Properties

Label 570.2.k.b.533.6
Level $570$
Weight $2$
Character 570.533
Analytic conductor $4.551$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [570,2,Mod(77,570)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(570, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("570.77");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.k (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 533.6
Character \(\chi\) \(=\) 570.533
Dual form 570.2.k.b.77.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.577604 - 1.63290i) q^{3} +1.00000i q^{4} +(2.23603 + 0.0135681i) q^{5} +(-1.56306 + 0.746209i) q^{6} +(3.38538 - 3.38538i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.33275 - 1.88634i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.577604 - 1.63290i) q^{3} +1.00000i q^{4} +(2.23603 + 0.0135681i) q^{5} +(-1.56306 + 0.746209i) q^{6} +(3.38538 - 3.38538i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.33275 - 1.88634i) q^{9} +(-1.57152 - 1.59070i) q^{10} +1.22574i q^{11} +(1.63290 + 0.577604i) q^{12} +(3.51689 + 3.51689i) q^{13} -4.78765 q^{14} +(1.31369 - 3.64338i) q^{15} -1.00000 q^{16} +(0.826034 + 0.826034i) q^{17} +(0.315656 + 2.98335i) q^{18} +1.00000i q^{19} +(-0.0135681 + 2.23603i) q^{20} +(-3.57259 - 7.48341i) q^{21} +(0.866730 - 0.866730i) q^{22} +(-1.04719 + 1.04719i) q^{23} +(-0.746209 - 1.56306i) q^{24} +(4.99963 + 0.0606771i) q^{25} -4.97363i q^{26} +(-4.42762 + 2.71959i) q^{27} +(3.38538 + 3.38538i) q^{28} -8.14348 q^{29} +(-3.50518 + 1.64734i) q^{30} +7.41990 q^{31} +(0.707107 + 0.707107i) q^{32} +(2.00152 + 0.707993i) q^{33} -1.16819i q^{34} +(7.61574 - 7.52387i) q^{35} +(1.88634 - 2.33275i) q^{36} +(-5.83375 + 5.83375i) q^{37} +(0.707107 - 0.707107i) q^{38} +(7.77411 - 3.71137i) q^{39} +(1.59070 - 1.57152i) q^{40} +3.53572i q^{41} +(-2.76537 + 7.81778i) q^{42} +(-2.68748 - 2.68748i) q^{43} -1.22574 q^{44} +(-5.19049 - 4.24956i) q^{45} +1.48094 q^{46} +(-6.84848 - 6.84848i) q^{47} +(-0.577604 + 1.63290i) q^{48} -15.9216i q^{49} +(-3.49237 - 3.57818i) q^{50} +(1.82595 - 0.871713i) q^{51} +(-3.51689 + 3.51689i) q^{52} +(-3.40629 + 3.40629i) q^{53} +(5.05384 + 1.20776i) q^{54} +(-0.0166309 + 2.74079i) q^{55} -4.78765i q^{56} +(1.63290 + 0.577604i) q^{57} +(5.75831 + 5.75831i) q^{58} -9.91906 q^{59} +(3.64338 + 1.31369i) q^{60} -10.5422 q^{61} +(-5.24666 - 5.24666i) q^{62} +(-14.2832 + 1.51125i) q^{63} -1.00000i q^{64} +(7.81614 + 7.91158i) q^{65} +(-0.914660 - 1.91591i) q^{66} +(6.00309 - 6.00309i) q^{67} +(-0.826034 + 0.826034i) q^{68} +(1.10509 + 2.31481i) q^{69} +(-10.7053 - 0.0649592i) q^{70} +8.35839i q^{71} +(-2.98335 + 0.315656i) q^{72} +(-3.99393 - 3.99393i) q^{73} +8.25017 q^{74} +(2.98689 - 8.12887i) q^{75} -1.00000 q^{76} +(4.14960 + 4.14960i) q^{77} +(-8.12146 - 2.87279i) q^{78} -6.75057i q^{79} +(-2.23603 - 0.0135681i) q^{80} +(1.88342 + 8.80072i) q^{81} +(2.50013 - 2.50013i) q^{82} +(0.717790 - 0.717790i) q^{83} +(7.48341 - 3.57259i) q^{84} +(1.83583 + 1.85824i) q^{85} +3.80067i q^{86} +(-4.70370 + 13.2975i) q^{87} +(0.866730 + 0.866730i) q^{88} -0.384471 q^{89} +(0.665336 + 6.67513i) q^{90} +23.8120 q^{91} +(-1.04719 - 1.04719i) q^{92} +(4.28576 - 12.1160i) q^{93} +9.68521i q^{94} +(-0.0135681 + 2.23603i) q^{95} +(1.56306 - 0.746209i) q^{96} +(-12.5444 + 12.5444i) q^{97} +(-11.2583 + 11.2583i) q^{98} +(2.31217 - 2.85934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) 0.577604 1.63290i 0.333480 0.942757i
\(4\) 1.00000i 0.500000i
\(5\) 2.23603 + 0.0135681i 0.999982 + 0.00606782i
\(6\) −1.56306 + 0.746209i −0.638119 + 0.304639i
\(7\) 3.38538 3.38538i 1.27955 1.27955i 0.338638 0.940917i \(-0.390034\pi\)
0.940917 0.338638i \(-0.109966\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −2.33275 1.88634i −0.777582 0.628781i
\(10\) −1.57152 1.59070i −0.496957 0.503025i
\(11\) 1.22574i 0.369575i 0.982779 + 0.184787i \(0.0591597\pi\)
−0.982779 + 0.184787i \(0.940840\pi\)
\(12\) 1.63290 + 0.577604i 0.471379 + 0.166740i
\(13\) 3.51689 + 3.51689i 0.975410 + 0.975410i 0.999705 0.0242950i \(-0.00773410\pi\)
−0.0242950 + 0.999705i \(0.507734\pi\)
\(14\) −4.78765 −1.27955
\(15\) 1.31369 3.64338i 0.339194 0.940716i
\(16\) −1.00000 −0.250000
\(17\) 0.826034 + 0.826034i 0.200343 + 0.200343i 0.800147 0.599804i \(-0.204755\pi\)
−0.599804 + 0.800147i \(0.704755\pi\)
\(18\) 0.315656 + 2.98335i 0.0744008 + 0.703182i
\(19\) 1.00000i 0.229416i
\(20\) −0.0135681 + 2.23603i −0.00303391 + 0.499991i
\(21\) −3.57259 7.48341i −0.779604 1.63301i
\(22\) 0.866730 0.866730i 0.184787 0.184787i
\(23\) −1.04719 + 1.04719i −0.218353 + 0.218353i −0.807804 0.589451i \(-0.799344\pi\)
0.589451 + 0.807804i \(0.299344\pi\)
\(24\) −0.746209 1.56306i −0.152319 0.319059i
\(25\) 4.99963 + 0.0606771i 0.999926 + 0.0121354i
\(26\) 4.97363i 0.975410i
\(27\) −4.42762 + 2.71959i −0.852096 + 0.523386i
\(28\) 3.38538 + 3.38538i 0.639777 + 0.639777i
\(29\) −8.14348 −1.51221 −0.756103 0.654453i \(-0.772899\pi\)
−0.756103 + 0.654453i \(0.772899\pi\)
\(30\) −3.50518 + 1.64734i −0.639955 + 0.300761i
\(31\) 7.41990 1.33265 0.666327 0.745660i \(-0.267866\pi\)
0.666327 + 0.745660i \(0.267866\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 2.00152 + 0.707993i 0.348419 + 0.123246i
\(34\) 1.16819i 0.200343i
\(35\) 7.61574 7.52387i 1.28730 1.27177i
\(36\) 1.88634 2.33275i 0.314390 0.388791i
\(37\) −5.83375 + 5.83375i −0.959063 + 0.959063i −0.999194 0.0401316i \(-0.987222\pi\)
0.0401316 + 0.999194i \(0.487222\pi\)
\(38\) 0.707107 0.707107i 0.114708 0.114708i
\(39\) 7.77411 3.71137i 1.24485 0.594295i
\(40\) 1.59070 1.57152i 0.251512 0.248478i
\(41\) 3.53572i 0.552187i 0.961131 + 0.276093i \(0.0890399\pi\)
−0.961131 + 0.276093i \(0.910960\pi\)
\(42\) −2.76537 + 7.81778i −0.426706 + 1.20631i
\(43\) −2.68748 2.68748i −0.409836 0.409836i 0.471845 0.881681i \(-0.343588\pi\)
−0.881681 + 0.471845i \(0.843588\pi\)
\(44\) −1.22574 −0.184787
\(45\) −5.19049 4.24956i −0.773753 0.633488i
\(46\) 1.48094 0.218353
\(47\) −6.84848 6.84848i −0.998953 0.998953i 0.00104620 0.999999i \(-0.499667\pi\)
−0.999999 + 0.00104620i \(0.999667\pi\)
\(48\) −0.577604 + 1.63290i −0.0833699 + 0.235689i
\(49\) 15.9216i 2.27452i
\(50\) −3.49237 3.57818i −0.493895 0.506031i
\(51\) 1.82595 0.871713i 0.255685 0.122064i
\(52\) −3.51689 + 3.51689i −0.487705 + 0.487705i
\(53\) −3.40629 + 3.40629i −0.467890 + 0.467890i −0.901230 0.433340i \(-0.857335\pi\)
0.433340 + 0.901230i \(0.357335\pi\)
\(54\) 5.05384 + 1.20776i 0.687741 + 0.164355i
\(55\) −0.0166309 + 2.74079i −0.00224251 + 0.369568i
\(56\) 4.78765i 0.639777i
\(57\) 1.63290 + 0.577604i 0.216283 + 0.0765055i
\(58\) 5.75831 + 5.75831i 0.756103 + 0.756103i
\(59\) −9.91906 −1.29135 −0.645676 0.763612i \(-0.723424\pi\)
−0.645676 + 0.763612i \(0.723424\pi\)
\(60\) 3.64338 + 1.31369i 0.470358 + 0.169597i
\(61\) −10.5422 −1.34979 −0.674894 0.737915i \(-0.735811\pi\)
−0.674894 + 0.737915i \(0.735811\pi\)
\(62\) −5.24666 5.24666i −0.666327 0.666327i
\(63\) −14.2832 + 1.51125i −1.79952 + 0.190400i
\(64\) 1.00000i 0.125000i
\(65\) 7.81614 + 7.91158i 0.969473 + 0.981310i
\(66\) −0.914660 1.91591i −0.112587 0.235833i
\(67\) 6.00309 6.00309i 0.733394 0.733394i −0.237896 0.971291i \(-0.576458\pi\)
0.971291 + 0.237896i \(0.0764579\pi\)
\(68\) −0.826034 + 0.826034i −0.100171 + 0.100171i
