Properties

Label 135.4.e.c.91.2
Level $135$
Weight $4$
Character 135.91
Analytic conductor $7.965$
Analytic rank $0$
Dimension $14$
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] = [135,4,Mod(46,135)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(135, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("135.46");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 135.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.96525785077\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + 209529 x^{6} - 55412 x^{5} + 765088 x^{4} + 276096 x^{3} + 1572480 x^{2} + \cdots + 82944 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{13} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 91.2
Root \(2.13089 - 3.69081i\) of defining polynomial
Character \(\chi\) \(=\) 135.91
Dual form 135.4.e.c.46.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.13089 - 3.69081i) q^{2} +(-5.08138 + 8.80120i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-15.3820 - 26.6423i) q^{7} +9.21718 q^{8} +O(q^{10})\) \(q+(-2.13089 - 3.69081i) q^{2} +(-5.08138 + 8.80120i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-15.3820 - 26.6423i) q^{7} +9.21718 q^{8} +21.3089 q^{10} +(20.3573 + 35.2599i) q^{11} +(-31.6089 + 54.7482i) q^{13} +(-65.5545 + 113.544i) q^{14} +(21.0102 + 36.3908i) q^{16} +6.58990 q^{17} +75.3803 q^{19} +(-25.4069 - 44.0060i) q^{20} +(86.7584 - 150.270i) q^{22} +(-31.1814 + 54.0077i) q^{23} +(-12.5000 - 21.6506i) q^{25} +269.420 q^{26} +312.646 q^{28} +(24.8042 + 42.9621i) q^{29} +(-51.5021 + 89.2043i) q^{31} +(126.410 - 218.948i) q^{32} +(-14.0423 - 24.3221i) q^{34} +153.820 q^{35} -282.029 q^{37} +(-160.627 - 278.214i) q^{38} +(-23.0430 + 39.9116i) q^{40} +(-78.7700 + 136.434i) q^{41} +(168.907 + 292.555i) q^{43} -413.773 q^{44} +265.776 q^{46} +(22.2579 + 38.5518i) q^{47} +(-301.710 + 522.577i) q^{49} +(-53.2722 + 92.2702i) q^{50} +(-321.234 - 556.393i) q^{52} -26.2752 q^{53} -203.573 q^{55} +(-141.778 - 245.567i) q^{56} +(105.710 - 183.095i) q^{58} +(-212.963 + 368.863i) q^{59} +(-425.297 - 736.637i) q^{61} +438.981 q^{62} -741.296 q^{64} +(-158.045 - 273.741i) q^{65} +(-48.1538 + 83.4048i) q^{67} +(-33.4858 + 57.9990i) q^{68} +(-327.773 - 567.719i) q^{70} -952.164 q^{71} -50.8558 q^{73} +(600.973 + 1040.92i) q^{74} +(-383.036 + 663.437i) q^{76} +(626.271 - 1084.73i) q^{77} +(98.6395 + 170.849i) q^{79} -210.102 q^{80} +671.400 q^{82} +(-98.8693 - 171.247i) q^{83} +(-16.4747 + 28.5351i) q^{85} +(719.844 - 1246.81i) q^{86} +(187.637 + 324.997i) q^{88} -1364.54 q^{89} +1944.83 q^{91} +(-316.889 - 548.868i) q^{92} +(94.8583 - 164.299i) q^{94} +(-188.451 + 326.406i) q^{95} +(715.579 + 1239.42i) q^{97} +2571.64 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 2 q^{2} - 36 q^{4} - 35 q^{5} - 22 q^{7} + 36 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 2 q^{2} - 36 q^{4} - 35 q^{5} - 22 q^{7} + 36 q^{8} + 20 q^{10} - 23 q^{11} - 96 q^{13} + 21 q^{14} - 324 q^{16} + 322 q^{17} + 558 q^{19} - 180 q^{20} - 311 q^{22} - 96 q^{23} - 175 q^{25} - 716 q^{26} + 674 q^{28} + 296 q^{29} - 244 q^{31} + 314 q^{32} - 125 q^{34} + 220 q^{35} + 808 q^{37} - 305 q^{38} - 90 q^{40} + 47 q^{41} - 525 q^{43} + 110 q^{44} + 1434 q^{46} - 164 q^{47} - 1225 q^{49} - 50 q^{50} - 1682 q^{52} + 1012 q^{53} + 230 q^{55} + 981 q^{56} - 1183 q^{58} + 85 q^{59} - 828 q^{61} - 1572 q^{62} + 4472 q^{64} - 480 q^{65} - 1093 q^{67} - 2473 q^{68} + 105 q^{70} + 656 q^{71} + 4170 q^{73} + 1316 q^{74} - 2789 q^{76} - 24 q^{77} - 2110 q^{79} + 3240 q^{80} - 124 q^{82} - 1290 q^{83} - 805 q^{85} + 2569 q^{86} - 2271 q^{88} - 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 517 q^{94} - 1395 q^{95} - 1787 q^{97} + 2558 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/135\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(82\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.13089 3.69081i −0.753383 1.30490i −0.946174 0.323658i \(-0.895087\pi\)
0.192791 0.981240i \(-0.438246\pi\)
\(3\) 0 0
\(4\) −5.08138 + 8.80120i −0.635172 + 1.10015i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −15.3820 26.6423i −0.830548 1.43855i −0.897604 0.440802i \(-0.854694\pi\)
0.0670561 0.997749i \(-0.478639\pi\)
\(8\) 9.21718 0.407346
\(9\) 0 0
\(10\) 21.3089 0.673846
\(11\) 20.3573 + 35.2599i 0.557996 + 0.966478i 0.997664 + 0.0683175i \(0.0217631\pi\)
−0.439667 + 0.898161i \(0.644904\pi\)
\(12\) 0 0
\(13\) −31.6089 + 54.7482i −0.674364 + 1.16803i 0.302290 + 0.953216i \(0.402249\pi\)
−0.976654 + 0.214817i \(0.931085\pi\)
\(14\) −65.5545 + 113.544i −1.25144 + 2.16756i
\(15\) 0 0
\(16\) 21.0102 + 36.3908i 0.328285 + 0.568606i
\(17\) 6.58990 0.0940168 0.0470084 0.998894i \(-0.485031\pi\)
0.0470084 + 0.998894i \(0.485031\pi\)
\(18\) 0 0
\(19\) 75.3803 0.910180 0.455090 0.890445i \(-0.349607\pi\)
0.455090 + 0.890445i \(0.349607\pi\)
\(20\) −25.4069 44.0060i −0.284058 0.492002i
\(21\) 0 0
\(22\) 86.7584 150.270i 0.840770 1.45626i
\(23\) −31.1814 + 54.0077i −0.282686 + 0.489626i −0.972045 0.234793i \(-0.924559\pi\)
0.689360 + 0.724419i \(0.257892\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 269.420 2.03222
\(27\) 0 0
\(28\) 312.646 2.11016
\(29\) 24.8042 + 42.9621i 0.158828 + 0.275099i 0.934446 0.356104i \(-0.115895\pi\)
−0.775618 + 0.631202i \(0.782562\pi\)
\(30\) 0 0
\(31\) −51.5021 + 89.2043i −0.298389 + 0.516824i −0.975767 0.218810i \(-0.929783\pi\)
0.677379 + 0.735634i \(0.263116\pi\)
\(32\) 126.410 218.948i 0.698321 1.20953i
\(33\) 0 0
\(34\) −14.0423 24.3221i −0.0708306 0.122682i
\(35\) 153.820 0.742865
\(36\) 0 0
\(37\) −282.029 −1.25312 −0.626559 0.779374i \(-0.715537\pi\)
−0.626559 + 0.779374i \(0.715537\pi\)
\(38\) −160.627 278.214i −0.685714 1.18769i
\(39\) 0 0
\(40\) −23.0430 + 39.9116i −0.0910853 + 0.157764i
\(41\) −78.7700 + 136.434i −0.300044 + 0.519692i −0.976146 0.217117i \(-0.930335\pi\)
0.676102 + 0.736808i \(0.263668\pi\)
\(42\) 0 0
\(43\) 168.907 + 292.555i 0.599025 + 1.03754i 0.992965 + 0.118406i \(0.0377783\pi\)
