Properties

Label 208.4.w.b.49.1
Level $208$
Weight $4$
Character 208.49
Analytic conductor $12.272$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [208,4,Mod(17,208)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(208, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("208.17");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 208 = 2^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 208.w (of order \(6\), 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: \(12.2723972812\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 208.49
Dual form 208.4.w.b.17.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{3} +1.73205i q^{5} +(12.0000 + 6.92820i) q^{7} +(11.5000 - 19.9186i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{3} +1.73205i q^{5} +(12.0000 + 6.92820i) q^{7} +(11.5000 - 19.9186i) q^{9} +(-12.0000 + 6.92820i) q^{11} +(45.5000 - 11.2583i) q^{13} +(-3.00000 + 1.73205i) q^{15} +(-58.5000 + 101.325i) q^{17} +(99.0000 + 57.1577i) q^{19} +27.7128i q^{21} +(-39.0000 - 67.5500i) q^{23} +122.000 q^{25} +100.000 q^{27} +(70.5000 + 122.110i) q^{29} +155.885i q^{31} +(-24.0000 - 13.8564i) q^{33} +(-12.0000 + 20.7846i) q^{35} +(-124.500 + 71.8801i) q^{37} +(65.0000 + 67.5500i) q^{39} +(235.500 - 135.966i) q^{41} +(52.0000 - 90.0666i) q^{43} +(34.5000 + 19.9186i) q^{45} +301.377i q^{47} +(-75.5000 - 130.770i) q^{49} -234.000 q^{51} +93.0000 q^{53} +(-12.0000 - 20.7846i) q^{55} +228.631i q^{57} +(246.000 + 142.028i) q^{59} +(-72.5000 + 125.574i) q^{61} +(276.000 - 159.349i) q^{63} +(19.5000 + 78.8083i) q^{65} +(681.000 - 393.176i) q^{67} +(78.0000 - 135.100i) q^{69} +(-915.000 - 528.275i) q^{71} -458.993i q^{73} +(122.000 + 211.310i) q^{75} -192.000 q^{77} -1276.00 q^{79} +(-210.500 - 364.597i) q^{81} -789.815i q^{83} +(-175.500 - 101.325i) q^{85} +(-141.000 + 244.219i) q^{87} +(-846.000 + 488.438i) q^{89} +(624.000 + 180.133i) q^{91} +(-270.000 + 155.885i) q^{93} +(-99.0000 + 171.473i) q^{95} +(174.000 + 100.459i) q^{97} +318.697i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} + 24 q^{7} + 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} + 24 q^{7} + 23 q^{9} - 24 q^{11} + 91 q^{13} - 6 q^{15} - 117 q^{17} + 198 q^{19} - 78 q^{23} + 244 q^{25} + 200 q^{27} + 141 q^{29} - 48 q^{33} - 24 q^{35} - 249 q^{37} + 130 q^{39} + 471 q^{41} + 104 q^{43} + 69 q^{45} - 151 q^{49} - 468 q^{51} + 186 q^{53} - 24 q^{55} + 492 q^{59} - 145 q^{61} + 552 q^{63} + 39 q^{65} + 1362 q^{67} + 156 q^{69} - 1830 q^{71} + 244 q^{75} - 384 q^{77} - 2552 q^{79} - 421 q^{81} - 351 q^{85} - 282 q^{87} - 1692 q^{89} + 1248 q^{91} - 540 q^{93} - 198 q^{95} + 348 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/208\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(79\) \(145\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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 0
\(3\) 1.00000 + 1.73205i 0.192450 + 0.333333i 0.946062 0.323987i \(-0.105023\pi\)
−0.753612 + 0.657320i \(0.771690\pi\)
\(4\) 0 0
\(5\) 1.73205i 0.154919i 0.996995 + 0.0774597i \(0.0246809\pi\)
−0.996995 + 0.0774597i \(0.975319\pi\)
\(6\) 0 0
\(7\) 12.0000 + 6.92820i 0.647939 + 0.374088i 0.787666 0.616102i \(-0.211289\pi\)
−0.139727 + 0.990190i \(0.544623\pi\)
\(8\) 0 0
\(9\) 11.5000 19.9186i 0.425926 0.737725i
\(10\) 0 0
\(11\) −12.0000 + 6.92820i −0.328921 + 0.189903i −0.655362 0.755315i \(-0.727484\pi\)
0.326441 + 0.945218i \(0.394151\pi\)
\(12\) 0 0
\(13\) 45.5000 11.2583i 0.970725 0.240192i
\(14\) 0 0
\(15\) −3.00000 + 1.73205i −0.0516398 + 0.0298142i
\(16\) 0 0
\(17\) −58.5000 + 101.325i −0.834608 + 1.44558i 0.0597414 + 0.998214i \(0.480972\pi\)
−0.894349 + 0.447369i \(0.852361\pi\)
\(18\) 0 0
\(19\) 99.0000 + 57.1577i 1.19538 + 0.690151i 0.959521 0.281637i \(-0.0908774\pi\)
0.235856 + 0.971788i \(0.424211\pi\)
\(20\) 0 0
\(21\) 27.7128i 0.287973i
\(22\) 0 0
\(23\) −39.0000 67.5500i −0.353568 0.612398i 0.633304 0.773903i \(-0.281698\pi\)
−0.986872 + 0.161506i \(0.948365\pi\)
\(24\) 0 0
\(25\) 122.000 0.976000
\(26\) 0 0
\(27\) 100.000 0.712778
\(28\) 0 0
\(29\) 70.5000 + 122.110i 0.451432 + 0.781903i 0.998475 0.0552014i \(-0.0175801\pi\)
−0.547043 + 0.837104i \(0.684247\pi\)
\(30\) 0 0
\(31\) 155.885i 0.903151i 0.892233 + 0.451576i \(0.149138\pi\)