\(69\) 1.10509 + 2.31481i 0.133038 + 0.278671i
\(70\) −10.7053 0.0649592i −1.27953 0.00776411i
\(71\) 8.35839i 0.991958i 0.868334 + 0.495979i \(0.165191\pi\)
−0.868334 + 0.495979i \(0.834809\pi\)
\(72\) −2.98335 + 0.315656i −0.351591 + 0.0372004i
\(73\) −3.99393 3.99393i −0.467454 0.467454i 0.433635 0.901089i \(-0.357231\pi\)
−0.901089 + 0.433635i \(0.857231\pi\)
\(74\) 8.25017 0.959063
\(75\) 2.98689 8.12887i 0.344896 0.938641i
\(76\) −1.00000 −0.114708
\(77\) 4.14960 + 4.14960i 0.472891 + 0.472891i
\(78\) −8.12146 2.87279i −0.919575 0.325279i
\(79\) 6.75057i 0.759498i −0.925090 0.379749i \(-0.876010\pi\)
0.925090 0.379749i \(-0.123990\pi\)
\(80\) −2.23603 0.0135681i −0.249995 0.00151695i
\(81\) 1.88342 + 8.80072i 0.209269 + 0.977858i
\(82\) 2.50013 2.50013i 0.276093 0.276093i
\(83\) 0.717790 0.717790i 0.0787877 0.0787877i −0.666615 0.745402i \(-0.732257\pi\)
0.745402 + 0.666615i \(0.232257\pi\)
\(84\) 7.48341 3.57259i 0.816507 0.389802i
\(85\) 1.83583 + 1.85824i 0.199123 + 0.201555i
\(86\) 3.80067i 0.409836i
\(87\) −4.70370 + 13.2975i −0.504290 + 1.42564i
\(88\) 0.866730 + 0.866730i 0.0923937 + 0.0923937i
\(89\) −0.384471 −0.0407539 −0.0203769 0.999792i \(-0.506487\pi\)
−0.0203769 + 0.999792i \(0.506487\pi\)
\(90\) 0.665336 + 6.67513i 0.0701326 + 0.703620i
\(91\) 23.8120 2.49618
\(92\) −1.04719 1.04719i −0.109177 0.109177i
\(93\) 4.28576 12.1160i 0.444413 1.25637i
\(94\) 9.68521i 0.998953i
\(95\) −0.0135681 + 2.23603i −0.00139205 + 0.229412i
\(96\) 1.56306 0.746209i 0.159530 0.0761597i
\(97\) −12.5444 + 12.5444i −1.27369 + 1.27369i −0.329554 + 0.944137i \(0.606899\pi\)
−0.944137 + 0.329554i \(0.893101\pi\)
\(98\) −11.2583 + 11.2583i −1.13726 + 1.13726i
\(99\) 2.31217 2.85934i 0.232382 0.287375i
\(100\) −0.0606771 + 4.99963i −0.00606771 + 0.499963i
\(101\) 1.19949i 0.119354i 0.998218 + 0.0596768i \(0.0190070\pi\)
−0.998218 + 0.0596768i \(0.980993\pi\)
\(102\) −1.90754 0.674750i −0.188875 0.0668102i
\(103\) 13.1711 + 13.1711i 1.29778 + 1.29778i 0.929853 + 0.367931i \(0.119934\pi\)
0.367931 + 0.929853i \(0.380066\pi\)
\(104\) 4.97363 0.487705
\(105\) −7.88688 16.7816i −0.769681 1.63772i
\(106\) 4.81722 0.467890
\(107\) 9.98389 + 9.98389i 0.965179 + 0.965179i 0.999414 0.0342348i \(-0.0108994\pi\)
−0.0342348 + 0.999414i \(0.510899\pi\)
\(108\) −2.71959 4.42762i −0.261693 0.426048i
\(109\) 8.95394i 0.857632i −0.903392 0.428816i \(-0.858931\pi\)
0.903392 0.428816i \(-0.141069\pi\)
\(110\) 1.94979 1.92627i 0.185905 0.183663i
\(111\) 6.15635 + 12.8956i 0.584335 + 1.22399i
\(112\) −3.38538 + 3.38538i −0.319889 + 0.319889i
\(113\) 13.3747 13.3747i 1.25818 1.25818i 0.306225 0.951959i \(-0.400934\pi\)
0.951959 0.306225i \(-0.0990661\pi\)
\(114\) −0.746209 1.56306i −0.0698889 0.146394i
\(115\) −2.35574 + 2.32733i −0.219674 + 0.217024i
\(116\) 8.14348i 0.756103i
\(117\) −1.56996 14.8381i −0.145142 1.37178i
\(118\) 7.01383 + 7.01383i 0.645676 + 0.645676i
\(119\) 5.59288 0.512699
\(120\) −1.64734 3.50518i −0.150381 0.319978i
\(121\) 9.49756 0.863414
\(122\) 7.45445 + 7.45445i 0.674894 + 0.674894i
\(123\) 5.77349 + 2.04225i 0.520578 + 0.184143i
\(124\) 7.41990i 0.666327i
\(125\) 11.1785 + 0.203511i 0.999834 + 0.0182026i
\(126\) 11.1684 + 9.03116i 0.994959 + 0.804560i
\(127\) −6.46428 + 6.46428i −0.573612 + 0.573612i −0.933136 0.359524i \(-0.882939\pi\)
0.359524 + 0.933136i \(0.382939\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −5.94069 + 2.83609i −0.523048 + 0.249704i
\(130\) 0.0674826 11.1212i 0.00591861 0.975392i
\(131\) 4.64733i 0.406039i −0.979175 0.203020i \(-0.934924\pi\)
0.979175 0.203020i \(-0.0650755\pi\)
\(132\) −0.707993 + 2.00152i −0.0616229 + 0.174210i
\(133\) 3.38538 + 3.38538i 0.293550 + 0.293550i
\(134\) −8.48965 −0.733394
\(135\) −9.93718 + 6.02101i −0.855256 + 0.518206i
\(136\) 1.16819 0.100171
\(137\) −0.825480 0.825480i −0.0705255 0.0705255i 0.670964 0.741490i \(-0.265880\pi\)
−0.741490 + 0.670964i \(0.765880\pi\)
\(138\) 0.855399 2.41824i 0.0728164 0.205854i
\(139\) 3.47441i 0.294695i 0.989085 + 0.147348i \(0.0470736\pi\)
−0.989085 + 0.147348i \(0.952926\pi\)
\(140\) 7.52387 + 7.61574i 0.635883 + 0.643648i
\(141\) −15.1386 + 7.22720i −1.27490 + 0.608640i
\(142\) 5.91027 5.91027i 0.495979 0.495979i
\(143\) −4.31080 + 4.31080i −0.360487 + 0.360487i
\(144\) 2.33275 + 1.88634i 0.194396 + 0.157195i
\(145\) −18.2090 0.110491i −1.51218 0.00917579i
\(146\) 5.64827i 0.467454i
\(147\) −25.9985 9.19640i −2.14432 0.758506i
\(148\) −5.83375 5.83375i −0.479531 0.479531i
\(149\) −1.10597 −0.0906042 −0.0453021 0.998973i \(-0.514425\pi\)
−0.0453021 + 0.998973i \(0.514425\pi\)
\(150\) −7.86003 + 3.63593i −0.641768 + 0.296872i
\(151\) 3.28699 0.267491 0.133746 0.991016i \(-0.457299\pi\)
0.133746 + 0.991016i \(0.457299\pi\)
\(152\) 0.707107 + 0.707107i 0.0573539 + 0.0573539i
\(153\) −0.368745 3.48511i −0.0298113 0.281755i
\(154\) 5.86842i 0.472891i
\(155\) 16.5911 + 0.100674i 1.33263 + 0.00808630i
\(156\) 3.71137 + 7.77411i 0.297148 + 0.622427i
\(157\) −12.0134 + 12.0134i −0.958773 + 0.958773i −0.999183 0.0404098i \(-0.987134\pi\)
0.0404098 + 0.999183i \(0.487134\pi\)
\(158\) −4.77337 + 4.77337i −0.379749 + 0.379749i
\(159\) 3.59466 + 7.52963i 0.285075 + 0.597138i
\(160\) 1.57152 + 1.59070i 0.124239 + 0.125756i
\(161\) 7.09025i 0.558790i
\(162\) 4.89127 7.55483i 0.384295 0.593564i
\(163\) 3.82552 + 3.82552i 0.299638 + 0.299638i 0.840872 0.541234i \(-0.182043\pi\)
−0.541234 + 0.840872i \(0.682043\pi\)
\(164\) −3.53572 −0.276093
\(165\) 4.46584 + 1.61025i 0.347665 + 0.125358i
\(166\) −1.01511 −0.0787877
\(167\) 14.1056 + 14.1056i 1.09152 + 1.09152i 0.995366 + 0.0961553i \(0.0306545\pi\)
0.0961553 + 0.995366i \(0.469345\pi\)
\(168\) −7.81778 2.76537i −0.603155 0.213353i
\(169\) 11.7370i 0.902849i
\(170\) 0.0158500 2.61210i 0.00121564 0.200339i
\(171\) 1.88634 2.33275i 0.144252 0.178390i
\(172\) 2.68748 2.68748i 0.204918 0.204918i
\(173\) 6.57463 6.57463i 0.499860 0.499860i −0.411535 0.911394i \(-0.635007\pi\)
0.911394 + 0.411535i \(0.135007\pi\)
\(174\) 12.7288 6.07674i 0.964966 0.460676i
\(175\) 17.1311 16.7203i 1.29499 1.26393i
\(176\) 1.22574i 0.0923937i
\(177\) −5.72929 + 16.1969i −0.430639 + 1.21743i
\(178\) 0.271862 + 0.271862i 0.0203769 + 0.0203769i
\(179\) −11.2885 −0.843741 −0.421870 0.906656i \(-0.638626\pi\)
−0.421870 + 0.906656i \(0.638626\pi\)
\(180\) 4.24956 5.19049i 0.316744 0.386876i
\(181\) −9.96083 −0.740383 −0.370191 0.928956i \(-0.620708\pi\)
−0.370191 + 0.928956i \(0.620708\pi\)
\(182\) −16.8377 16.8377i −1.24809 1.24809i
\(183\) −6.08920 + 17.2144i −0.450127 + 1.27252i
\(184\) 1.48094i 0.109177i
\(185\) −13.1236 + 12.9653i −0.964865 + 0.953226i
\(186\) −11.5978 + 5.53680i −0.850391 + 0.405978i
\(187\) −1.01250 + 1.01250i −0.0740416 + 0.0740416i
\(188\) 6.84848 6.84848i 0.499477 0.499477i
\(189\) −5.78233 + 24.1961i −0.420602 + 1.76000i
\(190\) 1.59070 1.57152i 0.115402 0.114010i
\(191\) 10.1454i 0.734095i −0.930202 0.367048i \(-0.880369\pi\)
0.930202 0.367048i \(-0.119631\pi\)
\(192\) −1.63290 0.577604i −0.117845 0.0416850i
\(193\) 1.33016 + 1.33016i 0.0957468 + 0.0957468i 0.753358 0.657611i \(-0.228433\pi\)
−0.657611 + 0.753358i \(0.728433\pi\)
\(194\) 17.7405 1.27369
\(195\) 17.4335 8.19325i 1.24844 0.586731i
\(196\) 15.9216 1.13726
