Properties

Label 144.4.i.d.49.3
Level $144$
Weight $4$
Character 144.49
Analytic conductor $8.496$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [144,4,Mod(49,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("144.49");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 144.i (of order \(3\), degree \(2\), not 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: \(8.49627504083\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.6831243.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 13x^{4} + 49x^{2} + 48 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.3
Root \(-1.23396i\) of defining polynomial
Character \(\chi\) \(=\) 144.49
Dual form 144.4.i.d.97.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.14739 + 3.13036i) q^{3} +(6.92194 - 11.9892i) q^{5} +(15.3540 + 26.5939i) q^{7} +(7.40171 + 25.9656i) q^{9} +O(q^{10})\) \(q+(4.14739 + 3.13036i) q^{3} +(6.92194 - 11.9892i) q^{5} +(15.3540 + 26.5939i) q^{7} +(7.40171 + 25.9656i) q^{9} +(-21.9523 - 38.0225i) q^{11} +(6.11853 - 10.5976i) q^{13} +(66.2383 - 28.0555i) q^{15} +76.0286 q^{17} +44.1789 q^{19} +(-19.5694 + 158.359i) q^{21} +(-39.3135 + 68.0930i) q^{23} +(-33.3265 - 57.7232i) q^{25} +(-50.5840 + 130.860i) q^{27} +(46.3903 + 80.3504i) q^{29} +(-71.5329 + 123.899i) q^{31} +(27.9793 - 226.413i) q^{33} +425.118 q^{35} -32.4741 q^{37} +(58.5502 - 24.7992i) q^{39} +(167.778 - 290.599i) q^{41} +(-249.166 - 431.567i) q^{43} +(362.540 + 90.9925i) q^{45} +(-140.882 - 244.016i) q^{47} +(-299.990 + 519.599i) q^{49} +(315.320 + 237.997i) q^{51} -628.565 q^{53} -607.810 q^{55} +(183.227 + 138.296i) q^{57} +(252.327 - 437.043i) q^{59} +(-185.951 - 322.076i) q^{61} +(-576.882 + 595.517i) q^{63} +(-84.7041 - 146.712i) q^{65} +(-81.3304 + 140.868i) q^{67} +(-376.204 + 159.343i) q^{69} -433.512 q^{71} -629.645 q^{73} +(42.4763 - 343.725i) q^{75} +(674.111 - 1167.59i) q^{77} +(86.3649 + 149.588i) q^{79} +(-619.429 + 384.380i) q^{81} +(-87.4288 - 151.431i) q^{83} +(526.265 - 911.518i) q^{85} +(-59.1267 + 478.463i) q^{87} +336.716 q^{89} +375.775 q^{91} +(-684.522 + 289.933i) q^{93} +(305.804 - 529.668i) q^{95} +(-42.1594 - 73.0222i) q^{97} +(824.794 - 851.437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{3} + 6 q^{5} + 6 q^{7} + 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{3} + 6 q^{5} + 6 q^{7} + 39 q^{9} - 51 q^{11} + 12 q^{13} + 180 q^{15} - 222 q^{17} - 30 q^{19} - 120 q^{21} - 210 q^{23} - 3 q^{25} - 648 q^{27} + 456 q^{29} - 48 q^{31} - 603 q^{33} + 1104 q^{35} - 96 q^{37} + 36 q^{39} + 897 q^{41} - 129 q^{43} + 1494 q^{45} - 522 q^{47} - 225 q^{49} + 1647 q^{51} - 2208 q^{53} + 216 q^{55} - 645 q^{57} - 453 q^{59} - 402 q^{61} - 1896 q^{63} + 1110 q^{65} + 213 q^{67} - 198 q^{69} - 120 q^{71} + 750 q^{73} - 921 q^{75} + 1128 q^{77} - 552 q^{79} - 549 q^{81} + 612 q^{83} + 1188 q^{85} + 1386 q^{87} - 924 q^{89} + 264 q^{91} - 1998 q^{93} + 2184 q^{95} + 93 q^{97} + 1854 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0
\(3\) 4.14739 + 3.13036i 0.798166 + 0.602438i
\(4\) 0 0
\(5\) 6.92194 11.9892i 0.619117 1.07234i −0.370530 0.928821i \(-0.620824\pi\)
0.989647 0.143522i \(-0.0458427\pi\)
\(6\) 0 0
\(7\) 15.3540 + 26.5939i 0.829038 + 1.43594i 0.898794 + 0.438372i \(0.144445\pi\)
−0.0697558 + 0.997564i \(0.522222\pi\)
\(8\) 0 0
\(9\) 7.40171 + 25.9656i 0.274137 + 0.961691i
\(10\) 0 0
\(11\) −21.9523 38.0225i −0.601715 1.04220i −0.992561 0.121745i \(-0.961151\pi\)
0.390846 0.920456i \(-0.372182\pi\)
\(12\) 0 0
\(13\) 6.11853 10.5976i 0.130536 0.226096i −0.793347 0.608770i \(-0.791663\pi\)
0.923883 + 0.382674i \(0.124997\pi\)
\(14\) 0 0
\(15\) 66.2383 28.0555i 1.14018 0.482927i
\(16\) 0 0
\(17\) 76.0286 1.08468 0.542342 0.840158i \(-0.317538\pi\)
0.542342 + 0.840158i \(0.317538\pi\)
\(18\) 0 0
\(19\) 44.1789 0.533439 0.266720 0.963774i \(-0.414060\pi\)
0.266720 + 0.963774i \(0.414060\pi\)
\(20\) 0 0
\(21\) −19.5694 + 158.359i −0.203352 + 1.64556i
\(22\) 0 0
\(23\) −39.3135 + 68.0930i −0.356410 + 0.617321i −0.987358 0.158504i \(-0.949333\pi\)
0.630948 + 0.775825i \(0.282666\pi\)
\(24\) 0 0
\(25\) −33.3265 57.7232i −0.266612 0.461786i
\(26\) 0 0
\(27\) −50.5840 + 130.860i −0.360552 + 0.932739i
\(28\) 0 0
\(29\) 46.3903 + 80.3504i 0.297050 + 0.514506i 0.975460 0.220178i \(-0.0706637\pi\)
