Properties

Label 225.4.h.a.91.5
Level $225$
Weight $4$
Character 225.91
Analytic conductor $13.275$
Analytic rank $0$
Dimension $28$
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] = [225,4,Mod(46,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.46");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.5
Character \(\chi\) \(=\) 225.91
Dual form 225.4.h.a.136.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.08389 + 0.787491i) q^{2} +(-1.91746 - 5.90135i) q^{4} +(3.83217 - 10.5031i) q^{5} -12.2101 q^{7} +(5.88101 - 18.0999i) q^{8} +O(q^{10})\) \(q+(1.08389 + 0.787491i) q^{2} +(-1.91746 - 5.90135i) q^{4} +(3.83217 - 10.5031i) q^{5} -12.2101 q^{7} +(5.88101 - 18.0999i) q^{8} +(12.4247 - 8.36635i) q^{10} +(-2.00821 - 1.45905i) q^{11} +(-69.2682 + 50.3263i) q^{13} +(-13.2344 - 9.61535i) q^{14} +(-19.5320 + 14.1909i) q^{16} +(1.71458 - 5.27694i) q^{17} +(-7.45887 + 22.9561i) q^{19} +(-69.3303 - 2.47571i) q^{20} +(-1.02769 - 3.16290i) q^{22} +(-83.6143 - 60.7493i) q^{23} +(-95.6289 - 80.4991i) q^{25} -114.710 q^{26} +(23.4124 + 72.0561i) q^{28} +(35.3035 + 108.653i) q^{29} +(47.5487 - 146.340i) q^{31} -184.596 q^{32} +(6.01395 - 4.36939i) q^{34} +(-46.7912 + 128.244i) q^{35} +(277.229 - 201.419i) q^{37} +(-26.1623 + 19.0080i) q^{38} +(-167.567 - 131.130i) q^{40} +(28.0530 - 20.3817i) q^{41} -154.740 q^{43} +(-4.75970 + 14.6489i) q^{44} +(-42.7890 - 131.691i) q^{46} +(-104.613 - 321.965i) q^{47} -193.913 q^{49} +(-40.2588 - 162.559i) q^{50} +(429.812 + 312.277i) q^{52} +(-199.512 - 614.036i) q^{53} +(-23.0204 + 15.5011i) q^{55} +(-71.8077 + 221.001i) q^{56} +(-47.2982 + 145.569i) q^{58} +(536.260 - 389.616i) q^{59} +(289.370 + 210.239i) q^{61} +(166.779 - 121.172i) q^{62} +(-43.8256 - 31.8411i) q^{64} +(263.133 + 920.387i) q^{65} +(-164.205 + 505.370i) q^{67} -34.4287 q^{68} +(-151.707 + 102.154i) q^{70} +(196.164 + 603.732i) q^{71} +(-779.001 - 565.977i) q^{73} +459.101 q^{74} +149.774 q^{76} +(24.5205 + 17.8152i) q^{77} +(175.752 + 540.908i) q^{79} +(74.1975 + 259.528i) q^{80} +46.4568 q^{82} +(98.8352 - 304.184i) q^{83} +(-48.8535 - 38.2305i) q^{85} +(-167.721 - 121.856i) q^{86} +(-38.2190 + 27.7677i) q^{88} +(-1079.81 - 784.525i) q^{89} +(845.772 - 614.489i) q^{91} +(-198.176 + 609.922i) q^{92} +(140.156 - 431.355i) q^{94} +(212.525 + 166.313i) q^{95} +(123.390 + 379.754i) q^{97} +(-210.180 - 152.705i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.08389 + 0.787491i 0.383212 + 0.278420i 0.762668 0.646790i \(-0.223889\pi\)
−0.379456 + 0.925210i \(0.623889\pi\)
\(3\) 0 0
\(4\) −1.91746 5.90135i −0.239683 0.737669i
\(5\) 3.83217 10.5031i 0.342760 0.939423i
\(6\) 0 0
\(7\) −12.2101 −0.659284 −0.329642 0.944106i \(-0.606928\pi\)
−0.329642 + 0.944106i \(0.606928\pi\)
\(8\) 5.88101 18.0999i 0.259906 0.799909i
\(9\) 0 0
\(10\) 12.4247 8.36635i 0.392904 0.264567i
\(11\) −2.00821 1.45905i −0.0550454 0.0399928i 0.559922 0.828545i \(-0.310831\pi\)
−0.614968 + 0.788552i \(0.710831\pi\)
\(12\) 0 0
\(13\) −69.2682 + 50.3263i −1.47781 + 1.07369i −0.499557 + 0.866281i \(0.666504\pi\)
−0.978254 + 0.207411i \(0.933496\pi\)
\(14\) −13.2344 9.61535i −0.252646 0.183558i
\(15\) 0 0
\(16\) −19.5320 + 14.1909i −0.305188 + 0.221732i
\(17\) 1.71458 5.27694i 0.0244616 0.0752850i −0.938080 0.346417i \(-0.887398\pi\)
0.962542 + 0.271132i \(0.0873981\pi\)
\(18\) 0 0
\(19\) −7.45887 + 22.9561i −0.0900623 + 0.277183i −0.985935 0.167127i \(-0.946551\pi\)
0.895873 + 0.444310i \(0.146551\pi\)
\(20\) −69.3303 2.47571i −0.775137 0.0276793i
\(21\) 0 0
\(22\) −1.02769 3.16290i −0.00995927 0.0306515i
\(23\) −83.6143 60.7493i −0.758034 0.550744i 0.140273 0.990113i \(-0.455202\pi\)
−0.898307 + 0.439369i \(0.855202\pi\)
\(24\) 0 0
\(25\) −95.6289 80.4991i −0.765031 0.643993i
\(26\) −114.710 −0.865253
\(27\) 0 0
\(28\) 23.4124 + 72.0561i 0.158019 + 0.486333i
\(29\) 35.3035 + 108.653i 0.226059 + 0.695737i 0.998182 + 0.0602646i \(0.0191945\pi\)
−0.772124 + 0.635472i \(0.780806\pi\)
\(30\) 0 0
\(31\) 47.5487 146.340i 0.275484 0.847852i −0.713607 0.700546i \(-0.752940\pi\)
0.989091 0.147306i \(-0.0470602\pi\)
\(32\) −184.596 −1.01976
\(33\) 0 0
\(34\) 6.01395 4.36939i 0.0303348 0.0220395i
\(35\) −46.7912 + 128.244i −0.225976 + 0.619346i
\(36\) 0 0
\(37\) 277.229 201.419i 1.23179 0.894948i 0.234767 0.972052i \(-0.424567\pi\)
0.997023 + 0.0771043i \(0.0245674\pi\)
\(38\) −26.1623 + 19.0080i −0.111686 + 0.0811449i
\(39\) 0 0
\(40\) −167.567 131.130i −0.662368 0.518339i
\(41\) 28.0530 20.3817i 0.106857 0.0776363i −0.533073 0.846069i \(-0.678963\pi\)
0.639931 + 0.768433i \(0.278963\pi\)
\(42\) 0 0
\(43\) −154.740 −0.548783 −0.274391 0.961618i \(-0.588476\pi\)
−0.274391 + 0.961618i \(0.588476\pi\)
\(44\) −4.75970 + 14.6489i −0.0163080 + 0.0501908i
\(45\) 0 0
\(46\) −42.7890 131.691i −0.137150 0.422104i
\(47\) −104.613 321.965i −0.324666 0.999221i −0.971591 0.236667i \(-0.923945\pi\)
0.646924 0.762554i \(-0.276055\pi\)
\(48\) 0 0
\(49\) −193.913 −0.565345
\(50\) −40.2588 162.559i −0.113869 0.459786i
\(51\) 0 0
\(52\) 429.812 + 312.277i 1.14624 + 0.832789i
\(53\) −199.512 614.036i −0.517078 1.59140i −0.779469 0.626441i \(-0.784511\pi\)
0.262390 0.964962i \(-0.415489\pi\)
\(54\) 0 0
\(55\) −23.0204 + 15.5011i −0.0564375 + 0.0380030i
\(56\) −71.8077 + 221.001i −0.171352 + 0.527367i
\(57\) 0 0
\(58\) −47.2982 + 145.569i −0.107079 + 0.329554i
\(59\) 536.260 389.616i 1.18331 0.859724i 0.190767 0.981635i \(-0.438903\pi\)
0.992541 + 0.121912i \(0.0389025\pi\)
\(60\) 0 0
\(61\) 289.370 + 210.239i 0.607377 + 0.441285i 0.848490 0.529212i \(-0.177512\pi\)
−0.241113 + 0.970497i \(0.577512\pi\)
\(62\) 166.779 121.172i 0.341628 0.248207i
\(63\) 0 0
\(64\) −43.8256 31.8411i −0.0855968 0.0621897i
\(65\) 263.133 + 920.387i 0.502117 + 1.75631i
\(66\) 0 0
\(67\) −164.205 + 505.370i −0.299415 + 0.921504i 0.682288 + 0.731083i \(0.260985\pi\)
−0.981703 + 0.190420i \(0.939015\pi\)
\(68\) −34.4287 −0.0613984
\(69\) 0 0
\(70\) −151.707 + 102.154i −0.259035 + 0.174425i
\(71\) 196.164 + 603.732i 0.327893 + 1.00915i 0.970118 + 0.242635i \(0.0780118\pi\)
−0.642224 + 0.766517i \(0.721988\pi\)
\(72\) 0 0
