Properties

Label 225.4.h.d.91.4
Level $225$
Weight $4$
Character 225.91
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 91.4
Character \(\chi\) \(=\) 225.91
Dual form 225.4.h.d.136.4

$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

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

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 0.00261710 0.999997i \(-0.499167\pi\)
−0.950245 + 0.311505i \(0.899167\pi\)
\(3\) 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 −0.187546 0.982256i \(-0.560053\pi\)
−0.992136 + 0.125167i \(0.960053\pi\)
\(12\) 0 0
\(13\) −29.8370 + 21.6778i −0.636560 + 0.462488i −0.858667 0.512534i \(-0.828707\pi\)
0.222107 + 0.975022i \(0.428707\pi\)
\(14\) −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 −0.678655 0.734458i \(-0.737437\pi\)
0.980746 0.195286i \(-0.0625634\pi\)
\(18\) 0 0
\(19\) −1.49479 + 4.60048i −0.0180488 + 0.0555485i −0.959675 0.281111i \(-0.909297\pi\)
0.941626 + 0.336659i \(0.109297\pi\)
\(20\) 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 0.240760 0.970585i \(-0.422603\pi\)
−0.848682 + 0.528903i \(0.822603\pi\)
\(24\) 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 0.970276 + 0.241999i \(0.0778031\pi\)
−0.642727 + 0.766096i \(0.722197\pi\)
\(30\) 0 0
\(31\) −97.3566 + 299.633i −0.564057 + 1.73599i 0.106680 + 0.994293i \(0.465978\pi\)
−0.670737 + 0.741695i \(0.734022\pi\)
\(32\) −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 −0.0394231 0.999223i \(-0.512552\pi\)
0.938135 + 0.346270i \(0.112552\pi\)
\(38\) 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 −0.983242 0.182307i \(-0.941644\pi\)
−0.130454 + 0.991454i \(0.541644\pi\)
\(42\) 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 0.999276 + 0.0380490i \(0.0121143\pi\)
−0.786067 + 0.618142i \(0.787886\pi\)
\(48\) 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 0.906945 + 0.421249i \(0.138408\pi\)
−0.486130 + 0.873886i \(0.661592\pi\)
\(54\) 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 −0.625635 0.780116i \(-0.715160\pi\)
0.548602 + 0.836084i \(0.315160\pi\)
\(60\) 0 0
\(61\) 502.015 + 364.735i 1.05371 + 0.765566i 0.972915 0.231165i \(-0.0742536\pi\)
0.0807964 + 0.996731i \(0.474254\pi\)
\(62\) 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 −0.863919 0.503631i \(-0.831997\pi\)
0.994952 + 0.100353i \(0.0319973\pi\)
\(68\) 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 0.970329 + 0.241788i \(0.0777339\pi\)
−0.642893 + 0.765956i \(0.722266\pi\)
\(72\) 0 0
\(73\) −770.064 559.484i −1.23465 0.897022i −0.237416 0.971408i \(-0.576300\pi\)
−0.997230 + 0.0743856i \(0.976300\pi\)
\(74\) −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 −0.924316 0.381627i \(-0.875364\pi\)
0.523473 0.852043i \(-0.324636\pi\)
\(80\) −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 −0.902218 0.431280i \(-0.858062\pi\)
0.983410 + 0.181398i \(0.0580622\pi\)
\(84\) 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 0.0840133 0.996465i \(-0.473226\pi\)
−0.921733 + 0.387826i \(0.873226\pi\)
\(90\) 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 0.908833 0.417161i \(-0.136975\pi\)
−0.980462 + 0.196708i \(0.936975\pi\)
\(98\) 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 −0.924650 0.380817i \(-0.875643\pi\)
0.524219 0.851584i \(-0.324357\pi\)
\(104\) −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 −0.833109 0.553109i \(-0.813441\pi\)
0.268593 + 0.963254i \(0.413441\pi\)
\(110\) 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 −0.754962 0.655768i \(-0.772345\pi\)
0.390376 + 0.920655i \(0.372345\pi\)
\(114\) 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 0.893577 0.448910i \(-0.148187\pi\)
−0.150808 + 0.988563i \(0.548187\pi\)
