Properties

Label 201.2.p.a.80.1
Level $201$
Weight $2$
Character 201.80
Analytic conductor $1.605$
Analytic rank $0$
Dimension $20$
CM discriminant -3
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [201,2,Mod(2,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([33, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 201.p (of order \(66\), degree \(20\), 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: \(1.60499308063\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{33})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{66}]$

Embedding invariants

Embedding label 80.1
Root \(-0.327068 - 0.945001i\) of defining polynomial
Character \(\chi\) \(=\) 201.80
Dual form 201.2.p.a.98.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.30900 - 1.13425i) q^{3} +(-0.471518 + 1.94362i) q^{4} +(-0.816487 + 2.03949i) q^{7} +(0.426945 + 2.96946i) q^{9} +O(q^{10})\) \(q+(-1.30900 - 1.13425i) q^{3} +(-0.471518 + 1.94362i) q^{4} +(-0.816487 + 2.03949i) q^{7} +(0.426945 + 2.96946i) q^{9} +(2.82177 - 2.00938i) q^{12} +(0.682051 + 7.14276i) q^{13} +(-3.55534 - 1.83291i) q^{16} +(2.43315 - 0.974087i) q^{19} +(3.38207 - 1.74358i) q^{21} +(-2.07708 + 4.54816i) q^{25} +(2.80925 - 4.37128i) q^{27} +(-3.57900 - 2.54860i) q^{28} +(0.332790 - 3.48513i) q^{31} +(-5.97283 - 0.570336i) q^{36} +(-5.22813 - 9.05539i) q^{37} +(7.20888 - 10.1235i) q^{39} +(-0.137621 + 0.468693i) q^{43} +(2.57495 + 6.43192i) q^{48} +(1.57329 + 1.50013i) q^{49} +(-14.2044 - 2.04229i) q^{52} +(-4.28985 - 1.48473i) q^{57} +(15.4785 + 0.737330i) q^{61} +(-6.40478 - 1.55378i) q^{63} +(5.23889 - 6.04600i) q^{64} +(6.05134 + 5.51192i) q^{67} +(-0.725040 + 15.2205i) q^{73} +(7.87764 - 3.59760i) q^{75} +(0.745984 + 5.18843i) q^{76} +(14.3547 - 10.2219i) q^{79} +(-8.63544 + 2.53559i) q^{81} +(1.79415 + 7.39560i) q^{84} +(-15.1244 - 4.44094i) q^{91} +(-4.38864 + 4.18456i) q^{93} +(-9.48859 + 5.47824i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 2 q^{4} - 6 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 2 q^{4} - 6 q^{7} + 6 q^{9} - 6 q^{12} - 3 q^{13} + 4 q^{16} - 8 q^{19} + 6 q^{21} + 10 q^{25} - 12 q^{28} + 15 q^{31} + 6 q^{36} + 10 q^{37} - 3 q^{39} - 12 q^{48} - 5 q^{49} - 154 q^{52} - 75 q^{57} + 15 q^{61} - 15 q^{63} + 16 q^{64} + 5 q^{67} + 60 q^{73} - 32 q^{76} + 134 q^{79} - 18 q^{81} + 186 q^{84} - 12 q^{91} - 15 q^{93} + 9 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{19}{66}\right)\)

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 −0.618159 0.786053i \(-0.712121\pi\)
0.618159 + 0.786053i \(0.287879\pi\)
\(3\) −1.30900 1.13425i −0.755750 0.654861i
\(4\) −0.471518 + 1.94362i −0.235759 + 0.971812i
\(5\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(6\) 0 0
\(7\) −0.816487 + 2.03949i −0.308603 + 0.770853i 0.690277 + 0.723545i \(0.257489\pi\)
−0.998880 + 0.0473083i \(0.984936\pi\)
\(8\) 0 0
\(9\) 0.426945 + 2.96946i 0.142315 + 0.989821i
\(10\) 0 0
\(11\) 0 0 0.998867 0.0475819i \(-0.0151515\pi\)
−0.998867 + 0.0475819i \(0.984848\pi\)
\(12\) 2.82177 2.00938i 0.814576 0.580057i
\(13\) 0.682051 + 7.14276i 0.189167 + 1.98104i 0.193731 + 0.981055i \(0.437941\pi\)
−0.00456441 + 0.999990i \(0.501453\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −3.55534 1.83291i −0.888835 0.458227i
\(17\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(18\) 0 0
\(19\) 2.43315 0.974087i 0.558203 0.223471i −0.0753671 0.997156i \(-0.524013\pi\)
0.633571 + 0.773685i \(0.281589\pi\)
\(20\) 0 0
\(21\) 3.38207 1.74358i 0.738028 0.380480i
\(22\) 0 0
\(23\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(24\) 0 0
\(25\) −2.07708 + 4.54816i −0.415415 + 0.909632i
\(26\) 0 0
\(27\) 2.80925 4.37128i 0.540641 0.841254i
\(28\) −3.57900 2.54860i −0.676368 0.481640i
\(29\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0 0
\(31\) 0.332790 3.48513i 0.0597708 0.625948i −0.915108 0.403210i \(-0.867894\pi\)
0.974878 0.222738i \(-0.0714995\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −5.97283 0.570336i −0.995472 0.0950560i
