Properties

Label 100.4.i.a.9.4
Level $100$
Weight $4$
Character 100.9
Analytic conductor $5.900$
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] = [100,4,Mod(9,100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(100, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("100.9");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 100.i (of order \(10\), degree \(4\), 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: \(5.90019100057\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 9.4
Character \(\chi\) \(=\) 100.9
Dual form 100.4.i.a.89.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.776927 + 0.252439i) q^{3} +(-4.16996 - 10.3736i) q^{5} +1.56595i q^{7} +(-21.3036 + 15.4779i) q^{9} +O(q^{10})\) \(q+(-0.776927 + 0.252439i) q^{3} +(-4.16996 - 10.3736i) q^{5} +1.56595i q^{7} +(-21.3036 + 15.4779i) q^{9} +(-28.6951 - 20.8482i) q^{11} +(-34.1181 - 46.9595i) q^{13} +(5.85845 + 7.00686i) q^{15} +(-21.7409 - 7.06405i) q^{17} +(44.6035 - 137.275i) q^{19} +(-0.395306 - 1.21663i) q^{21} +(-78.6996 + 108.321i) q^{23} +(-90.2228 + 86.5150i) q^{25} +(25.6086 - 35.2472i) q^{27} +(15.4001 + 47.3967i) q^{29} +(46.9860 - 144.608i) q^{31} +(27.5569 + 8.95379i) q^{33} +(16.2445 - 6.52994i) q^{35} +(246.292 + 338.992i) q^{37} +(38.3617 + 27.8714i) q^{39} +(-8.27027 + 6.00871i) q^{41} -151.479i q^{43} +(249.397 + 156.452i) q^{45} +(179.302 - 58.2587i) q^{47} +340.548 q^{49} +18.6743 q^{51} +(-506.519 + 164.578i) q^{53} +(-96.6134 + 384.608i) q^{55} +117.913i q^{57} +(448.410 - 325.789i) q^{59} +(-434.696 - 315.825i) q^{61} +(-24.2376 - 33.3602i) q^{63} +(-344.868 + 549.747i) q^{65} +(620.780 + 201.704i) q^{67} +(33.7995 - 104.024i) q^{69} +(-192.972 - 593.908i) q^{71} +(-180.947 + 249.052i) q^{73} +(48.2568 - 89.9916i) q^{75} +(32.6472 - 44.9350i) q^{77} +(-201.806 - 621.096i) q^{79} +(208.707 - 642.335i) q^{81} +(-1006.07 - 326.891i) q^{83} +(17.3793 + 254.988i) q^{85} +(-23.9295 - 32.9362i) q^{87} +(-190.914 - 138.707i) q^{89} +(73.5361 - 53.4271i) q^{91} +124.211i q^{93} +(-1610.03 + 109.735i) q^{95} +(-427.524 + 138.911i) q^{97} +933.997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 6 q^{5} + 122 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 6 q^{5} + 122 q^{9} + 20 q^{11} + 68 q^{15} - 160 q^{17} + 2 q^{19} - 108 q^{21} + 290 q^{23} + 654 q^{25} + 600 q^{27} + 62 q^{29} - 378 q^{31} - 1280 q^{33} - 278 q^{35} + 680 q^{37} + 592 q^{39} - 528 q^{41} - 1044 q^{45} - 1810 q^{47} - 2796 q^{49} + 1664 q^{51} - 510 q^{53} - 1350 q^{55} + 144 q^{59} - 1346 q^{61} + 1660 q^{63} + 1142 q^{65} + 1890 q^{67} + 956 q^{69} + 786 q^{71} + 3720 q^{73} - 78 q^{75} + 2160 q^{77} + 896 q^{79} + 348 q^{81} + 570 q^{83} + 224 q^{85} + 3240 q^{87} - 2512 q^{89} - 2212 q^{91} + 1536 q^{95} - 2250 q^{97} - 2540 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(77\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.776927 + 0.252439i −0.149520 + 0.0485819i −0.382821 0.923823i \(-0.625047\pi\)
0.233301 + 0.972405i \(0.425047\pi\)
\(4\) 0 0
\(5\) −4.16996 10.3736i −0.372973 0.927842i
\(6\) 0 0
\(7\) 1.56595i 0.0845531i 0.999106 + 0.0422766i \(0.0134611\pi\)
−0.999106 + 0.0422766i \(0.986539\pi\)
\(8\) 0 0
\(9\) −21.3036 + 15.4779i −0.789021 + 0.573257i
\(10\) 0 0
\(11\) −28.6951 20.8482i −0.786537 0.571453i 0.120397 0.992726i \(-0.461583\pi\)
−0.906934 + 0.421273i \(0.861583\pi\)
\(12\) 0 0
\(13\) −34.1181 46.9595i −0.727897 1.00186i −0.999224 0.0393770i \(-0.987463\pi\)
0.271328 0.962487i \(-0.412537\pi\)
\(14\) 0 0
\(15\) 5.85845 + 7.00686i 0.100843 + 0.120611i
\(16\) 0 0
\(17\) −21.7409 7.06405i −0.310173 0.100781i 0.149794 0.988717i \(-0.452139\pi\)
−0.459967 + 0.887936i \(0.652139\pi\)
\(18\) 0 0
\(19\) 44.6035 137.275i 0.538565 1.65753i −0.197252 0.980353i \(-0.563202\pi\)
0.735817 0.677180i \(-0.236798\pi\)
\(20\) 0 0
\(21\) −0.395306 1.21663i −0.00410775 0.0126424i
\(22\) 0 0
\(23\) −78.6996 + 108.321i −0.713478 + 0.982018i 0.286237 + 0.958159i \(0.407595\pi\)
−0.999715 + 0.0238596i \(0.992405\pi\)
\(24\) 0 0
\(25\) −90.2228 + 86.5150i −0.721782 + 0.692120i
\(26\) 0 0
\(27\) 25.6086 35.2472i 0.182532 0.251234i
\(28\) 0 0
\(29\) 15.4001 + 47.3967i 0.0986115 + 0.303495i 0.988178 0.153311i \(-0.0489935\pi\)
−0.889567 + 0.456806i \(0.848994\pi\)
\(30\) 0 0
\(31\) 46.9860 144.608i 0.272224 0.837819i −0.717717 0.696335i \(-0.754813\pi\)
0.989941 0.141483i \(-0.0451872\pi\)
\(32\) 0 0
\(33\) 27.5569 + 8.95379i 0.145365 + 0.0472320i
\(34\) 0 0
\(35\) 16.2445 6.52994i 0.0784520 0.0315360i
\(36\) 0 0
\(37\) 246.292 + 338.992i 1.09433 + 1.50622i 0.842693 + 0.538394i \(0.180969\pi\)
0.251636 + 0.967822i \(0.419031\pi\)
\(38\) 0 0
\(39\) 38.3617 + 27.8714i 0.157507 + 0.114436i
\(40\) 0 0
\(41\) −8.27027 + 6.00871i −0.0315024 + 0.0228879i −0.603425 0.797420i \(-0.706198\pi\)
0.571923 + 0.820308i \(0.306198\pi\)
\(42\) 0 0
\(43\) 151.479i 0.537219i −0.963249 0.268609i \(-0.913436\pi\)
0.963249 0.268609i \(-0.0865641\pi\)
\(44\) 0 0
\(45\) 249.397 + 156.452i 0.826176 + 0.518278i
\(46\) 0 0
\(47\) 179.302 58.2587i 0.556465 0.180806i −0.0172651 0.999851i \(-0.505496\pi\)
0.573730 + 0.819045i \(0.305496\pi\)
\(48\) 0 0
\(49\) 340.548 0.992851
\(50\) 0 0
\(51\) 18.6743 0.0512732
\(52\) 0 0
\(53\) −506.519 + 164.578i −1.31275 + 0.426538i −0.879999 0.474976i \(-0.842457\pi\)
−0.432751 + 0.901514i \(0.642457\pi\)
\(54\) 0 0
\(55\) −96.6134 + 384.608i −0.236861 + 0.942919i
\(56\) 0 0
\(57\) 117.913i 0.273998i
\(58\) 0 0
\(59\) 448.410 325.789i 0.989458 0.718883i 0.0296555 0.999560i \(-0.490559\pi\)