−0.678409 + 0.734684i \(0.737330\pi\)
\(30\) 0 0
\(31\) −71.5329 + 123.899i −0.414442 + 0.717834i −0.995370 0.0961208i \(-0.969356\pi\)
0.580928 + 0.813955i \(0.302690\pi\)
\(32\) 0 0
\(33\) 27.9793 226.413i 0.147593 1.19434i
\(34\) 0 0
\(35\) 425.118 2.05309
\(36\) 0 0
\(37\) −32.4741 −0.144289 −0.0721447 0.997394i \(-0.522984\pi\)
−0.0721447 + 0.997394i \(0.522984\pi\)
\(38\) 0 0
\(39\) 58.5502 24.7992i 0.240398 0.101822i
\(40\) 0 0
\(41\) 167.778 290.599i 0.639084 1.10693i −0.346550 0.938031i \(-0.612647\pi\)
0.985634 0.168895i \(-0.0540197\pi\)
\(42\) 0 0
\(43\) −249.166 431.567i −0.883660 1.53054i −0.847242 0.531208i \(-0.821738\pi\)
−0.0364186 0.999337i \(-0.511595\pi\)
\(44\) 0 0
\(45\) 362.540 + 90.9925i 1.20098 + 0.301430i
\(46\) 0 0
\(47\) −140.882 244.016i −0.437230 0.757305i 0.560244 0.828327i \(-0.310707\pi\)
−0.997475 + 0.0710223i \(0.977374\pi\)
\(48\) 0 0
\(49\) −299.990 + 519.599i −0.874608 + 1.51487i
\(50\) 0 0
\(51\) 315.320 + 237.997i 0.865758 + 0.653455i
\(52\) 0 0
\(53\) −628.565 −1.62906 −0.814529 0.580123i \(-0.803005\pi\)
−0.814529 + 0.580123i \(0.803005\pi\)
\(54\) 0 0
\(55\) −607.810 −1.49013
\(56\) 0 0
\(57\) 183.227 + 138.296i 0.425773 + 0.321364i
\(58\) 0 0
\(59\) 252.327 437.043i 0.556782 0.964375i −0.440980 0.897517i \(-0.645369\pi\)
0.997762 0.0668584i \(-0.0212976\pi\)
\(60\) 0 0
\(61\) −185.951 322.076i −0.390304 0.676026i 0.602186 0.798356i \(-0.294297\pi\)
−0.992489 + 0.122330i \(0.960963\pi\)
\(62\) 0 0
\(63\) −576.882 + 595.517i −1.15366 + 1.19092i
\(64\) 0 0
\(65\) −84.7041 146.712i −0.161635 0.279960i
\(66\) 0 0
\(67\) −81.3304 + 140.868i −0.148300 + 0.256863i −0.930599 0.366040i \(-0.880713\pi\)
0.782299 + 0.622903i \(0.214047\pi\)
\(68\) 0 0
\(69\) −376.204 + 159.343i −0.656372 + 0.278009i
\(70\) 0 0
\(71\) −433.512 −0.724626 −0.362313 0.932056i \(-0.618013\pi\)
−0.362313 + 0.932056i \(0.618013\pi\)
\(72\) 0 0
\(73\) −629.645 −1.00951 −0.504756 0.863262i \(-0.668418\pi\)
−0.504756 + 0.863262i \(0.668418\pi\)
\(74\) 0 0
\(75\) 42.4763 343.725i 0.0653965 0.529199i
\(76\) 0 0
\(77\) 674.111 1167.59i 0.997689 1.72805i
\(78\) 0 0
\(79\) 86.3649 + 149.588i 0.122998 + 0.213038i 0.920948 0.389684i \(-0.127416\pi\)
−0.797951 + 0.602723i \(0.794083\pi\)
\(80\) 0 0
\(81\) −619.429 + 384.380i −0.849697 + 0.527271i
\(82\) 0 0
\(83\) −87.4288 151.431i −0.115621 0.200262i 0.802407 0.596778i \(-0.203553\pi\)
−0.918028 + 0.396516i \(0.870219\pi\)
\(84\) 0 0
\(85\) 526.265 911.518i 0.671547 1.16315i
\(86\) 0 0
\(87\) −59.1267 + 478.463i −0.0728626 + 0.589616i
\(88\) 0 0
\(89\) 336.716 0.401032 0.200516 0.979690i \(-0.435738\pi\)
0.200516 + 0.979690i \(0.435738\pi\)
\(90\) 0 0
\(91\) 375.775 0.432879
\(92\) 0 0
\(93\) −684.522 + 289.933i −0.763244 + 0.323275i
\(94\) 0 0
\(95\) 305.804 529.668i 0.330261 0.572029i
\(96\) 0 0
\(97\) −42.1594 73.0222i −0.0441303 0.0764358i 0.843117 0.537731i \(-0.180718\pi\)
−0.887247 + 0.461295i \(0.847385\pi\)
\(98\) 0 0
\(99\) 824.794 851.437i 0.837322 0.864370i
\(100\) 0 0
\(101\) 874.902 + 1515.38i 0.861941 + 1.49293i 0.870053 + 0.492959i \(0.164085\pi\)
−0.00811161 + 0.999967i \(0.502582\pi\)
\(102\) 0 0
\(103\) 55.6978 96.4714i 0.0532822 0.0922875i −0.838154 0.545433i \(-0.816365\pi\)
0.891436 + 0.453146i \(0.149698\pi\)
\(104\) 0 0
\(105\) 1763.13 + 1330.77i 1.63870 + 1.23686i
\(106\) 0 0
\(107\) −895.520 −0.809095 −0.404548 0.914517i \(-0.632571\pi\)
−0.404548 + 0.914517i \(0.632571\pi\)
\(108\) 0 0
\(109\) −716.957 −0.630019 −0.315009 0.949089i \(-0.602008\pi\)
−0.315009 + 0.949089i \(0.602008\pi\)
\(110\) 0 0
\(111\) −134.683 101.656i −0.115167 0.0869254i
\(112\) 0 0
\(113\) −115.526 + 200.096i −0.0961746 + 0.166579i −0.910098 0.414393i \(-0.863994\pi\)
0.813924 + 0.580972i \(0.197327\pi\)
\(114\) 0 0
\(115\) 544.252 + 942.672i 0.441320 + 0.764388i
\(116\) 0 0
\(117\) 320.461 + 80.4312i 0.253219 + 0.0635544i
\(118\) 0 0
\(119\) 1167.34 + 2021.90i 0.899245 + 1.55754i
\(120\) 0 0
\(121\) −298.306 + 516.681i −0.224122 + 0.388190i
\(122\) 0 0
\(123\) 1605.52 680.025i 1.17695 0.498502i
\(124\) 0 0
\(125\) 807.748 0.577978
\(126\) 0 0
\(127\) −1715.22 −1.19843 −0.599217 0.800586i \(-0.704522\pi\)
−0.599217 + 0.800586i \(0.704522\pi\)
\(128\) 0 0
\(129\) 317.574 2569.86i 0.216750 1.75398i
\(130\) 0 0
\(131\) 666.435 1154.30i 0.444479 0.769859i −0.553537 0.832824i \(-0.686722\pi\)