\(197\) 3.67465 + 3.67465i 0.261808 + 0.261808i 0.825788 0.563980i \(-0.190731\pi\)
−0.563980 + 0.825788i \(0.690731\pi\)
\(198\) −3.65681 + 0.386912i −0.259878 + 0.0274966i
\(199\) 0.894086i 0.0633801i 0.999498 + 0.0316900i \(0.0100889\pi\)
−0.999498 + 0.0316900i \(0.989911\pi\)
\(200\) 3.57818 3.49237i 0.253015 0.246948i
\(201\) −6.33506 13.2699i −0.446841 0.935985i
\(202\) 0.848167 0.848167i 0.0596768 0.0596768i
\(203\) −27.5688 + 27.5688i −1.93495 + 1.93495i
\(204\) 0.871713 + 1.82595i 0.0610321 + 0.127842i
\(205\) −0.0479729 + 7.90597i −0.00335057 + 0.552177i
\(206\) 18.6267i 1.29778i
\(207\) 4.41817 0.467469i 0.307084 0.0324913i
\(208\) −3.51689 3.51689i −0.243852 0.243852i
\(209\) −1.22574 −0.0847863
\(210\) −6.28951 + 17.4432i −0.434017 + 1.20370i
\(211\) −0.656325 −0.0451833 −0.0225916 0.999745i \(-0.507192\pi\)
−0.0225916 + 0.999745i \(0.507192\pi\)
\(212\) −3.40629 3.40629i −0.233945 0.233945i
\(213\) 13.6484 + 4.82784i 0.935176 + 0.330798i
\(214\) 14.1194i 0.965179i
\(215\) −5.97281 6.04574i −0.407342 0.412316i
\(216\) −1.20776 + 5.05384i −0.0821775 + 0.343870i
\(217\) 25.1192 25.1192i 1.70520 1.70520i
\(218\) −6.33139 + 6.33139i −0.428816 + 0.428816i
\(219\) −8.82861 + 4.21479i −0.596582 + 0.284809i
\(220\) −2.74079 0.0166309i −0.184784 0.00112126i
\(221\) 5.81014i 0.390832i
\(222\) 4.76533 13.4717i 0.319828 0.904163i
\(223\) −5.81309 5.81309i −0.389273 0.389273i 0.485155 0.874428i \(-0.338763\pi\)
−0.874428 + 0.485155i \(0.838763\pi\)
\(224\) 4.78765 0.319889
\(225\) −11.5484 9.57256i −0.769895 0.638171i
\(226\) −18.9147 −1.25818
\(227\) −11.1211 11.1211i −0.738133 0.738133i 0.234083 0.972217i \(-0.424791\pi\)
−0.972217 + 0.234083i \(0.924791\pi\)
\(228\) −0.577604 + 1.63290i −0.0382528 + 0.108142i
\(229\) 15.9766i 1.05576i −0.849318 0.527881i \(-0.822987\pi\)
0.849318 0.527881i \(-0.177013\pi\)
\(230\) 3.31143 + 0.0200935i 0.218349 + 0.00132493i
\(231\) 9.17273 4.37907i 0.603521 0.288122i
\(232\) −5.75831 + 5.75831i −0.378051 + 0.378051i
\(233\) 10.3048 10.3048i 0.675090 0.675090i −0.283795 0.958885i \(-0.591593\pi\)
0.958885 + 0.283795i \(0.0915935\pi\)
\(234\) −9.38198 + 11.6022i −0.613319 + 0.758462i
\(235\) −15.2205 15.4063i −0.992873 1.00500i
\(236\) 9.91906i 0.645676i
\(237\) −11.0230 3.89915i −0.716022 0.253277i
\(238\) −3.95477 3.95477i −0.256349 0.256349i
\(239\) 16.1045 1.04172 0.520858 0.853644i \(-0.325612\pi\)
0.520858 + 0.853644i \(0.325612\pi\)
\(240\) −1.31369 + 3.64338i −0.0847985 + 0.235179i
\(241\) −19.9193 −1.28312 −0.641559 0.767074i \(-0.721712\pi\)
−0.641559 + 0.767074i \(0.721712\pi\)
\(242\) −6.71579 6.71579i −0.431707 0.431707i
\(243\) 15.4586 + 2.00789i 0.991670 + 0.128806i
\(244\) 10.5422i 0.674894i
\(245\) 0.216026 35.6012i 0.0138014 2.27448i
\(246\) −2.63839 5.52656i −0.168218 0.352361i
\(247\) −3.51689 + 3.51689i −0.223774 + 0.223774i
\(248\) 5.24666 5.24666i 0.333163 0.333163i
\(249\) −0.757484 1.58668i −0.0480036 0.100552i
\(250\) −7.76048 8.04829i −0.490816 0.509018i
\(251\) 17.8998i 1.12982i −0.825151 0.564912i \(-0.808910\pi\)
0.825151 0.564912i \(-0.191090\pi\)
\(252\) −1.51125 14.2832i −0.0951998 0.899759i
\(253\) −1.28358 1.28358i −0.0806979 0.0806979i
\(254\) 9.14187 0.573612
\(255\) 4.09471 1.92440i 0.256421 0.120511i
\(256\) 1.00000 0.0625000
\(257\) 14.5464 + 14.5464i 0.907378 + 0.907378i 0.996060 0.0886822i \(-0.0282655\pi\)
−0.0886822 + 0.996060i \(0.528266\pi\)
\(258\) 6.20612 + 2.19528i 0.386376 + 0.136672i
\(259\) 39.4990i 2.45435i
\(260\) −7.91158 + 7.81614i −0.490655 + 0.484737i
\(261\) 18.9967 + 15.3614i 1.17586 + 0.950846i
\(262\) −3.28616 + 3.28616i −0.203020 + 0.203020i
\(263\) −6.05674 + 6.05674i −0.373475 + 0.373475i −0.868741 0.495266i \(-0.835070\pi\)
0.495266 + 0.868741i \(0.335070\pi\)
\(264\) 1.91591 0.914660i 0.117916 0.0562934i
\(265\) −7.66277 + 7.57034i −0.470720 + 0.465042i
\(266\) 4.78765i 0.293550i
\(267\) −0.222072 + 0.627804i −0.0135906 + 0.0384210i
\(268\) 6.00309 + 6.00309i 0.366697 + 0.366697i
\(269\) 9.51326 0.580034 0.290017 0.957022i \(-0.406339\pi\)
0.290017 + 0.957022i \(0.406339\pi\)
\(270\) 11.2841 + 2.76915i 0.686731 + 0.168525i
\(271\) 0.405502 0.0246325 0.0123162 0.999924i \(-0.496080\pi\)
0.0123162 + 0.999924i \(0.496080\pi\)
\(272\) −0.826034 0.826034i −0.0500857 0.0500857i
\(273\) 13.7539 38.8828i 0.832426 2.35329i
\(274\) 1.16740i 0.0705255i
\(275\) −0.0743744 + 6.12825i −0.00448494 + 0.369548i
\(276\) −2.31481 + 1.10509i −0.139335 + 0.0665189i
\(277\) 3.15621 3.15621i 0.189639 0.189639i −0.605901 0.795540i \(-0.707187\pi\)
0.795540 + 0.605901i \(0.207187\pi\)
\(278\) 2.45678 2.45678i 0.147348 0.147348i
\(279\) −17.3088 13.9965i −1.03625 0.837947i
\(280\) 0.0649592 10.7053i 0.00388205 0.639765i
\(281\) 11.9223i 0.711227i −0.934633 0.355613i \(-0.884272\pi\)
0.934633 0.355613i \(-0.115728\pi\)
\(282\) 15.8150 + 5.59422i 0.941770 + 0.333131i
\(283\) 11.1386 + 11.1386i 0.662120 + 0.662120i 0.955879 0.293759i \(-0.0949063\pi\)
−0.293759 + 0.955879i \(0.594906\pi\)
\(284\) −8.35839 −0.495979
\(285\) 3.64338 + 1.31369i 0.215815 + 0.0778165i
\(286\) 6.09639 0.360487
\(287\) 11.9698 + 11.9698i 0.706553 + 0.706553i
\(288\) −0.315656 2.98335i −0.0186002 0.175795i
\(289\) 15.6353i 0.919726i
\(290\) 12.7976 + 12.9539i 0.751501 + 0.760677i
\(291\) 13.2381 + 27.7295i 0.776031 + 1.62553i
\(292\) 3.99393 3.99393i 0.233727 0.233727i
\(293\) −3.32969 + 3.32969i −0.194522 + 0.194522i −0.797647 0.603125i \(-0.793922\pi\)
0.603125 + 0.797647i \(0.293922\pi\)
\(294\) 11.8809 + 24.8866i 0.692907 + 1.45141i
\(295\) −22.1793 0.134582i −1.29133 0.00783569i
\(296\) 8.25017i 0.479531i
\(297\) −3.33352 5.42712i −0.193430 0.314913i
\(298\) 0.782036 + 0.782036i 0.0453021 + 0.0453021i
\(299\) −7.36568 −0.425968
\(300\) 8.12887 + 2.98689i 0.469320 + 0.172448i
\(301\) −18.1963 −1.04882
\(302\) −2.32425 2.32425i −0.133746 0.133746i
\(303\) 1.95865 + 0.692830i 0.112522 + 0.0398020i
\(304\) 1.00000i 0.0573539i
\(305\) −23.5726 0.143037i −1.34976 0.00819027i
\(306\) −2.20360 + 2.72509i −0.125972 + 0.155783i
\(307\) −1.69015 + 1.69015i −0.0964621 + 0.0964621i −0.753691 0.657229i \(-0.771728\pi\)
0.657229 + 0.753691i \(0.271728\pi\)
\(308\) −4.14960 + 4.14960i −0.236446 + 0.236446i
\(309\) 29.1147 13.8994i 1.65628 0.790711i
\(310\) −11.6605 11.8029i −0.662271 0.670358i
\(311\) 14.3337i 0.812790i −0.913697 0.406395i \(-0.866786\pi\)
0.913697 0.406395i \(-0.133214\pi\)
\(312\) 2.87279 8.12146i 0.162640 0.459787i
\(313\) 1.56414 + 1.56414i 0.0884102 + 0.0884102i 0.749929 0.661519i \(-0.230088\pi\)
−0.661519 + 0.749929i \(0.730088\pi\)
\(314\) 16.9895 0.958773
\(315\) −31.9582 + 3.18540i −1.80064 + 0.179477i
\(316\) 6.75057 0.379749
\(317\) −21.5987 21.5987i −1.21311 1.21311i −0.969999 0.243107i \(-0.921833\pi\)
−0.243107 0.969999i \(-0.578167\pi\)
\(318\) 2.78245 7.86606i 0.156032 0.441107i
\(319\) 9.98179i 0.558873i
\(320\) 0.0135681 2.23603i 0.000758477 0.124998i
\(321\) 22.0695 10.5360i 1.23180 0.588062i
\(322\) 5.01356 5.01356i 0.279395 0.279395i
\(323\) −0.826034 + 0.826034i −0.0459618 + 0.0459618i
\(324\) −8.80072 + 1.88342i −0.488929 + 0.104635i
\(325\) 17.3698 + 17.7966i 0.963501 + 0.987175i
\(326\) 5.41010i 0.299638i
\(327\) −14.6209 5.17183i −0.808538 0.286003i
\(328\) 2.50013 + 2.50013i 0.138047 + 0.138047i
\(329\) −46.3694 −2.55643
