Properties

Label 208.4.i.a.113.1
Level $208$
Weight $4$
Character 208.113
Analytic conductor $12.272$
Analytic rank $0$
Dimension $2$
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(81,208)]
 
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, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("208.81");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 208 = 2^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 208.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: \(12.2723972812\)
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 113.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 208.113
Dual form 208.4.i.a.81.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.50000 + 2.59808i) q^{3} +2.00000 q^{5} +(-2.50000 - 4.33013i) q^{7} +(9.00000 + 15.5885i) q^{9} +O(q^{10})\) \(q+(-1.50000 + 2.59808i) q^{3} +2.00000 q^{5} +(-2.50000 - 4.33013i) q^{7} +(9.00000 + 15.5885i) q^{9} +(6.50000 - 11.2583i) q^{11} +(-13.0000 + 45.0333i) q^{13} +(-3.00000 + 5.19615i) q^{15} +(-13.5000 - 23.3827i) q^{17} +(37.5000 + 64.9519i) q^{19} +15.0000 q^{21} +(-93.5000 + 161.947i) q^{23} -121.000 q^{25} -135.000 q^{27} +(6.50000 - 11.2583i) q^{29} +104.000 q^{31} +(19.5000 + 33.7750i) q^{33} +(-5.00000 - 8.66025i) q^{35} +(-211.500 + 366.329i) q^{37} +(-97.5000 - 101.325i) q^{39} +(-97.5000 + 168.875i) q^{41} +(99.5000 + 172.339i) q^{43} +(18.0000 + 31.1769i) q^{45} -388.000 q^{47} +(159.000 - 275.396i) q^{49} +81.0000 q^{51} +618.000 q^{53} +(13.0000 - 22.5167i) q^{55} -225.000 q^{57} +(245.500 + 425.218i) q^{59} +(-87.5000 - 151.554i) q^{61} +(45.0000 - 77.9423i) q^{63} +(-26.0000 + 90.0666i) q^{65} +(408.500 - 707.543i) q^{67} +(-280.500 - 485.840i) q^{69} +(39.5000 + 68.4160i) q^{71} +230.000 q^{73} +(181.500 - 314.367i) q^{75} -65.0000 q^{77} -764.000 q^{79} +(-40.5000 + 70.1481i) q^{81} +732.000 q^{83} +(-27.0000 - 46.7654i) q^{85} +(19.5000 + 33.7750i) q^{87} +(520.500 - 901.532i) q^{89} +(227.500 - 56.2917i) q^{91} +(-156.000 + 270.200i) q^{93} +(75.0000 + 129.904i) q^{95} +(48.5000 + 84.0045i) q^{97} +234.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{3} + 4 q^{5} - 5 q^{7} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{3} + 4 q^{5} - 5 q^{7} + 18 q^{9} + 13 q^{11} - 26 q^{13} - 6 q^{15} - 27 q^{17} + 75 q^{19} + 30 q^{21} - 187 q^{23} - 242 q^{25} - 270 q^{27} + 13 q^{29} + 208 q^{31} + 39 q^{33} - 10 q^{35} - 423 q^{37} - 195 q^{39} - 195 q^{41} + 199 q^{43} + 36 q^{45} - 776 q^{47} + 318 q^{49} + 162 q^{51} + 1236 q^{53} + 26 q^{55} - 450 q^{57} + 491 q^{59} - 175 q^{61} + 90 q^{63} - 52 q^{65} + 817 q^{67} - 561 q^{69} + 79 q^{71} + 460 q^{73} + 363 q^{75} - 130 q^{77} - 1528 q^{79} - 81 q^{81} + 1464 q^{83} - 54 q^{85} + 39 q^{87} + 1041 q^{89} + 455 q^{91} - 312 q^{93} + 150 q^{95} + 97 q^{97} + 468 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(53\) \(79\) \(145\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) 0 0
\(5\) 2.00000 0.178885 0.0894427 0.995992i \(-0.471491\pi\)
0.0894427 + 0.995992i \(0.471491\pi\)
\(6\) 0 0
\(7\) −2.50000 4.33013i −0.134987 0.233805i 0.790605 0.612326i \(-0.209766\pi\)
−0.925593 + 0.378521i \(0.876433\pi\)
\(8\) 0 0
\(9\) 9.00000 + 15.5885i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) 6.50000 11.2583i 0.178166 0.308592i −0.763087 0.646296i \(-0.776317\pi\)
0.941252 + 0.337704i \(0.109650\pi\)
\(12\) 0 0
\(13\) −13.0000 + 45.0333i −0.277350 + 0.960769i
\(14\) 0 0
\(15\) −3.00000 + 5.19615i −0.0516398 + 0.0894427i
\(16\) 0 0
\(17\) −13.5000 23.3827i −0.192602 0.333596i 0.753510 0.657437i \(-0.228359\pi\)
−0.946112 + 0.323840i \(0.895026\pi\)
\(18\) 0 0
\(19\) 37.5000 + 64.9519i 0.452794 + 0.784263i 0.998558 0.0536762i \(-0.0170939\pi\)
−0.545764 + 0.837939i \(0.683761\pi\)
\(20\) 0 0
\(21\) 15.0000 0.155870
\(22\) 0 0
\(23\) −93.5000 + 161.947i −0.847656 + 1.46818i 0.0356377 + 0.999365i \(0.488654\pi\)
−0.883294 + 0.468819i \(0.844680\pi\)
\(24\) 0 0
\(25\) −121.000 −0.968000
\(26\) 0 0
\(27\) −135.000 −0.962250
\(28\) 0 0
\(29\) 6.50000 11.2583i 0.0416214 0.0720903i −0.844464 0.535612i \(-0.820081\pi\)
0.886086 + 0.463522i \(0.153414\pi\)
\(30\) 0 0
\(31\) 104.000 0.602547 0.301273 0.953538i \(-0.402588\pi\)