−0.892233 + 0.451576i \(0.850862\pi\)
\(32\) 0 0
\(33\) −24.0000 13.8564i −0.126602 0.0730937i
\(34\) 0 0
\(35\) −12.0000 + 20.7846i −0.0579534 + 0.100378i
\(36\) 0 0
\(37\) −124.500 + 71.8801i −0.553180 + 0.319379i −0.750404 0.660980i \(-0.770141\pi\)
0.197223 + 0.980359i \(0.436808\pi\)
\(38\) 0 0
\(39\) 65.0000 + 67.5500i 0.266880 + 0.277350i
\(40\) 0 0
\(41\) 235.500 135.966i 0.897047 0.517910i 0.0208059 0.999784i \(-0.493377\pi\)
0.876241 + 0.481873i \(0.160043\pi\)
\(42\) 0 0
\(43\) 52.0000 90.0666i 0.184417 0.319419i −0.758963 0.651134i \(-0.774294\pi\)
0.943380 + 0.331714i \(0.107627\pi\)
\(44\) 0 0
\(45\) 34.5000 + 19.9186i 0.114288 + 0.0659842i
\(46\) 0 0
\(47\) 301.377i 0.935326i 0.883907 + 0.467663i \(0.154904\pi\)
−0.883907 + 0.467663i \(0.845096\pi\)
\(48\) 0 0
\(49\) −75.5000 130.770i −0.220117 0.381253i
\(50\) 0 0
\(51\) −234.000 −0.642481
\(52\) 0 0
\(53\) 93.0000 0.241029 0.120514 0.992712i \(-0.461546\pi\)
0.120514 + 0.992712i \(0.461546\pi\)
\(54\) 0 0
\(55\) −12.0000 20.7846i −0.0294196 0.0509563i
\(56\) 0 0
\(57\) 228.631i 0.531279i
\(58\) 0 0
\(59\) 246.000 + 142.028i 0.542822 + 0.313398i 0.746222 0.665698i \(-0.231866\pi\)
−0.203400 + 0.979096i \(0.565199\pi\)
\(60\) 0 0
\(61\) −72.5000 + 125.574i −0.152175 + 0.263575i −0.932027 0.362389i \(-0.881961\pi\)
0.779852 + 0.625964i \(0.215294\pi\)
\(62\) 0 0
\(63\) 276.000 159.349i 0.551948 0.318667i
\(64\) 0 0
\(65\) 19.5000 + 78.8083i 0.0372104 + 0.150384i
\(66\) 0 0
\(67\) 681.000 393.176i 1.24175 0.716926i 0.272301 0.962212i \(-0.412215\pi\)
0.969451 + 0.245286i \(0.0788819\pi\)
\(68\) 0 0
\(69\) 78.0000 135.100i 0.136088 0.235712i
\(70\) 0 0
\(71\) −915.000 528.275i −1.52944 0.883025i −0.999385 0.0350641i \(-0.988836\pi\)
−0.530059 0.847961i \(-0.677830\pi\)
\(72\) 0 0
\(73\) 458.993i 0.735906i −0.929844 0.367953i \(-0.880059\pi\)
0.929844 0.367953i \(-0.119941\pi\)
\(74\) 0 0
\(75\) 122.000 + 211.310i 0.187831 + 0.325333i
\(76\) 0 0
\(77\) −192.000 −0.284161
\(78\) 0 0
\(79\) −1276.00 −1.81723 −0.908615 0.417634i \(-0.862859\pi\)
−0.908615 + 0.417634i \(0.862859\pi\)
\(80\) 0 0
\(81\) −210.500 364.597i −0.288752 0.500133i
\(82\) 0 0
\(83\) 789.815i 1.04450i −0.852793 0.522250i \(-0.825093\pi\)
0.852793 0.522250i \(-0.174907\pi\)
\(84\) 0 0
\(85\) −175.500 101.325i −0.223949 0.129297i
\(86\) 0 0
\(87\) −141.000 + 244.219i −0.173756 + 0.300955i
\(88\) 0 0
\(89\) −846.000 + 488.438i −1.00759 + 0.581734i −0.910486 0.413540i \(-0.864292\pi\)
−0.0971073 + 0.995274i \(0.530959\pi\)
\(90\) 0 0
\(91\) 624.000 + 180.133i 0.718824 + 0.207507i
\(92\) 0 0
\(93\) −270.000 + 155.885i −0.301050 + 0.173812i
\(94\) 0 0
\(95\) −99.0000 + 171.473i −0.106918 + 0.185187i
\(96\) 0 0
\(97\) 174.000 + 100.459i 0.182134 + 0.105155i 0.588295 0.808646i \(-0.299799\pi\)
−0.406161 + 0.913802i \(0.633133\pi\)
\(98\) 0 0
\(99\) 318.697i 0.323538i
\(100\) 0 0
\(101\) −214.500 371.525i −0.211322 0.366021i 0.740806 0.671719i \(-0.234444\pi\)
−0.952129 + 0.305698i \(0.901110\pi\)
\(102\) 0 0
\(103\) −182.000 −0.174107 −0.0870534 0.996204i \(-0.527745\pi\)
−0.0870534 + 0.996204i \(0.527745\pi\)
\(104\) 0 0
\(105\) −48.0000 −0.0446126
\(106\) 0 0
\(107\) −753.000 1304.23i −0.680330 1.17837i −0.974880 0.222729i \(-0.928503\pi\)
0.294551 0.955636i \(-0.404830\pi\)
\(108\) 0 0
\(109\) 1551.92i 1.36373i −0.731477 0.681866i \(-0.761169\pi\)
0.731477 0.681866i \(-0.238831\pi\)
\(110\) 0 0
\(111\) −249.000 143.760i −0.212919 0.122929i
\(112\) 0 0
\(113\) 343.500 594.959i 0.285962 0.495302i −0.686880 0.726771i \(-0.741020\pi\)
0.972842 + 0.231470i \(0.0743534\pi\)
\(114\) 0 0
\(115\) 117.000 67.5500i 0.0948722 0.0547745i
\(116\) 0 0
\(117\) 299.000 1035.77i 0.236261 0.818433i
\(118\) 0 0
\(119\) −1404.00 + 810.600i −1.08155 + 0.624433i
\(120\) 0 0
\(121\) −569.500 + 986.403i −0.427874 + 0.741099i
\(122\) 0 0
\(123\) 471.000 + 271.932i 0.345273 + 0.199344i
\(124\) 0 0
\(125\) 427.817i 0.306121i
\(126\) 0 0
\(127\) 143.000 + 247.683i 0.0999149 + 0.173058i 0.911649 0.410969i \(-0.134810\pi\)
−0.811734 + 0.584027i \(0.801476\pi\)
\(128\) 0 0
\(129\) 208.000 0.141964
\(130\) 0 0
\(131\) 1974.00 1.31656 0.658279 0.752774i \(-0.271285\pi\)
0.658279 + 0.752774i \(0.271285\pi\)
