Properties

Label 225.4.e.d.151.2
Level $225$
Weight $4$
Character 225.151
Analytic conductor $13.275$
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] = [225,4,Mod(76,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.76");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(14\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{6} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 151.2
Root \(2.13089 + 3.69081i\) of defining polynomial
Character \(\chi\) \(=\) 225.151
Dual form 225.4.e.d.76.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.13089 + 3.69081i) q^{2} +(-4.39640 + 2.76977i) q^{3} +(-5.08138 - 8.80120i) q^{4} +(-0.854448 - 22.1284i) q^{6} +(15.3820 - 26.6423i) q^{7} +9.21718 q^{8} +(11.6567 - 24.3541i) q^{9} +O(q^{10})\) \(q+(-2.13089 + 3.69081i) q^{2} +(-4.39640 + 2.76977i) q^{3} +(-5.08138 - 8.80120i) q^{4} +(-0.854448 - 22.1284i) q^{6} +(15.3820 - 26.6423i) q^{7} +9.21718 q^{8} +(11.6567 - 24.3541i) q^{9} +(-20.3573 + 35.2599i) q^{11} +(46.7171 + 24.6194i) q^{12} +(31.6089 + 54.7482i) q^{13} +(65.5545 + 113.544i) q^{14} +(21.0102 - 36.3908i) q^{16} +6.58990 q^{17} +(65.0470 + 94.9186i) q^{18} +75.3803 q^{19} +(6.16789 + 159.735i) q^{21} +(-86.7584 - 150.270i) q^{22} +(-31.1814 - 54.0077i) q^{23} +(-40.5225 + 25.5295i) q^{24} -269.420 q^{26} +(16.2075 + 139.357i) q^{27} -312.646 q^{28} +(-24.8042 + 42.9621i) q^{29} +(-51.5021 - 89.2043i) q^{31} +(126.410 + 218.948i) q^{32} +(-8.16291 - 211.402i) q^{33} +(-14.0423 + 24.3221i) q^{34} +(-273.577 + 21.1590i) q^{36} +282.029 q^{37} +(-160.627 + 278.214i) q^{38} +(-290.606 - 153.146i) q^{39} +(78.7700 + 136.434i) q^{41} +(-602.695 - 317.613i) q^{42} +(-168.907 + 292.555i) q^{43} +413.773 q^{44} +265.776 q^{46} +(22.2579 - 38.5518i) q^{47} +(8.42472 + 218.182i) q^{48} +(-301.710 - 522.577i) q^{49} +(-28.9719 + 18.2525i) q^{51} +(321.234 - 556.393i) q^{52} -26.2752 q^{53} +(-548.876 - 237.135i) q^{54} +(141.778 - 245.567i) q^{56} +(-331.402 + 208.786i) q^{57} +(-105.710 - 183.095i) q^{58} +(212.963 + 368.863i) q^{59} +(-425.297 + 736.637i) q^{61} +438.981 q^{62} +(-469.546 - 685.176i) q^{63} -741.296 q^{64} +(797.638 + 420.346i) q^{66} +(48.1538 + 83.4048i) q^{67} +(-33.4858 - 57.9990i) q^{68} +(286.675 + 151.075i) q^{69} +952.164 q^{71} +(107.442 - 224.476i) q^{72} +50.8558 q^{73} +(-600.973 + 1040.92i) q^{74} +(-383.036 - 663.437i) q^{76} +(626.271 + 1084.73i) q^{77} +(1184.48 - 746.233i) q^{78} +(98.6395 - 170.849i) q^{79} +(-457.241 - 567.778i) q^{81} -671.400 q^{82} +(-98.8693 + 171.247i) q^{83} +(1374.52 - 865.959i) q^{84} +(-719.844 - 1246.81i) q^{86} +(-9.94603 - 257.581i) q^{87} +(-187.637 + 324.997i) q^{88} +1364.54 q^{89} +1944.83 q^{91} +(-316.889 + 548.868i) q^{92} +(473.499 + 249.529i) q^{93} +(94.8583 + 164.299i) q^{94} +(-1162.18 - 612.458i) q^{96} +(-715.579 + 1239.42i) q^{97} +2571.64 q^{98} +(621.422 + 906.799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 2 q^{2} + 5 q^{3} - 36 q^{4} - 31 q^{6} + 22 q^{7} + 36 q^{8} + 17 q^{9} + 23 q^{11} - 287 q^{12} + 96 q^{13} - 21 q^{14} - 324 q^{16} + 322 q^{17} + 89 q^{18} + 558 q^{19} + 180 q^{21} + 311 q^{22} - 96 q^{23} + 48 q^{24} + 716 q^{26} + 470 q^{27} - 674 q^{28} - 296 q^{29} - 244 q^{31} + 314 q^{32} + 211 q^{33} - 125 q^{34} - 2399 q^{36} - 808 q^{37} - 305 q^{38} + 634 q^{39} - 47 q^{41} - 1941 q^{42} + 525 q^{43} - 110 q^{44} + 1434 q^{46} - 164 q^{47} - 2051 q^{48} - 1225 q^{49} + 1517 q^{51} + 1682 q^{52} + 1012 q^{53} - 4066 q^{54} - 981 q^{56} - 337 q^{57} + 1183 q^{58} - 85 q^{59} - 828 q^{61} - 1572 q^{62} + 828 q^{63} + 4472 q^{64} + 4930 q^{66} + 1093 q^{67} - 2473 q^{68} - 822 q^{69} - 656 q^{71} + 4626 q^{72} - 4170 q^{73} - 1316 q^{74} - 2789 q^{76} - 24 q^{77} + 5314 q^{78} - 2110 q^{79} - 2167 q^{81} + 124 q^{82} - 1290 q^{83} + 5775 q^{84} - 2569 q^{86} - 3604 q^{87} + 2271 q^{88} + 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 696 q^{93} + 517 q^{94} - 593 q^{96} + 1787 q^{97} + 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.13089 + 3.69081i −0.753383 + 1.30490i 0.192791 + 0.981240i \(0.438246\pi\)
−0.946174 + 0.323658i \(0.895087\pi\)
\(3\) −4.39640 + 2.76977i −0.846088 + 0.533043i
\(4\) −5.08138 8.80120i −0.635172 1.10015i
\(5\) 0 0
\(6\) −0.854448 22.1284i −0.0581378 1.50564i
\(7\) 15.3820 26.6423i 0.830548 1.43855i −0.0670561 0.997749i \(-0.521361\pi\)
0.897604 0.440802i \(-0.145306\pi\)
\(8\) 9.21718 0.407346
\(9\) 11.6567 24.3541i 0.431731 0.902003i
\(10\) 0 0
\(11\) −20.3573 + 35.2599i −0.557996 + 0.966478i 0.439667 + 0.898161i \(0.355096\pi\)
−0.997664 + 0.0683175i \(0.978237\pi\)
\(12\) 46.7171 + 24.6194i 1.12384 + 0.592250i
\(13\) 31.6089 + 54.7482i 0.674364 + 1.16803i 0.976654 + 0.214817i \(0.0689155\pi\)
−0.302290 + 0.953216i \(0.597751\pi\)
\(14\) 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 \(0.485031\pi\)
\(18\) 65.0470 + 94.9186i 0.851763 + 1.24292i
\(19\) 75.3803 0.910180 0.455090 0.890445i \(-0.349607\pi\)
0.455090 + 0.890445i \(0.349607\pi\)
\(20\) 0 0
\(21\) 6.16789 + 159.735i 0.0640926 + 1.65986i
\(22\) −86.7584 150.270i −0.840770 1.45626i
\(23\) −31.1814 54.0077i −0.282686 0.489626i 0.689360 0.724419i \(-0.257892\pi\)
−0.972045 + 0.234793i \(0.924559\pi\)
\(24\) −40.5225 + 25.5295i −0.344651 + 0.217133i
\(25\) 0 0
\(26\) −269.420 −2.03222
\(27\) 16.2075 + 139.357i 0.115524 + 0.993305i
\(28\) −312.646 −2.11016
\(29\) −24.8042 + 42.9621i −0.158828 + 0.275099i −0.934446 0.356104i \(-0.884105\pi\)
0.775618 + 0.631202i \(0.217438\pi\)
\(30\) 0 0
\(31\) −51.5021 89.2043i −0.298389 0.516824i 0.677379 0.735634i \(-0.263116\pi\)
−0.975767 + 0.218810i \(0.929783\pi\)
\(32\) 126.410 + 218.948i 0.698321 + 1.20953i
\(33\) −8.16291 211.402i −0.0430600 1.11516i
\(34\) −14.0423 + 24.3221i −0.0708306 + 0.122682i
\(35\) 0 0
\(36\) −273.577 + 21.1590i −1.26656 + 0.0979582i
\(37\) 282.029 1.25312 0.626559 0.779374i \(-0.284463\pi\)
0.626559 + 0.779374i \(0.284463\pi\)
\(38\) −160.627 + 278.214i −0.685714 + 1.18769i
\(39\) −290.606 153.146i −1.19318 0.628794i
\(40\) 0 0
\(41\) 78.7700 + 136.434i 0.300044 + 0.519692i 0.976146 0.217117i \(-0.0696653\pi\)