−0.393940 + 0.919136i \(0.628888\pi\)
\(44\) −413.773 −1.41770
\(45\) 0 0
\(46\) 265.776 0.851882
\(47\) 22.2579 + 38.5518i 0.0690777 + 0.119646i 0.898496 0.438983i \(-0.144661\pi\)
−0.829418 + 0.558629i \(0.811328\pi\)
\(48\) 0 0
\(49\) −301.710 + 522.577i −0.879620 + 1.52355i
\(50\) −53.2722 + 92.2702i −0.150677 + 0.260980i
\(51\) 0 0
\(52\) −321.234 556.393i −0.856675 1.48380i
\(53\) −26.2752 −0.0680978 −0.0340489 0.999420i \(-0.510840\pi\)
−0.0340489 + 0.999420i \(0.510840\pi\)
\(54\) 0 0
\(55\) −203.573 −0.499087
\(56\) −141.778 245.567i −0.338320 0.585988i
\(57\) 0 0
\(58\) 105.710 183.095i 0.239317 0.414509i
\(59\) −212.963 + 368.863i −0.469923 + 0.813930i −0.999409 0.0343889i \(-0.989052\pi\)
0.529486 + 0.848319i \(0.322385\pi\)
\(60\) 0 0
\(61\) −425.297 736.637i −0.892684 1.54617i −0.836644 0.547746i \(-0.815486\pi\)
−0.0560400 0.998429i \(-0.517847\pi\)
\(62\) 438.981 0.899204
\(63\) 0 0
\(64\) −741.296 −1.44784
\(65\) −158.045 273.741i −0.301585 0.522360i
\(66\) 0 0
\(67\) −48.1538 + 83.4048i −0.0878048 + 0.152082i −0.906583 0.422028i \(-0.861319\pi\)
0.818778 + 0.574110i \(0.194652\pi\)
\(68\) −33.4858 + 57.9990i −0.0597168 + 0.103433i
\(69\) 0 0
\(70\) −327.773 567.719i −0.559662 0.969363i
\(71\) −952.164 −1.59156 −0.795782 0.605583i \(-0.792940\pi\)
−0.795782 + 0.605583i \(0.792940\pi\)
\(72\) 0 0
\(73\) −50.8558 −0.0815373 −0.0407686 0.999169i \(-0.512981\pi\)
−0.0407686 + 0.999169i \(0.512981\pi\)
\(74\) 600.973 + 1040.92i 0.944077 + 1.63519i
\(75\) 0 0
\(76\) −383.036 + 663.437i −0.578121 + 1.00134i
\(77\) 626.271 1084.73i 0.926886 1.60541i
\(78\) 0 0
\(79\) 98.6395 + 170.849i 0.140479 + 0.243316i 0.927677 0.373384i \(-0.121803\pi\)
−0.787198 + 0.616700i \(0.788469\pi\)
\(80\) −210.102 −0.293627
\(81\) 0 0
\(82\) 671.400 0.904192
\(83\) −98.8693 171.247i −0.130751 0.226467i 0.793215 0.608941i \(-0.208405\pi\)
−0.923966 + 0.382474i \(0.875072\pi\)
\(84\) 0 0
\(85\) −16.4747 + 28.5351i −0.0210228 + 0.0364125i
\(86\) 719.844 1246.81i 0.902590 1.56333i
\(87\) 0 0
\(88\) 187.637 + 324.997i 0.227298 + 0.393691i
\(89\) −1364.54 −1.62519 −0.812593 0.582832i \(-0.801944\pi\)
−0.812593 + 0.582832i \(0.801944\pi\)
\(90\) 0 0
\(91\) 1944.83 2.24037
\(92\) −316.889 548.868i −0.359108 0.621993i
\(93\) 0 0
\(94\) 94.8583 164.299i 0.104084 0.180279i
\(95\) −188.451 + 326.406i −0.203522 + 0.352511i
\(96\) 0 0
\(97\) 715.579 + 1239.42i 0.749031 + 1.29736i 0.948288 + 0.317413i \(0.102814\pi\)
−0.199256 + 0.979947i \(0.563853\pi\)
\(98\) 2571.64 2.65076
\(99\) 0 0
\(100\) 254.069 0.254069
\(101\) 553.808 + 959.224i 0.545604 + 0.945013i 0.998569 + 0.0534851i \(0.0170329\pi\)
−0.452965 + 0.891528i \(0.649634\pi\)
\(102\) 0 0
\(103\) −264.437 + 458.018i −0.252969 + 0.438154i −0.964342 0.264660i \(-0.914740\pi\)
0.711373 + 0.702814i \(0.248074\pi\)
\(104\) −291.345 + 504.624i −0.274699 + 0.475793i
\(105\) 0 0
\(106\) 55.9896 + 96.9769i 0.0513037 + 0.0888607i
\(107\) −490.910 −0.443533 −0.221766 0.975100i \(-0.571182\pi\)
−0.221766 + 0.975100i \(0.571182\pi\)
\(108\) 0 0
\(109\) −351.634 −0.308994 −0.154497 0.987993i \(-0.549376\pi\)
−0.154497 + 0.987993i \(0.549376\pi\)
\(110\) 433.792 + 751.349i 0.376004 + 0.651258i
\(111\) 0 0
\(112\) 646.357 1119.52i 0.545313 0.944509i
\(113\) 881.226 1526.33i 0.733618 1.27066i −0.221710 0.975113i \(-0.571164\pi\)
0.955327 0.295550i \(-0.0955030\pi\)
\(114\) 0 0
\(115\) −155.907 270.039i −0.126421 0.218967i
\(116\) −504.158 −0.403533
\(117\) 0 0
\(118\) 1815.20 1.41613
\(119\) −101.366 175.570i −0.0780854 0.135248i
\(120\) 0 0
\(121\) −163.340 + 282.914i −0.122720 + 0.212557i
\(122\) −1812.52 + 3139.38i −1.34507 + 2.32972i
\(123\) 0 0
\(124\) −523.403 906.561i −0.379056 0.656545i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1506.12 −1.05234 −0.526169 0.850380i \(-0.676372\pi\)
−0.526169 + 0.850380i \(0.676372\pi\)
\(128\) 568.343 + 984.399i 0.392460 + 0.679761i
\(129\) 0 0
\(130\) −673.551 + 1166.62i −0.454418 + 0.787075i
\(131\) 637.562 1104.29i 0.425222 0.736506i −0.571219 0.820798i \(-0.693529\pi\)
0.996441 + 0.0842915i \(0.0268627\pi\)
\(132\) 0 0
\(133\) −1159.50 2008.31i −0.755948 1.30934i
\(134\) 410.441 0.264603
\(135\) 0 0
\(136\) 60.7403 0.0382973
\(137\) 719.712 + 1246.58i 0.448826 + 0.777389i 0.998310 0.0581150i \(-0.0185090\pi\)
−0.549484 + 0.835504i \(0.685176\pi\)
\(138\) 0 0
\(139\) 1269.75 2199.27i 0.774811 1.34201i −0.160090 0.987102i \(-0.551178\pi\)
0.934901 0.354909i \(-0.115488\pi\)
\(140\) −781.616 + 1353.80i −0.471847 + 0.817263i
\(141\) 0 0
\(142\) 2028.96 + 3514.25i 1.19906 + 2.07683i
\(143\) −2573.89 −1.50517
\(144\) 0 0
\(145\) −248.042 −0.142060
\(146\) 108.368 + 187.699i 0.0614288 + 0.106398i
\(147\) 0 0
\(148\) 1433.10 2482.20i 0.795945 1.37862i
\(149\) 46.8796 81.1979i 0.0257754 0.0446442i −0.852850 0.522156i \(-0.825128\pi\)
0.878625 + 0.477512i \(0.158461\pi\)
\(150\) 0 0
\(151\) 534.065 + 925.027i 0.287825 + 0.498527i 0.973290 0.229578i \(-0.0737345\pi\)
−0.685465 + 0.728105i \(0.740401\pi\)
\(152\) 694.794 0.370758
\(153\) 0 0
\(154\) −5338.06 −2.79320
\(155\) −257.510 446.021i −0.133443 0.231131i
\(156\) 0 0
\(157\) −90.8574 + 157.370i −0.0461861 + 0.0799966i −0.888194 0.459468i \(-0.848040\pi\)
0.842008 + 0.539465i \(0.181373\pi\)
\(158\) 420.380 728.119i 0.211668 0.366621i
\(159\) 0 0
\(160\) 632.048 + 1094.74i 0.312299 + 0.540917i
\(161\) 1918.52 0.939136
\(162\) 0 0
\(163\) −1103.07 −0.530056 −0.265028 0.964241i \(-0.585381\pi\)
−0.265028 + 0.964241i \(0.585381\pi\)
\(164\) −800.520 1386.54i −0.381159 0.660187i
\(165\) 0 0
\(166\) −421.359 + 729.816i −0.197011 + 0.341233i
\(167\) −2020.85 + 3500.22i −0.936396 + 1.62189i −0.164270 + 0.986415i \(0.552527\pi\)
−0.772126 + 0.635470i \(0.780806\pi\)
\(168\) 0 0
\(169\) −899.745 1558.40i −0.409534 0.709333i
\(170\) 140.423 0.0633529
\(171\) 0 0
\(172\) −3433.12 −1.52194
\(173\) −1373.88 2379.63i −0.603780 1.04578i −0.992243 0.124314i \(-0.960327\pi\)
0.388463 0.921465i \(-0.373006\pi\)
\(174\) 0 0
\(175\) −384.549 + 666.059i −0.166110 + 0.287710i
