Properties

Label 2100.2.bo.i.1349.16
Level $2100$
Weight $2$
Character 2100.1349
Analytic conductor $16.769$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2100,2,Mod(1349,2100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2100.1349");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.bo (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(16.7685844245\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1349.16
Character \(\chi\) \(=\) 2100.1349
Dual form 2100.2.bo.i.1949.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.68420 - 0.404332i) q^{3} +(-2.10133 + 1.60761i) q^{7} +(2.67303 - 1.36195i) q^{9} +O(q^{10})\) \(q+(1.68420 - 0.404332i) q^{3} +(-2.10133 + 1.60761i) q^{7} +(2.67303 - 1.36195i) q^{9} +(-2.05856 + 1.18851i) q^{11} +0.748179 q^{13} +(6.53402 - 3.77242i) q^{17} +(6.11872 + 3.53264i) q^{19} +(-2.88904 + 3.55717i) q^{21} +(-1.63394 + 2.83006i) q^{23} +(3.95123 - 3.37458i) q^{27} -2.48504i q^{29} +(-6.84372 + 3.95123i) q^{31} +(-2.98646 + 2.83402i) q^{33} +(-3.73959 - 2.15905i) q^{37} +(1.26008 - 0.302513i) q^{39} +10.8663 q^{41} +3.03200i q^{43} +(5.59088 + 3.22790i) q^{47} +(1.83117 - 6.75624i) q^{49} +(9.47926 - 8.99541i) q^{51} +(0.0540095 + 0.0935472i) q^{53} +(11.7335 + 3.47567i) q^{57} +(6.60248 + 11.4358i) q^{59} +(6.90005 + 3.98375i) q^{61} +(-3.42743 + 7.15910i) q^{63} +(5.09859 - 2.94367i) q^{67} +(-1.60758 + 5.42703i) q^{69} +13.9589i q^{71} +(0.780701 + 1.35221i) q^{73} +(2.41505 - 5.80681i) q^{77} +(1.27644 - 2.21086i) q^{79} +(5.29018 - 7.28107i) q^{81} +0.901948i q^{83} +(-1.00478 - 4.18529i) q^{87} +(2.43223 - 4.21274i) q^{89} +(-1.57217 + 1.20278i) q^{91} +(-9.92856 + 9.42178i) q^{93} -12.9183 q^{97} +(-3.88390 + 5.98057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 18 q^{9} + 36 q^{19} - 22 q^{21} - 36 q^{31} - 24 q^{39} + 36 q^{49} - 2 q^{51} + 72 q^{61} + 14 q^{81} + 40 q^{91} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).

\(n\) \(701\) \(1051\) \(1177\) \(1501\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.68420 0.404332i 0.972371 0.233441i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.10133 + 1.60761i −0.794228 + 0.607620i
\(8\) 0 0
\(9\) 2.67303 1.36195i 0.891010 0.453983i
\(10\) 0 0
\(11\) −2.05856 + 1.18851i −0.620679 + 0.358349i −0.777133 0.629336i \(-0.783327\pi\)
0.156455 + 0.987685i \(0.449994\pi\)
\(12\) 0 0
\(13\) 0.748179 0.207508 0.103754 0.994603i \(-0.466915\pi\)
0.103754 + 0.994603i \(0.466915\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.53402 3.77242i 1.58473 0.914946i 0.590578 0.806980i \(-0.298900\pi\)
0.994155 0.107966i \(-0.0344336\pi\)
\(18\) 0 0
\(19\) 6.11872 + 3.53264i 1.40373 + 0.810444i 0.994773 0.102109i \(-0.0325591\pi\)
0.408957 + 0.912553i \(0.365892\pi\)
\(20\) 0 0
\(21\) −2.88904 + 3.55717i −0.630440 + 0.776238i
\(22\) 0 0
\(23\) −1.63394 + 2.83006i −0.340699 + 0.590109i −0.984563 0.175032i \(-0.943997\pi\)
0.643863 + 0.765141i \(0.277331\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3.95123 3.37458i 0.760414 0.649439i
\(28\) 0 0
\(29\) 2.48504i 0.461460i −0.973018 0.230730i \(-0.925889\pi\)
0.973018 0.230730i \(-0.0741114\pi\)
\(30\) 0 0
\(31\) −6.84372 + 3.95123i −1.22917 + 0.709661i −0.966856 0.255322i \(-0.917819\pi\)
−0.262313 + 0.964983i \(0.584485\pi\)
\(32\) 0 0
\(33\) −2.98646 + 2.83402i −0.519876 + 0.493340i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.73959 2.15905i −0.614784 0.354946i 0.160051 0.987109i \(-0.448834\pi\)
−0.774835 + 0.632163i \(0.782167\pi\)
\(38\) 0 0
\(39\) 1.26008 0.302513i 0.201774 0.0484409i
\(40\) 0 0
\(41\) 10.8663 1.69703 0.848514 0.529173i \(-0.177498\pi\)
0.848514 + 0.529173i \(0.177498\pi\)
\(42\) 0 0
\(43\) 3.03200i 0.462375i 0.972909 + 0.231188i \(0.0742611\pi\)
−0.972909 + 0.231188i \(0.925739\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.59088 + 3.22790i 0.815514 + 0.470837i 0.848867 0.528606i \(-0.177285\pi\)
−0.0333530 + 0.999444i \(0.510619\pi\)
\(48\) 0 0
\(49\) 1.83117 6.75624i 0.261596 0.965178i
\(50\) 0 0
\(51\) 9.47926 8.99541i 1.32736 1.25961i
\(52\) 0 0
\(53\) 0.0540095 + 0.0935472i 0.00741878 + 0.0128497i 0.869711 0.493561i \(-0.164305\pi\)
−0.862292 + 0.506411i \(0.830972\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 11.7335 + 3.47567i 1.55414 + 0.460363i
\(58\) 0 0
\(59\) 6.60248 + 11.4358i 0.859570 + 1.48882i 0.872340 + 0.488900i \(0.162602\pi\)
−0.0127699 + 0.999918i \(0.504065\pi\)
\(60\) 0 0
\(61\) 6.90005 + 3.98375i 0.883461 + 0.510067i 0.871798 0.489865i \(-0.162954\pi\)
0.0116632 + 0.999932i \(0.496287\pi\)
\(62\) 0 0
\(63\) −3.42743 + 7.15910i −0.431816 + 0.901962i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 5.09859 2.94367i 0.622892 0.359627i −0.155102 0.987898i \(-0.549571\pi\)
0.777994 + 0.628272i \(0.216237\pi\)
\(68\) 0 0
\(69\) −1.60758 + 5.42703i −0.193530 + 0.653338i
\(70\) 0 0
\(71\) 13.9589i 1.65662i 0.560273 + 0.828308i \(0.310696\pi\)
−0.560273 + 0.828308i \(0.689304\pi\)
\(72\) 0 0
\(73\) 0.780701 + 1.35221i 0.0913742 + 0.158265i 0.908090 0.418776i \(-0.137541\pi\)
−0.816715 + 0.577041i \(0.804207\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.41505 5.80681i 0.275220 0.661747i
