Properties

Label 405.4.e.m.271.1
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
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] = [405,4,Mod(136,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.136");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (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: \(23.8957735523\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.m.136.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.50000 + 4.33013i) q^{2} +(-8.50000 + 14.7224i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-4.50000 - 7.79423i) q^{7} -45.0000 q^{8} +O(q^{10})\) \(q+(2.50000 + 4.33013i) q^{2} +(-8.50000 + 14.7224i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-4.50000 - 7.79423i) q^{7} -45.0000 q^{8} -25.0000 q^{10} +(4.00000 + 6.92820i) q^{11} +(-21.5000 + 37.2391i) q^{13} +(22.5000 - 38.9711i) q^{14} +(-44.5000 - 77.0763i) q^{16} -122.000 q^{17} -59.0000 q^{19} +(-42.5000 - 73.6122i) q^{20} +(-20.0000 + 34.6410i) q^{22} +(106.500 - 184.463i) q^{23} +(-12.5000 - 21.6506i) q^{25} -215.000 q^{26} +153.000 q^{28} +(-112.000 - 193.990i) q^{29} +(18.0000 - 31.1769i) q^{31} +(42.5000 - 73.6122i) q^{32} +(-305.000 - 528.275i) q^{34} +45.0000 q^{35} +206.000 q^{37} +(-147.500 - 255.477i) q^{38} +(112.500 - 194.856i) q^{40} +(-206.500 + 357.668i) q^{41} +(196.000 + 339.482i) q^{43} -136.000 q^{44} +1065.00 q^{46} +(155.500 + 269.334i) q^{47} +(131.000 - 226.899i) q^{49} +(62.5000 - 108.253i) q^{50} +(-365.500 - 633.065i) q^{52} -377.000 q^{53} -40.0000 q^{55} +(202.500 + 350.740i) q^{56} +(560.000 - 969.948i) q^{58} +(-168.500 + 291.851i) q^{59} +(-20.0000 - 34.6410i) q^{61} +180.000 q^{62} -287.000 q^{64} +(-107.500 - 186.195i) q^{65} +(-174.000 + 301.377i) q^{67} +(1037.00 - 1796.14i) q^{68} +(112.500 + 194.856i) q^{70} +62.0000 q^{71} -1214.00 q^{73} +(515.000 + 892.006i) q^{74} +(501.500 - 868.623i) q^{76} +(36.0000 - 62.3538i) q^{77} +(147.000 + 254.611i) q^{79} +445.000 q^{80} -2065.00 q^{82} +(-267.000 - 462.458i) q^{83} +(305.000 - 528.275i) q^{85} +(-980.000 + 1697.41i) q^{86} +(-180.000 - 311.769i) q^{88} -810.000 q^{89} +387.000 q^{91} +(1810.50 + 3135.88i) q^{92} +(-777.500 + 1346.67i) q^{94} +(147.500 - 255.477i) q^{95} +(464.000 + 803.672i) q^{97} +1310.00 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 5 q^{2} - 17 q^{4} - 5 q^{5} - 9 q^{7} - 90 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 5 q^{2} - 17 q^{4} - 5 q^{5} - 9 q^{7} - 90 q^{8} - 50 q^{10} + 8 q^{11} - 43 q^{13} + 45 q^{14} - 89 q^{16} - 244 q^{17} - 118 q^{19} - 85 q^{20} - 40 q^{22} + 213 q^{23} - 25 q^{25} - 430 q^{26} + 306 q^{28} - 224 q^{29} + 36 q^{31} + 85 q^{32} - 610 q^{34} + 90 q^{35} + 412 q^{37} - 295 q^{38} + 225 q^{40} - 413 q^{41} + 392 q^{43} - 272 q^{44} + 2130 q^{46} + 311 q^{47} + 262 q^{49} + 125 q^{50} - 731 q^{52} - 754 q^{53} - 80 q^{55} + 405 q^{56} + 1120 q^{58} - 337 q^{59} - 40 q^{61} + 360 q^{62} - 574 q^{64} - 215 q^{65} - 348 q^{67} + 2074 q^{68} + 225 q^{70} + 124 q^{71} - 2428 q^{73} + 1030 q^{74} + 1003 q^{76} + 72 q^{77} + 294 q^{79} + 890 q^{80} - 4130 q^{82} - 534 q^{83} + 610 q^{85} - 1960 q^{86} - 360 q^{88} - 1620 q^{89} + 774 q^{91} + 3621 q^{92} - 1555 q^{94} + 295 q^{95} + 928 q^{97} + 2620 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.50000 + 4.33013i 0.883883 + 1.53093i 0.846988 + 0.531612i \(0.178414\pi\)
0.0368954 + 0.999319i \(0.488253\pi\)
\(3\) 0 0
\(4\) −8.50000 + 14.7224i −1.06250 + 1.84030i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −4.50000 7.79423i −0.242977 0.420849i 0.718584 0.695440i \(-0.244791\pi\)
−0.961561 + 0.274592i \(0.911457\pi\)
\(8\) −45.0000 −1.98874
\(9\) 0 0
\(10\) −25.0000 −0.790569
\(11\) 4.00000 + 6.92820i 0.109640 + 0.189903i 0.915625 0.402034i \(-0.131697\pi\)
−0.805984 + 0.591937i \(0.798363\pi\)
\(12\) 0 0
\(13\) −21.5000 + 37.2391i −0.458694 + 0.794482i −0.998892 0.0470560i \(-0.985016\pi\)
0.540198 + 0.841538i \(0.318349\pi\)
\(14\) 22.5000 38.9711i 0.429527 0.743963i
\(15\) 0 0
\(16\) −44.5000 77.0763i −0.695312 1.20432i
\(17\) −122.000 −1.74055 −0.870275 0.492566i \(-0.836059\pi\)
−0.870275 + 0.492566i \(0.836059\pi\)
\(18\) 0 0
\(19\) −59.0000 −0.712396 −0.356198 0.934410i \(-0.615927\pi\)
−0.356198 + 0.934410i \(0.615927\pi\)
\(20\) −42.5000 73.6122i −0.475164 0.823009i
\(21\) 0 0
\(22\) −20.0000 + 34.6410i −0.193819 + 0.335704i
\(23\) 106.500 184.463i 0.965512 1.67232i 0.257280 0.966337i \(-0.417174\pi\)
0.708232 0.705980i \(-0.249493\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −215.000 −1.62173
\(27\) 0 0
\(28\) 153.000 1.03265
\(29\) −112.000 193.990i −0.717168 1.24217i −0.962117 0.272636i \(-0.912105\pi\)