\(132\) 0 0
\(133\) 792.000 + 1371.78i 0.516354 + 0.894352i
\(134\) 0 0
\(135\) 173.205i 0.110423i
\(136\) 0 0
\(137\) −733.500 423.486i −0.457424 0.264094i 0.253536 0.967326i \(-0.418406\pi\)
−0.710961 + 0.703232i \(0.751740\pi\)
\(138\) 0 0
\(139\) 118.000 204.382i 0.0720045 0.124716i −0.827775 0.561060i \(-0.810394\pi\)
0.899780 + 0.436344i \(0.143727\pi\)
\(140\) 0 0
\(141\) −522.000 + 301.377i −0.311775 + 0.180004i
\(142\) 0 0
\(143\) −468.000 + 450.333i −0.273679 + 0.263348i
\(144\) 0 0
\(145\) −211.500 + 122.110i −0.121132 + 0.0699355i
\(146\) 0 0
\(147\) 151.000 261.540i 0.0847229 0.146744i
\(148\) 0 0
\(149\) −40.5000 23.3827i −0.0222677 0.0128563i 0.488825 0.872382i \(-0.337426\pi\)
−0.511093 + 0.859526i \(0.670759\pi\)
\(150\) 0 0
\(151\) 1770.16i 0.953995i −0.878905 0.476998i \(-0.841725\pi\)
0.878905 0.476998i \(-0.158275\pi\)
\(152\) 0 0
\(153\) 1345.50 + 2330.47i 0.710962 + 1.23142i
\(154\) 0 0
\(155\) −270.000 −0.139916
\(156\) 0 0
\(157\) 1211.00 0.615594 0.307797 0.951452i \(-0.400408\pi\)
0.307797 + 0.951452i \(0.400408\pi\)
\(158\) 0 0
\(159\) 93.0000 + 161.081i 0.0463860 + 0.0803430i
\(160\) 0 0
\(161\) 1080.80i 0.529062i
\(162\) 0 0
\(163\) 870.000 + 502.295i 0.418059 + 0.241367i 0.694247 0.719737i \(-0.255738\pi\)
−0.276187 + 0.961104i \(0.589071\pi\)
\(164\) 0 0
\(165\) 24.0000 41.5692i 0.0113236 0.0196131i
\(166\) 0 0
\(167\) −792.000 + 457.261i −0.366987 + 0.211880i −0.672141 0.740423i \(-0.734625\pi\)
0.305154 + 0.952303i \(0.401292\pi\)
\(168\) 0 0
\(169\) 1943.50 1024.51i 0.884615 0.466321i
\(170\) 0 0
\(171\) 2277.00 1314.63i 1.01828 0.587906i
\(172\) 0 0
\(173\) −1287.00 + 2229.15i −0.565600 + 0.979648i 0.431394 + 0.902164i \(0.358022\pi\)
−0.996994 + 0.0774841i \(0.975311\pi\)
\(174\) 0 0
\(175\) 1464.00 + 845.241i 0.632389 + 0.365110i
\(176\) 0 0
\(177\) 568.113i 0.241254i
\(178\) 0 0
\(179\) 1872.00 + 3242.40i 0.781675 + 1.35390i 0.930965 + 0.365108i \(0.118968\pi\)
−0.149290 + 0.988793i \(0.547699\pi\)
\(180\) 0 0
\(181\) −637.000 −0.261590 −0.130795 0.991409i \(-0.541753\pi\)
−0.130795 + 0.991409i \(0.541753\pi\)
\(182\) 0 0
\(183\) −290.000 −0.117144
\(184\) 0 0
\(185\) −124.500 215.640i −0.0494780 0.0856983i
\(186\) 0 0
\(187\) 1621.20i 0.633978i
\(188\) 0 0
\(189\) 1200.00 + 692.820i 0.461837 + 0.266642i
\(190\) 0 0
\(191\) −1299.00 + 2249.93i −0.492106 + 0.852353i −0.999959 0.00909077i \(-0.997106\pi\)
0.507852 + 0.861444i \(0.330440\pi\)
\(192\) 0 0
\(193\) 967.500 558.586i 0.360840 0.208331i −0.308609 0.951189i \(-0.599863\pi\)
0.669449 + 0.742858i \(0.266530\pi\)
\(194\) 0 0
\(195\) −117.000 + 112.583i −0.0429669 + 0.0413449i
\(196\) 0 0
\(197\) 1776.00 1025.37i 0.642308 0.370837i −0.143195 0.989695i \(-0.545738\pi\)
0.785503 + 0.618858i \(0.212404\pi\)
\(198\) 0 0
\(199\) −1261.00 + 2184.12i −0.449196 + 0.778030i −0.998334 0.0577019i \(-0.981623\pi\)
0.549138 + 0.835732i \(0.314956\pi\)
\(200\) 0 0
\(201\) 1362.00 + 786.351i 0.477951 + 0.275945i
\(202\) 0 0
\(203\) 1953.75i 0.675500i
\(204\) 0 0
\(205\) 235.500 + 407.898i 0.0802343 + 0.138970i
\(206\) 0 0
\(207\) −1794.00 −0.602375
\(208\) 0 0
\(209\) −1584.00 −0.524247
\(210\) 0 0
\(211\) 521.000 + 902.398i 0.169986 + 0.294425i 0.938415 0.345511i \(-0.112294\pi\)
−0.768428 + 0.639936i \(0.778961\pi\)
\(212\) 0 0
\(213\) 2113.10i 0.679753i
\(214\) 0 0
\(215\) 156.000 + 90.0666i 0.0494842 + 0.0285697i
\(216\) 0 0
\(217\) −1080.00 + 1870.61i −0.337858 + 0.585187i
\(218\) 0 0
\(219\) 795.000 458.993i 0.245302 0.141625i
\(220\) 0 0
\(221\) −1521.00 + 5268.90i −0.462957 + 1.60373i
\(222\) 0 0
\(223\) 2085.00 1203.78i 0.626107 0.361483i −0.153136 0.988205i \(-0.548937\pi\)
0.779243 + 0.626722i \(0.215604\pi\)
\(224\) 0 0
\(225\) 1403.00 2430.07i 0.415704 0.720020i
\(226\) 0 0
\(227\) −2085.00 1203.78i −0.609631 0.351971i 0.163190 0.986595i \(-0.447822\pi\)
−0.772821 + 0.634624i \(0.781155\pi\)
\(228\) 0 0
\(229\) 2508.01i 0.723729i −0.932231 0.361864i \(-0.882140\pi\)
0.932231 0.361864i \(-0.117860\pi\)
\(230\) 0 0
\(231\) −192.000 332.554i −0.0546869 0.0947205i
\(232\) 0 0
\(233\) −5850.00 −1.64483 −0.822417 0.568885i \(-0.807375\pi\)
−0.822417 + 0.568885i \(0.807375\pi\)
\(234\) 0 0
\(235\) −522.000 −0.144900
\(236\) 0 0
