Properties

Label 294.4.e.k.67.2
Level $294$
Weight $4$
Character 294.67
Analytic conductor $17.347$
Analytic rank $0$
Dimension $4$
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] = [294,4,Mod(67,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.67");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.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: \(17.3465615417\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 294.67
Dual form 294.4.e.k.79.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.29289 - 3.97141i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.29289 - 3.97141i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-4.58579 + 7.94282i) q^{10} +(3.24264 - 5.61642i) q^{11} +(-6.00000 - 10.3923i) q^{12} +45.2132 q^{13} +13.7574 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-40.7782 + 70.6299i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(2.52691 + 4.37674i) q^{19} +18.3431 q^{20} -12.9706 q^{22} +(-53.1249 - 92.0150i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(51.9853 - 90.0411i) q^{25} +(-45.2132 - 78.3116i) q^{26} +27.0000 q^{27} -268.132 q^{29} +(-13.7574 - 23.8284i) q^{30} +(-146.184 + 253.198i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(9.72792 + 16.8493i) q^{33} +163.113 q^{34} +36.0000 q^{36} +(-57.2792 - 99.2105i) q^{37} +(5.05382 - 8.75348i) q^{38} +(-67.8198 + 117.467i) q^{39} +(-18.3431 - 31.7713i) q^{40} -161.605 q^{41} -471.294 q^{43} +(12.9706 + 22.4657i) q^{44} +(-20.6360 + 35.7427i) q^{45} +(-106.250 + 184.030i) q^{46} +(-173.002 - 299.648i) q^{47} +48.0000 q^{48} -207.941 q^{50} +(-122.335 - 211.890i) q^{51} +(-90.4264 + 156.623i) q^{52} +(-202.765 + 351.198i) q^{53} +(-27.0000 - 46.7654i) q^{54} -29.7401 q^{55} -15.1615 q^{57} +(268.132 + 464.418i) q^{58} +(126.718 - 219.482i) q^{59} +(-27.5147 + 47.6569i) q^{60} +(375.609 + 650.573i) q^{61} +584.735 q^{62} +64.0000 q^{64} +(-103.669 - 179.560i) q^{65} +(19.4558 - 33.6985i) q^{66} +(-5.82338 + 10.0864i) q^{67} +(-163.113 - 282.519i) q^{68} +318.749 q^{69} -681.661 q^{71} +(-36.0000 - 62.3538i) q^{72} +(-342.729 + 593.623i) q^{73} +(-114.558 + 198.421i) q^{74} +(155.956 + 270.123i) q^{75} -20.2153 q^{76} +271.279 q^{78} +(-0.132034 - 0.228690i) q^{79} +(-36.6863 + 63.5425i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(161.605 + 279.908i) q^{82} -437.137 q^{83} +374.000 q^{85} +(471.294 + 816.304i) q^{86} +(402.198 - 696.627i) q^{87} +(25.9411 - 44.9313i) q^{88} +(29.2563 + 50.6734i) q^{89} +82.5442 q^{90} +424.999 q^{92} +(-438.551 - 759.593i) q^{93} +(-346.004 + 599.297i) q^{94} +(11.5879 - 20.0708i) q^{95} +(-48.0000 - 83.1384i) q^{96} -1280.09 q^{97} -58.3675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 12 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 12 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9} - 24 q^{10} - 4 q^{11} - 24 q^{12} + 96 q^{13} + 72 q^{15} - 32 q^{16} - 132 q^{17} - 36 q^{18} - 120 q^{19} + 96 q^{20} + 16 q^{22} + 76 q^{23} - 48 q^{24} + 174 q^{25} - 96 q^{26} + 108 q^{27} - 224 q^{29} - 72 q^{30} - 432 q^{31} - 64 q^{32} - 12 q^{33} + 528 q^{34} + 144 q^{36} + 280 q^{37} - 240 q^{38} - 144 q^{39} - 96 q^{40} + 72 q^{41} - 256 q^{43} - 16 q^{44} - 108 q^{45} + 152 q^{46} + 264 q^{47} + 192 q^{48} - 696 q^{50} - 396 q^{51} - 192 q^{52} - 268 q^{53} - 108 q^{54} + 96 q^{55} + 720 q^{57} + 224 q^{58} - 336 q^{59} - 144 q^{60} + 504 q^{61} + 1728 q^{62} + 256 q^{64} - 228 q^{65} - 24 q^{66} + 384 q^{67} - 528 q^{68} - 456 q^{69} - 792 q^{71} - 144 q^{72} + 312 q^{73} + 560 q^{74} + 522 q^{75} + 960 q^{76} + 576 q^{78} + 848 q^{79} - 192 q^{80} - 162 q^{81} - 72 q^{82} - 1296 q^{83} + 1496 q^{85} + 256 q^{86} + 336 q^{87} - 32 q^{88} + 612 q^{89} + 432 q^{90} - 608 q^{92} - 1296 q^{93} + 528 q^{94} - 904 q^{95} - 192 q^{96} - 4368 q^{97} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −2.29289 3.97141i −0.205083 0.355213i 0.745076 0.666979i \(-0.232413\pi\)
−0.950159 + 0.311766i \(0.899080\pi\)
\(6\) 6.00000 0.408248
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) −4.58579 + 7.94282i −0.145015 + 0.251174i
\(11\) 3.24264 5.61642i 0.0888812 0.153947i −0.818157 0.574994i \(-0.805004\pi\)
0.907038 + 0.421048i \(0.138338\pi\)
\(12\) −6.00000 10.3923i −0.144338 0.250000i
\(13\) 45.2132 0.964607 0.482303 0.876004i \(-0.339800\pi\)
0.482303 + 0.876004i \(0.339800\pi\)
\(14\) 0 0
\(15\) 13.7574 0.236809
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −40.7782 + 70.6299i −0.581774 + 1.00766i 0.413495 + 0.910506i \(0.364308\pi\)
−0.995269 + 0.0971560i \(0.969025\pi\)
\(18\) −9.00000 + 15.5885i −0.117851 + 0.204124i
\(19\) 2.52691 + 4.37674i 0.0305112 + 0.0528470i 0.880878 0.473344i \(-0.156953\pi\)
−0.850367 + 0.526191i \(0.823620\pi\)
\(20\) 18.3431 0.205083
\(21\) 0 0
\(22\) −12.9706 −0.125697
\(23\) −53.1249 92.0150i −0.481622 0.834194i 0.518156 0.855286i \(-0.326619\pi\)
−0.999778 + 0.0210927i \(0.993286\pi\)
\(24\) −12.0000 + 20.7846i −0.102062 + 0.176777i
\(25\) 51.9853 90.0411i 0.415882 0.720329i
\(26\) −45.2132 78.3116i −0.341040 0.590699i
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −268.132 −1.71693 −0.858463 0.512875i \(-0.828580\pi\)
−0.858463 + 0.512875i \(0.828580\pi\)
\(30\) −13.7574 23.8284i −0.0837246 0.145015i
\(31\) −146.184 + 253.198i −0.846948 + 1.46696i 0.0369712 + 0.999316i \(0.488229\pi\)
−0.883919 + 0.467640i \(0.845104\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 9.72792 + 16.8493i 0.0513156 + 0.0888812i
\(34\) 163.113 0.822753
\(35\) 0 0
\(36\) 36.0000 0.166667
\(37\) −57.2792 99.2105i −0.254504 0.440814i 0.710257 0.703943i \(-0.248579\pi\)
−0.964761 + 0.263129i \(0.915246\pi\)
\(38\) 5.05382 8.75348i 0.0215747 0.0373685i
\(39\) −67.8198 + 117.467i −0.278458 + 0.482303i
\(40\) −18.3431 31.7713i −0.0725077 0.125587i
\(41\) −161.605 −0.615573 −0.307786 0.951456i \(-0.599588\pi\)
−0.307786 + 0.951456i \(0.599588\pi\)
\(42\) 0 0
\(43\) −471.294 −1.67143 −0.835716 0.549162i \(-0.814947\pi\)
−0.835716 + 0.549162i \(0.814947\pi\)
\(44\) 12.9706 + 22.4657i 0.0444406 + 0.0769734i
\(45\) −20.6360 + 35.7427i −0.0683609 + 0.118404i
\(46\) −106.250 + 184.030i −0.340558 + 0.589864i
\(47\) −173.002 299.648i −0.536914 0.929962i −0.999068 0.0431624i \(-0.986257\pi\)
0.462154 0.886800i \(-0.347077\pi\)
\(48\) 48.0000 0.144338
\(49\) 0 0
\(50\) −207.941 −0.588146
\(51\) −122.335 211.890i −0.335887 0.581774i
\(52\) −90.4264 + 156.623i −0.241152 + 0.417687i
\(53\) −202.765 + 351.198i −0.525507 + 0.910204i 0.474052 + 0.880497i \(0.342791\pi\)
−0.999559 + 0.0297072i \(0.990543\pi\)
\(54\) −27.0000 46.7654i −0.0680414 0.117851i
\(55\) −29.7401 −0.0729119
\(56\) 0 0
\(57\) −15.1615 −0.0352313
