Properties

Label 315.3.ca.b.172.3
Level $315$
Weight $3$
Character 315.172
Analytic conductor $8.583$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,3,Mod(37,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.37");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 315.ca (of order \(12\), 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: \(8.58312832735\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 172.3
Character \(\chi\) \(=\) 315.172
Dual form 315.3.ca.b.163.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.770020 + 2.87375i) q^{2} +(-4.20143 - 2.42570i) q^{4} +(4.72092 - 1.64709i) q^{5} +(-6.80154 - 1.65502i) q^{7} +(1.79111 - 1.79111i) q^{8} +O(q^{10})\) \(q+(-0.770020 + 2.87375i) q^{2} +(-4.20143 - 2.42570i) q^{4} +(4.72092 - 1.64709i) q^{5} +(-6.80154 - 1.65502i) q^{7} +(1.79111 - 1.79111i) q^{8} +(1.09812 + 14.8351i) q^{10} +(-6.96127 + 12.0573i) q^{11} +(7.79302 - 7.79302i) q^{13} +(9.99344 - 18.2715i) q^{14} +(-5.93477 - 10.2793i) q^{16} +(-25.8415 + 6.92421i) q^{17} +(-28.5616 + 16.4901i) q^{19} +(-23.8300 - 4.53140i) q^{20} +(-29.2893 - 29.2893i) q^{22} +(-20.4773 - 5.48688i) q^{23} +(19.5742 - 15.5516i) q^{25} +(16.3944 + 28.3960i) q^{26} +(24.5616 + 23.4519i) q^{28} +18.1531i q^{29} +(-11.5772 + 20.0522i) q^{31} +(43.8970 - 11.7622i) q^{32} -79.5940i q^{34} +(-34.8355 + 3.38952i) q^{35} +(5.40117 - 20.1574i) q^{37} +(-25.3954 - 94.7768i) q^{38} +(5.50557 - 11.4058i) q^{40} +1.69819 q^{41} +(26.7992 - 26.7992i) q^{43} +(58.4946 - 33.7719i) q^{44} +(31.5359 - 54.6218i) q^{46} +(-2.75524 + 10.2827i) q^{47} +(43.5218 + 22.5134i) q^{49} +(29.6188 + 68.2264i) q^{50} +(-51.6453 + 13.8383i) q^{52} +(-11.5451 - 43.0869i) q^{53} +(-13.0042 + 68.3872i) q^{55} +(-15.1466 + 9.21797i) q^{56} +(-52.1677 - 13.9783i) q^{58} +(9.04603 + 5.22273i) q^{59} +(40.5827 + 70.2914i) q^{61} +(-48.7105 - 48.7105i) q^{62} +87.7280i q^{64} +(23.9544 - 49.6260i) q^{65} +(-40.9029 + 10.9599i) q^{67} +(125.367 + 33.5921i) q^{68} +(17.0834 - 102.719i) q^{70} +20.1105 q^{71} +(-1.68295 - 6.28085i) q^{73} +(53.7685 + 31.0433i) q^{74} +160.000 q^{76} +(67.3023 - 70.4869i) q^{77} +(-10.5341 + 6.08184i) q^{79} +(-44.9486 - 38.7528i) q^{80} +(-1.30764 + 4.88019i) q^{82} +(-20.6649 + 20.6649i) q^{83} +(-110.591 + 75.2519i) q^{85} +(56.3783 + 97.6501i) q^{86} +(9.12749 + 34.0643i) q^{88} +(-145.002 + 83.7168i) q^{89} +(-65.9021 + 40.1069i) q^{91} +(72.7245 + 72.7245i) q^{92} +(-27.4284 - 15.8358i) q^{94} +(-107.677 + 124.892i) q^{95} +(-66.3082 - 66.3082i) q^{97} +(-98.2105 + 107.735i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.770020 + 2.87375i −0.385010 + 1.43688i 0.453141 + 0.891439i \(0.350303\pi\)
−0.838151 + 0.545438i \(0.816363\pi\)
\(3\) 0 0
\(4\) −4.20143 2.42570i −1.05036 0.606424i
\(5\) 4.72092 1.64709i 0.944184 0.329418i
\(6\) 0 0
\(7\) −6.80154 1.65502i −0.971648 0.236431i
\(8\) 1.79111 1.79111i 0.223889 0.223889i
\(9\) 0 0
\(10\) 1.09812 + 14.8351i 0.109812 + 1.48351i
\(11\) −6.96127 + 12.0573i −0.632842 + 1.09612i 0.354126 + 0.935198i \(0.384779\pi\)
−0.986968 + 0.160917i \(0.948555\pi\)
\(12\) 0 0
\(13\) 7.79302 7.79302i 0.599463 0.599463i −0.340707 0.940170i \(-0.610666\pi\)
0.940170 + 0.340707i \(0.110666\pi\)
\(14\) 9.99344 18.2715i 0.713817 1.30511i
\(15\) 0 0
\(16\) −5.93477 10.2793i −0.370923 0.642458i
\(17\) −25.8415 + 6.92421i −1.52009 + 0.407307i −0.919771 0.392455i \(-0.871626\pi\)
−0.600318 + 0.799761i \(0.704959\pi\)
\(18\) 0 0
\(19\) −28.5616 + 16.4901i −1.50324 + 0.867898i −0.503251 + 0.864140i \(0.667863\pi\)
−0.999993 + 0.00375778i \(0.998804\pi\)
\(20\) −23.8300 4.53140i −1.19150 0.226570i
\(21\) 0 0
\(22\) −29.2893 29.2893i −1.33133 1.33133i
\(23\) −20.4773 5.48688i −0.890318 0.238560i −0.215464 0.976512i \(-0.569127\pi\)
−0.674854 + 0.737952i \(0.735793\pi\)
\(24\) 0 0
\(25\) 19.5742 15.5516i 0.782968 0.622062i
\(26\) 16.3944 + 28.3960i 0.630555 + 1.09215i
\(27\) 0 0
\(28\) 24.5616 + 23.4519i 0.877201 + 0.837569i
\(29\) 18.1531i 0.625971i 0.949758 + 0.312985i \(0.101329\pi\)
−0.949758 + 0.312985i \(0.898671\pi\)
\(30\) 0 0
\(31\) −11.5772 + 20.0522i −0.373457 + 0.646846i −0.990095 0.140401i \(-0.955161\pi\)
0.616638 + 0.787247i \(0.288494\pi\)
\(32\) 43.8970 11.7622i 1.37178 0.367567i
\(33\) 0 0
\(34\) 79.5940i 2.34100i
\(35\) −34.8355 + 3.38952i −0.995300 + 0.0968434i
\(36\) 0 0
\(37\) 5.40117 20.1574i 0.145978 0.544796i −0.853732 0.520712i \(-0.825667\pi\)
0.999710 0.0240837i \(-0.00766681\pi\)
\(38\) −25.3954 94.7768i −0.668299 2.49413i
\(39\) 0 0
\(40\) 5.50557 11.4058i 0.137639 0.285145i
\(41\) 1.69819 0.0414193 0.0207097 0.999786i \(-0.493407\pi\)
0.0207097 + 0.999786i \(0.493407\pi\)
\(42\) 0 0
\(43\) 26.7992 26.7992i 0.623236 0.623236i −0.323121 0.946358i \(-0.604732\pi\)
0.946358 + 0.323121i \(0.104732\pi\)
\(44\) 58.4946 33.7719i 1.32942 0.767542i
\(45\) 0 0
\(46\) 31.5359 54.6218i 0.685563 1.18743i
\(47\) −2.75524 + 10.2827i −0.0586222 + 0.218781i −0.989023 0.147763i \(-0.952793\pi\)
0.930401 + 0.366544i \(0.119459\pi\)
\(48\) 0 0
\(49\) 43.5218 + 22.5134i 0.888200 + 0.459456i
\(50\) 29.6188 + 68.2264i 0.592376 + 1.36453i
\(51\) 0 0
\(52\) −51.6453 + 13.8383i −0.993179 + 0.266122i
\(53\) −11.5451 43.0869i −0.217832 0.812961i −0.985150 0.171694i \(-0.945076\pi\)
0.767318 0.641267i \(-0.221591\pi\)
\(54\) 0 0
\(55\) −13.0042 + 68.3872i −0.236440 + 1.24340i
\(56\) −15.1466 + 9.21797i −0.270475 + 0.164607i
\(57\) 0 0
\(58\) −52.1677 13.9783i −0.899443 0.241005i
\(59\) 9.04603 + 5.22273i 0.153323 + 0.0885208i 0.574698 0.818365i \(-0.305119\pi\)
−0.421376 + 0.906886i \(0.638453\pi\)
\(60\) 0 0
\(61\) 40.5827 + 70.2914i 0.665291 + 1.15232i 0.979206 + 0.202867i \(0.0650258\pi\)
−0.313915 + 0.949451i \(0.601641\pi\)
\(62\) −48.7105 48.7105i −0.785654 0.785654i
\(63\) 0 0
\(64\) 87.7280i 1.37075i
\(65\) 23.9544 49.6260i 0.368530 0.763477i
\(66\) 0 0
\(67\) −40.9029 + 10.9599i −0.610491 + 0.163581i −0.550801 0.834636i \(-0.685678\pi\)
−0.0596898 + 0.998217i \(0.519011\pi\)
\(68\) 125.367 + 33.5921i 1.84364 + 0.494001i
\(69\) 0 0
\(70\) 17.0834 102.719i 0.244048 1.46741i
\(71\) 20.1105 0.283247 0.141623 0.989921i \(-0.454768\pi\)
0.141623 + 0.989921i \(0.454768\pi\)
