i
\(341\) 20.5123 + 16.1137i 1.11081 + 0.872605i
\(342\) 5.12049 + 4.30151i 0.276884 + 0.232599i
\(343\) −10.3497 −0.558829
\(344\) 5.79463 10.0366i 0.312425 0.541137i
\(345\) −0.179070 0.384299i −0.00964081 0.0206900i
\(346\) −1.30405 2.25868i −0.0701061 0.121427i
\(347\) −14.1185 + 24.4539i −0.757919 + 1.31275i 0.185992 + 0.982551i \(0.440450\pi\)
−0.943910 + 0.330202i \(0.892883\pi\)
\(348\) −0.311692 + 3.55116i −0.0167084 + 0.190362i
\(349\) 14.1084 0.755205 0.377602 0.925968i \(-0.376749\pi\)
0.377602 + 0.925968i \(0.376749\pi\)
\(350\) −2.85385 + 1.64767i −0.152545 + 0.0880718i
\(351\) 5.53650 + 20.7324i 0.295516 + 1.10661i
\(352\) 4.05727 2.34247i 0.216253 0.124854i
\(353\) −11.1592 + 19.3283i −0.593943 + 1.02874i 0.399752 + 0.916623i \(0.369096\pi\)
−0.993695 + 0.112116i \(0.964237\pi\)
\(354\) −1.05082 0.736234i −0.0558506 0.0391304i
\(355\) −4.83225 + 8.36971i −0.256469 + 0.444218i
\(356\) −0.149606 −0.00792909
\(357\) −31.2717 + 14.5715i −1.65507 + 0.771207i
\(358\) −16.4505 9.49768i −0.869434 0.501968i
\(359\) −4.93899 + 2.85152i −0.260670 + 0.150498i −0.624640 0.780913i \(-0.714754\pi\)
0.363970 + 0.931411i \(0.381421\pi\)
\(360\) 1.02448 + 2.81965i 0.0539946 + 0.148609i
\(361\) 7.01543 + 12.1511i 0.369233 + 0.639530i
\(362\) −8.30014 14.3763i −0.436245 0.755599i
\(363\) −15.5310 10.8814i −0.815166 0.571127i
\(364\) 13.6090i 0.713307i
\(365\) 0.167642 0.290365i 0.00877480 0.0151984i
\(366\) −0.954291 + 10.8724i −0.0498816 + 0.568309i
\(367\) 27.7580 16.0261i 1.44896 0.836555i 0.450537 0.892758i \(-0.351233\pi\)
0.998419 + 0.0562025i \(0.0178992\pi\)
\(368\) −0.244780 −0.0127600
\(369\) 22.2616 8.08838i 1.15889 0.421064i
\(370\) 8.54454i 0.444210i
\(371\) 6.56798 0.340993
\(372\) 2.79250 + 9.23049i 0.144784 + 0.478579i
\(373\) −22.0309 −1.14072 −0.570359 0.821396i \(-0.693196\pi\)
−0.570359 + 0.821396i \(0.693196\pi\)
\(374\) 28.3179i 1.46428i
\(375\) 1.72542 + 0.151443i 0.0891002 + 0.00782049i
\(376\) −3.99299 −0.205923
\(377\) 7.36092 4.24983i 0.379107 0.218877i
\(378\) −12.1181 + 12.0977i −0.623287 + 0.622237i
\(379\) 11.4743 19.8741i 0.589397 1.02087i −0.404915 0.914355i \(-0.632699\pi\)
0.994312 0.106511i \(-0.0339679\pi\)
\(380\) 2.22916i 0.114353i
\(381\) −0.420768 + 0.600560i −0.0215566 + 0.0307676i
\(382\) −8.43140 14.6036i −0.431388 0.747186i
\(383\) −5.15835 8.93453i −0.263579 0.456533i 0.703611 0.710585i \(-0.251570\pi\)
−0.967190 + 0.254052i \(0.918236\pi\)
\(384\) 1.72542 + 0.151443i 0.0880498 + 0.00772830i
\(385\) 13.3701 7.71924i 0.681404 0.393409i
\(386\) −5.99887 3.46345i −0.305335 0.176285i
\(387\) −26.6211 22.3633i −1.35323 1.13679i
\(388\) 7.67331 0.389553
\(389\) 12.7371 22.0613i 0.645798 1.11855i −0.338319 0.941031i \(-0.609858\pi\)
0.984117 0.177523i \(-0.0568083\pi\)
\(390\) 4.10442 5.85822i 0.207836 0.296642i
\(391\) −0.739781 + 1.28134i −0.0374123 + 0.0648001i
\(392\) −3.34226 + 1.92965i −0.168810 + 0.0974623i
\(393\) −2.06551 + 2.94809i −0.104191 + 0.148711i
\(394\) 12.8333 7.40933i 0.646534 0.373276i
\(395\) −12.8409 −0.646096
\(396\) −4.79960 13.2099i −0.241189 0.663822i
\(397\) 3.16333 5.47906i 0.158763 0.274986i −0.775660 0.631151i \(-0.782583\pi\)
0.934423 + 0.356165i \(0.115916\pi\)
\(398\) −9.50589 16.4647i −0.476487 0.825300i
\(399\) 11.5328 5.37389i 0.577363 0.269031i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) −25.4504 −1.27093 −0.635465 0.772130i \(-0.719192\pi\)
−0.635465 + 0.772130i \(0.719192\pi\)
\(402\) −2.79113 5.98999i −0.139209 0.298753i
\(403\) 14.2042 18.0816i 0.707562 0.900710i
\(404\) 5.06959i 0.252222i
\(405\) 8.86502 1.55287i 0.440506 0.0771626i
\(406\) 5.87364 + 3.39115i 0.291504 + 0.168300i
\(407\) 40.0306i 1.98425i
\(408\) 6.00736 8.57426i 0.297408 0.424489i
\(409\) 31.9037 + 18.4196i 1.57754 + 0.910790i 0.995202 + 0.0978399i \(0.0311933\pi\)
0.582333 + 0.812950i \(0.302140\pi\)
\(410\) −6.83739 3.94757i −0.337675 0.194957i
\(411\) 30.6622 14.2875i 1.51246 0.704752i
\(412\) −9.37875 16.2445i −0.462058 0.800307i
\(413\) −2.11408 + 1.22056i −0.104027 + 0.0600600i
\(414\) −0.127923 + 0.723112i −0.00628709 + 0.0355390i
\(415\) 2.46393 + 1.42255i 0.120949 + 0.0698301i
\(416\) −2.06489 3.57649i −0.101239 0.175352i
\(417\) −38.8727 3.41193i −1.90361 0.167083i
\(418\) 10.4435i 0.510807i
\(419\) 8.72337i 0.426164i 0.977034 + 0.213082i \(0.0683502\pi\)
−0.977034 + 0.213082i \(0.931650\pi\)
\(420\) 5.68585 + 0.499058i 0.277441 + 0.0243515i
\(421\) −2.19810 3.80721i −0.107129 0.185552i 0.807477 0.589899i \(-0.200832\pi\)
−0.914606 + 0.404347i \(0.867499\pi\)
