Properties

Label 225.4.h.d.136.3
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 136.3
Character \(\chi\) \(=\) 225.136
Dual form 225.4.h.d.91.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.54222 + 2.57358i) q^{2} +(3.45191 - 10.6239i) q^{4} +(10.9424 - 2.29411i) q^{5} -21.8567 q^{7} +(4.28988 + 13.2029i) q^{8} +O(q^{10})\) \(q+(-3.54222 + 2.57358i) q^{2} +(3.45191 - 10.6239i) q^{4} +(10.9424 - 2.29411i) q^{5} -21.8567 q^{7} +(4.28988 + 13.2029i) q^{8} +(-32.8565 + 36.2875i) q^{10} +(17.2752 - 12.5512i) q^{11} +(-62.3251 - 45.2819i) q^{13} +(77.4214 - 56.2500i) q^{14} +(23.1234 + 16.8001i) q^{16} +(36.3807 + 111.968i) q^{17} +(33.1410 + 101.998i) q^{19} +(13.3999 - 124.170i) q^{20} +(-28.8912 + 88.9181i) q^{22} +(82.9046 - 60.2337i) q^{23} +(114.474 - 50.2064i) q^{25} +337.306 q^{26} +(-75.4476 + 232.204i) q^{28} +(-77.0758 + 237.215i) q^{29} +(44.9716 + 138.408i) q^{31} -236.204 q^{32} +(-417.027 - 302.988i) q^{34} +(-239.166 + 50.1419i) q^{35} +(-44.0318 - 31.9910i) q^{37} +(-379.891 - 276.007i) q^{38} +(77.2308 + 134.631i) q^{40} +(45.9645 + 33.3952i) q^{41} -233.645 q^{43} +(-73.7099 - 226.856i) q^{44} +(-138.650 + 426.722i) q^{46} +(-76.4532 + 235.299i) q^{47} +134.717 q^{49} +(-276.283 + 472.450i) q^{50} +(-696.211 + 505.827i) q^{52} +(-46.1009 + 141.884i) q^{53} +(160.239 - 176.972i) q^{55} +(-93.7629 - 288.573i) q^{56} +(-337.471 - 1038.63i) q^{58} +(235.190 + 170.875i) q^{59} +(-181.693 + 132.008i) q^{61} +(-515.503 - 374.535i) q^{62} +(651.698 - 473.486i) q^{64} +(-785.871 - 352.513i) q^{65} +(273.377 + 841.368i) q^{67} +1315.12 q^{68} +(718.136 - 793.126i) q^{70} +(11.8621 - 36.5077i) q^{71} +(-742.038 + 539.122i) q^{73} +238.302 q^{74} +1198.01 q^{76} +(-377.580 + 274.328i) q^{77} +(283.101 - 871.295i) q^{79} +(291.568 + 130.787i) q^{80} -248.761 q^{82} +(243.885 + 750.602i) q^{83} +(654.961 + 1141.74i) q^{85} +(827.621 - 601.302i) q^{86} +(239.821 + 174.240i) q^{88} +(409.198 - 297.300i) q^{89} +(1362.22 + 989.714i) q^{91} +(-353.737 - 1088.69i) q^{92} +(-334.745 - 1030.24i) q^{94} +(596.638 + 1040.07i) q^{95} +(5.01798 - 15.4438i) q^{97} +(-477.198 + 346.705i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.54222 + 2.57358i −1.25236 + 0.909896i −0.998357 0.0573059i \(-0.981749\pi\)
−0.254008 + 0.967202i \(0.581749\pi\)
\(3\) 0 0
\(4\) 3.45191 10.6239i 0.431489 1.32799i
\(5\) 10.9424 2.29411i 0.978722 0.205192i
\(6\) 0 0
\(7\) −21.8567 −1.18015 −0.590077 0.807347i \(-0.700902\pi\)
−0.590077 + 0.807347i \(0.700902\pi\)
\(8\) 4.28988 + 13.2029i 0.189588 + 0.583492i
\(9\) 0 0
\(10\) −32.8565 + 36.2875i −1.03901 + 1.14751i
\(11\) 17.2752 12.5512i 0.473516 0.344029i −0.325294 0.945613i \(-0.605463\pi\)
0.798810 + 0.601584i \(0.205463\pi\)
\(12\) 0 0
\(13\) −62.3251 45.2819i −1.32968 0.966071i −0.999757 0.0220647i \(-0.992976\pi\)
−0.329927 0.944007i \(-0.607024\pi\)
\(14\) 77.4214 56.2500i 1.47798 1.07382i
\(15\) 0 0
\(16\) 23.1234 + 16.8001i 0.361303 + 0.262502i
\(17\) 36.3807 + 111.968i 0.519036 + 1.59743i 0.775817 + 0.630958i \(0.217338\pi\)
−0.256781 + 0.966470i \(0.582662\pi\)
\(18\) 0 0
\(19\) 33.1410 + 101.998i 0.400162 + 1.23157i 0.924868 + 0.380288i \(0.124175\pi\)
−0.524707 + 0.851283i \(0.675825\pi\)
\(20\) 13.3999 124.170i 0.149816 1.38827i
\(21\) 0 0
\(22\) −28.8912 + 88.9181i −0.279983 + 0.861700i
\(23\) 82.9046 60.2337i 0.751600 0.546069i −0.144722 0.989472i \(-0.546229\pi\)
0.896322 + 0.443403i \(0.146229\pi\)
\(24\) 0 0
\(25\) 114.474 50.2064i 0.915793 0.401651i
\(26\) 337.306 2.54427
\(27\) 0 0
\(28\) −75.4476 + 232.204i −0.509223 + 1.56723i
\(29\) −77.0758 + 237.215i −0.493539 + 1.51896i 0.325683 + 0.945479i \(0.394406\pi\)
−0.819222 + 0.573477i \(0.805594\pi\)
\(30\) 0 0
\(31\) 44.9716 + 138.408i 0.260553 + 0.801899i 0.992685 + 0.120736i \(0.0385254\pi\)
−0.732132 + 0.681163i \(0.761475\pi\)
\(32\) −236.204 −1.30485
\(33\) 0 0
\(34\) −417.027 302.988i −2.10352 1.52829i
\(35\) −239.166 + 50.1419i −1.15504 + 0.242158i
\(36\) 0 0
\(37\) −44.0318 31.9910i −0.195643 0.142143i 0.485651 0.874153i \(-0.338582\pi\)
−0.681294 + 0.732010i \(0.738582\pi\)
\(38\) −379.891 276.007i −1.62175 1.17827i
\(39\) 0 0
\(40\) 77.2308 + 134.631i 0.305282 + 0.532174i
\(41\) 45.9645 + 33.3952i 0.175084 + 0.127206i 0.671876 0.740664i \(-0.265489\pi\)
−0.496792 + 0.867870i \(0.665489\pi\)
\(42\) 0 0
\(43\) −233.645 −0.828615 −0.414308 0.910137i \(-0.635976\pi\)
−0.414308 + 0.910137i \(0.635976\pi\)
\(44\) −73.7099 226.856i −0.252550 0.777268i
\(45\) 0 0
\(46\) −138.650 + 426.722i −0.444411 + 1.36776i
\(47\) −76.4532 + 235.299i −0.237273 + 0.730252i 0.759538 + 0.650463i \(0.225425\pi\)
−0.996812 + 0.0797898i \(0.974575\pi\)
\(48\) 0 0
\(49\) 134.717 0.392761
\(50\) −276.283 + 472.450i −0.781445 + 1.33629i
\(51\) 0 0
