Properties

Label 105.4.u.a.52.4
Level $105$
Weight $4$
Character 105.52
Analytic conductor $6.195$
Analytic rank $0$
Dimension $96$
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] = [105,4,Mod(52,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.52");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.u (of order \(12\), degree \(4\), 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: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 52.4
Character \(\chi\) \(=\) 105.52
Dual form 105.4.u.a.103.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.17018 + 4.36716i) q^{2} +(2.89778 - 0.776457i) q^{3} +(-10.7746 - 6.22070i) q^{4} +(-6.73223 - 8.92620i) q^{5} +13.5637i q^{6} +(-1.57380 - 18.4533i) q^{7} +(14.1991 - 14.1991i) q^{8} +(7.79423 - 4.50000i) q^{9} +O(q^{10})\) \(q+(-1.17018 + 4.36716i) q^{2} +(2.89778 - 0.776457i) q^{3} +(-10.7746 - 6.22070i) q^{4} +(-6.73223 - 8.92620i) q^{5} +13.5637i q^{6} +(-1.57380 - 18.4533i) q^{7} +(14.1991 - 14.1991i) q^{8} +(7.79423 - 4.50000i) q^{9} +(46.8601 - 18.9555i) q^{10} +(19.3043 - 33.4361i) q^{11} +(-36.0524 - 9.66022i) q^{12} +(-34.4805 - 34.4805i) q^{13} +(82.4300 + 14.7206i) q^{14} +(-26.4393 - 20.6389i) q^{15} +(-4.37136 - 7.57141i) q^{16} +(20.7911 + 77.5933i) q^{17} +(10.5316 + 39.3044i) q^{18} +(-41.7160 - 72.2543i) q^{19} +(17.0097 + 138.055i) q^{20} +(-18.8887 - 52.2515i) q^{21} +(123.431 + 123.431i) q^{22} +(50.8102 + 13.6146i) q^{23} +(30.1208 - 52.1708i) q^{24} +(-34.3541 + 120.186i) q^{25} +(190.930 - 110.234i) q^{26} +(19.0919 - 19.0919i) q^{27} +(-97.8353 + 208.616i) q^{28} +83.4317i q^{29} +(121.072 - 91.3136i) q^{30} +(-81.2237 - 46.8945i) q^{31} +(193.351 - 51.8083i) q^{32} +(29.9780 - 111.879i) q^{33} -363.192 q^{34} +(-154.122 + 138.280i) q^{35} -111.973 q^{36} +(42.2257 - 157.588i) q^{37} +(364.361 - 97.6303i) q^{38} +(-126.690 - 73.1443i) q^{39} +(-222.336 - 31.1524i) q^{40} -412.940i q^{41} +(250.294 - 21.3465i) q^{42} +(31.4152 - 31.4152i) q^{43} +(-415.992 + 240.173i) q^{44} +(-92.6405 - 39.2778i) q^{45} +(-118.914 + 205.965i) q^{46} +(-406.470 - 108.913i) q^{47} +(-18.5461 - 18.5461i) q^{48} +(-338.046 + 58.0835i) q^{49} +(-484.673 - 290.669i) q^{50} +(120.496 + 208.705i) q^{51} +(157.020 + 586.006i) q^{52} +(146.952 + 548.432i) q^{53} +(61.0364 + 105.718i) q^{54} +(-428.419 + 52.7851i) q^{55} +(-284.366 - 239.673i) q^{56} +(-176.986 - 176.986i) q^{57} +(-364.360 - 97.6299i) q^{58} +(280.188 - 485.300i) q^{59} +(156.484 + 386.846i) q^{60} +(204.399 - 118.010i) q^{61} +(299.842 - 299.842i) q^{62} +(-95.3063 - 136.747i) q^{63} +835.080i q^{64} +(-75.6493 + 539.911i) q^{65} +(453.515 + 261.837i) q^{66} +(956.795 - 256.372i) q^{67} +(258.670 - 965.369i) q^{68} +157.808 q^{69} +(-423.539 - 834.889i) q^{70} -738.029 q^{71} +(46.7751 - 174.567i) q^{72} +(608.633 - 163.083i) q^{73} +(638.802 + 368.812i) q^{74} +(-6.23097 + 374.948i) q^{75} +1038.01i q^{76} +(-647.386 - 303.606i) q^{77} +(467.682 - 467.682i) q^{78} +(-153.129 + 88.4091i) q^{79} +(-38.1550 + 89.9921i) q^{80} +(40.5000 - 70.1481i) q^{81} +(1803.38 + 483.213i) q^{82} +(712.405 + 712.405i) q^{83} +(-121.523 + 680.488i) q^{84} +(552.643 - 707.961i) q^{85} +(100.434 + 173.957i) q^{86} +(64.7812 + 241.767i) q^{87} +(-200.658 - 748.866i) q^{88} +(489.207 + 847.331i) q^{89} +(279.938 - 358.614i) q^{90} +(-582.013 + 690.544i) q^{91} +(-462.766 - 462.766i) q^{92} +(-271.780 - 72.8231i) q^{93} +(951.283 - 1647.67i) q^{94} +(-364.114 + 858.798i) q^{95} +(520.062 - 300.258i) q^{96} +(-1266.78 + 1266.78i) q^{97} +(141.914 - 1544.27i) q^{98} -347.478i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 48 q^{5} - 4 q^{7} + 168 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 48 q^{5} - 4 q^{7} + 168 q^{8} - 72 q^{10} + 56 q^{11} - 168 q^{15} + 880 q^{16} + 96 q^{21} + 624 q^{22} - 64 q^{23} + 152 q^{25} + 912 q^{26} + 628 q^{28} + 48 q^{30} - 528 q^{31} - 672 q^{32} - 108 q^{33} - 1616 q^{35} - 3456 q^{36} - 552 q^{37} - 4044 q^{38} + 2052 q^{40} - 1068 q^{42} + 720 q^{43} + 2560 q^{46} + 240 q^{47} - 3528 q^{50} + 336 q^{51} + 4644 q^{52} + 1728 q^{53} + 4896 q^{56} + 1392 q^{57} + 512 q^{58} + 420 q^{60} - 2592 q^{61} - 288 q^{63} - 824 q^{65} - 4104 q^{66} - 3784 q^{67} - 8844 q^{68} - 2256 q^{70} - 128 q^{71} - 756 q^{72} - 3312 q^{73} - 1872 q^{75} - 6600 q^{77} - 1200 q^{78} + 12108 q^{80} + 3888 q^{81} + 6084 q^{82} + 4768 q^{85} - 1088 q^{86} + 5652 q^{87} + 4844 q^{88} + 10128 q^{91} - 2152 q^{92} + 1368 q^{93} - 7872 q^{95} + 20184 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17018 + 4.36716i −0.413720 + 1.54402i 0.373666 + 0.927564i \(0.378101\pi\)
−0.787386 + 0.616461i \(0.788566\pi\)
\(3\) 2.89778 0.776457i 0.557678 0.149429i
\(4\) −10.7746 6.22070i −1.34682 0.777588i
\(5\) −6.73223 8.92620i −0.602149 0.798384i
\(6\) 13.5637i 0.922890i
\(7\) −1.57380 18.4533i −0.0849771 0.996383i
\(8\) 14.1991 14.1991i 0.627517 0.627517i
\(9\) 7.79423 4.50000i 0.288675 0.166667i
\(10\) 46.8601 18.9555i 1.48184 0.599425i
\(11\) 19.3043 33.4361i 0.529134 0.916487i −0.470288 0.882513i \(-0.655850\pi\)
0.999423 0.0339746i \(-0.0108165\pi\)
\(12\) −36.0524 9.66022i −0.867286 0.232389i
\(13\) −34.4805 34.4805i −0.735629 0.735629i 0.236100 0.971729i \(-0.424131\pi\)
−0.971729 + 0.236100i \(0.924131\pi\)
\(14\) 82.4300 + 14.7206i 1.57360 + 0.281017i
\(15\) −26.4393 20.6389i −0.455107 0.355262i
\(16\) −4.37136 7.57141i −0.0683024 0.118303i
\(17\) 20.7911 + 77.5933i 0.296622 + 1.10701i 0.939921 + 0.341393i \(0.110899\pi\)
−0.643299 + 0.765615i \(0.722435\pi\)
\(18\) 10.5316 + 39.3044i 0.137907 + 0.514675i
\(19\) −41.7160 72.2543i −0.503701 0.872435i −0.999991 0.00427834i \(-0.998638\pi\)
0.496290 0.868157i \(-0.334695\pi\)
\(20\) 17.0097 + 138.055i 0.190174 + 1.54350i
\(21\) −18.8887 52.2515i −0.196279 0.542962i
\(22\) 123.431 + 123.431i 1.19617 + 1.19617i
\(23\) 50.8102 + 13.6146i 0.460638 + 0.123427i 0.481673 0.876351i \(-0.340029\pi\)
−0.0210349 + 0.999779i \(0.506696\pi\)
\(24\) 30.1208 52.1708i 0.256183 0.443722i
\(25\) −34.3541 + 120.186i −0.274833 + 0.961492i
\(26\) 190.930 110.234i 1.44017 0.831485i
\(27\) 19.0919 19.0919i 0.136083 0.136083i
\(28\) −97.8353 + 208.616i −0.660326 + 1.40803i
\(29\) 83.4317i 0.534237i 0.963664 + 0.267119i \(0.0860716\pi\)
−0.963664 + 0.267119i \(0.913928\pi\)
\(30\) 121.072 91.3136i 0.736820 0.555717i
\(31\) −81.2237 46.8945i −0.470587 0.271694i 0.245898 0.969296i \(-0.420917\pi\)
−0.716485 + 0.697602i \(0.754250\pi\)
\(32\) 193.351 51.8083i 1.06813 0.286203i
\(33\) 29.9780 111.879i 0.158136 0.590173i
\(34\) −363.192 −1.83197
\(35\) −154.122 + 138.280i −0.744327 + 0.667815i
\(36\) −111.973 −0.518392
\(37\) 42.2257 157.588i 0.187618 0.700199i −0.806437 0.591320i \(-0.798607\pi\)
0.994055 0.108879i \(-0.0347262\pi\)
\(38\) 364.361 97.6303i 1.55545 0.416782i
\(39\) −126.690 73.1443i −0.520168 0.300319i
\(40\) −222.336 31.1524i −0.878858 0.123141i
\(41\) 412.940i 1.57294i −0.617630 0.786469i \(-0.711907\pi\)
0.617630 0.786469i \(-0.288093\pi\)
\(42\) 250.294 21.3465i 0.919551 0.0784245i
\(43\) 31.4152 31.4152i 0.111413 0.111413i −0.649202 0.760616i \(-0.724897\pi\)
0.760616 + 0.649202i \(0.224897\pi\)
\(44\) −415.992 + 240.173i −1.42530 + 0.822897i
\(45\) −92.6405 39.2778i −0.306889 0.130115i
\(46\) −118.914 + 205.965i −0.381150 + 0.660171i
\(47\) −406.470 108.913i −1.26148 0.338013i −0.434721 0.900565i \(-0.643153\pi\)
−0.826762 + 0.562552i \(0.809820\pi\)
\(48\) −18.5461 18.5461i −0.0557687 0.0557687i
\(49\) −338.046 + 58.0835i −0.985558 + 0.169340i
\(50\) −484.673 290.669i −1.37086 0.822137i
\(51\) 120.496 + 208.705i 0.330839 + 0.573030i
\(52\) 157.020 + 586.006i 0.418745 + 1.56278i
\(53\) 146.952 + 548.432i 0.380856 + 1.42137i 0.844596 + 0.535404i \(0.179840\pi\)
