Properties

Label 225.4.h.d.91.3
Level $225$
Weight $4$
Character 225.91
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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 91.3
Character \(\chi\) \(=\) 225.91
Dual form 225.4.h.d.136.3

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.54222 2.57358i −1.25236 0.909896i −0.254008 0.967202i \(-0.581749\pi\)
−0.998357 + 0.0573059i \(0.981749\pi\)
\(3\) 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 0.798810 0.601584i \(-0.205463\pi\)
−0.325294 + 0.945613i \(0.605463\pi\)
\(12\) 0 0
\(13\) −62.3251 + 45.2819i −1.32968 + 0.966071i −0.329927 + 0.944007i \(0.607024\pi\)
−0.999757 + 0.0220647i \(0.992976\pi\)
\(14\) 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 −0.256781 0.966470i \(-0.582662\pi\)
0.775817 0.630958i \(-0.217338\pi\)
\(18\) 0 0
\(19\) 33.1410 101.998i 0.400162 1.23157i −0.524707 0.851283i \(-0.675825\pi\)
0.924868 0.380288i \(-0.124175\pi\)
\(20\) 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 0.896322 0.443403i \(-0.146229\pi\)
−0.144722 + 0.989472i \(0.546229\pi\)
\(24\) 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 −0.819222 0.573477i \(-0.805594\pi\)
0.325683 0.945479i \(-0.394406\pi\)
\(30\) 0 0
\(31\) 44.9716 138.408i 0.260553 0.801899i −0.732132 0.681163i \(-0.761475\pi\)
0.992685 0.120736i \(-0.0385254\pi\)
\(32\) −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 −0.681294 0.732010i \(-0.738582\pi\)
0.485651 + 0.874153i \(0.338582\pi\)
\(38\) −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 −0.496792 0.867870i \(-0.665489\pi\)
0.671876 + 0.740664i \(0.265489\pi\)
\(42\) 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 −0.996812 0.0797898i \(-0.974575\pi\)
0.759538 0.650463i \(-0.225425\pi\)
\(48\) 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 0.873375 0.487048i \(-0.161926\pi\)
−0.992855 + 0.119327i \(0.961926\pi\)
\(54\) 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 −0.297247 0.954801i \(-0.596068\pi\)
0.816215 + 0.577748i \(0.196068\pi\)
\(60\) 0 0
\(61\) −181.693 132.008i −0.381368 0.277080i 0.380541 0.924764i \(-0.375738\pi\)
−0.761909 + 0.647684i \(0.775738\pi\)
\(62\) −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 −0.312977 0.949761i \(-0.601326\pi\)
0.811459 0.584410i \(-0.198674\pi\)
\(68\) 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 0.960481 0.278346i \(-0.0897862\pi\)
−0.940653 + 0.339370i \(0.889786\pi\)
\(72\) 0 0
\(73\) −742.038 539.122i −1.18971 0.864376i −0.196478 0.980508i \(-0.562950\pi\)
−0.993234 + 0.116132i \(0.962950\pi\)
\(74\) 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 0.922404 + 0.386226i \(0.126221\pi\)
−0.519223 + 0.854639i \(0.673779\pi\)
\(80\) 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 −0.650015 0.759921i \(-0.725237\pi\)
0.972544 0.232720i \(-0.0747626\pi\)
\(84\) 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 0.804168 0.594403i \(-0.202611\pi\)
−0.316809 + 0.948489i \(0.602611\pi\)
\(90\) 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 0.953648 0.300923i \(-0.0972947\pi\)
−0.948396 + 0.317089i \(0.897295\pi\)
\(98\) −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 0.999575 0.0291682i \(-0.00928585\pi\)
−0.825817 + 0.563938i \(0.809286\pi\)
\(104\) 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 −0.950260 0.311459i \(-0.899182\pi\)
0.00256836 + 0.999997i \(0.499182\pi\)
\(110\) −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 0.228088 0.973640i \(-0.426753\pi\)
0.996470 + 0.0839467i \(0.0267526\pi\)
\(114\) 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 0.683177 0.730253i \(-0.260598\pi\)
−0.483399 + 0.875400i \(0.660598\pi\)
\(128\) −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 −0.872166 0.489210i \(-0.837285\pi\)
