Properties

Label 230.5.d.a.91.10
Level $230$
Weight $5$
Character 230.91
Analytic conductor $23.775$
Analytic rank $0$
Dimension $32$
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] = [230,5,Mod(91,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("230.91");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 230.d (of order \(2\), degree \(1\), 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: \(23.7750915093\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.10
Character \(\chi\) \(=\) 230.91
Dual form 230.5.d.a.91.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.82843 q^{2} +0.828614 q^{3} +8.00000 q^{4} +11.1803i q^{5} -2.34367 q^{6} -16.9191i q^{7} -22.6274 q^{8} -80.3134 q^{9} +O(q^{10})\) \(q-2.82843 q^{2} +0.828614 q^{3} +8.00000 q^{4} +11.1803i q^{5} -2.34367 q^{6} -16.9191i q^{7} -22.6274 q^{8} -80.3134 q^{9} -31.6228i q^{10} -34.1074i q^{11} +6.62891 q^{12} +274.959 q^{13} +47.8544i q^{14} +9.26419i q^{15} +64.0000 q^{16} +6.91652i q^{17} +227.161 q^{18} +302.833i q^{19} +89.4427i q^{20} -14.0194i q^{21} +96.4702i q^{22} +(-328.833 - 414.379i) q^{23} -18.7494 q^{24} -125.000 q^{25} -777.702 q^{26} -133.667 q^{27} -135.353i q^{28} +266.017 q^{29} -26.2031i q^{30} +583.049 q^{31} -181.019 q^{32} -28.2618i q^{33} -19.5629i q^{34} +189.161 q^{35} -642.507 q^{36} +1130.86i q^{37} -856.542i q^{38} +227.835 q^{39} -252.982i q^{40} +1769.42 q^{41} +39.6528i q^{42} +3303.32i q^{43} -272.859i q^{44} -897.931i q^{45} +(930.081 + 1172.04i) q^{46} +1722.09 q^{47} +53.0313 q^{48} +2114.74 q^{49} +353.553 q^{50} +5.73113i q^{51} +2199.67 q^{52} +2677.50i q^{53} +378.066 q^{54} +381.332 q^{55} +382.835i q^{56} +250.932i q^{57} -752.409 q^{58} +1276.66 q^{59} +74.1135i q^{60} -4181.52i q^{61} -1649.11 q^{62} +1358.83i q^{63} +512.000 q^{64} +3074.14i q^{65} +79.9366i q^{66} +6231.09i q^{67} +55.3322i q^{68} +(-272.476 - 343.360i) q^{69} -535.029 q^{70} +7815.96 q^{71} +1817.28 q^{72} +5456.59 q^{73} -3198.55i q^{74} -103.577 q^{75} +2422.67i q^{76} -577.066 q^{77} -644.415 q^{78} +11504.8i q^{79} +715.542i q^{80} +6394.63 q^{81} -5004.66 q^{82} +2467.58i q^{83} -112.155i q^{84} -77.3291 q^{85} -9343.19i q^{86} +220.425 q^{87} +771.762i q^{88} +242.783i q^{89} +2539.73i q^{90} -4652.06i q^{91} +(-2630.67 - 3315.03i) q^{92} +483.123 q^{93} -4870.81 q^{94} -3385.78 q^{95} -149.995 q^{96} +13642.0i q^{97} -5981.40 q^{98} +2739.28i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 256 q^{4} + 64 q^{6} + 832 q^{9} - 408 q^{13} + 2048 q^{16} + 1024 q^{18} + 1332 q^{23} + 512 q^{24} - 4000 q^{25} + 2208 q^{27} + 3732 q^{29} - 412 q^{31} + 300 q^{35} + 6656 q^{36} - 9208 q^{39} - 6156 q^{41} + 4480 q^{46} + 5184 q^{47} - 13820 q^{49} - 3264 q^{52} - 3328 q^{54} - 6000 q^{55} + 3200 q^{58} - 30468 q^{59} - 10752 q^{62} + 16384 q^{64} - 1168 q^{69} + 4800 q^{70} - 37644 q^{71} + 8192 q^{72} + 19984 q^{73} + 27528 q^{77} + 15744 q^{78} + 69056 q^{81} - 17408 q^{82} + 3300 q^{85} + 28936 q^{87} + 10656 q^{92} + 40648 q^{93} - 23808 q^{94} - 21600 q^{95} + 4096 q^{96} + 43008 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.82843 −0.707107
\(3\) 0.828614 0.0920682 0.0460341 0.998940i \(-0.485342\pi\)
0.0460341 + 0.998940i \(0.485342\pi\)
\(4\) 8.00000 0.500000
\(5\) 11.1803i 0.447214i
\(6\) −2.34367 −0.0651021
\(7\) 16.9191i 0.345288i −0.984984 0.172644i \(-0.944769\pi\)
0.984984 0.172644i \(-0.0552310\pi\)
\(8\) −22.6274 −0.353553
\(9\) −80.3134 −0.991523
\(10\) 31.6228i 0.316228i
\(11\) 34.1074i 0.281879i −0.990018 0.140940i \(-0.954988\pi\)
0.990018 0.140940i \(-0.0450123\pi\)
\(12\) 6.62891 0.0460341
\(13\) 274.959 1.62698 0.813489 0.581580i \(-0.197565\pi\)
0.813489 + 0.581580i \(0.197565\pi\)
\(14\) 47.8544i 0.244155i
\(15\) 9.26419i 0.0411742i
\(16\) 64.0000 0.250000
\(17\) 6.91652i 0.0239326i 0.999928 + 0.0119663i \(0.00380908\pi\)
−0.999928 + 0.0119663i \(0.996191\pi\)
\(18\) 227.161 0.701113
\(19\) 302.833i 0.838874i 0.907784 + 0.419437i \(0.137772\pi\)
−0.907784 + 0.419437i \(0.862228\pi\)
\(20\) 89.4427i 0.223607i
\(21\) 14.0194i 0.0317900i
\(22\) 96.4702i 0.199319i
\(23\) −328.833 414.379i −0.621613 0.783324i
\(24\) −18.7494 −0.0325510
\(25\) −125.000 −0.200000
\(26\) −777.702 −1.15045
\(27\) −133.667 −0.183356
\(28\) 135.353i 0.172644i
\(29\) 266.017 0.316310 0.158155 0.987414i \(-0.449445\pi\)
0.158155 + 0.987414i \(0.449445\pi\)
\(30\) 26.2031i 0.0291145i
\(31\) 583.049 0.606711 0.303355 0.952877i \(-0.401893\pi\)
0.303355 + 0.952877i \(0.401893\pi\)
\(32\) −181.019 −0.176777
\(33\) 28.2618i 0.0259521i
\(34\) 19.5629i 0.0169229i
\(35\) 189.161 0.154417
\(36\) −642.507 −0.495762
\(37\) 1130.86i 0.826048i 0.910720 + 0.413024i \(0.135527\pi\)
−0.910720 + 0.413024i \(0.864473\pi\)
\(38\) 856.542i 0.593173i
\(39\) 227.835 0.149793
\(40\) 252.982i 0.158114i
\(41\) 1769.42 1.05260 0.526299 0.850300i \(-0.323579\pi\)
0.526299 + 0.850300i \(0.323579\pi\)
\(42\) 39.6528i 0.0224789i
\(43\) 3303.32i 1.78654i 0.449519 + 0.893271i \(0.351595\pi\)
−0.449519 + 0.893271i \(0.648405\pi\)
\(44\) 272.859i 0.140940i
\(45\) 897.931i 0.443423i
\(46\) 930.081 + 1172.04i 0.439547 + 0.553894i
\(47\) 1722.09 0.779579 0.389790 0.920904i \(-0.372548\pi\)
0.389790 + 0.920904i \(0.372548\pi\)
\(48\) 53.0313 0.0230171
\(49\) 2114.74 0.880776
\(50\) 353.553 0.141421
\(51\) 5.73113i 0.00220343i
\(52\) 2199.67 0.813489
\(53\) 2677.50i 0.953185i 0.879124 + 0.476592i \(0.158128\pi\)