\(176\) −855.423 + 1481.64i −0.366363 + 0.634560i
\(177\) 0 0
\(178\) 2907.69 + 5036.27i 1.22439 + 2.12070i
\(179\) 2838.32 1.18517 0.592587 0.805506i \(-0.298107\pi\)
0.592587 + 0.805506i \(0.298107\pi\)
\(180\) 0 0
\(181\) 3442.25 1.41359 0.706796 0.707417i \(-0.250140\pi\)
0.706796 + 0.707417i \(0.250140\pi\)
\(182\) −4144.21 7177.99i −1.68785 2.92345i
\(183\) 0 0
\(184\) −287.405 + 497.799i −0.115151 + 0.199447i
\(185\) 705.073 1221.22i 0.280206 0.485330i
\(186\) 0 0
\(187\) 134.153 + 232.359i 0.0524610 + 0.0908652i
\(188\) −452.403 −0.175505
\(189\) 0 0
\(190\) 1606.27 0.613322
\(191\) −373.148 646.311i −0.141361 0.244845i 0.786648 0.617402i \(-0.211815\pi\)
−0.928010 + 0.372557i \(0.878481\pi\)
\(192\) 0 0
\(193\) −53.9538 + 93.4506i −0.0201227 + 0.0348535i −0.875911 0.482472i \(-0.839739\pi\)
0.855789 + 0.517326i \(0.173072\pi\)
\(194\) 3049.64 5282.13i 1.12861 1.95482i
\(195\) 0 0
\(196\) −3066.20 5310.82i −1.11742 1.93543i
\(197\) 3361.02 1.21555 0.607774 0.794110i \(-0.292063\pi\)
0.607774 + 0.794110i \(0.292063\pi\)
\(198\) 0 0
\(199\) 1368.99 0.487663 0.243831 0.969818i \(-0.421596\pi\)
0.243831 + 0.969818i \(0.421596\pi\)
\(200\) −115.215 199.558i −0.0407346 0.0705544i
\(201\) 0 0
\(202\) 2360.21 4088.00i 0.822097 1.42391i
\(203\) 763.074 1321.68i 0.263829 0.456965i
\(204\) 0 0
\(205\) −393.850 682.168i −0.134184 0.232413i
\(206\) 2253.94 0.762329
\(207\) 0 0
\(208\) −2656.44 −0.885534
\(209\) 1534.54 + 2657.90i 0.507877 + 0.879669i
\(210\) 0 0
\(211\) −1251.27 + 2167.27i −0.408252 + 0.707114i −0.994694 0.102878i \(-0.967195\pi\)
0.586442 + 0.809991i \(0.300528\pi\)
\(212\) 133.514 231.254i 0.0432538 0.0749178i
\(213\) 0 0
\(214\) 1046.07 + 1811.85i 0.334150 + 0.578765i
\(215\) −1689.07 −0.535784
\(216\) 0 0
\(217\) 3168.81 0.991305
\(218\) 749.292 + 1297.81i 0.232791 + 0.403206i
\(219\) 0 0
\(220\) 1034.43 1791.69i 0.317006 0.549071i
\(221\) −208.299 + 360.785i −0.0634015 + 0.109815i
\(222\) 0 0
\(223\) −937.263 1623.39i −0.281452 0.487489i 0.690291 0.723532i \(-0.257483\pi\)
−0.971743 + 0.236043i \(0.924149\pi\)
\(224\) −7777.72 −2.31996
\(225\) 0 0
\(226\) −7511.18 −2.21078
\(227\) 2539.37 + 4398.32i 0.742484 + 1.28602i 0.951361 + 0.308078i \(0.0996859\pi\)
−0.208877 + 0.977942i \(0.566981\pi\)
\(228\) 0 0
\(229\) −432.933 + 749.861i −0.124930 + 0.216385i −0.921706 0.387890i \(-0.873204\pi\)
0.796776 + 0.604275i \(0.206537\pi\)
\(230\) −664.441 + 1150.85i −0.190487 + 0.329933i
\(231\) 0 0
\(232\) 228.625 + 395.990i 0.0646981 + 0.112060i
\(233\) −1142.10 −0.321122 −0.160561 0.987026i \(-0.551330\pi\)
−0.160561 + 0.987026i \(0.551330\pi\)
\(234\) 0 0
\(235\) −222.579 −0.0617849
\(236\) −2164.29 3748.66i −0.596964 1.03397i
\(237\) 0 0
\(238\) −431.998 + 748.242i −0.117657 + 0.203787i
\(239\) −1574.68 + 2727.43i −0.426183 + 0.738171i −0.996530 0.0832330i \(-0.973475\pi\)
0.570347 + 0.821404i \(0.306809\pi\)
\(240\) 0 0
\(241\) −2252.18 3900.90i −0.601975 1.04265i −0.992522 0.122068i \(-0.961047\pi\)
0.390547 0.920583i \(-0.372286\pi\)
\(242\) 1392.24 0.369821
\(243\) 0 0
\(244\) 8644.39 2.26803
\(245\) −1508.55 2612.88i −0.393378 0.681351i
\(246\) 0 0
\(247\) −2382.69 + 4126.94i −0.613793 + 1.06312i
\(248\) −474.704 + 822.212i −0.121547 + 0.210526i
\(249\) 0 0
\(250\) −266.361 461.351i −0.0673846 0.116714i
\(251\) −886.861 −0.223021 −0.111510 0.993763i \(-0.535569\pi\)
−0.111510 + 0.993763i \(0.535569\pi\)
\(252\) 0 0
\(253\) −2539.08 −0.630950
\(254\) 3209.38 + 5558.81i 0.792813 + 1.37319i
\(255\) 0 0
\(256\) −543.033 + 940.561i −0.132576 + 0.229629i
\(257\) 1131.02 1958.98i 0.274517 0.475478i −0.695496 0.718530i \(-0.744815\pi\)
0.970013 + 0.243052i \(0.0781486\pi\)
\(258\) 0 0
\(259\) 4338.17 + 7513.92i 1.04077 + 1.80267i
\(260\) 3212.34 0.766233
\(261\) 0 0
\(262\) −5434.30 −1.28142
\(263\) 3640.31 + 6305.20i 0.853503 + 1.47831i 0.878027 + 0.478611i \(0.158859\pi\)
−0.0245245 + 0.999699i \(0.507807\pi\)
\(264\) 0 0
\(265\) 65.6881 113.775i 0.0152271 0.0263742i
\(266\) −4941.52 + 8558.96i −1.13904 + 1.97287i
\(267\) 0 0
\(268\) −489.375 847.622i −0.111542 0.193197i
\(269\) 106.781 0.0242028 0.0121014 0.999927i \(-0.496148\pi\)
0.0121014 + 0.999927i \(0.496148\pi\)
\(270\) 0 0
\(271\) 5908.85 1.32449 0.662246 0.749287i \(-0.269603\pi\)
0.662246 + 0.749287i \(0.269603\pi\)
\(272\) 138.455 + 239.811i 0.0308643 + 0.0534585i
\(273\) 0 0
\(274\) 3067.25 5312.64i 0.676276 1.17134i
\(275\) 508.933 881.498i 0.111599 0.193296i
\(276\) 0 0
\(277\) −1645.04 2849.30i −0.356827 0.618042i 0.630602 0.776106i \(-0.282808\pi\)
−0.987429 + 0.158064i \(0.949475\pi\)
\(278\) −10822.8 −2.33492
\(279\) 0 0
\(280\) 1417.78 0.302603
\(281\) 169.861 + 294.209i 0.0360608 + 0.0624591i 0.883493 0.468445i \(-0.155186\pi\)
−0.847432 + 0.530904i \(0.821852\pi\)
\(282\) 0 0
\(283\) −1299.83 + 2251.37i −0.273028 + 0.472898i −0.969636 0.244554i \(-0.921358\pi\)
0.696608 + 0.717452i \(0.254692\pi\)
\(284\) 4838.30 8380.19i 1.01092 1.75096i
\(285\) 0 0
\(286\) 5484.67 + 9499.73i 1.13397 + 1.96409i
\(287\) 4846.55 0.996804
\(288\) 0 0
\(289\) −4869.57 −0.991161
\(290\) 528.550 + 915.475i 0.107026 + 0.185374i
\(291\) 0 0
\(292\) 258.418 447.592i 0.0517902 0.0897033i
\(293\) 89.0427 154.227i 0.0177540 0.0307509i −0.857012 0.515297i \(-0.827682\pi\)
0.874766 + 0.484546i \(0.161015\pi\)
\(294\) 0 0
\(295\) −1064.82 1844.31i −0.210156 0.364001i
\(296\) −2599.52 −0.510452
\(297\) 0 0
\(298\) −399.581 −0.0776749
\(299\) −1971.22 3414.25i −0.381266 0.660372i
\(300\) 0 0
\(301\) 5196.24 9000.16i 0.995038 1.72346i
\(302\) 2276.07 3942.26i 0.433685 0.751164i
\(303\) 0 0
\(304\) 1583.76 + 2743.15i 0.298798 + 0.517534i
\(305\) 4252.97 0.798441
\(306\) 0 0
\(307\) 1537.60 0.285848 0.142924 0.989734i \(-0.454349\pi\)
0.142924 + 0.989734i \(0.454349\pi\)
\(308\) 6364.64 + 11023.9i 1.17746 + 2.03943i
\(309\) 0 0
\(310\) −1097.45 + 1900.84i −0.201068 + 0.348260i
\(311\) 472.662 818.674i 0.0861807 0.149269i −0.819713 0.572774i \(-0.805867\pi\)
0.905894 + 0.423505i \(0.139200\pi\)