0.993148 + 0.116867i \(0.0372851\pi\)
\(132\) 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 −0.312945 + 0.949771i \(0.601316\pi\)
−0.999991 + 0.00413341i \(0.998684\pi\)
\(138\) 0 0
\(139\) −1405.38 1021.07i −0.857576 0.623065i 0.0696487 0.997572i \(-0.477812\pi\)
−0.927224 + 0.374506i \(0.877812\pi\)
\(140\) −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 −0.0812166 0.996696i \(-0.525881\pi\)
0.922817 + 0.385238i \(0.125881\pi\)
\(164\) 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 −0.828244 0.560368i \(-0.810660\pi\)
0.999439 + 0.0334827i \(0.0106599\pi\)
\(168\) 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 0.261260 0.965268i \(-0.415862\pi\)
−0.837291 + 0.546757i \(0.815862\pi\)
\(174\) 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 0.920149 + 0.391568i \(0.128067\pi\)
−0.514258 + 0.857635i \(0.671933\pi\)
\(180\) 0 0
\(181\) −142.108 + 437.363i −0.0583579 + 0.179607i −0.975986 0.217833i \(-0.930101\pi\)
0.917628 + 0.397440i \(0.130101\pi\)
\(182\) −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 −0.188585 0.982057i \(-0.560390\pi\)
0.875715 + 0.482827i \(0.160390\pi\)
\(192\) 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 0.985804 0.167903i \(-0.0536994\pi\)
−0.896223 + 0.443605i \(0.853699\pi\)
\(198\) 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 0.294700 0.955590i \(-0.404780\pi\)
−0.817752 + 0.575570i \(0.804780\pi\)
\(212\) 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 −0.939096 0.343654i \(-0.888335\pi\)
−0.617031 0.786939i \(-0.711665\pi\)
\(224\) 5162.64 1.53993
\(225\) 0 0
\(226\) −7960.82 −2.34312
\(227\) 2378.84 + 1728.33i 0.695548 + 0.505345i 0.878479 0.477780i \(-0.158559\pi\)
−0.182931 + 0.983126i \(0.558559\pi\)
\(228\) 0 0
\(229\) −97.7803 300.937i −0.0282162 0.0868405i 0.935957 0.352115i \(-0.114537\pi\)
−0.964173 + 0.265275i \(0.914537\pi\)
\(230\) −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 −0.846174 0.532907i \(-0.821099\pi\)
0.997804 + 0.0662375i \(0.0210995\pi\)
\(234\) 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 0.510978 0.859594i \(-0.329283\pi\)
−0.659621 + 0.751598i \(0.729283\pi\)
\(240\) 0 0
\(241\) −1023.83 + 743.856i −0.273654 + 0.198822i −0.716145 0.697952i \(-0.754095\pi\)
0.442491 + 0.896773i \(0.354095\pi\)
\(242\) −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 −0.978683 0.205377i \(-0.934158\pi\)
−0.107104 + 0.994248i \(0.534158\pi\)
\(264\) 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 −0.723310 0.690524i \(-0.757380\pi\)
0.991050 0.133495i \(-0.0426200\pi\)
\(270\) 0 0
\(271\) 1514.67 + 4661.67i 0.339518 + 1.04493i 0.964453 + 0.264253i \(0.0851255\pi\)
−0.624935 + 0.780677i \(0.714874\pi\)
\(272\) −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 0.983557 0.180598i \(-0.0578032\pi\)
0.132177 + 0.991226i \(0.457803\pi\)
\(278\) 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 0.791367 + 0.611342i \(0.209370\pi\)
−0.999567 + 0.0294325i \(0.990630\pi\)
\(282\) 0 0
\(283\) −1794.88 + 5524.08i −0.377013 + 1.16033i 0.565097 + 0.825024i \(0.308839\pi\)
−0.942110 + 0.335303i \(0.891161\pi\)
\(284\) −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 −0.0102048 0.999948i \(-0.503248\pi\)
−0.954160 + 0.299296i \(0.903248\pi\)
\(312\) 0 0
\(313\) −8090.51 + 5878.10i −1.46103 + 1.06150i −0.477939 + 0.878393i \(0.658616\pi\)
−0.983093 + 0.183109i \(0.941384\pi\)
\(314\) 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 −0.955863 0.293812i \(-0.905076\pi\)
0.946008 + 0.324144i \(0.105076\pi\)
\(318\) 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 −0.931716 0.363187i \(-0.881689\pi\)
0.967250 + 0.253825i \(0.0816886\pi\)
\(332\) 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 −0.442472 0.896782i \(-0.645898\pi\)