−0.463740 + 0.885971i \(0.653493\pi\)
\(54\) 61.0364 + 105.718i 0.153815 + 0.266415i
\(55\) −428.419 + 52.7851i −1.05033 + 0.129410i
\(56\) −284.366 239.673i −0.678572 0.571923i
\(57\) −176.986 176.986i −0.411270 0.411270i
\(58\) −364.360 97.6299i −0.824876 0.221025i
\(59\) 280.188 485.300i 0.618261 1.07086i −0.371542 0.928416i \(-0.621171\pi\)
0.989803 0.142443i \(-0.0454959\pi\)
\(60\) 156.484 + 386.846i 0.336700 + 0.832360i
\(61\) 204.399 118.010i 0.429025 0.247698i −0.269906 0.962887i \(-0.586993\pi\)
0.698931 + 0.715189i \(0.253659\pi\)
\(62\) 299.842 299.842i 0.614193 0.614193i
\(63\) −95.3063 136.747i −0.190595 0.273468i
\(64\) 835.080i 1.63102i
\(65\) −75.6493 + 539.911i −0.144356 + 1.03027i
\(66\) 453.515 + 261.837i 0.845817 + 0.488332i
\(67\) 956.795 256.372i 1.74464 0.467476i 0.761173 0.648548i \(-0.224624\pi\)
0.983470 + 0.181073i \(0.0579569\pi\)
\(68\) 258.670 965.369i 0.461299 1.72159i
\(69\) 157.808 0.275331
\(70\) −423.539 834.889i −0.723180 1.42555i
\(71\) −738.029 −1.23363 −0.616816 0.787107i \(-0.711578\pi\)
−0.616816 + 0.787107i \(0.711578\pi\)
\(72\) 46.7751 174.567i 0.0765624 0.285735i
\(73\) 608.633 163.083i 0.975824 0.261471i 0.264539 0.964375i \(-0.414780\pi\)
0.711285 + 0.702904i \(0.248114\pi\)
\(74\) 638.802 + 368.812i 1.00350 + 0.579373i
\(75\) −6.23097 + 374.948i −0.00959321 + 0.577271i
\(76\) 1038.01i 1.56669i
\(77\) −647.386 303.606i −0.958137 0.449340i
\(78\) 467.682 467.682i 0.678904 0.678904i
\(79\) −153.129 + 88.4091i −0.218081 + 0.125909i −0.605061 0.796179i \(-0.706851\pi\)
0.386981 + 0.922088i \(0.373518\pi\)
\(80\) −38.1550 + 89.9921i −0.0533232 + 0.125768i
\(81\) 40.5000 70.1481i 0.0555556 0.0962250i
\(82\) 1803.38 + 483.213i 2.42865 + 0.650756i
\(83\) 712.405 + 712.405i 0.942128 + 0.942128i 0.998415 0.0562866i \(-0.0179261\pi\)
−0.0562866 + 0.998415i \(0.517926\pi\)
\(84\) −121.523 + 680.488i −0.157849 + 0.883897i
\(85\) 552.643 707.961i 0.705207 0.903402i
\(86\) 100.434 + 173.957i 0.125931 + 0.218119i
\(87\) 64.7812 + 241.767i 0.0798307 + 0.297932i
\(88\) −200.658 748.866i −0.243071 0.907152i
\(89\) 489.207 + 847.331i 0.582650 + 1.00918i 0.995164 + 0.0982280i \(0.0313174\pi\)
−0.412514 + 0.910951i \(0.635349\pi\)
\(90\) 279.938 358.614i 0.327868 0.420013i
\(91\) −582.013 + 690.544i −0.670457 + 0.795480i
\(92\) −462.766 462.766i −0.524421 0.524421i
\(93\) −271.780 72.8231i −0.303035 0.0811979i
\(94\) 951.283 1647.67i 1.04380 1.80792i
\(95\) −364.114 + 858.798i −0.393235 + 0.927482i
\(96\) 520.062 300.258i 0.552902 0.319218i
\(97\) −1266.78 + 1266.78i −1.32600 + 1.32600i −0.417164 + 0.908831i \(0.636976\pi\)
−0.908831 + 0.417164i \(0.863024\pi\)
\(98\) 141.914 1544.27i 0.146281 1.59178i
\(99\) 347.478i 0.352756i
\(100\) 1117.80 1081.25i 1.11780 1.08125i
\(101\) −332.434 191.931i −0.327509 0.189088i 0.327225 0.944946i \(-0.393886\pi\)
−0.654735 + 0.755859i \(0.727220\pi\)
\(102\) −1052.45 + 282.003i −1.02165 + 0.273749i
\(103\) 154.776 577.631i 0.148063 0.552579i −0.851537 0.524295i \(-0.824329\pi\)
0.999600 0.0282845i \(-0.00900442\pi\)
\(104\) −979.184 −0.923240
\(105\) −339.244 + 520.373i −0.315303 + 0.483650i
\(106\) −2567.05 −2.35221
\(107\) −440.222 + 1642.93i −0.397737 + 1.48437i 0.419331 + 0.907834i \(0.362265\pi\)
−0.817068 + 0.576541i \(0.804402\pi\)
\(108\) −324.472 + 86.9419i −0.289095 + 0.0774629i
\(109\) −650.138 375.357i −0.571302 0.329841i 0.186367 0.982480i \(-0.440329\pi\)
−0.757669 + 0.652639i \(0.773662\pi\)
\(110\) 270.805 1932.74i 0.234729 1.67527i
\(111\) 489.442i 0.418521i
\(112\) −132.838 + 92.5817i −0.112071 + 0.0781085i
\(113\) 924.567 924.567i 0.769698 0.769698i −0.208355 0.978053i \(-0.566811\pi\)
0.978053 + 0.208355i \(0.0668109\pi\)
\(114\) 980.032 565.822i 0.805161 0.464860i
\(115\) −220.540 545.199i −0.178830 0.442087i
\(116\) 519.004 898.941i 0.415416 0.719522i
\(117\) −423.912 113.587i −0.334963 0.0897530i
\(118\) 1791.51 + 1791.51i 1.39765 + 1.39765i
\(119\) 1399.13 505.779i 1.07780 0.389619i
\(120\) −668.467 + 82.3613i −0.508520 + 0.0626544i
\(121\) −79.8148 138.243i −0.0599660 0.103864i
\(122\) 276.184 + 1030.73i 0.204955 + 0.764903i
\(123\) −320.630 1196.61i −0.235043 0.877192i
\(124\) 583.433 + 1010.54i 0.422531 + 0.731846i
\(125\) 1304.09 502.471i 0.933130 0.359539i
\(126\) 708.721 256.200i 0.501094 0.181143i
\(127\) 355.909 + 355.909i 0.248676 + 0.248676i 0.820427 0.571751i \(-0.193736\pi\)
−0.571751 + 0.820427i \(0.693736\pi\)
\(128\) −2100.12 562.724i −1.45020 0.388580i
\(129\) 66.6417 115.427i 0.0454843 0.0787811i
\(130\) −2269.36 962.164i −1.53104 0.649134i
\(131\) −197.652 + 114.114i −0.131824 + 0.0761085i −0.564462 0.825459i \(-0.690916\pi\)
0.432638 + 0.901568i \(0.357583\pi\)
\(132\) −1018.97 + 1018.97i −0.671892 + 0.671892i
\(133\) −1267.67 + 883.511i −0.826476 + 0.576016i
\(134\) 4478.48i 2.88718i
\(135\) −298.949 41.8870i −0.190588 0.0267042i
\(136\) 1396.97 + 806.540i 0.880802 + 0.508531i
\(137\) 846.689 226.870i 0.528011 0.141480i 0.0150415 0.999887i \(-0.495212\pi\)
0.512970 + 0.858407i \(0.328545\pi\)
\(138\) −184.663 + 689.172i −0.113910 + 0.425118i
\(139\) 1381.39 0.842933 0.421467 0.906844i \(-0.361515\pi\)
0.421467 + 0.906844i \(0.361515\pi\)
\(140\) 2520.80 531.155i 1.52176 0.320649i
\(141\) −1262.43 −0.754010
\(142\) 863.624 3223.09i 0.510378 1.90476i
\(143\) −1818.52 + 487.270i −1.06344 + 0.284948i
\(144\) −68.1427 39.3422i −0.0394344 0.0227675i
\(145\) 744.728 561.682i 0.426526 0.321691i
\(146\) 2848.84i 1.61487i
\(147\) −934.484 + 430.791i −0.524319 + 0.241708i
\(148\) −1435.27 + 1435.27i −0.797154 + 0.797154i
\(149\) −1185.88 + 684.668i −0.652021 + 0.376444i −0.789230 0.614098i \(-0.789520\pi\)
0.137209 + 0.990542i \(0.456187\pi\)
\(150\) −1630.17 465.967i −0.887351 0.253641i
\(151\) 1505.27 2607.20i 0.811238 1.40511i −0.100759 0.994911i \(-0.532127\pi\)
0.911998 0.410195i \(-0.134539\pi\)
\(152\) −1618.27 433.615i −0.863549 0.231387i
\(153\) 511.220 + 511.220i 0.270129 + 0.270129i
\(154\) 2083.45 2471.97i 1.09019 1.29349i
\(155\) 128.227 + 1040.72i 0.0664478 + 0.539309i
\(156\) 910.017 + 1576.20i 0.467049 + 0.808953i
\(157\) 193.602 + 722.533i 0.0984149 + 0.367289i 0.997515 0.0704536i \(-0.0224447\pi\)
−0.899100 + 0.437743i \(0.855778\pi\)
\(158\) −206.909 772.194i −0.104182 0.388813i
\(159\) 851.667 + 1475.13i 0.424790 + 0.735758i
\(160\) −1764.14 1377.11i −0.871671 0.680437i
\(161\) 171.268 959.042i 0.0838374 0.469460i
\(162\) 258.956 + 258.956i 0.125589 + 0.125589i
\(163\) 2891.63 + 774.809i 1.38951 + 0.372318i 0.874566 0.484907i \(-0.161147\pi\)
0.514942 + 0.857225i \(0.327813\pi\)
\(164\) −2568.78 + 4449.25i −1.22310 + 2.11847i
\(165\) −1200.48 + 485.608i −0.566406 + 0.229118i
\(166\) −3944.83 + 2277.55i −1.84445 + 1.06489i
\(167\) 187.527 187.527i 0.0868940 0.0868940i −0.662324 0.749218i \(-0.730430\pi\)
0.749218 + 0.662324i \(0.230430\pi\)
\(168\) −1010.13 473.721i −0.463886 0.217550i
\(169\) 180.814i 0.0823005i
\(170\) 2445.09 + 3241.92i 1.10312 + 1.46261i
\(171\) −650.288 375.444i −0.290812 0.167900i
\(172\) −533.910 + 143.061i −0.236687 + 0.0634202i
\(173\) 432.171 1612.89i 0.189927 0.708817i −0.803595 0.595177i \(-0.797082\pi\)
0.993522 0.113641i \(-0.0362512\pi\)
\(174\) −1131.64 −0.493042
\(175\) 2271.90 + 444.797i 0.981369 + 0.192134i
\(176\) −337.545 −0.144565
\(177\) 435.108 1623.85i 0.184773 0.689581i
\(178\) −4272.89 + 1144.92i −1.79925 + 0.482108i
\(179\) 1049.59 + 605.980i 0.438267 + 0.253034i 0.702862 0.711326i \(-0.251905\pi\)
−0.264595 + 0.964360i \(0.585238\pi\)
\(180\) 753.826 + 999.490i 0.312149 + 0.413876i
\(181\) 3068.84i 1.26025i −0.776493 0.630126i \(-0.783003\pi\)
0.776493 0.630126i \(-0.216997\pi\)
\(182\) −2334.66 3349.80i −0.950859 1.36431i
\(183\) 500.672 500.672i 0.202245 0.202245i
\(184\) 914.774 528.145i 0.366511 0.211605i