\(78\) 0 0
\(79\) 1.27644 2.21086i 0.143611 0.248742i −0.785243 0.619188i \(-0.787462\pi\)
0.928854 + 0.370446i \(0.120795\pi\)
\(80\) 0 0
\(81\) 5.29018 7.28107i 0.587798 0.809008i
\(82\) 0 0
\(83\) 0.901948i 0.0990016i 0.998774 + 0.0495008i \(0.0157630\pi\)
−0.998774 + 0.0495008i \(0.984237\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −1.00478 4.18529i −0.107724 0.448710i
\(88\) 0 0
\(89\) 2.43223 4.21274i 0.257816 0.446550i −0.707841 0.706372i \(-0.750331\pi\)
0.965656 + 0.259822i \(0.0836640\pi\)
\(90\) 0 0
\(91\) −1.57217 + 1.20278i −0.164808 + 0.126086i
\(92\) 0 0
\(93\) −9.92856 + 9.42178i −1.02954 + 0.976993i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −12.9183 −1.31166 −0.655829 0.754909i \(-0.727681\pi\)
−0.655829 + 0.754909i \(0.727681\pi\)
\(98\) 0 0
\(99\) −3.88390 + 5.98057i −0.390346 + 0.601070i
\(100\) 0 0
\(101\) 1.56718 + 2.71443i 0.155940 + 0.270096i 0.933401 0.358835i \(-0.116826\pi\)
−0.777461 + 0.628931i \(0.783493\pi\)
\(102\) 0 0
\(103\) 7.89048 13.6667i 0.777472 1.34662i −0.155922 0.987769i \(-0.549835\pi\)
0.933394 0.358852i \(-0.116832\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.92544 11.9952i 0.669508 1.15962i −0.308534 0.951213i \(-0.599839\pi\)
0.978042 0.208408i \(-0.0668282\pi\)
\(108\) 0 0
\(109\) −0.863166 1.49505i −0.0826763 0.143200i 0.821722 0.569888i \(-0.193013\pi\)
−0.904399 + 0.426688i \(0.859680\pi\)
\(110\) 0 0
\(111\) −7.17117 2.12423i −0.680657 0.201623i
\(112\) 0 0
\(113\) −4.93811 −0.464539 −0.232269 0.972652i \(-0.574615\pi\)
−0.232269 + 0.972652i \(0.574615\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.99991 1.01898i 0.184891 0.0942050i
\(118\) 0 0
\(119\) −7.66554 + 18.4313i −0.702699 + 1.68959i
\(120\) 0 0
\(121\) −2.67489 + 4.63305i −0.243172 + 0.421186i
\(122\) 0 0
\(123\) 18.3009 4.39359i 1.65014 0.396157i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 15.9416i 1.41458i −0.706921 0.707292i \(-0.749917\pi\)
0.706921 0.707292i \(-0.250083\pi\)
\(128\) 0 0
\(129\) 1.22593 + 5.10648i 0.107938 + 0.449600i
\(130\) 0 0
\(131\) −4.17025 + 7.22309i −0.364357 + 0.631084i −0.988673 0.150087i \(-0.952044\pi\)
0.624316 + 0.781172i \(0.285378\pi\)
\(132\) 0 0
\(133\) −18.5366 + 2.41328i −1.60732 + 0.209258i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.01096 + 6.94718i 0.342679 + 0.593537i 0.984929 0.172958i \(-0.0553323\pi\)
−0.642250 + 0.766495i \(0.721999\pi\)
\(138\) 0 0
\(139\) 4.61654i 0.391570i −0.980647 0.195785i \(-0.937275\pi\)
0.980647 0.195785i \(-0.0627254\pi\)
\(140\) 0 0
\(141\) 10.7213 + 3.17584i 0.902895 + 0.267454i
\(142\) 0 0
\(143\) −1.54017 + 0.889218i −0.128796 + 0.0743601i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0.352278 12.1192i 0.0290554 0.999578i
\(148\) 0 0
\(149\) 15.6215 + 9.01906i 1.27976 + 0.738870i 0.976804 0.214134i \(-0.0686931\pi\)
0.302956 + 0.953004i \(0.402026\pi\)
\(150\) 0 0
\(151\) 2.12850 + 3.68667i 0.173215 + 0.300017i 0.939542 0.342434i \(-0.111251\pi\)
−0.766327 + 0.642451i \(0.777918\pi\)
\(152\) 0 0
\(153\) 12.3278 18.9828i 0.996643 1.53467i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −8.32830 14.4250i −0.664671 1.15124i −0.979374 0.202054i \(-0.935238\pi\)
0.314703 0.949190i \(-0.398095\pi\)
\(158\) 0 0
\(159\) 0.128787 + 0.135714i 0.0102135 + 0.0107628i
\(160\) 0 0
\(161\) −1.11620 8.57363i −0.0879690 0.675697i
\(162\) 0 0
\(163\) −13.9950 8.07999i −1.09617 0.632874i −0.160957 0.986961i \(-0.551458\pi\)
−0.935212 + 0.354087i \(0.884792\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 17.4029i 1.34668i −0.739335 0.673338i \(-0.764860\pi\)
0.739335 0.673338i \(-0.235140\pi\)
\(168\) 0 0
\(169\) −12.4402 −0.956941
\(170\) 0 0
\(171\) 21.1668 + 1.10948i 1.61867 + 0.0848438i
\(172\) 0 0
\(173\) −17.0267 9.83038i −1.29452 0.747390i −0.315066 0.949070i \(-0.602027\pi\)
−0.979451 + 0.201680i \(0.935360\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 15.7437 + 16.5906i 1.18337 + 1.24702i
\(178\) 0 0
\(179\) 5.84722 3.37589i 0.437042 0.252326i −0.265300 0.964166i \(-0.585471\pi\)
0.702342 + 0.711840i \(0.252138\pi\)
\(180\) 0 0
\(181\) 7.71256i 0.573270i 0.958040 + 0.286635i \(0.0925367\pi\)
−0.958040 + 0.286635i \(0.907463\pi\)
\(182\) 0 0
\(183\) 13.2318 + 3.91950i 0.978123 + 0.289737i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −8.96711 + 15.5315i −0.655740 + 1.13577i
\(188\) 0 0
\(189\) −2.87781 + 13.4431i −0.209330 + 0.977845i
\(190\) 0 0
\(191\) −12.7009 7.33284i −0.919001 0.530586i −0.0356850 0.999363i \(-0.511361\pi\)
−0.883316 + 0.468777i \(0.844695\pi\)
\(192\) 0 0
\(193\) −9.21969 + 5.32299i −0.663648 + 0.383157i −0.793666 0.608354i \(-0.791830\pi\)
0.130018 + 0.991512i \(0.458497\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 7.53462 0.536820 0.268410 0.963305i \(-0.413502\pi\)
0.268410 + 0.963305i \(0.413502\pi\)
\(198\) 0 0
\(199\) −0.993782 + 0.573760i −0.0704473 + 0.0406728i −0.534810 0.844972i \(-0.679617\pi\)
0.464363 + 0.885645i \(0.346283\pi\)
\(200\) 0 0
\(201\) 7.39680 7.01924i 0.521730 0.495099i
\(202\) 0 0
