Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1690,2,Mod(1689,1690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1690.1689");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1690 = 2 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1690.c (of order \(2\), degree \(1\), 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: | \(13.4947179416\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 130) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1689.4 | ||
Root | \(-0.854638 - 0.854638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1690.1689 |
Dual form | 1690.2.c.b.1689.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.539189i | 0.311301i | 0.987812 | + | 0.155650i | \(0.0497473\pi\) | ||||
−0.987812 | + | 0.155650i | \(0.950253\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.17009 | − | 0.539189i | 0.970492 | − | 0.241133i | ||||
\(6\) | − | 0.539189i | − | 0.220123i | ||||||
\(7\) | 0.709275 | 0.268081 | 0.134040 | − | 0.990976i | \(-0.457205\pi\) | ||||
0.134040 | + | 0.990976i | \(0.457205\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.70928 | 0.903092 | ||||||||
\(10\) | −2.17009 | + | 0.539189i | −0.686242 | + | 0.170506i | ||||
\(11\) | 4.51026i | 1.35989i | 0.733261 | + | 0.679947i | \(0.237997\pi\) | ||||
−0.733261 | + | 0.679947i | \(0.762003\pi\) | |||||||
\(12\) | 0.539189i | 0.155650i | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.709275 | −0.189562 | ||||||||
\(15\) | 0.290725 | + | 1.17009i | 0.0750648 | + | 0.302115i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.17009i | − | 0.768859i | −0.923154 | − | 0.384429i | \(-0.874398\pi\) | ||
0.923154 | − | 0.384429i | \(-0.125602\pi\) | |||||||
\(18\) | −2.70928 | −0.638582 | ||||||||
\(19\) | 0.120638i | 0.0276763i | 0.999904 | + | 0.0138381i | \(0.00440496\pi\) | ||||
−0.999904 | + | 0.0138381i | \(0.995595\pi\) | |||||||
\(20\) | 2.17009 | − | 0.539189i | 0.485246 | − | 0.120566i | ||||
\(21\) | 0.382433i | 0.0834538i | ||||||||
\(22\) | − | 4.51026i | − | 0.961591i | ||||||
\(23\) | 4.97107i | 1.03654i | 0.855217 | + | 0.518270i | \(0.173424\pi\) | ||||
−0.855217 | + | 0.518270i | \(0.826576\pi\) | |||||||
\(24\) | − | 0.539189i | − | 0.110061i | ||||||
\(25\) | 4.41855 | − | 2.34017i | 0.883710 | − | 0.468035i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.07838i | 0.592434i | ||||||||
\(28\) | 0.709275 | 0.134040 | ||||||||
\(29\) | 7.26180 | 1.34848 | 0.674241 | − | 0.738512i | \(-0.264471\pi\) | ||||
0.674241 | + | 0.738512i | \(0.264471\pi\) | |||||||
\(30\) | −0.290725 | − | 1.17009i | −0.0530788 | − | 0.213628i | ||||
\(31\) | 9.66701i | 1.73625i | 0.496348 | + | 0.868124i | \(0.334674\pi\) | ||||
−0.496348 | + | 0.868124i | \(0.665326\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.43188 | −0.423336 | ||||||||
\(34\) | 3.17009i | 0.543665i | ||||||||
\(35\) | 1.53919 | − | 0.382433i | 0.260170 | − | 0.0646430i | ||||
\(36\) | 2.70928 | 0.451546 | ||||||||
\(37\) | −6.95774 | −1.14385 | −0.571923 | − | 0.820308i | \(-0.693802\pi\) | ||||
−0.571923 | + | 0.820308i | \(0.693802\pi\) | |||||||
\(38\) | − | 0.120638i | − | 0.0195701i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.17009 | + | 0.539189i | −0.343121 | + | 0.0852532i | ||||
\(41\) | 0.447480i | 0.0698847i | 0.999389 | + | 0.0349423i | \(0.0111248\pi\) | ||||
−0.999389 | + | 0.0349423i | \(0.988875\pi\) | |||||||
\(42\) | − | 0.382433i | − | 0.0590108i | ||||||
\(43\) | 2.00000i | 0.304997i | 0.988304 | + | 0.152499i | \(0.0487319\pi\) | ||||
−0.988304 | + | 0.152499i | \(0.951268\pi\) | |||||||
\(44\) | 4.51026i | 0.679947i | ||||||||
\(45\) | 5.87936 | − | 1.46081i | 0.876444 | − | 0.217765i | ||||
\(46\) | − | 4.97107i | − | 0.732944i | ||||||
\(47\) | −4.70928 | −0.686918 | −0.343459 | − | 0.939168i | \(-0.611599\pi\) | ||||
−0.343459 | + | 0.939168i | \(0.611599\pi\) | |||||||
\(48\) | 0.539189i | 0.0778252i | ||||||||
\(49\) | −6.49693 | −0.928133 | ||||||||
\(50\) | −4.41855 | + | 2.34017i | −0.624877 | + | 0.330950i | ||||
\(51\) | 1.70928 | 0.239346 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 9.58864i | − | 1.31710i | −0.752537 | − | 0.658550i | \(-0.771170\pi\) | ||
0.752537 | − | 0.658550i | \(-0.228830\pi\) | |||||||
\(54\) | − | 3.07838i | − | 0.418914i | ||||||
\(55\) | 2.43188 | + | 9.78765i | 0.327915 | + | 1.31977i | ||||
\(56\) | −0.709275 | −0.0947809 | ||||||||
\(57\) | −0.0650468 | −0.00861565 | ||||||||
\(58\) | −7.26180 | −0.953520 | ||||||||
\(59\) | − | 5.75872i | − | 0.749722i | −0.927081 | − | 0.374861i | \(-0.877690\pi\) | ||
0.927081 | − | 0.374861i | \(-0.122310\pi\) | |||||||
\(60\) | 0.290725 | + | 1.17009i | 0.0375324 | + | 0.151058i | ||||
\(61\) | 7.06278 | 0.904296 | 0.452148 | − | 0.891943i | \(-0.350658\pi\) | ||||
0.452148 | + | 0.891943i | \(0.350658\pi\) | |||||||
\(62\) | − | 9.66701i | − | 1.22771i | ||||||
\(63\) | 1.92162 | 0.242102 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.43188 | 0.299344 | ||||||||
\(67\) | 2.92162 | 0.356933 | 0.178466 | − | 0.983946i | \(-0.442886\pi\) | ||||
0.178466 | + | 0.983946i | \(0.442886\pi\) | |||||||
\(68\) | − | 3.17009i | − | 0.384429i | ||||||
\(69\) | −2.68035 | −0.322676 | ||||||||
\(70\) | −1.53919 | + | 0.382433i | −0.183968 | + | 0.0457095i | ||||
\(71\) | − | 8.18342i | − | 0.971193i | −0.874183 | − | 0.485596i | \(-0.838602\pi\) | ||
0.874183 | − | 0.485596i | \(-0.161398\pi\) | |||||||
\(72\) | −2.70928 | −0.319291 | ||||||||
\(73\) | −6.74539 | −0.789488 | −0.394744 | − | 0.918791i | \(-0.629167\pi\) | ||||
−0.394744 | + | 0.918791i | \(0.629167\pi\) | |||||||
\(74\) | 6.95774 | 0.808821 | ||||||||
\(75\) | 1.26180 | + | 2.38243i | 0.145700 | + | 0.275100i | ||||
\(76\) | 0.120638i | 0.0138381i | ||||||||
\(77\) | 3.19902i | 0.364562i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.0072 | 1.80095 | 0.900475 | − | 0.434908i | \(-0.143219\pi\) | ||||
0.900475 | + | 0.434908i | \(0.143219\pi\) | |||||||
\(80\) | 2.17009 | − | 0.539189i | 0.242623 | − | 0.0602831i | ||||
\(81\) | 6.46800 | 0.718667 | ||||||||
\(82\) | − | 0.447480i | − | 0.0494159i | ||||||
\(83\) | −0.355771 | −0.0390510 | −0.0195255 | − | 0.999809i | \(-0.506216\pi\) | ||||
−0.0195255 | + | 0.999809i | \(0.506216\pi\) | |||||||
\(84\) | 0.382433i | 0.0417269i | ||||||||
\(85\) | −1.70928 | − | 6.87936i | −0.185397 | − | 0.746172i | ||||
\(86\) | − | 2.00000i | − | 0.215666i | ||||||
\(87\) | 3.91548i | 0.419783i | ||||||||
\(88\) | − | 4.51026i | − | 0.480795i | ||||||
\(89\) | 3.63090i | 0.384874i | 0.981309 | + | 0.192437i | \(0.0616392\pi\) | ||||
−0.981309 | + | 0.192437i | \(0.938361\pi\) | |||||||
\(90\) | −5.87936 | + | 1.46081i | −0.619739 | + | 0.153983i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.97107i | 0.518270i | ||||||||
\(93\) | −5.21235 | −0.540495 | ||||||||
\(94\) | 4.70928 | 0.485725 | ||||||||
\(95\) | 0.0650468 | + | 0.261795i | 0.00667366 | + | 0.0268596i | ||||
\(96\) | − | 0.539189i | − | 0.0550307i | ||||||
\(97\) | 7.90829 | 0.802965 | 0.401483 | − | 0.915867i | \(-0.368495\pi\) | ||||
0.401483 | + | 0.915867i | \(0.368495\pi\) | |||||||
\(98\) | 6.49693 | 0.656289 | ||||||||
\(99\) | 12.2195i | 1.22811i | ||||||||
\(100\) | 4.41855 | − | 2.34017i | 0.441855 | − | 0.234017i | ||||
\(101\) | −6.14116 | −0.611068 | −0.305534 | − | 0.952181i | \(-0.598835\pi\) | ||||
−0.305534 | + | 0.952181i | \(0.598835\pi\) | |||||||
\(102\) | −1.70928 | −0.169243 | ||||||||
\(103\) | − | 17.6803i | − | 1.74210i | −0.491198 | − | 0.871048i | \(-0.663441\pi\) | ||
0.491198 | − | 0.871048i | \(-0.336559\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.206204 | + | 0.829914i | 0.0201234 | + | 0.0809913i | ||||
\(106\) | 9.58864i | 0.931331i | ||||||||
\(107\) | 0.539189i | 0.0521254i | 0.999660 | + | 0.0260627i | \(0.00829695\pi\) | ||||
−0.999660 | + | 0.0260627i | \(0.991703\pi\) | |||||||
\(108\) | 3.07838i | 0.296217i | ||||||||
\(109\) | 11.0205i | 1.05557i | 0.849377 | + | 0.527787i | \(0.176978\pi\) | ||||
−0.849377 | + | 0.527787i | \(0.823022\pi\) | |||||||
\(110\) | −2.43188 | − | 9.78765i | −0.231871 | − | 0.933216i | ||||
\(111\) | − | 3.75154i | − | 0.356080i | ||||||
\(112\) | 0.709275 | 0.0670202 | ||||||||
