Properties

Label 378.4.k.d.269.2
Level $378$
Weight $4$
Character 378.269
Analytic conductor $22.303$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [378,4,Mod(215,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.215");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 378.k (of order \(6\), 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: \(22.3027219822\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 2 x^{19} + 2 x^{18} - 32 x^{17} - 669 x^{16} + 1752 x^{15} - 1654 x^{14} + 13878 x^{13} + 494085 x^{12} - 780096 x^{11} + 556152 x^{10} - 2898760 x^{9} + \cdots + 2458624 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{18}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.2
Root \(-4.83258 + 1.29489i\) of defining polynomial
Character \(\chi\) \(=\) 378.269
Dual form 378.4.k.d.215.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.73205 + 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-3.43124 - 5.94308i) q^{5} +(-18.5152 - 0.434813i) q^{7} +8.00000i q^{8} +O(q^{10})\) \(q+(-1.73205 + 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-3.43124 - 5.94308i) q^{5} +(-18.5152 - 0.434813i) q^{7} +8.00000i q^{8} +(11.8862 + 6.86248i) q^{10} +(28.6032 + 16.5141i) q^{11} +65.9110i q^{13} +(32.5040 - 17.7620i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-7.20650 + 12.4820i) q^{17} +(-44.9254 + 25.9377i) q^{19} -27.4499 q^{20} -66.0562 q^{22} +(174.131 - 100.535i) q^{23} +(38.9532 - 67.4689i) q^{25} +(-65.9110 - 114.161i) q^{26} +(-38.5365 + 63.2688i) q^{28} -227.304i q^{29} +(-24.5744 - 14.1881i) q^{31} +(27.7128 + 16.0000i) q^{32} -28.8260i q^{34} +(60.9458 + 111.529i) q^{35} +(-101.081 - 175.078i) q^{37} +(51.8754 - 89.8508i) q^{38} +(47.5446 - 27.4499i) q^{40} +34.6120 q^{41} -483.052 q^{43} +(114.413 - 66.0562i) q^{44} +(-201.070 + 348.263i) q^{46} +(-95.7687 - 165.876i) q^{47} +(342.622 + 16.1012i) q^{49} +155.813i q^{50} +(228.322 + 131.822i) q^{52} +(-75.4532 - 43.5629i) q^{53} -226.655i q^{55} +(3.47850 - 148.121i) q^{56} +(227.304 + 393.702i) q^{58} +(292.449 - 506.536i) q^{59} +(303.713 - 175.349i) q^{61} +56.7523 q^{62} -64.0000 q^{64} +(391.714 - 226.156i) q^{65} +(315.762 - 546.916i) q^{67} +(28.8260 + 49.9281i) q^{68} +(-217.090 - 132.228i) q^{70} -932.935i q^{71} +(191.352 + 110.477i) q^{73} +(350.156 + 202.163i) q^{74} +207.501i q^{76} +(-522.412 - 318.197i) q^{77} +(228.057 + 395.007i) q^{79} +(-54.8998 + 95.0893i) q^{80} +(-59.9498 + 34.6120i) q^{82} +1363.85 q^{83} +98.9088 q^{85} +(836.670 - 483.052i) q^{86} +(-132.112 + 228.825i) q^{88} +(358.658 + 621.215i) q^{89} +(28.6589 - 1220.35i) q^{91} -804.279i q^{92} +(331.752 + 191.537i) q^{94} +(308.299 + 177.997i) q^{95} -9.90916i q^{97} +(-609.540 + 314.734i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 40 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 40 q^{4} + 4 q^{7} - 24 q^{10} - 160 q^{16} + 408 q^{19} + 240 q^{22} - 646 q^{25} + 56 q^{28} - 102 q^{31} + 194 q^{37} - 96 q^{40} - 2332 q^{43} - 624 q^{46} + 2840 q^{49} - 648 q^{52} + 96 q^{58} + 1878 q^{61} - 1280 q^{64} - 386 q^{67} + 3672 q^{70} + 1788 q^{73} + 814 q^{79} - 672 q^{82} - 4560 q^{85} + 480 q^{88} + 2724 q^{91} - 1536 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73205 + 1.00000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 2.00000 3.46410i 0.250000 0.433013i
\(5\) −3.43124 5.94308i −0.306899 0.531565i 0.670783 0.741654i \(-0.265958\pi\)
−0.977682 + 0.210088i \(0.932625\pi\)
\(6\) 0 0
\(7\) −18.5152 0.434813i −0.999724 0.0234777i
\(8\) 8.00000i 0.353553i
\(9\) 0 0
\(10\) 11.8862 + 6.86248i 0.375873 + 0.217011i
\(11\) 28.6032 + 16.5141i 0.784017 + 0.452652i 0.837852 0.545898i \(-0.183811\pi\)
−0.0538351 + 0.998550i \(0.517145\pi\)
\(12\) 0 0
\(13\) 65.9110i 1.40619i 0.711097 + 0.703093i \(0.248198\pi\)
−0.711097 + 0.703093i \(0.751802\pi\)
\(14\) 32.5040 17.7620i 0.620504 0.339079i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −7.20650 + 12.4820i −0.102814 + 0.178078i −0.912843 0.408311i \(-0.866118\pi\)
0.810029 + 0.586390i \(0.199451\pi\)
\(18\) 0 0
\(19\) −44.9254 + 25.9377i −0.542452 + 0.313185i −0.746072 0.665865i \(-0.768063\pi\)
0.203620 + 0.979050i \(0.434729\pi\)
\(20\) −27.4499 −0.306899
\(21\) 0 0
\(22\) −66.0562 −0.640147
\(23\) 174.131 100.535i 1.57865 0.911433i 0.583600 0.812041i \(-0.301644\pi\)
0.995048 0.0993915i \(-0.0316896\pi\)
\(24\) 0 0
\(25\) 38.9532 67.4689i 0.311626 0.539752i
\(26\) −65.9110 114.161i −0.497162 0.861110i
\(27\) 0 0
\(28\) −38.5365 + 63.2688i −0.260097 + 0.427024i
\(29\) 227.304i 1.45549i −0.685847 0.727746i \(-0.740568\pi\)
0.685847 0.727746i \(-0.259432\pi\)
\(30\) 0 0
\(31\) −24.5744 14.1881i −0.142377 0.0822017i 0.427119 0.904195i \(-0.359528\pi\)
−0.569497 + 0.821994i \(0.692862\pi\)
\(32\) 27.7128 + 16.0000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 28.8260i 0.145400i
\(35\) 60.9458 + 111.529i 0.294335 + 0.538624i
\(36\) 0 0
\(37\) −101.081 175.078i −0.449126 0.777910i 0.549203 0.835689i \(-0.314931\pi\)
−0.998329 + 0.0577792i \(0.981598\pi\)
\(38\) 51.8754 89.8508i 0.221455 0.383572i
\(39\) 0 0
\(40\) 47.5446 27.4499i 0.187937 0.108505i
\(41\) 34.6120 0.131841 0.0659206 0.997825i \(-0.479002\pi\)
0.0659206 + 0.997825i \(0.479002\pi\)
\(42\) 0 0
\(43\) −483.052 −1.71313 −0.856566 0.516038i \(-0.827406\pi\)
−0.856566 + 0.516038i \(0.827406\pi\)
\(44\) 114.413 66.0562i 0.392008 0.226326i
\(45\) 0 0
\(46\) −201.070 + 348.263i −0.644480 + 1.11627i
\(47\) −95.7687 165.876i −0.297219 0.514799i 0.678280 0.734804i \(-0.262726\pi\)
−0.975499 + 0.220005i \(0.929393\pi\)
\(48\) 0 0
\(49\) 342.622 + 16.1012i 0.998898 + 0.0469424i
\(50\) 155.813i 0.440705i
\(51\) 0 0
\(52\) 228.322 + 131.822i 0.608897 + 0.351547i
\(53\) −75.4532 43.5629i −0.195553 0.112902i 0.399027 0.916939i \(-0.369348\pi\)
−0.594579 + 0.804037i \(0.702681\pi\)
\(54\) 0 0
\(55\) 226.655i 0.555675i
\(56\) 3.47850 148.121i 0.00830061 0.353456i
\(57\) 0 0
\(58\) 227.304 + 393.702i 0.514594 + 0.891303i