\(203\) 3.99497 + 5.22188i 0.280392 + 0.366504i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.513161 + 9.79018i −0.0356671 + 0.680465i
\(208\) 0 0
\(209\) −16.7943 −1.16169
\(210\) 0 0
\(211\) −11.1248 −0.765862 −0.382931 0.923777i \(-0.625085\pi\)
−0.382931 + 0.923777i \(0.625085\pi\)
\(212\) 0 0
\(213\) 5.64404 + 23.5095i 0.386723 + 1.61085i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 8.02888 19.3049i 0.545036 1.31050i
\(218\) 0 0
\(219\) 1.86160 + 1.96173i 0.125795 + 0.132561i
\(220\) 0 0
\(221\) 4.88862 2.82245i 0.328844 0.189858i
\(222\) 0 0
\(223\) −10.6904 −0.715883 −0.357942 0.933744i \(-0.616521\pi\)
−0.357942 + 0.933744i \(0.616521\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.5979 + 6.69603i −0.769777 + 0.444431i −0.832795 0.553581i \(-0.813261\pi\)
0.0630180 + 0.998012i \(0.479927\pi\)
\(228\) 0 0
\(229\) −8.32905 4.80878i −0.550399 0.317773i 0.198884 0.980023i \(-0.436268\pi\)
−0.749283 + 0.662250i \(0.769602\pi\)
\(230\) 0 0
\(231\) 1.71953 10.7563i 0.113137 0.707712i
\(232\) 0 0
\(233\) −10.7087 + 18.5481i −0.701552 + 1.21512i 0.266369 + 0.963871i \(0.414176\pi\)
−0.967921 + 0.251253i \(0.919157\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1.25586 4.23964i 0.0815766 0.275394i
\(238\) 0 0
\(239\) 25.2806i 1.63527i −0.575738 0.817634i \(-0.695285\pi\)
0.575738 0.817634i \(-0.304715\pi\)
\(240\) 0 0
\(241\) −19.7291 + 11.3906i −1.27086 + 0.733733i −0.975150 0.221543i \(-0.928891\pi\)
−0.295713 + 0.955277i \(0.595557\pi\)
\(242\) 0 0
\(243\) 5.96573 14.4017i 0.382702 0.923872i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 4.57790 + 2.64305i 0.291285 + 0.168173i
\(248\) 0 0
\(249\) 0.364687 + 1.51906i 0.0231111 + 0.0962663i
\(250\) 0 0
\(251\) 16.4201 1.03643 0.518215 0.855251i \(-0.326597\pi\)
0.518215 + 0.855251i \(0.326597\pi\)
\(252\) 0 0
\(253\) 7.76780i 0.488357i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.2616 + 5.92452i 0.640100 + 0.369562i 0.784653 0.619935i \(-0.212841\pi\)
−0.144553 + 0.989497i \(0.546175\pi\)
\(258\) 0 0
\(259\) 11.3290 1.47493i 0.703951 0.0916474i
\(260\) 0 0
\(261\) −3.38450 6.64258i −0.209495 0.411165i
\(262\) 0 0
\(263\) 2.76844 + 4.79507i 0.170709 + 0.295677i 0.938668 0.344822i \(-0.112061\pi\)
−0.767959 + 0.640499i \(0.778727\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 2.39300 8.07851i 0.146449 0.494397i
\(268\) 0 0
\(269\) −0.504112 0.873148i −0.0307363 0.0532368i 0.850248 0.526382i \(-0.176452\pi\)
−0.880984 + 0.473145i \(0.843119\pi\)
\(270\) 0 0
\(271\) 0.991979 + 0.572720i 0.0602585 + 0.0347902i 0.529827 0.848106i \(-0.322257\pi\)
−0.469568 + 0.882896i \(0.655590\pi\)
\(272\) 0 0
\(273\) −2.16152 + 2.66140i −0.130821 + 0.161075i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −8.08299 + 4.66672i −0.485660 + 0.280396i −0.722772 0.691086i \(-0.757132\pi\)
0.237112 + 0.971482i \(0.423799\pi\)
\(278\) 0 0
\(279\) −12.9121 + 19.8826i −0.773028 + 1.19034i
\(280\) 0 0
\(281\) 0.922818i 0.0550507i 0.999621 + 0.0275253i \(0.00876270\pi\)
−0.999621 + 0.0275253i \(0.991237\pi\)
\(282\) 0 0
\(283\) 3.77681 + 6.54162i 0.224508 + 0.388859i 0.956172 0.292807i \(-0.0945892\pi\)
−0.731664 + 0.681666i \(0.761256\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −22.8336 + 17.4688i −1.34783 + 1.03115i
\(288\) 0 0
\(289\) 19.9623 34.5757i 1.17425 2.03386i
\(290\) 0 0
\(291\) −21.7570 + 5.22330i −1.27542 + 0.306195i
\(292\) 0 0
\(293\) 21.3909i 1.24967i −0.780758 0.624834i \(-0.785167\pi\)
0.780758 0.624834i \(-0.214833\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −4.12310 + 11.6428i −0.239247 + 0.675586i
\(298\) 0 0
\(299\) −1.22248 + 2.11739i −0.0706977 + 0.122452i
\(300\) 0 0
\(301\) −4.87427 6.37122i −0.280949 0.367231i
\(302\) 0 0
\(303\) 3.73696 + 3.93797i 0.214683 + 0.226230i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −16.7500 −0.955972 −0.477986 0.878368i \(-0.658633\pi\)
−0.477986 + 0.878368i \(0.658633\pi\)
\(308\) 0 0
\(309\) 7.76322 26.2078i 0.441634 1.49091i
\(310\) 0 0
\(311\) 2.52577 + 4.37477i 0.143224 + 0.248070i 0.928709 0.370810i \(-0.120920\pi\)
−0.785485 + 0.618880i \(0.787587\pi\)
\(312\) 0 0
\(313\) 7.50546 12.9998i 0.424234 0.734795i −0.572115 0.820174i \(-0.693877\pi\)
0.996349 + 0.0853790i \(0.0272101\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.7324 + 22.0531i −0.715121 + 1.23863i 0.247792 + 0.968813i \(0.420295\pi\)
−0.962913 + 0.269812i \(0.913038\pi\)
\(318\) 0 0
\(319\) 2.95349 + 5.11559i 0.165364 + 0.286418i
\(320\) 0 0
\(321\) 6.81374 23.0025i 0.380306 1.28387i
\(322\) 0 0
\(323\) 53.3065 2.96605
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −2.05824 2.16895i −0.113821 0.119943i
\(328\) 0 0
\(329\) −16.9375 + 2.20509i −0.933794 + 0.121571i
\(330\) 0 0
\(331\) −5.45134 + 9.44199i −0.299633 + 0.518979i −0.976052 0.217538i \(-0.930197\pi\)
0.676419 + 0.736517i \(0.263531\pi\)
\(332\) 0 0
\(333\) −12.9365 0.678080i −0.708918 0.0371585i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 18.4210i 1.00345i 0.865026 + 0.501727i \(0.167302\pi\)
−0.865026 + 0.501727i \(0.832698\pi\)
\(338\) 0 0
\(339\) −8.31675 + 1.99664i −0.451704 + 0.108443i
\(340\) 0 0