\(312\) 0 0
\(313\) −992.767 1719.52i −0.179280 0.310521i 0.762354 0.647160i \(-0.224043\pi\)
−0.941634 + 0.336638i \(0.890710\pi\)
\(314\) 774.428 0.139183
\(315\) 0 0
\(316\) −2004.90 −0.356913
\(317\) −2591.62 4488.81i −0.459179 0.795321i 0.539739 0.841833i \(-0.318523\pi\)
−0.998918 + 0.0465112i \(0.985190\pi\)
\(318\) 0 0
\(319\) −1009.89 + 1749.19i −0.177251 + 0.307008i
\(320\) 1853.24 3209.91i 0.323748 0.560748i
\(321\) 0 0
\(322\) −4088.16 7080.91i −0.707529 1.22548i
\(323\) 496.748 0.0855722
\(324\) 0 0
\(325\) 1580.45 0.269746
\(326\) 2350.52 + 4071.22i 0.399336 + 0.691670i
\(327\) 0 0
\(328\) −726.037 + 1257.53i −0.122222 + 0.211694i
\(329\) 684.741 1186.01i 0.114745 0.198744i
\(330\) 0 0
\(331\) 1086.68 + 1882.19i 0.180451 + 0.312551i 0.942034 0.335517i \(-0.108911\pi\)
−0.761583 + 0.648067i \(0.775578\pi\)
\(332\) 2009.57 0.332197
\(333\) 0 0
\(334\) 17224.8 2.82186
\(335\) −240.769 417.024i −0.0392675 0.0680133i
\(336\) 0 0
\(337\) 3925.16 6798.57i 0.634472 1.09894i −0.352155 0.935942i \(-0.614551\pi\)
0.986627 0.162995i \(-0.0521156\pi\)
\(338\) −3834.52 + 6641.58i −0.617071 + 1.06880i
\(339\) 0 0
\(340\) −167.429 289.995i −0.0267062 0.0462565i
\(341\) −4193.78 −0.665999
\(342\) 0 0
\(343\) 8011.53 1.26117
\(344\) 1556.85 + 2696.54i 0.244010 + 0.422638i
\(345\) 0 0
\(346\) −5855.16 + 10141.4i −0.909756 + 1.57574i
\(347\) −4686.12 + 8116.60i −0.724969 + 1.25568i 0.234018 + 0.972232i \(0.424813\pi\)
−0.958987 + 0.283451i \(0.908521\pi\)
\(348\) 0 0
\(349\) 588.952 + 1020.10i 0.0903321 + 0.156460i 0.907651 0.419726i \(-0.137874\pi\)
−0.817319 + 0.576186i \(0.804540\pi\)
\(350\) 3277.73 0.500577
\(351\) 0 0
\(352\) 10293.4 1.55864
\(353\) −3631.06 6289.19i −0.547484 0.948271i −0.998446 0.0557274i \(-0.982252\pi\)
0.450962 0.892543i \(-0.351081\pi\)
\(354\) 0 0
\(355\) 2380.41 4122.99i 0.355885 0.616410i
\(356\) 6933.77 12009.6i 1.03227 1.78795i
\(357\) 0 0
\(358\) −6048.15 10475.7i −0.892890 1.54653i
\(359\) 1939.95 0.285199 0.142600 0.989780i \(-0.454454\pi\)
0.142600 + 0.989780i \(0.454454\pi\)
\(360\) 0 0
\(361\) −1176.81 −0.171572
\(362\) −7335.05 12704.7i −1.06498 1.84459i
\(363\) 0 0
\(364\) −9882.41 + 17116.8i −1.42302 + 2.46474i
\(365\) 127.139 220.212i 0.0182323 0.0315792i
\(366\) 0 0
\(367\) −3250.97 5630.85i −0.462396 0.800893i 0.536684 0.843783i \(-0.319677\pi\)
−0.999080 + 0.0428901i \(0.986343\pi\)
\(368\) −2620.51 −0.371205
\(369\) 0 0
\(370\) −6009.73 −0.844409
\(371\) 404.165 + 700.034i 0.0565585 + 0.0979622i
\(372\) 0 0
\(373\) −6659.02 + 11533.8i −0.924372 + 1.60106i −0.131805 + 0.991276i \(0.542077\pi\)
−0.792568 + 0.609784i \(0.791256\pi\)
\(374\) 571.729 990.263i 0.0790465 0.136913i
\(375\) 0 0
\(376\) 205.155 + 355.339i 0.0281385 + 0.0487373i
\(377\) −3136.13 −0.428432
\(378\) 0 0
\(379\) −3198.42 −0.433488 −0.216744 0.976228i \(-0.569544\pi\)
−0.216744 + 0.976228i \(0.569544\pi\)
\(380\) −1915.18 3317.19i −0.258544 0.447811i
\(381\) 0 0
\(382\) −1590.27 + 2754.43i −0.212999 + 0.368924i
\(383\) −1170.25 + 2026.93i −0.156128 + 0.270422i −0.933469 0.358658i \(-0.883235\pi\)
0.777341 + 0.629079i \(0.216568\pi\)
\(384\) 0 0
\(385\) 3131.36 + 5423.67i 0.414516 + 0.717963i
\(386\) 459.878 0.0606403
\(387\) 0 0
\(388\) −14544.5 −1.90305
\(389\) 1995.97 + 3457.12i 0.260153 + 0.450599i 0.966282 0.257484i \(-0.0828936\pi\)
−0.706129 + 0.708083i \(0.749560\pi\)
\(390\) 0 0
\(391\) −205.482 + 355.906i −0.0265772 + 0.0460330i
\(392\) −2780.91 + 4816.69i −0.358310 + 0.620611i
\(393\) 0 0
\(394\) −7161.96 12404.9i −0.915773 1.58616i
\(395\) −986.395 −0.125648
\(396\) 0 0
\(397\) −4960.90 −0.627155 −0.313577 0.949563i \(-0.601528\pi\)
−0.313577 + 0.949563i \(0.601528\pi\)
\(398\) −2917.16 5052.66i −0.367397 0.636350i
\(399\) 0 0
\(400\) 525.256 909.769i 0.0656569 0.113721i
\(401\) 413.811 716.742i 0.0515330 0.0892578i −0.839108 0.543965i \(-0.816923\pi\)
0.890641 + 0.454707i \(0.150256\pi\)
\(402\) 0 0
\(403\) −3255.85 5639.30i −0.402445 0.697056i
\(404\) −11256.4 −1.38621
\(405\) 0 0
\(406\) −6504.11 −0.795058
\(407\) −5741.36 9944.33i −0.699235 1.21111i
\(408\) 0 0
\(409\) 4183.82 7246.59i 0.505811 0.876090i −0.494167 0.869367i \(-0.664527\pi\)
0.999977 0.00672263i \(-0.00213989\pi\)
\(410\) −1678.50 + 2907.25i −0.202184 + 0.350192i
\(411\) 0 0
\(412\) −2687.41 4654.73i −0.321357 0.556607i
\(413\) 13103.2 1.56117
\(414\) 0 0
\(415\) 988.693 0.116947
\(416\) 7991.34 + 13841.4i 0.941845 + 1.63132i
\(417\) 0 0
\(418\) 6539.87 11327.4i 0.765252 1.32546i
\(419\) 2100.36 3637.93i 0.244891 0.424163i −0.717210 0.696857i \(-0.754581\pi\)
0.962101 + 0.272694i \(0.0879145\pi\)
\(420\) 0 0
\(421\) −3469.38 6009.14i −0.401632 0.695648i 0.592291 0.805724i \(-0.298224\pi\)
−0.993923 + 0.110077i \(0.964890\pi\)
\(422\) 10665.3 1.23028
\(423\) 0 0
\(424\) −242.184 −0.0277394
\(425\) −82.3737 142.675i −0.00940168 0.0162842i
\(426\) 0 0
\(427\) −13083.8 + 22661.8i −1.48283 + 2.56835i
\(428\) 2494.50 4320.60i 0.281720 0.487953i
\(429\) 0 0
\(430\) 3599.22 + 6234.03i 0.403651 + 0.699144i
\(431\) −6827.09 −0.762991 −0.381496 0.924371i \(-0.624591\pi\)
−0.381496 + 0.924371i \(0.624591\pi\)
\(432\) 0 0
\(433\) −2199.59 −0.244124 −0.122062 0.992522i \(-0.538951\pi\)
−0.122062 + 0.992522i \(0.538951\pi\)
\(434\) −6752.39 11695.5i −0.746832 1.29355i
\(435\) 0 0
\(436\) 1786.78 3094.80i 0.196265 0.339940i
\(437\) −2350.46 + 4071.12i −0.257295 + 0.445648i
\(438\) 0 0
\(439\) −4162.16 7209.07i −0.452504 0.783759i 0.546037 0.837761i \(-0.316136\pi\)
−0.998541 + 0.0540018i \(0.982802\pi\)
\(440\) −1876.37 −0.203301
\(441\) 0 0
\(442\) 1775.45 0.191063
\(443\) −5433.41 9410.93i −0.582729 1.00932i −0.995154 0.0983247i \(-0.968652\pi\)
0.412426 0.910991i \(-0.364682\pi\)
\(444\) 0 0
\(445\) 3411.36 5908.65i 0.363402 0.629431i
\(446\) −3994.41 + 6918.51i −0.424082 + 0.734532i
\(447\) 0 0
\(448\) 11402.6 + 19749.9i 1.20250 + 2.08280i
\(449\) 4947.73 0.520040 0.260020 0.965603i \(-0.416271\pi\)
0.260020 + 0.965603i \(0.416271\pi\)
\(450\) 0 0