\(59\) 292.449 506.536i 0.645315 1.11772i −0.338913 0.940818i \(-0.610059\pi\)
0.984229 0.176901i \(-0.0566073\pi\)
\(60\) 0 0
\(61\) 303.713 175.349i 0.637483 0.368051i −0.146162 0.989261i \(-0.546692\pi\)
0.783644 + 0.621210i \(0.213359\pi\)
\(62\) 56.7523 0.116251
\(63\) 0 0
\(64\) −64.0000 −0.125000
\(65\) 391.714 226.156i 0.747480 0.431558i
\(66\) 0 0
\(67\) 315.762 546.916i 0.575768 0.997260i −0.420190 0.907436i \(-0.638036\pi\)
0.995958 0.0898233i \(-0.0286302\pi\)
\(68\) 28.8260 + 49.9281i 0.0514068 + 0.0890392i
\(69\) 0 0
\(70\) −217.090 132.228i −0.370675 0.225775i
\(71\) 932.935i 1.55942i −0.626139 0.779712i \(-0.715366\pi\)
0.626139 0.779712i \(-0.284634\pi\)
\(72\) 0 0
\(73\) 191.352 + 110.477i 0.306795 + 0.177128i 0.645491 0.763768i \(-0.276653\pi\)
−0.338697 + 0.940896i \(0.609986\pi\)
\(74\) 350.156 + 202.163i 0.550065 + 0.317580i
\(75\) 0 0
\(76\) 207.501i 0.313185i
\(77\) −522.412 318.197i −0.773174 0.470934i
\(78\) 0 0
\(79\) 228.057 + 395.007i 0.324790 + 0.562553i 0.981470 0.191616i \(-0.0613729\pi\)
−0.656680 + 0.754170i \(0.728040\pi\)
\(80\) −54.8998 + 95.0893i −0.0767248 + 0.132891i
\(81\) 0 0
\(82\) −59.9498 + 34.6120i −0.0807360 + 0.0466129i
\(83\) 1363.85 1.80364 0.901822 0.432107i \(-0.142230\pi\)
0.901822 + 0.432107i \(0.142230\pi\)
\(84\) 0 0
\(85\) 98.9088 0.126214
\(86\) 836.670 483.052i 1.04907 0.605684i
\(87\) 0 0
\(88\) −132.112 + 228.825i −0.160037 + 0.277192i
\(89\) 358.658 + 621.215i 0.427165 + 0.739872i 0.996620 0.0821507i \(-0.0261789\pi\)
−0.569455 + 0.822023i \(0.692846\pi\)
\(90\) 0 0
\(91\) 28.6589 1220.35i 0.0330140 1.40580i
\(92\) 804.279i 0.911433i
\(93\) 0 0
\(94\) 331.752 + 191.537i 0.364018 + 0.210166i
\(95\) 308.299 + 177.997i 0.332956 + 0.192232i
\(96\) 0 0
\(97\) 9.90916i 0.0103724i −0.999987 0.00518620i \(-0.998349\pi\)
0.999987 0.00518620i \(-0.00165083\pi\)
\(98\) −609.540 + 314.734i −0.628294 + 0.324417i
\(99\) 0 0
\(100\) −155.813 269.876i −0.155813 0.269876i
\(101\) −47.7022 + 82.6226i −0.0469955 + 0.0813985i −0.888566 0.458748i \(-0.848298\pi\)
0.841571 + 0.540147i \(0.181631\pi\)
\(102\) 0 0
\(103\) 983.832 568.016i 0.941163 0.543381i 0.0508385 0.998707i \(-0.483811\pi\)
0.890325 + 0.455326i \(0.150477\pi\)
\(104\) −527.288 −0.497162
\(105\) 0 0
\(106\) 174.252 0.159668
\(107\) −1799.33 + 1038.84i −1.62568 + 0.938584i −0.640313 + 0.768114i \(0.721195\pi\)
−0.985363 + 0.170470i \(0.945471\pi\)
\(108\) 0 0
\(109\) 59.1994 102.536i 0.0520208 0.0901027i −0.838842 0.544374i \(-0.816767\pi\)
0.890863 + 0.454272i \(0.150100\pi\)
\(110\) 226.655 + 392.577i 0.196461 + 0.340280i
\(111\) 0 0
\(112\) 142.096 + 260.032i 0.119882 + 0.219381i
\(113\) 112.853i 0.0939496i 0.998896 + 0.0469748i \(0.0149580\pi\)
−0.998896 + 0.0469748i \(0.985042\pi\)
\(114\) 0 0
\(115\) −1194.97 689.918i −0.968972 0.559436i
\(116\) −787.403 454.608i −0.630246 0.363873i
\(117\) 0 0
\(118\) 1169.80i 0.912614i
\(119\) 138.857 227.973i 0.106966 0.175616i
\(120\) 0 0
\(121\) −120.072 207.970i −0.0902117 0.156251i
\(122\) −350.697 + 607.426i −0.260251 + 0.450768i
\(123\) 0 0
\(124\) −98.2978 + 56.7523i −0.0711887 + 0.0411008i
\(125\) −1392.44 −0.996349
\(126\) 0 0
\(127\) −857.420 −0.599084 −0.299542 0.954083i \(-0.596834\pi\)
−0.299542 + 0.954083i \(0.596834\pi\)
\(128\) 110.851 64.0000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −452.313 + 783.429i −0.305157 + 0.528548i
\(131\) 357.900 + 619.902i 0.238702 + 0.413443i 0.960342 0.278825i \(-0.0899449\pi\)
−0.721640 + 0.692268i \(0.756612\pi\)
\(132\) 0 0
\(133\) 843.078 460.706i 0.549655 0.300363i
\(134\) 1263.05i 0.814259i
\(135\) 0 0
\(136\) −99.8562 57.6520i −0.0629603 0.0363501i
\(137\) 114.971 + 66.3786i 0.0716982 + 0.0413950i 0.535421 0.844586i \(-0.320153\pi\)
−0.463722 + 0.885981i \(0.653486\pi\)
\(138\) 0 0
\(139\) 2907.60i 1.77424i −0.461540 0.887119i \(-0.652703\pi\)
0.461540 0.887119i \(-0.347297\pi\)
\(140\) 508.239 + 11.9356i 0.306815 + 0.00720528i
\(141\) 0 0
\(142\) 932.935 + 1615.89i 0.551339 + 0.954948i
\(143\) −1088.46 + 1885.27i −0.636514 + 1.10247i
\(144\) 0 0
\(145\) −1350.88 + 779.933i −0.773688 + 0.446689i
\(146\) −441.908 −0.250497
\(147\) 0 0
\(148\) −808.651 −0.449126
\(149\) 2517.63 1453.55i 1.38424 0.799192i 0.391583 0.920143i \(-0.371928\pi\)
0.992659 + 0.120951i \(0.0385943\pi\)
\(150\) 0 0
\(151\) −451.859 + 782.642i −0.243521 + 0.421791i −0.961715 0.274052i \(-0.911636\pi\)
0.718193 + 0.695843i \(0.244969\pi\)
\(152\) −207.501 359.403i −0.110728 0.191786i
\(153\) 0 0
\(154\) 1223.04 + 28.7221i 0.639971 + 0.0150292i
\(155\) 194.730i 0.100911i
\(156\) 0 0
\(157\) 2157.41 + 1245.58i 1.09669 + 0.633174i 0.935350 0.353725i \(-0.115085\pi\)
0.161340 + 0.986899i \(0.448418\pi\)
\(158\) −790.013 456.114i −0.397785 0.229661i
\(159\) 0 0
\(160\) 219.599i 0.108505i
\(161\) −3267.78 + 1785.70i −1.59961 + 0.874119i
\(162\) 0 0
\(163\) 727.153 + 1259.47i 0.349417 + 0.605208i 0.986146 0.165879i \(-0.0530463\pi\)
−0.636729 + 0.771088i \(0.719713\pi\)
\(164\) 69.2241 119.900i 0.0329603 0.0570890i
\(165\) 0 0
\(166\) −2362.27 + 1363.85i −1.10450 + 0.637685i
\(167\) −1402.20 −0.649733 −0.324866 0.945760i \(-0.605319\pi\)
−0.324866 + 0.945760i \(0.605319\pi\)
\(168\) 0 0
\(169\) −2147.26 −0.977362
\(170\) −171.315 + 98.9088i −0.0772898 + 0.0446233i
\(171\) 0 0
\(172\) −966.103 + 1673.34i −0.428283 + 0.741808i
\(173\) 1458.60 + 2526.36i 0.641012 + 1.11027i 0.985207 + 0.171367i \(0.0548185\pi\)
−0.344195 + 0.938898i \(0.611848\pi\)
\(174\) 0 0
\(175\) −750.561 + 1232.26i −0.324212 + 0.532287i
\(176\) 528.450i 0.226326i
\(177\) 0 0
\(178\) −1242.43 717.317i −0.523169 0.302052i
\(179\) −2921.84 1686.93i −1.22005 0.704396i −0.255121 0.966909i \(-0.582115\pi\)
−0.964928 + 0.262513i \(0.915449\pi\)
\(180\) 0 0
\(181\) 3857.00i 1.58392i −0.610576 0.791958i \(-0.709062\pi\)
0.610576 0.791958i \(-0.290938\pi\)
\(182\) 1170.71 + 2142.37i 0.476808 + 0.872545i
\(183\) 0 0
\(184\) 804.279 + 1393.05i 0.322240 + 0.558136i