\(113\) | 14.0000i | 1.31701i | 0.752577 | + | 0.658505i | \(0.228811\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0.0650468 | 0.00609219 | ||||||||
\(115\) | 2.68035 | + | 10.7877i | 0.249944 | + | 1.00595i | ||||
\(116\) | 7.26180 | 0.674241 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.75872i | 0.530133i | ||||||||
\(119\) | − | 2.24846i | − | 0.206116i | ||||||
\(120\) | −0.290725 | − | 1.17009i | −0.0265394 | − | 0.106814i | ||||
\(121\) | −9.34244 | −0.849313 | ||||||||
\(122\) | −7.06278 | −0.639434 | ||||||||
\(123\) | −0.241276 | −0.0217552 | ||||||||
\(124\) | 9.66701i | 0.868124i | ||||||||
\(125\) | 8.32684 | − | 7.46081i | 0.744775 | − | 0.667315i | ||||
\(126\) | −1.92162 | −0.171192 | ||||||||
\(127\) | 12.1773i | 1.08056i | 0.841486 | + | 0.540279i | \(0.181681\pi\) | ||||
−0.841486 | + | 0.540279i | \(0.818319\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.07838 | −0.0949459 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.4547 | −1.52502 | −0.762511 | − | 0.646976i | \(-0.776034\pi\) | ||||
−0.762511 | + | 0.646976i | \(0.776034\pi\) | |||||||
\(132\) | −2.43188 | −0.211668 | ||||||||
\(133\) | 0.0855657i | 0.00741948i | ||||||||
\(134\) | −2.92162 | −0.252390 | ||||||||
\(135\) | 1.65983 | + | 6.68035i | 0.142855 | + | 0.574953i | ||||
\(136\) | 3.17009i | 0.271833i | ||||||||
\(137\) | −9.35350 | −0.799124 | −0.399562 | − | 0.916706i | \(-0.630838\pi\) | ||||
−0.399562 | + | 0.916706i | \(0.630838\pi\) | |||||||
\(138\) | 2.68035 | 0.228166 | ||||||||
\(139\) | 2.64423 | 0.224281 | 0.112140 | − | 0.993692i | \(-0.464229\pi\) | ||||
0.112140 | + | 0.993692i | \(0.464229\pi\) | |||||||
\(140\) | 1.53919 | − | 0.382433i | 0.130085 | − | 0.0323215i | ||||
\(141\) | − | 2.53919i | − | 0.213838i | ||||||
\(142\) | 8.18342i | 0.686737i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.70928 | 0.225773 | ||||||||
\(145\) | 15.7587 | − | 3.91548i | 1.30869 | − | 0.325163i | ||||
\(146\) | 6.74539 | 0.558253 | ||||||||
\(147\) | − | 3.50307i | − | 0.288928i | ||||||
\(148\) | −6.95774 | −0.571923 | ||||||||
\(149\) | 9.23513i | 0.756572i | 0.925689 | + | 0.378286i | \(0.123486\pi\) | ||||
−0.925689 | + | 0.378286i | \(0.876514\pi\) | |||||||
\(150\) | −1.26180 | − | 2.38243i | −0.103025 | − | 0.194525i | ||||
\(151\) | 9.42574i | 0.767056i | 0.923529 | + | 0.383528i | \(0.125291\pi\) | ||||
−0.923529 | + | 0.383528i | \(0.874709\pi\) | |||||||
\(152\) | − | 0.120638i | − | 0.00978505i | ||||||
\(153\) | − | 8.58864i | − | 0.694350i | ||||||
\(154\) | − | 3.19902i | − | 0.257784i | ||||||
\(155\) | 5.21235 | + | 20.9783i | 0.418666 | + | 1.68501i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 5.77205i | − | 0.460660i | −0.973113 | − | 0.230330i | \(-0.926019\pi\) | ||
0.973113 | − | 0.230330i | \(-0.0739806\pi\) | |||||||
\(158\) | −16.0072 | −1.27346 | ||||||||
\(159\) | 5.17009 | 0.410015 | ||||||||
\(160\) | −2.17009 | + | 0.539189i | −0.171560 | + | 0.0426266i | ||||
\(161\) | 3.52586i | 0.277877i | ||||||||
\(162\) | −6.46800 | −0.508174 | ||||||||
\(163\) | 16.8215 | 1.31756 | 0.658781 | − | 0.752335i | \(-0.271072\pi\) | ||||
0.658781 | + | 0.752335i | \(0.271072\pi\) | |||||||
\(164\) | 0.447480i | 0.0349423i | ||||||||
\(165\) | −5.27739 | + | 1.31124i | −0.410845 | + | 0.102080i | ||||
\(166\) | 0.355771 | 0.0276132 | ||||||||
\(167\) | 18.1194 | 1.40212 | 0.701061 | − | 0.713101i | \(-0.252710\pi\) | ||||
0.701061 | + | 0.713101i | \(0.252710\pi\) | |||||||
\(168\) | − | 0.382433i | − | 0.0295054i | ||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.70928 | + | 6.87936i | 0.131095 | + | 0.527623i | ||||
\(171\) | 0.326842i | 0.0249942i | ||||||||
\(172\) | 2.00000i | 0.152499i | ||||||||
\(173\) | 10.3041i | 0.783403i | 0.920092 | + | 0.391701i | \(0.128113\pi\) | ||||
−0.920092 | + | 0.391701i | \(0.871887\pi\) | |||||||
\(174\) | − | 3.91548i | − | 0.296832i | ||||||
\(175\) | 3.13397 | − | 1.65983i | 0.236906 | − | 0.125471i | ||||
\(176\) | 4.51026i | 0.339974i | ||||||||
\(177\) | 3.10504 | 0.233389 | ||||||||
\(178\) | − | 3.63090i | − | 0.272147i | ||||||
\(179\) | 1.26180 | 0.0943110 | 0.0471555 | − | 0.998888i | \(-0.484984\pi\) | ||||
0.0471555 | + | 0.998888i | \(0.484984\pi\) | |||||||
\(180\) | 5.87936 | − | 1.46081i | 0.438222 | − | 0.108882i | ||||
\(181\) | −2.38243 | −0.177085 | −0.0885424 | − | 0.996072i | \(-0.528221\pi\) | ||||
−0.0885424 | + | 0.996072i | \(0.528221\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.80817i | 0.281508i | ||||||||
\(184\) | − | 4.97107i | − | 0.366472i | ||||||
\(185\) | −15.0989 | + | 3.75154i | −1.11009 | + | 0.275818i | ||||
\(186\) | 5.21235 | 0.382188 | ||||||||
\(187\) | 14.2979 | 1.04557 | ||||||||
\(188\) | −4.70928 | −0.343459 | ||||||||
\(189\) | 2.18342i | 0.158820i | ||||||||
\(190\) | −0.0650468 | − | 0.261795i | −0.00471899 | − | 0.0189926i | ||||
\(191\) | −11.0856 | −0.802123 | −0.401062 | − | 0.916051i | \(-0.631359\pi\) | ||||
−0.401062 | + | 0.916051i | \(0.631359\pi\) | |||||||
\(192\) | 0.539189i | 0.0389126i | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | −7.90829 | −0.567782 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.49693 | −0.464066 | ||||||||
\(197\) | 8.69368 | 0.619399 | 0.309699 | − | 0.950835i | \(-0.399772\pi\) | ||||
0.309699 | + | 0.950835i | \(0.399772\pi\) | |||||||
\(198\) | − | 12.2195i | − | 0.868405i | ||||||
\(199\) | 21.5174 | 1.52533 | 0.762666 | − | 0.646793i | \(-0.223890\pi\) | ||||
0.762666 | + | 0.646793i | \(0.223890\pi\) | |||||||
\(200\) | −4.41855 | + | 2.34017i | −0.312439 | + | 0.165475i | ||||
\(201\) | 1.57531i | 0.111114i | ||||||||
\(202\) | 6.14116 | 0.432090 | ||||||||
\(203\) | 5.15061 | 0.361502 | ||||||||
\(204\) | 1.70928 | 0.119673 | ||||||||
\(205\) | 0.241276 | + | 0.971071i | 0.0168515 | + | 0.0678225i | ||||
\(206\) | 17.6803i | 1.23185i | ||||||||
\(207\) | 13.4680i | 0.936091i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.544109 | −0.0376368 | ||||||||
\(210\) | −0.206204 | − | 0.829914i | −0.0142294 | − | 0.0572695i | ||||
\(211\) | −5.58864 | −0.384738 | −0.192369 | − | 0.981323i | \(-0.561617\pi\) | ||||
−0.192369 | + | 0.981323i | \(0.561617\pi\) | |||||||
\(212\) | − | 9.58864i | − | 0.658550i | ||||||
\(213\) | 4.41241 | 0.302333 | ||||||||
\(214\) | − | 0.539189i | − | 0.0368582i | ||||||
\(215\) | 1.07838 | + | 4.34017i | 0.0735448 | + | 0.295997i | ||||
\(216\) | − | 3.07838i | − | 0.209457i | ||||||
\(217\) | 6.85658i | 0.465455i | ||||||||
\(218\) | − | 11.0205i | − | 0.746404i | ||||||
\(219\) | − | 3.63704i | − | 0.245768i | ||||||
\(220\) | 2.43188 | + | 9.78765i | 0.163957 | + | 0.659883i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.75154i | 0.251787i | ||||||||
\(223\) | −24.7093 | −1.65466 | −0.827328 | − | 0.561720i | \(-0.810140\pi\) | ||||
−0.827328 | + | 0.561720i | \(0.810140\pi\) | |||||||
\(224\) | −0.709275 | −0.0473905 | ||||||||
\(225\) | 11.9711 | − | 6.34017i | 0.798071 | − | 0.422678i | ||||
\(226\) | − | 14.0000i | − | 0.931266i | ||||||
\(227\) | 28.6947 | 1.90454 | 0.952268 | − | 0.305264i | \(-0.0987447\pi\) | ||||
0.952268 | + | 0.305264i | \(0.0987447\pi\) | |||||||
\(228\) | −0.0650468 | −0.00430783 | ||||||||
\(229\) | − | 1.89988i | − | 0.125548i | −0.998028 | − | 0.0627738i | \(-0.980005\pi\) | ||
0.998028 | − | 0.0627738i | \(-0.0199947\pi\) | |||||||
\(230\) | −2.68035 | − | 10.7877i | −0.176737 | − | 0.711317i | ||||
\(231\) | −1.72487 | −0.113488 | ||||||||
\(232\) | −7.26180 | −0.476760 | ||||||||
\(233\) | − | 22.2485i | − | 1.45755i | −0.684756 | − | 0.728773i | \(-0.740091\pi\) | ||
0.684756 | − | 0.728773i | \(-0.259909\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2195 | + | 2.53919i | −0.666649 | + | 0.165638i | ||||
\(236\) | − | 5.75872i | − | 0.374861i | ||||||
\(237\) | 8.63090i | 0.560637i | ||||||||
\(238\) | 2.24846i | 0.145746i | ||||||||
\(239\) | − | 24.8710i | − | 1.60877i | −0.594110 | − | 0.804384i | \(-0.702495\pi\) | ||
0.594110 | − | 0.804384i | \(-0.297505\pi\) | |||||||
\(240\) | 0.290725 | + | 1.17009i | 0.0187662 | + | 0.0755288i | ||||
\(241\) | 2.95055i | 0.190062i | 0.995474 | + | 0.0950309i | \(0.0302950\pi\) | ||||
−0.995474 | + | 0.0950309i | \(0.969705\pi\) | |||||||
\(242\) | 9.34244 | 0.600555 | ||||||||