\(72\) 0 0
\(73\) −1.68295 6.28085i −0.0230541 0.0860390i 0.953440 0.301582i \(-0.0975146\pi\)
−0.976494 + 0.215543i \(0.930848\pi\)
\(74\) 53.7685 + 31.0433i 0.726602 + 0.419504i
\(75\) 0 0
\(76\) 160.000 2.10526
\(77\) 67.3023 70.4869i 0.874056 0.915415i
\(78\) 0 0
\(79\) −10.5341 + 6.08184i −0.133342 + 0.0769853i −0.565187 0.824963i \(-0.691196\pi\)
0.431845 + 0.901948i \(0.357863\pi\)
\(80\) −44.9486 38.7528i −0.561857 0.484410i
\(81\) 0 0
\(82\) −1.30764 + 4.88019i −0.0159469 + 0.0595145i
\(83\) −20.6649 + 20.6649i −0.248975 + 0.248975i −0.820550 0.571575i \(-0.806333\pi\)
0.571575 + 0.820550i \(0.306333\pi\)
\(84\) 0 0
\(85\) −110.591 + 75.2519i −1.30107 + 0.885317i
\(86\) 56.3783 + 97.6501i 0.655562 + 1.13547i
\(87\) 0 0
\(88\) 9.12749 + 34.0643i 0.103721 + 0.387094i
\(89\) −145.002 + 83.7168i −1.62923 + 0.940638i −0.644911 + 0.764257i \(0.723106\pi\)
−0.984322 + 0.176381i \(0.943561\pi\)
\(90\) 0 0
\(91\) −65.9021 + 40.1069i −0.724199 + 0.440735i
\(92\) 72.7245 + 72.7245i 0.790484 + 0.790484i
\(93\) 0 0
\(94\) −27.4284 15.8358i −0.291791 0.168466i
\(95\) −107.677 + 124.892i −1.13344 + 1.31465i
\(96\) 0 0
\(97\) −66.3082 66.3082i −0.683589 0.683589i 0.277218 0.960807i \(-0.410588\pi\)
−0.960807 + 0.277218i \(0.910588\pi\)
\(98\) −98.2105 + 107.735i −1.00215 + 1.09934i
\(99\) 0 0
\(100\) −119.963 + 17.8577i −1.19963 + 0.178577i
\(101\) 22.9150 39.6899i 0.226881 0.392969i −0.730001 0.683446i \(-0.760481\pi\)
0.956882 + 0.290477i \(0.0938138\pi\)
\(102\) 0 0
\(103\) −21.1782 5.67468i −0.205614 0.0550940i 0.154542 0.987986i \(-0.450610\pi\)
−0.360156 + 0.932892i \(0.617276\pi\)
\(104\) 27.9163i 0.268426i
\(105\) 0 0
\(106\) 132.711 1.25199
\(107\) −26.1382 + 97.5490i −0.244282 + 0.911673i 0.729461 + 0.684022i \(0.239771\pi\)
−0.973743 + 0.227650i \(0.926896\pi\)
\(108\) 0 0
\(109\) 109.890 + 63.4449i 1.00816 + 0.582064i 0.910654 0.413171i \(-0.135579\pi\)
0.0975104 + 0.995235i \(0.468912\pi\)
\(110\) −186.515 90.0304i −1.69559 0.818458i
\(111\) 0 0
\(112\) 23.3531 + 79.7374i 0.208510 + 0.711941i
\(113\) 10.2422 10.2422i 0.0906391 0.0906391i −0.660333 0.750973i \(-0.729585\pi\)
0.750973 + 0.660333i \(0.229585\pi\)
\(114\) 0 0
\(115\) −105.709 + 7.82482i −0.919210 + 0.0680419i
\(116\) 44.0340 76.2692i 0.379604 0.657493i
\(117\) 0 0
\(118\) −21.9745 + 21.9745i −0.186224 + 0.186224i
\(119\) 187.222 4.32709i 1.57329 0.0363621i
\(120\) 0 0
\(121\) −36.4184 63.0786i −0.300979 0.521311i
\(122\) −233.250 + 62.4991i −1.91188 + 0.512287i
\(123\) 0 0
\(124\) 97.2812 56.1654i 0.784526 0.452946i
\(125\) 66.7935 105.658i 0.534348 0.845265i
\(126\) 0 0
\(127\) 138.223 + 138.223i 1.08837 + 1.08837i 0.995697 + 0.0926732i \(0.0295412\pi\)
0.0926732 + 0.995697i \(0.470459\pi\)
\(128\) −76.5208 20.5037i −0.597819 0.160185i
\(129\) 0 0
\(130\) 124.168 + 107.052i 0.955135 + 0.823478i
\(131\) −11.0263 19.0981i −0.0841704 0.145787i 0.820867 0.571119i \(-0.193491\pi\)
−0.905037 + 0.425332i \(0.860157\pi\)
\(132\) 0 0
\(133\) 221.554 64.8877i 1.66582 0.487878i
\(134\) 125.984i 0.940181i
\(135\) 0 0
\(136\) −33.8829 + 58.6870i −0.249139 + 0.431522i
\(137\) −207.089 + 55.4894i −1.51160 + 0.405032i −0.916966 0.398965i \(-0.869370\pi\)
−0.594634 + 0.803997i \(0.702703\pi\)
\(138\) 0 0
\(139\) 203.695i 1.46543i −0.680534 0.732716i \(-0.738252\pi\)
0.680534 0.732716i \(-0.261748\pi\)
\(140\) 154.581 + 70.2595i 1.10415 + 0.501854i
\(141\) 0 0
\(142\) −15.4855 + 57.7926i −0.109053 + 0.406990i
\(143\) 39.7132 + 148.212i 0.277715 + 1.03645i
\(144\) 0 0
\(145\) 29.8998 + 85.6996i 0.206206 + 0.591032i
\(146\) 19.3455 0.132504
\(147\) 0 0
\(148\) −71.5885 + 71.5885i −0.483706 + 0.483706i
\(149\) 106.635 61.5658i 0.715672 0.413193i −0.0974859 0.995237i \(-0.531080\pi\)
0.813157 + 0.582044i \(0.197747\pi\)
\(150\) 0 0
\(151\) −50.6434 + 87.7170i −0.335387 + 0.580907i −0.983559 0.180587i \(-0.942200\pi\)
0.648172 + 0.761494i \(0.275534\pi\)
\(152\) −21.6215 + 80.6925i −0.142247 + 0.530872i
\(153\) 0 0
\(154\) 150.738 + 247.687i 0.978818 + 1.60836i
\(155\) −21.6271 + 113.734i −0.139529 + 0.733765i
\(156\) 0 0
\(157\) 70.0141 18.7602i 0.445950 0.119492i −0.0288540 0.999584i \(-0.509186\pi\)
0.474804 + 0.880092i \(0.342519\pi\)
\(158\) −9.36628 34.9554i −0.0592802 0.221237i
\(159\) 0 0
\(160\) 187.861 127.830i 1.17413 0.798940i
\(161\) 130.196 + 71.2096i 0.808673 + 0.442295i
\(162\) 0 0
\(163\) −175.917 47.1369i −1.07925 0.289183i −0.324960 0.945728i \(-0.605351\pi\)
−0.754287 + 0.656545i \(0.772017\pi\)
\(164\) −7.13484 4.11930i −0.0435051 0.0251177i
\(165\) 0 0
\(166\) −43.4735 75.2984i −0.261889 0.453605i
\(167\) 188.951 + 188.951i 1.13144 + 1.13144i 0.989938 + 0.141505i \(0.0451940\pi\)
0.141505 + 0.989938i \(0.454806\pi\)
\(168\) 0 0
\(169\) 47.5377i 0.281288i
\(170\) −131.098 375.757i −0.771167 2.21033i
\(171\) 0 0
\(172\) −177.601 + 47.5882i −1.03257 + 0.276675i
\(173\) −8.81487 2.36194i −0.0509530 0.0136528i 0.233253 0.972416i \(-0.425063\pi\)
−0.284206 + 0.958763i \(0.591730\pi\)
\(174\) 0 0
\(175\) −158.873 + 73.3788i −0.907844 + 0.419307i
\(176\) 165.254 0.938944
\(177\) 0 0
\(178\) −128.927 481.163i −0.724310 2.70316i
\(179\) 232.008 + 133.950i 1.29613 + 0.748322i 0.979734 0.200304i \(-0.0641931\pi\)
0.316398 + 0.948626i \(0.397526\pi\)
\(180\) 0 0
\(181\) −226.975 −1.25401 −0.627004 0.779016i \(-0.715719\pi\)
−0.627004 + 0.779016i \(0.715719\pi\)
\(182\) −64.5115 220.270i −0.354459 1.21027i
\(183\) 0 0
\(184\) −46.5047 + 26.8495i −0.252743 + 0.145921i
\(185\) −7.70259 104.058i −0.0416356 0.562475i
\(186\) 0 0
\(187\) 96.4026 359.779i 0.515522 1.92395i
\(188\) 36.5187 36.5187i 0.194248 0.194248i
\(189\) 0 0
\(190\) −275.995 405.605i −1.45261 2.13477i
\(191\) −77.8090 134.769i −0.407377 0.705597i 0.587218 0.809429i \(-0.300223\pi\)
−0.994595 + 0.103831i \(0.966890\pi\)
\(192\) 0 0
\(193\) 54.4390 + 203.169i 0.282067 + 1.05269i 0.950956 + 0.309327i \(0.100104\pi\)
−0.668889 + 0.743363i \(0.733230\pi\)
\(194\) 241.612 139.495i 1.24542 0.719045i
\(195\) 0 0
\(196\) −128.243 200.159i −0.654303 1.02122i
\(197\) 98.6199 + 98.6199i 0.500609 + 0.500609i 0.911627 0.411018i \(-0.134827\pi\)
−0.411018 + 0.911627i \(0.634827\pi\)
\(198\) 0 0