\(73\) −779.001 565.977i −1.24897 0.907433i −0.250812 0.968036i \(-0.580698\pi\)
−0.998162 + 0.0606028i \(0.980698\pi\)
\(74\) 459.101 0.721208
\(75\) 0 0
\(76\) 149.774 0.226056
\(77\) 24.5205 + 17.8152i 0.0362905 + 0.0263666i
\(78\) 0 0
\(79\) 175.752 + 540.908i 0.250299 + 0.770340i 0.994720 + 0.102630i \(0.0327257\pi\)
−0.744421 + 0.667711i \(0.767274\pi\)
\(80\) 74.1975 + 259.528i 0.103694 + 0.362702i
\(81\) 0 0
\(82\) 46.4568 0.0625645
\(83\) 98.8352 304.184i 0.130706 0.402271i −0.864192 0.503163i \(-0.832170\pi\)
0.994897 + 0.100892i \(0.0321696\pi\)
\(84\) 0 0
\(85\) −48.8535 38.2305i −0.0623400 0.0487844i
\(86\) −167.721 121.856i −0.210300 0.152792i
\(87\) 0 0
\(88\) −38.2190 + 27.7677i −0.0462973 + 0.0336369i
\(89\) −1079.81 784.525i −1.28606 0.934376i −0.286341 0.958128i \(-0.592439\pi\)
−0.999718 + 0.0237515i \(0.992439\pi\)
\(90\) 0 0
\(91\) 845.772 614.489i 0.974296 0.707868i
\(92\) −198.176 + 609.922i −0.224579 + 0.691182i
\(93\) 0 0
\(94\) 140.156 431.355i 0.153787 0.473307i
\(95\) 212.525 + 166.313i 0.229523 + 0.179614i
\(96\) 0 0
\(97\) 123.390 + 379.754i 0.129158 + 0.397507i 0.994636 0.103440i \(-0.0329850\pi\)
−0.865478 + 0.500947i \(0.832985\pi\)
\(98\) −210.180 152.705i −0.216647 0.157403i
\(99\) 0 0
\(100\) −291.688 + 718.694i −0.291688 + 0.718694i
\(101\) 131.408 0.129461 0.0647307 0.997903i \(-0.479381\pi\)
0.0647307 + 0.997903i \(0.479381\pi\)
\(102\) 0 0
\(103\) 5.82218 + 17.9188i 0.00556967 + 0.0171417i 0.953803 0.300434i \(-0.0971314\pi\)
−0.948233 + 0.317575i \(0.897131\pi\)
\(104\) 503.533 + 1549.72i 0.474764 + 1.46117i
\(105\) 0 0
\(106\) 267.299 822.661i 0.244928 0.753810i
\(107\) 1832.09 1.65528 0.827640 0.561259i \(-0.189683\pi\)
0.827640 + 0.561259i \(0.189683\pi\)
\(108\) 0 0
\(109\) 1082.18 786.250i 0.950954 0.690909i −7.79623e−5 1.00000i \(-0.500025\pi\)
0.951032 + 0.309091i \(0.100025\pi\)
\(110\) −37.1584 1.32689i −0.0322083 0.00115013i
\(111\) 0 0
\(112\) 238.488 173.272i 0.201206 0.146184i
\(113\) 29.3061 21.2921i 0.0243972 0.0177256i −0.575520 0.817788i \(-0.695200\pi\)
0.599917 + 0.800062i \(0.295200\pi\)
\(114\) 0 0
\(115\) −958.478 + 645.405i −0.777205 + 0.523342i
\(116\) 573.506 416.677i 0.459041 0.333513i
\(117\) 0 0
\(118\) 888.065 0.692822
\(119\) −20.9352 + 64.4319i −0.0161271 + 0.0496342i
\(120\) 0 0
\(121\) −409.398 1260.00i −0.307586 0.946654i
\(122\) 148.083 + 455.752i 0.109892 + 0.338212i
\(123\) 0 0
\(124\) −954.776 −0.691463
\(125\) −1211.95 + 695.911i −0.867204 + 0.497953i
\(126\) 0 0
\(127\) 1130.69 + 821.496i 0.790021 + 0.573984i 0.907970 0.419036i \(-0.137632\pi\)
−0.117949 + 0.993020i \(0.537632\pi\)
\(128\) 433.920 + 1335.47i 0.299637 + 0.922187i
\(129\) 0 0
\(130\) −439.590 + 1204.81i −0.296574 + 0.812838i
\(131\) 877.005 2699.14i 0.584918 1.80019i −0.0146799 0.999892i \(-0.504673\pi\)
0.599598 0.800301i \(-0.295327\pi\)
\(132\) 0 0
\(133\) 91.0736 280.296i 0.0593766 0.182742i
\(134\) −575.953 + 418.455i −0.371304 + 0.269768i
\(135\) 0 0
\(136\) −85.4284 62.0674i −0.0538634 0.0391341i
\(137\) −655.541 + 476.279i −0.408808 + 0.297016i −0.773119 0.634261i \(-0.781304\pi\)
0.364311 + 0.931277i \(0.381304\pi\)
\(138\) 0 0
\(139\) 2540.67 + 1845.91i 1.55034 + 1.12639i 0.943410 + 0.331628i \(0.107598\pi\)
0.606927 + 0.794758i \(0.292402\pi\)
\(140\) 846.530 + 30.2287i 0.511035 + 0.0182485i
\(141\) 0 0
\(142\) −262.813 + 808.855i −0.155315 + 0.478012i
\(143\) 212.534 0.124287
\(144\) 0 0
\(145\) 1276.48 + 45.5818i 0.731075 + 0.0261059i
\(146\) −398.648 1226.91i −0.225975 0.695479i
\(147\) 0 0
\(148\) −1720.22 1249.81i −0.955414 0.694149i
\(149\) 1008.26 0.554362 0.277181 0.960818i \(-0.410600\pi\)
0.277181 + 0.960818i \(0.410600\pi\)
\(150\) 0 0
\(151\) −2162.97 −1.16570 −0.582848 0.812581i \(-0.698062\pi\)
−0.582848 + 0.812581i \(0.698062\pi\)
\(152\) 371.636 + 270.009i 0.198314 + 0.144083i
\(153\) 0 0
\(154\) 12.5482 + 38.6193i 0.00656598 + 0.0202080i
\(155\) −1354.80 1060.21i −0.702067 0.549406i
\(156\) 0 0
\(157\) −2618.64 −1.33115 −0.665575 0.746331i \(-0.731814\pi\)
−0.665575 + 0.746331i \(0.731814\pi\)
\(158\) −235.465 + 724.686i −0.118561 + 0.364892i
\(159\) 0 0
\(160\) −707.405 + 1938.83i −0.349533 + 0.957987i
\(161\) 1020.94 + 741.756i 0.499759 + 0.363096i
\(162\) 0 0
\(163\) 261.518 190.004i 0.125667 0.0913022i −0.523176 0.852224i \(-0.675253\pi\)
0.648843 + 0.760922i \(0.275253\pi\)
\(164\) −174.070 126.469i −0.0828818 0.0602171i
\(165\) 0 0
\(166\) 346.668 251.869i 0.162088 0.117764i
\(167\) −49.1296 + 151.205i −0.0227650 + 0.0700636i −0.961794 0.273775i \(-0.911727\pi\)
0.939029 + 0.343839i \(0.111727\pi\)
\(168\) 0 0
\(169\) 1586.44 4882.55i 0.722092 2.22237i
\(170\) −22.8455 79.9092i −0.0103069 0.0360515i
\(171\) 0 0
\(172\) 296.709 + 913.176i 0.131534 + 0.404820i
\(173\) −2663.82 1935.38i −1.17067 0.850545i −0.179585 0.983743i \(-0.557475\pi\)
−0.991089 + 0.133198i \(0.957475\pi\)
\(174\) 0 0
\(175\) 1167.64 + 982.903i 0.504373 + 0.424574i
\(176\) 59.9297 0.0256669
\(177\) 0 0
\(178\) −552.583 1700.67i −0.232684 0.716129i
\(179\) −871.102 2680.98i −0.363739 1.11947i −0.950767 0.309906i \(-0.899702\pi\)
0.587028 0.809566i \(-0.300298\pi\)
\(180\) 0 0
\(181\) 129.046 397.161i 0.0529938 0.163098i −0.921057 0.389428i \(-0.872673\pi\)
0.974051 + 0.226330i \(0.0726727\pi\)
\(182\) 1400.63 0.570447
\(183\) 0 0
\(184\) −1591.29 + 1156.14i −0.637563 + 0.463217i
\(185\) −1053.13 3683.63i −0.418526 1.46392i
\(186\) 0 0
\(187\) −11.1426 + 8.09555i −0.00435736 + 0.00316580i
\(188\) −1699.43 + 1234.71i −0.659277 + 0.478992i
\(189\) 0 0
\(190\) 99.3841 + 347.626i 0.0379478 + 0.132734i
\(191\) 421.982 306.588i 0.159861 0.116146i −0.504979 0.863132i \(-0.668500\pi\)
0.664840 + 0.746986i \(0.268500\pi\)
\(192\) 0 0
\(193\) −4528.65 −1.68901 −0.844506 0.535547i \(-0.820106\pi\)
−0.844506 + 0.535547i \(0.820106\pi\)
\(194\) −165.312 + 508.779i −0.0611791 + 0.188290i
\(195\) 0 0
\(196\) 371.822 + 1144.35i 0.135504 + 0.417037i
\(197\) 859.280 + 2644.59i 0.310767 + 0.956444i 0.977462 + 0.211112i \(0.0677086\pi\)
−0.666694 + 0.745331i \(0.732291\pi\)
\(198\) 0 0
