Properties

Label 2100.2.ce.e.493.2
Level $2100$
Weight $2$
Character 2100.493
Analytic conductor $16.769$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2100,2,Mod(157,2100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2100, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2100.157");
 
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.ce (of order \(12\), 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: \(16.7685844245\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 420)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 493.2
Character \(\chi\) \(=\) 2100.493
Dual form 2100.2.ce.e.1657.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{3} +(1.70817 - 2.02043i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{3} +(1.70817 - 2.02043i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(1.21556 - 2.10542i) q^{11} +(0.728866 - 0.728866i) q^{13} +(7.33552 - 1.96555i) q^{17} +(1.84965 + 3.20369i) q^{19} +(-2.39370 - 1.12704i) q^{21} +(-0.759994 + 2.83634i) q^{23} +(0.707107 + 0.707107i) q^{27} +1.99120i q^{29} +(6.02262 + 3.47716i) q^{31} +(-2.34829 - 0.629222i) q^{33} +(-8.22068 - 2.20273i) q^{37} +(-0.892675 - 0.515386i) q^{39} -1.08701i q^{41} +(-5.91785 - 5.91785i) q^{43} +(1.28906 - 4.81085i) q^{47} +(-1.16431 - 6.90249i) q^{49} +(-3.79715 - 6.57685i) q^{51} +(6.56972 - 1.76035i) q^{53} +(2.61580 - 2.61580i) q^{57} +(-1.39403 + 2.41454i) q^{59} +(0.217574 - 0.125616i) q^{61} +(-0.469102 + 2.60383i) q^{63} +(2.08758 + 7.79096i) q^{67} +2.93639 q^{69} +14.5737 q^{71} +(-1.73216 - 6.46450i) q^{73} +(-2.17747 - 6.05238i) q^{77} +(9.54459 - 5.51057i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-9.90994 + 9.90994i) q^{83} +(1.92335 - 0.515361i) q^{87} +(-5.81468 - 10.0713i) q^{89} +(-0.227598 - 2.71765i) q^{91} +(1.79991 - 6.71736i) q^{93} +(-10.8833 - 10.8833i) q^{97} +2.43113i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 8 q^{11} - 8 q^{21} - 16 q^{23} + 24 q^{31} - 12 q^{33} - 20 q^{37} + 24 q^{43} - 12 q^{47} - 8 q^{51} - 40 q^{53} + 16 q^{57} - 24 q^{61} + 12 q^{63} - 16 q^{71} + 60 q^{73} + 84 q^{77} + 16 q^{81} + 48 q^{87} + 40 q^{91} - 8 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(701\) \(1051\) \(1177\) \(1501\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.258819 0.965926i −0.149429 0.557678i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.70817 2.02043i 0.645628 0.763652i
\(8\) 0 0
\(9\) −0.866025 + 0.500000i −0.288675 + 0.166667i
\(10\) 0 0
\(11\) 1.21556 2.10542i 0.366506 0.634808i −0.622510 0.782612i \(-0.713887\pi\)
0.989017 + 0.147804i \(0.0472204\pi\)
\(12\) 0 0
\(13\) 0.728866 0.728866i 0.202151 0.202151i −0.598770 0.800921i \(-0.704344\pi\)
0.800921 + 0.598770i \(0.204344\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.33552 1.96555i 1.77913 0.476715i 0.788702 0.614776i \(-0.210753\pi\)
0.990424 + 0.138060i \(0.0440867\pi\)
\(18\) 0 0
\(19\) 1.84965 + 3.20369i 0.424339 + 0.734977i 0.996358 0.0852629i \(-0.0271730\pi\)
−0.572019 + 0.820240i \(0.693840\pi\)
\(20\) 0 0
\(21\) −2.39370 1.12704i −0.522347 0.245940i
\(22\) 0 0
\(23\) −0.759994 + 2.83634i −0.158470 + 0.591417i 0.840313 + 0.542101i \(0.182371\pi\)
−0.998783 + 0.0493165i \(0.984296\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 0 0
\(29\) 1.99120i 0.369757i 0.982761 + 0.184878i \(0.0591891\pi\)
−0.982761 + 0.184878i \(0.940811\pi\)
\(30\) 0 0
\(31\) 6.02262 + 3.47716i 1.08169 + 0.624517i 0.931353 0.364117i \(-0.118629\pi\)
0.150342 + 0.988634i \(0.451963\pi\)
\(32\) 0 0
\(33\) −2.34829 0.629222i −0.408785 0.109534i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.22068 2.20273i −1.35147 0.362126i −0.490794 0.871276i \(-0.663293\pi\)
−0.860678 + 0.509150i \(0.829960\pi\)
\(38\) 0 0
\(39\) −0.892675 0.515386i −0.142942 0.0825278i
\(40\) 0 0
\(41\) 1.08701i 0.169762i −0.996391 0.0848810i \(-0.972949\pi\)
0.996391 0.0848810i \(-0.0270510\pi\)
\(42\) 0 0
\(43\) −5.91785 5.91785i −0.902464 0.902464i 0.0931848 0.995649i \(-0.470295\pi\)
−0.995649 + 0.0931848i \(0.970295\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.28906 4.81085i 0.188029 0.701735i −0.805932 0.592007i \(-0.798336\pi\)
0.993962 0.109727i \(-0.0349978\pi\)
\(48\) 0 0
\(49\) −1.16431 6.90249i −0.166329 0.986070i
\(50\) 0 0
\(51\) −3.79715 6.57685i −0.531707 0.920943i
\(52\) 0 0
\(53\) 6.56972 1.76035i 0.902420 0.241803i 0.222365 0.974964i \(-0.428622\pi\)
0.680055 + 0.733161i \(0.261956\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.61580 2.61580i 0.346472 0.346472i
\(58\) 0 0
\(59\) −1.39403 + 2.41454i −0.181488 + 0.314346i −0.942387 0.334523i \(-0.891425\pi\)
0.760900 + 0.648870i \(0.224758\pi\)
\(60\) 0 0
\(61\) 0.217574 0.125616i 0.0278575 0.0160835i −0.486007 0.873955i \(-0.661547\pi\)
0.513864 + 0.857872i \(0.328214\pi\)
\(62\) 0 0
\(63\) −0.469102 + 2.60383i −0.0591013 + 0.328052i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 2.08758 + 7.79096i 0.255039 + 0.951818i 0.968069 + 0.250684i \(0.0806556\pi\)
−0.713030 + 0.701133i \(0.752678\pi\)
\(68\) 0 0
\(69\) 2.93639 0.353500
\(70\) 0 0
\(71\) 14.5737 1.72958 0.864790 0.502133i \(-0.167451\pi\)
0.864790 + 0.502133i \(0.167451\pi\)
\(72\) 0 0