−0.676102 + 0.736808i \(0.736332\pi\)
\(42\) −602.695 317.613i −2.21423 1.16688i
\(43\) −168.907 + 292.555i −0.599025 + 1.03754i 0.393940 + 0.919136i \(0.371112\pi\)
−0.992965 + 0.118406i \(0.962222\pi\)
\(44\) 413.773 1.41770
\(45\) 0 0
\(46\) 265.776 0.851882
\(47\) 22.2579 38.5518i 0.0690777 0.119646i −0.829418 0.558629i \(-0.811328\pi\)
0.898496 + 0.438983i \(0.144661\pi\)
\(48\) 8.42472 + 218.182i 0.0253334 + 0.656081i
\(49\) −301.710 522.577i −0.879620 1.52355i
\(50\) 0 0
\(51\) −28.9719 + 18.2525i −0.0795465 + 0.0501150i
\(52\) 321.234 556.393i 0.856675 1.48380i
\(53\) −26.2752 −0.0680978 −0.0340489 0.999420i \(-0.510840\pi\)
−0.0340489 + 0.999420i \(0.510840\pi\)
\(54\) −548.876 237.135i −1.38319 0.597592i
\(55\) 0 0
\(56\) 141.778 245.567i 0.338320 0.585988i
\(57\) −331.402 + 208.786i −0.770093 + 0.485165i
\(58\) −105.710 183.095i −0.239317 0.414509i
\(59\) 212.963 + 368.863i 0.469923 + 0.813930i 0.999409 0.0343889i \(-0.0109485\pi\)
−0.529486 + 0.848319i \(0.677615\pi\)
\(60\) 0 0
\(61\) −425.297 + 736.637i −0.892684 + 1.54617i −0.0560400 + 0.998429i \(0.517847\pi\)
−0.836644 + 0.547746i \(0.815486\pi\)
\(62\) 438.981 0.899204
\(63\) −469.546 685.176i −0.939004 1.37022i
\(64\) −741.296 −1.44784
\(65\) 0 0
\(66\) 797.638 + 420.346i 1.48761 + 0.783955i
\(67\) 48.1538 + 83.4048i 0.0878048 + 0.152082i 0.906583 0.422028i \(-0.138681\pi\)
−0.818778 + 0.574110i \(0.805348\pi\)
\(68\) −33.4858 57.9990i −0.0597168 0.103433i
\(69\) 286.675 + 151.075i 0.500169 + 0.263583i
\(70\) 0 0
\(71\) 952.164 1.59156 0.795782 0.605583i \(-0.207060\pi\)
0.795782 + 0.605583i \(0.207060\pi\)
\(72\) 107.442 224.476i 0.175864 0.367427i
\(73\) 50.8558 0.0815373 0.0407686 0.999169i \(-0.487019\pi\)
0.0407686 + 0.999169i \(0.487019\pi\)
\(74\) −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
\(78\) 1184.48 746.233i 1.71944 1.08326i
\(79\) 98.6395 170.849i 0.140479 0.243316i −0.787198 0.616700i \(-0.788469\pi\)
0.927677 + 0.373384i \(0.121803\pi\)
\(80\) 0 0
\(81\) −457.241 567.778i −0.627217 0.778844i
\(82\) −671.400 −0.904192
\(83\) −98.8693 + 171.247i −0.130751 + 0.226467i −0.923966 0.382474i \(-0.875072\pi\)
0.793215 + 0.608941i \(0.208405\pi\)
\(84\) 1374.52 865.959i 1.78539 1.12481i
\(85\) 0 0
\(86\) −719.844 1246.81i −0.902590 1.56333i
\(87\) −9.94603 257.581i −0.0122566 0.317420i
\(88\) −187.637 + 324.997i −0.227298 + 0.393691i
\(89\) 1364.54 1.62519 0.812593 0.582832i \(-0.198056\pi\)
0.812593 + 0.582832i \(0.198056\pi\)
\(90\) 0 0
\(91\) 1944.83 2.24037
\(92\) −316.889 + 548.868i −0.359108 + 0.621993i
\(93\) 473.499 + 249.529i 0.527953 + 0.278225i
\(94\) 94.8583 + 164.299i 0.104084 + 0.180279i
\(95\) 0 0
\(96\) −1162.18 612.458i −1.23557 0.651132i
\(97\) −715.579 + 1239.42i −0.749031 + 1.29736i 0.199256 + 0.979947i \(0.436147\pi\)
−0.948288 + 0.317413i \(0.897186\pi\)
\(98\) 2571.64 2.65076
\(99\) 621.422 + 906.799i 0.630862 + 0.920573i
\(100\) 0 0
\(101\) −553.808 + 959.224i −0.545604 + 0.945013i 0.452965 + 0.891528i \(0.350366\pi\)
−0.998569 + 0.0534851i \(0.982967\pi\)
\(102\) −5.63073 145.824i −0.00546593 0.141556i
\(103\) 264.437 + 458.018i 0.252969 + 0.438154i 0.964342 0.264660i \(-0.0852597\pi\)
−0.711373 + 0.702814i \(0.751926\pi\)
\(104\) 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 \(0.571182\pi\)
\(108\) 1144.15 850.770i 1.01941 0.758013i
\(109\) −351.634 −0.308994 −0.154497 0.987993i \(-0.549376\pi\)
−0.154497 + 0.987993i \(0.549376\pi\)
\(110\) 0 0
\(111\) −1239.91 + 781.157i −1.06025 + 0.667965i
\(112\) −646.357 1119.52i −0.545313 0.944509i
\(113\) 881.226 + 1526.33i 0.733618 + 1.27066i 0.955327 + 0.295550i \(0.0955030\pi\)
−0.221710 + 0.975113i \(0.571164\pi\)
\(114\) −64.4085 1668.04i −0.0529159 1.37041i
\(115\) 0 0
\(116\) 504.158 0.403533
\(117\) 1701.80 131.620i 1.34471 0.104002i
\(118\) −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
\(123\) −724.195 381.642i −0.530882 0.279769i
\(124\) −523.403 + 906.561i −0.379056 + 0.656545i
\(125\) 0 0
\(126\) 3529.40 272.971i 2.49543 0.193001i
\(127\) 1506.12 1.05234 0.526169 0.850380i \(-0.323628\pi\)
0.526169 + 0.850380i \(0.323628\pi\)
\(128\) 568.343 984.399i 0.392460 0.679761i
\(129\) −67.7286 1754.03i −0.0462262 1.19716i
\(130\) 0 0
\(131\) −637.562 1104.29i −0.425222 0.736506i 0.571219 0.820798i \(-0.306471\pi\)
−0.996441 + 0.0842915i \(0.973137\pi\)
\(132\) −1819.11 + 1146.06i −1.19950 + 0.755692i
\(133\) 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 −0.549484 0.835504i \(-0.685176\pi\)
0.998310 + 0.0581150i \(0.0185090\pi\)
\(138\) −1168.46 + 736.140i −0.720768 + 0.454090i
\(139\) 1269.75 + 2199.27i 0.774811 + 1.34201i 0.934901 + 0.354909i \(0.115488\pi\)
−0.160090 + 0.987102i \(0.551178\pi\)
\(140\) 0 0
\(141\) 8.92502 + 231.139i 0.00533065 + 0.138052i
\(142\) −2028.96 + 3514.25i −1.19906 + 2.07683i
\(143\) −2573.89 −1.50517
\(144\) −641.353 935.882i −0.371153 0.541598i
\(145\) 0 0
\(146\) −108.368 + 187.699i −0.0614288 + 0.106398i
\(147\) 2773.86 + 1461.79i 1.55635 + 0.820180i
\(148\) −1433.10 2482.20i −0.795945 1.37862i
\(149\) −46.8796 81.1979i −0.0257754 0.0446442i 0.852850 0.522156i \(-0.174872\pi\)
−0.878625 + 0.477512i \(0.841539\pi\)
\(150\) 0 0
\(151\) 534.065 925.027i 0.287825 0.498527i −0.685465 0.728105i \(-0.740401\pi\)
0.973290 + 0.229578i \(0.0737345\pi\)
\(152\) 694.794 0.370758
\(153\) 76.8166 160.491i 0.0405899 0.0848034i
\(154\) −5338.06 −2.79320
\(155\) 0 0
\(156\) 128.809 + 3335.87i 0.0661087 + 1.71207i
\(157\) 90.8574 + 157.370i 0.0461861 + 0.0799966i 0.888194 0.459468i \(-0.151960\pi\)
−0.842008 + 0.539465i \(0.818627\pi\)
\(158\) 420.380 + 728.119i 0.211668 + 0.366621i
\(159\) 115.517 72.7764i 0.0576167 0.0362990i
\(160\) 0 0
\(161\) −1918.52 −0.939136
\(162\) 3069.89 477.719i 1.48885 0.231686i
\(163\) 1103.07 0.530056 0.265028 0.964241i \(-0.414619\pi\)
0.265028 + 0.964241i \(0.414619\pi\)
\(164\) 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 −0.772126 0.635470i \(-0.780806\pi\)
−0.164270 0.986415i \(-0.552527\pi\)
\(168\) 56.8506 + 1472.31i 0.0261078 + 0.676137i
\(169\) −899.745 + 1558.40i −0.409534 + 0.709333i
\(170\) 0 0
\(171\) 878.687 1835.82i 0.392953 0.820985i