0.959802 + 0.280677i \(0.0905590\pi\)
\(60\) 0 0
\(61\) −434.696 315.825i −0.912413 0.662907i 0.0292111 0.999573i \(-0.490700\pi\)
−0.941624 + 0.336667i \(0.890700\pi\)
\(62\) 0 0
\(63\) −24.2376 33.3602i −0.0484707 0.0667142i
\(64\) 0 0
\(65\) −344.868 + 549.747i −0.658086 + 1.04904i
\(66\) 0 0
\(67\) 620.780 + 201.704i 1.13195 + 0.367792i 0.814315 0.580423i \(-0.197113\pi\)
0.317631 + 0.948214i \(0.397113\pi\)
\(68\) 0 0
\(69\) 33.7995 104.024i 0.0589707 0.181493i
\(70\) 0 0
\(71\) −192.972 593.908i −0.322558 0.992731i −0.972531 0.232774i \(-0.925220\pi\)
0.649973 0.759957i \(-0.274780\pi\)
\(72\) 0 0
\(73\) −180.947 + 249.052i −0.290113 + 0.399306i −0.929051 0.369952i \(-0.879374\pi\)
0.638938 + 0.769258i \(0.279374\pi\)
\(74\) 0 0
\(75\) 48.2568 89.9916i 0.0742961 0.138551i
\(76\) 0 0
\(77\) 32.6472 44.9350i 0.0483181 0.0665042i
\(78\) 0 0
\(79\) −201.806 621.096i −0.287405 0.884541i −0.985668 0.168700i \(-0.946043\pi\)
0.698263 0.715842i \(-0.253957\pi\)
\(80\) 0 0
\(81\) 208.707 642.335i 0.286292 0.881118i
\(82\) 0 0
\(83\) −1006.07 326.891i −1.33048 0.432300i −0.444401 0.895828i \(-0.646583\pi\)
−0.886082 + 0.463528i \(0.846583\pi\)
\(84\) 0 0
\(85\) 17.3793 + 254.988i 0.0221770 + 0.325381i
\(86\) 0 0
\(87\) −23.9295 32.9362i −0.0294887 0.0405877i
\(88\) 0 0
\(89\) −190.914 138.707i −0.227380 0.165201i 0.468262 0.883590i \(-0.344880\pi\)
−0.695643 + 0.718388i \(0.744880\pi\)
\(90\) 0 0
\(91\) 73.5361 53.4271i 0.0847108 0.0615460i
\(92\) 0 0
\(93\) 124.211i 0.138495i
\(94\) 0 0
\(95\) −1610.03 + 109.735i −1.73880 + 0.118512i
\(96\) 0 0
\(97\) −427.524 + 138.911i −0.447510 + 0.145405i −0.524098 0.851658i \(-0.675598\pi\)
0.0765876 + 0.997063i \(0.475598\pi\)
\(98\) 0 0
\(99\) 933.997 0.948184
\(100\) 0 0
\(101\) −779.325 −0.767780 −0.383890 0.923379i \(-0.625416\pi\)
−0.383890 + 0.923379i \(0.625416\pi\)
\(102\) 0 0
\(103\) 15.2644 4.95969i 0.0146024 0.00474459i −0.301707 0.953401i \(-0.597556\pi\)
0.316309 + 0.948656i \(0.397556\pi\)
\(104\) 0 0
\(105\) −10.9724 + 9.17402i −0.0101980 + 0.00852660i
\(106\) 0 0
\(107\) 192.417i 0.173847i −0.996215 0.0869236i \(-0.972296\pi\)
0.996215 0.0869236i \(-0.0277036\pi\)
\(108\) 0 0
\(109\) 170.017 123.524i 0.149400 0.108546i −0.510574 0.859834i \(-0.670567\pi\)
0.659974 + 0.751288i \(0.270567\pi\)
\(110\) 0 0
\(111\) −276.926 201.198i −0.236799 0.172044i
\(112\) 0 0
\(113\) −625.409 860.802i −0.520651 0.716615i 0.465019 0.885301i \(-0.346048\pi\)
−0.985670 + 0.168686i \(0.946048\pi\)
\(114\) 0 0
\(115\) 1451.85 + 364.704i 1.17727 + 0.295729i
\(116\) 0 0
\(117\) 1453.67 + 472.328i 1.14865 + 0.373220i
\(118\) 0 0
\(119\) 11.0619 34.0451i 0.00852139 0.0262261i
\(120\) 0 0
\(121\) −22.5397 69.3701i −0.0169344 0.0521188i
\(122\) 0 0
\(123\) 4.90857 6.75606i 0.00359830 0.00495263i
\(124\) 0 0
\(125\) 1273.70 + 575.170i 0.911384 + 0.411558i
\(126\) 0 0
\(127\) −158.906 + 218.716i −0.111029 + 0.152818i −0.860915 0.508749i \(-0.830108\pi\)
0.749886 + 0.661567i \(0.230108\pi\)
\(128\) 0 0
\(129\) 38.2393 + 117.688i 0.0260991 + 0.0803248i
\(130\) 0 0
\(131\) −81.9275 + 252.147i −0.0546415 + 0.168169i −0.974653 0.223722i \(-0.928179\pi\)
0.920011 + 0.391892i \(0.128179\pi\)
\(132\) 0 0
\(133\) 214.966 + 69.8466i 0.140150 + 0.0455374i
\(134\) 0 0
\(135\) −472.427 118.673i −0.301186 0.0756577i
\(136\) 0 0
\(137\) 1258.12 + 1731.66i 0.784589 + 1.07989i 0.994761 + 0.102229i \(0.0325976\pi\)
−0.210172 + 0.977664i \(0.567402\pi\)
\(138\) 0 0
\(139\) 649.615 + 471.973i 0.396400 + 0.288001i 0.768073 0.640362i \(-0.221216\pi\)
−0.371673 + 0.928364i \(0.621216\pi\)
\(140\) 0 0
\(141\) −124.598 + 90.5254i −0.0744185 + 0.0540682i
\(142\) 0 0
\(143\) 2058.81i 1.20396i
\(144\) 0 0
\(145\) 427.456 357.397i 0.244816 0.204691i
\(146\) 0 0
\(147\) −264.581 + 85.9675i −0.148451 + 0.0482346i
\(148\) 0 0
\(149\) −1322.85 −0.727329 −0.363664 0.931530i \(-0.618474\pi\)
−0.363664 + 0.931530i \(0.618474\pi\)
\(150\) 0 0
\(151\) 3124.98 1.68416 0.842078 0.539356i \(-0.181332\pi\)
0.842078 + 0.539356i \(0.181332\pi\)
\(152\) 0 0
\(153\) 572.496 186.015i 0.302507 0.0982905i
\(154\) 0 0
\(155\) −1696.03 + 115.597i −0.878895 + 0.0599030i
\(156\) 0 0
\(157\) 2679.00i 1.36183i −0.732363 0.680915i \(-0.761582\pi\)
0.732363 0.680915i \(-0.238418\pi\)
\(158\) 0 0
\(159\) 351.982 255.730i 0.175560 0.127552i
\(160\) 0 0
\(161\) −169.624 123.239i −0.0830327 0.0603268i
\(162\) 0 0
\(163\) 1470.51 + 2023.99i 0.706622 + 0.972581i 0.999863 + 0.0165430i \(0.00526605\pi\)
−0.293241 + 0.956038i \(0.594734\pi\)
\(164\) 0 0
\(165\) −22.0285 323.201i −0.0103934 0.152492i
\(166\) 0 0
\(167\) −3182.68 1034.12i −1.47475 0.479176i −0.542211 0.840242i \(-0.682413\pi\)
−0.932540 + 0.361066i \(0.882413\pi\)
\(168\) 0 0
\(169\) −362.243 + 1114.87i −0.164881 + 0.507451i
\(170\) 0 0
\(171\) 1174.53 + 3614.82i 0.525254 + 1.61656i
\(172\) 0 0
\(173\) 1420.60 1955.29i 0.624315 0.859295i −0.373343 0.927693i \(-0.621789\pi\)
0.997658 + 0.0683977i \(0.0217887\pi\)
\(174\) 0 0
\(175\) −135.478 141.284i −0.0585209 0.0610290i
\(176\) 0 0
\(177\) −266.140 + 366.310i −0.113019 + 0.155557i
\(178\) 0 0
\(179\) 6.32806 + 19.4758i 0.00264235 + 0.00813233i 0.952369 0.304948i \(-0.0986391\pi\)
−0.949727 + 0.313080i \(0.898639\pi\)
\(180\) 0 0
\(181\) 495.928 1526.31i 0.203658 0.626794i −0.796108 0.605154i \(-0.793111\pi\)
0.999766 0.0216394i \(-0.00688858\pi\)
\(182\) 0 0
\(183\) 417.454 + 135.639i 0.168629 + 0.0547908i
\(184\) 0 0
\(185\) 2489.54 3968.52i 0.989375 1.57714i
\(186\) 0 0
\(187\) 476.586 + 655.964i 0.186371 + 0.256518i