0.998016 + 0.0629650i \(0.0200557\pi\)
\(132\) 0 0
\(133\) 678.323 + 1174.89i 0.442241 + 0.765984i
\(134\) 0 0
\(135\) 1218.76 + 1512.26i 0.776992 + 0.964110i
\(136\) 0 0
\(137\) −1259.49 2181.50i −0.785443 1.36043i −0.928734 0.370746i \(-0.879102\pi\)
0.143292 0.989680i \(-0.454231\pi\)
\(138\) 0 0
\(139\) 311.442 539.433i 0.190044 0.329166i −0.755220 0.655471i \(-0.772470\pi\)
0.945265 + 0.326305i \(0.105804\pi\)
\(140\) 0 0
\(141\) 179.562 1453.04i 0.107247 0.867859i
\(142\) 0 0
\(143\) −537.263 −0.314183
\(144\) 0 0
\(145\) 1284.44 0.735636
\(146\) 0 0
\(147\) −2870.71 + 1215.90i −1.61069 + 0.682217i
\(148\) 0 0
\(149\) −1204.47 + 2086.21i −0.662243 + 1.14704i 0.317781 + 0.948164i \(0.397062\pi\)
−0.980025 + 0.198875i \(0.936271\pi\)
\(150\) 0 0
\(151\) 33.8218 + 58.5810i 0.0182277 + 0.0315712i 0.874995 0.484131i \(-0.160864\pi\)
−0.856768 + 0.515703i \(0.827531\pi\)
\(152\) 0 0
\(153\) 562.741 + 1974.13i 0.297352 + 1.04313i
\(154\) 0 0
\(155\) 990.293 + 1715.24i 0.513176 + 0.888847i
\(156\) 0 0
\(157\) 2.19676 3.80490i 0.00111669 0.00193417i −0.865467 0.500967i \(-0.832978\pi\)
0.866583 + 0.499033i \(0.166311\pi\)
\(158\) 0 0
\(159\) −2606.91 1967.64i −1.30026 0.981406i
\(160\) 0 0
\(161\) −2414.48 −1.18191
\(162\) 0 0
\(163\) 2863.88 1.37617 0.688087 0.725628i \(-0.258451\pi\)
0.688087 + 0.725628i \(0.258451\pi\)
\(164\) 0 0
\(165\) −2520.82 1902.66i −1.18937 0.897710i
\(166\) 0 0
\(167\) 214.757 371.970i 0.0995114 0.172359i −0.811971 0.583698i \(-0.801605\pi\)
0.911483 + 0.411339i \(0.134939\pi\)
\(168\) 0 0
\(169\) 1023.63 + 1772.97i 0.465920 + 0.806998i
\(170\) 0 0
\(171\) 327.000 + 1147.13i 0.146236 + 0.513003i
\(172\) 0 0
\(173\) 1287.14 + 2229.40i 0.565663 + 0.979756i 0.996988 + 0.0775599i \(0.0247129\pi\)
−0.431325 + 0.902197i \(0.641954\pi\)
\(174\) 0 0
\(175\) 1023.39 1772.56i 0.442063 0.765676i
\(176\) 0 0
\(177\) 2414.60 1022.71i 1.02538 0.434305i
\(178\) 0 0
\(179\) −807.448 −0.337159 −0.168580 0.985688i \(-0.553918\pi\)
−0.168580 + 0.985688i \(0.553918\pi\)
\(180\) 0 0
\(181\) 4296.57 1.76443 0.882215 0.470847i \(-0.156052\pi\)
0.882215 + 0.470847i \(0.156052\pi\)
\(182\) 0 0
\(183\) 237.003 1917.87i 0.0957365 0.774714i
\(184\) 0 0
\(185\) −224.784 + 389.337i −0.0893321 + 0.154728i
\(186\) 0 0
\(187\) −1669.00 2890.79i −0.652671 1.13046i
\(188\) 0 0
\(189\) −4256.74 + 663.993i −1.63826 + 0.255547i
\(190\) 0 0
\(191\) −153.147 265.259i −0.0580176 0.100489i 0.835558 0.549402i \(-0.185145\pi\)
−0.893575 + 0.448913i \(0.851811\pi\)
\(192\) 0 0
\(193\) 856.177 1482.94i 0.319321 0.553080i −0.661026 0.750363i \(-0.729879\pi\)
0.980347 + 0.197283i \(0.0632119\pi\)
\(194\) 0 0
\(195\) 107.960 873.626i 0.0396469 0.320829i
\(196\) 0 0
\(197\) −263.636 −0.0953466 −0.0476733 0.998863i \(-0.515181\pi\)
−0.0476733 + 0.998863i \(0.515181\pi\)
\(198\) 0 0
\(199\) 3835.87 1.36642 0.683211 0.730221i \(-0.260583\pi\)
0.683211 + 0.730221i \(0.260583\pi\)
\(200\) 0 0
\(201\) −778.278 + 329.643i −0.273112 + 0.115678i
\(202\) 0 0
\(203\) −1424.55 + 2467.40i −0.492532 + 0.853091i
\(204\) 0 0
\(205\) −2322.69 4023.02i −0.791336 1.37063i
\(206\) 0 0
\(207\) −2059.07 516.796i −0.691377 0.173526i
\(208\) 0 0
\(209\) −969.829 1679.79i −0.320978 0.555951i
\(210\) 0 0
\(211\) −2034.66 + 3524.14i −0.663848 + 1.14982i 0.315748 + 0.948843i \(0.397745\pi\)
−0.979596 + 0.200976i \(0.935589\pi\)
\(212\) 0 0
\(213\) −1797.95 1357.05i −0.578372 0.436542i
\(214\) 0 0
\(215\) −6898.84 −2.18836
\(216\) 0 0
\(217\) −4393.27 −1.37435
\(218\) 0 0
\(219\) −2611.38 1971.01i −0.805758 0.608168i
\(220\) 0 0
\(221\) 465.183 805.720i 0.141591 0.245243i
\(222\) 0 0
\(223\) 3078.07 + 5331.38i 0.924318 + 1.60097i 0.792654 + 0.609672i \(0.208699\pi\)
0.131664 + 0.991294i \(0.457968\pi\)
\(224\) 0 0
\(225\) 1252.15 1292.60i 0.371007 0.382991i
\(226\) 0 0
\(227\) 12.1307 + 21.0110i 0.00354689 + 0.00614339i 0.867793 0.496925i \(-0.165538\pi\)
−0.864247 + 0.503069i \(0.832204\pi\)
\(228\) 0 0
\(229\) 316.209 547.691i 0.0912476 0.158045i −0.816789 0.576937i \(-0.804248\pi\)
0.908036 + 0.418891i \(0.137581\pi\)
\(230\) 0 0
\(231\) 6450.79 2732.26i 1.83736 0.778223i
\(232\) 0 0
\(233\) −3163.59 −0.889502 −0.444751 0.895654i \(-0.646708\pi\)
−0.444751 + 0.895654i \(0.646708\pi\)
\(234\) 0 0