\(52\) −696.211 + 505.827i −1.85667 + 1.34895i
\(53\) −46.1009 + 141.884i −0.119480 + 0.367722i −0.992855 0.119327i \(-0.961926\pi\)
0.873375 + 0.487048i \(0.161926\pi\)
\(54\) 0 0
\(55\) 160.239 176.972i 0.392848 0.433871i
\(56\) −93.7629 288.573i −0.223743 0.688609i
\(57\) 0 0
\(58\) −337.471 1038.63i −0.764002 2.35136i
\(59\) 235.190 + 170.875i 0.518968 + 0.377052i 0.816215 0.577748i \(-0.196068\pi\)
−0.297247 + 0.954801i \(0.596068\pi\)
\(60\) 0 0
\(61\) −181.693 + 132.008i −0.381368 + 0.277080i −0.761909 0.647684i \(-0.775738\pi\)
0.380541 + 0.924764i \(0.375738\pi\)
\(62\) −515.503 374.535i −1.05595 0.767194i
\(63\) 0 0
\(64\) 651.698 473.486i 1.27285 0.924778i
\(65\) −785.871 352.513i −1.49962 0.672675i
\(66\) 0 0
\(67\) 273.377 + 841.368i 0.498482 + 1.53417i 0.811459 + 0.584410i \(0.198674\pi\)
−0.312977 + 0.949761i \(0.601326\pi\)
\(68\) 1315.12 2.34532
\(69\) 0 0
\(70\) 718.136 793.126i 1.22619 1.35424i
\(71\) 11.8621 36.5077i 0.0198278 0.0610235i −0.940653 0.339370i \(-0.889786\pi\)
0.960481 + 0.278346i \(0.0897862\pi\)
\(72\) 0 0
\(73\) −742.038 + 539.122i −1.18971 + 0.864376i −0.993234 0.116132i \(-0.962950\pi\)
−0.196478 + 0.980508i \(0.562950\pi\)
\(74\) 238.302 0.374351
\(75\) 0 0
\(76\) 1198.01 1.80818
\(77\) −377.580 + 274.328i −0.558821 + 0.406007i
\(78\) 0 0
\(79\) 283.101 871.295i 0.403181 1.24086i −0.519223 0.854639i \(-0.673779\pi\)
0.922404 0.386226i \(-0.126221\pi\)
\(80\) 291.568 + 130.787i 0.407479 + 0.182780i
\(81\) 0 0
\(82\) −248.761 −0.335013
\(83\) 243.885 + 750.602i 0.322529 + 0.992642i 0.972544 + 0.232720i \(0.0747626\pi\)
−0.650015 + 0.759921i \(0.725237\pi\)
\(84\) 0 0
\(85\) 654.961 + 1141.74i 0.835771 + 1.45694i
\(86\) 827.621 601.302i 1.03773 0.753954i
\(87\) 0 0
\(88\) 239.821 + 174.240i 0.290511 + 0.211069i
\(89\) 409.198 297.300i 0.487358 0.354087i −0.316809 0.948489i \(-0.602611\pi\)
0.804168 + 0.594403i \(0.202611\pi\)
\(90\) 0 0
\(91\) 1362.22 + 989.714i 1.56923 + 1.14011i
\(92\) −353.737 1088.69i −0.400866 1.23374i
\(93\) 0 0
\(94\) −334.745 1030.24i −0.367301 1.13044i
\(95\) 596.638 + 1040.07i 0.644355 + 1.12326i
\(96\) 0 0
\(97\) 5.01798 15.4438i 0.00525257 0.0161657i −0.948396 0.317089i \(-0.897295\pi\)
0.953648 + 0.300923i \(0.0972947\pi\)
\(98\) −477.198 + 346.705i −0.491881 + 0.357372i
\(99\) 0 0
\(100\) −138.233 1389.47i −0.138233 1.38947i
\(101\) −968.668 −0.954317 −0.477159 0.878817i \(-0.658333\pi\)
−0.477159 + 0.878817i \(0.658333\pi\)
\(102\) 0 0
\(103\) 181.635 559.014i 0.173757 0.534769i −0.825817 0.563938i \(-0.809286\pi\)
0.999575 + 0.0291682i \(0.00928585\pi\)
\(104\) 330.485 1017.13i 0.311603 0.959014i
\(105\) 0 0
\(106\) −201.849 621.228i −0.184956 0.569236i
\(107\) 1331.12 1.20266 0.601330 0.799001i \(-0.294638\pi\)
0.601330 + 0.799001i \(0.294638\pi\)
\(108\) 0 0
\(109\) −1078.47 783.552i −0.947691 0.688538i 0.00256836 0.999997i \(-0.499182\pi\)
−0.950260 + 0.311459i \(0.899182\pi\)
\(110\) −112.152 + 1039.26i −0.0972119 + 0.900815i
\(111\) 0 0
\(112\) −505.403 367.196i −0.426393 0.309793i
\(113\) 1470.95 + 1068.71i 1.22456 + 0.889694i 0.996470 0.0839467i \(-0.0267526\pi\)
0.228088 + 0.973640i \(0.426753\pi\)
\(114\) 0 0
\(115\) 768.996 849.296i 0.623558 0.688672i
\(116\) 2254.09 + 1637.69i 1.80420 + 1.31083i
\(117\) 0 0
\(118\) −1272.86 −0.993016
\(119\) −795.163 2447.26i −0.612542 1.88521i
\(120\) 0 0
\(121\) −270.401 + 832.208i −0.203156 + 0.625250i
\(122\) 303.866 935.203i 0.225498 0.694011i
\(123\) 0 0
\(124\) 1625.67 1.17734
\(125\) 1137.45 811.998i 0.813891 0.581018i
\(126\) 0 0
\(127\) 285.926 207.737i 0.199778 0.145147i −0.483399 0.875400i \(-0.660598\pi\)
0.683177 + 0.730253i \(0.260598\pi\)
\(128\) −505.980 + 1557.24i −0.349396 + 1.07533i
\(129\) 0 0
\(130\) 3690.95 773.818i 2.49014 0.522064i
\(131\) 181.395 + 558.278i 0.120982 + 0.372343i 0.993148 0.116867i \(-0.0372851\pi\)
−0.872166 + 0.489210i \(0.837285\pi\)
\(132\) 0 0
\(133\) −724.355 2229.33i −0.472252 1.45344i
\(134\) −3133.68 2276.76i −2.02022 1.46777i
\(135\) 0 0
\(136\) −1322.24 + 960.661i −0.833683 + 0.605706i
\(137\) −2105.35 1529.63i −1.31294 0.953905i −0.999991 0.00413341i \(-0.998684\pi\)
−0.312945 0.949771i \(-0.601316\pi\)
\(138\) 0 0
\(139\) −1405.38 + 1021.07i −0.857576 + 0.623065i −0.927224 0.374506i \(-0.877812\pi\)
0.0696487 + 0.997572i \(0.477812\pi\)
\(140\) −292.879 + 2713.96i −0.176805 + 1.63837i
\(141\) 0 0
\(142\) 51.9373 + 159.846i 0.0306935 + 0.0944649i
\(143\) −1645.02 −0.961983
\(144\) 0 0
\(145\) −299.199 + 2772.53i −0.171360 + 1.58791i
\(146\) 1240.99 3819.38i 0.703460 2.16503i
\(147\) 0 0
\(148\) −491.863 + 357.359i −0.273182 + 0.198478i
\(149\) −341.168 −0.187581 −0.0937905 0.995592i \(-0.529898\pi\)
−0.0937905 + 0.995592i \(0.529898\pi\)
\(150\) 0 0