\(243\) | 12.7226i | 0.816156i | ||||||||
\(244\) | 7.06278 | 0.452148 | ||||||||
\(245\) | −14.0989 | + | 3.50307i | −0.900745 | + | 0.223803i | ||||
\(246\) | 0.241276 | 0.0153832 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 9.66701i | − | 0.613856i | ||||||
\(249\) | − | 0.191828i | − | 0.0121566i | ||||||
\(250\) | −8.32684 | + | 7.46081i | −0.526636 | + | 0.471863i | ||||
\(251\) | −16.5597 | −1.04524 | −0.522620 | − | 0.852566i | \(-0.675045\pi\) | ||||
−0.522620 | + | 0.852566i | \(0.675045\pi\) | |||||||
\(252\) | 1.92162 | 0.121051 | ||||||||
\(253\) | −22.4208 | −1.40958 | ||||||||
\(254\) | − | 12.1773i | − | 0.764070i | ||||||
\(255\) | 3.70928 | − | 0.921622i | 0.232284 | − | 0.0577142i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 0.523590i | − | 0.0326607i | −0.999867 | − | 0.0163303i | \(-0.994802\pi\) | ||
0.999867 | − | 0.0163303i | \(-0.00519834\pi\) | |||||||
\(258\) | 1.07838 | 0.0671369 | ||||||||
\(259\) | −4.93495 | −0.306643 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.6742 | 1.21780 | ||||||||
\(262\) | 17.4547 | 1.07835 | ||||||||
\(263\) | − | 28.7815i | − | 1.77474i | −0.461054 | − | 0.887372i | \(-0.652529\pi\) | ||
0.461054 | − | 0.887372i | \(-0.347471\pi\) | |||||||
\(264\) | 2.43188 | 0.149672 | ||||||||
\(265\) | −5.17009 | − | 20.8082i | −0.317596 | − | 1.27824i | ||||
\(266\) | − | 0.0855657i | − | 0.00524637i | ||||||
\(267\) | −1.95774 | −0.119812 | ||||||||
\(268\) | 2.92162 | 0.178466 | ||||||||
\(269\) | −10.0566 | −0.613164 | −0.306582 | − | 0.951844i | \(-0.599185\pi\) | ||||
−0.306582 | + | 0.951844i | \(0.599185\pi\) | |||||||
\(270\) | −1.65983 | − | 6.68035i | −0.101014 | − | 0.406553i | ||||
\(271\) | − | 18.1256i | − | 1.10105i | −0.834819 | − | 0.550525i | \(-0.814428\pi\) | ||
0.834819 | − | 0.550525i | \(-0.185572\pi\) | |||||||
\(272\) | − | 3.17009i | − | 0.192215i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.35350 | 0.565066 | ||||||||
\(275\) | 10.5548 | + | 19.9288i | 0.636478 | + | 1.20175i | ||||
\(276\) | −2.68035 | −0.161338 | ||||||||
\(277\) | 24.7165i | 1.48507i | 0.669808 | + | 0.742534i | \(0.266376\pi\) | ||||
−0.669808 | + | 0.742534i | \(0.733624\pi\) | |||||||
\(278\) | −2.64423 | −0.158590 | ||||||||
\(279\) | 26.1906i | 1.56799i | ||||||||
\(280\) | −1.53919 | + | 0.382433i | −0.0919841 | + | 0.0228548i | ||||
\(281\) | − | 22.9854i | − | 1.37120i | −0.727980 | − | 0.685598i | \(-0.759541\pi\) | ||
0.727980 | − | 0.685598i | \(-0.240459\pi\) | |||||||
\(282\) | 2.53919i | 0.151206i | ||||||||
\(283\) | 18.0989i | 1.07587i | 0.842987 | + | 0.537934i | \(0.180795\pi\) | ||||
−0.842987 | + | 0.537934i | \(0.819205\pi\) | |||||||
\(284\) | − | 8.18342i | − | 0.485596i | ||||||
\(285\) | −0.141157 | + | 0.0350725i | −0.00836142 | + | 0.00207751i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.317387i | 0.0187347i | ||||||||
\(288\) | −2.70928 | −0.159646 | ||||||||
\(289\) | 6.95055 | 0.408856 | ||||||||
\(290\) | −15.7587 | + | 3.91548i | −0.925384 | + | 0.229925i | ||||
\(291\) | 4.26406i | 0.249964i | ||||||||
\(292\) | −6.74539 | −0.394744 | ||||||||
\(293\) | −17.8443 | −1.04247 | −0.521237 | − | 0.853412i | \(-0.674529\pi\) | ||||
−0.521237 | + | 0.853412i | \(0.674529\pi\) | |||||||
\(294\) | 3.50307i | 0.204303i | ||||||||
\(295\) | −3.10504 | − | 12.4969i | −0.180782 | − | 0.727599i | ||||
\(296\) | 6.95774 | 0.404410 | ||||||||
\(297\) | −13.8843 | −0.805648 | ||||||||
\(298\) | − | 9.23513i | − | 0.534977i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.26180 | + | 2.38243i | 0.0728498 | + | 0.137550i | ||||
\(301\) | 1.41855i | 0.0817639i | ||||||||
\(302\) | − | 9.42574i | − | 0.542390i | ||||||
\(303\) | − | 3.31124i | − | 0.190226i | ||||||
\(304\) | 0.120638i | 0.00691907i | ||||||||
\(305\) | 15.3268 | − | 3.80817i | 0.877612 | − | 0.218055i | ||||
\(306\) | 8.58864i | 0.490980i | ||||||||
\(307\) | 3.44521 | 0.196629 | 0.0983143 | − | 0.995155i | \(-0.468655\pi\) | ||||
0.0983143 | + | 0.995155i | \(0.468655\pi\) | |||||||
\(308\) | 3.19902i | 0.182281i | ||||||||
\(309\) | 9.53305 | 0.542316 | ||||||||
\(310\) | −5.21235 | − | 20.9783i | −0.296041 | − | 1.19149i | ||||
\(311\) | −17.8238 | −1.01069 | −0.505347 | − | 0.862916i | \(-0.668635\pi\) | ||||
−0.505347 | + | 0.862916i | \(0.668635\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 32.2245i | − | 1.82143i | −0.413031 | − | 0.910717i | \(-0.635530\pi\) | ||
0.413031 | − | 0.910717i | \(-0.364470\pi\) | |||||||
\(314\) | 5.77205i | 0.325736i | ||||||||
\(315\) | 4.17009 | − | 1.03612i | 0.234958 | − | 0.0583786i | ||||
\(316\) | 16.0072 | 0.900475 | ||||||||
\(317\) | −1.90602 | −0.107053 | −0.0535265 | − | 0.998566i | \(-0.517046\pi\) | ||||
−0.0535265 | + | 0.998566i | \(0.517046\pi\) | |||||||
\(318\) | −5.17009 | −0.289924 | ||||||||
\(319\) | 32.7526i | 1.83379i | ||||||||
\(320\) | 2.17009 | − | 0.539189i | 0.121312 | − | 0.0301416i | ||||
\(321\) | −0.290725 | −0.0162267 | ||||||||
\(322\) | − | 3.52586i | − | 0.196488i | ||||||
\(323\) | 0.382433 | 0.0212792 | ||||||||
\(324\) | 6.46800 | 0.359333 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −16.8215 | −0.931657 | ||||||||
\(327\) | −5.94214 | −0.328601 | ||||||||
\(328\) | − | 0.447480i | − | 0.0247080i | ||||||
\(329\) | −3.34017 | −0.184150 | ||||||||
\(330\) | 5.27739 | − | 1.31124i | 0.290511 | − | 0.0721816i | ||||
\(331\) | − | 0.711543i | − | 0.0391099i | −0.999809 | − | 0.0195550i | \(-0.993775\pi\) | ||
0.999809 | − | 0.0195550i | \(-0.00622494\pi\) | |||||||
\(332\) | −0.355771 | −0.0195255 | ||||||||
\(333\) | −18.8504 | −1.03300 | ||||||||
\(334\) | −18.1194 | −0.991450 | ||||||||
\(335\) | 6.34017 | − | 1.57531i | 0.346401 | − | 0.0860682i | ||||
\(336\) | 0.382433i | 0.0208635i | ||||||||
\(337\) | − | 9.85043i | − | 0.536587i | −0.963337 | − | 0.268294i | \(-0.913540\pi\) | ||
0.963337 | − | 0.268294i | \(-0.0864597\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.54864 | −0.409986 | ||||||||
\(340\) | −1.70928 | − | 6.87936i | −0.0926985 | − | 0.373086i | ||||
\(341\) | −43.6007 | −2.36111 | ||||||||
\(342\) | − | 0.326842i | − | 0.0176736i | ||||||
\(343\) | −9.57304 | −0.516896 | ||||||||
\(344\) | − | 2.00000i | − | 0.107833i | ||||||
\(345\) | −5.81658 | + | 1.44521i | −0.313154 | + | 0.0778076i | ||||
\(346\) | − | 10.3041i | − | 0.553949i | ||||||
\(347\) | − | 25.5330i | − | 1.37069i | −0.728221 | − | 0.685343i | \(-0.759652\pi\) | ||
0.728221 | − | 0.685343i | \(-0.240348\pi\) | |||||||
\(348\) | 3.91548i | 0.209892i | ||||||||
\(349\) | − | 18.0566i | − | 0.966550i | −0.875469 | − | 0.483275i | \(-0.839447\pi\) | ||
0.875469 | − | 0.483275i | \(-0.160553\pi\) | |||||||
\(350\) | −3.13397 | + | 1.65983i | −0.167518 | + | 0.0887215i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 4.51026i | − | 0.240398i | ||||||
\(353\) | −14.6465 | −0.779554 | −0.389777 | − | 0.920909i | \(-0.627448\pi\) | ||||
−0.389777 | + | 0.920909i | \(0.627448\pi\) | |||||||
\(354\) | −3.10504 | −0.165031 | ||||||||
\(355\) | −4.41241 | − | 17.7587i | −0.234186 | − | 0.942535i | ||||
\(356\) | 3.63090i | 0.192437i | ||||||||
\(357\) | 1.21235 | 0.0641642 | ||||||||
\(358\) | −1.26180 | −0.0666879 | ||||||||
\(359\) | − | 13.4186i | − | 0.708204i | −0.935207 | − | 0.354102i | \(-0.884787\pi\) | ||
0.935207 | − | 0.354102i | \(-0.115213\pi\) | |||||||
\(360\) | −5.87936 | + | 1.46081i | −0.309870 | + | 0.0769915i | ||||
\(361\) | 18.9854 | 0.999234 | ||||||||
\(362\) | 2.38243 | 0.125218 | ||||||||
\(363\) | − | 5.03734i | − | 0.264392i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.6381 | + | 3.63704i | −0.766192 | + | 0.190371i | ||||
\(366\) | − | 3.80817i | − | 0.199056i | ||||||
\(367\) | 21.5441i | 1.12459i | 0.826936 | + | 0.562297i | \(0.190082\pi\) | ||||
−0.826936 | + | 0.562297i | \(0.809918\pi\) | |||||||
\(368\) | 4.97107i | 0.259135i | ||||||||
\(369\) | 1.21235i | 0.0631123i | ||||||||
\(370\) | 15.0989 | − | 3.75154i | 0.784954 | − | 0.195033i | ||||
\(371\) | − | 6.80098i | − | 0.353090i | ||||||
\(372\) | −5.21235 | −0.270248 | ||||||||
\(373\) | 21.3340i | 1.10463i | 0.833634 | + | 0.552317i | \(0.186256\pi\) | ||||
−0.833634 | + | 0.552317i | \(0.813744\pi\) | |||||||