\(235\) −3900.72 −1.08279
\(236\) 0 0
\(237\) −110.076 + 890.755i −0.0301697 + 0.244138i
\(238\) 0 0
\(239\) 1110.57 1923.57i 0.300573 0.520608i −0.675693 0.737183i \(-0.736155\pi\)
0.976266 + 0.216575i \(0.0694887\pi\)
\(240\) 0 0
\(241\) 300.730 + 520.879i 0.0803805 + 0.139223i 0.903413 0.428771i \(-0.141053\pi\)
−0.823033 + 0.567994i \(0.807720\pi\)
\(242\) 0 0
\(243\) −3772.26 344.861i −0.995847 0.0910406i
\(244\) 0 0
\(245\) 4153.03 + 7193.26i 1.08297 + 1.87576i
\(246\) 0 0
\(247\) 270.310 468.191i 0.0696332 0.120608i
\(248\) 0 0
\(249\) 111.432 901.727i 0.0283604 0.229497i
\(250\) 0 0
\(251\) −1350.71 −0.339665 −0.169833 0.985473i \(-0.554323\pi\)
−0.169833 + 0.985473i \(0.554323\pi\)
\(252\) 0 0
\(253\) 3452.09 0.857830
\(254\) 0 0
\(255\) 5036.01 2133.02i 1.23673 0.523824i
\(256\) 0 0
\(257\) 3521.95 6100.20i 0.854838 1.48062i −0.0219564 0.999759i \(-0.506990\pi\)
0.876795 0.480865i \(-0.159677\pi\)
\(258\) 0 0
\(259\) −498.607 863.613i −0.119621 0.207190i
\(260\) 0 0
\(261\) −1742.98 + 1799.28i −0.413363 + 0.426716i
\(262\) 0 0
\(263\) 1162.13 + 2012.87i 0.272472 + 0.471935i 0.969494 0.245114i \(-0.0788255\pi\)
−0.697022 + 0.717050i \(0.745492\pi\)
\(264\) 0 0
\(265\) −4350.89 + 7535.97i −1.00858 + 1.74691i
\(266\) 0 0
\(267\) 1396.49 + 1054.04i 0.320090 + 0.241597i
\(268\) 0 0
\(269\) −3675.87 −0.833167 −0.416584 0.909097i \(-0.636773\pi\)
−0.416584 + 0.909097i \(0.636773\pi\)
\(270\) 0 0
\(271\) 1881.48 0.421741 0.210871 0.977514i \(-0.432370\pi\)
0.210871 + 0.977514i \(0.432370\pi\)
\(272\) 0 0
\(273\) 1558.49 + 1176.31i 0.345509 + 0.260782i
\(274\) 0 0
\(275\) −1463.19 + 2534.31i −0.320849 + 0.555727i
\(276\) 0 0
\(277\) −732.008 1267.87i −0.158780 0.275015i 0.775649 0.631165i \(-0.217423\pi\)
−0.934429 + 0.356149i \(0.884089\pi\)
\(278\) 0 0
\(279\) −3746.58 940.337i −0.803948 0.201780i
\(280\) 0 0
\(281\) 4116.28 + 7129.61i 0.873867 + 1.51358i 0.857965 + 0.513709i \(0.171729\pi\)
0.0159023 + 0.999874i \(0.494938\pi\)
\(282\) 0 0
\(283\) 844.364 1462.48i 0.177358 0.307192i −0.763617 0.645669i \(-0.776578\pi\)
0.940975 + 0.338477i \(0.109912\pi\)
\(284\) 0 0
\(285\) 2926.34 1239.46i 0.608215 0.257612i
\(286\) 0 0
\(287\) 10304.2 2.11930
\(288\) 0 0
\(289\) 867.343 0.176540
\(290\) 0 0
\(291\) 53.7342 434.825i 0.0108246 0.0875942i
\(292\) 0 0
\(293\) −255.866 + 443.173i −0.0510166 + 0.0883633i −0.890406 0.455167i \(-0.849579\pi\)
0.839389 + 0.543531i \(0.182913\pi\)
\(294\) 0 0
\(295\) −3493.18 6050.37i −0.689427 1.19412i
\(296\) 0 0
\(297\) 6086.04 949.340i 1.18905 0.185476i
\(298\) 0 0
\(299\) 481.082 + 833.258i 0.0930491 + 0.161166i
\(300\) 0 0
\(301\) 7651.37 13252.6i 1.46518 2.53776i
\(302\) 0 0
\(303\) −1115.11 + 9023.61i −0.211423 + 1.71087i
\(304\) 0 0
\(305\) −5148.55 −0.966575
\(306\) 0 0
\(307\) 3171.98 0.589690 0.294845 0.955545i \(-0.404732\pi\)
0.294845 + 0.955545i \(0.404732\pi\)
\(308\) 0 0
\(309\) 532.991 225.751i 0.0981255 0.0415615i
\(310\) 0 0
\(311\) 2530.39 4382.76i 0.461367 0.799112i −0.537662 0.843160i \(-0.680692\pi\)
0.999029 + 0.0440487i \(0.0140257\pi\)
\(312\) 0 0
\(313\) 4732.92 + 8197.66i 0.854698 + 1.48038i 0.876925 + 0.480628i \(0.159591\pi\)
−0.0222263 + 0.999753i \(0.507075\pi\)
\(314\) 0 0
\(315\) 3146.60 + 11038.5i 0.562828 + 1.97443i
\(316\) 0 0
\(317\) −3208.57 5557.40i −0.568489 0.984652i −0.996716 0.0809808i \(-0.974195\pi\)
0.428226 0.903671i \(-0.359139\pi\)
\(318\) 0 0
\(319\) 2036.75 3527.75i 0.357479 0.619172i
\(320\) 0 0
\(321\) −3714.07 2803.30i −0.645792 0.487430i
\(322\) 0 0
\(323\) 3358.86 0.578613
\(324\) 0 0
\(325\) −815.637 −0.139210
\(326\) 0 0
\(327\) −2973.50 2244.33i −0.502860 0.379547i
\(328\) 0 0
\(329\) 4326.22 7493.23i 0.724961 1.25567i
\(330\) 0 0
\(331\) 3332.37 + 5771.83i 0.553364 + 0.958455i 0.998029 + 0.0627575i \(0.0199895\pi\)
−0.444665 + 0.895697i \(0.646677\pi\)
\(332\) 0 0
\(333\) −240.364 843.211i −0.0395551 0.138762i
\(334\) 0 0
\(335\) 1125.93 + 1950.17i 0.183630 + 0.318056i
\(336\) 0 0
\(337\) −5244.05 + 9082.95i −0.847660 + 1.46819i 0.0356314 + 0.999365i \(0.488656\pi\)
−0.883291 + 0.468825i \(0.844678\pi\)
\(338\) 0 0
\(339\) −1105.50 + 468.241i −0.177117 + 0.0750187i
\(340\) 0 0
\(341\) 6281.25 0.997503
\(342\) 0 0
\(343\) −7891.37 −1.24226
\(344\) 0 0
\(345\) −693.676 + 5613.33i −0.108250 + 0.875976i