0.244949 0.969536i \(-0.421229\pi\)
\(30\) 0 0
\(31\) 18.0000 31.1769i 0.104287 0.180630i −0.809160 0.587589i \(-0.800077\pi\)
0.913447 + 0.406958i \(0.133411\pi\)
\(32\) 42.5000 73.6122i 0.234782 0.406654i
\(33\) 0 0
\(34\) −305.000 528.275i −1.53844 2.66466i
\(35\) 45.0000 0.217325
\(36\) 0 0
\(37\) 206.000 0.915302 0.457651 0.889132i \(-0.348691\pi\)
0.457651 + 0.889132i \(0.348691\pi\)
\(38\) −147.500 255.477i −0.629675 1.09063i
\(39\) 0 0
\(40\) 112.500 194.856i 0.444695 0.770235i
\(41\) −206.500 + 357.668i −0.786582 + 1.36240i 0.141467 + 0.989943i \(0.454818\pi\)
−0.928049 + 0.372458i \(0.878515\pi\)
\(42\) 0 0
\(43\) 196.000 + 339.482i 0.695110 + 1.20397i 0.970144 + 0.242531i \(0.0779776\pi\)
−0.275034 + 0.961435i \(0.588689\pi\)
\(44\) −136.000 −0.465972
\(45\) 0 0
\(46\) 1065.00 3.41360
\(47\) 155.500 + 269.334i 0.482596 + 0.835881i 0.999800 0.0199813i \(-0.00636066\pi\)
−0.517204 + 0.855862i \(0.673027\pi\)
\(48\) 0 0
\(49\) 131.000 226.899i 0.381924 0.661512i
\(50\) 62.5000 108.253i 0.176777 0.306186i
\(51\) 0 0
\(52\) −365.500 633.065i −0.974726 1.68827i
\(53\) −377.000 −0.977074 −0.488537 0.872543i \(-0.662469\pi\)
−0.488537 + 0.872543i \(0.662469\pi\)
\(54\) 0 0
\(55\) −40.0000 −0.0980654
\(56\) 202.500 + 350.740i 0.483218 + 0.836958i
\(57\) 0 0
\(58\) 560.000 969.948i 1.26779 2.19587i
\(59\) −168.500 + 291.851i −0.371811 + 0.643995i −0.989844 0.142157i \(-0.954596\pi\)
0.618033 + 0.786152i \(0.287930\pi\)
\(60\) 0 0
\(61\) −20.0000 34.6410i −0.0419793 0.0727103i 0.844272 0.535914i \(-0.180033\pi\)
−0.886252 + 0.463204i \(0.846700\pi\)
\(62\) 180.000 0.368710
\(63\) 0 0
\(64\) −287.000 −0.560547
\(65\) −107.500 186.195i −0.205134 0.355303i
\(66\) 0 0
\(67\) −174.000 + 301.377i −0.317276 + 0.549538i −0.979919 0.199398i \(-0.936101\pi\)
0.662643 + 0.748936i \(0.269435\pi\)
\(68\) 1037.00 1796.14i 1.84933 3.20314i
\(69\) 0 0
\(70\) 112.500 + 194.856i 0.192090 + 0.332710i
\(71\) 62.0000 0.103634 0.0518172 0.998657i \(-0.483499\pi\)
0.0518172 + 0.998657i \(0.483499\pi\)
\(72\) 0 0
\(73\) −1214.00 −1.94641 −0.973205 0.229939i \(-0.926147\pi\)
−0.973205 + 0.229939i \(0.926147\pi\)
\(74\) 515.000 + 892.006i 0.809021 + 1.40127i
\(75\) 0 0
\(76\) 501.500 868.623i 0.756921 1.31103i
\(77\) 36.0000 62.3538i 0.0532803 0.0922841i
\(78\) 0 0
\(79\) 147.000 + 254.611i 0.209352 + 0.362608i 0.951511 0.307616i \(-0.0995313\pi\)
−0.742159 + 0.670224i \(0.766198\pi\)
\(80\) 445.000 0.621906
\(81\) 0 0
\(82\) −2065.00 −2.78099
\(83\) −267.000 462.458i −0.353097 0.611582i 0.633693 0.773584i \(-0.281538\pi\)
−0.986790 + 0.162002i \(0.948205\pi\)
\(84\) 0 0
\(85\) 305.000 528.275i 0.389199 0.674112i
\(86\) −980.000 + 1697.41i −1.22879 + 2.12833i
\(87\) 0 0
\(88\) −180.000 311.769i −0.218046 0.377667i
\(89\) −810.000 −0.964717 −0.482359 0.875974i \(-0.660220\pi\)
−0.482359 + 0.875974i \(0.660220\pi\)
\(90\) 0 0
\(91\) 387.000 0.445809
\(92\) 1810.50 + 3135.88i 2.05171 + 3.55367i
\(93\) 0 0
\(94\) −777.500 + 1346.67i −0.853117 + 1.47764i
\(95\) 147.500 255.477i 0.159297 0.275910i
\(96\) 0 0
\(97\) 464.000 + 803.672i 0.485691 + 0.841242i 0.999865 0.0164441i \(-0.00523456\pi\)
−0.514173 + 0.857686i \(0.671901\pi\)
\(98\) 1310.00 1.35031
\(99\) 0 0
\(100\) 425.000 0.425000
\(101\) 498.000 + 862.561i 0.490622 + 0.849783i 0.999942 0.0107948i \(-0.00343616\pi\)
−0.509319 + 0.860578i \(0.670103\pi\)
\(102\) 0 0
\(103\) 216.500 374.989i 0.207110 0.358726i −0.743693 0.668522i \(-0.766927\pi\)
0.950803 + 0.309796i \(0.100261\pi\)
\(104\) 967.500 1675.76i 0.912223 1.58002i
\(105\) 0 0
\(106\) −942.500 1632.46i −0.863620 1.49583i
\(107\) −1686.00 −1.52329 −0.761644 0.647996i \(-0.775607\pi\)
−0.761644 + 0.647996i \(0.775607\pi\)
\(108\) 0 0
\(109\) 656.000 0.576453 0.288227 0.957562i \(-0.406934\pi\)
0.288227 + 0.957562i \(0.406934\pi\)
\(110\) −100.000 173.205i −0.0866784 0.150131i
\(111\) 0 0
\(112\) −400.500 + 693.686i −0.337890 + 0.585243i
\(113\) −509.000 + 881.614i −0.423741 + 0.733940i −0.996302 0.0859216i \(-0.972617\pi\)
0.572561 + 0.819862i \(0.305950\pi\)
\(114\) 0 0
\(115\) 532.500 + 922.317i 0.431790 + 0.747883i
\(116\) 3808.00 3.04796
\(117\) 0 0
\(118\) −1685.00 −1.31455
\(119\) 549.000 + 950.896i 0.422914 + 0.732508i
\(120\) 0 0
\(121\) 633.500 1097.25i 0.475958 0.824383i
\(122\) 100.000 173.205i 0.0742096 0.128535i
\(123\) 0 0
\(124\) 306.000 + 530.008i 0.221610 + 0.383839i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1361.00 −0.950939 −0.475469 0.879732i \(-0.657722\pi\)
−0.475469 + 0.879732i \(0.657722\pi\)
\(128\) −1057.50 1831.64i −0.730240 1.26481i
\(129\) 0 0
\(130\) 537.500 930.977i 0.362630 0.628093i