\(37\) −5.22813 9.05539i −0.859500 1.48870i −0.872407 0.488780i \(-0.837442\pi\)
0.0129071 0.999917i \(-0.495891\pi\)
\(38\) 0 0
\(39\) 7.20888 10.1235i 1.15435 1.62105i
\(40\) 0 0
\(41\) 0 0 −0.690079 0.723734i \(-0.742424\pi\)
0.690079 + 0.723734i \(0.257576\pi\)
\(42\) 0 0
\(43\) −0.137621 + 0.468693i −0.0209869 + 0.0714749i −0.969321 0.245800i \(-0.920949\pi\)
0.948334 + 0.317275i \(0.102768\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(48\) 2.57495 + 6.43192i 0.371662 + 0.928368i
\(49\) 1.57329 + 1.50013i 0.224755 + 0.214304i
\(50\) 0 0
\(51\) 0 0
\(52\) −14.2044 2.04229i −1.96980 0.283214i
\(53\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −4.28985 1.48473i −0.568204 0.196657i
\(58\) 0 0
\(59\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(60\) 0 0
\(61\) 15.4785 + 0.737330i 1.98181 + 0.0944054i 0.996902 0.0786561i \(-0.0250629\pi\)
0.984911 + 0.173061i \(0.0553659\pi\)
\(62\) 0 0
\(63\) −6.40478 1.55378i −0.806926 0.195758i
\(64\) 5.23889 6.04600i 0.654861 0.755750i
\(65\) 0 0
\(66\) 0 0
\(67\) 6.05134 + 5.51192i 0.739289 + 0.673388i
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(72\) 0 0
\(73\) −0.725040 + 15.2205i −0.0848595 + 1.78142i 0.409644 + 0.912245i \(0.365653\pi\)
−0.494504 + 0.869176i \(0.664650\pi\)
\(74\) 0 0
\(75\) 7.87764 3.59760i 0.909632 0.415415i
\(76\) 0.745984 + 5.18843i 0.0855702 + 0.595154i
\(77\) 0 0
\(78\) 0 0
\(79\) 14.3547 10.2219i 1.61503 1.15006i 0.731307 0.682048i \(-0.238911\pi\)
0.883723 0.468010i \(-0.155029\pi\)
\(80\) 0 0
\(81\) −8.63544 + 2.53559i −0.959493 + 0.281733i
\(82\) 0 0
\(83\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(84\) 1.79415 + 7.39560i 0.195758 + 0.806926i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(90\) 0 0
\(91\) −15.1244 4.44094i −1.58547 0.465537i
\(92\) 0 0
\(93\) −4.38864 + 4.18456i −0.455080 + 0.433918i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −9.48859 + 5.47824i −0.963421 + 0.556231i −0.897224 0.441575i \(-0.854420\pi\)
−0.0661967 + 0.997807i \(0.521086\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −7.86053 6.18159i −0.786053 0.618159i
\(101\) 0 0 0.618159 0.786053i \(-0.287879\pi\)
−0.618159 + 0.786053i \(0.712121\pi\)
\(102\) 0 0
\(103\) −6.24672 0.596490i −0.615508 0.0587739i −0.217355 0.976093i \(-0.569743\pi\)
−0.398153 + 0.917319i \(0.630349\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(108\) 7.17151 + 7.52126i 0.690079 + 0.723734i
\(109\) 17.6383 + 8.05513i 1.68944 + 0.771541i 0.998832 + 0.0483110i \(0.0153839\pi\)
0.690607 + 0.723230i \(0.257343\pi\)
\(110\) 0 0
\(111\) −3.42749 + 17.7835i −0.325323 + 1.68793i
\(112\) 6.64108 5.75453i 0.627523 0.543752i
\(113\) 0 0 −0.458227 0.888835i \(-0.651515\pi\)
0.458227 + 0.888835i \(0.348485\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −20.9190 + 5.07489i −1.93396 + 0.469173i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 10.9502 1.04562i 0.995472 0.0950560i
\(122\) 0 0
\(123\) 0 0
\(124\) 6.61686 + 2.29012i 0.594212 + 0.205659i
\(125\) 0 0
\(126\) 0 0
\(127\) −18.6291 7.45795i −1.65306 0.661786i −0.657289 0.753639i \(-0.728297\pi\)
−0.995773 + 0.0918526i \(0.970721\pi\)
\(128\) 0 0
\(129\) 0.711760 0.457421i 0.0626670 0.0402736i
\(130\) 0 0
\(131\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(132\) 0 0
\(133\) 5.75771i 0.499257i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(138\) 0 0
\(139\) 10.8320 + 16.8550i 0.918760 + 1.42962i 0.902951 + 0.429744i \(0.141396\pi\)
0.0158092 + 0.999875i \(0.494968\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 3.92482 11.3400i 0.327068 0.945001i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.357906 3.74816i −0.0295196 0.309143i
\(148\) 20.0654 5.89174i 1.64937 0.484298i
\(149\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(150\) 0 0
\(151\) −5.75525 23.7234i −0.468355 1.93059i −0.346544 0.938034i \(-0.612645\pi\)
−0.121811 0.992553i \(-0.538870\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 16.2771 + 18.7847i 1.30321 + 1.50398i
\(157\) 18.2449 + 3.51641i 1.45610 + 0.280640i 0.855039 0.518564i \(-0.173533\pi\)