\(330\) −2.01921 4.29644i −0.111154 0.236511i
\(331\) −6.37126 −0.350196 −0.175098 0.984551i \(-0.556024\pi\)
−0.175098 + 0.984551i \(0.556024\pi\)
\(332\) 0.717790 + 0.717790i 0.0393939 + 0.0393939i
\(333\) 24.6131 2.60421i 1.34879 0.142710i
\(334\) 19.9483i 1.09152i
\(335\) 13.5045 13.3416i 0.737831 0.728931i
\(336\) 3.57259 + 7.48341i 0.194901 + 0.408254i
\(337\) 1.13280 1.13280i 0.0617073 0.0617073i −0.675580 0.737287i \(-0.736107\pi\)
0.737287 + 0.675580i \(0.236107\pi\)
\(338\) 8.29934 8.29934i 0.451424 0.451424i
\(339\) −14.1143 29.5648i −0.766583 1.60574i
\(340\) −1.85824 + 1.83583i −0.100777 + 0.0995617i
\(341\) 9.09487i 0.492515i
\(342\) −2.98335 + 0.315656i −0.161321 + 0.0170687i
\(343\) −30.2032 30.2032i −1.63082 1.63082i
\(344\) −3.80067 −0.204918
\(345\) 2.43961 + 5.19098i 0.131344 + 0.279473i
\(346\) −9.29793 −0.499860
\(347\) 22.1434 + 22.1434i 1.18872 + 1.18872i 0.977422 + 0.211296i \(0.0677683\pi\)
0.211296 + 0.977422i \(0.432232\pi\)
\(348\) −13.2975 4.70370i −0.712821 0.252145i
\(349\) 19.6754i 1.05320i 0.850113 + 0.526600i \(0.176533\pi\)
−0.850113 + 0.526600i \(0.823467\pi\)
\(350\) −23.9365 0.290501i −1.27946 0.0155279i
\(351\) −25.1360 6.00695i −1.34166 0.320627i
\(352\) −0.866730 + 0.866730i −0.0461969 + 0.0461969i
\(353\) −24.9047 + 24.9047i −1.32554 + 1.32554i −0.416330 + 0.909214i \(0.636684\pi\)
−0.909214 + 0.416330i \(0.863316\pi\)
\(354\) 15.5041 7.40169i 0.824035 0.393396i
\(355\) −0.113407 + 18.6896i −0.00601902 + 0.991940i
\(356\) 0.384471i 0.0203769i
\(357\) 3.23047 9.13264i 0.170975 0.483350i
\(358\) 7.98216 + 7.98216i 0.421870 + 0.421870i
\(359\) 20.9304 1.10466 0.552331 0.833625i \(-0.313739\pi\)
0.552331 + 0.833625i \(0.313739\pi\)
\(360\) −6.67513 + 0.665336i −0.351810 + 0.0350663i
\(361\) −1.00000 −0.0526316
\(362\) 7.04337 + 7.04337i 0.370191 + 0.370191i
\(363\) 5.48583 15.5086i 0.287931 0.813990i
\(364\) 23.8120i 1.24809i
\(365\) −8.87634 8.98472i −0.464609 0.470282i
\(366\) 16.4781 7.86667i 0.861325 0.411198i
\(367\) 26.3718 26.3718i 1.37660 1.37660i 0.526301 0.850298i \(-0.323578\pi\)
0.850298 0.526301i \(-0.176422\pi\)
\(368\) 1.04719 1.04719i 0.0545883 0.0545883i
\(369\) 6.66958 8.24795i 0.347205 0.429371i
\(370\) 18.4476 + 0.111939i 0.959045 + 0.00581942i
\(371\) 23.0632i 1.19738i
\(372\) 12.1160 + 4.28576i 0.628184 + 0.222206i
\(373\) −6.66242 6.66242i −0.344967 0.344967i 0.513264 0.858231i \(-0.328436\pi\)
−0.858231 + 0.513264i \(0.828436\pi\)
\(374\) 1.43190 0.0740416
\(375\) 6.78905 18.1358i 0.350585 0.936531i
\(376\) −9.68521 −0.499477
\(377\) −28.6397 28.6397i −1.47502 1.47502i
\(378\) 21.1979 13.0205i 1.09030 0.669701i
\(379\) 0.205871i 0.0105749i −0.999986 0.00528745i \(-0.998317\pi\)
0.999986 0.00528745i \(-0.00168305\pi\)
\(380\) −2.23603 0.0135681i −0.114706 0.000696027i
\(381\) 6.82175 + 14.2893i 0.349489 + 0.732065i
\(382\) −7.17388 + 7.17388i −0.367048 + 0.367048i
\(383\) 8.26926 8.26926i 0.422539 0.422539i −0.463538 0.886077i \(-0.653420\pi\)
0.886077 + 0.463538i \(0.153420\pi\)
\(384\) 0.746209 + 1.56306i 0.0380798 + 0.0797648i
\(385\) 9.22232 + 9.33493i 0.470013 + 0.475752i
\(386\) 1.88113i 0.0957468i
\(387\) 1.19970 + 11.3387i 0.0609843 + 0.576379i
\(388\) −12.5444 12.5444i −0.636846 0.636846i
\(389\) 25.3999 1.28782 0.643912 0.765099i \(-0.277310\pi\)
0.643912 + 0.765099i \(0.277310\pi\)
\(390\) −18.1208 6.53383i −0.917584 0.330853i
\(391\) −1.73002 −0.0874910
\(392\) −11.2583 11.2583i −0.568630 0.568630i
\(393\) −7.58865 2.68432i −0.382797 0.135406i
\(394\) 5.19674i 0.261808i
\(395\) 0.0915921 15.0944i 0.00460850 0.759484i
\(396\) 2.85934 + 2.31217i 0.143687 + 0.116191i
\(397\) 14.4297 14.4297i 0.724206 0.724206i −0.245253 0.969459i \(-0.578871\pi\)
0.969459 + 0.245253i \(0.0788711\pi\)
\(398\) 0.632214 0.632214i 0.0316900 0.0316900i
\(399\) 7.48341 3.57259i 0.374639 0.178853i
\(400\) −4.99963 0.0606771i −0.249982 0.00303385i
\(401\) 8.03063i 0.401030i −0.979691 0.200515i \(-0.935738\pi\)
0.979691 0.200515i \(-0.0642616\pi\)
\(402\) −4.90366 + 13.8628i −0.244572 + 0.691413i
\(403\) 26.0950 + 26.0950i 1.29988 + 1.29988i
\(404\) −1.19949 −0.0596768
\(405\) 4.09197 + 19.7042i 0.203332 + 0.979110i
\(406\) 38.9882 1.93495
\(407\) −7.15067 7.15067i −0.354445 0.354445i
\(408\) 0.674750 1.90754i 0.0334051 0.0944373i
\(409\) 13.8653i 0.685596i 0.939409 + 0.342798i \(0.111375\pi\)
−0.939409 + 0.342798i \(0.888625\pi\)
\(410\) 5.62429 5.55644i 0.277764 0.274413i
\(411\) −1.82473 + 0.871129i −0.0900073 + 0.0429696i
\(412\) −13.1711 + 13.1711i −0.648892 + 0.648892i
\(413\) −33.5798 + 33.5798i −1.65235 + 1.65235i
\(414\) −3.45467 2.79357i −0.169788 0.137296i
\(415\) 1.61474 1.59526i 0.0792643 0.0783082i
\(416\) 4.97363i 0.243852i
\(417\) 5.67337 + 2.00683i 0.277826 + 0.0982749i
\(418\) 0.866730 + 0.866730i 0.0423931 + 0.0423931i
\(419\) −17.7272 −0.866028 −0.433014 0.901387i \(-0.642550\pi\)
−0.433014 + 0.901387i \(0.642550\pi\)
\(420\) 16.7816 7.88688i 0.818858 0.384840i
\(421\) 2.65269 0.129284 0.0646420 0.997909i \(-0.479409\pi\)
0.0646420 + 0.997909i \(0.479409\pi\)
\(422\) 0.464092 + 0.464092i 0.0225916 + 0.0225916i
\(423\) 3.05719 + 28.8943i 0.148646 + 1.40489i
\(424\) 4.81722i 0.233945i
\(425\) 4.07974 + 4.17999i 0.197897 + 0.202759i
\(426\) −6.23711 13.0647i −0.302189 0.632987i
\(427\) −35.6893 + 35.6893i −1.72713 + 1.72713i
\(428\) −9.98389 + 9.98389i −0.482590 + 0.482590i
\(429\) 4.54918 + 9.52905i 0.219637 + 0.460067i
\(430\) −0.0515677 + 8.49839i −0.00248681 + 0.409829i
\(431\) 17.0087i 0.819280i −0.912247 0.409640i \(-0.865654\pi\)
0.912247 0.409640i \(-0.134346\pi\)
\(432\) 4.42762 2.71959i 0.213024 0.130846i
\(433\) 13.8732 + 13.8732i 0.666705 + 0.666705i 0.956952 0.290247i \(-0.0937375\pi\)
−0.290247 + 0.956952i \(0.593738\pi\)
\(434\) −35.5239 −1.70520
\(435\) −10.6980 + 29.6698i −0.512931 + 1.42256i
\(436\) 8.95394 0.428816
\(437\) −1.04719 1.04719i −0.0500937 0.0500937i
\(438\) 9.22308 + 3.26246i 0.440696 + 0.155887i
\(439\) 7.44257i 0.355214i −0.984101 0.177607i \(-0.943164\pi\)
0.984101 0.177607i \(-0.0568357\pi\)
\(440\) 1.92627 + 1.94979i 0.0918314 + 0.0929526i
\(441\) −30.0337 + 37.1412i −1.43017 + 1.76863i
\(442\) 4.10839 4.10839i 0.195416 0.195416i
\(443\) 14.0091 14.0091i 0.665593 0.665593i −0.291100 0.956693i \(-0.594021\pi\)
0.956693 + 0.291100i \(0.0940213\pi\)
\(444\) −12.8956 + 6.15635i −0.611996 + 0.292168i
\(445\) −0.859688 0.00521653i −0.0407531 0.000247287i
\(446\) 8.22095i 0.389273i
\(447\) −0.638810 + 1.80593i −0.0302147 + 0.0854178i
\(448\) −3.38538 3.38538i −0.159944 0.159944i
\(449\) −17.0757 −0.805851 −0.402926 0.915233i \(-0.632007\pi\)
−0.402926 + 0.915233i \(0.632007\pi\)
\(450\) 1.39714 + 14.9348i 0.0658619 + 0.704033i
\(451\) −4.33388 −0.204074
\(452\) 13.3747 + 13.3747i 0.629092 + 0.629092i
\(453\) 1.89858 5.36734i 0.0892030 0.252179i
\(454\) 15.7276i 0.738133i
\(455\) 53.2444 + 0.323083i 2.49613 + 0.0151464i
\(456\) 1.56306 0.746209i 0.0731972 0.0349445i
\(457\) −4.57545 + 4.57545i −0.214030 + 0.214030i −0.805977 0.591947i \(-0.798360\pi\)
0.591947 + 0.805977i \(0.298360\pi\)
\(458\) −11.2971 + 11.2971i −0.527881 + 0.527881i
\(459\) −5.90384 1.41089i −0.275568 0.0658547i
\(460\) −2.32733 2.35574i −0.108512 0.109837i
\(461\) 0.120191i 0.00559787i −0.999996 0.00279893i \(-0.999109\pi\)