\(131\) −955.500 + 1654.97i −0.637270 + 1.10378i 0.348759 + 0.937212i \(0.386603\pi\)
−0.986029 + 0.166572i \(0.946730\pi\)
\(132\) 0 0
\(133\) 265.500 + 459.859i 0.173096 + 0.299811i
\(134\) −1740.00 −1.12174
\(135\) 0 0
\(136\) 5490.00 3.46150
\(137\) −327.000 566.381i −0.203923 0.353206i 0.745866 0.666096i \(-0.232036\pi\)
−0.949789 + 0.312891i \(0.898703\pi\)
\(138\) 0 0
\(139\) 366.500 634.797i 0.223641 0.387358i −0.732270 0.681015i \(-0.761539\pi\)
0.955911 + 0.293657i \(0.0948723\pi\)
\(140\) −382.500 + 662.509i −0.230908 + 0.399945i
\(141\) 0 0
\(142\) 155.000 + 268.468i 0.0916008 + 0.158657i
\(143\) −344.000 −0.201166
\(144\) 0 0
\(145\) 1120.00 0.641455
\(146\) −3035.00 5256.77i −1.72040 2.97982i
\(147\) 0 0
\(148\) −1751.00 + 3032.82i −0.972509 + 1.68443i
\(149\) 563.000 975.145i 0.309549 0.536154i −0.668715 0.743519i \(-0.733155\pi\)
0.978264 + 0.207365i \(0.0664887\pi\)
\(150\) 0 0
\(151\) 1273.00 + 2204.90i 0.686061 + 1.18829i 0.973102 + 0.230375i \(0.0739952\pi\)
−0.287041 + 0.957918i \(0.592671\pi\)
\(152\) 2655.00 1.41677
\(153\) 0 0
\(154\) 360.000 0.188374
\(155\) 90.0000 + 155.885i 0.0466385 + 0.0807803i
\(156\) 0 0
\(157\) −611.500 + 1059.15i −0.310847 + 0.538403i −0.978546 0.206028i \(-0.933946\pi\)
0.667699 + 0.744432i \(0.267279\pi\)
\(158\) −735.000 + 1273.06i −0.370085 + 0.641006i
\(159\) 0 0
\(160\) 212.500 + 368.061i 0.104998 + 0.181861i
\(161\) −1917.00 −0.938390
\(162\) 0 0
\(163\) 3176.00 1.52616 0.763078 0.646306i \(-0.223687\pi\)
0.763078 + 0.646306i \(0.223687\pi\)
\(164\) −3510.50 6080.36i −1.67149 2.89510i
\(165\) 0 0
\(166\) 1335.00 2312.29i 0.624193 1.08113i
\(167\) −66.0000 + 114.315i −0.0305822 + 0.0529700i −0.880911 0.473281i \(-0.843069\pi\)
0.850329 + 0.526251i \(0.176403\pi\)
\(168\) 0 0
\(169\) 174.000 + 301.377i 0.0791989 + 0.137177i
\(170\) 3050.00 1.37603
\(171\) 0 0
\(172\) −6664.00 −2.95422
\(173\) 496.500 + 859.963i 0.218198 + 0.377929i 0.954257 0.298988i \(-0.0966489\pi\)
−0.736059 + 0.676917i \(0.763316\pi\)
\(174\) 0 0
\(175\) −112.500 + 194.856i −0.0485954 + 0.0841698i
\(176\) 356.000 616.610i 0.152469 0.264084i
\(177\) 0 0
\(178\) −2025.00 3507.40i −0.852698 1.47692i
\(179\) −3101.00 −1.29486 −0.647429 0.762126i \(-0.724156\pi\)
−0.647429 + 0.762126i \(0.724156\pi\)
\(180\) 0 0
\(181\) 2846.00 1.16874 0.584369 0.811488i \(-0.301342\pi\)
0.584369 + 0.811488i \(0.301342\pi\)
\(182\) 967.500 + 1675.76i 0.394043 + 0.682503i
\(183\) 0 0
\(184\) −4792.50 + 8300.85i −1.92015 + 3.32580i
\(185\) −515.000 + 892.006i −0.204668 + 0.354495i
\(186\) 0 0
\(187\) −488.000 845.241i −0.190835 0.330535i
\(188\) −5287.00 −2.05103
\(189\) 0 0
\(190\) 1475.00 0.563199
\(191\) −1540.00 2667.36i −0.583406 1.01049i −0.995072 0.0991537i \(-0.968386\pi\)
0.411666 0.911335i \(-0.364947\pi\)
\(192\) 0 0
\(193\) −1294.00 + 2241.27i −0.482612 + 0.835909i −0.999801 0.0199626i \(-0.993645\pi\)
0.517189 + 0.855872i \(0.326979\pi\)
\(194\) −2320.00 + 4018.36i −0.858589 + 1.48712i
\(195\) 0 0
\(196\) 2227.00 + 3857.28i 0.811589 + 1.40571i
\(197\) −1335.00 −0.482816 −0.241408 0.970424i \(-0.577609\pi\)
−0.241408 + 0.970424i \(0.577609\pi\)
\(198\) 0 0
\(199\) −5204.00 −1.85378 −0.926889 0.375336i \(-0.877527\pi\)
−0.926889 + 0.375336i \(0.877527\pi\)
\(200\) 562.500 + 974.279i 0.198874 + 0.344459i
\(201\) 0 0
\(202\) −2490.00 + 4312.81i −0.867306 + 1.50222i
\(203\) −1008.00 + 1745.91i −0.348511 + 0.603639i
\(204\) 0 0
\(205\) −1032.50 1788.34i −0.351770 0.609284i
\(206\) 2165.00 0.732246
\(207\) 0 0
\(208\) 3827.00 1.27574
\(209\) −236.000 408.764i −0.0781075 0.135286i
\(210\) 0 0
\(211\) −818.500 + 1417.68i −0.267051 + 0.462547i −0.968099 0.250568i \(-0.919383\pi\)
0.701048 + 0.713115i \(0.252716\pi\)
\(212\) 3204.50 5550.36i 1.03814 1.79811i
\(213\) 0 0
\(214\) −4215.00 7300.59i −1.34641 2.33205i
\(215\) −1960.00 −0.621725
\(216\) 0 0
\(217\) −324.000 −0.101357
\(218\) 1640.00 + 2840.56i 0.509518 + 0.882510i
\(219\) 0 0
\(220\) 340.000 588.897i 0.104195 0.180470i
\(221\) 2623.00 4543.17i 0.798380 1.38284i
\(222\) 0 0
\(223\) 2240.00 + 3879.79i 0.672652 + 1.16507i 0.977149 + 0.212555i \(0.0681784\pi\)
−0.304497 + 0.952513i \(0.598488\pi\)
\(224\) −765.000 −0.228186
\(225\) 0 0
\(226\) −5090.00 −1.49815
\(227\) 1868.00 + 3235.47i 0.546183 + 0.946017i 0.998531 + 0.0541753i \(0.0172530\pi\)
−0.452349 + 0.891841i \(0.649414\pi\)
\(228\) 0 0
\(229\) 690.000 1195.12i 0.199111 0.344871i −0.749129 0.662424i \(-0.769528\pi\)
0.948241 + 0.317553i \(0.102861\pi\)
\(230\) −2662.50 + 4611.59i −0.763305 + 1.32208i
\(231\) 0 0
\(232\) 5040.00 + 8729.54i 1.42626 + 2.47035i
\(233\) −2904.00 −0.816512 −0.408256 0.912867i \(-0.633863\pi\)