\(199\) 4988.03 1.77685 0.888423 0.459026i \(-0.151801\pi\)
0.888423 + 0.459026i \(0.151801\pi\)
\(200\) −2019.42 + 1257.46i −0.713972 + 0.444578i
\(201\) 0 0
\(202\) 142.432 + 103.483i 0.0496112 + 0.0360446i
\(203\) −431.060 1326.67i −0.149037 0.458688i
\(204\) 0 0
\(205\) −106.567 372.749i −0.0363070 0.126995i
\(206\) −7.80032 + 24.0069i −0.00263822 + 0.00811961i
\(207\) 0 0
\(208\) 638.776 1965.95i 0.212938 0.655356i
\(209\) 48.4731 35.2178i 0.0160428 0.0116558i
\(210\) 0 0
\(211\) −3035.52 2205.44i −0.990398 0.719566i −0.0303898 0.999538i \(-0.509675\pi\)
−0.960008 + 0.279972i \(0.909675\pi\)
\(212\) −3241.08 + 2354.79i −1.04999 + 0.762865i
\(213\) 0 0
\(214\) 1985.78 + 1442.76i 0.634324 + 0.460863i
\(215\) −592.991 + 1625.25i −0.188101 + 0.515539i
\(216\) 0 0
\(217\) −580.575 + 1786.83i −0.181622 + 0.558975i
\(218\) 1792.13 0.556780
\(219\) 0 0
\(220\) 135.618 + 106.128i 0.0415607 + 0.0325235i
\(221\) 146.803 + 451.812i 0.0446833 + 0.137521i
\(222\) 0 0
\(223\) −1324.82 962.540i −0.397833 0.289042i 0.370825 0.928703i \(-0.379075\pi\)
−0.768658 + 0.639660i \(0.779075\pi\)
\(224\) 2253.94 0.672312
\(225\) 0 0
\(226\) 48.5319 0.0142845
\(227\) −3068.69 2229.54i −0.897252 0.651892i 0.0405064 0.999179i \(-0.487103\pi\)
−0.937759 + 0.347287i \(0.887103\pi\)
\(228\) 0 0
\(229\) 27.8795 + 85.8041i 0.00804509 + 0.0247603i 0.954998 0.296611i \(-0.0958564\pi\)
−0.946953 + 0.321371i \(0.895856\pi\)
\(230\) −1547.13 55.2465i −0.443543 0.0158385i
\(231\) 0 0
\(232\) 2174.23 0.615280
\(233\) −1118.15 + 3441.31i −0.314388 + 0.967587i 0.661617 + 0.749842i \(0.269870\pi\)
−0.976006 + 0.217746i \(0.930130\pi\)
\(234\) 0 0
\(235\) −3782.51 135.070i −1.04997 0.0374935i
\(236\) −3327.52 2417.59i −0.917810 0.666828i
\(237\) 0 0
\(238\) −73.4310 + 53.3507i −0.0199993 + 0.0145303i
\(239\) −1189.87 864.489i −0.322034 0.233971i 0.415009 0.909817i \(-0.363778\pi\)
−0.737043 + 0.675846i \(0.763778\pi\)
\(240\) 0 0
\(241\) 3192.76 2319.68i 0.853377 0.620014i −0.0726983 0.997354i \(-0.523161\pi\)
0.926075 + 0.377340i \(0.123161\pi\)
\(242\) 548.494 1688.09i 0.145696 0.448408i
\(243\) 0 0
\(244\) 685.840 2110.80i 0.179944 0.553811i
\(245\) −743.109 + 2036.69i −0.193778 + 0.531098i
\(246\) 0 0
\(247\) −638.630 1965.50i −0.164514 0.506323i
\(248\) −2369.10 1721.25i −0.606605 0.440724i
\(249\) 0 0
\(250\) −1861.65 200.113i −0.470963 0.0506251i
\(251\) −3410.52 −0.857649 −0.428825 0.903388i \(-0.641072\pi\)
−0.428825 + 0.903388i \(0.641072\pi\)
\(252\) 0 0
\(253\) 79.2789 + 243.995i 0.0197005 + 0.0606318i
\(254\) 578.623 + 1780.82i 0.142937 + 0.439915i
\(255\) 0 0
\(256\) −715.268 + 2201.37i −0.174626 + 0.537443i
\(257\) 6919.87 1.67957 0.839785 0.542918i \(-0.182681\pi\)
0.839785 + 0.542918i \(0.182681\pi\)
\(258\) 0 0
\(259\) −3385.00 + 2459.35i −0.812099 + 0.590024i
\(260\) 4926.98 3317.65i 1.17522 0.791353i
\(261\) 0 0
\(262\) 3076.13 2234.94i 0.725358 0.527003i
\(263\) 3081.19 2238.62i 0.722413 0.524863i −0.164742 0.986337i \(-0.552679\pi\)
0.887154 + 0.461473i \(0.152679\pi\)
\(264\) 0 0
\(265\) −7213.83 257.598i −1.67223 0.0597138i
\(266\) 319.444 232.090i 0.0736330 0.0534975i
\(267\) 0 0
\(268\) 3297.22 0.751529
\(269\) −799.222 + 2459.75i −0.181150 + 0.557523i −0.999861 0.0166834i \(-0.994689\pi\)
0.818711 + 0.574206i \(0.194689\pi\)
\(270\) 0 0
\(271\) 329.230 + 1013.27i 0.0737981 + 0.227127i 0.981151 0.193242i \(-0.0619004\pi\)
−0.907353 + 0.420370i \(0.861900\pi\)
\(272\) 41.3950 + 127.401i 0.00922772 + 0.0284000i
\(273\) 0 0
\(274\) −1085.60 −0.239356
\(275\) 74.5909 + 301.187i 0.0163564 + 0.0660446i
\(276\) 0 0
\(277\) 1996.88 + 1450.82i 0.433144 + 0.314698i 0.782905 0.622141i \(-0.213737\pi\)
−0.349761 + 0.936839i \(0.613737\pi\)
\(278\) 1300.17 + 4001.51i 0.280500 + 0.863290i
\(279\) 0 0
\(280\) 2046.01 + 1601.12i 0.436688 + 0.341732i
\(281\) −960.683 + 2956.68i −0.203948 + 0.627689i 0.795806 + 0.605551i \(0.207047\pi\)
−0.999755 + 0.0221378i \(0.992953\pi\)
\(282\) 0 0
\(283\) −1994.41 + 6138.15i −0.418923 + 1.28931i 0.489772 + 0.871851i \(0.337080\pi\)
−0.908695 + 0.417461i \(0.862920\pi\)
\(284\) 3186.69 2315.27i 0.665829 0.483753i
\(285\) 0 0
\(286\) 230.363 + 167.369i 0.0476282 + 0.0346039i
\(287\) −342.530 + 248.863i −0.0704493 + 0.0511844i
\(288\) 0 0
\(289\) 3949.79 + 2869.69i 0.803948 + 0.584102i
\(290\) 1347.67 + 1054.62i 0.272888 + 0.213550i
\(291\) 0 0
\(292\) −1846.32 + 5682.39i −0.370027 + 1.13883i
\(293\) −835.063 −0.166501 −0.0832507 0.996529i \(-0.526530\pi\)
−0.0832507 + 0.996529i \(0.526530\pi\)
\(294\) 0 0
\(295\) −2037.12 7125.46i −0.402054 1.40631i
\(296\) −2015.27 6202.36i −0.395727 1.21792i
\(297\) 0 0
\(298\) 1092.84 + 793.996i 0.212438 + 0.154346i
\(299\) 8849.10 1.71156
\(300\) 0 0
\(301\) 1889.39 0.361803
\(302\) −2344.42 1703.32i −0.446709 0.324553i
\(303\) 0 0
\(304\) −180.079 554.227i −0.0339745 0.104563i
\(305\) 3317.07 2233.60i 0.622738 0.419329i
\(306\) 0 0
\(307\) 2681.88 0.498577 0.249289 0.968429i \(-0.419803\pi\)
0.249289 + 0.968429i \(0.419803\pi\)
\(308\) 58.1164 178.864i 0.0107516 0.0330900i
\(309\) 0 0
\(310\) −633.552 2216.04i −0.116075 0.406009i
\(311\) 6580.24 + 4780.83i 1.19978 + 0.871691i 0.994263 0.106963i \(-0.0341126\pi\)
0.205516 + 0.978654i \(0.434113\pi\)
\(312\) 0 0
\(313\) −6248.59 + 4539.87i −1.12841 + 0.819835i −0.985462 0.169895i \(-0.945657\pi\)
−0.142944 + 0.989731i \(0.545657\pi\)
\(314\) −2838.32 2062.16i −0.510113 0.370619i
\(315\) 0 0
\(316\) 2855.09 2074.34i 0.508263 0.369275i
\(317\) −995.186 + 3062.87i −0.176326 + 0.542674i −0.999692 0.0248365i \(-0.992093\pi\)
0.823366 + 0.567511i \(0.192093\pi\)
\(318\) 0 0
\(319\) 87.6335 269.708i 0.0153810 0.0473378i
\(320\) −502.377 + 338.282i −0.0877616 + 0.0590955i
\(321\) 0 0
\(322\) 522.458 + 1607.96i 0.0904206 + 0.278286i
\(323\) 108.349 + 78.7200i 0.0186647 + 0.0135607i
\(324\) 0 0
\(325\) 10675.3 + 763.379i 1.82202 + 0.130291i
\(326\) 433.083 0.0735774
\(327\) 0 0
\(328\) −203.927 627.622i −0.0343292 0.105654i
\(329\) 1277.33 + 3931.22i 0.214047 + 0.658770i
\(330\) 0 0
\(331\) 1297.25 3992.52i 0.215417 0.662987i −0.783706 0.621132i \(-0.786673\pi\)
0.999124 0.0418550i \(-0.0133268\pi\)
