Properties

Label 225.4.h.d.46.7
Level $225$
Weight $4$
Character 225.46
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 46.7
Character \(\chi\) \(=\) 225.46
Dual form 225.4.h.d.181.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.426412 + 1.31236i) q^{2} +(4.93167 + 3.58307i) q^{4} +(10.9704 - 2.15653i) q^{5} -13.9864 q^{7} +(-15.7361 + 11.4329i) q^{8} +O(q^{10})\) \(q+(-0.426412 + 1.31236i) q^{2} +(4.93167 + 3.58307i) q^{4} +(10.9704 - 2.15653i) q^{5} -13.9864 q^{7} +(-15.7361 + 11.4329i) q^{8} +(-1.84776 + 15.3167i) q^{10} +(-8.55501 + 26.3296i) q^{11} +(19.3615 + 59.5885i) q^{13} +(5.96399 - 18.3553i) q^{14} +(6.77575 + 20.8536i) q^{16} +(76.5125 - 55.5896i) q^{17} +(-93.8251 + 68.1679i) q^{19} +(61.8293 + 28.6723i) q^{20} +(-30.9060 - 22.4545i) q^{22} +(35.1368 - 108.140i) q^{23} +(115.699 - 47.3159i) q^{25} -86.4576 q^{26} +(-68.9765 - 50.1144i) q^{28} +(161.223 + 117.135i) q^{29} +(-214.777 + 156.045i) q^{31} -185.864 q^{32} +(40.3278 + 124.116i) q^{34} +(-153.437 + 30.1622i) q^{35} +(88.0113 + 270.871i) q^{37} +(-49.4528 - 152.200i) q^{38} +(-147.976 + 159.359i) q^{40} +(100.917 + 310.590i) q^{41} +113.898 q^{43} +(-136.531 + 99.1958i) q^{44} +(126.936 + 92.2244i) q^{46} +(45.5242 + 33.0753i) q^{47} -147.379 q^{49} +(12.7603 + 172.015i) q^{50} +(-118.025 + 363.244i) q^{52} +(-386.969 - 281.150i) q^{53} +(-37.0712 + 307.295i) q^{55} +(220.092 - 159.906i) q^{56} +(-222.471 + 161.635i) q^{58} +(-173.406 - 533.690i) q^{59} +(160.923 - 495.270i) q^{61} +(-113.204 - 348.405i) q^{62} +(25.0486 - 77.0916i) q^{64} +(340.907 + 611.955i) q^{65} +(565.942 - 411.181i) q^{67} +576.516 q^{68} +(25.8436 - 214.226i) q^{70} +(-47.8348 - 34.7540i) q^{71} +(226.377 - 696.716i) q^{73} -393.010 q^{74} -706.964 q^{76} +(119.654 - 368.258i) q^{77} +(192.738 + 140.032i) q^{79} +(119.304 + 214.160i) q^{80} -450.638 q^{82} +(-282.783 + 205.454i) q^{83} +(719.492 - 774.841i) q^{85} +(-48.5673 + 149.475i) q^{86} +(-166.403 - 512.135i) q^{88} +(-240.108 + 738.975i) q^{89} +(-270.798 - 833.431i) q^{91} +(560.756 - 407.413i) q^{92} +(-62.8188 + 45.6405i) q^{94} +(-882.291 + 950.165i) q^{95} +(478.367 + 347.554i) q^{97} +(62.8443 - 193.415i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.426412 + 1.31236i −0.150759 + 0.463990i −0.997707 0.0676872i \(-0.978438\pi\)
0.846947 + 0.531677i \(0.178438\pi\)
\(3\) 0 0
\(4\) 4.93167 + 3.58307i 0.616459 + 0.447884i
\(5\) 10.9704 2.15653i 0.981221 0.192886i
\(6\) 0 0
\(7\) −13.9864 −0.755197 −0.377599 0.925969i \(-0.623250\pi\)
−0.377599 + 0.925969i \(0.623250\pi\)
\(8\) −15.7361 + 11.4329i −0.695444 + 0.505269i
\(9\) 0 0
\(10\) −1.84776 + 15.3167i −0.0584312 + 0.484356i
\(11\) −8.55501 + 26.3296i −0.234494 + 0.721698i 0.762694 + 0.646759i \(0.223876\pi\)
−0.997188 + 0.0749390i \(0.976124\pi\)
\(12\) 0 0
\(13\) 19.3615 + 59.5885i 0.413070 + 1.27130i 0.913966 + 0.405790i \(0.133004\pi\)
−0.500897 + 0.865507i \(0.666996\pi\)
\(14\) 5.96399 18.3553i 0.113853 0.350404i
\(15\) 0 0
\(16\) 6.77575 + 20.8536i 0.105871 + 0.325838i
\(17\) 76.5125 55.5896i 1.09159 0.793086i 0.111922 0.993717i \(-0.464299\pi\)
0.979667 + 0.200631i \(0.0642992\pi\)
\(18\) 0 0
\(19\) −93.8251 + 68.1679i −1.13289 + 0.823094i −0.986113 0.166075i \(-0.946891\pi\)
−0.146779 + 0.989169i \(0.546891\pi\)
\(20\) 61.8293 + 28.6723i 0.691273 + 0.320567i
\(21\) 0 0
\(22\) −30.9060 22.4545i −0.299509 0.217606i
\(23\) 35.1368 108.140i 0.318545 0.980380i −0.655726 0.754999i \(-0.727637\pi\)
0.974271 0.225381i \(-0.0723628\pi\)
\(24\) 0 0
\(25\) 115.699 47.3159i 0.925590 0.378528i
\(26\) −86.4576 −0.652143
\(27\) 0 0
\(28\) −68.9765 50.1144i −0.465548 0.338240i
\(29\) 161.223 + 117.135i 1.03236 + 0.750051i 0.968779 0.247925i \(-0.0797488\pi\)
0.0635781 + 0.997977i \(0.479749\pi\)
\(30\) 0 0
\(31\) −214.777 + 156.045i −1.24436 + 0.904080i −0.997881 0.0650678i \(-0.979274\pi\)
−0.246479 + 0.969148i \(0.579274\pi\)
\(32\) −185.864 −1.02676
\(33\) 0 0
\(34\) 40.3278 + 124.116i 0.203417 + 0.626052i
\(35\) −153.437 + 30.1622i −0.741015 + 0.145667i
\(36\) 0 0
\(37\) 88.0113 + 270.871i 0.391053 + 1.20354i 0.931993 + 0.362477i \(0.118069\pi\)
−0.540939 + 0.841062i \(0.681931\pi\)
\(38\) −49.4528 152.200i −0.211113 0.649740i
\(39\) 0 0
\(40\) −147.976 + 159.359i −0.584925 + 0.629922i
\(41\) 100.917 + 310.590i 0.384404 + 1.18307i 0.936912 + 0.349565i \(0.113671\pi\)
−0.552508 + 0.833507i \(0.686329\pi\)
\(42\) 0 0
\(43\) 113.898 0.403935 0.201968 0.979392i \(-0.435266\pi\)
0.201968 + 0.979392i \(0.435266\pi\)
\(44\) −136.531 + 99.1958i −0.467793 + 0.339871i
\(45\) 0 0
\(46\) 126.936 + 92.2244i 0.406863 + 0.295603i
\(47\) 45.5242 + 33.0753i 0.141285 + 0.102649i 0.656183 0.754602i \(-0.272170\pi\)
−0.514898 + 0.857252i \(0.672170\pi\)
\(48\) 0 0
\(49\) −147.379 −0.429677