−0.879124 + 0.476592i \(0.841872\pi\)
\(54\) 378.066 0.129652
\(55\) 381.332 0.126060
\(56\) 382.835i 0.122078i
\(57\) 250.932i 0.0772336i
\(58\) −752.409 −0.223665
\(59\) 1276.66 0.366751 0.183375 0.983043i \(-0.441298\pi\)
0.183375 + 0.983043i \(0.441298\pi\)
\(60\) 74.1135i 0.0205871i
\(61\) 4181.52i 1.12376i −0.827218 0.561881i \(-0.810078\pi\)
0.827218 0.561881i \(-0.189922\pi\)
\(62\) −1649.11 −0.429009
\(63\) 1358.83i 0.342361i
\(64\) 512.000 0.125000
\(65\) 3074.14i 0.727607i
\(66\) 79.9366i 0.0183509i
\(67\) 6231.09i 1.38808i 0.719936 + 0.694040i \(0.244171\pi\)
−0.719936 + 0.694040i \(0.755829\pi\)
\(68\) 55.3322i 0.0119663i
\(69\) −272.476 343.360i −0.0572308 0.0721193i
\(70\) −535.029 −0.109190
\(71\) 7815.96 1.55048 0.775239 0.631668i \(-0.217630\pi\)
0.775239 + 0.631668i \(0.217630\pi\)
\(72\) 1817.28 0.350556
\(73\) 5456.59 1.02394 0.511971 0.859003i \(-0.328916\pi\)
0.511971 + 0.859003i \(0.328916\pi\)
\(74\) 3198.55i 0.584104i
\(75\) −103.577 −0.0184136
\(76\) 2422.67i 0.419437i
\(77\) −577.066 −0.0973294
\(78\) −644.415 −0.105920
\(79\) 11504.8i 1.84342i 0.387878 + 0.921711i \(0.373208\pi\)
−0.387878 + 0.921711i \(0.626792\pi\)
\(80\) 715.542i 0.111803i
\(81\) 6394.63 0.974642
\(82\) −5004.66 −0.744299
\(83\) 2467.58i 0.358192i 0.983832 + 0.179096i \(0.0573172\pi\)
−0.983832 + 0.179096i \(0.942683\pi\)
\(84\) 112.155i 0.0158950i
\(85\) −77.3291 −0.0107030
\(86\) 9343.19i 1.26328i
\(87\) 220.425 0.0291221
\(88\) 771.762i 0.0996593i
\(89\) 242.783i 0.0306505i 0.999883 + 0.0153252i \(0.00487837\pi\)
−0.999883 + 0.0153252i \(0.995122\pi\)
\(90\) 2539.73i 0.313547i
\(91\) 4652.06i 0.561775i
\(92\) −2630.67 3315.03i −0.310807 0.391662i
\(93\) 483.123 0.0558588
\(94\) −4870.81 −0.551246
\(95\) −3385.78 −0.375156
\(96\) −149.995 −0.0162755
\(97\) 13642.0i 1.44989i 0.688809 + 0.724943i \(0.258134\pi\)
−0.688809 + 0.724943i \(0.741866\pi\)
\(98\) −5981.40 −0.622803
\(99\) 2739.28i 0.279490i
\(100\) −1000.00 −0.100000
\(101\) −2916.56 −0.285909 −0.142954 0.989729i \(-0.545660\pi\)
−0.142954 + 0.989729i \(0.545660\pi\)
\(102\) 16.2101i 0.00155806i
\(103\) 16819.4i 1.58539i −0.609621 0.792693i \(-0.708678\pi\)
0.609621 0.792693i \(-0.291322\pi\)
\(104\) −6221.62 −0.575224
\(105\) 156.742 0.0142169
\(106\) 7573.10i 0.674003i
\(107\) 12039.3i 1.05156i −0.850621 0.525780i \(-0.823774\pi\)
0.850621 0.525780i \(-0.176226\pi\)
\(108\) −1069.33 −0.0916780
\(109\) 15109.6i 1.27174i −0.771794 0.635872i \(-0.780641\pi\)
0.771794 0.635872i \(-0.219359\pi\)
\(110\) −1078.57 −0.0891380
\(111\) 937.046i 0.0760527i
\(112\) 1082.82i 0.0863219i
\(113\) 5430.98i 0.425325i −0.977126 0.212663i \(-0.931787\pi\)
0.977126 0.212663i \(-0.0682135\pi\)
\(114\) 709.743i 0.0546124i
\(115\) 4632.89 3676.47i 0.350313 0.277994i
\(116\) 2128.13 0.158155
\(117\) −22082.9 −1.61319
\(118\) −3610.94 −0.259332
\(119\) 117.021 0.00826364
\(120\) 209.625i 0.0145573i
\(121\) 13477.7 0.920544
\(122\) 11827.1i 0.794620i
\(123\) 1466.16 0.0969108
\(124\) 4664.39 0.303355
\(125\) 1397.54i 0.0894427i
\(126\) 3843.35i 0.242086i
\(127\) −17536.1 −1.08724 −0.543621 0.839331i \(-0.682947\pi\)
−0.543621 + 0.839331i \(0.682947\pi\)
\(128\) −1448.15 −0.0883883
\(129\) 2737.17i 0.164484i
\(130\) 8694.98i 0.514496i
\(131\) −26126.8 −1.52245 −0.761226 0.648487i \(-0.775402\pi\)
−0.761226 + 0.648487i \(0.775402\pi\)
\(132\) 226.095i 0.0129761i
\(133\) 5123.67 0.289653
\(134\) 17624.2i 0.981521i
\(135\) 1494.44i 0.0819993i
\(136\) 156.503i 0.00846146i
\(137\) 17590.7i 0.937220i 0.883405 + 0.468610i \(0.155245\pi\)
−0.883405 + 0.468610i \(0.844755\pi\)
\(138\) 770.678 + 971.168i 0.0404683 + 0.0509960i
\(139\) −6189.98 −0.320376 −0.160188 0.987087i \(-0.551210\pi\)
−0.160188 + 0.987087i \(0.551210\pi\)
\(140\) 1513.29 0.0772087
\(141\) 1426.95 0.0717745
\(142\) −22106.9 −1.09635
\(143\) 9378.14i 0.458611i
\(144\) −5140.06 −0.247881
\(145\) 2974.16i 0.141458i
\(146\) −15433.6 −0.724036
\(147\) 1752.31 0.0810915
\(148\) 9046.87i 0.413024i
\(149\) 30482.6i 1.37303i −0.727117 0.686513i \(-0.759140\pi\)
0.727117 0.686513i \(-0.240860\pi\)
\(150\) 292.959 0.0130204
\(151\) 6831.67 0.299621 0.149811 0.988715i \(-0.452134\pi\)
0.149811 + 0.988715i \(0.452134\pi\)
\(152\) 6852.34i 0.296587i
\(153\) 555.490i 0.0237297i
\(154\) 1632.19 0.0688222
\(155\) 6518.69i 0.271329i
\(156\) 1822.68 0.0748965
\(157\) 44251.0i 1.79524i 0.440766 + 0.897622i \(0.354707\pi\)
−0.440766 + 0.897622i \(0.645293\pi\)
\(158\) 32540.5i 1.30350i
\(159\) 2218.61i 0.0877580i
\(160\) 2023.86i 0.0790569i
\(161\) −7010.91 + 5563.56i −0.270472 + 0.214635i
\(162\) −18086.7 −0.689176
\(163\) 3576.65 0.134618 0.0673088 0.997732i \(-0.478559\pi\)
0.0673088 + 0.997732i \(0.478559\pi\)
\(164\) 14155.3 0.526299
\(165\) 315.977 0.0116061
\(166\) 6979.38i 0.253280i
\(167\) −14455.8 −0.518332 −0.259166 0.965833i \(-0.583448\pi\)
−0.259166 + 0.965833i \(0.583448\pi\)
\(168\) 317.223i 0.0112395i
\(169\) 47041.6 1.64706
\(170\) 218.720 0.00756816
\(171\) 24321.6i 0.831763i
\(172\) 26426.5i 0.893271i
\(173\) −9552.18 −0.319161 −0.159581 0.987185i \(-0.551014\pi\)
−0.159581 + 0.987185i \(0.551014\pi\)
\(174\) −623.457 −0.0205924
\(175\) 2114.89i 0.0690575i
\(176\) 2182.87i 0.0704698i
\(177\) 1057.86 0.0337661
\(178\) 686.693i 0.0216732i
\(179\) −24503.7 −0.764761 −0.382380 0.924005i \(-0.624896\pi\)
−0.382380 + 0.924005i \(0.624896\pi\)
\(180\) 7183.45i 0.221711i
\(181\) 3317.62i 0.101267i −0.998717 0.0506337i \(-0.983876\pi\)
