Properties

Label 225.4.h.d.136.4
Level $225$
Weight $4$
Character 225.136
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,4,Mod(46,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.46");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), 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: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 136.4
Character \(\chi\) \(=\) 225.136
Dual form 225.4.h.d.91.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.68030 + 1.94735i) q^{2} +(0.919680 - 2.83048i) q^{4} +(-2.31093 + 10.9389i) q^{5} +10.7752 q^{7} +(-5.14333 - 15.8295i) q^{8} +O(q^{10})\) \(q+(-2.68030 + 1.94735i) q^{2} +(0.919680 - 2.83048i) q^{4} +(-2.31093 + 10.9389i) q^{5} +10.7752 q^{7} +(-5.14333 - 15.8295i) q^{8} +(-15.1079 - 33.8197i) q^{10} +(-43.0382 + 31.2691i) q^{11} +(-29.8370 - 21.6778i) q^{13} +(-28.8808 + 20.9831i) q^{14} +(63.8733 + 46.4067i) q^{16} +(21.1745 + 65.1683i) q^{17} +(-1.49479 - 4.60048i) q^{19} +(28.8371 + 16.6014i) q^{20} +(54.4633 - 167.621i) q^{22} +(-67.0563 + 48.7193i) q^{23} +(-114.319 - 50.5582i) q^{25} +122.186 q^{26} +(9.90977 - 30.4991i) q^{28} +(51.1534 - 157.434i) q^{29} +(-97.3566 - 299.633i) q^{31} -128.416 q^{32} +(-183.659 - 133.436i) q^{34} +(-24.9009 + 117.869i) q^{35} +(202.266 + 146.955i) q^{37} +(12.9652 + 9.41977i) q^{38} +(185.044 - 19.6814i) q^{40} +(-292.377 - 212.424i) q^{41} +180.805 q^{43} +(48.9253 + 150.576i) q^{44} +(84.8573 - 261.164i) q^{46} +(68.6994 - 211.435i) q^{47} -226.894 q^{49} +(404.863 - 87.1085i) q^{50} +(-88.7992 + 64.5164i) q^{52} +(162.370 - 499.723i) q^{53} +(-242.591 - 543.051i) q^{55} +(-55.4206 - 170.567i) q^{56} +(169.473 + 521.583i) q^{58} +(-34.9106 - 25.3641i) q^{59} +(502.015 - 364.735i) q^{61} +(844.434 + 613.517i) q^{62} +(-166.794 + 121.183i) q^{64} +(306.083 - 276.288i) q^{65} +(71.8608 + 221.165i) q^{67} +203.932 q^{68} +(-162.791 - 364.415i) q^{70} +(195.891 - 602.890i) q^{71} +(-770.064 + 559.484i) q^{73} -828.305 q^{74} -14.3963 q^{76} +(-463.747 + 336.932i) q^{77} +(-281.459 + 866.243i) q^{79} +(-655.245 + 591.461i) q^{80} +1197.32 q^{82} +(61.3942 + 188.952i) q^{83} +(-761.802 + 81.0258i) q^{85} +(-484.612 + 352.091i) q^{86} +(716.334 + 520.447i) q^{88} +(-703.370 + 511.028i) q^{89} +(-321.500 - 233.584i) q^{91} +(76.2288 + 234.608i) q^{92} +(227.603 + 700.490i) q^{94} +(53.7785 - 5.71992i) q^{95} +(-68.4303 + 210.607i) q^{97} +(608.144 - 441.842i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68030 + 1.94735i −0.947627 + 0.688492i −0.950245 0.311505i \(-0.899167\pi\)
0.00261710 + 0.999997i \(0.499167\pi\)
\(3\) 0 0
\(4\) 0.919680 2.83048i 0.114960 0.353811i
\(5\) −2.31093 + 10.9389i −0.206696 + 0.978405i
\(6\) 0 0
\(7\) 10.7752 0.581808 0.290904 0.956752i \(-0.406044\pi\)
0.290904 + 0.956752i \(0.406044\pi\)
\(8\) −5.14333 15.8295i −0.227305 0.699573i
\(9\) 0 0
\(10\) −15.1079 33.8197i −0.477753 1.06947i
\(11\) −43.0382 + 31.2691i −1.17968 + 0.857089i −0.992136 0.125167i \(-0.960053\pi\)
−0.187546 + 0.982256i \(0.560053\pi\)
\(12\) 0 0
\(13\) −29.8370 21.6778i −0.636560 0.462488i 0.222107 0.975022i \(-0.428707\pi\)
−0.858667 + 0.512534i \(0.828707\pi\)
\(14\) −28.8808 + 20.9831i −0.551337 + 0.400570i
\(15\) 0 0
\(16\) 63.8733 + 46.4067i 0.998020 + 0.725104i
\(17\) 21.1745 + 65.1683i 0.302092 + 0.929743i 0.980746 + 0.195286i \(0.0625634\pi\)
−0.678655 + 0.734458i \(0.737437\pi\)
\(18\) 0 0
\(19\) −1.49479 4.60048i −0.0180488 0.0555485i 0.941626 0.336659i \(-0.109297\pi\)
−0.959675 + 0.281111i \(0.909297\pi\)
\(20\) 28.8371 + 16.6014i 0.322408 + 0.185609i
\(21\) 0 0
\(22\) 54.4633 167.621i 0.527800 1.62440i
\(23\) −67.0563 + 48.7193i −0.607922 + 0.441681i −0.848682 0.528903i \(-0.822603\pi\)
0.240760 + 0.970585i \(0.422603\pi\)
\(24\) 0 0
\(25\) −114.319 50.5582i −0.914553 0.404465i
\(26\) 122.186 0.921641
\(27\) 0 0
\(28\) 9.90977 30.4991i 0.0668847 0.205850i
\(29\) 51.1534 157.434i 0.327550 1.00809i −0.642727 0.766096i \(-0.722197\pi\)
0.970276 0.241999i \(-0.0778031\pi\)
\(30\) 0 0
\(31\) −97.3566 299.633i −0.564057 1.73599i −0.670737 0.741695i \(-0.734022\pi\)
0.106680 0.994293i \(-0.465978\pi\)
\(32\) −128.416 −0.709405
\(33\) 0 0
\(34\) −183.659 133.436i −0.926391 0.673062i
\(35\) −24.9009 + 117.869i −0.120258 + 0.569244i
\(36\) 0 0
\(37\) 202.266 + 146.955i 0.898712 + 0.652952i 0.938135 0.346270i \(-0.112552\pi\)
−0.0394231 + 0.999223i \(0.512552\pi\)
\(38\) 12.9652 + 9.41977i 0.0553483 + 0.0402129i
\(39\) 0 0
\(40\) 185.044 19.6814i 0.731449 0.0777974i
\(41\) −292.377 212.424i −1.11370 0.809148i −0.130454 0.991454i \(-0.541644\pi\)
−0.983242 + 0.182307i \(0.941644\pi\)
\(42\) 0 0
\(43\) 180.805 0.641223 0.320611 0.947211i \(-0.396112\pi\)
0.320611 + 0.947211i \(0.396112\pi\)
\(44\) 48.9253 + 150.576i 0.167631 + 0.515915i
\(45\) 0 0
\(46\) 84.8573 261.164i 0.271990 0.837099i