\(346\) 0 0
\(347\) 1074.48 1861.05i 0.166228 0.287915i −0.770863 0.637001i \(-0.780175\pi\)
0.937091 + 0.349086i \(0.113508\pi\)
\(348\) 0 0
\(349\) 1388.53 + 2405.00i 0.212969 + 0.368874i 0.952642 0.304093i \(-0.0983532\pi\)
−0.739673 + 0.672966i \(0.765020\pi\)
\(350\) 0 0
\(351\) 1077.30 + 1336.74i 0.163823 + 0.203276i
\(352\) 0 0
\(353\) −3898.72 6752.78i −0.587841 1.01817i −0.994515 0.104597i \(-0.966645\pi\)
0.406673 0.913574i \(-0.366689\pi\)
\(354\) 0 0
\(355\) −3000.75 + 5197.45i −0.448629 + 0.777047i
\(356\) 0 0
\(357\) −1487.84 + 12039.8i −0.220573 + 1.78491i
\(358\) 0 0
\(359\) −2309.31 −0.339500 −0.169750 0.985487i \(-0.554296\pi\)
−0.169750 + 0.985487i \(0.554296\pi\)
\(360\) 0 0
\(361\) −4907.22 −0.715443
\(362\) 0 0
\(363\) −2854.59 + 1209.07i −0.412747 + 0.174821i
\(364\) 0 0
\(365\) −4358.36 + 7548.91i −0.625006 + 1.08254i
\(366\) 0 0
\(367\) −3105.66 5379.16i −0.441728 0.765095i 0.556090 0.831122i \(-0.312301\pi\)
−0.997818 + 0.0660271i \(0.978968\pi\)
\(368\) 0 0
\(369\) 8787.44 + 2205.52i 1.23972 + 0.311151i
\(370\) 0 0
\(371\) −9650.99 16716.0i −1.35055 2.33922i
\(372\) 0 0
\(373\) −4349.61 + 7533.75i −0.603792 + 1.04580i 0.388450 + 0.921470i \(0.373011\pi\)
−0.992241 + 0.124328i \(0.960323\pi\)
\(374\) 0 0
\(375\) 3350.05 + 2528.54i 0.461322 + 0.348196i
\(376\) 0 0
\(377\) 1135.36 0.155104
\(378\) 0 0
\(379\) −5954.77 −0.807061 −0.403531 0.914966i \(-0.632217\pi\)
−0.403531 + 0.914966i \(0.632217\pi\)
\(380\) 0 0
\(381\) −7113.69 5369.26i −0.956550 0.721983i
\(382\) 0 0
\(383\) 2128.35 3686.41i 0.283952 0.491819i −0.688403 0.725329i \(-0.741688\pi\)
0.972354 + 0.233510i \(0.0750211\pi\)
\(384\) 0 0
\(385\) −9332.31 16164.0i −1.23537 2.13973i
\(386\) 0 0
\(387\) 9361.67 9664.08i 1.22967 1.26939i
\(388\) 0 0
\(389\) −801.019 1387.41i −0.104404 0.180834i 0.809090 0.587684i \(-0.199960\pi\)
−0.913495 + 0.406851i \(0.866627\pi\)
\(390\) 0 0
\(391\) −2988.95 + 5177.02i −0.386593 + 0.669598i
\(392\) 0 0
\(393\) 6377.34 2701.15i 0.818560 0.346705i
\(394\) 0 0
\(395\) 2391.25 0.304600
\(396\) 0 0
\(397\) −7987.87 −1.00982 −0.504912 0.863171i \(-0.668475\pi\)
−0.504912 + 0.863171i \(0.668475\pi\)
\(398\) 0 0
\(399\) −864.557 + 6996.13i −0.108476 + 0.877805i
\(400\) 0 0
\(401\) 3534.75 6122.36i 0.440191 0.762434i −0.557512 0.830169i \(-0.688244\pi\)
0.997703 + 0.0677350i \(0.0215772\pi\)
\(402\) 0 0
\(403\) 875.352 + 1516.15i 0.108200 + 0.187407i
\(404\) 0 0
\(405\) 320.739 + 10087.1i 0.0393523 + 1.23761i
\(406\) 0 0
\(407\) 712.881 + 1234.75i 0.0868211 + 0.150379i
\(408\) 0 0
\(409\) 5932.38 10275.2i 0.717207 1.24224i −0.244896 0.969549i \(-0.578754\pi\)
0.962102 0.272689i \(-0.0879129\pi\)
\(410\) 0 0
\(411\) 1605.28 12990.2i 0.192659 1.55903i
\(412\) 0 0
\(413\) 15496.9 1.84637
\(414\) 0 0
\(415\) −2420.71 −0.286332
\(416\) 0 0
\(417\) 2980.29 1262.31i 0.349989 0.148239i
\(418\) 0 0
\(419\) −6171.30 + 10689.0i −0.719541 + 1.24628i 0.241641 + 0.970366i \(0.422314\pi\)
−0.961182 + 0.275916i \(0.911019\pi\)
\(420\) 0 0
\(421\) −2732.93 4733.58i −0.316377 0.547982i 0.663352 0.748308i \(-0.269133\pi\)
−0.979729 + 0.200326i \(0.935800\pi\)
\(422\) 0 0
\(423\) 5293.25 5464.24i 0.608432 0.628086i
\(424\) 0 0
\(425\) −2533.77 4388.61i −0.289190 0.500892i
\(426\) 0 0
\(427\) 5710.17 9890.30i 0.647153 1.12090i
\(428\) 0 0
\(429\) −2228.24 1681.82i −0.250770 0.189276i
\(430\) 0 0
\(431\) −8997.67 −1.00557 −0.502787 0.864410i \(-0.667692\pi\)
−0.502787 + 0.864410i \(0.667692\pi\)
\(432\) 0 0
\(433\) −10967.4 −1.21723 −0.608615 0.793466i \(-0.708275\pi\)
−0.608615 + 0.793466i \(0.708275\pi\)
\(434\) 0 0
\(435\) 5327.09 + 4020.77i 0.587160 + 0.443175i
\(436\) 0 0
\(437\) −1736.83 + 3008.28i −0.190123 + 0.329303i
\(438\) 0 0
\(439\) 3563.51 + 6172.18i 0.387419 + 0.671029i 0.992102 0.125437i \(-0.0400333\pi\)
−0.604683 + 0.796467i \(0.706700\pi\)
\(440\) 0 0
\(441\) −15712.2 3943.53i −1.69659 0.425821i
\(442\) 0 0
\(443\) 4434.28 + 7680.39i 0.475573 + 0.823716i 0.999608 0.0279799i \(-0.00890744\pi\)
−0.524036 + 0.851696i \(0.675574\pi\)
\(444\) 0 0
\(445\) 2330.73 4036.94i 0.248286 0.430043i
\(446\) 0 0
\(447\) −11526.0 + 4881.89i −1.21960 + 0.516567i
\(448\) 0 0
\(449\) 9835.05 1.03373 0.516865 0.856067i \(-0.327099\pi\)
0.516865 + 0.856067i \(0.327099\pi\)
\(450\) 0 0
\(451\) −14732.4 −1.53819