\(58\) 268.132 + 464.418i 0.607025 + 1.05140i
\(59\) 126.718 219.482i 0.279614 0.484307i −0.691674 0.722209i \(-0.743127\pi\)
0.971289 + 0.237903i \(0.0764600\pi\)
\(60\) −27.5147 + 47.6569i −0.0592022 + 0.102541i
\(61\) 375.609 + 650.573i 0.788390 + 1.36553i 0.926953 + 0.375177i \(0.122418\pi\)
−0.138563 + 0.990354i \(0.544248\pi\)
\(62\) 584.735 1.19776
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −103.669 179.560i −0.197824 0.342641i
\(66\) 19.4558 33.6985i 0.0362856 0.0628485i
\(67\) −5.82338 + 10.0864i −0.0106185 + 0.0183918i −0.871286 0.490776i \(-0.836713\pi\)
0.860667 + 0.509168i \(0.170047\pi\)
\(68\) −163.113 282.519i −0.290887 0.503831i
\(69\) 318.749 0.556129
\(70\) 0 0
\(71\) −681.661 −1.13941 −0.569706 0.821848i \(-0.692943\pi\)
−0.569706 + 0.821848i \(0.692943\pi\)
\(72\) −36.0000 62.3538i −0.0589256 0.102062i
\(73\) −342.729 + 593.623i −0.549498 + 0.951758i 0.448811 + 0.893627i \(0.351848\pi\)
−0.998309 + 0.0581315i \(0.981486\pi\)
\(74\) −114.558 + 198.421i −0.179961 + 0.311702i
\(75\) 155.956 + 270.123i 0.240110 + 0.415882i
\(76\) −20.2153 −0.0305112
\(77\) 0 0
\(78\) 271.279 0.393799
\(79\) −0.132034 0.228690i −0.000188038 0.000325692i 0.865931 0.500163i \(-0.166727\pi\)
−0.866119 + 0.499837i \(0.833393\pi\)
\(80\) −36.6863 + 63.5425i −0.0512707 + 0.0888034i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 161.605 + 279.908i 0.217638 + 0.376960i
\(83\) −437.137 −0.578097 −0.289048 0.957314i \(-0.593339\pi\)
−0.289048 + 0.957314i \(0.593339\pi\)
\(84\) 0 0
\(85\) 374.000 0.477247
\(86\) 471.294 + 816.304i 0.590941 + 1.02354i
\(87\) 402.198 696.627i 0.495634 0.858463i
\(88\) 25.9411 44.9313i 0.0314242 0.0544284i
\(89\) 29.2563 + 50.6734i 0.0348445 + 0.0603525i 0.882922 0.469520i \(-0.155573\pi\)
−0.848077 + 0.529873i \(0.822240\pi\)
\(90\) 82.5442 0.0966769
\(91\) 0 0
\(92\) 424.999 0.481622
\(93\) −438.551 759.593i −0.488985 0.846948i
\(94\) −346.004 + 599.297i −0.379655 + 0.657582i
\(95\) 11.5879 20.0708i 0.0125146 0.0216760i
\(96\) −48.0000 83.1384i −0.0510310 0.0883883i
\(97\) −1280.09 −1.33993 −0.669966 0.742391i \(-0.733692\pi\)
−0.669966 + 0.742391i \(0.733692\pi\)
\(98\) 0 0
\(99\) −58.3675 −0.0592541
\(100\) 207.941 + 360.165i 0.207941 + 0.360165i
\(101\) 653.194 1131.37i 0.643518 1.11461i −0.341124 0.940018i \(-0.610808\pi\)
0.984642 0.174587i \(-0.0558590\pi\)
\(102\) −244.669 + 423.779i −0.237508 + 0.411376i
\(103\) 379.487 + 657.291i 0.363029 + 0.628785i 0.988458 0.151496i \(-0.0484092\pi\)
−0.625429 + 0.780281i \(0.715076\pi\)
\(104\) 361.706 0.341040
\(105\) 0 0
\(106\) 811.058 0.743178
\(107\) −631.257 1093.37i −0.570336 0.987850i −0.996531 0.0832192i \(-0.973480\pi\)
0.426196 0.904631i \(-0.359854\pi\)
\(108\) −54.0000 + 93.5307i −0.0481125 + 0.0833333i
\(109\) 1052.76 1823.44i 0.925105 1.60233i 0.133713 0.991020i \(-0.457310\pi\)
0.791392 0.611309i \(-0.209357\pi\)
\(110\) 29.7401 + 51.5114i 0.0257783 + 0.0446493i
\(111\) 343.675 0.293876
\(112\) 0 0
\(113\) 1535.76 1.27852 0.639258 0.768992i \(-0.279241\pi\)
0.639258 + 0.768992i \(0.279241\pi\)
\(114\) 15.1615 + 26.2604i 0.0124562 + 0.0215747i
\(115\) −243.619 + 421.961i −0.197545 + 0.342157i
\(116\) 536.264 928.837i 0.429232 0.743451i
\(117\) −203.459 352.402i −0.160768 0.278458i
\(118\) −506.871 −0.395435
\(119\) 0 0
\(120\) 110.059 0.0837246
\(121\) 644.471 + 1116.26i 0.484200 + 0.838659i
\(122\) 751.217 1301.15i 0.557476 0.965576i
\(123\) 242.408 419.862i 0.177701 0.307786i
\(124\) −584.735 1012.79i −0.423474 0.733478i
\(125\) −1050.01 −0.751326
\(126\) 0 0
\(127\) 24.1749 0.0168911 0.00844557 0.999964i \(-0.497312\pi\)
0.00844557 + 0.999964i \(0.497312\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 706.940 1224.46i 0.482501 0.835716i
\(130\) −207.338 + 359.120i −0.139883 + 0.242284i
\(131\) −790.764 1369.64i −0.527400 0.913483i −0.999490 0.0319327i \(-0.989834\pi\)
0.472090 0.881550i \(-0.343500\pi\)
\(132\) −77.8234 −0.0513156
\(133\) 0 0
\(134\) 23.2935 0.0150168
\(135\) −61.9081 107.228i −0.0394682 0.0683609i
\(136\) −326.225 + 565.039i −0.205688 + 0.356262i
\(137\) 372.594 645.352i 0.232357 0.402454i −0.726144 0.687542i \(-0.758690\pi\)
0.958501 + 0.285089i \(0.0920230\pi\)
\(138\) −318.749 552.090i −0.196621 0.340558i
\(139\) −1373.60 −0.838179 −0.419090 0.907945i \(-0.637651\pi\)
−0.419090 + 0.907945i \(0.637651\pi\)
\(140\) 0 0
\(141\) 1038.01 0.619975
\(142\) 681.661 + 1180.67i 0.402843 + 0.697745i
\(143\) 146.610 253.936i 0.0857354 0.148498i
\(144\) −72.0000 + 124.708i −0.0416667 + 0.0721688i
\(145\) 614.798 + 1064.86i 0.352112 + 0.609875i
\(146\) 1370.91 0.777107
\(147\) 0 0
\(148\) 458.234 0.254504
\(149\) −310.265 537.395i −0.170590 0.295470i 0.768036 0.640406i \(-0.221234\pi\)
−0.938626 + 0.344936i \(0.887901\pi\)
\(150\) 311.912 540.247i 0.169783 0.294073i
\(151\) 969.632 1679.45i 0.522567 0.905112i −0.477089 0.878855i \(-0.658308\pi\)
0.999655 0.0262568i \(-0.00835877\pi\)
\(152\) 20.2153 + 35.0139i 0.0107873 + 0.0186842i
\(153\) 734.007 0.387849
\(154\) 0 0
\(155\) 1340.74 0.694777
\(156\) −271.279 469.869i −0.139229 0.241152i
\(157\) 206.422 357.533i 0.104931 0.181747i −0.808779 0.588113i \(-0.799871\pi\)
0.913710 + 0.406366i \(0.133204\pi\)
\(158\) −0.264069 + 0.457380i −0.000132963 + 0.000230299i
\(159\) −608.294 1053.60i −0.303401 0.525507i
\(160\) 146.745 0.0725077
\(161\) 0 0
\(162\) 162.000 0.0785674
\(163\) 1953.72 + 3383.94i 0.938817 + 1.62608i 0.767682 + 0.640831i \(0.221410\pi\)
0.171135 + 0.985248i \(0.445257\pi\)
\(164\) 323.210 559.817i 0.153893 0.266551i
\(165\) 44.6102 77.2671i 0.0210479 0.0364560i
\(166\) 437.137 + 757.144i 0.204388 + 0.354011i
\(167\) −1286.41 −0.596082 −0.298041 0.954553i \(-0.596333\pi\)
−0.298041 + 0.954553i \(0.596333\pi\)
\(168\) 0 0
\(169\) −152.766 −0.0695340
\(170\) −374.000 647.787i −0.168732 0.292253i
\(171\) 22.7422 39.3907i 0.0101704 0.0176157i
\(172\) 942.587 1632.61i 0.417858 0.723751i
\(173\) 625.628 + 1083.62i 0.274946 + 0.476220i 0.970121 0.242620i \(-0.0780068\pi\)
−0.695176 + 0.718840i \(0.744673\pi\)
\(174\) −1608.79 −0.700932
\(175\) 0 0
\(176\) −103.765 −0.0444406
\(177\) 380.153 + 658.445i 0.161436 + 0.279614i
\(178\) 58.5126 101.347i 0.0246388 0.0426757i
\(179\) −1811.76 + 3138.05i −0.756520 + 1.31033i 0.188095 + 0.982151i \(0.439769\pi\)
−0.944615 + 0.328180i \(0.893565\pi\)
\(180\) −82.5442 142.971i −0.0341804 0.0592022i
\(181\) 181.727 0.0746280 0.0373140 0.999304i \(-0.488120\pi\)
0.0373140 + 0.999304i \(0.488120\pi\)
\(182\) 0 0
\(183\) −2253.65 −0.910354
\(184\) −424.999 736.120i −0.170279 0.294932i
\(185\) −262.670 + 454.958i −0.104389 + 0.180806i
\(186\) −877.103 + 1519.19i −0.345765 + 0.598882i
\(187\) 264.458 + 458.055i 0.103418 + 0.179124i