0.998717 0.0506337i \(-0.0161241\pi\)
\(182\) 13158.0i 0.397235i
\(183\) 3464.87i 0.103463i
\(184\) 7440.65 + 9376.32i 0.219773 + 0.276947i
\(185\) −12643.4 −0.369420
\(186\) −1366.48 −0.0394981
\(187\) 235.904 0.00674610
\(188\) 13776.7 0.389790
\(189\) 2261.52i 0.0633106i
\(190\) 9576.44 0.265275
\(191\) 23907.6i 0.655344i −0.944792 0.327672i \(-0.893736\pi\)
0.944792 0.327672i \(-0.106264\pi\)
\(192\) 424.250 0.0115085
\(193\) 12502.0 0.335634 0.167817 0.985818i \(-0.446328\pi\)
0.167817 + 0.985818i \(0.446328\pi\)
\(194\) 38585.3i 1.02522i
\(195\) 2547.27i 0.0669895i
\(196\) 16918.0 0.440388
\(197\) −17516.7 −0.451357 −0.225679 0.974202i \(-0.572460\pi\)
−0.225679 + 0.974202i \(0.572460\pi\)
\(198\) 7747.85i 0.197629i
\(199\) 8686.79i 0.219358i −0.993967 0.109679i \(-0.965018\pi\)
0.993967 0.109679i \(-0.0349823\pi\)
\(200\) 2828.43 0.0707107
\(201\) 5163.17i 0.127798i
\(202\) 8249.26 0.202168
\(203\) 4500.76i 0.109218i
\(204\) 45.8490i 0.00110172i
\(205\) 19782.7i 0.470736i
\(206\) 47572.3i 1.12104i
\(207\) 26409.7 + 33280.2i 0.616344 + 0.776684i
\(208\) 17597.4 0.406744
\(209\) 10328.9 0.236461
\(210\) −443.332 −0.0100529
\(211\) 68036.4 1.52819 0.764094 0.645105i \(-0.223186\pi\)
0.764094 + 0.645105i \(0.223186\pi\)
\(212\) 21420.0i 0.476592i
\(213\) 6476.41 0.142750
\(214\) 34052.3i 0.743565i
\(215\) −36932.2 −0.798966
\(216\) 3024.53 0.0648261
\(217\) 9864.66i 0.209490i
\(218\) 42736.4i 0.899259i
\(219\) 4521.40 0.0942725
\(220\) 3050.66 0.0630301
\(221\) 1901.76i 0.0389378i
\(222\) 2650.37i 0.0537774i
\(223\) −1496.04 −0.0300838 −0.0150419 0.999887i \(-0.504788\pi\)
−0.0150419 + 0.999887i \(0.504788\pi\)
\(224\) 3062.68i 0.0610388i
\(225\) 10039.2 0.198305
\(226\) 15361.1i 0.300750i
\(227\) 16836.2i 0.326732i 0.986566 + 0.163366i \(0.0522352\pi\)
−0.986566 + 0.163366i \(0.947765\pi\)
\(228\) 2007.46i 0.0386168i
\(229\) 19026.6i 0.362820i −0.983408 0.181410i \(-0.941934\pi\)
0.983408 0.181410i \(-0.0580661\pi\)
\(230\) −13103.8 + 10398.6i −0.247709 + 0.196571i
\(231\) −478.165 −0.00896094
\(232\) −6019.27 −0.111833
\(233\) 64511.4 1.18830 0.594148 0.804356i \(-0.297489\pi\)
0.594148 + 0.804356i \(0.297489\pi\)
\(234\) 62459.9 1.14070
\(235\) 19253.6i 0.348639i
\(236\) 10213.3 0.183375
\(237\) 9533.03i 0.169721i
\(238\) −330.986 −0.00584327
\(239\) 5760.10 0.100840 0.0504202 0.998728i \(-0.483944\pi\)
0.0504202 + 0.998728i \(0.483944\pi\)
\(240\) 592.908i 0.0102935i
\(241\) 31647.1i 0.544878i −0.962173 0.272439i \(-0.912170\pi\)
0.962173 0.272439i \(-0.0878303\pi\)
\(242\) −38120.7 −0.650923
\(243\) 16125.7 0.273090
\(244\) 33452.2i 0.561881i
\(245\) 23643.6i 0.393895i
\(246\) −4146.93 −0.0685263
\(247\) 83266.9i 1.36483i
\(248\) −13192.9 −0.214505
\(249\) 2044.67i 0.0329781i
\(250\) 3952.85i 0.0632456i
\(251\) 33172.4i 0.526538i −0.964722 0.263269i \(-0.915199\pi\)
0.964722 0.263269i \(-0.0848007\pi\)
\(252\) 10870.6i 0.171180i
\(253\) −14133.4 + 11215.6i −0.220803 + 0.175220i
\(254\) 49599.7 0.768796
\(255\) −64.0760 −0.000985405
\(256\) 4096.00 0.0625000
\(257\) −111070. −1.68163 −0.840815 0.541323i \(-0.817924\pi\)
−0.840815 + 0.541323i \(0.817924\pi\)
\(258\) 7741.90i 0.116308i
\(259\) 19133.1 0.285224
\(260\) 24593.1i 0.363803i
\(261\) −21364.7 −0.313629
\(262\) 73897.8 1.07654
\(263\) 128554.i 1.85855i −0.369384 0.929277i \(-0.620431\pi\)
0.369384 0.929277i \(-0.379569\pi\)
\(264\) 639.492i 0.00917545i
\(265\) −29935.3 −0.426277
\(266\) −14491.9 −0.204815
\(267\) 201.173i 0.00282194i
\(268\) 49848.8i 0.694040i
\(269\) 27040.9 0.373694 0.186847 0.982389i \(-0.440173\pi\)
0.186847 + 0.982389i \(0.440173\pi\)
\(270\) 4226.91i 0.0579823i
\(271\) 19692.1 0.268135 0.134068 0.990972i \(-0.457196\pi\)
0.134068 + 0.990972i \(0.457196\pi\)
\(272\) 442.658i 0.00598315i
\(273\) 3854.76i 0.0517217i
\(274\) 49753.9i 0.662714i
\(275\) 4263.42i 0.0563758i
\(276\) −2179.81 2746.88i −0.0286154 0.0360596i
\(277\) −24505.9 −0.319382 −0.159691 0.987167i \(-0.551050\pi\)
−0.159691 + 0.987167i \(0.551050\pi\)
\(278\) 17507.9 0.226540
\(279\) −46826.7 −0.601568
\(280\) −4280.23 −0.0545948
\(281\) 106703.i 1.35133i 0.737207 + 0.675667i \(0.236144\pi\)
−0.737207 + 0.675667i \(0.763856\pi\)
\(282\) −4036.02 −0.0507522
\(283\) 34820.1i 0.434767i −0.976086 0.217383i \(-0.930248\pi\)
0.976086 0.217383i \(-0.0697522\pi\)
\(284\) 62527.6 0.775239
\(285\) −2805.51 −0.0345399
\(286\) 26525.4i 0.324287i
\(287\) 29936.9i 0.363449i
\(288\) 14538.3 0.175278
\(289\) 83473.2 0.999427
\(290\) 8412.19i 0.100026i
\(291\) 11303.9i 0.133488i
\(292\) 43652.7 0.511971
\(293\) 97143.9i 1.13157i 0.824554 + 0.565783i \(0.191426\pi\)
−0.824554 + 0.565783i \(0.808574\pi\)
\(294\) −4956.27 −0.0573404
\(295\) 14273.5i 0.164016i
\(296\) 25588.4i 0.292052i
\(297\) 4559.01i 0.0516842i
\(298\) 86217.7i 0.970876i
\(299\) −90415.8 113937.i −1.01135 1.27445i
\(300\) −828.614 −0.00920682
\(301\) 55889.1 0.616871
\(302\) −19322.9 −0.211864
\(303\) −2416.70 −0.0263231
\(304\) 19381.3i 0.209718i
\(305\) 46750.8 0.502562
\(306\) 1571.16i 0.0167795i
\(307\) −124144. −1.31719 −0.658594 0.752498i \(-0.728849\pi\)
−0.658594 + 0.752498i \(0.728849\pi\)
\(308\) −4616.53 −0.0486647
\(309\) 13936.8i 0.145964i
\(310\) 18437.6i 0.191859i
\(311\) −82226.6 −0.850142 −0.425071 0.905160i \(-0.639751\pi\)
−0.425071 + 0.905160i \(0.639751\pi\)
\(312\) −5155.32 −0.0529598
\(313\) 108944.i 1.11203i −0.831173 0.556014i \(-0.812330\pi\)