\(199\) 35.8210 + 20.6813i 0.180005 + 0.103926i 0.587295 0.809373i \(-0.300193\pi\)
−0.407290 + 0.913299i \(0.633526\pi\)
\(200\) 7.20499 62.9140i 0.0360250 0.314570i
\(201\) 0 0
\(202\) 96.4140 + 96.4140i 0.477297 + 0.477297i
\(203\) 30.0438 123.469i 0.147999 0.608223i
\(204\) 0 0
\(205\) 8.01703 2.79707i 0.0391075 0.0136443i
\(206\) 32.6153 56.4913i 0.158327 0.274230i
\(207\) 0 0
\(208\) −126.357 33.8572i −0.607485 0.162775i
\(209\) 459.167i 2.19697i
\(210\) 0 0
\(211\) 326.483 1.54731 0.773655 0.633607i \(-0.218426\pi\)
0.773655 + 0.633607i \(0.218426\pi\)
\(212\) −56.0099 + 209.032i −0.264198 + 0.985999i
\(213\) 0 0
\(214\) −260.205 150.229i −1.21591 0.702006i
\(215\) 82.3761 170.657i 0.383145 0.793755i
\(216\) 0 0
\(217\) 111.929 117.226i 0.515803 0.540210i
\(218\) −266.943 + 266.943i −1.22451 + 1.22451i
\(219\) 0 0
\(220\) 220.523 255.780i 1.00238 1.16264i
\(221\) −147.423 + 255.344i −0.667072 + 1.15540i
\(222\) 0 0
\(223\) −39.2007 + 39.2007i −0.175788 + 0.175788i −0.789517 0.613729i \(-0.789669\pi\)
0.613729 + 0.789517i \(0.289669\pi\)
\(224\) −318.033 + 7.35042i −1.41979 + 0.0328144i
\(225\) 0 0
\(226\) 21.5469 + 37.3203i 0.0953403 + 0.165134i
\(227\) 3.48231 0.933082i 0.0153406 0.00411049i −0.251141 0.967951i \(-0.580806\pi\)
0.266481 + 0.963840i \(0.414139\pi\)
\(228\) 0 0
\(229\) 46.0053 26.5612i 0.200896 0.115988i −0.396177 0.918174i \(-0.629663\pi\)
0.597074 + 0.802186i \(0.296330\pi\)
\(230\) 58.9116 309.807i 0.256137 1.34699i
\(231\) 0 0
\(232\) 32.5143 + 32.5143i 0.140148 + 0.140148i
\(233\) −124.839 33.4506i −0.535791 0.143565i −0.0192298 0.999815i \(-0.506121\pi\)
−0.516561 + 0.856250i \(0.672788\pi\)
\(234\) 0 0
\(235\) 3.92924 + 53.0820i 0.0167202 + 0.225881i
\(236\) −25.3375 43.8859i −0.107362 0.185957i
\(237\) 0 0
\(238\) −131.730 + 541.361i −0.553485 + 2.27463i
\(239\) 365.148i 1.52782i −0.645325 0.763908i \(-0.723278\pi\)
0.645325 0.763908i \(-0.276722\pi\)
\(240\) 0 0
\(241\) −196.782 + 340.837i −0.816525 + 1.41426i 0.0917031 + 0.995786i \(0.470769\pi\)
−0.908228 + 0.418476i \(0.862564\pi\)
\(242\) 209.315 56.0859i 0.864939 0.231760i
\(243\) 0 0
\(244\) 393.766i 1.61379i
\(245\) 242.545 + 34.5995i 0.989978 + 0.141222i
\(246\) 0 0
\(247\) −94.0739 + 351.089i −0.380866 + 1.42141i
\(248\) 15.1798 + 56.6516i 0.0612087 + 0.228434i
\(249\) 0 0
\(250\) 252.203 + 273.307i 1.00881 + 1.09323i
\(251\) −353.349 −1.40777 −0.703883 0.710316i \(-0.748552\pi\)
−0.703883 + 0.710316i \(0.748552\pi\)
\(252\) 0 0
\(253\) 208.705 208.705i 0.824920 0.824920i
\(254\) −503.653 + 290.784i −1.98289 + 1.14482i
\(255\) 0 0
\(256\) −57.6108 + 99.7848i −0.225042 + 0.389784i
\(257\) 14.5977 54.4792i 0.0568002 0.211981i −0.931693 0.363247i \(-0.881668\pi\)
0.988493 + 0.151266i \(0.0483348\pi\)
\(258\) 0 0
\(259\) −70.0972 + 128.163i −0.270646 + 0.494836i
\(260\) −221.021 + 150.394i −0.850079 + 0.578439i
\(261\) 0 0
\(262\) 63.3739 16.9810i 0.241885 0.0648129i
\(263\) −73.5553 274.512i −0.279678 1.04377i −0.952641 0.304097i \(-0.901645\pi\)
0.672963 0.739676i \(-0.265021\pi\)
\(264\) 0 0
\(265\) −125.472 184.394i −0.473477 0.695827i
\(266\) 15.8701 + 686.658i 0.0596620 + 2.58142i
\(267\) 0 0
\(268\) 198.436 + 53.1708i 0.740433 + 0.198399i
\(269\) 228.544 + 131.950i 0.849607 + 0.490521i 0.860518 0.509419i \(-0.170140\pi\)
−0.0109111 + 0.999940i \(0.503473\pi\)
\(270\) 0 0
\(271\) 50.4495 + 87.3810i 0.186160 + 0.322439i 0.943967 0.330040i \(-0.107062\pi\)
−0.757807 + 0.652479i \(0.773729\pi\)
\(272\) 224.540 + 224.540i 0.825514 + 0.825514i
\(273\) 0 0
\(274\) 637.851i 2.32792i
\(275\) 51.2480 + 344.270i 0.186356 + 1.25189i
\(276\) 0 0
\(277\) 253.335 67.8808i 0.914566 0.245057i 0.229305 0.973355i \(-0.426355\pi\)
0.685261 + 0.728297i \(0.259688\pi\)
\(278\) 585.370 + 156.849i 2.10565 + 0.564206i
\(279\) 0 0
\(280\) −56.3231 + 68.4651i −0.201154 + 0.244518i
\(281\) −394.591 −1.40424 −0.702119 0.712060i \(-0.747762\pi\)
−0.702119 + 0.712060i \(0.747762\pi\)
\(282\) 0 0
\(283\) −79.1013 295.210i −0.279510 1.04315i −0.952758 0.303729i \(-0.901768\pi\)
0.673249 0.739416i \(-0.264898\pi\)
\(284\) −84.4929 48.7820i −0.297510 0.171768i
\(285\) 0 0
\(286\) −456.504 −1.59617
\(287\) −11.5503 2.81054i −0.0402450 0.00979282i
\(288\) 0 0
\(289\) 369.558 213.364i 1.27875 0.738285i
\(290\) −269.303 + 19.9344i −0.928631 + 0.0687393i
\(291\) 0 0
\(292\) −8.16464 + 30.4709i −0.0279611 + 0.104352i
\(293\) −232.731 + 232.731i −0.794304 + 0.794304i −0.982191 0.187887i \(-0.939836\pi\)
0.187887 + 0.982191i \(0.439836\pi\)
\(294\) 0 0
\(295\) 51.3079 + 9.75647i 0.173925 + 0.0330728i
\(296\) −26.4301 45.7782i −0.0892908 0.154656i
\(297\) 0 0
\(298\) 94.8138 + 353.850i 0.318167 + 1.18742i
\(299\) −202.339 + 116.821i −0.676720 + 0.390705i
\(300\) 0 0
\(301\) −226.629 + 137.922i −0.752919 + 0.458214i
\(302\) −213.081 213.081i −0.705565 0.705565i
\(303\) 0 0
\(304\) 339.014 + 195.730i 1.11518 + 0.643847i
\(305\) 307.364 + 264.997i 1.00775 + 0.868842i
\(306\) 0 0
\(307\) 192.175 + 192.175i 0.625976 + 0.625976i 0.947053 0.321077i \(-0.104045\pi\)
−0.321077 + 0.947053i \(0.604045\pi\)
\(308\) −453.746 + 132.891i −1.47320 + 0.431464i
\(309\) 0 0
\(310\) −310.189 149.728i −1.00061 0.482993i
\(311\) −69.8332 + 120.955i −0.224544 + 0.388922i −0.956183 0.292771i \(-0.905423\pi\)
0.731638 + 0.681693i \(0.238756\pi\)
\(312\) 0 0
\(313\) −47.2333 12.6561i −0.150905 0.0404349i 0.182576 0.983192i \(-0.441557\pi\)
−0.333481 + 0.942757i \(0.608223\pi\)
\(314\) 215.649i 0.686780i
\(315\) 0 0
\(316\) 59.0108 0.186743
\(317\) 77.1789 288.036i 0.243467 0.908630i −0.730681 0.682719i \(-0.760797\pi\)
0.974148 0.225911i \(-0.0725359\pi\)
\(318\) 0 0
\(319\) −218.877 126.369i −0.686136 0.396141i
\(320\) 144.496 + 414.157i 0.451549 + 1.29424i
\(321\) 0 0
\(322\) −304.893 + 319.319i −0.946871 + 0.991675i
\(323\) 623.895 623.895i 1.93156 1.93156i
\(324\) 0 0
\(325\) 31.3485 273.736i 0.0964571 0.842263i
\(326\) 270.920 469.247i 0.831042 1.43941i
\(327\) 0 0
\(328\) 3.04165 3.04165i 0.00927331 0.00927331i
\(329\) 35.7580 65.3782i 0.108687 0.198718i
\(330\) 0 0
\(331\) −43.7659 75.8048i −0.132223 0.229018i 0.792310 0.610119i \(-0.208878\pi\)
−0.924533 + 0.381101i \(0.875545\pi\)