\(73\) −1.73216 6.46450i −0.202734 0.756612i −0.990128 0.140163i \(-0.955237\pi\)
0.787395 0.616449i \(-0.211429\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.17747 6.05238i −0.248146 0.689733i
\(78\) 0 0
\(79\) 9.54459 5.51057i 1.07385 0.619987i 0.144619 0.989487i \(-0.453804\pi\)
0.929231 + 0.369500i \(0.120471\pi\)
\(80\) 0 0
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) 0 0
\(83\) −9.90994 + 9.90994i −1.08776 + 1.08776i −0.0919976 + 0.995759i \(0.529325\pi\)
−0.995759 + 0.0919976i \(0.970675\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 1.92335 0.515361i 0.206205 0.0552525i
\(88\) 0 0
\(89\) −5.81468 10.0713i −0.616354 1.06756i −0.990145 0.140044i \(-0.955276\pi\)
0.373791 0.927513i \(-0.378058\pi\)
\(90\) 0 0
\(91\) −0.227598 2.71765i −0.0238587 0.284887i
\(92\) 0 0
\(93\) 1.79991 6.71736i 0.186642 0.696558i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −10.8833 10.8833i −1.10503 1.10503i −0.993794 0.111236i \(-0.964519\pi\)
−0.111236 0.993794i \(-0.535481\pi\)
\(98\) 0 0
\(99\) 2.43113i 0.244338i
\(100\) 0 0
\(101\) 5.44655 + 3.14457i 0.541952 + 0.312896i 0.745870 0.666092i \(-0.232034\pi\)
−0.203918 + 0.978988i \(0.565367\pi\)
\(102\) 0 0
\(103\) −14.5741 3.90512i −1.43603 0.384782i −0.544887 0.838510i \(-0.683427\pi\)
−0.891141 + 0.453727i \(0.850094\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 14.1277 + 3.78551i 1.36578 + 0.365960i 0.865935 0.500156i \(-0.166724\pi\)
0.499844 + 0.866115i \(0.333391\pi\)
\(108\) 0 0
\(109\) −10.3565 5.97935i −0.991976 0.572718i −0.0861118 0.996285i \(-0.527444\pi\)
−0.905864 + 0.423568i \(0.860778\pi\)
\(110\) 0 0
\(111\) 8.51068i 0.807798i
\(112\) 0 0
\(113\) 5.10715 + 5.10715i 0.480441 + 0.480441i 0.905272 0.424832i \(-0.139667\pi\)
−0.424832 + 0.905272i \(0.639667\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.266783 + 0.995650i −0.0246641 + 0.0920478i
\(118\) 0 0
\(119\) 8.55907 18.1784i 0.784609 1.66641i
\(120\) 0 0
\(121\) 2.54481 + 4.40773i 0.231346 + 0.400703i
\(122\) 0 0
\(123\) −1.04997 + 0.281338i −0.0946724 + 0.0253674i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0.0263367 0.0263367i 0.00233701 0.00233701i −0.705937 0.708274i \(-0.749474\pi\)
0.708274 + 0.705937i \(0.249474\pi\)
\(128\) 0 0
\(129\) −4.18455 + 7.24786i −0.368429 + 0.638138i
\(130\) 0 0
\(131\) 8.58485 4.95646i 0.750062 0.433048i −0.0756546 0.997134i \(-0.524105\pi\)
0.825716 + 0.564086i \(0.190771\pi\)
\(132\) 0 0
\(133\) 9.63237 + 1.73535i 0.835232 + 0.150474i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.71987 13.8828i −0.317810 1.18608i −0.921345 0.388747i \(-0.872908\pi\)
0.603535 0.797337i \(-0.293759\pi\)
\(138\) 0 0
\(139\) −11.0917 −0.940787 −0.470394 0.882457i \(-0.655888\pi\)
−0.470394 + 0.882457i \(0.655888\pi\)
\(140\) 0 0
\(141\) −4.98056 −0.419439
\(142\) 0 0
\(143\) −0.648585 2.42055i −0.0542374 0.202417i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −6.36595 + 2.91113i −0.525055 + 0.240106i
\(148\) 0 0
\(149\) 7.66332 4.42442i 0.627804 0.362463i −0.152097 0.988366i \(-0.548603\pi\)
0.779901 + 0.625903i \(0.215269\pi\)
\(150\) 0 0
\(151\) −0.901062 + 1.56068i −0.0733274 + 0.127007i −0.900358 0.435151i \(-0.856695\pi\)
0.827030 + 0.562157i \(0.190028\pi\)
\(152\) 0 0
\(153\) −5.36998 + 5.36998i −0.434137 + 0.434137i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 11.0832 2.96972i 0.884532 0.237010i 0.212171 0.977233i \(-0.431947\pi\)
0.672361 + 0.740223i \(0.265280\pi\)
\(158\) 0 0
\(159\) −3.40074 5.89025i −0.269696 0.467127i
\(160\) 0 0
\(161\) 4.43243 + 6.38047i 0.349325 + 0.502851i
\(162\) 0 0
\(163\) 0.0813198 0.303489i 0.00636946 0.0237711i −0.962668 0.270685i \(-0.912750\pi\)
0.969037 + 0.246914i \(0.0794165\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.10159 2.10159i −0.162626 0.162626i 0.621103 0.783729i \(-0.286685\pi\)
−0.783729 + 0.621103i \(0.786685\pi\)
\(168\) 0 0
\(169\) 11.9375i 0.918270i
\(170\) 0 0
\(171\) −3.20369 1.84965i −0.244992 0.141446i
\(172\) 0 0
\(173\) −9.48720 2.54209i −0.721298 0.193271i −0.120547 0.992708i \(-0.538465\pi\)
−0.600751 + 0.799436i \(0.705132\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 2.69307 + 0.721606i 0.202423 + 0.0542392i
\(178\) 0 0
\(179\) −15.8512 9.15169i −1.18477 0.684030i −0.227660 0.973741i \(-0.573107\pi\)
−0.957114 + 0.289711i \(0.906441\pi\)
\(180\) 0 0
\(181\) 20.1817i 1.50009i −0.661387 0.750045i \(-0.730032\pi\)
0.661387 0.750045i \(-0.269968\pi\)
\(182\) 0 0
\(183\) −0.177648 0.177648i −0.0131321 0.0131321i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 4.77850 17.8336i 0.349439 1.30412i
\(188\) 0 0
\(189\) 2.63652 0.220803i 0.191779 0.0160611i
\(190\) 0 0
\(191\) −1.24147 2.15029i −0.0898297 0.155590i 0.817609 0.575773i \(-0.195299\pi\)
−0.907439 + 0.420184i \(0.861966\pi\)
\(192\) 0 0
\(193\) 12.8390 3.44019i 0.924169 0.247630i 0.234802 0.972043i \(-0.424556\pi\)
0.689366 + 0.724413i \(0.257889\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5.45204 5.45204i 0.388442 0.388442i −0.485690 0.874131i \(-0.661431\pi\)
0.874131 + 0.485690i \(0.161431\pi\)
\(198\) 0 0
\(199\) −6.32953 + 10.9631i −0.448689 + 0.777152i −0.998301 0.0582681i \(-0.981442\pi\)