\(451\) −6414.18 −0.669694
\(452\) 8955.69 + 15511.7i 0.931947 + 1.61418i
\(453\) 0 0
\(454\) 10822.2 18744.7i 1.11875 1.93773i
\(455\) −4862.07 + 8421.35i −0.500961 + 0.867690i
\(456\) 0 0
\(457\) 7098.85 + 12295.6i 0.726630 + 1.25856i 0.958299 + 0.285766i \(0.0922480\pi\)
−0.231669 + 0.972795i \(0.574419\pi\)
\(458\) 3690.13 0.376481
\(459\) 0 0
\(460\) 3168.89 0.321196
\(461\) −9114.02 15785.9i −0.920786 1.59485i −0.798202 0.602390i \(-0.794215\pi\)
−0.122584 0.992458i \(-0.539118\pi\)
\(462\) 0 0
\(463\) −2170.59 + 3759.58i −0.217875 + 0.377370i −0.954158 0.299303i \(-0.903246\pi\)
0.736283 + 0.676674i \(0.236579\pi\)
\(464\) −1042.28 + 1805.29i −0.104282 + 0.180621i
\(465\) 0 0
\(466\) 2433.69 + 4215.28i 0.241928 + 0.419032i
\(467\) −4919.63 −0.487481 −0.243740 0.969841i \(-0.578374\pi\)
−0.243740 + 0.969841i \(0.578374\pi\)
\(468\) 0 0
\(469\) 2962.80 0.291704
\(470\) 474.291 + 821.497i 0.0465477 + 0.0806230i
\(471\) 0 0
\(472\) −1962.92 + 3399.88i −0.191421 + 0.331551i
\(473\) −6876.98 + 11911.3i −0.668508 + 1.15789i
\(474\) 0 0
\(475\) −942.254 1632.03i −0.0910180 0.157648i
\(476\) 2060.31 0.198391
\(477\) 0 0
\(478\) 13421.9 1.28432
\(479\) 2286.41 + 3960.19i 0.218098 + 0.377757i 0.954226 0.299085i \(-0.0966814\pi\)
−0.736128 + 0.676842i \(0.763348\pi\)
\(480\) 0 0
\(481\) 8914.64 15440.6i 0.845057 1.46368i
\(482\) −9598.31 + 16624.8i −0.907035 + 1.57103i
\(483\) 0 0
\(484\) −1659.99 2875.19i −0.155897 0.270021i
\(485\) −7155.79 −0.669954
\(486\) 0 0
\(487\) 15751.5 1.46564 0.732822 0.680421i \(-0.238203\pi\)
0.732822 + 0.680421i \(0.238203\pi\)
\(488\) −3920.04 6789.72i −0.363631 0.629828i
\(489\) 0 0
\(490\) −6429.10 + 11135.5i −0.592729 + 1.02664i
\(491\) 7654.18 13257.4i 0.703520 1.21853i −0.263703 0.964604i \(-0.584944\pi\)
0.967223 0.253928i \(-0.0817227\pi\)
\(492\) 0 0
\(493\) 163.457 + 283.116i 0.0149325 + 0.0258639i
\(494\) 20309.0 1.84968
\(495\) 0 0
\(496\) −4328.28 −0.391826
\(497\) 14646.2 + 25367.9i 1.32187 + 2.28955i
\(498\) 0 0
\(499\) −8866.05 + 15356.5i −0.795389 + 1.37765i 0.127203 + 0.991877i \(0.459400\pi\)
−0.922592 + 0.385777i \(0.873933\pi\)
\(500\) −635.172 + 1100.15i −0.0568115 + 0.0984005i
\(501\) 0 0
\(502\) 1889.80 + 3273.23i 0.168020 + 0.291019i
\(503\) 10511.5 0.931775 0.465887 0.884844i \(-0.345735\pi\)
0.465887 + 0.884844i \(0.345735\pi\)
\(504\) 0 0
\(505\) −5538.08 −0.488003
\(506\) 5410.49 + 9371.25i 0.475347 + 0.823326i
\(507\) 0 0
\(508\) 7653.18 13255.7i 0.668416 1.15773i
\(509\) 9815.42 17000.8i 0.854737 1.48045i −0.0221524 0.999755i \(-0.507052\pi\)
0.876889 0.480693i \(-0.159615\pi\)
\(510\) 0 0
\(511\) 782.262 + 1354.92i 0.0677206 + 0.117296i
\(512\) 13722.1 1.18444
\(513\) 0 0
\(514\) −9640.30 −0.827267
\(515\) −1322.19 2290.09i −0.113131 0.195949i
\(516\) 0 0
\(517\) −906.223 + 1569.62i −0.0770902 + 0.133524i
\(518\) 18488.3 32022.7i 1.56820 2.71621i
\(519\) 0 0
\(520\) −1456.73 2523.12i −0.122849 0.212781i
\(521\) −88.4336 −0.00743636 −0.00371818 0.999993i \(-0.501184\pi\)
−0.00371818 + 0.999993i \(0.501184\pi\)
\(522\) 0 0
\(523\) 21346.4 1.78473 0.892363 0.451317i \(-0.149046\pi\)
0.892363 + 0.451317i \(0.149046\pi\)
\(524\) 6479.39 + 11222.6i 0.540178 + 0.935616i
\(525\) 0 0
\(526\) 15514.2 26871.4i 1.28603 2.22747i
\(527\) −339.394 + 587.847i −0.0280535 + 0.0485902i
\(528\) 0 0
\(529\) 4138.94 + 7168.86i 0.340178 + 0.589205i
\(530\) −559.896 −0.0458874
\(531\) 0 0
\(532\) 23567.4 1.92063
\(533\) −4979.67 8625.03i −0.404678 0.700923i
\(534\) 0 0
\(535\) 1227.27 2125.70i 0.0991770 0.171780i
\(536\) −443.842 + 768.757i −0.0357669 + 0.0619501i
\(537\) 0 0
\(538\) −227.538 394.108i −0.0182340 0.0315821i
\(539\) −24568.0 −1.96330
\(540\) 0 0
\(541\) −14432.6 −1.14696 −0.573480 0.819220i \(-0.694407\pi\)
−0.573480 + 0.819220i \(0.694407\pi\)
\(542\) −12591.1 21808.4i −0.997850 1.72833i
\(543\) 0 0
\(544\) 833.027 1442.84i 0.0656539 0.113716i
\(545\) 879.084 1522.62i 0.0690933 0.119673i
\(546\) 0 0
\(547\) 8284.80 + 14349.7i 0.647592 + 1.12166i 0.983696 + 0.179837i \(0.0575571\pi\)
−0.336105 + 0.941825i \(0.609110\pi\)
\(548\) −14628.5 −1.14033
\(549\) 0 0
\(550\) −4337.92 −0.336308
\(551\) 1869.75 + 3238.50i 0.144562 + 0.250389i
\(552\) 0 0
\(553\) 3034.54 5255.98i 0.233349 0.404172i
\(554\) −7010.80 + 12143.1i −0.537654 + 0.931245i
\(555\) 0 0
\(556\) 12904.1 + 22350.6i 0.984277 + 1.70482i
\(557\) −11597.0 −0.882191 −0.441096 0.897460i \(-0.645410\pi\)
−0.441096 + 0.897460i \(0.645410\pi\)
\(558\) 0 0
\(559\) −21355.9 −1.61584
\(560\) 3231.79 + 5597.62i 0.243871 + 0.422397i
\(561\) 0 0
\(562\) 723.912 1253.85i 0.0543352 0.0941113i
\(563\) −11524.6 + 19961.3i −0.862709 + 1.49426i 0.00659429 + 0.999978i \(0.497901\pi\)
−0.869304 + 0.494278i \(0.835432\pi\)
\(564\) 0 0
\(565\) 4406.13 + 7631.64i 0.328084 + 0.568258i
\(566\) 11079.2 0.822778
\(567\) 0 0
\(568\) −8776.27 −0.648317
\(569\) 7366.96 + 12759.9i 0.542775 + 0.940114i 0.998743 + 0.0501179i \(0.0159597\pi\)
−0.455968 + 0.889996i \(0.650707\pi\)
\(570\) 0 0
\(571\) −7555.94 + 13087.3i −0.553776 + 0.959169i 0.444221 + 0.895917i \(0.353480\pi\)
−0.997998 + 0.0632515i \(0.979853\pi\)
\(572\) 13078.9 22653.3i 0.956043 1.65591i
\(573\) 0 0
\(574\) −10327.5 17887.7i −0.750975 1.30073i
\(575\) 1559.07 0.113074
\(576\) 0 0
\(577\) −26150.5 −1.88676 −0.943380 0.331715i \(-0.892373\pi\)
−0.943380 + 0.331715i \(0.892373\pi\)
\(578\) 10376.5 + 17972.7i 0.746724 + 1.29336i
\(579\) 0 0
\(580\) 1260.39 2183.07i 0.0902328 0.156288i
\(581\) −3041.61 + 5268.22i −0.217190 + 0.376184i
\(582\) 0 0
\(583\) −534.894 926.463i −0.0379983 0.0658150i
\(584\) −468.747 −0.0332139
\(585\) 0 0
\(586\) −758.961 −0.0535023
\(587\) 1045.77 + 1811.33i 0.0735326 + 0.127362i 0.900447 0.434965i \(-0.143239\pi\)
−0.826915 + 0.562327i \(0.809906\pi\)
\(588\) 0 0
\(589\) −3882.24 + 6724.24i −0.271587 + 0.470403i
\(590\) −4538.01 + 7860.06i −0.316656 + 0.548464i
\(591\) 0 0
\(592\) −5925.50 10263.3i −0.411379 0.712530i
\(593\) −3260.34 −0.225778 −0.112889 0.993608i \(-0.536010\pi\)