0.601060 + 0.799204i \(0.294745\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 10.8396 18.7747i 0.849019 1.47054i −0.0330650 0.999453i \(-0.510527\pi\)
0.882084 0.471091i \(-0.156140\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(168\) 0 0
\(169\) −37.7887 + 7.28318i −2.90682 + 0.560244i
\(170\) 0 0
\(171\) 3.93134 + 6.80928i 0.300637 + 0.520719i
\(172\) −0.846071 0.488479i −0.0645123 0.0372462i
\(173\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(174\) 0 0
\(175\) −7.58000 7.94968i −0.572994 0.600939i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(180\) 0 0
\(181\) −7.92125 22.8870i −0.588782 1.70117i −0.706129 0.708083i \(-0.749560\pi\)
0.117348 0.993091i \(-0.462561\pi\)
\(182\) 0 0
\(183\) −19.4249 18.5216i −1.43593 1.36916i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 6.62145 + 9.29852i 0.481640 + 0.676368i
\(190\) 0 0
\(191\) 0 0 −0.945001 0.327068i \(-0.893939\pi\)
0.945001 + 0.327068i \(0.106061\pi\)
\(192\) −13.7154 + 1.97197i −0.989821 + 0.142315i
\(193\) −7.76952 17.0129i −0.559262 1.22461i −0.952320 0.305100i \(-0.901310\pi\)
0.393058 0.919514i \(-0.371417\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −3.65751 + 2.35054i −0.261251 + 0.167896i
\(197\) 0 0 −0.971812 0.235759i \(-0.924242\pi\)
0.971812 + 0.235759i \(0.0757576\pi\)
\(198\) 0 0
\(199\) −14.0500 + 11.0490i −0.995975 + 0.783243i −0.976269 0.216563i \(-0.930515\pi\)
−0.0197060 + 0.999806i \(0.506273\pi\)
\(200\) 0 0
\(201\) −1.66928 14.0788i −0.117742 0.993044i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 10.6671 26.6451i 0.739629 1.84750i
\(209\) 0 0
\(210\) 0 0
\(211\) 1.01717 2.93892i 0.0700249 0.202324i −0.904558 0.426350i \(-0.859799\pi\)
0.974583 + 0.224027i \(0.0719203\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 6.83616 + 3.52428i 0.464069 + 0.239244i
\(218\) 0 0
\(219\) 18.2129 19.1012i 1.23072 1.29074i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 19.2927 + 22.2650i 1.29193 + 1.49097i 0.770097 + 0.637927i \(0.220208\pi\)
0.521837 + 0.853045i \(0.325247\pi\)
\(224\) 0 0
\(225\) −14.3924 4.22599i −0.959493 0.281733i
\(226\) 0 0
\(227\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(228\) 4.90850 7.63777i 0.325073 0.505824i
\(229\) 15.1505 + 10.7886i 1.00117 + 0.712933i 0.958187 0.286143i \(-0.0923732\pi\)
0.0429870 + 0.999076i \(0.486313\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.189251 0.981929i \(-0.560606\pi\)
0.189251 + 0.981929i \(0.439394\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −30.3845 2.90137i −1.97369 0.188464i
\(238\) 0 0
\(239\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 0 0
\(241\) −9.50813 6.11050i −0.612473 0.393612i 0.197311 0.980341i \(-0.436779\pi\)
−0.809784 + 0.586729i \(0.800415\pi\)
\(242\) 0 0
\(243\) 14.1798 + 6.47568i 0.909632 + 0.415415i
\(244\) −8.73146 + 29.7366i −0.558974 + 1.90369i
\(245\) 0 0
\(246\) 0 0
\(247\) 8.61720 + 16.7150i 0.548299 + 1.06355i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.971812 0.235759i \(-0.0757576\pi\)
−0.971812 + 0.235759i \(0.924242\pi\)
\(252\) 6.03993 11.7158i 0.380480 0.738028i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 9.28091 + 13.0332i 0.580057 + 0.814576i
\(257\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(258\) 0 0
\(259\) 22.7370 3.26909i 1.41281 0.203132i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −13.5664 + 9.16256i −0.828700 + 0.559692i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 2.79145 + 2.41880i 0.169568 + 0.146932i 0.735511 0.677513i \(-0.236942\pi\)
−0.565943 + 0.824445i \(0.691488\pi\)
\(272\) 0 0
\(273\) 14.7607 + 22.9681i 0.893358 + 1.39009i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −2.00223 13.9258i −0.120302 0.836720i −0.957214 0.289382i \(-0.906550\pi\)
0.836912 0.547338i \(-0.184359\pi\)
\(278\) 0 0
\(279\) 10.4911 0.499751i 0.628083 0.0299193i
\(280\) 0 0
\(281\) 0 0 −0.0950560 0.995472i \(-0.530303\pi\)
0.0950560 + 0.995472i \(0.469697\pi\)
\(282\) 0 0