\(47\) 68.6994 211.435i 0.213209 0.656191i −0.786067 0.618142i \(-0.787886\pi\)
0.999276 0.0380490i \(-0.0121143\pi\)
\(48\) 0 0
\(49\) −226.894 −0.661499
\(50\) 404.863 87.1085i 1.14513 0.246380i
\(51\) 0 0
\(52\) −88.7992 + 64.5164i −0.236812 + 0.172054i
\(53\) 162.370 499.723i 0.420815 1.29514i −0.486130 0.873886i \(-0.661592\pi\)
0.906945 0.421249i \(-0.138408\pi\)
\(54\) 0 0
\(55\) −242.591 543.051i −0.594745 1.33136i
\(56\) −55.4206 170.567i −0.132248 0.407017i
\(57\) 0 0
\(58\) 169.473 + 521.583i 0.383670 + 1.18081i
\(59\) −34.9106 25.3641i −0.0770335 0.0559681i 0.548602 0.836084i \(-0.315160\pi\)
−0.625635 + 0.780116i \(0.715160\pi\)
\(60\) 0 0
\(61\) 502.015 364.735i 1.05371 0.765566i 0.0807964 0.996731i \(-0.474254\pi\)
0.972915 + 0.231165i \(0.0742536\pi\)
\(62\) 844.434 + 613.517i 1.72973 + 1.25672i
\(63\) 0 0
\(64\) −166.794 + 121.183i −0.325769 + 0.236685i
\(65\) 306.083 276.288i 0.584075 0.527219i
\(66\) 0 0
\(67\) 71.8608 + 221.165i 0.131033 + 0.403277i 0.994952 0.100353i \(-0.0319973\pi\)
−0.863919 + 0.503631i \(0.831997\pi\)
\(68\) 203.932 0.363681
\(69\) 0 0
\(70\) −162.791 364.415i −0.277960 0.622228i
\(71\) 195.891 602.890i 0.327436 1.00774i −0.642893 0.765956i \(-0.722266\pi\)
0.970329 0.241788i \(-0.0777339\pi\)
\(72\) 0 0
\(73\) −770.064 + 559.484i −1.23465 + 0.897022i −0.997230 0.0743856i \(-0.976300\pi\)
−0.237416 + 0.971408i \(0.576300\pi\)
\(74\) −828.305 −1.30120
\(75\) 0 0
\(76\) −14.3963 −0.0217286
\(77\) −463.747 + 336.932i −0.686349 + 0.498661i
\(78\) 0 0
\(79\) −281.459 + 866.243i −0.400844 + 1.23367i 0.523473 + 0.852043i \(0.324636\pi\)
−0.924316 + 0.381627i \(0.875364\pi\)
\(80\) −655.245 + 591.461i −0.915733 + 0.826592i
\(81\) 0 0
\(82\) 1197.32 1.61246
\(83\) 61.3942 + 188.952i 0.0811915 + 0.249882i 0.983410 0.181398i \(-0.0580622\pi\)
−0.902218 + 0.431280i \(0.858062\pi\)
\(84\) 0 0
\(85\) −761.802 + 81.0258i −0.972107 + 0.103394i
\(86\) −484.612 + 352.091i −0.607640 + 0.441476i
\(87\) 0 0
\(88\) 716.334 + 520.447i 0.867744 + 0.630453i
\(89\) −703.370 + 511.028i −0.837719 + 0.608639i −0.921733 0.387826i \(-0.873226\pi\)
0.0840133 + 0.996465i \(0.473226\pi\)
\(90\) 0 0
\(91\) −321.500 233.584i −0.370356 0.269079i
\(92\) 76.2288 + 234.608i 0.0863848 + 0.265865i
\(93\) 0 0
\(94\) 227.603 + 700.490i 0.249739 + 0.768617i
\(95\) 53.7785 5.71992i 0.0580796 0.00617738i
\(96\) 0 0
\(97\) −68.4303 + 210.607i −0.0716293 + 0.220452i −0.980462 0.196708i \(-0.936975\pi\)
0.908833 + 0.417161i \(0.136975\pi\)
\(98\) 608.144 441.842i 0.626855 0.455437i
\(99\) 0 0
\(100\) −248.241 + 277.081i −0.248241 + 0.277081i
\(101\) −800.883 −0.789019 −0.394509 0.918892i \(-0.629085\pi\)
−0.394509 + 0.918892i \(0.629085\pi\)
\(102\) 0 0
\(103\) −418.585 + 1288.27i −0.400431 + 1.23240i 0.524219 + 0.851584i \(0.324357\pi\)
−0.924650 + 0.380817i \(0.875643\pi\)
\(104\) −189.689 + 583.801i −0.178851 + 0.550446i
\(105\) 0 0
\(106\) 537.935 + 1655.59i 0.492914 + 1.51703i
\(107\) −1010.72 −0.913177 −0.456589 0.889678i \(-0.650929\pi\)
−0.456589 + 0.889678i \(0.650929\pi\)
\(108\) 0 0
\(109\) −642.415 466.742i −0.564515 0.410144i 0.268593 0.963254i \(-0.413441\pi\)
−0.833109 + 0.553109i \(0.813441\pi\)
\(110\) 1707.73 + 983.129i 1.48023 + 0.852160i
\(111\) 0 0
\(112\) 688.250 + 500.043i 0.580656 + 0.421871i
\(113\) −437.943 318.184i −0.364586 0.264887i 0.390376 0.920655i \(-0.372345\pi\)
−0.754962 + 0.655768i \(0.772345\pi\)
\(114\) 0 0
\(115\) −377.973 846.110i −0.306488 0.686088i
\(116\) −398.570 289.578i −0.319019 0.231781i
\(117\) 0 0
\(118\) 142.963 0.111533
\(119\) 228.160 + 702.204i 0.175759 + 0.540932i
\(120\) 0 0
\(121\) 463.229 1425.67i 0.348031 1.07113i
\(122\) −635.281 + 1955.19i −0.471440 + 1.45094i
\(123\) 0 0
\(124\) −937.643 −0.679055
\(125\) 817.235 1133.69i 0.584766 0.811202i
\(126\) 0 0
\(127\) 1063.06 772.361i 0.742769 0.539654i −0.150808 0.988563i \(-0.548187\pi\)
0.893577 + 0.448910i \(0.148187\pi\)
\(128\) 528.533 1626.66i 0.364970 1.12326i
\(129\) 0 0
\(130\) −282.364 + 1336.58i −0.190500 + 0.901738i
\(131\) −103.644 318.984i −0.0691255 0.212746i 0.910526 0.413451i \(-0.135677\pi\)
−0.979652 + 0.200705i \(0.935677\pi\)
\(132\) 0 0
\(133\) −16.1067 49.5713i −0.0105009 0.0323186i
\(134\) −623.293 452.849i −0.401823 0.291942i
\(135\) 0 0
\(136\) 922.677 670.364i 0.581756 0.422671i
\(137\) 973.264 + 707.118i 0.606946 + 0.440972i 0.848337 0.529456i \(-0.177604\pi\)
−0.241392 + 0.970428i \(0.577604\pi\)
\(138\) 0 0
\(139\) −1583.61 + 1150.56i −0.966334 + 0.702083i −0.954613 0.297848i \(-0.903731\pi\)
−0.0117211 + 0.999931i \(0.503731\pi\)
\(140\) 310.726 + 178.884i 0.187580 + 0.107989i
\(141\) 0 0
\(142\) 648.991 + 1997.39i 0.383536 + 1.18040i
\(143\) 1961.97 1.14733
\(144\) 0 0
\(145\) 1603.94 + 923.381i 0.918622 + 0.528846i
\(146\) 974.487 2999.16i 0.552391 1.70009i