\(422\) −0.276731 0.159771i −0.0134711 0.00777752i
\(423\) −2.08676 + 11.7958i −0.101462 + 0.573532i
\(424\) −1.72608 + 0.996554i −0.0838260 + 0.0483969i
\(425\) −3.02223 5.23465i −0.146600 0.253918i
\(426\) 15.1731 7.07012i 0.735137 0.342548i
\(427\) 17.9830 + 10.3825i 0.870260 + 0.502445i
\(428\) −3.66151 2.11397i −0.176986 0.102183i
\(429\) −19.2290 + 27.4454i −0.928383 + 1.32508i
\(430\) 11.5893i 0.558883i
\(431\) −12.3311 7.11935i −0.593967 0.342927i 0.172698 0.984975i \(-0.444752\pi\)
−0.766665 + 0.642048i \(0.778085\pi\)
\(432\) 1.34909 5.01796i 0.0649084 0.241427i
\(433\) 16.3649i 0.786448i 0.919443 + 0.393224i \(0.128640\pi\)
−0.919443 + 0.393224i \(0.871360\pi\)
\(434\) 18.1623 + 2.60163i 0.871820 + 0.124882i
\(435\) −1.50564 3.23124i −0.0721901 0.154926i
\(436\) −5.84653 −0.279998
\(437\) 0.272827 0.472550i 0.0130511 0.0226051i
\(438\) −0.526389 + 0.245279i −0.0251519 + 0.0117199i
\(439\) −6.66688 11.5474i −0.318193 0.551126i 0.661918 0.749576i \(-0.269743\pi\)
−0.980111 + 0.198450i \(0.936409\pi\)
\(440\) −2.34247 + 4.05727i −0.111673 + 0.193423i
\(441\) 3.95377 + 10.8819i 0.188275 + 0.518186i
\(442\) −24.9622 −1.18733
\(443\) 18.7900 10.8484i 0.892742 0.515425i 0.0179037 0.999840i \(-0.494301\pi\)
0.874838 + 0.484415i \(0.160967\pi\)
\(444\) −8.49210 + 12.1207i −0.403017 + 0.575224i
\(445\) 0.129562 0.0748029i 0.00614185 0.00354600i
\(446\) 0.692562 1.19955i 0.0327937 0.0568004i
\(447\) 15.3969 21.9759i 0.728250 1.03943i
\(448\) 1.64767 2.85385i 0.0778452 0.134832i
\(449\) 5.51787 0.260405 0.130202 0.991487i \(-0.458437\pi\)
0.130202 + 0.991487i \(0.458437\pi\)
\(450\) −2.29705 1.92965i −0.108284 0.0909648i
\(451\) 32.0327 + 18.4941i 1.50836 + 0.870854i
\(452\) 5.58805 3.22626i 0.262840 0.151751i
\(453\) 31.5221 + 2.76676i 1.48104 + 0.129994i
\(454\) −4.55194 7.88419i −0.213633 0.370024i
\(455\) −6.80451 11.7858i −0.319000 0.552525i
\(456\) −2.21548 + 3.16214i −0.103749 + 0.148081i
\(457\) 17.8127i 0.833241i 0.909081 + 0.416620i \(0.136786\pi\)
−0.909081 + 0.416620i \(0.863214\pi\)
\(458\) −3.99401 + 6.91782i −0.186628 + 0.323249i
\(459\) −22.1900 22.2275i −1.03574 1.03749i
\(460\) 0.211986 0.122390i 0.00988389 0.00570646i
\(461\) −10.7060 −0.498630 −0.249315 0.968422i \(-0.580205\pi\)
−0.249315 + 0.968422i \(0.580205\pi\)
\(462\) −26.6378 2.33805i −1.23930 0.108776i
\(463\) 23.2499i 1.08051i 0.841500 + 0.540257i \(0.181673\pi\)
−0.841500 + 0.540257i \(0.818327\pi\)
\(464\) −2.05814 −0.0955469
\(465\) −7.03362 6.59759i −0.326176 0.305956i
\(466\) −15.9529 −0.739003
\(467\) 1.78177i 0.0824507i −0.999150 0.0412253i \(-0.986874\pi\)
0.999150 0.0412253i \(-0.0131262\pi\)
\(468\) −11.6445 + 4.23085i −0.538268 + 0.195571i
\(469\) −12.5728 −0.580560
\(470\) 3.45803 1.99650i 0.159507 0.0920914i
\(471\) 2.77954 31.6677i 0.128074 1.45917i
\(472\) 0.370390 0.641535i 0.0170486 0.0295290i
\(473\) 54.2949i 2.49648i
\(474\) 18.2153 + 12.7621i 0.836655 + 0.586183i
\(475\) 1.11458 + 1.93051i 0.0511404 + 0.0885778i
\(476\) −9.95929 17.2500i −0.456483 0.790652i
\(477\) 2.04189 + 5.61988i 0.0934917 + 0.257316i
\(478\) 7.83393 4.52292i 0.358316 0.206874i
\(479\) −30.8844 17.8311i −1.41115 0.814725i −0.415649 0.909525i \(-0.636445\pi\)
−0.995496 + 0.0948002i \(0.969779\pi\)
\(480\) −1.56998 + 0.731555i −0.0716593 + 0.0333908i
\(481\) 35.2870 1.60895
\(482\) −7.71462 + 13.3621i −0.351391 + 0.608628i
\(483\) 1.14424 + 0.801684i 0.0520647 + 0.0364779i
\(484\) 5.47431 9.48178i 0.248832 0.430990i
\(485\) −6.64528 + 3.83666i −0.301747 + 0.174214i
\(486\) −14.1187 6.60781i −0.640436 0.299737i
\(487\) 9.14547 5.28014i 0.414421 0.239266i −0.278267 0.960504i \(-0.589760\pi\)
0.692687 + 0.721238i \(0.256427\pi\)
\(488\) −6.30131 −0.285247
\(489\) −0.258128 + 2.94089i −0.0116729 + 0.132992i
\(490\) 1.92965 3.34226i 0.0871729 0.150988i
\(491\) −8.01143 13.8762i −0.361551 0.626224i 0.626665 0.779288i \(-0.284419\pi\)
−0.988216 + 0.153064i \(0.951086\pi\)
\(492\) 5.77573 + 12.3952i 0.260390 + 0.558818i
\(493\) −6.22018 + 10.7737i −0.280143 + 0.485221i
\(494\) 9.20591 0.414194
\(495\) 10.7615 + 9.04031i 0.483695 + 0.406332i
\(496\) −5.16785 + 2.07204i −0.232043 + 0.0930373i
\(497\) 31.8479i 1.42857i
\(498\) −2.08134 4.46673i −0.0932673 0.200159i
\(499\) 15.8026 + 9.12364i 0.707422 + 0.408430i 0.810106 0.586284i \(-0.199410\pi\)
−0.102684 + 0.994714i \(0.532743\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) −17.8343 12.4952i −0.796778 0.558244i
\(502\) 3.28729 + 1.89792i 0.146719 + 0.0847082i
\(503\) −30.0423 17.3449i −1.33952 0.773371i −0.352782 0.935706i \(-0.614764\pi\)