\(151\) 3335.13 1.79741 0.898705 0.438554i \(-0.144509\pi\)
0.898705 + 0.438554i \(0.144509\pi\)
\(152\) −1204.49 + 875.115i −0.642745 + 0.466982i
\(153\) 0 0
\(154\) 631.469 1943.46i 0.330423 1.01694i
\(155\) 809.623 + 1411.35i 0.419552 + 0.731373i
\(156\) 0 0
\(157\) −1141.72 −0.580379 −0.290190 0.956969i \(-0.593718\pi\)
−0.290190 + 0.956969i \(0.593718\pi\)
\(158\) 1239.54 + 3814.90i 0.624128 + 1.92087i
\(159\) 0 0
\(160\) −2584.64 + 541.878i −1.27709 + 0.267745i
\(161\) −1812.02 + 1316.51i −0.887003 + 0.644446i
\(162\) 0 0
\(163\) 1751.41 + 1272.47i 0.841601 + 0.611459i 0.922817 0.385238i \(-0.125881\pi\)
−0.0812166 + 0.996696i \(0.525881\pi\)
\(164\) 513.452 373.045i 0.244475 0.177621i
\(165\) 0 0
\(166\) −2795.63 2031.14i −1.30712 0.949682i
\(167\) 369.459 + 1137.08i 0.171195 + 0.526885i 0.999439 0.0334827i \(-0.0106599\pi\)
−0.828244 + 0.560368i \(0.810660\pi\)
\(168\) 0 0
\(169\) 1155.06 + 3554.92i 0.525746 + 1.61808i
\(170\) −5258.38 2358.72i −2.37235 1.06415i
\(171\) 0 0
\(172\) −806.521 + 2482.22i −0.357539 + 1.10039i
\(173\) −1310.74 + 952.305i −0.576031 + 0.418511i −0.837291 0.546757i \(-0.815862\pi\)
0.261260 + 0.965268i \(0.415862\pi\)
\(174\) 0 0
\(175\) −2502.03 + 1097.35i −1.08078 + 0.474010i
\(176\) 610.324 0.261391
\(177\) 0 0
\(178\) −684.347 + 2106.20i −0.288168 + 0.886891i
\(179\) 972.050 2991.66i 0.405891 1.24920i −0.514258 0.857635i \(-0.671933\pi\)
0.920149 0.391568i \(-0.128067\pi\)
\(180\) 0 0
\(181\) −142.108 437.363i −0.0583579 0.179607i 0.917628 0.397440i \(-0.130101\pi\)
−0.975986 + 0.217833i \(0.930101\pi\)
\(182\) −7372.40 −3.00263
\(183\) 0 0
\(184\) 1150.91 + 836.186i 0.461121 + 0.335024i
\(185\) −555.206 249.045i −0.220646 0.0989739i
\(186\) 0 0
\(187\) 2033.82 + 1477.65i 0.795334 + 0.577844i
\(188\) 2235.88 + 1624.46i 0.867385 + 0.630192i
\(189\) 0 0
\(190\) −4790.13 2148.68i −1.82901 0.820429i
\(191\) 1813.80 + 1317.80i 0.687130 + 0.499229i 0.875715 0.482827i \(-0.160390\pi\)
−0.188585 + 0.982057i \(0.560390\pi\)
\(192\) 0 0
\(193\) 3741.08 1.39528 0.697639 0.716449i \(-0.254234\pi\)
0.697639 + 0.716449i \(0.254234\pi\)
\(194\) 21.9709 + 67.6194i 0.00813102 + 0.0250247i
\(195\) 0 0
\(196\) 465.032 1431.22i 0.169472 0.521582i
\(197\) 247.694 762.324i 0.0895811 0.275702i −0.896223 0.443605i \(-0.853699\pi\)
0.985804 + 0.167903i \(0.0536994\pi\)
\(198\) 0 0
\(199\) −2298.96 −0.818941 −0.409471 0.912323i \(-0.634287\pi\)
−0.409471 + 0.912323i \(0.634287\pi\)
\(200\) 1153.95 + 1296.01i 0.407983 + 0.458209i
\(201\) 0 0
\(202\) 3431.24 2492.94i 1.19515 0.868330i
\(203\) 1684.63 5184.75i 0.582451 1.79260i
\(204\) 0 0
\(205\) 579.576 + 259.977i 0.197460 + 0.0885735i
\(206\) 795.274 + 2447.60i 0.268977 + 0.827827i
\(207\) 0 0
\(208\) −680.428 2094.14i −0.226823 0.698090i
\(209\) 1852.71 + 1346.07i 0.613179 + 0.445501i
\(210\) 0 0
\(211\) −1603.13 + 1164.74i −0.523052 + 0.380020i −0.817752 0.575570i \(-0.804780\pi\)
0.294700 + 0.955590i \(0.404780\pi\)
\(212\) 1348.22 + 979.541i 0.436775 + 0.317336i
\(213\) 0 0
\(214\) −4715.13 + 3425.74i −1.50617 + 1.09429i
\(215\) −2556.64 + 536.008i −0.810984 + 0.170025i
\(216\) 0 0
\(217\) −982.932 3025.15i −0.307492 0.946363i
\(218\) 5836.70 1.81335
\(219\) 0 0
\(220\) −1327.00 2313.26i −0.406665 0.708908i
\(221\) 2802.70 8625.81i 0.853076 2.62550i
\(222\) 0 0
\(223\) −5182.06 + 3764.99i −1.55613 + 1.13059i −0.617031 + 0.786939i \(0.711665\pi\)
−0.939096 + 0.343654i \(0.888335\pi\)
\(224\) 5162.64 1.53993
\(225\) 0 0
\(226\) −7960.82 −2.34312
\(227\) 2378.84 1728.33i 0.695548 0.505345i −0.182931 0.983126i \(-0.558559\pi\)
0.878479 + 0.477780i \(0.158559\pi\)
\(228\) 0 0
\(229\) −97.7803 + 300.937i −0.0282162 + 0.0868405i −0.964173 0.265275i \(-0.914537\pi\)
0.935957 + 0.352115i \(0.114537\pi\)
\(230\) −538.225 + 4987.46i −0.154302 + 1.42984i
\(231\) 0 0
\(232\) −3462.57 −0.979867
\(233\) 539.286 + 1659.75i 0.151630 + 0.466670i 0.997804 0.0662375i \(-0.0210995\pi\)
−0.846174 + 0.532907i \(0.821099\pi\)
\(234\) 0 0
\(235\) −296.782 + 2750.14i −0.0823828 + 0.763400i
\(236\) 2627.22 1908.79i 0.724650 0.526489i
\(237\) 0 0
\(238\) 9114.85 + 6622.33i 2.48247 + 1.80362i
\(239\) −549.214 + 399.027i −0.148643 + 0.107996i −0.659621 0.751598i \(-0.729283\pi\)
0.510978 + 0.859594i \(0.329283\pi\)
\(240\) 0 0
\(241\) −1023.83 743.856i −0.273654 0.198822i 0.442491 0.896773i \(-0.354095\pi\)
−0.716145 + 0.697952i \(0.754095\pi\)
\(242\) −1183.93 3643.76i −0.314487 0.967892i
\(243\) 0 0
\(244\) 775.249 + 2385.97i 0.203403 + 0.626009i
\(245\) 1474.13 309.057i 0.384404 0.0805915i
\(246\) 0 0
\(247\) 2553.12 7857.70i 0.657697 2.02418i
\(248\) −1634.47 + 1187.51i −0.418504 + 0.304061i
\(249\) 0 0
\(250\) −1939.35 + 5803.58i −0.490621 + 1.46820i
\(251\) 1923.82 0.483787 0.241893 0.970303i \(-0.422232\pi\)