\(147\) 0 0
\(148\) 601.974 437.359i 0.334337 0.242910i
\(149\) −2620.38 −1.44074 −0.720369 0.693591i \(-0.756028\pi\)
−0.720369 + 0.693591i \(0.756028\pi\)
\(150\) 0 0
\(151\) −562.774 −0.303298 −0.151649 0.988434i \(-0.548458\pi\)
−0.151649 + 0.988434i \(0.548458\pi\)
\(152\) −65.1353 + 47.3235i −0.0347577 + 0.0252529i
\(153\) 0 0
\(154\) 586.855 1806.15i 0.307078 0.945090i
\(155\) 3502.64 372.543i 1.81509 0.193054i
\(156\) 0 0
\(157\) −2954.02 −1.50163 −0.750817 0.660510i \(-0.770340\pi\)
−0.750817 + 0.660510i \(0.770340\pi\)
\(158\) −932.482 2869.89i −0.469521 1.44504i
\(159\) 0 0
\(160\) 296.761 1404.73i 0.146631 0.694085i
\(161\) −722.548 + 524.962i −0.353694 + 0.256974i
\(162\) 0 0
\(163\) −620.436 450.773i −0.298137 0.216609i 0.428653 0.903469i \(-0.358988\pi\)
−0.726789 + 0.686860i \(0.758988\pi\)
\(164\) −870.156 + 632.205i −0.414316 + 0.301018i
\(165\) 0 0
\(166\) −532.510 386.891i −0.248981 0.180895i
\(167\) 605.341 + 1863.05i 0.280495 + 0.863276i 0.987713 + 0.156280i \(0.0499502\pi\)
−0.707217 + 0.706996i \(0.750050\pi\)
\(168\) 0 0
\(169\) −258.594 795.871i −0.117703 0.362254i
\(170\) 1884.07 1700.67i 0.850009 0.767266i
\(171\) 0 0
\(172\) 166.283 511.767i 0.0737150 0.226871i
\(173\) 1944.34 1412.65i 0.854483 0.620818i −0.0718957 0.997412i \(-0.522905\pi\)
0.926378 + 0.376594i \(0.122905\pi\)
\(174\) 0 0
\(175\) −1231.82 544.776i −0.532095 0.235321i
\(176\) −4200.08 −1.79883
\(177\) 0 0
\(178\) 890.089 2739.41i 0.374803 1.15353i
\(179\) −104.154 + 320.554i −0.0434908 + 0.133851i −0.970444 0.241325i \(-0.922418\pi\)
0.926953 + 0.375176i \(0.122418\pi\)
\(180\) 0 0
\(181\) −324.908 999.965i −0.133427 0.410645i 0.861915 0.507052i \(-0.169265\pi\)
−0.995342 + 0.0964070i \(0.969265\pi\)
\(182\) 1316.58 0.536218
\(183\) 0 0
\(184\) 1116.10 + 810.891i 0.447172 + 0.324890i
\(185\) −2074.95 + 1872.97i −0.824612 + 0.744341i
\(186\) 0 0
\(187\) −2949.06 2142.62i −1.15325 0.837882i
\(188\) −535.282 388.905i −0.207657 0.150871i
\(189\) 0 0
\(190\) −133.004 + 120.057i −0.0507848 + 0.0458412i
\(191\) 2116.22 + 1537.53i 0.801699 + 0.582468i 0.911412 0.411495i \(-0.134993\pi\)
−0.109713 + 0.993963i \(0.534993\pi\)
\(192\) 0 0
\(193\) 1585.88 0.591472 0.295736 0.955270i \(-0.404435\pi\)
0.295736 + 0.955270i \(0.404435\pi\)
\(194\) −226.711 697.746i −0.0839017 0.258223i
\(195\) 0 0
\(196\) −208.670 + 642.221i −0.0760460 + 0.234045i
\(197\) −639.374 + 1967.79i −0.231236 + 0.711672i 0.766362 + 0.642409i \(0.222065\pi\)
−0.997598 + 0.0692631i \(0.977935\pi\)
\(198\) 0 0
\(199\) 5111.28 1.82075 0.910374 0.413786i \(-0.135794\pi\)
0.910374 + 0.413786i \(0.135794\pi\)
\(200\) −212.331 + 2069.66i −0.0750704 + 0.731734i
\(201\) 0 0
\(202\) 2146.60 1559.60i 0.747696 0.543233i
\(203\) 551.190 1696.39i 0.190571 0.586518i
\(204\) 0 0
\(205\) 2999.35 2707.38i 1.02187 0.922398i
\(206\) −1386.78 4268.08i −0.469038 1.44355i
\(207\) 0 0
\(208\) −899.789 2769.27i −0.299948 0.923145i
\(209\) 208.186 + 151.256i 0.0689019 + 0.0500602i
\(210\) 0 0
\(211\) −4179.26 + 3036.41i −1.36357 + 0.990688i −0.365356 + 0.930868i \(0.619053\pi\)
−0.998209 + 0.0598201i \(0.980947\pi\)
\(212\) −1265.13 919.170i −0.409856 0.297778i
\(213\) 0 0
\(214\) 2709.03 1968.22i 0.865352 0.628715i
\(215\) −417.829 + 1977.81i −0.132538 + 0.627375i
\(216\) 0 0
\(217\) −1049.04 3228.61i −0.328173 1.01001i
\(218\) 2630.77 0.817331
\(219\) 0 0
\(220\) −1760.20 + 187.216i −0.539423 + 0.0573733i
\(221\) 780.925 2403.44i 0.237695 0.731551i
\(222\) 0 0
\(223\) −3917.06 + 2845.91i −1.17626 + 0.854602i −0.991745 0.128228i \(-0.959071\pi\)
−0.184514 + 0.982830i \(0.559071\pi\)
\(224\) −1383.71 −0.412737
\(225\) 0 0
\(226\) 1793.43 0.527865
\(227\) −418.579 + 304.115i −0.122388 + 0.0889200i −0.647295 0.762239i \(-0.724100\pi\)
0.524907 + 0.851159i \(0.324100\pi\)
\(228\) 0 0
\(229\) 841.230 2589.04i 0.242751 0.747111i −0.753247 0.657738i \(-0.771514\pi\)
0.995998 0.0893736i \(-0.0284865\pi\)
\(230\) 2660.75 + 1531.78i 0.762802 + 0.439141i
\(231\) 0 0
\(232\) −2755.20 −0.779690
\(233\) 1792.83 + 5517.77i 0.504087 + 1.55142i 0.802300 + 0.596922i \(0.203610\pi\)
−0.298212 + 0.954500i \(0.596390\pi\)
\(234\) 0 0
\(235\) 2154.11 + 1240.11i 0.597951 + 0.344237i
\(236\) −103.899 + 75.4872i −0.0286579 + 0.0208212i
\(237\) 0 0
\(238\) −1978.97 1437.81i −0.538982 0.391593i
\(239\) −3885.12 + 2822.71i −1.05150 + 0.763957i −0.972497 0.232917i \(-0.925173\pi\)
−0.0790005 + 0.996875i \(0.525173\pi\)
\(240\) 0 0
\(241\) −891.648 647.821i −0.238324 0.173153i 0.462212 0.886769i \(-0.347056\pi\)
−0.700536 + 0.713617i \(0.747056\pi\)
\(242\) 1534.69 + 4723.29i 0.407660 + 1.25465i
\(243\) 0 0
\(244\) −570.684 1756.38i −0.149731 0.460824i
\(245\) 524.338 2481.97i 0.136729 0.647214i
\(246\) 0 0
\(247\) −55.1285 + 169.668i −0.0142014 + 0.0437074i
\(248\) −4242.31 + 3082.22i −1.08624 + 0.789198i