0.999996 0.00279893i \(-0.000890930\pi\)
\(462\) −9.58257 3.38963i −0.445822 0.157700i
\(463\) −5.82164 5.82164i −0.270555 0.270555i 0.558769 0.829323i \(-0.311274\pi\)
−0.829323 + 0.558769i \(0.811274\pi\)
\(464\) 8.14348 0.378051
\(465\) 9.74747 27.0335i 0.452028 1.25365i
\(466\) −14.5732 −0.675090
\(467\) 1.26700 + 1.26700i 0.0586298 + 0.0586298i 0.735814 0.677184i \(-0.236800\pi\)
−0.677184 + 0.735814i \(0.736800\pi\)
\(468\) 14.8381 1.56996i 0.685890 0.0725712i
\(469\) 40.6455i 1.87684i
\(470\) −0.131410 + 21.6564i −0.00606147 + 0.998935i
\(471\) 12.6777 + 26.5557i 0.584159 + 1.22362i
\(472\) −7.01383 + 7.01383i −0.322838 + 0.322838i
\(473\) 3.29415 3.29415i 0.151465 0.151465i
\(474\) 5.03734 + 10.5516i 0.231373 + 0.484650i
\(475\) −0.0606771 + 4.99963i −0.00278406 + 0.229399i
\(476\) 5.59288i 0.256349i
\(477\) 14.3714 1.52058i 0.658023 0.0696227i
\(478\) −11.3876 11.3876i −0.520858 0.520858i
\(479\) 4.76857 0.217881 0.108941 0.994048i \(-0.465254\pi\)
0.108941 + 0.994048i \(0.465254\pi\)
\(480\) 3.50518 1.64734i 0.159989 0.0751903i
\(481\) −41.0333 −1.87096
\(482\) 14.0851 + 14.0851i 0.641559 + 0.641559i
\(483\) 11.5777 + 4.09536i 0.526803 + 0.186345i
\(484\) 9.49756i 0.431707i
\(485\) −28.2198 + 27.8794i −1.28140 + 1.26594i
\(486\) −9.51109 12.3507i −0.431432 0.560238i
\(487\) 18.6777 18.6777i 0.846368 0.846368i −0.143310 0.989678i \(-0.545775\pi\)
0.989678 + 0.143310i \(0.0457747\pi\)
\(488\) −7.45445 + 7.45445i −0.337447 + 0.337447i
\(489\) 8.45634 4.03707i 0.382409 0.182563i
\(490\) −25.3266 + 25.0211i −1.14414 + 1.13034i
\(491\) 42.9796i 1.93964i 0.243814 + 0.969822i \(0.421601\pi\)
−0.243814 + 0.969822i \(0.578399\pi\)
\(492\) −2.04225 + 5.77349i −0.0920716 + 0.260289i
\(493\) −6.72679 6.72679i −0.302959 0.302959i
\(494\) 4.97363 0.223774
\(495\) 5.20886 6.36220i 0.234121 0.285960i
\(496\) −7.41990 −0.333163
\(497\) 28.2963 + 28.2963i 1.26926 + 1.26926i
\(498\) −0.586331 + 1.65757i −0.0262741 + 0.0742777i
\(499\) 20.8455i 0.933173i −0.884475 0.466587i \(-0.845484\pi\)
0.884475 0.466587i \(-0.154516\pi\)
\(500\) −0.203511 + 11.1785i −0.00910128 + 0.499917i
\(501\) 31.1805 14.8856i 1.39304 0.665040i
\(502\) −12.6570 + 12.6570i −0.564912 + 0.564912i
\(503\) 15.7847 15.7847i 0.703804 0.703804i −0.261421 0.965225i \(-0.584191\pi\)
0.965225 + 0.261421i \(0.0841911\pi\)
\(504\) −9.03116 + 11.1684i −0.402280 + 0.497480i
\(505\) −0.0162747 + 2.68209i −0.000724216 + 0.119351i
\(506\) 1.81525i 0.0806979i
\(507\) 19.1654 + 6.77936i 0.851167 + 0.301082i
\(508\) −6.46428 6.46428i −0.286806 0.286806i
\(509\) −4.31039 −0.191055 −0.0955274 0.995427i \(-0.530454\pi\)
−0.0955274 + 0.995427i \(0.530454\pi\)
\(510\) −4.25615 1.53464i −0.188466 0.0679551i
\(511\) −27.0420 −1.19627
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −2.71959 4.42762i −0.120073 0.195484i
\(514\) 20.5717i 0.907378i
\(515\) 29.2722 + 29.6296i 1.28989 + 1.30563i
\(516\) −2.83609 5.94069i −0.124852 0.261524i
\(517\) 8.39446 8.39446i 0.369188 0.369188i
\(518\) 27.9300 27.9300i 1.22717 1.22717i
\(519\) −6.93820 14.5333i −0.304553 0.637939i
\(520\) 11.1212 + 0.0674826i 0.487696 + 0.00295931i
\(521\) 11.7874i 0.516417i −0.966089 0.258208i \(-0.916868\pi\)
0.966089 0.258208i \(-0.0831321\pi\)
\(522\) −2.57053 24.2948i −0.112509 1.06336i
\(523\) −9.59018 9.59018i −0.419349 0.419349i 0.465630 0.884979i \(-0.345828\pi\)
−0.884979 + 0.465630i \(0.845828\pi\)
\(524\) 4.64733 0.203020
\(525\) −17.4076 37.6311i −0.759729 1.64236i
\(526\) 8.56553 0.373475
\(527\) 6.12909 + 6.12909i 0.266987 + 0.266987i
\(528\) −2.00152 0.707993i −0.0871048 0.0308114i
\(529\) 20.8068i 0.904644i
\(530\) 10.7714 + 0.0653603i 0.467881 + 0.00283907i
\(531\) 23.1387 + 18.7107i 1.00413 + 0.811977i
\(532\) −3.38538 + 3.38538i −0.146775 + 0.146775i
\(533\) −12.4347 + 12.4347i −0.538609 + 0.538609i
\(534\) 0.600953 0.286896i 0.0260058 0.0124152i
\(535\) 22.1888 + 22.4597i 0.959305 + 0.971018i
\(536\) 8.48965i 0.366697i
\(537\) −6.52027 + 18.4330i −0.281370 + 0.795443i
\(538\) −6.72689 6.72689i −0.290017 0.290017i
\(539\) 19.5158 0.840605
\(540\) −6.02101 9.93718i −0.259103 0.427628i
\(541\) −29.8151 −1.28185 −0.640925 0.767603i \(-0.721449\pi\)
−0.640925 + 0.767603i \(0.721449\pi\)
\(542\) −0.286733 0.286733i −0.0123162 0.0123162i
\(543\) −5.75341 + 16.2651i −0.246903 + 0.698001i
\(544\) 1.16819i 0.0500857i
\(545\) 0.121488 20.0212i 0.00520395 0.857616i
\(546\) −37.2198 + 17.7688i −1.59286 + 0.760433i
\(547\) −9.70052 + 9.70052i −0.414764 + 0.414764i −0.883395 0.468630i \(-0.844748\pi\)
0.468630 + 0.883395i \(0.344748\pi\)
\(548\) 0.825480 0.825480i 0.0352628 0.0352628i
\(549\) 24.5922 + 19.8862i 1.04957 + 0.848721i
\(550\) 4.38592 4.28074i 0.187016 0.182531i
\(551\) 8.14348i 0.346924i
\(552\) 2.41824 + 0.855399i 0.102927 + 0.0364082i
\(553\) −22.8533 22.8533i −0.971819 0.971819i
\(554\) −4.46356 −0.189639
\(555\) 13.5908 + 28.9183i 0.576898 + 1.22751i
\(556\) −3.47441 −0.147348
\(557\) 19.7758 + 19.7758i 0.837928 + 0.837928i 0.988586 0.150658i \(-0.0481393\pi\)
−0.150658 + 0.988586i \(0.548139\pi\)
\(558\) 2.34213 + 22.1361i 0.0991504 + 0.937097i
\(559\) 18.9031i 0.799517i
\(560\) −7.61574 + 7.52387i −0.321824 + 0.317942i
\(561\) 1.06849 + 2.23815i 0.0451119 + 0.0944946i
\(562\) −8.43036 + 8.43036i −0.355613 + 0.355613i
\(563\) 26.3822 26.3822i 1.11188 1.11188i 0.118981 0.992896i \(-0.462037\pi\)
0.992896 0.118981i \(-0.0379629\pi\)
\(564\) −7.22720 15.1386i −0.304320 0.637451i
\(565\) 30.0876 29.7247i 1.26580 1.25053i
\(566\) 15.7523i 0.662120i
\(567\) 36.1699 + 23.4177i 1.51899 + 0.983452i
\(568\) 5.91027 + 5.91027i 0.247990 + 0.247990i
\(569\) −21.7175 −0.910445 −0.455222 0.890378i \(-0.650440\pi\)
−0.455222 + 0.890378i \(0.650440\pi\)
\(570\) −1.64734 3.50518i −0.0689993 0.146816i
\(571\) −15.2769 −0.639319 −0.319660 0.947532i \(-0.603569\pi\)
−0.319660 + 0.947532i \(0.603569\pi\)
\(572\) −4.31080 4.31080i −0.180243 0.180243i
\(573\) −16.5665 5.86002i −0.692073 0.244806i
\(574\) 16.9278i 0.706553i
\(575\) −5.29908 + 5.17200i −0.220987 + 0.215687i
\(576\) −1.88634 + 2.33275i −0.0785976 + 0.0971978i
\(577\) 7.00181 7.00181i 0.291489 0.291489i −0.546179 0.837668i \(-0.683918\pi\)
0.837668 + 0.546179i \(0.183918\pi\)
\(578\) −11.0559 + 11.0559i −0.459863 + 0.459863i
\(579\) 2.94032 1.40371i 0.122196 0.0583364i
\(580\) 0.110491 18.2090i 0.00458790 0.756089i
\(581\) 4.85999i 0.201626i
\(582\) 10.2470 28.9685i 0.424750 1.20078i
\(583\) −4.17523 4.17523i −0.172920 0.172920i
\(584\) −5.64827 −0.233727
\(585\) −3.30914 33.1996i −0.136816 1.37264i
\(586\) 4.70889 0.194522
\(587\) −5.53868 5.53868i −0.228606 0.228606i 0.583504 0.812110i \(-0.301681\pi\)
−0.812110 + 0.583504i \(0.801681\pi\)
\(588\) 9.19640 25.9985i 0.379253 1.07216i
\(589\) 7.41990i 0.305732i
\(590\) 15.5880 + 15.7783i 0.641746 + 0.649582i
\(591\) 8.12283 3.87785i 0.334129 0.159514i
\(592\) 5.83375 5.83375i 0.239766 0.239766i
\(593\) 31.4864 31.4864i 1.29299 1.29299i 0.360061 0.932929i \(-0.382756\pi\)
0.932929 0.360061i \(-0.117244\pi\)
\(594\) −1.48040 + 6.19470i −0.0607415 + 0.254172i
\(595\) 12.5058 + 0.0758846i 0.512689 + 0.00311096i
\(596\) 1.10597i 0.0453021i
\(597\) 1.45996 + 0.516428i 0.0597520 + 0.0211360i
\(598\) 5.20832 + 5.20832i 0.212984 + 0.212984i
\(599\) −31.3766 −1.28201 −0.641007 0.767535i \(-0.721483\pi\)