−0.112889 + 0.993608i \(0.536010\pi\)
\(594\) 0 0
\(595\) 1013.66 0.0698417
\(596\) 476.426 + 825.194i 0.0327436 + 0.0567135i
\(597\) 0 0
\(598\) −8400.90 + 14550.8i −0.574479 + 0.995026i
\(599\) −11499.6 + 19917.9i −0.784410 + 1.35864i 0.144941 + 0.989440i \(0.453701\pi\)
−0.929351 + 0.369197i \(0.879633\pi\)
\(600\) 0 0
\(601\) 7146.93 + 12378.9i 0.485074 + 0.840173i 0.999853 0.0171500i \(-0.00545928\pi\)
−0.514779 + 0.857323i \(0.672126\pi\)
\(602\) −44290.5 −2.99858
\(603\) 0 0
\(604\) −10855.1 −0.731274
\(605\) −816.702 1414.57i −0.0548821 0.0950586i
\(606\) 0 0
\(607\) 8217.04 14232.3i 0.549455 0.951685i −0.448856 0.893604i \(-0.648169\pi\)
0.998312 0.0580809i \(-0.0184981\pi\)
\(608\) 9528.80 16504.4i 0.635598 1.10089i
\(609\) 0 0
\(610\) −9062.62 15696.9i −0.601532 1.04188i
\(611\) −2814.19 −0.186334
\(612\) 0 0
\(613\) 3674.45 0.242104 0.121052 0.992646i \(-0.461373\pi\)
0.121052 + 0.992646i \(0.461373\pi\)
\(614\) −3276.45 5674.99i −0.215353 0.373003i
\(615\) 0 0
\(616\) 5772.46 9998.19i 0.377563 0.653958i
\(617\) 4313.78 7471.69i 0.281469 0.487519i −0.690278 0.723544i \(-0.742512\pi\)
0.971747 + 0.236026i \(0.0758450\pi\)
\(618\) 0 0
\(619\) 654.905 + 1134.33i 0.0425248 + 0.0736551i 0.886504 0.462720i \(-0.153127\pi\)
−0.843980 + 0.536375i \(0.819793\pi\)
\(620\) 5234.03 0.339038
\(621\) 0 0
\(622\) −4028.76 −0.259708
\(623\) 20989.4 + 36354.7i 1.34979 + 2.33791i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −4230.95 + 7328.23i −0.270132 + 0.467883i
\(627\) 0 0
\(628\) −923.362 1599.31i −0.0586722 0.101623i
\(629\) −1858.54 −0.117814
\(630\) 0 0
\(631\) 14447.2 0.911463 0.455731 0.890117i \(-0.349378\pi\)
0.455731 + 0.890117i \(0.349378\pi\)
\(632\) 909.179 + 1574.74i 0.0572234 + 0.0991138i
\(633\) 0 0
\(634\) −11044.9 + 19130.3i −0.691875 + 1.19836i
\(635\) 3765.31 6521.71i 0.235310 0.407569i
\(636\) 0 0
\(637\) −19073.4 33036.2i −1.18637 2.05485i
\(638\) 8607.88 0.534152
\(639\) 0 0
\(640\) −5683.43 −0.351027
\(641\) −10036.6 17383.8i −0.618440 1.07117i −0.989770 0.142669i \(-0.954431\pi\)
0.371330 0.928501i \(-0.378902\pi\)
\(642\) 0 0
\(643\) 8867.96 15359.8i 0.543885 0.942037i −0.454791 0.890598i \(-0.650286\pi\)
0.998676 0.0514386i \(-0.0163807\pi\)
\(644\) −9748.75 + 16885.3i −0.596513 + 1.03319i
\(645\) 0 0
\(646\) −1058.52 1833.40i −0.0644686 0.111663i
\(647\) 11456.8 0.696158 0.348079 0.937465i \(-0.386834\pi\)
0.348079 + 0.937465i \(0.386834\pi\)
\(648\) 0 0
\(649\) −17341.4 −1.04886
\(650\) −3367.75 5833.12i −0.203222 0.351990i
\(651\) 0 0
\(652\) 5605.12 9708.36i 0.336677 0.583142i
\(653\) 14536.0 25177.0i 0.871113 1.50881i 0.0102660 0.999947i \(-0.496732\pi\)
0.860847 0.508864i \(-0.169935\pi\)
\(654\) 0 0
\(655\) 3187.81 + 5521.45i 0.190165 + 0.329376i
\(656\) −6619.90 −0.393999
\(657\) 0 0
\(658\) −5836.43 −0.345787
\(659\) −2177.54 3771.62i −0.128718 0.222946i 0.794462 0.607314i \(-0.207753\pi\)
−0.923180 + 0.384368i \(0.874419\pi\)
\(660\) 0 0
\(661\) −13647.7 + 23638.5i −0.803075 + 1.39097i 0.114508 + 0.993422i \(0.463471\pi\)
−0.917583 + 0.397545i \(0.869862\pi\)
\(662\) 4631.19 8021.46i 0.271898 0.470941i
\(663\) 0 0
\(664\) −911.297 1578.41i −0.0532608 0.0922504i
\(665\) 11595.0 0.676141
\(666\) 0 0
\(667\) −3093.72 −0.179594
\(668\) −20537.4 35571.8i −1.18955 2.06035i
\(669\) 0 0
\(670\) −1026.10 + 1777.26i −0.0591669 + 0.102480i
\(671\) 17315.8 29991.9i 0.996230 1.72552i
\(672\) 0 0
\(673\) 8880.01 + 15380.6i 0.508617 + 0.880951i 0.999950 + 0.00997909i \(0.00317650\pi\)
−0.491333 + 0.870972i \(0.663490\pi\)
\(674\) −33456.3 −1.91200
\(675\) 0 0
\(676\) 18287.8 1.04050
\(677\) 968.667 + 1677.78i 0.0549910 + 0.0952472i 0.892210 0.451620i \(-0.149154\pi\)
−0.837219 + 0.546867i \(0.815820\pi\)
\(678\) 0 0
\(679\) 22014.0 38129.4i 1.24421 2.15504i
\(680\) −151.851 + 263.013i −0.00856355 + 0.0148325i
\(681\) 0 0
\(682\) 8936.48 + 15478.4i 0.501753 + 0.869061i
\(683\) 2125.71 0.119090 0.0595448 0.998226i \(-0.481035\pi\)
0.0595448 + 0.998226i \(0.481035\pi\)
\(684\) 0 0
\(685\) −7197.12 −0.401442
\(686\) −17071.7 29569.0i −0.950146 1.64570i
\(687\) 0 0
\(688\) −7097.55 + 12293.3i −0.393301 + 0.681218i
\(689\) 830.532 1438.52i 0.0459227 0.0795405i
\(690\) 0 0
\(691\) −6913.13 11973.9i −0.380590 0.659201i 0.610557 0.791973i \(-0.290946\pi\)
−0.991147 + 0.132771i \(0.957612\pi\)
\(692\) 27924.8 1.53402
\(693\) 0 0
\(694\) 39942.4 2.18472
\(695\) 6348.74 + 10996.3i 0.346506 + 0.600166i
\(696\) 0 0
\(697\) −519.086 + 899.084i −0.0282092 + 0.0488597i
\(698\) 2509.98 4347.42i 0.136109 0.235748i
\(699\) 0 0
\(700\) −3908.08 6768.99i −0.211016 0.365491i
\(701\) 24464.0 1.31810 0.659052 0.752097i \(-0.270958\pi\)
0.659052 + 0.752097i \(0.270958\pi\)
\(702\) 0 0
\(703\) −21259.5 −1.14056
\(704\) −15090.8 26138.0i −0.807892 1.39931i
\(705\) 0 0
\(706\) −15474.8 + 26803.1i −0.824931 + 1.42882i
\(707\) 17037.3 29509.5i 0.906300 1.56976i
\(708\) 0 0
\(709\) 14749.1 + 25546.2i 0.781263 + 1.35319i 0.931206 + 0.364492i \(0.118757\pi\)
−0.149944 + 0.988695i \(0.547909\pi\)
\(710\) −20289.6 −1.07247
\(711\) 0 0
\(712\) −12577.3 −0.662012
\(713\) −3211.81 5563.02i −0.168700 0.292198i
\(714\) 0 0
\(715\) 6434.72 11145.3i 0.336566 0.582950i
\(716\) −14422.6 + 24980.7i −0.752790 + 1.30387i
\(717\) 0 0
\(718\) −4133.81 7159.98i −0.214864 0.372156i
\(719\) 3857.66 0.200093 0.100046 0.994983i \(-0.468101\pi\)
0.100046 + 0.994983i \(0.468101\pi\)
\(720\) 0 0
\(721\) 16270.2 0.840410
\(722\) 2507.66 + 4343.39i 0.129260 + 0.223884i
\(723\) 0 0
\(724\) −17491.4 + 30295.9i −0.897874 + 1.55516i
\(725\) 620.105 1074.05i 0.0317657 0.0550197i
\(726\) 0 0
\(727\) −4372.55 7573.48i −0.223066 0.386361i 0.732672 0.680582i \(-0.238273\pi\)
−0.955737 + 0.294221i \(0.904940\pi\)
\(728\) 17925.8 0.912604
\(729\) 0 0
\(730\) −1083.68 −0.0549436
\(731\) 1113.08 + 1927.91i 0.0563184 + 0.0975463i
\(732\) 0 0
\(733\) 4709.20 8156.58i 0.237296 0.411010i −0.722641 0.691223i \(-0.757072\pi\)
0.959938 + 0.280214i \(0.0904054\pi\)