\(283\) −3.03154 + 21.0848i −0.180206 + 1.25336i 0.676068 + 0.736839i \(0.263682\pi\)
−0.856274 + 0.516522i \(0.827227\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −15.1102 + 7.78985i −0.888835 + 0.458227i
\(290\) 0 0
\(291\) 18.6342 + 3.59146i 1.09236 + 0.210535i
\(292\) −29.2410 8.58593i −1.71120 0.502453i
\(293\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 3.27793 + 17.0075i 0.189251 + 0.981929i
\(301\) −0.843526 0.663357i −0.0486201 0.0382352i
\(302\) 0 0
\(303\) 0 0
\(304\) −10.4361 0.996527i −0.598551 0.0571547i
\(305\) 0 0
\(306\) 0 0
\(307\) −19.1966 + 26.9578i −1.09561 + 1.53856i −0.279960 + 0.960012i \(0.590321\pi\)
−0.815646 + 0.578551i \(0.803618\pi\)
\(308\) 0 0
\(309\) 7.50037 + 7.86616i 0.426681 + 0.447490i
\(310\) 0 0
\(311\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(312\) 0 0
\(313\) 13.4766 11.6776i 0.761744 0.660055i −0.184747 0.982786i \(-0.559147\pi\)
0.946491 + 0.322731i \(0.104601\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 13.0991 + 32.7200i 0.736882 + 1.84064i
\(317\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.856474 17.9796i −0.0475819 0.998867i
\(325\) −33.9031 11.7340i −1.88060 0.650883i
\(326\) 0 0
\(327\) −13.9519 30.5504i −0.771541 1.68944i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −23.8823 5.79379i −1.31269 0.318455i −0.482481 0.875907i \(-0.660264\pi\)
−0.830210 + 0.557451i \(0.811779\pi\)
\(332\) 0 0
\(333\) 24.6575 19.3909i 1.35122 1.06261i
\(334\) 0 0
\(335\) 0 0
\(336\) −15.2202 −0.830332
\(337\) 22.0887 + 28.0881i 1.20325 + 1.53006i 0.782211 + 0.623014i \(0.214092\pi\)
0.421039 + 0.907043i \(0.361666\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −18.3323 + 8.37210i −0.989853 + 0.452051i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.814576 0.580057i \(-0.196970\pi\)
−0.814576 + 0.580057i \(0.803030\pi\)
\(348\) 0 0
\(349\) 0.117428 0.0344801i 0.00628580 0.00184568i −0.278588 0.960411i \(-0.589866\pi\)
0.284874 + 0.958565i \(0.408048\pi\)
\(350\) 0 0
\(351\) 33.1391 + 17.0844i 1.76883 + 0.911896i
\(352\) 0 0
\(353\) 0 0 0.690079 0.723734i \(-0.257576\pi\)
−0.690079 + 0.723734i \(0.742424\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(360\) 0 0
\(361\) −8.77956 + 8.37129i −0.462082 + 0.440594i
\(362\) 0 0
\(363\) −15.5198 11.0516i −0.814576 0.580057i
\(364\) 15.7629 27.3022i 0.826203 1.43103i
\(365\) 0 0
\(366\) 0 0
\(367\) −5.65738 29.3533i −0.295313 1.53223i −0.761865 0.647736i \(-0.775716\pi\)
0.466552 0.884494i \(-0.345496\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −6.06388 10.5030i −0.314398 0.544553i
\(373\) 15.6267 + 9.02205i 0.809117 + 0.467144i 0.846649 0.532151i \(-0.178616\pi\)
−0.0375318 + 0.999295i \(0.511950\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −4.73268 + 24.5555i −0.243101 + 1.26133i 0.631076 + 0.775721i \(0.282614\pi\)
−0.874177 + 0.485608i \(0.838598\pi\)
\(380\) 0 0
\(381\) 15.9262 + 30.8925i 0.815923 + 1.58267i
\(382\) 0 0
\(383\) 0 0 −0.371662 0.928368i \(-0.621212\pi\)
0.371662 + 0.928368i \(0.378788\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.45052 0.208554i −0.0737342 0.0106014i
\(388\) −6.17360 21.0253i −0.313417 1.06740i
\(389\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 8.63457 5.54910i 0.433357 0.278501i −0.305722 0.952121i \(-0.598898\pi\)
0.739078 + 0.673620i \(0.235261\pi\)
\(398\) 0 0
\(399\) 6.53069 7.53682i 0.326944 0.377313i
\(400\) 15.7211 12.3632i 0.786053 0.618159i
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 25.1204 1.25134
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 3.30319 8.25096i 0.163332 0.407984i −0.824013 0.566571i \(-0.808270\pi\)
0.987345 + 0.158587i \(0.0506939\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 4.10479 11.8600i 0.202229 0.584301i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 4.93869 34.3493i 0.241849 1.68209i
\(418\) 0 0
\(419\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(420\) 0 0
\(421\) 38.0436 15.2304i 1.85413 0.742282i 0.907384 0.420303i \(-0.138076\pi\)
