Properties

Label 490.4.c.e.99.9
Level $490$
Weight $4$
Character 490.99
Analytic conductor $28.911$
Analytic rank $0$
Dimension $12$
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] = [490,4,Mod(99,490)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(490, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("490.99");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 490.c (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: \(28.9109359028\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 185x^{10} + 12748x^{8} + 405460x^{6} + 5908496x^{4} + 33016000x^{2} + 60840000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 99.9
Root \(-2.20031i\) of defining polynomial
Character \(\chi\) \(=\) 490.99
Dual form 490.4.c.e.99.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000i q^{2} -1.20031i q^{3} -4.00000 q^{4} +(-11.1276 + 1.08430i) q^{5} +2.40061 q^{6} -8.00000i q^{8} +25.5593 q^{9} +O(q^{10})\) \(q+2.00000i q^{2} -1.20031i q^{3} -4.00000 q^{4} +(-11.1276 + 1.08430i) q^{5} +2.40061 q^{6} -8.00000i q^{8} +25.5593 q^{9} +(-2.16860 - 22.2553i) q^{10} -26.4409 q^{11} +4.80123i q^{12} -55.0319i q^{13} +(1.30149 + 13.3566i) q^{15} +16.0000 q^{16} +49.4218i q^{17} +51.1185i q^{18} +5.46016 q^{19} +(44.5105 - 4.33720i) q^{20} -52.8818i q^{22} +1.07321i q^{23} -9.60246 q^{24} +(122.649 - 24.1314i) q^{25} +110.064 q^{26} -63.0873i q^{27} +246.181 q^{29} +(-26.7132 + 2.60299i) q^{30} -228.745 q^{31} +32.0000i q^{32} +31.7372i q^{33} -98.8437 q^{34} -102.237 q^{36} +381.237i q^{37} +10.9203i q^{38} -66.0552 q^{39} +(8.67440 + 89.0211i) q^{40} +48.5643 q^{41} +233.878i q^{43} +105.764 q^{44} +(-284.414 + 27.7139i) q^{45} -2.14643 q^{46} +245.153i q^{47} -19.2049i q^{48} +(48.2628 + 245.297i) q^{50} +59.3214 q^{51} +220.127i q^{52} +269.630i q^{53} +126.175 q^{54} +(294.225 - 28.6699i) q^{55} -6.55387i q^{57} +492.362i q^{58} +784.534 q^{59} +(-5.20597 - 53.4263i) q^{60} -425.992 q^{61} -457.489i q^{62} -64.0000 q^{64} +(59.6711 + 612.375i) q^{65} -63.4744 q^{66} +918.344i q^{67} -197.687i q^{68} +1.28819 q^{69} +200.821 q^{71} -204.474i q^{72} +778.434i q^{73} -762.474 q^{74} +(-28.9651 - 147.216i) q^{75} -21.8407 q^{76} -132.110i q^{78} -189.419 q^{79} +(-178.042 + 17.3488i) q^{80} +614.376 q^{81} +97.1287i q^{82} -611.073i q^{83} +(-53.5881 - 549.948i) q^{85} -467.757 q^{86} -295.493i q^{87} +211.527i q^{88} +292.327 q^{89} +(-55.4278 - 568.828i) q^{90} -4.29286i q^{92} +274.564i q^{93} -490.307 q^{94} +(-60.7587 + 5.92046i) q^{95} +38.4098 q^{96} -1429.73i q^{97} -675.810 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 48 q^{4} - 8 q^{5} - 28 q^{6} - 62 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 48 q^{4} - 8 q^{5} - 28 q^{6} - 62 q^{9} + 12 q^{10} + 62 q^{11} + 86 q^{15} + 192 q^{16} + 186 q^{19} + 32 q^{20} + 112 q^{24} - 126 q^{25} - 236 q^{26} - 338 q^{29} - 28 q^{30} - 652 q^{31} + 272 q^{34} + 248 q^{36} + 868 q^{39} - 48 q^{40} - 396 q^{41} - 248 q^{44} + 664 q^{45} - 376 q^{46} + 160 q^{50} + 1448 q^{51} + 1540 q^{54} - 298 q^{55} + 1336 q^{59} - 344 q^{60} - 314 q^{61} - 768 q^{64} - 1862 q^{65} - 1600 q^{66} - 90 q^{69} + 2216 q^{71} + 1012 q^{74} - 4550 q^{75} - 744 q^{76} + 1772 q^{79} - 128 q^{80} - 1228 q^{81} + 2282 q^{85} - 396 q^{86} + 6094 q^{89} - 100 q^{90} + 3604 q^{94} - 1166 q^{95} - 448 q^{96} - 8546 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 0.707107i
\(3\) 1.20031i 0.230999i −0.993308 0.115500i \(-0.963153\pi\)
0.993308 0.115500i \(-0.0368469\pi\)
\(4\) −4.00000 −0.500000
\(5\) −11.1276 + 1.08430i −0.995286 + 0.0969827i
\(6\) 2.40061 0.163341
\(7\) 0 0
\(8\) 8.00000i 0.353553i
\(9\) 25.5593 0.946639
\(10\) −2.16860 22.2553i −0.0685772 0.703774i
\(11\) −26.4409 −0.724749 −0.362374 0.932033i \(-0.618034\pi\)
−0.362374 + 0.932033i \(0.618034\pi\)
\(12\) 4.80123i 0.115500i
\(13\) 55.0319i 1.17408i −0.809556 0.587042i \(-0.800292\pi\)
0.809556 0.587042i \(-0.199708\pi\)
\(14\) 0 0
\(15\) 1.30149 + 13.3566i 0.0224029 + 0.229910i
\(16\) 16.0000 0.250000
\(17\) 49.4218i 0.705091i 0.935795 + 0.352546i \(0.114684\pi\)
−0.935795 + 0.352546i \(0.885316\pi\)
\(18\) 51.1185i 0.669375i
\(19\) 5.46016 0.0659288 0.0329644 0.999457i \(-0.489505\pi\)
0.0329644 + 0.999457i \(0.489505\pi\)
\(20\) 44.5105 4.33720i 0.497643 0.0484914i
\(21\) 0 0
\(22\) 52.8818i 0.512475i
\(23\) 1.07321i 0.00972959i 0.999988 + 0.00486480i \(0.00154852\pi\)
−0.999988 + 0.00486480i \(0.998451\pi\)
\(24\) −9.60246 −0.0816706
\(25\) 122.649 24.1314i 0.981189 0.193051i
\(26\) 110.064 0.830203
\(27\) 63.0873i 0.449672i
\(28\) 0 0
\(29\) 246.181 1.57637 0.788185 0.615439i \(-0.211021\pi\)
0.788185 + 0.615439i \(0.211021\pi\)
\(30\) −26.7132 + 2.60299i −0.162571 + 0.0158413i
\(31\) −228.745 −1.32528 −0.662641 0.748937i \(-0.730565\pi\)
−0.662641 + 0.748937i \(0.730565\pi\)
\(32\) 32.0000i 0.176777i
\(33\) 31.7372i 0.167416i
\(34\) −98.8437 −0.498575
\(35\) 0 0
\(36\) −102.237 −0.473320
\(37\) 381.237i 1.69392i 0.531658 + 0.846959i \(0.321569\pi\)
−0.531658 + 0.846959i \(0.678431\pi\)
\(38\) 10.9203i 0.0466187i
\(39\) −66.0552 −0.271213
\(40\) 8.67440 + 89.0211i 0.0342886 + 0.351887i
\(41\) 48.5643 0.184987 0.0924936 0.995713i \(-0.470516\pi\)
0.0924936 + 0.995713i \(0.470516\pi\)
\(42\) 0 0
\(43\) 233.878i 0.829445i 0.909948 + 0.414722i \(0.136121\pi\)
−0.909948 + 0.414722i \(0.863879\pi\)
\(44\) 105.764 0.362374
\(45\) −284.414 + 27.7139i −0.942177 + 0.0918077i
\(46\) −2.14643 −0.00687986
\(47\) 245.153i 0.760836i 0.924815 + 0.380418i \(0.124220\pi\)
−0.924815 + 0.380418i \(0.875780\pi\)
\(48\) 19.2049i 0.0577498i
\(49\) 0 0
\(50\) 48.2628 + 245.297i 0.136508 + 0.693805i