\(249\) 0 0
\(250\) 17.2584 + 4630.06i 0.00436607 + 1.17132i
\(251\) −5994.06 −1.50734 −0.753668 0.657255i \(-0.771717\pi\)
−0.753668 + 0.657255i \(0.771717\pi\)
\(252\) 0 0
\(253\) 1362.58 4193.58i 0.338595 1.04209i
\(254\) −1345.27 + 4140.31i −0.332322 + 1.02278i
\(255\) 0 0
\(256\) 1241.37 + 3820.54i 0.303068 + 0.932748i
\(257\) 4844.17 1.17576 0.587881 0.808948i \(-0.299962\pi\)
0.587881 + 0.808948i \(0.299962\pi\)
\(258\) 0 0
\(259\) 2179.46 + 1583.47i 0.522878 + 0.379893i
\(260\) −500.529 1120.46i −0.119390 0.267261i
\(261\) 0 0
\(262\) 898.970 + 653.140i 0.211979 + 0.154012i
\(263\) −6370.39 4628.36i −1.49359 1.08516i −0.972847 0.231449i \(-0.925653\pi\)
−0.520748 0.853711i \(-0.674347\pi\)
\(264\) 0 0
\(265\) 5091.19 + 2930.97i 1.18019 + 0.679427i
\(266\) 139.703 + 101.500i 0.0322021 + 0.0233962i
\(267\) 0 0
\(268\) 692.093 0.157747
\(269\) −276.633 851.389i −0.0627012 0.192974i 0.914799 0.403910i \(-0.132349\pi\)
−0.977500 + 0.210935i \(0.932349\pi\)
\(270\) 0 0
\(271\) −288.006 + 886.391i −0.0645576 + 0.198688i −0.978133 0.207983i \(-0.933310\pi\)
0.913575 + 0.406670i \(0.133310\pi\)
\(272\) −1671.76 + 5145.15i −0.372667 + 1.14695i
\(273\) 0 0
\(274\) −3985.64 −0.878764
\(275\) 6501.00 1398.72i 1.42554 0.306713i
\(276\) 0 0
\(277\) −6357.04 + 4618.66i −1.37891 + 1.00184i −0.381928 + 0.924192i \(0.624740\pi\)
−0.996981 + 0.0776436i \(0.975260\pi\)
\(278\) 2004.01 6167.70i 0.432347 1.33063i
\(279\) 0 0
\(280\) 1993.89 212.071i 0.425563 0.0452631i
\(281\) −357.780 1101.13i −0.0759550 0.233765i 0.905869 0.423557i \(-0.139219\pi\)
−0.981824 + 0.189792i \(0.939219\pi\)
\(282\) 0 0
\(283\) −1284.25 3952.50i −0.269754 0.830219i −0.990560 0.137081i \(-0.956228\pi\)
0.720805 0.693137i \(-0.243772\pi\)
\(284\) −1526.31 1108.93i −0.318909 0.231701i
\(285\) 0 0
\(286\) −5258.67 + 3820.65i −1.08724 + 0.789928i
\(287\) −3150.43 2288.92i −0.647957 0.470769i
\(288\) 0 0
\(289\) 176.152 127.982i 0.0358542 0.0260496i
\(290\) −6097.18 + 648.500i −1.23462 + 0.131315i
\(291\) 0 0
\(292\) 875.398 + 2694.20i 0.175441 + 0.539952i
\(293\) 5554.75 1.10755 0.553775 0.832666i \(-0.313187\pi\)
0.553775 + 0.832666i \(0.313187\pi\)
\(294\) 0 0
\(295\) 358.131 323.269i 0.0706821 0.0638016i
\(296\) 1285.91 3957.61i 0.252506 0.777134i
\(297\) 0 0
\(298\) 7023.40 5102.80i 1.36528 0.991937i
\(299\) 3056.88 0.591251
\(300\) 0 0
\(301\) 1948.22 0.373068
\(302\) 1508.40 1095.92i 0.287413 0.208818i
\(303\) 0 0
\(304\) 118.016 363.216i 0.0222654 0.0685258i
\(305\) 2829.68 + 6334.37i 0.531236 + 1.18920i
\(306\) 0 0
\(307\) −4614.58 −0.857877 −0.428938 0.903334i \(-0.641112\pi\)
−0.428938 + 0.903334i \(0.641112\pi\)
\(308\) 527.181 + 1622.50i 0.0975290 + 0.300164i
\(309\) 0 0
\(310\) −8662.64 + 7819.38i −1.58711 + 1.43262i
\(311\) −3714.99 + 2699.10i −0.677356 + 0.492128i −0.872480 0.488651i \(-0.837489\pi\)
0.195123 + 0.980779i \(0.437489\pi\)
\(312\) 0 0
\(313\) 4066.76 + 2954.67i 0.734399 + 0.533572i 0.890952 0.454098i \(-0.150038\pi\)
−0.156553 + 0.987670i \(0.550038\pi\)
\(314\) 7917.65 5752.51i 1.42299 1.03386i
\(315\) 0 0
\(316\) 2193.03 + 1593.33i 0.390405 + 0.283645i
\(317\) −2340.29 7202.67i −0.414649 1.27616i −0.912564 0.408933i \(-0.865901\pi\)
0.497915 0.867226i \(-0.334099\pi\)
\(318\) 0 0
\(319\) 2721.26 + 8375.19i 0.477622 + 1.46997i
\(320\) −940.157 2104.59i −0.164239 0.367656i
\(321\) 0 0
\(322\) 914.358 2814.10i 0.158246 0.487031i
\(323\) 268.154 194.825i 0.0461935 0.0335615i
\(324\) 0 0
\(325\) 2314.95 + 3986.69i 0.395108 + 0.680436i
\(326\) 2540.76 0.431656
\(327\) 0 0
\(328\) −1858.78 + 5720.75i −0.312909 + 0.963035i
\(329\) 740.252 2278.26i 0.124047 0.381777i
\(330\) 0 0
\(331\) −338.723 1042.48i −0.0562475 0.173112i 0.918986 0.394291i \(-0.129010\pi\)
−0.975233 + 0.221179i \(0.929010\pi\)
\(332\) 591.289 0.0977446
\(333\) 0 0
\(334\) −5250.50 3814.71i −0.860163 0.624945i
\(335\) −2585.37 + 274.981i −0.421653 + 0.0448472i
\(336\) 0 0
\(337\) 146.017 + 106.088i 0.0236025 + 0.0171482i 0.599524 0.800357i \(-0.295357\pi\)
−0.575921 + 0.817505i \(0.695357\pi\)
\(338\) 2242.95 + 1629.60i 0.360947 + 0.262244i
\(339\) 0 0
\(340\) −471.272 + 2230.79i −0.0751716 + 0.355828i
\(341\) 13559.3 + 9851.40i 2.15330 + 1.56447i
\(342\) 0 0
\(343\) −6140.75 −0.966674
\(344\) −929.942 2862.07i −0.145753 0.448582i
\(345\) 0 0
\(346\) −2460.49 + 7572.62i −0.382303 + 1.17661i
\(347\) 2198.19 6765.33i 0.340072 1.04663i −0.624097 0.781347i \(-0.714533\pi\)
0.964169 0.265287i \(-0.0854668\pi\)
\(348\) 0 0
\(349\) 10139.8 1.55522 0.777612 0.628745i \(-0.216431\pi\)
0.777612 + 0.628745i \(0.216431\pi\)
\(350\) 4362.50 938.614i 0.666244 0.143346i
\(351\) 0 0
\(352\) 5526.79 4015.45i 0.836872 0.608023i
\(353\) 1307.23 4023.24i 0.197102 0.606617i −0.802844 0.596189i \(-0.796681\pi\)
0.999946 0.0104274i \(-0.00331921\pi\)
\(354\) 0 0