−0.408256 + 0.912867i \(0.633863\pi\)
\(234\) 0 0
\(235\) −1555.00 −0.431647
\(236\) −2864.50 4961.46i −0.790098 1.36849i
\(237\) 0 0
\(238\) −2745.00 + 4754.48i −0.747613 + 1.29490i
\(239\) 2983.00 5166.71i 0.807340 1.39835i −0.107360 0.994220i \(-0.534240\pi\)
0.914700 0.404133i \(-0.132427\pi\)
\(240\) 0 0
\(241\) 1609.00 + 2786.87i 0.430061 + 0.744888i 0.996878 0.0789557i \(-0.0251586\pi\)
−0.566817 + 0.823844i \(0.691825\pi\)
\(242\) 6335.00 1.68277
\(243\) 0 0
\(244\) 680.000 0.178412
\(245\) 655.000 + 1134.49i 0.170802 + 0.295837i
\(246\) 0 0
\(247\) 1268.50 2197.11i 0.326772 0.565986i
\(248\) −810.000 + 1402.96i −0.207399 + 0.359226i
\(249\) 0 0
\(250\) 312.500 + 541.266i 0.0790569 + 0.136931i
\(251\) 6123.00 1.53976 0.769881 0.638187i \(-0.220315\pi\)
0.769881 + 0.638187i \(0.220315\pi\)
\(252\) 0 0
\(253\) 1704.00 0.423437
\(254\) −3402.50 5893.30i −0.840519 1.45582i
\(255\) 0 0
\(256\) 4139.50 7169.82i 1.01062 1.75045i
\(257\) 699.000 1210.70i 0.169659 0.293858i −0.768641 0.639681i \(-0.779067\pi\)
0.938300 + 0.345822i \(0.112400\pi\)
\(258\) 0 0
\(259\) −927.000 1605.61i −0.222398 0.385204i
\(260\) 3655.00 0.871821
\(261\) 0 0
\(262\) −9555.00 −2.25309
\(263\) 1605.50 + 2780.81i 0.376423 + 0.651985i 0.990539 0.137232i \(-0.0438205\pi\)
−0.614116 + 0.789216i \(0.710487\pi\)
\(264\) 0 0
\(265\) 942.500 1632.46i 0.218480 0.378419i
\(266\) −1327.50 + 2299.30i −0.305993 + 0.529996i
\(267\) 0 0
\(268\) −2958.00 5123.41i −0.674211 1.16777i
\(269\) 4018.00 0.910713 0.455356 0.890309i \(-0.349512\pi\)
0.455356 + 0.890309i \(0.349512\pi\)
\(270\) 0 0
\(271\) 2314.00 0.518692 0.259346 0.965784i \(-0.416493\pi\)
0.259346 + 0.965784i \(0.416493\pi\)
\(272\) 5429.00 + 9403.30i 1.21023 + 2.09617i
\(273\) 0 0
\(274\) 1635.00 2831.90i 0.360489 0.624385i
\(275\) 100.000 173.205i 0.0219281 0.0379806i
\(276\) 0 0
\(277\) 2173.50 + 3764.61i 0.471455 + 0.816584i 0.999467 0.0326534i \(-0.0103957\pi\)
−0.528012 + 0.849237i \(0.677062\pi\)
\(278\) 3665.00 0.790691
\(279\) 0 0
\(280\) −2025.00 −0.432203
\(281\) −775.500 1343.21i −0.164635 0.285156i 0.771891 0.635755i \(-0.219311\pi\)
−0.936526 + 0.350599i \(0.885978\pi\)
\(282\) 0 0
\(283\) −2190.00 + 3793.19i −0.460007 + 0.796756i −0.998961 0.0455799i \(-0.985486\pi\)
0.538954 + 0.842335i \(0.318820\pi\)
\(284\) −527.000 + 912.791i −0.110112 + 0.190719i
\(285\) 0 0
\(286\) −860.000 1489.56i −0.177807 0.307971i
\(287\) 3717.00 0.764486
\(288\) 0 0
\(289\) 9971.00 2.02951
\(290\) 2800.00 + 4849.74i 0.566971 + 0.982023i
\(291\) 0 0
\(292\) 10319.0 17873.0i 2.06806 3.58199i
\(293\) −2524.50 + 4372.56i −0.503354 + 0.871836i 0.496638 + 0.867958i \(0.334568\pi\)
−0.999992 + 0.00387777i \(0.998766\pi\)
\(294\) 0 0
\(295\) −842.500 1459.25i −0.166279 0.288003i
\(296\) −9270.00 −1.82030
\(297\) 0 0
\(298\) 5630.00 1.09442
\(299\) 4579.50 + 7931.93i 0.885750 + 1.53416i
\(300\) 0 0
\(301\) 1764.00 3055.34i 0.337792 0.585072i
\(302\) −6365.00 + 11024.5i −1.21280 + 2.10063i
\(303\) 0 0
\(304\) 2625.50 + 4547.50i 0.495338 + 0.857951i
\(305\) 200.000 0.0375474
\(306\) 0 0
\(307\) 5428.00 1.00910 0.504548 0.863384i \(-0.331659\pi\)
0.504548 + 0.863384i \(0.331659\pi\)
\(308\) 612.000 + 1060.02i 0.113221 + 0.196104i
\(309\) 0 0
\(310\) −450.000 + 779.423i −0.0824461 + 0.142801i
\(311\) 9.00000 15.5885i 0.00164097 0.00284225i −0.865204 0.501420i \(-0.832811\pi\)
0.866845 + 0.498578i \(0.166144\pi\)
\(312\) 0 0
\(313\) 1058.00 + 1832.51i 0.191060 + 0.330925i 0.945602 0.325327i \(-0.105474\pi\)
−0.754542 + 0.656252i \(0.772141\pi\)
\(314\) −6115.00 −1.09901
\(315\) 0 0
\(316\) −4998.00 −0.889745
\(317\) −2207.50 3823.50i −0.391122 0.677443i 0.601476 0.798891i \(-0.294579\pi\)
−0.992598 + 0.121448i \(0.961246\pi\)
\(318\) 0 0
\(319\) 896.000 1551.92i 0.157261 0.272385i
\(320\) 717.500 1242.75i 0.125342 0.217099i
\(321\) 0 0
\(322\) −4792.50 8300.85i −0.829427 1.43661i
\(323\) 7198.00 1.23996
\(324\) 0 0
\(325\) 1075.00 0.183478
\(326\) 7940.00 + 13752.5i 1.34894 + 2.33644i
\(327\) 0 0
\(328\) 9292.50 16095.1i 1.56431 2.70946i
\(329\) 1399.50 2424.01i 0.234520 0.406200i
\(330\) 0 0
\(331\) −1740.00 3013.77i −0.288940 0.500458i 0.684617 0.728903i \(-0.259969\pi\)
−0.973557 + 0.228445i \(0.926636\pi\)
\(332\) 9078.00 1.50066
\(333\) 0 0
\(334\) −660.000 −0.108125
\(335\) −870.000 1506.88i −0.141890 0.245761i
\(336\) 0 0
\(337\) −3161.00 + 5475.01i −0.510951 + 0.884994i 0.488968 + 0.872302i \(0.337373\pi\)
−0.999919 + 0.0126922i \(0.995960\pi\)
\(338\) −870.000 + 1506.88i −0.140005 + 0.242496i
\(339\) 0 0
\(340\) 5185.00 + 8980.68i 0.827047 + 1.43249i
\(341\) 288.000 0.0457363
\(342\) 0 0