\(237\) −1276.00 2210.10i −0.349726 0.605744i
\(238\) 0 0
\(239\) 5383.21i 1.45695i −0.685072 0.728475i \(-0.740229\pi\)
0.685072 0.728475i \(-0.259771\pi\)
\(240\) 0 0
\(241\) 4258.50 + 2458.65i 1.13823 + 0.657159i 0.945992 0.324189i \(-0.105091\pi\)
0.192240 + 0.981348i \(0.438425\pi\)
\(242\) 0 0
\(243\) 1771.00 3067.46i 0.467530 0.809785i
\(244\) 0 0
\(245\) 226.500 130.770i 0.0590635 0.0341003i
\(246\) 0 0
\(247\) 5148.00 + 1486.10i 1.32615 + 0.382827i
\(248\) 0 0
\(249\) 1368.00 789.815i 0.348167 0.201014i
\(250\) 0 0
\(251\) −1989.00 + 3445.05i −0.500178 + 0.866333i 0.499822 + 0.866128i \(0.333399\pi\)
−1.00000 0.000205037i \(0.999935\pi\)
\(252\) 0 0
\(253\) 936.000 + 540.400i 0.232592 + 0.134287i
\(254\) 0 0
\(255\) 405.300i 0.0995328i
\(256\) 0 0
\(257\) −1033.50 1790.07i −0.250848 0.434482i 0.712911 0.701254i \(-0.247376\pi\)
−0.963760 + 0.266772i \(0.914043\pi\)
\(258\) 0 0
\(259\) −1992.00 −0.477903
\(260\) 0 0
\(261\) 3243.00 0.769106
\(262\) 0 0
\(263\) −1026.00 1777.08i −0.240555 0.416653i 0.720318 0.693644i \(-0.243996\pi\)
−0.960872 + 0.276991i \(0.910663\pi\)
\(264\) 0 0
\(265\) 161.081i 0.0373400i
\(266\) 0 0
\(267\) −1692.00 976.877i −0.387823 0.223910i
\(268\) 0 0
\(269\) −1665.00 + 2883.86i −0.377386 + 0.653652i −0.990681 0.136202i \(-0.956510\pi\)
0.613295 + 0.789854i \(0.289844\pi\)
\(270\) 0 0
\(271\) −2430.00 + 1402.96i −0.544694 + 0.314479i −0.746979 0.664848i \(-0.768496\pi\)
0.202285 + 0.979327i \(0.435163\pi\)
\(272\) 0 0
\(273\) 312.000 + 1260.93i 0.0691689 + 0.279543i
\(274\) 0 0
\(275\) −1464.00 + 845.241i −0.321027 + 0.185345i
\(276\) 0 0
\(277\) −188.500 + 326.492i −0.0408876 + 0.0708194i −0.885745 0.464172i \(-0.846352\pi\)
0.844857 + 0.534992i \(0.179685\pi\)
\(278\) 0 0
\(279\) 3105.00 + 1792.67i 0.666278 + 0.384676i
\(280\) 0 0
\(281\) 36.3731i 0.00772183i 0.999993 + 0.00386092i \(0.00122897\pi\)
−0.999993 + 0.00386092i \(0.998771\pi\)
\(282\) 0 0
\(283\) −3562.00 6169.56i −0.748194 1.29591i −0.948688 0.316215i \(-0.897588\pi\)
0.200493 0.979695i \(-0.435745\pi\)
\(284\) 0 0
\(285\) −396.000 −0.0823053
\(286\) 0 0
\(287\) 3768.00 0.774976
\(288\) 0 0
\(289\) −4388.00 7600.24i −0.893141 1.54696i
\(290\) 0 0
\(291\) 401.836i 0.0809486i
\(292\) 0 0
\(293\) −7207.50 4161.25i −1.43709 0.829703i −0.439441 0.898271i \(-0.644823\pi\)
−0.997646 + 0.0685685i \(0.978157\pi\)
\(294\) 0 0
\(295\) −246.000 + 426.084i −0.0485514 + 0.0840936i
\(296\) 0 0
\(297\) −1200.00 + 692.820i −0.234448 + 0.135359i
\(298\) 0 0
\(299\) −2535.00 2634.45i −0.490310 0.509546i
\(300\) 0 0
\(301\) 1248.00 720.533i 0.238982 0.137976i
\(302\) 0 0
\(303\) 429.000 743.050i 0.0813380 0.140882i
\(304\) 0 0
\(305\) −217.500 125.574i −0.0408328 0.0235748i
\(306\) 0 0
\(307\) 2220.49i 0.412801i −0.978468 0.206401i \(-0.933825\pi\)
0.978468 0.206401i \(-0.0661750\pi\)
\(308\) 0 0
\(309\) −182.000 315.233i −0.0335069 0.0580356i
\(310\) 0 0
\(311\) −4914.00 −0.895972 −0.447986 0.894041i \(-0.647859\pi\)
−0.447986 + 0.894041i \(0.647859\pi\)
\(312\) 0 0
\(313\) −518.000 −0.0935434 −0.0467717 0.998906i \(-0.514893\pi\)
−0.0467717 + 0.998906i \(0.514893\pi\)
\(314\) 0 0
\(315\) 276.000 + 478.046i 0.0493677 + 0.0855074i
\(316\) 0 0
\(317\) 3916.17i 0.693861i −0.937891 0.346930i \(-0.887224\pi\)
0.937891 0.346930i \(-0.112776\pi\)
\(318\) 0 0
\(319\) −1692.00 976.877i −0.296971 0.171456i
\(320\) 0 0
\(321\) 1506.00 2608.47i 0.261859 0.453553i
\(322\) 0 0
\(323\) −11583.0 + 6687.45i −1.99534 + 1.15201i
\(324\) 0 0
\(325\) 5551.00 1373.52i 0.947428 0.234428i
\(326\) 0 0
\(327\) 2688.00 1551.92i 0.454577 0.262450i
\(328\) 0 0
\(329\) −2088.00 + 3616.52i −0.349894 + 0.606034i
\(330\) 0 0
\(331\) 6456.00 + 3727.37i 1.07207 + 0.618958i 0.928745 0.370719i \(-0.120889\pi\)
0.143321 + 0.989676i \(0.454222\pi\)
\(332\) 0 0
\(333\) 3306.48i 0.544127i
\(334\) 0 0
\(335\) 681.000 + 1179.53i 0.111066 + 0.192371i
\(336\) 0 0
\(337\) −3575.00 −0.577871 −0.288936 0.957349i \(-0.593301\pi\)
−0.288936 + 0.957349i \(0.593301\pi\)
\(338\) 0 0
\(339\) 1374.00 0.220134
\(340\) 0 0
\(341\) −1080.00 1870.61i −0.171511 0.297066i
\(342\) 0 0
\(343\) 6845.06i 1.07755i
\(344\) 0 0
\(345\) 234.000 + 135.100i 0.0365163 + 0.0210827i
\(346\) 0 0