0.946747 0.321979i \(-0.104348\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −14.1417 + 30.9661i −0.684366 + 1.49855i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −18.0000 + 10.3923i −0.866025 + 0.500000i
\(433\) 1.81441 19.0013i 0.0871947 0.913145i −0.840996 0.541041i \(-0.818030\pi\)
0.928191 0.372104i \(-0.121363\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −23.9729 + 30.4840i −1.14809 + 1.45992i
\(437\) 0 0
\(438\) 0 0
\(439\) −18.4497 31.9558i −0.880555 1.52517i −0.850725 0.525610i \(-0.823837\pi\)
−0.0298292 0.999555i \(-0.509496\pi\)
\(440\) 0 0
\(441\) −3.78286 + 5.31229i −0.180136 + 0.252966i
\(442\) 0 0
\(443\) 0 0 −0.690079 0.723734i \(-0.742424\pi\)
0.690079 + 0.723734i \(0.257576\pi\)
\(444\) −32.9483 15.0470i −1.56366 0.714098i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 8.05324 + 15.6211i 0.380480 + 0.738028i
\(449\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −19.3748 + 37.5818i −0.910306 + 1.76575i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −14.3468 20.1472i −0.671114 0.942448i 0.328884 0.944370i \(-0.393327\pi\)
−0.999998 + 0.00192256i \(0.999388\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(462\) 0 0
\(463\) −25.1908 1.19999i −1.17072 0.0557680i −0.546802 0.837262i \(-0.684155\pi\)
−0.623913 + 0.781494i \(0.714458\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(468\) 43.0515i 1.99006i
\(469\) −16.1823 + 7.84122i −0.747230 + 0.362074i
\(470\) 0 0
\(471\) −19.8940 25.2972i −0.916666 1.16564i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −0.623535 + 13.0896i −0.0286098 + 0.600593i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(480\) 0 0
\(481\) 61.1146 43.5195i 2.78659 1.98432i
\(482\) 0 0
\(483\) 0 0
\(484\) −3.13093 + 21.7761i −0.142315 + 0.989821i
\(485\) 0 0
\(486\) 0 0
\(487\) 28.9440 30.3556i 1.31158 1.37554i 0.430486 0.902597i \(-0.358342\pi\)
0.881092 0.472946i \(-0.156809\pi\)
\(488\) 0 0
\(489\) −35.4841 + 12.2812i −1.60465 + 0.555374i
\(490\) 0 0
\(491\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −7.57110 + 11.7809i −0.339952 + 0.528976i
\(497\) 0 0
\(498\) 0 0
\(499\) 13.9923 8.07843i 0.626379 0.361640i −0.152969 0.988231i \(-0.548884\pi\)
0.779349 + 0.626591i \(0.215550\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.618159 0.786053i \(-0.287879\pi\)
−0.618159 + 0.786053i \(0.712121\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 57.7262 + 33.3283i 2.56371 + 1.48016i
\(508\) 23.2794 32.6913i 1.03286 1.45044i
\(509\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(510\) 0 0
\(511\) −30.4499 13.9060i −1.34703 0.615166i
\(512\) 0 0
\(513\) 2.57733 13.3725i 0.113792 0.590408i
\(514\) 0 0
\(515\) 0 0
\(516\) 0.553446 + 1.59908i 0.0243641 + 0.0703954i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(522\) 0 0
\(523\) 43.2397 4.12889i 1.89074 0.180544i 0.915595 0.402102i \(-0.131720\pi\)
0.975147 + 0.221558i \(0.0711142\pi\)
\(524\) 0 0
\(525\) 0.905260 + 19.0037i 0.0395088 + 0.829391i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 21.3525 + 8.54824i 0.928368 + 0.371662i
\(530\) 0 0
\(531\) 0 0
\(532\) −11.1908 2.71486i −0.485184 0.117704i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −25.0515 38.9809i −1.07705 1.67592i −0.612887 0.790171i \(-0.709992\pi\)
−0.464162 0.885750i \(-0.653645\pi\)
\(542\) 0 0
\(543\) −15.5907 + 38.9436i −0.669060 + 1.67123i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −33.1181 + 1.57761i −1.41603 + 0.0674536i −0.741577 0.670868i \(-0.765922\pi\)
−0.674449 + 0.738321i \(0.735619\pi\)
\(548\) 0 0
\(549\) 4.41897 + 46.2775i 0.188597 + 1.97508i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 9.12707 + 37.6223i 0.388123 + 1.59986i
\(554\) 0 0
\(555\) 0 0
\(556\) −37.8672 + 13.1060i −1.60593 + 0.555816i
\(557\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(558\) 0 0
\(559\) −3.44162 0.663318i −0.145565 0.0280554i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1.87942 19.6821i 0.0789280 0.826572i
\(568\) 0 0
\(569\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(570\) 0 0