\(188\) 0 0
\(189\) 55.1952 + 40.1017i 0.0212427 + 0.0154337i
\(190\) 0 0
\(191\) −3149.57 + 2288.29i −1.19317 + 0.866886i −0.993595 0.112998i \(-0.963955\pi\)
−0.199570 + 0.979883i \(0.563955\pi\)
\(192\) 0 0
\(193\) 4353.01i 1.62351i −0.584000 0.811753i \(-0.698513\pi\)
0.584000 0.811753i \(-0.301487\pi\)
\(194\) 0 0
\(195\) 129.160 514.171i 0.0474324 0.188823i
\(196\) 0 0
\(197\) −4717.04 + 1532.66i −1.70596 + 0.554302i −0.989653 0.143479i \(-0.954171\pi\)
−0.716312 + 0.697781i \(0.754171\pi\)
\(198\) 0 0
\(199\) −2522.45 −0.898552 −0.449276 0.893393i \(-0.648318\pi\)
−0.449276 + 0.893393i \(0.648318\pi\)
\(200\) 0 0
\(201\) −533.219 −0.187116
\(202\) 0 0
\(203\) −74.2207 + 24.1158i −0.0256614 + 0.00833791i
\(204\) 0 0
\(205\) 96.8186 + 60.7364i 0.0329859 + 0.0206927i
\(206\) 0 0
\(207\) 3525.73i 1.18384i
\(208\) 0 0
\(209\) −4141.85 + 3009.23i −1.37080 + 0.995947i
\(210\) 0 0
\(211\) −601.096 436.722i −0.196119 0.142489i 0.485392 0.874297i \(-0.338677\pi\)
−0.681511 + 0.731808i \(0.738677\pi\)
\(212\) 0 0
\(213\) 299.851 + 412.709i 0.0964574 + 0.132762i
\(214\) 0 0
\(215\) −1571.39 + 631.664i −0.498454 + 0.200368i
\(216\) 0 0
\(217\) 226.448 + 73.5776i 0.0708402 + 0.0230174i
\(218\) 0 0
\(219\) 77.7121 239.173i 0.0239785 0.0737984i
\(220\) 0 0
\(221\) 410.034 + 1261.96i 0.124805 + 0.384110i
\(222\) 0 0
\(223\) −893.614 + 1229.95i −0.268345 + 0.369345i −0.921830 0.387594i \(-0.873306\pi\)
0.653485 + 0.756939i \(0.273306\pi\)
\(224\) 0 0
\(225\) 582.992 3239.54i 0.172738 0.959864i
\(226\) 0 0
\(227\) 3636.30 5004.94i 1.06322 1.46339i 0.186456 0.982463i \(-0.440300\pi\)
0.876760 0.480928i \(-0.159700\pi\)
\(228\) 0 0
\(229\) 228.735 + 703.973i 0.0660053 + 0.203143i 0.978620 0.205678i \(-0.0659399\pi\)
−0.912614 + 0.408821i \(0.865940\pi\)
\(230\) 0 0
\(231\) −14.0212 + 43.1527i −0.00399361 + 0.0122911i
\(232\) 0 0
\(233\) 3869.85 + 1257.39i 1.08808 + 0.353539i 0.797504 0.603313i \(-0.206153\pi\)
0.290576 + 0.956852i \(0.406153\pi\)
\(234\) 0 0
\(235\) −1352.03 1617.07i −0.375306 0.448876i
\(236\) 0 0
\(237\) 313.578 + 431.602i 0.0859454 + 0.118294i
\(238\) 0 0
\(239\) −1509.61 1096.80i −0.408571 0.296844i 0.364452 0.931222i \(-0.381256\pi\)
−0.773023 + 0.634378i \(0.781256\pi\)
\(240\) 0 0
\(241\) −1663.23 + 1208.40i −0.444555 + 0.322988i −0.787442 0.616388i \(-0.788595\pi\)
0.342887 + 0.939377i \(0.388595\pi\)
\(242\) 0 0
\(243\) 1728.07i 0.456196i
\(244\) 0 0
\(245\) −1420.07 3532.70i −0.370307 0.921209i
\(246\) 0 0
\(247\) −7968.17 + 2589.02i −2.05264 + 0.666944i
\(248\) 0 0
\(249\) 864.160 0.219935
\(250\) 0 0
\(251\) 6414.16 1.61298 0.806490 0.591247i \(-0.201364\pi\)
0.806490 + 0.591247i \(0.201364\pi\)
\(252\) 0 0
\(253\) 4516.59 1467.53i 1.12235 0.364675i
\(254\) 0 0
\(255\) −77.8713 193.720i −0.0191235 0.0475734i
\(256\) 0 0
\(257\) 2669.98i 0.648050i −0.946048 0.324025i \(-0.894964\pi\)
0.946048 0.324025i \(-0.105036\pi\)
\(258\) 0 0
\(259\) −530.844 + 385.680i −0.127355 + 0.0925290i
\(260\) 0 0
\(261\) −1061.68 771.357i −0.251787 0.182934i
\(262\) 0 0
\(263\) −1834.73 2525.30i −0.430169 0.592077i 0.537823 0.843058i \(-0.319247\pi\)
−0.967992 + 0.250981i \(0.919247\pi\)
\(264\) 0 0
\(265\) 3819.43 + 4568.14i 0.885380 + 1.05894i
\(266\) 0 0
\(267\) 183.341 + 59.5712i 0.0420236 + 0.0136543i
\(268\) 0 0
\(269\) −1221.38 + 3759.01i −0.276835 + 0.852011i 0.711893 + 0.702288i \(0.247838\pi\)
−0.988728 + 0.149723i \(0.952162\pi\)
\(270\) 0 0
\(271\) 2211.00 + 6804.77i 0.495605 + 1.52531i 0.816012 + 0.578035i \(0.196180\pi\)
−0.320407 + 0.947280i \(0.603820\pi\)
\(272\) 0 0
\(273\) −43.6451 + 60.0723i −0.00967590 + 0.0133177i
\(274\) 0 0
\(275\) 4392.64 601.574i 0.963223 0.131914i
\(276\) 0 0
\(277\) −2073.39 + 2853.77i −0.449739 + 0.619013i −0.972341 0.233564i \(-0.924961\pi\)
0.522602 + 0.852577i \(0.324961\pi\)
\(278\) 0 0
\(279\) 1237.27 + 3807.91i 0.265495 + 0.817111i
\(280\) 0 0
\(281\) −437.184 + 1345.52i −0.0928122 + 0.285647i −0.986677 0.162689i \(-0.947983\pi\)
0.893865 + 0.448336i \(0.147983\pi\)
\(282\) 0 0
\(283\) 6802.11 + 2210.14i 1.42878 + 0.464237i 0.918379 0.395702i \(-0.129499\pi\)
0.510396 + 0.859939i \(0.329499\pi\)
\(284\) 0 0
\(285\) 1223.18 491.691i 0.254227 0.102194i
\(286\) 0 0
\(287\) −9.40931 12.9508i −0.00193524 0.00266363i
\(288\) 0 0
\(289\) −3551.93 2580.63i −0.722966 0.525266i
\(290\) 0 0
\(291\) 297.089 215.847i 0.0598476 0.0434818i
\(292\) 0 0
\(293\) 338.223i 0.0674375i −0.999431 0.0337188i \(-0.989265\pi\)
0.999431 0.0337188i \(-0.0107351\pi\)
\(294\) 0 0
\(295\) −5249.45 3293.09i −1.03605 0.649937i
\(296\) 0 0
\(297\) −1469.68 + 477.529i −0.287137 + 0.0932965i
\(298\) 0 0
\(299\) 7771.77 1.50319
\(300\) 0 0
\(301\) 237.209 0.0454235
\(302\) 0 0
\(303\) 605.479 196.732i 0.114798 0.0373002i
\(304\) 0 0
\(305\) −1463.58 + 5826.34i −0.274767 + 1.09382i
\(306\) 0 0
\(307\) 6906.15i 1.28389i −0.766750 0.641946i \(-0.778127\pi\)
0.766750 0.641946i \(-0.221873\pi\)
\(308\) 0 0
\(309\) −10.6073 + 7.70664i −0.00195284 + 0.00141882i
\(310\) 0 0
\(311\) 2107.51 + 1531.20i 0.384264 + 0.279184i 0.763101 0.646279i \(-0.223676\pi\)
−0.378837 + 0.925463i \(0.623676\pi\)
\(312\) 0 0
\(313\) 1582.88 + 2178.64i 0.285845 + 0.393432i 0.927659 0.373429i \(-0.121818\pi\)
−0.641814 + 0.766860i \(0.721818\pi\)
\(314\) 0 0
\(315\) −244.995 + 390.542i −0.0438220 + 0.0698558i
\(316\) 0 0
\(317\) 9301.43 + 3022.22i 1.64801 + 0.535472i 0.978308 0.207154i \(-0.0664201\pi\)
0.669706 + 0.742626i \(0.266420\pi\)
\(318\) 0 0
\(319\) 546.229 1681.12i 0.0958714 0.295062i
\(320\) 0 0