\(347\) −3483.00 + 6032.73i −0.538839 + 0.933297i 0.460128 + 0.887853i \(0.347804\pi\)
−0.998967 + 0.0454442i \(0.985530\pi\)
\(348\) 0 0
\(349\) −5760.00 + 3325.54i −0.883455 + 0.510063i −0.871796 0.489869i \(-0.837045\pi\)
−0.0116588 + 0.999932i \(0.503711\pi\)
\(350\) 0 0
\(351\) 4550.00 1125.83i 0.691912 0.171204i
\(352\) 0 0
\(353\) 4876.50 2815.45i 0.735269 0.424508i −0.0850777 0.996374i \(-0.527114\pi\)
0.820347 + 0.571867i \(0.193781\pi\)
\(354\) 0 0
\(355\) 915.000 1584.83i 0.136798 0.236940i
\(356\) 0 0
\(357\) −2808.00 1621.20i −0.416289 0.240344i
\(358\) 0 0
\(359\) 7129.12i 1.04808i −0.851694 0.524040i \(-0.824424\pi\)
0.851694 0.524040i \(-0.175576\pi\)
\(360\) 0 0
\(361\) 3104.50 + 5377.15i 0.452617 + 0.783956i
\(362\) 0 0
\(363\) −2278.00 −0.329377
\(364\) 0 0
\(365\) 795.000 0.114006
\(366\) 0 0
\(367\) 1.00000 + 1.73205i 0.000142233 + 0.000246355i 0.866097 0.499877i \(-0.166621\pi\)
−0.865954 + 0.500123i \(0.833288\pi\)
\(368\) 0 0
\(369\) 6254.44i 0.882366i
\(370\) 0 0
\(371\) 1116.00 + 644.323i 0.156172 + 0.0901660i
\(372\) 0 0
\(373\) −1749.50 + 3030.22i −0.242857 + 0.420641i −0.961527 0.274711i \(-0.911418\pi\)
0.718670 + 0.695351i \(0.244751\pi\)
\(374\) 0 0
\(375\) −741.000 + 427.817i −0.102040 + 0.0589129i
\(376\) 0 0
\(377\) 4582.50 + 4762.27i 0.626023 + 0.650582i
\(378\) 0 0
\(379\) −4779.00 + 2759.16i −0.647706 + 0.373953i −0.787577 0.616216i \(-0.788665\pi\)
0.139871 + 0.990170i \(0.455331\pi\)
\(380\) 0 0
\(381\) −286.000 + 495.367i −0.0384573 + 0.0666100i
\(382\) 0 0
\(383\) 6378.00 + 3682.34i 0.850915 + 0.491276i 0.860960 0.508673i \(-0.169864\pi\)
−0.0100443 + 0.999950i \(0.503197\pi\)
\(384\) 0 0
\(385\) 332.554i 0.0440221i
\(386\) 0 0
\(387\) −1196.00 2071.53i −0.157096 0.272098i
\(388\) 0 0
\(389\) −1209.00 −0.157580 −0.0787901 0.996891i \(-0.525106\pi\)
−0.0787901 + 0.996891i \(0.525106\pi\)
\(390\) 0 0
\(391\) 9126.00 1.18036
\(392\) 0 0
\(393\) 1974.00 + 3419.07i 0.253372 + 0.438853i
\(394\) 0 0
\(395\) 2210.10i 0.281524i
\(396\) 0 0
\(397\) 10128.0 + 5847.40i 1.28038 + 0.739226i 0.976917 0.213618i \(-0.0685248\pi\)
0.303460 + 0.952844i \(0.401858\pi\)
\(398\) 0 0
\(399\) −1584.00 + 2743.57i −0.198745 + 0.344236i
\(400\) 0 0
\(401\) −2581.50 + 1490.43i −0.321481 + 0.185607i −0.652053 0.758174i \(-0.726092\pi\)
0.330571 + 0.943781i \(0.392759\pi\)
\(402\) 0 0
\(403\) 1755.00 + 7092.75i 0.216930 + 0.876712i
\(404\) 0 0
\(405\) 631.500 364.597i 0.0774802 0.0447332i
\(406\) 0 0
\(407\) 996.000 1725.12i 0.121302 0.210101i
\(408\) 0 0
\(409\) 37.5000 + 21.6506i 0.00453363 + 0.00261749i 0.502265 0.864714i \(-0.332500\pi\)
−0.497731 + 0.867331i \(0.665833\pi\)
\(410\) 0 0
\(411\) 1693.95i 0.203300i
\(412\) 0 0
\(413\) 1968.00 + 3408.68i 0.234477 + 0.406126i
\(414\) 0 0
\(415\) 1368.00 0.161813
\(416\) 0 0
\(417\) 472.000 0.0554291
\(418\) 0 0
\(419\) −4731.00 8194.33i −0.551610 0.955416i −0.998159 0.0606569i \(-0.980680\pi\)
0.446549 0.894759i \(-0.352653\pi\)
\(420\) 0 0
\(421\) 7068.50i 0.818284i −0.912471 0.409142i \(-0.865828\pi\)
0.912471 0.409142i \(-0.134172\pi\)
\(422\) 0 0
\(423\) 6003.00 + 3465.83i 0.690014 + 0.398380i
\(424\) 0 0
\(425\) −7137.00 + 12361.6i −0.814577 + 1.41089i
\(426\) 0 0
\(427\) −1740.00 + 1004.59i −0.197200 + 0.113854i
\(428\) 0 0
\(429\) −1248.00 360.267i −0.140452 0.0405451i
\(430\) 0 0
\(431\) 8598.00 4964.06i 0.960907 0.554780i 0.0644552 0.997921i \(-0.479469\pi\)
0.896452 + 0.443140i \(0.146136\pi\)
\(432\) 0 0
\(433\) 3308.50 5730.49i 0.367197 0.636004i −0.621929 0.783074i \(-0.713651\pi\)
0.989126 + 0.147070i \(0.0469841\pi\)
\(434\) 0 0
\(435\) −423.000 244.219i −0.0466237 0.0269182i
\(436\) 0 0
\(437\) 8916.60i 0.976061i
\(438\) 0 0
\(439\) 6994.00 + 12114.0i 0.760377 + 1.31701i 0.942656 + 0.333765i \(0.108319\pi\)
−0.182280 + 0.983247i \(0.558348\pi\)
\(440\) 0 0
\(441\) −3473.00 −0.375013
\(442\) 0 0
\(443\) −2004.00 −0.214928 −0.107464 0.994209i \(-0.534273\pi\)
−0.107464 + 0.994209i \(0.534273\pi\)
\(444\) 0 0
\(445\) −846.000 1465.31i −0.0901219 0.156096i
\(446\) 0 0
\(447\) 93.5307i 0.00989676i
\(448\) 0 0
\(449\) 7866.00 + 4541.44i 0.826769 + 0.477336i 0.852745 0.522327i \(-0.174936\pi\)
−0.0259758 + 0.999663i \(0.508269\pi\)
\(450\) 0 0
\(451\) −1884.00 + 3263.18i −0.196705 + 0.340704i