\(172\) 3433.12 1.52194
\(173\) −1373.88 + 2379.63i −0.603780 + 1.04578i 0.388463 + 0.921465i \(0.373006\pi\)
−0.992243 + 0.124314i \(0.960327\pi\)
\(174\) 971.875 + 512.167i 0.423435 + 0.223145i
\(175\) 0 0
\(176\) 855.423 + 1481.64i 0.366363 + 0.634560i
\(177\) −1957.94 1031.81i −0.831456 0.438168i
\(178\) −2907.69 + 5036.27i −1.22439 + 2.12070i
\(179\) −2838.32 −1.18517 −0.592587 0.805506i \(-0.701893\pi\)
−0.592587 + 0.805506i \(0.701893\pi\)
\(180\) 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
\(183\) −170.537 4416.53i −0.0688876 1.78404i
\(184\) −287.405 497.799i −0.115151 0.199447i
\(185\) 0 0
\(186\) −1929.94 + 1215.88i −0.760806 + 0.479314i
\(187\) −134.153 + 232.359i −0.0524610 + 0.0908652i
\(188\) −452.403 −0.175505
\(189\) 3962.10 + 1711.77i 1.52487 + 0.658801i
\(190\) 0 0
\(191\) 373.148 646.311i 0.141361 0.244845i −0.786648 0.617402i \(-0.788185\pi\)
0.928010 + 0.372557i \(0.121519\pi\)
\(192\) 3259.04 2053.22i 1.22500 0.771763i
\(193\) 53.9538 + 93.4506i 0.0201227 + 0.0348535i 0.875911 0.482472i \(-0.160261\pi\)
−0.855789 + 0.517326i \(0.826928\pi\)
\(194\) −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 \(0.292063\pi\)
\(198\) −4671.00 + 361.264i −1.67653 + 0.129666i
\(199\) 1368.99 0.487663 0.243831 0.969818i \(-0.421596\pi\)
0.243831 + 0.969818i \(0.421596\pi\)
\(200\) 0 0
\(201\) −442.716 233.306i −0.155357 0.0818714i
\(202\) −2360.21 4088.00i −0.822097 1.42391i
\(203\) 763.074 + 1321.68i 0.263829 + 0.456965i
\(204\) 307.861 + 162.239i 0.105660 + 0.0556815i
\(205\) 0 0
\(206\) −2253.94 −0.762329
\(207\) −1678.78 + 129.840i −0.563688 + 0.0435966i
\(208\) 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 0.586442 0.809991i \(-0.300528\pi\)
−0.994694 + 0.102878i \(0.967195\pi\)
\(212\) 133.514 + 231.254i 0.0432538 + 0.0749178i
\(213\) −4186.10 + 2637.28i −1.34660 + 0.848372i
\(214\) 1046.07 1811.85i 0.334150 0.578765i
\(215\) 0 0
\(216\) 149.388 + 1284.48i 0.0470581 + 0.404619i
\(217\) −3168.81 −0.991305
\(218\) 749.292 1297.81i 0.232791 0.403206i
\(219\) −223.583 + 140.859i −0.0689877 + 0.0434629i
\(220\) 0 0
\(221\) 208.299 + 360.785i 0.0634015 + 0.109815i
\(222\) −240.979 6240.85i −0.0728535 1.88675i
\(223\) 937.263 1623.39i 0.281452 0.487489i −0.690291 0.723532i \(-0.742517\pi\)
0.971743 + 0.236043i \(0.0758507\pi\)
\(224\) 7777.72 2.31996
\(225\) 0 0
\(226\) −7511.18 −2.21078
\(227\) 2539.37 4398.32i 0.742484 1.28602i −0.208877 0.977942i \(-0.566981\pi\)
0.951361 0.308078i \(-0.0996859\pi\)
\(228\) 3521.55 + 1855.82i 1.02290 + 0.539055i
\(229\) −432.933 749.861i −0.124930 0.216385i 0.796776 0.604275i \(-0.206537\pi\)
−0.921706 + 0.387890i \(0.873204\pi\)
\(230\) 0 0
\(231\) −5757.80 3034.30i −1.63998 0.864252i
\(232\) −228.625 + 395.990i −0.0646981 + 0.112060i
\(233\) −1142.10 −0.321122 −0.160561 0.987026i \(-0.551330\pi\)
−0.160561 + 0.987026i \(0.551330\pi\)
\(234\) −3140.56 + 6561.48i −0.877371 + 1.83307i
\(235\) 0 0
\(236\) 2164.29 3748.66i 0.596964 1.03397i
\(237\) 39.5527 + 1024.33i 0.0108406 + 0.280748i
\(238\) 431.998 + 748.242i 0.117657 + 0.203787i
\(239\) 1574.68 + 2727.43i 0.426183 + 0.738171i 0.996530 0.0832330i \(-0.0265246\pi\)
−0.570347 + 0.821404i \(0.693191\pi\)
\(240\) 0 0
\(241\) −2252.18 + 3900.90i −0.601975 + 1.04265i 0.390547 + 0.920583i \(0.372286\pi\)
−0.992522 + 0.122068i \(0.961047\pi\)
\(242\) 1392.24 0.369821
\(243\) 3582.83 + 1229.72i 0.945839 + 0.324637i
\(244\) 8644.39 2.26803
\(245\) 0 0
\(246\) 2951.75 1859.63i 0.765027 0.481973i
\(247\) 2382.69 + 4126.94i 0.613793 + 1.06312i
\(248\) −474.704 822.212i −0.121547 0.210526i
\(249\) −39.6448 1026.72i −0.0100899 0.261307i
\(250\) 0 0
\(251\) 886.861 0.223021 0.111510 0.993763i \(-0.464431\pi\)
0.111510 + 0.993763i \(0.464431\pi\)
\(252\) −3644.43 + 7614.21i −0.911023 + 1.90337i
\(253\) 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 0.970013 0.243052i \(-0.0781486\pi\)
−0.695496 + 0.718530i \(0.744815\pi\)
\(258\) 6618.09 + 3487.66i 1.59699 + 0.841598i
\(259\) 4338.17 7513.92i 1.04077 1.80267i
\(260\) 0 0
\(261\) 757.166 + 1104.88i 0.179569 + 0.262032i
\(262\) 5434.30 1.28142
\(263\) 3640.31 6305.20i 0.853503 1.47831i −0.0245245 0.999699i \(-0.507807\pi\)
0.878027 0.478611i \(-0.158859\pi\)
\(264\) −75.2391 1948.53i −0.0175403 0.454257i
\(265\) 0 0
\(266\) 4941.52 + 8558.96i 1.13904 + 1.97287i
\(267\) −5999.09 + 3779.48i −1.37505 + 0.866293i
\(268\) 489.375 847.622i 0.111542 0.193197i
\(269\) −106.781 −0.0242028 −0.0121014 0.999927i \(-0.503852\pi\)
−0.0121014 + 0.999927i \(0.503852\pi\)
\(270\) 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
\(273\) −8550.25 + 5386.73i −1.89555 + 1.19421i
\(274\) 3067.25 + 5312.64i 0.676276 + 1.17134i
\(275\) 0 0
\(276\) −127.067 3290.75i −0.0277120 0.717681i
\(277\) 1645.04 2849.30i 0.356827 0.618042i −0.630602 0.776106i \(-0.717192\pi\)
0.987429 + 0.158064i \(0.0505254\pi\)
\(278\) −10822.8 −2.33492
\(279\) −2772.83 + 214.456i −0.595000 + 0.0460184i
\(280\) 0 0
\(281\) −169.861 + 294.209i −0.0360608 + 0.0624591i −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(282\) −872.107 459.590i −0.184160 0.0970504i
\(283\) 1299.83 + 2251.37i 0.273028 + 0.472898i 0.969636 0.244554i \(-0.0786415\pi\)
−0.696608 + 0.717452i \(0.745308\pi\)
\(284\) −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
\(288\) 6805.80 526.373i 1.39248 0.107697i
\(289\) −4869.57 −0.991161
\(290\) 0 0
\(291\) −286.934 7430.98i −0.0578020 1.49695i
\(292\) −258.418 447.592i −0.0517902 0.0897033i
\(293\) 89.0427 + 154.227i 0.0177540 + 0.0307509i 0.874766 0.484546i \(-0.161015\pi\)
−0.857012 + 0.515297i \(0.827682\pi\)
\(294\) −11306.0 + 7122.86i −2.24278 + 1.41297i
\(295\) 0 0
\(296\) 2599.52 0.510452
\(297\) −5243.65 2265.45i −1.02447 0.442609i
\(298\) 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
\(303\) −222.067 5751.06i −0.0421037 1.09039i
\(304\) 1583.76 2743.15i 0.298798 0.517534i
\(305\) 0 0
\(306\) 428.653 + 625.504i 0.0800800 + 0.116855i
\(307\) −1537.60 −0.285848 −0.142924 0.989734i \(-0.545651\pi\)
−0.142924 + 0.989734i \(0.545651\pi\)
\(308\) 6364.64 11023.9i 1.17746 2.03943i