\(128\) 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 −0.979652 0.200705i \(-0.935677\pi\)
0.910526 + 0.413451i \(0.135677\pi\)
\(132\) 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 −0.241392 0.970428i \(-0.577604\pi\)
0.848337 + 0.529456i \(0.177604\pi\)
\(138\) 0 0
\(139\) −1583.61 1150.56i −0.966334 0.702083i −0.0117211 0.999931i \(-0.503731\pi\)
−0.954613 + 0.297848i \(0.903731\pi\)
\(140\) 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 −0.726789 0.686860i \(-0.758988\pi\)
0.428653 + 0.903469i \(0.358988\pi\)
\(164\) −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 −0.707217 0.706996i \(-0.750050\pi\)
0.987713 0.156280i \(-0.0499502\pi\)
\(168\) 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 0.926378 0.376594i \(-0.122905\pi\)
−0.0718957 + 0.997412i \(0.522905\pi\)
\(174\) 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 0.926953 0.375176i \(-0.122418\pi\)
−0.970444 + 0.241325i \(0.922418\pi\)
\(180\) 0 0
\(181\) −324.908 + 999.965i −0.133427 + 0.410645i −0.995342 0.0964070i \(-0.969265\pi\)
0.861915 + 0.507052i \(0.169265\pi\)
\(182\) 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 −0.109713 0.993963i \(-0.534993\pi\)
0.911412 + 0.411495i \(0.134993\pi\)
\(192\) 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 −0.997598 0.0692631i \(-0.977935\pi\)
0.766362 0.642409i \(-0.222065\pi\)
\(198\) 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 −0.998209 0.0598201i \(-0.980947\pi\)
−0.365356 0.930868i \(-0.619053\pi\)
\(212\) −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 −0.184514 0.982830i \(-0.559071\pi\)
−0.991745 + 0.128228i \(0.959071\pi\)
\(224\) −1383.71 −0.412737
\(225\) 0 0
\(226\) 1793.43 0.527865
\(227\) −418.579 304.115i −0.122388 0.0889200i 0.524907 0.851159i \(-0.324100\pi\)
−0.647295 + 0.762239i \(0.724100\pi\)
\(228\) 0 0
\(229\) 841.230 + 2589.04i 0.242751 + 0.747111i 0.995998 + 0.0893736i \(0.0284865\pi\)
−0.753247 + 0.657738i \(0.771514\pi\)
\(230\) 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 −0.298212 0.954500i \(-0.596390\pi\)
0.802300 0.596922i \(-0.203610\pi\)
\(234\) 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 −0.0790005 0.996875i \(-0.525173\pi\)
−0.972497 + 0.232917i \(0.925173\pi\)
\(240\) 0 0
\(241\) −891.648 + 647.821i −0.238324 + 0.173153i −0.700536 0.713617i \(-0.747056\pi\)
0.462212 + 0.886769i \(0.347056\pi\)
\(242\) 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 −0.520748 + 0.853711i \(0.674347\pi\)
−0.972847 + 0.231449i \(0.925653\pi\)
\(264\) 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 −0.977500 0.210935i \(-0.932349\pi\)
0.914799 + 0.403910i \(0.132349\pi\)
\(270\) 0 0
\(271\) −288.006 886.391i −0.0645576 0.198688i 0.913575 0.406670i \(-0.133310\pi\)
−0.978133 + 0.207983i \(0.933310\pi\)
\(272\) −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 −0.996981 0.0776436i \(-0.975260\pi\)
−0.381928 0.924192i \(-0.624740\pi\)
\(278\) 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 −0.981824 0.189792i \(-0.939219\pi\)
0.905869 + 0.423557i \(0.139219\pi\)
\(282\) 0 0
\(283\) −1284.25 + 3952.50i −0.269754 + 0.830219i 0.720805 + 0.693137i \(0.243772\pi\)
−0.990560 + 0.137081i \(0.956228\pi\)
\(284\) −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 0.195123 0.980779i \(-0.437489\pi\)
−0.872480 + 0.488651i \(0.837489\pi\)
\(312\) 0 0
\(313\) 4066.76 2954.67i 0.734399 0.533572i −0.156553 0.987670i \(-0.550038\pi\)
0.890952 + 0.454098i \(0.150038\pi\)
\(314\) 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 0.497915 + 0.867226i \(0.334099\pi\)
−0.912564 + 0.408933i \(0.865901\pi\)
\(318\) 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 −0.975233 0.221179i \(-0.929010\pi\)
0.918986 + 0.394291i \(0.129010\pi\)