\(185\) −1690.94 + 684.006i −0.672001 + 0.271833i
\(186\) 636.061 1101.69i 0.250743 0.434300i
\(187\) 2995.77 + 802.715i 1.17151 + 0.313906i
\(188\) 3702.02 + 3702.02i 1.43616 + 1.43616i
\(189\) −382.354 322.261i −0.147154 0.124027i
\(190\) −3324.43 2595.09i −1.26937 0.990883i
\(191\) 188.360 + 326.249i 0.0713574 + 0.123595i 0.899496 0.436928i \(-0.143934\pi\)
−0.828139 + 0.560523i \(0.810600\pi\)
\(192\) 648.404 + 2419.88i 0.243721 + 0.909580i
\(193\) −479.735 1790.39i −0.178923 0.667748i −0.995850 0.0910078i \(-0.970991\pi\)
0.816928 0.576740i \(-0.195675\pi\)
\(194\) −4049.86 7014.56i −1.49878 2.59596i
\(195\) 200.003 + 1623.28i 0.0734488 + 0.596131i
\(196\) 4003.62 + 1477.06i 1.45905 + 0.538287i
\(197\) −1948.20 1948.20i −0.704586 0.704586i 0.260805 0.965391i \(-0.416012\pi\)
−0.965391 + 0.260805i \(0.916012\pi\)
\(198\) 1517.49 + 406.611i 0.544664 + 0.145942i
\(199\) 2581.45 4471.20i 0.919569 1.59274i 0.119497 0.992835i \(-0.461872\pi\)
0.800071 0.599905i \(-0.204795\pi\)
\(200\) 1218.74 + 2194.34i 0.430890 + 0.775815i
\(201\) 2573.52 1485.82i 0.903094 0.521401i
\(202\) 1227.20 1227.20i 0.427453 0.427453i
\(203\) 1539.59 131.305i 0.532305 0.0453980i
\(204\) 2998.27i 1.02902i
\(205\) −3685.99 + 2780.01i −1.25581 + 0.947143i
\(206\) 2341.49 + 1351.86i 0.791939 + 0.457226i
\(207\) 457.292 122.531i 0.153546 0.0411425i
\(208\) −110.340 + 411.793i −0.0367821 + 0.137273i
\(209\) −3221.20 −1.06610
\(210\) −1875.58 2090.46i −0.616320 0.686932i
\(211\) 1316.10 0.429403 0.214702 0.976680i \(-0.431122\pi\)
0.214702 + 0.976680i \(0.431122\pi\)
\(212\) 1828.29 6823.26i 0.592298 2.21049i
\(213\) −2138.64 + 573.048i −0.687969 + 0.184341i
\(214\) −6659.80 3845.04i −2.12736 1.22823i
\(215\) −491.913 68.9240i −0.156038 0.0218631i
\(216\) 542.175i 0.170789i
\(217\) −737.527 + 1572.64i −0.230722 + 0.491973i
\(218\) 2400.02 2400.02i 0.745642 0.745642i
\(219\) 1637.06 945.156i 0.505124 0.291633i
\(220\) 4944.39 + 2096.33i 1.51523 + 0.642429i
\(221\) 1958.57 3392.34i 0.596144 1.03255i
\(222\) 2137.47 + 572.734i 0.646206 + 0.173150i
\(223\) 2362.48 + 2362.48i 0.709431 + 0.709431i 0.966416 0.256984i \(-0.0827289\pi\)
−0.256984 + 0.966416i \(0.582729\pi\)
\(224\) −1260.33 3486.43i −0.375934 1.03994i
\(225\) 273.075 + 1091.35i 0.0809112 + 0.323364i
\(226\) 2955.82 + 5119.64i 0.869993 + 1.50687i
\(227\) −927.009 3459.64i −0.271047 1.01156i −0.958444 0.285280i \(-0.907913\pi\)
0.687397 0.726282i \(-0.258753\pi\)
\(228\) 805.972 + 3007.93i 0.234109 + 0.873705i
\(229\) 721.608 + 1249.86i 0.208232 + 0.360669i 0.951158 0.308705i \(-0.0998957\pi\)
−0.742925 + 0.669374i \(0.766562\pi\)
\(230\) 2639.04 325.154i 0.756579 0.0932175i
\(231\) −2111.72 377.116i −0.601476 0.107413i
\(232\) 1184.65 + 1184.65i 0.335243 + 0.335243i
\(233\) −5460.44 1463.12i −1.53530 0.411383i −0.610557 0.791973i \(-0.709054\pi\)
−0.924744 + 0.380590i \(0.875721\pi\)
\(234\) 992.103 1718.37i 0.277162 0.480058i
\(235\) 1764.27 + 4361.46i 0.489736 + 1.21068i
\(236\) −6037.82 + 3485.94i −1.66537 + 0.961505i
\(237\) −375.088 + 375.088i −0.102804 + 0.102804i
\(238\) 571.590 + 6702.07i 0.155675 + 1.82534i
\(239\) 3858.74i 1.04436i 0.852836 + 0.522178i \(0.174880\pi\)
−0.852836 + 0.522178i \(0.825120\pi\)
\(240\) −40.6896 + 290.403i −0.0109438 + 0.0781059i
\(241\) −1117.34 645.098i −0.298649 0.172425i 0.343187 0.939267i \(-0.388494\pi\)
−0.641836 + 0.766842i \(0.721827\pi\)
\(242\) 697.128 186.795i 0.185178 0.0496183i
\(243\) 62.8930 234.720i 0.0166032 0.0619642i
\(244\) −2936.41 −0.770427
\(245\) 2794.27 + 2626.44i 0.728651 + 0.684886i
\(246\) 5600.98 1.45165
\(247\) −1052.97 + 3929.76i −0.271252 + 1.01233i
\(248\) −1819.16 + 487.443i −0.465794 + 0.124809i
\(249\) 2617.54 + 1511.24i 0.666185 + 0.384622i
\(250\) 668.358 + 6283.15i 0.169083 + 1.58952i
\(251\) 2795.67i 0.703032i −0.936182 0.351516i \(-0.885666\pi\)
0.936182 0.351516i \(-0.114334\pi\)
\(252\) 176.222 + 2066.26i 0.0440515 + 0.516517i
\(253\) 1436.08 1436.08i 0.356859 0.356859i
\(254\) −1970.79 + 1137.84i −0.486844 + 0.281079i
\(255\) 1051.74 2480.62i 0.258283 0.609185i
\(256\) 1574.70 2727.45i 0.384447 0.665882i
\(257\) 3460.57 + 927.257i 0.839939 + 0.225061i 0.653045 0.757319i \(-0.273491\pi\)
0.186894 + 0.982380i \(0.440158\pi\)
\(258\) 426.105 + 426.105i 0.102822 + 0.102822i
\(259\) −2974.47 531.189i −0.713609 0.127438i
\(260\) 4173.71 5346.72i 0.995549 1.27534i
\(261\) 375.443 + 650.286i 0.0890396 + 0.154221i
\(262\) −267.068 996.711i −0.0629752 0.235027i
\(263\) 1560.02 + 5822.07i 0.365760 + 1.36504i 0.866387 + 0.499373i \(0.166436\pi\)
−0.500627 + 0.865663i \(0.666897\pi\)
\(264\) −1162.92 2014.25i −0.271110 0.469577i
\(265\) 3906.10 5003.89i 0.905470 1.15995i
\(266\) −2375.03 6570.00i −0.547452 1.51441i
\(267\) 2075.53 + 2075.53i 0.475732 + 0.475732i
\(268\) −11903.9 3189.63i −2.71323 0.727007i
\(269\) 3266.46 5657.68i 0.740371 1.28236i −0.211955 0.977279i \(-0.567983\pi\)
0.952326 0.305081i \(-0.0986836\pi\)
\(270\) 532.751 1256.54i 0.120082 0.283225i
\(271\) 1400.35 808.494i 0.313894 0.181227i −0.334774 0.942299i \(-0.608660\pi\)
0.648668 + 0.761072i \(0.275326\pi\)
\(272\) 496.606 496.606i 0.110703 0.110703i
\(273\) −1150.37 + 2452.95i −0.255031 + 0.543807i
\(274\) 3963.10i 0.873795i
\(275\) 3355.38 + 3468.79i 0.735772 + 0.760639i
\(276\) −1700.31 981.676i −0.370822 0.214094i
\(277\) −1993.75 + 534.223i −0.432465 + 0.115879i −0.468483 0.883473i \(-0.655199\pi\)
0.0360181 + 0.999351i \(0.488533\pi\)
\(278\) −1616.47 + 6032.74i −0.348738 + 1.30151i
\(279\) −844.101 −0.181129
\(280\) −224.952 + 4151.84i −0.0480123 + 0.886143i
\(281\) −1707.65 −0.362526 −0.181263 0.983435i \(-0.558019\pi\)
−0.181263 + 0.983435i \(0.558019\pi\)
\(282\) 1477.26 5513.21i 0.311949 1.16421i
\(283\) 3322.02 890.132i 0.697786 0.186971i 0.107548 0.994200i \(-0.465700\pi\)
0.590239 + 0.807229i \(0.299034\pi\)
\(284\) 7951.94 + 4591.06i 1.66148 + 0.959257i
\(285\) −388.302 + 2771.32i −0.0807054 + 0.575997i
\(286\) 8511.95i 1.75987i
\(287\) −7620.10 + 649.885i −1.56725 + 0.133664i
\(288\) 1273.89 1273.89i 0.260641 0.260641i
\(289\) −1333.67 + 769.993i −0.271457 + 0.156726i
\(290\) 1581.49 + 3909.62i 0.320235 + 0.791657i
\(291\) −2687.24 + 4654.43i −0.541335 + 0.937620i
\(292\) −7572.25 2028.98i −1.51758 0.406634i
\(293\) −3697.62 3697.62i −0.737260 0.737260i 0.234787 0.972047i \(-0.424561\pi\)
−0.972047 + 0.234787i \(0.924561\pi\)
\(294\) −787.824 4585.14i −0.156282 0.909561i
\(295\) −6218.18 + 766.137i −1.22724 + 0.151208i
\(296\) −1638.04 2837.18i −0.321653 0.557120i
\(297\) −269.802 1006.91i −0.0527121 0.196724i
\(298\) −1602.37 5980.11i −0.311485 1.16248i
\(299\) −1282.53 2221.40i −0.248062 0.429655i
\(300\) 2399.58 4001.15i 0.461799 0.770021i
\(301\) −629.154 530.272i −0.120478 0.101543i
\(302\) 9624.63 + 9624.63i 1.83389 + 1.83389i
\(303\) −1112.35 298.053i −0.210900 0.0565105i
\(304\) −364.711 + 631.698i −0.0688080 + 0.119179i
\(305\) −2429.44 1030.03i −0.456095 0.193376i
\(306\) −2830.80 + 1634.36i −0.528843 + 0.305328i
\(307\) −6817.56 + 6817.56i −1.26742 + 1.26742i −0.320008 + 0.947415i \(0.603686\pi\)
−0.947415 + 0.320008i \(0.896314\pi\)
\(308\) 5086.67 + 7298.43i 0.941038 + 1.35022i
\(309\) 1794.02i 0.330286i
\(310\) −4695.05 657.844i −0.860197 0.120526i
\(311\) 1173.84 + 677.715i 0.214026 + 0.123568i 0.603181 0.797604i \(-0.293900\pi\)
−0.389155 + 0.921172i \(0.627233\pi\)
\(312\) −2837.46 + 760.295i −0.514870 + 0.137959i
\(313\) 1530.87 5713.30i 0.276454 1.03174i −0.678407 0.734687i \(-0.737329\pi\)
0.954861 0.297054i \(-0.0960041\pi\)
\(314\) −3381.97 −0.607820
\(315\) −579.007 + 1771.33i −0.103566 + 0.316836i
\(316\) 2199.87 0.391621
\(317\) −1509.30 + 5632.80i −0.267416 + 0.998011i 0.693339 + 0.720612i \(0.256139\pi\)