0.549612 + 0.835420i \(0.314776\pi\)
\(200\) 0 0
\(201\) 6.98519 4.03290i 0.492697 0.284459i
\(202\) 0 0
\(203\) 4.02309 + 3.40131i 0.282366 + 0.238725i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.759994 2.83634i −0.0528233 0.197139i
\(208\) 0 0
\(209\) 8.99349 0.622093
\(210\) 0 0
\(211\) −5.37636 −0.370124 −0.185062 0.982727i \(-0.559249\pi\)
−0.185062 + 0.982727i \(0.559249\pi\)
\(212\) 0 0
\(213\) −3.77195 14.0771i −0.258450 0.964548i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 17.3130 6.22872i 1.17529 0.422833i
\(218\) 0 0
\(219\) −5.79591 + 3.34627i −0.391651 + 0.226120i
\(220\) 0 0
\(221\) 3.91399 6.77924i 0.263284 0.456021i
\(222\) 0 0
\(223\) −17.2847 + 17.2847i −1.15747 + 1.15747i −0.172452 + 0.985018i \(0.555169\pi\)
−0.985018 + 0.172452i \(0.944831\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.81901 0.487401i 0.120732 0.0323499i −0.197947 0.980213i \(-0.563427\pi\)
0.318679 + 0.947863i \(0.396761\pi\)
\(228\) 0 0
\(229\) 12.5383 + 21.7171i 0.828557 + 1.43510i 0.899170 + 0.437600i \(0.144171\pi\)
−0.0706123 + 0.997504i \(0.522495\pi\)
\(230\) 0 0
\(231\) −5.28258 + 3.66975i −0.347568 + 0.241452i
\(232\) 0 0
\(233\) 5.80563 21.6669i 0.380340 1.41945i −0.465044 0.885287i \(-0.653962\pi\)
0.845384 0.534159i \(-0.179372\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −7.79312 7.79312i −0.506218 0.506218i
\(238\) 0 0
\(239\) 6.38917i 0.413281i 0.978417 + 0.206641i \(0.0662531\pi\)
−0.978417 + 0.206641i \(0.933747\pi\)
\(240\) 0 0
\(241\) −16.1337 9.31479i −1.03926 0.600018i −0.119638 0.992818i \(-0.538173\pi\)
−0.919624 + 0.392799i \(0.871507\pi\)
\(242\) 0 0
\(243\) −0.965926 0.258819i −0.0619642 0.0166032i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 3.68321 + 0.986914i 0.234357 + 0.0627958i
\(248\) 0 0
\(249\) 12.1371 + 7.00738i 0.769160 + 0.444075i
\(250\) 0 0
\(251\) 31.5776i 1.99316i 0.0826181 + 0.996581i \(0.473672\pi\)
−0.0826181 + 0.996581i \(0.526328\pi\)
\(252\) 0 0
\(253\) 5.04786 + 5.04786i 0.317356 + 0.317356i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4.81126 + 17.9559i −0.300118 + 1.12006i 0.636949 + 0.770906i \(0.280196\pi\)
−0.937067 + 0.349150i \(0.886470\pi\)
\(258\) 0 0
\(259\) −18.4928 + 12.8467i −1.14909 + 0.798256i
\(260\) 0 0
\(261\) −0.995601 1.72443i −0.0616261 0.106740i
\(262\) 0 0
\(263\) −5.52178 + 1.47956i −0.340488 + 0.0912334i −0.425011 0.905188i \(-0.639730\pi\)
0.0845235 + 0.996421i \(0.473063\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −8.22319 + 8.22319i −0.503251 + 0.503251i
\(268\) 0 0
\(269\) 1.22482 2.12145i 0.0746785 0.129347i −0.826268 0.563277i \(-0.809540\pi\)
0.900946 + 0.433930i \(0.142874\pi\)
\(270\) 0 0
\(271\) −21.9156 + 12.6530i −1.33128 + 0.768613i −0.985495 0.169702i \(-0.945720\pi\)
−0.345782 + 0.938315i \(0.612386\pi\)
\(272\) 0 0
\(273\) −2.56614 + 0.923223i −0.155310 + 0.0558760i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 8.27697 + 30.8901i 0.497315 + 1.85600i 0.516660 + 0.856191i \(0.327175\pi\)
−0.0193451 + 0.999813i \(0.506158\pi\)
\(278\) 0 0
\(279\) −6.95433 −0.416345
\(280\) 0 0
\(281\) 12.3044 0.734020 0.367010 0.930217i \(-0.380382\pi\)
0.367010 + 0.930217i \(0.380382\pi\)
\(282\) 0 0
\(283\) −0.584999 2.18325i −0.0347746 0.129780i 0.946356 0.323125i \(-0.104733\pi\)
−0.981131 + 0.193344i \(0.938067\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.19623 1.85679i −0.129639 0.109603i
\(288\) 0 0
\(289\) 35.2241 20.3366i 2.07201 1.19627i
\(290\) 0 0
\(291\) −7.69564 + 13.3292i −0.451126 + 0.781374i
\(292\) 0 0
\(293\) 3.19458 3.19458i 0.186629 0.186629i −0.607608 0.794237i \(-0.707871\pi\)
0.794237 + 0.607608i \(0.207871\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 2.34829 0.629222i 0.136262 0.0365112i
\(298\) 0 0
\(299\) 1.51338 + 2.62124i 0.0875208 + 0.151590i
\(300\) 0 0
\(301\) −22.0653 + 1.84793i −1.27182 + 0.106513i
\(302\) 0 0
\(303\) 1.62775 6.07484i 0.0935117 0.348990i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 5.74597 + 5.74597i 0.327940 + 0.327940i 0.851803 0.523863i \(-0.175510\pi\)
−0.523863 + 0.851803i \(0.675510\pi\)
\(308\) 0 0
\(309\) 15.0882i 0.858338i
\(310\) 0 0
\(311\) 12.5238 + 7.23064i 0.710161 + 0.410012i 0.811121 0.584879i \(-0.198858\pi\)
−0.100959 + 0.994891i \(0.532191\pi\)
\(312\) 0 0
\(313\) 1.14185 + 0.305958i 0.0645412 + 0.0172938i 0.290945 0.956740i \(-0.406030\pi\)
−0.226404 + 0.974033i \(0.572697\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.53996 2.28828i −0.479652 0.128522i 0.0108885 0.999941i \(-0.496534\pi\)
−0.490541 + 0.871418i \(0.663201\pi\)
\(318\) 0 0
\(319\) 4.19231 + 2.42043i 0.234725 + 0.135518i
\(320\) 0 0
\(321\) 14.6261i 0.816350i
\(322\) 0 0
\(323\) 19.8652 + 19.8652i 1.10533 + 1.10533i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −3.09514 + 11.5512i −0.171162 + 0.638784i
\(328\) 0 0
\(329\) −7.51807 10.8222i −0.414484 0.596649i
\(330\) 0 0
\(331\) −10.9304 18.9320i −0.600789 1.04060i −0.992702 0.120595i \(-0.961520\pi\)
0.391913 0.920002i \(-0.371814\pi\)
\(332\) 0 0
\(333\) 8.22068 2.20273i 0.450491 0.120709i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −18.0987 + 18.0987i −0.985900 + 0.985900i −0.999902 0.0140019i \(-0.995543\pi\)