\(332\) −1984.61 −0.328071
\(333\) 0 0
\(334\) −172.324 + 125.201i −0.0282309 + 0.0205110i
\(335\) 4678.67 + 3661.31i 0.763054 + 0.597131i
\(336\) 0 0
\(337\) −1039.69 + 755.378i −0.168058 + 0.122101i −0.668635 0.743591i \(-0.733121\pi\)
0.500577 + 0.865692i \(0.333121\pi\)
\(338\) 5564.48 4042.83i 0.895467 0.650595i
\(339\) 0 0
\(340\) −131.937 + 361.607i −0.0210449 + 0.0576791i
\(341\) −309.006 + 224.506i −0.0490721 + 0.0356530i
\(342\) 0 0
\(343\) 6555.77 1.03201
\(344\) −910.028 + 2800.78i −0.142632 + 0.438976i
\(345\) 0 0
\(346\) −1363.19 4195.47i −0.211808 0.651878i
\(347\) 96.1696 + 295.980i 0.0148780 + 0.0457897i 0.958220 0.286033i \(-0.0923366\pi\)
−0.943342 + 0.331822i \(0.892337\pi\)
\(348\) 0 0
\(349\) −3853.76 −0.591081 −0.295540 0.955330i \(-0.595500\pi\)
−0.295540 + 0.955330i \(0.595500\pi\)
\(350\) 491.564 + 1984.86i 0.0750719 + 0.303129i
\(351\) 0 0
\(352\) 370.709 + 269.336i 0.0561331 + 0.0407831i
\(353\) −371.671 1143.89i −0.0560398 0.172473i 0.919119 0.393980i \(-0.128902\pi\)
−0.975159 + 0.221508i \(0.928902\pi\)
\(354\) 0 0
\(355\) 7092.77 + 253.276i 1.06041 + 0.0378661i
\(356\) −2559.27 + 7876.61i −0.381014 + 1.17264i
\(357\) 0 0
\(358\) 1167.07 3591.86i 0.172295 0.530268i
\(359\) 8830.61 6415.81i 1.29822 0.943213i 0.298285 0.954477i \(-0.403585\pi\)
0.999937 + 0.0112636i \(0.00358538\pi\)
\(360\) 0 0
\(361\) 5077.70 + 3689.17i 0.740298 + 0.537858i
\(362\) 452.632 328.856i 0.0657177 0.0477467i
\(363\) 0 0
\(364\) −5248.05 3812.93i −0.755694 0.549044i
\(365\) −8929.76 + 6012.98i −1.28056 + 0.862284i
\(366\) 0 0
\(367\) −44.8963 + 138.177i −0.00638575 + 0.0196533i −0.954199 0.299174i \(-0.903289\pi\)
0.947813 + 0.318827i \(0.103289\pi\)
\(368\) 2495.24 0.353461
\(369\) 0 0
\(370\) 1759.35 4821.97i 0.247201 0.677520i
\(371\) 2436.07 + 7497.45i 0.340901 + 1.04919i
\(372\) 0 0
\(373\) 2847.26 + 2068.66i 0.395243 + 0.287161i 0.767601 0.640929i \(-0.221451\pi\)
−0.372358 + 0.928089i \(0.621451\pi\)
\(374\) −18.4525 −0.00255122
\(375\) 0 0
\(376\) −6442.75 −0.883669
\(377\) −7913.51 5749.50i −1.08108 0.785450i
\(378\) 0 0
\(379\) −124.955 384.571i −0.0169354 0.0521217i 0.942232 0.334962i \(-0.108723\pi\)
−0.959167 + 0.282840i \(0.908723\pi\)
\(380\) 573.959 1573.08i 0.0774828 0.212362i
\(381\) 0 0
\(382\) 698.816 0.0935982
\(383\) 1292.81 3978.86i 0.172479 0.530836i −0.827030 0.562158i \(-0.809971\pi\)
0.999509 + 0.0313212i \(0.00997146\pi\)
\(384\) 0 0
\(385\) 281.081 189.270i 0.0372083 0.0250547i
\(386\) −4908.55 3566.27i −0.647250 0.470255i
\(387\) 0 0
\(388\) 2004.47 1456.33i 0.262272 0.190551i
\(389\) −8299.40 6029.87i −1.08174 0.785929i −0.103754 0.994603i \(-0.533085\pi\)
−0.977985 + 0.208674i \(0.933085\pi\)
\(390\) 0 0
\(391\) −463.934 + 337.067i −0.0600054 + 0.0435965i
\(392\) −1140.41 + 3509.81i −0.146937 + 0.452225i
\(393\) 0 0
\(394\) −1151.23 + 3543.12i −0.147203 + 0.453045i
\(395\) 6354.70 + 226.920i 0.809468 + 0.0289053i
\(396\) 0 0
\(397\) −3149.37 9692.75i −0.398142 1.22535i −0.926488 0.376325i \(-0.877188\pi\)
0.528346 0.849029i \(-0.322812\pi\)
\(398\) 5406.47 + 3928.03i 0.680909 + 0.494710i
\(399\) 0 0
\(400\) 3010.18 + 215.255i 0.376273 + 0.0269069i
\(401\) −5912.32 −0.736277 −0.368139 0.929771i \(-0.620005\pi\)
−0.368139 + 0.929771i \(0.620005\pi\)
\(402\) 0 0
\(403\) 4071.13 + 12529.6i 0.503219 + 1.54875i
\(404\) −251.970 775.485i −0.0310297 0.0954996i
\(405\) 0 0
\(406\) 577.516 1777.41i 0.0705952 0.217270i
\(407\) −850.616 −0.103596
\(408\) 0 0
\(409\) −4576.30 + 3324.88i −0.553260 + 0.401967i −0.828986 0.559269i \(-0.811082\pi\)
0.275726 + 0.961236i \(0.411082\pi\)
\(410\) 178.030 487.939i 0.0214446 0.0587746i
\(411\) 0 0
\(412\) 94.5814 68.7174i 0.0113099 0.00821714i
\(413\) −6547.80 + 4757.25i −0.780136 + 0.566802i
\(414\) 0 0
\(415\) −2816.11 2203.76i −0.333102 0.260670i
\(416\) 12786.7 9290.05i 1.50701 1.09491i
\(417\) 0 0
\(418\) 80.2731 0.00939303
\(419\) −4234.75 + 13033.2i −0.493749 + 1.51960i 0.325148 + 0.945663i \(0.394586\pi\)
−0.818897 + 0.573940i \(0.805414\pi\)
\(420\) 0 0
\(421\) 2847.48 + 8763.66i 0.329639 + 1.01452i 0.969303 + 0.245869i \(0.0790734\pi\)
−0.639664 + 0.768654i \(0.720927\pi\)
\(422\) −1553.41 4780.89i −0.179191 0.551493i
\(423\) 0 0
\(424\) −12287.3 −1.40737
\(425\) −588.752 + 366.606i −0.0671969 + 0.0418423i
\(426\) 0 0
\(427\) −3533.23 2567.04i −0.400434 0.290932i
\(428\) −3512.97 10811.8i −0.396743 1.22105i
\(429\) 0 0
\(430\) −1922.60 + 1294.61i −0.215619 + 0.145190i
\(431\) −2337.94 + 7195.44i −0.261287 + 0.804158i 0.731239 + 0.682121i \(0.238942\pi\)
−0.992526 + 0.122036i \(0.961058\pi\)
\(432\) 0 0
\(433\) 1250.50 3848.63i 0.138788 0.427144i −0.857372 0.514697i \(-0.827905\pi\)
0.996160 + 0.0875525i \(0.0279046\pi\)
\(434\) −2036.39 + 1479.52i −0.225230 + 0.163639i
\(435\) 0 0
\(436\) −6714.97 4878.71i −0.737589 0.535890i
\(437\) 2018.23 1466.33i 0.220927 0.160513i
\(438\) 0 0
\(439\) −3157.92 2294.36i −0.343324 0.249440i 0.402739 0.915315i \(-0.368058\pi\)
−0.746063 + 0.665875i \(0.768058\pi\)
\(440\) 145.185 + 507.828i 0.0157305 + 0.0550221i
\(441\) 0 0
\(442\) −196.680 + 605.320i −0.0211654 + 0.0651405i
\(443\) −2288.91 −0.245484 −0.122742 0.992439i \(-0.539169\pi\)
−0.122742 + 0.992439i \(0.539169\pi\)
\(444\) 0 0
\(445\) −12377.9 + 8334.84i −1.31858 + 0.887887i
\(446\) −677.968 2086.57i −0.0719792 0.221529i
\(447\) 0 0
\(448\) 535.115 + 388.784i 0.0564326 + 0.0410007i
\(449\) −10025.3 −1.05373 −0.526863 0.849950i \(-0.676632\pi\)
−0.526863 + 0.849950i \(0.676632\pi\)
\(450\) 0 0
\(451\) −86.0745 −0.00898690
\(452\) −181.846 132.119i −0.0189232 0.0137485i
\(453\) 0 0
\(454\) −1570.38 4833.13i −0.162338 0.499626i
\(455\) −3212.88 11238.0i −0.331038 1.15791i
\(456\) 0 0
\(457\) −3293.06 −0.337075 −0.168537 0.985695i \(-0.553904\pi\)
−0.168537 + 0.985695i \(0.553904\pi\)
\(458\) −37.3518 + 114.957i −0.00381077 + 0.0117283i
\(459\) 0 0
\(460\) 5646.61 + 4418.77i 0.572336 + 0.447884i
\(461\) −672.561 488.644i −0.0679486 0.0493676i 0.553292 0.832987i \(-0.313371\pi\)
−0.621241 + 0.783620i \(0.713371\pi\)
\(462\) 0 0