0.831173 0.556014i \(-0.187670\pi\)
\(314\) 125161.i 1.26943i
\(315\) −15192.2 −0.153108
\(316\) 92038.4i 0.921711i
\(317\) 107217. 1.06695 0.533476 0.845815i \(-0.320885\pi\)
0.533476 + 0.845815i \(0.320885\pi\)
\(318\) 6275.18i 0.0620543i
\(319\) 9073.13i 0.0891612i
\(320\) 5724.33i 0.0559017i
\(321\) 9975.94i 0.0968152i
\(322\) 19829.8 15736.1i 0.191253 0.151770i
\(323\) −2094.56 −0.0200764
\(324\) 51157.0 0.487321
\(325\) −34369.9 −0.325396
\(326\) −10116.3 −0.0951890
\(327\) 12520.0i 0.117087i
\(328\) −40037.3 −0.372149
\(329\) 29136.2i 0.269179i
\(330\) −893.718 −0.00820678
\(331\) −128870. −1.17624 −0.588120 0.808773i \(-0.700132\pi\)
−0.588120 + 0.808773i \(0.700132\pi\)
\(332\) 19740.7i 0.179096i
\(333\) 90823.2i 0.819046i
\(334\) 40887.1 0.366516
\(335\) −69665.8 −0.620769
\(336\) 897.242i 0.00794750i
\(337\) 91307.7i 0.803984i 0.915643 + 0.401992i \(0.131682\pi\)
−0.915643 + 0.401992i \(0.868318\pi\)
\(338\) −133054. −1.16465
\(339\) 4500.18i 0.0391589i
\(340\) −618.633 −0.00535149
\(341\) 19886.3i 0.171019i
\(342\) 68791.8i 0.588145i
\(343\) 76402.3i 0.649409i
\(344\) 74745.5i 0.631638i
\(345\) 3838.88 3046.37i 0.0322527 0.0255944i
\(346\) 27017.6 0.225681
\(347\) −199317. −1.65534 −0.827668 0.561219i \(-0.810333\pi\)
−0.827668 + 0.561219i \(0.810333\pi\)
\(348\) 1763.40 0.0145611
\(349\) 186033. 1.52735 0.763674 0.645602i \(-0.223393\pi\)
0.763674 + 0.645602i \(0.223393\pi\)
\(350\) 5981.80i 0.0488310i
\(351\) −36752.9 −0.298316
\(352\) 6174.09i 0.0498296i
\(353\) 125942. 1.01069 0.505347 0.862916i \(-0.331365\pi\)
0.505347 + 0.862916i \(0.331365\pi\)
\(354\) −2992.07 −0.0238762
\(355\) 87385.0i 0.693395i
\(356\) 1942.26i 0.0153252i
\(357\) 96.9655 0.000760818
\(358\) 69306.9 0.540767
\(359\) 70779.3i 0.549183i −0.961561 0.274592i \(-0.911457\pi\)
0.961561 0.274592i \(-0.0885427\pi\)
\(360\) 20317.9i 0.156774i
\(361\) 38612.9 0.296291
\(362\) 9383.64i 0.0716068i
\(363\) 11167.8 0.0847529
\(364\) 37216.5i 0.280888i
\(365\) 61006.5i 0.457921i
\(366\) 9800.12i 0.0731593i
\(367\) 31425.9i 0.233322i 0.993172 + 0.116661i \(0.0372191\pi\)
−0.993172 + 0.116661i \(0.962781\pi\)
\(368\) −21045.3 26520.2i −0.155403 0.195831i
\(369\) −142108. −1.04367
\(370\) 35760.9 0.261219
\(371\) 45300.8 0.329123
\(372\) 3864.98 0.0279294
\(373\) 173293.i 1.24556i 0.782399 + 0.622778i \(0.213996\pi\)
−0.782399 + 0.622778i \(0.786004\pi\)
\(374\) −667.239 −0.00477021
\(375\) 1158.02i 0.00823483i
\(376\) −38966.5 −0.275623
\(377\) 73143.8 0.514630
\(378\) 6396.54i 0.0447673i
\(379\) 12563.7i 0.0874663i 0.999043 + 0.0437331i \(0.0139251\pi\)
−0.999043 + 0.0437331i \(0.986075\pi\)
\(380\) −27086.2 −0.187578
\(381\) −14530.7 −0.100100
\(382\) 67620.9i 0.463398i
\(383\) 155679.i 1.06129i −0.847595 0.530643i \(-0.821950\pi\)
0.847595 0.530643i \(-0.178050\pi\)
\(384\) −1199.96 −0.00813776
\(385\) 6451.79i 0.0435270i
\(386\) −35361.1 −0.237329
\(387\) 265300.i 1.77140i
\(388\) 109136.i 0.724943i
\(389\) 271059.i 1.79129i 0.444773 + 0.895644i \(0.353285\pi\)
−0.444773 + 0.895644i \(0.646715\pi\)
\(390\) 7204.78i 0.0473687i
\(391\) 2866.06 2274.38i 0.0187470 0.0148768i
\(392\) −47851.2 −0.311401
\(393\) −21649.0 −0.140169
\(394\) 49544.8 0.319158
\(395\) −128628. −0.824403
\(396\) 21914.2i 0.139745i
\(397\) 232055. 1.47234 0.736172 0.676794i \(-0.236631\pi\)
0.736172 + 0.676794i \(0.236631\pi\)
\(398\) 24570.0i 0.155109i
\(399\) 4245.54 0.0266678
\(400\) −8000.00 −0.0500000
\(401\) 313994.i 1.95268i −0.216231 0.976342i \(-0.569377\pi\)
0.216231 0.976342i \(-0.430623\pi\)
\(402\) 14603.7i 0.0903669i
\(403\) 160315. 0.987105
\(404\) −23332.4 −0.142954
\(405\) 71494.1i 0.435873i
\(406\) 12730.1i 0.0772288i
\(407\) 38570.6 0.232846
\(408\) 129.681i 0.000779031i
\(409\) −278472. −1.66470 −0.832349 0.554251i \(-0.813005\pi\)
−0.832349 + 0.554251i \(0.813005\pi\)
\(410\) 55953.8i 0.332860i
\(411\) 14575.9i 0.0862881i
\(412\) 134555.i 0.792693i
\(413\) 21599.9i 0.126635i
\(414\) −74698.0 94130.5i −0.435821 0.549199i
\(415\) −27588.4 −0.160188
\(416\) −49772.9 −0.287612
\(417\) −5129.11 −0.0294964
\(418\) −29214.4 −0.167203
\(419\) 92205.6i 0.525206i 0.964904 + 0.262603i \(0.0845809\pi\)
−0.964904 + 0.262603i \(0.915419\pi\)
\(420\) 1253.93 0.00710846
\(421\) 273540.i 1.54332i 0.636035 + 0.771660i \(0.280573\pi\)
−0.636035 + 0.771660i \(0.719427\pi\)
\(422\) −192436. −1.08059
\(423\) −138307. −0.772971
\(424\) 60584.8i 0.337002i
\(425\) 864.566i 0.00478652i
\(426\) −18318.1 −0.100939
\(427\) −70747.6 −0.388021
\(428\) 96314.4i 0.525780i
\(429\) 7770.86i 0.0422235i
\(430\) 104460. 0.564954
\(431\) 108915.i 0.586316i −0.956064 0.293158i \(-0.905294\pi\)
0.956064 0.293158i \(-0.0947061\pi\)
\(432\) −8554.66 −0.0458390
\(433\) 152308.i 0.812359i −0.913793 0.406179i \(-0.866861\pi\)
0.913793 0.406179i \(-0.133139\pi\)
\(434\) 27901.5i 0.148132i
\(435\) 2464.43i 0.0130238i
\(436\) 120877.i 0.635872i
\(437\) 125488. 99581.8i 0.657110 0.521455i
\(438\) −12788.5 −0.0666607
\(439\) 130401. 0.676632 0.338316 0.941033i \(-0.390143\pi\)
0.338316 + 0.941033i \(0.390143\pi\)
\(440\) −8628.56 −0.0445690
\(441\) −169842. −0.873310
\(442\) 5379.00i 0.0275332i
\(443\) −253547. −1.29197 −0.645983 0.763352i \(-0.723552\pi\)
−0.645983 + 0.763352i \(0.723552\pi\)
\(444\) 7496.37i 0.0380264i
\(445\) −2714.39 −0.0137073
\(446\) 4231.44 0.0212725
\(447\) 25258.3i 0.126412i
\(448\) 8662.58i 0.0431610i
\(449\) 102672. 0.509282 0.254641 0.967036i \(-0.418043\pi\)