\(332\) 136.949 36.6954i 0.412498 0.110528i
\(333\) 0 0
\(334\) −688.494 + 397.502i −2.06136 + 1.19013i
\(335\) −175.047 + 119.112i −0.522530 + 0.355557i
\(336\) 0 0
\(337\) 170.978 + 170.978i 0.507354 + 0.507354i 0.913713 0.406359i \(-0.133202\pi\)
−0.406359 + 0.913713i \(0.633202\pi\)
\(338\) −136.612 36.6050i −0.404177 0.108299i
\(339\) 0 0
\(340\) 647.179 47.9056i 1.90347 0.140899i
\(341\) −161.183 279.178i −0.472678 0.818703i
\(342\) 0 0
\(343\) −258.755 225.155i −0.754389 0.656428i
\(344\) 96.0004i 0.279071i
\(345\) 0 0
\(346\) 13.5753 23.5130i 0.0392348 0.0679567i
\(347\) −64.4278 + 17.2634i −0.185671 + 0.0497504i −0.350456 0.936579i \(-0.613974\pi\)
0.164785 + 0.986329i \(0.447307\pi\)
\(348\) 0 0
\(349\) 445.265i 1.27583i 0.770106 + 0.637915i \(0.220203\pi\)
−0.770106 + 0.637915i \(0.779797\pi\)
\(350\) −88.5374 513.064i −0.252964 1.46590i
\(351\) 0 0
\(352\) −163.759 + 611.157i −0.465224 + 1.73624i
\(353\) −95.8678 357.784i −0.271580 1.01355i −0.958099 0.286439i \(-0.907529\pi\)
0.686518 0.727112i \(-0.259138\pi\)
\(354\) 0 0
\(355\) 94.9401 33.1238i 0.267437 0.0933064i
\(356\) 812.287 2.28170
\(357\) 0 0
\(358\) −563.589 + 563.589i −1.57427 + 1.57427i
\(359\) −507.313 + 292.897i −1.41313 + 0.815870i −0.995682 0.0928320i \(-0.970408\pi\)
−0.417446 + 0.908702i \(0.637075\pi\)
\(360\) 0 0
\(361\) 363.345 629.331i 1.00649 1.74330i
\(362\) 174.776 652.272i 0.482806 1.80186i
\(363\) 0 0
\(364\) 374.170 8.64786i 1.02794 0.0237579i
\(365\) −18.2902 26.8794i −0.0501101 0.0736422i
\(366\) 0 0
\(367\) −291.219 + 78.0318i −0.793511 + 0.212621i −0.632733 0.774370i \(-0.718067\pi\)
−0.160778 + 0.986991i \(0.551400\pi\)
\(368\) 65.1268 + 243.056i 0.176975 + 0.660479i
\(369\) 0 0
\(370\) 304.968 + 57.9913i 0.824238 + 0.156733i
\(371\) 7.21478 + 312.165i 0.0194469 + 0.841414i
\(372\) 0 0
\(373\) −510.035 136.663i −1.36739 0.366390i −0.500862 0.865527i \(-0.666984\pi\)
−0.866523 + 0.499137i \(0.833650\pi\)
\(374\) 959.686 + 554.075i 2.56600 + 1.48148i
\(375\) 0 0
\(376\) 13.4825 + 23.3524i 0.0358577 + 0.0621074i
\(377\) 141.468 + 141.468i 0.375246 + 0.375246i
\(378\) 0 0
\(379\) 177.062i 0.467182i 0.972335 + 0.233591i \(0.0750476\pi\)
−0.972335 + 0.233591i \(0.924952\pi\)
\(380\) 755.346 263.534i 1.98775 0.693509i
\(381\) 0 0
\(382\) 447.208 119.829i 1.17070 0.313688i
\(383\) −260.649 69.8407i −0.680545 0.182352i −0.0980450 0.995182i \(-0.531259\pi\)
−0.582500 + 0.812830i \(0.697926\pi\)
\(384\) 0 0
\(385\) 201.631 443.616i 0.523716 1.15225i
\(386\) −625.777 −1.62118
\(387\) 0 0
\(388\) 117.746 + 439.433i 0.303468 + 1.13256i
\(389\) 161.408 + 93.1891i 0.414931 + 0.239561i 0.692906 0.721028i \(-0.256330\pi\)
−0.277975 + 0.960588i \(0.589663\pi\)
\(390\) 0 0
\(391\) 567.157 1.45053
\(392\) 118.276 37.6284i 0.301725 0.0959909i
\(393\) 0 0
\(394\) −359.349 + 207.470i −0.912053 + 0.526574i
\(395\) −39.7131 + 46.0624i −0.100540 + 0.116614i
\(396\) 0 0
\(397\) 176.603 659.091i 0.444844 1.66018i −0.271506 0.962437i \(-0.587522\pi\)
0.716349 0.697742i \(-0.245812\pi\)
\(398\) −87.0158 + 87.0158i −0.218633 + 0.218633i
\(399\) 0 0
\(400\) −276.028 108.915i −0.690070 0.272287i
\(401\) −63.9305 110.731i −0.159428 0.276137i 0.775235 0.631673i \(-0.217632\pi\)
−0.934662 + 0.355536i \(0.884298\pi\)
\(402\) 0 0
\(403\) 66.0463 + 246.488i 0.163887 + 0.611634i
\(404\) −192.551 + 111.170i −0.476612 + 0.275172i
\(405\) 0 0
\(406\) 331.686 + 181.412i 0.816961 + 0.446829i
\(407\) 205.445 + 205.445i 0.504778 + 0.504778i
\(408\) 0 0
\(409\) −67.5742 39.0140i −0.165218 0.0953887i 0.415111 0.909771i \(-0.363743\pi\)
−0.580329 + 0.814382i \(0.697076\pi\)
\(410\) 1.86482 + 25.1928i 0.00454835 + 0.0614458i
\(411\) 0 0
\(412\) 75.2137 + 75.2137i 0.182558 + 0.182558i
\(413\) −52.8832 50.4939i −0.128046 0.122261i
\(414\) 0 0
\(415\) −63.5206 + 131.595i −0.153062 + 0.317095i
\(416\) 250.427 433.752i 0.601988 1.04267i
\(417\) 0 0
\(418\) 1319.53 + 353.568i 3.15678 + 0.845856i
\(419\) 38.0855i 0.0908962i 0.998967 + 0.0454481i \(0.0144716\pi\)
−0.998967 + 0.0454481i \(0.985528\pi\)
\(420\) 0 0
\(421\) −151.613 −0.360126 −0.180063 0.983655i \(-0.557630\pi\)
−0.180063 + 0.983655i \(0.557630\pi\)
\(422\) −251.398 + 938.231i −0.595730 + 2.22330i
\(423\) 0 0
\(424\) −97.8519 56.4948i −0.230783 0.133242i
\(425\) −398.145 + 537.412i −0.936811 + 1.26450i
\(426\) 0 0
\(427\) −159.691 545.255i −0.373985 1.27694i
\(428\) 346.442 346.442i 0.809444 0.809444i
\(429\) 0 0
\(430\) 426.996 + 368.138i 0.993014 + 0.856136i
\(431\) 268.299 464.707i 0.622503 1.07821i −0.366515 0.930412i \(-0.619449\pi\)
0.989018 0.147795i \(-0.0472175\pi\)
\(432\) 0 0
\(433\) 421.429 421.429i 0.973278 0.973278i −0.0263739 0.999652i \(-0.508396\pi\)
0.999652 + 0.0263739i \(0.00839605\pi\)
\(434\) 250.690 + 411.923i 0.577626 + 0.949132i
\(435\) 0 0
\(436\) −307.796 533.119i −0.705955 1.22275i
\(437\) 675.344 180.958i 1.54541 0.414092i
\(438\) 0 0
\(439\) −411.292 + 237.460i −0.936884 + 0.540910i −0.888982 0.457942i \(-0.848587\pi\)
−0.0479017 + 0.998852i \(0.515253\pi\)
\(440\) 99.1970 + 145.781i 0.225448 + 0.331320i
\(441\) 0 0
\(442\) −620.277 620.277i −1.40334 1.40334i
\(443\) 90.9998 + 24.3833i 0.205417 + 0.0550414i 0.360060 0.932929i \(-0.382756\pi\)
−0.154643 + 0.987970i \(0.549423\pi\)
\(444\) 0 0
\(445\) −546.653 + 634.051i −1.22843 + 1.42483i
\(446\) −82.4678 142.839i −0.184905 0.320266i
\(447\) 0 0
\(448\) 145.192 596.685i 0.324088 1.33189i
\(449\) 521.631i 1.16176i −0.813989 0.580881i \(-0.802708\pi\)
0.813989 0.580881i \(-0.197292\pi\)
\(450\) 0 0
\(451\) −11.8216 + 20.4756i −0.0262119 + 0.0454003i
\(452\) −67.8765 + 18.1875i −0.150169 + 0.0402377i
\(453\) 0 0
\(454\) 10.7258i 0.0236251i
\(455\) −245.059 + 297.888i −0.538591 + 0.654699i
\(456\) 0 0
\(457\) −107.539 + 401.339i −0.235314 + 0.878204i 0.742693 + 0.669632i \(0.233548\pi\)
−0.978007 + 0.208572i \(0.933118\pi\)
\(458\) 40.9053 + 152.661i 0.0893128 + 0.333320i
\(459\) 0 0
\(460\) 463.110 + 223.543i 1.00676 + 0.485963i
\(461\) −280.539 −0.608544 −0.304272 0.952585i \(-0.598413\pi\)
−0.304272 + 0.952585i \(0.598413\pi\)
\(462\) 0 0
\(463\) −326.436 + 326.436i −0.705045 + 0.705045i −0.965489 0.260444i \(-0.916131\pi\)