\(185\) −693.669 + 1201.47i −0.275673 + 0.477480i
\(186\) 0 0
\(187\) −412.258 + 238.017i −0.161215 + 0.0930777i
\(188\) −766.149 −0.297219
\(189\) 0 0
\(190\) −711.987 −0.271858
\(191\) 1849.52 1067.82i 0.700662 0.404527i −0.106932 0.994266i \(-0.534103\pi\)
0.807594 + 0.589739i \(0.200769\pi\)
\(192\) 0 0
\(193\) 566.229 980.737i 0.211182 0.365777i −0.740903 0.671612i \(-0.765602\pi\)
0.952085 + 0.305835i \(0.0989355\pi\)
\(194\) 9.90916 + 17.1632i 0.00366720 + 0.00635177i
\(195\) 0 0
\(196\) 741.020 1154.67i 0.270051 0.420800i
\(197\) 1972.82i 0.713490i 0.934202 + 0.356745i \(0.116114\pi\)
−0.934202 + 0.356745i \(0.883886\pi\)
\(198\) 0 0
\(199\) 1006.36 + 581.025i 0.358489 + 0.206974i 0.668418 0.743786i \(-0.266972\pi\)
−0.309929 + 0.950760i \(0.600305\pi\)
\(200\) 539.752 + 311.626i 0.190831 + 0.110176i
\(201\) 0 0
\(202\) 190.809i 0.0664616i
\(203\) −98.8346 + 4208.56i −0.0341716 + 1.45509i
\(204\) 0 0
\(205\) −118.762 205.702i −0.0404620 0.0700822i
\(206\) −1136.03 + 1967.66i −0.384228 + 0.665503i
\(207\) 0 0
\(208\) 913.290 527.288i 0.304448 0.175773i
\(209\) −1713.35 −0.567055
\(210\) 0 0
\(211\) −3561.70 −1.16207 −0.581037 0.813877i \(-0.697353\pi\)
−0.581037 + 0.813877i \(0.697353\pi\)
\(212\) −301.813 + 174.252i −0.0977764 + 0.0564512i
\(213\) 0 0
\(214\) 2077.68 3598.65i 0.663679 1.14953i
\(215\) 1657.46 + 2870.81i 0.525759 + 0.910641i
\(216\) 0 0
\(217\) 448.831 + 273.379i 0.140408 + 0.0855217i
\(218\) 236.797i 0.0735686i
\(219\) 0 0
\(220\) −785.155 453.309i −0.240614 0.138919i
\(221\) −822.703 474.988i −0.250412 0.144575i
\(222\) 0 0
\(223\) 479.700i 0.144050i 0.997403 + 0.0720249i \(0.0229461\pi\)
−0.997403 + 0.0720249i \(0.977054\pi\)
\(224\) −506.150 308.292i −0.150976 0.0919583i
\(225\) 0 0
\(226\) −112.853 195.467i −0.0332162 0.0575321i
\(227\) 2054.69 3558.83i 0.600769 1.04056i −0.391935 0.919993i \(-0.628194\pi\)
0.992705 0.120570i \(-0.0384724\pi\)
\(228\) 0 0
\(229\) −1965.47 + 1134.77i −0.567170 + 0.327456i −0.756018 0.654550i \(-0.772858\pi\)
0.188848 + 0.982006i \(0.439525\pi\)
\(230\) 2759.67 0.791162
\(231\) 0 0
\(232\) 1818.43 0.514594
\(233\) −292.043 + 168.611i −0.0821133 + 0.0474081i −0.540494 0.841348i \(-0.681763\pi\)
0.458381 + 0.888756i \(0.348429\pi\)
\(234\) 0 0
\(235\) −657.210 + 1138.32i −0.182433 + 0.315983i
\(236\) −1169.80 2026.15i −0.322658 0.558859i
\(237\) 0 0
\(238\) −12.5339 + 533.718i −0.00341367 + 0.145360i
\(239\) 1119.50i 0.302990i −0.988458 0.151495i \(-0.951591\pi\)
0.988458 0.151495i \(-0.0484088\pi\)
\(240\) 0 0
\(241\) 3778.92 + 2181.76i 1.01005 + 0.583152i 0.911206 0.411951i \(-0.135153\pi\)
0.0988426 + 0.995103i \(0.468486\pi\)
\(242\) 415.941 + 240.144i 0.110486 + 0.0637893i
\(243\) 0 0
\(244\) 1402.79i 0.368051i
\(245\) −1079.93 2091.48i −0.281608 0.545386i
\(246\) 0 0
\(247\) −1709.58 2961.08i −0.440396 0.762789i
\(248\) 113.505 196.596i 0.0290627 0.0503380i
\(249\) 0 0
\(250\) 2411.78 1392.44i 0.610137 0.352263i
\(251\) −3878.06 −0.975222 −0.487611 0.873061i \(-0.662132\pi\)
−0.487611 + 0.873061i \(0.662132\pi\)
\(252\) 0 0
\(253\) 6640.95 1.65025
\(254\) 1485.09 857.420i 0.366863 0.211808i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 300.225 + 520.005i 0.0728698 + 0.126214i 0.900158 0.435564i \(-0.143451\pi\)
−0.827288 + 0.561778i \(0.810118\pi\)
\(258\) 0 0
\(259\) 1795.41 + 3285.55i 0.430739 + 0.788240i
\(260\) 1809.25i 0.431558i
\(261\) 0 0
\(262\) −1239.80 715.801i −0.292349 0.168788i
\(263\) −3050.60 1761.27i −0.715240 0.412944i 0.0977581 0.995210i \(-0.468833\pi\)
−0.812998 + 0.582266i \(0.802166\pi\)
\(264\) 0 0
\(265\) 597.899i 0.138599i
\(266\) −999.549 + 1641.04i −0.230399 + 0.378267i
\(267\) 0 0
\(268\) −1263.05 2187.66i −0.287884 0.498630i
\(269\) 2938.40 5089.46i 0.666012 1.15357i −0.312998 0.949754i \(-0.601333\pi\)
0.979010 0.203813i \(-0.0653335\pi\)
\(270\) 0 0
\(271\) 2902.80 1675.93i 0.650673 0.375666i −0.138041 0.990427i \(-0.544080\pi\)
0.788714 + 0.614760i \(0.210747\pi\)
\(272\) 230.608 0.0514068
\(273\) 0 0
\(274\) −265.515 −0.0585413
\(275\) 2228.37 1286.55i 0.488640 0.282116i
\(276\) 0 0
\(277\) −2396.31 + 4150.53i −0.519785 + 0.900293i 0.479951 + 0.877295i \(0.340654\pi\)
−0.999736 + 0.0229980i \(0.992679\pi\)
\(278\) 2907.60 + 5036.11i 0.627288 + 1.08649i
\(279\) 0 0
\(280\) −892.232 + 487.566i −0.190432 + 0.104063i
\(281\) 6132.70i 1.30194i −0.759102 0.650971i \(-0.774362\pi\)
0.759102 0.650971i \(-0.225638\pi\)
\(282\) 0 0
\(283\) −2487.31 1436.05i −0.522458 0.301641i 0.215482 0.976508i \(-0.430868\pi\)
−0.737940 + 0.674867i \(0.764201\pi\)
\(284\) −3231.78 1865.87i −0.675250 0.389856i
\(285\) 0 0
\(286\) 4353.83i 0.900166i
\(287\) −640.847 15.0498i −0.131805 0.00309533i
\(288\) 0 0
\(289\) 2352.63 + 4074.88i 0.478859 + 0.829408i
\(290\) 1559.87 2701.77i 0.315857 0.547080i
\(291\) 0 0
\(292\) 765.407 441.908i 0.153397 0.0885640i
\(293\) 4741.31 0.945360 0.472680 0.881234i \(-0.343287\pi\)
0.472680 + 0.881234i \(0.343287\pi\)
\(294\) 0 0
\(295\) −4013.85 −0.792187
\(296\) 1400.62 808.651i 0.275033 0.158790i
\(297\) 0 0
\(298\) −2907.10 + 5035.25i −0.565114 + 0.978806i
\(299\) 6626.35 + 11477.2i 1.28165 + 2.21987i
\(300\) 0 0
\(301\) 8943.77 + 210.037i 1.71266 + 0.0402204i
\(302\) 1807.43i 0.344391i
\(303\) 0 0
\(304\) 718.806 + 415.003i 0.135613 + 0.0782962i
\(305\) −2084.22 1203.33i −0.391286 0.225909i
\(306\) 0 0
\(307\) 6632.39i 1.23300i −0.787355 0.616499i \(-0.788550\pi\)
0.787355 0.616499i \(-0.211450\pi\)
\(308\) −2147.09 + 1173.29i −0.397214 + 0.217060i
\(309\) 0 0
\(310\) −194.730 337.283i −0.0356773 0.0617948i
\(311\) 3785.11 6556.00i 0.690140 1.19536i −0.281651 0.959517i \(-0.590882\pi\)
0.971792 0.235841i \(-0.0757846\pi\)
\(312\) 0 0
\(313\) −5933.44 + 3425.67i −1.07150 + 0.618628i −0.928590 0.371108i \(-0.878978\pi\)
−0.142906 + 0.989736i \(0.545645\pi\)
\(314\) −4982.33 −0.895443
\(315\) 0 0
\(316\) 1824.46 0.324790
\(317\) 4568.52 2637.63i 0.809443 0.467332i −0.0373193 0.999303i \(-0.511882\pi\)