0.241893 + 0.970303i \(0.422232\pi\)
\(252\) 0 0
\(253\) 676.190 2081.10i 0.168031 0.517145i
\(254\) −478.186 + 1471.70i −0.118126 + 0.363555i
\(255\) 0 0
\(256\) −223.982 689.346i −0.0546832 0.168297i
\(257\) −489.131 −0.118720 −0.0593602 0.998237i \(-0.518906\pi\)
−0.0593602 + 0.998237i \(0.518906\pi\)
\(258\) 0 0
\(259\) 962.392 + 699.218i 0.230888 + 0.167750i
\(260\) −6457.82 + 7132.17i −1.54037 + 1.70122i
\(261\) 0 0
\(262\) −2079.31 1510.71i −0.490307 0.356229i
\(263\) −4631.04 3364.65i −1.08579 0.788870i −0.107104 0.994248i \(-0.534158\pi\)
−0.978683 + 0.205377i \(0.934158\pi\)
\(264\) 0 0
\(265\) −178.958 + 1658.32i −0.0414842 + 0.384413i
\(266\) 8303.18 + 6032.62i 1.91391 + 1.39054i
\(267\) 0 0
\(268\) 9882.28 2.25245
\(269\) 1181.25 + 3635.51i 0.267740 + 0.824019i 0.991050 + 0.133495i \(0.0426200\pi\)
−0.723310 + 0.690524i \(0.757380\pi\)
\(270\) 0 0
\(271\) 1514.67 4661.67i 0.339518 1.04493i −0.624935 0.780677i \(-0.714874\pi\)
0.964453 0.264253i \(-0.0851255\pi\)
\(272\) −1039.84 + 3200.29i −0.231799 + 0.713404i
\(273\) 0 0
\(274\) 11394.2 2.51223
\(275\) 1347.41 2304.11i 0.295462 0.505248i
\(276\) 0 0
\(277\) 5143.76 3737.16i 1.11573 0.810628i 0.132177 0.991226i \(-0.457803\pi\)
0.983557 + 0.180598i \(0.0578032\pi\)
\(278\) 2350.38 7233.72i 0.507073 1.56061i
\(279\) 0 0
\(280\) −1688.01 2942.59i −0.360279 0.628047i
\(281\) −980.710 3018.32i −0.208200 0.640775i −0.999567 0.0294325i \(-0.990630\pi\)
0.791367 0.611342i \(-0.209370\pi\)
\(282\) 0 0
\(283\) −1794.88 5524.08i −0.377013 1.16033i −0.942110 0.335303i \(-0.891161\pi\)
0.565097 0.825024i \(-0.308839\pi\)
\(284\) −346.908 252.043i −0.0724830 0.0526620i
\(285\) 0 0
\(286\) 5827.03 4233.58i 1.20475 0.875304i
\(287\) −1004.63 729.909i −0.206626 0.150123i
\(288\) 0 0
\(289\) −7238.62 + 5259.16i −1.47336 + 1.07046i
\(290\) −6075.49 10590.9i −1.23022 2.14456i
\(291\) 0 0
\(292\) 3166.13 + 9744.34i 0.634533 + 1.95289i
\(293\) 8177.25 1.63044 0.815222 0.579148i \(-0.196615\pi\)
0.815222 + 0.579148i \(0.196615\pi\)
\(294\) 0 0
\(295\) 2965.56 + 1330.24i 0.585293 + 0.262541i
\(296\) 233.483 718.585i 0.0458476 0.141104i
\(297\) 0 0
\(298\) 1208.49 878.022i 0.234920 0.170679i
\(299\) −7894.53 −1.52693
\(300\) 0 0
\(301\) 5106.71 0.977893
\(302\) −11813.8 + 8583.20i −2.25101 + 1.63546i
\(303\) 0 0
\(304\) −947.240 + 2915.31i −0.178710 + 0.550014i
\(305\) −1685.33 + 1861.31i −0.316399 + 0.349438i
\(306\) 0 0
\(307\) 6696.78 1.24497 0.622485 0.782632i \(-0.286123\pi\)
0.622485 + 0.782632i \(0.286123\pi\)
\(308\) 1611.06 + 4958.33i 0.298047 + 0.917295i
\(309\) 0 0
\(310\) −6500.09 2915.71i −1.19090 0.534197i
\(311\) −5289.10 + 3842.76i −0.964365 + 0.700652i −0.954160 0.299296i \(-0.903248\pi\)
−0.0102048 + 0.999948i \(0.503248\pi\)
\(312\) 0 0
\(313\) −8090.51 5878.10i −1.46103 1.06150i −0.983093 0.183109i \(-0.941384\pi\)
−0.477939 0.878393i \(-0.658616\pi\)
\(314\) 4044.24 2938.31i 0.726846 0.528085i
\(315\) 0 0
\(316\) −8279.31 6015.27i −1.47388 1.07084i
\(317\) −55.6242 171.194i −0.00985542 0.0303319i 0.946008 0.324144i \(-0.105076\pi\)
−0.955863 + 0.293812i \(0.905076\pi\)
\(318\) 0 0
\(319\) 1645.83 + 5065.33i 0.288867 + 0.889041i
\(320\) 6044.94 6676.17i 1.05601 1.16628i
\(321\) 0 0
\(322\) 3030.45 9326.76i 0.524473 1.61416i
\(323\) −10214.8 + 7421.48i −1.75965 + 1.27846i
\(324\) 0 0
\(325\) −9408.05 2054.48i −1.60574 0.350652i
\(326\) −9478.68 −1.61036
\(327\) 0 0
\(328\) −243.731 + 750.126i −0.0410298 + 0.126277i
\(329\) 1671.02 5142.87i 0.280019 0.861810i
\(330\) 0 0
\(331\) 213.987 + 658.583i 0.0355341 + 0.109363i 0.967250 0.253825i \(-0.0816886\pi\)
−0.931716 + 0.363187i \(0.881689\pi\)
\(332\) 8816.19 1.45738
\(333\) 0 0
\(334\) −4235.06 3076.95i −0.693809 0.504082i
\(335\) 4921.60 + 8579.46i 0.802675 + 1.39924i
\(336\) 0 0
\(337\) 1693.17 + 1230.16i 0.273688 + 0.198846i 0.716160 0.697937i \(-0.245898\pi\)
−0.442472 + 0.896782i \(0.645898\pi\)
\(338\) −13240.4 9619.68i −2.13071 1.54805i
\(339\) 0 0
\(340\) 14390.6 3017.04i 2.29542 0.481241i
\(341\) 2514.08 + 1826.59i 0.399253 + 0.290074i
\(342\) 0 0
\(343\) 4552.38 0.716634
\(344\) −1002.31 3084.79i −0.157095 0.483490i
\(345\) 0 0
\(346\) 2192.09 6746.55i 0.340599 1.04826i
\(347\) −662.825 + 2039.97i −0.102543 + 0.315594i −0.989146 0.146937i \(-0.953059\pi\)
0.886603 + 0.462531i \(0.153059\pi\)
\(348\) 0 0
\(349\) −6207.24 −0.952051 −0.476026 0.879431i \(-0.657923\pi\)
−0.476026 + 0.879431i \(0.657923\pi\)
\(350\) 6038.64 10326.2i 0.922225 1.57703i
\(351\) 0 0
\(352\) −4080.47 + 2964.63i −0.617868 + 0.448908i
\(353\) −4011.53 + 12346.2i −0.604851 + 1.86154i −0.107038 + 0.994255i \(0.534137\pi\)
−0.497813 + 0.867284i \(0.665863\pi\)
\(354\) 0 0
\(355\) 46.0472 426.697i 0.00688432 0.0637936i
\(356\) −1745.97 5373.53i −0.259933 0.799990i