0.260444 + 0.965489i \(0.416131\pi\)
\(464\) 186.602 107.735i 0.402160 0.232187i
\(465\) 0 0
\(466\) 192.257 333.000i 0.412570 0.714592i
\(467\) −109.999 + 410.520i −0.235543 + 0.879058i 0.742360 + 0.670001i \(0.233706\pi\)
−0.977903 + 0.209057i \(0.932960\pi\)
\(468\) 0 0
\(469\) 296.342 6.84907i 0.631858 0.0146036i
\(470\) −155.570 29.5825i −0.331000 0.0629415i
\(471\) 0 0
\(472\) 25.5569 6.84795i 0.0541459 0.0145084i
\(473\) 136.569 + 509.681i 0.288728 + 1.07755i
\(474\) 0 0
\(475\) −302.625 + 766.958i −0.637105 + 1.61465i
\(476\) −797.096 435.963i −1.67457 0.915889i
\(477\) 0 0
\(478\) 1049.35 + 281.171i 2.19529 + 0.588225i
\(479\) −183.280 105.817i −0.382630 0.220912i 0.296332 0.955085i \(-0.404237\pi\)
−0.678962 + 0.734173i \(0.737570\pi\)
\(480\) 0 0
\(481\) −114.996 199.179i −0.239077 0.414093i
\(482\) −827.956 827.956i −1.71775 1.71775i
\(483\) 0 0
\(484\) 353.361i 0.730084i
\(485\) −422.251 203.820i −0.870621 0.420248i
\(486\) 0 0
\(487\) −46.3134 + 12.4096i −0.0950993 + 0.0254818i −0.306055 0.952014i \(-0.599009\pi\)
0.210956 + 0.977496i \(0.432342\pi\)
\(488\) 198.588 + 53.2114i 0.406942 + 0.109040i
\(489\) 0 0
\(490\) −286.195 + 670.371i −0.584071 + 1.36810i
\(491\) 784.457 1.59767 0.798836 0.601549i \(-0.205449\pi\)
0.798836 + 0.601549i \(0.205449\pi\)
\(492\) 0 0
\(493\) −125.696 469.105i −0.254962 0.951531i
\(494\) −936.504 540.691i −1.89576 1.09452i
\(495\) 0 0
\(496\) 274.831 0.554095
\(497\) −136.782 33.2833i −0.275216 0.0669684i
\(498\) 0 0
\(499\) 50.6730 29.2561i 0.101549 0.0586294i −0.448365 0.893850i \(-0.647994\pi\)
0.549914 + 0.835221i \(0.314660\pi\)
\(500\) −536.923 + 281.894i −1.07385 + 0.563789i
\(501\) 0 0
\(502\) 272.086 1015.44i 0.542004 2.02279i
\(503\) −144.269 + 144.269i −0.286816 + 0.286816i −0.835820 0.549004i \(-0.815007\pi\)
0.549004 + 0.835820i \(0.315007\pi\)
\(504\) 0 0
\(505\) 42.8070 225.116i 0.0847664 0.445774i
\(506\) 439.059 + 760.473i 0.867706 + 1.50291i
\(507\) 0 0
\(508\) −245.447 916.021i −0.483164 1.80319i
\(509\) −38.7059 + 22.3469i −0.0760431 + 0.0439035i −0.537539 0.843239i \(-0.680646\pi\)
0.461496 + 0.887142i \(0.347313\pi\)
\(510\) 0 0
\(511\) 1.05171 + 45.5047i 0.00205814 + 0.0890503i
\(512\) −466.464 466.464i −0.911063 0.911063i
\(513\) 0 0
\(514\) 145.319 + 83.9001i 0.282722 + 0.163230i
\(515\) −109.327 + 8.09265i −0.212286 + 0.0157139i
\(516\) 0 0
\(517\) −104.801 104.801i −0.202711 0.202711i
\(518\) −314.331 300.130i −0.606817 0.579401i
\(519\) 0 0
\(520\) −45.9806 131.791i −0.0884242 0.253443i
\(521\) −139.872 + 242.266i −0.268469 + 0.465001i −0.968467 0.249143i \(-0.919851\pi\)
0.699998 + 0.714145i \(0.253184\pi\)
\(522\) 0 0
\(523\) −238.051 63.7856i −0.455165 0.121961i 0.0239502 0.999713i \(-0.492376\pi\)
−0.479115 + 0.877752i \(0.659042\pi\)
\(524\) 106.986i 0.204172i
\(525\) 0 0
\(526\) 845.520 1.60745
\(527\) 160.325 598.343i 0.304223 1.13537i
\(528\) 0 0
\(529\) −68.9129 39.7869i −0.130270 0.0752115i
\(530\) 626.519 218.587i 1.18211 0.412429i
\(531\) 0 0
\(532\) −1088.24 264.802i −2.04557 0.497749i
\(533\) 13.2340 13.2340i 0.0248293 0.0248293i
\(534\) 0 0
\(535\) 37.2756 + 503.573i 0.0696740 + 0.941258i
\(536\) −53.6312 + 92.8919i −0.100058 + 0.173306i
\(537\) 0 0
\(538\) −555.176 + 555.176i −1.03193 + 1.03193i
\(539\) −574.416 + 368.033i −1.06571 + 0.682807i
\(540\) 0 0
\(541\) −391.651 678.360i −0.723939 1.25390i −0.959409 0.282018i \(-0.908996\pi\)
0.235470 0.971882i \(-0.424337\pi\)
\(542\) −289.959 + 77.6942i −0.534979 + 0.143347i
\(543\) 0 0
\(544\) −1052.92 + 607.904i −1.93552 + 1.11747i
\(545\) 623.281 + 118.520i 1.14363 + 0.217468i
\(546\) 0 0
\(547\) −32.2224 32.2224i −0.0589074 0.0589074i 0.677039 0.735947i \(-0.263263\pi\)
−0.735947 + 0.677039i \(0.763263\pi\)
\(548\) 1004.67 + 269.201i 1.83334 + 0.491243i
\(549\) 0 0
\(550\) −1028.81 117.820i −1.87056 0.214219i
\(551\) −299.347 518.484i −0.543279 0.940986i
\(552\) 0 0
\(553\) 81.7133 23.9318i 0.147764 0.0432763i
\(554\) 780.291i 1.40847i
\(555\) 0 0
\(556\) −494.103 + 855.811i −0.888674 + 1.53923i
\(557\) −805.560 + 215.849i −1.44625 + 0.387521i −0.894717 0.446634i \(-0.852623\pi\)
−0.551531 + 0.834155i \(0.685956\pi\)
\(558\) 0 0
\(559\) 417.693i 0.747214i
\(560\) 241.583 + 337.969i 0.431398 + 0.603517i
\(561\) 0 0
\(562\) 303.843 1133.96i 0.540646 2.01772i
\(563\) −217.180 810.525i −0.385754 1.43965i −0.836975 0.547241i \(-0.815678\pi\)
0.451221 0.892412i \(-0.350989\pi\)
\(564\) 0 0
\(565\) 31.4829 65.2226i 0.0557219 0.115438i
\(566\) 909.271 1.60649
\(567\) 0 0
\(568\) 36.0201 36.0201i 0.0634157 0.0634157i
\(569\) 663.998 383.359i 1.16696 0.673742i 0.213995 0.976835i \(-0.431352\pi\)
0.952961 + 0.303093i \(0.0980191\pi\)
\(570\) 0 0
\(571\) −525.520 + 910.227i −0.920350 + 1.59409i −0.121476 + 0.992594i \(0.538763\pi\)
−0.798874 + 0.601498i \(0.794571\pi\)
\(572\) 192.665 719.034i 0.336826 1.25705i
\(573\) 0 0
\(574\) 16.9708 31.0286i 0.0295658 0.0540568i
\(575\) −486.156 + 211.053i −0.845490 + 0.367048i
\(576\) 0 0
\(577\) −191.449 + 51.2986i −0.331801 + 0.0889058i −0.420873 0.907119i \(-0.638276\pi\)
0.0890726 + 0.996025i \(0.471610\pi\)
\(578\) 328.590 + 1226.31i 0.568494 + 2.12165i
\(579\) 0 0
\(580\) 82.2591 432.589i 0.141826 0.745843i
\(581\) 174.754 106.352i 0.300782 0.183051i
\(582\) 0 0
\(583\) 599.879 + 160.737i 1.02895 + 0.275707i
\(584\) −14.2640 8.23534i −0.0244247 0.0141016i
\(585\) 0 0
\(586\) −489.604 848.019i −0.835502 1.44713i
\(587\) −425.592 425.592i −0.725029 0.725029i 0.244596 0.969625i \(-0.421345\pi\)
−0.969625 + 0.244596i \(0.921345\pi\)
\(588\) 0 0
\(589\) 763.632i 1.29649i
\(590\) −67.5458 + 139.934i −0.114484 + 0.237176i
\(591\) 0 0
\(592\) −239.260 + 64.1094i −0.404155 + 0.108293i
\(593\) 521.131 + 139.637i 0.878805 + 0.235475i 0.669892 0.742459i \(-0.266341\pi\)
0.208914 + 0.977934i \(0.433007\pi\)
\(594\) 0 0
\(595\) 876.732 328.799i 1.47350 0.552603i
\(596\) −597.360 −1.00228
\(597\) 0 0
\(598\) −179.909 671.428i −0.300851 1.12279i
\(599\) −329.578 190.282i −0.550213 0.317666i 0.198995 0.980001i \(-0.436232\pi\)
−0.749208 + 0.662335i \(0.769566\pi\)
\(600\) 0 0
\(601\) −566.492 −0.942582 −0.471291 0.881978i \(-0.656212\pi\)
−0.471291 + 0.881978i \(0.656212\pi\)