−0.960755 + 0.277399i \(0.910528\pi\)
\(318\) −7438.73 + 1993.20i −1.31177 + 0.351488i
\(319\) 2789.63 + 1610.59i 0.489622 + 0.282683i
\(320\) 7454.09 5621.95i 1.30218 0.982114i
\(321\) 5102.66i 0.887236i
\(322\) 3987.87 + 1870.20i 0.690172 + 0.323672i
\(323\) 4739.13 4739.13i 0.816384 0.816384i
\(324\) −872.740 + 503.877i −0.149647 + 0.0863986i
\(325\) 5328.64 2959.55i 0.909477 0.505126i
\(326\) −6767.43 + 11721.5i −1.14973 + 1.99140i
\(327\) −2175.40 582.898i −0.367890 0.0985759i
\(328\) −5863.38 5863.38i −0.987045 0.987045i
\(329\) −1370.10 + 7672.10i −0.229593 + 1.28564i
\(330\) −715.959 5810.92i −0.119431 0.969335i
\(331\) 1758.33 + 3045.51i 0.291983 + 0.505729i 0.974278 0.225347i \(-0.0723517\pi\)
−0.682296 + 0.731076i \(0.739018\pi\)
\(332\) −3244.20 12107.5i −0.536291 2.00147i
\(333\) −380.031 1418.29i −0.0625392 0.233400i
\(334\) 599.522 + 1038.40i 0.0982167 + 0.170116i
\(335\) −8729.80 6814.59i −1.42376 1.11140i
\(336\) −313.048 + 371.424i −0.0508279 + 0.0603061i
\(337\) −5527.15 5527.15i −0.893422 0.893422i 0.101422 0.994844i \(-0.467661\pi\)
−0.994844 + 0.101422i \(0.967661\pi\)
\(338\) −789.644 211.585i −0.127074 0.0340494i
\(339\) 1961.30 3397.07i 0.314228 0.544259i
\(340\) −10358.5 + 4190.15i −1.65226 + 0.668361i
\(341\) −3135.94 + 1810.53i −0.498008 + 0.287525i
\(342\) 2400.58 2400.58i 0.379557 0.379557i
\(343\) 1603.85 + 6146.65i 0.252477 + 0.967603i
\(344\) 892.134i 0.139827i
\(345\) −1062.40 1408.62i −0.165790 0.219820i
\(346\) 6538.01 + 3774.72i 1.01585 + 0.586504i
\(347\) −1969.11 + 527.622i −0.304633 + 0.0816261i −0.407897 0.913028i \(-0.633738\pi\)
0.103265 + 0.994654i \(0.467071\pi\)
\(348\) 805.969 3007.92i 0.124151 0.463337i
\(349\) −762.358 −0.116929 −0.0584643 0.998289i \(-0.518620\pi\)
−0.0584643 + 0.998289i \(0.518620\pi\)
\(350\) −4601.02 + 9401.26i −0.702672 + 1.43577i
\(351\) −1316.60 −0.200213
\(352\) 2000.25 7465.04i 0.302880 1.13036i
\(353\) 319.095 85.5012i 0.0481125 0.0128917i −0.234683 0.972072i \(-0.575405\pi\)
0.282795 + 0.959180i \(0.408738\pi\)
\(354\) 6582.44 + 3800.38i 0.988285 + 0.570587i
\(355\) 4968.58 + 6587.79i 0.742830 + 0.984912i
\(356\) 12172.8i 1.81225i
\(357\) 3661.65 2552.00i 0.542843 0.378336i
\(358\) −3874.61 + 3874.61i −0.572010 + 0.572010i
\(359\) 8345.62 4818.35i 1.22692 0.708364i 0.260538 0.965464i \(-0.416100\pi\)
0.966385 + 0.257100i \(0.0827669\pi\)
\(360\) −1873.12 + 757.701i −0.274228 + 0.110929i
\(361\) −50.9524 + 88.2521i −0.00742854 + 0.0128666i
\(362\) 13402.1 + 3591.09i 1.94586 + 0.521391i
\(363\) −338.626 338.626i −0.0489621 0.0489621i
\(364\) 10566.6 3819.79i 1.52154 0.550031i
\(365\) −5553.17 4334.87i −0.796346 0.621637i
\(366\) 1600.64 + 2772.39i 0.228598 + 0.395943i
\(367\) −970.801 3623.08i −0.138080 0.515322i −0.999966 0.00822014i \(-0.997383\pi\)
0.861886 0.507102i \(-0.169283\pi\)
\(368\) −119.028 444.219i −0.0168608 0.0629254i
\(369\) −1858.23 3218.55i −0.262156 0.454068i
\(370\) −1008.47 8185.00i −0.141697 1.15005i
\(371\) 9889.08 3574.86i 1.38387 0.500263i
\(372\) 2475.30 + 2475.30i 0.344995 + 0.344995i
\(373\) −5717.11 1531.89i −0.793621 0.212650i −0.160839 0.986981i \(-0.551420\pi\)
−0.632781 + 0.774331i \(0.718087\pi\)
\(374\) −7011.17 + 12143.7i −0.969356 + 1.67897i
\(375\) 3388.81 2468.62i 0.466660 0.339944i
\(376\) −7317.97 + 4225.03i −1.00371 + 0.579493i
\(377\) 2876.77 2876.77i 0.393001 0.393001i
\(378\) 1854.79 1292.70i 0.252381 0.175898i
\(379\) 9473.48i 1.28396i 0.766722 + 0.641979i \(0.221886\pi\)
−0.766722 + 0.641979i \(0.778114\pi\)
\(380\) 9265.50 6988.13i 1.25082 0.943378i
\(381\) 1307.69 + 754.998i 0.175840 + 0.101522i
\(382\) −1645.20 + 440.829i −0.220355 + 0.0590440i
\(383\) 663.707 2476.99i 0.0885479 0.330465i −0.907415 0.420237i \(-0.861947\pi\)
0.995962 + 0.0897716i \(0.0286137\pi\)
\(384\) −6522.60 −0.866810
\(385\) 1648.30 + 7822.65i 0.218195 + 1.03553i
\(386\) 8380.31 1.10504
\(387\) 103.489 386.226i 0.0135934 0.0507311i
\(388\) 21529.2 5768.73i 2.81696 0.754801i
\(389\) 10784.1 + 6226.21i 1.40559 + 0.811521i 0.994959 0.100279i \(-0.0319736\pi\)
0.410635 + 0.911800i \(0.365307\pi\)
\(390\) −7323.17 1026.08i −0.950828 0.133225i
\(391\) 4225.59i 0.546541i
\(392\) −3975.22 + 5624.68i −0.512191 + 0.724718i
\(393\) −484.146 + 484.146i −0.0621423 + 0.0621423i
\(394\) 10787.8 6228.36i 1.37940 0.796397i
\(395\) 1820.06 + 771.670i 0.231841 + 0.0982961i
\(396\) −2161.56 + 3743.93i −0.274299 + 0.475100i
\(397\) −13241.2 3547.98i −1.67395 0.448534i −0.707779 0.706434i \(-0.750303\pi\)
−0.966171 + 0.257901i \(0.916969\pi\)
\(398\) 16505.7 + 16505.7i 2.07878 + 2.07878i
\(399\) −2987.43 + 3544.51i −0.374834 + 0.444731i
\(400\) 1060.16 265.269i 0.132519 0.0331586i
\(401\) 955.935 + 1655.73i 0.119045 + 0.206192i 0.919390 0.393348i \(-0.128683\pi\)
−0.800344 + 0.599541i \(0.795350\pi\)
\(402\) 3477.35 + 12977.6i 0.431428 + 1.61011i
\(403\) 1183.69 + 4417.58i 0.146312 + 0.546043i
\(404\) 2387.89 + 4135.95i 0.294065 + 0.509335i
\(405\) −898.811 + 110.742i −0.110277 + 0.0135872i
\(406\) −1228.16 + 6877.28i −0.150130 + 0.840674i
\(407\) −4454.00 4454.00i −0.542448 0.542448i
\(408\) 4674.35 + 1252.49i 0.567193 + 0.151979i
\(409\) −6050.07 + 10479.0i −0.731434 + 1.26688i 0.224836 + 0.974397i \(0.427815\pi\)
−0.956270 + 0.292485i \(0.905518\pi\)
\(410\) −7827.49 19350.4i −0.942859 2.33085i
\(411\) 2277.36 1314.84i 0.273319 0.157801i
\(412\) −5260.91 + 5260.91i −0.629094 + 0.629094i
\(413\) −9396.34 4406.62i −1.11952 0.525026i
\(414\) 2140.45i 0.254100i
\(415\) 1563.00 11155.1i 0.184878 1.31948i
\(416\) −8453.24 4880.48i −0.996284 0.575205i
\(417\) 4002.95 1072.59i 0.470085 0.125959i
\(418\) 3769.37 14067.5i 0.441067 1.64609i
\(419\) −3652.75 −0.425891 −0.212946 0.977064i \(-0.568306\pi\)
−0.212946 + 0.977064i \(0.568306\pi\)
\(420\) 6892.30 3496.46i 0.800737 0.406214i
\(421\) 15908.6 1.84166 0.920831 0.389961i \(-0.127512\pi\)
0.920831 + 0.389961i \(0.127512\pi\)
\(422\) −1540.07 + 5747.62i −0.177653 + 0.663009i
\(423\) −3658.23 + 980.219i −0.420494 + 0.112671i
\(424\) 9873.81 + 5700.65i 1.13093 + 0.652943i
\(425\) −10039.9 166.846i −1.14590 0.0190428i
\(426\) 10010.4i 1.13851i
\(427\) −2499.34 3586.10i −0.283259 0.406425i
\(428\) 14963.4 14963.4i 1.68991 1.68991i
\(429\) −4891.32 + 2824.00i −0.550478 + 0.317818i
\(430\) 876.627 2067.61i 0.0983133 0.231881i
\(431\) −4523.39 + 7834.74i −0.505532 + 0.875606i 0.494448 + 0.869207i \(0.335370\pi\)
−0.999980 + 0.00639914i \(0.997963\pi\)
\(432\) −228.010 61.0951i −0.0253938 0.00680425i
\(433\) −3918.73 3918.73i −0.434924 0.434924i 0.455375 0.890300i \(-0.349505\pi\)
−0.890300 + 0.455375i \(0.849505\pi\)
\(434\) −6004.95 5061.17i −0.664164 0.559779i
\(435\) 1721.94 2205.88i 0.189794 0.243135i
\(436\) 4669.97 + 8088.63i 0.512961 + 0.888475i
\(437\) −1135.89 4239.20i −0.124341 0.464047i
\(438\) 2212.00 + 8255.29i 0.241309 + 0.900578i
\(439\) −3221.24 5579.35i −0.350208 0.606578i 0.636078 0.771625i \(-0.280556\pi\)
−0.986286 + 0.165047i \(0.947222\pi\)
\(440\) −5333.65 + 6832.65i −0.577891 + 0.740305i
\(441\) −2373.43 + 1973.92i −0.256283 + 0.213144i
\(442\) 12523.0 + 12523.0i 1.34765 + 1.34765i
\(443\) −7918.55 2121.77i −0.849259 0.227558i −0.192161 0.981363i \(-0.561550\pi\)
−0.657098 + 0.753805i \(0.728216\pi\)
\(444\) −3044.67 + 5273.53i −0.325437 + 0.563673i
\(445\) 4270.00 10071.2i 0.454870 1.07285i
\(446\) −13081.8 + 7552.80i −1.38888 + 0.801873i
\(447\) −2904.80 + 2904.80i −0.307366 + 0.307366i
\(448\) 15410.0 1314.25i 1.62512 0.138599i
\(449\) 9021.47i 0.948217i −0.880467 0.474108i \(-0.842770\pi\)
0.880467 0.474108i \(-0.157230\pi\)
\(450\) −5085.67 84.5148i −0.532757 0.00885347i
\(451\) −13807.1 7971.54i −1.44158 0.832295i
\(452\) −15713.3 + 4210.36i −1.63515 + 0.438138i
\(453\) 2337.55 8723.86i 0.242445 0.904819i