0.254641 + 0.967036i \(0.418043\pi\)
\(450\) −28395.1 −0.140223
\(451\) 60350.1i 0.296705i
\(452\) 43447.8i 0.212663i
\(453\) 5660.81 0.0275856
\(454\) 47619.9i 0.231035i
\(455\) 52011.6 0.251234
\(456\) 5677.94i 0.0273062i
\(457\) 45739.5i 0.219008i 0.993986 + 0.109504i \(0.0349262\pi\)
−0.993986 + 0.109504i \(0.965074\pi\)
\(458\) 53815.5i 0.256552i
\(459\) 924.508i 0.00438819i
\(460\) 37063.1 29411.8i 0.175157 0.138997i
\(461\) 156031. 0.734192 0.367096 0.930183i \(-0.380352\pi\)
0.367096 + 0.930183i \(0.380352\pi\)
\(462\) 1352.45 0.00633634
\(463\) 234327. 1.09310 0.546549 0.837427i \(-0.315941\pi\)
0.546549 + 0.837427i \(0.315941\pi\)
\(464\) 17025.1 0.0790775
\(465\) 5401.48i 0.0249808i
\(466\) −182466. −0.840252
\(467\) 385291.i 1.76667i 0.468744 + 0.883334i \(0.344707\pi\)
−0.468744 + 0.883334i \(0.655293\pi\)
\(468\) −176663. −0.806593
\(469\) 105424. 0.479287
\(470\) 54457.3i 0.246525i
\(471\) 36667.0i 0.165285i
\(472\) −28887.5 −0.129666
\(473\) 112667. 0.503589
\(474\) 26963.5i 0.120011i
\(475\) 37854.2i 0.167775i
\(476\) 936.171 0.00413182
\(477\) 215039.i 0.945105i
\(478\) −16292.0 −0.0713049
\(479\) 82157.1i 0.358075i −0.983842 0.179038i \(-0.942702\pi\)
0.983842 0.179038i \(-0.0572984\pi\)
\(480\) 1677.00i 0.00727863i
\(481\) 310940.i 1.34396i
\(482\) 89511.4i 0.385287i
\(483\) −5809.34 + 4610.05i −0.0249019 + 0.0197611i
\(484\) 107822. 0.460272
\(485\) −152522. −0.648408
\(486\) −45610.3 −0.193104
\(487\) −228829. −0.964837 −0.482418 0.875941i \(-0.660242\pi\)
−0.482418 + 0.875941i \(0.660242\pi\)
\(488\) 94617.0i 0.397310i
\(489\) 2963.67 0.0123940
\(490\) 66874.1i 0.278526i
\(491\) 225264. 0.934390 0.467195 0.884154i \(-0.345265\pi\)
0.467195 + 0.884154i \(0.345265\pi\)
\(492\) 11729.3 0.0484554
\(493\) 1839.91i 0.00757013i
\(494\) 235514.i 0.965080i
\(495\) −30626.1 −0.124992
\(496\) 37315.1 0.151678
\(497\) 132239.i 0.535361i
\(498\) 5783.21i 0.0233190i
\(499\) −211941. −0.851163 −0.425582 0.904920i \(-0.639930\pi\)
−0.425582 + 0.904920i \(0.639930\pi\)
\(500\) 11180.3i 0.0447214i
\(501\) −11978.3 −0.0477220
\(502\) 93825.8i 0.372319i
\(503\) 149353.i 0.590306i 0.955450 + 0.295153i \(0.0953706\pi\)
−0.955450 + 0.295153i \(0.904629\pi\)
\(504\) 30746.8i 0.121043i
\(505\) 32608.1i 0.127862i
\(506\) 39975.2 31722.6i 0.156131 0.123899i
\(507\) 38979.3 0.151642
\(508\) −140289. −0.543621
\(509\) −375302. −1.44859 −0.724295 0.689490i \(-0.757835\pi\)
−0.724295 + 0.689490i \(0.757835\pi\)
\(510\) 181.234 0.000696787
\(511\) 92320.5i 0.353555i
\(512\) −11585.2 −0.0441942
\(513\) 40478.7i 0.153813i
\(514\) 314153. 1.18909
\(515\) 188046. 0.709006
\(516\) 21897.4i 0.0822419i
\(517\) 58736.0i 0.219747i
\(518\) −54116.6 −0.201684
\(519\) −7915.07 −0.0293846
\(520\) 69559.8i 0.257248i
\(521\) 80213.3i 0.295509i 0.989024 + 0.147755i \(0.0472046\pi\)
−0.989024 + 0.147755i \(0.952795\pi\)
\(522\) 60428.5 0.221769
\(523\) 61120.2i 0.223451i −0.993739 0.111725i \(-0.964362\pi\)
0.993739 0.111725i \(-0.0356377\pi\)
\(524\) −209014. −0.761226
\(525\) 1752.42i 0.00635800i
\(526\) 363606.i 1.31420i
\(527\) 4032.67i 0.0145202i
\(528\) 1808.76i 0.00648803i
\(529\) −63578.2 + 272523.i −0.227194 + 0.973850i
\(530\) 84669.9 0.301424
\(531\) −102533. −0.363642
\(532\) 40989.3 0.144826
\(533\) 486517. 1.71255
\(534\) 569.003i 0.00199541i
\(535\) 134603. 0.470272
\(536\) 140994.i 0.490761i
\(537\) −20304.1 −0.0704102
\(538\) −76483.1 −0.264241
\(539\) 72128.4i 0.248272i
\(540\) 11955.5i 0.0409997i
\(541\) 211761. 0.723521 0.361760 0.932271i \(-0.382176\pi\)
0.361760 + 0.932271i \(0.382176\pi\)
\(542\) −55697.7 −0.189600
\(543\) 2749.03i 0.00932350i
\(544\) 1252.02i 0.00423073i
\(545\) 168930. 0.568741
\(546\) 10902.9i 0.0365727i
\(547\) 475518. 1.58925 0.794624 0.607101i \(-0.207668\pi\)
0.794624 + 0.607101i \(0.207668\pi\)
\(548\) 140725.i 0.468610i
\(549\) 335832.i 1.11424i
\(550\) 12058.8i 0.0398637i
\(551\) 80558.8i 0.265344i
\(552\) 6165.43 + 7769.35i 0.0202342 + 0.0254980i
\(553\) 194651. 0.636511
\(554\) 69313.1 0.225837
\(555\) −10476.5 −0.0340118
\(556\) −49519.9 −0.160188
\(557\) 329137.i 1.06088i 0.847722 + 0.530441i \(0.177974\pi\)
−0.847722 + 0.530441i \(0.822026\pi\)
\(558\) 132446. 0.425373
\(559\) 908277.i 2.90666i
\(560\) 12106.3 0.0386043
\(561\) 195.474 0.000621102
\(562\) 301801.i 0.955537i
\(563\) 187233.i 0.590697i −0.955390 0.295348i \(-0.904564\pi\)
0.955390 0.295348i \(-0.0954357\pi\)
\(564\) 11415.6 0.0358872
\(565\) 60720.1 0.190211
\(566\) 98486.0i 0.307427i
\(567\) 108191.i 0.336532i
\(568\) −176855. −0.548177
\(569\) 354702.i 1.09557i 0.836620 + 0.547784i \(0.184528\pi\)
−0.836620 + 0.547784i \(0.815472\pi\)
\(570\) 7935.17 0.0244234
\(571\) 142525.i 0.437139i −0.975821 0.218570i \(-0.929861\pi\)
0.975821 0.218570i \(-0.0701391\pi\)
\(572\) 75025.1i 0.229305i
\(573\) 19810.2i 0.0603363i
\(574\) 84674.4i 0.256997i
\(575\) 41104.2 + 51797.3i 0.124323 + 0.156665i
\(576\) −41120.5 −0.123940
\(577\) 397881. 1.19509 0.597546 0.801834i \(-0.296142\pi\)
0.597546 + 0.801834i \(0.296142\pi\)
\(578\) −236098. −0.706702
\(579\) 10359.4 0.0309012
\(580\) 23793.3i 0.0707291i
\(581\) 41749.3 0.123679
\(582\) 31972.3i 0.0943905i
\(583\) 91322.3 0.268683
\(584\) −123468. −0.362018
\(585\) 246894.i 0.721439i
\(586\) 274764.i 0.800139i
\(587\) 49627.5 0.144028 0.0720139 0.997404i \(-0.477057\pi\)
0.0720139 + 0.997404i \(0.477057\pi\)
\(588\) 14018.5 0.0405458
\(589\) 176567.i 0.508954i