\(355\) 6142.26 + 3536.07i 0.918302 + 0.528662i
\(356\) 799.582 + 2460.86i 0.119039 + 0.366363i
\(357\) 0 0
\(358\) −345.066 1062.00i −0.0509422 0.156784i
\(359\) −5057.37 3674.40i −0.743504 0.540187i 0.150302 0.988640i \(-0.451975\pi\)
−0.893807 + 0.448453i \(0.851975\pi\)
\(360\) 0 0
\(361\) 5530.12 4017.87i 0.806257 0.585780i
\(362\) 2818.13 + 2047.49i 0.409165 + 0.297276i
\(363\) 0 0
\(364\) −956.832 + 695.179i −0.137779 + 0.100102i
\(365\) −4340.57 9716.58i −0.622455 1.39339i
\(366\) 0 0
\(367\) 4058.64 + 12491.2i 0.577273 + 1.77666i 0.628306 + 0.777966i \(0.283749\pi\)
−0.0510334 + 0.998697i \(0.516251\pi\)
\(368\) −6544.01 −0.926983
\(369\) 0 0
\(370\) 1914.16 9060.75i 0.268952 1.27310i
\(371\) 1749.57 5384.63i 0.244834 0.753520i
\(372\) 0 0
\(373\) −2397.18 + 1741.65i −0.332765 + 0.241768i −0.741603 0.670839i \(-0.765934\pi\)
0.408838 + 0.912607i \(0.365934\pi\)
\(374\) 12076.8 1.66972
\(375\) 0 0
\(376\) −3700.26 −0.507517
\(377\) −4939.08 + 3588.46i −0.674737 + 0.490225i
\(378\) 0 0
\(379\) −2124.88 + 6539.71i −0.287989 + 0.886338i 0.697498 + 0.716586i \(0.254296\pi\)
−0.985487 + 0.169751i \(0.945704\pi\)
\(380\) 33.2689 157.480i 0.00449121 0.0212593i
\(381\) 0 0
\(382\) −8666.20 −1.16074
\(383\) 1713.45 + 5273.46i 0.228599 + 0.703555i 0.997906 + 0.0646760i \(0.0206014\pi\)
−0.769308 + 0.638879i \(0.779399\pi\)
\(384\) 0 0
\(385\) −2613.97 5851.51i −0.346027 0.774598i
\(386\) −4250.63 + 3088.26i −0.560495 + 0.407224i
\(387\) 0 0
\(388\) 533.185 + 387.382i 0.0697639 + 0.0506864i
\(389\) −8335.61 + 6056.17i −1.08646 + 0.789358i −0.978798 0.204830i \(-0.934336\pi\)
−0.107660 + 0.994188i \(0.534336\pi\)
\(390\) 0 0
\(391\) −4594.83 3338.34i −0.594298 0.431783i
\(392\) 1166.99 + 3591.63i 0.150362 + 0.462767i
\(393\) 0 0
\(394\) −2118.26 6519.35i −0.270854 0.833604i
\(395\) −8825.31 5080.69i −1.12418 0.647182i
\(396\) 0 0
\(397\) 4175.65 12851.3i 0.527884 1.62466i −0.230657 0.973035i \(-0.574088\pi\)
0.758541 0.651625i \(-0.225912\pi\)
\(398\) −13699.7 + 9953.44i −1.72539 + 1.25357i
\(399\) 0 0
\(400\) −4955.71 8534.49i −0.619463 1.06681i
\(401\) −6139.20 −0.764531 −0.382266 0.924053i \(-0.624856\pi\)
−0.382266 + 0.924053i \(0.624856\pi\)
\(402\) 0 0
\(403\) −3590.56 + 11050.6i −0.443818 + 1.36593i
\(404\) −736.557 + 2266.89i −0.0907056 + 0.279163i
\(405\) 0 0
\(406\) 1826.11 + 5620.18i 0.223222 + 0.687007i
\(407\) −13300.3 −1.61983
\(408\) 0 0
\(409\) 1441.33 + 1047.19i 0.174252 + 0.126602i 0.671493 0.741011i \(-0.265653\pi\)
−0.497241 + 0.867613i \(0.665653\pi\)
\(410\) −2766.92 + 13097.4i −0.333289 + 1.57764i
\(411\) 0 0
\(412\) 3261.47 + 2369.60i 0.390003 + 0.283354i
\(413\) −376.170 273.304i −0.0448187 0.0325627i
\(414\) 0 0
\(415\) −2208.81 + 234.930i −0.261268 + 0.0277886i
\(416\) 3831.54 + 2783.78i 0.451579 + 0.328091i
\(417\) 0 0
\(418\) −852.546 −0.0997594
\(419\) 1708.09 + 5256.97i 0.199155 + 0.612936i 0.999903 + 0.0139343i \(0.00443558\pi\)
−0.800748 + 0.599001i \(0.795564\pi\)
\(420\) 0 0
\(421\) 4706.54 14485.2i 0.544852 1.67688i −0.176490 0.984302i \(-0.556474\pi\)
0.721342 0.692579i \(-0.243526\pi\)
\(422\) 5288.70 16277.0i 0.610071 1.87761i
\(423\) 0 0
\(424\) −8745.50 −1.00170
\(425\) 874.142 8520.53i 0.0997697 0.972485i
\(426\) 0 0
\(427\) 5409.33 3930.10i 0.613058 0.445412i
\(428\) −929.539 + 2860.83i −0.104979 + 0.323092i
\(429\) 0 0
\(430\) −2731.58 6114.78i −0.306346 0.685770i
\(431\) 5032.73 + 15489.1i 0.562455 + 1.73106i 0.675395 + 0.737456i \(0.263973\pi\)
−0.112941 + 0.993602i \(0.536027\pi\)
\(432\) 0 0
\(433\) 2693.63 + 8290.15i 0.298955 + 0.920090i 0.981864 + 0.189586i \(0.0607147\pi\)
−0.682909 + 0.730504i \(0.739285\pi\)
\(434\) 9098.98 + 6610.79i 1.00637 + 0.731171i
\(435\) 0 0
\(436\) −1911.92 + 1389.09i −0.210010 + 0.152581i
\(437\) 324.367 + 235.666i 0.0355070 + 0.0257974i
\(438\) 0 0
\(439\) 4496.39 3266.82i 0.488840 0.355163i −0.315898 0.948793i \(-0.602306\pi\)
0.804738 + 0.593630i \(0.202306\pi\)
\(440\) −7348.52 + 6633.19i −0.796198 + 0.718693i
\(441\) 0 0
\(442\) 2587.23 + 7962.66i 0.278420 + 0.856889i
\(443\) 14955.5 1.60397 0.801984 0.597346i \(-0.203778\pi\)
0.801984 + 0.597346i \(0.203778\pi\)
\(444\) 0 0
\(445\) −3964.64 8875.04i −0.422342 0.945432i
\(446\) 4956.90 15255.8i 0.526269 1.61969i
\(447\) 0 0
\(448\) −1797.24 + 1305.77i −0.189535 + 0.137705i
\(449\) −1838.79 −0.193269 −0.0966347 0.995320i \(-0.530808\pi\)
−0.0966347 + 0.995320i \(0.530808\pi\)
\(450\) 0 0
\(451\) 19225.7 2.00732
\(452\) −1303.38 + 946.964i −0.135633 + 0.0985430i
\(453\) 0 0
\(454\) 529.696 1630.24i 0.0547574 0.168526i
\(455\) 3298.11 2977.06i 0.339820 0.306740i
\(456\) 0 0
\(457\) 2881.50 0.294947 0.147474 0.989066i \(-0.452886\pi\)
0.147474 + 0.989066i \(0.452886\pi\)
\(458\) 2787.02 + 8577.56i 0.284342 + 0.875115i
\(459\) 0 0
\(460\) −2742.51 + 291.695i −0.277979 + 0.0295660i