\(309\) −2431.18 1281.20i −0.447589 0.235874i
\(310\) 0 0
\(311\) −472.662 818.674i −0.0861807 0.149269i 0.819713 0.572774i \(-0.194133\pi\)
−0.905894 + 0.423505i \(0.860800\pi\)
\(312\) −2678.57 1411.57i −0.486038 0.256137i
\(313\) 992.767 1719.52i 0.179280 0.310521i −0.762354 0.647160i \(-0.775957\pi\)
0.941634 + 0.336638i \(0.109290\pi\)
\(314\) −774.428 −0.139183
\(315\) 0 0
\(316\) −2004.90 −0.356913
\(317\) −2591.62 + 4488.81i −0.459179 + 0.795321i −0.998918 0.0465112i \(-0.985190\pi\)
0.539739 + 0.841833i \(0.318523\pi\)
\(318\) 22.4508 + 581.428i 0.00395906 + 0.102531i
\(319\) −1009.89 1749.19i −0.177251 0.307008i
\(320\) 0 0
\(321\) 2158.24 1359.71i 0.375268 0.236422i
\(322\) 4088.16 7080.91i 0.707529 1.22548i
\(323\) 496.748 0.0855722
\(324\) −2673.71 + 6909.37i −0.458455 + 1.18473i
\(325\) 0 0
\(326\) −2350.52 + 4071.22i −0.399336 + 0.691670i
\(327\) 1545.92 973.945i 0.261437 0.164707i
\(328\) 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 −0.761583 0.648067i \(-0.775578\pi\)
0.942034 + 0.335517i \(0.108911\pi\)
\(332\) 2009.57 0.332197
\(333\) 3287.54 6868.56i 0.541009 1.13032i
\(334\) 17224.8 2.82186
\(335\) 0 0
\(336\) 5942.47 + 3131.61i 0.964846 + 0.508463i
\(337\) −3925.16 6798.57i −0.634472 1.09894i −0.986627 0.162995i \(-0.947884\pi\)
0.352155 0.935942i \(-0.385449\pi\)
\(338\) −3834.52 6641.58i −0.617071 1.06880i
\(339\) −8101.81 4269.56i −1.29802 0.684043i
\(340\) 0 0
\(341\) 4193.78 0.665999
\(342\) 4903.26 + 7154.99i 0.775257 + 1.13128i
\(343\) −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 −0.958987 0.283451i \(-0.908521\pi\)
0.234018 0.972232i \(-0.424813\pi\)
\(348\) −2216.48 + 1396.40i −0.341425 + 0.215101i
\(349\) 588.952 1020.10i 0.0903321 0.156460i −0.817319 0.576186i \(-0.804540\pi\)
0.907651 + 0.419726i \(0.137874\pi\)
\(350\) 0 0
\(351\) −7117.23 + 5292.25i −1.08231 + 0.804784i
\(352\) −10293.4 −1.55864
\(353\) −3631.06 + 6289.19i −0.547484 + 0.948271i 0.450962 + 0.892543i \(0.351081\pi\)
−0.998446 + 0.0557274i \(0.982252\pi\)
\(354\) 7980.37 5027.70i 1.19817 0.754856i
\(355\) 0 0
\(356\) −6933.77 12009.6i −1.03227 1.78795i
\(357\) 40.6458 + 1052.64i 0.00602578 + 0.156055i
\(358\) 6048.15 10475.7i 0.892890 1.54653i
\(359\) −1939.95 −0.285199 −0.142600 0.989780i \(-0.545546\pi\)
−0.142600 + 0.989780i \(0.545546\pi\)
\(360\) 0 0
\(361\) −1176.81 −0.171572
\(362\) −7335.05 + 12704.7i −1.06498 + 1.84459i
\(363\) 1501.72 + 791.388i 0.217134 + 0.114427i
\(364\) −9882.41 17116.8i −1.42302 2.46474i
\(365\) 0 0
\(366\) 16664.0 + 8781.72i 2.37989 + 1.25417i
\(367\) 3250.97 5630.85i 0.462396 0.800893i −0.536684 0.843783i \(-0.680323\pi\)
0.999080 + 0.0428901i \(0.0136565\pi\)
\(368\) −2620.51 −0.371205
\(369\) 4240.91 328.000i 0.598301 0.0462737i
\(370\) 0 0
\(371\) −404.165 + 700.034i −0.0565585 + 0.0979622i
\(372\) −209.875 5435.32i −0.0292514 0.757548i
\(373\) 6659.02 + 11533.8i 0.924372 + 1.60106i 0.792568 + 0.609784i \(0.208744\pi\)
0.131805 + 0.991276i \(0.457923\pi\)
\(374\) −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
\(378\) −14760.6 + 10975.7i −2.00848 + 1.49347i
\(379\) −3198.42 −0.433488 −0.216744 0.976228i \(-0.569544\pi\)
−0.216744 + 0.976228i \(0.569544\pi\)
\(380\) 0 0
\(381\) −6621.53 + 4171.62i −0.890370 + 0.560941i
\(382\) 1590.27 + 2754.43i 0.212999 + 0.368924i
\(383\) −1170.25 2026.93i −0.156128 0.270422i 0.777341 0.629079i \(-0.216568\pi\)
−0.933469 + 0.358658i \(0.883235\pi\)
\(384\) 227.895 + 5902.00i 0.0302858 + 0.784336i
\(385\) 0 0
\(386\) −459.878 −0.0606403
\(387\) 5156.01 + 7523.81i 0.677248 + 0.988261i
\(388\) 14544.5 1.90305
\(389\) −1995.97 + 3457.12i −0.260153 + 0.450599i −0.966282 0.257484i \(-0.917106\pi\)
0.706129 + 0.708083i \(0.250440\pi\)
\(390\) 0 0
\(391\) −205.482 355.906i −0.0265772 0.0460330i
\(392\) −2780.91 4816.69i −0.358310 0.620611i
\(393\) 5861.61 + 3089.00i 0.752365 + 0.396488i
\(394\) −7161.96 + 12404.9i −0.915773 + 1.58616i
\(395\) 0 0
\(396\) 4823.24 10077.1i 0.612063 1.27876i
\(397\) 4960.90 0.627155 0.313577 0.949563i \(-0.398472\pi\)
0.313577 + 0.949563i \(0.398472\pi\)
\(398\) −2917.16 + 5052.66i −0.367397 + 0.636350i
\(399\) 464.937 + 12040.9i 0.0583358 + 1.51077i
\(400\) 0 0
\(401\) −413.811 716.742i −0.0515330 0.0892578i 0.839108 0.543965i \(-0.183077\pi\)
−0.890641 + 0.454707i \(0.849744\pi\)
\(402\) 1804.47 1136.83i 0.223877 0.141044i
\(403\) 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
\(408\) −267.039 + 168.237i −0.0324029 + 0.0204141i
\(409\) 4183.82 + 7246.59i 0.505811 + 0.876090i 0.999977 + 0.00672263i \(0.00213989\pi\)
−0.494167 + 0.869367i \(0.664527\pi\)
\(410\) 0 0
\(411\) 288.592 + 7473.90i 0.0346354 + 0.896983i
\(412\) 2687.41 4654.73i 0.321357 0.556607i
\(413\) 13103.2 1.56117
\(414\) 3098.08 6472.74i 0.367784 0.768400i
\(415\) 0 0
\(416\) −7991.34 + 13841.4i −0.941845 + 1.63132i
\(417\) −11673.8 6151.96i −1.37091 0.722453i
\(418\) −6539.87 11327.4i −0.765252 1.32546i
\(419\) −2100.36 3637.93i −0.244891 0.424163i 0.717210 0.696857i \(-0.245419\pi\)
−0.962101 + 0.272694i \(0.912085\pi\)
\(420\) 0 0
\(421\) −3469.38 + 6009.14i −0.401632 + 0.695648i −0.993923 0.110077i \(-0.964890\pi\)
0.592291 + 0.805724i \(0.298224\pi\)
\(422\) 10665.3 1.23028
\(423\) −679.440 991.459i −0.0780981 0.113963i
\(424\) −242.184 −0.0277394
\(425\) 0 0
\(426\) −813.575 21069.8i −0.0925301 2.39633i
\(427\) 13083.8 + 22661.8i 1.48283 + 2.56835i
\(428\) 2494.50 + 4320.60i 0.281720 + 0.487953i
\(429\) 11315.9 7129.09i 1.27351 0.802321i
\(430\) 0 0
\(431\) 6827.09 0.762991 0.381496 0.924371i \(-0.375409\pi\)
0.381496 + 0.924371i \(0.375409\pi\)
\(432\) 5411.83 + 2338.11i 0.602724 + 0.260399i
\(433\) 2199.59 0.244124 0.122062 0.992522i \(-0.461049\pi\)
0.122062 + 0.992522i \(0.461049\pi\)
\(434\) 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
\(438\) −43.4536 1125.36i −0.00474040 0.122766i
\(439\) −4162.16 + 7209.07i −0.452504 + 0.783759i −0.998541 0.0540018i \(-0.982802\pi\)
0.546037 + 0.837761i \(0.316136\pi\)
\(440\) 0 0
\(441\) −16243.8 + 1256.33i −1.75400 + 0.135658i
\(442\) −1775.45 −0.191063
\(443\) −5433.41 + 9410.93i −0.582729 + 1.00932i 0.412426 + 0.910991i \(0.364682\pi\)