\(321\) 48.5735 + 149.494i 0.00844582 + 0.0259936i
\(322\) 0 0
\(323\) −1939.44 + 2669.41i −0.334097 + 0.459845i
\(324\) 0 0
\(325\) 7140.94 + 1285.09i 1.21879 + 0.219336i
\(326\) 0 0
\(327\) −100.908 + 138.888i −0.0170649 + 0.0234879i
\(328\) 0 0
\(329\) 91.2299 + 280.777i 0.0152877 + 0.0470509i
\(330\) 0 0
\(331\) 2943.03 9057.71i 0.488712 1.50410i −0.337821 0.941210i \(-0.609690\pi\)
0.826532 0.562889i \(-0.190310\pi\)
\(332\) 0 0
\(333\) −10493.8 3409.65i −1.72690 0.561103i
\(334\) 0 0
\(335\) −496.240 7280.82i −0.0809328 1.18744i
\(336\) 0 0
\(337\) 5377.32 + 7401.25i 0.869203 + 1.19635i 0.979296 + 0.202434i \(0.0648851\pi\)
−0.110093 + 0.993921i \(0.535115\pi\)
\(338\) 0 0
\(339\) 703.197 + 510.903i 0.112662 + 0.0818538i
\(340\) 0 0
\(341\) −4363.09 + 3169.97i −0.692888 + 0.503412i
\(342\) 0 0
\(343\) 1070.40i 0.168502i
\(344\) 0 0
\(345\) −1220.05 + 83.1549i −0.190391 + 0.0129765i
\(346\) 0 0
\(347\) −3784.12 + 1229.54i −0.585425 + 0.190216i −0.586729 0.809783i \(-0.699585\pi\)
0.00130455 + 0.999999i \(0.499585\pi\)
\(348\) 0 0
\(349\) −12466.3 −1.91205 −0.956025 0.293286i \(-0.905251\pi\)
−0.956025 + 0.293286i \(0.905251\pi\)
\(350\) 0 0
\(351\) −2528.91 −0.384567
\(352\) 0 0
\(353\) −4554.49 + 1479.84i −0.686718 + 0.223128i −0.631534 0.775348i \(-0.717574\pi\)
−0.0551835 + 0.998476i \(0.517574\pi\)
\(354\) 0 0
\(355\) −5356.27 + 4478.39i −0.800792 + 0.669545i
\(356\) 0 0
\(357\) 29.2430i 0.00433531i
\(358\) 0 0
\(359\) 6367.03 4625.92i 0.936042 0.680074i −0.0114230 0.999935i \(-0.503636\pi\)
0.947465 + 0.319861i \(0.103636\pi\)
\(360\) 0 0
\(361\) −11306.0 8214.29i −1.64835 1.19759i
\(362\) 0 0
\(363\) 35.0234 + 48.2056i 0.00506405 + 0.00697007i
\(364\) 0 0
\(365\) 3338.11 + 838.531i 0.478697 + 0.120249i
\(366\) 0 0
\(367\) 1605.00 + 521.497i 0.228285 + 0.0741742i 0.420926 0.907095i \(-0.361705\pi\)
−0.192641 + 0.981269i \(0.561705\pi\)
\(368\) 0 0
\(369\) 83.1839 256.014i 0.0117355 0.0361180i
\(370\) 0 0
\(371\) −257.720 793.181i −0.0360651 0.110997i
\(372\) 0 0
\(373\) 5649.85 7776.35i 0.784285 1.07948i −0.210512 0.977591i \(-0.567513\pi\)
0.994796 0.101884i \(-0.0324870\pi\)
\(374\) 0 0
\(375\) −1134.76 125.334i −0.156264 0.0172593i
\(376\) 0 0
\(377\) 1700.31 2340.27i 0.232282 0.319708i
\(378\) 0 0
\(379\) −3329.83 10248.2i −0.451298 1.38895i −0.875427 0.483350i \(-0.839420\pi\)
0.424129 0.905602i \(-0.360580\pi\)
\(380\) 0 0
\(381\) 68.2462 210.040i 0.00917680 0.0282433i
\(382\) 0 0
\(383\) −7462.73 2424.79i −0.995634 0.323501i −0.234515 0.972113i \(-0.575350\pi\)
−0.761120 + 0.648611i \(0.775350\pi\)
\(384\) 0 0
\(385\) −602.275 151.291i −0.0797268 0.0200273i
\(386\) 0 0
\(387\) 2344.59 + 3227.05i 0.307965 + 0.423877i
\(388\) 0 0
\(389\) 11716.3 + 8512.42i 1.52710 + 1.10950i 0.957824 + 0.287357i \(0.0927764\pi\)
0.569276 + 0.822146i \(0.307224\pi\)
\(390\) 0 0
\(391\) 2476.18 1799.05i 0.320271 0.232691i
\(392\) 0 0
\(393\) 216.581i 0.0277992i
\(394\) 0 0
\(395\) −5601.47 + 4683.41i −0.713520 + 0.596576i
\(396\) 0 0
\(397\) −10826.5 + 3517.73i −1.36868 + 0.444710i −0.898931 0.438091i \(-0.855655\pi\)
−0.469747 + 0.882801i \(0.655655\pi\)
\(398\) 0 0
\(399\) −184.645 −0.0231674
\(400\) 0 0
\(401\) 9387.67 1.16907 0.584536 0.811368i \(-0.301277\pi\)
0.584536 + 0.811368i \(0.301277\pi\)
\(402\) 0 0
\(403\) −8393.80 + 2727.31i −1.03753 + 0.337114i
\(404\) 0 0
\(405\) −7533.62 + 513.470i −0.924318 + 0.0629988i
\(406\) 0 0
\(407\) 14862.2i 1.81005i
\(408\) 0 0
\(409\) 2771.64 2013.71i 0.335082 0.243452i −0.407502 0.913204i \(-0.633600\pi\)
0.742584 + 0.669753i \(0.233600\pi\)
\(410\) 0 0
\(411\) −1414.61 1027.77i −0.169775 0.123349i
\(412\) 0 0
\(413\) 510.168 + 702.186i 0.0607838 + 0.0836618i
\(414\) 0 0
\(415\) 804.230 + 11799.6i 0.0951279 + 1.39571i
\(416\) 0 0
\(417\) −623.847 202.700i −0.0732612 0.0238040i
\(418\) 0 0
\(419\) 4711.09 14499.2i 0.549288 1.69053i −0.161282 0.986908i \(-0.551563\pi\)
0.710570 0.703626i \(-0.248437\pi\)
\(420\) 0 0
\(421\) −1380.41 4248.48i −0.159804 0.491825i 0.838812 0.544421i \(-0.183250\pi\)
−0.998616 + 0.0525960i \(0.983250\pi\)
\(422\) 0 0
\(423\) −2918.04 + 4016.34i −0.335414 + 0.461658i
\(424\) 0 0
\(425\) 2572.67 1243.58i 0.293630 0.141935i
\(426\) 0 0
\(427\) 494.566 680.711i 0.0560508 0.0771474i
\(428\) 0 0
\(429\) −519.724 1599.55i −0.0584907 0.180016i
\(430\) 0 0
\(431\) 2231.16 6866.80i 0.249353 0.767430i −0.745537 0.666464i \(-0.767807\pi\)
0.994890 0.100965i \(-0.0321932\pi\)
\(432\) 0 0
\(433\) −3036.92 986.754i −0.337055 0.109516i 0.135599 0.990764i \(-0.456704\pi\)
−0.472654 + 0.881248i \(0.656704\pi\)
\(434\) 0 0
\(435\) −241.881 + 385.578i −0.0266605 + 0.0424990i
\(436\) 0 0
\(437\) 11359.5 + 15635.0i 1.24347 + 1.71149i
\(438\) 0 0
\(439\) 1051.45 + 763.925i 0.114312 + 0.0830527i 0.643473 0.765469i \(-0.277493\pi\)
−0.529160 + 0.848522i \(0.677493\pi\)
\(440\) 0 0
\(441\) −7254.88 + 5270.98i −0.783380 + 0.569159i
\(442\) 0 0
\(443\) 4847.79i 0.519923i 0.965619 + 0.259961i \(0.0837098\pi\)
−0.965619 + 0.259961i \(0.916290\pi\)
\(444\) 0 0
\(445\) −642.786 + 2558.87i −0.0684742 + 0.272589i
\(446\) 0 0
\(447\) 1027.76 333.938i 0.108750 0.0353350i
\(448\) 0 0
\(449\) 2344.41 0.246414 0.123207 0.992381i \(-0.460682\pi\)
0.123207 + 0.992381i \(0.460682\pi\)
\(450\) 0 0
\(451\) 362.588 0.0378572
\(452\) 0 0
\(453\) −2427.88 + 788.867i −0.251814 + 0.0818195i
\(454\) 0 0
\(455\) −860.874 540.044i −0.0886998 0.0556432i
\(456\) 0 0
\(457\) 8691.80i 0.889684i 0.895609 + 0.444842i \(0.146740\pi\)
−0.895609 + 0.444842i \(0.853260\pi\)