−0.641007 + 0.767535i \(0.721483\pi\)
\(600\) −3.63593 7.86003i −0.148436 0.320884i
\(601\) −36.3695 −1.48354 −0.741771 0.670654i \(-0.766014\pi\)
−0.741771 + 0.670654i \(0.766014\pi\)
\(602\) 12.8667 + 12.8667i 0.524408 + 0.524408i
\(603\) −25.3276 + 2.67981i −1.03142 + 0.109130i
\(604\) 3.28699i 0.133746i
\(605\) 21.2368 + 0.128863i 0.863399 + 0.00523904i
\(606\) −0.895070 1.87488i −0.0363597 0.0761618i
\(607\) 8.74748 8.74748i 0.355049 0.355049i −0.506935 0.861984i \(-0.669222\pi\)
0.861984 + 0.506935i \(0.169222\pi\)
\(608\) −0.707107 + 0.707107i −0.0286770 + 0.0286770i
\(609\) 29.0933 + 60.9410i 1.17892 + 2.46945i
\(610\) 16.5672 + 16.7695i 0.670786 + 0.678977i
\(611\) 48.1707i 1.94878i
\(612\) 3.48511 0.368745i 0.140877 0.0149056i
\(613\) −1.37399 1.37399i −0.0554951 0.0554951i 0.678815 0.734310i \(-0.262494\pi\)
−0.734310 + 0.678815i \(0.762494\pi\)
\(614\) 2.39024 0.0964621
\(615\) 12.8820 + 4.64485i 0.519451 + 0.187299i
\(616\) 5.86842 0.236446
\(617\) 11.8837 + 11.8837i 0.478419 + 0.478419i 0.904626 0.426207i \(-0.140150\pi\)
−0.426207 + 0.904626i \(0.640150\pi\)
\(618\) −30.4156 10.7589i −1.22350 0.432785i
\(619\) 4.06759i 0.163490i −0.996653 0.0817450i \(-0.973951\pi\)
0.996653 0.0817450i \(-0.0260493\pi\)
\(620\) −0.100674 + 16.5911i −0.00404315 + 0.666314i
\(621\) 1.78862 7.48446i 0.0717750 0.300341i
\(622\) −10.1355 + 10.1355i −0.406395 + 0.406395i
\(623\) −1.30158 + 1.30158i −0.0521468 + 0.0521468i
\(624\) −7.77411 + 3.71137i −0.311214 + 0.148574i
\(625\) 24.9926 + 0.606726i 0.999705 + 0.0242690i
\(626\) 2.21202i 0.0884102i
\(627\) −0.707993 + 2.00152i −0.0282745 + 0.0799329i
\(628\) −12.0134 12.0134i −0.479387 0.479387i
\(629\) −9.63775 −0.384282
\(630\) 24.8503 + 20.3454i 0.990059 + 0.810582i
\(631\) −5.67496 −0.225917 −0.112958 0.993600i \(-0.536033\pi\)
−0.112958 + 0.993600i \(0.536033\pi\)
\(632\) −4.77337 4.77337i −0.189875 0.189875i
\(633\) −0.379096 + 1.07172i −0.0150677 + 0.0425969i
\(634\) 30.5452i 1.21311i
\(635\) −14.5420 + 14.3666i −0.577082 + 0.570121i
\(636\) −7.52963 + 3.59466i −0.298569 + 0.142537i
\(637\) 55.9947 55.9947i 2.21859 2.21859i
\(638\) −7.05819 + 7.05819i −0.279437 + 0.279437i
\(639\) 15.7668 19.4980i 0.623724 0.771329i
\(640\) −1.59070 + 1.57152i −0.0628781 + 0.0621196i
\(641\) 1.58825i 0.0627323i −0.999508 0.0313661i \(-0.990014\pi\)
0.999508 0.0313661i \(-0.00998579\pi\)
\(642\) −23.0555 8.15539i −0.909930 0.321868i
\(643\) −8.25666 8.25666i −0.325611 0.325611i 0.525304 0.850915i \(-0.323952\pi\)
−0.850915 + 0.525304i \(0.823952\pi\)
\(644\) −7.09025 −0.279395
\(645\) −13.3220 + 6.26098i −0.524554 + 0.246526i
\(646\) 1.16819 0.0459618
\(647\) −12.9377 12.9377i −0.508635 0.508635i 0.405472 0.914107i \(-0.367107\pi\)
−0.914107 + 0.405472i \(0.867107\pi\)
\(648\) 7.55483 + 4.89127i 0.296782 + 0.192147i
\(649\) 12.1582i 0.477251i
\(650\) 0.301786 24.8663i 0.0118370 0.975338i
\(651\) −26.5083 55.5262i −1.03894 2.17624i
\(652\) −3.82552 + 3.82552i −0.149819 + 0.149819i
\(653\) 16.2867 16.2867i 0.637350 0.637350i −0.312551 0.949901i \(-0.601184\pi\)
0.949901 + 0.312551i \(0.101184\pi\)
\(654\) 6.68151 + 13.9956i 0.261268 + 0.547271i
\(655\) 0.0630553 10.3916i 0.00246377 0.406032i
\(656\) 3.53572i 0.138047i
\(657\) 1.78291 + 16.8508i 0.0695579 + 0.657410i
\(658\) 32.7882 + 32.7882i 1.27822 + 1.27822i
\(659\) −40.1270 −1.56313 −0.781563 0.623827i \(-0.785577\pi\)
−0.781563 + 0.623827i \(0.785577\pi\)
\(660\) −1.61025 + 4.46584i −0.0626788 + 0.173833i
\(661\) −17.8333 −0.693634 −0.346817 0.937933i \(-0.612737\pi\)
−0.346817 + 0.937933i \(0.612737\pi\)
\(662\) 4.50516 + 4.50516i 0.175098 + 0.175098i
\(663\) 9.48740 + 3.35596i 0.368460 + 0.130335i
\(664\) 1.01511i 0.0393939i
\(665\) 7.52387 + 7.61574i 0.291763 + 0.295326i
\(666\) −19.2456 15.5626i −0.745750 0.603040i
\(667\) 8.52773 8.52773i 0.330195 0.330195i
\(668\) −14.1056 + 14.1056i −0.545761 + 0.545761i
\(669\) −12.8499 + 6.13455i −0.496805 + 0.237176i
\(670\) −18.9831 0.115188i −0.733381 0.00445010i
\(671\) 12.9220i 0.498848i
\(672\) 2.76537 7.81778i 0.106676 0.301577i
\(673\) 15.7599 + 15.7599i 0.607498 + 0.607498i 0.942292 0.334793i \(-0.108667\pi\)
−0.334793 + 0.942292i \(0.608667\pi\)
\(674\) −1.60201 −0.0617073
\(675\) −22.3015 + 13.3283i −0.858385 + 0.513007i
\(676\) −11.7370 −0.451424
\(677\) 28.0078 + 28.0078i 1.07643 + 1.07643i 0.996827 + 0.0795985i \(0.0253638\pi\)
0.0795985 + 0.996827i \(0.474636\pi\)
\(678\) −10.9252 + 30.8858i −0.419579 + 1.18616i
\(679\) 84.9352i 3.25951i
\(680\) 2.61210 + 0.0158500i 0.100169 + 0.000607822i
\(681\) −24.5833 + 11.7361i −0.942033 + 0.449728i
\(682\) 6.43105 6.43105i 0.246258 0.246258i
\(683\) −11.0403 + 11.0403i −0.422444 + 0.422444i −0.886045 0.463600i \(-0.846557\pi\)
0.463600 + 0.886045i \(0.346557\pi\)
\(684\) 2.33275 + 1.88634i 0.0891948 + 0.0721261i
\(685\) −1.83459 1.85700i −0.0700963 0.0709521i
\(686\) 42.7137i 1.63082i
\(687\) −26.0882 9.22813i −0.995327 0.352075i
\(688\) 2.68748 + 2.68748i 0.102459 + 0.102459i
\(689\) −23.9591 −0.912769
\(690\) 1.94551 5.39564i 0.0740642 0.205409i
\(691\) −34.6717 −1.31897 −0.659486 0.751717i \(-0.729226\pi\)
−0.659486 + 0.751717i \(0.729226\pi\)
\(692\) 6.57463 + 6.57463i 0.249930 + 0.249930i
\(693\) −1.85240 17.5075i −0.0703669 0.665057i
\(694\) 31.3154i 1.18872i
\(695\) −0.0471409 + 7.76887i −0.00178816 + 0.294690i
\(696\) 6.07674 + 12.7288i 0.230338 + 0.482483i
\(697\) −2.92063 + 2.92063i −0.110627 + 0.110627i
\(698\) 13.9126 13.9126i 0.526600 0.526600i
\(699\) −10.8747 22.7788i −0.411317 0.861575i
\(700\) 16.7203 + 17.1311i 0.631966 + 0.647494i
\(701\) 2.11730i 0.0799692i 0.999200 + 0.0399846i \(0.0127309\pi\)
−0.999200 + 0.0399846i \(0.987269\pi\)
\(702\) 13.5263 + 22.0214i 0.510516 + 0.831143i
\(703\) −5.83375 5.83375i −0.220024 0.220024i
\(704\) 1.22574 0.0461969
\(705\) −33.9484 + 15.9548i −1.27857 + 0.600893i
\(706\) 35.2206 1.32554
\(707\) 4.06073 + 4.06073i 0.152719 + 0.152719i
\(708\) −16.1969 5.72929i −0.608715 0.215320i
\(709\) 14.5305i 0.545705i 0.962056 + 0.272852i \(0.0879670\pi\)
−0.962056 + 0.272852i \(0.912033\pi\)
\(710\) 13.2957 13.1353i 0.498979 0.492960i
\(711\) −12.7339 + 15.7474i −0.477558 + 0.590572i
\(712\) −0.271862 + 0.271862i −0.0101885 + 0.0101885i
\(713\) −7.77001 + 7.77001i −0.290989 + 0.290989i
\(714\) −8.74204 + 4.17346i −0.327163 + 0.156188i
\(715\) −9.69755 + 9.58057i −0.362668 + 0.358293i
\(716\) 11.2885i 0.421870i
\(717\) 9.30204 26.2971i 0.347391 0.982085i
\(718\) −14.8000 14.8000i −0.552331 0.552331i
\(719\) −2.51322 −0.0937272 −0.0468636 0.998901i \(-0.514923\pi\)
−0.0468636 + 0.998901i \(0.514923\pi\)
\(720\) 5.19049 + 4.24956i 0.193438 + 0.158372i
\(721\) 89.1782 3.32117
\(722\) 0.707107 + 0.707107i 0.0263158 + 0.0263158i
\(723\) −11.5055 + 32.5264i −0.427894 + 1.20967i
\(724\) 9.96083i 0.370191i
\(725\) −40.7144 0.494122i −1.51209 0.0183512i
\(726\) −14.8453 + 7.08717i −0.550961 + 0.263029i
\(727\) −7.64794 + 7.64794i −0.283646 + 0.283646i −0.834561 0.550915i \(-0.814279\pi\)
0.550915 + 0.834561i \(0.314279\pi\)
\(728\) 16.8377 16.8377i 0.624045 0.624045i
\(729\) 12.2076 24.0826i 0.452135 0.891950i
\(730\) −0.0766361 + 12.6297i −0.00283643 + 0.467446i
\(731\) 4.43990i 0.164215i
\(732\) −17.2144 6.08920i −0.636261 0.225063i