\(454\) 16193.6 1.67401
\(455\) 10082.2 + 546.265i 1.03881 + 0.0562841i
\(456\) −5026.08 −0.516158
\(457\) 806.142 3008.56i 0.0825158 0.307953i −0.912316 0.409486i \(-0.865708\pi\)
0.994832 + 0.101533i \(0.0323747\pi\)
\(458\) −6302.75 + 1688.82i −0.643031 + 0.172300i
\(459\) 1878.34 + 1084.46i 0.191010 + 0.110280i
\(460\) −1015.30 + 7246.20i −0.102910 + 0.734469i
\(461\) 1056.67i 0.106755i 0.998574 + 0.0533776i \(0.0169987\pi\)
−0.998574 + 0.0533776i \(0.983001\pi\)
\(462\) 4118.01 8780.92i 0.414691 0.884254i
\(463\) 4783.03 4783.03i 0.480100 0.480100i −0.425064 0.905163i \(-0.639748\pi\)
0.905163 + 0.425064i \(0.139748\pi\)
\(464\) 631.696 364.710i 0.0632020 0.0364897i
\(465\) 1179.65 + 2916.22i 0.117645 + 0.290831i
\(466\) 12779.4 22134.5i 1.27037 2.20034i
\(467\) 9772.64 + 2618.57i 0.968359 + 0.259471i 0.708135 0.706077i \(-0.249537\pi\)
0.260224 + 0.965548i \(0.416204\pi\)
\(468\) 3860.88 + 3860.88i 0.381344 + 0.381344i
\(469\) −6236.71 17252.5i −0.614040 1.69861i
\(470\) −21111.7 + 2601.16i −2.07194 + 0.255282i
\(471\) 1122.03 + 1943.42i 0.109768 + 0.190123i
\(472\) −2912.40 10869.2i −0.284013 1.05995i
\(473\) −443.952 1656.85i −0.0431563 0.161061i
\(474\) −1199.15 2076.99i −0.116200 0.201264i
\(475\) 10117.1 2531.47i 0.977273 0.244530i
\(476\) −18221.3 3254.01i −1.75456 0.313335i
\(477\) 3613.32 + 3613.32i 0.346840 + 0.346840i
\(478\) −16851.7 4515.41i −1.61251 0.432071i
\(479\) −1182.06 + 2047.38i −0.112755 + 0.195297i −0.916880 0.399163i \(-0.869301\pi\)
0.804125 + 0.594460i \(0.202634\pi\)
\(480\) −6181.34 2620.77i −0.587788 0.249211i
\(481\) −6889.69 + 3977.77i −0.653104 + 0.377070i
\(482\) 4124.74 4124.74i 0.389785 0.389785i
\(483\) −248.358 2912.07i −0.0233968 0.274335i
\(484\) 1986.02i 0.186515i
\(485\) 19835.7 + 2779.27i 1.85710 + 0.260206i
\(486\) 951.464 + 549.328i 0.0888051 + 0.0512716i
\(487\) 12270.3 3287.81i 1.14172 0.305923i 0.362079 0.932148i \(-0.382067\pi\)
0.779643 + 0.626224i \(0.215401\pi\)
\(488\) 1226.65 4577.90i 0.113786 0.424655i
\(489\) 8980.90 0.830533
\(490\) −14739.9 + 9129.63i −1.35894 + 0.841703i
\(491\) −5861.11 −0.538714 −0.269357 0.963040i \(-0.586811\pi\)
−0.269357 + 0.963040i \(0.586811\pi\)
\(492\) −3989.09 + 14887.5i −0.365533 + 1.36419i
\(493\) −6473.74 + 1734.63i −0.591405 + 0.158467i
\(494\) −15929.7 9197.02i −1.45083 0.837639i
\(495\) −3101.66 + 2339.30i −0.281635 + 0.212412i
\(496\) 819.970i 0.0742293i
\(497\) 1161.51 + 13619.0i 0.104831 + 1.22917i
\(498\) −9662.82 + 9662.82i −0.869480 + 0.869480i
\(499\) −10907.2 + 6297.30i −0.978508 + 0.564942i −0.901819 0.432113i \(-0.857768\pi\)
−0.0766887 + 0.997055i \(0.524435\pi\)
\(500\) −17176.7 2698.43i −1.53633 0.241355i
\(501\) 397.806 689.020i 0.0354743 0.0614434i
\(502\) 12209.1 + 3271.43i 1.08550 + 0.290858i
\(503\) −7660.55 7660.55i −0.679059 0.679059i 0.280728 0.959787i \(-0.409424\pi\)
−0.959787 + 0.280728i \(0.909424\pi\)
\(504\) −3294.94 588.420i −0.291207 0.0520045i
\(505\) 524.810 + 4259.50i 0.0462450 + 0.375337i
\(506\) 4591.11 + 7952.04i 0.403359 + 0.698638i
\(507\) 140.394 + 523.959i 0.0122981 + 0.0458971i
\(508\) −1620.76 6048.78i −0.141555 0.528289i
\(509\) 5787.83 + 10024.8i 0.504010 + 0.872971i 0.999989 + 0.00463649i \(0.00147584\pi\)
−0.495979 + 0.868334i \(0.665191\pi\)
\(510\) 9602.54 + 7495.86i 0.833740 + 0.650828i
\(511\) −3967.28 10974.6i −0.343448 0.950075i
\(512\) −2230.58 2230.58i −0.192536 0.192536i
\(513\) −2175.91 583.033i −0.187268 0.0501784i
\(514\) −8098.96 + 14027.8i −0.694999 + 1.20377i
\(515\) −6198.04 + 2507.19i −0.530327 + 0.214524i
\(516\) −1436.07 + 829.116i −0.122518 + 0.0707360i
\(517\) −11488.3 + 11488.3i −0.977279 + 0.977279i
\(518\) 5800.45 12368.4i 0.492002 1.04911i
\(519\) 5009.34i 0.423672i
\(520\) 6592.10 + 8740.40i 0.555928 + 0.737100i
\(521\) 15690.1 + 9058.67i 1.31938 + 0.761742i 0.983628 0.180210i \(-0.0576777\pi\)
0.335748 + 0.941952i \(0.391011\pi\)
\(522\) −3279.24 + 878.669i −0.274959 + 0.0736749i
\(523\) −2185.34 + 8155.81i −0.182712 + 0.681891i 0.812397 + 0.583105i \(0.198162\pi\)
−0.995109 + 0.0987856i \(0.968504\pi\)
\(524\) 2839.48 0.236724
\(525\) 6928.83 475.111i 0.575998 0.0394963i
\(526\) −27251.4 −2.25897
\(527\) 1949.97 7277.40i 0.161181 0.601534i
\(528\) −978.129 + 262.089i −0.0806204 + 0.0216022i
\(529\) −8140.61 4699.98i −0.669073 0.386289i
\(530\) 17282.0 + 22914.0i 1.41638 + 1.87796i
\(531\) 5043.39i 0.412174i
\(532\) 19154.7 1633.62i 1.56102 0.133132i
\(533\) −14238.4 + 14238.4i −1.15710 + 1.15710i
\(534\) −11492.9 + 6635.43i −0.931361 + 0.537722i
\(535\) 17628.8 7131.08i 1.42460 0.576268i
\(536\) 9945.36 17225.9i 0.801444 1.38814i
\(537\) 3511.99 + 941.034i 0.282223 + 0.0756213i
\(538\) 20885.7 + 20885.7i 1.67369 + 1.67369i
\(539\) −4583.68 + 12424.2i −0.366295 + 0.992855i
\(540\) 2960.48 + 2310.99i 0.235924 + 0.184165i
\(541\) −1462.87 2533.76i −0.116254 0.201358i 0.802026 0.597289i \(-0.203755\pi\)
−0.918280 + 0.395931i \(0.870422\pi\)
\(542\) 1892.16 + 7061.64i 0.149954 + 0.559638i
\(543\) −2382.83 8892.83i −0.188318 0.702814i
\(544\) 8039.96 + 13925.6i 0.633659 + 1.09753i
\(545\) 1026.36 + 8330.25i 0.0806690 + 0.654732i
\(546\) −9366.30 7894.22i −0.734140 0.618757i
\(547\) 11390.3 + 11390.3i 0.890337 + 0.890337i 0.994555 0.104218i \(-0.0332339\pi\)
−0.104218 + 0.994555i \(0.533234\pi\)
\(548\) −10534.0 2822.58i −0.821150 0.220026i
\(549\) 1062.09 1839.59i 0.0825660 0.143008i
\(550\) −19075.1 + 10594.4i −1.47885 + 0.821358i
\(551\) 6028.30 3480.44i 0.466087 0.269096i
\(552\) 2240.73 2240.73i 0.172775 0.172775i
\(553\) 1872.43 + 2686.59i 0.143985 + 0.206592i
\(554\) 9332.16i 0.715677i
\(555\) −4368.86 + 3295.04i −0.334140 + 0.252012i
\(556\) −14883.9 8593.20i −1.13528 0.655455i
\(557\) 13106.7 3511.92i 0.997034 0.267154i 0.276831 0.960918i \(-0.410716\pi\)
0.720202 + 0.693764i \(0.244049\pi\)
\(558\) 987.748 3686.32i 0.0749367 0.279668i
\(559\) −2166.42 −0.163918
\(560\) 1720.70 + 562.454i 0.129844 + 0.0424429i
\(561\) 9304.36 0.700232
\(562\) 1998.25 7457.57i 0.149984 0.559749i
\(563\) 7608.60 2038.72i 0.569564 0.152614i 0.0374672 0.999298i \(-0.488071\pi\)
0.532096 + 0.846684i \(0.321404\pi\)
\(564\) 13602.1 + 7853.17i 1.01552 + 0.586309i
\(565\) −14477.3 2028.47i −1.07799 0.151041i
\(566\) 15549.4i 1.15475i
\(567\) −1358.20 636.958i −0.100598 0.0471777i
\(568\) −10479.3 + 10479.3i −0.774125 + 0.774125i
\(569\) −3943.73 + 2276.91i −0.290562 + 0.167756i −0.638195 0.769874i \(-0.720319\pi\)
0.347633 + 0.937631i \(0.386985\pi\)
\(570\) −11648.4 4938.72i −0.855964 0.362913i
\(571\) 7554.25 13084.3i 0.553652 0.958954i −0.444355 0.895851i \(-0.646567\pi\)
0.998007 0.0631031i \(-0.0200997\pi\)
\(572\) 22624.9 + 6062.33i 1.65384 + 0.443145i
\(573\) 799.144 + 799.144i 0.0582631 + 0.0582631i
\(574\) 6078.71 34038.7i 0.442022 2.47517i
\(575\) −3381.83 + 5638.99i −0.245273 + 0.408977i
\(576\) 3757.86 + 6508.80i 0.271836 + 0.470833i
\(577\) −212.586 793.380i −0.0153380 0.0572424i 0.957833 0.287327i \(-0.0927665\pi\)
−0.973171 + 0.230084i \(0.926100\pi\)
\(578\) −1802.06 6725.37i −0.129681 0.483977i
\(579\) −2780.33 4815.67i −0.199562 0.345652i
\(580\) −11518.2 + 1419.15i −0.824598 + 0.101598i
\(581\) 12025.0 14267.4i 0.858661 1.01878i
\(582\) −17182.1 17182.1i −1.22375 1.22375i
\(583\) 21174.2 + 5673.61i 1.50420 + 0.403048i
\(584\) 6326.41 10957.7i 0.448269 0.776424i
\(585\) 1839.97 + 4548.61i 0.130040 + 0.321473i
\(586\) 20475.0 11821.2i 1.44337 0.833329i
\(587\) 5660.66 5660.66i 0.398025 0.398025i −0.479511 0.877536i \(-0.659186\pi\)
0.877536 + 0.479511i \(0.159186\pi\)
\(588\) 12748.5 + 1171.55i 0.894113 + 0.0821666i
\(589\) 7825.01i 0.547409i
\(590\) 3930.53 28052.3i 0.274267 1.95745i
\(591\) −7158.14 4132.76i −0.498218 0.287646i
\(592\) −1377.75 + 369.167i −0.0956506 + 0.0256295i