\(188\) 1384.02 0.536914
\(189\) 0 0
\(190\) −46.3515 −0.0176984
\(191\) −740.640 1282.83i −0.280580 0.485979i 0.690948 0.722905i \(-0.257194\pi\)
−0.971528 + 0.236926i \(0.923860\pi\)
\(192\) −96.0000 + 166.277i −0.0360844 + 0.0625000i
\(193\) 178.354 308.918i 0.0665192 0.115215i −0.830848 0.556500i \(-0.812144\pi\)
0.897367 + 0.441285i \(0.145477\pi\)
\(194\) 1280.09 + 2217.18i 0.473738 + 0.820538i
\(195\) 622.014 0.228428
\(196\) 0 0
\(197\) 4890.53 1.76871 0.884355 0.466816i \(-0.154599\pi\)
0.884355 + 0.466816i \(0.154599\pi\)
\(198\) 58.3675 + 101.096i 0.0209495 + 0.0362856i
\(199\) −1771.43 + 3068.20i −0.631020 + 1.09296i 0.356323 + 0.934363i \(0.384030\pi\)
−0.987344 + 0.158596i \(0.949303\pi\)
\(200\) 415.882 720.329i 0.147037 0.254675i
\(201\) −17.4701 30.2592i −0.00613059 0.0106185i
\(202\) −2612.78 −0.910071
\(203\) 0 0
\(204\) 978.676 0.335887
\(205\) 370.543 + 641.800i 0.126243 + 0.218660i
\(206\) 758.975 1314.58i 0.256700 0.444618i
\(207\) −478.124 + 828.135i −0.160541 + 0.278065i
\(208\) −361.706 626.493i −0.120576 0.208843i
\(209\) 32.7755 0.0108475
\(210\) 0 0
\(211\) −4289.50 −1.39953 −0.699765 0.714373i \(-0.746712\pi\)
−0.699765 + 0.714373i \(0.746712\pi\)
\(212\) −811.058 1404.79i −0.262753 0.455102i
\(213\) 1022.49 1771.01i 0.328920 0.569706i
\(214\) −1262.51 + 2186.74i −0.403288 + 0.698516i
\(215\) 1080.63 + 1871.70i 0.342782 + 0.593715i
\(216\) 216.000 0.0680414
\(217\) 0 0
\(218\) −4211.05 −1.30830
\(219\) −1028.19 1780.87i −0.317253 0.549498i
\(220\) 59.4802 103.023i 0.0182280 0.0315718i
\(221\) −1843.71 + 3193.40i −0.561183 + 0.971998i
\(222\) −343.675 595.263i −0.103901 0.179961i
\(223\) 5795.73 1.74041 0.870204 0.492692i \(-0.163987\pi\)
0.870204 + 0.492692i \(0.163987\pi\)
\(224\) 0 0
\(225\) −935.735 −0.277255
\(226\) −1535.76 2660.02i −0.452024 0.782929i
\(227\) −2052.02 + 3554.21i −0.599989 + 1.03921i 0.392833 + 0.919610i \(0.371495\pi\)
−0.992822 + 0.119601i \(0.961838\pi\)
\(228\) 30.3229 52.5209i 0.00880783 0.0152556i
\(229\) 648.416 + 1123.09i 0.187111 + 0.324086i 0.944286 0.329126i \(-0.106754\pi\)
−0.757175 + 0.653213i \(0.773421\pi\)
\(230\) 974.478 0.279370
\(231\) 0 0
\(232\) −2145.06 −0.607025
\(233\) 739.167 + 1280.27i 0.207830 + 0.359972i 0.951031 0.309096i \(-0.100027\pi\)
−0.743201 + 0.669069i \(0.766693\pi\)
\(234\) −406.919 + 704.804i −0.113680 + 0.196900i
\(235\) −793.351 + 1374.12i −0.220223 + 0.381438i
\(236\) 506.871 + 877.927i 0.139807 + 0.242153i
\(237\) 0.792206 0.000217128
\(238\) 0 0
\(239\) −3776.92 −1.02221 −0.511106 0.859518i \(-0.670764\pi\)
−0.511106 + 0.859518i \(0.670764\pi\)
\(240\) −110.059 190.628i −0.0296011 0.0512707i
\(241\) 1998.19 3460.97i 0.534086 0.925065i −0.465121 0.885247i \(-0.653989\pi\)
0.999207 0.0398173i \(-0.0126776\pi\)
\(242\) 1288.94 2232.51i 0.342381 0.593022i
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) −3004.87 −0.788390
\(245\) 0 0
\(246\) −969.631 −0.251306
\(247\) 114.250 + 197.886i 0.0294313 + 0.0509766i
\(248\) −1169.47 + 2025.58i −0.299441 + 0.518647i
\(249\) 655.706 1135.72i 0.166882 0.289048i
\(250\) 1050.01 + 1818.67i 0.265634 + 0.460091i
\(251\) 5423.58 1.36388 0.681939 0.731409i \(-0.261137\pi\)
0.681939 + 0.731409i \(0.261137\pi\)
\(252\) 0 0
\(253\) −689.060 −0.171229
\(254\) −24.1749 41.8721i −0.00597192 0.0103437i
\(255\) −561.000 + 971.681i −0.137769 + 0.238624i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −2982.11 5165.17i −0.723809 1.25367i −0.959462 0.281837i \(-0.909056\pi\)
0.235653 0.971837i \(-0.424277\pi\)
\(258\) −2827.76 −0.682359
\(259\) 0 0
\(260\) 829.352 0.197824
\(261\) 1206.59 + 2089.88i 0.286154 + 0.495634i
\(262\) −1581.53 + 2739.29i −0.372928 + 0.645930i
\(263\) −2583.00 + 4473.89i −0.605608 + 1.04894i 0.386347 + 0.922353i \(0.373737\pi\)
−0.991955 + 0.126590i \(0.959597\pi\)
\(264\) 77.8234 + 134.794i 0.0181428 + 0.0314242i
\(265\) 1859.67 0.431089
\(266\) 0 0
\(267\) −175.538 −0.0402350
\(268\) −23.2935 40.3455i −0.00530924 0.00919588i
\(269\) −1941.65 + 3363.03i −0.440090 + 0.762259i −0.997696 0.0678474i \(-0.978387\pi\)
0.557605 + 0.830106i \(0.311720\pi\)
\(270\) −123.816 + 214.456i −0.0279082 + 0.0483384i
\(271\) −2763.83 4787.09i −0.619522 1.07304i −0.989573 0.144032i \(-0.953993\pi\)
0.370051 0.929011i \(-0.379340\pi\)
\(272\) 1304.90 0.290887
\(273\) 0 0
\(274\) −1490.38 −0.328602
\(275\) −337.139 583.942i −0.0739282 0.128047i
\(276\) −637.499 + 1104.18i −0.139032 + 0.240811i
\(277\) −1134.06 + 1964.25i −0.245989 + 0.426066i −0.962409 0.271603i \(-0.912446\pi\)
0.716420 + 0.697669i \(0.245779\pi\)
\(278\) 1373.60 + 2379.14i 0.296341 + 0.513278i
\(279\) 2631.31 0.564632
\(280\) 0 0
\(281\) 725.656 0.154053 0.0770267 0.997029i \(-0.475457\pi\)
0.0770267 + 0.997029i \(0.475457\pi\)
\(282\) −1038.01 1797.89i −0.219194 0.379655i
\(283\) −2118.50 + 3669.35i −0.444988 + 0.770742i −0.998051 0.0623972i \(-0.980125\pi\)
0.553063 + 0.833139i \(0.313459\pi\)
\(284\) 1363.32 2361.34i 0.284853 0.493380i
\(285\) 34.7636 + 60.2124i 0.00722533 + 0.0125146i
\(286\) −586.441 −0.121248
\(287\) 0 0
\(288\) 288.000 0.0589256
\(289\) −869.219 1505.53i −0.176922 0.306438i
\(290\) 1229.60 2129.72i 0.248981 0.431247i
\(291\) 1920.14 3325.77i 0.386805 0.669966i
\(292\) −1370.91 2374.49i −0.274749 0.475879i
\(293\) −4373.78 −0.872079 −0.436039 0.899928i \(-0.643619\pi\)
−0.436039 + 0.899928i \(0.643619\pi\)
\(294\) 0 0
\(295\) −1162.20 −0.229376
\(296\) −458.234 793.684i −0.0899807 0.155851i
\(297\) 87.5513 151.643i 0.0171052 0.0296271i
\(298\) −620.530 + 1074.79i −0.120625 + 0.208929i
\(299\) −2401.95 4160.29i −0.464576 0.804669i
\(300\) −1247.65 −0.240110
\(301\) 0 0
\(302\) −3878.53 −0.739021
\(303\) 1959.58 + 3394.10i 0.371535 + 0.643518i
\(304\) 40.4306 70.0278i 0.00762781 0.0132117i
\(305\) 1722.46 2983.39i 0.323370 0.560093i
\(306\) −734.007 1271.34i −0.137125 0.237508i
\(307\) 4133.47 0.768435 0.384217 0.923243i \(-0.374471\pi\)
0.384217 + 0.923243i \(0.374471\pi\)
\(308\) 0 0
\(309\) −2276.92 −0.419190
\(310\) −1340.74 2322.22i −0.245641 0.425462i
\(311\) −2531.62 + 4384.89i −0.461591 + 0.799499i −0.999040 0.0437972i \(-0.986054\pi\)
0.537450 + 0.843296i \(0.319388\pi\)
\(312\) −542.558 + 939.739i −0.0984498 + 0.170520i
\(313\) −3705.78 6418.60i −0.669211 1.15911i −0.978125 0.208017i \(-0.933299\pi\)
0.308914 0.951090i \(-0.400034\pi\)
\(314\) −825.686 −0.148395
\(315\) 0 0
\(316\) 1.05627 0.000188038
\(317\) 3368.53 + 5834.46i 0.596831 + 1.03374i 0.993286 + 0.115687i \(0.0369069\pi\)
−0.396455 + 0.918054i \(0.629760\pi\)
\(318\) −1216.59 + 2107.19i −0.214537 + 0.371589i
\(319\) −869.456 + 1505.94i −0.152602 + 0.264315i
\(320\) −146.745 254.170i −0.0256353 0.0444017i
\(321\) 3787.54 0.658567