\(341\) 9.39213 16.2677i 0.508613 0.880943i
\(342\) 0 0
\(343\) 7.01353 + 17.1409i 0.378695 + 0.925522i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.79206 8.30010i −0.257252 0.445573i 0.708253 0.705959i \(-0.249484\pi\)
−0.965505 + 0.260386i \(0.916150\pi\)
\(348\) 0 0
\(349\) 16.5601i 0.886441i 0.896413 + 0.443220i \(0.146164\pi\)
−0.896413 + 0.443220i \(0.853836\pi\)
\(350\) 0 0
\(351\) 2.95623 2.52479i 0.157792 0.134764i
\(352\) 0 0
\(353\) 15.5984 9.00574i 0.830219 0.479327i −0.0237089 0.999719i \(-0.507547\pi\)
0.853928 + 0.520392i \(0.174214\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −5.45792 + 34.1413i −0.288864 + 1.80695i
\(358\) 0 0
\(359\) −3.47735 2.00765i −0.183527 0.105960i 0.405422 0.914130i \(-0.367125\pi\)
−0.588949 + 0.808170i \(0.700458\pi\)
\(360\) 0 0
\(361\) 15.4592 + 26.7760i 0.813640 + 1.40927i
\(362\) 0 0
\(363\) −2.63175 + 8.88451i −0.138131 + 0.466316i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 17.0259 + 29.4897i 0.888744 + 1.53935i 0.841361 + 0.540473i \(0.181755\pi\)
0.0473832 + 0.998877i \(0.484912\pi\)
\(368\) 0 0
\(369\) 29.0459 14.7993i 1.51207 0.770423i
\(370\) 0 0
\(371\) −0.263879 0.109747i −0.0136999 0.00569779i
\(372\) 0 0
\(373\) −11.6169 6.70705i −0.601503 0.347278i 0.168130 0.985765i \(-0.446227\pi\)
−0.769632 + 0.638487i \(0.779561\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.85925i 0.0957564i
\(378\) 0 0
\(379\) 15.3945 0.790764 0.395382 0.918517i \(-0.370612\pi\)
0.395382 + 0.918517i \(0.370612\pi\)
\(380\) 0 0
\(381\) −6.44569 26.8487i −0.330223 1.37550i
\(382\) 0 0
\(383\) 21.1422 + 12.2065i 1.08032 + 0.623722i 0.930982 0.365065i \(-0.118953\pi\)
0.149336 + 0.988787i \(0.452287\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4.12943 + 8.10462i 0.209911 + 0.411981i
\(388\) 0 0
\(389\) 30.1938 17.4324i 1.53089 0.883857i 0.531564 0.847018i \(-0.321604\pi\)
0.999321 0.0368391i \(-0.0117289\pi\)
\(390\) 0 0
\(391\) 24.6556i 1.24689i
\(392\) 0 0
\(393\) −4.10299 + 13.8513i −0.206969 + 0.698704i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 11.2631 19.5083i 0.565281 0.979095i −0.431743 0.901997i \(-0.642101\pi\)
0.997024 0.0770980i \(-0.0245654\pi\)
\(398\) 0 0
\(399\) −30.2434 + 11.5594i −1.51407 + 0.578692i
\(400\) 0 0
\(401\) −15.8774 9.16683i −0.792881 0.457770i 0.0480950 0.998843i \(-0.484685\pi\)
−0.840976 + 0.541073i \(0.818018\pi\)
\(402\) 0 0
\(403\) −5.12033 + 2.95623i −0.255062 + 0.147260i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 10.2642 0.508778
\(408\) 0 0
\(409\) −9.37130 + 5.41052i −0.463381 + 0.267533i −0.713465 0.700691i \(-0.752875\pi\)
0.250084 + 0.968224i \(0.419542\pi\)
\(410\) 0 0
\(411\) 9.56420 + 10.0786i 0.471767 + 0.497143i
\(412\) 0 0
\(413\) −32.2584 13.4162i −1.58733 0.660169i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.86662 7.77516i −0.0914086 0.380751i
\(418\) 0 0
\(419\) −34.1164 −1.66670 −0.833348 0.552749i \(-0.813579\pi\)
−0.833348 + 0.552749i \(0.813579\pi\)
\(420\) 0 0
\(421\) −29.9892 −1.46158 −0.730792 0.682600i \(-0.760849\pi\)
−0.730792 + 0.682600i \(0.760849\pi\)
\(422\) 0 0
\(423\) 19.3408 + 1.01377i 0.940384 + 0.0492910i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −20.9036 + 2.72144i −1.01160 + 0.131700i
\(428\) 0 0
\(429\) −2.23441 + 2.12036i −0.107878 + 0.102372i
\(430\) 0 0
\(431\) −32.6954 + 18.8767i −1.57488 + 0.909258i −0.579324 + 0.815097i \(0.696684\pi\)
−0.995557 + 0.0941612i \(0.969983\pi\)
\(432\) 0 0
\(433\) 0.221375 0.0106386 0.00531930 0.999986i \(-0.498307\pi\)
0.00531930 + 0.999986i \(0.498307\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −19.9952 + 11.5442i −0.956501 + 0.552236i
\(438\) 0 0
\(439\) 12.5292 + 7.23374i 0.597987 + 0.345248i 0.768249 0.640151i \(-0.221128\pi\)
−0.170262 + 0.985399i \(0.554462\pi\)
\(440\) 0 0
\(441\) −4.30690 20.5536i −0.205090 0.978743i
\(442\) 0 0
\(443\) −5.55285 + 9.61783i −0.263824 + 0.456957i −0.967255 0.253807i \(-0.918317\pi\)
0.703431 + 0.710764i \(0.251651\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 29.9563 + 8.87359i 1.41688 + 0.419707i
\(448\) 0 0
\(449\) 31.1416i 1.46966i −0.678250 0.734831i \(-0.737261\pi\)
0.678250 0.734831i \(-0.262739\pi\)
\(450\) 0 0
\(451\) −22.3689 + 12.9147i −1.05331 + 0.608128i
\(452\) 0 0
\(453\) 5.07545 + 5.34845i 0.238466 + 0.251292i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −16.4171 9.47844i −0.767962 0.443383i 0.0641853 0.997938i \(-0.479555\pi\)
−0.832147 + 0.554555i \(0.812888\pi\)
\(458\) 0 0
\(459\) 13.0871 36.9553i 0.610851 1.72492i
\(460\) 0 0
\(461\) −15.1960 −0.707746 −0.353873 0.935293i \(-0.615136\pi\)
−0.353873 + 0.935293i \(0.615136\pi\)
\(462\) 0 0
\(463\) 29.3400i 1.36355i −0.731564 0.681773i \(-0.761209\pi\)
0.731564 0.681773i \(-0.238791\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −14.5382 8.39365i −0.672749 0.388412i 0.124369 0.992236i \(-0.460309\pi\)
−0.797117 + 0.603824i \(0.793643\pi\)
\(468\) 0 0
\(469\) −5.98153 + 14.3822i −0.276201 + 0.664107i
\(470\) 0 0
\(471\) −19.8590 20.9272i −0.915055 0.964274i
\(472\) 0 0
\(473\) −3.60356 6.24154i −0.165692 0.286986i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.271776 + 0.176496i 0.0124438 + 0.00808121i