\(51\) 59.3214 0.162876
\(52\) 220.127i 0.587042i
\(53\) 269.630i 0.698803i 0.936973 + 0.349402i \(0.113615\pi\)
−0.936973 + 0.349402i \(0.886385\pi\)
\(54\) 126.175 0.317966
\(55\) 294.225 28.6699i 0.721332 0.0702881i
\(56\) 0 0
\(57\) 6.55387i 0.0152295i
\(58\) 492.362i 1.11466i
\(59\) 784.534 1.73115 0.865573 0.500783i \(-0.166954\pi\)
0.865573 + 0.500783i \(0.166954\pi\)
\(60\) −5.20597 53.4263i −0.0112015 0.114955i
\(61\) −425.992 −0.894142 −0.447071 0.894498i \(-0.647533\pi\)
−0.447071 + 0.894498i \(0.647533\pi\)
\(62\) 457.489i 0.937116i
\(63\) 0 0
\(64\) −64.0000 −0.125000
\(65\) 59.6711 + 612.375i 0.113866 + 1.16855i
\(66\) −63.4744 −0.118381
\(67\) 918.344i 1.67453i 0.546797 + 0.837265i \(0.315847\pi\)
−0.546797 + 0.837265i \(0.684153\pi\)
\(68\) 197.687i 0.352546i
\(69\) 1.28819 0.00224753
\(70\) 0 0
\(71\) 200.821 0.335676 0.167838 0.985815i \(-0.446321\pi\)
0.167838 + 0.985815i \(0.446321\pi\)
\(72\) 204.474i 0.334688i
\(73\) 778.434i 1.24807i 0.781398 + 0.624033i \(0.214507\pi\)
−0.781398 + 0.624033i \(0.785493\pi\)
\(74\) −762.474 −1.19778
\(75\) −28.9651 147.216i −0.0445947 0.226654i
\(76\) −21.8407 −0.0329644
\(77\) 0 0
\(78\) 132.110i 0.191776i
\(79\) −189.419 −0.269764 −0.134882 0.990862i \(-0.543066\pi\)
−0.134882 + 0.990862i \(0.543066\pi\)
\(80\) −178.042 + 17.3488i −0.248822 + 0.0242457i
\(81\) 614.376 0.842765
\(82\) 97.1287i 0.130806i
\(83\) 611.073i 0.808120i −0.914732 0.404060i \(-0.867599\pi\)
0.914732 0.404060i \(-0.132401\pi\)
\(84\) 0 0
\(85\) −53.5881 549.948i −0.0683817 0.701768i
\(86\) −467.757 −0.586506
\(87\) 295.493i 0.364140i
\(88\) 211.527i 0.256237i
\(89\) 292.327 0.348164 0.174082 0.984731i \(-0.444304\pi\)
0.174082 + 0.984731i \(0.444304\pi\)
\(90\) −55.4278 568.828i −0.0649178 0.666220i
\(91\) 0 0
\(92\) 4.29286i 0.00486480i
\(93\) 274.564i 0.306139i
\(94\) −490.307 −0.537992
\(95\) −60.7587 + 5.92046i −0.0656180 + 0.00639396i
\(96\) 38.4098 0.0408353
\(97\) 1429.73i 1.49657i −0.663380 0.748283i \(-0.730879\pi\)
0.663380 0.748283i \(-0.269121\pi\)
\(98\) 0 0
\(99\) −675.810 −0.686075
\(100\) −490.594 + 96.5256i −0.490594 + 0.0965256i
\(101\) 806.329 0.794384 0.397192 0.917736i \(-0.369985\pi\)
0.397192 + 0.917736i \(0.369985\pi\)
\(102\) 118.643i 0.115170i
\(103\) 1510.14i 1.44465i 0.691554 + 0.722325i \(0.256927\pi\)
−0.691554 + 0.722325i \(0.743073\pi\)
\(104\) −440.255 −0.415101
\(105\) 0 0
\(106\) −539.261 −0.494129
\(107\) 621.127i 0.561184i 0.959827 + 0.280592i \(0.0905307\pi\)
−0.959827 + 0.280592i \(0.909469\pi\)
\(108\) 252.349i 0.224836i
\(109\) 1542.81 1.35573 0.677863 0.735189i \(-0.262906\pi\)
0.677863 + 0.735189i \(0.262906\pi\)
\(110\) 57.3398 + 588.450i 0.0497012 + 0.510059i
\(111\) 457.602 0.391294
\(112\) 0 0
\(113\) 1295.03i 1.07810i 0.842272 + 0.539052i \(0.181217\pi\)
−0.842272 + 0.539052i \(0.818783\pi\)
\(114\) 13.1077 0.0107689
\(115\) −1.16369 11.9423i −0.000943602 0.00968373i
\(116\) −984.725 −0.788185
\(117\) 1406.57i 1.11143i
\(118\) 1569.07i 1.22411i
\(119\) 0 0
\(120\) 106.853 10.4119i 0.0812856 0.00792064i
\(121\) −631.878 −0.474740
\(122\) 851.984i 0.632254i
\(123\) 58.2921i 0.0427319i
\(124\) 914.979 0.662641
\(125\) −1338.62 + 401.513i −0.957841 + 0.287299i
\(126\) 0 0
\(127\) 191.946i 0.134114i −0.997749 0.0670568i \(-0.978639\pi\)
0.997749 0.0670568i \(-0.0213609\pi\)
\(128\) 128.000i 0.0883883i
\(129\) 280.726 0.191601
\(130\) −1224.75 + 119.342i −0.826289 + 0.0805154i
\(131\) −1495.46 −0.997400 −0.498700 0.866775i \(-0.666189\pi\)
−0.498700 + 0.866775i \(0.666189\pi\)
\(132\) 126.949i 0.0837082i
\(133\) 0 0
\(134\) −1836.69 −1.18407
\(135\) 68.4055 + 702.012i 0.0436104 + 0.447552i
\(136\) 395.375 0.249287
\(137\) 1167.66i 0.728174i −0.931365 0.364087i \(-0.881381\pi\)
0.931365 0.364087i \(-0.118619\pi\)
\(138\) 2.57637i 0.00158924i
\(139\) 2084.75 1.27213 0.636066 0.771635i \(-0.280561\pi\)
0.636066 + 0.771635i \(0.280561\pi\)
\(140\) 0 0
\(141\) 294.259 0.175753
\(142\) 401.641i 0.237359i
\(143\) 1455.09i 0.850916i
\(144\) 408.948 0.236660
\(145\) −2739.42 + 266.934i −1.56894 + 0.152881i
\(146\) −1556.87 −0.882516
\(147\) 0 0
\(148\) 1524.95i 0.846959i
\(149\) 1183.29 0.650597 0.325299 0.945611i \(-0.394535\pi\)
0.325299 + 0.945611i \(0.394535\pi\)
\(150\) 294.432 57.9302i 0.160268 0.0315332i
\(151\) −1485.42 −0.800544 −0.400272 0.916396i \(-0.631084\pi\)
−0.400272 + 0.916396i \(0.631084\pi\)
\(152\) 43.6813i 0.0233094i
\(153\) 1263.19i 0.667467i
\(154\) 0 0
\(155\) 2545.39 248.028i 1.31903 0.128530i
\(156\) 264.221 0.135606
\(157\) 235.071i 0.119495i 0.998214 + 0.0597475i \(0.0190295\pi\)
−0.998214 + 0.0597475i \(0.980970\pi\)
\(158\) 378.839i 0.190752i
\(159\) 323.639 0.161423
\(160\) −34.6976 356.084i −0.0171443 0.175943i
\(161\) 0 0
\(162\) 1228.75i 0.595925i
\(163\) 3514.51i 1.68882i −0.535699 0.844409i \(-0.679952\pi\)
0.535699 0.844409i \(-0.320048\pi\)
\(164\) −194.257 −0.0924936
\(165\) −34.4127 353.160i −0.0162365 0.166627i
\(166\) 1222.15 0.571427
\(167\) 1675.24i 0.776249i 0.921607 + 0.388125i \(0.126877\pi\)
−0.921607 + 0.388125i \(0.873123\pi\)
\(168\) 0 0
\(169\) −831.507 −0.378474
\(170\) 1099.90 107.176i 0.496225 0.0483532i
\(171\) 139.558 0.0624108
\(172\) 935.514i 0.414722i
\(173\) 746.748i 0.328175i −0.986446 0.164087i \(-0.947532\pi\)
0.986446 0.164087i \(-0.0524679\pi\)
\(174\) 590.986 0.257486
\(175\) 0 0
\(176\) −423.055 −0.181187
\(177\) 941.682i 0.399893i
\(178\) 584.653i 0.246189i
\(179\) 3652.52 1.52515 0.762576 0.646898i \(-0.223934\pi\)
0.762576 + 0.646898i \(0.223934\pi\)
\(180\) 1137.66 110.856i 0.471088 0.0459038i
\(181\) −767.005 −0.314978 −0.157489 0.987521i \(-0.550340\pi\)