\(50\) 12.7603 + 172.015i 0.0360915 + 0.486531i
\(51\) 0 0
\(52\) −118.025 + 363.244i −0.314753 + 0.968709i
\(53\) −386.969 281.150i −1.00291 0.728658i −0.0402011 0.999192i \(-0.512800\pi\)
−0.962711 + 0.270534i \(0.912800\pi\)
\(54\) 0 0
\(55\) −37.0712 + 307.295i −0.0908850 + 0.753376i
\(56\) 220.092 159.906i 0.525197 0.381578i
\(57\) 0 0
\(58\) −222.471 + 161.635i −0.503654 + 0.365926i
\(59\) −173.406 533.690i −0.382637 1.17764i −0.938180 0.346148i \(-0.887489\pi\)
0.555543 0.831488i \(-0.312511\pi\)
\(60\) 0 0
\(61\) 160.923 495.270i 0.337772 1.03955i −0.627569 0.778561i \(-0.715950\pi\)
0.965341 0.260993i \(-0.0840500\pi\)
\(62\) −113.204 348.405i −0.231885 0.713669i
\(63\) 0 0
\(64\) 25.0486 77.0916i 0.0489230 0.150570i
\(65\) 340.907 + 611.955i 0.650528 + 1.16775i
\(66\) 0 0
\(67\) 565.942 411.181i 1.03195 0.749758i 0.0632546 0.997997i \(-0.479852\pi\)
0.968699 + 0.248239i \(0.0798520\pi\)
\(68\) 576.516 1.02813
\(69\) 0 0
\(70\) 25.8436 214.226i 0.0441271 0.365784i
\(71\) −47.8348 34.7540i −0.0799570 0.0580921i 0.547089 0.837075i \(-0.315736\pi\)
−0.627046 + 0.778983i \(0.715736\pi\)
\(72\) 0 0
\(73\) 226.377 696.716i 0.362951 1.11705i −0.588304 0.808640i \(-0.700204\pi\)
0.951254 0.308407i \(-0.0997959\pi\)
\(74\) −393.010 −0.617385
\(75\) 0 0
\(76\) −706.964 −1.06703
\(77\) 119.654 368.258i 0.177089 0.545024i
\(78\) 0 0
\(79\) 192.738 + 140.032i 0.274489 + 0.199428i 0.716510 0.697577i \(-0.245738\pi\)
−0.442021 + 0.897005i \(0.645738\pi\)
\(80\) 119.304 + 214.160i 0.166733 + 0.299298i
\(81\) 0 0
\(82\) −450.638 −0.606886
\(83\) −282.783 + 205.454i −0.373969 + 0.271705i −0.758855 0.651260i \(-0.774241\pi\)
0.384886 + 0.922964i \(0.374241\pi\)
\(84\) 0 0
\(85\) 719.492 774.841i 0.918115 0.988745i
\(86\) −48.5673 + 149.475i −0.0608971 + 0.187422i
\(87\) 0 0
\(88\) −166.403 512.135i −0.201575 0.620383i
\(89\) −240.108 + 738.975i −0.285970 + 0.880126i 0.700136 + 0.714010i \(0.253123\pi\)
−0.986106 + 0.166116i \(0.946877\pi\)
\(90\) 0 0
\(91\) −270.798 833.431i −0.311949 0.960080i
\(92\) 560.756 407.413i 0.635466 0.461693i
\(93\) 0 0
\(94\) −62.8188 + 45.6405i −0.0689283 + 0.0500794i
\(95\) −882.291 + 950.165i −0.952854 + 1.02616i
\(96\) 0 0
\(97\) 478.367 + 347.554i 0.500730 + 0.363802i 0.809296 0.587401i \(-0.199849\pi\)
−0.308565 + 0.951203i \(0.599849\pi\)
\(98\) 62.8443 193.415i 0.0647779 0.199366i
\(99\) 0 0
\(100\) 740.124 + 181.210i 0.740124 + 0.181210i
\(101\) 1781.73 1.75534 0.877668 0.479270i \(-0.159098\pi\)
0.877668 + 0.479270i \(0.159098\pi\)
\(102\) 0 0
\(103\) −300.280 218.166i −0.287257 0.208704i 0.434820 0.900518i \(-0.356812\pi\)
−0.722076 + 0.691813i \(0.756812\pi\)
\(104\) −985.945 716.331i −0.929614 0.675404i
\(105\) 0 0
\(106\) 533.978 387.958i 0.489288 0.355489i
\(107\) 1427.47 1.28971 0.644854 0.764306i \(-0.276918\pi\)
0.644854 + 0.764306i \(0.276918\pi\)
\(108\) 0 0
\(109\) 85.3484 + 262.675i 0.0749991 + 0.230823i 0.981527 0.191322i \(-0.0612773\pi\)
−0.906528 + 0.422145i \(0.861277\pi\)
\(110\) −387.475 179.685i −0.335857 0.155748i
\(111\) 0 0
\(112\) −94.7687 291.668i −0.0799536 0.246072i
\(113\) −430.521 1325.01i −0.358407 1.10306i −0.954007 0.299783i \(-0.903086\pi\)
0.595600 0.803281i \(-0.296914\pi\)
\(114\) 0 0
\(115\) 152.257 1262.11i 0.123461 1.02341i
\(116\) 375.395 + 1155.35i 0.300470 + 0.924752i
\(117\) 0 0
\(118\) 774.337 0.604097
\(119\) −1070.14 + 777.501i −0.824365 + 0.598936i
\(120\) 0 0
\(121\) 456.741 + 331.841i 0.343156 + 0.249317i
\(122\) 581.354 + 422.378i 0.431420 + 0.313445i
\(123\) 0 0
\(124\) −1618.33 −1.17202
\(125\) 1167.22 768.582i 0.835196 0.549953i
\(126\) 0 0
\(127\) 269.996 830.961i 0.188648 0.580598i −0.811345 0.584568i \(-0.801264\pi\)
0.999992 + 0.00397069i \(0.00126391\pi\)
\(128\) −1112.44 808.239i −0.768181 0.558116i
\(129\) 0 0
\(130\) −948.473 + 186.448i −0.639897 + 0.125789i
\(131\) 1869.82 1358.50i 1.24707 0.906052i 0.249026 0.968497i \(-0.419890\pi\)
0.998048 + 0.0624445i \(0.0198896\pi\)
\(132\) 0 0
\(133\) 1312.28 953.426i 0.855556 0.621598i
\(134\) 298.294 + 918.054i 0.192303 + 0.591849i
\(135\) 0 0
\(136\) −568.456 + 1749.53i −0.358417 + 1.10309i
\(137\) −2.56402 7.89125i −0.00159897 0.00492113i 0.950254 0.311477i \(-0.100824\pi\)
−0.951853 + 0.306555i \(0.900824\pi\)
\(138\) 0 0
\(139\) 655.033 2015.98i 0.399706 1.23017i −0.525529 0.850776i \(-0.676133\pi\)
0.925235 0.379394i \(-0.123867\pi\)
\(140\) −864.772 401.024i −0.522047 0.242091i
\(141\) 0 0
\(142\) 66.0071 47.9570i 0.0390084 0.0283413i
\(143\) −1734.58 −1.01436
\(144\) 0 0
\(145\) 2021.28 + 937.338i 1.15765 + 0.536839i
\(146\) 817.813 + 594.176i 0.463580 + 0.336811i
\(147\) 0 0
\(148\) −536.506 + 1651.20i −0.297977 + 0.917078i
\(149\) −2602.21 −1.43075 −0.715373 0.698743i \(-0.753743\pi\)
−0.715373 + 0.698743i \(0.753743\pi\)
\(150\) 0 0