\(374\) | −14.2979 | −0.739327 | ||||||||
\(375\) | 4.02279 | + | 4.48974i | 0.207736 | + | 0.231849i | ||||
\(376\) | 4.70928 | 0.242862 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | − | 2.18342i | − | 0.112303i | ||||||
\(379\) | − | 8.11223i | − | 0.416697i | −0.978055 | − | 0.208349i | \(-0.933191\pi\) | ||
0.978055 | − | 0.208349i | \(-0.0668088\pi\) | |||||||
\(380\) | 0.0650468 | + | 0.261795i | 0.00333683 | + | 0.0134298i | ||||
\(381\) | −6.56585 | −0.336379 | ||||||||
\(382\) | 11.0856 | 0.567187 | ||||||||
\(383\) | −24.9399 | −1.27437 | −0.637184 | − | 0.770712i | \(-0.719901\pi\) | ||||
−0.637184 | + | 0.770712i | \(0.719901\pi\) | |||||||
\(384\) | − | 0.539189i | − | 0.0275154i | ||||||
\(385\) | 1.72487 | + | 6.94214i | 0.0879077 | + | 0.353804i | ||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | 5.41855i | 0.275440i | ||||||||
\(388\) | 7.90829 | 0.401483 | ||||||||
\(389\) | 13.5330 | 0.686153 | 0.343076 | − | 0.939308i | \(-0.388531\pi\) | ||||
0.343076 | + | 0.939308i | \(0.388531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.7587 | 0.796953 | ||||||||
\(392\) | 6.49693 | 0.328144 | ||||||||
\(393\) | − | 9.41136i | − | 0.474740i | ||||||
\(394\) | −8.69368 | −0.437981 | ||||||||
\(395\) | 34.7370 | − | 8.63090i | 1.74781 | − | 0.434268i | ||||
\(396\) | 12.2195i | 0.614055i | ||||||||
\(397\) | 4.59478 | 0.230605 | 0.115303 | − | 0.993330i | \(-0.463216\pi\) | ||||
0.115303 | + | 0.993330i | \(0.463216\pi\) | |||||||
\(398\) | −21.5174 | −1.07857 | ||||||||
\(399\) | −0.0461361 | −0.00230969 | ||||||||
\(400\) | 4.41855 | − | 2.34017i | 0.220928 | − | 0.117009i | ||||
\(401\) | − | 29.7031i | − | 1.48330i | −0.670785 | − | 0.741652i | \(-0.734043\pi\) | ||
0.670785 | − | 0.741652i | \(-0.265957\pi\) | |||||||
\(402\) | − | 1.57531i | − | 0.0785691i | ||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.14116 | −0.305534 | ||||||||
\(405\) | 14.0361 | − | 3.48747i | 0.697460 | − | 0.173294i | ||||
\(406\) | −5.15061 | −0.255621 | ||||||||
\(407\) | − | 31.3812i | − | 1.55551i | ||||||
\(408\) | −1.70928 | −0.0846217 | ||||||||
\(409\) | 10.3112i | 0.509858i | 0.966960 | + | 0.254929i | \(0.0820521\pi\) | ||||
−0.966960 | + | 0.254929i | \(0.917948\pi\) | |||||||
\(410\) | −0.241276 | − | 0.971071i | −0.0119158 | − | 0.0479578i | ||||
\(411\) | − | 5.04331i | − | 0.248768i | ||||||
\(412\) | − | 17.6803i | − | 0.871048i | ||||||
\(413\) | − | 4.08452i | − | 0.200986i | ||||||
\(414\) | − | 13.4680i | − | 0.661916i | ||||||
\(415\) | −0.772055 | + | 0.191828i | −0.0378987 | + | 0.00941646i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.42574i | 0.0698187i | ||||||||
\(418\) | 0.544109 | 0.0266133 | ||||||||
\(419\) | −38.0905 | −1.86084 | −0.930421 | − | 0.366492i | \(-0.880559\pi\) | ||||
−0.930421 | + | 0.366492i | \(0.880559\pi\) | |||||||
\(420\) | 0.206204 | + | 0.829914i | 0.0100617 | + | 0.0404956i | ||||
\(421\) | − | 26.7103i | − | 1.30178i | −0.759171 | − | 0.650891i | \(-0.774396\pi\) | ||
0.759171 | − | 0.650891i | \(-0.225604\pi\) | |||||||
\(422\) | 5.58864 | 0.272051 | ||||||||
\(423\) | −12.7587 | −0.620350 | ||||||||
\(424\) | 9.58864i | 0.465665i | ||||||||
\(425\) | −7.41855 | − | 14.0072i | −0.359853 | − | 0.679448i | ||||
\(426\) | −4.41241 | −0.213782 | ||||||||
\(427\) | 5.00946 | 0.242425 | ||||||||
\(428\) | 0.539189i | 0.0260627i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.07838 | − | 4.34017i | −0.0520040 | − | 0.209302i | ||||
\(431\) | − | 20.7187i | − | 0.997986i | −0.866606 | − | 0.498993i | \(-0.833703\pi\) | ||
0.866606 | − | 0.498993i | \(-0.166297\pi\) | |||||||
\(432\) | 3.07838i | 0.148109i | ||||||||
\(433\) | 15.8576i | 0.762069i | 0.924561 | + | 0.381034i | \(0.124432\pi\) | ||||
−0.924561 | + | 0.381034i | \(0.875568\pi\) | |||||||
\(434\) | − | 6.85658i | − | 0.329126i | ||||||
\(435\) | 2.11118 | + | 8.49693i | 0.101223 | + | 0.407397i | ||||
\(436\) | 11.0205i | 0.527787i | ||||||||
\(437\) | −0.599701 | −0.0286876 | ||||||||
\(438\) | 3.63704i | 0.173785i | ||||||||
\(439\) | −9.73925 | −0.464829 | −0.232415 | − | 0.972617i | \(-0.574663\pi\) | ||||
−0.232415 | + | 0.972617i | \(0.574663\pi\) | |||||||
\(440\) | −2.43188 | − | 9.78765i | −0.115935 | − | 0.466608i | ||||
\(441\) | −17.6020 | −0.838189 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.23060i | 0.438559i | 0.975662 | + | 0.219279i | \(0.0703707\pi\) | ||||
−0.975662 | + | 0.219279i | \(0.929629\pi\) | |||||||
\(444\) | − | 3.75154i | − | 0.178040i | ||||||
\(445\) | 1.95774 | + | 7.87936i | 0.0928058 | + | 0.373518i | ||||
\(446\) | 24.7093 | 1.17002 | ||||||||
\(447\) | −4.97948 | −0.235521 | ||||||||
\(448\) | 0.709275 | 0.0335101 | ||||||||
\(449\) | − | 2.92389i | − | 0.137987i | −0.997617 | − | 0.0689934i | \(-0.978021\pi\) | ||
0.997617 | − | 0.0689934i | \(-0.0219788\pi\) | |||||||
\(450\) | −11.9711 | + | 6.34017i | −0.564322 | + | 0.298879i | ||||
\(451\) | −2.01825 | −0.0950358 | ||||||||
\(452\) | 14.0000i | 0.658505i | ||||||||
\(453\) | −5.08225 | −0.238785 | ||||||||
\(454\) | −28.6947 | −1.34671 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0650468 | 0.00304609 | ||||||||
\(457\) | 11.6526 | 0.545087 | 0.272544 | − | 0.962143i | \(-0.412135\pi\) | ||||
0.272544 | + | 0.962143i | \(0.412135\pi\) | |||||||
\(458\) | 1.89988i | 0.0887756i | ||||||||
\(459\) | 9.75872 | 0.455498 | ||||||||
\(460\) | 2.68035 | + | 10.7877i | 0.124972 | + | 0.502977i | ||||
\(461\) | − | 30.2979i | − | 1.41111i | −0.708653 | − | 0.705557i | \(-0.750697\pi\) | ||
0.708653 | − | 0.705557i | \(-0.249303\pi\) | |||||||
\(462\) | 1.72487 | 0.0802484 | ||||||||
\(463\) | 7.04331 | 0.327330 | 0.163665 | − | 0.986516i | \(-0.447668\pi\) | ||||
0.163665 | + | 0.986516i | \(0.447668\pi\) | |||||||
\(464\) | 7.26180 | 0.337120 | ||||||||
\(465\) | −11.3112 | + | 2.81044i | −0.524546 | + | 0.130331i | ||||
\(466\) | 22.2485i | 1.03064i | ||||||||
\(467\) | 3.90110i | 0.180522i | 0.995918 | + | 0.0902608i | \(0.0287700\pi\) | ||||
−0.995918 | + | 0.0902608i | \(0.971230\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.07223 | 0.0956869 | ||||||||
\(470\) | 10.2195 | − | 2.53919i | 0.471392 | − | 0.117124i | ||||
\(471\) | 3.11223 | 0.143404 | ||||||||
\(472\) | 5.75872i | 0.265067i | ||||||||
\(473\) | −9.02052 | −0.414764 | ||||||||
\(474\) | − | 8.63090i | − | 0.396430i | ||||||
\(475\) | 0.282314 | + | 0.533046i | 0.0129535 | + | 0.0244578i | ||||
\(476\) | − | 2.24846i | − | 0.103058i | ||||||
\(477\) | − | 25.9783i | − | 1.18946i | ||||||
\(478\) | 24.8710i | 1.13757i | ||||||||
\(479\) | 17.5103i | 0.800064i | 0.916501 | + | 0.400032i | \(0.131001\pi\) | ||||
−0.916501 | + | 0.400032i | \(0.868999\pi\) | |||||||
\(480\) | −0.290725 | − | 1.17009i | −0.0132697 | − | 0.0534069i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 2.95055i | − | 0.134394i | ||||||
\(483\) | −1.90110 | −0.0865032 | ||||||||
\(484\) | −9.34244 | −0.424656 | ||||||||
\(485\) | 17.1617 | − | 4.26406i | 0.779272 | − | 0.193621i | ||||
\(486\) | − | 12.7226i | − | 0.577109i | ||||||
\(487\) | −38.5318 | −1.74604 | −0.873022 | − | 0.487681i | \(-0.837843\pi\) | ||||
−0.873022 | + | 0.487681i | \(0.837843\pi\) | |||||||
\(488\) | −7.06278 | −0.319717 | ||||||||
\(489\) | 9.06997i | 0.410158i | ||||||||
\(490\) | 14.0989 | − | 3.50307i | 0.636923 | − | 0.158253i | ||||
\(491\) | −6.82377 | −0.307952 | −0.153976 | − | 0.988075i | \(-0.549208\pi\) | ||||
−0.153976 | + | 0.988075i | \(0.549208\pi\) | |||||||
\(492\) | −0.241276 | −0.0108776 | ||||||||
\(493\) | − | 23.0205i | − | 1.03679i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.58864 | + | 26.5174i | 0.296137 | + | 1.19187i | ||||
\(496\) | 9.66701i | 0.434062i | ||||||||
\(497\) | − | 5.80430i | − | 0.260358i | ||||||
\(498\) | 0.191828i | 0.00859602i | ||||||||
\(499\) | − | 9.57918i | − | 0.428823i | −0.976743 | − | 0.214412i | \(-0.931217\pi\) | ||
0.976743 | − | 0.214412i | \(-0.0687834\pi\) | |||||||
\(500\) | 8.32684 | − | 7.46081i | 0.372388 | − | 0.333658i | ||||
\(501\) | 9.76979i | 0.436482i | ||||||||
\(502\) | 16.5597 | 0.739096 | ||||||||
\(503\) | − | 16.6742i | − | 0.743466i | −0.928340 | − | 0.371733i | \(-0.878764\pi\) | ||
0.928340 | − | 0.371733i | \(-0.121236\pi\) | |||||||