\(590\) 40371.5i 0.115977i
\(591\) −14514.6 −0.0415557
\(592\) 72375.0i 0.206512i
\(593\) 315575. 0.897415 0.448708 0.893679i \(-0.351884\pi\)
0.448708 + 0.893679i \(0.351884\pi\)
\(594\) 12894.8i 0.0365463i
\(595\) 1308.34i 0.00369561i
\(596\) 243860.i 0.686513i
\(597\) 7198.00i 0.0201959i
\(598\) 255734. + 322263.i 0.715133 + 0.901173i
\(599\) −276969. −0.771931 −0.385965 0.922513i \(-0.626132\pi\)
−0.385965 + 0.922513i \(0.626132\pi\)
\(600\) 2343.67 0.00651021
\(601\) 284226. 0.786890 0.393445 0.919348i \(-0.371283\pi\)
0.393445 + 0.919348i \(0.371283\pi\)
\(602\) −158078. −0.436193
\(603\) 500440.i 1.37631i
\(604\) 54653.3 0.149811
\(605\) 150685.i 0.411680i
\(606\) 6835.46 0.0186133
\(607\) −264420. −0.717657 −0.358828 0.933404i \(-0.616824\pi\)
−0.358828 + 0.933404i \(0.616824\pi\)
\(608\) 54818.7i 0.148293i
\(609\) 3729.40i 0.0100555i
\(610\) −132231. −0.355365
\(611\) 473505. 1.26836
\(612\) 4443.92i 0.0118649i
\(613\) 321222.i 0.854839i 0.904053 + 0.427420i \(0.140577\pi\)
−0.904053 + 0.427420i \(0.859423\pi\)
\(614\) 351131. 0.931393
\(615\) 16392.2i 0.0433398i
\(616\) 13057.5 0.0344111
\(617\) 246378.i 0.647190i 0.946196 + 0.323595i \(0.104891\pi\)
−0.946196 + 0.323595i \(0.895109\pi\)
\(618\) 39419.1i 0.103212i
\(619\) 518214.i 1.35247i −0.736685 0.676236i \(-0.763610\pi\)
0.736685 0.676236i \(-0.236390\pi\)
\(620\) 52149.5i 0.135665i
\(621\) 43954.0 + 55388.5i 0.113977 + 0.143627i
\(622\) 232572. 0.601141
\(623\) 4107.66 0.0105832
\(624\) 14581.4 0.0374482
\(625\) 15625.0 0.0400000
\(626\) 308141.i 0.786322i
\(627\) 8558.63 0.0217705
\(628\) 354008.i 0.897622i
\(629\) −7821.62 −0.0197695
\(630\) 42970.0 0.108264
\(631\) 173044.i 0.434607i −0.976104 0.217304i \(-0.930274\pi\)
0.976104 0.217304i \(-0.0697262\pi\)
\(632\) 260324.i 0.651748i
\(633\) 56376.0 0.140698
\(634\) −303256. −0.754450
\(635\) 196060.i 0.486229i
\(636\) 17748.9i 0.0438790i
\(637\) 581469. 1.43300
\(638\) 25662.7i 0.0630465i
\(639\) −627726. −1.53733
\(640\) 16190.9i 0.0395285i
\(641\) 228416.i 0.555917i −0.960593 0.277958i \(-0.910342\pi\)
0.960593 0.277958i \(-0.0896577\pi\)
\(642\) 28216.2i 0.0684587i
\(643\) 631308.i 1.52693i 0.645849 + 0.763465i \(0.276503\pi\)
−0.645849 + 0.763465i \(0.723497\pi\)
\(644\) −56087.3 + 44508.5i −0.135236 + 0.107318i
\(645\) −30602.5 −0.0735594
\(646\) 5924.30 0.0141962
\(647\) 49159.1 0.117434 0.0587172 0.998275i \(-0.481299\pi\)
0.0587172 + 0.998275i \(0.481299\pi\)
\(648\) −144694. −0.344588
\(649\) 43543.5i 0.103379i
\(650\) 97212.8 0.230089
\(651\) 8174.00i 0.0192873i
\(652\) 28613.2 0.0673088
\(653\) −473169. −1.10966 −0.554829 0.831964i \(-0.687217\pi\)
−0.554829 + 0.831964i \(0.687217\pi\)
\(654\) 35412.0i 0.0827932i
\(655\) 292107.i 0.680861i
\(656\) 113243. 0.263149
\(657\) −438237. −1.01526
\(658\) 82409.7i 0.190338i
\(659\) 448560.i 1.03288i 0.856323 + 0.516440i \(0.172743\pi\)
−0.856323 + 0.516440i \(0.827257\pi\)
\(660\) 2527.82 0.00580307
\(661\) 135040.i 0.309071i −0.987987 0.154536i \(-0.950612\pi\)
0.987987 0.154536i \(-0.0493881\pi\)
\(662\) 364500. 0.831728
\(663\) 1575.83i 0.00358494i
\(664\) 55835.0i 0.126640i
\(665\) 57284.3i 0.129537i
\(666\) 256887.i 0.579153i
\(667\) −87475.2 110232.i −0.196623 0.247773i
\(668\) −115646. −0.259166
\(669\) −1239.64 −0.00276977
\(670\) 197045. 0.438950
\(671\) −142621. −0.316765
\(672\) 2537.78i 0.00561973i
\(673\) −597311. −1.31877 −0.659387 0.751803i \(-0.729184\pi\)
−0.659387 + 0.751803i \(0.729184\pi\)
\(674\) 258257.i 0.568502i
\(675\) 16708.3 0.0366712
\(676\) 376333. 0.823529
\(677\) 735875.i 1.60556i −0.596274 0.802781i \(-0.703353\pi\)
0.596274 0.802781i \(-0.296647\pi\)
\(678\) 12728.4i 0.0276895i
\(679\) 230810. 0.500627
\(680\) 1749.76 0.00378408
\(681\) 13950.7i 0.0300817i
\(682\) 56246.9i 0.120929i
\(683\) −393705. −0.843975 −0.421988 0.906602i \(-0.638667\pi\)
−0.421988 + 0.906602i \(0.638667\pi\)
\(684\) 194573.i 0.415882i
\(685\) −196670. −0.419137
\(686\) 216098.i 0.459201i
\(687\) 15765.7i 0.0334042i
\(688\) 211412.i 0.446635i
\(689\) 736202.i 1.55081i
\(690\) −10858.0 + 8616.45i −0.0228061 + 0.0180980i
\(691\) 41361.1 0.0866236 0.0433118 0.999062i \(-0.486209\pi\)
0.0433118 + 0.999062i \(0.486209\pi\)
\(692\) −76417.4 −0.159581
\(693\) 46346.1 0.0965043
\(694\) 563754. 1.17050
\(695\) 69206.1i 0.143276i
\(696\) −4987.65 −0.0102962
\(697\) 12238.2i 0.0251914i
\(698\) −526180. −1.08000
\(699\) 53455.1 0.109404
\(700\) 16919.1i 0.0345288i
\(701\) 528870.i 1.07625i −0.842865 0.538124i \(-0.819133\pi\)
0.842865 0.538124i \(-0.180867\pi\)
\(702\) 103953. 0.210941
\(703\) −342462. −0.692950
\(704\) 17463.0i 0.0352349i
\(705\) 15953.8i 0.0320985i
\(706\) −356216. −0.714668
\(707\) 49345.5i 0.0987208i
\(708\) 8462.87 0.0168831
\(709\) 26402.1i 0.0525225i 0.999655 + 0.0262613i \(0.00836018\pi\)
−0.999655 + 0.0262613i \(0.991640\pi\)
\(710\) 247162.i 0.490304i
\(711\) 923989.i 1.82780i
\(712\) 5493.54i 0.0108366i
\(713\) −191726. 241603.i −0.377139 0.475251i
\(714\) −274.260 −0.000537980
\(715\) 104851. 0.205097
\(716\) −196030. −0.382380
\(717\) 4772.90 0.00928419
\(718\) 200194.i 0.388331i
\(719\) 395915. 0.765850 0.382925 0.923779i \(-0.374917\pi\)
0.382925 + 0.923779i \(0.374917\pi\)
\(720\) 57467.6i 0.110856i
\(721\) −284568. −0.547414
\(722\) −109214. −0.209509
\(723\) 26223.2i 0.0501660i
\(724\) 26540.9i 0.0506337i
\(725\) −33252.1 −0.0632620
\(726\) −31587.3 −0.0599293
\(727\) 485482.i 0.918554i −0.888293 0.459277i \(-0.848109\pi\)