−0.995154 + 0.0983247i \(0.968652\pi\)
\(444\) 13175.6 + 6943.39i 1.40830 + 0.742159i
\(445\) 0 0
\(446\) 3994.41 + 6918.51i 0.424082 + 0.734532i
\(447\) 431.001 + 227.133i 0.0456055 + 0.0240336i
\(448\) −11402.6 + 19749.9i −1.20250 + 2.08280i
\(449\) −4947.73 −0.520040 −0.260020 0.965603i \(-0.583729\pi\)
−0.260020 + 0.965603i \(0.583729\pi\)
\(450\) 0 0
\(451\) −6414.18 −0.669694
\(452\) 8955.69 15511.7i 0.931947 1.61418i
\(453\) 214.150 + 5546.03i 0.0222112 + 0.575221i
\(454\) 10822.2 + 18744.7i 1.11875 + 1.93773i
\(455\) 0 0
\(456\) −3054.59 + 1924.42i −0.313694 + 0.197630i
\(457\) −7098.85 + 12295.6i −0.726630 + 1.25856i 0.231669 + 0.972795i \(0.425581\pi\)
−0.958299 + 0.285766i \(0.907752\pi\)
\(458\) 3690.13 0.376481
\(459\) 106.806 + 918.347i 0.0108612 + 0.0933873i
\(460\) 0 0
\(461\) 9114.02 15785.9i 0.920786 1.59485i 0.122584 0.992458i \(-0.460882\pi\)
0.798202 0.602390i \(-0.205785\pi\)
\(462\) 23468.3 14785.2i 2.36329 1.48890i
\(463\) 2170.59 + 3759.58i 0.217875 + 0.377370i 0.954158 0.299303i \(-0.0967542\pi\)
−0.736283 + 0.676674i \(0.763421\pi\)
\(464\) 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 \(0.578374\pi\)
\(468\) −9805.90 14309.1i −0.968542 1.41333i
\(469\) 2962.80 0.291704
\(470\) 0 0
\(471\) −835.324 440.206i −0.0817191 0.0430650i
\(472\) 1962.92 + 3399.88i 0.191421 + 0.331551i
\(473\) −6876.98 11911.3i −0.668508 1.15789i
\(474\) −3864.88 2036.75i −0.374515 0.197365i
\(475\) 0 0
\(476\) −2060.31 −0.198391
\(477\) −306.283 + 639.909i −0.0293999 + 0.0614244i
\(478\) −13421.9 −1.28432
\(479\) −2286.41 + 3960.19i −0.218098 + 0.377757i −0.954226 0.299085i \(-0.903319\pi\)
0.736128 + 0.676842i \(0.236652\pi\)
\(480\) 0 0
\(481\) 8914.64 + 15440.6i 0.845057 + 1.46368i
\(482\) −9598.31 16624.8i −0.907035 1.57103i
\(483\) 8434.61 5313.87i 0.794592 0.500600i
\(484\) −1659.99 + 2875.19i −0.155897 + 0.270021i
\(485\) 0 0
\(486\) −12173.3 + 10603.1i −1.13620 + 0.989646i
\(487\) −15751.5 −1.46564 −0.732822 0.680421i \(-0.761797\pi\)
−0.732822 + 0.680421i \(0.761797\pi\)
\(488\) −3920.04 + 6789.72i −0.363631 + 0.629828i
\(489\) −4849.55 + 3055.26i −0.448475 + 0.282543i
\(490\) 0 0
\(491\) −7654.18 13257.4i −0.703520 1.21853i −0.967223 0.253928i \(-0.918277\pi\)
0.263703 0.964604i \(-0.415056\pi\)
\(492\) 320.994 + 8313.05i 0.0294137 + 0.761751i
\(493\) −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
\(498\) 3873.89 + 2041.49i 0.348580 + 0.183698i
\(499\) −8866.05 15356.5i −0.795389 1.37765i −0.922592 0.385777i \(-0.873933\pi\)
0.127203 0.991877i \(-0.459400\pi\)
\(500\) 0 0
\(501\) 18579.3 + 9791.07i 1.65681 + 0.873119i
\(502\) −1889.80 + 3273.23i −0.168020 + 0.291019i
\(503\) 10511.5 0.931775 0.465887 0.884844i \(-0.345735\pi\)
0.465887 + 0.884844i \(0.345735\pi\)
\(504\) −4327.89 6315.39i −0.382499 0.558155i
\(505\) 0 0
\(506\) −5410.49 + 9371.25i −0.475347 + 0.823326i
\(507\) −360.782 9343.47i −0.0316033 0.818457i
\(508\) −7653.18 13255.7i −0.668416 1.15773i
\(509\) −9815.42 17000.8i −0.854737 1.48045i −0.876889 0.480693i \(-0.840385\pi\)
0.0221524 0.999755i \(-0.492948\pi\)
\(510\) 0 0
\(511\) 782.262 1354.92i 0.0677206 0.117296i
\(512\) 13722.1 1.18444
\(513\) 1221.73 + 10504.8i 0.105147 + 0.904086i
\(514\) −9640.30 −0.827267
\(515\) 0 0
\(516\) −15093.4 + 9508.96i −1.28769 + 0.811257i
\(517\) 906.223 + 1569.62i 0.0770902 + 0.133524i
\(518\) 18488.3 + 32022.7i 1.56820 + 2.71621i
\(519\) −550.900 14267.1i −0.0465931 1.20666i
\(520\) 0 0
\(521\) 88.4336 0.00743636 0.00371818 0.999993i \(-0.498816\pi\)
0.00371818 + 0.999993i \(0.498816\pi\)
\(522\) −5691.34 + 440.179i −0.477209 + 0.0369082i
\(523\) −21346.4 −1.78473 −0.892363 0.451317i \(-0.850954\pi\)
−0.892363 + 0.451317i \(0.850954\pi\)
\(524\) −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
\(528\) −7864.58 4144.55i −0.648224 0.341606i
\(529\) 4138.94 7168.86i 0.340178 0.589205i
\(530\) 0 0
\(531\) 11465.8 886.783i 0.937047 0.0724729i
\(532\) −23567.4 −1.92063
\(533\) −4979.67 + 8625.03i −0.404678 + 0.700923i
\(534\) −1165.93 30195.1i −0.0944847 2.44695i
\(535\) 0 0
\(536\) 443.842 + 768.757i 0.0357669 + 0.0619501i
\(537\) 12478.4 7861.51i 1.00276 0.631749i
\(538\) 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
\(543\) −15133.5 + 9534.24i −1.19602 + 0.753505i
\(544\) 833.027 + 1442.84i 0.0656539 + 0.113716i
\(545\) 0 0
\(546\) −1661.75 43035.9i −0.130250 3.37320i
\(547\) −8284.80 + 14349.7i −0.647592 + 1.12166i 0.336105 + 0.941825i \(0.390890\pi\)
−0.983696 + 0.179837i \(0.942443\pi\)
\(548\) −14628.5 −1.14033
\(549\) 12982.5 + 18944.5i 1.00925 + 1.47273i
\(550\) 0 0
\(551\) −1869.75 + 3238.50i −0.144562 + 0.250389i
\(552\) 2642.34 + 1392.48i 0.203742 + 0.107369i
\(553\) −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 \(0.645410\pi\)
\(558\) 5117.08 10691.0i 0.388214 0.811084i
\(559\) −21355.9 −1.61584
\(560\) 0 0
\(561\) −53.7928 1393.12i −0.00404836 0.104844i
\(562\) −723.912 1253.85i −0.0543352 0.0941113i
\(563\) −11524.6 19961.3i −0.862709 1.49426i −0.869304 0.494278i \(-0.835432\pi\)
0.00659429 0.999978i \(-0.497901\pi\)
\(564\) 1988.95 1253.05i 0.148493 0.0935516i
\(565\) 0 0
\(566\) −11079.2 −0.822778
\(567\) −22160.2 + 3448.45i −1.64134 + 0.255417i
\(568\) 8776.27 0.648317
\(569\) −7366.96 + 12759.9i −0.542775 + 0.940114i 0.455968 + 0.889996i \(0.349293\pi\)
−0.998743 + 0.0501179i \(0.984040\pi\)
\(570\) 0 0
\(571\) −7555.94 13087.3i −0.553776 0.959169i −0.997998 0.0632515i \(-0.979853\pi\)
0.444221 0.895917i \(-0.353480\pi\)
\(572\) 13078.9 + 22653.3i 0.956043 + 1.65591i
\(573\) 149.625 + 3874.98i 0.0109087 + 0.282512i
\(574\) −10327.5 + 17887.7i −0.750975 + 1.30073i
\(575\) 0 0
\(576\) −8641.09 + 18053.6i −0.625079 + 1.30596i
\(577\) 26150.5 1.88676 0.943380 0.331715i \(-0.107627\pi\)
0.943380 + 0.331715i \(0.107627\pi\)
\(578\) 10376.5 17972.7i 0.746724 1.29336i
\(579\) −496.039 261.407i −0.0356040 0.0187629i
\(580\) 0 0
\(581\) 3041.61 + 5268.22i 0.217190 + 0.376184i
\(582\) 28037.7 + 14775.6i 1.99691 + 1.05235i
\(583\) 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 −0.826915 0.562327i \(-0.809906\pi\)
0.900447 + 0.434965i \(0.143239\pi\)