\(332\) 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 −0.575921 0.817505i \(-0.695357\pi\)
0.599524 + 0.800357i \(0.295357\pi\)
\(338\) 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 0.964169 + 0.265287i \(0.0854668\pi\)
−0.624097 + 0.781347i \(0.714533\pi\)
\(348\) 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 0.999946 + 0.0104274i \(0.00331921\pi\)
−0.802844 + 0.596189i \(0.796681\pi\)
\(354\) 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 −0.893807 0.448453i \(-0.851975\pi\)
0.150302 + 0.988640i \(0.451975\pi\)
\(360\) 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 −0.0510334 0.998697i \(-0.516251\pi\)
0.628306 0.777966i \(-0.283749\pi\)
\(368\) −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 0.408838 0.912607i \(-0.365934\pi\)
−0.741603 + 0.670839i \(0.765934\pi\)
\(374\) 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 −0.985487 0.169751i \(-0.945704\pi\)
0.697498 0.716586i \(-0.254296\pi\)
\(380\) 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 −0.769308 0.638879i \(-0.779399\pi\)
0.997906 0.0646760i \(-0.0206014\pi\)
\(384\) 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 −0.107660 0.994188i \(-0.534336\pi\)
−0.978798 + 0.204830i \(0.934336\pi\)
\(390\) 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 0.758541 + 0.651625i \(0.225912\pi\)
−0.230657 + 0.973035i \(0.574088\pi\)
\(398\) −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 −0.497241 0.867613i \(-0.665653\pi\)
0.671493 + 0.741011i \(0.265653\pi\)
\(410\) −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 −0.800748 0.599001i \(-0.795564\pi\)
0.999903 0.0139343i \(-0.00443558\pi\)
\(420\) 0 0
\(421\) 4706.54 + 14485.2i 0.544852 + 1.67688i 0.721342 + 0.692579i \(0.243526\pi\)
−0.176490 + 0.984302i \(0.556474\pi\)
\(422\) 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 −0.112941 0.993602i \(-0.536027\pi\)
0.675395 0.737456i \(-0.263973\pi\)
\(432\) 0 0
\(433\) 2693.63 8290.15i 0.298955 0.920090i −0.682909 0.730504i \(-0.739285\pi\)
0.981864 0.189586i \(-0.0607147\pi\)
\(434\) 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 0.804738 0.593630i \(-0.202306\pi\)
−0.315898 + 0.948793i \(0.602306\pi\)
\(440\) −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 −0.218901 0.975747i \(-0.570247\pi\)
−0.995635 + 0.0933353i \(0.970247\pi\)
\(462\) 0 0
\(463\) 2417.11 1756.13i 0.242619 0.176273i −0.459830 0.888007i \(-0.652090\pi\)
0.702449 + 0.711734i \(0.252090\pi\)
\(464\) 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 0.649171 + 0.760642i \(0.275116\pi\)
−0.972285 + 0.233800i \(0.924884\pi\)
\(468\) 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 0.999938 + 0.0111759i \(0.00355749\pi\)
−0.802397 + 0.596790i \(0.796443\pi\)
\(480\) 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 −0.872579 0.488473i \(-0.837554\pi\)
0.194924 + 0.980818i \(0.437554\pi\)
\(488\) −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 0.399527 0.916721i \(-0.369174\pi\)
0.995314 0.0966906i \(-0.0308257\pi\)
\(492\) 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 −0.989318 0.145774i \(-0.953433\pi\)
0.714692 0.699440i \(-0.246567\pi\)
\(504\) 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 −0.511958 0.859011i \(-0.671080\pi\)
0.658764 + 0.752350i \(0.271080\pi\)
\(510\) 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 0.775129 + 0.631803i \(0.217685\pi\)
−0.255728 + 0.966749i \(0.582315\pi\)
\(522\) 0 0
\(523\) 1489.75 + 1082.36i 0.124555 + 0.0904942i 0.648318 0.761369i \(-0.275473\pi\)
−0.523764 + 0.851863i \(0.675473\pi\)
\(524\) −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 −0.482337 0.875986i \(-0.660212\pi\)
0.684062 + 0.729424i \(0.260212\pi\)
\(542\) −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 −0.999992 0.00402194i \(-0.998720\pi\)