\(452\) 0 0
\(453\) 3066.00 1770.16i 0.317998 0.183596i
\(454\) 0 0
\(455\) −312.000 + 1080.80i −0.0321468 + 0.111360i
\(456\) 0 0
\(457\) 2185.50 1261.80i 0.223705 0.129156i −0.383959 0.923350i \(-0.625440\pi\)
0.607665 + 0.794194i \(0.292106\pi\)
\(458\) 0 0
\(459\) −5850.00 + 10132.5i −0.594890 + 1.03038i
\(460\) 0 0
\(461\) 16963.5 + 9793.88i 1.71382 + 0.989472i 0.929270 + 0.369400i \(0.120437\pi\)
0.784545 + 0.620072i \(0.212897\pi\)
\(462\) 0 0
\(463\) 8632.54i 0.866497i 0.901274 + 0.433249i \(0.142633\pi\)
−0.901274 + 0.433249i \(0.857367\pi\)
\(464\) 0 0
\(465\) −270.000 467.654i −0.0269268 0.0466385i
\(466\) 0 0
\(467\) −5460.00 −0.541025 −0.270512 0.962716i \(-0.587193\pi\)
−0.270512 + 0.962716i \(0.587193\pi\)
\(468\) 0 0
\(469\) 10896.0 1.07277
\(470\) 0 0
\(471\) 1211.00 + 2097.51i 0.118471 + 0.205198i
\(472\) 0 0
\(473\) 1441.07i 0.140085i
\(474\) 0 0
\(475\) 12078.0 + 6973.24i 1.16669 + 0.673587i
\(476\) 0 0
\(477\) 1069.50 1852.43i 0.102660 0.177813i
\(478\) 0 0
\(479\) 2211.00 1276.52i 0.210904 0.121766i −0.390827 0.920464i \(-0.627811\pi\)
0.601732 + 0.798698i \(0.294478\pi\)
\(480\) 0 0
\(481\) −4855.50 + 4672.21i −0.460274 + 0.442899i
\(482\) 0 0
\(483\) 1872.00 1080.80i 0.176354 0.101818i
\(484\) 0 0
\(485\) −174.000 + 301.377i −0.0162906 + 0.0282161i
\(486\) 0 0
\(487\) −9378.00 5414.39i −0.872603 0.503798i −0.00439074 0.999990i \(-0.501398\pi\)
−0.868212 + 0.496193i \(0.834731\pi\)
\(488\) 0 0
\(489\) 2009.18i 0.185804i
\(490\) 0 0
\(491\) 5694.00 + 9862.30i 0.523354 + 0.906475i 0.999631 + 0.0271797i \(0.00865264\pi\)
−0.476277 + 0.879295i \(0.658014\pi\)
\(492\) 0 0
\(493\) −16497.0 −1.50707
\(494\) 0 0
\(495\) −552.000 −0.0501223
\(496\) 0 0
\(497\) −7320.00 12678.6i −0.660658 1.14429i
\(498\) 0 0
\(499\) 17677.3i 1.58586i −0.609311 0.792931i \(-0.708554\pi\)
0.609311 0.792931i \(-0.291446\pi\)
\(500\) 0 0
\(501\) −1584.00 914.523i −0.141253 0.0815526i
\(502\) 0 0
\(503\) 1938.00 3356.71i 0.171792 0.297552i −0.767255 0.641343i \(-0.778378\pi\)
0.939046 + 0.343791i \(0.111711\pi\)
\(504\) 0 0
\(505\) 643.500 371.525i 0.0567037 0.0327379i
\(506\) 0 0
\(507\) 3718.00 + 2341.73i 0.325685 + 0.205128i
\(508\) 0 0
\(509\) −14779.5 + 8532.95i −1.28701 + 0.743058i −0.978120 0.208039i \(-0.933292\pi\)
−0.308893 + 0.951097i \(0.599958\pi\)
\(510\) 0 0
\(511\) 3180.00 5507.92i 0.275293 0.476822i
\(512\) 0 0
\(513\) 9900.00 + 5715.77i 0.852038 + 0.491925i
\(514\) 0 0
\(515\) 315.233i 0.0269725i
\(516\) 0 0
\(517\) −2088.00 3616.52i −0.177621 0.307649i
\(518\) 0 0
\(519\) −5148.00 −0.435399
\(520\) 0 0
\(521\) 2121.00 0.178355 0.0891773 0.996016i \(-0.471576\pi\)
0.0891773 + 0.996016i \(0.471576\pi\)
\(522\) 0 0
\(523\) −5732.00 9928.12i −0.479241 0.830069i 0.520476 0.853876i \(-0.325755\pi\)
−0.999717 + 0.0238072i \(0.992421\pi\)
\(524\) 0 0
\(525\) 3380.96i 0.281062i
\(526\) 0 0
\(527\) −15795.0 9119.25i −1.30558 0.753777i
\(528\) 0 0
\(529\) 3041.50 5268.03i 0.249979 0.432977i
\(530\) 0 0
\(531\) 5658.00 3266.65i 0.462404 0.266969i
\(532\) 0 0
\(533\) 9184.50 8837.79i 0.746388 0.718212i
\(534\) 0 0
\(535\) 2259.00 1304.23i 0.182552 0.105396i
\(536\) 0 0
\(537\) −3744.00 + 6484.80i −0.300867 + 0.521117i
\(538\) 0 0
\(539\) 1812.00 + 1046.16i 0.144802 + 0.0836016i
\(540\) 0 0
\(541\) 4764.87i 0.378665i 0.981913 + 0.189333i \(0.0606324\pi\)
−0.981913 + 0.189333i \(0.939368\pi\)
\(542\) 0 0
\(543\) −637.000 1103.32i −0.0503431 0.0871968i
\(544\) 0 0
\(545\) 2688.00 0.211268
\(546\) 0 0
\(547\) −6554.00 −0.512301 −0.256151 0.966637i \(-0.582454\pi\)
−0.256151 + 0.966637i \(0.582454\pi\)
\(548\) 0 0
\(549\) 1667.50 + 2888.19i 0.129631 + 0.224527i
\(550\) 0 0
\(551\) 16118.5i 1.24622i
\(552\) 0 0
\(553\) −15312.0 8840.39i −1.17745 0.679804i
\(554\) 0 0
\(555\) 249.000 431.281i 0.0190441 0.0329853i
\(556\) 0 0
\(557\) −15685.5 + 9056.03i −1.19321 + 0.688898i −0.959032 0.283297i \(-0.908572\pi\)
−0.234174 + 0.972195i \(0.575239\pi\)
\(558\) 0 0
\(559\) 1352.00 4683.47i 0.102296 0.354364i
\(560\) 0 0
\(561\) 2808.00 1621.20i 0.211326 0.122009i
\(562\) 0 0
\(563\) −6084.00 + 10537.8i −0.455435 + 0.788837i −0.998713 0.0507160i \(-0.983850\pi\)
0.543278 + 0.839553i \(0.317183\pi\)
\(564\) 0 0