\(463\) 7302.69 5305.71i 0.733012 0.532565i −0.157503 0.987519i \(-0.550344\pi\)
0.890515 + 0.454954i \(0.150344\pi\)
\(464\) −2231.43 1621.23i −0.223258 0.162206i
\(465\) 0 0
\(466\) −3921.95 + 2849.46i −0.389873 + 0.283259i
\(467\) −406.581 + 1251.33i −0.0402876 + 0.123992i −0.969177 0.246364i \(-0.920764\pi\)
0.928890 + 0.370356i \(0.120764\pi\)
\(468\) 0 0
\(469\) 2004.95 6170.62i 0.197399 0.607532i
\(470\) −3993.45 3125.09i −0.391924 0.306702i
\(471\) 0 0
\(472\) −3898.25 11997.6i −0.380152 1.16999i
\(473\) 310.751 + 225.774i 0.0302080 + 0.0219474i
\(474\) 0 0
\(475\) 2561.23 1594.83i 0.247404 0.154054i
\(476\) 420.378 0.0404790
\(477\) 0 0
\(478\) −608.906 1874.02i −0.0582651 0.179321i
\(479\) −2883.48 8874.45i −0.275052 0.846522i −0.989206 0.146533i \(-0.953188\pi\)
0.714154 0.699989i \(-0.246812\pi\)
\(480\) 0 0
\(481\) −9066.51 + 27903.8i −0.859454 + 2.64513i
\(482\) 5287.32 0.499649
\(483\) 0 0
\(484\) −6650.67 + 4831.99i −0.624593 + 0.453794i
\(485\) 4461.43 + 159.313i 0.417698 + 0.0149155i
\(486\) 0 0
\(487\) 1662.91 1208.18i 0.154731 0.112418i −0.507726 0.861519i \(-0.669514\pi\)
0.662457 + 0.749100i \(0.269514\pi\)
\(488\) 5507.09 4001.14i 0.510849 0.371154i
\(489\) 0 0
\(490\) −2409.32 + 1622.35i −0.222126 + 0.149572i
\(491\) 2888.29 2098.47i 0.265472 0.192877i −0.447084 0.894492i \(-0.647537\pi\)
0.712556 + 0.701615i \(0.247537\pi\)
\(492\) 0 0
\(493\) 633.886 0.0579083
\(494\) 855.611 2633.30i 0.0779266 0.239833i
\(495\) 0 0
\(496\) 1147.97 + 3533.07i 0.103922 + 0.319838i
\(497\) −2395.19 7371.63i −0.216175 0.665317i
\(498\) 0 0
\(499\) −316.957 −0.0284347 −0.0142174 0.999899i \(-0.504526\pi\)
−0.0142174 + 0.999899i \(0.504526\pi\)
\(500\) 6430.69 + 5817.78i 0.575179 + 0.520358i
\(501\) 0 0
\(502\) −3696.62 2685.75i −0.328662 0.238787i
\(503\) 3270.63 + 10066.0i 0.289921 + 0.892285i 0.984880 + 0.173236i \(0.0554223\pi\)
−0.694959 + 0.719049i \(0.744578\pi\)
\(504\) 0 0
\(505\) 503.578 1380.19i 0.0443741 0.121619i
\(506\) −106.215 + 326.895i −0.00933165 + 0.0287199i
\(507\) 0 0
\(508\) 2679.87 8247.79i 0.234055 0.720348i
\(509\) −11989.3 + 8710.74i −1.04404 + 0.758540i −0.971070 0.238794i \(-0.923248\pi\)
−0.0729705 + 0.997334i \(0.523248\pi\)
\(510\) 0 0
\(511\) 9511.68 + 6910.64i 0.823428 + 0.598256i
\(512\) 6579.32 4780.15i 0.567905 0.412607i
\(513\) 0 0
\(514\) 7500.37 + 5449.34i 0.643632 + 0.467626i
\(515\) 210.514 + 7.51724i 0.0180124 + 0.000643202i
\(516\) 0 0
\(517\) −259.679 + 799.209i −0.0220903 + 0.0679868i
\(518\) −5605.67 −0.475481
\(519\) 0 0
\(520\) 18206.4 + 650.131i 1.53539 + 0.0548272i
\(521\) −1266.26 3897.16i −0.106480 0.327711i 0.883595 0.468252i \(-0.155116\pi\)
−0.990075 + 0.140541i \(0.955116\pi\)
\(522\) 0 0
\(523\) −4884.26 3548.62i −0.408363 0.296693i 0.364576 0.931174i \(-0.381214\pi\)
−0.772939 + 0.634481i \(0.781214\pi\)
\(524\) −17610.2 −1.46814
\(525\) 0 0
\(526\) 5102.56 0.422970
\(527\) −690.700 501.823i −0.0570918 0.0414796i
\(528\) 0 0
\(529\) −458.945 1412.49i −0.0377204 0.116092i
\(530\) −7616.13 5960.03i −0.624195 0.488467i
\(531\) 0 0
\(532\) −1828.75 −0.149035
\(533\) −917.446 + 2823.61i −0.0745573 + 0.229464i
\(534\) 0 0
\(535\) 7020.89 19242.6i 0.567364 1.55501i
\(536\) 8181.44 + 5944.17i 0.659300 + 0.479009i
\(537\) 0 0
\(538\) −2803.30 + 2036.72i −0.224645 + 0.163214i
\(539\) 389.419 + 282.930i 0.0311196 + 0.0226097i
\(540\) 0 0
\(541\) −3971.18 + 2885.23i −0.315590 + 0.229290i −0.734291 0.678834i \(-0.762485\pi\)
0.418701 + 0.908124i \(0.362485\pi\)
\(542\) −441.089 + 1357.53i −0.0349564 + 0.107585i
\(543\) 0 0
\(544\) −316.505 + 974.104i −0.0249450 + 0.0767727i
\(545\) −4110.94 14379.3i −0.323107 1.13016i
\(546\) 0 0
\(547\) −5430.58 16713.6i −0.424488 1.30644i −0.903484 0.428623i \(-0.858999\pi\)
0.478995 0.877817i \(-0.341001\pi\)
\(548\) 4067.66 + 2955.33i 0.317084 + 0.230375i
\(549\) 0 0
\(550\) −156.334 + 385.193i −0.0121202 + 0.0298630i
\(551\) −2757.57 −0.213206
\(552\) 0 0
\(553\) −2145.95 6604.54i −0.165018 0.507873i
\(554\) 1021.89 + 3145.05i 0.0783680 + 0.241192i
\(555\) 0 0
\(556\) 6021.68 18532.8i 0.459310 1.41361i
\(557\) 23625.5 1.79721 0.898603 0.438764i \(-0.144583\pi\)
0.898603 + 0.438764i \(0.144583\pi\)
\(558\) 0 0
\(559\) 10718.6 7787.50i 0.810997 0.589224i
\(560\) −905.959 3168.87i −0.0683638 0.239123i
\(561\) 0 0
\(562\) −3369.63 + 2448.18i −0.252917 + 0.183755i
\(563\) −18736.1 + 13612.6i −1.40254 + 1.01901i −0.408188 + 0.912898i \(0.633839\pi\)
−0.994355 + 0.106109i \(0.966161\pi\)
\(564\) 0 0
\(565\) −111.327 389.399i −0.00828947 0.0289950i
\(566\) −6995.45 + 5082.49i −0.519507 + 0.377444i
\(567\) 0 0
\(568\) 12081.1 0.892452
\(569\) 2625.00 8078.93i 0.193402 0.595231i −0.806589 0.591112i \(-0.798689\pi\)
0.999992 0.00411844i \(-0.00131094\pi\)
\(570\) 0 0
\(571\) 4777.92 + 14704.9i 0.350174 + 1.07773i 0.958755 + 0.284234i \(0.0917393\pi\)
−0.608580 + 0.793492i \(0.708261\pi\)
\(572\) −407.526 1254.24i −0.0297894 0.0916823i
\(573\) 0 0
\(574\) −567.242 −0.0412478
\(575\) 3105.68 + 12540.3i 0.225245 + 0.909505i
\(576\) 0 0
\(577\) −21389.0 15540.0i −1.54322 1.12121i −0.948278 0.317440i \(-0.897177\pi\)
−0.594937 0.803772i \(-0.702823\pi\)
\(578\) 2021.28 + 6220.85i 0.145457 + 0.447670i
\(579\) 0 0
\(580\) −2178.61 7620.35i −0.155969 0.545548i
\(581\) −1206.79 + 3714.11i −0.0861722 + 0.265211i
\(582\) 0 0
\(583\) −495.248 + 1524.22i −0.0351819 + 0.108279i
\(584\) −14825.4 + 10771.3i −1.05048 + 0.763219i
\(585\) 0 0
\(586\) −905.115 657.605i −0.0638054 0.0463573i
\(587\) −4812.71 + 3496.64i −0.338402 + 0.245863i −0.743987 0.668194i \(-0.767068\pi\)
0.405585 + 0.914057i \(0.367068\pi\)
\(588\) 0 0
\(589\) 3004.73 + 2183.06i 0.210200 + 0.152719i
\(590\) 3403.22 9327.41i 0.237472 0.650853i
\(591\) 0 0
\(592\) −2556.55 + 7868.24i −0.177489 + 0.546255i
\(593\) 11755.3 0.814054 0.407027 0.913416i \(-0.366566\pi\)
0.407027 + 0.913416i \(0.366566\pi\)
\(594\) 0 0
\(595\) 596.506 + 466.798i 0.0410998 + 0.0321628i
\(596\) −1933.30 5950.10i −0.132871 0.408936i
\(597\) 0 0
\(598\) 9591.43 + 6968.58i 0.655891 + 0.476533i
\(599\) 10184.4 0.694698 0.347349 0.937736i \(-0.387082\pi\)
0.347349 + 0.937736i \(0.387082\pi\)