−0.986736 + 0.162335i \(0.948098\pi\)
\(504\) −7.56957 6.35888i −0.337176 0.283247i
\(505\) −2.53480 4.39040i −0.112797 0.195370i
\(506\) −0.993140 + 0.573389i −0.0441504 + 0.0254903i
\(507\) 5.75216 + 4.03011i 0.255462 + 0.178984i
\(508\) −0.366646 0.211683i −0.0162673 0.00939193i
\(509\) −9.89991 17.1472i −0.438806 0.760034i 0.558792 0.829308i \(-0.311265\pi\)
−0.997598 + 0.0692738i \(0.977932\pi\)
\(510\) −0.915391 + 10.4292i −0.0405342 + 0.461813i
\(511\) 1.10488i 0.0488770i
\(512\) 1.00000i 0.0441942i
\(513\) 8.18354 + 8.19736i 0.361312 + 0.361922i
\(514\) 15.5105 + 26.8650i 0.684139 + 1.18496i
\(515\) 16.2445 + 9.37875i 0.715817 + 0.413277i
\(516\) 11.5181 16.4397i 0.507057 0.723720i
\(517\) −16.2007 + 9.35345i −0.712504 + 0.411364i
\(518\) 14.0786 + 24.3849i 0.618579 + 1.07141i
\(519\) −1.90797 4.09465i −0.0837505 0.179735i
\(520\) 3.57649 + 2.06489i 0.156839 + 0.0905512i
\(521\) 27.2181 + 15.7144i 1.19245 + 0.688460i 0.958861 0.283876i \(-0.0916204\pi\)
0.233587 + 0.972336i \(0.424954\pi\)
\(522\) −1.07560 + 6.08002i −0.0470776 + 0.266115i
\(523\) 30.9522i 1.35345i −0.736237 0.676723i \(-0.763399\pi\)
0.736237 0.676723i \(-0.236601\pi\)
\(524\) −1.79983 1.03913i −0.0786260 0.0453947i
\(525\) −5.17362 + 2.41073i −0.225795 + 0.105213i
\(526\) 21.5086i 0.937818i
\(527\) −4.77201 + 33.3141i −0.207872 + 1.45118i
\(528\) 7.35524 3.42729i 0.320096 0.149154i
\(529\) −22.9401 −0.997395
\(530\) 0.996554 1.72608i 0.0432875 0.0749762i
\(531\) −1.70161 1.42945i −0.0738435 0.0620328i
\(532\) 3.67293 + 6.36169i 0.159242 + 0.275814i
\(533\) 16.3026 28.2369i 0.706142 1.22307i
\(534\) −0.258132 0.0226568i −0.0111705 0.000980454i
\(535\) 4.22795 0.182790
\(536\) 3.30418 1.90767i 0.142719 0.0823987i
\(537\) −26.9456 18.8788i −1.16279 0.814679i
\(538\) −23.4194 + 13.5212i −1.00968 + 0.582940i
\(539\) −9.04031 + 15.6583i −0.389394 + 0.674449i
\(540\) 1.34063 + 5.02023i 0.0576916 + 0.216036i
\(541\) 21.6449 37.4901i 0.930588 1.61183i 0.148270 0.988947i \(-0.452630\pi\)
0.782318 0.622879i \(-0.214037\pi\)
\(542\) 16.9825 0.729463
\(543\) −12.1440 26.0620i −0.521149 1.11843i
\(544\) 5.23465 + 3.02223i 0.224434 + 0.129577i
\(545\) 5.06324 2.92326i 0.216885 0.125219i
\(546\) −2.06099 + 23.4812i −0.0882024 + 1.00490i
\(547\) 2.09475 + 3.62821i 0.0895650 + 0.155131i 0.907327 0.420425i \(-0.138119\pi\)
−0.817762 + 0.575556i \(0.804786\pi\)
\(548\) 9.76518 + 16.9138i 0.417148 + 0.722522i
\(549\) −3.29310 + 18.6149i −0.140546 + 0.794465i
\(550\) 4.68494i 0.199766i
\(551\) 2.29396 3.97326i 0.0977261 0.169267i
\(552\) −0.422348 0.0370703i −0.0179763 0.00157781i
\(553\) 36.6461 21.1576i 1.55835 0.899714i
\(554\) −23.1214 −0.982336
\(555\) 1.29401 14.7429i 0.0549278 0.625801i
\(556\) 22.5295i 0.955462i
\(557\) 33.3611 1.41356 0.706778 0.707435i \(-0.250148\pi\)
0.706778 + 0.707435i \(0.250148\pi\)
\(558\) 3.42033 + 16.3494i 0.144794 + 0.692123i
\(559\) −47.8610 −2.02430
\(560\) 3.29535i 0.139254i
\(561\) 4.28855 48.8602i 0.181063 2.06288i
\(562\) 26.0722 1.09979
\(563\) 3.50089 2.02124i 0.147545 0.0851851i −0.424410 0.905470i \(-0.639518\pi\)
0.571955 + 0.820285i \(0.306185\pi\)
\(564\) −6.88957 0.604711i −0.290103 0.0254629i
\(565\) −3.22626 + 5.58805i −0.135730 + 0.235091i
\(566\) 14.5905i 0.613284i
\(567\) −22.7409 + 19.0383i −0.955026 + 0.799534i
\(568\) 4.83225 + 8.36971i 0.202757 + 0.351185i
\(569\) −1.92967 3.34229i −0.0808961 0.140116i 0.822739 0.568419i \(-0.192445\pi\)
−0.903635 + 0.428303i \(0.859112\pi\)
\(570\) 0.337591 3.84623i 0.0141401 0.161101i
\(571\) 27.2167 15.7136i 1.13898 0.657593i 0.192805 0.981237i \(-0.438241\pi\)
0.946179 + 0.323644i \(0.104908\pi\)
\(572\) −16.7556 9.67385i −0.700587 0.404484i
\(573\) −12.3361 26.4742i −0.515346 1.10598i
\(574\) 26.0172 1.08594
\(575\) −0.122390 + 0.211986i −0.00510402 + 0.00884042i
\(576\) 2.95413 + 0.522605i 0.123089 + 0.0217752i
\(577\) 0.696828 1.20694i 0.0290093 0.0502457i −0.851156 0.524912i \(-0.824098\pi\)
0.880166 + 0.474667i \(0.157431\pi\)
\(578\) 16.9182 9.76772i 0.703703 0.406283i
\(579\) −9.82604 6.88438i −0.408356 0.286105i
\(580\) 1.78240 1.02907i 0.0740103 0.0427299i
\(581\) −9.37558 −0.388965
\(582\) 13.2397 + 1.16207i 0.548802 + 0.0481694i
\(583\) −4.66879 + 8.08658i −0.193362 + 0.334912i
\(584\) −0.167642 0.290365i −0.00693709 0.0120154i
\(585\) 7.96903 9.48628i 0.329479 0.392210i
\(586\) 14.2780 24.7303i 0.589821 1.02160i
\(587\) 44.2243 1.82533 0.912666 0.408706i \(-0.134020\pi\)
0.912666 + 0.408706i \(0.134020\pi\)
\(588\) −6.05903 + 2.82330i −0.249870 + 0.116431i
\(589\) 1.75989 12.2860i 0.0725149 0.506237i