−0.157489 + 0.987521i \(0.550340\pi\)
\(182\) 0 0
\(183\) 511.321i 0.206546i
\(184\) 8.58571 0.00343993
\(185\) −413.375 4242.27i −0.164281 1.68593i
\(186\) −549.128 −0.216473
\(187\) 1306.76i 0.511014i
\(188\) 980.613i 0.380418i
\(189\) 0 0
\(190\) −11.8409 121.517i −0.00452121 0.0463989i
\(191\) 339.746 0.128708 0.0643538 0.997927i \(-0.479501\pi\)
0.0643538 + 0.997927i \(0.479501\pi\)
\(192\) 76.8197i 0.0288749i
\(193\) 2244.39i 0.837070i 0.908201 + 0.418535i \(0.137456\pi\)
−0.908201 + 0.418535i \(0.862544\pi\)
\(194\) 2859.46 1.05823
\(195\) 735.038 71.6236i 0.269934 0.0263029i
\(196\) 0 0
\(197\) 2130.15i 0.770389i −0.922835 0.385194i \(-0.874134\pi\)
0.922835 0.385194i \(-0.125866\pi\)
\(198\) 1351.62i 0.485129i
\(199\) −1913.46 −0.681615 −0.340807 0.940133i \(-0.610700\pi\)
−0.340807 + 0.940133i \(0.610700\pi\)
\(200\) −193.051 981.189i −0.0682539 0.346903i
\(201\) 1102.29 0.386815
\(202\) 1612.66i 0.561714i
\(203\) 0 0
\(204\) −237.286 −0.0814378
\(205\) −540.406 + 52.6583i −0.184115 + 0.0179406i
\(206\) −3020.29 −1.02152
\(207\) 27.4306i 0.00921041i
\(208\) 880.510i 0.293521i
\(209\) −144.372 −0.0477818
\(210\) 0 0
\(211\) 4018.96 1.31126 0.655632 0.755080i \(-0.272402\pi\)
0.655632 + 0.755080i \(0.272402\pi\)
\(212\) 1078.52i 0.349402i
\(213\) 241.046i 0.0775410i
\(214\) −1242.25 −0.396817
\(215\) −253.594 2602.51i −0.0804418 0.825535i
\(216\) −504.698 −0.158983
\(217\) 0 0
\(218\) 3085.61i 0.958642i
\(219\) 934.360 0.288302
\(220\) −1176.90 + 114.680i −0.360666 + 0.0351441i
\(221\) 2719.78 0.827837
\(222\) 915.203i 0.276687i
\(223\) 4659.51i 1.39921i 0.714530 + 0.699604i \(0.246640\pi\)
−0.714530 + 0.699604i \(0.753360\pi\)
\(224\) 0 0
\(225\) 3134.81 616.781i 0.928832 0.182750i
\(226\) −2590.05 −0.762335
\(227\) 3692.30i 1.07959i −0.841797 0.539794i \(-0.818502\pi\)
0.841797 0.539794i \(-0.181498\pi\)
\(228\) 26.2155i 0.00761475i
\(229\) 1454.34 0.419675 0.209837 0.977736i \(-0.432707\pi\)
0.209837 + 0.977736i \(0.432707\pi\)
\(230\) 23.8847 2.32737i 0.00684743 0.000667228i
\(231\) 0 0
\(232\) 1969.45i 0.557331i
\(233\) 6402.66i 1.80023i −0.435657 0.900113i \(-0.643484\pi\)
0.435657 0.900113i \(-0.356516\pi\)
\(234\) 2813.15 0.785903
\(235\) −265.820 2727.98i −0.0737880 0.757249i
\(236\) −3138.14 −0.865573
\(237\) 227.361i 0.0623152i
\(238\) 0 0
\(239\) −1077.42 −0.291601 −0.145801 0.989314i \(-0.546576\pi\)
−0.145801 + 0.989314i \(0.546576\pi\)
\(240\) 20.8239 + 213.705i 0.00560073 + 0.0574776i
\(241\) 1129.47 0.301891 0.150946 0.988542i \(-0.451768\pi\)
0.150946 + 0.988542i \(0.451768\pi\)
\(242\) 1263.76i 0.335692i
\(243\) 2440.80i 0.644350i
\(244\) 1703.97 0.447071
\(245\) 0 0
\(246\) 116.584 0.0302160
\(247\) 300.483i 0.0774060i
\(248\) 1829.96i 0.468558i
\(249\) −733.475 −0.186675
\(250\) −803.026 2677.25i −0.203151 0.677296i
\(251\) 5190.33 1.30522 0.652610 0.757694i \(-0.273674\pi\)
0.652610 + 0.757694i \(0.273674\pi\)
\(252\) 0 0
\(253\) 28.3768i 0.00705151i
\(254\) 383.891 0.0948326
\(255\) −660.107 + 64.3222i −0.162108 + 0.0157961i
\(256\) 256.000 0.0625000
\(257\) 6646.83i 1.61330i 0.591030 + 0.806649i \(0.298721\pi\)
−0.591030 + 0.806649i \(0.701279\pi\)
\(258\) 561.452i 0.135482i
\(259\) 0 0
\(260\) −238.684 2449.50i −0.0569330 0.584275i
\(261\) 6292.21 1.49225
\(262\) 2990.93i 0.705268i
\(263\) 5975.55i 1.40102i −0.713643 0.700510i \(-0.752956\pi\)
0.713643 0.700510i \(-0.247044\pi\)
\(264\) 253.898 0.0591906
\(265\) −292.360 3000.35i −0.0677719 0.695509i
\(266\) 0 0
\(267\) 350.882i 0.0804255i
\(268\) 3673.38i 0.837265i
\(269\) 5039.87 1.14233 0.571164 0.820836i \(-0.306492\pi\)
0.571164 + 0.820836i \(0.306492\pi\)
\(270\) −1404.02 + 136.811i −0.316467 + 0.0308372i
\(271\) −564.058 −0.126436 −0.0632179 0.998000i \(-0.520136\pi\)
−0.0632179 + 0.998000i \(0.520136\pi\)
\(272\) 790.749i 0.176273i
\(273\) 0 0
\(274\) 2335.32 0.514897
\(275\) −3242.94 + 638.056i −0.711115 + 0.139914i
\(276\) −5.15275 −0.00112376
\(277\) 4707.89i 1.02119i −0.859821 0.510596i \(-0.829425\pi\)
0.859821 0.510596i \(-0.170575\pi\)
\(278\) 4169.50i 0.899533i
\(279\) −5846.54 −1.25456
\(280\) 0 0
\(281\) −1993.69 −0.423250 −0.211625 0.977351i \(-0.567876\pi\)
−0.211625 + 0.977351i \(0.567876\pi\)
\(282\) 588.519i 0.124276i
\(283\) 7285.39i 1.53029i 0.643859 + 0.765144i \(0.277332\pi\)
−0.643859 + 0.765144i \(0.722668\pi\)
\(284\) −803.282 −0.167838
\(285\) 7.10637 + 72.9291i 0.00147700 + 0.0151577i
\(286\) −2910.19 −0.601688
\(287\) 0 0
\(288\) 817.896i 0.167344i
\(289\) 2470.48 0.502846
\(290\) −533.869 5478.83i −0.108103 1.10941i
\(291\) −1716.11 −0.345706
\(292\) 3113.74i 0.624033i
\(293\) 8519.76i 1.69874i 0.527801 + 0.849368i \(0.323017\pi\)
−0.527801 + 0.849368i \(0.676983\pi\)
\(294\) 0 0
\(295\) −8730.01 + 850.670i −1.72299 + 0.167891i
\(296\) 3049.90 0.598891
\(297\) 1668.08i 0.325899i
\(298\) 2366.58i 0.460042i
\(299\) 59.0610 0.0114234
\(300\) 115.860 + 588.864i 0.0222973 + 0.113327i
\(301\) 0 0
\(302\) 2970.85i 0.566070i
\(303\) 967.843i 0.183502i
\(304\) 87.3626 0.0164822
\(305\) 4740.28 461.903i 0.889927 0.0867164i
\(306\) −2526.37 −0.471971
\(307\) 1738.43i 0.323183i 0.986858 + 0.161592i \(0.0516627\pi\)
−0.986858 + 0.161592i \(0.948337\pi\)
\(308\) 0 0
\(309\) 1812.64 0.333713
\(310\) 496.056 + 5090.77i 0.0908841 + 0.932699i
\(311\) −3990.34 −0.727562 −0.363781 0.931485i \(-0.618514\pi\)
−0.363781 + 0.931485i \(0.618514\pi\)
\(312\) 528.441i 0.0958881i
\(313\) 243.187i 0.0439160i −0.999759 0.0219580i \(-0.993010\pi\)
0.999759 0.0219580i \(-0.00699002\pi\)
\(314\) −470.142 −0.0844957
\(315\) 0 0
\(316\) 757.677 0.134882
\(317\) 5328.16i 0.944036i 0.881589 + 0.472018i \(0.156474\pi\)