\(461\) −12021.6 + 8734.19i −1.21454 + 0.882412i −0.995635 0.0933353i \(-0.970247\pi\)
−0.218901 + 0.975747i \(0.570247\pi\)
\(462\) 0 0
\(463\) 2417.11 + 1756.13i 0.242619 + 0.176273i 0.702449 0.711734i \(-0.252090\pi\)
−0.459830 + 0.888007i \(0.652090\pi\)
\(464\) 10573.3 7681.96i 1.05787 0.768591i
\(465\) 0 0
\(466\) −15550.3 11298.0i −1.54583 1.12311i
\(467\) −3260.85 10035.9i −0.323114 0.994442i −0.972285 0.233800i \(-0.924884\pi\)
0.649171 0.760642i \(-0.275116\pi\)
\(468\) 0 0
\(469\) 774.317 + 2383.10i 0.0762359 + 0.234630i
\(470\) −8188.57 + 870.941i −0.803639 + 0.0854756i
\(471\) 0 0
\(472\) −221.944 + 683.075i −0.0216437 + 0.0666124i
\(473\) −7781.54 + 5653.62i −0.756439 + 0.549585i
\(474\) 0 0
\(475\) −61.7090 + 601.497i −0.00596085 + 0.0581022i
\(476\) 2197.41 0.211593
\(477\) 0 0
\(478\) 4916.48 15131.4i 0.470449 1.44789i
\(479\) 2070.90 6373.57i 0.197540 0.607966i −0.802397 0.596790i \(-0.796443\pi\)
0.999938 0.0111759i \(-0.00355749\pi\)
\(480\) 0 0
\(481\) −2849.34 8769.37i −0.270101 0.831287i
\(482\) 3651.41 0.345057
\(483\) 0 0
\(484\) −3609.32 2622.33i −0.338967 0.246274i
\(485\) −2145.67 1235.25i −0.200886 0.115649i
\(486\) 0 0
\(487\) −7282.87 5291.31i −0.677655 0.492345i 0.194924 0.980818i \(-0.437554\pi\)
−0.872579 + 0.488473i \(0.837554\pi\)
\(488\) −8355.61 6070.71i −0.775083 0.563131i
\(489\) 0 0
\(490\) 3427.89 + 7673.49i 0.316033 + 0.707455i
\(491\) 15175.6 + 11025.8i 1.39484 + 1.01341i 0.995314 + 0.0966906i \(0.0308257\pi\)
0.399527 + 0.916721i \(0.369174\pi\)
\(492\) 0 0
\(493\) 11342.8 1.03622
\(494\) −182.642 562.115i −0.0166345 0.0511958i
\(495\) 0 0
\(496\) 7686.47 23656.5i 0.695832 2.14155i
\(497\) 2110.77 6496.28i 0.190505 0.586314i
\(498\) 0 0
\(499\) −21413.5 −1.92104 −0.960522 0.278203i \(-0.910261\pi\)
−0.960522 + 0.278203i \(0.910261\pi\)
\(500\) −2457.30 3355.80i −0.219787 0.300152i
\(501\) 0 0
\(502\) 16065.8 11672.5i 1.42839 1.03779i
\(503\) −3098.09 + 9534.95i −0.274626 + 0.845213i 0.714692 + 0.699440i \(0.246567\pi\)
−0.989318 + 0.145774i \(0.953433\pi\)
\(504\) 0 0
\(505\) 1850.79 8760.79i 0.163087 0.771980i
\(506\) 4514.25 + 13893.4i 0.396607 + 1.22063i
\(507\) 0 0
\(508\) −1208.48 3719.31i −0.105546 0.324838i
\(509\) 1685.86 + 1224.85i 0.146806 + 0.106661i 0.658764 0.752350i \(-0.271080\pi\)
−0.511958 + 0.859011i \(0.671080\pi\)
\(510\) 0 0
\(511\) −8297.62 + 6028.57i −0.718327 + 0.521895i
\(512\) 302.589 + 219.843i 0.0261185 + 0.0189762i
\(513\) 0 0
\(514\) −12983.8 + 9433.28i −1.11418 + 0.809502i
\(515\) −13125.0 7555.98i −1.12302 0.646517i
\(516\) 0 0
\(517\) 3654.68 + 11247.9i 0.310895 + 0.956836i
\(518\) −8925.18 −0.757046
\(519\) 0 0
\(520\) −5947.79 3424.11i −0.501592 0.288764i
\(521\) 6176.74 19010.0i 0.519401 1.59855i −0.255728 0.966749i \(-0.582315\pi\)
0.775129 0.631803i \(-0.217685\pi\)
\(522\) 0 0
\(523\) 1489.75 1082.36i 0.124555 0.0904942i −0.523764 0.851863i \(-0.675473\pi\)
0.648318 + 0.761369i \(0.275473\pi\)
\(524\) −998.199 −0.0832186
\(525\) 0 0
\(526\) 26087.6 2.16249
\(527\) 17465.1 12689.1i 1.44363 1.04886i
\(528\) 0 0
\(529\) −1636.83 + 5037.63i −0.134530 + 0.414041i
\(530\) −19353.5 + 2058.45i −1.58616 + 0.168705i
\(531\) 0 0
\(532\) −155.124 −0.0126418
\(533\) 4118.74 + 12676.2i 0.334713 + 1.03014i
\(534\) 0 0
\(535\) 2335.71 11056.2i 0.188750 0.893457i
\(536\) 3131.33 2275.05i 0.252338 0.183334i
\(537\) 0 0
\(538\) 2399.41 + 1743.27i 0.192279 + 0.139699i
\(539\) 9765.12 7094.77i 0.780359 0.566964i
\(540\) 0 0
\(541\) 2538.38 + 1844.24i 0.201725 + 0.146562i 0.684062 0.729424i \(-0.260212\pi\)
−0.482337 + 0.875986i \(0.660212\pi\)
\(542\) −954.172 2936.64i −0.0756184 0.232730i
\(543\) 0 0
\(544\) −2719.14 8368.65i −0.214305 0.659564i
\(545\) 6590.22 5948.70i 0.517970 0.467549i
\(546\) 0 0
\(547\) −2473.52 + 7612.71i −0.193345 + 0.595056i 0.806646 + 0.591034i \(0.201280\pi\)
−0.999992 + 0.00402194i \(0.998720\pi\)
\(548\) 2896.58 2104.49i 0.225795 0.164050i
\(549\) 0 0
\(550\) −14700.8 + 16408.7i −1.13972 + 1.27213i
\(551\) −800.735 −0.0619101
\(552\) 0 0
\(553\) −3032.79 + 9333.97i −0.233214 + 0.717759i
\(554\) 8044.61 24758.8i 0.616936 1.89873i
\(555\) 0 0
\(556\) 1800.23 + 5540.55i 0.137315 + 0.422611i
\(557\) −7336.30 −0.558077 −0.279039 0.960280i \(-0.590016\pi\)
−0.279039 + 0.960280i \(0.590016\pi\)
\(558\) 0 0
\(559\) −5394.68 3919.47i −0.408177 0.296558i
\(560\) −7060.42 + 6373.13i −0.532781 + 0.480918i
\(561\) 0 0
\(562\) 3103.24 + 2254.64i 0.232922 + 0.169228i
\(563\) −1287.19 935.199i −0.0963564 0.0700070i 0.538564 0.842585i \(-0.318967\pi\)
−0.634920 + 0.772578i \(0.718967\pi\)
\(564\) 0 0
\(565\) 4492.65 4055.32i 0.334526 0.301962i
\(566\) 11139.1 + 8093.00i 0.827225 + 0.601014i
\(567\) 0 0
\(568\) −10551.0 −0.779419
\(569\) −2067.73 6363.82i −0.152344 0.468866i 0.845538 0.533915i \(-0.179280\pi\)