\(504\) | −1.92162 | −0.0855959 | ||||||||
\(505\) | −13.3268 | + | 3.31124i | −0.593037 | + | 0.147348i | ||||
\(506\) | 22.4208 | 0.996727 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.1773i | 0.540279i | ||||||||
\(509\) | 23.6598i | 1.04870i | 0.851502 | + | 0.524352i | \(0.175692\pi\) | ||||
−0.851502 | + | 0.524352i | \(0.824308\pi\) | |||||||
\(510\) | −3.70928 | + | 0.921622i | −0.164249 | + | 0.0408101i | ||||
\(511\) | −4.78434 | −0.211647 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.371370 | −0.0163964 | ||||||||
\(514\) | 0.523590i | 0.0230946i | ||||||||
\(515\) | −9.53305 | − | 38.3679i | −0.420076 | − | 1.69069i | ||||
\(516\) | −1.07838 | −0.0474729 | ||||||||
\(517\) | − | 21.2401i | − | 0.934136i | ||||||
\(518\) | 4.93495 | 0.216829 | ||||||||
\(519\) | −5.55583 | −0.243874 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.0472 | −1.05353 | −0.526763 | − | 0.850012i | \(-0.676594\pi\) | ||||
−0.526763 | + | 0.850012i | \(0.676594\pi\) | |||||||
\(522\) | −19.6742 | −0.861116 | ||||||||
\(523\) | − | 23.3340i | − | 1.02033i | −0.860078 | − | 0.510163i | \(-0.829585\pi\) | ||
0.860078 | − | 0.510163i | \(-0.170415\pi\) | |||||||
\(524\) | −17.4547 | −0.762511 | ||||||||
\(525\) | 0.894960 | + | 1.68980i | 0.0390593 | + | 0.0737490i | ||||
\(526\) | 28.7815i | 1.25493i | ||||||||
\(527\) | 30.6453 | 1.33493 | ||||||||
\(528\) | −2.43188 | −0.105834 | ||||||||
\(529\) | −1.71154 | −0.0744149 | ||||||||
\(530\) | 5.17009 | + | 20.8082i | 0.224574 | + | 0.903849i | ||||
\(531\) | − | 15.6020i | − | 0.677068i | ||||||
\(532\) | 0.0855657i | 0.00370974i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1.95774 | 0.0847197 | ||||||||
\(535\) | 0.290725 | + | 1.17009i | 0.0125691 | + | 0.0505873i | ||||
\(536\) | −2.92162 | −0.126195 | ||||||||
\(537\) | 0.680346i | 0.0293591i | ||||||||
\(538\) | 10.0566 | 0.433572 | ||||||||
\(539\) | − | 29.3028i | − | 1.26216i | ||||||
\(540\) | 1.65983 | + | 6.68035i | 0.0714276 | + | 0.287476i | ||||
\(541\) | 33.1494i | 1.42520i | 0.701569 | + | 0.712602i | \(0.252483\pi\) | ||||
−0.701569 | + | 0.712602i | \(0.747517\pi\) | |||||||
\(542\) | 18.1256i | 0.778559i | ||||||||
\(543\) | − | 1.28458i | − | 0.0551267i | ||||||
\(544\) | 3.17009i | 0.135916i | ||||||||
\(545\) | 5.94214 | + | 23.9155i | 0.254533 | + | 1.02443i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.6742i | 1.86737i | 0.358090 | + | 0.933687i | \(0.383428\pi\) | ||||
−0.358090 | + | 0.933687i | \(0.616572\pi\) | |||||||
\(548\) | −9.35350 | −0.399562 | ||||||||
\(549\) | 19.1350 | 0.816662 | ||||||||
\(550\) | −10.5548 | − | 19.9288i | −0.450058 | − | 0.849767i | ||||
\(551\) | 0.876050i | 0.0373210i | ||||||||
\(552\) | 2.68035 | 0.114083 | ||||||||
\(553\) | 11.3535 | 0.482800 | ||||||||
\(554\) | − | 24.7165i | − | 1.05010i | ||||||
\(555\) | −2.02279 | − | 8.14116i | −0.0858625 | − | 0.345573i | ||||
\(556\) | 2.64423 | 0.112140 | ||||||||
\(557\) | −22.3991 | −0.949079 | −0.474540 | − | 0.880234i | \(-0.657385\pi\) | ||||
−0.474540 | + | 0.880234i | \(0.657385\pi\) | |||||||
\(558\) | − | 26.1906i | − | 1.10874i | ||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.53919 | − | 0.382433i | 0.0650426 | − | 0.0161608i | ||||
\(561\) | 7.70928i | 0.325486i | ||||||||
\(562\) | 22.9854i | 0.969583i | ||||||||
\(563\) | 0.241276i | 0.0101686i | 0.999987 | + | 0.00508429i | \(0.00161839\pi\) | ||||
−0.999987 | + | 0.00508429i | \(0.998382\pi\) | |||||||
\(564\) | − | 2.53919i | − | 0.106919i | ||||||
\(565\) | 7.54864 | + | 30.3812i | 0.317574 | + | 1.27815i | ||||
\(566\) | − | 18.0989i | − | 0.760753i | ||||||
\(567\) | 4.58759 | 0.192661 | ||||||||
\(568\) | 8.18342i | 0.343369i | ||||||||
\(569\) | 27.1711 | 1.13907 | 0.569537 | − | 0.821966i | \(-0.307123\pi\) | ||||
0.569537 | + | 0.821966i | \(0.307123\pi\) | |||||||
\(570\) | 0.141157 | − | 0.0350725i | 0.00591242 | − | 0.00146902i | ||||
\(571\) | −2.25461 | −0.0943524 | −0.0471762 | − | 0.998887i | \(-0.515022\pi\) | ||||
−0.0471762 | + | 0.998887i | \(0.515022\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 5.97721i | − | 0.249702i | ||||||
\(574\) | − | 0.317387i | − | 0.0132475i | ||||||
\(575\) | 11.6332 | + | 21.9649i | 0.485137 | + | 0.916001i | ||||
\(576\) | 2.70928 | 0.112886 | ||||||||
\(577\) | −7.86481 | −0.327416 | −0.163708 | − | 0.986509i | \(-0.552346\pi\) | ||||
−0.163708 | + | 0.986509i | \(0.552346\pi\) | |||||||
\(578\) | −6.95055 | −0.289105 | ||||||||
\(579\) | 7.54864i | 0.313711i | ||||||||
\(580\) | 15.7587 | − | 3.91548i | 0.654345 | − | 0.162581i | ||||
\(581\) | −0.252340 | −0.0104688 | ||||||||
\(582\) | − | 4.26406i | − | 0.176751i | ||||||
\(583\) | 43.2472 | 1.79112 | ||||||||
\(584\) | 6.74539 | 0.279126 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.8443 | 0.737141 | ||||||||
\(587\) | 11.2039 | 0.462436 | 0.231218 | − | 0.972902i | \(-0.425729\pi\) | ||||
0.231218 | + | 0.972902i | \(0.425729\pi\) | |||||||
\(588\) | − | 3.50307i | − | 0.144464i | ||||||
\(589\) | −1.16621 | −0.0480529 | ||||||||
\(590\) | 3.10504 | + | 12.4969i | 0.127832 | + | 0.514490i | ||||
\(591\) | 4.68753i | 0.192819i | ||||||||
\(592\) | −6.95774 | −0.285961 | ||||||||
\(593\) | −13.4186 | −0.551034 | −0.275517 | − | 0.961296i | \(-0.588849\pi\) | ||||
−0.275517 | + | 0.961296i | \(0.588849\pi\) | |||||||
\(594\) | 13.8843 | 0.569679 | ||||||||
\(595\) | −1.21235 | − | 4.87936i | −0.0497014 | − | 0.200034i | ||||
\(596\) | 9.23513i | 0.378286i | ||||||||
\(597\) | 11.6020i | 0.474837i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.5753 | −1.20841 | −0.604207 | − | 0.796827i | \(-0.706510\pi\) | ||||
−0.604207 | + | 0.796827i | \(0.706510\pi\) | |||||||
\(600\) | −1.26180 | − | 2.38243i | −0.0515126 | − | 0.0972624i | ||||
\(601\) | 24.9832 | 1.01909 | 0.509543 | − | 0.860445i | \(-0.329815\pi\) | ||||
0.509543 | + | 0.860445i | \(0.329815\pi\) | |||||||
\(602\) | − | 1.41855i | − | 0.0578158i | ||||||
\(603\) | 7.91548 | 0.322343 | ||||||||
\(604\) | 9.42574i | 0.383528i | ||||||||
\(605\) | −20.2739 | + | 5.03734i | −0.824251 | + | 0.204797i | ||||
\(606\) | 3.31124i | 0.134510i | ||||||||
\(607\) | 10.3919i | 0.421794i | 0.977508 | + | 0.210897i | \(0.0676384\pi\) | ||||
−0.977508 | + | 0.210897i | \(0.932362\pi\) | |||||||
\(608\) | − | 0.120638i | − | 0.00489252i | ||||||
\(609\) | 2.77715i | 0.112536i | ||||||||
\(610\) | −15.3268 | + | 3.80817i | −0.620566 | + | 0.154188i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | − | 8.58864i | − | 0.347175i | ||||||
\(613\) | −30.5285 | −1.23303 | −0.616517 | − | 0.787341i | \(-0.711457\pi\) | ||||
−0.616517 | + | 0.787341i | \(0.711457\pi\) | |||||||
\(614\) | −3.44521 | −0.139037 | ||||||||
\(615\) | −0.523590 | + | 0.130094i | −0.0211132 | + | 0.00524588i | ||||
\(616\) | − | 3.19902i | − | 0.128892i | ||||||
\(617\) | −7.30283 | −0.294001 | −0.147000 | − | 0.989136i | \(-0.546962\pi\) | ||||
−0.147000 | + | 0.989136i | \(0.546962\pi\) | |||||||
\(618\) | −9.53305 | −0.383475 | ||||||||
\(619\) | − | 24.5103i | − | 0.985151i | −0.870270 | − | 0.492575i | \(-0.836056\pi\) | ||
0.870270 | − | 0.492575i | \(-0.163944\pi\) | |||||||
\(620\) | 5.21235 | + | 20.9783i | 0.209333 | + | 0.842507i | ||||
\(621\) | −15.3028 | −0.614082 | ||||||||
\(622\) | 17.8238 | 0.714668 | ||||||||
\(623\) | 2.57531i | 0.103177i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.0472 | − | 20.6803i | 0.561887 | − | 0.827214i | ||||
\(626\) | 32.2245i | 1.28795i | ||||||||
\(627\) | − | 0.293378i | − | 0.0117164i | ||||||
\(628\) | − | 5.77205i | − | 0.230330i | ||||||
\(629\) | 22.0566i | 0.879456i | ||||||||
\(630\) | −4.17009 | + | 1.03612i | −0.166140 | + | 0.0412799i | ||||
\(631\) | 3.07838i | 0.122548i | 0.998121 | + | 0.0612741i | \(0.0195164\pi\) | ||||
−0.998121 | + | 0.0612741i | \(0.980484\pi\) | |||||||
\(632\) | −16.0072 | −0.636732 | ||||||||
\(633\) | − | 3.01333i | − | 0.119769i | ||||||
\(634\) | 1.90602 | 0.0756979 | ||||||||
\(635\) | 6.56585 | + | 26.4257i | 0.260558 | + | 1.04867i | ||||
\(636\) | 5.17009 | 0.205007 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 32.7526i | − | 1.29669i | ||||||
\(639\) | − | 22.1711i | − | 0.877076i | ||||||