\(590\) 0.740780i 0.0304974i
\(591\) 23.2649 10.8407i 0.956992 0.445925i
\(592\) −7.39979 4.27227i −0.304130 0.175589i
\(593\) 14.8656i 0.610459i −0.952279 0.305229i \(-0.901267\pi\)
0.952279 0.305229i \(-0.0987332\pi\)
\(594\) −6.28077 23.5195i −0.257703 0.965015i
\(595\) 17.2500 + 9.95929i 0.707181 + 0.408291i
\(596\) 13.4165 + 7.74601i 0.549560 + 0.317289i
\(597\) −13.9082 29.8481i −0.569223 1.22160i
\(598\) 0.505443 + 0.875452i 0.0206691 + 0.0357999i
\(599\) −23.8479 + 13.7686i −0.974397 + 0.562568i −0.900574 0.434703i \(-0.856853\pi\)
−0.0738230 + 0.997271i \(0.523520\pi\)
\(600\) 0.993862 1.41853i 0.0405743 0.0579114i
\(601\) −30.8947 17.8371i −1.26022 0.727589i −0.287105 0.957899i \(-0.592693\pi\)
−0.973117 + 0.230310i \(0.926026\pi\)
\(602\) −19.0953 33.0740i −0.778266 1.34800i
\(603\) −3.90872 10.7579i −0.159175 0.438096i
\(604\) 18.2693i 0.743367i
\(605\) 10.9486i 0.445125i
\(606\) −0.767755 + 8.74716i −0.0311879 + 0.355329i
\(607\) 22.4644 + 38.9094i 0.911801 + 1.57929i 0.811519 + 0.584327i \(0.198641\pi\)
0.100282 + 0.994959i \(0.468025\pi\)
\(608\) −1.93051 1.11458i −0.0782924 0.0452022i
\(609\) 9.62091 + 6.74067i 0.389859 + 0.273146i
\(610\) 5.45710 3.15066i 0.220951 0.127566i
\(611\) 8.24507 + 14.2809i 0.333560 + 0.577742i
\(612\) 11.6637 13.8844i 0.471477 0.561244i
\(613\) 36.0994 + 20.8420i 1.45804 + 0.841800i 0.998915 0.0465721i \(-0.0148297\pi\)
0.459125 + 0.888372i \(0.348163\pi\)
\(614\) 8.12397 + 4.69037i 0.327857 + 0.189288i
\(615\) −11.1995 7.84668i −0.451608 0.316409i
\(616\) 15.4385i 0.622034i
\(617\) −37.6159 21.7175i −1.51436 0.874316i −0.999858 0.0168256i \(-0.994644\pi\)
−0.514501 0.857490i \(-0.672023\pi\)
\(618\) −13.7221 29.4488i −0.551985 1.18461i
\(619\) 38.4345i 1.54481i −0.635129 0.772406i \(-0.719053\pi\)
0.635129 0.772406i \(-0.280947\pi\)
\(620\) 3.43947 4.37836i 0.138132 0.175839i
\(621\) −0.330231 + 1.22830i −0.0132517 + 0.0492899i
\(622\) −1.63457 −0.0655403
\(623\) −0.246502 + 0.426953i −0.00987587 + 0.0171055i
\(624\) −3.02115 6.48364i −0.120943 0.259553i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −6.17384 + 10.6934i −0.246756 + 0.427394i
\(627\) −1.58159 + 18.0193i −0.0631627 + 0.719623i
\(628\) 18.3537 0.732391
\(629\) −44.7277 + 25.8236i −1.78341 + 1.02965i
\(630\) 9.73488 + 1.72217i 0.387847 + 0.0686127i
\(631\) 5.86942 3.38871i 0.233658 0.134902i −0.378601 0.925560i \(-0.623595\pi\)
0.612258 + 0.790658i \(0.290261\pi\)
\(632\) −6.42046 + 11.1206i −0.255392 + 0.442352i
\(633\) −0.453280 0.317580i −0.0180163 0.0126227i
\(634\) −17.0459 + 29.5244i −0.676979 + 1.17256i
\(635\) 0.423367 0.0168008
\(636\) −3.12913 + 1.45807i −0.124078 + 0.0578162i
\(637\) 13.8028 + 7.96903i 0.546885 + 0.315744i
\(638\) −8.35045 + 4.82113i −0.330597 + 0.190870i
\(639\) 27.2506 9.90105i 1.07802 0.391680i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 1.51314 + 2.62083i 0.0597653 + 0.103517i 0.894360 0.447348i \(-0.147631\pi\)
−0.834595 + 0.550865i \(0.814298\pi\)
\(642\) −5.99748 4.20200i −0.236702 0.165840i
\(643\) 8.47085i 0.334058i −0.985952 0.167029i \(-0.946583\pi\)
0.985952 0.167029i \(-0.0534173\pi\)
\(644\) −0.403318 + 0.698566i −0.0158929 + 0.0275274i
\(645\) −1.75511 + 19.9963i −0.0691075 + 0.787354i
\(646\) −11.6689 + 6.73702i −0.459106 + 0.265065i
\(647\) 30.7071 1.20722 0.603611 0.797279i \(-0.293728\pi\)
0.603611 + 0.797279i \(0.293728\pi\)
\(648\) 3.08769 8.45377i 0.121296 0.332095i
\(649\) 3.47051i 0.136229i
\(650\) −4.12977 −0.161983
\(651\) 30.9436 + 7.23945i 1.21278 + 0.283737i
\(652\) −1.70445 −0.0667515
\(653\) 20.6155i 0.806748i 0.915035 + 0.403374i \(0.132163\pi\)
−0.915035 + 0.403374i \(0.867837\pi\)
\(654\) −10.0877 0.885417i −0.394460 0.0346225i
\(655\) 2.07827 0.0812046
\(656\) −6.83739 + 3.94757i −0.266955 + 0.154127i
\(657\) −0.945387 + 0.343491i −0.0368831 + 0.0134009i
\(658\) −6.57914 + 11.3954i −0.256482 + 0.444239i
\(659\) 45.9699i 1.79073i 0.445331 + 0.895366i \(0.353086\pi\)
−0.445331 + 0.895366i \(0.646914\pi\)
\(660\) −4.65618 + 6.64574i −0.181242 + 0.258685i
\(661\) −1.62902 2.82155i −0.0633616 0.109745i 0.832604 0.553868i \(-0.186849\pi\)
−0.895966 + 0.444123i \(0.853515\pi\)
\(662\) 11.0835 + 19.1972i 0.430773 + 0.746121i
\(663\) −43.0702 3.78036i −1.67271 0.146817i
\(664\) 2.46393 1.42255i 0.0956189 0.0552056i
\(665\) −6.36169 3.67293i −0.246696 0.142430i
\(666\) −16.4880 + 19.6272i −0.638898 + 0.760540i
\(667\) 0.503792 0.0195069
\(668\) 6.28618 10.8880i 0.243220 0.421269i
\(669\) 1.37662 1.96484i 0.0532233 0.0759653i
\(670\) −1.90767 + 3.30418i −0.0736996 + 0.127651i