\(478\) 0 0
\(479\) −1.07579 1.86333i −0.0491542 0.0851376i 0.840401 0.541964i \(-0.182319\pi\)
−0.889556 + 0.456827i \(0.848986\pi\)
\(480\) 0 0
\(481\) −2.79788 1.61536i −0.127572 0.0736540i
\(482\) 0 0
\(483\) −5.34650 13.9884i −0.243274 0.636492i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 3.02174 1.74460i 0.136928 0.0790555i −0.429971 0.902843i \(-0.641476\pi\)
0.566899 + 0.823787i \(0.308143\pi\)
\(488\) 0 0
\(489\) −26.8373 7.94967i −1.21362 0.359497i
\(490\) 0 0
\(491\) 26.1361i 1.17950i −0.807584 0.589752i \(-0.799225\pi\)
0.807584 0.589752i \(-0.200775\pi\)
\(492\) 0 0
\(493\) −9.37460 16.2373i −0.422211 0.731290i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −22.4405 29.3322i −1.00659 1.31573i
\(498\) 0 0
\(499\) 7.15545 12.3936i 0.320322 0.554814i −0.660232 0.751061i \(-0.729542\pi\)
0.980554 + 0.196247i \(0.0628756\pi\)
\(500\) 0 0
\(501\) −7.03656 29.3099i −0.314370 1.30947i
\(502\) 0 0
\(503\) 39.3226i 1.75331i −0.481123 0.876653i \(-0.659771\pi\)
0.481123 0.876653i \(-0.340229\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −20.9518 + 5.02999i −0.930501 + 0.223390i
\(508\) 0 0
\(509\) 17.4284 30.1868i 0.772498 1.33801i −0.163692 0.986512i \(-0.552340\pi\)
0.936190 0.351495i \(-0.114326\pi\)
\(510\) 0 0
\(511\) −3.81435 1.58638i −0.168737 0.0701774i
\(512\) 0 0
\(513\) 36.0977 6.68985i 1.59375 0.295364i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −15.3455 −0.674896
\(518\) 0 0
\(519\) −32.6511 9.67183i −1.43322 0.424546i
\(520\) 0 0
\(521\) −12.3030 21.3094i −0.539005 0.933584i −0.998958 0.0456406i \(-0.985467\pi\)
0.459953 0.887943i \(-0.347866\pi\)
\(522\) 0 0
\(523\) −13.8335 + 23.9603i −0.604897 + 1.04771i 0.387171 + 0.922008i \(0.373452\pi\)
−0.992068 + 0.125704i \(0.959881\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −29.8114 + 51.6348i −1.29860 + 2.24925i
\(528\) 0 0
\(529\) 6.16050 + 10.6703i 0.267848 + 0.463926i
\(530\) 0 0
\(531\) 33.2237 + 21.5761i 1.44178 + 0.936322i
\(532\) 0 0
\(533\) 8.12993 0.352146
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 8.48288 8.04989i 0.366063 0.347378i
\(538\) 0 0
\(539\) 4.26029 + 16.0845i 0.183504 + 0.692808i
\(540\) 0 0
\(541\) 7.90334 13.6890i 0.339791 0.588536i −0.644602 0.764518i \(-0.722977\pi\)
0.984393 + 0.175983i \(0.0563103\pi\)
\(542\) 0 0
\(543\) 3.11844 + 12.9895i 0.133825 + 0.557431i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 13.9288i 0.595553i −0.954636 0.297776i \(-0.903755\pi\)
0.954636 0.297776i \(-0.0962450\pi\)
\(548\) 0 0
\(549\) 23.8697 + 1.25115i 1.01873 + 0.0533978i
\(550\) 0 0
\(551\) 8.77875 15.2052i 0.373987 0.647765i
\(552\) 0 0
\(553\) 0.871984 + 6.69778i 0.0370805 + 0.284818i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 17.2950 + 29.9559i 0.732814 + 1.26927i 0.955676 + 0.294421i \(0.0951269\pi\)
−0.222862 + 0.974850i \(0.571540\pi\)
\(558\) 0 0
\(559\) 2.26848i 0.0959464i
\(560\) 0 0
\(561\) −8.82248 + 29.7838i −0.372485 + 1.25747i
\(562\) 0 0
\(563\) −25.0789 + 14.4793i −1.05695 + 0.610229i −0.924586 0.380972i \(-0.875589\pi\)
−0.132361 + 0.991202i \(0.542256\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.588712 + 23.8045i 0.0247236 + 0.999694i
\(568\) 0 0
\(569\) 10.1544 + 5.86266i 0.425696 + 0.245775i 0.697511 0.716574i \(-0.254291\pi\)
−0.271816 + 0.962349i \(0.587624\pi\)
\(570\) 0 0
\(571\) 17.5541 + 30.4045i 0.734614 + 1.27239i 0.954892 + 0.296952i \(0.0959703\pi\)
−0.220278 + 0.975437i \(0.570696\pi\)
\(572\) 0 0
\(573\) −24.3556 7.21457i −1.01747 0.301393i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 10.0423 + 17.3937i 0.418065 + 0.724110i 0.995745 0.0921536i \(-0.0293751\pi\)
−0.577680 + 0.816263i \(0.696042\pi\)
\(578\) 0 0
\(579\) −13.3755 + 12.6928i −0.555867 + 0.527494i
\(580\) 0 0
\(581\) −1.44998 1.89529i −0.0601554 0.0786298i
\(582\) 0 0
\(583\) −0.222363 0.128382i −0.00920935 0.00531702i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 32.7111i 1.35013i −0.737757 0.675066i \(-0.764115\pi\)
0.737757 0.675066i \(-0.235885\pi\)
\(588\) 0 0
\(589\) −55.8331 −2.30056
\(590\) 0 0
\(591\) 12.6898 3.04649i 0.521988 0.125316i
\(592\) 0 0
\(593\) 3.86664 + 2.23240i 0.158784 + 0.0916738i 0.577286 0.816542i \(-0.304112\pi\)
−0.418503 + 0.908216i \(0.637445\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1.44173 + 1.36814i −0.0590062 + 0.0559944i
\(598\) 0 0
\(599\) −31.6126 + 18.2515i −1.29165 + 0.745737i −0.978947 0.204112i \(-0.934569\pi\)
−0.312707 + 0.949850i \(0.601236\pi\)
\(600\) 0 0
\(601\) 32.4566i 1.32393i −0.749534 0.661966i \(-0.769722\pi\)
0.749534 0.661966i \(-0.230278\pi\)
\(602\) 0 0
\(603\) 9.61955 14.8125i 0.391738 0.603213i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −10.4608 + 18.1187i −0.424593 + 0.735416i −0.996382 0.0849841i \(-0.972916\pi\)
0.571790 + 0.820400i \(0.306249\pi\)
\(608\) 0 0
\(609\) 8.83970 + 7.17937i 0.358203 + 0.290923i
\(610\) 0 0
\(611\) 4.18298 + 2.41505i 0.169225 + 0.0977023i
\(612\) 0 0
\(613\) 33.6783 19.4442i 1.36025 0.785343i 0.370596 0.928794i \(-0.379153\pi\)