\(452\) 0 0
\(453\) −43.1075 + 348.833i −0.00447101 + 0.0361801i
\(454\) 0 0
\(455\) 2601.09 4505.23i 0.268003 0.464194i
\(456\) 0 0
\(457\) 4443.25 + 7695.93i 0.454806 + 0.787747i 0.998677 0.0514218i \(-0.0163753\pi\)
−0.543871 + 0.839169i \(0.683042\pi\)
\(458\) 0 0
\(459\) −3845.83 + 9949.07i −0.391085 + 1.01173i
\(460\) 0 0
\(461\) −932.894 1615.82i −0.0942499 0.163246i 0.815045 0.579397i \(-0.196712\pi\)
−0.909295 + 0.416151i \(0.863379\pi\)
\(462\) 0 0
\(463\) −6811.70 + 11798.2i −0.683729 + 1.18425i 0.290105 + 0.956995i \(0.406310\pi\)
−0.973834 + 0.227259i \(0.927024\pi\)
\(464\) 0 0
\(465\) −1262.18 + 10213.7i −0.125875 + 1.01860i
\(466\) 0 0
\(467\) 9328.97 0.924397 0.462199 0.886776i \(-0.347061\pi\)
0.462199 + 0.886776i \(0.347061\pi\)
\(468\) 0 0
\(469\) −4994.99 −0.491785
\(470\) 0 0
\(471\) 21.0215 8.90377i 0.00205652 0.000871048i
\(472\) 0 0
\(473\) −10939.5 + 18947.8i −1.06342 + 1.84190i
\(474\) 0 0
\(475\) −1472.33 2550.15i −0.142221 0.246335i
\(476\) 0 0
\(477\) −4652.46 16321.1i −0.446586 1.56665i
\(478\) 0 0
\(479\) 1330.15 + 2303.89i 0.126881 + 0.219765i 0.922467 0.386077i \(-0.126170\pi\)
−0.795586 + 0.605841i \(0.792837\pi\)
\(480\) 0 0
\(481\) −198.694 + 344.147i −0.0188350 + 0.0326232i
\(482\) 0 0
\(483\) −10013.8 7558.19i −0.943361 0.712028i
\(484\) 0 0
\(485\) −1167.30 −0.109287
\(486\) 0 0
\(487\) 20450.7 1.90289 0.951447 0.307813i \(-0.0995971\pi\)
0.951447 + 0.307813i \(0.0995971\pi\)
\(488\) 0 0
\(489\) 11877.6 + 8964.97i 1.09842 + 0.829059i
\(490\) 0 0
\(491\) 10327.4 17887.7i 0.949228 1.64411i 0.202173 0.979350i \(-0.435200\pi\)
0.747055 0.664762i \(-0.231467\pi\)
\(492\) 0 0
\(493\) 3526.99 + 6108.92i 0.322206 + 0.558077i
\(494\) 0 0
\(495\) −4498.83 15782.2i −0.408500 1.43304i
\(496\) 0 0
\(497\) −6656.15 11528.8i −0.600743 1.04052i
\(498\) 0 0
\(499\) 8733.31 15126.5i 0.783480 1.35703i −0.146423 0.989222i \(-0.546776\pi\)
0.929903 0.367805i \(-0.119891\pi\)
\(500\) 0 0
\(501\) 2055.08 870.439i 0.183262 0.0776215i
\(502\) 0 0
\(503\) −19951.2 −1.76855 −0.884275 0.466966i \(-0.845347\pi\)
−0.884275 + 0.466966i \(0.845347\pi\)
\(504\) 0 0
\(505\) 24224.1 2.13457
\(506\) 0 0
\(507\) −1304.66 + 10557.5i −0.114284 + 0.924806i
\(508\) 0 0
\(509\) 3638.88 6302.73i 0.316878 0.548848i −0.662957 0.748657i \(-0.730699\pi\)
0.979835 + 0.199809i \(0.0640322\pi\)
\(510\) 0 0
\(511\) −9667.57 16744.7i −0.836924 1.44959i
\(512\) 0 0
\(513\) −2234.75 + 5781.24i −0.192332 + 0.497560i
\(514\) 0 0
\(515\) −771.074 1335.54i −0.0659759 0.114274i
\(516\) 0 0
\(517\) −6185.39 + 10713.4i −0.526176 + 0.911364i
\(518\) 0 0
\(519\) −1640.53 + 13275.4i −0.138750 + 1.12278i
\(520\) 0 0
\(521\) −11664.5 −0.980866 −0.490433 0.871479i \(-0.663161\pi\)
−0.490433 + 0.871479i \(0.663161\pi\)
\(522\) 0 0
\(523\) 8925.51 0.746243 0.373122 0.927782i \(-0.378287\pi\)
0.373122 + 0.927782i \(0.378287\pi\)
\(524\) 0 0
\(525\) 9793.16 4147.94i 0.814112 0.344821i
\(526\) 0 0
\(527\) −5438.55 + 9419.84i −0.449539 + 0.778624i
\(528\) 0 0
\(529\) 2992.39 + 5182.98i 0.245943 + 0.425986i
\(530\) 0 0
\(531\) 13215.8 + 3316.97i 1.08007 + 0.271081i
\(532\) 0 0
\(533\) −2053.10 3556.08i −0.166848 0.288988i
\(534\) 0 0
\(535\) −6198.74 + 10736.5i −0.500925 + 0.867627i
\(536\) 0 0
\(537\) −3348.80 2527.60i −0.269109 0.203118i
\(538\) 0 0
\(539\) 26341.9 2.10506
\(540\) 0 0
\(541\) 12334.1 0.980193 0.490097 0.871668i \(-0.336962\pi\)
0.490097 + 0.871668i \(0.336962\pi\)
\(542\) 0 0
\(543\) 17819.6 + 13449.8i 1.40831 + 1.06296i
\(544\) 0 0
\(545\) −4962.74 + 8595.71i −0.390056 + 0.675596i
\(546\) 0 0
\(547\) 2284.81 + 3957.41i 0.178595 + 0.309336i 0.941400 0.337293i \(-0.109511\pi\)
−0.762804 + 0.646629i \(0.776178\pi\)
\(548\) 0 0
\(549\) 6986.55 7212.24i 0.543131 0.560675i
\(550\) 0 0
\(551\) 2049.47 + 3549.79i 0.158458 + 0.274458i
\(552\) 0 0
\(553\) −2652.09 + 4593.56i −0.203939 + 0.353233i
\(554\) 0 0
\(555\) −2151.03 + 911.079i −0.164516 + 0.0696813i
\(556\) 0 0
\(557\) −8154.40 −0.620310 −0.310155 0.950686i \(-0.600381\pi\)
−0.310155 + 0.950686i \(0.600381\pi\)
\(558\) 0 0
\(559\) −6098.10 −0.461399
\(560\) 0 0
\(561\) 2127.22 17213.8i 0.160092 1.29549i
\(562\) 0 0
\(563\) −8086.82 + 14006.8i −0.605362 + 1.04852i 0.386632 + 0.922234i \(0.373638\pi\)
−0.991994 + 0.126284i \(0.959695\pi\)
\(564\) 0 0