\(640\) | −2.17009 | + | 0.539189i | −0.0857802 | + | 0.0213133i | ||||
\(641\) | 2.46800 | 0.0974801 | 0.0487401 | − | 0.998811i | \(-0.484479\pi\) | ||||
0.0487401 | + | 0.998811i | \(0.484479\pi\) | |||||||
\(642\) | 0.290725 | 0.0114740 | ||||||||
\(643\) | −18.8215 | −0.742248 | −0.371124 | − | 0.928583i | \(-0.621027\pi\) | ||||
−0.371124 | + | 0.928583i | \(0.621027\pi\) | |||||||
\(644\) | 3.52586i | 0.138938i | ||||||||
\(645\) | −2.34017 | + | 0.581449i | −0.0921442 | + | 0.0228945i | ||||
\(646\) | −0.382433 | −0.0150466 | ||||||||
\(647\) | 11.7031i | 0.460098i | 0.973179 | + | 0.230049i | \(0.0738886\pi\) | ||||
−0.973179 | + | 0.230049i | \(0.926111\pi\) | |||||||
\(648\) | −6.46800 | −0.254087 | ||||||||
\(649\) | 25.9733 | 1.01954 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.69699 | −0.144896 | ||||||||
\(652\) | 16.8215 | 0.658781 | ||||||||
\(653\) | − | 14.6937i | − | 0.575008i | −0.957779 | − | 0.287504i | \(-0.907175\pi\) | ||
0.957779 | − | 0.287504i | \(-0.0928255\pi\) | |||||||
\(654\) | 5.94214 | 0.232356 | ||||||||
\(655\) | −37.8781 | + | 9.41136i | −1.48002 | + | 0.367732i | ||||
\(656\) | 0.447480i | 0.0174712i | ||||||||
\(657\) | −18.2751 | −0.712981 | ||||||||
\(658\) | 3.34017 | 0.130213 | ||||||||
\(659\) | −18.7877 | −0.731863 | −0.365932 | − | 0.930642i | \(-0.619250\pi\) | ||||
−0.365932 | + | 0.930642i | \(0.619250\pi\) | |||||||
\(660\) | −5.27739 | + | 1.31124i | −0.205422 | + | 0.0510401i | ||||
\(661\) | 5.84202i | 0.227228i | 0.993525 | + | 0.113614i | \(0.0362428\pi\) | ||||
−0.993525 | + | 0.113614i | \(0.963757\pi\) | |||||||
\(662\) | 0.711543i | 0.0276549i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.355771 | 0.0138066 | ||||||||
\(665\) | 0.0461361 | + | 0.185685i | 0.00178908 | + | 0.00720055i | ||||
\(666\) | 18.8504 | 0.730439 | ||||||||
\(667\) | 36.0989i | 1.39775i | ||||||||
\(668\) | 18.1194 | 0.701061 | ||||||||
\(669\) | − | 13.3230i | − | 0.515096i | ||||||
\(670\) | −6.34017 | + | 1.57531i | −0.244942 | + | 0.0608594i | ||||
\(671\) | 31.8550i | 1.22975i | ||||||||
\(672\) | − | 0.382433i | − | 0.0147527i | ||||||
\(673\) | − | 40.8925i | − | 1.57629i | −0.615489 | − | 0.788145i | \(-0.711042\pi\) | ||
0.615489 | − | 0.788145i | \(-0.288958\pi\) | |||||||
\(674\) | 9.85043i | 0.379424i | ||||||||
\(675\) | 7.20394 | + | 13.6020i | 0.277280 | + | 0.523540i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 28.2700i | − | 1.08651i | −0.839569 | − | 0.543253i | \(-0.817193\pi\) | ||
0.839569 | − | 0.543253i | \(-0.182807\pi\) | |||||||
\(678\) | 7.54864 | 0.289904 | ||||||||
\(679\) | 5.60916 | 0.215260 | ||||||||
\(680\) | 1.70928 | + | 6.87936i | 0.0655477 | + | 0.263811i | ||||
\(681\) | 15.4719i | 0.592884i | ||||||||
\(682\) | 43.6007 | 1.66956 | ||||||||
\(683\) | 41.5052 | 1.58815 | 0.794075 | − | 0.607819i | \(-0.207955\pi\) | ||||
0.794075 | + | 0.607819i | \(0.207955\pi\) | |||||||
\(684\) | 0.326842i | 0.0124971i | ||||||||
\(685\) | −20.2979 | + | 5.04331i | −0.775543 | + | 0.192695i | ||||
\(686\) | 9.57304 | 0.365500 | ||||||||
\(687\) | 1.02439 | 0.0390831 | ||||||||
\(688\) | 2.00000i | 0.0762493i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 5.81658 | − | 1.44521i | 0.221434 | − | 0.0550183i | ||||
\(691\) | − | 24.1084i | − | 0.917125i | −0.888662 | − | 0.458562i | \(-0.848365\pi\) | ||
0.888662 | − | 0.458562i | \(-0.151635\pi\) | |||||||
\(692\) | 10.3041i | 0.391701i | ||||||||
\(693\) | 8.66701i | 0.329233i | ||||||||
\(694\) | 25.5330i | 0.969221i | ||||||||
\(695\) | 5.73820 | − | 1.42574i | 0.217663 | − | 0.0540813i | ||||
\(696\) | − | 3.91548i | − | 0.148416i | ||||||
\(697\) | 1.41855 | 0.0537314 | ||||||||
\(698\) | 18.0566i | 0.683454i | ||||||||
\(699\) | 11.9961 | 0.453735 | ||||||||
\(700\) | 3.13397 | − | 1.65983i | 0.118453 | − | 0.0627356i | ||||
\(701\) | 14.1822 | 0.535654 | 0.267827 | − | 0.963467i | \(-0.413694\pi\) | ||||
0.267827 | + | 0.963467i | \(0.413694\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.839369i | − | 0.0316574i | ||||||
\(704\) | 4.51026i | 0.169987i | ||||||||
\(705\) | −1.36910 | − | 5.51026i | −0.0515634 | − | 0.207528i | ||||
\(706\) | 14.6465 | 0.551228 | ||||||||
\(707\) | −4.35577 | −0.163816 | ||||||||
\(708\) | 3.10504 | 0.116695 | ||||||||
\(709\) | − | 46.4957i | − | 1.74618i | −0.487556 | − | 0.873091i | \(-0.662112\pi\) | ||
0.487556 | − | 0.873091i | \(-0.337888\pi\) | |||||||
\(710\) | 4.41241 | + | 17.7587i | 0.165595 | + | 0.666473i | ||||
\(711\) | 43.3679 | 1.62642 | ||||||||
\(712\) | − | 3.63090i | − | 0.136074i | ||||||
\(713\) | −48.0554 | −1.79969 | ||||||||
\(714\) | −1.21235 | −0.0453709 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.26180 | 0.0471555 | ||||||||
\(717\) | 13.4101 | 0.500811 | ||||||||
\(718\) | 13.4186i | 0.500776i | ||||||||
\(719\) | −12.7214 | −0.474428 | −0.237214 | − | 0.971457i | \(-0.576234\pi\) | ||||
−0.237214 | + | 0.971457i | \(0.576234\pi\) | |||||||
\(720\) | 5.87936 | − | 1.46081i | 0.219111 | − | 0.0544412i | ||||
\(721\) | − | 12.5402i | − | 0.467023i | ||||||
\(722\) | −18.9854 | −0.706565 | ||||||||
\(723\) | −1.59090 | −0.0591664 | ||||||||
\(724\) | −2.38243 | −0.0885424 | ||||||||
\(725\) | 32.0866 | − | 16.9939i | 1.19167 | − | 0.631136i | ||||
\(726\) | 5.03734i | 0.186953i | ||||||||
\(727\) | 13.2595i | 0.491769i | 0.969299 | + | 0.245884i | \(0.0790783\pi\) | ||||
−0.969299 | + | 0.245884i | \(0.920922\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.5441 | 0.464597 | ||||||||
\(730\) | 14.6381 | − | 3.63704i | 0.541780 | − | 0.134613i | ||||
\(731\) | 6.34017 | 0.234500 | ||||||||
\(732\) | 3.80817i | 0.140754i | ||||||||
\(733\) | −31.5848 | −1.16661 | −0.583305 | − | 0.812253i | \(-0.698241\pi\) | ||||
−0.583305 | + | 0.812253i | \(0.698241\pi\) | |||||||
\(734\) | − | 21.5441i | − | 0.795208i | ||||||
\(735\) | −1.88882 | − | 7.60197i | −0.0696701 | − | 0.280403i | ||||
\(736\) | − | 4.97107i | − | 0.183236i | ||||||
\(737\) | 13.1773i | 0.485391i | ||||||||
\(738\) | − | 1.21235i | − | 0.0446271i | ||||||
\(739\) | 2.83218i | 0.104183i | 0.998642 | + | 0.0520917i | \(0.0165888\pi\) | ||||
−0.998642 | + | 0.0520917i | \(0.983411\pi\) | |||||||
\(740\) | −15.0989 | + | 3.75154i | −0.555046 | + | 0.137909i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.80098i | 0.249672i | ||||||||
\(743\) | −20.8020 | −0.763152 | −0.381576 | − | 0.924337i | \(-0.624619\pi\) | ||||
−0.381576 | + | 0.924337i | \(0.624619\pi\) | |||||||
\(744\) | 5.21235 | 0.191094 | ||||||||
\(745\) | 4.97948 | + | 20.0410i | 0.182434 | + | 0.734247i | ||||
\(746\) | − | 21.3340i | − | 0.781094i | ||||||
\(747\) | −0.963883 | −0.0352666 | ||||||||
\(748\) | 14.2979 | 0.522783 | ||||||||
\(749\) | 0.382433i | 0.0139738i | ||||||||
\(750\) | −4.02279 | − | 4.48974i | −0.146891 | − | 0.163942i | ||||
\(751\) | −36.2823 | −1.32396 | −0.661980 | − | 0.749521i | \(-0.730284\pi\) | ||||
−0.661980 | + | 0.749521i | \(0.730284\pi\) | |||||||
\(752\) | −4.70928 | −0.171730 | ||||||||
\(753\) | − | 8.92881i | − | 0.325384i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.08225 | + | 20.4547i | 0.184962 | + | 0.744422i | ||||
\(756\) | 2.18342i | 0.0794101i | ||||||||
\(757\) | − | 40.8687i | − | 1.48540i | −0.669626 | − | 0.742699i | \(-0.733545\pi\) | ||
0.669626 | − | 0.742699i | \(-0.266455\pi\) | |||||||
\(758\) | 8.11223i | 0.294649i | ||||||||
\(759\) | − | 12.0891i | − | 0.438805i | ||||||
\(760\) | −0.0650468 | − | 0.261795i | −0.00235949 | − | 0.00949631i | ||||
\(761\) | − | 35.6225i | − | 1.29131i | −0.763627 | − | 0.645657i | \(-0.776584\pi\) | ||
0.763627 | − | 0.645657i | \(-0.223416\pi\) | |||||||
\(762\) | 6.56585 | 0.237856 | ||||||||
\(763\) | 7.81658i | 0.282979i | ||||||||
\(764\) | −11.0856 | −0.401062 | ||||||||
\(765\) | −4.63090 | − | 18.6381i | −0.167430 | − | 0.673861i | ||||
\(766\) | 24.9399 | 0.901114 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.539189i | 0.0194563i | ||||||||
\(769\) | − | 3.36910i | − | 0.121493i | −0.998153 | − | 0.0607465i | \(-0.980652\pi\) | ||
0.998153 | − | 0.0607465i | \(-0.0193481\pi\) | |||||||
\(770\) | −1.72487 | − | 6.94214i | −0.0621601 | − | 0.250177i | ||||
\(771\) | 0.282314 | 0.0101673 | ||||||||