\(733\) 24.3729 + 24.3729i 0.900235 + 0.900235i 0.995456 0.0952214i \(-0.0303559\pi\)
−0.0952214 + 0.995456i \(0.530356\pi\)
\(734\) −37.2954 −1.37660
\(735\) −58.0086 20.9161i −2.13968 0.771504i
\(736\) −1.48094 −0.0545883
\(737\) 7.35823 + 7.35823i 0.271044 + 0.271044i
\(738\) −10.5483 + 1.11607i −0.388288 + 0.0410831i
\(739\) 30.8274i 1.13401i 0.823716 + 0.567003i \(0.191897\pi\)
−0.823716 + 0.567003i \(0.808103\pi\)
\(740\) −12.9653 13.1236i −0.476613 0.482432i
\(741\) 3.71137 + 7.77411i 0.136341 + 0.285589i
\(742\) 16.3081 16.3081i 0.598691 0.598691i
\(743\) −23.0214 + 23.0214i −0.844574 + 0.844574i −0.989450 0.144876i \(-0.953722\pi\)
0.144876 + 0.989450i \(0.453722\pi\)
\(744\) −5.53680 11.5978i −0.202989 0.425195i
\(745\) −2.47297 0.0150058i −0.0906026 0.000549770i
\(746\) 9.42209i 0.344967i
\(747\) −3.02842 + 0.320425i −0.110804 + 0.0117237i
\(748\) −1.01250 1.01250i −0.0370208 0.0370208i
\(749\) 67.5986 2.47000
\(750\) −17.6246 + 8.02339i −0.643558 + 0.292973i
\(751\) 43.6630 1.59329 0.796643 0.604450i \(-0.206607\pi\)
0.796643 + 0.604450i \(0.206607\pi\)
\(752\) 6.84848 + 6.84848i 0.249738 + 0.249738i
\(753\) −29.2286 10.3390i −1.06515 0.376773i
\(754\) 40.5027i 1.47502i
\(755\) 7.34980 + 0.0445981i 0.267486 + 0.00162309i
\(756\) −24.1961 5.78233i −0.880002 0.210301i
\(757\) −8.25576 + 8.25576i −0.300061 + 0.300061i −0.841038 0.540977i \(-0.818055\pi\)
0.540977 + 0.841038i \(0.318055\pi\)
\(758\) −0.145573 + 0.145573i −0.00528745 + 0.00528745i
\(759\) −2.83736 + 1.35456i −0.102990 + 0.0491674i
\(760\) 1.57152 + 1.59070i 0.0570049 + 0.0577009i
\(761\) 45.4398i 1.64719i −0.567176 0.823596i \(-0.691964\pi\)
0.567176 0.823596i \(-0.308036\pi\)
\(762\) 5.28038 14.9278i 0.191288 0.540777i
\(763\) −30.3125 30.3125i −1.09739 1.09739i
\(764\) 10.1454 0.367048
\(765\) −0.777238 7.79781i −0.0281011 0.281930i
\(766\) −11.6945 −0.422539
\(767\) −34.8842 34.8842i −1.25960 1.25960i
\(768\) 0.577604 1.63290i 0.0208425 0.0589223i
\(769\) 14.3253i 0.516582i 0.966067 + 0.258291i \(0.0831593\pi\)
−0.966067 + 0.258291i \(0.916841\pi\)
\(770\) 0.0796231 13.1220i 0.00286942 0.472882i
\(771\) 32.1549 15.3508i 1.15803 0.552845i
\(772\) −1.33016 + 1.33016i −0.0478734 + 0.0478734i
\(773\) −30.7793 + 30.7793i −1.10706 + 1.10706i −0.113520 + 0.993536i \(0.536212\pi\)
−0.993536 + 0.113520i \(0.963788\pi\)
\(774\) 7.16936 8.86600i 0.257697 0.318682i
\(775\) 37.0968 + 0.450218i 1.33256 + 0.0161723i
\(776\) 17.7405i 0.636846i
\(777\) 64.4980 + 22.8148i 2.31385 + 0.818475i
\(778\) −17.9604 17.9604i −0.643912 0.643912i
\(779\) −3.53572 −0.126680
\(780\) 8.19325 + 17.4335i 0.293365 + 0.624219i
\(781\) −10.2452 −0.366603
\(782\) 1.22331 + 1.22331i 0.0437455 + 0.0437455i
\(783\) 36.0562 22.1469i 1.28854 0.791467i
\(784\) 15.9216i 0.568630i
\(785\) −27.0253 + 26.6993i −0.964573 + 0.952938i
\(786\) 3.46788 + 7.26408i 0.123695 + 0.259101i
\(787\) −4.68011 + 4.68011i −0.166828 + 0.166828i −0.785583 0.618756i \(-0.787637\pi\)
0.618756 + 0.785583i \(0.287637\pi\)
\(788\) −3.67465 + 3.67465i −0.130904 + 0.130904i
\(789\) 6.39168 + 13.3885i 0.227550 + 0.476642i
\(790\) −10.7382 + 10.6086i −0.382046 + 0.377438i
\(791\) 90.5568i 3.21983i
\(792\) −0.386912 3.65681i −0.0137483 0.129939i
\(793\) −37.0757 37.0757i −1.31660 1.31660i
\(794\) −20.4067 −0.724206
\(795\) 7.93558 + 16.8852i 0.281446 + 0.598857i
\(796\) −0.894086 −0.0316900
\(797\) −0.135863 0.135863i −0.00481251 0.00481251i 0.704696 0.709509i \(-0.251083\pi\)
−0.709509 + 0.704696i \(0.751083\pi\)
\(798\) −7.81778 2.76537i −0.276746 0.0978930i
\(799\) 11.3142i 0.400266i
\(800\) 3.49237 + 3.57818i 0.123474 + 0.126508i
\(801\) 0.896874 + 0.725245i 0.0316895 + 0.0256253i
\(802\) −5.67851 + 5.67851i −0.200515 + 0.200515i
\(803\) 4.89552 4.89552i 0.172759 0.172759i
\(804\) 13.2699 6.33506i 0.467992 0.223420i
\(805\) −0.0962009 + 15.8540i −0.00339064 + 0.558780i
\(806\) 36.9039i 1.29988i
\(807\) 5.49490 15.5342i 0.193430 0.546831i
\(808\) 0.848167 + 0.848167i 0.0298384 + 0.0298384i
\(809\) −19.5668 −0.687933 −0.343967 0.938982i \(-0.611771\pi\)
−0.343967 + 0.938982i \(0.611771\pi\)
\(810\) 11.0395 16.8264i 0.387889 0.591221i
\(811\) 19.4917 0.684447 0.342223 0.939619i \(-0.388820\pi\)
0.342223 + 0.939619i \(0.388820\pi\)
\(812\) −27.5688 27.5688i −0.967475 0.967475i
\(813\) 0.234220 0.662146i 0.00821444 0.0232225i
\(814\) 10.1126i 0.354445i
\(815\) 8.50206 + 8.60587i 0.297814 + 0.301451i
\(816\) −1.82595 + 0.871713i −0.0639212 + 0.0305161i
\(817\) 2.68748 2.68748i 0.0940229 0.0940229i
\(818\) 9.80426 9.80426i 0.342798 0.342798i
\(819\) −55.5475 44.9177i −1.94099 1.56955i
\(820\) −7.90597 0.0479729i −0.276088 0.00167529i
\(821\) 1.40866i 0.0491626i 0.999698 + 0.0245813i \(0.00782525\pi\)
−0.999698 + 0.0245813i \(0.992175\pi\)
\(822\) 1.90626 + 0.674298i 0.0664884 + 0.0235188i
\(823\) −33.6212 33.6212i −1.17196 1.17196i −0.981741 0.190220i \(-0.939080\pi\)
−0.190220 0.981741i \(-0.560920\pi\)
\(824\) 18.6267 0.648892
\(825\) 9.96389 + 3.66115i 0.346898 + 0.127465i
\(826\) 47.4890 1.65235
\(827\) −27.8950 27.8950i −0.970006 0.970006i 0.0295575 0.999563i \(-0.490590\pi\)
−0.999563 + 0.0295575i \(0.990590\pi\)
\(828\) 0.467469 + 4.41817i 0.0162457 + 0.153542i
\(829\) 17.3145i 0.601357i −0.953725 0.300679i \(-0.902787\pi\)
0.953725 0.300679i \(-0.0972132\pi\)
\(830\) −2.26981 0.0137731i −0.0787863 0.000478070i
\(831\) −3.33075 6.97684i −0.115542 0.242024i
\(832\) 3.51689 3.51689i 0.121926 0.121926i
\(833\) 13.1518 13.1518i 0.455683 0.455683i
\(834\) −2.59263 5.43072i −0.0897756 0.188051i
\(835\) 31.3490 + 31.7318i 1.08488 + 1.09812i
\(836\) 1.22574i 0.0423931i
\(837\) −32.8525 + 20.1791i −1.13555 + 0.697492i
\(838\) 12.5350 + 12.5350i 0.433014 + 0.433014i
\(839\) 24.7985 0.856141 0.428070 0.903745i \(-0.359194\pi\)
0.428070 + 0.903745i \(0.359194\pi\)
\(840\) −17.4432 6.28951i −0.601849 0.217009i
\(841\) 37.3162 1.28677
\(842\) −1.87573 1.87573i −0.0646420 0.0646420i
\(843\) −19.4680 6.88639i −0.670514 0.237180i
\(844\) 0.656325i 0.0225916i
\(845\) −0.159249 + 26.2443i −0.00547832 + 0.902832i
\(846\) 18.2696 22.5932i 0.628123 0.776769i
\(847\) 32.1529 32.1529i 1.10479 1.10479i
\(848\) 3.40629 3.40629i 0.116972 0.116972i
\(849\) 24.6219 11.7545i 0.845023 0.403415i
\(850\) 0.0708823 5.84051i 0.00243124 0.200328i
\(851\) 12.2180i 0.418829i
\(852\) −4.82784 + 13.6484i −0.165399 + 0.467588i
\(853\) 26.5568 + 26.5568i 0.909288 + 0.909288i 0.996215 0.0869270i \(-0.0277047\pi\)
−0.0869270 + 0.996215i \(0.527705\pi\)
\(854\) 50.4723 1.72713
\(855\) 4.24956 5.19049i 0.145332 0.177511i
\(856\) 14.1194 0.482590
\(857\) −29.8963 29.8963i −1.02124 1.02124i −0.999769 0.0214701i \(-0.993165\pi\)
−0.0214701 0.999769i \(-0.506835\pi\)
\(858\) 3.52130 9.95481i 0.120215 0.339852i
\(859\) 54.0727i 1.84494i −0.386074 0.922468i \(-0.626169\pi\)
0.386074 0.922468i \(-0.373831\pi\)
\(860\) 6.04574 5.97281i 0.206158 0.203671i
\(861\) 26.4593 12.6317i 0.901730 0.430487i
\(862\) −12.0270 + 12.0270i −0.409640 + 0.409640i
\(863\) 35.2140 35.2140i 1.19870 1.19870i 0.224142 0.974557i \(-0.428042\pi\)
0.974557 0.224142i \(-0.0719579\pi\)
\(864\) −5.05384 1.20776i −0.171935 0.0410888i
\(865\) 14.7902 14.6118i 0.502884 0.496817i
\(866\) 19.6197i 0.666705i
\(867\) −25.5310 9.03103i −0.867078 0.306710i
\(868\) 25.1192 + 25.1192i 0.852601 + 0.852601i