\(671\) −25.5662 + 14.7606i −0.986970 + 0.569828i
\(672\) 3.27512 4.67456i 0.126341 0.180325i
\(673\) −28.5117 + 16.4612i −1.09905 + 0.634534i −0.935970 0.352079i \(-0.885475\pi\)
−0.163076 + 0.986614i \(0.552141\pi\)
\(674\) 24.0073 0.924727
\(675\) −3.67114 3.67733i −0.141302 0.141541i
\(676\) −2.02750 + 3.51174i −0.0779808 + 0.135067i
\(677\) 2.98095 + 5.16316i 0.114567 + 0.198436i 0.917607 0.397490i \(-0.130118\pi\)
−0.803039 + 0.595926i \(0.796785\pi\)
\(678\) 10.1303 4.72038i 0.389052 0.181285i
\(679\) 12.6431 21.8985i 0.485198 0.840388i
\(680\) −6.04445 −0.231794
\(681\) −6.65999 14.2929i −0.255211 0.547705i
\(682\) −16.1137 + 20.5123i −0.617025 + 0.785458i
\(683\) 32.4819i 1.24289i 0.783459 + 0.621443i \(0.213453\pi\)
−0.783459 + 0.621443i \(0.786547\pi\)
\(684\) −4.30151 + 5.12049i −0.164472 + 0.195787i
\(685\) −16.9138 9.76518i −0.646243 0.373109i
\(686\) 10.3497i 0.395152i
\(687\) −7.93899 + 11.3313i −0.302891 + 0.432315i
\(688\) 10.0366 + 5.79463i 0.382641 + 0.220918i
\(689\) 7.12832 + 4.11554i 0.271567 + 0.156790i
\(690\) 0.384299 0.179070i 0.0146300 0.00681708i
\(691\) 8.97812 + 15.5506i 0.341544 + 0.591571i 0.984720 0.174147i \(-0.0557169\pi\)
−0.643176 + 0.765719i \(0.722384\pi\)
\(692\) 2.25868 1.30405i 0.0858621 0.0495725i
\(693\) −45.6073 8.06823i −1.73248 0.306487i
\(694\) −24.4539 14.1185i −0.928257 0.535929i
\(695\) 11.2647 + 19.5111i 0.427296 + 0.740098i
\(696\) −3.55116 0.311692i −0.134606 0.0118146i
\(697\) 47.7218i 1.80759i
\(698\) 14.1084i 0.534010i
\(699\) −27.5254 2.41595i −1.04110 0.0913797i
\(700\) −1.64767 2.85385i −0.0622762 0.107866i
\(701\) −17.0045 9.81756i −0.642251 0.370804i 0.143230 0.989689i \(-0.454251\pi\)
−0.785481 + 0.618885i \(0.787584\pi\)
\(702\) −20.7324 + 5.53650i −0.782494 + 0.208962i
\(703\) 16.4953 9.52357i 0.622133 0.359188i
\(704\) 2.34247 + 4.05727i 0.0882851 + 0.152914i
\(705\) 6.26890 2.92109i 0.236100 0.110015i
\(706\) −19.3283 11.1592i −0.727428 0.419981i
\(707\) 14.4679 + 8.35303i 0.544120 + 0.314148i
\(708\) 0.736234 1.05082i 0.0276694 0.0394923i
\(709\) 2.09339i 0.0786187i 0.999227 + 0.0393094i \(0.0125158\pi\)
−0.999227 + 0.0393094i \(0.987484\pi\)
\(710\) −8.36971 4.83225i −0.314110 0.181351i
\(711\) 29.4962 + 24.7785i 1.10619 + 0.929267i
\(712\) 0.149606i 0.00560672i
\(713\) 1.26499 0.507194i 0.0473741 0.0189946i
\(714\) −14.5715 31.2717i −0.545326 1.17031i
\(715\) 19.3477 0.723563
\(716\) 9.49768 16.4505i 0.354945 0.614783i
\(717\) 14.2018 6.61753i 0.530375 0.247136i
\(718\) −2.85152 4.93899i −0.106418 0.184321i
\(719\) −4.88475 + 8.46063i −0.182170 + 0.315528i −0.942619 0.333869i \(-0.891646\pi\)
0.760449 + 0.649398i \(0.224979\pi\)
\(720\) −2.81965 + 1.02448i −0.105082 + 0.0381800i
\(721\) −61.8124 −2.30202
\(722\) −12.1511 + 7.01543i −0.452216 + 0.261087i
\(723\) −15.3345 + 21.8869i −0.570298 + 0.813983i
\(724\) 14.3763 8.30014i 0.534289 0.308472i
\(725\) −1.02907 + 1.78240i −0.0382188 + 0.0661968i
\(726\) 10.8814 15.5310i 0.403847 0.576409i
\(727\) −9.42776 + 16.3294i −0.349656 + 0.605622i −0.986188 0.165628i \(-0.947035\pi\)
0.636532 + 0.771250i \(0.280368\pi\)
\(728\) −13.6090 −0.504384
\(729\) −23.3599 13.5394i −0.865181 0.501460i
\(730\) 0.290365 + 0.167642i 0.0107469 + 0.00620472i
\(731\) 60.6657 35.0254i 2.24380 1.29546i
\(732\) −10.8724 0.954291i −0.401855 0.0352716i
\(733\) −7.30224 12.6479i −0.269714 0.467159i 0.699074 0.715050i \(-0.253596\pi\)
−0.968788 + 0.247891i \(0.920263\pi\)
\(734\) 16.0261 + 27.7580i 0.591534 + 1.02457i
\(735\) 3.83562 5.47456i 0.141479 0.201932i
\(736\) 0.244780i 0.00902271i
\(737\) 8.93730 15.4799i 0.329210 0.570208i
\(738\) 8.08838 + 22.2616i 0.297737 + 0.819459i
\(739\) −41.8282 + 24.1495i −1.53868 + 0.888355i −0.539759 + 0.841819i \(0.681485\pi\)
−0.998917 + 0.0465355i \(0.985182\pi\)
\(740\) 8.54454 0.314104
\(741\) 15.8840 + 1.39417i 0.583515 + 0.0512162i
\(742\) 6.56798i 0.241118i
\(743\) 6.41688 0.235412 0.117706 0.993048i \(-0.462446\pi\)
0.117706 + 0.993048i \(0.462446\pi\)
\(744\) −9.23049 + 2.79250i −0.338406 + 0.102378i
\(745\) −15.4920 −0.567584
\(746\) 22.0309i 0.806609i
\(747\) −2.91473 8.02219i −0.106644 0.293516i
\(748\) 28.3179 1.03540
\(749\) −12.0659 + 6.96627i −0.440880 + 0.254542i
\(750\) −0.151443 + 1.72542i −0.00552992 + 0.0630033i
\(751\) −8.51988 + 14.7569i −0.310895 + 0.538486i −0.978556 0.205979i \(-0.933962\pi\)
0.667661 + 0.744465i \(0.267295\pi\)
\(752\) 3.99299i 0.145609i
\(753\) 5.38452 + 3.77254i 0.196223 + 0.137479i
\(754\) 4.24983 + 7.36092i 0.154770 + 0.268069i
\(755\) −9.13464 15.8217i −0.332444 0.575809i