\(322\) 0 0
\(323\) −412.171 −0.0710026
\(324\) −162.000 280.592i −0.0277778 0.0481125i
\(325\) 2350.42 4071.05i 0.401163 0.694834i
\(326\) 3907.44 6767.88i 0.663844 1.14981i
\(327\) 3158.29 + 5470.32i 0.534110 + 0.925105i
\(328\) −1292.84 −0.217638
\(329\) 0 0
\(330\) −178.441 −0.0297662
\(331\) −5587.97 9678.65i −0.927923 1.60721i −0.786791 0.617219i \(-0.788259\pi\)
−0.141132 0.989991i \(-0.545074\pi\)
\(332\) 874.274 1514.29i 0.144524 0.250323i
\(333\) −515.513 + 892.895i −0.0848346 + 0.146938i
\(334\) 1286.41 + 2228.14i 0.210747 + 0.365024i
\(335\) 53.4095 0.00871067
\(336\) 0 0
\(337\) 9379.78 1.51617 0.758085 0.652156i \(-0.226135\pi\)
0.758085 + 0.652156i \(0.226135\pi\)
\(338\) 152.766 + 264.599i 0.0245840 + 0.0425807i
\(339\) −2303.64 + 3990.03i −0.369076 + 0.639258i
\(340\) −748.000 + 1295.57i −0.119312 + 0.206654i
\(341\) 948.043 + 1642.06i 0.150555 + 0.260770i
\(342\) −90.9688 −0.0143831
\(343\) 0 0
\(344\) −3770.35 −0.590941
\(345\) −730.858 1265.88i −0.114052 0.197545i
\(346\) 1251.26 2167.24i 0.194416 0.336738i
\(347\) −2840.73 + 4920.29i −0.439476 + 0.761195i −0.997649 0.0685293i \(-0.978169\pi\)
0.558173 + 0.829725i \(0.311503\pi\)
\(348\) 1608.79 + 2786.51i 0.247817 + 0.429232i
\(349\) −704.250 −0.108016 −0.0540080 0.998541i \(-0.517200\pi\)
−0.0540080 + 0.998541i \(0.517200\pi\)
\(350\) 0 0
\(351\) 1220.76 0.185639
\(352\) 103.765 + 179.725i 0.0157121 + 0.0272142i
\(353\) 2142.48 3710.89i 0.323039 0.559520i −0.658074 0.752953i \(-0.728629\pi\)
0.981114 + 0.193433i \(0.0619622\pi\)
\(354\) 760.307 1316.89i 0.114152 0.197717i
\(355\) 1562.98 + 2707.15i 0.233674 + 0.404735i
\(356\) −234.051 −0.0348445
\(357\) 0 0
\(358\) 7247.03 1.06988
\(359\) −2330.64 4036.78i −0.342636 0.593463i 0.642285 0.766465i \(-0.277986\pi\)
−0.984921 + 0.173003i \(0.944653\pi\)
\(360\) −165.088 + 285.941i −0.0241692 + 0.0418623i
\(361\) 3416.73 5917.95i 0.498138 0.862801i
\(362\) −181.727 314.760i −0.0263850 0.0457001i
\(363\) −3866.82 −0.559106
\(364\) 0 0
\(365\) 3143.36 0.450770
\(366\) 2253.65 + 3903.44i 0.321859 + 0.557476i
\(367\) 3467.65 6006.15i 0.493215 0.854274i −0.506754 0.862091i \(-0.669155\pi\)
0.999969 + 0.00781688i \(0.00248822\pi\)
\(368\) −849.998 + 1472.24i −0.120405 + 0.208548i
\(369\) 727.223 + 1259.59i 0.102595 + 0.177701i
\(370\) 1050.68 0.147628
\(371\) 0 0
\(372\) 3508.41 0.488985
\(373\) 1540.55 + 2668.31i 0.213852 + 0.370402i 0.952917 0.303232i \(-0.0980657\pi\)
−0.739065 + 0.673634i \(0.764732\pi\)
\(374\) 528.916 916.109i 0.0731272 0.126660i
\(375\) 1575.02 2728.01i 0.216889 0.375663i
\(376\) −1384.02 2397.19i −0.189828 0.328791i
\(377\) −12123.1 −1.65616
\(378\) 0 0
\(379\) 941.827 0.127647 0.0638237 0.997961i \(-0.479670\pi\)
0.0638237 + 0.997961i \(0.479670\pi\)
\(380\) 46.3515 + 80.2832i 0.00625732 + 0.0108380i
\(381\) −36.2623 + 62.8082i −0.00487605 + 0.00844557i
\(382\) −1481.28 + 2565.65i −0.198400 + 0.343639i
\(383\) 338.763 + 586.755i 0.0451958 + 0.0782814i 0.887738 0.460348i \(-0.152276\pi\)
−0.842543 + 0.538630i \(0.818942\pi\)
\(384\) 384.000 0.0510310
\(385\) 0 0
\(386\) −713.416 −0.0940724
\(387\) 2120.82 + 3673.37i 0.278572 + 0.482501i
\(388\) 2560.18 4434.36i 0.334983 0.580208i
\(389\) 5932.71 10275.8i 0.773266 1.33934i −0.162498 0.986709i \(-0.551955\pi\)
0.935764 0.352627i \(-0.114711\pi\)
\(390\) −622.014 1077.36i −0.0807613 0.139883i
\(391\) 8665.34 1.12078
\(392\) 0 0
\(393\) 4744.58 0.608989
\(394\) −4890.53 8470.64i −0.625333 1.08311i
\(395\) −0.605481 + 1.04872i −7.71268e−5 + 0.000133587i
\(396\) 116.735 202.191i 0.0148135 0.0256578i
\(397\) 2570.38 + 4452.03i 0.324947 + 0.562824i 0.981502 0.191454i \(-0.0613203\pi\)
−0.656555 + 0.754278i \(0.727987\pi\)
\(398\) 7085.70 0.892397
\(399\) 0 0
\(400\) −1663.53 −0.207941
\(401\) 6190.99 + 10723.1i 0.770981 + 1.33538i 0.937026 + 0.349260i \(0.113567\pi\)
−0.166045 + 0.986118i \(0.553100\pi\)
\(402\) −34.9403 + 60.5183i −0.00433498 + 0.00750840i
\(403\) −6609.44 + 11447.9i −0.816971 + 1.41504i
\(404\) 2612.78 + 4525.46i 0.321759 + 0.557303i
\(405\) 371.449 0.0455739
\(406\) 0 0
\(407\) −742.944 −0.0904824
\(408\) −978.676 1695.12i −0.118754 0.205688i
\(409\) 7937.82 13748.7i 0.959657 1.66217i 0.236326 0.971674i \(-0.424057\pi\)
0.723331 0.690501i \(-0.242610\pi\)
\(410\) 741.087 1283.60i 0.0892675 0.154616i
\(411\) 1117.78 + 1936.06i 0.134151 + 0.232357i
\(412\) −3035.90 −0.363029
\(413\) 0 0
\(414\) 1912.50 0.227039
\(415\) 1002.31 + 1736.05i 0.118558 + 0.205348i
\(416\) −723.411 + 1252.99i −0.0852600 + 0.147675i
\(417\) 2060.39 3568.71i 0.241962 0.419090i
\(418\) −32.7755 56.7688i −0.00383517 0.00664271i
\(419\) −16111.9 −1.87857 −0.939283 0.343145i \(-0.888508\pi\)
−0.939283 + 0.343145i \(0.888508\pi\)
\(420\) 0 0
\(421\) 8691.58 1.00618 0.503090 0.864234i \(-0.332197\pi\)
0.503090 + 0.864234i \(0.332197\pi\)
\(422\) 4289.50 + 7429.62i 0.494809 + 0.857034i
\(423\) −1557.02 + 2696.84i −0.178971 + 0.309987i
\(424\) −1622.12 + 2809.59i −0.185795 + 0.321806i
\(425\) 4239.73 + 7343.43i 0.483899 + 0.838138i
\(426\) −4089.97 −0.465163
\(427\) 0 0
\(428\) 5050.06 0.570336
\(429\) 439.831 + 761.809i 0.0494993 + 0.0857354i
\(430\) 2161.25 3743.40i 0.242383 0.419820i
\(431\) 2097.55 3633.07i 0.234421 0.406029i −0.724683 0.689082i \(-0.758014\pi\)
0.959104 + 0.283053i \(0.0913472\pi\)
\(432\) −216.000 374.123i −0.0240563 0.0416667i
\(433\) −5426.54 −0.602270 −0.301135 0.953582i \(-0.597365\pi\)
−0.301135 + 0.953582i \(0.597365\pi\)
\(434\) 0 0
\(435\) −3688.79 −0.406584
\(436\) 4211.05 + 7293.76i 0.462553 + 0.801165i
\(437\) 268.484 465.028i 0.0293898 0.0509046i
\(438\) −2056.37 + 3561.74i −0.224332 + 0.388554i
\(439\) 1885.62 + 3265.99i 0.205002 + 0.355073i 0.950133 0.311844i \(-0.100947\pi\)
−0.745132 + 0.666917i \(0.767613\pi\)
\(440\) −237.921 −0.0257783
\(441\) 0 0
\(442\) 7374.85 0.793633
\(443\) 2965.15 + 5135.79i 0.318010 + 0.550810i 0.980073 0.198639i \(-0.0636520\pi\)
−0.662063 + 0.749449i \(0.730319\pi\)
\(444\) −687.351 + 1190.53i −0.0734690 + 0.127252i
\(445\) 134.163 232.377i 0.0142920 0.0247545i
\(446\) −5795.73 10038.5i −0.615327 1.06578i
\(447\) 1861.59 0.196980
\(448\) 0 0
\(449\) −529.065 −0.0556083 −0.0278041 0.999613i \(-0.508851\pi\)
−0.0278041 + 0.999613i \(0.508851\pi\)
\(450\) 935.735 + 1620.74i 0.0980244 + 0.169783i
\(451\) −524.027 + 907.642i −0.0547128 + 0.0947654i
\(452\) −3071.53 + 5320.04i −0.319629 + 0.553614i
\(453\) 2908.90 + 5038.36i 0.301704 + 0.522567i
\(454\) 8208.09 0.848512
\(455\) 0 0
\(456\) −121.292 −0.0124562
\(457\) −5028.59 8709.77i −0.514721 0.891523i −0.999854 0.0170824i \(-0.994562\pi\)
0.485133 0.874440i \(-0.338771\pi\)
\(458\) 1296.83 2246.18i 0.132308 0.229164i