\(357\) 0 0
\(358\) 4256.05 + 13098.8i 0.628322 + 1.93378i
\(359\) 2265.91 + 1646.28i 0.333120 + 0.242026i 0.741753 0.670673i \(-0.233995\pi\)
−0.408633 + 0.912699i \(0.633995\pi\)
\(360\) 0 0
\(361\) −3756.13 + 2728.99i −0.547620 + 0.397869i
\(362\) 1628.96 + 1183.51i 0.236509 + 0.171834i
\(363\) 0 0
\(364\) 15216.9 11055.7i 2.19116 1.59197i
\(365\) −6882.90 + 7601.63i −0.987034 + 1.09010i
\(366\) 0 0
\(367\) −2800.19 8618.09i −0.398280 1.22578i −0.926378 0.376595i \(-0.877095\pi\)
0.528098 0.849183i \(-0.322905\pi\)
\(368\) 2928.97 0.414900
\(369\) 0 0
\(370\) 2607.60 546.691i 0.366386 0.0768138i
\(371\) 1007.61 3101.12i 0.141005 0.433968i
\(372\) 0 0
\(373\) 726.587 527.896i 0.100861 0.0732800i −0.536212 0.844084i \(-0.680145\pi\)
0.637073 + 0.770804i \(0.280145\pi\)
\(374\) −11007.1 −1.52183
\(375\) 0 0
\(376\) −3434.60 −0.471080
\(377\) 15545.3 11294.3i 2.12367 1.54294i
\(378\) 0 0
\(379\) 2096.07 6451.03i 0.284084 0.874319i −0.702588 0.711597i \(-0.747972\pi\)
0.986672 0.162723i \(-0.0520276\pi\)
\(380\) 13109.2 2748.38i 1.76970 0.371023i
\(381\) 0 0
\(382\) −9816.34 −1.31478
\(383\) 2095.27 + 6448.58i 0.279539 + 0.860331i 0.987983 + 0.154564i \(0.0493974\pi\)
−0.708444 + 0.705767i \(0.750603\pi\)
\(384\) 0 0
\(385\) −3502.31 + 3868.03i −0.463621 + 0.512034i
\(386\) −13251.7 + 9627.94i −1.74740 + 1.26956i
\(387\) 0 0
\(388\) −146.751 106.621i −0.0192015 0.0139507i
\(389\) −3113.57 + 2262.14i −0.405820 + 0.294846i −0.771907 0.635735i \(-0.780697\pi\)
0.366087 + 0.930581i \(0.380697\pi\)
\(390\) 0 0
\(391\) 9760.38 + 7091.33i 1.26241 + 0.917197i
\(392\) 577.921 + 1778.66i 0.0744628 + 0.229173i
\(393\) 0 0
\(394\) 1084.51 + 3337.78i 0.138672 + 0.426789i
\(395\) 1098.96 10183.6i 0.139987 1.29719i
\(396\) 0 0
\(397\) −2105.97 + 6481.51i −0.266236 + 0.819389i 0.725171 + 0.688569i \(0.241761\pi\)
−0.991406 + 0.130820i \(0.958239\pi\)
\(398\) 8143.44 5916.56i 1.02561 0.745151i
\(399\) 0 0
\(400\) 3490.51 + 762.237i 0.436313 + 0.0952796i
\(401\) −14456.1 −1.80025 −0.900127 0.435627i \(-0.856527\pi\)
−0.900127 + 0.435627i \(0.856527\pi\)
\(402\) 0 0
\(403\) 3464.52 10662.7i 0.428239 1.31798i
\(404\) −3343.76 + 10291.0i −0.411778 + 1.26732i
\(405\) 0 0
\(406\) 7376.02 + 22701.0i 0.901639 + 2.77496i
\(407\) −1162.18 −0.141541
\(408\) 0 0
\(409\) −10118.6 7351.62i −1.22331 0.888788i −0.226941 0.973909i \(-0.572872\pi\)
−0.996371 + 0.0851209i \(0.972872\pi\)
\(410\) −2722.06 + 570.687i −0.327885 + 0.0687420i
\(411\) 0 0
\(412\) −5311.92 3859.33i −0.635193 0.461494i
\(413\) −5140.48 3734.78i −0.612462 0.444980i
\(414\) 0 0
\(415\) 4390.67 + 7653.92i 0.519348 + 0.905340i
\(416\) 14721.4 + 10695.7i 1.73504 + 1.26058i
\(417\) 0 0
\(418\) −10026.9 −1.17328
\(419\) −3297.18 10147.7i −0.384434 1.18317i −0.936890 0.349624i \(-0.886309\pi\)
0.552456 0.833542i \(-0.313691\pi\)
\(420\) 0 0
\(421\) 1024.54 3153.20i 0.118606 0.365030i −0.874076 0.485788i \(-0.838533\pi\)
0.992682 + 0.120758i \(0.0385326\pi\)
\(422\) 2681.09 8251.55i 0.309274 0.951846i
\(423\) 0 0
\(424\) −2071.05 −0.237214
\(425\) 9786.17 + 10990.9i 1.11694 + 1.25444i
\(426\) 0 0
\(427\) 3971.22 2885.26i 0.450073 0.326997i
\(428\) 4594.92 14141.7i 0.518934 1.59712i
\(429\) 0 0
\(430\) 7676.74 8478.37i 0.860942 0.950845i
\(431\) 3822.49 + 11764.4i 0.427199 + 1.31478i 0.900873 + 0.434083i \(0.142928\pi\)
−0.473674 + 0.880701i \(0.657072\pi\)
\(432\) 0 0
\(433\) −174.988 538.559i −0.0194213 0.0597725i 0.940876 0.338751i \(-0.110004\pi\)
−0.960297 + 0.278978i \(0.910004\pi\)
\(434\) 11267.2 + 8186.12i 1.24618 + 0.905406i
\(435\) 0 0
\(436\) −12047.1 + 8752.76i −1.32329 + 0.961425i
\(437\) 8891.23 + 6459.86i 0.973285 + 0.707133i
\(438\) 0 0
\(439\) 8114.02 5895.18i 0.882144 0.640915i −0.0516738 0.998664i \(-0.516456\pi\)
0.933818 + 0.357749i \(0.116456\pi\)
\(440\) 3023.95 + 1356.43i 0.327639 + 0.146967i
\(441\) 0 0
\(442\) 12271.4 + 37767.5i 1.32057 + 4.06429i
\(443\) 1985.26 0.212918 0.106459 0.994317i \(-0.466049\pi\)
0.106459 + 0.994317i \(0.466049\pi\)
\(444\) 0 0
\(445\) 3795.59 4191.93i 0.404333 0.446554i
\(446\) 8666.53 26672.8i 0.920117 2.83183i
\(447\) 0 0
\(448\) −14244.0 + 10348.9i −1.50216 + 1.09138i
\(449\) 8871.95 0.932501 0.466251 0.884653i \(-0.345605\pi\)
0.466251 + 0.884653i \(0.345605\pi\)
\(450\) 0 0
\(451\) 1213.19 0.126668
\(452\) 16431.4 11938.1i 1.70989 1.24230i
\(453\) 0 0
\(454\) −3978.40 + 12244.3i −0.411268 + 1.26575i
\(455\) 17176.6 + 7704.79i 1.76978 + 0.793859i
\(456\) 0 0
\(457\) −16226.8 −1.66096 −0.830481 0.557047i \(-0.811934\pi\)
−0.830481 + 0.557047i \(0.811934\pi\)
\(458\) −428.124 1317.63i −0.0436789 0.134430i
\(459\) 0 0
\(460\) −6368.33 11101.4i −0.645489 1.12523i
\(461\) −11687.2 + 8491.23i −1.18075 + 0.857865i −0.992256 0.124209i \(-0.960361\pi\)