0.301273 + 0.953538i \(0.402588\pi\)
\(32\) 0 0
\(33\) 19.5000 + 33.7750i 0.102864 + 0.178166i
\(34\) 0 0
\(35\) −5.00000 8.66025i −0.0241473 0.0418243i
\(36\) 0 0
\(37\) −211.500 + 366.329i −0.939740 + 1.62768i −0.173785 + 0.984784i \(0.555600\pi\)
−0.765955 + 0.642894i \(0.777734\pi\)
\(38\) 0 0
\(39\) −97.5000 101.325i −0.400320 0.416025i
\(40\) 0 0
\(41\) −97.5000 + 168.875i −0.371389 + 0.643264i −0.989779 0.142607i \(-0.954452\pi\)
0.618391 + 0.785871i \(0.287785\pi\)
\(42\) 0 0
\(43\) 99.5000 + 172.339i 0.352875 + 0.611197i 0.986752 0.162237i \(-0.0518709\pi\)
−0.633877 + 0.773434i \(0.718538\pi\)
\(44\) 0 0
\(45\) 18.0000 + 31.1769i 0.0596285 + 0.103280i
\(46\) 0 0
\(47\) −388.000 −1.20416 −0.602081 0.798435i \(-0.705662\pi\)
−0.602081 + 0.798435i \(0.705662\pi\)
\(48\) 0 0
\(49\) 159.000 275.396i 0.463557 0.802904i
\(50\) 0 0
\(51\) 81.0000 0.222397
\(52\) 0 0
\(53\) 618.000 1.60168 0.800838 0.598881i \(-0.204388\pi\)
0.800838 + 0.598881i \(0.204388\pi\)
\(54\) 0 0
\(55\) 13.0000 22.5167i 0.0318713 0.0552027i
\(56\) 0 0
\(57\) −225.000 −0.522842
\(58\) 0 0
\(59\) 245.500 + 425.218i 0.541718 + 0.938284i 0.998806 + 0.0488617i \(0.0155594\pi\)
−0.457087 + 0.889422i \(0.651107\pi\)
\(60\) 0 0
\(61\) −87.5000 151.554i −0.183659 0.318108i 0.759465 0.650549i \(-0.225461\pi\)
−0.943124 + 0.332441i \(0.892128\pi\)
\(62\) 0 0
\(63\) 45.0000 77.9423i 0.0899915 0.155870i
\(64\) 0 0
\(65\) −26.0000 + 90.0666i −0.0496139 + 0.171868i
\(66\) 0 0
\(67\) 408.500 707.543i 0.744869 1.29015i −0.205387 0.978681i \(-0.565845\pi\)
0.950256 0.311470i \(-0.100821\pi\)
\(68\) 0 0
\(69\) −280.500 485.840i −0.489395 0.847656i
\(70\) 0 0
\(71\) 39.5000 + 68.4160i 0.0660252 + 0.114359i 0.897148 0.441729i \(-0.145635\pi\)
−0.831123 + 0.556088i \(0.812302\pi\)
\(72\) 0 0
\(73\) 230.000 0.368760 0.184380 0.982855i \(-0.440972\pi\)
0.184380 + 0.982855i \(0.440972\pi\)
\(74\) 0 0
\(75\) 181.500 314.367i 0.279438 0.484000i
\(76\) 0 0
\(77\) −65.0000 −0.0962005
\(78\) 0 0
\(79\) −764.000 −1.08806 −0.544030 0.839066i \(-0.683102\pi\)
−0.544030 + 0.839066i \(0.683102\pi\)
\(80\) 0 0
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 732.000 0.968041 0.484021 0.875057i \(-0.339176\pi\)
0.484021 + 0.875057i \(0.339176\pi\)
\(84\) 0 0
\(85\) −27.0000 46.7654i −0.0344537 0.0596755i
\(86\) 0 0
\(87\) 19.5000 + 33.7750i 0.0240301 + 0.0416214i
\(88\) 0 0
\(89\) 520.500 901.532i 0.619920 1.07373i −0.369580 0.929199i \(-0.620498\pi\)
0.989500 0.144534i \(-0.0461683\pi\)
\(90\) 0 0
\(91\) 227.500 56.2917i 0.262071 0.0648458i
\(92\) 0 0
\(93\) −156.000 + 270.200i −0.173940 + 0.301273i
\(94\) 0 0
\(95\) 75.0000 + 129.904i 0.0809983 + 0.140293i
\(96\) 0 0
\(97\) 48.5000 + 84.0045i 0.0507673 + 0.0879316i 0.890292 0.455389i \(-0.150500\pi\)
−0.839525 + 0.543321i \(0.817167\pi\)
\(98\) 0 0
\(99\) 234.000 0.237554
\(100\) 0 0
\(101\) 404.500 700.615i 0.398507 0.690235i −0.595035 0.803700i \(-0.702862\pi\)
0.993542 + 0.113465i \(0.0361950\pi\)
\(102\) 0 0
\(103\) −1288.00 −1.23214 −0.616070 0.787691i \(-0.711276\pi\)
−0.616070 + 0.787691i \(0.711276\pi\)
\(104\) 0 0
\(105\) 30.0000 0.0278829
\(106\) 0 0
\(107\) 638.500 1105.91i 0.576880 0.999185i −0.418955 0.908007i \(-0.637603\pi\)
0.995835 0.0911779i \(-0.0290632\pi\)
\(108\) 0 0
\(109\) 826.000 0.725839 0.362920 0.931820i \(-0.381780\pi\)
0.362920 + 0.931820i \(0.381780\pi\)
\(110\) 0 0
\(111\) −634.500 1098.99i −0.542559 0.939740i
\(112\) 0 0
\(113\) −473.500 820.126i −0.394187 0.682752i 0.598810 0.800891i \(-0.295640\pi\)
−0.992997 + 0.118139i \(0.962307\pi\)
\(114\) 0 0
\(115\) −187.000 + 323.894i −0.151633 + 0.262637i
\(116\) 0 0
\(117\) −819.000 + 202.650i −0.647150 + 0.160128i
\(118\) 0 0
\(119\) −67.5000 + 116.913i −0.0519976 + 0.0900625i
\(120\) 0 0
\(121\) 581.000 + 1006.32i 0.436514 + 0.756064i
\(122\) 0 0
\(123\) −292.500 506.625i −0.214421 0.371389i
\(124\) 0 0
\(125\) −492.000 −0.352047
\(126\) 0 0
\(127\) 588.500 1019.31i 0.411188 0.712199i −0.583832 0.811875i \(-0.698447\pi\)
0.995020 + 0.0996756i \(0.0317805\pi\)
\(128\) 0 0
\(129\) −597.000 −0.407464
\(130\) 0 0
\(131\) 1420.00 0.947069 0.473534 0.880775i \(-0.342978\pi\)
0.473534 + 0.880775i \(0.342978\pi\)
\(132\) 0 0