\(756\) −12.0977 12.1181i −0.439988 0.440730i
\(757\) 17.9616 10.3701i 0.652826 0.376909i −0.136712 0.990611i \(-0.543653\pi\)
0.789538 + 0.613701i \(0.210320\pi\)
\(758\) 19.8741 + 11.4743i 0.721861 + 0.416767i
\(759\) −1.80042 + 0.838932i −0.0653510 + 0.0304513i
\(760\) 2.22916 0.0808601
\(761\) −11.5689 + 20.0379i −0.419372 + 0.726373i −0.995876 0.0907205i \(-0.971083\pi\)
0.576504 + 0.817094i \(0.304416\pi\)
\(762\) −0.600560 0.420768i −0.0217560 0.0152428i
\(763\) −9.63317 + 16.6851i −0.348744 + 0.604043i
\(764\) 14.6036 8.43140i 0.528340 0.305037i
\(765\) −3.15886 + 17.8561i −0.114209 + 0.645589i
\(766\) 8.93453 5.15835i 0.322818 0.186379i
\(767\) −3.05925 −0.110463
\(768\) −0.151443 + 1.72542i −0.00546473 + 0.0622606i
\(769\) 19.5619 33.8822i 0.705420 1.22182i −0.261120 0.965306i \(-0.584092\pi\)
0.966540 0.256517i \(-0.0825749\pi\)
\(770\) 7.71924 + 13.3701i 0.278182 + 0.481826i
\(771\) 22.6936 + 48.7023i 0.817289 + 1.75397i
\(772\) 3.46345 5.99887i 0.124652 0.215904i
\(773\) 17.0109 0.611839 0.305920 0.952057i \(-0.401036\pi\)
0.305920 + 0.952057i \(0.401036\pi\)
\(774\) 22.3633 26.6211i 0.803831 0.956875i
\(775\) −0.789485 + 5.51151i −0.0283592 + 0.197979i
\(776\) 7.67331i 0.275456i
\(777\) 20.5986 + 44.2062i 0.738969 + 1.58589i
\(778\) 22.0613 + 12.7371i 0.790937 + 0.456648i
\(779\) 17.5995i 0.630568i
\(780\) 5.85822 + 4.10442i 0.209758 + 0.146962i
\(781\) 39.2116 + 22.6388i 1.40310 + 0.810080i
\(782\) −1.28134 0.739781i −0.0458206 0.0264545i
\(783\) −2.77663 + 10.3277i −0.0992286 + 0.369081i
\(784\) −1.92965 3.34226i −0.0689162 0.119366i
\(785\) −15.8947 + 9.17683i −0.567307 + 0.327535i
\(786\) −2.94809 2.06551i −0.105155 0.0736743i
\(787\) 12.8119 + 7.39695i 0.456695 + 0.263673i 0.710653 0.703542i \(-0.248399\pi\)
−0.253959 + 0.967215i \(0.581733\pi\)
\(788\) 7.40933 + 12.8333i 0.263946 + 0.457168i
\(789\) −3.25732 + 37.1112i −0.115964 + 1.32120i
\(790\) 12.8409i 0.456859i
\(791\) 21.2633i 0.756036i
\(792\) 13.2099 4.79960i 0.469393 0.170546i
\(793\) 13.0115 + 22.5366i 0.462052 + 0.800297i
\(794\) 5.47906 + 3.16333i 0.194444 + 0.112263i
\(795\) 1.98087 2.82729i 0.0702544 0.100274i
\(796\) 16.4647 9.50589i 0.583575 0.336927i
\(797\) 11.4621 + 19.8529i 0.406007 + 0.703226i 0.994438 0.105322i \(-0.0335873\pi\)
−0.588431 + 0.808548i \(0.700254\pi\)
\(798\) 5.37389 + 11.5328i 0.190234 + 0.408257i
\(799\) −20.9019 12.0677i −0.739456 0.426925i
\(800\) 0.866025 + 0.500000i 0.0306186 + 0.0176777i
\(801\) −0.441955 0.0781848i −0.0156157 0.00276252i
\(802\) 25.4504i 0.898683i
\(803\) −1.36034 0.785394i −0.0480054 0.0277159i
\(804\) 5.98999 2.79113i 0.211250 0.0984354i
\(805\) 0.806635i 0.0284302i
\(806\) 18.0816 + 14.2042i 0.636898 + 0.500322i
\(807\) −42.4559 + 19.7830i −1.49452 + 0.696394i
\(808\) −5.06959 −0.178348
\(809\) 25.3510 43.9092i 0.891294 1.54377i 0.0529687 0.998596i \(-0.483132\pi\)
0.838325 0.545170i \(-0.183535\pi\)
\(810\) 1.55287 + 8.86502i 0.0545622 + 0.311485i
\(811\) −8.64545 14.9744i −0.303583 0.525821i 0.673362 0.739313i \(-0.264850\pi\)
−0.976945 + 0.213492i \(0.931516\pi\)
\(812\) −3.39115 + 5.87364i −0.119006 + 0.206124i
\(813\) 29.3020 + 2.57189i 1.02767 + 0.0902001i
\(814\) −40.0306 −1.40307
\(815\) 1.47610 0.852226i 0.0517055 0.0298522i
\(816\) 8.57426 + 6.00736i 0.300159 + 0.210299i
\(817\) −22.3732 + 12.9171i −0.782737 + 0.451914i
\(818\) −18.4196 + 31.9037i −0.644026 + 1.11549i
\(819\) −7.11215 + 40.2028i −0.248519 + 1.40480i
\(820\) 3.94757 6.83739i 0.137855 0.238772i
\(821\) −37.4349 −1.30649 −0.653244 0.757147i \(-0.726593\pi\)
−0.653244 + 0.757147i \(0.726593\pi\)
\(822\) 14.2875 + 30.6622i 0.498335 + 1.06947i
\(823\) −28.5790 16.5001i −0.996202 0.575157i −0.0890794 0.996025i \(-0.528393\pi\)
−0.907122 + 0.420867i \(0.861726\pi\)
\(824\) 16.2445 9.37875i 0.565903 0.326724i
\(825\) 0.709501 8.08347i 0.0247017 0.281430i
\(826\) −1.22056 2.11408i −0.0424689 0.0735582i
\(827\) −21.9755 38.0628i −0.764165 1.32357i −0.940687 0.339275i \(-0.889818\pi\)
0.176523 0.984297i \(-0.443515\pi\)
\(828\) −0.723112 0.127923i −0.0251299 0.00444564i
\(829\) 8.72147i 0.302909i 0.988464 + 0.151455i \(0.0483957\pi\)
−0.988464 + 0.151455i \(0.951604\pi\)
\(830\) −1.42255 + 2.46393i −0.0493774 + 0.0855241i
\(831\) −39.8941 3.50158i −1.38391 0.121469i
\(832\) 3.57649 2.06489i 0.123992 0.0715870i
\(833\) −23.3274 −0.808247
\(834\) 3.41193 38.8727i 0.118146 1.34605i
\(835\) 12.5724i 0.435084i
\(836\) −10.4435 −0.361195
\(837\) 3.42550 + 28.7274i 0.118403 + 0.992966i
\(838\) −8.72337 −0.301344
\(839\) 42.4663i 1.46610i −0.680175 0.733050i \(-0.738096\pi\)