0.846762 + 0.531971i \(0.178549\pi\)
\(318\) 0 0
\(319\) 3753.71 6501.61i 0.658832 1.14113i
\(320\) 219.599 + 380.357i 0.0383624 + 0.0664456i
\(321\) 0 0
\(322\) 3874.26 6360.71i 0.670510 1.10083i
\(323\) 747.679i 0.128799i
\(324\) 0 0
\(325\) 4446.95 + 2567.45i 0.758992 + 0.438204i
\(326\) −2518.93 1454.31i −0.427947 0.247075i
\(327\) 0 0
\(328\) 276.896i 0.0466129i
\(329\) 1701.05 + 3112.87i 0.285051 + 0.521635i
\(330\) 0 0
\(331\) 3089.55 + 5351.25i 0.513042 + 0.888614i 0.999886 + 0.0151252i \(0.00481468\pi\)
−0.486844 + 0.873489i \(0.661852\pi\)
\(332\) 2727.71 4724.53i 0.450911 0.781001i
\(333\) 0 0
\(334\) 2428.68 1402.20i 0.397878 0.229715i
\(335\) −4333.82 −0.706811
\(336\) 0 0
\(337\) −3792.02 −0.612951 −0.306475 0.951879i \(-0.599150\pi\)
−0.306475 + 0.951879i \(0.599150\pi\)
\(338\) 3719.17 2147.26i 0.598509 0.345550i
\(339\) 0 0
\(340\) 197.818 342.630i 0.0315534 0.0546522i
\(341\) −468.605 811.648i −0.0744175 0.128895i
\(342\) 0 0
\(343\) −6336.70 447.093i −0.997520 0.0703813i
\(344\) 3864.41i 0.605684i
\(345\) 0 0
\(346\) −5052.73 2917.19i −0.785076 0.453264i
\(347\) −6380.27 3683.65i −0.987062 0.569881i −0.0826675 0.996577i \(-0.526344\pi\)
−0.904395 + 0.426696i \(0.859677\pi\)
\(348\) 0 0
\(349\) 9408.31i 1.44302i 0.692402 + 0.721512i \(0.256553\pi\)
−0.692402 + 0.721512i \(0.743447\pi\)
\(350\) 67.7494 2884.90i 0.0103467 0.440584i
\(351\) 0 0
\(352\) 528.450 + 915.302i 0.0800184 + 0.138596i
\(353\) −1411.89 + 2445.47i −0.212883 + 0.368723i −0.952615 0.304177i \(-0.901619\pi\)
0.739733 + 0.672901i \(0.234952\pi\)
\(354\) 0 0
\(355\) −5544.51 + 3201.12i −0.828935 + 0.478586i
\(356\) 2869.27 0.427165
\(357\) 0 0
\(358\) 6747.71 0.996167
\(359\) 9971.93 5757.30i 1.46601 0.846402i 0.466734 0.884398i \(-0.345431\pi\)
0.999278 + 0.0379953i \(0.0120972\pi\)
\(360\) 0 0
\(361\) −2083.97 + 3609.55i −0.303830 + 0.526250i
\(362\) 3857.00 + 6680.52i 0.559999 + 0.969946i
\(363\) 0 0
\(364\) −4170.11 2539.98i −0.600475 0.365745i
\(365\) 1516.29i 0.217442i
\(366\) 0 0
\(367\) −7817.42 4513.39i −1.11190 0.641954i −0.172577 0.984996i \(-0.555209\pi\)
−0.939320 + 0.343042i \(0.888543\pi\)
\(368\) −2786.10 1608.56i −0.394662 0.227858i
\(369\) 0 0
\(370\) 2774.67i 0.389861i
\(371\) 1378.09 + 839.382i 0.192848 + 0.117462i
\(372\) 0 0
\(373\) 1982.76 + 3434.23i 0.275236 + 0.476723i 0.970195 0.242327i \(-0.0779105\pi\)
−0.694958 + 0.719050i \(0.744577\pi\)
\(374\) 476.034 824.515i 0.0658159 0.113996i
\(375\) 0 0
\(376\) 1327.01 766.149i 0.182009 0.105083i
\(377\) 14981.8 2.04669
\(378\) 0 0
\(379\) −12103.7 −1.64044 −0.820221 0.572047i \(-0.806149\pi\)
−0.820221 + 0.572047i \(0.806149\pi\)
\(380\) 1233.20 711.987i 0.166478 0.0961162i
\(381\) 0 0
\(382\) −2135.64 + 3699.03i −0.286044 + 0.495443i
\(383\) −2263.10 3919.81i −0.301930 0.522958i 0.674643 0.738144i \(-0.264297\pi\)
−0.976573 + 0.215186i \(0.930964\pi\)
\(384\) 0 0
\(385\) −98.5523 + 4196.55i −0.0130459 + 0.555521i
\(386\) 2264.92i 0.298656i
\(387\) 0 0
\(388\) −34.3263 19.8183i −0.00449138 0.00259310i
\(389\) −2027.54 1170.60i −0.264268 0.152575i 0.362012 0.932173i \(-0.382090\pi\)
−0.626280 + 0.779598i \(0.715423\pi\)
\(390\) 0 0
\(391\) 2898.02i 0.374831i
\(392\) −128.810 + 2740.98i −0.0165966 + 0.353164i
\(393\) 0 0
\(394\) −1972.82 3417.02i −0.252257 0.436922i
\(395\) 1565.04 2710.72i 0.199356 0.345294i
\(396\) 0 0
\(397\) 9683.92 5591.01i 1.22424 0.706813i 0.258418 0.966033i \(-0.416799\pi\)
0.965818 + 0.259220i \(0.0834655\pi\)
\(398\) −2324.10 −0.292705
\(399\) 0 0
\(400\) −1246.50 −0.155813
\(401\) 9808.28 5662.81i 1.22145 0.705205i 0.256224 0.966617i \(-0.417521\pi\)
0.965227 + 0.261412i \(0.0841881\pi\)
\(402\) 0 0
\(403\) 935.150 1619.73i 0.115591 0.200209i
\(404\) 190.809 + 330.490i 0.0234977 + 0.0406993i
\(405\) 0 0
\(406\) −4037.38 7388.28i −0.493526 0.903139i
\(407\) 6677.06i 0.813193i
\(408\) 0 0
\(409\) 9068.41 + 5235.65i 1.09634 + 0.632974i 0.935258 0.353967i \(-0.115168\pi\)
0.161084 + 0.986941i \(0.448501\pi\)
\(410\) 411.404 + 237.524i 0.0495556 + 0.0286109i
\(411\) 0 0
\(412\) 4544.12i 0.543381i
\(413\) −5634.98 + 9251.44i −0.671379 + 1.10226i
\(414\) 0 0
\(415\) −4679.71 8105.50i −0.553537 0.958755i
\(416\) −1054.58 + 1826.58i −0.124291 + 0.215278i
\(417\) 0 0
\(418\) 2967.60 1713.35i 0.347249 0.200484i
\(419\) −10355.8 −1.20743 −0.603717 0.797199i \(-0.706314\pi\)
−0.603717 + 0.797199i \(0.706314\pi\)
\(420\) 0 0
\(421\) 2613.96 0.302604 0.151302 0.988488i \(-0.451653\pi\)
0.151302 + 0.988488i \(0.451653\pi\)
\(422\) 6169.05 3561.70i 0.711623 0.410855i
\(423\) 0 0
\(424\) 348.503 603.626i 0.0399170 0.0691383i
\(425\) 561.432 + 972.430i 0.0640788 + 0.110988i
\(426\) 0 0
\(427\) −5699.53 + 3114.55i −0.645948 + 0.352983i
\(428\) 8310.73i 0.938584i
\(429\) 0 0
\(430\) −5741.63 3314.93i −0.643920 0.371768i
\(431\) −3344.94 1931.20i −0.373829 0.215830i 0.301301 0.953529i \(-0.402579\pi\)
−0.675130 + 0.737699i \(0.735912\pi\)
\(432\) 0 0
\(433\) 17569.5i 1.94997i 0.222280 + 0.974983i \(0.428650\pi\)
−0.222280 + 0.974983i \(0.571350\pi\)
\(434\) −1050.78 24.6766i −0.116219 0.00272930i
\(435\) 0 0
\(436\) −236.797 410.145i −0.0260104 0.0450514i
\(437\) −5215.28 + 9033.13i −0.570894 + 0.988817i
\(438\) 0 0
\(439\) −9969.18 + 5755.71i −1.08383 + 0.625752i −0.931928 0.362643i \(-0.881874\pi\)
−0.151906 + 0.988395i \(0.548541\pi\)
\(440\) 1813.24 0.196461
\(441\) 0 0
\(442\) 1899.95 0.204460
\(443\) 6386.93 3687.49i 0.684993 0.395481i −0.116740 0.993162i \(-0.537245\pi\)
0.801734 + 0.597681i \(0.203911\pi\)
\(444\) 0 0
\(445\) 2461.28 4263.07i 0.262193 0.454132i
\(446\) −479.700 830.865i −0.0509293 0.0882121i
\(447\) 0 0
\(448\) 1184.97 + 27.8280i 0.124966 + 0.00293471i
\(449\) 10388.6i 1.09192i −0.837813 0.545958i \(-0.816166\pi\)
0.837813 0.545958i \(-0.183834\pi\)
\(450\) 0 0
\(451\) 990.015 + 571.585i 0.103366 + 0.0596783i
\(452\) 390.934 + 225.706i 0.0406814 + 0.0234874i
\(453\) 0 0