\(151\) −635.859 −0.342685 −0.171343 0.985211i \(-0.554811\pi\)
−0.171343 + 0.985211i \(0.554811\pi\)
\(152\) 697.080 2145.39i 0.371978 1.14483i
\(153\) 0 0
\(154\) 432.265 + 314.059i 0.226188 + 0.164335i
\(155\) −2019.68 + 2175.05i −1.04661 + 1.12712i
\(156\) 0 0
\(157\) −1282.78 −0.652081 −0.326040 0.945356i \(-0.605715\pi\)
−0.326040 + 0.945356i \(0.605715\pi\)
\(158\) −265.958 + 193.230i −0.133915 + 0.0972946i
\(159\) 0 0
\(160\) −2039.00 + 400.821i −1.00748 + 0.198048i
\(161\) −491.439 + 1512.49i −0.240564 + 0.740380i
\(162\) 0 0
\(163\) 127.898 + 393.629i 0.0614584 + 0.189150i 0.977072 0.212911i \(-0.0682943\pi\)
−0.915613 + 0.402060i \(0.868294\pi\)
\(164\) −615.176 + 1893.32i −0.292910 + 0.901483i
\(165\) 0 0
\(166\) −149.048 458.721i −0.0696888 0.214480i
\(167\) 2674.52 1943.15i 1.23929 0.900394i 0.241735 0.970342i \(-0.422284\pi\)
0.997551 + 0.0699486i \(0.0222835\pi\)
\(168\) 0 0
\(169\) −1398.51 + 1016.08i −0.636553 + 0.462483i
\(170\) 710.072 + 1274.63i 0.320353 + 0.575059i
\(171\) 0 0
\(172\) 561.706 + 408.103i 0.249010 + 0.180916i
\(173\) 757.000 2329.81i 0.332680 1.02388i −0.635173 0.772370i \(-0.719071\pi\)
0.967853 0.251515i \(-0.0809287\pi\)
\(174\) 0 0
\(175\) −1618.21 + 661.782i −0.699003 + 0.285863i
\(176\) −607.035 −0.259983
\(177\) 0 0
\(178\) −867.418 630.216i −0.365257 0.265375i
\(179\) −2319.38 1685.13i −0.968486 0.703646i −0.0133796 0.999910i \(-0.504259\pi\)
−0.955106 + 0.296265i \(0.904259\pi\)
\(180\) 0 0
\(181\) 1470.27 1068.21i 0.603779 0.438671i −0.243439 0.969916i \(-0.578276\pi\)
0.847218 + 0.531245i \(0.178276\pi\)
\(182\) 1209.23 0.492497
\(183\) 0 0
\(184\) 683.442 + 2103.42i 0.273826 + 0.842751i
\(185\) 1549.66 + 2781.76i 0.615855 + 1.10551i
\(186\) 0 0
\(187\) 809.088 + 2490.12i 0.316398 + 0.973772i
\(188\) 105.999 + 326.233i 0.0411213 + 0.126558i
\(189\) 0 0
\(190\) −870.740 1563.05i −0.332474 0.596817i
\(191\) 298.679 + 919.239i 0.113150 + 0.348240i 0.991557 0.129674i \(-0.0413931\pi\)
−0.878407 + 0.477914i \(0.841393\pi\)
\(192\) 0 0
\(193\) −1504.57 −0.561148 −0.280574 0.959832i \(-0.590525\pi\)
−0.280574 + 0.959832i \(0.590525\pi\)
\(194\) −660.099 + 479.590i −0.244290 + 0.177487i
\(195\) 0 0
\(196\) −726.826 528.070i −0.264878 0.192445i
\(197\) −640.764 465.542i −0.231739 0.168368i 0.465856 0.884860i \(-0.345746\pi\)
−0.697595 + 0.716492i \(0.745746\pi\)
\(198\) 0 0
\(199\) 3270.72 1.16510 0.582551 0.812794i \(-0.302055\pi\)
0.582551 + 0.812794i \(0.302055\pi\)
\(200\) −1279.69 + 2067.35i −0.452437 + 0.730917i
\(201\) 0 0
\(202\) −759.752 + 2338.28i −0.264633 + 0.814458i
\(203\) −2254.94 1638.31i −0.779633 0.566437i
\(204\) 0 0
\(205\) 1776.89 + 3189.66i 0.605383 + 1.08671i
\(206\) 414.356 301.047i 0.140143 0.101820i
\(207\) 0 0
\(208\) −1111.45 + 807.513i −0.370505 + 0.269187i
\(209\) −992.161 3053.56i −0.328369 1.01062i
\(210\) 0 0
\(211\) −1098.34 + 3380.33i −0.358354 + 1.10290i 0.595686 + 0.803218i \(0.296880\pi\)
−0.954039 + 0.299681i \(0.903120\pi\)
\(212\) −901.027 2773.07i −0.291900 0.898375i
\(213\) 0 0
\(214\) −608.691 + 1873.36i −0.194436 + 0.598411i
\(215\) 1249.50 245.624i 0.396350 0.0779135i
\(216\) 0 0
\(217\) 3003.97 2182.51i 0.939737 0.682759i
\(218\) −381.119 −0.118407
\(219\) 0 0
\(220\) −1283.88 + 1382.65i −0.393452 + 0.423720i
\(221\) 4793.89 + 3482.97i 1.45915 + 1.06013i
\(222\) 0 0
\(223\) −1769.03 + 5444.53i −0.531225 + 1.63494i 0.220441 + 0.975400i \(0.429250\pi\)
−0.751667 + 0.659543i \(0.770750\pi\)
\(224\) 2599.57 0.775408
\(225\) 0 0
\(226\) 1922.47 0.565844
\(227\) −397.881 + 1224.55i −0.116336 + 0.358045i −0.992223 0.124470i \(-0.960277\pi\)
0.875887 + 0.482516i \(0.160277\pi\)
\(228\) 0 0
\(229\) −1106.51 803.928i −0.319303 0.231987i 0.416575 0.909101i \(-0.363230\pi\)
−0.735878 + 0.677114i \(0.763230\pi\)
\(230\) 1591.42 + 737.996i 0.456240 + 0.211574i
\(231\) 0 0
\(232\) −3876.22 −1.09692
\(233\) 2138.13 1553.45i 0.601175 0.436779i −0.245121 0.969493i \(-0.578828\pi\)
0.846296 + 0.532713i \(0.178828\pi\)
\(234\) 0 0
\(235\) 570.746 + 264.674i 0.158431 + 0.0734700i
\(236\) 1057.06 3253.31i 0.291564 0.897341i
\(237\) 0 0
\(238\) −564.043 1735.94i −0.153620 0.472792i
\(239\) −128.836 + 396.516i −0.0348690 + 0.107316i −0.966976 0.254867i \(-0.917968\pi\)
0.932107 + 0.362183i \(0.117968\pi\)
\(240\) 0 0
\(241\) 331.859 + 1021.36i 0.0887010 + 0.272994i 0.985561 0.169321i \(-0.0541575\pi\)
−0.896860 + 0.442315i \(0.854157\pi\)
\(242\) −630.256 + 457.908i −0.167415 + 0.121634i
\(243\) 0 0
\(244\) 2568.20 1865.91i 0.673822 0.489560i
\(245\) −1616.81 + 317.828i −0.421609 + 0.0828787i
\(246\) 0 0
\(247\) −5878.61 4271.06i −1.51436 1.10025i
\(248\) 1595.70 4911.07i 0.408578 1.25747i
\(249\) 0 0
\(250\) 510.940 + 1859.55i 0.129259 + 0.470433i
\(251\) 3269.53 0.822194 0.411097 0.911592i \(-0.365146\pi\)