\(133\) 187.500 324.760i 0.122243 0.211731i
\(134\) 0 0
\(135\) −270.000 −0.172133
\(136\) 0 0
\(137\) 1204.50 + 2086.26i 0.751149 + 1.30103i 0.947266 + 0.320447i \(0.103833\pi\)
−0.196118 + 0.980580i \(0.562833\pi\)
\(138\) 0 0
\(139\) 1413.50 + 2448.25i 0.862529 + 1.49394i 0.869480 + 0.493968i \(0.164454\pi\)
−0.00695133 + 0.999976i \(0.502213\pi\)
\(140\) 0 0
\(141\) 582.000 1008.05i 0.347612 0.602081i
\(142\) 0 0
\(143\) 422.500 + 439.075i 0.247072 + 0.256764i
\(144\) 0 0
\(145\) 13.0000 22.5167i 0.00744546 0.0128959i
\(146\) 0 0
\(147\) 477.000 + 826.188i 0.267635 + 0.463557i
\(148\) 0 0
\(149\) −427.500 740.452i −0.235048 0.407115i 0.724239 0.689549i \(-0.242191\pi\)
−0.959287 + 0.282434i \(0.908858\pi\)
\(150\) 0 0
\(151\) −2064.00 −1.11236 −0.556179 0.831063i \(-0.687733\pi\)
−0.556179 + 0.831063i \(0.687733\pi\)
\(152\) 0 0
\(153\) 243.000 420.888i 0.128401 0.222397i
\(154\) 0 0
\(155\) 208.000 0.107787
\(156\) 0 0
\(157\) −1894.00 −0.962788 −0.481394 0.876504i \(-0.659869\pi\)
−0.481394 + 0.876504i \(0.659869\pi\)
\(158\) 0 0
\(159\) −927.000 + 1605.61i −0.462364 + 0.800838i
\(160\) 0 0
\(161\) 935.000 0.457691
\(162\) 0 0
\(163\) −492.500 853.035i −0.236660 0.409907i 0.723094 0.690750i \(-0.242719\pi\)
−0.959754 + 0.280843i \(0.909386\pi\)
\(164\) 0 0
\(165\) 39.0000 + 67.5500i 0.0184009 + 0.0318713i
\(166\) 0 0
\(167\) −1177.50 + 2039.49i −0.545615 + 0.945033i 0.452953 + 0.891534i \(0.350371\pi\)
−0.998568 + 0.0534983i \(0.982963\pi\)
\(168\) 0 0
\(169\) −1859.00 1170.87i −0.846154 0.532939i
\(170\) 0 0
\(171\) −675.000 + 1169.13i −0.301863 + 0.522842i
\(172\) 0 0
\(173\) 1944.50 + 3367.97i 0.854553 + 1.48013i 0.877059 + 0.480382i \(0.159502\pi\)
−0.0225069 + 0.999747i \(0.507165\pi\)
\(174\) 0 0
\(175\) 302.500 + 523.945i 0.130668 + 0.226323i
\(176\) 0 0
\(177\) −1473.00 −0.625522
\(178\) 0 0
\(179\) 1114.50 1930.37i 0.465372 0.806048i −0.533846 0.845582i \(-0.679254\pi\)
0.999218 + 0.0395333i \(0.0125871\pi\)
\(180\) 0 0
\(181\) −1038.00 −0.426265 −0.213132 0.977023i \(-0.568367\pi\)
−0.213132 + 0.977023i \(0.568367\pi\)
\(182\) 0 0
\(183\) 525.000 0.212072
\(184\) 0 0
\(185\) −423.000 + 732.657i −0.168106 + 0.291168i
\(186\) 0 0
\(187\) −351.000 −0.137260
\(188\) 0 0
\(189\) 337.500 + 584.567i 0.129892 + 0.224979i
\(190\) 0 0
\(191\) −1070.50 1854.16i −0.405543 0.702421i 0.588842 0.808248i \(-0.299584\pi\)
−0.994384 + 0.105828i \(0.966251\pi\)
\(192\) 0 0
\(193\) −1313.50 + 2275.05i −0.489885 + 0.848506i −0.999932 0.0116407i \(-0.996295\pi\)
0.510047 + 0.860146i \(0.329628\pi\)
\(194\) 0 0
\(195\) −195.000 202.650i −0.0716115 0.0744208i
\(196\) 0 0
\(197\) −601.500 + 1041.83i −0.217539 + 0.376788i −0.954055 0.299632i \(-0.903136\pi\)
0.736516 + 0.676420i \(0.236469\pi\)
\(198\) 0 0
\(199\) 371.500 + 643.457i 0.132336 + 0.229213i 0.924577 0.380996i \(-0.124419\pi\)
−0.792240 + 0.610209i \(0.791085\pi\)
\(200\) 0 0
\(201\) 1225.50 + 2122.63i 0.430050 + 0.744869i
\(202\) 0 0
\(203\) −65.0000 −0.0224734
\(204\) 0 0
\(205\) −195.000 + 337.750i −0.0664361 + 0.115071i
\(206\) 0 0
\(207\) −3366.00 −1.13021
\(208\) 0 0
\(209\) 975.000 0.322690
\(210\) 0 0
\(211\) −177.500 + 307.439i −0.0579128 + 0.100308i −0.893528 0.449007i \(-0.851778\pi\)
0.835615 + 0.549315i \(0.185111\pi\)
\(212\) 0 0
\(213\) −237.000 −0.0762393
\(214\) 0 0
\(215\) 199.000 + 344.678i 0.0631241 + 0.109334i
\(216\) 0 0
\(217\) −260.000 450.333i −0.0813362 0.140878i
\(218\) 0 0
\(219\) −345.000 + 597.558i −0.106452 + 0.184380i
\(220\) 0 0
\(221\) 1228.50 303.975i 0.373927 0.0925229i
\(222\) 0 0
\(223\) −1141.50 + 1977.14i −0.342782 + 0.593717i −0.984948 0.172849i \(-0.944703\pi\)
0.642166 + 0.766566i \(0.278036\pi\)
\(224\) 0 0
\(225\) −1089.00 1886.20i −0.322667 0.558875i
\(226\) 0 0
\(227\) 1225.50 + 2122.63i 0.358323 + 0.620633i 0.987681 0.156482i \(-0.0500154\pi\)
−0.629358 + 0.777116i \(0.716682\pi\)
\(228\) 0 0
\(229\) −1878.00 −0.541929 −0.270964 0.962589i \(-0.587343\pi\)
−0.270964 + 0.962589i \(0.587343\pi\)
\(230\) 0 0
\(231\) 97.5000 168.875i 0.0277707 0.0481002i
\(232\) 0 0
\(233\) 1630.00 0.458304 0.229152 0.973391i \(-0.426405\pi\)
0.229152 + 0.973391i \(0.426405\pi\)
\(234\) 0 0
\(235\) −776.000 −0.215407
\(236\) 0 0