\(454\) 8218.77i 0.849616i
\(455\) −7350.99 + 4017.00i −0.757406 + 0.413890i
\(456\) 0 0
\(457\) −1264.70 2190.53i −0.129454 0.224220i 0.794011 0.607903i \(-0.207989\pi\)
−0.923465 + 0.383683i \(0.874656\pi\)
\(458\) 2269.53 3930.94i 0.231546 0.401050i
\(459\) 0 0
\(460\) −4779.89 + 2759.67i −0.484486 + 0.279718i
\(461\) −19385.0 −1.95845 −0.979227 0.202767i \(-0.935007\pi\)
−0.979227 + 0.202767i \(0.935007\pi\)
\(462\) 0 0
\(463\) 7386.83 0.741458 0.370729 0.928741i \(-0.379108\pi\)
0.370729 + 0.928741i \(0.379108\pi\)
\(464\) −3149.61 + 1818.43i −0.315123 + 0.181936i
\(465\) 0 0
\(466\) 337.223 584.087i 0.0335226 0.0580629i
\(467\) 6019.62 + 10426.3i 0.596477 + 1.03313i 0.993337 + 0.115249i \(0.0367667\pi\)
−0.396860 + 0.917879i \(0.629900\pi\)
\(468\) 0 0
\(469\) −6084.19 + 9988.93i −0.599023 + 0.983467i
\(470\) 2628.84i 0.257999i
\(471\) 0 0
\(472\) 4052.29 + 2339.59i 0.395173 + 0.228153i
\(473\) −13816.8 7977.14i −1.34312 0.775453i
\(474\) 0 0
\(475\) 4041.42i 0.390386i
\(476\) −512.008 936.960i −0.0493022 0.0902216i
\(477\) 0 0
\(478\) 1119.50 + 1939.04i 0.107123 + 0.185543i
\(479\) −7469.93 + 12938.3i −0.712546 + 1.23417i 0.251352 + 0.967896i \(0.419125\pi\)
−0.963898 + 0.266271i \(0.914208\pi\)
\(480\) 0 0
\(481\) 11539.6 6662.38i 1.09389 0.631556i
\(482\) −8727.04 −0.824701
\(483\) 0 0
\(484\) −960.574 −0.0902117
\(485\) −58.8909 + 34.0007i −0.00551360 + 0.00318328i
\(486\) 0 0
\(487\) 2645.81 4582.68i 0.246187 0.426409i −0.716278 0.697815i \(-0.754156\pi\)
0.962465 + 0.271407i \(0.0874889\pi\)
\(488\) 1402.79 + 2429.70i 0.130126 + 0.225384i
\(489\) 0 0
\(490\) 3961.96 + 2542.62i 0.365272 + 0.234416i
\(491\) 14095.0i 1.29552i 0.761845 + 0.647759i \(0.224294\pi\)
−0.761845 + 0.647759i \(0.775706\pi\)
\(492\) 0 0
\(493\) 2837.21 + 1638.06i 0.259192 + 0.149644i
\(494\) 5922.16 + 3419.16i 0.539373 + 0.311407i
\(495\) 0 0
\(496\) 454.018i 0.0411008i
\(497\) −405.652 + 17273.4i −0.0366116 + 1.55899i
\(498\) 0 0
\(499\) −4303.22 7453.40i −0.386050 0.668658i 0.605865 0.795568i \(-0.292827\pi\)
−0.991914 + 0.126910i \(0.959494\pi\)
\(500\) −2784.88 + 4823.56i −0.249087 + 0.431432i
\(501\) 0 0
\(502\) 6716.99 3878.06i 0.597199 0.344793i
\(503\) 9541.90 0.845830 0.422915 0.906169i \(-0.361007\pi\)
0.422915 + 0.906169i \(0.361007\pi\)
\(504\) 0 0
\(505\) 654.710 0.0576915
\(506\) −11502.5 + 6640.95i −1.01057 + 0.583451i
\(507\) 0 0
\(508\) −1714.84 + 2970.19i −0.149771 + 0.259411i
\(509\) 4949.39 + 8572.60i 0.430998 + 0.746510i 0.996960 0.0779213i \(-0.0248283\pi\)
−0.565962 + 0.824432i \(0.691495\pi\)
\(510\) 0 0
\(511\) −3494.87 2128.70i −0.302552 0.184282i
\(512\) 512.000i 0.0441942i
\(513\) 0 0
\(514\) −1040.01 600.450i −0.0892469 0.0515267i
\(515\) −6751.52 3897.99i −0.577685 0.333526i
\(516\) 0 0
\(517\) 6326.12i 0.538148i
\(518\) −6395.29 3895.33i −0.542458 0.330407i
\(519\) 0 0
\(520\) 1809.25 + 3133.72i 0.152579 + 0.264274i
\(521\) 4465.58 7734.61i 0.375510 0.650402i −0.614893 0.788610i \(-0.710801\pi\)
0.990403 + 0.138208i \(0.0441343\pi\)
\(522\) 0 0
\(523\) −7532.64 + 4348.97i −0.629789 + 0.363609i −0.780670 0.624943i \(-0.785122\pi\)
0.150882 + 0.988552i \(0.451789\pi\)
\(524\) 2863.20 0.238702
\(525\) 0 0
\(526\) 7045.06 0.583991
\(527\) 354.191 204.492i 0.0292767 0.0169029i
\(528\) 0 0
\(529\) 14131.0 24475.6i 1.16142 2.01164i
\(530\) −597.899 1035.59i −0.0490020 0.0848740i
\(531\) 0 0
\(532\) 90.2243 3841.92i 0.00735285 0.313099i
\(533\) 2281.32i 0.185393i
\(534\) 0 0
\(535\) 12347.8 + 7129.02i 0.997837 + 0.576102i
\(536\) 4375.33 + 2526.10i 0.352585 + 0.203565i
\(537\) 0 0
\(538\) 11753.6i 0.941884i
\(539\) 9534.18 + 6118.62i 0.761904 + 0.488957i
\(540\) 0 0
\(541\) −3981.40 6895.99i −0.316402 0.548025i 0.663332 0.748325i \(-0.269142\pi\)
−0.979735 + 0.200300i \(0.935808\pi\)
\(542\) −3351.86 + 5805.60i −0.265636 + 0.460096i
\(543\) 0 0
\(544\) −399.425 + 230.608i −0.0314801 + 0.0181751i
\(545\) −812.508 −0.0638606
\(546\) 0 0
\(547\) −10238.1 −0.800276 −0.400138 0.916455i \(-0.631038\pi\)
−0.400138 + 0.916455i \(0.631038\pi\)
\(548\) 459.885 265.515i 0.0358491 0.0206975i
\(549\) 0 0
\(550\) −2573.10 + 4456.74i −0.199486 + 0.345520i
\(551\) 5895.73 + 10211.7i 0.455838 + 0.789534i
\(552\) 0 0
\(553\) −4050.76 7412.77i −0.311493 0.570024i
\(554\) 9585.24i 0.735086i
\(555\) 0 0
\(556\) −10072.2 5815.19i −0.768268 0.443560i
\(557\) 2902.01 + 1675.47i 0.220758 + 0.127454i 0.606301 0.795235i \(-0.292653\pi\)
−0.385543 + 0.922690i \(0.625986\pi\)
\(558\) 0 0
\(559\) 31838.4i 2.40898i
\(560\) 1057.82 1736.72i 0.0798236 0.131053i
\(561\) 0 0
\(562\) 6132.70 + 10622.1i 0.460306 + 0.797274i
\(563\) 1477.19 2558.58i 0.110580 0.191529i −0.805425 0.592698i \(-0.798063\pi\)
0.916004 + 0.401169i \(0.131396\pi\)
\(564\) 0 0
\(565\) 670.693 387.225i 0.0499403 0.0288331i
\(566\) 5744.21 0.426585
\(567\) 0 0
\(568\) 7463.48 0.551339
\(569\) −10620.5 + 6131.74i −0.782485 + 0.451768i −0.837310 0.546728i \(-0.815873\pi\)
0.0548252 + 0.998496i \(0.482540\pi\)
\(570\) 0 0
\(571\) 6836.24 11840.7i 0.501029 0.867808i −0.498970 0.866619i \(-0.666288\pi\)
0.999999 0.00118894i \(-0.000378452\pi\)
\(572\) 4353.83 + 7541.06i 0.318257 + 0.551237i
\(573\) 0 0
\(574\) 1125.03 614.780i 0.0818081 0.0447046i
\(575\) 15664.6i 1.13610i
\(576\) 0 0
\(577\) 21055.8 + 12156.6i 1.51918 + 0.877096i 0.999745 + 0.0225837i \(0.00718923\pi\)
0.519431 + 0.854513i \(0.326144\pi\)
\(578\) −8149.76 4705.27i −0.586480 0.338604i
\(579\) 0 0
\(580\) 6239.47i 0.446689i
\(581\) −25252.0 593.021i −1.80315 0.0423454i
\(582\) 0 0
\(583\) −1438.80 2492.08i −0.102211 0.177035i
\(584\) −883.815 + 1530.81i −0.0626242 + 0.108468i
\(585\) 0 0
\(586\) −8212.19 + 4741.31i −0.578912 + 0.334235i
\(587\) −20911.9 −1.47040 −0.735200 0.677851i \(-0.762912\pi\)
−0.735200 + 0.677851i \(0.762912\pi\)
\(588\) 0 0
\(589\) 1472.02 0.102977
\(590\) 6952.19 4013.85i 0.485114 0.280080i
\(591\) 0 0
\(592\) −1617.30 + 2801.25i −0.112282 + 0.194477i