\(343\) −5445.00 −0.857150
\(344\) −8820.00 15276.7i −1.38239 2.39437i
\(345\) 0 0
\(346\) −2482.50 + 4299.82i −0.385723 + 0.668091i
\(347\) 5017.00 8689.70i 0.776158 1.34434i −0.157984 0.987442i \(-0.550499\pi\)
0.934142 0.356903i \(-0.116167\pi\)
\(348\) 0 0
\(349\) 1255.00 + 2173.72i 0.192489 + 0.333400i 0.946074 0.323949i \(-0.105011\pi\)
−0.753586 + 0.657350i \(0.771677\pi\)
\(350\) −1125.00 −0.171811
\(351\) 0 0
\(352\) 680.000 0.102966
\(353\) −1863.00 3226.81i −0.280899 0.486532i 0.690707 0.723135i \(-0.257299\pi\)
−0.971607 + 0.236603i \(0.923966\pi\)
\(354\) 0 0
\(355\) −155.000 + 268.468i −0.0231734 + 0.0401375i
\(356\) 6885.00 11925.2i 1.02501 1.77537i
\(357\) 0 0
\(358\) −7752.50 13427.7i −1.14450 1.98234i
\(359\) −10710.0 −1.57452 −0.787259 0.616622i \(-0.788501\pi\)
−0.787259 + 0.616622i \(0.788501\pi\)
\(360\) 0 0
\(361\) −3378.00 −0.492492
\(362\) 7115.00 + 12323.5i 1.03303 + 1.78926i
\(363\) 0 0
\(364\) −3289.50 + 5697.58i −0.473672 + 0.820424i
\(365\) 3035.00 5256.77i 0.435231 0.753841i
\(366\) 0 0
\(367\) 1080.00 + 1870.61i 0.153612 + 0.266063i 0.932553 0.361034i \(-0.117576\pi\)
−0.778941 + 0.627097i \(0.784243\pi\)
\(368\) −18957.0 −2.68533
\(369\) 0 0
\(370\) −5150.00 −0.723610
\(371\) 1696.50 + 2938.42i 0.237407 + 0.411200i
\(372\) 0 0
\(373\) −1697.00 + 2939.29i −0.235569 + 0.408018i −0.959438 0.281920i \(-0.909029\pi\)
0.723869 + 0.689938i \(0.242362\pi\)
\(374\) 2440.00 4226.20i 0.337351 0.584310i
\(375\) 0 0
\(376\) −6997.50 12120.0i −0.959757 1.66235i
\(377\) 9632.00 1.31584
\(378\) 0 0
\(379\) 9031.00 1.22399 0.611994 0.790863i \(-0.290368\pi\)
0.611994 + 0.790863i \(0.290368\pi\)
\(380\) 2507.50 + 4343.12i 0.338505 + 0.586308i
\(381\) 0 0
\(382\) 7700.00 13336.8i 1.03133 1.78631i
\(383\) 5152.50 8924.39i 0.687416 1.19064i −0.285255 0.958452i \(-0.592078\pi\)
0.972671 0.232188i \(-0.0745885\pi\)
\(384\) 0 0
\(385\) 180.000 + 311.769i 0.0238277 + 0.0412707i
\(386\) −12940.0 −1.70629
\(387\) 0 0
\(388\) −15776.0 −2.06419
\(389\) 1740.00 + 3013.77i 0.226790 + 0.392813i 0.956855 0.290565i \(-0.0938434\pi\)
−0.730065 + 0.683378i \(0.760510\pi\)
\(390\) 0 0
\(391\) −12993.0 + 22504.5i −1.68052 + 2.91075i
\(392\) −5895.00 + 10210.4i −0.759547 + 1.31557i
\(393\) 0 0
\(394\) −3337.50 5780.72i −0.426753 0.739158i
\(395\) −1470.00 −0.187250
\(396\) 0 0
\(397\) 3706.00 0.468511 0.234255 0.972175i \(-0.424735\pi\)
0.234255 + 0.972175i \(0.424735\pi\)
\(398\) −13010.0 22534.0i −1.63852 2.83801i
\(399\) 0 0
\(400\) −1112.50 + 1926.91i −0.139063 + 0.240863i
\(401\) −1339.50 + 2320.08i −0.166812 + 0.288926i −0.937297 0.348531i \(-0.886680\pi\)
0.770486 + 0.637457i \(0.220014\pi\)
\(402\) 0 0
\(403\) 774.000 + 1340.61i 0.0956717 + 0.165708i
\(404\) −16932.0 −2.08514
\(405\) 0 0
\(406\) −10080.0 −1.23217
\(407\) 824.000 + 1427.21i 0.100354 + 0.173819i
\(408\) 0 0
\(409\) 6249.50 10824.5i 0.755545 1.30864i −0.189558 0.981870i \(-0.560706\pi\)
0.945103 0.326773i \(-0.105961\pi\)
\(410\) 5162.50 8941.71i 0.621848 1.07707i
\(411\) 0 0
\(412\) 3680.50 + 6374.81i 0.440110 + 0.762292i
\(413\) 3033.00 0.361366
\(414\) 0 0
\(415\) 2670.00 0.315820
\(416\) 1827.50 + 3165.32i 0.215386 + 0.373059i
\(417\) 0 0
\(418\) 1180.00 2043.82i 0.138076 0.239154i
\(419\) 464.000 803.672i 0.0541000 0.0937039i −0.837707 0.546120i \(-0.816104\pi\)
0.891807 + 0.452416i \(0.149438\pi\)
\(420\) 0 0
\(421\) −3785.00 6555.81i −0.438170 0.758933i 0.559378 0.828912i \(-0.311040\pi\)
−0.997548 + 0.0699796i \(0.977707\pi\)
\(422\) −8185.00 −0.944170
\(423\) 0 0
\(424\) 16965.0 1.94314
\(425\) 1525.00 + 2641.38i 0.174055 + 0.301472i
\(426\) 0 0
\(427\) −180.000 + 311.769i −0.0204000 + 0.0353339i
\(428\) 14331.0 24822.0i 1.61849 2.80331i
\(429\) 0 0
\(430\) −4900.00 8487.05i −0.549533 0.951818i
\(431\) −2460.00 −0.274928 −0.137464 0.990507i \(-0.543895\pi\)
−0.137464 + 0.990507i \(0.543895\pi\)
\(432\) 0 0
\(433\) 1648.00 0.182905 0.0914525 0.995809i \(-0.470849\pi\)
0.0914525 + 0.995809i \(0.470849\pi\)
\(434\) −810.000 1402.96i −0.0895881 0.155171i
\(435\) 0 0
\(436\) −5576.00 + 9657.92i −0.612482 + 1.06085i
\(437\) −6283.50 + 10883.3i −0.687827 + 1.19135i
\(438\) 0 0
\(439\) −7913.00 13705.7i −0.860289 1.49006i −0.871650 0.490129i \(-0.836950\pi\)
0.0113610 0.999935i \(-0.496384\pi\)
\(440\) 1800.00 0.195026
\(441\) 0 0
\(442\) 26230.0 2.82270
\(443\) −6387.00 11062.6i −0.685001 1.18646i −0.973436 0.228957i \(-0.926468\pi\)
0.288435 0.957499i \(-0.406865\pi\)
\(444\) 0 0
\(445\) 2025.00 3507.40i 0.215717 0.373633i
\(446\) −11200.0 + 19399.0i −1.18909 + 2.05957i
\(447\) 0 0
\(448\) 1291.50 + 2236.94i 0.136200 + 0.235905i