\(237\) 1146.00 1984.93i 0.314096 0.544030i
\(238\) 0 0
\(239\) 5544.00 1.50047 0.750233 0.661173i \(-0.229941\pi\)
0.750233 + 0.661173i \(0.229941\pi\)
\(240\) 0 0
\(241\) −2761.50 4783.06i −0.738107 1.27844i −0.953347 0.301878i \(-0.902386\pi\)
0.215239 0.976561i \(-0.430947\pi\)
\(242\) 0 0
\(243\) −1944.00 3367.11i −0.513200 0.888889i
\(244\) 0 0
\(245\) 318.000 550.792i 0.0829236 0.143628i
\(246\) 0 0
\(247\) −3412.50 + 844.375i −0.879078 + 0.217515i
\(248\) 0 0
\(249\) −1098.00 + 1901.79i −0.279449 + 0.484021i
\(250\) 0 0
\(251\) 1087.50 + 1883.61i 0.273476 + 0.473674i 0.969749 0.244103i \(-0.0784934\pi\)
−0.696274 + 0.717776i \(0.745160\pi\)
\(252\) 0 0
\(253\) 1215.50 + 2105.31i 0.302047 + 0.523160i
\(254\) 0 0
\(255\) 162.000 0.0397837
\(256\) 0 0
\(257\) 2842.50 4923.35i 0.689923 1.19498i −0.281939 0.959432i \(-0.590978\pi\)
0.971862 0.235550i \(-0.0756891\pi\)
\(258\) 0 0
\(259\) 2115.00 0.507412
\(260\) 0 0
\(261\) 234.000 0.0554952
\(262\) 0 0
\(263\) 3058.50 5297.48i 0.717092 1.24204i −0.245055 0.969509i \(-0.578806\pi\)
0.962147 0.272531i \(-0.0878606\pi\)
\(264\) 0 0
\(265\) 1236.00 0.286517
\(266\) 0 0
\(267\) 1561.50 + 2704.60i 0.357911 + 0.619920i
\(268\) 0 0
\(269\) 2554.50 + 4424.52i 0.578999 + 1.00285i 0.995595 + 0.0937632i \(0.0298897\pi\)
−0.416596 + 0.909092i \(0.636777\pi\)
\(270\) 0 0
\(271\) 3774.50 6537.63i 0.846068 1.46543i −0.0386217 0.999254i \(-0.512297\pi\)
0.884690 0.466180i \(-0.154370\pi\)
\(272\) 0 0
\(273\) −195.000 + 675.500i −0.0432305 + 0.149755i
\(274\) 0 0
\(275\) −786.500 + 1362.26i −0.172464 + 0.298717i
\(276\) 0 0
\(277\) 490.500 + 849.571i 0.106395 + 0.184281i 0.914307 0.405022i \(-0.132736\pi\)
−0.807913 + 0.589302i \(0.799403\pi\)
\(278\) 0 0
\(279\) 936.000 + 1621.20i 0.200849 + 0.347881i
\(280\) 0 0
\(281\) −2762.00 −0.586360 −0.293180 0.956057i \(-0.594713\pi\)
−0.293180 + 0.956057i \(0.594713\pi\)
\(282\) 0 0
\(283\) 1962.50 3399.15i 0.412221 0.713988i −0.582911 0.812536i \(-0.698087\pi\)
0.995132 + 0.0985482i \(0.0314199\pi\)
\(284\) 0 0
\(285\) −450.000 −0.0935288
\(286\) 0 0
\(287\) 975.000 0.200531
\(288\) 0 0
\(289\) 2092.00 3623.45i 0.425809 0.737523i
\(290\) 0 0
\(291\) −291.000 −0.0586210
\(292\) 0 0
\(293\) −3855.50 6677.92i −0.768740 1.33150i −0.938247 0.345967i \(-0.887551\pi\)
0.169507 0.985529i \(-0.445782\pi\)
\(294\) 0 0
\(295\) 491.000 + 850.437i 0.0969055 + 0.167845i
\(296\) 0 0
\(297\) −877.500 + 1519.87i −0.171440 + 0.296943i
\(298\) 0 0
\(299\) −6077.50 6315.92i −1.17549 1.22160i
\(300\) 0 0
\(301\) 497.500 861.695i 0.0952672 0.165008i
\(302\) 0 0
\(303\) 1213.50 + 2101.84i 0.230078 + 0.398507i
\(304\) 0 0
\(305\) −175.000 303.109i −0.0328540 0.0569048i
\(306\) 0 0
\(307\) −10388.0 −1.93119 −0.965594 0.260056i \(-0.916259\pi\)
−0.965594 + 0.260056i \(0.916259\pi\)
\(308\) 0 0
\(309\) 1932.00 3346.32i 0.355688 0.616070i
\(310\) 0 0
\(311\) 7272.00 1.32591 0.662954 0.748660i \(-0.269303\pi\)
0.662954 + 0.748660i \(0.269303\pi\)
\(312\) 0 0
\(313\) 7910.00 1.42843 0.714217 0.699925i \(-0.246783\pi\)
0.714217 + 0.699925i \(0.246783\pi\)
\(314\) 0 0
\(315\) 90.0000 155.885i 0.0160982 0.0278829i
\(316\) 0 0
\(317\) 7398.00 1.31077 0.655383 0.755296i \(-0.272507\pi\)
0.655383 + 0.755296i \(0.272507\pi\)
\(318\) 0 0
\(319\) −84.5000 146.358i −0.0148310 0.0256881i
\(320\) 0 0
\(321\) 1915.50 + 3317.74i 0.333062 + 0.576880i
\(322\) 0 0
\(323\) 1012.50 1753.70i 0.174418 0.302101i
\(324\) 0 0
\(325\) 1573.00 5449.03i 0.268475 0.930024i
\(326\) 0 0
\(327\) −1239.00 + 2146.01i −0.209532 + 0.362920i
\(328\) 0 0
\(329\) 970.000 + 1680.09i 0.162547 + 0.281539i
\(330\) 0 0
\(331\) −1188.50 2058.54i −0.197359 0.341836i 0.750312 0.661084i \(-0.229903\pi\)
−0.947671 + 0.319248i \(0.896570\pi\)
\(332\) 0 0
\(333\) −7614.00 −1.25299
\(334\) 0 0
\(335\) 817.000 1415.09i 0.133246 0.230789i
\(336\) 0 0
\(337\) −7618.00 −1.23139 −0.615696 0.787984i \(-0.711125\pi\)
−0.615696 + 0.787984i \(0.711125\pi\)
\(338\) 0 0
\(339\) 2841.00 0.455168
\(340\) 0 0
\(341\) 676.000 1170.87i 0.107353 0.185941i
\(342\) 0 0
\(343\) −3305.00 −0.520272
\(344\) 0 0
\(345\) −561.000 971.681i −0.0875456 0.151633i
\(346\) 0 0
\(347\) 187.500 + 324.760i 0.0290073 + 0.0502421i 0.880165 0.474669i \(-0.157432\pi\)