−0.188494 + 0.982074i \(0.560361\pi\)
\(462\) 0 0
\(463\) −6186.58 4494.82i −0.620983 0.451170i 0.232282 0.972648i \(-0.425381\pi\)
−0.853265 + 0.521478i \(0.825381\pi\)
\(464\) −5767.50 + 4190.34i −0.577047 + 0.419249i
\(465\) 0 0
\(466\) −6181.77 4491.32i −0.614517 0.446473i
\(467\) 1061.82 + 3267.96i 0.105215 + 0.323818i 0.989781 0.142597i \(-0.0455453\pi\)
−0.884566 + 0.466415i \(0.845545\pi\)
\(468\) 0 0
\(469\) −5975.13 18389.6i −0.588285 1.81056i
\(470\) −6026.41 10505.4i −0.591442 1.03102i
\(471\) 0 0
\(472\) −1247.12 + 3838.23i −0.121617 + 0.374298i
\(473\) −4036.26 + 2932.51i −0.392362 + 0.285068i
\(474\) 0 0
\(475\) 8914.72 + 10012.2i 0.861127 + 0.967138i
\(476\) −28744.3 −2.76784
\(477\) 0 0
\(478\) 918.511 2826.89i 0.0878906 0.270500i
\(479\) 353.491 1087.93i 0.0337190 0.103776i −0.932780 0.360445i \(-0.882625\pi\)
0.966499 + 0.256669i \(0.0826249\pi\)
\(480\) 0 0
\(481\) 1295.68 + 3987.68i 0.122823 + 0.378010i
\(482\) 5541.00 0.523622
\(483\) 0 0
\(484\) 7907.89 + 5745.42i 0.742664 + 0.539577i
\(485\) 19.4792 180.504i 0.00182372 0.0168995i
\(486\) 0 0
\(487\) −3522.21 2559.03i −0.327734 0.238113i 0.411735 0.911304i \(-0.364923\pi\)
−0.739468 + 0.673191i \(0.764923\pi\)
\(488\) −2522.33 1832.58i −0.233977 0.169994i
\(489\) 0 0
\(490\) −4426.33 + 4888.54i −0.408084 + 0.450698i
\(491\) −7271.58 5283.11i −0.668354 0.485588i 0.201120 0.979567i \(-0.435542\pi\)
−0.869474 + 0.493979i \(0.835542\pi\)
\(492\) 0 0
\(493\) −29364.6 −2.68259
\(494\) 11178.7 + 34404.4i 1.01812 + 3.13345i
\(495\) 0 0
\(496\) −1285.38 + 3956.00i −0.116362 + 0.358124i
\(497\) −259.267 + 797.940i −0.0233998 + 0.0720171i
\(498\) 0 0
\(499\) −14839.0 −1.33123 −0.665616 0.746295i \(-0.731831\pi\)
−0.665616 + 0.746295i \(0.731831\pi\)
\(500\) −4700.21 14887.1i −0.420400 1.33154i
\(501\) 0 0
\(502\) −6814.60 + 4951.10i −0.605878 + 0.440196i
\(503\) 4080.30 12557.9i 0.361693 1.11318i −0.590333 0.807160i \(-0.701004\pi\)
0.952026 0.306017i \(-0.0989965\pi\)
\(504\) 0 0
\(505\) −10599.6 + 2222.23i −0.934011 + 0.195818i
\(506\) 2960.65 + 9111.95i 0.260113 + 0.800544i
\(507\) 0 0
\(508\) −1219.99 3754.74i −0.106552 0.327932i
\(509\) −9940.49 7222.19i −0.865628 0.628915i 0.0637826 0.997964i \(-0.479684\pi\)
−0.929410 + 0.369049i \(0.879684\pi\)
\(510\) 0 0
\(511\) 16218.5 11783.5i 1.40404 1.02010i
\(512\) −8029.89 5834.06i −0.693114 0.503577i
\(513\) 0 0
\(514\) 1732.61 1258.82i 0.148681 0.108023i
\(515\) 705.084 6533.66i 0.0603295 0.559044i
\(516\) 0 0
\(517\) 1632.53 + 5024.42i 0.138876 + 0.427415i
\(518\) −5208.50 −0.441792
\(519\) 0 0
\(520\) 1282.90 11888.0i 0.108190 1.00255i
\(521\) 2776.27 8544.47i 0.233456 0.718503i −0.763867 0.645374i \(-0.776702\pi\)
0.997322 0.0731289i \(-0.0232985\pi\)
\(522\) 0 0
\(523\) 10821.0 7861.90i 0.904719 0.657317i −0.0349548 0.999389i \(-0.511129\pi\)
0.939674 + 0.342072i \(0.111129\pi\)
\(524\) 6557.24 0.546669
\(525\) 0 0
\(526\) 25063.3 2.07759
\(527\) −13861.2 + 10070.8i −1.14574 + 0.832428i
\(528\) 0 0
\(529\) −514.739 + 1584.20i −0.0423062 + 0.130205i
\(530\) −3633.89 6334.69i −0.297823 0.519172i
\(531\) 0 0
\(532\) −26184.6 −2.13392
\(533\) −1352.55 4162.71i −0.109916 0.338287i
\(534\) 0 0
\(535\) 14565.7 3053.75i 1.17707 0.246776i
\(536\) −9935.74 + 7218.74i −0.800669 + 0.581720i
\(537\) 0 0
\(538\) −13540.5 9837.76i −1.08508 0.788356i
\(539\) 2327.27 1690.86i 0.185979 0.135121i
\(540\) 0 0
\(541\) −1366.44 992.774i −0.108591 0.0788959i 0.532165 0.846641i \(-0.321379\pi\)
−0.640755 + 0.767745i \(0.721379\pi\)
\(542\) 6631.86 + 20410.8i 0.525577 + 1.61756i
\(543\) 0 0
\(544\) −8593.24 26447.3i −0.677265 2.08441i
\(545\) −13598.6 6099.84i −1.06881 0.479429i
\(546\) 0 0
\(547\) −1264.47 + 3891.65i −0.0988392 + 0.304196i −0.988235 0.152942i \(-0.951125\pi\)
0.889396 + 0.457138i \(0.151125\pi\)
\(548\) −23518.1 + 17086.9i −1.83329 + 1.33196i
\(549\) 0 0
\(550\) 1156.96 + 11629.3i 0.0896965 + 0.901594i
\(551\) −26749.7 −2.06820
\(552\) 0 0
\(553\) −6187.66 + 19043.7i −0.475816 + 1.46441i
\(554\) −8602.47 + 26475.7i −0.659718 + 2.03040i
\(555\) 0 0
\(556\) 5996.49 + 18455.3i 0.457388 + 1.40770i
\(557\) 7123.59 0.541896 0.270948 0.962594i \(-0.412663\pi\)
0.270948 + 0.962594i \(0.412663\pi\)
\(558\) 0 0
\(559\) 14561.9 + 10579.9i 1.10180 + 0.800502i
\(560\) −6372.73 2858.57i −0.480887 0.215709i
\(561\) 0 0
\(562\) 11241.8 + 8167.61i 0.843781 + 0.613043i
\(563\) −3326.72 2417.00i −0.249031 0.180932i 0.456266 0.889843i \(-0.349186\pi\)
−0.705297 + 0.708912i \(0.749186\pi\)
\(564\) 0 0
\(565\) 18547.5 + 8319.73i 1.38106 + 0.619493i
\(566\) 20574.5 + 14948.3i 1.52794 + 1.11011i
\(567\) 0 0
\(568\) 532.895 0.0393658
\(569\) −1887.85 5810.22i −0.139091 0.428079i 0.857113 0.515129i \(-0.172256\pi\)
−0.996204 + 0.0870499i \(0.972256\pi\)
\(570\) 0 0