0.716160 + 0.697937i \(0.245898\pi\)
\(338\) −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 0.886603 0.462531i \(-0.153059\pi\)
−0.989146 + 0.146937i \(0.953059\pi\)
\(348\) 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 −0.497813 0.867284i \(-0.665863\pi\)
−0.107038 0.994255i \(-0.534137\pi\)
\(354\) 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 −0.408633 0.912699i \(-0.633995\pi\)
0.741753 + 0.670673i \(0.233995\pi\)
\(360\) 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 0.528098 + 0.849183i \(0.322905\pi\)
−0.926378 + 0.376595i \(0.877095\pi\)
\(368\) 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 0.637073 0.770804i \(-0.280145\pi\)
−0.536212 + 0.844084i \(0.680145\pi\)
\(374\) −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 0.986672 + 0.162723i \(0.0520276\pi\)
−0.702588 + 0.711597i \(0.747972\pi\)
\(380\) 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 −0.708444 0.705767i \(-0.750603\pi\)
0.987983 0.154564i \(-0.0493974\pi\)
\(384\) 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 0.366087 0.930581i \(-0.380697\pi\)
−0.771907 + 0.635735i \(0.780697\pi\)
\(390\) 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 −0.991406 0.130820i \(-0.958239\pi\)
0.725171 0.688569i \(-0.241761\pi\)
\(398\) 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 −0.996371 0.0851209i \(-0.972872\pi\)
−0.226941 + 0.973909i \(0.572872\pi\)
\(410\) −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 0.552456 + 0.833542i \(0.313691\pi\)
−0.936890 + 0.349624i \(0.886309\pi\)
\(420\) 0 0
\(421\) 1024.54 + 3153.20i 0.118606 + 0.365030i 0.992682 0.120758i \(-0.0385326\pi\)
−0.874076 + 0.485788i \(0.838533\pi\)
\(422\) 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 −0.473674 0.880701i \(-0.657072\pi\)
0.900873 0.434083i \(-0.142928\pi\)
\(432\) 0 0
\(433\) −174.988 + 538.559i −0.0194213 + 0.0597725i −0.960297 0.278978i \(-0.910004\pi\)
0.940876 + 0.338751i \(0.110004\pi\)
\(434\) 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 0.933818 0.357749i \(-0.116456\pi\)
−0.0516738 + 0.998664i \(0.516456\pi\)
\(440\) 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 −0.188494 0.982074i \(-0.560361\pi\)
−0.992256 + 0.124209i \(0.960361\pi\)
\(462\) 0 0
\(463\) −6186.58 + 4494.82i −0.620983 + 0.451170i −0.853265 0.521478i \(-0.825381\pi\)
0.232282 + 0.972648i \(0.425381\pi\)
\(464\) −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 −0.884566 0.466415i \(-0.845545\pi\)
0.989781 + 0.142597i \(0.0455453\pi\)
\(468\) 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 0.966499 0.256669i \(-0.0826249\pi\)
−0.932780 + 0.360445i \(0.882625\pi\)
\(480\) 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 −0.739468 0.673191i \(-0.764923\pi\)
0.411735 + 0.911304i \(0.364923\pi\)
\(488\) −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 −0.869474 0.493979i \(-0.835542\pi\)
0.201120 + 0.979567i \(0.435542\pi\)
\(492\) 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 0.952026 + 0.306017i \(0.0989965\pi\)
−0.590333 + 0.807160i \(0.701004\pi\)
\(504\) 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 −0.929410 0.369049i \(-0.879684\pi\)
0.0637826 + 0.997964i \(0.479684\pi\)
\(510\) 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 0.997322 + 0.0731289i \(0.0232985\pi\)
−0.763867 + 0.645374i \(0.776702\pi\)
\(522\) 0 0
\(523\) 10821.0 + 7861.90i 0.904719 + 0.657317i 0.939674 0.342072i \(-0.111129\pi\)
−0.0349548 + 0.999389i \(0.511129\pi\)
\(524\) 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 −0.640755 0.767745i \(-0.721379\pi\)
0.532165 + 0.846641i \(0.321379\pi\)
\(542\) 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 0.889396 0.457138i \(-0.151125\pi\)