0.0140019 + 0.999902i \(0.495543\pi\)
\(338\) 0 0
\(339\) 3.61130 6.25496i 0.196139 0.339723i
\(340\) 0 0
\(341\) 14.6418 8.45343i 0.792896 0.457779i
\(342\) 0 0
\(343\) −15.9349 9.43823i −0.860402 0.509617i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.08442 + 4.04711i 0.0582148 + 0.217261i 0.988905 0.148547i \(-0.0474596\pi\)
−0.930691 + 0.365807i \(0.880793\pi\)
\(348\) 0 0
\(349\) −33.8258 −1.81065 −0.905327 0.424715i \(-0.860374\pi\)
−0.905327 + 0.424715i \(0.860374\pi\)
\(350\) 0 0
\(351\) 1.03077 0.0550186
\(352\) 0 0
\(353\) 8.70598 + 32.4911i 0.463372 + 1.72933i 0.662230 + 0.749301i \(0.269610\pi\)
−0.198857 + 0.980028i \(0.563723\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −19.7743 3.56250i −1.04657 0.188548i
\(358\) 0 0
\(359\) 14.0177 8.09313i 0.739826 0.427139i −0.0821800 0.996618i \(-0.526188\pi\)
0.822006 + 0.569479i \(0.192855\pi\)
\(360\) 0 0
\(361\) 2.65757 4.60305i 0.139872 0.242266i
\(362\) 0 0
\(363\) 3.59890 3.59890i 0.188893 0.188893i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −15.6293 + 4.18786i −0.815842 + 0.218604i −0.642528 0.766262i \(-0.722114\pi\)
−0.173314 + 0.984867i \(0.555448\pi\)
\(368\) 0 0
\(369\) 0.543504 + 0.941376i 0.0282937 + 0.0490061i
\(370\) 0 0
\(371\) 7.66553 16.2807i 0.397974 0.845250i
\(372\) 0 0
\(373\) 0.962517 3.59216i 0.0498372 0.185995i −0.936520 0.350614i \(-0.885973\pi\)
0.986357 + 0.164619i \(0.0526395\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.45132 + 1.45132i 0.0747467 + 0.0747467i
\(378\) 0 0
\(379\) 0.149127i 0.00766015i 0.999993 + 0.00383007i \(0.00121915\pi\)
−0.999993 + 0.00383007i \(0.998781\pi\)
\(380\) 0 0
\(381\) −0.0322558 0.0186229i −0.00165251 0.000954080i
\(382\) 0 0
\(383\) 33.4767 + 8.97006i 1.71058 + 0.458349i 0.975567 0.219703i \(-0.0705089\pi\)
0.735014 + 0.678052i \(0.237176\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 8.08394 + 2.16608i 0.410930 + 0.110108i
\(388\) 0 0
\(389\) 28.3146 + 16.3474i 1.43561 + 0.828847i 0.997540 0.0700961i \(-0.0223306\pi\)
0.438065 + 0.898943i \(0.355664\pi\)
\(390\) 0 0
\(391\) 22.2998i 1.12775i
\(392\) 0 0
\(393\) −7.00950 7.00950i −0.353582 0.353582i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −4.73087 + 17.6559i −0.237436 + 0.886122i 0.739600 + 0.673047i \(0.235015\pi\)
−0.977036 + 0.213076i \(0.931652\pi\)
\(398\) 0 0
\(399\) −0.816819 9.75330i −0.0408921 0.488276i
\(400\) 0 0
\(401\) −0.590882 1.02344i −0.0295072 0.0511080i 0.850895 0.525336i \(-0.176060\pi\)
−0.880402 + 0.474228i \(0.842727\pi\)
\(402\) 0 0
\(403\) 6.92407 1.85530i 0.344913 0.0924190i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −14.6304 + 14.6304i −0.725203 + 0.725203i
\(408\) 0 0
\(409\) 8.11235 14.0510i 0.401130 0.694777i −0.592733 0.805399i \(-0.701951\pi\)
0.993863 + 0.110622i \(0.0352843\pi\)
\(410\) 0 0
\(411\) −12.4469 + 7.18624i −0.613962 + 0.354471i
\(412\) 0 0
\(413\) 2.49717 + 6.94100i 0.122878 + 0.341544i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 2.87075 + 10.7138i 0.140581 + 0.524656i
\(418\) 0 0
\(419\) −15.4289 −0.753750 −0.376875 0.926264i \(-0.623001\pi\)
−0.376875 + 0.926264i \(0.623001\pi\)
\(420\) 0 0
\(421\) 26.6085 1.29682 0.648409 0.761292i \(-0.275435\pi\)
0.648409 + 0.761292i \(0.275435\pi\)
\(422\) 0 0
\(423\) 1.28906 + 4.81085i 0.0626764 + 0.233912i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.117854 0.654167i 0.00570335 0.0316574i
\(428\) 0 0
\(429\) −2.17021 + 1.25297i −0.104779 + 0.0604940i
\(430\) 0 0
\(431\) −1.83304 + 3.17492i −0.0882944 + 0.152930i −0.906790 0.421582i \(-0.861475\pi\)
0.818496 + 0.574512i \(0.194808\pi\)
\(432\) 0 0
\(433\) 9.74318 9.74318i 0.468227 0.468227i −0.433112 0.901340i \(-0.642585\pi\)
0.901340 + 0.433112i \(0.142585\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −10.4925 + 2.81145i −0.501923 + 0.134490i
\(438\) 0 0
\(439\) 3.00918 + 5.21204i 0.143620 + 0.248757i 0.928857 0.370438i \(-0.120792\pi\)
−0.785237 + 0.619195i \(0.787459\pi\)
\(440\) 0 0
\(441\) 4.45956 + 5.39558i 0.212360 + 0.256932i
\(442\) 0 0
\(443\) −5.25355 + 19.6065i −0.249604 + 0.931534i 0.721410 + 0.692509i \(0.243495\pi\)
−0.971013 + 0.239025i \(0.923172\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −6.25708 6.25708i −0.295950 0.295950i
\(448\) 0 0
\(449\) 12.7251i 0.600534i 0.953855 + 0.300267i \(0.0970758\pi\)
−0.953855 + 0.300267i \(0.902924\pi\)
\(450\) 0 0
\(451\) −2.28861 1.32133i −0.107766 0.0622189i
\(452\) 0 0
\(453\) 1.74072 + 0.466424i 0.0817860 + 0.0219145i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −30.1623 8.08197i −1.41093 0.378058i −0.528675 0.848824i \(-0.677311\pi\)
−0.882258 + 0.470766i \(0.843978\pi\)
\(458\) 0 0
\(459\) 6.57685 + 3.79715i 0.306981 + 0.177236i
\(460\) 0 0
\(461\) 23.4059i 1.09012i 0.838397 + 0.545060i \(0.183493\pi\)
−0.838397 + 0.545060i \(0.816507\pi\)
\(462\) 0 0
\(463\) 16.8382 + 16.8382i 0.782539 + 0.782539i 0.980259 0.197720i \(-0.0633537\pi\)
−0.197720 + 0.980259i \(0.563354\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −10.0990 + 37.6898i −0.467324 + 1.74408i 0.181744 + 0.983346i \(0.441826\pi\)
−0.649068 + 0.760730i \(0.724841\pi\)
\(468\) 0 0