−0.881589 + 0.472018i \(0.843526\pi\)
\(318\) 647.279i 0.114143i
\(319\) −6509.26 −1.14247
\(320\) 712.169 69.3952i 0.124411 0.0121228i
\(321\) 745.544 0.129633
\(322\) 0 0
\(323\) 269.851i 0.0464858i
\(324\) −2457.50 −0.421383
\(325\) −1328.00 6749.58i −0.226658 1.15200i
\(326\) 7029.01 1.19417
\(327\) 1851.84i 0.313171i
\(328\) 388.515i 0.0654029i
\(329\) 0 0
\(330\) 706.320 68.8253i 0.117823 0.0114809i
\(331\) −11513.2 −1.91185 −0.955924 0.293614i \(-0.905142\pi\)
−0.955924 + 0.293614i \(0.905142\pi\)
\(332\) 2444.29i 0.404060i
\(333\) 9744.14i 1.60353i
\(334\) −3350.47 −0.548891
\(335\) −995.760 10219.0i −0.162401 1.66664i
\(336\) 0 0
\(337\) 8818.86i 1.42550i 0.701418 + 0.712750i \(0.252551\pi\)
−0.701418 + 0.712750i \(0.747449\pi\)
\(338\) 1663.01i 0.267621i
\(339\) 1554.43 0.249041
\(340\) 214.352 + 2199.79i 0.0341909 + 0.350884i
\(341\) 6048.22 0.960496
\(342\) 279.115i 0.0441311i
\(343\) 0 0
\(344\) 1871.03 0.293253
\(345\) −14.3345 + 1.39678i −0.00223693 + 0.000217971i
\(346\) 1493.50 0.232054
\(347\) 2160.48i 0.334237i 0.985937 + 0.167119i \(0.0534463\pi\)
−0.985937 + 0.167119i \(0.946554\pi\)
\(348\) 1181.97i 0.182070i
\(349\) −1837.74 −0.281868 −0.140934 0.990019i \(-0.545010\pi\)
−0.140934 + 0.990019i \(0.545010\pi\)
\(350\) 0 0
\(351\) −3471.81 −0.527953
\(352\) 846.109i 0.128119i
\(353\) 9588.21i 1.44569i 0.691009 + 0.722846i \(0.257166\pi\)
−0.691009 + 0.722846i \(0.742834\pi\)
\(354\) 1883.36 0.282767
\(355\) −2234.66 + 217.750i −0.334094 + 0.0325548i
\(356\) −1169.31 −0.174082
\(357\) 0 0
\(358\) 7305.04i 1.07845i
\(359\) −7047.23 −1.03604 −0.518020 0.855368i \(-0.673331\pi\)
−0.518020 + 0.855368i \(0.673331\pi\)
\(360\) 221.711 + 2275.31i 0.0324589 + 0.333110i
\(361\) −6829.19 −0.995653
\(362\) 1534.01i 0.222723i
\(363\) 758.448i 0.109664i
\(364\) 0 0
\(365\) −844.056 8662.13i −0.121041 1.24218i
\(366\) −1022.64 −0.146050
\(367\) 7554.28i 1.07447i −0.843433 0.537234i \(-0.819469\pi\)
0.843433 0.537234i \(-0.180531\pi\)
\(368\) 17.1714i 0.00243240i
\(369\) 1241.27 0.175116
\(370\) 8484.53 826.751i 1.19213 0.116164i
\(371\) 0 0
\(372\) 1098.26i 0.153070i
\(373\) 1288.31i 0.178837i 0.995994 + 0.0894184i \(0.0285008\pi\)
−0.995994 + 0.0894184i \(0.971499\pi\)
\(374\) 2613.52 0.361341
\(375\) 481.939 + 1606.76i 0.0663660 + 0.221260i
\(376\) 1961.23 0.268996
\(377\) 13547.8i 1.85079i
\(378\) 0 0
\(379\) −6985.61 −0.946773 −0.473386 0.880855i \(-0.656969\pi\)
−0.473386 + 0.880855i \(0.656969\pi\)
\(380\) 243.035 23.6818i 0.0328090 0.00319698i
\(381\) −230.394 −0.0309801
\(382\) 679.492i 0.0910101i
\(383\) 5684.58i 0.758403i 0.925314 + 0.379202i \(0.123801\pi\)
−0.925314 + 0.379202i \(0.876199\pi\)
\(384\) −153.639 −0.0204176
\(385\) 0 0
\(386\) −4488.77 −0.591898
\(387\) 5977.76i 0.785185i
\(388\) 5718.91i 0.748283i
\(389\) −2255.72 −0.294009 −0.147005 0.989136i \(-0.546963\pi\)
−0.147005 + 0.989136i \(0.546963\pi\)
\(390\) 143.247 + 1470.08i 0.0185990 + 0.190872i
\(391\) −53.0402 −0.00686025
\(392\) 0 0
\(393\) 1795.02i 0.230399i
\(394\) 4260.29 0.544747
\(395\) 2107.79 205.387i 0.268492 0.0261624i
\(396\) 2703.24 0.343038
\(397\) 9949.77i 1.25785i −0.777468 0.628923i \(-0.783496\pi\)
0.777468 0.628923i \(-0.216504\pi\)
\(398\) 3826.91i 0.481975i
\(399\) 0 0
\(400\) 1962.38 386.102i 0.245297 0.0482628i
\(401\) 10864.6 1.35300 0.676501 0.736442i \(-0.263496\pi\)
0.676501 + 0.736442i \(0.263496\pi\)
\(402\) 2204.59i 0.273520i
\(403\) 12588.2i 1.55599i
\(404\) −3225.32 −0.397192
\(405\) −6836.55 + 666.168i −0.838793 + 0.0817337i
\(406\) 0 0
\(407\) 10080.3i 1.22766i
\(408\) 474.571i 0.0575852i
\(409\) −951.004 −0.114973 −0.0574867 0.998346i \(-0.518309\pi\)
−0.0574867 + 0.998346i \(0.518309\pi\)
\(410\) −105.317 1080.81i −0.0126859 0.130189i
\(411\) −1401.55 −0.168208
\(412\) 6040.58i 0.722325i
\(413\) 0 0
\(414\) −54.8611 −0.00651275
\(415\) 662.586 + 6799.80i 0.0783737 + 0.804311i
\(416\) 1761.02 0.207551
\(417\) 2502.34i 0.293861i
\(418\) 288.743i 0.0337868i
\(419\) 985.724 0.114930 0.0574651 0.998348i \(-0.481698\pi\)
0.0574651 + 0.998348i \(0.481698\pi\)
\(420\) 0 0
\(421\) 3879.25 0.449081 0.224540 0.974465i \(-0.427912\pi\)
0.224540 + 0.974465i \(0.427912\pi\)
\(422\) 8037.93i 0.927204i
\(423\) 6265.94i 0.720237i
\(424\) 2157.04 0.247064
\(425\) 1192.62 + 6061.52i 0.136119 + 0.691828i
\(426\) 482.093 0.0548298
\(427\) 0 0
\(428\) 2484.51i 0.280592i
\(429\) 1746.56 0.196561
\(430\) 5205.03 507.189i 0.583741 0.0568810i
\(431\) −13821.6 −1.54470 −0.772349 0.635199i \(-0.780918\pi\)
−0.772349 + 0.635199i \(0.780918\pi\)
\(432\) 1009.40i 0.112418i
\(433\) 520.224i 0.0577375i 0.999583 + 0.0288688i \(0.00919049\pi\)
−0.999583 + 0.0288688i \(0.990810\pi\)
\(434\) 0 0
\(435\) 320.403 + 3288.14i 0.0353153 + 0.362424i
\(436\) −6171.23 −0.677863
\(437\) 5.85992i 0.000641460i
\(438\) 1868.72i 0.203860i
\(439\) −9569.21 −1.04035 −0.520175 0.854060i \(-0.674133\pi\)
−0.520175 + 0.854060i \(0.674133\pi\)
\(440\) −229.359 2353.80i −0.0248506 0.255029i
\(441\) 0 0
\(442\) 5439.55i 0.585369i
\(443\) 4313.29i 0.462597i −0.972883 0.231298i \(-0.925703\pi\)
0.972883 0.231298i \(-0.0742974\pi\)
\(444\) −1830.41 −0.195647
\(445\) −3252.90 + 316.970i −0.346522 + 0.0337659i
\(446\) −9319.01 −0.989390
\(447\) 1420.31i 0.150287i
\(448\) 0 0
\(449\) 4396.78 0.462131 0.231065 0.972938i \(-0.425779\pi\)
0.231065 + 0.972938i \(0.425779\pi\)
\(450\) 1233.56 + 6269.61i 0.129224 + 0.656783i
\(451\) −1284.09 −0.134069
\(452\) 5180.10i 0.539052i
\(453\) 1782.97i 0.184925i
\(454\) 7384.60 0.763384
\(455\) 0 0
\(456\) −52.4310 −0.00538444
\(457\) 8466.25i 0.866596i 0.901251 + 0.433298i \(0.142650\pi\)