\(458\) 0 0
\(459\) −805.742 + 585.406i −0.0819365 + 0.0595303i
\(460\) 0 0
\(461\) −10813.3 7856.33i −1.09246 0.793722i −0.112651 0.993635i \(-0.535934\pi\)
−0.979814 + 0.199913i \(0.935934\pi\)
\(462\) 0 0
\(463\) −2697.04 3712.16i −0.270718 0.372611i 0.651914 0.758293i \(-0.273966\pi\)
−0.922632 + 0.385682i \(0.873966\pi\)
\(464\) 0 0
\(465\) 1288.51 517.955i 0.128502 0.0516551i
\(466\) 0 0
\(467\) 18131.8 + 5891.39i 1.79666 + 0.583770i 0.999792 0.0203823i \(-0.00648834\pi\)
0.796869 + 0.604153i \(0.206488\pi\)
\(468\) 0 0
\(469\) −315.857 + 972.109i −0.0310979 + 0.0957096i
\(470\) 0 0
\(471\) 676.283 + 2081.39i 0.0661602 + 0.203620i
\(472\) 0 0
\(473\) −3158.08 + 4346.72i −0.306995 + 0.422543i
\(474\) 0 0
\(475\) 7852.13 + 16244.2i 0.758485 + 1.56913i
\(476\) 0 0
\(477\) 8243.33 11346.0i 0.791271 1.08909i
\(478\) 0 0
\(479\) 4236.57 + 13038.8i 0.404120 + 1.24375i 0.921627 + 0.388076i \(0.126860\pi\)
−0.517507 + 0.855679i \(0.673140\pi\)
\(480\) 0 0
\(481\) 7515.89 23131.5i 0.712464 2.19274i
\(482\) 0 0
\(483\) 162.896 + 52.9282i 0.0153458 + 0.00498616i
\(484\) 0 0
\(485\) 3223.77 + 3855.71i 0.301822 + 0.360987i
\(486\) 0 0
\(487\) 6580.50 + 9057.28i 0.612302 + 0.842761i 0.996764 0.0803794i \(-0.0256132\pi\)
−0.384463 + 0.923141i \(0.625613\pi\)
\(488\) 0 0
\(489\) −1653.41 1201.27i −0.152904 0.111091i
\(490\) 0 0
\(491\) −8449.70 + 6139.07i −0.776639 + 0.564261i −0.903968 0.427599i \(-0.859359\pi\)
0.127329 + 0.991860i \(0.459359\pi\)
\(492\) 0 0
\(493\) 1139.24i 0.104074i
\(494\) 0 0
\(495\) −3894.73 9688.90i −0.353647 0.879765i
\(496\) 0 0
\(497\) 930.028 302.184i 0.0839385 0.0272733i
\(498\) 0 0
\(499\) 13219.1 1.18591 0.592955 0.805236i \(-0.297961\pi\)
0.592955 + 0.805236i \(0.297961\pi\)
\(500\) 0 0
\(501\) 2733.76 0.243784
\(502\) 0 0
\(503\) 10619.1 3450.37i 0.941320 0.305853i 0.202136 0.979357i \(-0.435212\pi\)
0.739184 + 0.673504i \(0.235212\pi\)
\(504\) 0 0
\(505\) 3249.76 + 8084.40i 0.286361 + 0.712378i
\(506\) 0 0
\(507\) 957.617i 0.0838841i
\(508\) 0 0
\(509\) 8386.76 6093.34i 0.730328 0.530614i −0.159339 0.987224i \(-0.550936\pi\)
0.889667 + 0.456610i \(0.150936\pi\)
\(510\) 0 0
\(511\) −390.002 283.353i −0.0337626 0.0245300i
\(512\) 0 0
\(513\) −3696.34 5087.58i −0.318124 0.437860i
\(514\) 0 0
\(515\) −115.102 137.665i −0.00984852 0.0117791i
\(516\) 0 0
\(517\) −6359.68 2066.38i −0.541003 0.175782i
\(518\) 0 0
\(519\) −610.113 + 1877.73i −0.0516011 + 0.158812i
\(520\) 0 0
\(521\) 5294.58 + 16295.0i 0.445220 + 1.37025i 0.882242 + 0.470795i \(0.156033\pi\)
−0.437023 + 0.899451i \(0.643967\pi\)
\(522\) 0 0
\(523\) −5599.83 + 7707.51i −0.468190 + 0.644409i −0.976182 0.216953i \(-0.930388\pi\)
0.507992 + 0.861362i \(0.330388\pi\)
\(524\) 0 0
\(525\) 140.922 + 75.5675i 0.0117149 + 0.00628197i
\(526\) 0 0
\(527\) −2043.04 + 2812.00i −0.168873 + 0.232434i
\(528\) 0 0
\(529\) −1779.94 5478.08i −0.146292 0.450241i
\(530\) 0 0
\(531\) −4510.19 + 13880.9i −0.368598 + 1.13443i
\(532\) 0 0
\(533\) 564.332 + 183.363i 0.0458610 + 0.0149012i
\(534\) 0 0
\(535\) −1996.05 + 802.372i −0.161303 + 0.0648403i
\(536\) 0 0
\(537\) −9.83288 13.5338i −0.000790168 0.00108757i
\(538\) 0 0
\(539\) −9772.07 7099.82i −0.780914 0.567367i
\(540\) 0 0
\(541\) 4918.39 3573.42i 0.390865 0.283980i −0.374945 0.927047i \(-0.622338\pi\)
0.765810 + 0.643067i \(0.222338\pi\)
\(542\) 0 0
\(543\) 1311.02i 0.103612i
\(544\) 0 0
\(545\) −1990.36 1248.59i −0.156436 0.0981354i
\(546\) 0 0
\(547\) −20873.4 + 6782.18i −1.63160 + 0.530138i −0.974638 0.223789i \(-0.928157\pi\)
−0.656958 + 0.753927i \(0.728157\pi\)
\(548\) 0 0
\(549\) 14148.9 1.09993
\(550\) 0 0
\(551\) 7193.30 0.556161
\(552\) 0 0
\(553\) 972.603 316.018i 0.0747907 0.0243010i
\(554\) 0 0
\(555\) −932.379 + 3711.71i −0.0713104 + 0.283880i
\(556\) 0 0
\(557\) 16112.7i 1.22571i −0.790197 0.612853i \(-0.790022\pi\)
0.790197 0.612853i \(-0.209978\pi\)
\(558\) 0 0
\(559\) −7113.41 + 5168.19i −0.538220 + 0.391040i
\(560\) 0 0
\(561\) −535.863 389.327i −0.0403282 0.0293002i
\(562\) 0 0
\(563\) −5589.19 7692.85i −0.418394 0.575871i 0.546846 0.837233i \(-0.315828\pi\)
−0.965241 + 0.261362i \(0.915828\pi\)
\(564\) 0 0
\(565\) −6321.68 + 10077.3i −0.470717 + 0.750360i
\(566\) 0 0
\(567\) 1005.86 + 326.824i 0.0745013 + 0.0242069i
\(568\) 0 0
\(569\) −3051.12 + 9390.39i −0.224797 + 0.691855i 0.773515 + 0.633778i \(0.218497\pi\)
−0.998312 + 0.0580769i \(0.981503\pi\)
\(570\) 0 0
\(571\) −5095.76 15683.1i −0.373469 1.14942i −0.944506 0.328495i \(-0.893459\pi\)
0.571037 0.820925i \(-0.306541\pi\)
\(572\) 0 0
\(573\) 1869.33 2572.91i 0.136287 0.187583i
\(574\) 0 0
\(575\) −2270.87 16581.7i −0.164699 1.20262i
\(576\) 0 0
\(577\) −233.579 + 321.494i −0.0168527 + 0.0231958i −0.817360 0.576127i \(-0.804563\pi\)
0.800508 + 0.599323i \(0.204563\pi\)
\(578\) 0 0
\(579\) 1098.87 + 3381.97i 0.0788730 + 0.242746i
\(580\) 0 0
\(581\) 511.893 1575.45i 0.0365523 0.112497i
\(582\) 0 0
\(583\) 17965.8 + 5837.44i 1.27627 + 0.414686i
\(584\) 0 0
\(585\) −1162.04 17049.4i −0.0821272 1.20497i
\(586\) 0 0
\(587\) −2390.55 3290.30i −0.168089 0.231355i 0.716660 0.697423i \(-0.245670\pi\)
−0.884749 + 0.466068i \(0.845670\pi\)
\(588\) 0 0
\(589\) −17755.4 12900.0i −1.24210 0.902440i
\(590\) 0 0
\(591\) 3277.89 2381.53i 0.228146 0.165758i
\(592\) 0 0
\(593\) 11135.7i 0.771146i −0.922677 0.385573i \(-0.874004\pi\)
0.922677 0.385573i \(-0.125996\pi\)
\(594\) 0 0
\(595\) −399.298 + 27.2150i −0.0275120 + 0.00187514i
\(596\) 0 0
\(597\) 1959.76 636.765i 0.134351 0.0436533i
\(598\) 0 0