\(571\) −36.6490 + 7.06351i −1.53371 + 0.295599i −0.885056 0.465484i \(-0.845880\pi\)
−0.648655 + 0.761083i \(0.724668\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 20.1901 + 12.9754i 0.841254 + 0.540641i
\(577\) 23.0448 + 24.1687i 0.959369 + 1.00616i 0.999976 + 0.00698200i \(0.00222246\pi\)
−0.0406067 + 0.999175i \(0.512929\pi\)
\(578\) 0 0
\(579\) −9.12661 + 31.0824i −0.379289 + 1.29174i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.458227 0.888835i \(-0.348485\pi\)
−0.458227 + 0.888835i \(0.651515\pi\)
\(588\) 7.45377 + 1.07169i 0.307388 + 0.0441958i
\(589\) −2.58509 8.80402i −0.106517 0.362763i
\(590\) 0 0
\(591\) 0 0
\(592\) 1.99012 + 41.7777i 0.0817933 + 1.71705i
\(593\) 0 0 −0.945001 0.327068i \(-0.893939\pi\)
0.945001 + 0.327068i \(0.106061\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 30.9237 + 1.47308i 1.26562 + 0.0602890i
\(598\) 0 0
\(599\) 0 0 −0.971812 0.235759i \(-0.924242\pi\)
0.971812 + 0.235759i \(0.0757576\pi\)
\(600\) 0 0
\(601\) 33.6111 26.4320i 1.37102 1.07818i 0.383022 0.923739i \(-0.374883\pi\)
0.988001 0.154446i \(-0.0493591\pi\)
\(602\) 0 0
\(603\) −13.7839 + 20.3225i −0.561322 + 0.827597i
\(604\) 48.8231 1.98659
\(605\) 0 0
\(606\) 0 0
\(607\) −10.2694 + 42.3310i −0.416821 + 1.71816i 0.245901 + 0.969295i \(0.420916\pi\)
−0.662722 + 0.748866i \(0.730599\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 13.3131 38.4657i 0.537711 1.55361i −0.269287 0.963060i \(-0.586788\pi\)
0.806998 0.590554i \(-0.201091\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(618\) 0 0
\(619\) 32.4775 + 16.7433i 1.30538 + 0.672970i 0.963735 0.266860i \(-0.0859860\pi\)
0.341644 + 0.939829i \(0.389016\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −44.1854 + 22.7792i −1.76883 + 0.911896i
\(625\) −16.3715 18.8937i −0.654861 0.755750i
\(626\) 0 0
\(627\) 0 0
\(628\) −15.4374 + 33.8031i −0.616018 + 1.34889i
\(629\) 0 0
\(630\) 0 0
\(631\) 14.1520 + 10.0776i 0.563382 + 0.401183i 0.825960 0.563728i \(-0.190633\pi\)
−0.262578 + 0.964911i \(0.584573\pi\)
\(632\) 0 0
\(633\) −4.66495 + 2.69331i −0.185415 + 0.107049i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −9.64197 + 12.2608i −0.382029 + 0.485789i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(642\) 0 0
\(643\) −39.6763 25.4984i −1.56468 1.00556i −0.981100 0.193502i \(-0.938015\pi\)
−0.583579 0.812056i \(-0.698348\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.189251 0.981929i \(-0.439394\pi\)
−0.189251 + 0.981929i \(0.560606\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −4.95108 12.3672i −0.194048 0.484709i
\(652\) 31.3798 + 29.9206i 1.22893 + 1.17178i
\(653\) 0 0 0.971812 0.235759i \(-0.0757576\pi\)
−0.971812 + 0.235759i \(0.924242\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −45.5062 + 4.34531i −1.77537 + 0.169527i
\(658\) 0 0
\(659\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(660\) 0 0
\(661\) −28.4692 + 4.09325i −1.10732 + 0.159209i −0.671630 0.740887i \(-0.734405\pi\)
−0.435692 + 0.900096i \(0.643496\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 51.0275i 1.97284i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 37.2464 + 32.2742i 1.43574 + 1.24408i 0.922590 + 0.385782i \(0.126068\pi\)
0.513153 + 0.858297i \(0.328477\pi\)
\(674\) 0 0
\(675\) 14.0463 + 21.8564i 0.540641 + 0.841254i
\(676\) 3.66230 76.8811i 0.140858 2.95697i
\(677\) 0 0 0.371662 0.928368i \(-0.378788\pi\)
−0.371662 + 0.928368i \(0.621212\pi\)
\(678\) 0 0
\(679\) −3.42548 23.8248i −0.131458 0.914311i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.0950560 0.995472i \(-0.530303\pi\)
0.0950560 + 0.995472i \(0.469697\pi\)
\(684\) −15.0884 + 4.43034i −0.576918 + 0.169398i
\(685\) 0 0
\(686\) 0 0
\(687\) −7.59494 31.3068i −0.289765 1.19443i
\(688\) 1.34836 1.41412i 0.0514056 0.0539127i
\(689\) 0 0
\(690\) 0 0
\(691\) 44.9655 23.1813i 1.71057 0.881858i 0.730572 0.682836i \(-0.239254\pi\)
0.979995 0.199023i \(-0.0637767\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 19.0253 10.9843i 0.719088 0.415166i
\(701\) 0 0 0.0950560 0.995472i \(-0.469697\pi\)