\(449\) 8875.00 0.932822 0.466411 0.884568i \(-0.345547\pi\)
0.466411 + 0.884568i \(0.345547\pi\)
\(450\) 0 0
\(451\) −3304.00 −0.344965
\(452\) −8653.00 14987.4i −0.900449 1.55962i
\(453\) 0 0
\(454\) −9340.00 + 16177.4i −0.965524 + 1.67234i
\(455\) −967.500 + 1675.76i −0.0996859 + 0.172661i
\(456\) 0 0
\(457\) −5762.00 9980.08i −0.589792 1.02155i −0.994259 0.106997i \(-0.965876\pi\)
0.404467 0.914553i \(-0.367457\pi\)
\(458\) 6900.00 0.703965
\(459\) 0 0
\(460\) −18105.0 −1.83511
\(461\) 4272.00 + 7399.32i 0.431598 + 0.747550i 0.997011 0.0772577i \(-0.0246164\pi\)
−0.565413 + 0.824808i \(0.691283\pi\)
\(462\) 0 0
\(463\) −1261.50 + 2184.98i −0.126624 + 0.219319i −0.922367 0.386316i \(-0.873747\pi\)
0.795743 + 0.605635i \(0.207081\pi\)
\(464\) −9968.00 + 17265.1i −0.997312 + 1.72740i
\(465\) 0 0
\(466\) −7260.00 12574.7i −0.721702 1.25002i
\(467\) −2902.00 −0.287556 −0.143778 0.989610i \(-0.545925\pi\)
−0.143778 + 0.989610i \(0.545925\pi\)
\(468\) 0 0
\(469\) 3132.00 0.308363
\(470\) −3887.50 6733.35i −0.381526 0.660822i
\(471\) 0 0
\(472\) 7582.50 13133.3i 0.739434 1.28074i
\(473\) −1568.00 + 2715.86i −0.152424 + 0.264007i
\(474\) 0 0
\(475\) 737.500 + 1277.39i 0.0712396 + 0.123391i
\(476\) −18666.0 −1.79738
\(477\) 0 0
\(478\) 29830.0 2.85438
\(479\) −2181.00 3777.60i −0.208043 0.360340i 0.743055 0.669230i \(-0.233376\pi\)
−0.951098 + 0.308890i \(0.900043\pi\)
\(480\) 0 0
\(481\) −4429.00 + 7671.25i −0.419844 + 0.727191i
\(482\) −8045.00 + 13934.3i −0.760248 + 1.31679i
\(483\) 0 0
\(484\) 10769.5 + 18653.3i 1.01141 + 1.75181i
\(485\) −4640.00 −0.434416
\(486\) 0 0
\(487\) 5723.00 0.532513 0.266257 0.963902i \(-0.414213\pi\)
0.266257 + 0.963902i \(0.414213\pi\)
\(488\) 900.000 + 1558.85i 0.0834858 + 0.144602i
\(489\) 0 0
\(490\) −3275.00 + 5672.47i −0.301938 + 0.522971i
\(491\) 6669.50 11551.9i 0.613015 1.06177i −0.377714 0.925922i \(-0.623290\pi\)
0.990729 0.135851i \(-0.0433768\pi\)
\(492\) 0 0
\(493\) 13664.0 + 23666.7i 1.24827 + 2.16206i
\(494\) 12685.0 1.15531
\(495\) 0 0
\(496\) −3204.00 −0.290048
\(497\) −279.000 483.242i −0.0251808 0.0436144i
\(498\) 0 0
\(499\) 9818.50 17006.1i 0.880835 1.52565i 0.0304198 0.999537i \(-0.490316\pi\)
0.850415 0.526113i \(-0.176351\pi\)
\(500\) −1062.50 + 1840.30i −0.0950329 + 0.164602i
\(501\) 0 0
\(502\) 15307.5 + 26513.4i 1.36097 + 2.35727i
\(503\) −5416.00 −0.480094 −0.240047 0.970761i \(-0.577163\pi\)
−0.240047 + 0.970761i \(0.577163\pi\)
\(504\) 0 0
\(505\) −4980.00 −0.438826
\(506\) 4260.00 + 7378.54i 0.374269 + 0.648253i
\(507\) 0 0
\(508\) 11568.5 20037.2i 1.01037 1.75002i
\(509\) 3055.00 5291.42i 0.266032 0.460782i −0.701801 0.712373i \(-0.747621\pi\)
0.967834 + 0.251591i \(0.0809538\pi\)
\(510\) 0 0
\(511\) 5463.00 + 9462.19i 0.472933 + 0.819144i
\(512\) 24475.0 2.11260
\(513\) 0 0
\(514\) 6990.00 0.599836
\(515\) 1082.50 + 1874.94i 0.0926226 + 0.160427i
\(516\) 0 0
\(517\) −1244.00 + 2154.67i −0.105824 + 0.183293i
\(518\) 4635.00 8028.06i 0.393147 0.680951i
\(519\) 0 0
\(520\) 4837.50 + 8378.80i 0.407958 + 0.706605i
\(521\) 20375.0 1.71333 0.856665 0.515873i \(-0.172532\pi\)
0.856665 + 0.515873i \(0.172532\pi\)
\(522\) 0 0
\(523\) −19010.0 −1.58939 −0.794693 0.607011i \(-0.792368\pi\)
−0.794693 + 0.607011i \(0.792368\pi\)
\(524\) −16243.5 28134.6i −1.35420 2.34554i
\(525\) 0 0
\(526\) −8027.50 + 13904.0i −0.665429 + 1.15256i
\(527\) −2196.00 + 3803.58i −0.181517 + 0.314396i
\(528\) 0 0
\(529\) −16601.0 28753.8i −1.36443 2.36326i
\(530\) 9425.00 0.772445
\(531\) 0 0
\(532\) −9027.00 −0.735658
\(533\) −8879.50 15379.7i −0.721602 1.24985i
\(534\) 0 0
\(535\) 4215.00 7300.59i 0.340617 0.589967i
\(536\) 7830.00 13562.0i 0.630979 1.09289i
\(537\) 0 0
\(538\) 10045.0 + 17398.5i 0.804964 + 1.39424i
\(539\) 2096.00 0.167497
\(540\) 0 0
\(541\) 3288.00 0.261298 0.130649 0.991429i \(-0.458294\pi\)
0.130649 + 0.991429i \(0.458294\pi\)
\(542\) 5785.00 + 10019.9i 0.458463 + 0.794081i
\(543\) 0 0
\(544\) −5185.00 + 8980.68i −0.408649 + 0.707801i
\(545\) −1640.00 + 2840.56i −0.128899 + 0.223259i
\(546\) 0 0
\(547\) −1628.00 2819.78i −0.127255 0.220411i 0.795357 0.606141i \(-0.207283\pi\)
−0.922612 + 0.385729i \(0.873950\pi\)
\(548\) 11118.0 0.866674
\(549\) 0 0
\(550\) 1000.00 0.0775275
\(551\) 6608.00 + 11445.4i 0.510908 + 0.884918i
\(552\) 0 0
\(553\) 1323.00 2291.50i 0.101735 0.176211i
\(554\) −10867.5 + 18823.1i −0.833422 + 1.44353i
\(555\) 0 0
\(556\) 6230.50 + 10791.5i 0.475238 + 0.823136i
\(557\) 213.000 0.0162031 0.00810153 0.999967i \(-0.497421\pi\)
0.00810153 + 0.999967i \(0.497421\pi\)
\(558\) 0 0
\(559\) −16856.0 −1.27537
\(560\) −2002.50 3468.43i −0.151109 0.261729i
\(561\) 0 0
\(562\) 3877.50 6716.03i 0.291036 0.504090i