\(869\) 8.27445 0.280691
\(870\) 28.5443 13.4150i 0.967744 0.454813i
\(871\) 42.2244 1.43072
\(872\) −6.33139 6.33139i −0.214408 0.214408i
\(873\) 52.9260 5.59988i 1.79127 0.189527i
\(874\) 1.48094i 0.0500937i
\(875\) 38.5324 37.1545i 1.30263 1.25605i
\(876\) −4.21479 8.82861i −0.142405 0.298291i
\(877\) 6.50626 6.50626i 0.219701 0.219701i −0.588671 0.808372i \(-0.700349\pi\)
0.808372 + 0.588671i \(0.200349\pi\)
\(878\) −5.26269 + 5.26269i −0.177607 + 0.177607i
\(879\) 3.51382 + 7.36030i 0.118518 + 0.248257i
\(880\) 0.0166309 2.74079i 0.000560628 0.0923920i
\(881\) 40.0528i 1.34941i 0.738087 + 0.674706i \(0.235730\pi\)
−0.738087 + 0.674706i \(0.764270\pi\)
\(882\) 47.4998 5.02576i 1.59940 0.169226i
\(883\) −14.6050 14.6050i −0.491496 0.491496i 0.417281 0.908777i \(-0.362983\pi\)
−0.908777 + 0.417281i \(0.862983\pi\)
\(884\) −5.81014 −0.195416
\(885\) −13.0306 + 36.1389i −0.438019 + 1.21480i
\(886\) −19.8119 −0.665593
\(887\) 38.9555 + 38.9555i 1.30800 + 1.30800i 0.922857 + 0.385142i \(0.125847\pi\)
0.385142 + 0.922857i \(0.374153\pi\)
\(888\) 13.4717 + 4.76533i 0.452082 + 0.159914i
\(889\) 43.7681i 1.46794i
\(890\) 0.604203 + 0.611580i 0.0202529 + 0.0205002i
\(891\) −10.7874 + 2.30859i −0.361392 + 0.0773406i
\(892\) 5.81309 5.81309i 0.194637 0.194637i
\(893\) 6.84848 6.84848i 0.229176 0.229176i
\(894\) 1.72870 0.825282i 0.0578162 0.0276016i
\(895\) −25.2413 0.153163i −0.843725 0.00511967i
\(896\) 4.78765i 0.159944i
\(897\) −4.25444 + 12.0274i −0.142052 + 0.401584i
\(898\) 12.0743 + 12.0743i 0.402926 + 0.402926i
\(899\) −60.4238 −2.01525
\(900\) 9.57256 11.5484i 0.319085 0.384947i
\(901\) −5.62742 −0.187477
\(902\) 3.06452 + 3.06452i 0.102037 + 0.102037i
\(903\) −10.5102 + 29.7128i −0.349759 + 0.988779i
\(904\) 18.9147i 0.629092i
\(905\) −22.2727 0.135149i −0.740369 0.00449251i
\(906\) −5.13778 + 2.45278i −0.170691 + 0.0814882i
\(907\) 1.61743 1.61743i 0.0537059 0.0537059i −0.679744 0.733450i \(-0.737909\pi\)
0.733450 + 0.679744i \(0.237909\pi\)
\(908\) 11.1211 11.1211i 0.369067 0.369067i
\(909\) 2.26265 2.79811i 0.0750473 0.0928073i
\(910\) −37.4210 37.8779i −1.24049 1.25564i
\(911\) 28.2902i 0.937298i −0.883385 0.468649i \(-0.844741\pi\)
0.883385 0.468649i \(-0.155259\pi\)
\(912\) −1.63290 0.577604i −0.0540708 0.0191264i
\(913\) 0.879825 + 0.879825i 0.0291180 + 0.0291180i
\(914\) 6.47066 0.214030
\(915\) −13.8492 + 38.4092i −0.457840 + 1.26977i
\(916\) 15.9766 0.527881
\(917\) −15.7330 15.7330i −0.519550 0.519550i
\(918\) 3.17700 + 5.17229i 0.104857 + 0.170711i
\(919\) 32.0879i 1.05848i 0.848472 + 0.529241i \(0.177523\pi\)
−0.848472 + 0.529241i \(0.822477\pi\)
\(920\) −0.0200935 + 3.31143i −0.000662464 + 0.109175i
\(921\) 1.78362 + 3.73609i 0.0587722 + 0.123109i
\(922\) −0.0849881 + 0.0849881i −0.00279893 + 0.00279893i
\(923\) −29.3955 + 29.3955i −0.967566 + 0.967566i
\(924\) 4.37907 + 9.17273i 0.144061 + 0.301761i
\(925\) −29.5206 + 28.8126i −0.970631 + 0.947354i
\(926\) 8.23304i 0.270555i
\(927\) −5.87963 55.5699i −0.193112 1.82516i
\(928\) −5.75831 5.75831i −0.189026 0.189026i
\(929\) 46.3379 1.52030 0.760149 0.649749i \(-0.225126\pi\)
0.760149 + 0.649749i \(0.225126\pi\)
\(930\) −26.0081 + 12.2231i −0.852838 + 0.400810i
\(931\) 15.9216 0.521811
\(932\) 10.3048 + 10.3048i 0.337545 + 0.337545i
\(933\) −23.4056 8.27921i −0.766264 0.271049i
\(934\) 1.79181i 0.0586298i
\(935\) −2.27772 + 2.25025i −0.0744895 + 0.0735910i
\(936\) −11.6022 9.38198i −0.379231 0.306660i
\(937\) −35.8203 + 35.8203i −1.17020 + 1.17020i −0.188037 + 0.982162i \(0.560212\pi\)
−0.982162 + 0.188037i \(0.939788\pi\)
\(938\) −28.7407 + 28.7407i −0.938418 + 0.938418i
\(939\) 3.45754 1.65063i 0.112832 0.0538664i
\(940\) 15.4063 15.2205i 0.502498 0.496437i
\(941\) 36.8148i 1.20013i 0.799951 + 0.600065i \(0.204859\pi\)
−0.799951 + 0.600065i \(0.795141\pi\)
\(942\) 9.81321 27.7422i 0.319732 0.903891i
\(943\) −3.70256 3.70256i −0.120572 0.120572i
\(944\) 9.91906 0.322838
\(945\) −13.2577 + 54.0246i −0.431274 + 1.75742i
\(946\) −4.65863 −0.151465
\(947\) −14.0227 14.0227i −0.455676 0.455676i 0.441557 0.897233i \(-0.354426\pi\)
−0.897233 + 0.441557i \(0.854426\pi\)
\(948\) 3.89915 11.0230i 0.126639 0.358011i
\(949\) 28.0924i 0.911919i
\(950\) 3.57818 3.49237i 0.116091 0.113307i
\(951\) −47.7442 + 22.7931i −1.54821 + 0.739118i
\(952\) 3.95477 3.95477i 0.128175 0.128175i
\(953\) −2.01500 + 2.01500i −0.0652723 + 0.0652723i −0.738989 0.673717i \(-0.764697\pi\)
0.673717 + 0.738989i \(0.264697\pi\)
\(954\) −11.2374 9.08693i −0.363823 0.294200i
\(955\) 0.137653 22.6854i 0.00445436 0.734082i
\(956\) 16.1045i 0.520858i
\(957\) −16.2993 5.76552i −0.526882 0.186373i
\(958\) −3.37189 3.37189i −0.108941 0.108941i
\(959\) −5.58913 −0.180482
\(960\) −3.64338 1.31369i −0.117590 0.0423993i
\(961\) 24.0549 0.775965
\(962\) 29.0149 + 29.0149i 0.935479 + 0.935479i
\(963\) −4.45685 42.1229i −0.143620 1.35739i
\(964\) 19.9193i 0.641559i
\(965\) 2.95622 + 2.99231i 0.0951640 + 0.0963260i
\(966\) −5.29081 11.0825i −0.170229 0.356574i
\(967\) 3.86264 3.86264i 0.124214 0.124214i −0.642267 0.766481i \(-0.722006\pi\)
0.766481 + 0.642267i \(0.222006\pi\)
\(968\) 6.71579 6.71579i 0.215854 0.215854i
\(969\) 0.871713 + 1.82595i 0.0280035 + 0.0586581i
\(970\) 39.6682 + 0.240704i 1.27367 + 0.00772853i
\(971\) 4.62291i 0.148356i 0.997245 + 0.0741781i \(0.0236333\pi\)
−0.997245 + 0.0741781i \(0.976367\pi\)
\(972\) −2.00789 + 15.4586i −0.0644030 + 0.495835i
\(973\) 11.7622 + 11.7622i 0.377079 + 0.377079i
\(974\) −26.4143 −0.846368
\(975\) 39.0929 18.0838i 1.25197 0.579145i
\(976\) 10.5422 0.337447
\(977\) −40.0087 40.0087i −1.27999 1.27999i −0.940670 0.339323i \(-0.889802\pi\)
−0.339323 0.940670i \(-0.610198\pi\)
\(978\) −8.83418 3.12490i −0.282486 0.0999232i
\(979\) 0.471262i 0.0150616i
\(980\) 35.6012 + 0.216026i 1.13724 + 0.00690069i
\(981\) −16.8902 + 20.8873i −0.539262 + 0.666879i
\(982\) 30.3912 30.3912i 0.969822 0.969822i
\(983\) 12.9031 12.9031i 0.411545 0.411545i −0.470731 0.882277i \(-0.656010\pi\)
0.882277 + 0.470731i \(0.156010\pi\)
\(984\) 5.52656 2.63839i 0.176180 0.0841088i
\(985\) 8.16675 + 8.26647i 0.260214 + 0.263392i
\(986\) 9.51312i 0.302959i
\(987\) −26.7832 + 75.7168i −0.852518 + 2.41009i
\(988\) −3.51689 3.51689i −0.111887 0.111887i
\(989\) 5.62858 0.178978
\(990\) −8.18198 + 0.815530i −0.260040 + 0.0259192i
\(991\) 16.7867 0.533248 0.266624 0.963801i \(-0.414092\pi\)
0.266624 + 0.963801i \(0.414092\pi\)
\(992\) 5.24666 + 5.24666i 0.166582 + 0.166582i
\(993\) −3.68006 + 10.4036i −0.116783 + 0.330150i
\(994\) 40.0171i 1.26926i
\(995\) −0.0121310 + 1.99920i −0.000384579 + 0.0633789i
\(996\) 1.58668 0.757484i 0.0502759 0.0240018i
\(997\) 10.3397 10.3397i 0.327460 0.327460i −0.524160 0.851620i \(-0.675620\pi\)
0.851620 + 0.524160i \(0.175620\pi\)
\(998\) −14.7400 + 14.7400i −0.466587 + 0.466587i
\(999\) 9.96421 41.6951i 0.315254 1.31917i
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 570.2.k.b.533.6 yes 36
3.2 odd 2 inner 570.2.k.b.533.11 yes 36
5.2 odd 4 inner 570.2.k.b.77.11 yes 36
15.2 even 4 inner 570.2.k.b.77.6 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.k.b.77.6 36 15.2 even 4 inner
570.2.k.b.77.11 yes 36 5.2 odd 4 inner
570.2.k.b.533.6 yes 36 1.1 even 1 trivial
570.2.k.b.533.11 yes 36 3.2 odd 2 inner