\(459\) −1101.01 + 1907.01i −0.111962 + 0.193925i
\(460\) −974.478 1687.84i −0.0987723 0.171079i
\(461\) −5010.31 −0.506190 −0.253095 0.967441i \(-0.581448\pi\)
−0.253095 + 0.967441i \(0.581448\pi\)
\(462\) 0 0
\(463\) −7124.38 −0.715114 −0.357557 0.933891i \(-0.616390\pi\)
−0.357557 + 0.933891i \(0.616390\pi\)
\(464\) 2145.06 + 3715.35i 0.214616 + 0.371725i
\(465\) −2011.10 + 3483.33i −0.200565 + 0.347388i
\(466\) 1478.33 2560.55i 0.146958 0.254539i
\(467\) −3750.72 6496.44i −0.371654 0.643724i 0.618166 0.786048i \(-0.287876\pi\)
−0.989820 + 0.142323i \(0.954543\pi\)
\(468\) 1627.68 0.160768
\(469\) 0 0
\(470\) 3173.40 0.311443
\(471\) 619.265 + 1072.60i 0.0605822 + 0.104931i
\(472\) 1013.74 1755.85i 0.0988587 0.171228i
\(473\) −1528.24 + 2646.98i −0.148559 + 0.257312i
\(474\) −0.792206 1.37214i −7.67663e−5 0.000132963i
\(475\) 525.449 0.0507563
\(476\) 0 0
\(477\) 3649.76 0.350338
\(478\) 3776.92 + 6541.82i 0.361406 + 0.625974i
\(479\) 4086.90 7078.72i 0.389844 0.675230i −0.602584 0.798055i \(-0.705862\pi\)
0.992428 + 0.122826i \(0.0391956\pi\)
\(480\) −220.118 + 381.255i −0.0209312 + 0.0362538i
\(481\) −2589.78 4485.63i −0.245496 0.425212i
\(482\) −7992.76 −0.755312
\(483\) 0 0
\(484\) −5155.76 −0.484200
\(485\) 2935.11 + 5083.76i 0.274797 + 0.475962i
\(486\) −243.000 + 420.888i −0.0226805 + 0.0392837i
\(487\) 5984.39 10365.3i 0.556835 0.964467i −0.440923 0.897545i \(-0.645349\pi\)
0.997758 0.0669221i \(-0.0213179\pi\)
\(488\) 3004.87 + 5204.59i 0.278738 + 0.482788i
\(489\) −11722.3 −1.08405
\(490\) 0 0
\(491\) 2079.96 0.191176 0.0955878 0.995421i \(-0.469527\pi\)
0.0955878 + 0.995421i \(0.469527\pi\)
\(492\) 969.631 + 1679.45i 0.0888503 + 0.153893i
\(493\) 10933.9 18938.1i 0.998863 1.73008i
\(494\) 228.500 395.773i 0.0208111 0.0360459i
\(495\) 133.831 + 231.801i 0.0121520 + 0.0210479i
\(496\) 4677.88 0.423474
\(497\) 0 0
\(498\) −2622.82 −0.236007
\(499\) −6417.21 11114.9i −0.575699 0.997140i −0.995965 0.0897390i \(-0.971397\pi\)
0.420266 0.907401i \(-0.361937\pi\)
\(500\) 2100.02 3637.34i 0.187832 0.325334i
\(501\) 1929.62 3342.20i 0.172074 0.298041i
\(502\) −5423.58 9393.92i −0.482204 0.835202i
\(503\) 16808.8 1.48999 0.744997 0.667068i \(-0.232451\pi\)
0.744997 + 0.667068i \(0.232451\pi\)
\(504\) 0 0
\(505\) −5990.82 −0.527897
\(506\) 689.060 + 1193.49i 0.0605384 + 0.104856i
\(507\) 229.149 396.898i 0.0200727 0.0347670i
\(508\) −48.3498 + 83.7443i −0.00422278 + 0.00731408i
\(509\) 2135.13 + 3698.16i 0.185929 + 0.322039i 0.943889 0.330262i \(-0.107137\pi\)
−0.757960 + 0.652301i \(0.773804\pi\)
\(510\) 2244.00 0.194835
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 68.2266 + 118.172i 0.00587189 + 0.0101704i
\(514\) −5964.22 + 10330.3i −0.511811 + 0.886482i
\(515\) 1740.25 3014.20i 0.148902 0.257906i
\(516\) 2827.76 + 4897.83i 0.241250 + 0.417858i
\(517\) −2243.93 −0.190886
\(518\) 0 0
\(519\) −3753.77 −0.317480
\(520\) −829.352 1436.48i −0.0699414 0.121142i
\(521\) −7641.64 + 13235.7i −0.642584 + 1.11299i 0.342270 + 0.939602i \(0.388804\pi\)
−0.984854 + 0.173386i \(0.944529\pi\)
\(522\) 2413.19 4179.76i 0.202342 0.350466i
\(523\) 2249.66 + 3896.53i 0.188090 + 0.325781i 0.944613 0.328185i \(-0.106437\pi\)
−0.756524 + 0.653966i \(0.773104\pi\)
\(524\) 6326.11 0.527400
\(525\) 0 0
\(526\) 10332.0 0.856459
\(527\) −11922.2 20649.9i −0.985465 1.70687i
\(528\) 155.647 269.588i 0.0128289 0.0222203i
\(529\) 438.992 760.356i 0.0360805 0.0624933i
\(530\) −1859.67 3221.04i −0.152413 0.263987i
\(531\) −2280.92 −0.186410
\(532\) 0 0
\(533\) −7306.69 −0.593785
\(534\) 175.538 + 304.041i 0.0142252 + 0.0246388i
\(535\) −2894.81 + 5013.96i −0.233932 + 0.405182i
\(536\) −46.5870 + 80.6911i −0.00375420 + 0.00650247i
\(537\) −5435.27 9414.16i −0.436777 0.756520i
\(538\) 7766.59 0.622382
\(539\) 0 0
\(540\) 495.265 0.0394682
\(541\) −1985.41 3438.83i −0.157781 0.273284i 0.776287 0.630379i \(-0.217101\pi\)
−0.934068 + 0.357095i \(0.883767\pi\)
\(542\) −5527.65 + 9574.18i −0.438068 + 0.758757i
\(543\) −272.591 + 472.141i −0.0215432 + 0.0373140i
\(544\) −1304.90 2260.16i −0.102844 0.178131i
\(545\) −9655.50 −0.758892
\(546\) 0 0
\(547\) −2703.90 −0.211353 −0.105677 0.994401i \(-0.533701\pi\)
−0.105677 + 0.994401i \(0.533701\pi\)
\(548\) 1490.38 + 2581.41i 0.116178 + 0.201227i
\(549\) 3380.48 5855.16i 0.262797 0.455177i
\(550\) −674.278 + 1167.88i −0.0522751 + 0.0905432i
\(551\) −677.546 1173.54i −0.0523855 0.0907344i
\(552\) 2549.99 0.196621
\(553\) 0 0
\(554\) 4536.24 0.347881
\(555\) −788.011 1364.87i −0.0602688 0.104389i
\(556\) 2747.19 4758.28i 0.209545 0.362942i
\(557\) −395.412 + 684.874i −0.0300793 + 0.0520988i −0.880673 0.473724i \(-0.842909\pi\)
0.850594 + 0.525823i \(0.176243\pi\)
\(558\) −2631.31 4557.56i −0.199627 0.345765i
\(559\) −21308.7 −1.61227
\(560\) 0 0
\(561\) −1586.75 −0.119416
\(562\) −725.656 1256.87i −0.0544661 0.0943380i
\(563\) −3758.58 + 6510.05i −0.281359 + 0.487328i −0.971720 0.236137i \(-0.924119\pi\)
0.690361 + 0.723465i \(0.257452\pi\)
\(564\) −2076.03 + 3595.78i −0.154994 + 0.268457i
\(565\) −3521.34 6099.14i −0.262202 0.454146i
\(566\) 8473.99 0.629308
\(567\) 0 0
\(568\) −5453.29 −0.402843
\(569\) −6972.72 12077.1i −0.513728 0.889804i −0.999873 0.0159254i \(-0.994931\pi\)
0.486145 0.873878i \(-0.338403\pi\)
\(570\) 69.5273 120.425i 0.00510908 0.00884919i
\(571\) 1059.25 1834.67i 0.0776323 0.134463i −0.824596 0.565723i \(-0.808597\pi\)
0.902228 + 0.431259i \(0.141931\pi\)
\(572\) 586.441 + 1015.75i 0.0428677 + 0.0742490i
\(573\) 4443.84 0.323986
\(574\) 0 0
\(575\) −11046.8 −0.801192
\(576\) −288.000 498.831i −0.0208333 0.0360844i
\(577\) −11428.9 + 19795.4i −0.824592 + 1.42823i 0.0776391 + 0.996982i \(0.475262\pi\)
−0.902231 + 0.431253i \(0.858072\pi\)
\(578\) −1738.44 + 3011.06i −0.125103 + 0.216685i
\(579\) 535.062 + 926.755i 0.0384049 + 0.0665192i
\(580\) −4918.38 −0.352112
\(581\) 0 0
\(582\) −7680.54 −0.547025
\(583\) 1314.98 + 2277.62i 0.0934153 + 0.161800i
\(584\) −2741.83 + 4748.99i −0.194277 + 0.336497i
\(585\) −933.021 + 1616.04i −0.0659413 + 0.114214i
\(586\) 4373.78 + 7575.61i 0.308326 + 0.534037i
\(587\) 23955.3 1.68440 0.842199 0.539167i \(-0.181261\pi\)
0.842199 + 0.539167i \(0.181261\pi\)
\(588\) 0 0
\(589\) −1477.57 −0.103366
\(590\) 1162.20 + 2012.99i 0.0810968 + 0.140464i
\(591\) −7335.79 + 12706.0i −0.510582 + 0.884355i
\(592\) −916.468 + 1587.37i −0.0636260 + 0.110203i
\(593\) 5388.99 + 9334.01i 0.373186 + 0.646378i 0.990054 0.140689i \(-0.0449319\pi\)
−0.616867 + 0.787067i \(0.711599\pi\)
\(594\) −350.205 −0.0241904
\(595\) 0 0
\(596\) 2482.12 0.170590
\(597\) −5314.28 9204.60i −0.364320 0.631020i
\(598\) −4803.89 + 8320.59i −0.328505 + 0.568987i
\(599\) −3798.79 + 6579.69i −0.259122 + 0.448813i −0.966007 0.258516i \(-0.916767\pi\)