\(593\) 2269.12 + 3930.24i 0.157136 + 0.272168i 0.933835 0.357705i \(-0.116441\pi\)
−0.776699 + 0.629872i \(0.783107\pi\)
\(594\) 0 0
\(595\) −1831.31 43.0068i −0.126179 0.00296321i
\(596\) 11628.4i 0.799192i
\(597\) 0 0
\(598\) −22954.4 13252.7i −1.56969 0.906260i
\(599\) 19553.9 + 11289.4i 1.33380 + 0.770072i 0.985880 0.167451i \(-0.0535535\pi\)
0.347924 + 0.937523i \(0.386887\pi\)
\(600\) 0 0
\(601\) 3449.47i 0.234121i 0.993125 + 0.117061i \(0.0373471\pi\)
−0.993125 + 0.117061i \(0.962653\pi\)
\(602\) −15701.1 + 8579.98i −1.06301 + 0.580887i
\(603\) 0 0
\(604\) 1807.43 + 3130.57i 0.121761 + 0.210896i
\(605\) −823.990 + 1427.19i −0.0553718 + 0.0959068i
\(606\) 0 0
\(607\) 4570.23 2638.63i 0.305601 0.176439i −0.339355 0.940658i \(-0.610209\pi\)
0.644956 + 0.764219i \(0.276875\pi\)
\(608\) −1660.01 −0.110728
\(609\) 0 0
\(610\) 4813.30 0.319484
\(611\) 10933.1 6312.21i 0.723903 0.417946i
\(612\) 0 0
\(613\) −5405.00 + 9361.73i −0.356127 + 0.616830i −0.987310 0.158804i \(-0.949236\pi\)
0.631183 + 0.775634i \(0.282570\pi\)
\(614\) 6632.39 + 11487.6i 0.435931 + 0.755054i
\(615\) 0 0
\(616\) 2545.58 4179.30i 0.166500 0.273358i
\(617\) 19744.4i 1.28830i 0.764900 + 0.644149i \(0.222788\pi\)
−0.764900 + 0.644149i \(0.777212\pi\)
\(618\) 0 0
\(619\) 948.715 + 547.741i 0.0616027 + 0.0355664i 0.530485 0.847694i \(-0.322010\pi\)
−0.468882 + 0.883261i \(0.655343\pi\)
\(620\) 674.566 + 389.461i 0.0436955 + 0.0252276i
\(621\) 0 0
\(622\) 15140.4i 0.976006i
\(623\) −6370.50 11657.8i −0.409677 0.749697i
\(624\) 0 0
\(625\) −91.3572 158.235i −0.00584686 0.0101271i
\(626\) 6851.35 11866.9i 0.437436 0.757662i
\(627\) 0 0
\(628\) 8629.65 4982.33i 0.548345 0.316587i
\(629\) 2913.77 0.184705
\(630\) 0 0
\(631\) 4564.95 0.287999 0.144000 0.989578i \(-0.454004\pi\)
0.144000 + 0.989578i \(0.454004\pi\)
\(632\) −3160.05 + 1824.46i −0.198893 + 0.114831i
\(633\) 0 0
\(634\) −5275.27 + 9137.03i −0.330454 + 0.572363i
\(635\) 2942.01 + 5095.71i 0.183859 + 0.318452i
\(636\) 0 0
\(637\) −1061.25 + 22582.6i −0.0660098 + 1.40464i
\(638\) 15014.8i 0.931729i
\(639\) 0 0
\(640\) −760.714 439.198i −0.0469842 0.0271263i
\(641\) 4810.24 + 2777.20i 0.296401 + 0.171127i 0.640825 0.767687i \(-0.278592\pi\)
−0.344424 + 0.938814i \(0.611926\pi\)
\(642\) 0 0
\(643\) 27961.1i 1.71490i 0.514570 + 0.857449i \(0.327952\pi\)
−0.514570 + 0.857449i \(0.672048\pi\)
\(644\) −349.710 + 14891.3i −0.0213983 + 0.911182i
\(645\) 0 0
\(646\) 747.679 + 1295.02i 0.0455372 + 0.0788728i
\(647\) −10177.2 + 17627.5i −0.618406 + 1.07111i 0.371371 + 0.928485i \(0.378888\pi\)
−0.989777 + 0.142626i \(0.954445\pi\)
\(648\) 0 0
\(649\) 16729.9 9659.03i 1.01188 0.584207i
\(650\) −10269.8 −0.619714
\(651\) 0 0
\(652\) 5817.22 0.349417
\(653\) 10991.1 6345.71i 0.658674 0.380286i −0.133097 0.991103i \(-0.542492\pi\)
0.791772 + 0.610817i \(0.209159\pi\)
\(654\) 0 0
\(655\) 2456.08 4254.06i 0.146515 0.253771i
\(656\) −276.896 479.599i −0.0164802 0.0285445i
\(657\) 0 0
\(658\) −6059.17 3690.59i −0.358983 0.218654i
\(659\) 19546.6i 1.15543i −0.816239 0.577714i \(-0.803945\pi\)
0.816239 0.577714i \(-0.196055\pi\)
\(660\) 0 0
\(661\) −22849.3 13192.0i −1.34453 0.776264i −0.357060 0.934081i \(-0.616221\pi\)
−0.987468 + 0.157818i \(0.949554\pi\)
\(662\) −10702.5 6179.09i −0.628345 0.362775i
\(663\) 0 0
\(664\) 10910.8i 0.637685i
\(665\) −5630.82 3429.69i −0.328351 0.199996i
\(666\) 0 0
\(667\) −22851.9 39580.7i −1.32658 2.29771i
\(668\) −2804.40 + 4857.36i −0.162433 + 0.281343i
\(669\) 0 0
\(670\) 7506.39 4333.82i 0.432832 0.249896i
\(671\) 11582.9 0.666396
\(672\) 0 0
\(673\) 829.227 0.0474953 0.0237477 0.999718i \(-0.492440\pi\)
0.0237477 + 0.999718i \(0.492440\pi\)
\(674\) 6567.97 3792.02i 0.375354 0.216711i
\(675\) 0 0
\(676\) −4294.53 + 7438.34i −0.244340 + 0.423210i
\(677\) 745.967 + 1292.05i 0.0423484 + 0.0733495i 0.886423 0.462877i \(-0.153183\pi\)
−0.844074 + 0.536226i \(0.819849\pi\)
\(678\) 0 0
\(679\) −4.30863 + 183.470i −0.000243520 + 0.0103695i
\(680\) 791.271i 0.0446233i
\(681\) 0 0
\(682\) 1623.30 + 937.210i 0.0911425 + 0.0526212i
\(683\) −6008.93 3469.26i −0.336640 0.194359i 0.322145 0.946690i \(-0.395596\pi\)
−0.658785 + 0.752331i \(0.728929\pi\)
\(684\) 0 0
\(685\) 911.044i 0.0508163i
\(686\) 11422.6 5562.31i 0.635737 0.309577i
\(687\) 0 0
\(688\) 3864.41 + 6693.36i 0.214141 + 0.370904i
\(689\) 2871.28 4973.20i 0.158762 0.274984i
\(690\) 0 0
\(691\) −150.567 + 86.9299i −0.00828921 + 0.00478578i −0.504139 0.863623i \(-0.668190\pi\)
0.495850 + 0.868408i \(0.334857\pi\)
\(692\) 11668.8 0.641012
\(693\) 0 0
\(694\) 14734.6 0.805933
\(695\) −17280.1 + 9976.66i −0.943123 + 0.544513i
\(696\) 0 0
\(697\) −249.432 + 432.028i −0.0135551 + 0.0234781i
\(698\) −9408.31 16295.7i −0.510186 0.883668i
\(699\) 0 0
\(700\) 2767.55 + 5064.54i 0.149434 + 0.273460i
\(701\) 13902.8i 0.749076i 0.927211 + 0.374538i \(0.122199\pi\)
−0.927211 + 0.374538i \(0.877801\pi\)
\(702\) 0 0
\(703\) 9082.24 + 5243.63i 0.487259 + 0.281319i
\(704\) −1830.60 1056.90i −0.0980021 0.0565815i
\(705\) 0 0
\(706\) 5647.58i 0.301061i
\(707\) 919.138 1509.03i 0.0488936 0.0802728i
\(708\) 0 0
\(709\) −1902.55 3295.32i −0.100778 0.174553i 0.811227 0.584731i \(-0.198800\pi\)
−0.912006 + 0.410178i \(0.865467\pi\)
\(710\) 6402.25 11089.0i 0.338411 0.586146i
\(711\) 0 0
\(712\) −4969.72 + 2869.27i −0.261584 + 0.151026i
\(713\) −5705.58 −0.299685
\(714\) 0 0
\(715\) 14939.0 0.781382
\(716\) −11687.4 + 6747.71i −0.610025 + 0.352198i
\(717\) 0 0
\(718\) −11514.6 + 19943.9i −0.598497 + 1.03663i
\(719\) −15869.0 27485.9i −0.823107 1.42566i −0.903358 0.428888i \(-0.858906\pi\)
0.0802513 0.996775i \(-0.474428\pi\)
\(720\) 0 0
\(721\) −18462.8 + 10089.1i −0.953661 + 0.521135i
\(722\) 8335.89i 0.429681i
\(723\) 0 0
\(724\) −13361.0 7714.01i −0.685856 0.395979i
\(725\) −15335.9 8854.21i −0.785604 0.453569i
\(726\) 0 0
\(727\) 3362.88i 0.171558i −0.996314 0.0857789i \(-0.972662\pi\)
0.996314 0.0857789i \(-0.0273379\pi\)
\(728\) 9762.82 + 229.272i 0.497025 + 0.0116722i