\(772\) | 14.0000 | 0.503871 | ||||||||
\(773\) | 11.0794 | 0.398499 | 0.199250 | − | 0.979949i | \(-0.436150\pi\) | ||||
0.199250 | + | 0.979949i | \(0.436150\pi\) | |||||||
\(774\) | − | 5.41855i | − | 0.194766i | ||||||
\(775\) | 22.6225 | + | 42.7142i | 0.812624 | + | 1.53434i | ||||
\(776\) | −7.90829 | −0.283891 | ||||||||
\(777\) | − | 2.66087i | − | 0.0954582i | ||||||
\(778\) | −13.5330 | −0.485183 | ||||||||
\(779\) | −0.0539832 | −0.00193415 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.9093 | 1.32072 | ||||||||
\(782\) | −15.7587 | −0.563531 | ||||||||
\(783\) | 22.3545i | 0.798886i | ||||||||
\(784\) | −6.49693 | −0.232033 | ||||||||
\(785\) | −3.11223 | − | 12.5259i | −0.111080 | − | 0.447067i | ||||
\(786\) | 9.41136i | 0.335692i | ||||||||
\(787\) | 5.67089 | 0.202145 | 0.101073 | − | 0.994879i | \(-0.467773\pi\) | ||||
0.101073 | + | 0.994879i | \(0.467773\pi\) | |||||||
\(788\) | 8.69368 | 0.309699 | ||||||||
\(789\) | 15.5187 | 0.552479 | ||||||||
\(790\) | −34.7370 | + | 8.63090i | −1.23589 | + | 0.307074i | ||||
\(791\) | 9.92986i | 0.353065i | ||||||||
\(792\) | − | 12.2195i | − | 0.434202i | ||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −4.59478 | −0.163063 | ||||||||
\(795\) | 11.2195 | − | 2.78765i | 0.397916 | − | 0.0988679i | ||||
\(796\) | 21.5174 | 0.762666 | ||||||||
\(797\) | − | 27.3424i | − | 0.968519i | −0.874924 | − | 0.484259i | \(-0.839089\pi\) | ||
0.874924 | − | 0.484259i | \(-0.160911\pi\) | |||||||
\(798\) | 0.0461361 | 0.00163320 | ||||||||
\(799\) | 14.9288i | 0.528143i | ||||||||
\(800\) | −4.41855 | + | 2.34017i | −0.156219 | + | 0.0827376i | ||||
\(801\) | 9.83710i | 0.347577i | ||||||||
\(802\) | 29.7031i | 1.04885i | ||||||||
\(803\) | − | 30.4235i | − | 1.07362i | ||||||
\(804\) | 1.57531i | 0.0555568i | ||||||||
\(805\) | 1.90110 | + | 7.65142i | 0.0670051 | + | 0.269677i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 5.42243i | − | 0.190878i | ||||||
\(808\) | 6.14116 | 0.216045 | ||||||||
\(809\) | 5.02893 | 0.176808 | 0.0884039 | − | 0.996085i | \(-0.471823\pi\) | ||||
0.0884039 | + | 0.996085i | \(0.471823\pi\) | |||||||
\(810\) | −14.0361 | + | 3.48747i | −0.493179 | + | 0.122537i | ||||
\(811\) | 47.3390i | 1.66230i | 0.556052 | + | 0.831148i | \(0.312316\pi\) | ||||
−0.556052 | + | 0.831148i | \(0.687684\pi\) | |||||||
\(812\) | 5.15061 | 0.180751 | ||||||||
\(813\) | 9.77310 | 0.342758 | ||||||||
\(814\) | 31.3812i | 1.09991i | ||||||||
\(815\) | 36.5041 | − | 9.06997i | 1.27868 | − | 0.317707i | ||||
\(816\) | 1.70928 | 0.0598366 | ||||||||
\(817\) | −0.241276 | −0.00844119 | ||||||||
\(818\) | − | 10.3112i | − | 0.360524i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.241276 | + | 0.971071i | 0.00842573 | + | 0.0339113i | ||||
\(821\) | − | 20.6816i | − | 0.721792i | −0.932606 | − | 0.360896i | \(-0.882471\pi\) | ||
0.932606 | − | 0.360896i | \(-0.117529\pi\) | |||||||
\(822\) | 5.04331i | 0.175905i | ||||||||
\(823\) | − | 19.8371i | − | 0.691478i | −0.938331 | − | 0.345739i | \(-0.887628\pi\) | ||
0.938331 | − | 0.345739i | \(-0.112372\pi\) | |||||||
\(824\) | 17.6803i | 0.615924i | ||||||||
\(825\) | −10.7454 | + | 5.69102i | −0.374107 | + | 0.198136i | ||||
\(826\) | 4.08452i | 0.142119i | ||||||||
\(827\) | 39.6730 | 1.37956 | 0.689782 | − | 0.724017i | \(-0.257706\pi\) | ||||
0.689782 | + | 0.724017i | \(0.257706\pi\) | |||||||
\(828\) | 13.4680i | 0.468045i | ||||||||
\(829\) | −25.3874 | −0.881739 | −0.440870 | − | 0.897571i | \(-0.645330\pi\) | ||||
−0.440870 | + | 0.897571i | \(0.645330\pi\) | |||||||
\(830\) | 0.772055 | − | 0.191828i | 0.0267984 | − | 0.00665845i | ||||
\(831\) | −13.3268 | −0.462303 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.5958i | 0.713603i | ||||||||
\(834\) | − | 1.42574i | − | 0.0493693i | ||||||
\(835\) | 39.3207 | − | 9.76979i | 1.36075 | − | 0.338097i | ||||
\(836\) | −0.544109 | −0.0188184 | ||||||||
\(837\) | −29.7587 | −1.02861 | ||||||||
\(838\) | 38.0905 | 1.31581 | ||||||||
\(839\) | − | 23.0277i | − | 0.795005i | −0.917601 | − | 0.397502i | \(-0.869877\pi\) | ||
0.917601 | − | 0.397502i | \(-0.130123\pi\) | |||||||
\(840\) | −0.206204 | − | 0.829914i | −0.00711471 | − | 0.0286347i | ||||
\(841\) | 23.7337 | 0.818402 | ||||||||
\(842\) | 26.7103i | 0.920498i | ||||||||
\(843\) | 12.3935 | 0.426855 | ||||||||
\(844\) | −5.58864 | −0.192369 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.7587 | 0.438654 | ||||||||
\(847\) | −6.62636 | −0.227685 | ||||||||
\(848\) | − | 9.58864i | − | 0.329275i | ||||||
\(849\) | −9.75872 | −0.334919 | ||||||||
\(850\) | 7.41855 | + | 14.0072i | 0.254454 | + | 0.480443i | ||||
\(851\) | − | 34.5874i | − | 1.18564i | ||||||
\(852\) | 4.41241 | 0.151167 | ||||||||
\(853\) | 13.7047 | 0.469241 | 0.234621 | − | 0.972087i | \(-0.424615\pi\) | ||||
0.234621 | + | 0.972087i | \(0.424615\pi\) | |||||||
\(854\) | −5.00946 | −0.171420 | ||||||||
\(855\) | 0.176230 | + | 0.709275i | 0.00602692 | + | 0.0242567i | ||||
\(856\) | − | 0.539189i | − | 0.0184291i | ||||||
\(857\) | 17.8648i | 0.610250i | 0.952312 | + | 0.305125i | \(0.0986983\pi\) | ||||
−0.952312 | + | 0.305125i | \(0.901302\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.7187 | −0.468077 | −0.234039 | − | 0.972227i | \(-0.575194\pi\) | ||||
−0.234039 | + | 0.972227i | \(0.575194\pi\) | |||||||
\(860\) | 1.07838 | + | 4.34017i | 0.0367724 | + | 0.147999i | ||||
\(861\) | −0.171131 | −0.00583214 | ||||||||
\(862\) | 20.7187i | 0.705683i | ||||||||
\(863\) | −19.9383 | −0.678706 | −0.339353 | − | 0.940659i | \(-0.610208\pi\) | ||||
−0.339353 | + | 0.940659i | \(0.610208\pi\) | |||||||
\(864\) | − | 3.07838i | − | 0.104729i | ||||||
\(865\) | 5.55583 | + | 22.3607i | 0.188904 | + | 0.760286i | ||||
\(866\) | − | 15.8576i | − | 0.538864i | ||||||
\(867\) | 3.74766i | 0.127277i | ||||||||
\(868\) | 6.85658i | 0.232727i | ||||||||
\(869\) | 72.1966i | 2.44910i | ||||||||
\(870\) | −2.11118 | − | 8.49693i | −0.0715758 | − | 0.288073i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 11.0205i | − | 0.373202i | ||||||
\(873\) | 21.4257 | 0.725151 | ||||||||
\(874\) | 0.599701 | 0.0202852 | ||||||||
\(875\) | 5.90602 | − | 5.29177i | 0.199660 | − | 0.178894i | ||||
\(876\) | − | 3.63704i | − | 0.122884i | ||||||
\(877\) | 21.6163 | 0.729932 | 0.364966 | − | 0.931021i | \(-0.381081\pi\) | ||||
0.364966 | + | 0.931021i | \(0.381081\pi\) | |||||||
\(878\) | 9.73925 | 0.328684 | ||||||||
\(879\) | − | 9.62144i | − | 0.324523i | ||||||
\(880\) | 2.43188 | + | 9.78765i | 0.0819787 | + | 0.329942i | ||||
\(881\) | 7.99386 | 0.269320 | 0.134660 | − | 0.990892i | \(-0.457006\pi\) | ||||
0.134660 | + | 0.990892i | \(0.457006\pi\) | |||||||
\(882\) | 17.6020 | 0.592689 | ||||||||
\(883\) | 26.2713i | 0.884098i | 0.896991 | + | 0.442049i | \(0.145748\pi\) | ||||
−0.896991 | + | 0.442049i | \(0.854252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.73820 | − | 1.67420i | 0.226502 | − | 0.0562777i | ||||
\(886\) | − | 9.23060i | − | 0.310108i | ||||||
\(887\) | 17.1627i | 0.576268i | 0.957590 | + | 0.288134i | \(0.0930348\pi\) | ||||
−0.957590 | + | 0.288134i | \(0.906965\pi\) | |||||||
\(888\) | 3.75154i | 0.125893i | ||||||||
\(889\) | 8.63704i | 0.289677i | ||||||||
\(890\) | −1.95774 | − | 7.87936i | −0.0656236 | − | 0.264117i | ||||
\(891\) | 29.1724i | 0.977311i | ||||||||
\(892\) | −24.7093 | −0.827328 | ||||||||
\(893\) | − | 0.568118i | − | 0.0190114i | ||||||
\(894\) | 4.97948 | 0.166539 | ||||||||
\(895\) | 2.73820 | − | 0.680346i | 0.0915281 | − | 0.0227415i | ||||
\(896\) | −0.709275 | −0.0236952 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.92389i | 0.0975715i | ||||||||
\(899\) | 70.1999i | 2.34130i | ||||||||
\(900\) | 11.9711 | − | 6.34017i | 0.399036 | − | 0.211339i | ||||
\(901\) | −30.3968 | −1.01266 | ||||||||
\(902\) | 2.01825 | 0.0672004 | ||||||||
\(903\) | −0.764867 | −0.0254532 | ||||||||
\(904\) | − | 14.0000i | − | 0.465633i | ||||||
\(905\) | −5.17009 | + | 1.28458i | −0.171859 | + | 0.0427009i | ||||
\(906\) | 5.08225 | 0.168847 | ||||||||
\(907\) | − | 16.4136i | − | 0.545006i | −0.962155 | − | 0.272503i | \(-0.912149\pi\) | ||
0.962155 | − | 0.272503i | \(-0.0878514\pi\) | |||||||
\(908\) | 28.6947 | 0.952268 | ||||||||