\(599\) −12279.4 −0.837603 −0.418801 0.908078i \(-0.637550\pi\)
−0.418801 + 0.908078i \(0.637550\pi\)
\(600\) 0 0
\(601\) −1971.50 −0.133809 −0.0669045 0.997759i \(-0.521312\pi\)
−0.0669045 + 0.997759i \(0.521312\pi\)
\(602\) 0 0
\(603\) −16346.8 + 5311.40i −1.10397 + 0.358701i
\(604\) 0 0
\(605\) −625.627 + 523.088i −0.0420419 + 0.0351513i
\(606\) 0 0
\(607\) 3978.46i 0.266031i 0.991114 + 0.133015i \(0.0424660\pi\)
−0.991114 + 0.133015i \(0.957534\pi\)
\(608\) 0 0
\(609\) 51.5763 37.4724i 0.00343182 0.00249336i
\(610\) 0 0
\(611\) −8853.24 6432.25i −0.586192 0.425894i
\(612\) 0 0
\(613\) 11232.2 + 15459.8i 0.740073 + 1.01862i 0.998614 + 0.0526227i \(0.0167581\pi\)
−0.258542 + 0.966000i \(0.583242\pi\)
\(614\) 0 0
\(615\) −90.5532 22.7469i −0.00593733 0.00149145i
\(616\) 0 0
\(617\) −112.138 36.4359i −0.00731687 0.00237740i 0.305356 0.952238i \(-0.401224\pi\)
−0.312673 + 0.949861i \(0.601224\pi\)
\(618\) 0 0
\(619\) 195.101 600.460i 0.0126685 0.0389895i −0.944522 0.328447i \(-0.893475\pi\)
0.957191 + 0.289457i \(0.0934748\pi\)
\(620\) 0 0
\(621\) 1802.62 + 5547.88i 0.116484 + 0.358500i
\(622\) 0 0
\(623\) 217.208 298.961i 0.0139683 0.0192257i
\(624\) 0 0
\(625\) 655.302 15611.3i 0.0419393 0.999120i
\(626\) 0 0
\(627\) 2458.27 3383.52i 0.156577 0.215510i
\(628\) 0 0
\(629\) −2959.96 9109.82i −0.187633 0.577476i
\(630\) 0 0
\(631\) −2807.17 + 8639.59i −0.177103 + 0.545066i −0.999723 0.0235248i \(-0.992511\pi\)
0.822621 + 0.568591i \(0.192511\pi\)
\(632\) 0 0
\(633\) 577.253 + 187.561i 0.0362461 + 0.0117771i
\(634\) 0 0
\(635\) 2931.50 + 736.392i 0.183202 + 0.0460202i
\(636\) 0 0
\(637\) −11618.8 15992.0i −0.722693 0.994702i
\(638\) 0 0
\(639\) 13303.5 + 9665.54i 0.823595 + 0.598377i
\(640\) 0 0
\(641\) −3651.45 + 2652.93i −0.224998 + 0.163470i −0.694573 0.719422i \(-0.744407\pi\)
0.469576 + 0.882892i \(0.344407\pi\)
\(642\) 0 0
\(643\) 6553.26i 0.401921i −0.979599 0.200961i \(-0.935594\pi\)
0.979599 0.200961i \(-0.0644063\pi\)
\(644\) 0 0
\(645\) 1061.40 887.436i 0.0647944 0.0541748i
\(646\) 0 0
\(647\) −6759.24 + 2196.21i −0.410716 + 0.133450i −0.507085 0.861896i \(-0.669277\pi\)
0.0963691 + 0.995346i \(0.469277\pi\)
\(648\) 0 0
\(649\) −19659.3 −1.18905
\(650\) 0 0
\(651\) −194.508 −0.0117102
\(652\) 0 0
\(653\) −13453.8 + 4371.40i −0.806259 + 0.261969i −0.683013 0.730407i \(-0.739331\pi\)
−0.123247 + 0.992376i \(0.539331\pi\)
\(654\) 0 0
\(655\) 2957.30 201.561i 0.176414 0.0120239i
\(656\) 0 0
\(657\) 8106.39i 0.481370i
\(658\) 0 0
\(659\) −14599.7 + 10607.3i −0.863012 + 0.627015i −0.928703 0.370825i \(-0.879075\pi\)
0.0656910 + 0.997840i \(0.479075\pi\)
\(660\) 0 0
\(661\) 22268.2 + 16178.8i 1.31034 + 0.952017i 0.999999 + 0.00139082i \(0.000442713\pi\)
0.310339 + 0.950626i \(0.399557\pi\)
\(662\) 0 0
\(663\) −637.133 876.939i −0.0373216 0.0513687i
\(664\) 0 0
\(665\) −171.840 2521.23i −0.0100205 0.147021i
\(666\) 0 0
\(667\) −6346.03 2061.95i −0.368395 0.119699i
\(668\) 0 0
\(669\) 383.785 1181.17i 0.0221793 0.0682610i
\(670\) 0 0
\(671\) 5889.27 + 18125.3i 0.338827 + 1.04280i
\(672\) 0 0
\(673\) 13288.0 18289.3i 0.761091 1.04755i −0.236032 0.971745i \(-0.575847\pi\)
0.997123 0.0758065i \(-0.0241531\pi\)
\(674\) 0 0
\(675\) 738.934 + 5395.63i 0.0421357 + 0.307671i
\(676\) 0 0
\(677\) −8113.39 + 11167.1i −0.460595 + 0.633954i −0.974632 0.223813i \(-0.928149\pi\)
0.514037 + 0.857768i \(0.328149\pi\)
\(678\) 0 0
\(679\) −217.527 669.480i −0.0122944 0.0378384i
\(680\) 0 0
\(681\) −1561.70 + 4806.42i −0.0878774 + 0.270459i
\(682\) 0 0
\(683\) −7746.21 2516.90i −0.433969 0.141005i 0.0838826 0.996476i \(-0.473268\pi\)
−0.517851 + 0.855471i \(0.673268\pi\)
\(684\) 0 0
\(685\) 12717.2 20272.2i 0.709341 1.13075i
\(686\) 0 0
\(687\) −355.420 489.194i −0.0197382 0.0271673i
\(688\) 0 0
\(689\) 25010.0 + 18170.8i 1.38288 + 1.00472i
\(690\) 0 0
\(691\) −5632.18 + 4092.02i −0.310070 + 0.225279i −0.731926 0.681384i \(-0.761379\pi\)
0.421857 + 0.906662i \(0.361379\pi\)
\(692\) 0 0
\(693\) 1462.59i 0.0801719i
\(694\) 0 0
\(695\) 2187.18 8706.95i 0.119373 0.475213i
\(696\) 0 0
\(697\) 222.249 72.2131i 0.0120779 0.00392434i
\(698\) 0 0
\(699\) −3324.01 −0.179865
\(700\) 0 0
\(701\) −17301.5 −0.932193 −0.466096 0.884734i \(-0.654340\pi\)
−0.466096 + 0.884734i \(0.654340\pi\)
\(702\) 0 0
\(703\) 57520.8 18689.6i 3.08597 1.00269i
\(704\) 0 0
\(705\) 1458.64 + 915.037i 0.0779229 + 0.0488827i
\(706\) 0 0
\(707\) 1220.38i 0.0649182i
\(708\) 0 0
\(709\) −10399.9 + 7555.96i −0.550883 + 0.400240i −0.828111 0.560564i \(-0.810584\pi\)
0.277228 + 0.960804i \(0.410584\pi\)
\(710\) 0 0
\(711\) 13912.5 + 10108.0i 0.733838 + 0.533165i
\(712\) 0 0
\(713\) 11966.3 + 16470.2i 0.628528 + 0.865094i
\(714\) 0 0
\(715\) 21357.3 8585.18i 1.11709 0.449045i
\(716\) 0 0
\(717\) 1449.73 + 471.046i 0.0755107 + 0.0245349i
\(718\) 0 0
\(719\) −7217.90 + 22214.4i −0.374384 + 1.15224i 0.569509 + 0.821985i \(0.307133\pi\)
−0.943893 + 0.330251i \(0.892867\pi\)
\(720\) 0 0
\(721\) 7.76661 + 23.9032i 0.000401170 + 0.00123468i
\(722\) 0 0
\(723\) 987.157 1358.70i 0.0507784 0.0698904i
\(724\) 0 0
\(725\) −5489.97 2943.92i −0.281231 0.150806i
\(726\) 0 0
\(727\) −13476.7 + 18549.0i −0.687513 + 0.946281i −0.999993 0.00364359i \(-0.998840\pi\)
0.312480 + 0.949924i \(0.398840\pi\)
\(728\) 0 0
\(729\) 5198.86 + 16000.5i 0.264130 + 0.812907i
\(730\) 0 0
\(731\) −1070.06 + 3293.30i −0.0541417 + 0.166631i
\(732\) 0 0
\(733\) 20805.6 + 6760.13i 1.04839 + 0.340643i 0.782037 0.623232i \(-0.214181\pi\)
0.266354 + 0.963875i \(0.414181\pi\)
\(734\) 0 0