\(600\) 0 0
\(601\) −16384.2 −1.11202 −0.556012 0.831174i \(-0.687669\pi\)
−0.556012 + 0.831174i \(0.687669\pi\)
\(602\) 2047.89 + 1487.88i 0.138648 + 0.100733i
\(603\) 0 0
\(604\) 4147.42 + 12764.4i 0.279398 + 0.859897i
\(605\) −14802.7 528.589i −0.994737 0.0355210i
\(606\) 0 0
\(607\) 20161.1 1.34813 0.674066 0.738672i \(-0.264547\pi\)
0.674066 + 0.738672i \(0.264547\pi\)
\(608\) 1376.88 4237.61i 0.0918420 0.282661i
\(609\) 0 0
\(610\) 5354.27 + 191.195i 0.355390 + 0.0126906i
\(611\) 23449.6 + 17037.1i 1.55265 + 1.12807i
\(612\) 0 0
\(613\) 2555.01 1856.32i 0.168346 0.122310i −0.500422 0.865781i \(-0.666822\pi\)
0.668768 + 0.743471i \(0.266822\pi\)
\(614\) 2906.86 + 2111.96i 0.191061 + 0.138814i
\(615\) 0 0
\(616\) 466.658 339.047i 0.0305230 0.0221763i
\(617\) −2032.29 + 6254.74i −0.132604 + 0.408114i −0.995210 0.0977634i \(-0.968831\pi\)
0.862605 + 0.505877i \(0.168831\pi\)
\(618\) 0 0
\(619\) −6522.15 + 20073.1i −0.423502 + 1.30340i 0.480920 + 0.876764i \(0.340303\pi\)
−0.904422 + 0.426639i \(0.859697\pi\)
\(620\) −3658.86 + 10028.1i −0.237006 + 0.649576i
\(621\) 0 0
\(622\) 3367.39 + 10363.8i 0.217074 + 0.668085i
\(623\) 13184.5 + 9579.13i 0.847877 + 0.616019i
\(624\) 0 0
\(625\) 2664.79 + 15396.1i 0.170546 + 0.985350i
\(626\) −10347.9 −0.660678
\(627\) 0 0
\(628\) 5021.16 + 15453.5i 0.319054 + 0.981947i
\(629\) −587.542 1808.27i −0.0372446 0.114627i
\(630\) 0 0
\(631\) −8297.74 + 25537.8i −0.523499 + 1.61116i 0.243765 + 0.969834i \(0.421617\pi\)
−0.767265 + 0.641331i \(0.778383\pi\)
\(632\) 10824.0 0.681257
\(633\) 0 0
\(634\) −3490.65 + 2536.11i −0.218662 + 0.158867i
\(635\) 12961.2 8727.62i 0.810001 0.545425i
\(636\) 0 0
\(637\) 13432.0 9758.94i 0.835473 0.607007i
\(638\) 307.378 223.323i 0.0190740 0.0138581i
\(639\) 0 0
\(640\) 15689.4 + 560.251i 0.969027 + 0.0346029i
\(641\) 20566.4 14942.4i 1.26728 0.920732i 0.268188 0.963367i \(-0.413575\pi\)
0.999091 + 0.0426350i \(0.0135753\pi\)
\(642\) 0 0
\(643\) −10481.7 −0.642856 −0.321428 0.946934i \(-0.604163\pi\)
−0.321428 + 0.946934i \(0.604163\pi\)
\(644\) 2419.74 7447.21i 0.148061 0.455685i
\(645\) 0 0
\(646\) 55.4467 + 170.647i 0.00337697 + 0.0103932i
\(647\) −5847.14 17995.7i −0.355294 1.09348i −0.955839 0.293891i \(-0.905050\pi\)
0.600545 0.799591i \(-0.294950\pi\)
\(648\) 0 0
\(649\) −1645.40 −0.0995184
\(650\) 10969.6 + 9234.09i 0.661946 + 0.557217i
\(651\) 0 0
\(652\) −1622.73 1178.98i −0.0974710 0.0708168i
\(653\) 3911.37 + 12037.9i 0.234401 + 0.721411i 0.997200 + 0.0747761i \(0.0238242\pi\)
−0.762800 + 0.646635i \(0.776176\pi\)
\(654\) 0 0
\(655\) −24988.5 19554.8i −1.49066 1.16652i
\(656\) −258.699 + 796.193i −0.0153971 + 0.0473874i
\(657\) 0 0
\(658\) −1711.32 + 5266.89i −0.101389 + 0.312044i
\(659\) 9820.27 7134.84i 0.580491 0.421751i −0.258410 0.966035i \(-0.583199\pi\)
0.838901 + 0.544284i \(0.183199\pi\)
\(660\) 0 0
\(661\) −3379.82 2455.59i −0.198880 0.144495i 0.483888 0.875130i \(-0.339224\pi\)
−0.682768 + 0.730635i \(0.739224\pi\)
\(662\) 4550.14 3305.87i 0.267139 0.194088i
\(663\) 0 0
\(664\) −4924.44 3577.81i −0.287809 0.209105i
\(665\) −2594.96 2030.69i −0.151320 0.118416i
\(666\) 0 0
\(667\) 3648.72 11229.6i 0.211813 0.651892i
\(668\) 986.519 0.0571401
\(669\) 0 0
\(670\) 2187.91 + 7652.87i 0.126159 + 0.441278i
\(671\) −274.366 844.411i −0.0157851 0.0485814i
\(672\) 0 0
\(673\) −6124.43 4449.66i −0.350787 0.254862i 0.398412 0.917206i \(-0.369561\pi\)
−0.749199 + 0.662345i \(0.769561\pi\)
\(674\) −1721.76 −0.0983972
\(675\) 0 0
\(676\) −31855.6 −1.81245
\(677\) −26966.3 19592.1i −1.53087 1.11224i −0.955754 0.294168i \(-0.904958\pi\)
−0.575114 0.818073i \(-0.695042\pi\)
\(678\) 0 0
\(679\) −1506.60 4636.84i −0.0851517 0.262070i
\(680\) −979.275 + 659.408i −0.0552257 + 0.0371870i
\(681\) 0 0
\(682\) −511.724 −0.0287315
\(683\) 10789.5 33206.6i 0.604463 1.86035i 0.104023 0.994575i \(-0.466828\pi\)
0.500440 0.865771i \(-0.333172\pi\)
\(684\) 0 0
\(685\) 2490.24 + 8710.38i 0.138901 + 0.485849i
\(686\) 7105.72 + 5162.61i 0.395478 + 0.287331i
\(687\) 0 0
\(688\) 3022.39 2195.90i 0.167482 0.121683i
\(689\) 44722.0 + 32492.5i 2.47282 + 1.79661i
\(690\) 0 0
\(691\) 27262.3 19807.2i 1.50088 1.09045i 0.530846 0.847468i \(-0.321874\pi\)
0.970031 0.242982i \(-0.0781257\pi\)
\(692\) −6313.57 + 19431.2i −0.346829 + 1.06743i
\(693\) 0 0
\(694\) −128.844 + 396.542i −0.00704735 + 0.0216895i
\(695\) 29124.0 19611.0i 1.58955 1.07034i
\(696\) 0 0
\(697\) −59.4539 182.980i −0.00323095 0.00994386i
\(698\) −4177.05 3034.80i −0.226510 0.164569i
\(699\) 0 0
\(700\) 3561.54 8775.33i 0.192305 0.473823i
\(701\) −23077.6 −1.24341 −0.621704 0.783252i \(-0.713559\pi\)
−0.621704 + 0.783252i \(0.713559\pi\)
\(702\) 0 0
\(703\) 2555.96 + 7866.45i 0.137127 + 0.422032i
\(704\) 41.5532 + 127.888i 0.00222457 + 0.00684651i
\(705\) 0 0
\(706\) 497.950 1532.53i 0.0265447 0.0816963i
\(707\) −1604.51 −0.0853518
\(708\) 0 0
\(709\) 15178.3 11027.7i 0.803997 0.584138i −0.108087 0.994141i \(-0.534472\pi\)
0.912084 + 0.410003i \(0.134472\pi\)
\(710\) 7488.32 + 5860.02i 0.395819 + 0.309750i
\(711\) 0 0
\(712\) −20550.2 + 14930.6i −1.08167 + 0.785880i
\(713\) −12865.8 + 9347.55i −0.675776 + 0.490980i
\(714\) 0 0
\(715\) 814.467 2232.26i 0.0426005 0.116758i
\(716\) −14151.1 + 10281.4i −0.738618 + 0.536637i
\(717\) 0 0
\(718\) 14623.8 0.760104
\(719\) 4136.61 12731.2i 0.214561 0.660351i −0.784623 0.619973i \(-0.787144\pi\)
0.999184 0.0403783i \(-0.0128563\pi\)
\(720\) 0 0
\(721\) −71.0894 218.791i −0.00367199 0.0113012i
\(722\) 2598.48 + 7997.29i 0.133941 + 0.412227i
\(723\) 0 0
\(724\) −2591.23 −0.133014
\(725\) 5370.44 13232.3i 0.275108 0.677841i
\(726\) 0 0
\(727\) 8138.17 + 5912.73i 0.415169 + 0.301638i 0.775691 0.631113i \(-0.217401\pi\)
−0.360522 + 0.932751i \(0.617401\pi\)
\(728\) −6148.19 18922.2i −0.313004 0.963328i
\(729\) 0 0
\(730\) −14414.0 514.710i −0.730804 0.0260963i
\(731\) −265.314 + 816.554i −0.0134241 + 0.0413151i
\(732\) 0 0
\(733\) −884.238 + 2721.40i −0.0445567 + 0.137131i −0.970860 0.239647i \(-0.922968\pi\)
0.926303 + 0.376779i \(0.122968\pi\)
\(734\) −157.475 + 114.413i −0.00791897 + 0.00575347i