−0.851157 + 0.524911i \(0.824099\pi\)
\(348\) 0 0
\(349\) −4863.50 + 8423.83i −0.745952 + 1.29203i 0.203797 + 0.979013i \(0.434672\pi\)
−0.949749 + 0.313013i \(0.898662\pi\)
\(350\) 0 0
\(351\) 1755.00 6079.50i 0.266880 0.924500i
\(352\) 0 0
\(353\) −1131.50 + 1959.82i −0.170605 + 0.295497i −0.938632 0.344921i \(-0.887906\pi\)
0.768026 + 0.640418i \(0.221239\pi\)
\(354\) 0 0
\(355\) 79.0000 + 136.832i 0.0118109 + 0.0204572i
\(356\) 0 0
\(357\) −202.500 350.740i −0.0300208 0.0519976i
\(358\) 0 0
\(359\) 4488.00 0.659798 0.329899 0.944016i \(-0.392985\pi\)
0.329899 + 0.944016i \(0.392985\pi\)
\(360\) 0 0
\(361\) 617.000 1068.68i 0.0899548 0.155806i
\(362\) 0 0
\(363\) −3486.00 −0.504043
\(364\) 0 0
\(365\) 460.000 0.0659658
\(366\) 0 0
\(367\) −813.500 + 1409.02i −0.115707 + 0.200410i −0.918062 0.396437i \(-0.870247\pi\)
0.802355 + 0.596847i \(0.203580\pi\)
\(368\) 0 0
\(369\) −3510.00 −0.495185
\(370\) 0 0
\(371\) −1545.00 2676.02i −0.216206 0.374480i
\(372\) 0 0
\(373\) −1493.50 2586.82i −0.207320 0.359089i 0.743549 0.668681i \(-0.233141\pi\)
−0.950870 + 0.309592i \(0.899808\pi\)
\(374\) 0 0
\(375\) 738.000 1278.25i 0.101627 0.176023i
\(376\) 0 0
\(377\) 422.500 + 439.075i 0.0577185 + 0.0599828i
\(378\) 0 0
\(379\) −4433.50 + 7679.05i −0.600880 + 1.04076i 0.391808 + 0.920047i \(0.371850\pi\)
−0.992688 + 0.120708i \(0.961484\pi\)
\(380\) 0 0
\(381\) 1765.50 + 3057.94i 0.237400 + 0.411188i
\(382\) 0 0
\(383\) 5701.50 + 9875.29i 0.760661 + 1.31750i 0.942510 + 0.334177i \(0.108458\pi\)
−0.181850 + 0.983326i \(0.558208\pi\)
\(384\) 0 0
\(385\) −130.000 −0.0172089
\(386\) 0 0
\(387\) −1791.00 + 3102.10i −0.235250 + 0.407464i
\(388\) 0 0
\(389\) 2622.00 0.341750 0.170875 0.985293i \(-0.445341\pi\)
0.170875 + 0.985293i \(0.445341\pi\)
\(390\) 0 0
\(391\) 5049.00 0.653041
\(392\) 0 0
\(393\) −2130.00 + 3689.27i −0.273395 + 0.473534i
\(394\) 0 0
\(395\) −1528.00 −0.194638
\(396\) 0 0
\(397\) −329.500 570.711i −0.0416552 0.0721490i 0.844446 0.535641i \(-0.179930\pi\)
−0.886101 + 0.463492i \(0.846596\pi\)
\(398\) 0 0
\(399\) 562.500 + 974.279i 0.0705770 + 0.122243i
\(400\) 0 0
\(401\) 7342.50 12717.6i 0.914381 1.58376i 0.106577 0.994304i \(-0.466011\pi\)
0.807804 0.589451i \(-0.200656\pi\)
\(402\) 0 0
\(403\) −1352.00 + 4683.47i −0.167116 + 0.578908i
\(404\) 0 0
\(405\) −81.0000 + 140.296i −0.00993808 + 0.0172133i
\(406\) 0 0
\(407\) 2749.50 + 4762.27i 0.334859 + 0.579993i
\(408\) 0 0
\(409\) 3914.50 + 6780.11i 0.473251 + 0.819694i 0.999531 0.0306167i \(-0.00974712\pi\)
−0.526280 + 0.850311i \(0.676414\pi\)
\(410\) 0 0
\(411\) −7227.00 −0.867352
\(412\) 0 0
\(413\) 1227.50 2126.09i 0.146250 0.253313i
\(414\) 0 0
\(415\) 1464.00 0.173169
\(416\) 0 0
\(417\) −8481.00 −0.995962
\(418\) 0 0
\(419\) −1459.50 + 2527.93i −0.170170 + 0.294743i −0.938479 0.345336i \(-0.887765\pi\)
0.768309 + 0.640079i \(0.221098\pi\)
\(420\) 0 0
\(421\) −3110.00 −0.360029 −0.180014 0.983664i \(-0.557614\pi\)
−0.180014 + 0.983664i \(0.557614\pi\)
\(422\) 0 0
\(423\) −3492.00 6048.32i −0.401387 0.695223i
\(424\) 0 0
\(425\) 1633.50 + 2829.30i 0.186439 + 0.322921i
\(426\) 0 0
\(427\) −437.500 + 757.772i −0.0495834 + 0.0858810i
\(428\) 0 0
\(429\) −1774.50 + 439.075i −0.199706 + 0.0494143i
\(430\) 0 0
\(431\) −4567.50 + 7911.14i −0.510461 + 0.884145i 0.489465 + 0.872023i \(0.337192\pi\)
−0.999927 + 0.0121219i \(0.996141\pi\)
\(432\) 0 0
\(433\) 5834.50 + 10105.7i 0.647548 + 1.12159i 0.983707 + 0.179780i \(0.0575387\pi\)
−0.336159 + 0.941805i \(0.609128\pi\)
\(434\) 0 0
\(435\) 39.0000 + 67.5500i 0.00429864 + 0.00744546i
\(436\) 0 0
\(437\) −14025.0 −1.53526
\(438\) 0 0
\(439\) 6764.50 11716.5i 0.735426 1.27380i −0.219110 0.975700i \(-0.570315\pi\)
0.954536 0.298095i \(-0.0963512\pi\)
\(440\) 0 0
\(441\) 5724.00 0.618076
\(442\) 0 0
\(443\) 1932.00 0.207206 0.103603 0.994619i \(-0.466963\pi\)
0.103603 + 0.994619i \(0.466963\pi\)
\(444\) 0 0
\(445\) 1041.00 1803.06i 0.110895 0.192075i
\(446\) 0 0
\(447\) 2565.00 0.271410
\(448\) 0 0
\(449\) 2678.50 + 4639.30i 0.281528 + 0.487621i 0.971761 0.235966i \(-0.0758253\pi\)
−0.690233 + 0.723587i \(0.742492\pi\)
\(450\) 0 0
\(451\) 1267.50 + 2195.37i 0.132338 + 0.229215i
\(452\) 0 0