\(734\) −13854.9 + 23997.4i −0.696723 + 1.20676i
\(735\) 0 0
\(736\) 7883.26 + 13654.2i 0.394811 + 0.683832i
\(737\) −3921.13 −0.195979
\(738\) 0 0
\(739\) 6219.42 0.309587 0.154794 0.987947i \(-0.450529\pi\)
0.154794 + 0.987947i \(0.450529\pi\)
\(740\) 7165.49 + 12411.0i 0.355958 + 0.616537i
\(741\) 0 0
\(742\) 1722.46 2983.39i 0.0852204 0.147606i
\(743\) −14693.7 + 25450.3i −0.725518 + 1.25663i 0.233242 + 0.972419i \(0.425067\pi\)
−0.958760 + 0.284216i \(0.908267\pi\)
\(744\) 0 0
\(745\) 234.398 + 405.989i 0.0115271 + 0.0199655i
\(746\) 56758.5 2.78563
\(747\) 0 0
\(748\) −2726.72 −0.133287
\(749\) 7551.15 + 13079.0i 0.368375 + 0.638045i
\(750\) 0 0
\(751\) 10823.6 18747.0i 0.525909 0.910901i −0.473636 0.880721i \(-0.657059\pi\)
0.999544 0.0301801i \(-0.00960808\pi\)
\(752\) −935.287 + 1619.97i −0.0453543 + 0.0785559i
\(753\) 0 0
\(754\) 6682.75 + 11574.9i 0.322774 + 0.559061i
\(755\) −5340.65 −0.257438
\(756\) 0 0
\(757\) −13907.2 −0.667722 −0.333861 0.942622i \(-0.608352\pi\)
−0.333861 + 0.942622i \(0.608352\pi\)
\(758\) 6815.48 + 11804.8i 0.326582 + 0.565657i
\(759\) 0 0
\(760\) −1736.98 + 3008.55i −0.0829040 + 0.143594i
\(761\) −11953.0 + 20703.3i −0.569379 + 0.986193i 0.427249 + 0.904134i \(0.359483\pi\)
−0.996628 + 0.0820585i \(0.973851\pi\)
\(762\) 0 0
\(763\) 5408.82 + 9368.35i 0.256635 + 0.444504i
\(764\) 7584.42 0.359155
\(765\) 0 0
\(766\) 9974.70 0.470497
\(767\) −13463.1 23318.7i −0.633798 1.09777i
\(768\) 0 0
\(769\) 12555.8 21747.3i 0.588783 1.01980i −0.405609 0.914047i \(-0.632941\pi\)
0.994392 0.105755i \(-0.0337261\pi\)
\(770\) 13345.1 23114.5i 0.624579 1.08180i
\(771\) 0 0
\(772\) −548.319 949.716i −0.0255627 0.0442759i
\(773\) −14909.4 −0.693729 −0.346865 0.937915i \(-0.612754\pi\)
−0.346865 + 0.937915i \(0.612754\pi\)
\(774\) 0 0
\(775\) 2575.10 0.119355
\(776\) 6595.62 + 11424.0i 0.305115 + 0.528474i
\(777\) 0 0
\(778\) 8506.37 14733.5i 0.391990 0.678947i
\(779\) −5937.70 + 10284.4i −0.273094 + 0.473013i
\(780\) 0 0
\(781\) −19383.5 33573.2i −0.888087 1.53821i
\(782\) 1751.44 0.0800912
\(783\) 0 0
\(784\) −25356.0 −1.15506
\(785\) −454.287 786.848i −0.0206550 0.0357756i
\(786\) 0 0
\(787\) 1329.38 2302.56i 0.0602128 0.104292i −0.834348 0.551239i \(-0.814155\pi\)
0.894560 + 0.446947i \(0.147489\pi\)
\(788\) −17078.6 + 29581.0i −0.772082 + 1.33728i
\(789\) 0 0
\(790\) 2101.90 + 3640.60i 0.0946610 + 0.163958i
\(791\) −54220.0 −2.43722
\(792\) 0 0
\(793\) 53772.7 2.40798
\(794\) 10571.1 + 18309.7i 0.472488 + 0.818373i
\(795\) 0 0
\(796\) −6956.33 + 12048.7i −0.309750 + 0.536502i
\(797\) −7086.11 + 12273.5i −0.314935 + 0.545483i −0.979424 0.201815i \(-0.935316\pi\)
0.664489 + 0.747298i \(0.268649\pi\)
\(798\) 0 0
\(799\) 146.677 + 254.053i 0.00649446 + 0.0112487i
\(800\) −6320.48 −0.279329
\(801\) 0 0
\(802\) −3527.14 −0.155296
\(803\) −1035.29 1793.17i −0.0454975 0.0788040i
\(804\) 0 0
\(805\) −4796.31 + 8307.45i −0.209997 + 0.363726i
\(806\) −13875.7 + 24033.4i −0.606391 + 1.05030i
\(807\) 0 0
\(808\) 5104.55 + 8841.34i 0.222249 + 0.384947i
\(809\) 21077.7 0.916012 0.458006 0.888949i \(-0.348564\pi\)
0.458006 + 0.888949i \(0.348564\pi\)
\(810\) 0 0
\(811\) −11937.4 −0.516868 −0.258434 0.966029i \(-0.583206\pi\)
−0.258434 + 0.966029i \(0.583206\pi\)
\(812\) 7754.94 + 13431.9i 0.335154 + 0.580503i
\(813\) 0 0
\(814\) −24468.4 + 42380.5i −1.05358 + 1.82486i
\(815\) 2757.68 4776.44i 0.118524 0.205290i
\(816\) 0 0
\(817\) 12732.3 + 22052.9i 0.545221 + 0.944350i
\(818\) −35661.0 −1.52428
\(819\) 0 0
\(820\) 8005.20 0.340919
\(821\) 7400.25 + 12817.6i 0.314580 + 0.544869i 0.979348 0.202181i \(-0.0648029\pi\)
−0.664768 + 0.747050i \(0.731470\pi\)
\(822\) 0 0
\(823\) −16588.3 + 28731.8i −0.702591 + 1.21692i 0.264963 + 0.964259i \(0.414640\pi\)
−0.967554 + 0.252665i \(0.918693\pi\)
\(824\) −2437.37 + 4221.64i −0.103046 + 0.178480i
\(825\) 0 0
\(826\) −27921.4 48361.3i −1.17616 2.03717i
\(827\) 29001.3 1.21944 0.609718 0.792619i \(-0.291283\pi\)
0.609718 + 0.792619i \(0.291283\pi\)
\(828\) 0 0
\(829\) 13221.1 0.553904 0.276952 0.960884i \(-0.410676\pi\)
0.276952 + 0.960884i \(0.410676\pi\)
\(830\) −2106.80 3649.08i −0.0881060 0.152604i
\(831\) 0 0
\(832\) 23431.6 40584.7i 0.976374 1.69113i
\(833\) −1988.24 + 3443.73i −0.0826991 + 0.143239i
\(834\) 0 0
\(835\) −10104.3 17501.1i −0.418769 0.725329i
\(836\) −31190.3 −1.29036
\(837\) 0 0
\(838\) −17902.5 −0.737987
\(839\) −21062.0 36480.4i −0.866675 1.50112i −0.865375 0.501125i \(-0.832920\pi\)
−0.00129985 0.999999i \(-0.500414\pi\)
\(840\) 0 0
\(841\) 10964.0 18990.2i 0.449547 0.778638i
\(842\) −14785.7 + 25609.6i −0.605166 + 1.04818i
\(843\) 0 0
\(844\) −12716.4 22025.4i −0.518621 0.898278i
\(845\) 8997.45 0.366298
\(846\) 0 0
\(847\) 10050.0 0.407700
\(848\) −552.049 956.177i −0.0223555 0.0387208i
\(849\) 0 0
\(850\) −351.059 + 608.051i −0.0141661 + 0.0245365i
\(851\) 8794.07 15231.8i 0.354238 0.613559i
\(852\) 0 0
\(853\) −7215.84 12498.2i −0.289643 0.501677i 0.684081 0.729406i \(-0.260203\pi\)
−0.973725 + 0.227729i \(0.926870\pi\)
\(854\) 111521. 4.46857
\(855\) 0 0
\(856\) −4524.80 −0.180671
\(857\) 8056.71 + 13954.6i 0.321134 + 0.556220i 0.980722 0.195407i \(-0.0626027\pi\)
−0.659588 + 0.751627i \(0.729269\pi\)
\(858\) 0 0
\(859\) 11250.2 19485.9i 0.446858 0.773982i −0.551321 0.834293i \(-0.685876\pi\)
0.998180 + 0.0603115i \(0.0192094\pi\)
\(860\) 8582.80 14865.8i 0.340315 0.589443i
\(861\) 0 0
\(862\) 14547.8 + 25197.5i 0.574825 + 0.995626i
\(863\) 43396.8 1.71175 0.855877 0.517180i \(-0.173018\pi\)
0.855877 + 0.517180i \(0.173018\pi\)
\(864\) 0 0
\(865\) 13738.8 0.540038
\(866\) 4687.09 + 8118.28i 0.183919 + 0.318557i
\(867\) 0 0
\(868\) −16101.9 + 27889.4i −0.629649 + 1.09058i
\(869\) −4016.07 + 6956.04i −0.156773 + 0.271539i
\(870\) 0 0
\(871\) −3044.18 5272.67i −0.118425 0.205118i
\(872\) −3241.07 −0.125868
\(873\) 0 0
\(874\) 20034.3 0.775366
\(875\) −1922.75 3330.29i −0.0742865 0.128668i
\(876\) 0 0
\(877\) 1232.77 2135.21i 0.0474659 0.0822133i −0.841316 0.540543i \(-0.818219\pi\)