\(593\) −6753.23 + 25203.4i −0.467659 + 1.74533i 0.180261 + 0.983619i \(0.442306\pi\)
−0.647920 + 0.761708i \(0.724361\pi\)
\(594\) 4713.07 0.325555
\(595\) −13933.9 9083.88i −0.960061 0.625887i
\(596\) 17036.5 1.17087
\(597\) 4008.77 14960.9i 0.274821 1.02565i
\(598\) 11202.0 3001.57i 0.766026 0.205256i
\(599\) −8018.89 4629.71i −0.546984 0.315801i 0.200921 0.979607i \(-0.435607\pi\)
−0.747904 + 0.663806i \(0.768940\pi\)
\(600\) 5235.45 + 5412.40i 0.356227 + 0.368267i
\(601\) 22508.8i 1.52771i 0.645389 + 0.763854i \(0.276695\pi\)
−0.645389 + 0.763854i \(0.723305\pi\)
\(602\) 3052.00 2127.11i 0.206629 0.144011i
\(603\) 6303.80 6303.80i 0.425722 0.425722i
\(604\) −32437.2 + 18727.6i −2.18519 + 1.26162i
\(605\) −696.656 + 1643.13i −0.0468150 + 0.110418i
\(606\) 2603.29 4509.02i 0.174507 0.302255i
\(607\) −11256.7 3016.21i −0.752708 0.201687i −0.137989 0.990434i \(-0.544064\pi\)
−0.614719 + 0.788746i \(0.710730\pi\)
\(608\) −11809.2 11809.2i −0.787709 0.787709i
\(609\) 4359.43 1575.92i 0.290071 0.104859i
\(610\) 7341.20 9404.41i 0.487273 0.624219i
\(611\) 10259.9 + 17770.7i 0.679331 + 1.17664i
\(612\) −2328.03 8688.32i −0.153766 0.573864i
\(613\) 5896.55 + 22006.2i 0.388514 + 1.44996i 0.832552 + 0.553947i \(0.186879\pi\)
−0.444038 + 0.896008i \(0.646454\pi\)
\(614\) −21795.6 37751.1i −1.43257 2.48129i
\(615\) −8522.61 + 10917.9i −0.558805 + 0.715855i
\(616\) −13503.2 + 4881.36i −0.883216 + 0.319279i
\(617\) −8634.24 8634.24i −0.563373 0.563373i 0.366891 0.930264i \(-0.380422\pi\)
−0.930264 + 0.366891i \(0.880422\pi\)
\(618\) 7834.79 + 2099.32i 0.509970 + 0.136646i
\(619\) −1622.58 + 2810.38i −0.105358 + 0.182486i −0.913885 0.405974i \(-0.866932\pi\)
0.808526 + 0.588460i \(0.200266\pi\)
\(620\) 5092.44 12011.0i 0.329867 0.778022i
\(621\) 1229.99 710.135i 0.0794812 0.0458885i
\(622\) −4333.29 + 4333.29i −0.279339 + 0.279339i
\(623\) 14866.1 10361.0i 0.956017 0.666300i
\(624\) 1278.96i 0.0820502i
\(625\) −13264.6 8257.81i −0.848934 0.528500i
\(626\) 23159.5 + 13371.1i 1.47866 + 0.853704i
\(627\) −9334.32 + 2501.12i −0.594540 + 0.159307i
\(628\) 2408.68 8989.33i 0.153052 0.571199i
\(629\) 13105.7 0.830777
\(630\) −7058.16 4601.39i −0.446355 0.290990i
\(631\) −18151.9 −1.14519 −0.572597 0.819837i \(-0.694064\pi\)
−0.572597 + 0.819837i \(0.694064\pi\)
\(632\) −918.965 + 3429.62i −0.0578393 + 0.215859i
\(633\) 3813.77 1021.90i 0.239469 0.0641654i
\(634\) −22833.2 13182.7i −1.43032 0.825794i
\(635\) 780.854 5572.98i 0.0487988 0.348279i
\(636\) 21191.9i 1.32125i
\(637\) 13658.8 + 9653.27i 0.849576 + 0.600434i
\(638\) −10298.1 + 10298.1i −0.639036 + 0.639036i
\(639\) −5752.36 + 3321.13i −0.356119 + 0.205605i
\(640\) 9115.47 + 22534.4i 0.563001 + 1.39180i
\(641\) −4787.72 + 8292.58i −0.295014 + 0.510978i −0.974988 0.222257i \(-0.928657\pi\)
0.679975 + 0.733236i \(0.261991\pi\)
\(642\) −22284.1 5971.02i −1.36991 0.367067i
\(643\) −10557.7 10557.7i −0.647519 0.647519i 0.304874 0.952393i \(-0.401386\pi\)
−0.952393 + 0.304874i \(0.901386\pi\)
\(644\) −7811.25 + 9267.85i −0.477960 + 0.567088i
\(645\) −1478.97 + 182.223i −0.0902859 + 0.0111240i
\(646\) 15150.9 + 26242.1i 0.922762 + 1.59827i
\(647\) 3237.92 + 12084.1i 0.196748 + 0.734272i 0.991808 + 0.127741i \(0.0407727\pi\)
−0.795060 + 0.606531i \(0.792561\pi\)
\(648\) −420.975 1571.10i −0.0255208 0.0952449i
\(649\) −10817.7 18736.8i −0.654286 1.13326i
\(650\) 6689.35 + 26734.2i 0.403659 + 1.61324i
\(651\) −916.099 + 5129.83i −0.0551532 + 0.308839i
\(652\) −26336.2 26336.2i −1.58191 1.58191i
\(653\) 30306.4 + 8120.58i 1.81621 + 0.486651i 0.996307 0.0858590i \(-0.0273634\pi\)
0.819898 + 0.572510i \(0.194030\pi\)
\(654\) 5091.21 8818.24i 0.304407 0.527248i
\(655\) 2349.24 + 996.035i 0.140141 + 0.0594173i
\(656\) −3126.54 + 1805.11i −0.186084 + 0.107435i
\(657\) 4009.96 4009.96i 0.238118 0.238118i
\(658\) −31902.0 14961.2i −1.89008 0.886394i
\(659\) 22866.2i 1.35165i 0.737061 + 0.675826i \(0.236213\pi\)
−0.737061 + 0.675826i \(0.763787\pi\)
\(660\) 15955.4 + 2235.59i 0.941007 + 0.131849i
\(661\) 10029.1 + 5790.28i 0.590144 + 0.340720i 0.765154 0.643847i \(-0.222663\pi\)
−0.175011 + 0.984567i \(0.555996\pi\)
\(662\) −15357.8 + 4115.10i −0.901657 + 0.241598i
\(663\) 3041.49 11351.0i 0.178163 0.664912i
\(664\) 20231.0 1.18240
\(665\) 16420.7 + 5367.52i 0.957543 + 0.312998i
\(666\) 6638.62 0.386248
\(667\) −1135.89 + 4239.19i −0.0659396 + 0.246090i
\(668\) −3187.08 + 853.975i −0.184598 + 0.0494630i
\(669\) 8680.29 + 5011.57i 0.501644 + 0.289624i
\(670\) 39975.8 30150.1i 2.30507 1.73851i
\(671\) 9112.38i 0.524262i
\(672\) −6359.22 9124.30i −0.365048 0.523776i
\(673\) 139.882 139.882i 0.00801196 0.00801196i −0.703089 0.711101i \(-0.748197\pi\)
0.711101 + 0.703089i \(0.248197\pi\)
\(674\) 30605.7 17670.2i 1.74909 1.00984i
\(675\) 1638.70 + 2950.47i 0.0934424 + 0.168243i
\(676\) 1124.79 1948.19i 0.0639958 0.110844i
\(677\) −12399.9 3322.53i −0.703937 0.188619i −0.110944 0.993827i \(-0.535387\pi\)
−0.592993 + 0.805207i \(0.702054\pi\)
\(678\) 12540.5 + 12540.5i 0.710347 + 0.710347i
\(679\) 25369.8 + 21382.5i 1.43388 + 1.20852i
\(680\) −2205.37 17899.4i −0.124371 1.00943i
\(681\) −5372.53 9305.49i −0.302314 0.523623i
\(682\) −4237.29 15813.8i −0.237910 0.887890i
\(683\) 1586.44 + 5920.69i 0.0888779 + 0.331697i 0.996020 0.0891270i \(-0.0284077\pi\)
−0.907142 + 0.420824i \(0.861741\pi\)
\(684\) 4671.05 + 8090.50i 0.261114 + 0.452263i
\(685\) −7725.19 6030.38i −0.430897 0.336363i
\(686\) −28720.2 188.411i −1.59846 0.0104862i
\(687\) 3061.52 + 3061.52i 0.170021 + 0.170021i
\(688\) −375.184 100.530i −0.0207904 0.00557076i
\(689\) 13843.2 23977.2i 0.765436 1.32577i
\(690\) 7394.89 2991.33i 0.407998 0.165040i
\(691\) −5833.87 + 3368.18i −0.321173 + 0.185429i −0.651915 0.758292i \(-0.726034\pi\)
0.330742 + 0.943721i \(0.392701\pi\)
\(692\) −14689.7 + 14689.7i −0.806965 + 0.806965i
\(693\) −6412.11 + 546.861i −0.351480 + 0.0299762i
\(694\) 9216.84i 0.504130i
\(695\) −9299.82 12330.5i −0.507571 0.672984i
\(696\) 4352.70 + 2513.03i 0.237053 + 0.136862i
\(697\) 32041.4 8585.46i 1.74125 0.466568i
\(698\) 892.094 3329.34i 0.0483757 0.180541i
\(699\) −16959.2 −0.917675
\(700\) −21711.8 18925.3i −1.17233 1.02187i
\(701\) 19829.6 1.06841 0.534205 0.845355i \(-0.320611\pi\)
0.534205 + 0.845355i \(0.320611\pi\)
\(702\) 1540.65 5749.79i 0.0828321 0.309134i
\(703\) −13147.9 + 3522.97i −0.705381 + 0.189006i
\(704\) 27921.8 + 16120.7i 1.49480 + 0.863026i
\(705\) 8498.94 + 11268.7i 0.454026 + 0.601989i
\(706\) 1493.59i 0.0796204i
\(707\) −3018.57 + 6436.56i −0.160573 + 0.342393i
\(708\) −14789.6 + 14789.6i −0.785065 + 0.785065i
\(709\) −3288.67 + 1898.71i −0.174201 + 0.100575i −0.584565 0.811347i \(-0.698735\pi\)
0.410364 + 0.911922i \(0.365402\pi\)
\(710\) −34584.1 + 13989.7i −1.82805 + 0.739470i
\(711\) −795.682 + 1378.16i −0.0419696 + 0.0726935i
\(712\) 18977.6 + 5085.04i 0.998900 + 0.267654i
\(713\) −3488.55 3488.55i −0.183236 0.183236i
\(714\) 6860.21 + 18977.3i 0.359576 + 0.994688i
\(715\) 16592.2 + 12952.0i 0.867848 + 0.677453i
\(716\) −7539.24 13058.3i −0.393512 0.681583i
\(717\) 2996.15 + 11181.8i 0.156057 + 0.582414i
\(718\) 11276.6 + 42085.0i 0.586129 + 2.18746i
\(719\) −8770.35 15190.7i −0.454908 0.787923i 0.543775 0.839231i \(-0.316994\pi\)
−0.998683 + 0.0513075i \(0.983661\pi\)
\(720\) 107.576 + 873.116i 0.00556822 + 0.0451932i
\(721\) −10902.8 1947.04i −0.563163 0.100571i
\(722\) −325.788 325.788i −0.0167930 0.0167930i
\(723\) −3738.70 1001.78i −0.192315 0.0515307i
\(724\) −19090.4 + 33065.5i −0.979956 + 1.69733i
\(725\) −10027.4 2866.23i −0.513665 0.146826i
\(726\) 1875.08 1082.58i 0.0958552 0.0553420i
\(727\) 3993.19 3993.19i 0.203713 0.203713i −0.597876 0.801589i \(-0.703988\pi\)
0.801589 + 0.597876i \(0.203988\pi\)