\(602\) −221.846 757.478i −0.368516 1.25827i
\(603\) 0 0
\(604\) 425.550 245.691i 0.704552 0.406773i
\(605\) −275.825 237.805i −0.455909 0.393066i
\(606\) 0 0
\(607\) −278.422 + 1039.09i −0.458685 + 1.71184i 0.218336 + 0.975874i \(0.429937\pi\)
−0.677021 + 0.735963i \(0.736730\pi\)
\(608\) −1059.81 + 1059.81i −1.74311 + 1.74311i
\(609\) 0 0
\(610\) −998.212 + 679.236i −1.63641 + 1.11350i
\(611\) 58.6616 + 101.605i 0.0960092 + 0.166293i
\(612\) 0 0
\(613\) −108.584 405.242i −0.177136 0.661079i −0.996178 0.0873463i \(-0.972161\pi\)
0.819042 0.573733i \(-0.194505\pi\)
\(614\) −700.241 + 404.284i −1.14046 + 0.658444i
\(615\) 0 0
\(616\) −5.70396 246.795i −0.00925968 0.400642i
\(617\) 504.052 + 504.052i 0.816940 + 0.816940i 0.985663 0.168724i \(-0.0539645\pi\)
−0.168724 + 0.985663i \(0.553965\pi\)
\(618\) 0 0
\(619\) 210.689 + 121.641i 0.340369 + 0.196512i 0.660435 0.750883i \(-0.270372\pi\)
−0.320066 + 0.947395i \(0.603705\pi\)
\(620\) 366.748 425.383i 0.591529 0.686102i
\(621\) 0 0
\(622\) −293.821 293.821i −0.472381 0.472381i
\(623\) 1124.79 329.422i 1.80544 0.528768i
\(624\) 0 0
\(625\) 141.298 608.818i 0.226077 0.974109i
\(626\) 72.7413 125.992i 0.116200 0.201264i
\(627\) 0 0
\(628\) −339.666 91.0132i −0.540869 0.144926i
\(629\) 558.298i 0.887596i
\(630\) 0 0
\(631\) 912.593 1.44626 0.723132 0.690710i \(-0.242702\pi\)
0.723132 + 0.690710i \(0.242702\pi\)
\(632\) −7.97440 + 29.7609i −0.0126177 + 0.0470900i
\(633\) 0 0
\(634\) 768.315 + 443.587i 1.21185 + 0.699663i
\(635\) 880.205 + 424.874i 1.38615 + 0.669093i
\(636\) 0 0
\(637\) 514.613 163.719i 0.807870 0.257016i
\(638\) 531.693 531.693i 0.833375 0.833375i
\(639\) 0 0
\(640\) −395.020 + 29.2403i −0.617219 + 0.0456879i
\(641\) −114.103 + 197.632i −0.178007 + 0.308318i −0.941198 0.337856i \(-0.890298\pi\)
0.763191 + 0.646173i \(0.223632\pi\)
\(642\) 0 0
\(643\) 434.914 434.914i 0.676382 0.676382i −0.282797 0.959180i \(-0.591262\pi\)
0.959180 + 0.282797i \(0.0912624\pi\)
\(644\) −374.278 614.999i −0.581177 0.954967i
\(645\) 0 0
\(646\) 1312.51 + 2273.33i 2.03175 + 3.51909i
\(647\) 345.598 92.6027i 0.534155 0.143126i 0.0183485 0.999832i \(-0.494159\pi\)
0.515806 + 0.856705i \(0.327492\pi\)
\(648\) 0 0
\(649\) −125.944 + 72.7136i −0.194058 + 0.112039i
\(650\) 762.510 + 300.870i 1.17309 + 0.462877i
\(651\) 0 0
\(652\) 624.764 + 624.764i 0.958228 + 0.958228i
\(653\) 663.599 + 177.811i 1.01623 + 0.272298i 0.728231 0.685332i \(-0.240343\pi\)
0.288000 + 0.957630i \(0.407010\pi\)
\(654\) 0 0
\(655\) −83.5107 71.9995i −0.127497 0.109923i
\(656\) −10.0784 17.4563i −0.0153634 0.0266102i
\(657\) 0 0
\(658\) 160.347 + 153.102i 0.243688 + 0.232678i
\(659\) 619.112i 0.939471i 0.882807 + 0.469736i \(0.155651\pi\)
−0.882807 + 0.469736i \(0.844349\pi\)
\(660\) 0 0
\(661\) −249.541 + 432.217i −0.377520 + 0.653884i −0.990701 0.136059i \(-0.956556\pi\)
0.613181 + 0.789943i \(0.289890\pi\)
\(662\) 251.545 67.4013i 0.379978 0.101815i
\(663\) 0 0
\(664\) 74.0263i 0.111485i
\(665\) 939.065 671.250i 1.41213 1.00940i
\(666\) 0 0
\(667\) 99.6041 371.728i 0.149332 0.557313i
\(668\) −335.526 1252.20i −0.502285 1.87455i
\(669\) 0 0
\(670\) −207.507 594.762i −0.309712 0.887704i
\(671\) −1130.03 −1.68410
\(672\) 0 0
\(673\) 588.355 588.355i 0.874227 0.874227i −0.118703 0.992930i \(-0.537874\pi\)
0.992930 + 0.118703i \(0.0378735\pi\)
\(674\) −623.006 + 359.693i −0.924341 + 0.533669i
\(675\) 0 0
\(676\) 115.312 199.727i 0.170580 0.295454i
\(677\) 221.070 825.046i 0.326544 1.21868i −0.586206 0.810162i \(-0.699379\pi\)
0.912750 0.408518i \(-0.133954\pi\)
\(678\) 0 0
\(679\) 341.256 + 560.739i 0.502586 + 0.825830i
\(680\) −63.2961 + 332.865i −0.0930824 + 0.489507i
\(681\) 0 0
\(682\) 926.403 248.229i 1.35836 0.363972i
\(683\) 77.6050 + 289.626i 0.113624 + 0.424050i 0.999180 0.0404821i \(-0.0128894\pi\)
−0.885557 + 0.464532i \(0.846223\pi\)
\(684\) 0 0
\(685\) −886.256 + 603.055i −1.29380 + 0.880373i
\(686\) 846.287 570.225i 1.23365 0.831232i
\(687\) 0 0
\(688\) −434.524 116.430i −0.631576 0.169230i
\(689\) −425.748 245.806i −0.617922 0.356758i
\(690\) 0 0
\(691\) −422.621 732.000i −0.611607 1.05933i −0.990970 0.134086i \(-0.957190\pi\)
0.379363 0.925248i \(-0.376143\pi\)
\(692\) 31.3057 + 31.3057i 0.0452395 + 0.0452395i
\(693\) 0 0
\(694\) 198.443i 0.285941i
\(695\) −335.504 961.629i −0.482740 1.38364i
\(696\) 0 0
\(697\) −43.8839 + 11.7586i −0.0629611 + 0.0168704i
\(698\) −1279.58 342.863i −1.83321 0.491208i
\(699\) 0 0
\(700\) 845.488 + 77.0813i 1.20784 + 0.110116i
\(701\) 177.525 0.253245 0.126623 0.991951i \(-0.459586\pi\)
0.126623 + 0.991951i \(0.459586\pi\)
\(702\) 0 0
\(703\) 178.131 + 664.795i 0.253387 + 0.945654i
\(704\) −1057.76 610.698i −1.50250 0.867469i
\(705\) 0 0
\(706\) 1102.00 1.56091
\(707\) −221.545 + 232.028i −0.313359 + 0.328186i
\(708\) 0 0
\(709\) 488.278 281.907i 0.688685 0.397613i −0.114434 0.993431i \(-0.536505\pi\)
0.803119 + 0.595818i \(0.203172\pi\)
\(710\) 22.0838 + 298.341i 0.0311040 + 0.420198i
\(711\) 0 0
\(712\) −109.768 + 409.660i −0.154169 + 0.575365i
\(713\) 347.093 347.093i 0.486807 0.486807i
\(714\) 0 0
\(715\) 431.601 + 634.285i 0.603638 + 0.887112i
\(716\) −649.843 1125.56i −0.907602 1.57201i
\(717\) 0 0
\(718\) −451.074 1683.43i −0.628236 2.34461i
\(719\) −340.465 + 196.567i −0.473525 + 0.273390i −0.717714 0.696338i \(-0.754812\pi\)
0.244189 + 0.969728i \(0.421478\pi\)
\(720\) 0 0
\(721\) 134.653 + 73.6469i 0.186758 + 0.102146i
\(722\) 1528.76 + 1528.76i 2.11740 + 2.11740i
\(723\) 0 0
\(724\) 953.622 + 550.574i 1.31716 + 0.760461i
\(725\) 282.310 + 355.333i 0.389393 + 0.490115i
\(726\) 0 0
\(727\) −110.762 110.762i −0.152356 0.152356i 0.626814 0.779169i \(-0.284359\pi\)
−0.779169 + 0.626814i \(0.784359\pi\)
\(728\) −46.2020 + 189.874i −0.0634643 + 0.260815i
\(729\) 0 0
\(730\) 91.3287 31.8638i 0.125108 0.0436490i
\(731\) −506.968 + 878.094i −0.693527 + 1.20122i
\(732\) 0 0
\(733\) 673.766 + 180.535i 0.919190 + 0.246296i 0.687239 0.726431i \(-0.258822\pi\)
0.231951 + 0.972727i \(0.425489\pi\)
\(734\) 896.977i 1.22204i
\(735\) 0 0
\(736\) −963.429 −1.30901
\(737\) 152.590 569.472i 0.207042 0.772689i
\(738\) 0 0
\(739\) −701.070 404.763i −0.948675 0.547717i −0.0560056 0.998430i \(-0.517836\pi\)