\(735\) 0 0
\(736\) 15434.9 + 11214.1i 0.773013 + 0.561627i
\(737\) 1067.12 775.307i 0.0533349 0.0387501i
\(738\) 0 0
\(739\) −24379.0 17712.4i −1.21353 0.881680i −0.217982 0.975953i \(-0.569947\pi\)
−0.995546 + 0.0942726i \(0.969947\pi\)
\(740\) −19719.1 + 13278.1i −0.979577 + 0.659611i
\(741\) 0 0
\(742\) −3263.75 + 10044.8i −0.161477 + 0.496975i
\(743\) −1183.79 −0.0584508 −0.0292254 0.999573i \(-0.509304\pi\)
−0.0292254 + 0.999573i \(0.509304\pi\)
\(744\) 0 0
\(745\) 3863.83 10589.8i 0.190013 0.520781i
\(746\) 1457.06 + 4484.38i 0.0715106 + 0.220087i
\(747\) 0 0
\(748\) 69.1401 + 50.2333i 0.00337970 + 0.00245549i
\(749\) −22370.0 −1.09130
\(750\) 0 0
\(751\) 33092.2 1.60793 0.803964 0.594679i \(-0.202721\pi\)
0.803964 + 0.594679i \(0.202721\pi\)
\(752\) 6612.26 + 4804.08i 0.320644 + 0.232961i
\(753\) 0 0
\(754\) −4049.68 12463.6i −0.195598 0.601988i
\(755\) −8288.88 + 22717.8i −0.399554 + 1.09508i
\(756\) 0 0
\(757\) 14001.4 0.672246 0.336123 0.941818i \(-0.390884\pi\)
0.336123 + 0.941818i \(0.390884\pi\)
\(758\) 167.409 515.233i 0.00802188 0.0246888i
\(759\) 0 0
\(760\) 4260.10 2868.60i 0.203329 0.136914i
\(761\) −13651.0 9918.02i −0.650260 0.472441i 0.213100 0.977030i \(-0.431644\pi\)
−0.863360 + 0.504589i \(0.831644\pi\)
\(762\) 0 0
\(763\) −13213.5 + 9600.19i −0.626949 + 0.455505i
\(764\) −2618.41 1902.39i −0.123993 0.0900864i
\(765\) 0 0
\(766\) 4534.58 3294.56i 0.213892 0.155401i
\(767\) −17537.9 + 53976.0i −0.825627 + 2.54102i
\(768\) 0 0
\(769\) 2146.67 6606.78i 0.100665 0.309813i −0.888024 0.459797i \(-0.847922\pi\)
0.988688 + 0.149984i \(0.0479221\pi\)
\(770\) 453.708 + 16.2015i 0.0212344 + 0.000758260i
\(771\) 0 0
\(772\) 8683.52 + 26725.1i 0.404827 + 1.24593i
\(773\) −6808.98 4947.01i −0.316820 0.230183i 0.417997 0.908448i \(-0.362732\pi\)
−0.734817 + 0.678265i \(0.762732\pi\)
\(774\) 0 0
\(775\) −16327.3 + 10166.7i −0.756765 + 0.471224i
\(776\) 7599.16 0.351539
\(777\) 0 0
\(778\) −4247.16 13071.4i −0.195717 0.602356i
\(779\) 258.640 + 796.012i 0.0118957 + 0.0366111i
\(780\) 0 0
\(781\) 486.937 1498.64i 0.0223098 0.0686625i
\(782\) −768.290 −0.0351330
\(783\) 0 0
\(784\) 3787.52 2751.80i 0.172537 0.125355i
\(785\) −10035.1 + 27503.8i −0.456265 + 1.25051i
\(786\) 0 0
\(787\) 10033.4 7289.66i 0.454448 0.330176i −0.336901 0.941540i \(-0.609379\pi\)
0.791349 + 0.611364i \(0.209379\pi\)
\(788\) 13959.0 10141.8i 0.631053 0.458487i
\(789\) 0 0
\(790\) 6709.09 + 5250.23i 0.302150 + 0.236449i
\(791\) −357.831 + 259.979i −0.0160847 + 0.0116862i
\(792\) 0 0
\(793\) −30624.7 −1.37139
\(794\) 4219.39 12986.0i 0.188590 0.580421i
\(795\) 0 0
\(796\) −9564.38 29436.1i −0.425880 1.31072i
\(797\) −10310.5 31732.5i −0.458240 1.41032i −0.867289 0.497806i \(-0.834139\pi\)
0.409048 0.912513i \(-0.365861\pi\)
\(798\) 0 0
\(799\) −1878.35 −0.0831682
\(800\) 17652.8 + 14859.9i 0.780149 + 0.656719i
\(801\) 0 0
\(802\) −6408.29 4655.90i −0.282151 0.204994i
\(803\) 738.609 + 2273.21i 0.0324595 + 0.0999000i
\(804\) 0 0
\(805\) 11703.1 7880.46i 0.512399 0.345031i
\(806\) −5454.33 + 16786.7i −0.238363 + 0.733607i
\(807\) 0 0
\(808\) 772.812 2378.47i 0.0336478 0.103557i
\(809\) 11812.8 8582.52i 0.513371 0.372986i −0.300730 0.953709i \(-0.597230\pi\)
0.814101 + 0.580724i \(0.197230\pi\)
\(810\) 0 0
\(811\) −4741.12 3444.63i −0.205282 0.149146i 0.480395 0.877052i \(-0.340493\pi\)
−0.685676 + 0.727907i \(0.740493\pi\)
\(812\) −7002.57 + 5087.67i −0.302638 + 0.219879i
\(813\) 0 0
\(814\) −921.973 669.853i −0.0396992 0.0288431i
\(815\) −993.444 3474.87i −0.0426979 0.149349i
\(816\) 0 0
\(817\) 1154.19 3552.22i 0.0494246 0.152113i
\(818\) −7578.50 −0.323932
\(819\) 0 0
\(820\) −1995.39 + 1343.62i −0.0849779 + 0.0572210i
\(821\) −4761.16 14653.3i −0.202394 0.622905i −0.999810 0.0194753i \(-0.993800\pi\)
0.797416 0.603430i \(-0.206200\pi\)
\(822\) 0 0
\(823\) 33713.6 + 24494.3i 1.42792 + 1.03745i 0.990399 + 0.138241i \(0.0441447\pi\)
0.437525 + 0.899206i \(0.355855\pi\)
\(824\) 358.569 0.0151594
\(825\) 0 0
\(826\) −10843.4 −0.456767
\(827\) −12428.2 9029.60i −0.522576 0.379673i 0.294998 0.955498i \(-0.404681\pi\)
−0.817573 + 0.575825i \(0.804681\pi\)
\(828\) 0 0
\(829\) 4586.20 + 14114.9i 0.192142 + 0.591351i 0.999998 + 0.00197177i \(0.000627633\pi\)
−0.807856 + 0.589379i \(0.799372\pi\)
\(830\) −1316.91 4606.28i −0.0550729 0.192634i
\(831\) 0 0
\(832\) 4638.16 0.193268
\(833\) −332.480 + 1023.27i −0.0138292 + 0.0425620i
\(834\) 0 0
\(835\) 1399.85 + 1095.46i 0.0580164 + 0.0454010i
\(836\) −300.778 218.528i −0.0124433 0.00904060i
\(837\) 0 0
\(838\) −14853.5 + 10791.7i −0.612299 + 0.444861i
\(839\) 3570.89 + 2594.40i 0.146938 + 0.106757i 0.658825 0.752296i \(-0.271054\pi\)
−0.511888 + 0.859052i \(0.671054\pi\)
\(840\) 0 0
\(841\) 9171.97 6663.83i 0.376070 0.273231i
\(842\) −3814.94 + 11741.2i −0.156142 + 0.480556i
\(843\) 0 0
\(844\) −7194.54 + 22142.5i −0.293420 + 0.903053i
\(845\) −45202.3 35373.2i −1.84024 1.44009i
\(846\) 0 0
\(847\) 4998.79 + 15384.7i 0.202787 + 0.624113i
\(848\) 12610.6 + 9162.13i 0.510672 + 0.371025i
\(849\) 0 0
\(850\) −926.840 66.2775i −0.0374004 0.00267447i
\(851\) −35416.4 −1.42663
\(852\) 0 0
\(853\) −1784.63 5492.53i −0.0716350 0.220470i 0.908829 0.417169i \(-0.136978\pi\)
−0.980464 + 0.196699i \(0.936978\pi\)
\(854\) −1808.11 5564.78i −0.0724498 0.222977i
\(855\) 0 0
\(856\) 10774.5 33160.7i 0.430218 1.32407i
\(857\) 4100.45 0.163441 0.0817203 0.996655i \(-0.473959\pi\)
0.0817203 + 0.996655i \(0.473959\pi\)
\(858\) 0 0
\(859\) 7956.07 5780.42i 0.316016 0.229599i −0.418458 0.908236i \(-0.637429\pi\)
0.734473 + 0.678637i \(0.237429\pi\)
\(860\) 10728.2 + 383.092i 0.425381 + 0.0151899i
\(861\) 0 0
\(862\) −8200.41 + 5957.94i −0.324022 + 0.235416i
\(863\) 13882.1 10086.0i 0.547571 0.397834i −0.279318 0.960199i \(-0.590108\pi\)
0.826889 + 0.562365i \(0.190108\pi\)
\(864\) 0 0
\(865\) −30535.7 + 20561.6i −1.20028 + 0.808226i
\(866\) 4386.16 3186.73i 0.172111 0.125046i
\(867\) 0 0
\(868\) 11657.9 0.455870
\(869\) 436.266 1342.69i 0.0170303 0.0524138i
\(870\) 0 0
\(871\) −14059.2 43269.8i −0.546933 1.68329i