0.989657 + 0.143451i \(0.0458200\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12.8874 0.518828 0.259414 0.965766i \(-0.416471\pi\)
0.259414 + 0.965766i \(0.416471\pi\)
\(618\) 0 0
\(619\) −8.89767 + 5.13707i −0.357628 + 0.206476i −0.668040 0.744126i \(-0.732866\pi\)
0.310412 + 0.950602i \(0.399533\pi\)
\(620\) 0 0
\(621\) 3.09423 + 16.6961i 0.124167 + 0.669990i
\(622\) 0 0
\(623\) 1.66154 + 12.7624i 0.0665683 + 0.511316i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −28.2849 + 6.79049i −1.12959 + 0.271186i
\(628\) 0 0
\(629\) −32.5794 −1.29902
\(630\) 0 0
\(631\) 44.9308 1.78866 0.894332 0.447403i \(-0.147651\pi\)
0.894332 + 0.447403i \(0.147651\pi\)
\(632\) 0 0
\(633\) −18.7363 + 4.49811i −0.744701 + 0.178784i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.37004 5.05488i 0.0542831 0.200282i
\(638\) 0 0
\(639\) 19.0113 + 37.3126i 0.752076 + 1.47606i
\(640\) 0 0
\(641\) 33.7953 19.5118i 1.33484 0.770668i 0.348799 0.937197i \(-0.386589\pi\)
0.986036 + 0.166529i \(0.0532561\pi\)
\(642\) 0 0
\(643\) 12.2206 0.481932 0.240966 0.970534i \(-0.422536\pi\)
0.240966 + 0.970534i \(0.422536\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −14.6082 + 8.43406i −0.574308 + 0.331577i −0.758868 0.651244i \(-0.774247\pi\)
0.184560 + 0.982821i \(0.440914\pi\)
\(648\) 0 0
\(649\) −27.1832 15.6942i −1.06703 0.616052i
\(650\) 0 0
\(651\) 5.71662 35.7595i 0.224052 1.40153i
\(652\) 0 0
\(653\) −10.8531 + 18.7980i −0.424713 + 0.735624i −0.996394 0.0848520i \(-0.972958\pi\)
0.571681 + 0.820476i \(0.306292\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 3.92849 + 2.55123i 0.153265 + 0.0995331i
\(658\) 0 0
\(659\) 36.3752i 1.41698i −0.705722 0.708489i \(-0.749377\pi\)
0.705722 0.708489i \(-0.250623\pi\)
\(660\) 0 0
\(661\) 12.9940 7.50207i 0.505407 0.291797i −0.225537 0.974235i \(-0.572414\pi\)
0.730944 + 0.682438i \(0.239080\pi\)
\(662\) 0 0
\(663\) 7.09219 6.73018i 0.275438 0.261379i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 7.03281 + 4.06039i 0.272311 + 0.157219i
\(668\) 0 0
\(669\) −18.0048 + 4.32248i −0.696104 + 0.167117i
\(670\) 0 0
\(671\) −18.9389 −0.731127
\(672\) 0 0
\(673\) 0.119232i 0.00459606i −0.999997 0.00229803i \(-0.999269\pi\)
0.999997 0.00229803i \(-0.000731486\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −20.6622 11.9293i −0.794114 0.458482i 0.0472948 0.998881i \(-0.484940\pi\)
−0.841409 + 0.540399i \(0.818273\pi\)
\(678\) 0 0
\(679\) 27.1457 20.7677i 1.04176 0.796990i
\(680\) 0 0
\(681\) −16.8256 + 15.9668i −0.644760 + 0.611850i
\(682\) 0 0
\(683\) 14.6082 + 25.3022i 0.558968 + 0.968161i 0.997583 + 0.0694856i \(0.0221358\pi\)
−0.438615 + 0.898675i \(0.644531\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −15.9721 4.73122i −0.609374 0.180507i
\(688\) 0 0
\(689\) 0.0404088 + 0.0699901i 0.00153945 + 0.00266641i
\(690\) 0 0
\(691\) −36.0356 20.8052i −1.37086 0.791465i −0.379822 0.925059i \(-0.624015\pi\)
−0.991036 + 0.133594i \(0.957348\pi\)
\(692\) 0 0
\(693\) −1.45309 18.8110i −0.0551984 0.714569i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 71.0005 40.9922i 2.68934 1.55269i
\(698\) 0 0
\(699\) −10.5360 + 35.5685i −0.398509 + 1.34532i
\(700\) 0 0
\(701\) 14.6976i 0.555122i 0.960708 + 0.277561i \(0.0895261\pi\)
−0.960708 + 0.277561i \(0.910474\pi\)
\(702\) 0 0
\(703\) −15.2543 26.4213i −0.575328 0.996497i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7.65690 3.18450i −0.287967 0.119765i
\(708\) 0 0
\(709\) −18.6403 + 32.2859i −0.700050 + 1.21252i 0.268398 + 0.963308i \(0.413506\pi\)
−0.968448 + 0.249214i \(0.919828\pi\)
\(710\) 0 0
\(711\) 0.400885 7.64816i 0.0150343 0.286828i
\(712\) 0 0
\(713\) 25.8242i 0.967125i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −10.2218 42.5776i −0.381740 1.59009i
\(718\) 0 0
\(719\) −15.8612 + 27.4724i −0.591522 + 1.02455i 0.402505 + 0.915418i \(0.368139\pi\)
−0.994028 + 0.109129i \(0.965194\pi\)
\(720\) 0 0
\(721\) 5.39027 + 41.4031i 0.200744 + 1.54193i
\(722\) 0 0
\(723\) −28.6221 + 27.1611i −1.06447 + 1.01013i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −30.3126 −1.12423 −0.562117 0.827058i \(-0.690013\pi\)
−0.562117 + 0.827058i \(0.690013\pi\)
\(728\) 0 0
\(729\) 4.22437 26.6675i 0.156458 0.987685i
\(730\) 0 0
\(731\) 11.4380 + 19.8111i 0.423048 + 0.732741i
\(732\) 0 0
\(733\) 1.19316 2.06661i 0.0440703 0.0763321i −0.843149 0.537680i \(-0.819301\pi\)
0.887219 + 0.461348i \(0.152634\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6.99716 + 12.1194i −0.257744 + 0.446425i
\(738\) 0 0
\(739\) −2.29721 3.97889i −0.0845043 0.146366i 0.820676 0.571394i \(-0.193597\pi\)
−0.905180 + 0.425029i \(0.860264\pi\)
\(740\) 0 0
\(741\) 8.77875 + 2.60042i 0.322496 + 0.0955289i
\(742\) 0 0
\(743\) 12.5047 0.458753 0.229376 0.973338i \(-0.426331\pi\)
0.229376 + 0.973338i \(0.426331\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.22841 + 2.41093i 0.0449451 + 0.0882114i
\(748\) 0 0
\(749\) 4.73102 + 36.3393i 0.172868 + 1.32781i
\(750\) 0 0
\(751\) −17.3708 + 30.0872i −0.633871 + 1.09790i 0.352883 + 0.935668i \(0.385202\pi\)
−0.986753 + 0.162229i \(0.948132\pi\)
\(752\) 0 0