0.411097 + 0.911592i \(0.365146\pi\)
\(252\) 0 0
\(253\) 2546.69 + 1850.28i 0.632842 + 0.459787i
\(254\) 975.392 + 708.664i 0.240951 + 0.175061i
\(255\) 0 0
\(256\) 2059.69 1496.45i 0.502853 0.365344i
\(257\) −2452.88 −0.595357 −0.297678 0.954666i \(-0.596212\pi\)
−0.297678 + 0.954666i \(0.596212\pi\)
\(258\) 0 0
\(259\) −1230.97 3788.52i −0.295322 0.908909i
\(260\) −511.435 + 4239.45i −0.121992 + 1.01123i
\(261\) 0 0
\(262\) 985.533 + 3033.16i 0.232391 + 0.715226i
\(263\) −991.490 3051.49i −0.232463 0.715449i −0.997448 0.0714001i \(-0.977253\pi\)
0.764984 0.644049i \(-0.222747\pi\)
\(264\) 0 0
\(265\) −4851.51 2249.81i −1.12463 0.521527i
\(266\) 691.669 + 2128.74i 0.159432 + 0.490681i
\(267\) 0 0
\(268\) 4264.33 0.971961
\(269\) −5153.23 + 3744.04i −1.16802 + 0.848619i −0.990771 0.135547i \(-0.956721\pi\)
−0.177252 + 0.984165i \(0.556721\pi\)
\(270\) 0 0
\(271\) 1631.25 + 1185.17i 0.365651 + 0.265661i 0.755405 0.655258i \(-0.227440\pi\)
−0.389754 + 0.920919i \(0.627440\pi\)
\(272\) 1677.67 + 1218.90i 0.373985 + 0.271716i
\(273\) 0 0
\(274\) 11.4495 0.00252441
\(275\) 256.007 + 3451.09i 0.0561374 + 0.756759i
\(276\) 0 0
\(277\) 1503.94 4628.66i 0.326221 1.00400i −0.644666 0.764464i \(-0.723004\pi\)
0.970887 0.239539i \(-0.0769964\pi\)
\(278\) 2366.39 + 1719.28i 0.510527 + 0.370919i
\(279\) 0 0
\(280\) 2069.65 2228.87i 0.441733 0.475716i
\(281\) −4288.67 + 3115.90i −0.910464 + 0.661491i −0.941132 0.338039i \(-0.890236\pi\)
0.0306683 + 0.999530i \(0.490236\pi\)
\(282\) 0 0
\(283\) −477.121 + 346.649i −0.100219 + 0.0728132i −0.636766 0.771057i \(-0.719728\pi\)
0.536547 + 0.843870i \(0.319728\pi\)
\(284\) −111.379 342.791i −0.0232717 0.0716228i
\(285\) 0 0
\(286\) 739.646 2276.40i 0.152924 0.470651i
\(287\) −1411.47 4344.05i −0.290300 0.893453i
\(288\) 0 0
\(289\) 1245.76 3834.07i 0.253565 0.780392i
\(290\) −2092.03 + 2252.96i −0.423614 + 0.456202i
\(291\) 0 0
\(292\) 3612.80 2624.85i 0.724051 0.526054i
\(293\) −5328.13 −1.06236 −0.531182 0.847258i \(-0.678252\pi\)
−0.531182 + 0.847258i \(0.678252\pi\)
\(294\) 0 0
\(295\) −3053.25 5480.83i −0.602601 1.08172i
\(296\) −4481.81 3256.22i −0.880067 0.639406i
\(297\) 0 0
\(298\) 1109.61 3415.04i 0.215698 0.663852i
\(299\) 7124.20 1.37794
\(300\) 0 0
\(301\) −1593.02 −0.305051
\(302\) 271.138 834.477i 0.0516631 0.159003i
\(303\) 0 0
\(304\) −2057.28 1494.70i −0.388136 0.281997i
\(305\) 697.322 5780.34i 0.130913 1.08518i
\(306\) 0 0
\(307\) 3716.68 0.690952 0.345476 0.938428i \(-0.387717\pi\)
0.345476 + 0.938428i \(0.387717\pi\)
\(308\) 1909.59 1387.40i 0.353276 0.256670i
\(309\) 0 0
\(310\) −1993.23 3578.01i −0.365187 0.655540i
\(311\) −1016.45 + 3128.32i −0.185330 + 0.570388i −0.999954 0.00960189i \(-0.996944\pi\)
0.814624 + 0.579990i \(0.196944\pi\)
\(312\) 0 0
\(313\) −565.534 1740.54i −0.102127 0.314316i 0.886918 0.461927i \(-0.152842\pi\)
−0.989046 + 0.147611i \(0.952842\pi\)
\(314\) 546.991 1683.47i 0.0983074 0.302559i
\(315\) 0 0
\(316\) 448.774 + 1381.18i 0.0798908 + 0.245879i
\(317\) 3830.09 2782.73i 0.678610 0.493039i −0.194286 0.980945i \(-0.562239\pi\)
0.872896 + 0.487906i \(0.162239\pi\)
\(318\) 0 0
\(319\) −4463.40 + 3242.85i −0.783392 + 0.569168i
\(320\) 108.542 899.742i 0.0189615 0.157179i
\(321\) 0 0
\(322\) −1775.38 1289.89i −0.307262 0.223239i
\(323\) −3389.37 + 10431.4i −0.583868 + 1.79696i
\(324\) 0 0
\(325\) 5059.58 + 5978.20i 0.863554 + 1.02034i
\(326\) −571.120 −0.0970289
\(327\) 0 0
\(328\) −5138.99 3733.70i −0.865101 0.628533i
\(329\) −636.722 462.606i −0.106698 0.0775206i
\(330\) 0 0
\(331\) −3430.48 + 2492.39i −0.569656 + 0.413879i −0.834980 0.550280i \(-0.814521\pi\)
0.265324 + 0.964159i \(0.414521\pi\)
\(332\) −2130.75 −0.352229
\(333\) 0 0
\(334\) 1409.67 + 4338.52i 0.230940 + 0.710759i
\(335\) 5321.88 5731.29i 0.867957 0.934728i
\(336\) 0 0
\(337\) −152.626 469.735i −0.0246709 0.0759291i 0.937963 0.346735i \(-0.112710\pi\)
−0.962634 + 0.270806i \(0.912710\pi\)
\(338\) −737.118 2268.61i −0.118621 0.365078i
\(339\) 0 0
\(340\) 6324.60 1243.27i 1.00882 0.198312i
\(341\) −2271.18 6989.97i −0.360678 1.11005i
\(342\) 0 0
\(343\) 6858.66 1.07969
\(344\) −1792.30 + 1302.19i −0.280914 + 0.204096i
\(345\) 0 0
\(346\) 2734.76 + 1986.92i 0.424917 + 0.308721i
\(347\) 5680.75 + 4127.31i 0.878844 + 0.638517i 0.932945 0.360018i \(-0.117229\pi\)
−0.0541015 + 0.998535i \(0.517229\pi\)
\(348\) 0 0
\(349\) 9562.87 1.46673 0.733365 0.679835i \(-0.237949\pi\)
0.733365 + 0.679835i \(0.237949\pi\)
\(350\) −178.471 2405.87i −0.0272562 0.367427i
\(351\) 0 0
\(352\) 1590.07 4893.73i 0.240770 0.741013i
\(353\) 1305.15 + 948.244i 0.196787 + 0.142974i 0.681816 0.731524i \(-0.261191\pi\)
−0.485028 + 0.874498i \(0.661191\pi\)
\(354\) 0 0
\(355\) −599.714 278.108i −0.0896606 0.0415787i
\(356\) −3831.93 + 2784.06i −0.570483 + 0.414480i