\(563\) −8694.00 + 15058.4i −0.650814 + 1.12724i 0.332111 + 0.943240i \(0.392239\pi\)
−0.982926 + 0.184003i \(0.941094\pi\)
\(564\) 0 0
\(565\) −2545.00 4408.07i −0.189503 0.328228i
\(566\) −21900.0 −1.62637
\(567\) 0 0
\(568\) −2790.00 −0.206102
\(569\) 2176.50 + 3769.81i 0.160358 + 0.277748i 0.934997 0.354655i \(-0.115402\pi\)
−0.774639 + 0.632403i \(0.782069\pi\)
\(570\) 0 0
\(571\) 962.000 1666.23i 0.0705052 0.122119i −0.828618 0.559815i \(-0.810872\pi\)
0.899123 + 0.437696i \(0.144206\pi\)
\(572\) 2924.00 5064.52i 0.213739 0.370206i
\(573\) 0 0
\(574\) 9292.50 + 16095.1i 0.675717 + 1.17038i
\(575\) −5325.00 −0.386205
\(576\) 0 0
\(577\) 16832.0 1.21443 0.607214 0.794538i \(-0.292287\pi\)
0.607214 + 0.794538i \(0.292287\pi\)
\(578\) 24927.5 + 43175.7i 1.79385 + 3.10705i
\(579\) 0 0
\(580\) −9520.00 + 16489.1i −0.681546 + 1.18047i
\(581\) −2403.00 + 4162.12i −0.171589 + 0.297201i
\(582\) 0 0
\(583\) −1508.00 2611.93i −0.107127 0.185549i
\(584\) 54630.0 3.87090
\(585\) 0 0
\(586\) −25245.0 −1.77963
\(587\) 1053.00 + 1823.85i 0.0740408 + 0.128242i 0.900669 0.434506i \(-0.143077\pi\)
−0.826628 + 0.562749i \(0.809744\pi\)
\(588\) 0 0
\(589\) −1062.00 + 1839.44i −0.0742936 + 0.128680i
\(590\) 4212.50 7296.26i 0.293942 0.509123i
\(591\) 0 0
\(592\) −9167.00 15877.7i −0.636421 1.10231i
\(593\) 4694.00 0.325058 0.162529 0.986704i \(-0.448035\pi\)
0.162529 + 0.986704i \(0.448035\pi\)
\(594\) 0 0
\(595\) −5490.00 −0.378266
\(596\) 9571.00 + 16577.5i 0.657791 + 1.13933i
\(597\) 0 0
\(598\) −22897.5 + 39659.6i −1.56580 + 2.71205i
\(599\) −6613.00 + 11454.1i −0.451085 + 0.781302i −0.998454 0.0555895i \(-0.982296\pi\)
0.547369 + 0.836892i \(0.315630\pi\)
\(600\) 0 0
\(601\) 6645.50 + 11510.3i 0.451041 + 0.781226i 0.998451 0.0556387i \(-0.0177195\pi\)
−0.547410 + 0.836865i \(0.684386\pi\)
\(602\) 17640.0 1.19427
\(603\) 0 0
\(604\) −43282.0 −2.91576
\(605\) 3167.50 + 5486.27i 0.212855 + 0.368675i
\(606\) 0 0
\(607\) −3020.00 + 5230.79i −0.201941 + 0.349772i −0.949154 0.314813i \(-0.898058\pi\)
0.747213 + 0.664585i \(0.231392\pi\)
\(608\) −2507.50 + 4343.12i −0.167257 + 0.289698i
\(609\) 0 0
\(610\) 500.000 + 866.025i 0.0331876 + 0.0574825i
\(611\) −13373.0 −0.885456
\(612\) 0 0
\(613\) −23.0000 −0.00151543 −0.000757717 1.00000i \(-0.500241\pi\)
−0.000757717 1.00000i \(0.500241\pi\)
\(614\) 13570.0 + 23503.9i 0.891923 + 1.54486i
\(615\) 0 0
\(616\) −1620.00 + 2805.92i −0.105960 + 0.183529i
\(617\) 1509.00 2613.66i 0.0984604 0.170538i −0.812587 0.582840i \(-0.801942\pi\)
0.911048 + 0.412301i \(0.135275\pi\)
\(618\) 0 0
\(619\) 4719.50 + 8174.41i 0.306450 + 0.530787i 0.977583 0.210550i \(-0.0675253\pi\)
−0.671133 + 0.741337i \(0.734192\pi\)
\(620\) −3060.00 −0.198214
\(621\) 0 0
\(622\) 90.0000 0.00580172
\(623\) 3645.00 + 6313.33i 0.234404 + 0.406000i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −5290.00 + 9162.55i −0.337749 + 0.584999i
\(627\) 0 0
\(628\) −10395.5 18005.5i −0.660550 1.14411i
\(629\) −25132.0 −1.59313
\(630\) 0 0
\(631\) −9800.00 −0.618275 −0.309138 0.951017i \(-0.600040\pi\)
−0.309138 + 0.951017i \(0.600040\pi\)
\(632\) −6615.00 11457.5i −0.416346 0.721132i
\(633\) 0 0
\(634\) 11037.5 19117.5i 0.691412 1.19756i
\(635\) 3402.50 5893.30i 0.212636 0.368297i
\(636\) 0 0
\(637\) 5633.00 + 9756.64i 0.350373 + 0.606864i
\(638\) 8960.00 0.556003
\(639\) 0 0
\(640\) 10575.0 0.653146
\(641\) −11721.0 20301.4i −0.722233 1.25095i −0.960103 0.279648i \(-0.909782\pi\)
0.237869 0.971297i \(-0.423551\pi\)
\(642\) 0 0
\(643\) −15654.0 + 27113.5i −0.960083 + 1.66291i −0.237802 + 0.971314i \(0.576427\pi\)
−0.722282 + 0.691599i \(0.756907\pi\)
\(644\) 16294.5 28222.9i 0.997039 1.72692i
\(645\) 0 0
\(646\) 17995.0 + 31168.3i 1.09598 + 1.89829i
\(647\) 712.000 0.0432637 0.0216318 0.999766i \(-0.493114\pi\)
0.0216318 + 0.999766i \(0.493114\pi\)
\(648\) 0 0
\(649\) −2696.00 −0.163062
\(650\) 2687.50 + 4654.89i 0.162173 + 0.280892i
\(651\) 0 0
\(652\) −26996.0 + 46758.4i −1.62154 + 2.80859i
\(653\) −15739.0 + 27260.7i −0.943208 + 1.63368i −0.183907 + 0.982944i \(0.558875\pi\)
−0.759301 + 0.650740i \(0.774459\pi\)
\(654\) 0 0
\(655\) −4777.50 8274.87i −0.284996 0.493628i
\(656\) 36757.0 2.18768
\(657\) 0 0
\(658\) 13995.0 0.829152
\(659\) 8060.50 + 13961.2i 0.476468 + 0.825267i 0.999636 0.0269624i \(-0.00858343\pi\)
−0.523168 + 0.852229i \(0.675250\pi\)
\(660\) 0 0
\(661\) 9580.00 16593.0i 0.563720 0.976391i −0.433448 0.901179i \(-0.642703\pi\)
0.997168 0.0752127i \(-0.0239636\pi\)
\(662\) 8700.00 15068.8i 0.510778 0.884694i
\(663\) 0 0
\(664\) 12015.0 + 20810.6i 0.702218 + 1.21628i
\(665\) −2655.00 −0.154822
\(666\) 0 0