\(728\) 1541.04 + 18069.2i 0.0784543 + 0.919900i
\(729\) 729.000i 0.0370370i
\(730\) 25429.3 19179.0i 1.28929 0.972394i
\(731\) 3090.76 + 1784.45i 0.156383 + 0.0902878i
\(732\) −8509.06 + 2280.00i −0.429650 + 0.115124i
\(733\) 3105.65 11590.4i 0.156494 0.584042i −0.842479 0.538729i \(-0.818905\pi\)
0.998973 0.0453132i \(-0.0144286\pi\)
\(734\) 16958.6 0.852796
\(735\) 10136.5 + 5441.20i 0.508694 + 0.273064i
\(736\) 10529.6 0.527344
\(737\) 9898.20 36940.6i 0.494715 1.84630i
\(738\) 16230.4 4348.92i 0.809551 0.216919i
\(739\) −15999.3 9237.22i −0.796407 0.459806i 0.0458061 0.998950i \(-0.485414\pi\)
−0.842213 + 0.539144i \(0.818748\pi\)
\(740\) 22474.1 + 3148.95i 1.11644 + 0.156429i
\(741\) 12205.1i 0.605084i
\(742\) 4040.02 + 47370.4i 0.199884 + 2.34370i
\(743\) −9256.44 + 9256.44i −0.457047 + 0.457047i −0.897685 0.440638i \(-0.854752\pi\)
0.440638 + 0.897685i \(0.354752\pi\)
\(744\) −4893.05 + 2825.00i −0.241113 + 0.139206i
\(745\) 14095.1 + 5976.06i 0.693161 + 0.293887i
\(746\) 13380.1 23174.9i 0.656674 1.13739i
\(747\) 8758.47 + 2346.83i 0.428990 + 0.114948i
\(748\) −27284.7 27284.7i −1.33373 1.33373i
\(749\) 31010.3 + 5537.89i 1.51280 + 0.270160i
\(750\) 6815.35 + 17688.2i 0.331815 + 0.861176i
\(751\) −8451.47 14638.4i −0.410650 0.711267i 0.584311 0.811530i \(-0.301365\pi\)
−0.994961 + 0.100263i \(0.968032\pi\)
\(752\) 952.197 + 3553.65i 0.0461743 + 0.172325i
\(753\) −2170.72 8101.22i −0.105054 0.392065i
\(754\) 9196.99 + 15929.6i 0.444210 + 0.769395i
\(755\) −33406.2 + 4115.95i −1.61030 + 0.198404i
\(756\) 2115.02 + 5850.74i 0.101749 + 0.281467i
\(757\) −26269.9 26269.9i −1.26129 1.26129i −0.950470 0.310817i \(-0.899397\pi\)
−0.310817 0.950470i \(-0.600603\pi\)
\(758\) −41372.2 11085.7i −1.98246 0.531199i
\(759\) 3046.38 5276.48i 0.145687 0.252337i
\(760\) 7024.06 + 17364.2i 0.335249 + 0.828773i
\(761\) 11373.1 6566.28i 0.541755 0.312782i −0.204035 0.978964i \(-0.565406\pi\)
0.745790 + 0.666181i \(0.232072\pi\)
\(762\) −4827.43 + 4827.43i −0.229500 + 0.229500i
\(763\) −5903.38 + 12587.9i −0.280101 + 0.597264i
\(764\) 4686.93i 0.221946i
\(765\) 1121.60 8004.90i 0.0530086 0.378324i
\(766\) 10040.7 + 5797.03i 0.473612 + 0.273440i
\(767\) −26394.5 + 7072.37i −1.24257 + 0.332945i
\(768\) 2445.37 9126.24i 0.114895 0.428795i
\(769\) 5269.42 0.247100 0.123550 0.992338i \(-0.460572\pi\)
0.123550 + 0.992338i \(0.460572\pi\)
\(770\) −36091.6 1955.48i −1.68916 0.0915205i
\(771\) 10747.9 0.502046
\(772\) −5968.57 + 22275.0i −0.278256 + 1.03847i
\(773\) −13883.2 + 3719.98i −0.645980 + 0.173090i −0.566911 0.823779i \(-0.691862\pi\)
−0.0790693 + 0.996869i \(0.525195\pi\)
\(774\) 1565.61 + 903.905i 0.0727062 + 0.0419770i
\(775\) 8426.46 8150.97i 0.390564 0.377795i
\(776\) 35974.1i 1.66417i
\(777\) −9031.81 + 770.284i −0.417007 + 0.0355647i
\(778\) −39810.2 + 39810.2i −1.83453 + 1.83453i
\(779\) −29836.7 + 17226.2i −1.37229 + 0.792289i
\(780\) 7943.00 18734.3i 0.364622 0.859995i
\(781\) −14247.2 + 24676.8i −0.652757 + 1.13061i
\(782\) −18453.8 4944.69i −0.843872 0.226115i
\(783\) 1592.87 + 1592.87i 0.0727005 + 0.0727005i
\(784\) 1917.49 + 2305.58i 0.0873494 + 0.105028i
\(785\) 5146.10 6592.39i 0.233977 0.299736i
\(786\) −1547.81 2680.88i −0.0702397 0.121659i
\(787\) 6639.77 + 24780.0i 0.300740 + 1.12238i 0.936551 + 0.350532i \(0.113999\pi\)
−0.635811 + 0.771845i \(0.719334\pi\)
\(788\) 8871.85 + 33110.2i 0.401074 + 1.49683i
\(789\) 9041.18 + 15659.8i 0.407952 + 0.706594i
\(790\) −5499.80 + 7045.49i −0.247689 + 0.317301i
\(791\) −18516.4 15606.2i −0.832321 0.701508i
\(792\) −4933.87 4933.87i −0.221361 0.221361i
\(793\) −11116.8 2978.74i −0.497817 0.133390i
\(794\) 30989.2 53674.8i 1.38509 2.39905i
\(795\) 7433.69 17533.1i 0.331630 0.782181i
\(796\) −55628.0 + 32116.9i −2.47699 + 1.43009i
\(797\) −5875.40 + 5875.40i −0.261126 + 0.261126i −0.825511 0.564385i \(-0.809113\pi\)
0.564385 + 0.825511i \(0.309113\pi\)
\(798\) −11983.6 17194.3i −0.531599 0.762746i
\(799\) 33803.7i 1.49673i
\(800\) −415.756 + 25018.1i −0.0183740 + 1.10565i
\(801\) 7625.98 + 4402.86i 0.336393 + 0.194217i
\(802\) −8349.44 + 2237.23i −0.367617 + 0.0985027i
\(803\) 6296.41 23498.5i 0.276707 1.03268i
\(804\) −36971.4 −1.62174
\(805\) −9713.61 + 4927.72i −0.425292 + 0.215751i
\(806\) −20677.4 −0.903636
\(807\) 5072.54 18931.0i 0.221266 0.825777i
\(808\) −7445.51 + 1995.02i −0.324174 + 0.0868620i
\(809\) −1934.15 1116.68i −0.0840556 0.0485295i 0.457383 0.889270i \(-0.348787\pi\)
−0.541439 + 0.840740i \(0.682120\pi\)
\(810\) 568.141 4054.84i 0.0246450 0.175892i
\(811\) 7079.14i 0.306513i 0.988186 + 0.153257i \(0.0489761\pi\)
−0.988186 + 0.153257i \(0.951024\pi\)
\(812\) −17405.2 8162.57i −0.752221 0.352771i
\(813\) 3430.15 3430.15i 0.147971 0.147971i
\(814\) 24663.3 14239.4i 1.06198 0.613132i
\(815\) −12551.0 31027.5i −0.539439 1.33355i
\(816\) 1053.46 1824.65i 0.0451942 0.0782786i
\(817\) −3580.40 959.365i −0.153320 0.0410819i
\(818\) −38683.9 38683.9i −1.65349 1.65349i
\(819\) −1428.90 + 8001.32i −0.0609642 + 0.341378i
\(820\) 57008.5 7023.98i 2.42783 0.299132i
\(821\) −21268.7 36838.5i −0.904120 1.56598i −0.822094 0.569352i \(-0.807194\pi\)
−0.0820268 0.996630i \(-0.526139\pi\)
\(822\) 3077.18 + 11484.2i 0.130571 + 0.487296i
\(823\) 6978.20 + 26043.0i 0.295559 + 1.10304i 0.940773 + 0.339038i \(0.110102\pi\)
−0.645214 + 0.764002i \(0.723232\pi\)
\(824\) −6004.16 10399.5i −0.253841 0.439665i
\(825\) 12416.5 + 7446.47i 0.523985 + 0.314246i
\(826\) 30239.8 35878.8i 1.27382 1.51136i
\(827\) −18899.7 18899.7i −0.794688 0.794688i 0.187565 0.982252i \(-0.439941\pi\)
−0.982252 + 0.187565i \(0.939941\pi\)
\(828\) −5689.36 1524.46i −0.238791 0.0639838i
\(829\) 4710.37 8158.59i 0.197344 0.341809i −0.750323 0.661072i \(-0.770102\pi\)
0.947666 + 0.319263i \(0.103435\pi\)
\(830\) 46887.3 + 19879.4i 1.96082 + 0.831352i
\(831\) −5362.64 + 3096.12i −0.223860 + 0.129246i
\(832\) 28794.0 28794.0i 1.19982 1.19982i
\(833\) −11535.2 25022.5i −0.479798 1.04079i
\(834\) 18736.7i 0.777934i
\(835\) −2936.38 411.429i −0.121698 0.0170516i
\(836\) 34707.1 + 20038.1i 1.43585 + 0.828987i
\(837\) −2446.02 + 655.408i −0.101012 + 0.0270660i
\(838\) 4274.36 15952.1i 0.176200 0.657586i
\(839\) 9642.92 0.396795 0.198397 0.980122i \(-0.436426\pi\)
0.198397 + 0.980122i \(0.436426\pi\)
\(840\) 2571.87 + 12205.8i 0.105640 + 0.501357i
\(841\) 17428.1 0.714590
\(842\) −18615.9 + 69475.6i −0.761933 + 2.84357i
\(843\) −4948.39 + 1325.92i −0.202173 + 0.0541720i
\(844\) −14180.4 8187.07i −0.578330 0.333899i
\(845\) 1613.98 1217.28i 0.0657073 0.0495571i
\(846\) 17123.1i 0.695868i
\(847\) −2425.43 + 1690.41i −0.0983928 + 0.0685752i
\(848\) 3510.02 3510.02i 0.142140 0.142140i
\(849\) 8935.32 5158.81i 0.361201 0.208539i
\(850\) 12477.1 43650.7i 0.503485 1.76142i
\(851\) 4290.99 7432.22i 0.172848 0.299381i
\(852\) 26607.7 + 7129.52i 1.06991 + 0.286682i
\(853\) −897.027 897.027i −0.0360066 0.0360066i 0.688874 0.724881i \(-0.258105\pi\)
−0.724881 + 0.688874i \(0.758105\pi\)
\(854\) 18585.7 6718.67i 0.744720 0.269213i
\(855\) 1026.60 + 8332.18i 0.0410632 + 0.333280i
\(856\) 17077.4 + 29578.9i 0.681884 + 1.18106i
\(857\) 8415.12 + 31405.7i 0.335420 + 1.25181i 0.903413 + 0.428772i \(0.141054\pi\)
−0.567993 + 0.823034i \(0.692280\pi\)
\(858\) −6609.17 24665.7i −0.262976 0.981439i
\(859\) 6852.51 + 11868.9i 0.272182 + 0.471434i 0.969420 0.245406i \(-0.0789212\pi\)
−0.697238 + 0.716840i \(0.745588\pi\)
\(860\) 4871.39 + 3802.67i 0.193155 + 0.150779i
\(861\) −21576.7 + 7799.90i −0.854046 + 0.308734i
\(862\) −28922.4 28922.4i −1.14281 1.14281i
\(863\) 21779.0 + 5835.67i 0.859057 + 0.230184i 0.661350 0.750078i \(-0.269984\pi\)
0.197707 + 0.980261i \(0.436651\pi\)
\(864\) 2702.32 4680.56i 0.106406 0.184301i
\(865\) −17306.4 + 7000.67i −0.680272 + 0.275179i