−0.901251 + 0.433298i \(0.857350\pi\)
\(458\) 2908.68i 0.296755i
\(459\) 3117.89 0.317060
\(460\) 4.65474 + 47.7693i 0.000471801 + 0.00484186i
\(461\) 1231.15 0.124382 0.0621911 0.998064i \(-0.480191\pi\)
0.0621911 + 0.998064i \(0.480191\pi\)
\(462\) 0 0
\(463\) 9773.66i 0.981038i 0.871431 + 0.490519i \(0.163193\pi\)
−0.871431 + 0.490519i \(0.836807\pi\)
\(464\) 3938.90 0.394092
\(465\) −297.710 3055.25i −0.0296902 0.304696i
\(466\) 12805.3 1.27295
\(467\) 15981.9i 1.58363i 0.610760 + 0.791816i \(0.290864\pi\)
−0.610760 + 0.791816i \(0.709136\pi\)
\(468\) 5626.30i 0.555717i
\(469\) 0 0
\(470\) 5455.95 531.640i 0.535456 0.0521760i
\(471\) 282.157 0.0276032
\(472\) 6276.27i 0.612053i
\(473\) 6183.96i 0.601139i
\(474\) −454.723 −0.0440635
\(475\) 669.681 131.761i 0.0646886 0.0127276i
\(476\) 0 0
\(477\) 6891.55i 0.661515i
\(478\) 2154.85i 0.206193i
\(479\) −17543.5 −1.67345 −0.836727 0.547621i \(-0.815534\pi\)
−0.836727 + 0.547621i \(0.815534\pi\)
\(480\) −427.411 + 41.6478i −0.0406428 + 0.00396032i
\(481\) 20980.2 1.98880
\(482\) 2258.95i 0.213469i
\(483\) 0 0
\(484\) 2527.51 0.237370
\(485\) 1550.25 + 15909.5i 0.145141 + 1.48951i
\(486\) 4881.59 0.455625
\(487\) 14047.2i 1.30706i 0.756901 + 0.653529i \(0.226712\pi\)
−0.756901 + 0.653529i \(0.773288\pi\)
\(488\) 3407.93i 0.316127i
\(489\) −4218.49 −0.390116
\(490\) 0 0
\(491\) 6339.30 0.582665 0.291333 0.956622i \(-0.405901\pi\)
0.291333 + 0.956622i \(0.405901\pi\)
\(492\) 233.169i 0.0213660i
\(493\) 12166.7i 1.11148i
\(494\) 600.966 0.0547343
\(495\) 7520.17 732.781i 0.682841 0.0665375i
\(496\) −3659.91 −0.331321
\(497\) 0 0
\(498\) 1466.95i 0.131999i
\(499\) −18373.0 −1.64828 −0.824139 0.566388i \(-0.808340\pi\)
−0.824139 + 0.566388i \(0.808340\pi\)
\(500\) 5354.49 1606.05i 0.478920 0.143650i
\(501\) 2010.80 0.179313
\(502\) 10380.7i 0.922930i
\(503\) 6870.88i 0.609061i −0.952503 0.304530i \(-0.901500\pi\)
0.952503 0.304530i \(-0.0984995\pi\)
\(504\) 0 0
\(505\) −8972.54 + 874.303i −0.790639 + 0.0770415i
\(506\) 56.7535 0.00498617
\(507\) 998.063i 0.0874271i
\(508\) 767.783i 0.0670568i
\(509\) 3520.02 0.306527 0.153264 0.988185i \(-0.451022\pi\)
0.153264 + 0.988185i \(0.451022\pi\)
\(510\) −128.644 1320.21i −0.0111695 0.114628i
\(511\) 0 0
\(512\) 512.000i 0.0441942i
\(513\) 344.467i 0.0296464i
\(514\) −13293.7 −1.14077
\(515\) −1637.45 16804.3i −0.140106 1.43784i
\(516\) −1122.90 −0.0958005
\(517\) 6482.08i 0.551415i
\(518\) 0 0
\(519\) −896.327 −0.0758081
\(520\) 4899.00 477.368i 0.413145 0.0402577i
\(521\) 9451.97 0.794815 0.397407 0.917642i \(-0.369910\pi\)
0.397407 + 0.917642i \(0.369910\pi\)
\(522\) 12584.4i 1.05518i
\(523\) 2384.25i 0.199343i 0.995020 + 0.0996713i \(0.0317791\pi\)
−0.995020 + 0.0996713i \(0.968221\pi\)
\(524\) 5981.86 0.498700
\(525\) 0 0
\(526\) 11951.1 0.990671
\(527\) 11305.0i 0.934445i
\(528\) 507.795i 0.0418541i
\(529\) 12165.8 0.999905
\(530\) 6000.70 584.721i 0.491799 0.0479220i
\(531\) 20052.1 1.63877
\(532\) 0 0
\(533\) 2672.59i 0.217191i
\(534\) 701.763 0.0568694
\(535\) −673.488 6911.68i −0.0544251 0.558538i
\(536\) 7346.75 0.592036
\(537\) 4384.15i 0.352309i
\(538\) 10079.7i 0.807748i
\(539\) 0 0
\(540\) −273.622 2808.05i −0.0218052 0.223776i
\(541\) 5638.78 0.448115 0.224057 0.974576i \(-0.428070\pi\)
0.224057 + 0.974576i \(0.428070\pi\)
\(542\) 1128.12i 0.0894036i
\(543\) 920.642i 0.0727597i
\(544\) −1581.50 −0.124644
\(545\) −17167.8 + 1672.86i −1.34933 + 0.131482i
\(546\) 0 0
\(547\) 15979.0i 1.24902i −0.781017 0.624509i \(-0.785299\pi\)
0.781017 0.624509i \(-0.214701\pi\)
\(548\) 4670.64i 0.364087i
\(549\) −10888.0 −0.846430
\(550\) −1276.11 6485.88i −0.0989338 0.502834i
\(551\) 1344.19 0.103928
\(552\) 10.3055i 0.000794621i
\(553\) 0 0
\(554\) 9415.79 0.722091
\(555\) −5092.02 + 496.177i −0.389449 + 0.0379488i
\(556\) −8339.00 −0.636066
\(557\) 8033.56i 0.611118i −0.952173 0.305559i \(-0.901157\pi\)
0.952173 0.305559i \(-0.0988434\pi\)
\(558\) 11693.1i 0.887111i
\(559\) 12870.8 0.973838
\(560\) 0 0
\(561\) −1568.51 −0.118044
\(562\) 3987.37i 0.299283i
\(563\) 2495.23i 0.186788i −0.995629 0.0933939i \(-0.970228\pi\)
0.995629 0.0933939i \(-0.0297716\pi\)
\(564\) −1177.04 −0.0878763
\(565\) −1404.20 14410.6i −0.104557 1.07302i
\(566\) −14570.8 −1.08208
\(567\) 0 0
\(568\) 1606.56i 0.118680i
\(569\) 7234.24 0.532997 0.266498 0.963835i \(-0.414133\pi\)
0.266498 + 0.963835i \(0.414133\pi\)
\(570\) −145.858 + 14.2127i −0.0107181 + 0.00104440i
\(571\) −13910.5 −1.01950 −0.509750 0.860323i \(-0.670262\pi\)
−0.509750 + 0.860323i \(0.670262\pi\)
\(572\) 5820.37i 0.425458i
\(573\) 407.800i 0.0297314i
\(574\) 0 0
\(575\) 25.8981 + 131.628i 0.00187831 + 0.00954656i
\(576\) −1635.79 −0.118330
\(577\) 8862.92i 0.639459i 0.947509 + 0.319730i \(0.103592\pi\)
−0.947509 + 0.319730i \(0.896408\pi\)
\(578\) 4940.96i 0.355566i
\(579\) 2693.95 0.193362
\(580\) 10957.7 1067.74i 0.784469 0.0764403i
\(581\) 0 0
\(582\) 3432.23i 0.244451i
\(583\) 7129.27i 0.506457i
\(584\) 6227.47 0.441258
\(585\) 1525.15 + 15651.8i 0.107790 + 1.10620i
\(586\) −17039.5 −1.20119
\(587\) 4179.74i 0.293895i −0.989144 0.146948i \(-0.953055\pi\)
0.989144 0.146948i \(-0.0469449\pi\)
\(588\) 0 0
\(589\) −1248.98 −0.0873743
\(590\) −1701.34 17460.0i −0.118717 1.21833i
\(591\) −2556.83 −0.177959
\(592\) 6099.79i 0.423480i
\(593\) 8487.25i 0.587740i 0.955845 + 0.293870i \(0.0949432\pi\)
−0.955845 + 0.293870i \(0.905057\pi\)
\(594\) −3336.17 −0.230446
\(595\) 0 0
\(596\) −4733.17 −0.325299
\(597\) 2296.74i 0.157453i
\(598\) 118.122i 0.00807753i
\(599\) −17356.0 −1.18388 −0.591941 0.805981i \(-0.701638\pi\)
−0.591941 + 0.805981i \(0.701638\pi\)