\(453\) 3096.00 5362.43i 0.321110 0.556179i
\(454\) 0 0
\(455\) 455.000 112.583i 0.0468807 0.0116000i
\(456\) 0 0
\(457\) −9699.50 + 16800.0i −0.992830 + 1.71963i −0.392897 + 0.919582i \(0.628527\pi\)
−0.599933 + 0.800050i \(0.704806\pi\)
\(458\) 0 0
\(459\) 1822.50 + 3156.66i 0.185331 + 0.321003i
\(460\) 0 0
\(461\) 7774.50 + 13465.8i 0.785455 + 1.36045i 0.928727 + 0.370764i \(0.120904\pi\)
−0.143273 + 0.989683i \(0.545763\pi\)
\(462\) 0 0
\(463\) −4072.00 −0.408730 −0.204365 0.978895i \(-0.565513\pi\)
−0.204365 + 0.978895i \(0.565513\pi\)
\(464\) 0 0
\(465\) −312.000 + 540.400i −0.0311154 + 0.0538934i
\(466\) 0 0
\(467\) −15224.0 −1.50853 −0.754264 0.656571i \(-0.772006\pi\)
−0.754264 + 0.656571i \(0.772006\pi\)
\(468\) 0 0
\(469\) −4085.00 −0.402191
\(470\) 0 0
\(471\) 2841.00 4920.76i 0.277933 0.481394i
\(472\) 0 0
\(473\) 2587.00 0.251481
\(474\) 0 0
\(475\) −4537.50 7859.18i −0.438305 0.759166i
\(476\) 0 0
\(477\) 5562.00 + 9633.67i 0.533892 + 0.924728i
\(478\) 0 0
\(479\) −5167.50 + 8950.37i −0.492921 + 0.853764i −0.999967 0.00815506i \(-0.997404\pi\)
0.507046 + 0.861919i \(0.330737\pi\)
\(480\) 0 0
\(481\) −13747.5 14286.8i −1.30319 1.35431i
\(482\) 0 0
\(483\) −1402.50 + 2429.20i −0.132124 + 0.228846i
\(484\) 0 0
\(485\) 97.0000 + 168.009i 0.00908153 + 0.0157297i
\(486\) 0 0
\(487\) 3227.50 + 5590.19i 0.300312 + 0.520156i 0.976207 0.216843i \(-0.0695758\pi\)
−0.675894 + 0.736998i \(0.736243\pi\)
\(488\) 0 0
\(489\) 2955.00 0.273271
\(490\) 0 0
\(491\) 3888.50 6735.08i 0.357404 0.619043i −0.630122 0.776496i \(-0.716995\pi\)
0.987526 + 0.157454i \(0.0503285\pi\)
\(492\) 0 0
\(493\) −351.000 −0.0320654
\(494\) 0 0
\(495\) 468.000 0.0424950
\(496\) 0 0
\(497\) 197.500 342.080i 0.0178251 0.0308740i
\(498\) 0 0
\(499\) 3044.00 0.273082 0.136541 0.990634i \(-0.456401\pi\)
0.136541 + 0.990634i \(0.456401\pi\)
\(500\) 0 0
\(501\) −3532.50 6118.47i −0.315011 0.545615i
\(502\) 0 0
\(503\) 5673.50 + 9826.79i 0.502920 + 0.871083i 0.999994 + 0.00337525i \(0.00107438\pi\)
−0.497074 + 0.867708i \(0.665592\pi\)
\(504\) 0 0
\(505\) 809.000 1401.23i 0.0712872 0.123473i
\(506\) 0 0
\(507\) 5830.50 3073.52i 0.510733 0.269231i
\(508\) 0 0
\(509\) −363.500 + 629.600i −0.0316539 + 0.0548262i −0.881418 0.472336i \(-0.843411\pi\)
0.849764 + 0.527163i \(0.176744\pi\)
\(510\) 0 0
\(511\) −575.000 995.929i −0.0497779 0.0862178i
\(512\) 0 0
\(513\) −5062.50 8768.51i −0.435701 0.754657i
\(514\) 0 0
\(515\) −2576.00 −0.220412
\(516\) 0 0
\(517\) −2522.00 + 4368.23i −0.214540 + 0.371595i
\(518\) 0 0
\(519\) −11667.0 −0.986752
\(520\) 0 0
\(521\) 9582.00 0.805749 0.402874 0.915255i \(-0.368011\pi\)
0.402874 + 0.915255i \(0.368011\pi\)
\(522\) 0 0
\(523\) −5191.50 + 8991.94i −0.434051 + 0.751798i −0.997218 0.0745454i \(-0.976249\pi\)
0.563167 + 0.826343i \(0.309583\pi\)
\(524\) 0 0
\(525\) −1815.00 −0.150882
\(526\) 0 0
\(527\) −1404.00 2431.80i −0.116052 0.201007i
\(528\) 0 0
\(529\) −11401.0 19747.1i −0.937043 1.62301i
\(530\) 0 0
\(531\) −4419.00 + 7653.93i −0.361146 + 0.625522i
\(532\) 0 0
\(533\) −6337.50 6586.12i −0.515024 0.535228i
\(534\) 0 0
\(535\) 1277.00 2211.83i 0.103195 0.178740i
\(536\) 0 0
\(537\) 3343.50 + 5791.11i 0.268683 + 0.465372i
\(538\) 0 0
\(539\) −2067.00 3580.15i −0.165180 0.286100i
\(540\) 0 0
\(541\) 12230.0 0.971920 0.485960 0.873981i \(-0.338470\pi\)
0.485960 + 0.873981i \(0.338470\pi\)
\(542\) 0 0
\(543\) 1557.00 2696.80i 0.123052 0.213132i
\(544\) 0 0
\(545\) 1652.00 0.129842
\(546\) 0 0
\(547\) 14636.0 1.14404 0.572020 0.820239i \(-0.306160\pi\)
0.572020 + 0.820239i \(0.306160\pi\)
\(548\) 0 0
\(549\) 1575.00 2727.98i 0.122440 0.212072i
\(550\) 0 0
\(551\) 975.000 0.0753837
\(552\) 0 0
\(553\) 1910.00 + 3308.22i 0.146874 + 0.254394i
\(554\) 0 0
\(555\) −1269.00 2197.97i −0.0970559 0.168106i
\(556\) 0 0
\(557\) 382.500 662.509i 0.0290970 0.0503975i −0.851110 0.524987i \(-0.824070\pi\)
0.880207 + 0.474590i \(0.157403\pi\)
\(558\) 0 0
\(559\) −9054.50 + 2240.41i −0.685089 + 0.169515i
\(560\) 0 0
\(561\) 526.500 911.925i 0.0396236 0.0686301i
\(562\) 0 0
\(563\) 2957.50 + 5122.54i 0.221392 + 0.383462i 0.955231 0.295861i \(-0.0956066\pi\)
−0.733839 + 0.679324i \(0.762273\pi\)
\(564\) 0 0