−0.997882 + 0.0650485i \(0.979280\pi\)
\(570\) 0 0
\(571\) 2180.77 6711.72i 0.159829 0.491903i −0.838789 0.544456i \(-0.816736\pi\)
0.998618 + 0.0525535i \(0.0167360\pi\)
\(572\) 1804.39 5553.34i 0.131897 0.405938i
\(573\) 0 0
\(574\) 12901.4 0.938142
\(575\) 10129.0 2179.30i 0.734622 0.158058i
\(576\) 0 0
\(577\) 20208.4 14682.3i 1.45804 1.05933i 0.474168 0.880434i \(-0.342749\pi\)
0.983869 0.178891i \(-0.0572510\pi\)
\(578\) −222.914 + 686.058i −0.0160415 + 0.0493707i
\(579\) 0 0
\(580\) 4088.73 3690.72i 0.292716 0.264222i
\(581\) 661.537 + 2036.00i 0.0472379 + 0.145383i
\(582\) 0 0
\(583\) 8637.76 + 26584.3i 0.613619 + 1.88852i
\(584\) 12817.1 + 9312.14i 0.908174 + 0.659827i
\(585\) 0 0
\(586\) −14888.4 + 10817.0i −1.04954 + 0.762539i
\(587\) −6989.61 5078.25i −0.491468 0.357073i 0.314280 0.949330i \(-0.398237\pi\)
−0.805749 + 0.592258i \(0.798237\pi\)
\(588\) 0 0
\(589\) −1232.93 + 895.774i −0.0862511 + 0.0626651i
\(590\) −330.379 + 1563.86i −0.0230534 + 0.109124i
\(591\) 0 0
\(592\) 6099.71 + 18773.0i 0.423474 + 1.30332i
\(593\) −196.006 −0.0135733 −0.00678666 0.999977i \(-0.502160\pi\)
−0.00678666 + 0.999977i \(0.502160\pi\)
\(594\) 0 0
\(595\) −8208.60 + 873.072i −0.565580 + 0.0601554i
\(596\) −2409.91 + 7416.95i −0.165627 + 0.509749i
\(597\) 0 0
\(598\) −8193.35 + 5952.82i −0.560286 + 0.407072i
\(599\) 1180.26 0.0805079 0.0402539 0.999189i \(-0.487183\pi\)
0.0402539 + 0.999189i \(0.487183\pi\)
\(600\) 0 0
\(601\) −14145.6 −0.960083 −0.480042 0.877246i \(-0.659378\pi\)
−0.480042 + 0.877246i \(0.659378\pi\)
\(602\) −5221.81 + 3793.87i −0.353530 + 0.256855i
\(603\) 0 0
\(604\) −517.572 + 1592.92i −0.0348671 + 0.107310i
\(605\) 14524.8 + 8361.85i 0.976061 + 0.561913i
\(606\) 0 0
\(607\) −16501.7 −1.10343 −0.551716 0.834032i \(-0.686027\pi\)
−0.551716 + 0.834032i \(0.686027\pi\)
\(608\) 191.954 + 590.775i 0.0128039 + 0.0394064i
\(609\) 0 0
\(610\) −19919.6 11467.6i −1.32216 0.761163i
\(611\) −6633.23 + 4819.33i −0.439201 + 0.319098i
\(612\) 0 0
\(613\) −18875.6 13714.0i −1.24369 0.903592i −0.245849 0.969308i \(-0.579067\pi\)
−0.997838 + 0.0657164i \(0.979067\pi\)
\(614\) 12368.4 8986.20i 0.812948 0.590641i
\(615\) 0 0
\(616\) 7718.67 + 5607.94i 0.504861 + 0.366803i
\(617\) −4771.61 14685.5i −0.311342 0.958212i −0.977234 0.212164i \(-0.931949\pi\)
0.665892 0.746048i \(-0.268051\pi\)
\(618\) 0 0
\(619\) −564.315 1736.78i −0.0366425 0.112774i 0.931062 0.364860i \(-0.118883\pi\)
−0.967705 + 0.252086i \(0.918883\pi\)
\(620\) 2166.83 10256.8i 0.140358 0.664391i
\(621\) 0 0
\(622\) 4701.19 14468.8i 0.303055 0.932708i
\(623\) −7578.97 + 5506.45i −0.487392 + 0.354111i
\(624\) 0 0
\(625\) 10512.7 + 11559.5i 0.672816 + 0.739810i
\(626\) −16653.9 −1.06330
\(627\) 0 0
\(628\) −2716.76 + 8361.32i −0.172628 + 0.531294i
\(629\) −5293.92 + 16293.0i −0.335584 + 1.03282i
\(630\) 0 0
\(631\) 8156.90 + 25104.4i 0.514613 + 1.58382i 0.783984 + 0.620781i \(0.213184\pi\)
−0.269371 + 0.963036i \(0.586816\pi\)
\(632\) 15159.9 0.954156
\(633\) 0 0
\(634\) 20298.8 + 14747.9i 1.27156 + 0.923841i
\(635\) 5992.12 + 13413.6i 0.374472 + 0.838274i
\(636\) 0 0
\(637\) 6769.83 + 4918.57i 0.421084 + 0.305936i
\(638\) −23603.2 17148.7i −1.46467 1.06415i
\(639\) 0 0
\(640\) 16572.4 + 9540.67i 1.02357 + 0.589263i
\(641\) 9625.95 + 6993.66i 0.593139 + 0.430941i 0.843437 0.537228i \(-0.180529\pi\)
−0.250298 + 0.968169i \(0.580529\pi\)
\(642\) 0 0
\(643\) −5124.72 −0.314307 −0.157154 0.987574i \(-0.550232\pi\)
−0.157154 + 0.987574i \(0.550232\pi\)
\(644\) 821.383 + 2527.96i 0.0502594 + 0.154682i
\(645\) 0 0
\(646\) −339.339 + 1044.38i −0.0206674 + 0.0636076i
\(647\) −6325.15 + 19466.8i −0.384339 + 1.18287i 0.552620 + 0.833434i \(0.313628\pi\)
−0.936959 + 0.349440i \(0.886372\pi\)
\(648\) 0 0
\(649\) 2295.60 0.138845
\(650\) −13968.2 6177.50i −0.842890 0.372772i
\(651\) 0 0
\(652\) −1846.51 + 1341.57i −0.110912 + 0.0805826i
\(653\) 525.792 1618.22i 0.0315097 0.0969769i −0.934065 0.357104i \(-0.883764\pi\)
0.965574 + 0.260127i \(0.0837643\pi\)
\(654\) 0 0
\(655\) 3728.85 396.603i 0.222440 0.0236589i
\(656\) −8817.16 27136.4i −0.524775 1.61509i
\(657\) 0 0
\(658\) 2452.48 + 7547.95i 0.145300 + 0.447188i
\(659\) 10585.8 + 7691.06i 0.625744 + 0.454630i 0.854923 0.518754i \(-0.173604\pi\)
−0.229179 + 0.973384i \(0.573604\pi\)
\(660\) 0 0
\(661\) 4396.38 3194.16i 0.258698 0.187955i −0.450875 0.892587i \(-0.648888\pi\)
0.709573 + 0.704632i \(0.248888\pi\)
\(662\) 2937.96 + 2134.55i 0.172488 + 0.125320i
\(663\) 0 0
\(664\) 2675.25 1943.68i 0.156355 0.113599i
\(665\) 579.477 61.6335i 0.0337912 0.00359405i
\(666\) 0 0
\(667\) 4239.91 + 13049.1i 0.246132 + 0.757516i
\(668\) 5830.05 0.337682
\(669\) 0 0
\(670\) 6394.06 5771.64i 0.368693 0.332803i
\(671\) −10200.9 + 31395.1i −0.586886 + 1.80625i
\(672\) 0 0
\(673\) 18745.6 13619.5i 1.07369 0.780078i 0.0971147 0.995273i \(-0.469039\pi\)