\(909\) | −16.6381 | −0.551850 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.52359 | −0.149873 | −0.0749366 | − | 0.997188i | \(-0.523875\pi\) | ||||
−0.0749366 | + | 0.997188i | \(0.523875\pi\) | |||||||
\(912\) | −0.0650468 | −0.00215391 | ||||||||
\(913\) | − | 1.60462i | − | 0.0531052i | ||||||
\(914\) | −11.6526 | −0.385435 | ||||||||
\(915\) | 2.05332 | + | 8.26406i | 0.0678808 | + | 0.273201i | ||||
\(916\) | − | 1.89988i | − | 0.0627738i | ||||||
\(917\) | −12.3802 | −0.408829 | ||||||||
\(918\) | −9.75872 | −0.322086 | ||||||||
\(919\) | 7.64301 | 0.252120 | 0.126060 | − | 0.992023i | \(-0.459767\pi\) | ||||
0.126060 | + | 0.992023i | \(0.459767\pi\) | |||||||
\(920\) | −2.68035 | − | 10.7877i | −0.0883684 | − | 0.355658i | ||||
\(921\) | 1.85762i | 0.0612107i | ||||||||
\(922\) | 30.2979i | 0.997809i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.72487 | −0.0567442 | ||||||||
\(925\) | −30.7431 | + | 16.2823i | −1.01083 | + | 0.535359i | ||||
\(926\) | −7.04331 | −0.231457 | ||||||||
\(927\) | − | 47.9009i | − | 1.57327i | ||||||
\(928\) | −7.26180 | −0.238380 | ||||||||
\(929\) | − | 59.3295i | − | 1.94654i | −0.229669 | − | 0.973269i | \(-0.573764\pi\) | ||
0.229669 | − | 0.973269i | \(-0.426236\pi\) | |||||||
\(930\) | 11.3112 | − | 2.81044i | 0.370910 | − | 0.0921579i | ||||
\(931\) | − | 0.783777i | − | 0.0256873i | ||||||
\(932\) | − | 22.2485i | − | 0.728773i | ||||||
\(933\) | − | 9.61038i | − | 0.314630i | ||||||
\(934\) | − | 3.90110i | − | 0.127648i | ||||||
\(935\) | 31.0277 | − | 7.70928i | 1.01471 | − | 0.252120i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.75872i | 0.0574550i | 0.999587 | + | 0.0287275i | \(0.00914551\pi\) | ||||
−0.999587 | + | 0.0287275i | \(0.990854\pi\) | |||||||
\(938\) | −2.07223 | −0.0676609 | ||||||||
\(939\) | 17.3751 | 0.567014 | ||||||||
\(940\) | −10.2195 | + | 2.53919i | −0.333324 | + | 0.0828192i | ||||
\(941\) | 42.2967i | 1.37883i | 0.724365 | + | 0.689416i | \(0.242133\pi\) | ||||
−0.724365 | + | 0.689416i | \(0.757867\pi\) | |||||||
\(942\) | −3.11223 | −0.101402 | ||||||||
\(943\) | −2.22446 | −0.0724382 | ||||||||
\(944\) | − | 5.75872i | − | 0.187430i | ||||||
\(945\) | 1.17727 | + | 4.73820i | 0.0382967 | + | 0.154134i | ||||
\(946\) | 9.02052 | 0.293282 | ||||||||
\(947\) | 4.83832 | 0.157224 | 0.0786122 | − | 0.996905i | \(-0.474951\pi\) | ||||
0.0786122 | + | 0.996905i | \(0.474951\pi\) | |||||||
\(948\) | 8.63090i | 0.280319i | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.282314 | − | 0.533046i | −0.00915948 | − | 0.0172943i | ||||
\(951\) | − | 1.02771i | − | 0.0333257i | ||||||
\(952\) | 2.24846i | 0.0728731i | ||||||||
\(953\) | 25.9539i | 0.840728i | 0.907356 | + | 0.420364i | \(0.138098\pi\) | ||||
−0.907356 | + | 0.420364i | \(0.861902\pi\) | |||||||
\(954\) | 25.9783i | 0.841077i | ||||||||
\(955\) | −24.0566 | + | 5.97721i | −0.778454 | + | 0.193418i | ||||
\(956\) | − | 24.8710i | − | 0.804384i | ||||||
\(957\) | −17.6598 | −0.570861 | ||||||||
\(958\) | − | 17.5103i | − | 0.565731i | ||||||
\(959\) | −6.63421 | −0.214230 | ||||||||
\(960\) | 0.290725 | + | 1.17009i | 0.00938310 | + | 0.0377644i | ||||
\(961\) | −62.4512 | −2.01455 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.46081i | 0.0470740i | ||||||||
\(964\) | 2.95055i | 0.0950309i | ||||||||
\(965\) | 30.3812 | − | 7.54864i | 0.978006 | − | 0.242999i | ||||
\(966\) | 1.90110 | 0.0611670 | ||||||||
\(967\) | 29.9939 | 0.964537 | 0.482269 | − | 0.876023i | \(-0.339813\pi\) | ||||
0.482269 | + | 0.876023i | \(0.339813\pi\) | |||||||
\(968\) | 9.34244 | 0.300277 | ||||||||
\(969\) | 0.206204i | 0.00662422i | ||||||||
\(970\) | −17.1617 | + | 4.26406i | −0.551028 | + | 0.136911i | ||||
\(971\) | 15.7286 | 0.504754 | 0.252377 | − | 0.967629i | \(-0.418788\pi\) | ||||
0.252377 | + | 0.967629i | \(0.418788\pi\) | |||||||
\(972\) | 12.7226i | 0.408078i | ||||||||
\(973\) | 1.87549 | 0.0601253 | ||||||||
\(974\) | 38.5318 | 1.23464 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.06278 | 0.226074 | ||||||||
\(977\) | −27.5441 | −0.881214 | −0.440607 | − | 0.897700i | \(-0.645237\pi\) | ||||
−0.440607 | + | 0.897700i | \(0.645237\pi\) | |||||||
\(978\) | − | 9.06997i | − | 0.290026i | ||||||
\(979\) | −16.3763 | −0.523389 | ||||||||
\(980\) | −14.0989 | + | 3.50307i | −0.450373 | + | 0.111902i | ||||
\(981\) | 29.8576i | 0.953280i | ||||||||
\(982\) | 6.82377 | 0.217755 | ||||||||
\(983\) | 18.0289 | 0.575034 | 0.287517 | − | 0.957776i | \(-0.407170\pi\) | ||||
0.287517 | + | 0.957776i | \(0.407170\pi\) | |||||||
\(984\) | 0.241276 | 0.00769161 | ||||||||
\(985\) | 18.8660 | − | 4.68753i | 0.601122 | − | 0.149357i | ||||
\(986\) | 23.0205i | 0.733123i | ||||||||
\(987\) | − | 1.80098i | − | 0.0573260i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.94214 | −0.316142 | ||||||||
\(990\) | −6.58864 | − | 26.5174i | −0.209401 | − | 0.842780i | ||||
\(991\) | 11.6332 | 0.369540 | 0.184770 | − | 0.982782i | \(-0.440846\pi\) | ||||
0.184770 | + | 0.982782i | \(0.440846\pi\) | |||||||
\(992\) | − | 9.66701i | − | 0.306928i | ||||||
\(993\) | 0.383656 | 0.0121750 | ||||||||
\(994\) | 5.80430i | 0.184101i | ||||||||
\(995\) | 46.6947 | − | 11.6020i | 1.48032 | − | 0.367807i | ||||
\(996\) | − | 0.191828i | − | 0.00607830i | ||||||
\(997\) | 28.8648i | 0.914158i | 0.889426 | + | 0.457079i | \(0.151104\pi\) | ||||
−0.889426 | + | 0.457079i | \(0.848896\pi\) | |||||||
\(998\) | 9.57918i | 0.303224i | ||||||||
\(999\) | − | 21.4186i | − | 0.677653i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 1690.2.c.b.1689.4 | 6 | ||
5.4 | even | 2 | 1690.2.c.c.1689.3 | 6 | |||
13.2 | odd | 12 | 130.2.n.a.9.2 | ✓ | 12 | ||
13.5 | odd | 4 | 1690.2.b.c.339.5 | 6 | |||
13.6 | odd | 12 | 130.2.n.a.29.5 | yes | 12 | ||
13.8 | odd | 4 | 1690.2.b.b.339.2 | 6 | |||
13.12 | even | 2 | 1690.2.c.c.1689.4 | 6 | |||
39.2 | even | 12 | 1170.2.bp.h.919.5 | 12 | |||
39.32 | even | 12 | 1170.2.bp.h.289.2 | 12 | |||
52.15 | even | 12 | 1040.2.dh.b.529.4 | 12 | |||
52.19 | even | 12 | 1040.2.dh.b.289.3 | 12 | |||
65.2 | even | 12 | 650.2.e.k.451.2 | 6 | |||
65.8 | even | 4 | 8450.2.a.bt.1.2 | 3 | |||
65.18 | even | 4 | 8450.2.a.cb.1.2 | 3 | |||
65.19 | odd | 12 | 130.2.n.a.29.2 | yes | 12 | ||
65.28 | even | 12 | 650.2.e.j.451.2 | 6 | |||
65.32 | even | 12 | 650.2.e.k.601.2 | 6 | |||
65.34 | odd | 4 | 1690.2.b.b.339.5 | 6 | |||
65.44 | odd | 4 | 1690.2.b.c.339.2 | 6 | |||
65.47 | even | 4 | 8450.2.a.ca.1.2 | 3 | |||
65.54 | odd | 12 | 130.2.n.a.9.5 | yes | 12 | ||
65.57 | even | 4 | 8450.2.a.bu.1.2 | 3 | |||
65.58 | even | 12 | 650.2.e.j.601.2 | 6 | |||
65.64 | even | 2 | inner | 1690.2.c.b.1689.3 | 6 | ||
195.119 | even | 12 | 1170.2.bp.h.919.2 | 12 | |||
195.149 | even | 12 | 1170.2.bp.h.289.5 | 12 | |||
260.19 | even | 12 | 1040.2.dh.b.289.4 | 12 | |||
260.119 | even | 12 | 1040.2.dh.b.529.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.n.a.9.2 | ✓ | 12 | 13.2 | odd | 12 | ||
130.2.n.a.9.5 | yes | 12 | 65.54 | odd | 12 | ||
130.2.n.a.29.2 | yes | 12 | 65.19 | odd | 12 | ||
130.2.n.a.29.5 | yes | 12 | 13.6 | odd | 12 | ||
650.2.e.j.451.2 | 6 | 65.28 | even | 12 | |||
650.2.e.j.601.2 | 6 | 65.58 | even | 12 | |||
650.2.e.k.451.2 | 6 | 65.2 | even | 12 | |||
650.2.e.k.601.2 | 6 | 65.32 | even | 12 | |||
1040.2.dh.b.289.3 | 12 | 52.19 | even | 12 | |||
1040.2.dh.b.289.4 | 12 | 260.19 | even | 12 | |||
1040.2.dh.b.529.3 | 12 | 260.119 | even | 12 | |||
1040.2.dh.b.529.4 | 12 | 52.15 | even | 12 | |||
1170.2.bp.h.289.2 | 12 | 39.32 | even | 12 | |||
1170.2.bp.h.289.5 | 12 | 195.149 | even | 12 | |||
1170.2.bp.h.919.2 | 12 | 195.119 | even | 12 | |||
1170.2.bp.h.919.5 | 12 | 39.2 | even | 12 | |||
1690.2.b.b.339.2 | 6 | 13.8 | odd | 4 | |||
1690.2.b.b.339.5 | 6 | 65.34 | odd | 4 | |||
1690.2.b.c.339.2 | 6 | 65.44 | odd | 4 | |||
1690.2.b.c.339.5 | 6 | 13.5 | odd | 4 | |||
1690.2.c.b.1689.3 | 6 | 65.64 | even | 2 | inner | ||
1690.2.c.b.1689.4 | 6 | 1.1 | even | 1 | trivial | ||
1690.2.c.c.1689.3 | 6 | 5.4 | even | 2 | |||
1690.2.c.c.1689.4 | 6 | 13.12 | even | 2 | |||
8450.2.a.bt.1.2 | 3 | 65.8 | even | 4 | |||
8450.2.a.bu.1.2 | 3 | 65.57 | even | 4 | |||
8450.2.a.ca.1.2 | 3 | 65.47 | even | 4 | |||
8450.2.a.cb.1.2 | 3 | 65.18 | even | 4 |