\(469\) 19.3071 + 9.09048i 0.891518 + 0.419759i
\(470\) 0 0
\(471\) −5.73706 9.93688i −0.264350 0.457867i
\(472\) 0 0
\(473\) −19.6531 + 5.26603i −0.903650 + 0.242132i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −4.80937 + 4.80937i −0.220206 + 0.220206i
\(478\) 0 0
\(479\) 7.66084 13.2690i 0.350033 0.606275i −0.636222 0.771506i \(-0.719504\pi\)
0.986255 + 0.165231i \(0.0528371\pi\)
\(480\) 0 0
\(481\) −7.59727 + 4.38628i −0.346406 + 0.199997i
\(482\) 0 0
\(483\) 5.01586 5.93279i 0.228230 0.269951i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 4.32465 + 16.1398i 0.195968 + 0.731364i 0.992014 + 0.126127i \(0.0402548\pi\)
−0.796046 + 0.605237i \(0.793079\pi\)
\(488\) 0 0
\(489\) −0.314195 −0.0142084
\(490\) 0 0
\(491\) 0.188878 0.00852393 0.00426196 0.999991i \(-0.498643\pi\)
0.00426196 + 0.999991i \(0.498643\pi\)
\(492\) 0 0
\(493\) 3.91380 + 14.6065i 0.176269 + 0.657844i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 24.8944 29.4452i 1.11667 1.32080i
\(498\) 0 0
\(499\) −12.1410 + 7.00959i −0.543504 + 0.313792i −0.746498 0.665388i \(-0.768266\pi\)
0.202994 + 0.979180i \(0.434933\pi\)
\(500\) 0 0
\(501\) −1.48605 + 2.57391i −0.0663917 + 0.114994i
\(502\) 0 0
\(503\) 20.0052 20.0052i 0.891989 0.891989i −0.102721 0.994710i \(-0.532755\pi\)
0.994710 + 0.102721i \(0.0327549\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 11.5307 3.08965i 0.512098 0.137216i
\(508\) 0 0
\(509\) −6.58364 11.4032i −0.291815 0.505438i 0.682424 0.730956i \(-0.260926\pi\)
−0.974239 + 0.225518i \(0.927592\pi\)
\(510\) 0 0
\(511\) −16.0199 7.54276i −0.708679 0.333672i
\(512\) 0 0
\(513\) −0.957451 + 3.57325i −0.0422725 + 0.157763i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −8.56192 8.56192i −0.376553 0.376553i
\(518\) 0 0
\(519\) 9.82187i 0.431132i
\(520\) 0 0
\(521\) −22.6255 13.0628i −0.991242 0.572294i −0.0855965 0.996330i \(-0.527280\pi\)
−0.905645 + 0.424036i \(0.860613\pi\)
\(522\) 0 0
\(523\) 5.53573 + 1.48330i 0.242061 + 0.0648600i 0.377810 0.925883i \(-0.376677\pi\)
−0.135749 + 0.990743i \(0.543344\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 51.0136 + 13.6691i 2.22219 + 0.595434i
\(528\) 0 0
\(529\) 12.4514 + 7.18880i 0.541364 + 0.312556i
\(530\) 0 0
\(531\) 2.78807i 0.120992i
\(532\) 0 0
\(533\) −0.792283 0.792283i −0.0343176 0.0343176i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −4.73727 + 17.6797i −0.204428 + 0.762936i
\(538\) 0 0
\(539\) −15.9479 5.93907i −0.686926 0.255814i
\(540\) 0 0
\(541\) −14.1293 24.4727i −0.607468 1.05217i −0.991656 0.128910i \(-0.958852\pi\)
0.384188 0.923255i \(-0.374481\pi\)
\(542\) 0 0
\(543\) −19.4940 + 5.22340i −0.836567 + 0.224157i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −20.0515 + 20.0515i −0.857341 + 0.857341i −0.991024 0.133683i \(-0.957320\pi\)
0.133683 + 0.991024i \(0.457320\pi\)
\(548\) 0 0
\(549\) −0.125616 + 0.217574i −0.00536117 + 0.00928582i
\(550\) 0 0
\(551\) −6.37920 + 3.68303i −0.271763 + 0.156902i
\(552\) 0 0
\(553\) 5.17004 28.6972i 0.219853 1.22033i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.73283 21.3952i −0.242908 0.906544i −0.974423 0.224720i \(-0.927853\pi\)
0.731516 0.681825i \(-0.238813\pi\)
\(558\) 0 0
\(559\) −8.62664 −0.364868
\(560\) 0 0
\(561\) −18.4627 −0.779496
\(562\) 0 0
\(563\) 0.337839 + 1.26083i 0.0142382 + 0.0531378i 0.972679 0.232152i \(-0.0745768\pi\)
−0.958441 + 0.285290i \(0.907910\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.895662 2.48954i −0.0376143 0.104551i
\(568\) 0 0
\(569\) −0.426999 + 0.246528i −0.0179007 + 0.0103350i −0.508924 0.860812i \(-0.669956\pi\)
0.491023 + 0.871147i \(0.336623\pi\)
\(570\) 0 0
\(571\) −1.79895 + 3.11588i −0.0752839 + 0.130395i −0.901210 0.433383i \(-0.857320\pi\)
0.825926 + 0.563779i \(0.190653\pi\)
\(572\) 0 0
\(573\) −1.75571 + 1.75571i −0.0733456 + 0.0733456i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 12.2308 3.27724i 0.509177 0.136433i 0.00492102 0.999988i \(-0.498434\pi\)
0.504256 + 0.863554i \(0.331767\pi\)
\(578\) 0 0
\(579\) −6.64594 11.5111i −0.276196 0.478385i
\(580\) 0 0
\(581\) 3.09451 + 36.9502i 0.128382 + 1.53295i
\(582\) 0 0
\(583\) 4.27964 15.9718i 0.177245 0.661486i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2.84683 2.84683i −0.117501 0.117501i 0.645911 0.763413i \(-0.276478\pi\)
−0.763413 + 0.645911i \(0.776478\pi\)
\(588\) 0 0
\(589\) 25.7262i 1.06003i
\(590\) 0 0
\(591\) −6.67736 3.85517i −0.274670 0.158581i
\(592\) 0 0
\(593\) 30.7485 + 8.23903i 1.26269 + 0.338336i 0.827226 0.561870i \(-0.189918\pi\)
0.435463 + 0.900206i \(0.356585\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 12.2277 + 3.27641i 0.500447 + 0.134094i
\(598\) 0 0
\(599\) 33.3274 + 19.2416i 1.36172 + 0.786191i 0.989853 0.142095i \(-0.0453837\pi\)
0.371869 + 0.928285i \(0.378717\pi\)
\(600\) 0 0
\(601\) 45.6842i 1.86350i 0.363102 + 0.931750i \(0.381718\pi\)
−0.363102 + 0.931750i \(0.618282\pi\)
\(602\) 0 0
\(603\) −5.70338 5.70338i −0.232260 0.232260i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 6.42220 23.9680i 0.260669 0.972831i −0.704179 0.710023i \(-0.748685\pi\)
0.964848 0.262808i \(-0.0846487\pi\)
\(608\) 0 0
\(609\) 2.24416 4.76633i 0.0909381 0.193141i