0.976571 + 0.215195i \(0.0690386\pi\)
\(674\) −597.958 −0.0341728
\(675\) 0 0
\(676\) −2490.53 −0.141700
\(677\) −2643.89 + 1920.89i −0.150093 + 0.109049i −0.660297 0.751004i \(-0.729570\pi\)
0.510205 + 0.860053i \(0.329570\pi\)
\(678\) 0 0
\(679\) −737.352 + 2269.34i −0.0416745 + 0.128261i
\(680\) 5200.80 + 11642.2i 0.293296 + 0.656558i
\(681\) 0 0
\(682\) −55527.0 −3.11765
\(683\) 5489.83 + 16896.0i 0.307559 + 0.946568i 0.978710 + 0.205248i \(0.0658000\pi\)
−0.671151 + 0.741320i \(0.734200\pi\)
\(684\) 0 0
\(685\) −9984.24 + 9012.34i −0.556902 + 0.502691i
\(686\) 16459.0 11958.2i 0.916047 0.665547i
\(687\) 0 0
\(688\) 11548.6 + 8390.58i 0.639953 + 0.464953i
\(689\) −15677.5 + 11390.4i −0.866859 + 0.629810i
\(690\) 0 0
\(691\) −22646.8 16453.8i −1.24678 0.905837i −0.248747 0.968569i \(-0.580019\pi\)
−0.998030 + 0.0627318i \(0.980019\pi\)
\(692\) −2210.30 6802.61i −0.121421 0.373694i
\(693\) 0 0
\(694\) 7282.66 + 22413.7i 0.398337 + 1.22596i
\(695\) −8926.27 19981.9i −0.487184 1.09058i
\(696\) 0 0
\(697\) 7652.39 23551.6i 0.415861 1.27989i
\(698\) −27177.8 + 19745.8i −1.47377 + 1.07076i
\(699\) 0 0
\(700\) −2674.86 + 2985.62i −0.144429 + 0.161208i
\(701\) 12008.1 0.646988 0.323494 0.946230i \(-0.395142\pi\)
0.323494 + 0.946230i \(0.395142\pi\)
\(702\) 0 0
\(703\) 373.718 1150.19i 0.0200499 0.0617071i
\(704\) 3389.23 10431.0i 0.181444 0.558426i
\(705\) 0 0
\(706\) 4330.89 + 13329.1i 0.230872 + 0.710549i
\(707\) −8629.71 −0.459057
\(708\) 0 0
\(709\) 13731.7 + 9976.69i 0.727371 + 0.528466i 0.888731 0.458430i \(-0.151588\pi\)
−0.161359 + 0.986896i \(0.551588\pi\)
\(710\) −23349.0 + 2483.42i −1.23419 + 0.131269i
\(711\) 0 0
\(712\) 11707.0 + 8505.63i 0.616205 + 0.447699i
\(713\) 21126.3 + 15349.1i 1.10966 + 0.806213i
\(714\) 0 0
\(715\) −4533.99 + 21461.8i −0.237149 + 1.12256i
\(716\) 811.535 + 589.614i 0.0423582 + 0.0307750i
\(717\) 0 0
\(718\) 20710.6 1.07648
\(719\) −90.3053 277.931i −0.00468403 0.0144160i 0.948687 0.316216i \(-0.102412\pi\)
−0.953371 + 0.301800i \(0.902412\pi\)
\(720\) 0 0
\(721\) −4510.35 + 13881.4i −0.232974 + 0.717021i
\(722\) −6998.16 + 21538.1i −0.360727 + 1.11020i
\(723\) 0 0
\(724\) −3129.20 −0.160629
\(725\) −13807.4 + 15411.5i −0.707301 + 0.789474i
\(726\) 0 0
\(727\) −22594.0 + 16415.5i −1.15263 + 0.837436i −0.988829 0.149057i \(-0.952376\pi\)
−0.163803 + 0.986493i \(0.552376\pi\)
\(728\) −2043.94 + 6290.60i −0.104057 + 0.320254i
\(729\) 0 0
\(730\) 30555.6 + 17590.7i 1.54920 + 0.891864i
\(731\) 3828.46 + 11782.8i 0.193708 + 0.596172i
\(732\) 0 0
\(733\) −11190.6 34441.2i −0.563895 1.73549i −0.671211 0.741266i \(-0.734226\pi\)
0.107316 0.994225i \(-0.465774\pi\)
\(734\) −35203.1 25576.5i −1.77026 1.28617i
\(735\) 0 0
\(736\) 8611.10 6256.33i 0.431263 0.313331i
\(737\) −10008.4 7271.51i −0.500222 0.363432i
\(738\) 0 0
\(739\) 477.123 346.650i 0.0237500 0.0172554i −0.575847 0.817558i \(-0.695328\pi\)
0.599597 + 0.800302i \(0.295328\pi\)
\(740\) 3393.11 + 7595.64i 0.168558 + 0.377326i
\(741\) 0 0
\(742\) 5796.38 + 17839.4i 0.286781 + 0.882622i
\(743\) 15725.6 0.776468 0.388234 0.921561i \(-0.373085\pi\)
0.388234 + 0.921561i \(0.373085\pi\)
\(744\) 0 0
\(745\) 6055.53 28664.1i 0.297795 1.40963i
\(746\) 3033.54 9336.28i 0.148882 0.458211i
\(747\) 0 0
\(748\) −8776.85 + 6376.75i −0.429028 + 0.311707i
\(749\) −10890.7 −0.531294
\(750\) 0 0
\(751\) −15640.8 −0.759974 −0.379987 0.924992i \(-0.624072\pi\)
−0.379987 + 0.924992i \(0.624072\pi\)
\(752\) 14200.1 10316.9i 0.688594 0.500293i
\(753\) 0 0
\(754\) 6250.23 19236.2i 0.301883 0.929101i
\(755\) 1300.53 6156.13i 0.0626904 0.296748i
\(756\) 0 0
\(757\) −31252.3 −1.50051 −0.750255 0.661149i \(-0.770069\pi\)
−0.750255 + 0.661149i \(0.770069\pi\)
\(758\) −7039.78 21666.2i −0.337330 1.03820i
\(759\) 0 0
\(760\) −367.144 821.870i −0.0175233 0.0392268i
\(761\) −11969.7 + 8696.46i −0.570170 + 0.414253i −0.835167 0.549996i \(-0.814629\pi\)
0.264997 + 0.964249i \(0.414629\pi\)
\(762\) 0 0
\(763\) −6922.17 5029.25i −0.328440 0.238625i
\(764\) 6298.19 4575.90i 0.298247 0.216689i
\(765\) 0 0
\(766\) −14861.8 10797.8i −0.701018 0.509319i
\(767\) 491.790 + 1513.57i 0.0231519 + 0.0712542i
\(768\) 0 0
\(769\) −12997.7 40002.8i −0.609505 1.87586i −0.462207 0.886772i \(-0.652942\pi\)
−0.147298 0.989092i \(-0.547058\pi\)
\(770\) 18401.1 + 10593.4i 0.861209 + 0.495794i
\(771\) 0 0
\(772\) 1458.50 4488.81i 0.0679956 0.209269i
\(773\) 23657.9 17188.4i 1.10079 0.799774i 0.119605 0.992822i \(-0.461837\pi\)
0.981189 + 0.193047i \(0.0618371\pi\)
\(774\) 0 0
\(775\) −4019.16 + 39175.9i −0.186287 + 1.81580i
\(776\) 3685.77 0.170504
\(777\) 0 0
\(778\) 10548.4 32464.7i 0.486091 1.49603i
\(779\) −540.212 + 1662.60i −0.0248461 + 0.0764683i
\(780\) 0 0
\(781\) 10421.0 + 32072.6i 0.477456 + 1.46946i
\(782\) 18816.4 0.860453