\(357\) 0 0
\(358\) 3200.51 2325.31i 0.472493 0.343286i
\(359\) −2375.00 7309.50i −0.349158 1.07460i −0.959320 0.282321i \(-0.908896\pi\)
0.610162 0.792277i \(-0.291104\pi\)
\(360\) 0 0
\(361\) 2036.73 6268.42i 0.296943 0.913896i
\(362\) 774.940 + 2385.02i 0.112514 + 0.346281i
\(363\) 0 0
\(364\) 1650.75 5080.49i 0.237700 0.731566i
\(365\) 980.951 8131.43i 0.140672 1.16608i
\(366\) 0 0
\(367\) −6425.12 + 4668.12i −0.913865 + 0.663961i −0.941989 0.335643i \(-0.891046\pi\)
0.0281247 + 0.999604i \(0.491046\pi\)
\(368\) 2493.19 0.353170
\(369\) 0 0
\(370\) −4311.47 + 847.537i −0.605791 + 0.119085i
\(371\) 5412.32 + 3932.28i 0.757396 + 0.550280i
\(372\) 0 0
\(373\) −3174.37 + 9769.71i −0.440651 + 1.35618i 0.446533 + 0.894767i \(0.352659\pi\)
−0.887184 + 0.461417i \(0.847341\pi\)
\(374\) −3612.94 −0.499520
\(375\) 0 0
\(376\) −1094.52 −0.150121
\(377\) −3858.40 + 11874.9i −0.527103 + 1.62226i
\(378\) 0 0
\(379\) −9272.49 6736.86i −1.25672 0.913059i −0.258126 0.966111i \(-0.583105\pi\)
−0.998592 + 0.0530524i \(0.983105\pi\)
\(380\) −7755.67 + 1524.59i −1.04699 + 0.205815i
\(381\) 0 0
\(382\) −1333.73 −0.178638
\(383\) −3116.57 + 2264.32i −0.415795 + 0.302092i −0.775944 0.630802i \(-0.782726\pi\)
0.360149 + 0.932895i \(0.382726\pi\)
\(384\) 0 0
\(385\) 518.494 4297.97i 0.0686361 0.568948i
\(386\) 641.568 1974.54i 0.0845984 0.260367i
\(387\) 0 0
\(388\) 1113.84 + 3428.05i 0.145739 + 0.448538i
\(389\) −2243.60 + 6905.09i −0.292429 + 0.900005i 0.691644 + 0.722239i \(0.256887\pi\)
−0.984073 + 0.177766i \(0.943113\pi\)
\(390\) 0 0
\(391\) −3323.05 10227.3i −0.429806 1.32281i
\(392\) 2319.18 1684.98i 0.298817 0.217103i
\(393\) 0 0
\(394\) 884.189 642.401i 0.113058 0.0821414i
\(395\) 2416.39 + 1120.56i 0.307802 + 0.142738i
\(396\) 0 0
\(397\) 5893.38 + 4281.79i 0.745039 + 0.541302i 0.894285 0.447498i \(-0.147685\pi\)
−0.149246 + 0.988800i \(0.547685\pi\)
\(398\) −1394.67 + 4292.37i −0.175650 + 0.540595i
\(399\) 0 0
\(400\) 1770.65 + 2092.14i 0.221332 + 0.261517i
\(401\) −793.134 −0.0987711 −0.0493856 0.998780i \(-0.515726\pi\)
−0.0493856 + 0.998780i \(0.515726\pi\)
\(402\) 0 0
\(403\) −13456.9 9776.99i −1.66336 1.20850i
\(404\) 8786.91 + 6384.06i 1.08209 + 0.786186i
\(405\) 0 0
\(406\) 3111.58 2260.70i 0.380358 0.276346i
\(407\) −7884.87 −0.960291
\(408\) 0 0
\(409\) 1761.04 + 5419.93i 0.212905 + 0.655253i 0.999296 + 0.0375240i \(0.0119471\pi\)
−0.786391 + 0.617729i \(0.788053\pi\)
\(410\) −4943.67 + 971.815i −0.595490 + 0.117060i
\(411\) 0 0
\(412\) −699.177 2151.85i −0.0836068 0.257315i
\(413\) 2425.34 + 7464.43i 0.288966 + 0.889347i
\(414\) 0 0
\(415\) −2659.17 + 2863.74i −0.314539 + 0.338736i
\(416\) −3598.60 11075.3i −0.424124 1.30532i
\(417\) 0 0
\(418\) 4430.44 0.518421
\(419\) 11029.1 8013.13i 1.28594 0.934289i 0.286224 0.958163i \(-0.407600\pi\)
0.999715 + 0.0238738i \(0.00759998\pi\)
\(420\) 0 0
\(421\) 5536.49 + 4022.50i 0.640931 + 0.465664i 0.860170 0.510007i \(-0.170357\pi\)
−0.219239 + 0.975671i \(0.570357\pi\)
\(422\) −3967.87 2882.83i −0.457709 0.332545i
\(423\) 0 0
\(424\) 9303.75 1.06564
\(425\) 6222.13 10051.9i 0.710159 1.14727i
\(426\) 0 0
\(427\) −2250.74 + 6927.06i −0.255084 + 0.785068i
\(428\) 7039.81 + 5114.72i 0.795052 + 0.577639i
\(429\) 0 0
\(430\) −210.455 + 1744.53i −0.0236025 + 0.195649i
\(431\) 4408.94 3203.28i 0.492741 0.357997i −0.313497 0.949589i \(-0.601500\pi\)
0.806237 + 0.591592i \(0.201500\pi\)
\(432\) 0 0
\(433\) −3891.33 + 2827.21i −0.431883 + 0.313781i −0.782401 0.622775i \(-0.786005\pi\)
0.350519 + 0.936556i \(0.386005\pi\)
\(434\) 1583.32 + 4872.95i 0.175119 + 0.538961i
\(435\) 0 0
\(436\) −520.274 + 1601.24i −0.0571482 + 0.175884i
\(437\) 4074.96 + 12541.4i 0.446068 + 1.37286i
\(438\) 0 0
\(439\) −4451.87 + 13701.4i −0.484000 + 1.48960i 0.349424 + 0.936965i \(0.386377\pi\)
−0.833424 + 0.552634i \(0.813623\pi\)
\(440\) −2929.93 5259.46i −0.317453 0.569852i
\(441\) 0 0
\(442\) −6615.09 + 4806.14i −0.711873 + 0.517206i
\(443\) 12023.5 1.28951 0.644756 0.764389i \(-0.276959\pi\)
0.644756 + 0.764389i \(0.276959\pi\)
\(444\) 0 0
\(445\) −1040.45 + 8624.64i −0.110836 + 0.918758i
\(446\) −6390.85 4643.22i −0.678510 0.492966i
\(447\) 0 0
\(448\) −350.340 + 1078.24i −0.0369465 + 0.113710i
\(449\) 10740.5 1.12889 0.564447 0.825469i \(-0.309090\pi\)
0.564447 + 0.825469i \(0.309090\pi\)
\(450\) 0 0
\(451\) −9041.06 −0.943962
\(452\) 2624.40 8077.09i 0.273101 0.840518i
\(453\) 0 0
\(454\) −1437.39 1044.33i −0.148591 0.107957i
\(455\) −4768.08 8559.07i −0.491277 0.881880i
\(456\) 0 0
\(457\) 5957.31 0.609783 0.304892 0.952387i \(-0.401380\pi\)
0.304892 + 0.952387i \(0.401380\pi\)
\(458\) 1526.87 1109.34i 0.155778 0.113179i
\(459\) 0 0
\(460\) 5273.11 5678.77i 0.534479 0.575596i
\(461\) 3710.77 11420.6i 0.374898 1.15382i −0.568650 0.822580i \(-0.692534\pi\)