\(610\) 0 0
\(611\) −2.56691 4.44602i −0.103846 0.179867i
\(612\) 0 0
\(613\) 1.06899 0.286436i 0.0431762 0.0115690i −0.237166 0.971469i \(-0.576219\pi\)
0.280343 + 0.959900i \(0.409552\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.353089 0.353089i 0.0142148 0.0142148i −0.699964 0.714178i \(-0.746800\pi\)
0.714178 + 0.699964i \(0.246800\pi\)
\(618\) 0 0
\(619\) 11.6067 20.1034i 0.466513 0.808024i −0.532756 0.846269i \(-0.678844\pi\)
0.999268 + 0.0382453i \(0.0121768\pi\)
\(620\) 0 0
\(621\) −2.54299 + 1.46820i −0.102047 + 0.0589167i
\(622\) 0 0
\(623\) −30.2809 5.45536i −1.21318 0.218564i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −2.32769 8.68704i −0.0929588 0.346927i
\(628\) 0 0
\(629\) −64.6326 −2.57707
\(630\) 0 0
\(631\) 18.8761 0.751445 0.375723 0.926732i \(-0.377395\pi\)
0.375723 + 0.926732i \(0.377395\pi\)
\(632\) 0 0
\(633\) 1.39150 + 5.19316i 0.0553073 + 0.206410i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −5.87961 4.18237i −0.232959 0.165712i
\(638\) 0 0
\(639\) −12.6212 + 7.28685i −0.499287 + 0.288263i
\(640\) 0 0
\(641\) 18.7675 32.5062i 0.741271 1.28392i −0.210646 0.977562i \(-0.567557\pi\)
0.951917 0.306356i \(-0.0991099\pi\)
\(642\) 0 0
\(643\) −12.0570 + 12.0570i −0.475483 + 0.475483i −0.903684 0.428201i \(-0.859148\pi\)
0.428201 + 0.903684i \(0.359148\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −18.0130 + 4.82656i −0.708163 + 0.189752i −0.594884 0.803812i \(-0.702802\pi\)
−0.113279 + 0.993563i \(0.536135\pi\)
\(648\) 0 0
\(649\) 3.38908 + 5.87006i 0.133033 + 0.230420i
\(650\) 0 0
\(651\) −10.4974 15.1110i −0.411427 0.592247i
\(652\) 0 0
\(653\) 4.34601 16.2195i 0.170073 0.634719i −0.827266 0.561810i \(-0.810105\pi\)
0.997339 0.0729090i \(-0.0232283\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 4.73234 + 4.73234i 0.184626 + 0.184626i
\(658\) 0 0
\(659\) 47.4270i 1.84749i 0.383005 + 0.923746i \(0.374889\pi\)
−0.383005 + 0.923746i \(0.625111\pi\)
\(660\) 0 0
\(661\) 10.5554 + 6.09418i 0.410558 + 0.237036i 0.691030 0.722826i \(-0.257157\pi\)
−0.280471 + 0.959862i \(0.590491\pi\)
\(662\) 0 0
\(663\) −7.56125 2.02603i −0.293655 0.0786846i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −5.64772 1.51330i −0.218681 0.0585953i
\(668\) 0 0
\(669\) 21.1694 + 12.2221i 0.818455 + 0.472535i
\(670\) 0 0
\(671\) 0.610779i 0.0235789i
\(672\) 0 0
\(673\) −1.19597 1.19597i −0.0461011 0.0461011i 0.683680 0.729782i \(-0.260378\pi\)
−0.729782 + 0.683680i \(0.760378\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.45115 9.14780i 0.0942052 0.351578i −0.902693 0.430286i \(-0.858413\pi\)
0.996898 + 0.0787076i \(0.0250794\pi\)
\(678\) 0 0
\(679\) −40.5794 + 3.39845i −1.55730 + 0.130420i
\(680\) 0 0
\(681\) −0.941587 1.63088i −0.0360817 0.0624953i
\(682\) 0 0
\(683\) −20.7804 + 5.56809i −0.795139 + 0.213057i −0.633449 0.773785i \(-0.718361\pi\)
−0.161690 + 0.986842i \(0.551695\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 17.7319 17.7319i 0.676514 0.676514i
\(688\) 0 0
\(689\) 3.50538 6.07150i 0.133544 0.231306i
\(690\) 0 0
\(691\) 5.42242 3.13064i 0.206279 0.119095i −0.393302 0.919409i \(-0.628667\pi\)
0.599581 + 0.800314i \(0.295334\pi\)
\(692\) 0 0
\(693\) 4.91193 + 4.15278i 0.186589 + 0.157751i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −2.13656 7.97377i −0.0809281 0.302028i
\(698\) 0 0
\(699\) −22.4312 −0.848427
\(700\) 0 0
\(701\) −41.6155 −1.57180 −0.785899 0.618355i \(-0.787799\pi\)
−0.785899 + 0.618355i \(0.787799\pi\)
\(702\) 0 0
\(703\) −8.14855 30.4108i −0.307328 1.14697i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 15.6570 5.63294i 0.588843 0.211848i
\(708\) 0 0
\(709\) 0.279672 0.161469i 0.0105033 0.00606409i −0.494739 0.869042i \(-0.664736\pi\)
0.505242 + 0.862977i \(0.331403\pi\)
\(710\) 0 0
\(711\) −5.51057 + 9.54459i −0.206662 + 0.357950i
\(712\) 0 0
\(713\) −14.4396 + 14.4396i −0.540766 + 0.540766i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 6.17147 1.65364i 0.230478 0.0617563i
\(718\) 0 0
\(719\) 10.1034 + 17.4996i 0.376792 + 0.652623i 0.990594 0.136837i \(-0.0436938\pi\)
−0.613801 + 0.789460i \(0.710360\pi\)
\(720\) 0 0
\(721\) −32.7851 + 22.7754i −1.22098 + 0.848199i
\(722\) 0 0
\(723\) −4.82169 + 17.9948i −0.179321 + 0.669234i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 3.29844 + 3.29844i 0.122332 + 0.122332i 0.765622 0.643290i \(-0.222431\pi\)
−0.643290 + 0.765622i \(0.722431\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −55.0424 31.7787i −2.03582 1.17538i
\(732\) 0 0
\(733\) −14.6701 3.93084i −0.541852 0.145189i −0.0224964 0.999747i \(-0.507161\pi\)
−0.519356 + 0.854558i \(0.673828\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 18.9408 + 5.07518i 0.697695 + 0.186947i
\(738\) 0 0
\(739\) 15.6624 + 9.04272i 0.576153 + 0.332642i 0.759603 0.650387i \(-0.225393\pi\)
−0.183450 + 0.983029i \(0.558727\pi\)
\(740\) 0 0
\(741\) 3.81314i 0.140079i
\(742\) 0 0
\(743\) 4.73236 + 4.73236i 0.173613 + 0.173613i 0.788565 0.614952i \(-0.210824\pi\)
−0.614952 + 0.788565i \(0.710824\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 3.62729 13.5372i 0.132716 0.495301i
\(748\) 0 0
\(749\) 31.7810 22.0778i 1.16125 0.806707i
\(750\) 0 0