\(588\) −1229.49 31841.2i −0.0862303 2.23318i
\(589\) −3882.24 6724.24i −0.271587 0.470403i
\(590\) 0 0
\(591\) −14776.4 + 9309.26i −1.02846 + 0.647939i
\(592\) 5925.50 10263.3i 0.411379 0.712530i
\(593\) −3260.34 −0.225778 −0.112889 0.993608i \(-0.536010\pi\)
−0.112889 + 0.993608i \(0.536010\pi\)
\(594\) 19535.0 14525.9i 1.34938 1.00337i
\(595\) 0 0
\(596\) −476.426 + 825.194i −0.0327436 + 0.0567135i
\(597\) −6018.61 + 3791.78i −0.412606 + 0.259945i
\(598\) 8400.90 + 14550.8i 0.574479 + 0.995026i
\(599\) 11499.6 + 19917.9i 0.784410 + 1.35864i 0.929351 + 0.369197i \(0.120367\pi\)
−0.144941 + 0.989440i \(0.546299\pi\)
\(600\) 0 0
\(601\) 7146.93 12378.9i 0.485074 0.840173i −0.514779 0.857323i \(-0.672126\pi\)
0.999853 + 0.0171500i \(0.00545928\pi\)
\(602\) −44290.5 −2.99858
\(603\) 2592.56 200.513i 0.175087 0.0135415i
\(604\) −10855.1 −0.731274
\(605\) 0 0
\(606\) 21699.3 + 11435.3i 1.45457 + 0.766544i
\(607\) −8217.04 14232.3i −0.549455 0.951685i −0.998312 0.0580809i \(-0.981502\pi\)
0.448856 0.893604i \(-0.351831\pi\)
\(608\) 9528.80 + 16504.4i 0.635598 + 1.10089i
\(609\) −7015.54 3697.11i −0.466805 0.246001i
\(610\) 0 0
\(611\) 2814.19 0.186334
\(612\) −1802.85 + 139.435i −0.119078 + 0.00920971i
\(613\) −3674.45 −0.242104 −0.121052 0.992646i \(-0.538627\pi\)
−0.121052 + 0.992646i \(0.538627\pi\)
\(614\) 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 0.971747 0.236026i \(-0.0758450\pi\)
−0.690278 + 0.723544i \(0.742512\pi\)
\(618\) 9909.25 6242.91i 0.644998 0.406354i
\(619\) 654.905 1134.33i 0.0425248 0.0736551i −0.843980 0.536375i \(-0.819793\pi\)
0.886504 + 0.462720i \(0.153127\pi\)
\(620\) 0 0
\(621\) 7020.97 5220.67i 0.453691 0.337356i
\(622\) 4028.76 0.259708
\(623\) 20989.4 36354.7i 1.34979 2.33791i
\(624\) −11678.8 + 7357.73i −0.749240 + 0.472027i
\(625\) 0 0
\(626\) 4230.95 + 7328.23i 0.270132 + 0.467883i
\(627\) −615.323 15935.5i −0.0391924 1.01500i
\(628\) 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
\(633\) 11503.9 + 6062.45i 0.722339 + 0.380665i
\(634\) −11044.9 19130.3i −0.691875 1.19836i
\(635\) 0 0
\(636\) −1227.50 646.881i −0.0765310 0.0403309i
\(637\) 19073.4 33036.2i 1.18637 2.05485i
\(638\) 8607.88 0.534152
\(639\) 11099.1 23189.1i 0.687127 1.43560i
\(640\) 0 0
\(641\) 10036.6 17383.8i 0.618440 1.07117i −0.371330 0.928501i \(-0.621098\pi\)
0.989770 0.142669i \(-0.0455685\pi\)
\(642\) 419.457 + 10863.0i 0.0257860 + 0.667803i
\(643\) −8867.96 15359.8i −0.543885 0.942037i −0.998676 0.0514386i \(-0.983619\pi\)
0.454791 0.890598i \(-0.349714\pi\)
\(644\) 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 \(0.386834\pi\)
\(648\) −4214.48 5233.31i −0.255494 0.317259i
\(649\) −17341.4 −1.04886
\(650\) 0 0
\(651\) 13931.4 8776.89i 0.838731 0.528408i
\(652\) −5605.12 9708.36i −0.336677 0.583142i
\(653\) 14536.0 + 25177.0i 0.871113 + 1.50881i 0.860847 + 0.508864i \(0.169935\pi\)
0.0102660 + 0.999947i \(0.496732\pi\)
\(654\) 300.453 + 7781.08i 0.0179643 + 0.465236i
\(655\) 0 0
\(656\) 6619.90 0.393999
\(657\) 592.812 1238.55i 0.0352021 0.0735468i
\(658\) 5836.43 0.345787
\(659\) 2177.54 3771.62i 0.128718 0.222946i −0.794462 0.607314i \(-0.792247\pi\)
0.923180 + 0.384368i \(0.125581\pi\)
\(660\) 0 0
\(661\) −13647.7 23638.5i −0.803075 1.39097i −0.917583 0.397545i \(-0.869862\pi\)
0.114508 0.993422i \(-0.463471\pi\)
\(662\) 4631.19 + 8021.46i 0.271898 + 0.470941i
\(663\) −1915.06 1009.22i −0.112179 0.0591172i
\(664\) −911.297 + 1578.41i −0.0532608 + 0.0922504i
\(665\) 0 0
\(666\) 18345.2 + 26769.8i 1.06736 + 1.55752i
\(667\) 3093.72 0.179594
\(668\) −20537.4 + 35571.8i −1.18955 + 2.06035i
\(669\) 375.825 + 9733.06i 0.0217194 + 0.562484i
\(670\) 0 0
\(671\) −17315.8 29991.9i −0.996230 1.72552i
\(672\) −34194.0 + 21542.5i −1.96289 + 1.23664i
\(673\) −8880.01 + 15380.6i −0.508617 + 0.880951i 0.491333 + 0.870972i \(0.336510\pi\)
−0.999950 + 0.00997909i \(0.996824\pi\)
\(674\) 33456.3 1.91200
\(675\) 0 0
\(676\) 18287.8 1.04050
\(677\) 968.667 1677.78i 0.0549910 0.0952472i −0.837219 0.546867i \(-0.815820\pi\)
0.892210 + 0.451620i \(0.149154\pi\)
\(678\) 33022.2 20804.3i 1.87052 1.17844i
\(679\) 22014.0 + 38129.4i 1.24421 + 2.15504i
\(680\) 0 0
\(681\) 1018.24 + 26370.3i 0.0572968 + 1.48386i
\(682\) −8936.48 + 15478.4i −0.501753 + 0.869061i
\(683\) 2125.71 0.119090 0.0595448 0.998226i \(-0.481035\pi\)
0.0595448 + 0.998226i \(0.481035\pi\)
\(684\) −20622.3 + 1594.97i −1.15280 + 0.0891596i
\(685\) 0 0
\(686\) 17071.7 29569.0i 0.950146 1.64570i
\(687\) 3980.29 + 2097.57i 0.221045 + 0.116488i
\(688\) 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 −0.991147 0.132771i \(-0.957612\pi\)
0.610557 + 0.791973i \(0.290946\pi\)
\(692\) 27924.8 1.53402
\(693\) 33717.9 2607.81i 1.84825 0.142947i
\(694\) 39942.4 2.18472
\(695\) 0 0
\(696\) −91.6744 2374.17i −0.00499268 0.129300i
\(697\) 519.086 + 899.084i 0.0282092 + 0.0488597i
\(698\) 2509.98 + 4347.42i 0.136109 + 0.235748i
\(699\) 5021.14 3163.36i 0.271698 0.171172i
\(700\) 0 0
\(701\) −24464.0 −1.31810 −0.659052 0.752097i \(-0.729042\pi\)
−0.659052 + 0.752097i \(0.729042\pi\)
\(702\) −4366.64 37545.5i −0.234769 2.01861i
\(703\) 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
\(708\) 867.842 + 22475.2i 0.0460671 + 1.19304i
\(709\) 14749.1 25546.2i 0.781263 1.35319i −0.149944 0.988695i \(-0.547909\pi\)
0.931206 0.364492i \(-0.118757\pi\)
\(710\) 0 0
\(711\) −3011.05 4393.81i −0.158823 0.231759i
\(712\) 12577.3 0.662012
\(713\) −3211.81 + 5563.02i −0.168700 + 0.292198i
\(714\) −3971.70 2093.04i −0.208175 0.109706i
\(715\) 0 0
\(716\) 14422.6 + 24980.7i 0.752790 + 1.30387i
\(717\) −14477.3 7629.38i −0.754065 0.397384i
\(718\) 4133.81 7159.98i 0.214864 0.372156i
\(719\) −3857.66 −0.200093 −0.100046 0.994983i \(-0.531899\pi\)
−0.100046 + 0.994983i \(0.531899\pi\)
\(720\) 0 0
\(721\) 16270.2 0.840410
\(722\) 2507.66 4343.39i 0.129260 0.223884i
\(723\) −903.085 23387.9i −0.0464538 1.20305i
\(724\) −17491.4 30295.9i −0.897874 1.55516i
\(725\) 0 0
\(726\) −6120.86 + 3856.19i −0.312901 + 0.197130i
\(727\) 4372.55 7573.48i 0.223066 0.386361i −0.732672 0.680582i \(-0.761727\pi\)