\(872\) −7866.72 24211.3i −0.305505 0.940249i
\(873\) 0 0
\(874\) 3342.26 0.129352
\(875\) 14798.1 8497.15i 0.571733 0.328293i
\(876\) 0 0
\(877\) 7136.71 + 5185.12i 0.274789 + 0.199646i 0.716641 0.697442i \(-0.245679\pi\)
−0.441853 + 0.897088i \(0.645679\pi\)
\(878\) −1616.04 4973.67i −0.0621171 0.191177i
\(879\) 0 0
\(880\) 229.661 629.446i 0.00879758 0.0241121i
\(881\) 9227.88 28400.5i 0.352889 1.08608i −0.604335 0.796731i \(-0.706561\pi\)
0.957223 0.289350i \(-0.0934391\pi\)
\(882\) 0 0
\(883\) 2159.26 6645.52i 0.0822932 0.253272i −0.901441 0.432902i \(-0.857490\pi\)
0.983734 + 0.179629i \(0.0574898\pi\)
\(884\) 2384.81 1732.67i 0.0907352 0.0659230i
\(885\) 0 0
\(886\) −2480.92 1802.49i −0.0940723 0.0683476i
\(887\) 35503.0 25794.4i 1.34394 0.976428i 0.344648 0.938732i \(-0.387998\pi\)
0.999289 0.0376958i \(-0.0120018\pi\)
\(888\) 0 0
\(889\) −13805.9 10030.5i −0.520848 0.378418i
\(890\) −19979.9 713.461i −0.752503 0.0268711i
\(891\) 0 0
\(892\) −3139.98 + 9663.87i −0.117864 + 0.362747i
\(893\) 8171.33 0.306207
\(894\) 0 0
\(895\) −31496.7 1124.71i −1.17633 0.0420057i
\(896\) −5298.21 16306.2i −0.197546 0.607983i
\(897\) 0 0
\(898\) −10866.3 7894.83i −0.403801 0.293379i
\(899\) 17578.9 0.652157
\(900\) 0 0
\(901\) −3582.31 −0.132457
\(902\) −93.2951 67.7829i −0.00344389 0.00250213i
\(903\) 0 0
\(904\) −213.036 655.657i −0.00783790 0.0241226i
\(905\) −3676.89 2877.36i −0.135054 0.105687i
\(906\) 0 0
\(907\) 20572.4 0.753138 0.376569 0.926389i \(-0.377104\pi\)
0.376569 + 0.926389i \(0.377104\pi\)
\(908\) −7273.16 + 22384.5i −0.265824 + 0.818122i
\(909\) 0 0
\(910\) 5367.44 14710.9i 0.195526 0.535891i
\(911\) −5933.73 4311.11i −0.215799 0.156787i 0.474634 0.880183i \(-0.342580\pi\)
−0.690434 + 0.723396i \(0.742580\pi\)
\(912\) 0 0
\(913\) −642.302 + 466.660i −0.0232827 + 0.0169159i
\(914\) −3569.31 2593.26i −0.129171 0.0938483i
\(915\) 0 0
\(916\) 452.902 329.053i 0.0163366 0.0118692i
\(917\) −10708.3 + 32956.8i −0.385627 + 1.18684i
\(918\) 0 0
\(919\) −12333.6 + 37958.9i −0.442707 + 1.36251i 0.442271 + 0.896882i \(0.354173\pi\)
−0.884978 + 0.465632i \(0.845827\pi\)
\(920\) 6044.93 + 21144.0i 0.216625 + 0.757713i
\(921\) 0 0
\(922\) −344.178 1059.27i −0.0122938 0.0378365i
\(923\) −43971.5 31947.2i −1.56808 1.13928i
\(924\) 0 0
\(925\) −42725.2 3055.24i −1.51870 0.108601i
\(926\) 12093.5 0.429176
\(927\) 0 0
\(928\) −6516.90 20057.0i −0.230526 0.709485i
\(929\) −6378.19 19630.0i −0.225255 0.693263i −0.998266 0.0588699i \(-0.981250\pi\)
0.773011 0.634393i \(-0.218750\pi\)
\(930\) 0 0
\(931\) 1446.38 4451.49i 0.0509163 0.156704i
\(932\) 22452.4 0.789112
\(933\) 0 0
\(934\) −1426.10 + 1036.12i −0.0499607 + 0.0362986i
\(935\) 42.3279 + 148.055i 0.00148050 + 0.00517851i
\(936\) 0 0
\(937\) −21497.0 + 15618.5i −0.749494 + 0.544539i −0.895670 0.444719i \(-0.853303\pi\)
0.146176 + 0.989259i \(0.453303\pi\)
\(938\) 7032.45 5109.37i 0.244795 0.177854i
\(939\) 0 0
\(940\) 6455.74 + 22580.9i 0.224003 + 0.783519i
\(941\) 10502.5 7630.51i 0.363838 0.264344i −0.390813 0.920470i \(-0.627806\pi\)
0.754651 + 0.656126i \(0.227806\pi\)
\(942\) 0 0
\(943\) −3583.81 −0.123759
\(944\) −4945.28 + 15220.0i −0.170503 + 0.524755i
\(945\) 0 0
\(946\) 159.025 + 489.428i 0.00546547 + 0.0168210i
\(947\) −14382.2 44263.9i −0.493516 1.51888i −0.819257 0.573426i \(-0.805614\pi\)
0.325742 0.945459i \(-0.394386\pi\)
\(948\) 0 0
\(949\) 82443.5 2.82005
\(950\) 4032.00 + 288.324i 0.137700 + 0.00984682i
\(951\) 0 0
\(952\) 1043.09 + 757.849i 0.0355113 + 0.0258005i
\(953\) 11512.2 + 35430.8i 0.391307 + 1.20432i 0.931800 + 0.362972i \(0.118238\pi\)
−0.540493 + 0.841349i \(0.681762\pi\)
\(954\) 0 0
\(955\) −1603.00 5607.00i −0.0543163 0.189988i
\(956\) −2820.12 + 8679.45i −0.0954072 + 0.293633i
\(957\) 0 0
\(958\) 3863.18 11889.6i 0.130286 0.400978i
\(959\) 8004.23 5815.41i 0.269520 0.195818i
\(960\) 0 0
\(961\) 4946.94 + 3594.16i 0.166055 + 0.120646i
\(962\) −31801.1 + 23104.9i −1.06581 + 0.774356i
\(963\) 0 0
\(964\) −19811.2 14393.7i −0.661905 0.480902i
\(965\) −17354.5 + 47564.7i −0.578925 + 1.58670i
\(966\) 0 0
\(967\) −9790.75 + 30132.8i −0.325594 + 1.00207i 0.645578 + 0.763694i \(0.276616\pi\)
−0.971172 + 0.238380i \(0.923384\pi\)
\(968\) −25213.5 −0.837181
\(969\) 0 0
\(970\) 4710.24 + 3686.02i 0.155914 + 0.122011i
\(971\) −8373.85 25772.1i −0.276756 0.851766i −0.988750 0.149581i \(-0.952208\pi\)
0.711994 0.702186i \(-0.247792\pi\)
\(972\) 0 0
\(973\) −31021.9 22538.7i −1.02211 0.742608i
\(974\) 2753.84 0.0905943
\(975\) 0 0
\(976\) −8635.46 −0.283211
\(977\) 40154.6 + 29174.1i 1.31490 + 0.955333i 0.999981 + 0.00621630i \(0.00197872\pi\)
0.314923 + 0.949117i \(0.398021\pi\)
\(978\) 0 0
\(979\) 1023.82 + 3150.99i 0.0334233 + 0.102866i
\(980\) 13444.1 + 480.074i 0.438220 + 0.0156484i
\(981\) 0 0
\(982\) 4783.11 0.155433
\(983\) −10741.8 + 33059.7i −0.348534 + 1.07268i 0.611131 + 0.791530i \(0.290715\pi\)
−0.959665 + 0.281147i \(0.909285\pi\)
\(984\) 0 0
\(985\) 31069.2 + 1109.45i 1.00502 + 0.0358884i
\(986\) 687.061 + 499.179i 0.0221912 + 0.0161228i
\(987\) 0 0
\(988\) −10374.6 + 7537.56i −0.334068 + 0.242714i
\(989\) 12938.5 + 9400.36i 0.415996 + 0.302239i
\(990\) 0 0
\(991\) −15805.8 + 11483.6i −0.506646 + 0.368100i −0.811550 0.584283i \(-0.801376\pi\)
0.304904 + 0.952383i \(0.401376\pi\)
\(992\) −8777.33 + 27013.8i −0.280928 + 0.864607i
\(993\) 0 0
\(994\) 3208.97 9876.21i 0.102397 0.315145i
\(995\) 19115.0 52389.7i 0.609031 1.66921i
\(996\) 0 0
\(997\) 10317.8 + 31755.1i 0.327753 + 1.00872i 0.970183 + 0.242375i \(0.0779264\pi\)
−0.642430 + 0.766344i \(0.722074\pi\)
\(998\) −343.546 249.601i −0.0108965 0.00791680i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 225.4.h.a.91.5 28
3.2 odd 2 75.4.g.b.16.3 28
25.11 even 5 inner 225.4.h.a.136.5 28
75.11 odd 10 75.4.g.b.61.3 yes 28
75.44 odd 10 1875.4.a.f.1.6 14
75.56 odd 10 1875.4.a.g.1.9 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.4.g.b.16.3 28 3.2 odd 2
75.4.g.b.61.3 yes 28 75.11 odd 10
225.4.h.a.91.5 28 1.1 even 1 trivial
225.4.h.a.136.5 28 25.11 even 5 inner
1875.4.a.f.1.6 14 75.44 odd 10
1875.4.a.g.1.9 14 75.56 odd 10