\(729\) 0 0
\(730\) 1516.29 + 2626.29i 0.0768773 + 0.133155i
\(731\) 3481.11 6029.46i 0.176133 0.305072i
\(732\) 0 0
\(733\) −26902.9 + 15532.4i −1.35564 + 0.782676i −0.989032 0.147701i \(-0.952813\pi\)
−0.366603 + 0.930377i \(0.619479\pi\)
\(734\) 18053.6 0.907860
\(735\) 0 0
\(736\) 6434.23 0.322240
\(737\) 18063.6 10429.0i 0.902824 0.521246i
\(738\) 0 0
\(739\) −222.377 + 385.168i −0.0110694 + 0.0191727i −0.871507 0.490383i \(-0.836857\pi\)
0.860438 + 0.509556i \(0.170190\pi\)
\(740\) 2774.67 + 4805.88i 0.137837 + 0.238740i
\(741\) 0 0
\(742\) −3226.30 75.7669i −0.159624 0.00374864i
\(743\) 9748.08i 0.481322i −0.970609 0.240661i \(-0.922636\pi\)
0.970609 0.240661i \(-0.0773643\pi\)
\(744\) 0 0
\(745\) −17277.1 9974.97i −0.849645 0.490543i
\(746\) −6868.47 3965.51i −0.337094 0.194622i
\(747\) 0 0
\(748\) 1904.14i 0.0930777i
\(749\) 33766.5 18451.9i 1.64726 0.900159i
\(750\) 0 0
\(751\) −8765.46 15182.2i −0.425907 0.737693i 0.570598 0.821230i \(-0.306712\pi\)
−0.996505 + 0.0835371i \(0.973378\pi\)
\(752\) −1532.30 + 2654.02i −0.0743048 + 0.128700i
\(753\) 0 0
\(754\) −25949.3 + 14981.8i −1.25334 + 0.723615i
\(755\) 6201.74 0.298946
\(756\) 0 0
\(757\) 4717.30 0.226490 0.113245 0.993567i \(-0.463875\pi\)
0.113245 + 0.993567i \(0.463875\pi\)
\(758\) 20964.3 12103.7i 1.00456 0.579984i
\(759\) 0 0
\(760\) −1423.97 + 2466.39i −0.0679644 + 0.117718i
\(761\) −16185.3 28033.8i −0.770983 1.33538i −0.937025 0.349262i \(-0.886432\pi\)
0.166042 0.986119i \(-0.446901\pi\)
\(762\) 0 0
\(763\) −1140.67 + 1872.73i −0.0541219 + 0.0888565i
\(764\) 8542.55i 0.404527i
\(765\) 0 0
\(766\) 7839.62 + 4526.20i 0.369787 + 0.213497i
\(767\) 33386.3 + 19275.6i 1.57172 + 0.907434i
\(768\) 0 0
\(769\) 15910.1i 0.746076i −0.927816 0.373038i \(-0.878316\pi\)
0.927816 0.373038i \(-0.121684\pi\)
\(770\) −4025.85 7367.18i −0.188418 0.344798i
\(771\) 0 0
\(772\) −2264.92 3922.95i −0.105591 0.182889i
\(773\) 7751.27 13425.6i 0.360665 0.624690i −0.627406 0.778693i \(-0.715883\pi\)
0.988070 + 0.154003i \(0.0492165\pi\)
\(774\) 0 0
\(775\) −1914.51 + 1105.34i −0.0887369 + 0.0512323i
\(776\) 79.2732 0.00366720
\(777\) 0 0
\(778\) 4682.40 0.215774
\(779\) −1554.96 + 897.756i −0.0715176 + 0.0412907i
\(780\) 0 0
\(781\) 15406.5 26684.9i 0.705877 1.22261i
\(782\) −2898.02 5019.51i −0.132523 0.229536i
\(783\) 0 0
\(784\) −2517.87 4876.32i −0.114699 0.222135i
\(785\) 17095.6i 0.777283i
\(786\) 0 0
\(787\) −25807.5 14899.9i −1.16892 0.674874i −0.215491 0.976506i \(-0.569135\pi\)
−0.953424 + 0.301632i \(0.902469\pi\)
\(788\) 6834.05 + 3945.64i 0.308950 + 0.178373i
\(789\) 0 0
\(790\) 6260.15i 0.281932i
\(791\) 49.0699 2089.49i 0.00220572 0.0939237i
\(792\) 0 0
\(793\) 11557.4 + 20018.0i 0.517548 + 0.896420i
\(794\) −11182.0 + 19367.8i −0.499792 + 0.865666i
\(795\) 0 0
\(796\) 4025.46 2324.10i 0.179244 0.103487i
\(797\) 34495.2 1.53310 0.766550 0.642184i \(-0.221972\pi\)
0.766550 + 0.642184i \(0.221972\pi\)
\(798\) 0 0
\(799\) 2760.63 0.122233
\(800\) 2159.01 1246.50i 0.0954155 0.0550882i
\(801\) 0 0
\(802\) −11325.6 + 19616.6i −0.498655 + 0.863697i
\(803\) 3648.84 + 6319.98i 0.160355 + 0.277743i
\(804\) 0 0
\(805\) 21825.1 + 13293.5i 0.955571 + 0.582031i
\(806\) 3740.60i 0.163470i
\(807\) 0 0
\(808\) −660.980 381.617i −0.0287787 0.0166154i
\(809\) −8073.09 4661.00i −0.350846 0.202561i 0.314212 0.949353i \(-0.398260\pi\)
−0.665058 + 0.746792i \(0.731593\pi\)
\(810\) 0 0
\(811\) 13684.8i 0.592524i −0.955107 0.296262i \(-0.904260\pi\)
0.955107 0.296262i \(-0.0957401\pi\)
\(812\) 14381.2 + 8759.50i 0.621530 + 0.378569i
\(813\) 0 0
\(814\) 6677.06 + 11565.0i 0.287507 + 0.497977i
\(815\) 4990.07 8643.05i 0.214472 0.371476i
\(816\) 0 0
\(817\) 21701.3 12529.2i 0.929292 0.536527i
\(818\) −20942.6 −0.895160
\(819\) 0 0
\(820\) −950.097 −0.0404620
\(821\) 34689.6 20028.1i 1.47464 0.851381i 0.475044 0.879962i \(-0.342432\pi\)
0.999591 + 0.0285809i \(0.00909884\pi\)
\(822\) 0 0
\(823\) 3961.13 6860.88i 0.167772 0.290589i −0.769864 0.638208i \(-0.779676\pi\)
0.937636 + 0.347618i \(0.113009\pi\)
\(824\) 4544.12 + 7870.65i 0.192114 + 0.332751i
\(825\) 0 0
\(826\) 508.642 21658.9i 0.0214260 0.912362i
\(827\) 15771.5i 0.663155i 0.943428 + 0.331577i \(0.107581\pi\)
−0.943428 + 0.331577i \(0.892419\pi\)
\(828\) 0 0
\(829\) 30793.3 + 17778.5i 1.29010 + 0.744840i 0.978672 0.205429i \(-0.0658589\pi\)
0.311429 + 0.950269i \(0.399192\pi\)
\(830\) 16211.0 + 9359.42i 0.677942 + 0.391410i
\(831\) 0 0
\(832\) 4218.31i 0.175773i
\(833\) −2670.08 + 4160.58i −0.111060 + 0.173056i
\(834\) 0 0
\(835\) 4811.28 + 8333.38i 0.199403 + 0.345375i
\(836\) −3426.69 + 5935.20i −0.141764 + 0.245542i
\(837\) 0 0
\(838\) 17936.8 10355.8i 0.739399 0.426892i
\(839\) −24413.9 −1.00460 −0.502301 0.864693i \(-0.667513\pi\)
−0.502301 + 0.864693i \(0.667513\pi\)
\(840\) 0 0
\(841\) −27278.0 −1.11846
\(842\) −4527.50 + 2613.96i −0.185307 + 0.106987i
\(843\) 0 0
\(844\) −7123.41 + 12338.1i −0.290519 + 0.503193i
\(845\) 7367.77 + 12761.4i 0.299952 + 0.519531i
\(846\) 0 0
\(847\) 2132.72 + 3902.81i 0.0865184 + 0.158326i
\(848\) 1394.01i 0.0564512i
\(849\) 0 0
\(850\) −1944.86 1122.86i −0.0784801 0.0453105i
\(851\) −35202.9 20324.4i −1.41803 0.818697i
\(852\) 0 0
\(853\) 32086.8i 1.28796i −0.765041 0.643981i \(-0.777281\pi\)
0.765041 0.643981i \(-0.222719\pi\)
\(854\) 6757.33 11094.1i 0.270762 0.444534i
\(855\) 0 0
\(856\) −8310.73 14394.6i −0.331840 0.574763i
\(857\) 6399.64 11084.5i 0.255085 0.441820i −0.709834 0.704369i \(-0.751230\pi\)
0.964919 + 0.262549i \(0.0845633\pi\)
\(858\) 0 0
\(859\) −42677.2 + 24639.7i −1.69514 + 0.978690i −0.744899 + 0.667177i \(0.767502\pi\)
−0.950242 + 0.311513i \(0.899164\pi\)
\(860\) 13259.7 0.525759
\(861\) 0 0
\(862\) 7724.82 0.305230
\(863\) −10317.0 + 5956.55i −0.406948 + 0.234952i −0.689478 0.724307i \(-0.742160\pi\)
0.282529 + 0.959259i \(0.408826\pi\)
\(864\) 0 0
\(865\) 10009.6 17337.1i 0.393452 0.681479i
\(866\) −17569.5 30431.2i −0.689417 1.19411i