0.888782 + 0.458330i \(0.151552\pi\)
\(878\) −17738.2 + 30723.5i −0.681817 + 1.18094i
\(879\) 0 0
\(880\) −4277.12 7408.18i −0.163843 0.283784i
\(881\) −24512.9 −0.937412 −0.468706 0.883354i \(-0.655280\pi\)
−0.468706 + 0.883354i \(0.655280\pi\)
\(882\) 0 0
\(883\) 24236.1 0.923679 0.461840 0.886963i \(-0.347190\pi\)
0.461840 + 0.886963i \(0.347190\pi\)
\(884\) −2116.90 3666.57i −0.0805418 0.139502i
\(885\) 0 0
\(886\) −23156.0 + 40107.3i −0.878036 + 1.52080i
\(887\) 12599.3 21822.7i 0.476939 0.826082i −0.522712 0.852509i \(-0.675080\pi\)
0.999651 + 0.0264274i \(0.00841308\pi\)
\(888\) 0 0
\(889\) 23167.1 + 40126.7i 0.874017 + 1.51384i
\(890\) −29076.9 −1.09512
\(891\) 0 0
\(892\) 19050.3 0.715081
\(893\) 1677.81 + 2906.05i 0.0628731 + 0.108899i
\(894\) 0 0
\(895\) −7095.81 + 12290.3i −0.265013 + 0.459016i
\(896\) 17484.5 30284.0i 0.651914 1.12915i
\(897\) 0 0
\(898\) −10543.1 18261.1i −0.391789 0.678599i
\(899\) −5109.87 −0.189570
\(900\) 0 0
\(901\) −173.151 −0.00640233
\(902\) 13667.9 + 23673.5i 0.504536 + 0.873882i
\(903\) 0 0
\(904\) 8122.42 14068.5i 0.298836 0.517599i
\(905\) −8605.62 + 14905.4i −0.316089 + 0.547482i
\(906\) 0 0
\(907\) −13304.0 23043.3i −0.487049 0.843594i 0.512840 0.858484i \(-0.328593\pi\)
−0.999889 + 0.0148906i \(0.995260\pi\)
\(908\) −51614.0 −1.88642
\(909\) 0 0
\(910\) 41442.1 1.50966
\(911\) 12416.1 + 21505.2i 0.451550 + 0.782108i 0.998483 0.0550686i \(-0.0175378\pi\)
−0.546932 + 0.837177i \(0.684204\pi\)
\(912\) 0 0
\(913\) 4025.43 6972.25i 0.145917 0.252736i
\(914\) 30253.7 52401.0i 1.09486 1.89636i
\(915\) 0 0
\(916\) −4399.79 7620.66i −0.158704 0.274884i
\(917\) −39227.8 −1.41267
\(918\) 0 0
\(919\) −26107.2 −0.937102 −0.468551 0.883436i \(-0.655224\pi\)
−0.468551 + 0.883436i \(0.655224\pi\)
\(920\) −1437.02 2489.00i −0.0514970 0.0891954i
\(921\) 0 0
\(922\) −38841.9 + 67276.2i −1.38741 + 2.40306i
\(923\) 30096.9 52129.3i 1.07329 1.85900i
\(924\) 0 0
\(925\) 3525.37 + 6106.11i 0.125312 + 0.217046i
\(926\) 18501.2 0.656573
\(927\) 0 0
\(928\) 12542.0 0.443653
\(929\) −11680.8 20231.7i −0.412523 0.714511i 0.582642 0.812729i \(-0.302019\pi\)
−0.995165 + 0.0982184i \(0.968686\pi\)
\(930\) 0 0
\(931\) −22743.0 + 39392.0i −0.800613 + 1.38670i
\(932\) 5803.45 10051.9i 0.203968 0.353283i
\(933\) 0 0
\(934\) 10483.2 + 18157.4i 0.367260 + 0.636112i
\(935\) −1341.53 −0.0469226
\(936\) 0 0
\(937\) 10548.5 0.367775 0.183888 0.982947i \(-0.441132\pi\)
0.183888 + 0.982947i \(0.441132\pi\)
\(938\) −6313.40 10935.1i −0.219765 0.380644i
\(939\) 0 0
\(940\) 1131.01 1958.96i 0.0392441 0.0679727i
\(941\) −3245.07 + 5620.62i −0.112419 + 0.194715i −0.916745 0.399473i \(-0.869193\pi\)
0.804326 + 0.594188i \(0.202527\pi\)
\(942\) 0 0
\(943\) −4912.32 8508.38i −0.169636 0.293819i
\(944\) −17897.6 −0.617074
\(945\) 0 0
\(946\) 58616.4 2.01457
\(947\) 11753.0 + 20356.8i 0.403295 + 0.698528i 0.994121 0.108271i \(-0.0345314\pi\)
−0.590826 + 0.806799i \(0.701198\pi\)
\(948\) 0 0
\(949\) 1607.50 2784.26i 0.0549858 0.0952382i
\(950\) −4015.68 + 6955.35i −0.137143 + 0.237538i
\(951\) 0 0
\(952\) −934.305 1618.26i −0.0318078 0.0550927i
\(953\) −6740.26 −0.229106 −0.114553 0.993417i \(-0.536544\pi\)
−0.114553 + 0.993417i \(0.536544\pi\)
\(954\) 0 0
\(955\) 3731.48 0.126437
\(956\) −16003.1 27718.2i −0.541399 0.937731i
\(957\) 0 0
\(958\) 9744.19 16877.4i 0.328623 0.569191i
\(959\) 22141.2 38349.6i 0.745543 1.29132i
\(960\) 0 0
\(961\) 9590.57 + 16611.4i 0.321928 + 0.557596i
\(962\) −75984.4 −2.54661
\(963\) 0 0
\(964\) 45776.8 1.52943
\(965\) −269.769 467.253i −0.00899913 0.0155870i
\(966\) 0 0
\(967\) −8391.27 + 14534.1i −0.279054 + 0.483336i −0.971150 0.238470i \(-0.923354\pi\)
0.692096 + 0.721806i \(0.256688\pi\)
\(968\) −1505.54 + 2607.67i −0.0499895 + 0.0865844i
\(969\) 0 0
\(970\) 15248.2 + 26410.6i 0.504732 + 0.874221i
\(971\) 46282.7 1.52964 0.764822 0.644242i \(-0.222827\pi\)
0.764822 + 0.644242i \(0.222827\pi\)
\(972\) 0 0
\(973\) −78124.9 −2.57407
\(974\) −33564.7 58135.8i −1.10419 1.91252i
\(975\) 0 0
\(976\) 17871.2 30953.8i 0.586109 1.01517i
\(977\) 3383.98 5861.22i 0.110812 0.191931i −0.805286 0.592886i \(-0.797988\pi\)
0.916098 + 0.400955i \(0.131322\pi\)
\(978\) 0 0
\(979\) −27778.5 48113.7i −0.906848 1.57071i
\(980\) 30662.0 0.999452
\(981\) 0 0
\(982\) −65240.8 −2.12008
\(983\) −25037.4 43366.1i −0.812381 1.40708i −0.911194 0.411979i \(-0.864838\pi\)
0.0988128 0.995106i \(-0.468496\pi\)
\(984\) 0 0
\(985\) −8402.55 + 14553.6i −0.271805 + 0.470779i
\(986\) 696.618 1206.58i 0.0224998 0.0389708i
\(987\) 0 0
\(988\) −24214.7 41941.0i −0.779728 1.35053i
\(989\) −21067.0 −0.677343
\(990\) 0 0
\(991\) −2658.60 −0.0852200 −0.0426100 0.999092i \(-0.513567\pi\)
−0.0426100 + 0.999092i \(0.513567\pi\)
\(992\) 13020.7 + 22552.6i 0.416742 + 0.721819i
\(993\) 0 0
\(994\) 62418.7 108112.i 1.99175 3.44981i
\(995\) −3422.46 + 5927.88i −0.109045 + 0.188871i
\(996\) 0 0
\(997\) 30310.0 + 52498.5i 0.962817 + 1.66765i 0.715368 + 0.698748i \(0.246259\pi\)
0.247449 + 0.968901i \(0.420408\pi\)
\(998\) 75570.3 2.39693
\(999\) 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 135.4.e.c.91.2 14
3.2 odd 2 45.4.e.c.31.6 yes 14
9.2 odd 6 45.4.e.c.16.6 14
9.4 even 3 405.4.a.n.1.6 7
9.5 odd 6 405.4.a.m.1.2 7
9.7 even 3 inner 135.4.e.c.46.2 14
15.2 even 4 225.4.k.d.49.3 28
15.8 even 4 225.4.k.d.49.12 28
15.14 odd 2 225.4.e.d.76.2 14
45.2 even 12 225.4.k.d.124.12 28
45.4 even 6 2025.4.a.ba.1.2 7
45.14 odd 6 2025.4.a.bb.1.6 7
45.29 odd 6 225.4.e.d.151.2 14
45.38 even 12 225.4.k.d.124.3 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.e.c.16.6 14 9.2 odd 6
45.4.e.c.31.6 yes 14 3.2 odd 2
135.4.e.c.46.2 14 9.7 even 3 inner
135.4.e.c.91.2 14 1.1 even 1 trivial
225.4.e.d.76.2 14 15.14 odd 2
225.4.e.d.151.2 14 45.29 odd 6
225.4.k.d.49.3 28 15.2 even 4
225.4.k.d.49.12 28 15.8 even 4
225.4.k.d.124.3 28 45.38 even 12
225.4.k.d.124.12 28 45.2 even 12
405.4.a.m.1.2 7 9.5 odd 6
405.4.a.n.1.6 7 9.4 even 3
2025.4.a.ba.1.2 7 45.4 even 6
2025.4.a.bb.1.6 7 45.14 odd 6