\(735\) 1995.08 + 2386.17i 0.100122 + 0.119749i
\(736\) 0 0
\(737\) −13608.2 18730.1i −0.680142 0.936136i
\(738\) 0 0
\(739\) −20466.3 14869.7i −1.01876 0.740175i −0.0527349 0.998609i \(-0.516794\pi\)
−0.966029 + 0.258433i \(0.916794\pi\)
\(740\) 0 0
\(741\) 5537.12 4022.95i 0.274509 0.199442i
\(742\) 0 0
\(743\) 3971.78i 0.196111i 0.995181 + 0.0980555i \(0.0312623\pi\)
−0.995181 + 0.0980555i \(0.968738\pi\)
\(744\) 0 0
\(745\) 5516.23 + 13722.7i 0.271274 + 0.674846i
\(746\) 0 0
\(747\) 26492.4 8607.90i 1.29760 0.421615i
\(748\) 0 0
\(749\) 301.315 0.0146993
\(750\) 0 0
\(751\) 31873.9 1.54873 0.774364 0.632740i \(-0.218070\pi\)
0.774364 + 0.632740i \(0.218070\pi\)
\(752\) 0 0
\(753\) −4983.33 + 1619.18i −0.241172 + 0.0783616i
\(754\) 0 0
\(755\) −13031.1 32417.3i −0.628145 1.56263i
\(756\) 0 0
\(757\) 4967.00i 0.238479i −0.992866 0.119239i \(-0.961954\pi\)
0.992866 0.119239i \(-0.0380456\pi\)
\(758\) 0 0
\(759\) −3138.60 + 2280.33i −0.150097 + 0.109052i
\(760\) 0 0
\(761\) 20275.8 + 14731.2i 0.965829 + 0.701716i 0.954497 0.298220i \(-0.0963928\pi\)
0.0113320 + 0.999936i \(0.496393\pi\)
\(762\) 0 0
\(763\) 193.433 + 266.237i 0.00917789 + 0.0126323i
\(764\) 0 0
\(765\) −4316.93 5163.16i −0.204025 0.244019i
\(766\) 0 0
\(767\) −30597.8 9941.83i −1.44045 0.468029i
\(768\) 0 0
\(769\) 4397.19 13533.2i 0.206199 0.634615i −0.793463 0.608618i \(-0.791724\pi\)
0.999662 0.0259965i \(-0.00827587\pi\)
\(770\) 0 0
\(771\) 674.007 + 2074.38i 0.0314835 + 0.0968963i
\(772\) 0 0
\(773\) −14147.6 + 19472.5i −0.658283 + 0.906049i −0.999423 0.0339639i \(-0.989187\pi\)
0.341140 + 0.940012i \(0.389187\pi\)
\(774\) 0 0
\(775\) 8271.56 + 17111.9i 0.383385 + 0.793134i
\(776\) 0 0
\(777\) 315.066 433.651i 0.0145469 0.0200221i
\(778\) 0 0
\(779\) 455.964 + 1403.31i 0.0209713 + 0.0645429i
\(780\) 0 0
\(781\) −6844.56 + 21065.4i −0.313595 + 0.965146i
\(782\) 0 0
\(783\) 2064.98 + 670.952i 0.0942481 + 0.0306231i
\(784\) 0 0
\(785\) −27790.8 + 11171.3i −1.26356 + 0.507926i
\(786\) 0 0
\(787\) 13080.1 + 18003.2i 0.592445 + 0.815430i 0.994990 0.0999696i \(-0.0318746\pi\)
−0.402546 + 0.915400i \(0.631875\pi\)
\(788\) 0 0
\(789\) 2062.94 + 1498.81i 0.0930830 + 0.0676288i
\(790\) 0 0
\(791\) 1347.97 979.358i 0.0605920 0.0440227i
\(792\) 0 0
\(793\) 31188.5i 1.39664i
\(794\) 0 0
\(795\) −4120.59 2584.93i −0.183827 0.115318i
\(796\) 0 0
\(797\) 1809.10 587.811i 0.0804033 0.0261246i −0.268539 0.963269i \(-0.586541\pi\)
0.348942 + 0.937144i \(0.386541\pi\)
\(798\) 0 0
\(799\) −4309.73 −0.190822
\(800\) 0 0
\(801\) 6214.05 0.274111
\(802\) 0 0
\(803\) 10384.6 3374.16i 0.456369 0.148283i
\(804\) 0 0
\(805\) −571.107 + 2273.52i −0.0250048 + 0.0995416i
\(806\) 0 0
\(807\) 3228.80i 0.140842i
\(808\) 0 0
\(809\) 11667.8 8477.13i 0.507067 0.368405i −0.304643 0.952467i \(-0.598537\pi\)
0.811710 + 0.584061i \(0.198537\pi\)
\(810\) 0 0
\(811\) −30961.9 22495.1i −1.34059 0.973995i −0.999422 0.0339929i \(-0.989178\pi\)
−0.341168 0.940003i \(-0.610822\pi\)
\(812\) 0 0
\(813\) −3435.58 4728.67i −0.148205 0.203987i
\(814\) 0 0
\(815\) 14864.0 23694.4i 0.638851 1.01838i
\(816\) 0 0
\(817\) −20794.4 6756.51i −0.890458 0.289327i
\(818\) 0 0
\(819\) −739.640 + 2276.38i −0.0315569 + 0.0971221i
\(820\) 0 0
\(821\) 3651.70 + 11238.8i 0.155231 + 0.477753i 0.998184 0.0602342i \(-0.0191847\pi\)
−0.842953 + 0.537988i \(0.819185\pi\)
\(822\) 0 0
\(823\) 21930.1 30184.2i 0.928841 1.27844i −0.0314693 0.999505i \(-0.510019\pi\)
0.960310 0.278935i \(-0.0899814\pi\)
\(824\) 0 0
\(825\) −3260.90 + 1576.25i −0.137612 + 0.0665189i
\(826\) 0 0
\(827\) 19099.6 26288.3i 0.803092 1.10536i −0.189261 0.981927i \(-0.560609\pi\)
0.992353 0.123434i \(-0.0393907\pi\)
\(828\) 0 0
\(829\) 191.414 + 589.110i 0.00801938 + 0.0246811i 0.954986 0.296650i \(-0.0958696\pi\)
−0.946967 + 0.321332i \(0.895870\pi\)
\(830\) 0 0
\(831\) 890.467 2740.58i 0.0371720 0.114404i
\(832\) 0 0
\(833\) −7403.82 2405.65i −0.307956 0.100061i
\(834\) 0 0
\(835\) 2544.18 + 37328.1i 0.105443 + 1.54706i
\(836\) 0 0
\(837\) −3893.78 5359.33i −0.160799 0.221321i
\(838\) 0 0
\(839\) −5672.36 4121.21i −0.233411 0.169583i 0.464932 0.885346i \(-0.346079\pi\)
−0.698343 + 0.715764i \(0.746079\pi\)
\(840\) 0 0
\(841\) 17721.8 12875.7i 0.726632 0.527929i
\(842\) 0 0
\(843\) 1155.73i 0.0472188i
\(844\) 0 0
\(845\) 13075.7 891.206i 0.532331 0.0362821i
\(846\) 0 0
\(847\) 108.630 35.2960i 0.00440680 0.00143186i
\(848\) 0 0
\(849\) −5842.67 −0.236184
\(850\) 0 0
\(851\) −56103.0 −2.25991
\(852\) 0 0
\(853\) −5373.09 + 1745.82i −0.215676 + 0.0700772i −0.414862 0.909884i \(-0.636170\pi\)
0.199186 + 0.979962i \(0.436170\pi\)
\(854\) 0 0
\(855\) 32601.0 27257.8i 1.30401 1.09029i
\(856\) 0 0
\(857\) 16445.6i 0.655509i 0.944763 + 0.327755i \(0.106292\pi\)
−0.944763 + 0.327755i \(0.893708\pi\)
\(858\) 0 0
\(859\) −8964.34 + 6512.97i −0.356064 + 0.258696i −0.751409 0.659837i \(-0.770625\pi\)
0.395344 + 0.918533i \(0.370625\pi\)
\(860\) 0 0
\(861\) 10.5796 + 7.68655i 0.000418761 + 0.000304247i
\(862\) 0 0
\(863\) −23136.3 31844.4i −0.912594 1.25608i −0.966273 0.257520i \(-0.917095\pi\)
0.0536791 0.998558i \(-0.482905\pi\)
\(864\) 0 0
\(865\) −26207.3 6583.25i −1.03014 0.258772i
\(866\) 0 0
\(867\) 3411.04 + 1108.32i 0.133616 + 0.0434145i
\(868\) 0 0
\(869\) −7157.90 + 22029.7i −0.279419 + 0.859963i
\(870\) 0 0
\(871\) −11707.9 36033.3i −0.455463 1.40177i
\(872\) 0 0
\(873\) 6957.74 9576.50i 0.269741 0.371266i
\(874\) 0 0
\(875\) −900.685 + 1994.54i −0.0347985 + 0.0770603i
\(876\) 0 0
\(877\) −5869.40 + 8078.53i −0.225993 + 0.311052i −0.906923 0.421296i \(-0.861575\pi\)