0.706885 + 0.707329i \(0.250100\pi\)
\(600\) 1247.65 + 2160.99i 0.0848916 + 0.147037i
\(601\) 19956.1 1.35445 0.677225 0.735776i \(-0.263182\pi\)
0.677225 + 0.735776i \(0.263182\pi\)
\(602\) 0 0
\(603\) 104.821 0.00707899
\(604\) 3878.53 + 6717.81i 0.261283 + 0.452556i
\(605\) 2955.40 5118.91i 0.198602 0.343989i
\(606\) 3919.17 6788.20i 0.262715 0.455036i
\(607\) 118.155 + 204.651i 0.00790079 + 0.0136846i 0.869949 0.493142i \(-0.164152\pi\)
−0.862048 + 0.506827i \(0.830818\pi\)
\(608\) −161.722 −0.0107873
\(609\) 0 0
\(610\) −6889.85 −0.457314
\(611\) −7821.98 13548.1i −0.517911 0.897048i
\(612\) −1468.01 + 2542.68i −0.0969624 + 0.167944i
\(613\) −13207.5 + 22876.0i −0.870219 + 1.50726i −0.00844986 + 0.999964i \(0.502690\pi\)
−0.861770 + 0.507300i \(0.830644\pi\)
\(614\) −4133.47 7159.38i −0.271683 0.470568i
\(615\) −2223.26 −0.145773
\(616\) 0 0
\(617\) 18473.6 1.20538 0.602689 0.797976i \(-0.294096\pi\)
0.602689 + 0.797976i \(0.294096\pi\)
\(618\) 2276.92 + 3943.75i 0.148206 + 0.256700i
\(619\) −8023.96 + 13897.9i −0.521018 + 0.902430i 0.478683 + 0.877988i \(0.341114\pi\)
−0.999701 + 0.0244421i \(0.992219\pi\)
\(620\) −2681.47 + 4644.44i −0.173694 + 0.300847i
\(621\) −1434.37 2484.41i −0.0926882 0.160541i
\(622\) 10126.5 0.652788
\(623\) 0 0
\(624\) 2170.23 0.139229
\(625\) −4090.60 7085.13i −0.261798 0.453448i
\(626\) −7411.56 + 12837.2i −0.473204 + 0.819613i
\(627\) −49.1632 + 85.1532i −0.00313140 + 0.00542375i
\(628\) 825.686 + 1430.13i 0.0524657 + 0.0908733i
\(629\) 9342.97 0.592255
\(630\) 0 0
\(631\) −15065.7 −0.950487 −0.475243 0.879854i \(-0.657640\pi\)
−0.475243 + 0.879854i \(0.657640\pi\)
\(632\) −1.05627 1.82952i −6.64816e−5 0.000115149i
\(633\) 6434.24 11144.4i 0.404010 0.699765i
\(634\) 6737.05 11668.9i 0.422023 0.730965i
\(635\) −55.4304 96.0083i −0.00346408 0.00599996i
\(636\) 4866.35 0.303401
\(637\) 0 0
\(638\) 3477.82 0.215812
\(639\) 3067.47 + 5313.02i 0.189902 + 0.328920i
\(640\) −293.490 + 508.340i −0.0181269 + 0.0313967i
\(641\) 15599.2 27018.6i 0.961203 1.66485i 0.241715 0.970347i \(-0.422290\pi\)
0.719488 0.694505i \(-0.244377\pi\)
\(642\) −3787.54 6560.21i −0.232839 0.403288i
\(643\) −12497.9 −0.766517 −0.383259 0.923641i \(-0.625198\pi\)
−0.383259 + 0.923641i \(0.625198\pi\)
\(644\) 0 0
\(645\) −6483.75 −0.395810
\(646\) 412.171 + 713.902i 0.0251032 + 0.0434800i
\(647\) 4964.86 8599.39i 0.301683 0.522530i −0.674834 0.737969i \(-0.735785\pi\)
0.976517 + 0.215439i \(0.0691183\pi\)
\(648\) −324.000 + 561.184i −0.0196419 + 0.0340207i
\(649\) −821.801 1423.40i −0.0497049 0.0860915i
\(650\) −9401.68 −0.567330
\(651\) 0 0
\(652\) −15629.8 −0.938817
\(653\) 4072.79 + 7054.28i 0.244075 + 0.422750i 0.961871 0.273503i \(-0.0881825\pi\)
−0.717796 + 0.696253i \(0.754849\pi\)
\(654\) 6316.58 10940.6i 0.377673 0.654148i
\(655\) −3626.27 + 6280.89i −0.216321 + 0.374679i
\(656\) 1292.84 + 2239.27i 0.0769466 + 0.133275i
\(657\) 6169.11 0.366332
\(658\) 0 0
\(659\) −16975.8 −1.00347 −0.501733 0.865022i \(-0.667304\pi\)
−0.501733 + 0.865022i \(0.667304\pi\)
\(660\) 178.441 + 309.068i 0.0105239 + 0.0182280i
\(661\) −10318.9 + 17872.8i −0.607199 + 1.05170i 0.384501 + 0.923124i \(0.374373\pi\)
−0.991700 + 0.128574i \(0.958960\pi\)
\(662\) −11175.9 + 19357.3i −0.656141 + 1.13647i
\(663\) −5531.14 9580.21i −0.323999 0.561183i
\(664\) −3497.10 −0.204388
\(665\) 0 0
\(666\) 2062.05 0.119974
\(667\) 14244.5 + 24672.2i 0.826910 + 1.43225i
\(668\) 2572.83 4456.27i 0.149021 0.258111i
\(669\) −8693.60 + 15057.8i −0.502412 + 0.870204i
\(670\) −53.4095 92.5080i −0.00307969 0.00533417i
\(671\) 4871.86 0.280292
\(672\) 0 0
\(673\) −2150.29 −0.123161 −0.0615807 0.998102i \(-0.519614\pi\)
−0.0615807 + 0.998102i \(0.519614\pi\)
\(674\) −9379.78 16246.3i −0.536047 0.928461i
\(675\) 1403.60 2431.11i 0.0800366 0.138627i
\(676\) 305.532 529.198i 0.0173835 0.0301091i
\(677\) 13891.7 + 24061.1i 0.788628 + 1.36594i 0.926808 + 0.375536i \(0.122541\pi\)
−0.138180 + 0.990407i \(0.544125\pi\)
\(678\) 9214.58 0.521952
\(679\) 0 0
\(680\) 2992.00 0.168732
\(681\) −6156.06 10662.6i −0.346404 0.599989i
\(682\) 1896.09 3284.12i 0.106459 0.184392i
\(683\) −9090.89 + 15745.9i −0.509302 + 0.882137i 0.490640 + 0.871362i \(0.336763\pi\)
−0.999942 + 0.0107743i \(0.996570\pi\)
\(684\) 90.9688 + 157.563i 0.00508520 + 0.00880783i
\(685\) −3417.27 −0.190609
\(686\) 0 0
\(687\) −3890.49 −0.216058
\(688\) 3770.35 + 6530.43i 0.208929 + 0.361876i
\(689\) −9167.63 + 15878.8i −0.506907 + 0.877989i
\(690\) −1461.72 + 2531.77i −0.0806472 + 0.139685i
\(691\) −11967.6 20728.4i −0.658853 1.14117i −0.980913 0.194447i \(-0.937709\pi\)
0.322060 0.946719i \(-0.395625\pi\)
\(692\) −5005.02 −0.274946
\(693\) 0 0
\(694\) 11362.9 0.621513
\(695\) 3149.51 + 5455.11i 0.171896 + 0.297733i
\(696\) 3217.58 5573.02i 0.175233 0.303513i
\(697\) 6589.96 11414.1i 0.358124 0.620289i
\(698\) 704.250 + 1219.80i 0.0381895 + 0.0661461i
\(699\) −4435.00 −0.239982
\(700\) 0 0
\(701\) −20627.2 −1.11138 −0.555691 0.831389i \(-0.687546\pi\)
−0.555691 + 0.831389i \(0.687546\pi\)
\(702\) −1220.76 2114.41i −0.0656332 0.113680i
\(703\) 289.479 501.392i 0.0155305 0.0268995i
\(704\) 207.529 359.451i 0.0111101 0.0192433i
\(705\) −2380.05 4122.37i −0.127146 0.220223i
\(706\) −8569.93 −0.456846
\(707\) 0 0
\(708\) −3041.23 −0.161436
\(709\) 3292.32 + 5702.46i 0.174394 + 0.302060i 0.939952 0.341308i \(-0.110870\pi\)
−0.765557 + 0.643368i \(0.777537\pi\)
\(710\) 3125.95 5414.31i 0.165232 0.286191i
\(711\) −1.18831 + 2.05821i −6.26794e−5 + 0.000108564i
\(712\) 234.051 + 405.387i 0.0123194 + 0.0213378i
\(713\) 31064.0 1.63163
\(714\) 0 0
\(715\) −1344.65 −0.0703313
\(716\) −7247.03 12552.2i −0.378260 0.655165i
\(717\) 5665.38 9812.72i 0.295087 0.511106i
\(718\) −4661.27 + 8073.56i −0.242280 + 0.419642i
\(719\) −85.4430 147.992i −0.00443183 0.00767616i 0.863801 0.503833i \(-0.168077\pi\)
−0.868233 + 0.496157i \(0.834744\pi\)
\(720\) 660.353 0.0341804
\(721\) 0 0
\(722\) −13666.9 −0.704474
\(723\) 5994.57 + 10382.9i 0.308355 + 0.534086i
\(724\) −363.454 + 629.521i −0.0186570 + 0.0323149i
\(725\) −13938.9 + 24142.9i −0.714039 + 1.23675i
\(726\) 3866.82 + 6697.53i 0.197674 + 0.342381i
\(727\) −11127.5 −0.567671 −0.283836 0.958873i \(-0.591607\pi\)
−0.283836 + 0.958873i \(0.591607\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −3143.36 5444.46i −0.159371 0.276039i
\(731\) 19218.5 33287.4i 0.972396 1.68424i
\(732\) 4507.30 7806.88i 0.227588 0.394195i
\(733\) 11288.0 + 19551.3i 0.568800 + 0.985191i 0.996685 + 0.0813578i \(0.0259256\pi\)
−0.427885 + 0.903833i \(0.640741\pi\)
\(734\) −13870.6 −0.697511
\(735\) 0 0
\(736\) 3399.99 0.170279
\(737\) 37.7662 + 65.4130i 0.00188757 + 0.00326936i