0.955737 + 0.294221i \(0.0950602\pi\)
\(728\) 17925.8 0.912604
\(729\) −19157.6 + 4517.26i −0.973309 + 0.229501i
\(730\) 0 0
\(731\) −1113.08 + 1927.91i −0.0563184 + 0.0975463i
\(732\) −38004.2 + 23943.0i −1.91896 + 1.20896i
\(733\) −4709.20 8156.58i −0.237296 0.411010i 0.722641 0.691223i \(-0.242928\pi\)
−0.959938 + 0.280214i \(0.909595\pi\)
\(734\) 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
\(738\) −7826.33 + 16351.3i −0.390368 + 0.815584i
\(739\) 6219.42 0.309587 0.154794 0.987947i \(-0.450529\pi\)
0.154794 + 0.987947i \(0.450529\pi\)
\(740\) 0 0
\(741\) −21905.9 11544.2i −1.08601 0.572316i
\(742\) −1722.46 2983.39i −0.0852204 0.147606i
\(743\) −14693.7 25450.3i −0.725518 1.25663i −0.958760 0.284216i \(-0.908267\pi\)
0.233242 0.972419i \(-0.425067\pi\)
\(744\) 4364.33 + 2299.95i 0.215059 + 0.113334i
\(745\) 0 0
\(746\) −56758.5 −2.78563
\(747\) 3018.06 + 4404.05i 0.147825 + 0.215710i
\(748\) 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 0.999544 + 0.0301801i \(0.00960808\pi\)
−0.473636 + 0.880721i \(0.657059\pi\)
\(752\) −935.287 1619.97i −0.0453543 0.0785559i
\(753\) −3899.00 + 2456.40i −0.188695 + 0.118880i
\(754\) 6682.75 11574.9i 0.322774 0.559061i
\(755\) 0 0
\(756\) −5067.23 43569.4i −0.243774 2.09604i
\(757\) 13907.2 0.667722 0.333861 0.942622i \(-0.391648\pi\)
0.333861 + 0.942622i \(0.391648\pi\)
\(758\) 6815.48 11804.8i 0.326582 0.565657i
\(759\) −11162.8 + 7032.66i −0.533840 + 0.336324i
\(760\) 0 0
\(761\) 11953.0 + 20703.3i 0.569379 + 0.986193i 0.996628 + 0.0820585i \(0.0261494\pi\)
−0.427249 + 0.904134i \(0.640517\pi\)
\(762\) −1286.90 33328.0i −0.0611806 1.58445i
\(763\) −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
\(768\) 4992.53 + 2631.01i 0.234573 + 0.123618i
\(769\) 12555.8 + 21747.3i 0.588783 + 1.01980i 0.994392 + 0.105755i \(0.0337261\pi\)
−0.405609 + 0.914047i \(0.632941\pi\)
\(770\) 0 0
\(771\) −10398.3 5479.81i −0.485716 0.255967i
\(772\) 548.319 949.716i 0.0255627 0.0442759i
\(773\) −14909.4 −0.693729 −0.346865 0.937915i \(-0.612754\pi\)
−0.346865 + 0.937915i \(0.612754\pi\)
\(774\) −38755.8 + 2997.45i −1.79981 + 0.139200i
\(775\) 0 0
\(776\) −6595.62 + 11424.0i −0.305115 + 0.528474i
\(777\) 1739.53 + 45050.0i 0.0803155 + 2.08000i
\(778\) −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
\(783\) −6389.08 2760.32i −0.291605 0.125984i
\(784\) −25356.0 −1.15506
\(785\) 0 0
\(786\) −23891.4 + 15051.8i −1.08419 + 0.683052i
\(787\) −1329.38 2302.56i −0.0602128 0.104292i 0.834348 0.551239i \(-0.185845\pi\)
−0.894560 + 0.446947i \(0.852511\pi\)
\(788\) −17078.6 29581.0i −0.772082 1.33728i
\(789\) 1459.70 + 37803.1i 0.0658640 + 1.70573i
\(790\) 0 0
\(791\) 54220.0 2.43722
\(792\) 5727.76 + 8358.13i 0.256979 + 0.374991i
\(793\) −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 0.664489 0.747298i \(-0.268649\pi\)
−0.979424 + 0.201815i \(0.935316\pi\)
\(798\) −45431.3 23941.8i −2.01535 1.06207i
\(799\) 146.677 254.053i 0.00649446 0.0112487i
\(800\) 0 0
\(801\) 15906.1 33232.2i 0.701642 1.46592i
\(802\) 3527.14 0.155296
\(803\) −1035.29 + 1793.17i −0.0454975 + 0.0788040i
\(804\) 196.231 + 5081.95i 0.00860761 + 0.222918i
\(805\) 0 0
\(806\) 13875.7 + 24033.4i 0.606391 + 1.05030i
\(807\) 469.452 295.759i 0.0204777 0.0129011i
\(808\) −5104.55 + 8841.34i −0.222249 + 0.384947i
\(809\) −21077.7 −0.916012 −0.458006 0.888949i \(-0.651436\pi\)
−0.458006 + 0.888949i \(0.651436\pi\)
\(810\) 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
\(813\) −25977.7 + 16366.2i −1.12064 + 0.706011i
\(814\) −24468.4 42380.5i −1.05358 1.82486i
\(815\) 0 0
\(816\) 55.5180 + 1437.80i 0.00238176 + 0.0616826i
\(817\) −12732.3 + 22052.9i −0.545221 + 0.944350i
\(818\) −35661.0 −1.52428
\(819\) 22670.3 47364.5i 0.967235 2.02082i
\(820\) 0 0
\(821\) −7400.25 + 12817.6i −0.314580 + 0.544869i −0.979348 0.202181i \(-0.935197\pi\)
0.664768 + 0.747050i \(0.268530\pi\)
\(822\) −28199.7 14860.9i −1.19657 0.630576i
\(823\) 16588.3 + 28731.8i 0.702591 + 1.21692i 0.967554 + 0.252665i \(0.0813071\pi\)
−0.264963 + 0.964259i \(0.585360\pi\)
\(824\) 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 \(0.291283\pi\)
\(828\) 9673.27 + 14115.5i 0.406002 + 0.592450i
\(829\) 13221.1 0.553904 0.276952 0.960884i \(-0.410676\pi\)
0.276952 + 0.960884i \(0.410676\pi\)
\(830\) 0 0
\(831\) 659.632 + 17083.0i 0.0275360 + 0.713122i
\(832\) −23431.6 40584.7i −0.976374 1.69113i
\(833\) −1988.24 3443.73i −0.0826991 0.143239i
\(834\) 47581.3 29976.6i 1.97555 1.24461i
\(835\) 0 0
\(836\) 31190.3 1.29036
\(837\) 11596.5 8622.95i 0.478893 0.356096i
\(838\) 17902.5 0.737987
\(839\) 21062.0 36480.4i 0.866675 1.50112i 0.00129985 0.999999i \(-0.499586\pi\)
0.865375 0.501125i \(-0.167080\pi\)
\(840\) 0 0
\(841\) 10964.0 + 18990.2i 0.449547 + 0.778638i
\(842\) −14785.7 25609.6i −0.605166 1.04818i
\(843\) −68.1114 1763.94i −0.00278278 0.0720679i
\(844\) −12716.4 + 22025.4i −0.518621 + 0.898278i
\(845\) 0 0
\(846\) 5107.10 394.992i 0.207548 0.0160521i
\(847\) −10050.0 −0.407700
\(848\) −552.049 + 956.177i −0.0223555 + 0.0387208i
\(849\) −11950.4 6297.71i −0.483081 0.254578i
\(850\) 0 0
\(851\) −8794.07 15231.8i −0.354238 0.613559i
\(852\) 44482.4 + 23441.7i 1.78866 + 0.942605i
\(853\) 7215.84 12498.2i 0.289643 0.501677i −0.684081 0.729406i \(-0.739797\pi\)
0.973725 + 0.227729i \(0.0731300\pi\)
\(854\) −111521. −4.46857
\(855\) 0 0
\(856\) −4524.80 −0.180671
\(857\) 8056.71 13954.6i 0.321134 0.556220i −0.659588 0.751627i \(-0.729269\pi\)
0.980722 + 0.195407i \(0.0626027\pi\)
\(858\) 2199.25 + 56956.0i 0.0875074 + 2.26625i
\(859\) 11250.2 + 19485.9i 0.446858 + 0.773982i 0.998180 0.0603115i \(-0.0192094\pi\)
−0.551321 + 0.834293i \(0.685876\pi\)
\(860\) 0 0
\(861\) −21307.4 + 13423.8i −0.843384 + 0.531339i
\(862\) −14547.8 + 25197.5i −0.574825 + 0.995626i
\(863\) 43396.8 1.71175 0.855877 0.517180i \(-0.173018\pi\)
0.855877 + 0.517180i \(0.173018\pi\)
\(864\) −28463.1 + 21164.6i −1.12076 + 0.833375i
\(865\) 0 0
\(866\) −4687.09 + 8118.28i −0.183919 + 0.318557i
\(867\) 21408.6 13487.6i 0.838610 0.528331i
\(868\) 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
\(873\) 21843.6 + 31874.8i 0.846842 + 1.23574i