\(565\) 1030.50 + 594.959i 0.0767318 + 0.0443011i
\(566\) 0 0
\(567\) 5833.55i 0.432074i
\(568\) 0 0
\(569\) 3861.00 + 6687.45i 0.284467 + 0.492711i 0.972480 0.232988i \(-0.0748502\pi\)
−0.688013 + 0.725698i \(0.741517\pi\)
\(570\) 0 0
\(571\) −11440.0 −0.838440 −0.419220 0.907885i \(-0.637696\pi\)
−0.419220 + 0.907885i \(0.637696\pi\)
\(572\) 0 0
\(573\) −5196.00 −0.378824
\(574\) 0 0
\(575\) −4758.00 8241.10i −0.345082 0.597700i
\(576\) 0 0
\(577\) 15444.7i 1.11433i −0.830400 0.557167i \(-0.811888\pi\)
0.830400 0.557167i \(-0.188112\pi\)
\(578\) 0 0
\(579\) 1935.00 + 1117.17i 0.138887 + 0.0801867i
\(580\) 0 0
\(581\) 5472.00 9477.78i 0.390735 0.676772i
\(582\) 0 0
\(583\) −1116.00 + 644.323i −0.0792796 + 0.0457721i
\(584\) 0 0
\(585\) 1794.00 + 517.883i 0.126791 + 0.0366014i
\(586\) 0 0
\(587\) 12186.0 7035.59i 0.856848 0.494702i −0.00610719 0.999981i \(-0.501944\pi\)
0.862956 + 0.505280i \(0.168611\pi\)
\(588\) 0 0
\(589\) −8910.00 + 15432.6i −0.623311 + 1.07961i
\(590\) 0 0
\(591\) 3552.00 + 2050.75i 0.247225 + 0.142735i
\(592\) 0 0
\(593\) 26938.6i 1.86549i −0.360538 0.932745i \(-0.617407\pi\)
0.360538 0.932745i \(-0.382593\pi\)
\(594\) 0 0
\(595\) −1404.00 2431.80i −0.0967368 0.167553i
\(596\) 0 0
\(597\) −5044.00 −0.345791
\(598\) 0 0
\(599\) 10554.0 0.719908 0.359954 0.932970i \(-0.382792\pi\)
0.359954 + 0.932970i \(0.382792\pi\)
\(600\) 0 0
\(601\) 7415.50 + 12844.0i 0.503302 + 0.871745i 0.999993 + 0.00381713i \(0.00121503\pi\)
−0.496691 + 0.867928i \(0.665452\pi\)
\(602\) 0 0
\(603\) 18086.1i 1.22143i
\(604\) 0 0
\(605\) −1708.50 986.403i −0.114811 0.0662859i
\(606\) 0 0
\(607\) −3977.00 + 6888.37i −0.265933 + 0.460610i −0.967808 0.251691i \(-0.919013\pi\)
0.701874 + 0.712301i \(0.252347\pi\)
\(608\) 0 0
\(609\) −3384.00 + 1953.75i −0.225167 + 0.130000i
\(610\) 0 0
\(611\) 3393.00 + 13712.6i 0.224658 + 0.907945i
\(612\) 0 0
\(613\) 21841.5 12610.2i 1.43910 0.830866i 0.441315 0.897352i \(-0.354512\pi\)
0.997787 + 0.0664859i \(0.0211787\pi\)
\(614\) 0 0
\(615\) −471.000 + 815.796i −0.0308822 + 0.0534895i
\(616\) 0 0
\(617\) −15055.5 8692.30i −0.982353 0.567162i −0.0793731 0.996845i \(-0.525292\pi\)
−0.902980 + 0.429683i \(0.858625\pi\)
\(618\) 0 0
\(619\) 8209.92i 0.533093i −0.963822 0.266547i \(-0.914117\pi\)
0.963822 0.266547i \(-0.0858826\pi\)
\(620\) 0 0
\(621\) −3900.00 6755.00i −0.252015 0.436504i
\(622\) 0 0
\(623\) −13536.0 −0.870479
\(624\) 0 0
\(625\) 14509.0 0.928576
\(626\) 0 0
\(627\) −1584.00 2743.57i −0.100891 0.174749i
\(628\) 0 0
\(629\) 16819.9i 1.06622i
\(630\) 0 0
\(631\) −11142.0 6432.84i −0.702941 0.405843i 0.105501 0.994419i \(-0.466355\pi\)
−0.808442 + 0.588576i \(0.799689\pi\)
\(632\) 0 0
\(633\) −1042.00 + 1804.80i −0.0654278 + 0.113324i
\(634\) 0 0
\(635\) −429.000 + 247.683i −0.0268100 + 0.0154788i
\(636\) 0 0
\(637\) −4907.50 5100.02i −0.305247 0.317222i
\(638\) 0 0
\(639\) −21045.0 + 12150.3i −1.30286 + 0.752206i
\(640\) 0 0
\(641\) −3100.50 + 5370.22i −0.191049 + 0.330907i −0.945598 0.325337i \(-0.894522\pi\)
0.754549 + 0.656244i \(0.227856\pi\)
\(642\) 0 0
\(643\) 14568.0 + 8410.84i 0.893477 + 0.515849i 0.875078 0.483981i \(-0.160810\pi\)
0.0183989 + 0.999831i \(0.494143\pi\)
\(644\) 0 0
\(645\) 360.267i 0.0219930i
\(646\) 0 0
\(647\) −6747.00 11686.1i −0.409972 0.710092i 0.584914 0.811095i \(-0.301128\pi\)
−0.994886 + 0.101003i \(0.967795\pi\)
\(648\) 0 0
\(649\) −3936.00 −0.238061
\(650\) 0 0
\(651\) −4320.00 −0.260083
\(652\) 0 0
\(653\) 5667.00 + 9815.53i 0.339612 + 0.588226i 0.984360 0.176170i \(-0.0563708\pi\)
−0.644747 + 0.764396i \(0.723037\pi\)
\(654\) 0 0
\(655\) 3419.07i 0.203960i
\(656\) 0 0
\(657\) −9142.50 5278.42i −0.542896 0.313441i
\(658\) 0 0
\(659\) 6618.00 11462.7i 0.391200 0.677578i −0.601408 0.798942i \(-0.705393\pi\)
0.992608 + 0.121364i \(0.0387268\pi\)
\(660\) 0 0
\(661\) −10264.5 + 5926.21i −0.603998 + 0.348718i −0.770613 0.637304i \(-0.780050\pi\)
0.166615 + 0.986022i \(0.446716\pi\)
\(662\) 0 0
\(663\) −10647.0 + 2634.45i −0.623673 + 0.154319i
\(664\) 0 0
\(665\) −2376.00 + 1371.78i −0.138552 + 0.0799932i
\(666\) 0 0
\(667\) 5499.00 9524.55i 0.319224 0.552911i
\(668\) 0 0
\(669\) 4170.00 + 2407.55i 0.240989 + 0.139135i
\(670\) 0 0
\(671\) 2009.18i 0.115594i