−0.988235 + 0.152942i \(0.951125\pi\)
\(548\) −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 −0.705297 0.708912i \(-0.749186\pi\)
0.456266 + 0.889843i \(0.349186\pi\)
\(564\) 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 −0.996204 0.0870499i \(-0.972256\pi\)
0.857113 + 0.515129i \(0.172256\pi\)
\(570\) 0 0
\(571\) −4801.53 14777.6i −0.351905 1.08305i −0.957782 0.287494i \(-0.907178\pi\)
0.605877 0.795558i \(-0.292822\pi\)
\(572\) −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 0.975523 0.219896i \(-0.0705718\pi\)
0.0923197 + 0.995729i \(0.470572\pi\)
\(578\) 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 0.0541389 0.998533i \(-0.482759\pi\)
0.966392 + 0.257075i \(0.0827586\pi\)
\(588\) 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 −0.831027 0.556233i \(-0.812246\pi\)
0.272207 + 0.962239i \(0.412246\pi\)
\(614\) −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 0.553598 + 0.832784i \(0.313255\pi\)
−0.937368 + 0.348340i \(0.886745\pi\)
\(618\) 0 0
\(619\) 3661.02 11267.5i 0.237720 0.731628i −0.759029 0.651057i \(-0.774326\pi\)
0.996749 0.0805705i \(-0.0256742\pi\)
\(620\) 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 −0.888543 0.458793i \(-0.848282\pi\)
0.988518 + 0.151102i \(0.0482821\pi\)
\(632\) 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 0.383782 0.923424i \(-0.374621\pi\)
0.996823 0.0796450i \(-0.0253787\pi\)
\(642\) 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 0.963607 0.267324i \(-0.0861393\pi\)
−0.936703 + 0.350125i \(0.886139\pi\)
\(648\) 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 0.991628 0.129125i \(-0.0412168\pi\)
−0.878142 + 0.478400i \(0.841217\pi\)
\(654\) 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 −0.434626 0.900611i \(-0.643119\pi\)
0.722225 + 0.691658i \(0.243119\pi\)
\(660\) 0 0
\(661\) −781.067 567.479i −0.0459607 0.0333924i 0.564568 0.825387i \(-0.309043\pi\)
−0.610528 + 0.791994i \(0.709043\pi\)
\(662\) −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 0.962261 0.272130i \(-0.0877280\pi\)
0.0385441 + 0.999257i \(0.487728\pi\)
\(674\) −9163.49 −0.523686
\(675\) 0 0
\(676\) 41754.3 2.37564
\(677\) 10219.9 + 7425.17i 0.580180 + 0.421525i 0.838789 0.544457i \(-0.183264\pi\)
−0.258609 + 0.965982i \(0.583264\pi\)
\(678\) 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 −0.342746 0.939428i \(-0.611357\pi\)
0.829469 0.558552i \(-0.188643\pi\)
\(684\) 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 −0.771683 0.636007i \(-0.780585\pi\)
0.366415 + 0.930451i \(0.380585\pi\)
\(692\) 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 0.127359 0.991857i \(-0.459350\pi\)
0.982668 + 0.185375i \(0.0593501\pi\)
\(710\) 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 0.244298 + 0.969700i \(0.421443\pi\)
−0.767617 + 0.640909i \(0.778557\pi\)
\(720\) 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 0.819766 0.572699i \(-0.194104\pi\)
−0.291348 + 0.956617i \(0.594104\pi\)
\(728\) −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 −0.734566 0.678537i \(-0.762614\pi\)
0.993111 0.117181i \(-0.0373857\pi\)
\(734\) 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 0.996918 + 0.0784518i \(0.0249977\pi\)
0.382677 + 0.923882i \(0.375002\pi\)
\(740\) −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 0.162653 0.986683i \(-0.447995\pi\)
−0.888129 + 0.459594i \(0.847995\pi\)
\(762\) 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 −0.757664 0.652645i \(-0.773659\pi\)
0.996578 0.0826572i \(-0.0263407\pi\)
\(770\) 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 0.602263 0.798298i \(-0.294266\pi\)
−0.573117 + 0.819473i \(0.694266\pi\)
\(774\) 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