−0.892669 + 0.450713i \(0.851170\pi\)
\(740\) −220.051 + 455.876i −0.297366 + 0.616049i
\(741\) 0 0
\(742\) −902.640 219.640i −1.21650 0.296010i
\(743\) −615.379 + 615.379i −0.828235 + 0.828235i −0.987273 0.159037i \(-0.949161\pi\)
0.159037 + 0.987273i \(0.449161\pi\)
\(744\) 0 0
\(745\) 402.011 466.285i 0.539613 0.625885i
\(746\) 785.474 1360.48i 1.05291 1.82370i
\(747\) 0 0
\(748\) −1277.74 + 1277.74i −1.70821 + 1.70821i
\(749\) 339.225 620.224i 0.452904 0.828069i
\(750\) 0 0
\(751\) −666.673 1154.71i −0.887713 1.53756i −0.842572 0.538584i \(-0.818959\pi\)
−0.0451417 0.998981i \(-0.514374\pi\)
\(752\) 122.051 32.7035i 0.162302 0.0434887i
\(753\) 0 0
\(754\) −515.477 + 297.611i −0.683656 + 0.394709i
\(755\) −94.6059 + 497.519i −0.125306 + 0.658966i
\(756\) 0 0
\(757\) 897.927 + 897.927i 1.18617 + 1.18617i 0.978119 + 0.208047i \(0.0667106\pi\)
0.208047 + 0.978119i \(0.433289\pi\)
\(758\) −508.832 136.341i −0.671283 0.179870i
\(759\) 0 0
\(760\) 30.8343 + 416.555i 0.0405715 + 0.548099i
\(761\) 19.9063 + 34.4788i 0.0261581 + 0.0453072i 0.878808 0.477175i \(-0.158339\pi\)
−0.852650 + 0.522483i \(0.825006\pi\)
\(762\) 0 0
\(763\) −642.417 613.393i −0.841963 0.803923i
\(764\) 754.964i 0.988173i
\(765\) 0 0
\(766\) 401.410 695.262i 0.524034 0.907653i
\(767\) 111.197 29.7951i 0.144976 0.0388462i
\(768\) 0 0
\(769\) 246.046i 0.319956i 0.987121 + 0.159978i \(0.0511424\pi\)
−0.987121 + 0.159978i \(0.948858\pi\)
\(770\) 1119.58 + 921.031i 1.45401 + 1.19614i
\(771\) 0 0
\(772\) 264.105 985.653i 0.342105 1.27675i
\(773\) 203.881 + 760.894i 0.263753 + 0.984339i 0.963009 + 0.269468i \(0.0868479\pi\)
−0.699257 + 0.714871i \(0.746485\pi\)
\(774\) 0 0
\(775\) 85.2297 + 572.549i 0.109974 + 0.738773i
\(776\) −237.530 −0.306096
\(777\) 0 0
\(778\) −392.090 + 392.090i −0.503972 + 0.503972i
\(779\) −48.5031 + 28.0033i −0.0622633 + 0.0359477i
\(780\) 0 0
\(781\) −139.995 + 242.478i −0.179250 + 0.310471i
\(782\) −436.722 + 1629.87i −0.558469 + 2.08423i
\(783\) 0 0
\(784\) −26.8700 580.987i −0.0342730 0.741055i
\(785\) 299.631 203.885i 0.381696 0.259726i
\(786\) 0 0
\(787\) −831.602 + 222.827i −1.05667 + 0.283135i −0.745007 0.667057i \(-0.767554\pi\)
−0.311667 + 0.950192i \(0.600887\pi\)
\(788\) −175.123 653.567i −0.222237 0.829400i
\(789\) 0 0
\(790\) −101.792 149.595i −0.128851 0.189360i
\(791\) −86.6139 + 52.7118i −0.109499 + 0.0666394i
\(792\) 0 0
\(793\) 864.044 + 231.520i 1.08959 + 0.291954i
\(794\) 1758.08 + 1015.03i 2.21420 + 1.27837i
\(795\) 0 0
\(796\) −100.333 173.782i −0.126046 0.218319i
\(797\) −710.464 710.464i −0.891423 0.891423i 0.103234 0.994657i \(-0.467081\pi\)
−0.994657 + 0.103234i \(0.967081\pi\)
\(798\) 0 0
\(799\) 284.799i 0.356444i
\(800\) 676.328 912.901i 0.845410 1.14113i
\(801\) 0 0
\(802\) 367.441 98.4556i 0.458156 0.122763i
\(803\) 87.4453 + 23.4309i 0.108898 + 0.0291792i
\(804\) 0 0
\(805\) 731.935 + 121.730i 0.909236 + 0.151217i
\(806\) −759.204 −0.941940
\(807\) 0 0
\(808\) −30.0457 112.132i −0.0371853 0.138777i
\(809\) 836.414 + 482.904i 1.03389 + 0.596914i 0.918095 0.396359i \(-0.129727\pi\)
0.115790 + 0.993274i \(0.463060\pi\)
\(810\) 0 0
\(811\) −632.087 −0.779392 −0.389696 0.920944i \(-0.627420\pi\)
−0.389696 + 0.920944i \(0.627420\pi\)
\(812\) −425.726 + 445.871i −0.524293 + 0.549102i
\(813\) 0 0
\(814\) −748.594 + 432.201i −0.919649 + 0.530959i
\(815\) −908.130 + 67.2218i −1.11427 + 0.0824807i
\(816\) 0 0
\(817\) −323.508 + 1207.35i −0.395970 + 1.47778i
\(818\) 164.150 164.150i 0.200673 0.200673i
\(819\) 0 0
\(820\) −40.4679 7.69518i −0.0493510 0.00938437i
\(821\) 518.747 + 898.496i 0.631848 + 1.09439i 0.987174 + 0.159650i \(0.0510365\pi\)
−0.355326 + 0.934742i \(0.615630\pi\)
\(822\) 0 0
\(823\) 384.072 + 1433.38i 0.466673 + 1.74165i 0.651281 + 0.758837i \(0.274232\pi\)
−0.184607 + 0.982812i \(0.559101\pi\)
\(824\) −48.0964 + 27.7685i −0.0583695 + 0.0336996i
\(825\) 0 0
\(826\) 185.828 113.092i 0.224974 0.136915i
\(827\) 896.076 + 896.076i 1.08353 + 1.08353i 0.996178 + 0.0873480i \(0.0278392\pi\)
0.0873480 + 0.996178i \(0.472161\pi\)
\(828\) 0 0
\(829\) 566.312 + 326.960i 0.683127 + 0.394403i 0.801032 0.598621i \(-0.204285\pi\)
−0.117905 + 0.993025i \(0.537618\pi\)
\(830\) −329.258 283.873i −0.396697 0.342016i
\(831\) 0 0
\(832\) 683.666 + 683.666i 0.821714 + 0.821714i
\(833\) −1280.56 280.425i −1.53728 0.336644i
\(834\) 0 0
\(835\) 1203.24 + 580.803i 1.44101 + 0.695573i
\(836\) −1113.80 + 1929.16i −1.33230 + 2.30761i
\(837\) 0 0
\(838\) −109.448 29.3266i −0.130607 0.0349959i
\(839\) 1045.69i 1.24636i −0.782079 0.623179i \(-0.785841\pi\)
0.782079 0.623179i \(-0.214159\pi\)
\(840\) 0 0
\(841\) 511.463 0.608161
\(842\) 116.745 435.699i 0.138652 0.517457i
\(843\) 0 0
\(844\) −1371.69 791.948i −1.62523 0.938327i
\(845\) 78.2989 + 224.422i 0.0926614 + 0.265588i
\(846\) 0 0
\(847\) 143.305 + 489.305i 0.169191 + 0.577692i
\(848\) −374.387 + 374.387i −0.441494 + 0.441494i
\(849\) 0 0
\(850\) −1237.81 1557.99i −1.45625 1.83293i
\(851\) −221.203 + 383.135i −0.259933 + 0.450217i
\(852\) 0 0
\(853\) −707.639 + 707.639i −0.829588 + 0.829588i −0.987460 0.157871i \(-0.949537\pi\)
0.157871 + 0.987460i \(0.449537\pi\)
\(854\) 1689.89 39.0570i 1.97880 0.0457342i
\(855\) 0 0
\(856\) 127.904 + 221.537i 0.149421 + 0.258805i
\(857\) −1189.25 + 318.658i −1.38769 + 0.371829i −0.873907 0.486093i \(-0.838421\pi\)
−0.513779 + 0.857923i \(0.671755\pi\)
\(858\) 0 0
\(859\) −268.193 + 154.841i −0.312215 + 0.180258i −0.647917 0.761711i \(-0.724360\pi\)
0.335702 + 0.941968i \(0.391026\pi\)
\(860\) −760.061 + 517.185i −0.883792 + 0.601378i
\(861\) 0 0
\(862\) 1128.86 + 1128.86i 1.30958 + 1.30958i
\(863\) 1355.42 + 363.183i 1.57059 + 0.420837i 0.935996 0.352011i \(-0.114502\pi\)
0.634590 + 0.772849i \(0.281169\pi\)
\(864\) 0 0
\(865\) −45.5046 + 3.36835i −0.0526065 + 0.00389405i
\(866\) 886.576 + 1535.59i 1.02376 + 1.77320i
\(867\) 0 0
\(868\) −754.617 + 221.008i −0.869374 + 0.254618i
\(869\) 169.349i 0.194878i
\(870\) 0 0
\(871\) −233.346 + 404.168i −0.267906 + 0.464027i
\(872\) 310.461 83.1879i 0.356034 0.0953990i
\(873\) 0 0
\(874\) 2080.12i 2.37999i
\(875\) −629.164 + 608.093i −0.719045 + 0.694963i