\(667\) −47712.0 −2.76974
\(668\) −1122.00 1943.36i −0.0649873 0.112561i
\(669\) 0 0
\(670\) 4350.00 7534.42i 0.250829 0.434448i
\(671\) 160.000 277.128i 0.00920526 0.0159440i
\(672\) 0 0
\(673\) 6711.00 + 11623.8i 0.384383 + 0.665772i 0.991683 0.128701i \(-0.0410807\pi\)
−0.607300 + 0.794473i \(0.707747\pi\)
\(674\) −31610.0 −1.80649
\(675\) 0 0
\(676\) −5916.00 −0.336595
\(677\) −12952.5 22434.4i −0.735310 1.27359i −0.954587 0.297932i \(-0.903703\pi\)
0.219277 0.975663i \(-0.429630\pi\)
\(678\) 0 0
\(679\) 4176.00 7233.04i 0.236024 0.408805i
\(680\) −13725.0 + 23772.4i −0.774014 + 1.34063i
\(681\) 0 0
\(682\) 720.000 + 1247.08i 0.0404255 + 0.0700191i
\(683\) −9246.00 −0.517992 −0.258996 0.965878i \(-0.583392\pi\)
−0.258996 + 0.965878i \(0.583392\pi\)
\(684\) 0 0
\(685\) 3270.00 0.182395
\(686\) −13612.5 23577.5i −0.757621 1.31224i
\(687\) 0 0
\(688\) 17444.0 30213.9i 0.966637 1.67426i
\(689\) 8105.50 14039.1i 0.448178 0.776268i
\(690\) 0 0
\(691\) −12519.5 21684.4i −0.689239 1.19380i −0.972084 0.234632i \(-0.924612\pi\)
0.282845 0.959166i \(-0.408722\pi\)
\(692\) −16881.0 −0.927340
\(693\) 0 0
\(694\) 50170.0 2.74413
\(695\) 1832.50 + 3173.98i 0.100015 + 0.173232i
\(696\) 0 0
\(697\) 25193.0 43635.6i 1.36909 2.37133i
\(698\) −6275.00 + 10868.6i −0.340275 + 0.589374i
\(699\) 0 0
\(700\) −1912.50 3312.55i −0.103265 0.178861i
\(701\) 32930.0 1.77425 0.887125 0.461530i \(-0.152699\pi\)
0.887125 + 0.461530i \(0.152699\pi\)
\(702\) 0 0
\(703\) −12154.0 −0.652058
\(704\) −1148.00 1988.39i −0.0614586 0.106449i
\(705\) 0 0
\(706\) 9315.00 16134.1i 0.496565 0.860075i
\(707\) 4482.00 7763.05i 0.238420 0.412956i
\(708\) 0 0
\(709\) −941.000 1629.86i −0.0498448 0.0863338i 0.840026 0.542545i \(-0.182539\pi\)
−0.889871 + 0.456212i \(0.849206\pi\)
\(710\) −1550.00 −0.0819302
\(711\) 0 0
\(712\) 36450.0 1.91857
\(713\) −3834.00 6640.68i −0.201381 0.348802i
\(714\) 0 0
\(715\) 860.000 1489.56i 0.0449821 0.0779112i
\(716\) 26358.5 45654.3i 1.37579 2.38293i
\(717\) 0 0
\(718\) −26775.0 46375.7i −1.39169 2.41048i
\(719\) −1962.00 −0.101767 −0.0508833 0.998705i \(-0.516204\pi\)
−0.0508833 + 0.998705i \(0.516204\pi\)
\(720\) 0 0
\(721\) −3897.00 −0.201292
\(722\) −8445.00 14627.2i −0.435305 0.753971i
\(723\) 0 0
\(724\) −24191.0 + 41900.0i −1.24178 + 2.15083i
\(725\) −2800.00 + 4849.74i −0.143434 + 0.248434i
\(726\) 0 0
\(727\) 6870.50 + 11900.1i 0.350499 + 0.607082i 0.986337 0.164741i \(-0.0526787\pi\)
−0.635838 + 0.771823i \(0.719345\pi\)
\(728\) −17415.0 −0.886597
\(729\) 0 0
\(730\) 30350.0 1.53877
\(731\) −23912.0 41416.8i −1.20987 2.09556i
\(732\) 0 0
\(733\) 16229.0 28109.5i 0.817779 1.41643i −0.0895367 0.995984i \(-0.528539\pi\)
0.907315 0.420451i \(-0.138128\pi\)
\(734\) −5400.00 + 9353.07i −0.271550 + 0.470338i
\(735\) 0 0
\(736\) −9052.50 15679.4i −0.453369 0.785258i
\(737\) −2784.00 −0.139145
\(738\) 0 0
\(739\) 19612.0 0.976237 0.488118 0.872777i \(-0.337683\pi\)
0.488118 + 0.872777i \(0.337683\pi\)
\(740\) −8755.00 15164.1i −0.434919 0.753302i
\(741\) 0 0
\(742\) −8482.50 + 14692.1i −0.419680 + 0.726907i
\(743\) −18368.0 + 31814.3i −0.906940 + 1.57087i −0.0886488 + 0.996063i \(0.528255\pi\)
−0.818291 + 0.574804i \(0.805078\pi\)
\(744\) 0 0
\(745\) 2815.00 + 4875.72i 0.138434 + 0.239775i
\(746\) −16970.0 −0.832863
\(747\) 0 0
\(748\) 16592.0 0.811048
\(749\) 7587.00 + 13141.1i 0.370124 + 0.641074i
\(750\) 0 0
\(751\) 1873.00 3244.13i 0.0910076 0.157630i −0.816928 0.576740i \(-0.804325\pi\)
0.907935 + 0.419110i \(0.137658\pi\)
\(752\) 13839.5 23970.7i 0.671110 1.16240i
\(753\) 0 0
\(754\) 24080.0 + 41707.8i 1.16305 + 2.01447i
\(755\) −12730.0 −0.613632
\(756\) 0 0
\(757\) 5725.00 0.274873 0.137436 0.990511i \(-0.456114\pi\)
0.137436 + 0.990511i \(0.456114\pi\)
\(758\) 22577.5 + 39105.4i 1.08186 + 1.87384i
\(759\) 0 0
\(760\) −6637.50 + 11496.5i −0.316799 + 0.548712i
\(761\) −18661.5 + 32322.7i −0.888934 + 1.53968i −0.0477970 + 0.998857i \(0.515220\pi\)
−0.841137 + 0.540822i \(0.818113\pi\)
\(762\) 0 0
\(763\) −2952.00 5113.01i −0.140065 0.242600i
\(764\) 52360.0 2.47947
\(765\) 0 0
\(766\) 51525.0 2.43038
\(767\) −7245.50 12549.6i −0.341095 0.590794i
\(768\) 0 0
\(769\) 12293.0 21292.1i 0.576459 0.998456i −0.419423 0.907791i \(-0.637767\pi\)
0.995881 0.0906650i \(-0.0288993\pi\)
\(770\) −900.000 + 1558.85i −0.0421218 + 0.0729570i
\(771\) 0 0
\(772\) −21998.0 38101.7i −1.02555 1.77631i
\(773\) −3078.00 −0.143219 −0.0716093 0.997433i \(-0.522813\pi\)
−0.0716093 + 0.997433i \(0.522813\pi\)
\(774\) 0 0
\(775\) −900.000 −0.0417148
\(776\) −20880.0 36165.2i −0.965913 1.67301i
\(777\) 0 0
\(778\) −8700.00 + 15068.8i −0.400913 + 0.694401i