0.943548 0.331237i \(-0.107466\pi\)
\(462\) 0 0
\(463\) −2488.82 7659.79i −0.249817 0.768856i −0.994807 0.101781i \(-0.967546\pi\)
0.744990 0.667075i \(-0.232454\pi\)
\(464\) −1350.29 + 4155.76i −0.135098 + 0.415790i
\(465\) 0 0
\(466\) 1126.96 + 3468.41i 0.112028 + 0.344788i
\(467\) −15143.7 + 11002.5i −1.50057 + 1.09023i −0.530415 + 0.847738i \(0.677964\pi\)
−0.970154 + 0.242490i \(0.922036\pi\)
\(468\) 0 0
\(469\) −7915.52 + 5750.96i −0.779328 + 0.566215i
\(470\) −590.721 + 636.165i −0.0579743 + 0.0624343i
\(471\) 0 0
\(472\) 8830.39 + 6415.65i 0.861126 + 0.625645i
\(473\) −974.396 + 2998.88i −0.0947204 + 0.291520i
\(474\) 0 0
\(475\) −7630.01 + 12326.4i −0.737030 + 1.19068i
\(476\) −8063.41 −0.776441
\(477\) 0 0
\(478\) −465.435 338.159i −0.0445366 0.0323578i
\(479\) −11883.0 8633.47i −1.13350 0.823535i −0.147299 0.989092i \(-0.547058\pi\)
−0.986200 + 0.165557i \(0.947058\pi\)
\(480\) 0 0
\(481\) −14436.8 + 10488.9i −1.36852 + 0.994290i
\(482\) −1481.90 −0.140039
\(483\) 0 0
\(484\) 1063.48 + 3273.07i 0.0998763 + 0.307388i
\(485\) 5997.39 + 2781.19i 0.561500 + 0.260386i
\(486\) 0 0
\(487\) 1129.41 + 3475.96i 0.105089 + 0.323430i 0.989751 0.142802i \(-0.0456112\pi\)
−0.884662 + 0.466232i \(0.845611\pi\)
\(488\) 3130.09 + 9633.44i 0.290354 + 0.893617i
\(489\) 0 0
\(490\) 272.321 2257.36i 0.0251066 0.208117i
\(491\) 3658.40 + 11259.4i 0.336255 + 1.03489i 0.966101 + 0.258166i \(0.0831181\pi\)
−0.629846 + 0.776720i \(0.716882\pi\)
\(492\) 0 0
\(493\) 18847.1 1.72177
\(494\) 8111.89 5893.63i 0.738808 0.536775i
\(495\) 0 0
\(496\) −4709.38 3421.56i −0.426325 0.309743i
\(497\) 669.039 + 486.085i 0.0603833 + 0.0438710i
\(498\) 0 0
\(499\) −11497.8 −1.03149 −0.515744 0.856743i \(-0.672484\pi\)
−0.515744 + 0.856743i \(0.672484\pi\)
\(500\) 8510.24 + 391.842i 0.761179 + 0.0350474i
\(501\) 0 0
\(502\) −1394.17 + 4290.80i −0.123953 + 0.381490i
\(503\) 2539.40 + 1844.98i 0.225102 + 0.163546i 0.694620 0.719377i \(-0.255572\pi\)
−0.469518 + 0.882923i \(0.655572\pi\)
\(504\) 0 0
\(505\) 19546.3 3842.36i 1.72237 0.338579i
\(506\) −3514.17 + 2553.20i −0.308743 + 0.224315i
\(507\) 0 0
\(508\) 4308.92 3130.61i 0.376334 0.273422i
\(509\) −4595.77 14144.3i −0.400204 1.23170i −0.924834 0.380372i \(-0.875796\pi\)
0.524629 0.851331i \(-0.324204\pi\)
\(510\) 0 0
\(511\) −3166.21 + 9744.58i −0.274099 + 0.843591i
\(512\) −2313.72 7120.90i −0.199713 0.614653i
\(513\) 0 0
\(514\) 1045.94 3219.07i 0.0897557 0.276240i
\(515\) −3764.67 1745.80i −0.322119 0.149377i
\(516\) 0 0
\(517\) −1260.32 + 915.676i −0.107212 + 0.0778944i
\(518\) 5496.81 0.466247
\(519\) 0 0
\(520\) −12361.0 5732.21i −1.04243 0.483412i
\(521\) −14314.4 10400.0i −1.20370 0.874538i −0.209055 0.977904i \(-0.567039\pi\)
−0.994643 + 0.103366i \(0.967039\pi\)
\(522\) 0 0
\(523\) −6931.04 + 21331.5i −0.579490 + 1.78349i 0.0408650 + 0.999165i \(0.486989\pi\)
−0.620355 + 0.784321i \(0.713011\pi\)
\(524\) 14088.9 1.17458
\(525\) 0 0
\(526\) 4427.44 0.367007
\(527\) −7758.69 + 23878.8i −0.641316 + 1.97377i
\(528\) 0 0
\(529\) −616.356 447.809i −0.0506580 0.0368052i
\(530\) 5021.31 5407.59i 0.411531 0.443190i
\(531\) 0 0
\(532\) 9887.92 0.805819
\(533\) −16553.7 + 12026.9i −1.34525 + 0.977382i
\(534\) 0 0
\(535\) 15659.9 3078.38i 1.26549 0.248767i
\(536\) −4204.71 + 12940.8i −0.338836 + 1.04283i
\(537\) 0 0
\(538\) −2716.14 8359.41i −0.217660 0.669888i
\(539\) 1260.83 3880.44i 0.100757 0.310098i
\(540\) 0 0
\(541\) 3503.70 + 10783.3i 0.278440 + 0.856950i 0.988289 + 0.152596i \(0.0487633\pi\)
−0.709849 + 0.704354i \(0.751237\pi\)
\(542\) −2250.96 + 1635.42i −0.178389 + 0.129607i
\(543\) 0 0
\(544\) −14220.9 + 10332.1i −1.12080 + 0.814311i
\(545\) 1502.77 + 2697.60i 0.118113 + 0.212023i
\(546\) 0 0
\(547\) −9244.76 6716.71i −0.722627 0.525020i 0.164595 0.986361i \(-0.447368\pi\)
−0.887223 + 0.461342i \(0.847368\pi\)
\(548\) 15.6300 48.1041i 0.00121839 0.00374983i
\(549\) 0 0
\(550\) −4638.25 1135.62i −0.359592 0.0880414i
\(551\) −23111.6 −1.78691
\(552\) 0 0
\(553\) −2695.71 1958.55i −0.207294 0.150608i
\(554\) 5433.17 + 3947.43i 0.416667 + 0.302726i
\(555\) 0 0
\(556\) 10453.8 7595.14i 0.797375 0.579327i
\(557\) −1742.79 −0.132575 −0.0662875 0.997801i \(-0.521115\pi\)
−0.0662875 + 0.997801i \(0.521115\pi\)
\(558\) 0 0
\(559\) 2205.22 + 6786.98i 0.166853 + 0.513522i
\(560\) −1668.64 2995.34i −0.125916 0.226029i
\(561\) 0 0
\(562\) −2260.45 6956.94i −0.169664 0.522172i
\(563\) 1390.29 + 4278.88i 0.104074 + 0.320308i 0.989512 0.144450i \(-0.0461413\pi\)
−0.885438 + 0.464758i \(0.846141\pi\)
\(564\) 0 0
\(565\) −7580.40 13607.4i −0.564442 1.01322i
\(566\) −251.478 773.971i −0.0186757 0.0574778i
\(567\) 0 0
\(568\) 1150.07 0.0849578
\(569\) 4717.52 3427.48i 0.347573 0.252526i −0.400277 0.916394i \(-0.631086\pi\)