\(571\) −4801.53 + 14777.6i −0.351905 + 1.08305i 0.605877 + 0.795558i \(0.292822\pi\)
−0.957782 + 0.287494i \(0.907178\pi\)
\(572\) −5678.47 + 17476.5i −0.415085 + 1.27750i
\(573\) 0 0
\(574\) 5437.11 0.395367
\(575\) 6466.31 11057.5i 0.468980 0.801968i
\(576\) 0 0
\(577\) 14800.3 10753.1i 1.06784 0.775833i 0.0923197 0.995729i \(-0.470572\pi\)
0.975523 + 0.219896i \(0.0705718\pi\)
\(578\) 12105.9 37258.3i 0.871178 2.68121i
\(579\) 0 0
\(580\) 28422.3 + 12749.2i 2.03478 + 0.912728i
\(581\) −5330.54 16405.7i −0.380633 1.17147i
\(582\) 0 0
\(583\) 984.407 + 3029.69i 0.0699314 + 0.215227i
\(584\) −10301.2 7484.28i −0.729911 0.530311i
\(585\) 0 0
\(586\) −28965.6 + 21044.8i −2.04191 + 1.48353i
\(587\) 14513.9 + 10544.9i 1.02053 + 0.741459i 0.966392 0.257075i \(-0.0827586\pi\)
0.0541389 + 0.998533i \(0.482759\pi\)
\(588\) 0 0
\(589\) −12626.9 + 9173.98i −0.883332 + 0.641778i
\(590\) −13928.1 + 2920.08i −0.971886 + 0.203759i
\(591\) 0 0
\(592\) −480.713 1479.48i −0.0333736 0.102713i
\(593\) −4394.87 −0.304344 −0.152172 0.988354i \(-0.548627\pi\)
−0.152172 + 0.988354i \(0.548627\pi\)
\(594\) 0 0
\(595\) −14315.3 24954.8i −0.986338 1.71941i
\(596\) −1177.68 + 3624.54i −0.0809392 + 0.249105i
\(597\) 0 0
\(598\) 27964.2 20317.2i 1.91228 1.38935i
\(599\) 27492.5 1.87531 0.937657 0.347562i \(-0.112990\pi\)
0.937657 + 0.347562i \(0.112990\pi\)
\(600\) 0 0
\(601\) 1268.01 0.0860618 0.0430309 0.999074i \(-0.486299\pi\)
0.0430309 + 0.999074i \(0.486299\pi\)
\(602\) −18089.1 + 13142.5i −1.22468 + 0.889781i
\(603\) 0 0
\(604\) 11512.6 35432.0i 0.775563 2.38694i
\(605\) −1049.66 + 9726.71i −0.0705370 + 0.653632i
\(606\) 0 0
\(607\) −6975.77 −0.466454 −0.233227 0.972422i \(-0.574929\pi\)
−0.233227 + 0.972422i \(0.574929\pi\)
\(608\) −7828.03 24092.2i −0.522152 1.60702i
\(609\) 0 0
\(610\) 1179.57 10930.5i 0.0782942 0.725514i
\(611\) 15419.7 11203.1i 1.02097 0.741781i
\(612\) 0 0
\(613\) −8481.29 6162.02i −0.558819 0.406006i 0.272207 0.962239i \(-0.412246\pi\)
−0.831027 + 0.556233i \(0.812246\pi\)
\(614\) −23721.5 + 17234.7i −1.55916 + 1.13279i
\(615\) 0 0
\(616\) −5241.70 3808.32i −0.342848 0.249093i
\(617\) −5881.65 18101.9i −0.383771 1.18112i −0.937368 0.348340i \(-0.886745\pi\)
0.553598 0.832784i \(-0.313255\pi\)
\(618\) 0 0
\(619\) 3661.02 + 11267.5i 0.237720 + 0.731628i 0.996749 + 0.0805705i \(0.0256742\pi\)
−0.759029 + 0.651057i \(0.774326\pi\)
\(620\) 17788.8 3729.48i 1.15229 0.241580i
\(621\) 0 0
\(622\) 8845.55 27223.8i 0.570216 1.75494i
\(623\) −8943.74 + 6498.00i −0.575158 + 0.417876i
\(624\) 0 0
\(625\) 10583.6 11494.7i 0.677352 0.735659i
\(626\) 43786.1 2.79560
\(627\) 0 0
\(628\) −3941.13 + 12129.6i −0.250427 + 0.770736i
\(629\) 1980.06 6094.01i 0.125517 0.386302i
\(630\) 0 0
\(631\) 1584.65 + 4877.06i 0.0999748 + 0.307691i 0.988518 0.151102i \(-0.0482821\pi\)
−0.888543 + 0.458793i \(0.848282\pi\)
\(632\) 12718.1 0.800472
\(633\) 0 0
\(634\) 637.614 + 463.253i 0.0399414 + 0.0290191i
\(635\) 2652.16 2929.10i 0.165744 0.183052i
\(636\) 0 0
\(637\) −8396.27 6100.24i −0.522248 0.379436i
\(638\) −18865.9 13706.9i −1.17070 0.850565i
\(639\) 0 0
\(640\) −1964.15 + 18200.8i −0.121312 + 1.12414i
\(641\) 22405.6 + 16278.6i 1.38061 + 1.00307i 0.996823 + 0.0796450i \(0.0253787\pi\)
0.383782 + 0.923424i \(0.374621\pi\)
\(642\) 0 0
\(643\) 10803.6 0.662603 0.331302 0.943525i \(-0.392512\pi\)
0.331302 + 0.943525i \(0.392512\pi\)
\(644\) 7731.54 + 23795.2i 0.473083 + 1.45600i
\(645\) 0 0
\(646\) 17083.3 52577.0i 1.04046 3.20219i
\(647\) 442.759 1362.67i 0.0269037 0.0828010i −0.936703 0.350125i \(-0.886139\pi\)
0.963607 + 0.267324i \(0.0861393\pi\)
\(648\) 0 0
\(649\) 6207.64 0.375457
\(650\) 38612.8 16934.9i 2.33003 1.02191i
\(651\) 0 0
\(652\) 19564.3 14214.3i 1.17515 0.853797i
\(653\) 1893.71 5828.25i 0.113486 0.349275i −0.878142 0.478400i \(-0.841217\pi\)
0.991628 + 0.129125i \(0.0412168\pi\)
\(654\) 0 0
\(655\) 3265.66 + 5692.78i 0.194809 + 0.339596i
\(656\) 501.813 + 1544.42i 0.0298666 + 0.0919199i
\(657\) 0 0
\(658\) 7316.43 + 22517.7i 0.433471 + 1.33409i
\(659\) 4865.37 + 3534.90i 0.287599 + 0.208953i 0.722225 0.691658i \(-0.243119\pi\)
−0.434626 + 0.900611i \(0.643119\pi\)
\(660\) 0 0
\(661\) −781.067 + 567.479i −0.0459607 + 0.0333924i −0.610528 0.791994i \(-0.709043\pi\)
0.564568 + 0.825387i \(0.309043\pi\)
\(662\) −2452.90 1782.14i −0.144010 0.104630i
\(663\) 0 0
\(664\) −8863.89 + 6439.99i −0.518051 + 0.376386i
\(665\) −13040.6 22732.6i −0.760438 1.32561i
\(666\) 0 0
\(667\) 7898.40 + 24308.8i 0.458512 + 1.41115i
\(668\) 13355.5 0.773565
\(669\) 0 0
\(670\) −39513.3 17724.2i −2.27841 1.02201i
\(671\) −1481.94 + 4560.93i −0.0852601 + 0.262404i
\(672\) 0 0
\(673\) 17473.2 12695.0i 1.00080 0.727127i 0.0385441 0.999257i \(-0.487728\pi\)