0.806646 0.591034i \(-0.201280\pi\)
\(548\) 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 −0.634920 0.772578i \(-0.718967\pi\)
0.538564 + 0.842585i \(0.318967\pi\)
\(564\) 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 −0.997882 0.0650485i \(-0.979280\pi\)
0.845538 + 0.533915i \(0.179280\pi\)
\(570\) 0 0
\(571\) 2180.77 + 6711.72i 0.159829 + 0.491903i 0.998618 0.0525535i \(-0.0167360\pi\)
−0.838789 + 0.544456i \(0.816736\pi\)
\(572\) 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 0.983869 + 0.178891i \(0.0572510\pi\)
0.474168 + 0.880434i \(0.342749\pi\)
\(578\) −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 −0.805749 0.592258i \(-0.798237\pi\)
0.314280 + 0.949330i \(0.398237\pi\)
\(588\) 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 −0.997838 0.0657164i \(-0.979067\pi\)
−0.245849 + 0.969308i \(0.579067\pi\)
\(614\) 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 0.665892 + 0.746048i \(0.268051\pi\)
−0.977234 + 0.212164i \(0.931949\pi\)
\(618\) 0 0
\(619\) −564.315 + 1736.78i −0.0366425 + 0.112774i −0.967705 0.252086i \(-0.918883\pi\)
0.931062 + 0.364860i \(0.118883\pi\)
\(620\) 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 −0.269371 0.963036i \(-0.586816\pi\)
0.783984 0.620781i \(-0.213184\pi\)
\(632\) 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 −0.250298 0.968169i \(-0.580529\pi\)
0.843437 + 0.537228i \(0.180529\pi\)
\(642\) 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 −0.936959 0.349440i \(-0.886372\pi\)
0.552620 0.833434i \(-0.313628\pi\)
\(648\) 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 0.965574 0.260127i \(-0.0837643\pi\)
−0.934065 + 0.357104i \(0.883764\pi\)
\(654\) 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 −0.229179 0.973384i \(-0.573604\pi\)
0.854923 + 0.518754i \(0.173604\pi\)
\(660\) 0 0
\(661\) 4396.38 + 3194.16i 0.258698 + 0.187955i 0.709573 0.704632i \(-0.248888\pi\)
−0.450875 + 0.892587i \(0.648888\pi\)
\(662\) 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 0.976571 0.215195i \(-0.0690386\pi\)
0.0971147 + 0.995273i \(0.469039\pi\)
\(674\) −597.958 −0.0341728
\(675\) 0 0
\(676\) −2490.53 −0.141700
\(677\) −2643.89 1920.89i −0.150093 0.109049i 0.510205 0.860053i \(-0.329570\pi\)
−0.660297 + 0.751004i \(0.729570\pi\)
\(678\) 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 −0.671151 0.741320i \(-0.734200\pi\)
0.978710 0.205248i \(-0.0658000\pi\)
\(684\) 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 −0.998030 0.0627318i \(-0.980019\pi\)
−0.248747 + 0.968569i \(0.580019\pi\)
\(692\) −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 −0.161359 0.986896i \(-0.551588\pi\)
0.888731 + 0.458430i \(0.151588\pi\)
\(710\) −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 −0.953371 0.301800i \(-0.902412\pi\)
0.948687 + 0.316216i \(0.102412\pi\)
\(720\) 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 −0.163803 0.986493i \(-0.552376\pi\)
−0.988829 + 0.149057i \(0.952376\pi\)
\(728\) −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 0.107316 + 0.994225i \(0.465774\pi\)
−0.671211 + 0.741266i \(0.734226\pi\)
\(734\) −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 0.599597 0.800302i \(-0.295328\pi\)
−0.575847 + 0.817558i \(0.695328\pi\)
\(740\) 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 0.264997 0.964249i \(-0.414629\pi\)
−0.835167 + 0.549996i \(0.814629\pi\)
\(762\) 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 −0.147298 + 0.989092i \(0.547058\pi\)
−0.462207 + 0.886772i \(0.652942\pi\)
\(770\) 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 0.981189 0.193047i \(-0.0618371\pi\)
0.119605 + 0.992822i \(0.461837\pi\)
\(774\) 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