\(751\) 22.6070 + 39.1564i 0.824940 + 1.42884i 0.901965 + 0.431809i \(0.142124\pi\)
−0.0770253 + 0.997029i \(0.524542\pi\)
\(752\) 0 0
\(753\) 30.5017 8.17289i 1.11154 0.297837i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −13.8934 + 13.8934i −0.504964 + 0.504964i −0.912976 0.408012i \(-0.866222\pi\)
0.408012 + 0.912976i \(0.366222\pi\)
\(758\) 0 0
\(759\) 3.56938 6.18234i 0.129560 0.224405i
\(760\) 0 0
\(761\) −22.4013 + 12.9334i −0.812046 + 0.468835i −0.847666 0.530531i \(-0.821993\pi\)
0.0356201 + 0.999365i \(0.488659\pi\)
\(762\) 0 0
\(763\) −29.7716 + 10.7109i −1.07780 + 0.387762i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.743811 + 2.77594i 0.0268575 + 0.100233i
\(768\) 0 0
\(769\) −3.97934 −0.143499 −0.0717493 0.997423i \(-0.522858\pi\)
−0.0717493 + 0.997423i \(0.522858\pi\)
\(770\) 0 0
\(771\) 18.5893 0.669476
\(772\) 0 0
\(773\) 7.53332 + 28.1147i 0.270955 + 1.01122i 0.958504 + 0.285079i \(0.0920198\pi\)
−0.687549 + 0.726138i \(0.741314\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 17.1953 + 14.5377i 0.616876 + 0.521537i
\(778\) 0 0
\(779\) 3.48244 2.01059i 0.124771 0.0720367i
\(780\) 0 0
\(781\) 17.7153 30.6838i 0.633903 1.09795i
\(782\) 0 0
\(783\) −1.40799 + 1.40799i −0.0503175 + 0.0503175i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −29.3783 + 7.87190i −1.04722 + 0.280603i −0.741104 0.671390i \(-0.765698\pi\)
−0.306120 + 0.951993i \(0.599031\pi\)
\(788\) 0 0
\(789\) 2.85829 + 4.95070i 0.101758 + 0.176249i
\(790\) 0 0
\(791\) 19.0426 1.59477i 0.677075 0.0567037i
\(792\) 0 0
\(793\) 0.0670247 0.250140i 0.00238012 0.00888272i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −4.04054 4.04054i −0.143123 0.143123i 0.631915 0.775038i \(-0.282269\pi\)
−0.775038 + 0.631915i \(0.782269\pi\)
\(798\) 0 0
\(799\) 37.8238i 1.33811i
\(800\) 0 0
\(801\) 10.0713 + 5.81468i 0.355852 + 0.205451i
\(802\) 0 0
\(803\) −15.7160 4.21110i −0.554607 0.148606i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −2.36617 0.634013i −0.0832931 0.0223183i
\(808\) 0 0
\(809\) −37.9488 21.9098i −1.33421 0.770306i −0.348268 0.937395i \(-0.613230\pi\)
−0.985942 + 0.167089i \(0.946563\pi\)
\(810\) 0 0
\(811\) 1.74791i 0.0613774i 0.999529 + 0.0306887i \(0.00977005\pi\)
−0.999529 + 0.0306887i \(0.990230\pi\)
\(812\) 0 0
\(813\) 17.8940 + 17.8940i 0.627570 + 0.627570i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 8.01301 29.9049i 0.280340 1.04624i
\(818\) 0 0
\(819\) 1.55593 + 2.23976i 0.0543687 + 0.0782635i
\(820\) 0 0
\(821\) 13.5210 + 23.4191i 0.471886 + 0.817331i 0.999483 0.0321643i \(-0.0102400\pi\)
−0.527596 + 0.849495i \(0.676907\pi\)
\(822\) 0 0
\(823\) −2.50063 + 0.670043i −0.0871667 + 0.0233562i −0.302139 0.953264i \(-0.597701\pi\)
0.214972 + 0.976620i \(0.431034\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −37.3013 + 37.3013i −1.29709 + 1.29709i −0.366787 + 0.930305i \(0.619542\pi\)
−0.930305 + 0.366787i \(0.880458\pi\)
\(828\) 0 0
\(829\) 19.0559 33.0057i 0.661837 1.14634i −0.318295 0.947992i \(-0.603110\pi\)
0.980132 0.198344i \(-0.0635563\pi\)
\(830\) 0 0
\(831\) 27.6953 15.9899i 0.960738 0.554682i
\(832\) 0 0
\(833\) −22.1080 48.3449i −0.765996 1.67505i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1.79991 + 6.71736i 0.0622141 + 0.232186i
\(838\) 0 0
\(839\) 27.2101 0.939398 0.469699 0.882827i \(-0.344362\pi\)
0.469699 + 0.882827i \(0.344362\pi\)
\(840\) 0 0
\(841\) 25.0351 0.863280
\(842\) 0 0
\(843\) −3.18462 11.8852i −0.109684 0.409346i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 13.2525 + 2.38755i 0.455361 + 0.0820372i
\(848\) 0 0
\(849\) −1.95744 + 1.13013i −0.0671793 + 0.0387860i
\(850\) 0 0
\(851\) 12.4953 21.6426i 0.428335 0.741898i
\(852\) 0 0
\(853\) 12.1745 12.1745i 0.416848 0.416848i −0.467268 0.884116i \(-0.654762\pi\)
0.884116 + 0.467268i \(0.154762\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −33.5825 + 8.99840i −1.14716 + 0.307379i −0.781825 0.623498i \(-0.785711\pi\)
−0.365331 + 0.930878i \(0.619044\pi\)
\(858\) 0 0
\(859\) −16.7607 29.0304i −0.571869 0.990506i −0.996374 0.0850805i \(-0.972885\pi\)
0.424505 0.905426i \(-0.360448\pi\)
\(860\) 0 0
\(861\) −1.22510 + 2.60196i −0.0417513 + 0.0886747i
\(862\) 0 0
\(863\) 8.79609 32.8275i 0.299422 1.11746i −0.638219 0.769855i \(-0.720329\pi\)
0.937641 0.347605i \(-0.113005\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −28.7604 28.7604i −0.976753 0.976753i
\(868\) 0 0
\(869\) 26.7938i 0.908918i
\(870\) 0 0
\(871\) 7.20014 + 4.15700i 0.243967 + 0.140855i
\(872\) 0 0
\(873\) 14.8668 + 3.98356i 0.503166 + 0.134823i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 17.6931 + 4.74085i 0.597454 + 0.160087i 0.544858 0.838529i \(-0.316584\pi\)
0.0525963 + 0.998616i \(0.483250\pi\)
\(878\) 0 0
\(879\) −3.91255 2.25891i −0.131967 0.0761911i
\(880\) 0 0
\(881\) 17.5109i 0.589956i −0.955504 0.294978i \(-0.904688\pi\)
0.955504 0.294978i \(-0.0953123\pi\)
\(882\) 0 0
\(883\) 33.5448 + 33.5448i 1.12887 + 1.12887i 0.990361 + 0.138510i \(0.0442312\pi\)
0.138510 + 0.990361i \(0.455769\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 7.10104 26.5015i 0.238430 0.889832i −0.738143 0.674644i \(-0.764297\pi\)