\(565\) −947.000 1640.25i −0.0705143 0.122134i
\(566\) 0 0
\(567\) 405.000 0.0299972
\(568\) 0 0
\(569\) 608.500 1053.95i 0.0448324 0.0776520i −0.842738 0.538323i \(-0.819058\pi\)
0.887571 + 0.460671i \(0.152391\pi\)
\(570\) 0 0
\(571\) 23436.0 1.71763 0.858814 0.512287i \(-0.171202\pi\)
0.858814 + 0.512287i \(0.171202\pi\)
\(572\) 0 0
\(573\) 6423.00 0.468280
\(574\) 0 0
\(575\) 11313.5 19595.6i 0.820531 1.42120i
\(576\) 0 0
\(577\) 7854.00 0.566666 0.283333 0.959022i \(-0.408560\pi\)
0.283333 + 0.959022i \(0.408560\pi\)
\(578\) 0 0
\(579\) −3940.50 6825.15i −0.282835 0.489885i
\(580\) 0 0
\(581\) −1830.00 3169.65i −0.130673 0.226333i
\(582\) 0 0
\(583\) 4017.00 6957.65i 0.285364 0.494265i
\(584\) 0 0
\(585\) −1638.00 + 405.300i −0.115766 + 0.0286446i
\(586\) 0 0
\(587\) 8516.50 14751.0i 0.598831 1.03721i −0.394163 0.919040i \(-0.628966\pi\)
0.992994 0.118165i \(-0.0377011\pi\)
\(588\) 0 0
\(589\) 3900.00 + 6755.00i 0.272830 + 0.472555i
\(590\) 0 0
\(591\) −1804.50 3125.49i −0.125596 0.217539i
\(592\) 0 0
\(593\) −14506.0 −1.00454 −0.502268 0.864712i \(-0.667501\pi\)
−0.502268 + 0.864712i \(0.667501\pi\)
\(594\) 0 0
\(595\) −135.000 + 233.827i −0.00930161 + 0.0161109i
\(596\) 0 0
\(597\) −2229.00 −0.152809
\(598\) 0 0
\(599\) −15388.0 −1.04964 −0.524822 0.851212i \(-0.675868\pi\)
−0.524822 + 0.851212i \(0.675868\pi\)
\(600\) 0 0
\(601\) 3038.50 5262.84i 0.206228 0.357197i −0.744295 0.667851i \(-0.767214\pi\)
0.950523 + 0.310653i \(0.100548\pi\)
\(602\) 0 0
\(603\) 14706.0 0.993159
\(604\) 0 0
\(605\) 1162.00 + 2012.64i 0.0780860 + 0.135249i
\(606\) 0 0
\(607\) 5107.50 + 8846.45i 0.341527 + 0.591543i 0.984717 0.174165i \(-0.0557225\pi\)
−0.643189 + 0.765707i \(0.722389\pi\)
\(608\) 0 0
\(609\) 97.5000 168.875i 0.00648752 0.0112367i
\(610\) 0 0
\(611\) 5044.00 17472.9i 0.333974 1.15692i
\(612\) 0 0
\(613\) 1728.50 2993.85i 0.113888 0.197260i −0.803447 0.595377i \(-0.797003\pi\)
0.917335 + 0.398117i \(0.130336\pi\)
\(614\) 0 0
\(615\) −585.000 1013.25i −0.0383569 0.0664361i
\(616\) 0 0
\(617\) 3584.50 + 6208.54i 0.233884 + 0.405099i 0.958948 0.283583i \(-0.0915230\pi\)
−0.725064 + 0.688682i \(0.758190\pi\)
\(618\) 0 0
\(619\) −20212.0 −1.31242 −0.656211 0.754578i \(-0.727842\pi\)
−0.656211 + 0.754578i \(0.727842\pi\)
\(620\) 0 0
\(621\) 12622.5 21862.8i 0.815658 1.41276i
\(622\) 0 0
\(623\) −5205.00 −0.334725
\(624\) 0 0
\(625\) 14141.0 0.905024
\(626\) 0 0
\(627\) −1462.50 + 2533.12i −0.0931525 + 0.161345i
\(628\) 0 0
\(629\) 11421.0 0.723983
\(630\) 0 0
\(631\) −4472.50 7746.60i −0.282167 0.488728i 0.689751 0.724046i \(-0.257720\pi\)
−0.971918 + 0.235319i \(0.924387\pi\)
\(632\) 0 0
\(633\) −532.500 922.317i −0.0334360 0.0579128i
\(634\) 0 0
\(635\) 1177.00 2038.62i 0.0735556 0.127402i
\(636\) 0 0
\(637\) 10335.0 + 10740.4i 0.642838 + 0.668057i
\(638\) 0 0
\(639\) −711.000 + 1231.49i −0.0440168 + 0.0762393i
\(640\) 0 0
\(641\) −14121.5 24459.2i −0.870149 1.50714i −0.861842 0.507177i \(-0.830689\pi\)
−0.00830761 0.999965i \(-0.502644\pi\)
\(642\) 0 0
\(643\) 2615.50 + 4530.18i 0.160413 + 0.277843i 0.935017 0.354604i \(-0.115384\pi\)
−0.774604 + 0.632446i \(0.782051\pi\)
\(644\) 0 0
\(645\) −1194.00 −0.0728895
\(646\) 0 0
\(647\) −2435.50 + 4218.41i −0.147990 + 0.256326i −0.930484 0.366332i \(-0.880614\pi\)
0.782495 + 0.622657i \(0.213947\pi\)
\(648\) 0 0
\(649\) 6383.00 0.386063
\(650\) 0 0
\(651\) 1560.00 0.0939189
\(652\) 0 0
\(653\) −6127.50 + 10613.1i −0.367209 + 0.636025i −0.989128 0.147057i \(-0.953020\pi\)
0.621919 + 0.783082i \(0.286353\pi\)
\(654\) 0 0
\(655\) 2840.00 0.169417
\(656\) 0 0
\(657\) 2070.00 + 3585.35i 0.122920 + 0.212904i
\(658\) 0 0
\(659\) −1072.50 1857.62i −0.0633971 0.109807i 0.832585 0.553898i \(-0.186860\pi\)
−0.895982 + 0.444091i \(0.853527\pi\)
\(660\) 0 0
\(661\) −1055.50 + 1828.18i −0.0621092 + 0.107576i −0.895408 0.445247i \(-0.853116\pi\)
0.833299 + 0.552823i \(0.186449\pi\)
\(662\) 0 0
\(663\) −1053.00 + 3647.70i −0.0616819 + 0.213673i
\(664\) 0 0
\(665\) 375.000 649.519i 0.0218675 0.0378756i
\(666\) 0 0
\(667\) 1215.50 + 2105.31i 0.0705612 + 0.122216i
\(668\) 0 0
\(669\) −3424.50 5931.41i −0.197906 0.342782i
\(670\) 0 0
\(671\) −2275.00 −0.130887
\(672\) 0 0