\(876\) 0 0
\(877\) −164.653 + 614.493i −0.187746 + 0.700676i 0.806281 + 0.591533i \(0.201477\pi\)
−0.994026 + 0.109143i \(0.965189\pi\)
\(878\) −365.697 1364.80i −0.416512 1.55444i
\(879\) 0 0
\(880\) 780.152 272.188i 0.886536 0.309305i
\(881\) 947.178 1.07512 0.537559 0.843226i \(-0.319347\pi\)
0.537559 + 0.843226i \(0.319347\pi\)
\(882\) 0 0
\(883\) −1152.12 + 1152.12i −1.30478 + 1.30478i −0.379646 + 0.925132i \(0.623954\pi\)
−0.925132 + 0.379646i \(0.876046\pi\)
\(884\) 1238.77 715.207i 1.40133 0.809057i
\(885\) 0 0
\(886\) −140.143 + 242.735i −0.158175 + 0.273968i
\(887\) 10.7496 40.1181i 0.0121191 0.0452290i −0.959602 0.281363i \(-0.909214\pi\)
0.971721 + 0.236134i \(0.0758803\pi\)
\(888\) 0 0
\(889\) −711.367 1168.89i −0.800188 1.31484i
\(890\) −1401.17 2059.18i −1.57435 2.31368i
\(891\) 0 0
\(892\) 259.788 69.6100i 0.291242 0.0780381i
\(893\) −90.8683 339.125i −0.101756 0.379759i
\(894\) 0 0
\(895\) 1315.92 + 250.229i 1.47030 + 0.279585i
\(896\) 486.525 + 266.100i 0.542997 + 0.296987i
\(897\) 0 0
\(898\) 1499.04 + 401.666i 1.66931 + 0.447290i
\(899\) −364.011 210.162i −0.404907 0.233773i
\(900\) 0 0
\(901\) 596.686 + 1033.49i 0.662249 + 1.14705i
\(902\) −49.7389 49.7389i −0.0551429 0.0551429i
\(903\) 0 0
\(904\) 36.6899i 0.0405861i
\(905\) −1071.53 + 373.849i −1.18401 + 0.413093i
\(906\) 0 0
\(907\) 1521.13 407.585i 1.67710 0.449377i 0.710088 0.704112i \(-0.248655\pi\)
0.967011 + 0.254735i \(0.0819883\pi\)
\(908\) −16.8941 4.52675i −0.0186058 0.00498541i
\(909\) 0 0
\(910\) −667.357 933.619i −0.733359 1.02596i
\(911\) 1032.26 1.13311 0.566556 0.824023i \(-0.308276\pi\)
0.566556 + 0.824023i \(0.308276\pi\)
\(912\) 0 0
\(913\) −105.309 393.017i −0.115343 0.430468i
\(914\) −1070.54 618.079i −1.17127 0.676235i
\(915\) 0 0
\(916\) −257.717 −0.281351
\(917\) 43.3881 + 148.145i 0.0473153 + 0.161555i
\(918\) 0 0
\(919\) 181.801 104.963i 0.197824 0.114214i −0.397816 0.917465i \(-0.630232\pi\)
0.595640 + 0.803251i \(0.296898\pi\)
\(920\) −175.321 + 203.352i −0.190567 + 0.221034i
\(921\) 0 0
\(922\) 216.020 806.199i 0.234295 0.874403i
\(923\) 156.722 156.722i 0.169796 0.169796i
\(924\) 0 0
\(925\) −207.756 478.562i −0.224601 0.517365i
\(926\) −686.735 1189.46i −0.741614 1.28451i
\(927\) 0 0
\(928\) 213.520 + 796.868i 0.230086 + 0.858694i
\(929\) 194.809 112.473i 0.209698 0.121069i −0.391473 0.920189i \(-0.628034\pi\)
0.601171 + 0.799121i \(0.294701\pi\)
\(930\) 0 0
\(931\) −1614.30 + 74.6596i −1.73394 + 0.0801930i
\(932\) 443.363 + 443.363i 0.475711 + 0.475711i
\(933\) 0 0
\(934\) −1095.03 632.218i −1.17241 0.676893i
\(935\) −137.479 1857.27i −0.147037 1.98639i
\(936\) 0 0
\(937\) −650.762 650.762i −0.694516 0.694516i 0.268706 0.963222i \(-0.413404\pi\)
−0.963222 + 0.268706i \(0.913404\pi\)
\(938\) −208.506 + 856.887i −0.222288 + 0.913525i
\(939\) 0 0
\(940\) 112.252 232.551i 0.119417 0.247395i
\(941\) −175.589 + 304.130i −0.186599 + 0.323199i −0.944114 0.329619i \(-0.893080\pi\)
0.757515 + 0.652817i \(0.226413\pi\)
\(942\) 0 0
\(943\) −34.7744 9.31777i −0.0368764 0.00988099i
\(944\) 123.983i 0.131338i
\(945\) 0 0
\(946\) −1569.86 −1.65947
\(947\) −100.521 + 375.151i −0.106147 + 0.396147i −0.998473 0.0552454i \(-0.982406\pi\)
0.892326 + 0.451392i \(0.149073\pi\)
\(948\) 0 0
\(949\) −62.0620 35.8315i −0.0653973 0.0377571i
\(950\) −1971.02 1460.24i −2.07476 1.53710i
\(951\) 0 0
\(952\) 327.584 343.085i 0.344101 0.360383i
\(953\) −413.158 + 413.158i −0.433535 + 0.433535i −0.889829 0.456294i \(-0.849176\pi\)
0.456294 + 0.889829i \(0.349176\pi\)
\(954\) 0 0
\(955\) −589.307 508.076i −0.617075 0.532017i
\(956\) −885.739 + 1534.15i −0.926505 + 1.60475i
\(957\) 0 0
\(958\) 445.221 445.221i 0.464740 0.464740i
\(959\) 1500.36 34.6765i 1.56451 0.0361590i
\(960\) 0 0
\(961\) 212.439 + 367.955i 0.221060 + 0.382888i
\(962\) 660.940 177.098i 0.687048 0.184094i
\(963\) 0 0
\(964\) 1653.54 954.669i 1.71529 0.990321i
\(965\) 591.640 + 869.479i 0.613098 + 0.901015i
\(966\) 0 0
\(967\) −967.834 967.834i −1.00086 1.00086i −1.00000 0.000862358i \(-0.999726\pi\)
−0.000862358 1.00000i \(-0.500274\pi\)
\(968\) −178.210 47.7512i −0.184101 0.0493298i
\(969\) 0 0
\(970\) 910.871 1056.50i 0.939042 1.08918i
\(971\) −540.722 936.558i −0.556871 0.964529i −0.997755 0.0669653i \(-0.978668\pi\)
0.440884 0.897564i \(-0.354665\pi\)
\(972\) 0 0
\(973\) −337.119 + 1385.44i −0.346474 + 1.42389i
\(974\) 142.649i 0.146457i
\(975\) 0 0
\(976\) 481.699 834.327i 0.493544 0.854843i
\(977\) 314.733 84.3325i 0.322143 0.0863178i −0.0941240 0.995560i \(-0.530005\pi\)
0.416266 + 0.909243i \(0.363338\pi\)
\(978\) 0 0
\(979\) 2331.10i 2.38110i
\(980\) −935.107 733.707i −0.954190 0.748681i
\(981\) 0 0
\(982\) −604.048 + 2254.34i −0.615120 + 2.29566i
\(983\) 258.858 + 966.073i 0.263335 + 0.982780i 0.963261 + 0.268565i \(0.0865495\pi\)
−0.699926 + 0.714215i \(0.746784\pi\)
\(984\) 0 0
\(985\) 628.013 + 303.141i 0.637576 + 0.307757i
\(986\) 1444.88 1.46540
\(987\) 0 0
\(988\) 1246.88 1246.88i 1.26202 1.26202i
\(989\) −695.819 + 401.731i −0.703558 + 0.406199i
\(990\) 0 0
\(991\) 770.884 1335.21i 0.777885 1.34734i −0.155273 0.987872i \(-0.549626\pi\)
0.933158 0.359465i \(-0.117041\pi\)
\(992\) −272.345 + 1016.40i −0.274541 + 1.02460i
\(993\) 0 0
\(994\) 200.973 367.450i 0.202186 0.369668i
\(995\) 203.172 + 38.6343i 0.204193 + 0.0388284i
\(996\) 0 0
\(997\) −840.254 + 225.145i −0.842782 + 0.225823i −0.654282 0.756250i \(-0.727029\pi\)
−0.188500 + 0.982073i \(0.560363\pi\)
\(998\) 45.0555 + 168.150i 0.0451458 + 0.168486i
\(999\) 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 315.3.ca.b.172.3 64
3.2 odd 2 105.3.v.a.67.14 yes 64
5.3 odd 4 inner 315.3.ca.b.298.14 64
7.2 even 3 inner 315.3.ca.b.37.14 64
15.8 even 4 105.3.v.a.88.3 yes 64
21.2 odd 6 105.3.v.a.37.3 64
35.23 odd 12 inner 315.3.ca.b.163.3 64
105.23 even 12 105.3.v.a.58.14 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.v.a.37.3 64 21.2 odd 6
105.3.v.a.58.14 yes 64 105.23 even 12
105.3.v.a.67.14 yes 64 3.2 odd 2
105.3.v.a.88.3 yes 64 15.8 even 4
315.3.ca.b.37.14 64 7.2 even 3 inner
315.3.ca.b.163.3 64 35.23 odd 12 inner
315.3.ca.b.172.3 64 1.1 even 1 trivial
315.3.ca.b.298.14 64 5.3 odd 4 inner