0.962261 + 0.272130i \(0.0877280\pi\)
\(674\) −9163.49 −0.523686
\(675\) 0 0
\(676\) 41754.3 2.37564
\(677\) 10219.9 7425.17i 0.580180 0.421525i −0.258609 0.965982i \(-0.583264\pi\)
0.838789 + 0.544457i \(0.183264\pi\)
\(678\) 0 0
\(679\) −109.677 + 337.550i −0.00619883 + 0.0190781i
\(680\) −12264.6 + 13545.3i −0.691658 + 0.763883i
\(681\) 0 0
\(682\) −13606.3 −0.763947
\(683\) 8687.87 + 26738.5i 0.486723 + 1.49798i 0.829469 + 0.558552i \(0.188643\pi\)
−0.342746 + 0.939428i \(0.611357\pi\)
\(684\) 0 0
\(685\) −26546.8 11907.9i −1.48073 0.664203i
\(686\) −16125.6 + 11715.9i −0.897488 + 0.652063i
\(687\) 0 0
\(688\) −5402.66 3925.26i −0.299382 0.217513i
\(689\) 9298.01 6755.40i 0.514116 0.373527i
\(690\) 0 0
\(691\) −7361.39 5348.36i −0.405268 0.294445i 0.366415 0.930451i \(-0.380585\pi\)
−0.771683 + 0.636007i \(0.780585\pi\)
\(692\) 5592.65 + 17212.4i 0.307226 + 0.945545i
\(693\) 0 0
\(694\) −2902.13 8931.85i −0.158737 0.488542i
\(695\) −13035.9 + 14397.1i −0.711480 + 0.785775i
\(696\) 0 0
\(697\) −2066.98 + 6361.50i −0.112328 + 0.345709i
\(698\) 21987.4 15974.8i 1.19232 0.866268i
\(699\) 0 0
\(700\) 3021.33 + 30369.3i 0.163137 + 1.63979i
\(701\) −5984.06 −0.322418 −0.161209 0.986920i \(-0.551539\pi\)
−0.161209 + 0.986920i \(0.551539\pi\)
\(702\) 0 0
\(703\) 1803.74 5551.35i 0.0967702 0.297828i
\(704\) 5315.41 16359.2i 0.284563 0.875794i
\(705\) 0 0
\(706\) −17564.2 54057.1i −0.936314 2.88168i
\(707\) 21171.9 1.12624
\(708\) 0 0
\(709\) 20955.7 + 15225.2i 1.11003 + 0.806481i 0.982668 0.185375i \(-0.0593501\pi\)
0.127359 + 0.991857i \(0.459350\pi\)
\(710\) 935.027 + 1629.96i 0.0494238 + 0.0861568i
\(711\) 0 0
\(712\) 5680.63 + 4127.22i 0.299004 + 0.217239i
\(713\) 12065.2 + 8765.88i 0.633724 + 0.460427i
\(714\) 0 0
\(715\) −18000.5 + 3773.87i −0.941513 + 0.197391i
\(716\) −28427.7 20653.9i −1.48379 1.07804i
\(717\) 0 0
\(718\) −12263.2 −0.637406
\(719\) −10089.3 31051.6i −0.523319 1.61061i −0.767617 0.640909i \(-0.778557\pi\)
0.244298 0.969700i \(-0.421443\pi\)
\(720\) 0 0
\(721\) −3969.94 + 12218.2i −0.205060 + 0.631110i
\(722\) 6281.78 19333.3i 0.323800 0.996555i
\(723\) 0 0
\(724\) −5137.04 −0.263697
\(725\) 3086.54 + 31024.7i 0.158112 + 1.58928i
\(726\) 0 0
\(727\) 10358.1 7525.58i 0.528418 0.383918i −0.291348 0.956617i \(-0.594104\pi\)
0.819766 + 0.572699i \(0.194104\pi\)
\(728\) −7223.32 + 22231.1i −0.367739 + 1.13178i
\(729\) 0 0
\(730\) 4817.38 44640.3i 0.244246 2.26330i
\(731\) −8500.15 26160.8i −0.430081 1.32365i
\(732\) 0 0
\(733\) 5130.87 + 15791.2i 0.258544 + 0.795718i 0.993111 + 0.117181i \(0.0373857\pi\)
−0.734566 + 0.678537i \(0.762614\pi\)
\(734\) 32098.2 + 23320.7i 1.61412 + 1.17273i
\(735\) 0 0
\(736\) −19582.4 + 14227.4i −0.980727 + 0.712540i
\(737\) 15282.8 + 11103.6i 0.763839 + 0.554961i
\(738\) 0 0
\(739\) 27715.2 20136.3i 1.37959 1.00233i 0.382677 0.923882i \(-0.375002\pi\)
0.996918 0.0784518i \(-0.0249977\pi\)
\(740\) −4562.36 + 5038.77i −0.226643 + 0.250309i
\(741\) 0 0
\(742\) 4411.77 + 13578.0i 0.218276 + 0.671786i
\(743\) −12748.1 −0.629451 −0.314726 0.949183i \(-0.601913\pi\)
−0.314726 + 0.949183i \(0.601913\pi\)
\(744\) 0 0
\(745\) −3733.21 + 782.679i −0.183590 + 0.0384901i
\(746\) −1215.15 + 3739.85i −0.0596379 + 0.183547i
\(747\) 0 0
\(748\) 22719.0 16506.3i 1.11055 0.806859i
\(749\) −29094.0 −1.41932
\(750\) 0 0
\(751\) −14642.0 −0.711442 −0.355721 0.934592i \(-0.615765\pi\)
−0.355721 + 0.934592i \(0.615765\pi\)
\(752\) −5720.91 + 4156.49i −0.277421 + 0.201558i
\(753\) 0 0
\(754\) −25998.1 + 80014.0i −1.25570 + 3.86464i
\(755\) 36494.4 7651.16i 1.75916 0.368814i
\(756\) 0 0
\(757\) 4370.36 0.209833 0.104916 0.994481i \(-0.466542\pi\)
0.104916 + 0.994481i \(0.466542\pi\)
\(758\) 9177.47 + 28245.4i 0.439764 + 1.35345i
\(759\) 0 0
\(760\) −11172.5 + 12339.1i −0.533248 + 0.588931i
\(761\) −15230.0 + 11065.3i −0.725477 + 0.527090i −0.888129 0.459594i \(-0.847995\pi\)
0.162653 + 0.986683i \(0.447995\pi\)
\(762\) 0 0
\(763\) 23571.8 + 17125.9i 1.11842 + 0.812580i
\(764\) 20261.3 14720.7i 0.959459 0.697088i
\(765\) 0 0
\(766\) −24017.8 17450.0i −1.13290 0.823097i
\(767\) −6920.68 21299.7i −0.325804 1.00272i
\(768\) 0 0
\(769\) 5094.85 + 15680.3i 0.238914 + 0.735302i 0.996578 + 0.0826572i \(0.0263407\pi\)
−0.757664 + 0.652645i \(0.773659\pi\)
\(770\) 2451.29 22714.9i 0.114725 1.06310i
\(771\) 0 0
\(772\) 12913.9 39744.8i 0.602047 1.85291i
\(773\) 626.379 455.091i 0.0291452 0.0211753i −0.573117 0.819473i \(-0.694266\pi\)
0.602263 + 0.798298i \(0.294266\pi\)
\(774\) 0 0
\(775\) 12097.1 + 13586.3i 0.560696 + 0.629722i
\(776\) 225.429 0.0104284
\(777\) 0 0
\(778\) 5207.16 16026.0i 0.239956 0.738508i
\(779\) −1882.91 + 5795.01i −0.0866013 + 0.266531i
\(780\) 0 0
\(781\) −253.295 779.562i −0.0116051 0.0357169i
\(782\) −52823.5 −2.41556