\(565\) 1599.32 + 2770.11i 0.119087 + 0.206264i
\(566\) 0 0
\(567\) −19732.9 10571.3i −1.46156 0.782984i
\(568\) 0 0
\(569\) 4548.76 + 7878.69i 0.335139 + 0.580478i 0.983512 0.180845i \(-0.0578834\pi\)
−0.648372 + 0.761323i \(0.724550\pi\)
\(570\) 0 0
\(571\) −1647.54 + 2853.63i −0.120749 + 0.209143i −0.920063 0.391770i \(-0.871863\pi\)
0.799314 + 0.600913i \(0.205196\pi\)
\(572\) 0 0
\(573\) 195.194 1579.54i 0.0142310 0.115159i
\(574\) 0 0
\(575\) 5240.73 0.380093
\(576\) 0 0
\(577\) 15544.7 1.12155 0.560775 0.827968i \(-0.310503\pi\)
0.560775 + 0.827968i \(0.310503\pi\)
\(578\) 0 0
\(579\) 8193.04 3470.20i 0.588067 0.249079i
\(580\) 0 0
\(581\) 2684.76 4650.14i 0.191709 0.332049i
\(582\) 0 0
\(583\) 13798.4 + 23899.6i 0.980229 + 1.69781i
\(584\) 0 0
\(585\) 3182.51 3285.32i 0.224924 0.232190i
\(586\) 0 0
\(587\) −2344.33 4060.50i −0.164840 0.285511i 0.771759 0.635916i \(-0.219377\pi\)
−0.936598 + 0.350405i \(0.886044\pi\)
\(588\) 0 0
\(589\) −3160.25 + 5473.71i −0.221079 + 0.382921i
\(590\) 0 0
\(591\) −1093.40 825.275i −0.0761024 0.0574404i
\(592\) 0 0
\(593\) 16637.6 1.15215 0.576075 0.817397i \(-0.304584\pi\)
0.576075 + 0.817397i \(0.304584\pi\)
\(594\) 0 0
\(595\) 32321.1 2.22695
\(596\) 0 0
\(597\) 15908.9 + 12007.7i 1.09063 + 0.823184i
\(598\) 0 0
\(599\) −2933.73 + 5081.37i −0.200115 + 0.346610i −0.948565 0.316581i \(-0.897465\pi\)
0.748450 + 0.663191i \(0.230798\pi\)
\(600\) 0 0
\(601\) −10337.9 17905.8i −0.701649 1.21529i −0.967887 0.251385i \(-0.919114\pi\)
0.266238 0.963907i \(-0.414219\pi\)
\(602\) 0 0
\(603\) −4259.72 1069.13i −0.287677 0.0722029i
\(604\) 0 0
\(605\) 4129.71 + 7152.87i 0.277515 + 0.480671i
\(606\) 0 0
\(607\) 6303.86 10918.6i 0.421525 0.730103i −0.574564 0.818460i \(-0.694828\pi\)
0.996089 + 0.0883567i \(0.0281615\pi\)
\(608\) 0 0
\(609\) −13632.0 + 5773.90i −0.907056 + 0.384188i
\(610\) 0 0
\(611\) −3447.97 −0.228298
\(612\) 0 0
\(613\) 12469.7 0.821608 0.410804 0.911724i \(-0.365248\pi\)
0.410804 + 0.911724i \(0.365248\pi\)
\(614\) 0 0
\(615\) 2960.39 23955.9i 0.194104 1.57072i
\(616\) 0 0
\(617\) −9293.48 + 16096.8i −0.606388 + 1.05030i 0.385442 + 0.922732i \(0.374049\pi\)
−0.991830 + 0.127563i \(0.959284\pi\)
\(618\) 0 0
\(619\) −5972.96 10345.5i −0.387841 0.671761i 0.604318 0.796743i \(-0.293446\pi\)
−0.992159 + 0.124983i \(0.960112\pi\)
\(620\) 0 0
\(621\) −6922.00 8588.98i −0.447295 0.555014i
\(622\) 0 0
\(623\) 5169.94 + 8954.60i 0.332471 + 0.575856i
\(624\) 0 0
\(625\) 9757.00 16899.6i 0.624448 1.08158i
\(626\) 0 0
\(627\) 1236.09 10002.7i 0.0787318 0.637110i
\(628\) 0 0
\(629\) −2468.96 −0.156509
\(630\) 0 0
\(631\) −4285.35 −0.270360 −0.135180 0.990821i \(-0.543161\pi\)
−0.135180 + 0.990821i \(0.543161\pi\)
\(632\) 0 0
\(633\) −19470.4 + 8246.76i −1.22256 + 0.517819i
\(634\) 0 0
\(635\) −11872.7 + 20564.0i −0.741972 + 1.28513i
\(636\) 0 0
\(637\) 3671.00 + 6358.36i 0.228336 + 0.395490i
\(638\) 0 0
\(639\) −3208.73 11256.4i −0.198647 0.696866i
\(640\) 0 0
\(641\) 10879.1 + 18843.2i 0.670357 + 1.16109i 0.977803 + 0.209527i \(0.0671925\pi\)
−0.307446 + 0.951566i \(0.599474\pi\)
\(642\) 0 0
\(643\) −3671.54 + 6359.30i −0.225181 + 0.390025i −0.956374 0.292146i \(-0.905631\pi\)
0.731193 + 0.682171i \(0.238964\pi\)
\(644\) 0 0
\(645\) −28612.2 21595.8i −1.74667 1.31835i
\(646\) 0 0
\(647\) −9483.24 −0.576236 −0.288118 0.957595i \(-0.593030\pi\)
−0.288118 + 0.957595i \(0.593030\pi\)
\(648\) 0 0
\(649\) −22156.6 −1.34010
\(650\) 0 0
\(651\) −18220.6 13752.5i −1.09696 0.827962i
\(652\) 0 0
\(653\) −2392.09 + 4143.23i −0.143353 + 0.248295i −0.928757 0.370688i \(-0.879122\pi\)
0.785404 + 0.618984i \(0.212455\pi\)
\(654\) 0 0
\(655\) −9226.05 15980.0i −0.550369 0.953266i
\(656\) 0 0
\(657\) −4660.45 16349.1i −0.276745 0.970838i
\(658\) 0 0
\(659\) −16034.0 27771.6i −0.947791 1.64162i −0.750064 0.661365i \(-0.769977\pi\)
−0.197727 0.980257i \(-0.563356\pi\)
\(660\) 0 0
\(661\) 3762.64 6517.09i 0.221407 0.383488i −0.733829 0.679335i \(-0.762269\pi\)
0.955235 + 0.295847i \(0.0956019\pi\)
\(662\) 0 0
\(663\) 4451.49 1885.45i 0.260756 0.110445i
\(664\) 0 0
\(665\) 18781.3 1.09520
\(666\) 0 0
\(667\) −7295.07 −0.423487
\(668\) 0 0
\(669\) −3923.16 + 31746.8i −0.226723 + 1.83468i
\(670\) 0 0
\(671\) −8164.08 + 14140.6i −0.469703 + 0.813550i
\(672\) 0 0