0.888293 0.459277i \(-0.151891\pi\)
\(728\) 105264.i 0.198618i
\(729\) −504603. −0.949499
\(730\) 172552.i 0.323799i
\(731\) −22847.5 −0.0427566
\(732\) 27718.9i 0.0517314i
\(733\) 462501.i 0.860806i 0.902637 + 0.430403i \(0.141628\pi\)
−0.902637 + 0.430403i \(0.858372\pi\)
\(734\) 88885.9i 0.164984i
\(735\) 19591.4i 0.0362652i
\(736\) 59525.2 + 75010.5i 0.109887 + 0.138473i
\(737\) 212526. 0.391271
\(738\) 401942. 0.737990
\(739\) −1.02284e6 −1.87291 −0.936455 0.350787i \(-0.885914\pi\)
−0.936455 + 0.350787i \(0.885914\pi\)
\(740\) −101147. −0.184710
\(741\) 68996.1i 0.125657i
\(742\) −128130. −0.232725
\(743\) 994757.i 1.80194i 0.433886 + 0.900968i \(0.357142\pi\)
−0.433886 + 0.900968i \(0.642858\pi\)
\(744\) −10931.8 −0.0197491
\(745\) 340805. 0.614036
\(746\) 490146.i 0.880741i
\(747\) 198180.i 0.355156i
\(748\) 1887.24 0.00337305
\(749\) −203694. −0.363090
\(750\) 3275.38i 0.00582291i
\(751\) 103292.i 0.183142i 0.995799 + 0.0915712i \(0.0291889\pi\)
−0.995799 + 0.0915712i \(0.970811\pi\)
\(752\) 110214. 0.194895
\(753\) 27487.2i 0.0484775i
\(754\) −206882. −0.363898
\(755\) 76380.3i 0.133995i
\(756\) 18092.1i 0.0316553i
\(757\) 591075.i 1.03146i −0.856752 0.515728i \(-0.827522\pi\)
0.856752 0.515728i \(-0.172478\pi\)
\(758\) 35535.6i 0.0618480i
\(759\) −11711.1 + 9293.44i −0.0203289 + 0.0161322i
\(760\) 76611.5 0.132638
\(761\) 1318.58 0.00227686 0.00113843 0.999999i \(-0.499638\pi\)
0.00113843 + 0.999999i \(0.499638\pi\)
\(762\) 41099.0 0.0707817
\(763\) −255641. −0.439118
\(764\) 191261.i 0.327672i
\(765\) 6210.56 0.0106123
\(766\) 440327.i 0.750443i
\(767\) 351029. 0.596696
\(768\) 3394.00 0.00575426
\(769\) 876913.i 1.48287i −0.671024 0.741436i \(-0.734145\pi\)
0.671024 0.741436i \(-0.265855\pi\)
\(770\) 18248.4i 0.0307782i
\(771\) −92034.1 −0.154825
\(772\) 100016. 0.167817
\(773\) 387136.i 0.647894i −0.946075 0.323947i \(-0.894990\pi\)
0.946075 0.323947i \(-0.105010\pi\)
\(774\) 750383.i 1.25257i
\(775\) −72881.1 −0.121342
\(776\) 308683.i 0.512612i
\(777\) 15854.0 0.0262601
\(778\) 766672.i 1.26663i
\(779\) 535838.i 0.882996i
\(780\) 20378.2i 0.0334947i
\(781\) 266582.i 0.437047i
\(782\) −8106.44 + 6432.93i −0.0132561 + 0.0105195i
\(783\) −35557.5 −0.0579974
\(784\) 135344. 0.220194
\(785\) −494741. −0.802858
\(786\) 61232.7 0.0991148
\(787\) 959056.i 1.54844i −0.632916 0.774220i \(-0.718142\pi\)
0.632916 0.774220i \(-0.281858\pi\)
\(788\) −140134. −0.225679
\(789\) 106522.i 0.171114i
\(790\) 363814. 0.582941
\(791\) −91887.2 −0.146859
\(792\) 61982.8i 0.0988145i
\(793\) 1.14975e6i 1.82834i
\(794\) −656350. −1.04110
\(795\) −24804.8 −0.0392466
\(796\) 69494.4i 0.109679i
\(797\) 487707.i 0.767790i −0.923377 0.383895i \(-0.874582\pi\)
0.923377 0.383895i \(-0.125418\pi\)
\(798\) −12008.2 −0.0188570
\(799\) 11910.9i 0.0186574i
\(800\) 22627.4 0.0353553
\(801\) 19498.7i 0.0303907i
\(802\) 888108.i 1.38076i
\(803\) 186110.i 0.288628i
\(804\) 41305.4i 0.0638991i
\(805\) −62202.5 78384.4i −0.0959879 0.120959i
\(806\) −453439. −0.697989
\(807\) 22406.4 0.0344053
\(808\) 65994.1 0.101084
\(809\) −759228. −1.16005 −0.580023 0.814600i \(-0.696956\pi\)
−0.580023 + 0.814600i \(0.696956\pi\)
\(810\) 202216.i 0.308209i
\(811\) −713256. −1.08443 −0.542217 0.840238i \(-0.682415\pi\)
−0.542217 + 0.840238i \(0.682415\pi\)
\(812\) 36006.1i 0.0546090i
\(813\) 16317.2 0.0246867
\(814\) −109094. −0.164647
\(815\) 39988.2i 0.0602028i
\(816\) 366.792i 0.000550858i
\(817\) −1.00035e6 −1.49868
\(818\) 787639. 1.17712
\(819\) 373623.i 0.557013i
\(820\) 158261.i 0.235368i
\(821\) −29380.0 −0.0435879 −0.0217939 0.999762i \(-0.506938\pi\)
−0.0217939 + 0.999762i \(0.506938\pi\)
\(822\) 41226.8i 0.0610149i
\(823\) −48085.4 −0.0709927 −0.0354964 0.999370i \(-0.511301\pi\)
−0.0354964 + 0.999370i \(0.511301\pi\)
\(824\) 380579.i 0.560519i
\(825\) 3532.73i 0.00519042i
\(826\) 61093.8i 0.0895441i
\(827\) 35849.1i 0.0524165i 0.999657 + 0.0262082i \(0.00834330\pi\)
−0.999657 + 0.0262082i \(0.991657\pi\)
\(828\) 211278. + 266241.i 0.308172 + 0.388342i
\(829\) −576268. −0.838523 −0.419262 0.907865i \(-0.637711\pi\)
−0.419262 + 0.907865i \(0.637711\pi\)
\(830\) 78031.8 0.113270
\(831\) −20305.9 −0.0294050
\(832\) 140779. 0.203372
\(833\) 14626.7i 0.0210793i
\(834\) 14507.3 0.0208571
\(835\) 161620.i 0.231805i
\(836\) 82630.8 0.118230
\(837\) −77934.2 −0.111244
\(838\) 260797.i 0.371376i
\(839\) 87596.3i 0.124441i −0.998062 0.0622203i \(-0.980182\pi\)
0.998062 0.0622203i \(-0.0198181\pi\)
\(840\) −3546.66 −0.00502644
\(841\) −636516. −0.899948
\(842\) 773687.i 1.09129i
\(843\) 88415.3i 0.124415i
\(844\) 544292. 0.764094
\(845\) 525941.i 0.736586i
\(846\) 391191. 0.546573
\(847\) 228030.i 0.317853i
\(848\) 171360.i 0.238296i
\(849\) 28852.4i 0.0400282i
\(850\) 2445.36i 0.00338458i
\(851\) 468604. 371864.i 0.647063 0.513482i
\(852\) 51811.3 0.0713748
\(853\) −420184. −0.577486 −0.288743 0.957407i \(-0.593237\pi\)
−0.288743 + 0.957407i \(0.593237\pi\)
\(854\) 200104. 0.274373
\(855\) 271924. 0.371976
\(856\) 272418.i 0.371782i
\(857\) 230966. 0.314476 0.157238 0.987561i \(-0.449741\pi\)
0.157238 + 0.987561i \(0.449741\pi\)
\(858\) 21979.3i 0.0298565i
\(859\) −563067. −0.763086 −0.381543 0.924351i \(-0.624607\pi\)
−0.381543 + 0.924351i \(0.624607\pi\)
\(860\) −295458. −0.399483
\(861\) 24806.1i 0.0334621i
\(862\) 308057.i 0.414588i
\(863\) 126973. 0.170486 0.0852432 0.996360i \(-0.472833\pi\)