0.680175 0.733050i \(-0.261904\pi\)
\(840\) −0.499058 + 5.68585i −0.0172191 + 0.196180i
\(841\) −24.7640 −0.853933
\(842\) 3.80721 2.19810i 0.131205 0.0757514i
\(843\) 44.9854 + 3.94846i 1.54938 + 0.135992i
\(844\) 0.159771 0.276731i 0.00549953 0.00952547i
\(845\) 4.05500i 0.139496i
\(846\) −11.7958 2.08676i −0.405548 0.0717442i
\(847\) −18.0398 31.2458i −0.619853 1.07362i
\(848\) −0.996554 1.72608i −0.0342218 0.0592739i
\(849\) −2.20963 + 25.1747i −0.0758343 + 0.863993i
\(850\) 5.23465 3.02223i 0.179547 0.103662i
\(851\) 1.81132 + 1.04577i 0.0620913 + 0.0358484i
\(852\) 7.07012 + 15.1731i 0.242218 + 0.519820i
\(853\) 21.4819 0.735525 0.367762 0.929920i \(-0.380124\pi\)
0.367762 + 0.929920i \(0.380124\pi\)
\(854\) −10.3825 + 17.9830i −0.355282 + 0.615367i
\(855\) 1.16497 6.58523i 0.0398411 0.225210i
\(856\) 2.11397 3.66151i 0.0722541 0.125148i
\(857\) −16.4246 + 9.48276i −0.561054 + 0.323925i −0.753569 0.657369i \(-0.771669\pi\)
0.192514 + 0.981294i \(0.438336\pi\)
\(858\) −27.4454 19.2290i −0.936970 0.656466i
\(859\) −30.8514 + 17.8121i −1.05264 + 0.607741i −0.923387 0.383871i \(-0.874591\pi\)
−0.129251 + 0.991612i \(0.541257\pi\)
\(860\) −11.5893 −0.395190
\(861\) 44.8906 + 3.94013i 1.52987 + 0.134279i
\(862\) 7.11935 12.3311i 0.242486 0.419998i
\(863\) 2.53731 + 4.39475i 0.0863710 + 0.149599i 0.905975 0.423332i \(-0.139140\pi\)
−0.819604 + 0.572931i \(0.805806\pi\)
\(864\) 5.01796 + 1.34909i 0.170715 + 0.0458971i
\(865\) −1.30405 + 2.25868i −0.0443390 + 0.0767974i
\(866\) −16.3649 −0.556103
\(867\) 30.6702 14.2912i 1.04161 0.485356i
\(868\) −2.60163 + 18.1623i −0.0883050 + 0.616470i
\(869\) 60.1588i 2.04075i
\(870\) 3.23124 1.50564i 0.109549 0.0510461i
\(871\) −13.6455 7.87823i −0.462360 0.266943i
\(872\) 5.84653i 0.197988i
\(873\) 22.6680 + 4.01011i 0.767194 + 0.135722i
\(874\) 0.472550 + 0.272827i 0.0159842 + 0.00922851i
\(875\) 2.85385 + 1.64767i 0.0964779 + 0.0557015i
\(876\) −0.245279 0.526389i −0.00828722 0.0177850i
\(877\) 17.7228 + 30.6968i 0.598456 + 1.03656i 0.993049 + 0.117700i \(0.0375522\pi\)
−0.394593 + 0.918856i \(0.629114\pi\)
\(878\) 11.5474 6.66688i 0.389705 0.224996i
\(879\) 28.3808 40.5078i 0.957261 1.36629i
\(880\) −4.05727 2.34247i −0.136771 0.0789646i
\(881\) −3.31664 5.74459i −0.111741 0.193540i 0.804732 0.593639i \(-0.202309\pi\)
−0.916472 + 0.400099i \(0.868976\pi\)
\(882\) −10.8819 + 3.95377i −0.366413 + 0.133130i
\(883\) 35.2519i 1.18632i −0.805084 0.593160i \(-0.797880\pi\)
0.805084 0.593160i \(-0.202120\pi\)
\(884\) 24.9622i 0.839570i
\(885\) −0.112186 + 1.27816i −0.00377109 + 0.0429647i
\(886\) 10.8484 + 18.7900i 0.364460 + 0.631264i
\(887\) 2.63299 + 1.52016i 0.0884070 + 0.0510418i 0.543552 0.839376i \(-0.317079\pi\)
−0.455145 + 0.890417i \(0.650412\pi\)
\(888\) −12.1207 8.49210i −0.406745 0.284976i
\(889\) −1.20823 + 0.697570i −0.0405226 + 0.0233957i
\(890\) 0.0748029 + 0.129562i 0.00250740 + 0.00434294i
\(891\) −7.27509 41.5321i −0.243725 1.39138i
\(892\) 1.19955 + 0.692562i 0.0401640 + 0.0231887i
\(893\) 7.70850 + 4.45050i 0.257955 + 0.148930i
\(894\) 21.9759 + 15.3969i 0.734986 + 0.514950i
\(895\) 18.9954i 0.634945i
\(896\) 2.85385 + 1.64767i 0.0953406 + 0.0550449i
\(897\) 0.739518 + 1.58707i 0.0246918 + 0.0529906i
\(898\) 5.51787i 0.184134i
\(899\) 10.6362 4.26455i 0.354736 0.142231i
\(900\) 1.92965 2.29705i 0.0643218 0.0765683i
\(901\) −12.0473 −0.401352
\(902\) −18.4941 + 32.0327i −0.615786 + 1.06657i
\(903\) −27.9385 59.9584i −0.929736 1.99529i
\(904\) 3.22626 + 5.58805i 0.107304 + 0.185856i
\(905\) −8.30014 + 14.3763i −0.275906 + 0.477883i
\(906\) −2.76676 + 31.5221i −0.0919194 + 1.04725i
\(907\) −7.96679 −0.264533 −0.132267 0.991214i \(-0.542225\pi\)
−0.132267 + 0.991214i \(0.542225\pi\)
\(908\) 7.88419 4.55194i 0.261646 0.151061i
\(909\) −2.64940 + 14.9762i −0.0878749 + 0.496730i
\(910\) 11.7858 6.80451i 0.390694 0.225567i
\(911\) −21.6226 + 37.4515i −0.716390 + 1.24082i 0.246031 + 0.969262i \(0.420873\pi\)
−0.962421 + 0.271561i \(0.912460\pi\)
\(912\) −3.16214 2.21548i −0.104709 0.0733618i
\(913\) 6.66455 11.5433i 0.220564 0.382029i
\(914\) −17.8127 −0.589190
\(915\) 9.89292 4.60976i 0.327050 0.152394i
\(916\) −6.91782 3.99401i −0.228571 0.131966i
\(917\) −5.93107 + 3.42430i −0.195861 + 0.113080i
\(918\) 22.2275 22.1900i 0.733616 0.732379i
\(919\) 8.39359 + 14.5381i 0.276879 + 0.479569i 0.970607 0.240668i \(-0.0773665\pi\)
−0.693728 + 0.720237i \(0.744033\pi\)
\(920\) 0.122390 + 0.211986i 0.00403508 + 0.00698896i
\(921\) 13.3069 + 9.32317i 0.438478 + 0.307209i
\(922\) 10.7060i 0.352585i