\(738\) 1454.45 2519.17i 0.0725459 0.125653i
\(739\) 11468.2 19863.5i 0.570860 0.988758i −0.425618 0.904903i \(-0.639943\pi\)
0.996478 0.0838550i \(-0.0267233\pi\)
\(740\) −1050.68 1819.83i −0.0521943 0.0904032i
\(741\) −685.499 −0.0339844
\(742\) 0 0
\(743\) 16973.4 0.838081 0.419041 0.907967i \(-0.362366\pi\)
0.419041 + 0.907967i \(0.362366\pi\)
\(744\) −3508.41 6076.75i −0.172882 0.299441i
\(745\) −1422.81 + 2464.38i −0.0699700 + 0.121192i
\(746\) 3081.10 5336.63i 0.151216 0.261914i
\(747\) 1967.12 + 3407.15i 0.0963495 + 0.166882i
\(748\) −2115.66 −0.103418
\(749\) 0 0
\(750\) −6300.06 −0.306728
\(751\) 10598.9 + 18357.9i 0.514994 + 0.891995i 0.999849 + 0.0174007i \(0.00553909\pi\)
−0.484855 + 0.874595i \(0.661128\pi\)
\(752\) −2768.03 + 4794.37i −0.134228 + 0.232490i
\(753\) −8135.38 + 14090.9i −0.393718 + 0.681939i
\(754\) 12123.1 + 20997.8i 0.585541 + 1.01419i
\(755\) −8893.05 −0.428677
\(756\) 0 0
\(757\) −7962.24 −0.382289 −0.191144 0.981562i \(-0.561220\pi\)
−0.191144 + 0.981562i \(0.561220\pi\)
\(758\) −941.827 1631.29i −0.0451302 0.0781678i
\(759\) 1033.59 1790.23i 0.0494294 0.0856143i
\(760\) 92.7030 160.566i 0.00442460 0.00766362i
\(761\) −13428.1 23258.1i −0.639642 1.10789i −0.985511 0.169610i \(-0.945749\pi\)
0.345869 0.938283i \(-0.387584\pi\)
\(762\) 145.049 0.00689578
\(763\) 0 0
\(764\) 5925.12 0.280580
\(765\) −1683.00 2915.04i −0.0795412 0.137769i
\(766\) 677.526 1173.51i 0.0319582 0.0553533i
\(767\) 5729.32 9923.47i 0.269718 0.467165i
\(768\) −384.000 665.108i −0.0180422 0.0312500i
\(769\) −12183.6 −0.571331 −0.285666 0.958329i \(-0.592215\pi\)
−0.285666 + 0.958329i \(0.592215\pi\)
\(770\) 0 0
\(771\) 17892.7 0.835783
\(772\) 713.416 + 1235.67i 0.0332596 + 0.0576073i
\(773\) 8727.61 15116.7i 0.406093 0.703374i −0.588355 0.808603i \(-0.700224\pi\)
0.994448 + 0.105229i \(0.0335574\pi\)
\(774\) 4241.64 7346.74i 0.196980 0.341180i
\(775\) 15198.8 + 26325.1i 0.704461 + 1.22016i
\(776\) −10240.7 −0.473738
\(777\) 0 0
\(778\) −23730.8 −1.09356
\(779\) −408.362 707.304i −0.0187819 0.0325312i
\(780\) −1244.03 + 2154.72i −0.0571069 + 0.0989120i
\(781\) −2210.38 + 3828.49i −0.101272 + 0.175409i
\(782\) −8665.34 15008.8i −0.396256 0.686335i
\(783\) −7239.56 −0.330423
\(784\) 0 0
\(785\) −1893.21 −0.0860785
\(786\) −4744.58 8217.86i −0.215310 0.372928i
\(787\) −15490.5 + 26830.3i −0.701622 + 1.21524i 0.266275 + 0.963897i \(0.414207\pi\)
−0.967897 + 0.251348i \(0.919126\pi\)
\(788\) −9781.06 + 16941.3i −0.442177 + 0.765874i
\(789\) −7749.01 13421.7i −0.349648 0.605608i
\(790\) 2.42193 0.000109074
\(791\) 0 0
\(792\) −466.940 −0.0209495
\(793\) 16982.5 + 29414.5i 0.760486 + 1.31720i
\(794\) 5140.76 8904.07i 0.229772 0.397977i
\(795\) −2789.50 + 4831.56i −0.124445 + 0.215544i
\(796\) −7085.70 12272.8i −0.315510 0.546480i
\(797\) −10517.6 −0.467446 −0.233723 0.972303i \(-0.575091\pi\)
−0.233723 + 0.972303i \(0.575091\pi\)
\(798\) 0 0
\(799\) 28218.8 1.24945
\(800\) 1663.53 + 2881.32i 0.0735183 + 0.127337i
\(801\) 263.307 456.061i 0.0116148 0.0201175i
\(802\) 12382.0 21446.2i 0.545166 0.944255i
\(803\) 2222.69 + 3849.81i 0.0976800 + 0.169187i
\(804\) 139.761 0.00613059
\(805\) 0 0
\(806\) 26437.7 1.15537
\(807\) −5824.94 10089.1i −0.254086 0.440090i
\(808\) 5225.56 9050.93i 0.227518 0.394072i
\(809\) 20889.2 36181.2i 0.907819 1.57239i 0.0907320 0.995875i \(-0.471079\pi\)
0.817087 0.576514i \(-0.195587\pi\)
\(810\) −371.449 643.368i −0.0161128 0.0279082i
\(811\) −12935.4 −0.560079 −0.280039 0.959988i \(-0.590348\pi\)
−0.280039 + 0.959988i \(0.590348\pi\)
\(812\) 0 0
\(813\) 16583.0 0.715363
\(814\) 742.944 + 1286.82i 0.0319904 + 0.0554090i
\(815\) 8959.34 15518.0i 0.385070 0.666961i
\(816\) −1957.35 + 3390.23i −0.0839719 + 0.145444i
\(817\) −1190.92 2062.73i −0.0509975 0.0883302i
\(818\) −31751.3 −1.35716
\(819\) 0 0
\(820\) −2964.35 −0.126243
\(821\) 7249.61 + 12556.7i 0.308177 + 0.533778i 0.977964 0.208776i \(-0.0669478\pi\)
−0.669787 + 0.742554i \(0.733614\pi\)
\(822\) 2235.56 3872.11i 0.0948592 0.164301i
\(823\) 5988.57 10372.5i 0.253643 0.439323i −0.710883 0.703310i \(-0.751704\pi\)
0.964526 + 0.263987i \(0.0850377\pi\)
\(824\) 3035.90 + 5258.33i 0.128350 + 0.222309i
\(825\) 2022.84 0.0853649
\(826\) 0 0
\(827\) 27613.5 1.16108 0.580541 0.814231i \(-0.302841\pi\)
0.580541 + 0.814231i \(0.302841\pi\)
\(828\) −1912.50 3312.54i −0.0802703 0.139032i
\(829\) 338.918 587.023i 0.0141992 0.0245937i −0.858839 0.512246i \(-0.828813\pi\)
0.873038 + 0.487653i \(0.162147\pi\)
\(830\) 2004.62 3472.10i 0.0838329 0.145203i
\(831\) −3402.18 5892.75i −0.142022 0.245989i
\(832\) 2893.65 0.120576
\(833\) 0 0
\(834\) −8241.58 −0.342185
\(835\) 2949.61 + 5108.88i 0.122246 + 0.211736i
\(836\) −65.5509 + 113.538i −0.00271187 + 0.00469710i
\(837\) −3946.96 + 6836.34i −0.162995 + 0.282316i
\(838\) 16111.9 + 27906.7i 0.664173 + 1.15038i
\(839\) 42209.6 1.73687 0.868436 0.495801i \(-0.165126\pi\)
0.868436 + 0.495801i \(0.165126\pi\)
\(840\) 0 0
\(841\) 47505.8 1.94784
\(842\) −8691.58 15054.3i −0.355738 0.616157i
\(843\) −1088.48 + 1885.31i −0.0444714 + 0.0770267i
\(844\) 8578.99 14859.2i 0.349883 0.606015i
\(845\) 350.277 + 606.697i 0.0142602 + 0.0246994i
\(846\) 6228.08 0.253104
\(847\) 0 0
\(848\) 6488.46 0.262753
\(849\) −6355.50 11008.0i −0.256914 0.444988i
\(850\) 8479.46 14686.9i 0.342168 0.592653i
\(851\) −6085.90 + 10541.1i −0.245149 + 0.424611i
\(852\) 4089.97 + 7084.03i 0.164460 + 0.284853i
\(853\) −2796.45 −0.112249 −0.0561247 0.998424i \(-0.517874\pi\)
−0.0561247 + 0.998424i \(0.517874\pi\)
\(854\) 0 0
\(855\) −208.582 −0.00834310
\(856\) −5050.06 8746.95i −0.201644 0.349258i
\(857\) −11590.5 + 20075.4i −0.461989 + 0.800189i −0.999060 0.0433483i \(-0.986197\pi\)
0.537071 + 0.843537i \(0.319531\pi\)
\(858\) 879.661 1523.62i 0.0350013 0.0606241i
\(859\) 5948.75 + 10303.5i 0.236285 + 0.409257i 0.959645 0.281213i \(-0.0907369\pi\)
−0.723361 + 0.690471i \(0.757404\pi\)
\(860\) −8645.01 −0.342782
\(861\) 0 0
\(862\) −8390.21 −0.331521
\(863\) 14907.9 + 25821.3i 0.588033 + 1.01850i 0.994490 + 0.104833i \(0.0334308\pi\)
−0.406457 + 0.913670i \(0.633236\pi\)
\(864\) −432.000 + 748.246i −0.0170103 + 0.0294628i
\(865\) 2869.00 4969.25i 0.112773 0.195329i
\(866\) 5426.54 + 9399.04i 0.212934 + 0.368813i
\(867\) 5215.31 0.204292
\(868\) 0 0
\(869\) −1.71256 −6.68523e−5
\(870\) 3688.79 + 6389.17i 0.143749 + 0.248981i
\(871\) −263.294 + 456.038i −0.0102427 + 0.0177408i
\(872\) 8422.11 14587.5i 0.327074 0.566509i
\(873\) 5760.41 + 9977.32i 0.223322 + 0.386805i
\(874\) −1073.94 −0.0415634
\(875\) 0 0
\(876\) 8225.48 0.317253
\(877\) 5169.42 + 8953.70i 0.199041 + 0.344749i 0.948218 0.317621i \(-0.102884\pi\)
−0.749177 + 0.662370i \(0.769551\pi\)