\(600\) −1177.73 + 231.721i −0.0801342 + 0.0157666i
\(601\) −5769.08 −0.391557 −0.195779 0.980648i \(-0.562723\pi\)
−0.195779 + 0.980648i \(0.562723\pi\)
\(602\) 0 0
\(603\) 23472.2i 1.58518i
\(604\) 5941.70 0.400272
\(605\) 7031.31 685.146i 0.472502 0.0460415i
\(606\) 1935.69 0.129756
\(607\) 20810.7i 1.39157i −0.718253 0.695783i \(-0.755058\pi\)
0.718253 0.695783i \(-0.244942\pi\)
\(608\) 174.725i 0.0116547i
\(609\) 0 0
\(610\) 923.806 + 9480.56i 0.0613177 + 0.629274i
\(611\) 13491.2 0.893285
\(612\) 5052.74i 0.333734i
\(613\) 2273.33i 0.149786i −0.997192 0.0748929i \(-0.976138\pi\)
0.997192 0.0748929i \(-0.0238615\pi\)
\(614\) −3476.85 −0.228525
\(615\) 63.2062 + 648.654i 0.00414426 + 0.0425305i
\(616\) 0 0
\(617\) 9970.37i 0.650554i −0.945619 0.325277i \(-0.894542\pi\)
0.945619 0.325277i \(-0.105458\pi\)
\(618\) 3625.27i 0.235971i
\(619\) 4161.01 0.270186 0.135093 0.990833i \(-0.456867\pi\)
0.135093 + 0.990833i \(0.456867\pi\)
\(620\) −10181.5 + 992.111i −0.659517 + 0.0642648i
\(621\) 67.7061 0.00437513
\(622\) 7980.69i 0.514464i
\(623\) 0 0
\(624\) −1056.88 −0.0678031
\(625\) 14460.4 5919.36i 0.925463 0.378839i
\(626\) 486.373 0.0310533
\(627\) 173.290i 0.0110376i
\(628\) 940.284i 0.0597475i
\(629\) −18841.4 −1.19437
\(630\) 0 0
\(631\) −11476.1 −0.724018 −0.362009 0.932175i \(-0.617909\pi\)
−0.362009 + 0.932175i \(0.617909\pi\)
\(632\) 1515.35i 0.0953759i
\(633\) 4823.99i 0.302901i
\(634\) −10656.3 −0.667534
\(635\) 208.127 + 2135.90i 0.0130067 + 0.133481i
\(636\) −1294.56 −0.0807115
\(637\) 0 0
\(638\) 13018.5i 0.807849i
\(639\) 5132.83 0.317764
\(640\) 138.790 + 1424.34i 0.00857214 + 0.0879717i
\(641\) 8486.13 0.522905 0.261452 0.965216i \(-0.415799\pi\)
0.261452 + 0.965216i \(0.415799\pi\)
\(642\) 1491.09i 0.0916644i
\(643\) 25563.4i 1.56784i 0.620859 + 0.783922i \(0.286784\pi\)
−0.620859 + 0.783922i \(0.713216\pi\)
\(644\) 0 0
\(645\) −3123.82 + 304.391i −0.190698 + 0.0185820i
\(646\) −539.703 −0.0328705
\(647\) 19501.0i 1.18495i −0.805589 0.592475i \(-0.798151\pi\)
0.805589 0.592475i \(-0.201849\pi\)
\(648\) 4915.01i 0.297963i
\(649\) −20743.8 −1.25465
\(650\) 13499.2 2655.99i 0.814586 0.160272i
\(651\) 0 0
\(652\) 14058.0i 0.844409i
\(653\) 32575.7i 1.95220i −0.217329 0.976098i \(-0.569735\pi\)
0.217329 0.976098i \(-0.430265\pi\)
\(654\) 3703.68 0.221446
\(655\) 16641.0 1621.53i 0.992698 0.0967306i
\(656\) 777.030 0.0462468
\(657\) 19896.2i 1.18147i
\(658\) 0 0
\(659\) 16168.7 0.955759 0.477879 0.878425i \(-0.341406\pi\)
0.477879 + 0.878425i \(0.341406\pi\)
\(660\) 137.651 + 1412.64i 0.00811825 + 0.0833136i
\(661\) 14858.4 0.874317 0.437159 0.899384i \(-0.355985\pi\)
0.437159 + 0.899384i \(0.355985\pi\)
\(662\) 23026.4i 1.35188i
\(663\) 3264.57i 0.191230i
\(664\) −4888.58 −0.285714
\(665\) 0 0
\(666\) −19488.3 −1.13387
\(667\) 264.205i 0.0153374i
\(668\) 6700.94i 0.388125i
\(669\) 5592.84 0.323216
\(670\) 20438.0 1991.52i 1.17849 0.114835i
\(671\) 11263.6 0.648028
\(672\) 0 0
\(673\) 7945.78i 0.455108i −0.973766 0.227554i \(-0.926927\pi\)
0.973766 0.227554i \(-0.0730728\pi\)
\(674\) −17637.7 −1.00798
\(675\) −1522.38 7737.56i −0.0868097 0.441213i
\(676\) 3326.03 0.189237
\(677\) 10365.2i 0.588430i 0.955739 + 0.294215i \(0.0950582\pi\)
−0.955739 + 0.294215i \(0.904942\pi\)
\(678\) 3108.86i 0.176099i
\(679\) 0 0
\(680\) −4399.59 + 428.705i −0.248112 + 0.0241766i
\(681\) −4431.89 −0.249384
\(682\) 12096.4i 0.679173i
\(683\) 21394.4i 1.19858i −0.800531 0.599292i \(-0.795449\pi\)
0.800531 0.599292i \(-0.204551\pi\)
\(684\) −558.231 −0.0312054
\(685\) 1266.09 + 12993.3i 0.0706204 + 0.724742i
\(686\) 0 0
\(687\) 1745.66i 0.0969445i
\(688\) 3742.05i 0.207361i
\(689\) 14838.3 0.820454
\(690\) −2.79356 28.6689i −0.000154129 0.00158175i
\(691\) 22753.1 1.25263 0.626315 0.779570i \(-0.284562\pi\)
0.626315 + 0.779570i \(0.284562\pi\)
\(692\) 2986.99i 0.164087i
\(693\) 0 0
\(694\) −4320.95 −0.236342
\(695\) −23198.3 + 2260.50i −1.26613 + 0.123375i
\(696\) −2363.95 −0.128743
\(697\) 2400.14i 0.130433i
\(698\) 3675.47i 0.199310i
\(699\) −7685.16 −0.415851
\(700\) 0 0
\(701\) −11931.0 −0.642834 −0.321417 0.946938i \(-0.604159\pi\)
−0.321417 + 0.946938i \(0.604159\pi\)
\(702\) 6943.62i 0.373319i
\(703\) 2081.62i 0.111678i
\(704\) 1692.22 0.0905936
\(705\) −3274.41 + 319.065i −0.174924 + 0.0170450i
\(706\) −19176.4 −1.02226
\(707\) 0 0
\(708\) 3766.73i 0.199947i
\(709\) −8551.69 −0.452984 −0.226492 0.974013i \(-0.572726\pi\)
−0.226492 + 0.974013i \(0.572726\pi\)
\(710\) −435.500 4469.32i −0.0230197 0.236240i
\(711\) −4841.42 −0.255369
\(712\) 2338.61i 0.123094i
\(713\) 245.492i 0.0128945i
\(714\) 0 0
\(715\) −1577.76 16191.7i −0.0825241 0.846905i
\(716\) −14610.1 −0.762576
\(717\) 1293.24i 0.0673597i
\(718\) 14094.5i 0.732591i
\(719\) −21203.9 −1.09982 −0.549911 0.835223i \(-0.685338\pi\)
−0.549911 + 0.835223i \(0.685338\pi\)
\(720\) −4550.63 + 443.423i −0.235544 + 0.0229519i
\(721\) 0 0
\(722\) 13658.4i 0.704033i
\(723\) 1355.71i 0.0697366i
\(724\) 3068.02 0.157489
\(725\) 30193.8 5940.70i 1.54672 0.304320i
\(726\) −1516.90 −0.0775445
\(727\) 25557.6i 1.30382i 0.758295 + 0.651911i \(0.226033\pi\)
−0.758295 + 0.651911i \(0.773967\pi\)
\(728\) 0 0
\(729\) 13658.4 0.693921
\(730\) 17324.3 1688.11i 0.878356 0.0855888i
\(731\) −11558.7 −0.584834
\(732\) 2045.28i 0.103273i
\(733\) 12792.4i 0.644607i 0.946636 + 0.322303i \(0.104457\pi\)
−0.946636 + 0.322303i \(0.895543\pi\)
\(734\) 15108.6 0.759764
\(735\) 0 0
\(736\) −34.3428 −0.00171996
\(737\) 24281.8i 1.21361i
\(738\) 2482.54i 0.123826i
\(739\) −16767.3 −0.834636 −0.417318 0.908760i \(-0.637030\pi\)
−0.417318 + 0.908760i \(0.637030\pi\)