\(867\) 0 0
\(868\) 1844.68 1008.04i 0.0721341 0.0394182i
\(869\) 15064.6i 0.588069i
\(870\) 0 0
\(871\) 36047.8 + 20812.2i 1.40233 + 0.809638i
\(872\) 820.290 + 473.595i 0.0318561 + 0.0183921i
\(873\) 0 0
\(874\) 20861.1i 0.807366i
\(875\) 25781.2 + 605.451i 0.996075 + 0.0233920i
\(876\) 0 0
\(877\) −8249.14 14287.9i −0.317621 0.550136i 0.662370 0.749177i \(-0.269551\pi\)
−0.979991 + 0.199041i \(0.936217\pi\)
\(878\) 11511.4 19938.4i 0.442473 0.766386i
\(879\) 0 0
\(880\) −3140.62 + 1813.24i −0.120307 + 0.0694593i
\(881\) −21721.2 −0.830655 −0.415327 0.909672i \(-0.636333\pi\)
−0.415327 + 0.909672i \(0.636333\pi\)
\(882\) 0 0
\(883\) −30605.7 −1.16644 −0.583219 0.812315i \(-0.698207\pi\)
−0.583219 + 0.812315i \(0.698207\pi\)
\(884\) −3290.81 + 1899.95i −0.125206 + 0.0722876i
\(885\) 0 0
\(886\) −7374.99 + 12773.9i −0.279647 + 0.484363i
\(887\) 2826.08 + 4894.91i 0.106979 + 0.185293i 0.914545 0.404484i \(-0.132549\pi\)
−0.807566 + 0.589777i \(0.799216\pi\)
\(888\) 0 0
\(889\) 15875.3 + 372.817i 0.598919 + 0.0140651i
\(890\) 9845.14i 0.370798i
\(891\) 0 0
\(892\) 1661.73 + 959.400i 0.0623754 + 0.0360124i
\(893\) 8604.89 + 4968.04i 0.322454 + 0.186169i
\(894\) 0 0
\(895\) 23153.0i 0.864715i
\(896\) −2080.26 + 1136.77i −0.0775630 + 0.0423849i
\(897\) 0 0
\(898\) 10388.6 + 17993.7i 0.386051 + 0.668659i
\(899\) −3225.00 + 5585.86i −0.119644 + 0.207229i
\(900\) 0 0
\(901\) 1087.51 627.872i 0.0402110 0.0232158i
\(902\) −2286.34 −0.0843978
\(903\) 0 0
\(904\) −902.823 −0.0332162
\(905\) −22922.5 + 13234.3i −0.841954 + 0.486103i
\(906\) 0 0
\(907\) 17938.9 31071.2i 0.656728 1.13749i −0.324729 0.945807i \(-0.605273\pi\)
0.981458 0.191680i \(-0.0613935\pi\)
\(908\) −8218.77 14235.3i −0.300385 0.520282i
\(909\) 0 0
\(910\) 8715.29 14308.6i 0.317482 0.521238i
\(911\) 45908.2i 1.66960i −0.550554 0.834800i \(-0.685583\pi\)
0.550554 0.834800i \(-0.314417\pi\)
\(912\) 0 0
\(913\) 39010.6 + 22522.8i 1.41409 + 0.816424i
\(914\) 4381.06 + 2529.40i 0.158548 + 0.0915375i
\(915\) 0 0
\(916\) 9078.12i 0.327456i
\(917\) −6357.04 11633.2i −0.228929 0.418933i
\(918\) 0 0
\(919\) 21716.4 + 37613.9i 0.779498 + 1.35013i 0.932231 + 0.361862i \(0.117859\pi\)
−0.152734 + 0.988267i \(0.548808\pi\)
\(920\) 5519.34 9559.78i 0.197791 0.342583i
\(921\) 0 0
\(922\) 33575.7 19385.0i 1.19930 0.692418i
\(923\) 61490.7 2.19284
\(924\) 0 0
\(925\) −15749.8 −0.559837
\(926\) −12794.4 + 7386.83i −0.454048 + 0.262145i
\(927\) 0 0
\(928\) 3636.86 6299.23i 0.128648 0.222826i
\(929\) 19732.4 + 34177.5i 0.696877 + 1.20703i 0.969544 + 0.244917i \(0.0787608\pi\)
−0.272667 + 0.962108i \(0.587906\pi\)
\(930\) 0 0
\(931\) −15810.0 + 8163.46i −0.556556 + 0.287376i
\(932\) 1348.89i 0.0474081i
\(933\) 0 0
\(934\) −20852.6 12039.2i −0.730532 0.421773i
\(935\) 2829.11 + 1633.39i 0.0989537 + 0.0571309i
\(936\) 0 0
\(937\) 28000.6i 0.976242i 0.872776 + 0.488121i \(0.162318\pi\)
−0.872776 + 0.488121i \(0.837682\pi\)
\(938\) 549.189 23385.5i 0.0191169 0.814035i
\(939\) 0 0
\(940\) 2628.84 + 4553.29i 0.0912163 + 0.157991i
\(941\) 22909.8 39680.9i 0.793664 1.37467i −0.130019 0.991511i \(-0.541504\pi\)
0.923684 0.383156i \(-0.125163\pi\)
\(942\) 0 0
\(943\) 6027.04 3479.72i 0.208131 0.120164i
\(944\) −9358.36 −0.322658
\(945\) 0 0
\(946\) 31908.6 1.09666
\(947\) −21397.3 + 12353.7i −0.734234 + 0.423910i −0.819969 0.572408i \(-0.806009\pi\)
0.0857353 + 0.996318i \(0.472676\pi\)
\(948\) 0 0
\(949\) −7281.65 + 12612.2i −0.249075 + 0.431411i
\(950\) −4041.42 6999.95i −0.138022 0.239062i
\(951\) 0 0
\(952\) 1823.78 + 1110.85i 0.0620895 + 0.0378183i
\(953\) 48776.9i 1.65796i 0.559275 + 0.828982i \(0.311080\pi\)
−0.559275 + 0.828982i \(0.688920\pi\)
\(954\) 0 0
\(955\) −12692.3 7327.88i −0.430065 0.248298i
\(956\) −3878.08 2239.01i −0.131199 0.0757476i
\(957\) 0 0
\(958\) 29879.7i 1.00769i
\(959\) −2099.85 1279.00i −0.0707066 0.0430669i
\(960\) 0 0
\(961\) −14492.9 25102.4i −0.486486 0.842618i
\(962\) −13324.8 + 23079.2i −0.446577 + 0.773495i
\(963\) 0 0
\(964\) 15115.7 8727.04i 0.505024 0.291576i
\(965\) −7771.47 −0.259246
\(966\) 0 0
\(967\) 1312.29 0.0436406 0.0218203 0.999762i \(-0.493054\pi\)
0.0218203 + 0.999762i \(0.493054\pi\)
\(968\) 1663.76 960.574i 0.0552432 0.0318947i
\(969\) 0 0
\(970\) 68.0013 117.782i 0.00225092 0.00389871i
\(971\) −20988.7 36353.5i −0.693676 1.20148i −0.970625 0.240597i \(-0.922657\pi\)
0.276949 0.960885i \(-0.410677\pi\)
\(972\) 0 0
\(973\) −1264.26 + 53834.6i −0.0416550 + 1.77375i
\(974\) 10583.2i 0.348161i
\(975\) 0 0
\(976\) −4859.40 2805.58i −0.159371 0.0920127i
\(977\) 48936.5 + 28253.5i 1.60247 + 0.925188i 0.990991 + 0.133931i \(0.0427599\pi\)
0.611483 + 0.791258i \(0.290573\pi\)
\(978\) 0 0
\(979\) 23691.6i 0.773430i
\(980\) −9404.94 441.978i −0.306561 0.0144066i
\(981\) 0 0
\(982\) −14095.0 24413.3i −0.458035 0.793340i
\(983\) −11084.9 + 19199.5i −0.359667 + 0.622961i −0.987905 0.155060i \(-0.950443\pi\)
0.628238 + 0.778021i \(0.283776\pi\)
\(984\) 0 0
\(985\) 11724.6 6769.21i 0.379267 0.218970i
\(986\) −6552.26 −0.211629
\(987\) 0 0
\(988\) −13676.6 −0.440396
\(989\) −84114.4 + 48563.5i −2.70443 + 1.56140i
\(990\) 0 0
\(991\) 17799.4 30829.4i 0.570550 0.988222i −0.425959 0.904742i \(-0.640063\pi\)
0.996509 0.0834796i \(-0.0266033\pi\)
\(992\) −454.018 786.382i −0.0145313 0.0251690i
\(993\) 0 0
\(994\) −16570.8 30324.1i −0.528767 0.967629i
\(995\) 7974.54i 0.254080i
\(996\) 0 0
\(997\) −16868.4 9738.99i −0.535836 0.309365i 0.207554 0.978224i \(-0.433450\pi\)
−0.743390 + 0.668859i \(0.766783\pi\)
\(998\) 14906.8 + 8606.45i 0.472812 + 0.272978i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 378.4.k.d.269.2 yes 20
3.2 odd 2 inner 378.4.k.d.269.9 yes 20
7.5 odd 6 inner 378.4.k.d.215.9 yes 20
21.5 even 6 inner 378.4.k.d.215.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.4.k.d.215.2 20 21.5 even 6 inner
378.4.k.d.215.9 yes 20 7.5 odd 6 inner
378.4.k.d.269.2 yes 20 1.1 even 1 trivial
378.4.k.d.269.9 yes 20 3.2 odd 2 inner