0.747850 + 0.663868i \(0.231086\pi\)
\(570\) 0 0
\(571\) −21104.6 15333.4i −1.54676 1.12379i −0.945910 0.324430i \(-0.894827\pi\)
−0.600854 0.799359i \(-0.705173\pi\)
\(572\) −8554.37 6215.12i −0.625308 0.454313i
\(573\) 0 0
\(574\) 6302.83 0.458319
\(575\) −1051.46 14174.2i −0.0762590 1.02801i
\(576\) 0 0
\(577\) 691.064 2126.88i 0.0498603 0.153454i −0.923026 0.384737i \(-0.874292\pi\)
0.972887 + 0.231283i \(0.0742922\pi\)
\(578\) 4500.47 + 3269.78i 0.323867 + 0.235303i
\(579\) 0 0
\(580\) 6609.76 + 11865.0i 0.473199 + 0.849429i
\(581\) 3955.13 2873.57i 0.282420 0.205190i
\(582\) 0 0
\(583\) 10713.1 7783.52i 0.761048 0.552934i
\(584\) 4403.23 + 13551.7i 0.311998 + 0.960231i
\(585\) 0 0
\(586\) 2271.98 6992.43i 0.160161 0.492926i
\(587\) −3302.89 10165.2i −0.232240 0.714761i −0.997476 0.0710105i \(-0.977378\pi\)
0.765236 0.643750i \(-0.222622\pi\)
\(588\) 0 0
\(589\) 9514.25 29281.8i 0.665582 2.04845i
\(590\) 8494.77 1669.88i 0.592753 0.116522i
\(591\) 0 0
\(592\) −5052.30 + 3670.71i −0.350757 + 0.254840i
\(593\) −3071.33 −0.212689 −0.106344 0.994329i \(-0.533915\pi\)
−0.106344 + 0.994329i \(0.533915\pi\)
\(594\) 0 0
\(595\) −10063.1 + 10837.3i −0.693358 + 0.746697i
\(596\) −12833.2 9323.89i −0.881996 0.640808i
\(597\) 0 0
\(598\) −3037.84 + 9349.52i −0.207737 + 0.639348i
\(599\) 19658.8 1.34097 0.670483 0.741925i \(-0.266087\pi\)
0.670483 + 0.741925i \(0.266087\pi\)
\(600\) 0 0
\(601\) 24937.5 1.69255 0.846276 0.532745i \(-0.178840\pi\)
0.846276 + 0.532745i \(0.178840\pi\)
\(602\) 679.284 2090.62i 0.0459893 0.141541i
\(603\) 0 0
\(604\) −3135.85 2278.33i −0.211251 0.153483i
\(605\) 5726.25 + 2655.45i 0.384802 + 0.178446i
\(606\) 0 0
\(607\) −6767.35 −0.452518 −0.226259 0.974067i \(-0.572650\pi\)
−0.226259 + 0.974067i \(0.572650\pi\)
\(608\) 17438.7 12669.9i 1.16321 0.845122i
\(609\) 0 0
\(610\) 7288.55 + 3379.94i 0.483778 + 0.224344i
\(611\) −1089.49 + 3353.10i −0.0721375 + 0.222016i
\(612\) 0 0
\(613\) −7732.44 23798.0i −0.509478 1.56801i −0.793109 0.609080i \(-0.791539\pi\)
0.283631 0.958934i \(-0.408461\pi\)
\(614\) −1584.84 + 4877.63i −0.104168 + 0.320595i
\(615\) 0 0
\(616\) 2327.38 + 7162.94i 0.152229 + 0.468512i
\(617\) −8292.13 + 6024.59i −0.541051 + 0.393097i −0.824475 0.565898i \(-0.808530\pi\)
0.283424 + 0.958995i \(0.408530\pi\)
\(618\) 0 0
\(619\) 1384.10 1005.60i 0.0898732 0.0652967i −0.541941 0.840416i \(-0.682310\pi\)
0.631814 + 0.775120i \(0.282310\pi\)
\(620\) −17753.7 + 3489.98i −1.15001 + 0.226066i
\(621\) 0 0
\(622\) −3672.06 2667.91i −0.236714 0.171983i
\(623\) 3358.25 10335.6i 0.215964 0.664669i
\(624\) 0 0
\(625\) 11147.4 10948.8i 0.713434 0.700723i
\(626\) 2525.36 0.161236
\(627\) 0 0
\(628\) −6326.23 4596.28i −0.401981 0.292056i
\(629\) 21791.6 + 15832.5i 1.38138 + 1.00363i
\(630\) 0 0
\(631\) 132.282 96.1083i 0.00834557 0.00606341i −0.583605 0.812038i \(-0.698358\pi\)
0.591950 + 0.805975i \(0.298358\pi\)
\(632\) −4633.91 −0.291657
\(633\) 0 0
\(634\) 2018.74 + 6213.05i 0.126458 + 0.389199i
\(635\) 1169.96 9698.22i 0.0731159 0.606082i
\(636\) 0 0
\(637\) −2853.48 8782.11i −0.177487 0.546248i
\(638\) −2352.54 7240.38i −0.145984 0.449294i
\(639\) 0 0
\(640\) −13946.9 6467.67i −0.861408 0.399464i
\(641\) 902.479 + 2777.55i 0.0556097 + 0.171149i 0.975004 0.222189i \(-0.0713202\pi\)
−0.919394 + 0.393338i \(0.871320\pi\)
\(642\) 0 0
\(643\) 13783.9 0.845387 0.422693 0.906273i \(-0.361085\pi\)
0.422693 + 0.906273i \(0.361085\pi\)
\(644\) −7842.99 + 5698.26i −0.479902 + 0.348669i
\(645\) 0 0
\(646\) −12244.5 8896.15i −0.745748 0.541818i
\(647\) 15672.0 + 11386.4i 0.952288 + 0.691878i 0.951347 0.308122i \(-0.0997004\pi\)
0.000941137 1.00000i \(0.499700\pi\)
\(648\) 0 0
\(649\) 15535.4 0.939624
\(650\) −10003.0 + 4090.82i −0.603617 + 0.246854i
\(651\) 0 0
\(652\) −779.649 + 2399.51i −0.0468304 + 0.144129i
\(653\) −21129.9 15351.8i −1.26628 0.920003i −0.267228 0.963633i \(-0.586108\pi\)
−0.999048 + 0.0436299i \(0.986108\pi\)
\(654\) 0 0
\(655\) 17583.0 18935.6i 1.04889 1.12958i
\(656\) −5793.13 + 4208.96i −0.344792 + 0.250506i
\(657\) 0 0
\(658\) 878.612 638.349i 0.0520545 0.0378198i
\(659\) −1860.77 5726.87i −0.109993 0.338524i 0.880877 0.473346i \(-0.156954\pi\)
−0.990870 + 0.134822i \(0.956954\pi\)
\(660\) 0 0
\(661\) 7585.96 23347.2i 0.446384 1.37383i −0.434575 0.900636i \(-0.643101\pi\)
0.880959 0.473193i \(-0.156899\pi\)
\(662\) −1808.12 5564.81i −0.106155 0.326711i
\(663\) 0 0
\(664\) 2100.96 6466.08i 0.122791 0.377910i
\(665\) 12340.1 13289.4i 0.719593 0.774950i
\(666\) 0 0
\(667\) 18331.9 13318.9i 1.06419 0.773178i
\(668\) 20152.3 1.16724
\(669\) 0 0
\(670\) 5252.21 + 9428.12i 0.302851 + 0.543642i
\(671\) 11663.6 + 8474.08i 0.671039 + 0.487538i
\(672\) 0 0
\(673\) −8704.24 + 26788.9i −0.498549 + 1.53438i 0.312802 + 0.949818i \(0.398732\pi\)