\(740\) 1653.50 + 16969.1i 0.0821404 + 0.842967i
\(741\) −360.672 −0.0178807
\(742\) 0 0
\(743\) 17412.9i 0.859782i −0.902881 0.429891i \(-0.858552\pi\)
0.902881 0.429891i \(-0.141448\pi\)
\(744\) 2196.51 0.108237
\(745\) −13167.2 + 1283.04i −0.647530 + 0.0630967i
\(746\) −2576.62 −0.126457
\(747\) 15618.6i 0.764998i
\(748\) 5227.03i 0.255507i
\(749\) 0 0
\(750\) −3213.52 + 963.879i −0.156455 + 0.0469278i
\(751\) −21188.3 −1.02952 −0.514762 0.857333i \(-0.672120\pi\)
−0.514762 + 0.857333i \(0.672120\pi\)
\(752\) 3922.45i 0.190209i
\(753\) 6229.98i 0.301505i
\(754\) 27095.6 1.30871
\(755\) 16529.3 1610.65i 0.796770 0.0776390i
\(756\) 0 0
\(757\) 15675.9i 0.752642i 0.926489 + 0.376321i \(0.122811\pi\)
−0.926489 + 0.376321i \(0.877189\pi\)
\(758\) 13971.2i 0.669469i
\(759\) −34.0608 −0.00162889
\(760\) 47.3636 + 486.070i 0.00226061 + 0.0231995i
\(761\) −11122.5 −0.529815 −0.264908 0.964274i \(-0.585341\pi\)
−0.264908 + 0.964274i \(0.585341\pi\)
\(762\) 460.787i 0.0219063i
\(763\) 0 0
\(764\) −1358.98 −0.0643538
\(765\) −1369.67 14056.3i −0.0647328 0.664321i
\(766\) −11369.2 −0.536272
\(767\) 43174.4i 2.03251i
\(768\) 307.279i 0.0144375i
\(769\) −34411.5 −1.61367 −0.806833 0.590779i \(-0.798820\pi\)
−0.806833 + 0.590779i \(0.798820\pi\)
\(770\) 0 0
\(771\) 7978.24 0.372671
\(772\) 8977.54i 0.418535i
\(773\) 33325.4i 1.55062i −0.631579 0.775312i \(-0.717593\pi\)
0.631579 0.775312i \(-0.282407\pi\)
\(774\) −11955.5 −0.555210
\(775\) −28055.2 + 5519.93i −1.30035 + 0.255847i
\(776\) −11437.8 −0.529116
\(777\) 0 0
\(778\) 4511.44i 0.207896i
\(779\) 265.169 0.0121960
\(780\) −2940.15 + 286.494i −0.134967 + 0.0131515i
\(781\) −5309.88 −0.243281
\(782\) 106.080i 0.00485093i
\(783\) 15530.9i 0.708849i
\(784\) 0 0
\(785\) −254.887 2615.78i −0.0115889 0.118932i
\(786\) −3590.03 −0.162916
\(787\) 2874.46i 0.130195i 0.997879 + 0.0650976i \(0.0207359\pi\)
−0.997879 + 0.0650976i \(0.979264\pi\)
\(788\) 8520.58i 0.385194i
\(789\) −7172.50 −0.323635
\(790\) 410.775 + 4215.58i 0.0184996 + 0.189853i
\(791\) 0 0
\(792\) 5406.48i 0.242564i
\(793\) 23443.1i 1.04980i
\(794\) 19899.5 0.889431
\(795\) −3601.34 + 350.922i −0.160662 + 0.0156553i
\(796\) 7653.83 0.340807
\(797\) 3305.12i 0.146893i 0.997299 + 0.0734464i \(0.0233998\pi\)
−0.997299 + 0.0734464i \(0.976600\pi\)
\(798\) 0 0
\(799\) −12115.9 −0.536459
\(800\) 772.205 + 3924.75i 0.0341269 + 0.173451i
\(801\) 7471.65 0.329585
\(802\) 21729.2i 0.956716i
\(803\) 20582.5i 0.904534i
\(804\) −4409.18 −0.193408
\(805\) 0 0
\(806\) −25176.5 −1.10025
\(807\) 6049.39i 0.263877i
\(808\) 6450.64i 0.280857i
\(809\) 26393.2 1.14702 0.573508 0.819200i \(-0.305582\pi\)
0.573508 + 0.819200i \(0.305582\pi\)
\(810\) −1332.34 13673.1i −0.0577945 0.593116i
\(811\) 35281.8 1.52763 0.763817 0.645433i \(-0.223323\pi\)
0.763817 + 0.645433i \(0.223323\pi\)
\(812\) 0 0
\(813\) 677.043i 0.0292066i
\(814\) 20160.5 0.868090
\(815\) 3810.78 + 39108.1i 0.163786 + 1.68086i
\(816\) 949.142 0.0407189
\(817\) 1277.01i 0.0546843i
\(818\) 1902.01i 0.0812985i
\(819\) 0 0
\(820\) 2161.63 210.633i 0.0920576 0.00897029i
\(821\) 38385.0 1.63172 0.815862 0.578246i \(-0.196263\pi\)
0.815862 + 0.578246i \(0.196263\pi\)
\(822\) 2803.10i 0.118941i
\(823\) 21575.6i 0.913827i 0.889511 + 0.456913i \(0.151045\pi\)
−0.889511 + 0.456913i \(0.848955\pi\)
\(824\) 12081.2 0.510761
\(825\) 765.863 + 3892.52i 0.0323199 + 0.164267i
\(826\) 0 0
\(827\) 31906.7i 1.34160i 0.741638 + 0.670800i \(0.234049\pi\)
−0.741638 + 0.670800i \(0.765951\pi\)
\(828\) 109.722i 0.00460521i
\(829\) 26809.9 1.12322 0.561609 0.827403i \(-0.310183\pi\)
0.561609 + 0.827403i \(0.310183\pi\)
\(830\) −13599.6 + 1325.17i −0.568734 + 0.0554186i
\(831\) −5650.92 −0.235894
\(832\) 3522.04i 0.146761i
\(833\) 0 0
\(834\) 5004.68 0.207791
\(835\) −1816.46 18641.4i −0.0752828 0.772590i
\(836\) 577.487 0.0238909
\(837\) 14430.9i 0.595943i
\(838\) 1971.45i 0.0812680i
\(839\) 20507.0 0.843838 0.421919 0.906633i \(-0.361357\pi\)
0.421919 + 0.906633i \(0.361357\pi\)
\(840\) 0 0
\(841\) 36216.2 1.48494
\(842\) 7758.50i 0.317548i
\(843\) 2393.04i 0.0977705i
\(844\) −16075.9 −0.655632
\(845\) 9252.70 901.603i 0.376690 0.0367054i
\(846\) −12531.9 −0.509285
\(847\) 0 0
\(848\) 4314.09i 0.174701i
\(849\) 8744.71 0.353495
\(850\) −12123.0 + 2385.24i −0.489196 + 0.0962505i
\(851\) −409.149 −0.0164811
\(852\) 964.186i 0.0387705i
\(853\) 36776.8i 1.47622i −0.674681 0.738109i \(-0.735719\pi\)
0.674681 0.738109i \(-0.264281\pi\)
\(854\) 0 0
\(855\) −1552.95 + 151.322i −0.0621166 + 0.00605277i
\(856\) 4969.02 0.198408
\(857\) 26632.0i 1.06153i −0.847519 0.530765i \(-0.821905\pi\)
0.847519 0.530765i \(-0.178095\pi\)
\(858\) 3493.12i 0.138990i
\(859\) −2154.29 −0.0855687 −0.0427843 0.999084i \(-0.513623\pi\)
−0.0427843 + 0.999084i \(0.513623\pi\)
\(860\) 1014.38 + 10410.1i 0.0402209 + 0.412767i
\(861\) 0 0
\(862\) 27643.3i 1.09227i
\(863\) 37150.8i 1.46539i 0.680559 + 0.732693i \(0.261737\pi\)
−0.680559 + 0.732693i \(0.738263\pi\)
\(864\) 2018.79 0.0794916
\(865\) 809.699 + 8309.54i 0.0318273 + 0.326628i
\(866\) −1040.45 −0.0408266
\(867\) 2965.34i 0.116157i
\(868\) 0 0
\(869\) 5008.42 0.195511
\(870\) −6576.28 + 640.806i −0.256272 + 0.0249717i
\(871\) 50538.2 1.96604
\(872\) 12342.5i 0.479321i
\(873\) 36542.8i 1.41671i
\(874\) −11.7198 −0.000453581
\(875\) 0 0
\(876\) −3737.44 −0.144151
\(877\) 3945.86i 0.151930i −0.997111 0.0759648i \(-0.975796\pi\)
0.997111 0.0759648i \(-0.0242037\pi\)
\(878\) 19138.4i 0.735638i
\(879\) 10226.3 0.392407
\(880\) 4707.60 458.718i 0.180333 0.0175720i
\(881\) 25688.1 0.982353 0.491177 0.871060i \(-0.336567\pi\)
0.491177 + 0.871060i \(0.336567\pi\)
\(882\) 0 0