−0.0950560 + 0.995472i \(0.530303\pi\)
\(702\) 0 0
\(703\) −21.5416 16.9405i −0.812456 0.638923i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −29.6170 + 41.5913i −1.11229 + 1.56199i −0.324677 + 0.945825i \(0.605256\pi\)
−0.787614 + 0.616169i \(0.788684\pi\)
\(710\) 0 0
\(711\) 36.4823 + 38.2616i 1.36819 + 1.43492i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(720\) 0 0
\(721\) 6.31690 12.2531i 0.235254 0.456329i
\(722\) 0 0
\(723\) 5.51526 + 18.7832i 0.205115 + 0.698556i
\(724\) 48.2186 4.60432i 1.79203 0.171118i
\(725\) 0 0
\(726\) 0 0
\(727\) −50.0163 17.3108i −1.85500 0.642023i −0.990153 0.139992i \(-0.955292\pi\)
−0.864850 0.502031i \(-0.832586\pi\)
\(728\) 0 0
\(729\) −11.2162 24.5601i −0.415415 0.909632i
\(730\) 0 0
\(731\) 0 0
\(732\) 45.1583 29.0215i 1.66910 1.07266i
\(733\) −45.2214 10.9706i −1.67029 0.405208i −0.714589 0.699544i \(-0.753386\pi\)
−0.955702 + 0.294336i \(0.904902\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −16.4214 20.8815i −0.604072 0.768140i 0.383799 0.923417i \(-0.374616\pi\)
−0.987871 + 0.155277i \(0.950373\pi\)
\(740\) 0 0
\(741\) 7.67918 31.6540i 0.282102 1.16284i
\(742\) 0 0
\(743\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −52.5547 + 15.4314i −1.91775 + 0.563101i −0.948753 + 0.316017i \(0.897654\pi\)
−0.968994 + 0.247084i \(0.920528\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −21.1950 + 8.48518i −0.770853 + 0.308603i
\(757\) 26.7229 9.24888i 0.971259 0.336156i 0.205053 0.978751i \(-0.434263\pi\)
0.766206 + 0.642595i \(0.222142\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(762\) 0 0
\(763\) −30.8297 + 29.3961i −1.11611 + 1.06421i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 2.63427 27.5873i 0.0950560 0.995472i
\(769\) −6.39275 33.1687i −0.230528 1.19610i −0.894060 0.447947i \(-0.852155\pi\)
0.663532 0.748148i \(-0.269057\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 36.7301 7.07914i 1.32194 0.254784i
\(773\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(774\) 0 0
\(775\) 15.1597 + 8.75246i 0.544553 + 0.314398i
\(776\) 0 0
\(777\) −33.4707 21.5103i −1.20075 0.771678i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −2.84398 8.21714i −0.101571 0.293469i
\(785\) 0 0
\(786\) 0 0
\(787\) 50.9020 12.3487i 1.81446 0.440183i 0.822719 0.568448i \(-0.192456\pi\)
0.991740 + 0.128265i \(0.0409408\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 5.29052 + 111.062i 0.187872 + 3.94392i
\(794\) 0 0
\(795\) 0 0
\(796\) −14.8503 32.5176i −0.526355 1.15256i
\(797\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 28.1510 + 3.39397i 0.992811 + 0.119696i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(810\) 0 0
\(811\) 5.82335 14.5460i 0.204486 0.510780i −0.790306 0.612713i \(-0.790078\pi\)
0.994791 + 0.101932i \(0.0325026\pi\)
\(812\) 0 0
\(813\) −0.910463 6.33241i −0.0319313 0.222087i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0.121696 + 1.27445i 0.00425759 + 0.0445875i
\(818\) 0 0
\(819\) 6.72990 46.8075i 0.235162 1.63559i
\(820\) 0 0
\(821\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(822\) 0 0
\(823\) −51.8626 + 20.7627i −1.80782 + 0.723741i −0.819159 + 0.573567i \(0.805559\pi\)
−0.988660 + 0.150174i \(0.952017\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(828\) 0 0
\(829\) 18.4899 40.4872i 0.642181 1.40618i −0.256054 0.966663i \(-0.582422\pi\)
0.898234 0.439517i \(-0.144850\pi\)
\(830\) 0 0
\(831\) −13.1744 + 20.4998i −0.457017 + 0.711132i
\(832\) 46.7583 + 33.2964i 1.62105 + 1.15435i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −14.2996 11.2453i −0.494266 0.388695i
\(838\) 0 0
\(839\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(840\) 0 0
\(841\) −14.5000 25.1147i −0.500000 0.866025i
\(842\) 0 0
\(843\) 0 0
\(844\) 5.23254 + 3.36275i 0.180111 + 0.115751i
\(845\) 0 0
\(846\) 0 0
\(847\) −6.80817 + 23.1865i −0.233931 + 0.796697i
\(848\) 0 0
\(849\) 27.8837 24.1614i 0.956967 0.829217i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −28.4332 27.1110i −0.973535 0.928264i 0.0239089 0.999714i \(-0.492389\pi\)