0.976573 0.215188i \(-0.0690363\pi\)
\(888\) 0 0
\(889\) −0.00822399 0.0981993i −0.000275824 0.00329350i
\(890\) 0 0
\(891\) −1.21556 2.10542i −0.0407229 0.0705342i
\(892\) 0 0
\(893\) 17.7968 4.76864i 0.595547 0.159576i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 2.14024 2.14024i 0.0714604 0.0714604i
\(898\) 0 0
\(899\) −6.92373 + 11.9923i −0.230919 + 0.399964i
\(900\) 0 0
\(901\) 44.7323 25.8262i 1.49025 0.860395i
\(902\) 0 0
\(903\) 7.49589 + 20.8352i 0.249448 + 0.693352i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0.829631 + 3.09623i 0.0275475 + 0.102809i 0.978331 0.207048i \(-0.0663856\pi\)
−0.950783 + 0.309857i \(0.899719\pi\)
\(908\) 0 0
\(909\) −6.28914 −0.208597
\(910\) 0 0
\(911\) 51.5087 1.70656 0.853279 0.521454i \(-0.174610\pi\)
0.853279 + 0.521454i \(0.174610\pi\)
\(912\) 0 0
\(913\) 8.81841 + 32.9107i 0.291847 + 1.08919i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 4.65018 25.8116i 0.153562 0.852374i
\(918\) 0 0
\(919\) 41.7186 24.0862i 1.37617 0.794531i 0.384473 0.923136i \(-0.374383\pi\)
0.991696 + 0.128605i \(0.0410499\pi\)
\(920\) 0 0
\(921\) 4.06301 7.03734i 0.133881 0.231888i
\(922\) 0 0
\(923\) 10.6223 10.6223i 0.349637 0.349637i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 14.5741 3.90512i 0.478676 0.128261i
\(928\) 0 0
\(929\) −14.4707 25.0639i −0.474767 0.822321i 0.524815 0.851216i \(-0.324134\pi\)
−0.999582 + 0.0288955i \(0.990801\pi\)
\(930\) 0 0
\(931\) 19.9599 16.4973i 0.654159 0.540677i
\(932\) 0 0
\(933\) 3.74285 13.9685i 0.122536 0.457309i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −9.57644 9.57644i −0.312849 0.312849i 0.533164 0.846012i \(-0.321003\pi\)
−0.846012 + 0.533164i \(0.821003\pi\)
\(938\) 0 0
\(939\) 1.18213i 0.0385774i
\(940\) 0 0
\(941\) 13.8414 + 7.99136i 0.451218 + 0.260511i 0.708344 0.705867i \(-0.249442\pi\)
−0.257127 + 0.966378i \(0.582776\pi\)
\(942\) 0 0
\(943\) 3.08312 + 0.826119i 0.100400 + 0.0269021i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 7.97060 + 2.13572i 0.259010 + 0.0694015i 0.385987 0.922504i \(-0.373861\pi\)
−0.126977 + 0.991906i \(0.540528\pi\)
\(948\) 0 0
\(949\) −5.97426 3.44924i −0.193933 0.111967i
\(950\) 0 0
\(951\) 8.84122i 0.286696i
\(952\) 0 0
\(953\) −25.2246 25.2246i −0.817104 0.817104i 0.168584 0.985687i \(-0.446081\pi\)
−0.985687 + 0.168584i \(0.946081\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 1.25291 4.67592i 0.0405008 0.151151i
\(958\) 0 0
\(959\) −34.4034 16.1984i −1.11094 0.523072i
\(960\) 0 0
\(961\) 8.68132 + 15.0365i 0.280043 + 0.485048i
\(962\) 0 0
\(963\) −14.1277 + 3.78551i −0.455260 + 0.121987i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 16.3072 16.3072i 0.524405 0.524405i −0.394494 0.918899i \(-0.629080\pi\)
0.918899 + 0.394494i \(0.129080\pi\)
\(968\) 0 0
\(969\) 14.0468 24.3298i 0.451248 0.781585i
\(970\) 0 0
\(971\) −3.80744 + 2.19823i −0.122187 + 0.0705445i −0.559848 0.828596i \(-0.689140\pi\)
0.437661 + 0.899140i \(0.355807\pi\)
\(972\) 0 0
\(973\) −18.9466 + 22.4101i −0.607399 + 0.718434i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −10.6307 39.6743i −0.340106 1.26929i −0.898226 0.439534i \(-0.855144\pi\)
0.558120 0.829760i \(-0.311523\pi\)
\(978\) 0 0
\(979\) −28.2725 −0.903592
\(980\) 0 0
\(981\) 11.9587 0.381812
\(982\) 0 0
\(983\) −0.682478 2.54704i −0.0217677 0.0812380i 0.954188 0.299209i \(-0.0967228\pi\)
−0.975955 + 0.217971i \(0.930056\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −8.50765 + 10.0629i −0.270801 + 0.320305i
\(988\) 0 0
\(989\) 21.2826 12.2875i 0.676746 0.390720i
\(990\) 0 0
\(991\) 0.658365 1.14032i 0.0209136 0.0362235i −0.855379 0.518002i \(-0.826676\pi\)
0.876293 + 0.481779i \(0.160009\pi\)
\(992\) 0 0
\(993\) −15.4579 + 15.4579i −0.490542 + 0.490542i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 49.5044 13.2647i 1.56782 0.420096i 0.632692 0.774404i \(-0.281950\pi\)
0.935129 + 0.354307i \(0.115283\pi\)
\(998\) 0 0
\(999\) −4.25534 7.37046i −0.134633 0.233191i
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.ce.e.493.2 32
5.2 odd 4 inner 2100.2.ce.e.157.4 32
5.3 odd 4 420.2.bo.a.157.5 yes 32
5.4 even 2 420.2.bo.a.73.7 32
7.5 odd 6 inner 2100.2.ce.e.1993.4 32
15.8 even 4 1260.2.dq.c.577.7 32
15.14 odd 2 1260.2.dq.c.73.4 32
35.3 even 12 2940.2.x.c.97.15 32
35.4 even 6 2940.2.x.c.1273.15 32
35.12 even 12 inner 2100.2.ce.e.1657.2 32
35.18 odd 12 2940.2.x.c.97.4 32
35.19 odd 6 420.2.bo.a.313.5 yes 32
35.24 odd 6 2940.2.x.c.1273.4 32
35.33 even 12 420.2.bo.a.397.7 yes 32
105.68 odd 12 1260.2.dq.c.397.4 32
105.89 even 6 1260.2.dq.c.1153.7 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
420.2.bo.a.73.7 32 5.4 even 2
420.2.bo.a.157.5 yes 32 5.3 odd 4
420.2.bo.a.313.5 yes 32 35.19 odd 6
420.2.bo.a.397.7 yes 32 35.33 even 12
1260.2.dq.c.73.4 32 15.14 odd 2
1260.2.dq.c.397.4 32 105.68 odd 12
1260.2.dq.c.577.7 32 15.8 even 4
1260.2.dq.c.1153.7 32 105.89 even 6
2100.2.ce.e.157.4 32 5.2 odd 4 inner
2100.2.ce.e.493.2 32 1.1 even 1 trivial
2100.2.ce.e.1657.2 32 35.12 even 12 inner
2100.2.ce.e.1993.4 32 7.5 odd 6 inner
2940.2.x.c.97.4 32 35.18 odd 12
2940.2.x.c.97.15 32 35.3 even 12
2940.2.x.c.1273.4 32 35.24 odd 6
2940.2.x.c.1273.15 32 35.4 even 6