\(883\) 15521.1i 0.591537i −0.955260 0.295769i \(-0.904424\pi\)
0.955260 0.295769i \(-0.0955757\pi\)
\(884\) −10879.1 −0.413918
\(885\) 1021.07 + 10478.7i 0.0387828 + 0.398008i
\(886\) 8626.57 0.327105
\(887\) 31100.4i 1.17728i 0.808395 + 0.588641i \(0.200337\pi\)
−0.808395 + 0.588641i \(0.799663\pi\)
\(888\) 3660.81i 0.138343i
\(889\) 0 0
\(890\) −633.940 6505.81i −0.0238761 0.245028i
\(891\) −16244.7 −0.610793
\(892\) 18638.0i 0.699604i
\(893\) 1338.58i 0.0501610i
\(894\) 2840.63 0.106269
\(895\) −40643.9 + 3960.43i −1.51796 + 0.147913i
\(896\) 0 0
\(897\) 70.8913i 0.00263879i
\(898\) 8793.56i 0.326776i
\(899\) −56312.6 −2.08913
\(900\) −12539.2 + 2467.12i −0.464416 + 0.0913749i
\(901\) −13325.6 −0.492720
\(902\) 2568.17i 0.0948013i
\(903\) 0 0
\(904\) 10360.2 0.381167
\(905\) 8534.96 831.664i 0.313493 0.0305475i
\(906\) −3565.93 −0.130762
\(907\) 15230.5i 0.557577i 0.960353 + 0.278788i \(0.0899328\pi\)
−0.960353 + 0.278788i \(0.910067\pi\)
\(908\) 14769.2i 0.539794i
\(909\) 20609.2 0.751995
\(910\) 0 0
\(911\) 10133.5 0.368537 0.184269 0.982876i \(-0.441008\pi\)
0.184269 + 0.982876i \(0.441008\pi\)
\(912\) 104.862i 0.00380738i
\(913\) 16157.3i 0.585684i
\(914\) −16932.5 −0.612776
\(915\) −554.425 5689.80i −0.0200314 0.205572i
\(916\) −5817.36 −0.209837
\(917\) 0 0
\(918\) 6235.78i 0.224195i
\(919\) 20113.5 0.721961 0.360981 0.932573i \(-0.382442\pi\)
0.360981 + 0.932573i \(0.382442\pi\)
\(920\) −95.5387 + 9.30949i −0.00342371 + 0.000333614i
\(921\) 2086.65 0.0746550
\(922\) 2462.29i 0.0879515i
\(923\) 11051.5i 0.394112i
\(924\) 0 0
\(925\) 9199.78 + 46758.2i 0.327013 + 1.66205i
\(926\) −19547.3 −0.693698
\(927\) 38598.2i 1.36756i
\(928\) 7877.80i 0.278665i
\(929\) 34940.2 1.23396 0.616981 0.786978i \(-0.288356\pi\)
0.616981 + 0.786978i \(0.288356\pi\)
\(930\) 6110.49 595.419i 0.215453 0.0209942i
\(931\) 0 0
\(932\) 25610.7i 0.900113i
\(933\) 4789.64i 0.168066i
\(934\) −31963.9 −1.11980
\(935\) 1416.92 + 14541.1i 0.0495595 + 0.508605i
\(936\) −11252.6 −0.392951
\(937\) 6189.72i 0.215805i −0.994161 0.107902i \(-0.965587\pi\)
0.994161 0.107902i \(-0.0344134\pi\)
\(938\) 0 0
\(939\) −291.899 −0.0101446
\(940\) 1063.28 + 10911.9i 0.0368940 + 0.378625i
\(941\) −57065.9 −1.97694 −0.988468 0.151431i \(-0.951612\pi\)
−0.988468 + 0.151431i \(0.951612\pi\)
\(942\) 564.315i 0.0195184i
\(943\) 52.1199i 0.00179985i
\(944\) 12552.5 0.432786
\(945\) 0 0
\(946\) 12367.9 0.425069
\(947\) 14701.0i 0.504454i 0.967668 + 0.252227i \(0.0811630\pi\)
−0.967668 + 0.252227i \(0.918837\pi\)
\(948\) 909.446i 0.0311576i
\(949\) 42838.7 1.46533
\(950\) 263.523 + 1339.36i 0.00899979 + 0.0457417i
\(951\) 6395.43 0.218072
\(952\) 0 0
\(953\) 27816.6i 0.945507i −0.881195 0.472754i \(-0.843260\pi\)
0.881195 0.472754i \(-0.156740\pi\)
\(954\) −13783.1 −0.467762
\(955\) −3780.57 + 368.387i −0.128101 + 0.0124824i
\(956\) 4309.69 0.145801
\(957\) 7813.11i 0.263910i
\(958\) 35087.1i 1.18331i
\(959\) 0 0
\(960\) −83.2956 854.821i −0.00280037 0.0287388i
\(961\) 22533.1 0.756373
\(962\) 41960.4i 1.40630i
\(963\) 15875.6i 0.531238i
\(964\) −4517.89 −0.150946
\(965\) −2433.59 24974.7i −0.0811813 0.833124i
\(966\) 0 0
\(967\) 2846.67i 0.0946668i 0.998879 + 0.0473334i \(0.0150723\pi\)
−0.998879 + 0.0473334i \(0.984928\pi\)
\(968\) 5055.03i 0.167846i
\(969\) 323.904 0.0107382
\(970\) −31819.0 + 3100.51i −1.05324 + 0.102630i
\(971\) 976.436 0.0322712 0.0161356 0.999870i \(-0.494864\pi\)
0.0161356 + 0.999870i \(0.494864\pi\)
\(972\) 9763.18i 0.322175i
\(973\) 0 0
\(974\) −28094.3 −0.924230
\(975\) −8101.57 + 1594.00i −0.266111 + 0.0523579i
\(976\) −6815.87 −0.223536
\(977\) 24202.5i 0.792535i 0.918135 + 0.396267i \(0.129695\pi\)
−0.918135 + 0.396267i \(0.870305\pi\)
\(978\) 8436.97i 0.275853i
\(979\) −7729.38 −0.252331
\(980\) 0 0
\(981\) 39433.0 1.28338
\(982\) 12678.6i 0.412007i
\(983\) 47668.7i 1.54669i −0.633986 0.773344i \(-0.718582\pi\)
0.633986 0.773344i \(-0.281418\pi\)
\(984\) −466.337 −0.0151080
\(985\) 2309.72 + 23703.5i 0.0747144 + 0.766757i
\(986\) −24333.5 −0.785938
\(987\) 0 0
\(988\) 1201.93i 0.0387030i
\(989\) −251.002 −0.00807016
\(990\) 1465.56 + 15040.3i 0.0470491 + 0.482842i
\(991\) 25482.3 0.816824 0.408412 0.912798i \(-0.366083\pi\)
0.408412 + 0.912798i \(0.366083\pi\)
\(992\) 7319.83i 0.234279i
\(993\) 13819.4i 0.441635i
\(994\) 0 0
\(995\) 21292.3 2074.76i 0.678402 0.0661049i
\(996\) 2933.90 0.0933376
\(997\) 34022.5i 1.08075i 0.841425 + 0.540373i \(0.181717\pi\)
−0.841425 + 0.540373i \(0.818283\pi\)
\(998\) 36746.1i 1.16551i
\(999\) 24051.2 0.761708
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 490.4.c.e.99.9 12
5.2 odd 4 2450.4.a.cw.1.3 6
5.3 odd 4 2450.4.a.cx.1.4 6
5.4 even 2 inner 490.4.c.e.99.4 12
7.3 odd 6 70.4.i.a.9.4 24
7.5 odd 6 70.4.i.a.39.9 yes 24
7.6 odd 2 490.4.c.f.99.10 12
35.3 even 12 350.4.e.n.51.4 12
35.12 even 12 350.4.e.o.151.3 12
35.13 even 4 2450.4.a.cy.1.3 6
35.17 even 12 350.4.e.o.51.3 12
35.19 odd 6 70.4.i.a.39.4 yes 24
35.24 odd 6 70.4.i.a.9.9 yes 24
35.27 even 4 2450.4.a.cv.1.4 6
35.33 even 12 350.4.e.n.151.4 12
35.34 odd 2 490.4.c.f.99.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.4.i.a.9.4 24 7.3 odd 6
70.4.i.a.9.9 yes 24 35.24 odd 6
70.4.i.a.39.4 yes 24 35.19 odd 6
70.4.i.a.39.9 yes 24 7.5 odd 6
350.4.e.n.51.4 12 35.3 even 12
350.4.e.n.151.4 12 35.33 even 12
350.4.e.o.51.3 12 35.17 even 12
350.4.e.o.151.3 12 35.12 even 12
490.4.c.e.99.4 12 5.4 even 2 inner
490.4.c.e.99.9 12 1.1 even 1 trivial
490.4.c.f.99.3 12 35.34 odd 2
490.4.c.f.99.10 12 7.6 odd 2
2450.4.a.cv.1.4 6 35.27 even 4
2450.4.a.cw.1.3 6 5.2 odd 4
2450.4.a.cx.1.4 6 5.3 odd 4
2450.4.a.cy.1.3 6 35.13 even 4