\(753\) 27.6547 6.63919i 1.00779 0.241946i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 14.5066i 0.527250i −0.964625 0.263625i \(-0.915082\pi\)
0.964625 0.263625i \(-0.0849182\pi\)
\(758\) 0 0
\(759\) −3.14077 13.0825i −0.114003 0.474864i
\(760\) 0 0
\(761\) −20.2457 + 35.0666i −0.733906 + 1.27116i 0.221296 + 0.975207i \(0.428971\pi\)
−0.955202 + 0.295955i \(0.904362\pi\)
\(762\) 0 0
\(763\) 4.21725 + 1.75395i 0.152675 + 0.0634973i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.93984 + 8.55606i 0.178367 + 0.308941i
\(768\) 0 0
\(769\) 39.6907i 1.43128i −0.698468 0.715641i \(-0.746135\pi\)
0.698468 0.715641i \(-0.253865\pi\)
\(770\) 0 0
\(771\) 19.6780 + 5.82897i 0.708685 + 0.209925i
\(772\) 0 0
\(773\) −4.90181 + 2.83006i −0.176306 + 0.101790i −0.585556 0.810632i \(-0.699124\pi\)
0.409250 + 0.912422i \(0.365790\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 18.4839 7.06475i 0.663107 0.253447i
\(778\) 0 0
\(779\) 66.4877 + 38.3867i 2.38217 + 1.37535i
\(780\) 0 0
\(781\) −16.5903 28.7352i −0.593647 1.02823i
\(782\) 0 0
\(783\) −8.38596 9.81894i −0.299690 0.350900i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 1.59485 + 2.76237i 0.0568504 + 0.0984677i 0.893050 0.449958i \(-0.148561\pi\)
−0.836200 + 0.548425i \(0.815228\pi\)
\(788\) 0 0
\(789\) 6.60139 + 6.95647i 0.235016 + 0.247657i
\(790\) 0 0
\(791\) 10.3766 7.93857i 0.368949 0.282263i
\(792\) 0 0
\(793\) 5.16248 + 2.98056i 0.183325 + 0.105843i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 18.7853i 0.665410i −0.943031 0.332705i \(-0.892039\pi\)
0.943031 0.332705i \(-0.107961\pi\)
\(798\) 0 0
\(799\) 48.7079 1.72316
\(800\) 0 0
\(801\) 0.763875 14.5734i 0.0269902 0.514924i
\(802\) 0 0
\(803\) −3.21424 1.85574i −0.113428 0.0654877i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −1.20207 1.26672i −0.0423147 0.0445908i
\(808\) 0 0
\(809\) 24.5995 14.2025i 0.864873 0.499335i −0.000767968 1.00000i \(-0.500244\pi\)
0.865641 + 0.500665i \(0.166911\pi\)
\(810\) 0 0
\(811\) 46.9628i 1.64909i −0.565799 0.824543i \(-0.691432\pi\)
0.565799 0.824543i \(-0.308568\pi\)
\(812\) 0 0
\(813\) 1.90226 + 0.563482i 0.0667151 + 0.0197622i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −10.7110 + 18.5519i −0.374729 + 0.649050i
\(818\) 0 0
\(819\) −2.56433 + 5.35629i −0.0896050 + 0.187164i
\(820\) 0 0
\(821\) 16.9019 + 9.75831i 0.589880 + 0.340567i 0.765050 0.643971i \(-0.222714\pi\)
−0.175170 + 0.984538i \(0.556048\pi\)
\(822\) 0 0
\(823\) −21.7033 + 12.5304i −0.756529 + 0.436782i −0.828048 0.560657i \(-0.810549\pi\)
0.0715193 + 0.997439i \(0.477215\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 40.2141 1.39838 0.699191 0.714935i \(-0.253544\pi\)
0.699191 + 0.714935i \(0.253544\pi\)
\(828\) 0 0
\(829\) −5.52711 + 3.19108i −0.191964 + 0.110831i −0.592902 0.805275i \(-0.702018\pi\)
0.400937 + 0.916105i \(0.368684\pi\)
\(830\) 0 0
\(831\) −11.7264 + 11.1279i −0.406785 + 0.386022i
\(832\) 0 0
\(833\) −13.5225 51.0534i −0.468526 1.76889i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −13.7074 + 38.7069i −0.473796 + 1.33791i
\(838\) 0 0
\(839\) −15.2513 −0.526534 −0.263267 0.964723i \(-0.584800\pi\)
−0.263267 + 0.964723i \(0.584800\pi\)
\(840\) 0 0
\(841\) 22.8246 0.787055
\(842\) 0 0
\(843\) 0.373125 + 1.55421i 0.0128511 + 0.0535297i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −1.82732 14.0358i −0.0627873 0.482274i
\(848\) 0 0
\(849\) 9.00587 + 9.49028i 0.309081 + 0.325706i
\(850\) 0 0
\(851\) 12.2205 7.05551i 0.418913 0.241860i
\(852\) 0 0
\(853\) −16.7815 −0.574586 −0.287293 0.957843i \(-0.592755\pi\)
−0.287293 + 0.957843i \(0.592755\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 16.7758 9.68551i 0.573050 0.330851i −0.185317 0.982679i \(-0.559331\pi\)
0.758367 + 0.651828i \(0.225998\pi\)
\(858\) 0 0
\(859\) −42.4714 24.5208i −1.44910 0.836641i −0.450676 0.892688i \(-0.648817\pi\)
−0.998428 + 0.0560471i \(0.982150\pi\)
\(860\) 0 0
\(861\) −31.3931 + 38.6532i −1.06987 + 1.31730i
\(862\) 0 0
\(863\) 11.2358 19.4609i 0.382470 0.662458i −0.608944 0.793213i \(-0.708407\pi\)
0.991415 + 0.130755i \(0.0417401\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 19.6403 66.3036i 0.667020 2.25179i
\(868\) 0 0
\(869\) 6.06826i 0.205851i
\(870\) 0 0
\(871\) 3.81466 2.20239i 0.129255 0.0746253i
\(872\) 0 0
\(873\) −34.5311 + 17.5941i −1.16870 + 0.595471i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 26.8618 + 15.5087i 0.907059 + 0.523691i 0.879484 0.475929i \(-0.157888\pi\)
0.0275755 + 0.999620i \(0.491221\pi\)
\(878\) 0 0
\(879\) −8.64902 36.0264i −0.291724 1.21514i
\(880\) 0 0
\(881\) 21.8713 0.736864 0.368432 0.929655i \(-0.379895\pi\)
0.368432 + 0.929655i \(0.379895\pi\)
\(882\) 0 0
\(883\) 34.3430i 1.15573i 0.816131 + 0.577867i \(0.196115\pi\)
−0.816131 + 0.577867i \(0.803885\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 48.4807 + 27.9903i 1.62782 + 0.939824i 0.984741 + 0.174027i \(0.0556779\pi\)
0.643082 + 0.765797i \(0.277655\pi\)
\(888\) 0 0
\(889\) 25.6278 + 33.4985i 0.859530 + 1.12350i
\(890\) 0 0
\(891\) −2.23654 + 21.2759i −0.0749268 + 0.712771i
\(892\) 0 0