\(874\) 20034.3 0.775366
\(875\) 0 0
\(876\) 2375.84 + 1252.04i 0.0916348 + 0.0482905i
\(877\) −1232.77 2135.21i −0.0474659 0.0822133i 0.841316 0.540543i \(-0.181781\pi\)
−0.888782 + 0.458330i \(0.848448\pi\)
\(878\) −17738.2 30723.5i −0.681817 1.18094i
\(879\) −818.640 431.414i −0.0314130 0.0165543i
\(880\) 0 0
\(881\) 24512.9 0.937412 0.468706 0.883354i \(-0.344720\pi\)
0.468706 + 0.883354i \(0.344720\pi\)
\(882\) 29976.9 62629.9i 1.14442 2.39100i
\(883\) −24236.1 −0.923679 −0.461840 0.886963i \(-0.652810\pi\)
−0.461840 + 0.886963i \(0.652810\pi\)
\(884\) 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 0.999651 0.0264274i \(-0.00841308\pi\)
−0.522712 + 0.852509i \(0.675080\pi\)
\(888\) −11428.5 + 7200.07i −0.431888 + 0.272093i
\(889\) 23167.1 40126.7i 0.874017 1.51384i
\(890\) 0 0
\(891\) 29328.0 4563.86i 1.10272 0.171599i
\(892\) −19050.3 −0.715081
\(893\) 1677.81 2906.05i 0.0628731 0.108899i
\(894\) −1756.72 + 1106.75i −0.0657198 + 0.0414040i
\(895\) 0 0
\(896\) −17484.5 30284.0i −0.651914 1.12915i
\(897\) 790.423 + 20470.3i 0.0294219 + 0.761964i
\(898\) 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
\(903\) −47773.2 25175.9i −1.76057 0.927798i
\(904\) 8122.42 + 14068.5i 0.298836 + 0.517599i
\(905\) 0 0
\(906\) −20925.7 11027.6i −0.767338 0.404379i
\(907\) 13304.0 23043.3i 0.487049 0.843594i −0.512840 0.858484i \(-0.671407\pi\)
0.999889 + 0.0148906i \(0.00473999\pi\)
\(908\) −51614.0 −1.88642
\(909\) 16905.4 + 24668.9i 0.616851 + 0.900127i
\(910\) 0 0
\(911\) −12416.1 + 21505.2i −0.451550 + 0.782108i −0.998483 0.0550686i \(-0.982462\pi\)
0.546932 + 0.837177i \(0.315796\pi\)
\(912\) 635.058 + 16446.6i 0.0230580 + 0.597151i
\(913\) −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
\(918\) −3617.03 1562.70i −0.130043 0.0561837i
\(919\) −26107.2 −0.937102 −0.468551 0.883436i \(-0.655224\pi\)
−0.468551 + 0.883436i \(0.655224\pi\)
\(920\) 0 0
\(921\) 6759.91 4258.80i 0.241853 0.152369i
\(922\) 38841.9 + 67276.2i 1.38741 + 2.40306i
\(923\) 30096.9 + 52129.3i 1.07329 + 1.85900i
\(924\) 2552.11 + 66094.0i 0.0908637 + 2.35317i
\(925\) 0 0
\(926\) −18501.2 −0.656573
\(927\) 14237.1 1101.12i 0.504431 0.0390136i
\(928\) −12542.0 −0.443653
\(929\) 11680.8 20231.7i 0.412523 0.714511i −0.582642 0.812729i \(-0.697981\pi\)
0.995165 + 0.0982184i \(0.0313144\pi\)
\(930\) 0 0
\(931\) −22743.0 39392.0i −0.800613 1.38670i
\(932\) 5803.45 + 10051.9i 0.203968 + 0.353283i
\(933\) 4345.55 + 2290.06i 0.152483 + 0.0803570i
\(934\) 10483.2 18157.4i 0.367260 0.636112i
\(935\) 0 0
\(936\) 15685.8 1213.17i 0.547763 0.0423650i
\(937\) −10548.5 −0.367775 −0.183888 0.982947i \(-0.558868\pi\)
−0.183888 + 0.982947i \(0.558868\pi\)
\(938\) −6313.40 + 10935.1i −0.219765 + 0.380644i
\(939\) 398.082 + 10309.5i 0.0138348 + 0.358292i
\(940\) 0 0
\(941\) 3245.07 + 5620.62i 0.112419 + 0.194715i 0.916745 0.399473i \(-0.130807\pi\)
−0.804326 + 0.594188i \(0.797473\pi\)
\(942\) 3404.70 2144.99i 0.117761 0.0741906i
\(943\) 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 −0.590826 0.806799i \(-0.701198\pi\)
0.994121 + 0.108271i \(0.0345314\pi\)
\(948\) 8814.34 5553.11i 0.301979 0.190250i
\(949\) 1607.50 + 2784.26i 0.0549858 + 0.0952382i
\(950\) 0 0
\(951\) −1039.19 26912.8i −0.0354344 0.917674i
\(952\) 934.305 1618.26i 0.0318078 0.0550927i
\(953\) −6740.26 −0.229106 −0.114553 0.993417i \(-0.536544\pi\)
−0.114553 + 0.993417i \(0.536544\pi\)
\(954\) −1709.13 2494.01i −0.0580032 0.0846400i
\(955\) 0 0
\(956\) 16003.1 27718.2i 0.541399 0.937731i
\(957\) 9284.74 + 4892.95i 0.313619 + 0.165274i
\(958\) −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
\(963\) −5722.40 + 11955.6i −0.191487 + 0.400068i
\(964\) 45776.8 1.52943
\(965\) 0 0
\(966\) 1639.28 + 42453.8i 0.0545993 + 1.41400i
\(967\) 8391.27 + 14534.1i 0.279054 + 0.483336i 0.971150 0.238470i \(-0.0766458\pi\)
−0.692096 + 0.721806i \(0.743312\pi\)
\(968\) −1505.54 2607.67i −0.0499895 0.0865844i
\(969\) −2183.91 + 1375.88i −0.0724016 + 0.0456136i
\(970\) 0 0
\(971\) −46282.7 −1.52964 −0.764822 0.644242i \(-0.777173\pi\)
−0.764822 + 0.644242i \(0.777173\pi\)
\(972\) −7382.66 37781.9i −0.243620 1.24677i
\(973\) 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 0.916098 0.400955i \(-0.131322\pi\)
−0.805286 + 0.592886i \(0.797988\pi\)
\(978\) −942.517 24409.2i −0.0308163 0.798076i
\(979\) −27778.5 + 48113.7i −0.906848 + 1.57071i
\(980\) 0 0
\(981\) −4098.90 + 8563.71i −0.133402 + 0.278714i
\(982\) 65240.8 2.12008
\(983\) −25037.4 + 43366.1i −0.812381 + 1.40708i 0.0988128 + 0.995106i \(0.468496\pi\)
−0.911194 + 0.411979i \(0.864838\pi\)
\(984\) −6675.04 3517.67i −0.216252 0.113963i
\(985\) 0 0
\(986\) −696.618 1206.58i −0.0224998 0.0389708i
\(987\) 6295.36 + 3317.58i 0.203023 + 0.106991i
\(988\) 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
\(993\) 435.739 + 11284.7i 0.0139252 + 0.360634i
\(994\) 62418.7 + 108112.i 1.99175 + 3.44981i
\(995\) 0 0
\(996\) −8834.88 + 5566.05i −0.281068 + 0.177075i
\(997\) −30310.0 + 52498.5i −0.962817 + 1.66765i −0.247449 + 0.968901i \(0.579592\pi\)
−0.715368 + 0.698748i \(0.753741\pi\)
\(998\) 75570.3 2.39693
\(999\) 4571.00 + 39302.7i 0.144765 + 1.24473i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 225.4.e.d.151.2 14
5.2 odd 4 225.4.k.d.124.3 28
5.3 odd 4 225.4.k.d.124.12 28
5.4 even 2 45.4.e.c.16.6 14
9.2 odd 6 2025.4.a.ba.1.2 7
9.4 even 3 inner 225.4.e.d.76.2 14
9.7 even 3 2025.4.a.bb.1.6 7
15.14 odd 2 135.4.e.c.46.2 14
45.4 even 6 45.4.e.c.31.6 yes 14
45.13 odd 12 225.4.k.d.49.3 28
45.14 odd 6 135.4.e.c.91.2 14
45.22 odd 12 225.4.k.d.49.12 28
45.29 odd 6 405.4.a.n.1.6 7
45.34 even 6 405.4.a.m.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.e.c.16.6 14 5.4 even 2
45.4.e.c.31.6 yes 14 45.4 even 6
135.4.e.c.46.2 14 15.14 odd 2
135.4.e.c.91.2 14 45.14 odd 6
225.4.e.d.76.2 14 9.4 even 3 inner
225.4.e.d.151.2 14 1.1 even 1 trivial
225.4.k.d.49.3 28 45.13 odd 12
225.4.k.d.49.12 28 45.22 odd 12
225.4.k.d.124.3 28 5.2 odd 4
225.4.k.d.124.12 28 5.3 odd 4
405.4.a.m.1.2 7 45.34 even 6
405.4.a.n.1.6 7 45.29 odd 6
2025.4.a.ba.1.2 7 9.2 odd 6
2025.4.a.bb.1.6 7 9.7 even 3