0.0852432 + 0.996360i \(0.472833\pi\)
\(864\) 24196.2 0.0324131
\(865\) 106797.i 0.142733i
\(866\) 430793.i 0.574424i
\(867\) 69167.0 0.0920155
\(868\) 78917.3i 0.104745i
\(869\) 392398. 0.519622
\(870\) 6970.46i 0.00920922i
\(871\) 1.71330e6i 2.25838i
\(872\) 341891.i 0.449629i
\(873\) 1.09563e6i 1.43759i
\(874\) −354933. + 281660.i −0.464647 + 0.368724i
\(875\) −23645.2 −0.0308835
\(876\) 36171.2 0.0471363
\(877\) 189475. 0.246351 0.123175 0.992385i \(-0.460692\pi\)
0.123175 + 0.992385i \(0.460692\pi\)
\(878\) −368830. −0.478451
\(879\) 80494.8i 0.104181i
\(880\) 24405.2 0.0315150
\(881\) 1.05812e6i 1.36328i 0.731688 + 0.681640i \(0.238733\pi\)
−0.731688 + 0.681640i \(0.761267\pi\)
\(882\) 480387. 0.617524
\(883\) 672501. 0.862524 0.431262 0.902227i \(-0.358068\pi\)
0.431262 + 0.902227i \(0.358068\pi\)
\(884\) 15214.1i 0.0194689i
\(885\) 11827.2i 0.0151007i
\(886\) 717139. 0.913558
\(887\) 868186. 1.10348 0.551742 0.834015i \(-0.313963\pi\)
0.551742 + 0.834015i \(0.313963\pi\)
\(888\) 21202.9i 0.0268887i
\(889\) 296695.i 0.375411i
\(890\) 7677.46 0.00969254
\(891\) 218104.i 0.274731i
\(892\) −11968.3 −0.0150419
\(893\) 521507.i 0.653969i
\(894\) 71441.2i 0.0893869i
\(895\) 273960.i 0.342011i
\(896\) 24501.5i 0.0305194i
\(897\) −74919.8 94410.0i −0.0931133 0.117336i
\(898\) −290399. −0.360117
\(899\) 155101. 0.191909
\(900\) 80313.4 0.0991523
\(901\) −18519.0 −0.0228122
\(902\) 170696.i 0.209802i
\(903\) 46310.5 0.0567942
\(904\) 122889.i 0.150375i
\(905\) 37092.1 0.0452881
\(906\) −16011.2 −0.0195060
\(907\) 83304.6i 0.101264i −0.998717 0.0506319i \(-0.983876\pi\)
0.998717 0.0506319i \(-0.0161235\pi\)
\(908\) 134690.i 0.163366i
\(909\) 234238. 0.283485
\(910\) −147111. −0.177649
\(911\) 759069.i 0.914628i −0.889305 0.457314i \(-0.848812\pi\)
0.889305 0.457314i \(-0.151188\pi\)
\(912\) 16059.7i 0.0193084i
\(913\) 84162.8 0.100967
\(914\) 129371.i 0.154862i
\(915\) 38738.4 0.0462700
\(916\) 152213.i 0.181410i
\(917\) 442042.i 0.525684i
\(918\) 2614.90i 0.00310292i
\(919\) 89451.9i 0.105915i −0.998597 0.0529576i \(-0.983135\pi\)
0.998597 0.0529576i \(-0.0168648\pi\)
\(920\) −104830. + 83189.0i −0.123854 + 0.0982857i
\(921\) −102867. −0.121271
\(922\) −441323. −0.519152
\(923\) 2.14907e6 2.52259
\(924\) −3825.32 −0.00448047
\(925\) 141357.i 0.165210i
\(926\) −662776. −0.772938
\(927\) 1.35082e6i 1.57195i
\(928\) −48154.2 −0.0559163
\(929\) 742708. 0.860571 0.430285 0.902693i \(-0.358413\pi\)
0.430285 + 0.902693i \(0.358413\pi\)
\(930\) 15277.7i 0.0176641i
\(931\) 640415.i 0.738860i
\(932\) 516091. 0.594148
\(933\) −68134.1 −0.0782711
\(934\) 1.08977e6i 1.24922i
\(935\) 2637.49i 0.00301695i
\(936\) 499679. 0.570348
\(937\) 534562.i 0.608862i −0.952534 0.304431i \(-0.901534\pi\)
0.952534 0.304431i \(-0.0984663\pi\)
\(938\) −298185. −0.338907
\(939\) 90272.7i 0.102382i
\(940\) 154029.i 0.174319i
\(941\) 1.55592e6i 1.75714i 0.477611 + 0.878571i \(0.341503\pi\)
−0.477611 + 0.878571i \(0.658497\pi\)
\(942\) 103710.i 0.116874i
\(943\) −581843. 733208.i −0.654308 0.824525i
\(944\) 81706.2 0.0916877
\(945\) −25284.5 −0.0283133
\(946\) −318672. −0.356091
\(947\) 115842. 0.129171 0.0645857 0.997912i \(-0.479427\pi\)
0.0645857 + 0.997912i \(0.479427\pi\)
\(948\) 76264.3i 0.0848603i
\(949\) 1.50034e6 1.66593
\(950\) 107068.i 0.118635i
\(951\) 88841.5 0.0982324
\(952\) −2647.89 −0.00292164
\(953\) 158527.i 0.174550i 0.996184 + 0.0872748i \(0.0278158\pi\)
−0.996184 + 0.0872748i \(0.972184\pi\)
\(954\) 608222.i 0.668290i
\(955\) 267295. 0.293079
\(956\) 46080.8 0.0504202
\(957\) 7518.13i 0.00820891i
\(958\) 232376.i 0.253197i
\(959\) 297618. 0.323610
\(960\) 4743.26i 0.00514677i
\(961\) −583575. −0.631902
\(962\) 879472.i 0.950324i
\(963\) 966917.i 1.04265i
\(964\) 253177.i 0.272439i
\(965\) 139777.i 0.150100i
\(966\) 16431.3 13039.2i 0.0176083 0.0139732i
\(967\) 482715. 0.516223 0.258112 0.966115i \(-0.416900\pi\)
0.258112 + 0.966115i \(0.416900\pi\)
\(968\) −304965. −0.325462
\(969\) −1735.58 −0.00184840
\(970\) 431397. 0.458494
\(971\) 59475.4i 0.0630810i 0.999502 + 0.0315405i \(0.0100413\pi\)
−0.999502 + 0.0315405i \(0.989959\pi\)
\(972\) 129005. 0.136545
\(973\) 104729.i 0.110622i
\(974\) 647227. 0.682243
\(975\) −28479.4 −0.0299586
\(976\) 267617.i 0.280941i
\(977\) 935020.i 0.979562i −0.871845 0.489781i \(-0.837077\pi\)
0.871845 0.489781i \(-0.162923\pi\)
\(978\) −8382.51 −0.00876388
\(979\) 8280.67 0.00863973
\(980\) 189148.i 0.196948i
\(981\) 1.21350e6i 1.26096i
\(982\) −637142. −0.660713
\(983\) 330831.i 0.342373i 0.985239 + 0.171186i \(0.0547600\pi\)
−0.985239 + 0.171186i \(0.945240\pi\)
\(984\) −33175.5 −0.0342631
\(985\) 195843.i 0.201853i
\(986\) 5204.06i 0.00535289i
\(987\) 24142.7i 0.0247828i
\(988\) 666135.i 0.682415i
\(989\) 1.36882e6 1.08624e6i 1.39944 1.11054i
\(990\) 86623.6 0.0883824
\(991\) 1.44595e6 1.47234 0.736168 0.676799i \(-0.236634\pi\)
0.736168 + 0.676799i \(0.236634\pi\)
\(992\) −105543. −0.107252
\(993\) −106784. −0.108294
\(994\) 374028.i 0.378557i
\(995\) 97121.3 0.0980999
\(996\) 16357.4i 0.0164890i
\(997\) 1.39234e6 1.40073 0.700365 0.713785i \(-0.253021\pi\)
0.700365 + 0.713785i \(0.253021\pi\)
\(998\) 599458. 0.601863
\(999\) 151158.i 0.151461i
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 230.5.d.a.91.10 yes 32
23.22 odd 2 inner 230.5.d.a.91.7 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.5.d.a.91.7 32 23.22 odd 2 inner
230.5.d.a.91.10 yes 32 1.1 even 1 trivial