−0.997444 + 0.0714502i \(0.977237\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(858\) 0 0
\(859\) 10.6581 + 14.9673i 0.363651 + 0.510677i 0.955348 0.295484i \(-0.0954809\pi\)
−0.591696 + 0.806161i \(0.701542\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 28.6149 + 6.94189i 0.971812 + 0.235759i
\(868\) −10.0732 + 11.6252i −0.341908 + 0.394583i
\(869\) 0 0
\(870\) 0 0
\(871\) −35.2430 + 46.9827i −1.19416 + 1.59195i
\(872\) 0 0
\(873\) −20.3186 25.8371i −0.687679 0.874455i
\(874\) 0 0
\(875\) 0 0
\(876\) 28.5377 + 44.4056i 0.964201 + 1.50033i
\(877\) 2.35955 49.5330i 0.0796763 1.67261i −0.506357 0.862324i \(-0.669008\pi\)
0.586033 0.810287i \(-0.300689\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(882\) 0 0
\(883\) −36.3387 + 25.8767i −1.22289 + 0.870819i −0.994702 0.102797i \(-0.967221\pi\)
−0.228192 + 0.973616i \(0.573281\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(888\) 0 0
\(889\) 30.4208 31.9044i 1.02028 1.07004i
\(890\) 0 0
\(891\) 0 0
\(892\) −52.3715 + 26.9994i −1.75353 + 0.904007i
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 15.0000 25.9808i 0.500000 0.866025i
\(901\) 0 0
\(902\) 0 0
\(903\) 0.351760 + 1.82510i 0.0117058 + 0.0607356i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 57.7344 + 5.51296i 1.91704 + 0.183055i 0.984178 0.177183i \(-0.0566983\pi\)
0.932861 + 0.360238i \(0.117304\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(912\) 12.5305 + 13.1416i 0.414927 + 0.435162i
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −28.1128 + 24.3599i −0.928872 + 0.804872i
\(917\) 0 0
\(918\) 0 0
\(919\) −0.700819 1.75056i −0.0231179 0.0577457i 0.916360 0.400356i \(-0.131113\pi\)
−0.939478 + 0.342610i \(0.888689\pi\)
\(920\) 0 0
\(921\) 55.7052 13.5139i 1.83555 0.445299i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 52.0446 4.96966i 1.71122 0.163401i
\(926\) 0 0
\(927\) −0.895749 18.8041i −0.0294203 0.617607i
\(928\) 0 0
\(929\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(930\) 0 0
\(931\) 5.28930 + 2.11752i 0.173350 + 0.0693988i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 22.1714i 0.724307i 0.932119 + 0.362153i \(0.117958\pi\)
−0.932119 + 0.362153i \(0.882042\pi\)
\(938\) 0 0
\(939\) −30.8862 −1.00793
\(940\) 0 0
\(941\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(948\) 19.9660 57.6880i 0.648466 1.87362i
\(949\) −109.211 + 5.20234i −3.54513 + 0.168875i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 18.4044 + 3.54716i 0.593690 + 0.114424i
\(962\) 0 0
\(963\) 0 0
\(964\) 16.3598 15.5990i 0.526913 0.502410i
\(965\) 0 0
\(966\) 0 0
\(967\) 4.24681 7.35569i 0.136568 0.236543i −0.789627 0.613587i \(-0.789726\pi\)
0.926195 + 0.377044i \(0.123059\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(972\) −19.2723 + 24.5067i −0.618159 + 0.786053i
\(973\) −43.2196 + 8.32990i −1.38556 + 0.267044i
\(974\) 0 0
\(975\) 31.0697 + 53.8143i 0.995028 + 1.72344i
\(976\) −53.6797 30.9920i −1.71825 0.992030i
\(977\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −16.3888 + 55.8153i −0.523256 + 1.78205i
\(982\) 0 0
\(983\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −36.5509 + 8.86715i −1.16284 + 0.282102i
\(989\) 0 0
\(990\) 0 0
\(991\) 17.3752 + 59.1745i 0.551941 + 1.87974i 0.469031 + 0.883182i \(0.344603\pi\)
0.0829100 + 0.996557i \(0.473579\pi\)
\(992\) 0 0
\(993\) 24.6903 + 34.6726i 0.783521 + 1.10030i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 16.8556 + 36.9086i 0.533821 + 1.16891i 0.963937 + 0.266132i \(0.0857457\pi\)
−0.430115 + 0.902774i \(0.641527\pi\)
\(998\) 0 0
\(999\) −54.2708 2.58524i −1.71705 0.0817933i
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 201.2.p.a.80.1 20
3.2 odd 2 CM 201.2.p.a.80.1 20
67.31 odd 66 inner 201.2.p.a.98.1 yes 20
201.98 even 66 inner 201.2.p.a.98.1 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.2.p.a.80.1 20 1.1 even 1 trivial
201.2.p.a.80.1 20 3.2 odd 2 CM
201.2.p.a.98.1 yes 20 67.31 odd 66 inner
201.2.p.a.98.1 yes 20 201.98 even 66 inner