\(866\) 21699.3 12528.1i 0.851471 0.491597i
\(867\) −3266.81 + 3266.81i −0.127966 + 0.127966i
\(868\) 17729.5 12356.6i 0.693293 0.483193i
\(869\) 6826.72i 0.266491i
\(870\) 7618.45 + 10101.2i 0.296885 + 0.393637i
\(871\) −41830.7 24150.9i −1.62730 0.939522i
\(872\) −14561.1 + 3901.63i −0.565483 + 0.151521i
\(873\) −4173.05 + 15574.0i −0.161783 + 0.603781i
\(874\) 19842.5 0.767942
\(875\) −11324.6 23273.9i −0.437533 0.899202i
\(876\) −23518.1 −0.907082
\(877\) −3432.61 + 12810.7i −0.132168 + 0.493257i −0.999993 0.00361194i \(-0.998850\pi\)
0.867826 + 0.496869i \(0.165517\pi\)
\(878\) 28135.3 7538.83i 1.08146 0.289776i
\(879\) −13585.9 7843.84i −0.521322 0.300985i
\(880\) 2272.43 + 3012.99i 0.0870495 + 0.115418i
\(881\) 8865.99i 0.339050i −0.985526 0.169525i \(-0.945777\pi\)
0.985526 0.169525i \(-0.0542233\pi\)
\(882\) −5843.10 12675.0i −0.223070 0.483889i
\(883\) 16117.3 16117.3i 0.614260 0.614260i −0.329793 0.944053i \(-0.606979\pi\)
0.944053 + 0.329793i \(0.106979\pi\)
\(884\) −42205.5 + 24367.4i −1.60580 + 0.927108i
\(885\) −17424.0 + 7048.25i −0.661811 + 0.267711i
\(886\) 18532.2 32098.7i 0.702711 1.21713i
\(887\) −7962.66 2133.59i −0.301420 0.0807654i 0.104939 0.994479i \(-0.466535\pi\)
−0.406359 + 0.913713i \(0.633202\pi\)
\(888\) −6949.64 6949.64i −0.262629 0.262629i
\(889\) 6007.56 7127.82i 0.226645 0.268908i
\(890\) 38985.9 + 30432.8i 1.46832 + 1.14619i
\(891\) −1563.65 2708.32i −0.0587927 0.101832i
\(892\) −10758.4 40150.9i −0.403832 1.50712i
\(893\) 9086.85 + 33912.6i 0.340515 + 1.27082i
\(894\) −9286.60 16084.9i −0.347417 0.601743i
\(895\) −1656.97 13448.4i −0.0618842 0.502270i
\(896\) −7078.94 + 39639.6i −0.263941 + 1.47798i
\(897\) −5441.30 5441.30i −0.202541 0.202541i
\(898\) 39398.2 + 10556.7i 1.46407 + 0.392296i
\(899\) 3912.49 6776.63i 0.145149 0.251405i
\(900\) 3846.72 13457.6i 0.142471 0.498430i
\(901\) −39499.3 + 22804.9i −1.46050 + 0.843222i
\(902\) 50969.7 50969.7i 1.88149 1.88149i
\(903\) −2234.88 1048.10i −0.0823613 0.0386252i
\(904\) 26256.0i 0.965998i
\(905\) −27393.1 + 20660.2i −1.00616 + 0.758859i
\(906\) 35363.2 + 20416.9i 1.29676 + 0.748683i
\(907\) 47960.8 12851.1i 1.75580 0.470466i 0.769952 0.638101i \(-0.220280\pi\)
0.985849 + 0.167636i \(0.0536133\pi\)
\(908\) −11533.3 + 43042.8i −0.421526 + 1.57316i
\(909\) −3454.76 −0.126058
\(910\) −14183.6 + 43391.3i −0.516682 + 1.58067i
\(911\) 13361.9 0.485949 0.242974 0.970033i \(-0.421877\pi\)
0.242974 + 0.970033i \(0.421877\pi\)
\(912\) −566.365 + 2113.70i −0.0205638 + 0.0767453i
\(913\) 37572.6 10067.5i 1.36196 0.364936i
\(914\) 12195.6 + 7041.10i 0.441349 + 0.254813i
\(915\) −7839.74 1098.46i −0.283250 0.0396874i
\(916\) 17955.6i 0.647675i
\(917\) 2416.85 + 3467.73i 0.0870352 + 0.124879i
\(918\) −6934.01 + 6934.01i −0.249299 + 0.249299i
\(919\) −20340.6 + 11743.7i −0.730115 + 0.421532i −0.818464 0.574557i \(-0.805174\pi\)
0.0883490 + 0.996090i \(0.471841\pi\)
\(920\) −10872.8 4609.86i −0.389636 0.165198i
\(921\) −14462.2 + 25049.3i −0.517423 + 0.896203i
\(922\) −4614.66 1236.49i −0.164833 0.0441668i
\(923\) 25447.6 + 25447.6i 0.907496 + 0.907496i
\(924\) 20406.9 + 17199.6i 0.726557 + 0.612366i
\(925\) 17489.4 + 10488.8i 0.621672 + 0.372831i
\(926\) 15291.3 + 26485.2i 0.542659 + 0.939913i
\(927\) −1392.98 5198.68i −0.0493544 0.184193i
\(928\) 4322.46 + 16131.6i 0.152901 + 0.570633i
\(929\) −7462.40 12925.3i −0.263545 0.456474i 0.703636 0.710560i \(-0.251558\pi\)
−0.967181 + 0.254087i \(0.918225\pi\)
\(930\) −14116.0 + 1739.22i −0.497723 + 0.0613240i
\(931\) 18298.7 + 22002.3i 0.644164 + 0.774539i
\(932\) 49732.2 + 49732.2i 1.74789 + 1.74789i
\(933\) 3927.74 + 1052.43i 0.137822 + 0.0369294i
\(934\) −22871.4 + 39614.5i −0.801259 + 1.38782i
\(935\) −13003.0 32144.9i −0.454808 1.12433i
\(936\) −7631.99 + 4406.33i −0.266516 + 0.153873i
\(937\) 13442.5 13442.5i 0.468672 0.468672i −0.432812 0.901484i \(-0.642479\pi\)
0.901484 + 0.432812i \(0.142479\pi\)
\(938\) 82642.6 7048.22i 2.87673 0.245344i
\(939\) 17744.5i 0.616689i
\(940\) 8122.12 57967.8i 0.281824 2.01139i
\(941\) −3195.47 1844.90i −0.110701 0.0639130i 0.443627 0.896211i \(-0.353691\pi\)
−0.554328 + 0.832298i \(0.687025\pi\)
\(942\) −9800.19 + 2625.95i −0.338968 + 0.0908261i
\(943\) 5622.00 20981.6i 0.194144 0.724554i
\(944\) −4899.21 −0.168915
\(945\) −302.467 + 5582.51i −0.0104119 + 0.192168i
\(946\) 7755.23 0.266537
\(947\) −12206.7 + 45555.9i −0.418863 + 1.56322i 0.358106 + 0.933681i \(0.383423\pi\)
−0.776969 + 0.629538i \(0.783244\pi\)
\(948\) 6374.73 1708.10i 0.218398 0.0585196i
\(949\) −26609.2 15362.8i −0.910191 0.525499i
\(950\) −783.471 + 47145.3i −0.0267570 + 1.61010i
\(951\) 17494.5i 0.596528i
\(952\) 12684.8 27048.0i 0.431844 0.920829i
\(953\) −24250.5 + 24250.5i −0.824294 + 0.824294i −0.986721 0.162426i \(-0.948068\pi\)
0.162426 + 0.986721i \(0.448068\pi\)
\(954\) −20008.2 + 11551.7i −0.679023 + 0.392034i
\(955\) 1644.08 3877.73i 0.0557081 0.131393i
\(956\) 24004.1 41576.3i 0.812079 1.40656i
\(957\) 9334.29 + 2501.11i 0.315292 + 0.0844823i
\(958\) −7558.02 7558.02i −0.254894 0.254894i
\(959\) −5519.01 15267.1i −0.185837 0.514079i
\(960\) 17235.1 22078.9i 0.579438 0.742286i
\(961\) −10497.3 18181.9i −0.352365 0.610314i
\(962\) −9309.38 34743.1i −0.312003 1.16441i
\(963\) 3962.00 + 14786.4i 0.132579 + 0.494792i
\(964\) 8025.93 + 13901.3i 0.268151 + 0.464451i
\(965\) −12751.7 + 16335.6i −0.425381 + 0.544933i
\(966\) 13008.1 + 2323.02i 0.433260 + 0.0773726i
\(967\) 9621.23 + 9621.23i 0.319956 + 0.319956i 0.848750 0.528794i \(-0.177356\pi\)
−0.528794 + 0.848750i \(0.677356\pi\)
\(968\) −3096.23 829.632i −0.102806 0.0275469i
\(969\) 10053.2 17412.7i 0.333287 0.577271i
\(970\) −35348.8 + 83373.5i −1.17008 + 2.75975i
\(971\) 12347.0 7128.54i 0.408068 0.235598i −0.281891 0.959446i \(-0.590962\pi\)
0.689959 + 0.723848i \(0.257628\pi\)
\(972\) −2137.77 + 2137.77i −0.0705442 + 0.0705442i
\(973\) −2174.03 25491.1i −0.0716301 0.839884i
\(974\) 57433.5i 1.88941i
\(975\) 13143.3 12713.6i 0.431714 0.417600i
\(976\) −1787.00 1031.72i −0.0586070 0.0338367i
\(977\) 31938.1 8557.79i 1.04584 0.280233i 0.305311 0.952253i \(-0.401240\pi\)
0.740534 + 0.672019i \(0.234573\pi\)
\(978\) −10509.2 + 39221.0i −0.343608 + 1.28236i
\(979\) 37775.3 1.23320
\(980\) −13768.8 45681.1i −0.448804 1.48901i
\(981\) −6756.43 −0.219894
\(982\) 6858.54 25596.4i 0.222877 0.831787i
\(983\) −46820.0 + 12545.4i −1.51915 + 0.407056i −0.919463 0.393177i \(-0.871376\pi\)
−0.599689 + 0.800233i \(0.704709\pi\)
\(984\) −21543.4 12438.1i −0.697946 0.402959i
\(985\) −4274.29 + 30505.8i −0.138264 + 0.986796i
\(986\) 30301.7i 0.978705i
\(987\) 1986.80 + 23295.9i 0.0640736 + 0.751282i
\(988\) 35791.2 35791.2i 1.15250 1.15250i
\(989\) 2023.92 1168.51i 0.0650726 0.0375697i
\(990\) −6586.62 16282.8i −0.211451 0.522730i
\(991\) 5630.41 9752.16i 0.180480 0.312601i −0.761564 0.648090i \(-0.775568\pi\)
0.942044 + 0.335489i \(0.108901\pi\)
\(992\) −18134.2 4859.05i −0.580406 0.155519i
\(993\) 7459.94 + 7459.94i 0.238403 + 0.238403i
\(994\) −60835.7 10864.2i −1.94124 0.346671i
\(995\) −57289.8 + 7058.63i −1.82533 + 0.224898i
\(996\) −18801.9 32565.9i −0.598155 1.03603i
\(997\) −696.688 2600.07i −0.0221307 0.0825930i 0.953977 0.299879i \(-0.0969463\pi\)
−0.976108 + 0.217286i \(0.930280\pi\)
\(998\) −14737.9 55002.7i −0.467456 1.74457i
\(999\) −2202.49 3814.82i −0.0697535 0.120817i
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 105.4.u.a.52.4 96
5.3 odd 4 inner 105.4.u.a.73.21 yes 96
7.5 odd 6 inner 105.4.u.a.82.21 yes 96
35.33 even 12 inner 105.4.u.a.103.4 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.u.a.52.4 96 1.1 even 1 trivial
105.4.u.a.73.21 yes 96 5.3 odd 4 inner
105.4.u.a.82.21 yes 96 7.5 odd 6 inner
105.4.u.a.103.4 yes 96 35.33 even 12 inner