\(878\) 3771.24 6531.98i 0.144958 0.251075i
\(879\) 6560.67 11363.4i 0.251747 0.436039i
\(880\) 237.921 + 412.091i 0.00911399 + 0.0157859i
\(881\) 24140.2 0.923160 0.461580 0.887099i \(-0.347283\pi\)
0.461580 + 0.887099i \(0.347283\pi\)
\(882\) 0 0
\(883\) 12997.6 0.495361 0.247681 0.968842i \(-0.420332\pi\)
0.247681 + 0.968842i \(0.420332\pi\)
\(884\) −7374.85 12773.6i −0.280592 0.485999i
\(885\) 1743.30 3019.49i 0.0662152 0.114688i
\(886\) 5930.30 10271.6i 0.224867 0.389481i
\(887\) −22633.3 39202.0i −0.856766 1.48396i −0.874997 0.484129i \(-0.839137\pi\)
0.0182306 0.999834i \(-0.494197\pi\)
\(888\) 2749.40 0.103901
\(889\) 0 0
\(890\) −536.653 −0.0202120
\(891\) 262.654 + 454.930i 0.00987569 + 0.0171052i
\(892\) −11591.5 + 20077.0i −0.435102 + 0.753619i
\(893\) 874.322 1514.37i 0.0327638 0.0567486i
\(894\) −1861.59 3224.37i −0.0696430 0.120625i
\(895\) 16616.7 0.620596
\(896\) 0 0
\(897\) 14411.7 0.536446
\(898\) 529.065 + 916.367i 0.0196605 + 0.0340530i
\(899\) 39196.6 67890.4i 1.45415 2.51866i
\(900\) 1871.47 3241.48i 0.0693137 0.120055i
\(901\) −16536.7 28642.5i −0.611452 1.05907i
\(902\) 2096.11 0.0773756
\(903\) 0 0
\(904\) 12286.1 0.452024
\(905\) −416.681 721.712i −0.0153049 0.0265089i
\(906\) 5817.79 10076.7i 0.213337 0.369510i
\(907\) 13883.2 24046.5i 0.508253 0.880319i −0.491702 0.870764i \(-0.663625\pi\)
0.999954 0.00955575i \(-0.00304174\pi\)
\(908\) −8208.09 14216.8i −0.299994 0.519605i
\(909\) −11757.5 −0.429012
\(910\) 0 0
\(911\) 18531.2 0.673948 0.336974 0.941514i \(-0.390597\pi\)
0.336974 + 0.941514i \(0.390597\pi\)
\(912\) 121.292 + 210.084i 0.00440392 + 0.00762781i
\(913\) −1417.48 + 2455.14i −0.0513819 + 0.0889961i
\(914\) −10057.2 + 17419.5i −0.363963 + 0.630402i
\(915\) 5167.38 + 8950.17i 0.186698 + 0.323370i
\(916\) −5187.33 −0.187111
\(917\) 0 0
\(918\) 4404.04 0.158339
\(919\) 9046.70 + 15669.3i 0.324726 + 0.562442i 0.981457 0.191683i \(-0.0613947\pi\)
−0.656731 + 0.754125i \(0.728061\pi\)
\(920\) −1948.96 + 3375.69i −0.0698426 + 0.120971i
\(921\) −6200.20 + 10739.1i −0.221828 + 0.384217i
\(922\) 5010.31 + 8678.11i 0.178965 + 0.309977i
\(923\) −30820.1 −1.09908
\(924\) 0 0
\(925\) −11910.7 −0.423375
\(926\) 7124.38 + 12339.8i 0.252831 + 0.437916i
\(927\) 3415.39 5915.62i 0.121010 0.209595i
\(928\) 4290.11 7430.69i 0.151756 0.262850i
\(929\) −5311.26 9199.37i −0.187574 0.324888i 0.756867 0.653569i \(-0.226729\pi\)
−0.944441 + 0.328681i \(0.893396\pi\)
\(930\) 8044.41 0.283642
\(931\) 0 0
\(932\) −5913.34 −0.207830
\(933\) −7594.85 13154.7i −0.266500 0.461591i
\(934\) −7501.44 + 12992.9i −0.262799 + 0.455182i
\(935\) 1212.75 2100.54i 0.0424183 0.0734706i
\(936\) −1627.68 2819.22i −0.0568400 0.0984498i
\(937\) 16057.6 0.559851 0.279925 0.960022i \(-0.409690\pi\)
0.279925 + 0.960022i \(0.409690\pi\)
\(938\) 0 0
\(939\) 22234.7 0.772738
\(940\) −3173.40 5496.49i −0.110112 0.190719i
\(941\) −27576.6 + 47764.1i −0.955338 + 1.65469i −0.221745 + 0.975105i \(0.571175\pi\)
−0.733593 + 0.679589i \(0.762158\pi\)
\(942\) 1238.53 2145.20i 0.0428381 0.0741977i
\(943\) 8585.25 + 14870.1i 0.296473 + 0.513507i
\(944\) −4054.97 −0.139807
\(945\) 0 0
\(946\) 6112.94 0.210094
\(947\) −9392.86 16268.9i −0.322309 0.558256i 0.658655 0.752445i \(-0.271126\pi\)
−0.980964 + 0.194189i \(0.937792\pi\)
\(948\) −1.58441 + 2.74428i −5.42820e−5 + 9.40191e-5i
\(949\) −15495.9 + 26839.6i −0.530049 + 0.918072i
\(950\) −525.449 910.104i −0.0179451 0.0310818i
\(951\) −20211.2 −0.689161
\(952\) 0 0
\(953\) −36499.4 −1.24064 −0.620321 0.784348i \(-0.712998\pi\)
−0.620321 + 0.784348i \(0.712998\pi\)
\(954\) −3649.76 6321.57i −0.123863 0.214537i
\(955\) −3396.42 + 5882.76i −0.115084 + 0.199332i
\(956\) 7553.84 13083.6i 0.255553 0.442631i
\(957\) −2608.37 4517.83i −0.0881051 0.152602i
\(958\) −16347.6 −0.551323
\(959\) 0 0
\(960\) 880.471 0.0296011
\(961\) −27843.9 48227.0i −0.934641 1.61885i
\(962\) −5179.55 + 8971.25i −0.173592 + 0.300670i
\(963\) −5681.31 + 9840.32i −0.190112 + 0.329283i
\(964\) 7992.76 + 13843.9i 0.267043 + 0.462532i
\(965\) −1635.79 −0.0545677
\(966\) 0 0
\(967\) 26059.9 0.866627 0.433314 0.901243i \(-0.357344\pi\)
0.433314 + 0.901243i \(0.357344\pi\)
\(968\) 5155.76 + 8930.05i 0.171191 + 0.296511i
\(969\) 618.257 1070.85i 0.0204967 0.0355013i
\(970\) 5870.22 10167.5i 0.194311 0.336556i
\(971\) −10844.5 18783.2i −0.358410 0.620785i 0.629285 0.777174i \(-0.283348\pi\)
−0.987695 + 0.156390i \(0.950014\pi\)
\(972\) 972.000 0.0320750
\(973\) 0 0
\(974\) −23937.6 −0.787484
\(975\) 7051.26 + 12213.1i 0.231611 + 0.401163i
\(976\) 6009.74 10409.2i 0.197097 0.341383i
\(977\) −1059.59 + 1835.27i −0.0346975 + 0.0600978i −0.882853 0.469650i \(-0.844380\pi\)
0.848155 + 0.529748i \(0.177713\pi\)
\(978\) 11722.3 + 20303.7i 0.383270 + 0.663844i
\(979\) 379.471 0.0123881
\(980\) 0 0
\(981\) −18949.7 −0.616737
\(982\) −2079.96 3602.59i −0.0675908 0.117071i
\(983\) 24252.1 42005.8i 0.786898 1.36295i −0.140960 0.990015i \(-0.545019\pi\)
0.927859 0.372932i \(-0.121648\pi\)
\(984\) 1939.26 3358.90i 0.0628266 0.108819i
\(985\) −11213.5 19422.3i −0.362731 0.628269i
\(986\) −43735.7 −1.41261
\(987\) 0 0
\(988\) −913.998 −0.0294313
\(989\) 25037.4 + 43366.1i 0.804999 + 1.39430i
\(990\) 267.661 463.603i 0.00859275 0.0148831i
\(991\) −1021.92 + 1770.02i −0.0327572 + 0.0567372i −0.881939 0.471363i \(-0.843762\pi\)
0.849182 + 0.528100i \(0.177095\pi\)
\(992\) −4677.88 8102.33i −0.149721 0.259324i
\(993\) 33527.8 1.07147
\(994\) 0 0
\(995\) 16246.8 0.517645
\(996\) 2622.82 + 4542.86i 0.0834411 + 0.144524i
\(997\) 13369.5 23156.6i 0.424689 0.735583i −0.571702 0.820461i \(-0.693717\pi\)
0.996391 + 0.0848782i \(0.0270501\pi\)
\(998\) −12834.4 + 22229.9i −0.407081 + 0.705084i
\(999\) −1546.54 2678.68i −0.0489793 0.0848346i
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 294.4.e.k.67.2 4
3.2 odd 2 882.4.g.bk.361.1 4
7.2 even 3 inner 294.4.e.k.79.2 4
7.3 odd 6 294.4.a.l.1.2 2
7.4 even 3 294.4.a.o.1.1 yes 2
7.5 odd 6 294.4.e.m.79.1 4
7.6 odd 2 294.4.e.m.67.1 4
21.2 odd 6 882.4.g.bk.667.1 4
21.5 even 6 882.4.g.be.667.2 4
21.11 odd 6 882.4.a.t.1.2 2
21.17 even 6 882.4.a.bb.1.1 2
21.20 even 2 882.4.g.be.361.2 4
28.3 even 6 2352.4.a.bw.1.2 2
28.11 odd 6 2352.4.a.bu.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
294.4.a.l.1.2 2 7.3 odd 6
294.4.a.o.1.1 yes 2 7.4 even 3
294.4.e.k.67.2 4 1.1 even 1 trivial
294.4.e.k.79.2 4 7.2 even 3 inner
294.4.e.m.67.1 4 7.6 odd 2
294.4.e.m.79.1 4 7.5 odd 6
882.4.a.t.1.2 2 21.11 odd 6
882.4.a.bb.1.1 2 21.17 even 6
882.4.g.be.361.2 4 21.20 even 2
882.4.g.be.667.2 4 21.5 even 6
882.4.g.bk.361.1 4 3.2 odd 2
882.4.g.bk.667.1 4 21.2 odd 6
2352.4.a.bu.1.1 2 28.11 odd 6
2352.4.a.bw.1.2 2 28.3 even 6