\(893\) 22.8060 + 39.5012i 0.763175 + 1.32186i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −1.20276 + 4.06039i −0.0401590 + 0.135573i
\(898\) 0 0
\(899\) 9.81894 + 17.0069i 0.327480 + 0.567212i
\(900\) 0 0
\(901\) 0.705799 + 0.407493i 0.0235136 + 0.0135756i
\(902\) 0 0
\(903\) −10.7853 8.75956i −0.358913 0.291500i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0.856413 0.494450i 0.0284367 0.0164180i −0.485714 0.874118i \(-0.661440\pi\)
0.514151 + 0.857700i \(0.328107\pi\)
\(908\) 0 0
\(909\) 7.88602 + 5.12133i 0.261563 + 0.169864i
\(910\) 0 0
\(911\) 28.5096i 0.944567i 0.881447 + 0.472283i \(0.156570\pi\)
−0.881447 + 0.472283i \(0.843430\pi\)
\(912\) 0 0
\(913\) −1.07197 1.85671i −0.0354771 0.0614482i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −2.84885 21.8822i −0.0940774 0.722615i
\(918\) 0 0
\(919\) −1.40350 + 2.43093i −0.0462971 + 0.0801889i −0.888245 0.459369i \(-0.848075\pi\)
0.841948 + 0.539558i \(0.181409\pi\)
\(920\) 0 0
\(921\) −28.2102 + 6.77256i −0.929559 + 0.223163i
\(922\) 0 0
\(923\) 10.4438i 0.343761i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 2.47812 47.2780i 0.0813920 1.55281i
\(928\) 0 0
\(929\) 6.57702 11.3917i 0.215785 0.373751i −0.737730 0.675096i \(-0.764102\pi\)
0.953515 + 0.301345i \(0.0974356\pi\)
\(930\) 0 0
\(931\) 35.0718 34.8707i 1.14943 1.14284i
\(932\) 0 0
\(933\) 6.02276 + 6.34672i 0.197176 + 0.207782i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −20.2219 −0.660622 −0.330311 0.943872i \(-0.607154\pi\)
−0.330311 + 0.943872i \(0.607154\pi\)
\(938\) 0 0
\(939\) 7.38441 24.9290i 0.240981 0.813527i
\(940\) 0 0
\(941\) −22.8119 39.5113i −0.743646 1.28803i −0.950825 0.309729i \(-0.899762\pi\)
0.207179 0.978303i \(-0.433572\pi\)
\(942\) 0 0
\(943\) −17.7548 + 30.7523i −0.578177 + 1.00143i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 29.2959 50.7421i 0.951990 1.64890i 0.210880 0.977512i \(-0.432367\pi\)
0.741110 0.671383i \(-0.234300\pi\)
\(948\) 0 0
\(949\) 0.584105 + 1.01170i 0.0189608 + 0.0328411i
\(950\) 0 0
\(951\) −12.5270 + 42.2898i −0.406216 + 1.37134i
\(952\) 0 0
\(953\) −26.9224 −0.872101 −0.436051 0.899922i \(-0.643623\pi\)
−0.436051 + 0.899922i \(0.643623\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 7.04265 + 7.42147i 0.227657 + 0.239902i
\(958\) 0 0
\(959\) −19.5967 8.15025i −0.632811 0.263185i
\(960\) 0 0
\(961\) 15.7244 27.2354i 0.507238 0.878562i
\(962\) 0 0
\(963\) 2.17503 41.4957i 0.0700894 1.33718i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 17.4008i 0.559572i 0.960062 + 0.279786i \(0.0902635\pi\)
−0.960062 + 0.279786i \(0.909737\pi\)
\(968\) 0 0
\(969\) 89.7785 21.5535i 2.88410 0.692399i
\(970\) 0 0
\(971\) −12.6200 + 21.8585i −0.404996 + 0.701474i −0.994321 0.106422i \(-0.966060\pi\)
0.589325 + 0.807896i \(0.299394\pi\)
\(972\) 0 0
\(973\) 7.42160 + 9.70087i 0.237926 + 0.310996i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.74960 6.49450i −0.119960 0.207778i 0.799791 0.600278i \(-0.204943\pi\)
−0.919752 + 0.392501i \(0.871610\pi\)
\(978\) 0 0
\(979\) 11.5629i 0.369552i
\(980\) 0 0
\(981\) −4.34345 2.82072i −0.138676 0.0900586i
\(982\) 0 0
\(983\) −22.3498 + 12.9037i −0.712848 + 0.411563i −0.812115 0.583498i \(-0.801684\pi\)
0.0992666 + 0.995061i \(0.468350\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −27.6345 + 10.5622i −0.879615 + 0.336198i
\(988\) 0 0
\(989\) −8.58074 4.95409i −0.272852 0.157531i
\(990\) 0 0
\(991\) −11.4009 19.7469i −0.362161 0.627280i 0.626156 0.779698i \(-0.284627\pi\)
−0.988316 + 0.152418i \(0.951294\pi\)
\(992\) 0 0
\(993\) −5.36341 + 18.1063i −0.170203 + 0.574586i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 5.91662 + 10.2479i 0.187381 + 0.324554i 0.944376 0.328867i \(-0.106667\pi\)
−0.756995 + 0.653421i \(0.773333\pi\)
\(998\) 0 0
\(999\) −22.0618 + 4.08865i −0.698006 + 0.129359i
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 2100.2.bo.i.1349.16 32
3.2 odd 2 inner 2100.2.bo.i.1349.6 32
5.2 odd 4 2100.2.bi.m.1601.4 yes 16
5.3 odd 4 2100.2.bi.l.1601.5 yes 16
5.4 even 2 inner 2100.2.bo.i.1349.1 32
7.3 odd 6 inner 2100.2.bo.i.1949.11 32
15.2 even 4 2100.2.bi.m.1601.7 yes 16
15.8 even 4 2100.2.bi.l.1601.2 yes 16
15.14 odd 2 inner 2100.2.bo.i.1349.11 32
21.17 even 6 inner 2100.2.bo.i.1949.1 32
35.3 even 12 2100.2.bi.l.101.2 16
35.17 even 12 2100.2.bi.m.101.7 yes 16
35.24 odd 6 inner 2100.2.bo.i.1949.6 32
105.17 odd 12 2100.2.bi.m.101.4 yes 16
105.38 odd 12 2100.2.bi.l.101.5 yes 16
105.59 even 6 inner 2100.2.bo.i.1949.16 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2100.2.bi.l.101.2 16 35.3 even 12
2100.2.bi.l.101.5 yes 16 105.38 odd 12
2100.2.bi.l.1601.2 yes 16 15.8 even 4
2100.2.bi.l.1601.5 yes 16 5.3 odd 4
2100.2.bi.m.101.4 yes 16 105.17 odd 12
2100.2.bi.m.101.7 yes 16 35.17 even 12
2100.2.bi.m.1601.4 yes 16 5.2 odd 4
2100.2.bi.m.1601.7 yes 16 15.2 even 4
2100.2.bo.i.1349.1 32 5.4 even 2 inner
2100.2.bo.i.1349.6 32 3.2 odd 2 inner
2100.2.bo.i.1349.11 32 15.14 odd 2 inner
2100.2.bo.i.1349.16 32 1.1 even 1 trivial
2100.2.bo.i.1949.1 32 21.17 even 6 inner
2100.2.bo.i.1949.6 32 35.24 odd 6 inner
2100.2.bo.i.1949.11 32 7.3 odd 6 inner
2100.2.bo.i.1949.16 32 105.59 even 6 inner