\(673\) 11636.5 20155.0i 0.666499 1.15441i −0.312377 0.949958i \(-0.601125\pi\)
0.978876 0.204453i \(-0.0655414\pi\)
\(674\) 0 0
\(675\) 16335.0 0.931458
\(676\) 0 0
\(677\) −5910.00 −0.335509 −0.167755 0.985829i \(-0.553652\pi\)
−0.167755 + 0.985829i \(0.553652\pi\)
\(678\) 0 0
\(679\) 242.500 420.022i 0.0137059 0.0237393i
\(680\) 0 0
\(681\) −7353.00 −0.413756
\(682\) 0 0
\(683\) 8373.50 + 14503.3i 0.469111 + 0.812525i 0.999377 0.0353071i \(-0.0112409\pi\)
−0.530265 + 0.847832i \(0.677908\pi\)
\(684\) 0 0
\(685\) 2409.00 + 4172.51i 0.134370 + 0.232735i
\(686\) 0 0
\(687\) 2817.00 4879.19i 0.156441 0.270964i
\(688\) 0 0
\(689\) −8034.00 + 27830.6i −0.444225 + 1.53884i
\(690\) 0 0
\(691\) 5154.50 8927.86i 0.283772 0.491507i −0.688539 0.725200i \(-0.741747\pi\)
0.972311 + 0.233692i \(0.0750808\pi\)
\(692\) 0 0
\(693\) −585.000 1013.25i −0.0320668 0.0555414i
\(694\) 0 0
\(695\) 2827.00 + 4896.51i 0.154294 + 0.267245i
\(696\) 0 0
\(697\) 5265.00 0.286121
\(698\) 0 0
\(699\) −2445.00 + 4234.86i −0.132301 + 0.229152i
\(700\) 0 0
\(701\) −24294.0 −1.30895 −0.654473 0.756085i \(-0.727110\pi\)
−0.654473 + 0.756085i \(0.727110\pi\)
\(702\) 0 0
\(703\) −31725.0 −1.70204
\(704\) 0 0
\(705\) 1164.00 2016.11i 0.0621827 0.107704i
\(706\) 0 0
\(707\) −4045.00 −0.215174
\(708\) 0 0
\(709\) −6329.50 10963.0i −0.335274 0.580712i 0.648263 0.761416i \(-0.275496\pi\)
−0.983537 + 0.180704i \(0.942162\pi\)
\(710\) 0 0
\(711\) −6876.00 11909.6i −0.362687 0.628192i
\(712\) 0 0
\(713\) −9724.00 + 16842.5i −0.510753 + 0.884650i
\(714\) 0 0
\(715\) 845.000 + 878.150i 0.0441975 + 0.0459314i
\(716\) 0 0
\(717\) −8316.00 + 14403.7i −0.433147 + 0.750233i
\(718\) 0 0
\(719\) 6545.50 + 11337.1i 0.339508 + 0.588044i 0.984340 0.176279i \(-0.0564062\pi\)
−0.644833 + 0.764324i \(0.723073\pi\)
\(720\) 0 0
\(721\) 3220.00 + 5577.20i 0.166323 + 0.288080i
\(722\) 0 0
\(723\) 16569.0 0.852293
\(724\) 0 0
\(725\) −786.500 + 1362.26i −0.0402895 + 0.0697834i
\(726\) 0 0
\(727\) −10792.0 −0.550555 −0.275277 0.961365i \(-0.588770\pi\)
−0.275277 + 0.961365i \(0.588770\pi\)
\(728\) 0 0
\(729\) 9477.00 0.481481
\(730\) 0 0
\(731\) 2686.50 4653.15i 0.135929 0.235435i
\(732\) 0 0
\(733\) −2698.00 −0.135952 −0.0679761 0.997687i \(-0.521654\pi\)
−0.0679761 + 0.997687i \(0.521654\pi\)
\(734\) 0 0
\(735\) 954.000 + 1652.38i 0.0478759 + 0.0829236i
\(736\) 0 0
\(737\) −5310.50 9198.06i −0.265420 0.459721i
\(738\) 0 0
\(739\) 1420.50 2460.38i 0.0707090 0.122472i −0.828503 0.559984i \(-0.810807\pi\)
0.899212 + 0.437513i \(0.144141\pi\)
\(740\) 0 0
\(741\) 2925.00 10132.5i 0.145010 0.502330i
\(742\) 0 0
\(743\) −4595.50 + 7959.64i −0.226908 + 0.393016i −0.956890 0.290450i \(-0.906195\pi\)
0.729982 + 0.683466i \(0.239528\pi\)
\(744\) 0 0
\(745\) −855.000 1480.90i −0.0420467 0.0728270i
\(746\) 0 0
\(747\) 6588.00 + 11410.8i 0.322680 + 0.558899i
\(748\) 0 0
\(749\) −6385.00 −0.311486
\(750\) 0 0
\(751\) −829.500 + 1436.74i −0.0403048 + 0.0698099i −0.885474 0.464689i \(-0.846166\pi\)
0.845169 + 0.534499i \(0.179500\pi\)
\(752\) 0 0
\(753\) −6525.00 −0.315782
\(754\) 0 0
\(755\) −4128.00 −0.198985
\(756\) 0 0
\(757\) 6964.50 12062.9i 0.334384 0.579171i −0.648982 0.760804i \(-0.724805\pi\)
0.983366 + 0.181633i \(0.0581383\pi\)
\(758\) 0 0
\(759\) −7293.00 −0.348774
\(760\) 0 0
\(761\) −2293.50 3972.46i −0.109250 0.189227i 0.806217 0.591620i \(-0.201512\pi\)
−0.915467 + 0.402394i \(0.868178\pi\)
\(762\) 0 0
\(763\) −2065.00 3576.68i −0.0979791 0.169705i
\(764\) 0 0
\(765\) 486.000 841.777i 0.0229691 0.0397837i
\(766\) 0 0
\(767\) −22340.5 + 5527.84i −1.05172 + 0.260233i
\(768\) 0 0
\(769\) −7249.50 + 12556.5i −0.339953 + 0.588815i −0.984423 0.175814i \(-0.943744\pi\)
0.644471 + 0.764629i \(0.277078\pi\)
\(770\) 0 0
\(771\) 8527.50 + 14770.1i 0.398327 + 0.689923i
\(772\) 0 0
\(773\) −1529.50 2649.17i −0.0711673 0.123265i 0.828246 0.560365i \(-0.189339\pi\)
−0.899413 + 0.437100i \(0.856006\pi\)
\(774\) 0 0
\(775\) −12584.0 −0.583265
\(776\) 0 0
\(777\) −3172.50 + 5494.93i −0.146477 + 0.253706i
\(778\) 0 0
\(779\) −14625.0 −0.672651
\(780\) 0 0
\(781\) 1027.00 0.0470537
\(782\) 0 0
\(783\) −877.500 + 1519.87i −0.0400502 + 0.0693689i
\(784\) 0 0
\(785\) −3788.00 −0.172229
\(786\) 0 0
\(