−0.811351 + 0.584559i \(0.801268\pi\)
\(674\) 681.544 0.0389497
\(675\) 0 0
\(676\) −10537.6 −0.599547
\(677\) −3068.34 + 9443.37i −0.174189 + 0.536098i −0.999595 0.0284408i \(-0.990946\pi\)
0.825407 + 0.564538i \(0.190946\pi\)
\(678\) 0 0
\(679\) −6690.66 4861.05i −0.378150 0.274742i
\(680\) −2463.27 + 20418.9i −0.138915 + 1.15151i
\(681\) 0 0
\(682\) 10141.8 0.569429
\(683\) −9594.74 + 6970.99i −0.537529 + 0.390538i −0.823167 0.567800i \(-0.807795\pi\)
0.285637 + 0.958338i \(0.407795\pi\)
\(684\) 0 0
\(685\) −45.1460 81.0407i −0.00251816 0.00452030i
\(686\) −2924.62 + 9001.05i −0.162773 + 0.500964i
\(687\) 0 0
\(688\) 771.742 + 2375.18i 0.0427651 + 0.131617i
\(689\) 9260.98 28502.4i 0.512069 1.57599i
\(690\) 0 0
\(691\) −246.557 758.826i −0.0135738 0.0417758i 0.944040 0.329830i \(-0.106992\pi\)
−0.957614 + 0.288055i \(0.906992\pi\)
\(692\) 12081.1 8777.46i 0.663665 0.482181i
\(693\) 0 0
\(694\) −7838.86 + 5695.27i −0.428760 + 0.311512i
\(695\) 2838.43 23528.7i 0.154918 1.28417i
\(696\) 0 0
\(697\) 24987.0 + 18154.1i 1.35789 + 0.986564i
\(698\) −4077.72 + 12549.9i −0.221123 + 0.680548i
\(699\) 0 0
\(700\) −10351.7 2534.48i −0.558940 0.136849i
\(701\) 18597.0 1.00199 0.500997 0.865449i \(-0.332967\pi\)
0.500997 + 0.865449i \(0.332967\pi\)
\(702\) 0 0
\(703\) −26722.4 19414.9i −1.43365 1.04161i
\(704\) 1815.50 + 1319.04i 0.0971936 + 0.0706153i
\(705\) 0 0
\(706\) −1800.97 + 1308.48i −0.0960062 + 0.0697526i
\(707\) −24920.1 −1.32562
\(708\) 0 0
\(709\) 8099.16 + 24926.7i 0.429013 + 1.32037i 0.899099 + 0.437746i \(0.144223\pi\)
−0.470086 + 0.882621i \(0.655777\pi\)
\(710\) 620.703 668.453i 0.0328093 0.0353332i
\(711\) 0 0
\(712\) −4670.31 14373.7i −0.245825 0.756570i
\(713\) 9328.10 + 28708.9i 0.489958 + 1.50794i
\(714\) 0 0
\(715\) −19029.0 + 3740.67i −0.995307 + 0.195655i
\(716\) −5400.50 16621.0i −0.281880 0.867537i
\(717\) 0 0
\(718\) 10605.4 0.551241
\(719\) −16782.5 + 12193.2i −0.870491 + 0.632449i −0.930719 0.365736i \(-0.880817\pi\)
0.0602273 + 0.998185i \(0.480817\pi\)
\(720\) 0 0
\(721\) 4199.85 + 3051.37i 0.216936 + 0.157613i
\(722\) 7357.94 + 5345.86i 0.379272 + 0.275557i
\(723\) 0 0
\(724\) 11078.3 0.568679
\(725\) 24195.7 + 5924.00i 1.23945 + 0.303465i
\(726\) 0 0
\(727\) −3452.87 + 10626.8i −0.176148 + 0.542129i −0.999684 0.0251356i \(-0.991998\pi\)
0.823536 + 0.567264i \(0.191998\pi\)
\(728\) 13789.9 + 10018.9i 0.702042 + 0.510063i
\(729\) 0 0
\(730\) 10253.1 + 4754.70i 0.519841 + 0.241068i
\(731\) 8714.60 6331.53i 0.440932 0.320356i
\(732\) 0 0
\(733\) 22875.9 16620.3i 1.15272 0.837499i 0.163878 0.986481i \(-0.447600\pi\)
0.988840 + 0.148982i \(0.0475996\pi\)
\(734\) −3386.51 10422.6i −0.170298 0.524122i
\(735\) 0 0
\(736\) −6530.66 + 20099.3i −0.327070 + 1.00662i
\(737\) 5984.60 + 18418.7i 0.299112 + 0.920573i
\(738\) 0 0
\(739\) 12217.4 37601.2i 0.608151 1.87170i 0.134671 0.990890i \(-0.457002\pi\)
0.473480 0.880805i \(-0.342998\pi\)
\(740\) −2324.83 + 19271.3i −0.115490 + 0.957332i
\(741\) 0 0
\(742\) −7468.46 + 5426.15i −0.369509 + 0.268464i
\(743\) −35466.6 −1.75120 −0.875601 0.483036i \(-0.839534\pi\)
−0.875601 + 0.483036i \(0.839534\pi\)
\(744\) 0 0
\(745\) −28547.2 + 5611.74i −1.40388 + 0.275971i
\(746\) −11467.8 8331.85i −0.562823 0.408915i
\(747\) 0 0
\(748\) −4932.10 + 15179.5i −0.241090 + 0.742000i
\(749\) −19965.2 −0.973984
\(750\) 0 0
\(751\) 28967.6 1.40751 0.703756 0.710442i \(-0.251505\pi\)
0.703756 + 0.710442i \(0.251505\pi\)
\(752\) −381.278 + 1173.45i −0.0184891 + 0.0569036i
\(753\) 0 0
\(754\) −13938.9 10127.2i −0.673245 0.489141i
\(755\) −6975.62 + 1371.25i −0.336250 + 0.0660992i
\(756\) 0 0
\(757\) −15068.4 −0.723476 −0.361738 0.932280i \(-0.617817\pi\)
−0.361738 + 0.932280i \(0.617817\pi\)
\(758\) 12795.1 9296.18i 0.613112 0.445452i
\(759\) 0 0
\(760\) 3020.64 25039.1i 0.144171 1.19508i
\(761\) 998.600 3073.38i 0.0475680 0.146399i −0.924451 0.381300i \(-0.875477\pi\)
0.972019 + 0.234901i \(0.0754765\pi\)
\(762\) 0 0
\(763\) −1193.72 3673.90i −0.0566391 0.174317i
\(764\) −1820.71 + 5603.57i −0.0862186 + 0.265353i
\(765\) 0 0
\(766\) −1642.66 5055.60i −0.0774829 0.238468i
\(767\) 28444.4 20666.0i 1.33907 0.972891i
\(768\) 0 0
\(769\) 873.705 634.784i 0.0409709 0.0297671i −0.567111 0.823641i \(-0.691939\pi\)
0.608082 + 0.793874i \(0.291939\pi\)
\(770\) 5419.40 + 2513.16i 0.253638 + 0.117621i
\(771\) 0 0
\(772\) −7420.06 5390.99i −0.345925 0.251329i
\(773\) 4957.48 15257.6i 0.230670 0.709930i −0.766996 0.641652i \(-0.778249\pi\)
0.997666 0.0682784i \(-0.0217506\pi\)
\(774\) 0 0
\(775\) −17466.1 + 28216.6i −0.809548 + 1.30783i
\(776\) −11501.2 −0.532048
\(777\) 0 0
\(778\) −8105.27 5888.83i −0.373507 0.271368i
\(779\) −30640.8 22261.8i −1.40927 1.02389i
\(780\) 0 0
\(781\) 1324.29 962.151i 0.0606744 0.0440825i
\(782\) 14838.9 0.678566