0.680931 + 0.732348i \(0.261575\pi\)
\(878\) 0 0
\(879\) 85.3806 + 262.775i 0.00327624 + 0.0100832i
\(880\) 0 0
\(881\) −6916.28 + 21286.1i −0.264490 + 0.814015i 0.727321 + 0.686297i \(0.240765\pi\)
−0.991811 + 0.127718i \(0.959235\pi\)
\(882\) 0 0
\(883\) −31096.3 10103.8i −1.18514 0.385074i −0.350863 0.936427i \(-0.614112\pi\)
−0.834272 + 0.551353i \(0.814112\pi\)
\(884\) 0 0
\(885\) 4909.75 + 1233.33i 0.186485 + 0.0468450i
\(886\) 0 0
\(887\) −14028.5 19308.6i −0.531039 0.730912i 0.456249 0.889852i \(-0.349193\pi\)
−0.987288 + 0.158940i \(0.949193\pi\)
\(888\) 0 0
\(889\) −342.497 248.839i −0.0129212 0.00938783i
\(890\) 0 0
\(891\) −19380.4 + 14080.7i −0.728697 + 0.529429i
\(892\) 0 0
\(893\) 27212.2i 1.01973i
\(894\) 0 0
\(895\) 175.646 146.858i 0.00655999 0.00548483i
\(896\) 0 0
\(897\) −6038.10 + 1961.90i −0.224756 + 0.0730277i
\(898\) 0 0
\(899\) 7577.54 0.281118
\(900\) 0 0
\(901\) 12174.8 0.450167
\(902\) 0 0
\(903\) −184.294 + 59.8807i −0.00679171 + 0.00220676i
\(904\) 0 0
\(905\) −17901.3 + 1220.10i −0.657524 + 0.0448150i
\(906\) 0 0
\(907\) 50126.6i 1.83509i 0.397634 + 0.917544i \(0.369831\pi\)
−0.397634 + 0.917544i \(0.630169\pi\)
\(908\) 0 0
\(909\) 16602.4 12062.4i 0.605794 0.440135i
\(910\) 0 0
\(911\) 15483.8 + 11249.7i 0.563120 + 0.409131i 0.832599 0.553876i \(-0.186852\pi\)
−0.269480 + 0.963006i \(0.586852\pi\)
\(912\) 0 0
\(913\) 22054.1 + 30354.9i 0.799435 + 1.10033i
\(914\) 0 0
\(915\) −333.705 4896.11i −0.0120568 0.176897i
\(916\) 0 0
\(917\) −394.848 128.294i −0.0142192 0.00462011i
\(918\) 0 0
\(919\) −1119.36 + 3445.05i −0.0401789 + 0.123658i −0.969134 0.246534i \(-0.920708\pi\)
0.928955 + 0.370192i \(0.120708\pi\)
\(920\) 0 0
\(921\) 1743.38 + 5365.57i 0.0623739 + 0.191967i
\(922\) 0 0
\(923\) −21305.8 + 29324.9i −0.759793 + 1.04576i
\(924\) 0 0
\(925\) −51549.1 9276.84i −1.83235 0.329752i
\(926\) 0 0
\(927\) −248.420 + 341.920i −0.00880169 + 0.0121145i
\(928\) 0 0
\(929\) −15796.1 48615.5i −0.557863 1.71692i −0.688261 0.725463i \(-0.741626\pi\)
0.130399 0.991462i \(-0.458374\pi\)
\(930\) 0 0
\(931\) 15189.6 46748.8i 0.534715 1.64568i
\(932\) 0 0
\(933\) −2023.92 657.611i −0.0710183 0.0230753i
\(934\) 0 0
\(935\) 4817.35 7679.25i 0.168497 0.268597i
\(936\) 0 0
\(937\) −13605.4 18726.2i −0.474352 0.652889i 0.503055 0.864254i \(-0.332209\pi\)
−0.977407 + 0.211365i \(0.932209\pi\)
\(938\) 0 0
\(939\) −1779.75 1293.07i −0.0618531 0.0449389i
\(940\) 0 0
\(941\) 16989.1 12343.3i 0.588553 0.427609i −0.253245 0.967402i \(-0.581498\pi\)
0.841797 + 0.539794i \(0.181498\pi\)
\(942\) 0 0
\(943\) 1368.72i 0.0472660i
\(944\) 0 0
\(945\) 185.836 739.795i 0.00639709 0.0254662i
\(946\) 0 0
\(947\) 49202.7 15986.9i 1.68836 0.548580i 0.701853 0.712322i \(-0.252356\pi\)
0.986503 + 0.163742i \(0.0523564\pi\)
\(948\) 0 0
\(949\) 17868.9 0.611223
\(950\) 0 0
\(951\) −7989.46 −0.272425
\(952\) 0 0
\(953\) −42977.6 + 13964.3i −1.46084 + 0.474656i −0.928327 0.371765i \(-0.878753\pi\)
−0.532514 + 0.846421i \(0.678753\pi\)
\(954\) 0 0
\(955\) 36871.4 + 23130.2i 1.24935 + 0.783745i
\(956\) 0 0
\(957\) 1444.00i 0.0487751i
\(958\) 0 0
\(959\) −2711.68 + 1970.15i −0.0913084 + 0.0663394i
\(960\) 0 0
\(961\) 5397.62 + 3921.60i 0.181183 + 0.131637i
\(962\) 0 0
\(963\) 2978.22 + 4099.17i 0.0996592 + 0.137169i
\(964\) 0 0
\(965\) −45156.4 + 18151.9i −1.50636 + 0.605524i
\(966\) 0 0
\(967\) 17108.4 + 5558.85i 0.568944 + 0.184861i 0.579342 0.815085i \(-0.303310\pi\)
−0.0103977 + 0.999946i \(0.503310\pi\)
\(968\) 0 0
\(969\) 832.940 2563.53i 0.0276139 0.0849869i
\(970\) 0 0
\(971\) −7140.12 21975.0i −0.235981 0.726274i −0.996990 0.0775329i \(-0.975296\pi\)
0.761009 0.648741i \(-0.224704\pi\)
\(972\) 0 0
\(973\) −739.084 + 1017.26i −0.0243514 + 0.0335169i
\(974\) 0 0
\(975\) −5872.39 + 804.227i −0.192889 + 0.0264163i
\(976\) 0 0
\(977\) 12740.7 17536.0i 0.417206 0.574235i −0.547751 0.836641i \(-0.684516\pi\)
0.964958 + 0.262406i \(0.0845160\pi\)
\(978\) 0 0
\(979\) 2586.50 + 7960.44i 0.0844382 + 0.259874i
\(980\) 0 0
\(981\) −1710.06 + 5263.02i −0.0556554 + 0.171290i
\(982\) 0 0
\(983\) 20330.0 + 6605.62i 0.659641 + 0.214330i 0.619660 0.784870i \(-0.287270\pi\)
0.0399806 + 0.999200i \(0.487270\pi\)
\(984\) 0 0
\(985\) 35569.1 + 42541.5i 1.15058 + 1.37613i
\(986\) 0 0
\(987\) −141.758 195.113i −0.00457164 0.00629232i
\(988\) 0 0
\(989\) 16408.4 + 11921.4i 0.527559 + 0.383294i
\(990\) 0 0
\(991\) 21169.5 15380.5i 0.678578 0.493016i −0.194308 0.980941i \(-0.562246\pi\)
0.872886 + 0.487925i \(0.162246\pi\)
\(992\) 0 0
\(993\) 7780.12i 0.248635i
\(994\) 0 0
\(995\) 10518.5 + 26166.9i 0.335136 + 0.833714i
\(996\) 0 0
\(997\) 31795.7 10331.1i 1.01001 0.328173i 0.243152 0.969988i \(-0.421819\pi\)
0.766859 + 0.641816i \(0.221819\pi\)
\(998\) 0 0
\(999\) 18255.7 0.578164
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 100.4.i.a.9.4 32
5.2 odd 4 500.4.g.b.201.9 64
5.3 odd 4 500.4.g.b.201.8 64
5.4 even 2 500.4.i.a.49.5 32
25.2 odd 20 500.4.g.b.301.9 64
25.8 odd 20 2500.4.a.g.1.16 32
25.11 even 5 500.4.i.a.449.5 32
25.14 even 10 inner 100.4.i.a.89.4 yes 32
25.17 odd 20 2500.4.a.g.1.17 32
25.23 odd 20 500.4.g.b.301.8 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
100.4.i.a.9.4 32 1.1 even 1 trivial
100.4.i.a.89.4 yes 32 25.14 even 10 inner
500.4.g.b.201.8 64 5.3 odd 4
500.4.g.b.201.9 64 5.2 odd 4
500.4.g.b.301.8 64 25.23 odd 20
500.4.g.b.301.9 64 25.2 odd 20
500.4.i.a.49.5 32 5.4 even 2
500.4.i.a.449.5 32 25.11 even 5
2500.4.a.g.1.16 32 25.8 odd 20
2500.4.a.g.1.17 32 25.17 odd 20