\(673\) 3670.98 + 6358.32i 0.210261 + 0.364183i 0.951796 0.306731i \(-0.0992352\pi\)
−0.741535 + 0.670914i \(0.765902\pi\)
\(674\) 0 0
\(675\) 9239.43 1441.23i 0.526853 0.0821819i
\(676\) 0 0
\(677\) −4760.52 8245.45i −0.270253 0.468092i 0.698673 0.715441i \(-0.253774\pi\)
−0.968927 + 0.247348i \(0.920441\pi\)
\(678\) 0 0
\(679\) 1294.63 2242.36i 0.0731713 0.126736i
\(680\) 0 0
\(681\) −15.4612 + 125.114i −0.000870006 + 0.00704022i
\(682\) 0 0
\(683\) 1475.06 0.0826377 0.0413188 0.999146i \(-0.486844\pi\)
0.0413188 + 0.999146i \(0.486844\pi\)
\(684\) 0 0
\(685\) −34872.5 −1.94512
\(686\) 0 0
\(687\) 3025.91 1281.64i 0.168043 0.0711755i
\(688\) 0 0
\(689\) −3845.89 + 6661.28i −0.212651 + 0.368323i
\(690\) 0 0
\(691\) 17080.4 + 29584.0i 0.940329 + 1.62870i 0.764844 + 0.644215i \(0.222816\pi\)
0.175484 + 0.984482i \(0.443851\pi\)
\(692\) 0 0
\(693\) 35306.9 + 8861.53i 1.93535 + 0.485746i
\(694\) 0 0
\(695\) −4311.56 7467.84i −0.235319 0.407585i
\(696\) 0 0
\(697\) 12755.9 22093.8i 0.693205 1.20067i
\(698\) 0 0
\(699\) −13120.7 9903.19i −0.709970 0.535870i
\(700\) 0 0
\(701\) −29427.2 −1.58552 −0.792759 0.609535i \(-0.791356\pi\)
−0.792759 + 0.609535i \(0.791356\pi\)
\(702\) 0 0
\(703\) −1434.67 −0.0769696
\(704\) 0 0
\(705\) −16177.8 12210.7i −0.864244 0.652312i
\(706\) 0 0
\(707\) −26866.5 + 46534.1i −1.42916 + 2.47538i
\(708\) 0 0
\(709\) −9846.43 17054.5i −0.521566 0.903379i −0.999685 0.0250840i \(-0.992015\pi\)
0.478119 0.878295i \(-0.341319\pi\)
\(710\) 0 0
\(711\) −3244.91 + 3349.73i −0.171159 + 0.176687i
\(712\) 0 0
\(713\) −5624.42 9741.79i −0.295423 0.511687i
\(714\) 0 0
\(715\) −3718.90 + 6441.32i −0.194516 + 0.336912i
\(716\) 0 0
\(717\) 10627.4 4501.30i 0.553541 0.234455i
\(718\) 0 0
\(719\) 33746.9 1.75041 0.875206 0.483751i \(-0.160726\pi\)
0.875206 + 0.483751i \(0.160726\pi\)
\(720\) 0 0
\(721\) 3420.74 0.176692
\(722\) 0 0
\(723\) −383.295 + 3101.68i −0.0197163 + 0.159547i
\(724\) 0 0
\(725\) 3092.05 5355.60i 0.158395 0.274347i
\(726\) 0 0
\(727\) 10380.4 + 17979.4i 0.529558 + 0.917221i 0.999406 + 0.0344737i \(0.0109755\pi\)
−0.469848 + 0.882748i \(0.655691\pi\)
\(728\) 0 0
\(729\) −14565.5 13238.8i −0.740005 0.672602i
\(730\) 0 0
\(731\) −18943.7 32811.4i −0.958492 1.66016i
\(732\) 0 0
\(733\) −7122.02 + 12335.7i −0.358878 + 0.621596i −0.987774 0.155894i \(-0.950174\pi\)
0.628895 + 0.777490i \(0.283507\pi\)
\(734\) 0 0
\(735\) −5293.24 + 42833.8i −0.265638 + 2.14959i
\(736\) 0 0
\(737\) 7141.55 0.356937
\(738\) 0 0
\(739\) −27490.2 −1.36839 −0.684196 0.729298i \(-0.739847\pi\)
−0.684196 + 0.729298i \(0.739847\pi\)
\(740\) 0 0
\(741\) 2586.69 1095.60i 0.128238 0.0543157i
\(742\) 0 0
\(743\) 18234.0 31582.3i 0.900326 1.55941i 0.0732537 0.997313i \(-0.476662\pi\)
0.827072 0.562096i \(-0.190005\pi\)
\(744\) 0 0
\(745\) 16674.6 + 28881.2i 0.820013 + 1.42030i
\(746\) 0 0
\(747\) 3284.88 3390.99i 0.160894 0.166091i
\(748\) 0 0
\(749\) −13749.8 23815.4i −0.670771 1.16181i
\(750\) 0 0
\(751\) 19341.5 33500.5i 0.939791 1.62777i 0.173931 0.984758i \(-0.444353\pi\)
0.765860 0.643007i \(-0.222314\pi\)
\(752\) 0 0
\(753\) −5601.92 4228.20i −0.271109 0.204627i
\(754\) 0 0
\(755\) 936.449 0.0451402
\(756\) 0 0
\(757\) 37768.4 1.81337 0.906683 0.421813i \(-0.138606\pi\)
0.906683 + 0.421813i \(0.138606\pi\)
\(758\) 0 0
\(759\) 14317.2 + 10806.3i 0.684690 + 0.516789i
\(760\) 0 0
\(761\) 10406.6 18024.7i 0.495714 0.858603i −0.504273 0.863544i \(-0.668240\pi\)
0.999988 + 0.00494154i \(0.00157295\pi\)
\(762\) 0 0
\(763\) −11008.2 19066.7i −0.522310 0.904667i
\(764\) 0 0
\(765\) 27563.4 + 6918.03i 1.30269 + 0.326957i
\(766\) 0 0
\(767\) −3087.74 5348.12i −0.145361 0.251772i
\(768\) 0 0
\(769\) −3060.85 + 5301.55i −0.143533 + 0.248607i −0.928825 0.370519i \(-0.879180\pi\)
0.785291 + 0.619126i \(0.212513\pi\)
\(770\) 0 0
\(771\) 33702.7 14275.0i 1.57429 0.666796i
\(772\) 0 0
\(773\) −34251.2 −1.59370 −0.796850 0.604177i \(-0.793502\pi\)
−0.796850 + 0.604177i \(0.793502\pi\)
\(774\) 0 0
\(775\) 9535.78 0.441981
\(776\) 0 0
\(777\) 635.500 5142.56i 0.0293416 0.237437i
\(778\) 0 0
\(779\) 7412.23 12838.4i 0.340912 0.590478i
\(780\) 0 0
\(781\) 9516.59 + 16483.2i 0.436018 + 0.755206i
\(782\) 0 0
\(783\) −12861.2 + 2006.18i −0.587002 + 0.0915644i
\(784\) 0 0
\(785\) −30.4117 52.6746i −0.00138273 0.00239495i
\(786\) 0 0