\(672\) 0 0
\(673\) −4010.50 6946.39i −0.229708 0.397866i 0.728014 0.685563i \(-0.240444\pi\)
−0.957722 + 0.287697i \(0.907110\pi\)
\(674\) 0 0
\(675\) 12200.0 0.695671
\(676\) 0 0
\(677\) −21630.0 −1.22793 −0.613965 0.789333i \(-0.710426\pi\)
−0.613965 + 0.789333i \(0.710426\pi\)
\(678\) 0 0
\(679\) 1392.00 + 2411.01i 0.0786746 + 0.136268i
\(680\) 0 0
\(681\) 4815.10i 0.270947i
\(682\) 0 0
\(683\) 22983.0 + 13269.2i 1.28758 + 0.743387i 0.978223 0.207557i \(-0.0665514\pi\)
0.309361 + 0.950945i \(0.399885\pi\)
\(684\) 0 0
\(685\) 733.500 1270.46i 0.0409133 0.0708639i
\(686\) 0 0
\(687\) 4344.00 2508.01i 0.241243 0.139282i
\(688\) 0 0
\(689\) 4231.50 1047.02i 0.233973 0.0578933i
\(690\) 0 0
\(691\) 720.000 415.692i 0.0396383 0.0228852i −0.480050 0.877241i \(-0.659381\pi\)
0.519688 + 0.854356i \(0.326048\pi\)
\(692\) 0 0
\(693\) −2208.00 + 3824.37i −0.121032 + 0.209633i
\(694\) 0 0
\(695\) 354.000 + 204.382i 0.0193208 + 0.0111549i
\(696\) 0 0
\(697\) 31816.0i 1.72901i
\(698\) 0 0
\(699\) −5850.00 10132.5i −0.316548 0.548278i
\(700\) 0 0
\(701\) 30186.0 1.62640 0.813202 0.581981i \(-0.197722\pi\)
0.813202 + 0.581981i \(0.197722\pi\)
\(702\) 0 0
\(703\) −16434.0 −0.881679
\(704\) 0 0
\(705\) −522.000 904.131i −0.0278860 0.0483000i
\(706\) 0 0
\(707\) 5944.40i 0.316212i
\(708\) 0 0
\(709\) −10288.5 5940.07i −0.544983 0.314646i 0.202113 0.979362i \(-0.435219\pi\)
−0.747096 + 0.664716i \(0.768552\pi\)
\(710\) 0 0
\(711\) −14674.0 + 25416.1i −0.774006 + 1.34062i
\(712\) 0 0
\(713\) 10530.0 6079.50i 0.553088 0.319325i
\(714\) 0 0
\(715\) −780.000 810.600i −0.0407977 0.0423982i
\(716\) 0 0
\(717\) 9324.00 5383.21i 0.485650 0.280390i
\(718\) 0 0
\(719\) 9204.00 15941.8i 0.477401 0.826883i −0.522264 0.852784i \(-0.674912\pi\)
0.999665 + 0.0259014i \(0.00824561\pi\)
\(720\) 0 0
\(721\) −2184.00 1260.93i −0.112811 0.0651312i
\(722\) 0 0
\(723\) 9834.58i 0.505881i
\(724\) 0 0
\(725\) 8601.00 + 14897.4i 0.440597 + 0.763137i
\(726\) 0 0
\(727\) −21112.0 −1.07703 −0.538515 0.842616i \(-0.681014\pi\)
−0.538515 + 0.842616i \(0.681014\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) 0 0
\(731\) 6084.00 + 10537.8i 0.307832 + 0.533180i
\(732\) 0 0
\(733\) 23959.5i 1.20732i 0.797243 + 0.603658i \(0.206291\pi\)
−0.797243 + 0.603658i \(0.793709\pi\)
\(734\) 0 0
\(735\) 453.000 + 261.540i 0.0227335 + 0.0131252i
\(736\) 0 0
\(737\) −5448.00 + 9436.21i −0.272293 + 0.471625i
\(738\) 0 0
\(739\) −2742.00 + 1583.09i −0.136490 + 0.0788025i −0.566690 0.823931i \(-0.691776\pi\)
0.430200 + 0.902734i \(0.358443\pi\)
\(740\) 0 0
\(741\) 2574.00 + 10402.7i 0.127609 + 0.515726i
\(742\) 0 0
\(743\) 26070.0 15051.5i 1.28723 0.743185i 0.309075 0.951038i \(-0.399981\pi\)
0.978160 + 0.207852i \(0.0666474\pi\)
\(744\) 0 0
\(745\) 40.5000 70.1481i 0.00199168 0.00344970i
\(746\) 0 0
\(747\) −15732.0 9082.87i −0.770554 0.444880i
\(748\) 0 0
\(749\) 20867.7i 1.01801i
\(750\) 0 0
\(751\) 14248.0 + 24678.3i 0.692299 + 1.19910i 0.971083 + 0.238744i \(0.0767356\pi\)
−0.278783 + 0.960354i \(0.589931\pi\)
\(752\) 0 0
\(753\) −7956.00 −0.385037
\(754\) 0 0
\(755\) 3066.00 0.147792
\(756\) 0 0
\(757\) −8711.00 15087.9i −0.418239 0.724411i 0.577524 0.816374i \(-0.304019\pi\)
−0.995762 + 0.0919633i \(0.970686\pi\)
\(758\) 0 0
\(759\) 2161.60i 0.103374i
\(760\) 0 0
\(761\) 35790.0 + 20663.4i 1.70484 + 0.984292i 0.940695 + 0.339252i \(0.110174\pi\)
0.764149 + 0.645040i \(0.223159\pi\)
\(762\) 0 0
\(763\) 10752.0 18623.0i 0.510155 0.883615i
\(764\) 0 0
\(765\) −4036.50 + 2330.47i −0.190771 + 0.110142i
\(766\) 0 0
\(767\) 12792.0 + 3692.73i 0.602206 + 0.173842i
\(768\) 0 0
\(769\) −12186.0 + 7035.59i −0.571441 + 0.329922i −0.757725 0.652574i \(-0.773689\pi\)
0.186283 + 0.982496i \(0.440356\pi\)
\(770\) 0 0
\(771\) 2067.00 3580.15i 0.0965515 0.167232i
\(772\) 0 0
\(773\) 174.000 + 100.459i 0.00809618 + 0.00467433i 0.504043 0.863679i \(-0.331845\pi\)
−0.495946 + 0.868353i \(0.665179\pi\)
\(774\) 0 0
\(775\) 19017.9i 0.881476i
\(776\) 0 0
\(777\) −1992.00 3450.25i −0.0919725 0.159301i
\(778\) 0 0
\(779\) 31086.0 1.42975
\(780\) 0 0
\(781\) 14640.0 0.670756
\(782\) 0 0
\(783\) 7050.00 + 12211.0i 0.321771 + 0.557323i
\(784\) 0 0
\(785\) 2097.51i 0.0953675i
\(786\) 0 0
\(787\) 5979.00 +