\(923\) 19.9561 34.5650i 0.656863 1.13772i
\(924\) 2.33805 26.6378i 0.0769163 0.876320i
\(925\) −7.39979 + 4.27227i −0.243304 + 0.140471i
\(926\) −23.2499 −0.764038
\(927\) −19.2166 52.8896i −0.631156 1.73712i
\(928\) 2.05814i 0.0675618i
\(929\) 27.8352 0.913242 0.456621 0.889661i \(-0.349060\pi\)
0.456621 + 0.889661i \(0.349060\pi\)
\(930\) 6.59759 7.03362i 0.216344 0.230641i
\(931\) 8.60301 0.281952
\(932\) 15.9529i 0.522554i
\(933\) −2.82031 0.247544i −0.0923330 0.00810424i
\(934\) 1.78177 0.0583014
\(935\) −24.5240 + 14.1589i −0.802021 + 0.463047i
\(936\) −4.23085 11.6445i −0.138290 0.380613i
\(937\) 19.2733 33.3823i 0.629630 1.09055i −0.357996 0.933723i \(-0.616540\pi\)
0.987626 0.156828i \(-0.0501267\pi\)
\(938\) 12.5728i 0.410518i
\(939\) −12.2719 + 17.5156i −0.400478 + 0.571600i
\(940\) 1.99650 + 3.45803i 0.0651185 + 0.112789i
\(941\) 6.88657 + 11.9279i 0.224496 + 0.388838i 0.956168 0.292818i \(-0.0945931\pi\)
−0.731672 + 0.681657i \(0.761260\pi\)
\(942\) 31.6677 + 2.77954i 1.03179 + 0.0905622i
\(943\) 1.67366 0.966286i 0.0545018 0.0314666i
\(944\) 0.641535 + 0.370390i 0.0208802 + 0.0120552i
\(945\) 16.5359 + 4.44573i 0.537914 + 0.144620i
\(946\) 54.2949 1.76528
\(947\) −10.9849 + 19.0264i −0.356960 + 0.618273i −0.987451 0.157923i \(-0.949520\pi\)
0.630491 + 0.776196i \(0.282854\pi\)
\(948\) −12.7621 + 18.2153i −0.414494 + 0.591604i
\(949\) −0.692325 + 1.19914i −0.0224738 + 0.0389258i
\(950\) −1.93051 + 1.11458i −0.0626340 + 0.0361617i
\(951\) −33.8825 + 48.3603i −1.09872 + 1.56819i
\(952\) 17.2500 9.95929i 0.559075 0.322782i
\(953\) 44.4966 1.44138 0.720692 0.693255i \(-0.243824\pi\)
0.720692 + 0.693255i \(0.243824\pi\)
\(954\) −5.61988 + 2.04189i −0.181950 + 0.0661086i
\(955\) −8.43140 + 14.6036i −0.272834 + 0.472562i
\(956\) 4.52292 + 7.83393i 0.146282 + 0.253367i
\(957\) −15.1381 + 7.05385i −0.489346 + 0.228019i
\(958\) 17.8311 30.8844i 0.576098 0.997830i
\(959\) 64.3593 2.07827
\(960\) −0.731555 1.56998i −0.0236108 0.0506708i
\(961\) 22.4133 21.4160i 0.723010 0.690838i
\(962\) 35.2870i 1.13770i
\(963\) −9.71180 8.15848i −0.312958 0.262903i
\(964\) −13.3621 7.71462i −0.430365 0.248471i
\(965\) 6.92690i 0.222985i
\(966\) −0.801684 + 1.14424i −0.0257938 + 0.0368153i
\(967\) −46.3539 26.7624i −1.49064 0.860621i −0.490697 0.871330i \(-0.663258\pi\)
−0.999943 + 0.0107092i \(0.996591\pi\)
\(968\) 9.48178 + 5.47431i 0.304756 + 0.175951i
\(969\) −21.1539 + 9.85701i −0.679563 + 0.316653i
\(970\) −3.83666 6.64528i −0.123188 0.213367i
\(971\) −42.9055 + 24.7715i −1.37690 + 0.794955i −0.991785 0.127912i \(-0.959172\pi\)
−0.385118 + 0.922868i \(0.625839\pi\)
\(972\) 6.60781 14.1187i 0.211946 0.452856i
\(973\) −64.2958 37.1212i −2.06123 1.19005i
\(974\) 5.28014 + 9.14547i 0.169187 + 0.293040i
\(975\) −7.12558 0.625425i −0.228201 0.0200296i
\(976\) 6.30131i 0.201700i
\(977\) 9.46739i 0.302888i −0.988466 0.151444i \(-0.951608\pi\)
0.988466 0.151444i \(-0.0483924\pi\)
\(978\) −2.94089 0.258128i −0.0940393 0.00825401i
\(979\) −0.350447 0.606992i −0.0112003 0.0193995i
\(980\) 3.34226 + 1.92965i 0.106765 + 0.0616405i
\(981\) −17.2714 3.05543i −0.551433 0.0975522i
\(982\) 13.8762 8.01143i 0.442807 0.255655i
\(983\) −10.1810 17.6341i −0.324725 0.562440i 0.656732 0.754124i \(-0.271938\pi\)
−0.981457 + 0.191684i \(0.938605\pi\)
\(984\) −12.3952 + 5.77573i −0.395144 + 0.184124i
\(985\) −12.8333 7.40933i −0.408904 0.236081i
\(986\) −10.7737 6.22018i −0.343103 0.198091i
\(987\) −13.0775 + 18.6655i −0.416262 + 0.594129i
\(988\) 9.20591i 0.292879i
\(989\) −2.45676 1.41841i −0.0781203 0.0451028i
\(990\) −9.04031 + 10.7615i −0.287320 + 0.342024i
\(991\) 53.4053i 1.69647i 0.529617 + 0.848237i \(0.322336\pi\)
−0.529617 + 0.848237i \(0.677664\pi\)
\(992\) −2.07204 5.16785i −0.0657873 0.164079i
\(993\) 16.2164 + 34.8017i 0.514612 + 1.10440i
\(994\) 31.8479 1.01015
\(995\) −9.50589 + 16.4647i −0.301357 + 0.521966i
\(996\) 4.46673 2.08134i 0.141534 0.0659499i
\(997\) 27.9449 + 48.4020i 0.885024 + 1.53291i 0.845686 + 0.533680i \(0.179191\pi\)
0.0393377 + 0.999226i \(0.487475\pi\)
\(998\) −9.12364 + 15.8026i −0.288804 + 0.500223i
\(999\) −31.4211 + 31.3682i −0.994120 + 0.992445i
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.o.e.491.15 yes 40
3.2 odd 2 inner 930.2.o.e.491.9 yes 40
31.6 odd 6 inner 930.2.o.e.161.19 yes 40
93.68 even 6 inner 930.2.o.e.161.5 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.o.e.161.5 40 93.68 even 6 inner
930.2.o.e.161.19 yes 40 31.6 odd 6 inner
930.2.o.e.491.9 yes 40 3.2 odd 2 inner
930.2.o.e.491.15 yes 40 1.1 even 1 trivial