Properties

Label 1050.2.i.h.751.1
Level $1050$
Weight $2$
Character 1050.751
Analytic conductor $8.384$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1050,2,Mod(151,1050)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.i (of order \(3\), degree \(2\), 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: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 751.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1050.751
Dual form 1050.2.i.h.151.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{12} +4.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(1.50000 - 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(2.00000 - 1.73205i) q^{28} +(0.500000 + 0.866025i) q^{31} +(-0.500000 - 0.866025i) q^{32} -3.00000 q^{34} +1.00000 q^{36} +(-5.00000 + 8.66025i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(2.00000 + 3.46410i) q^{39} -9.00000 q^{41} +(-0.500000 - 2.59808i) q^{42} +10.0000 q^{43} +(1.50000 + 2.59808i) q^{46} +(-1.50000 + 2.59808i) q^{47} -1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +(-1.50000 + 2.59808i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.500000 + 2.59808i) q^{56} -2.00000 q^{57} +(3.00000 + 5.19615i) q^{59} +(-4.00000 + 6.92820i) q^{61} -1.00000 q^{62} +(-2.50000 - 0.866025i) q^{63} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +3.00000 q^{69} +3.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(7.00000 + 12.1244i) q^{73} +(-5.00000 - 8.66025i) q^{74} +2.00000 q^{76} -4.00000 q^{78} +(-5.50000 + 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} +(2.50000 + 0.866025i) q^{84} +(-5.00000 + 8.66025i) q^{86} +(7.50000 - 12.9904i) q^{89} +(2.00000 + 10.3923i) q^{91} -3.00000 q^{92} +(-0.500000 + 0.866025i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(0.500000 - 0.866025i) q^{96} +7.00000 q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + q^{7} + 2 q^{8} - q^{9} + q^{12} + 8 q^{13} - 5 q^{14} - q^{16} + 3 q^{17} - q^{18} - 2 q^{19} - 4 q^{21} + 3 q^{23} + q^{24} - 4 q^{26} - 2 q^{27} + 4 q^{28} + q^{31} - q^{32} - 6 q^{34} + 2 q^{36} - 10 q^{37} - 2 q^{38} + 4 q^{39} - 18 q^{41} - q^{42} + 20 q^{43} + 3 q^{46} - 3 q^{47} - 2 q^{48} - 13 q^{49} - 3 q^{51} - 4 q^{52} - 6 q^{53} + q^{54} + q^{56} - 4 q^{57} + 6 q^{59} - 8 q^{61} - 2 q^{62} - 5 q^{63} + 2 q^{64} - 4 q^{67} + 3 q^{68} + 6 q^{69} + 6 q^{71} - q^{72} + 14 q^{73} - 10 q^{74} + 4 q^{76} - 8 q^{78} - 11 q^{79} - q^{81} + 9 q^{82} + 5 q^{84} - 10 q^{86} + 15 q^{89} + 4 q^{91} - 6 q^{92} - q^{93} - 3 q^{94} + q^{96} + 14 q^{97} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) −2.50000 0.866025i −0.668153 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 0 0
\(21\) −2.00000 + 1.73205i −0.436436 + 0.377964i
\(22\) 0 0
\(23\) 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) −2.00000 + 3.46410i −0.392232 + 0.679366i
\(27\) −1.00000 −0.192450
\(28\) 2.00000 1.73205i 0.377964 0.327327i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −5.00000 + 8.66025i −0.821995 + 1.42374i 0.0821995 + 0.996616i \(0.473806\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) −1.00000 1.73205i −0.162221 0.280976i
\(39\) 2.00000 + 3.46410i 0.320256 + 0.554700i
\(40\) 0 0
\(41\) −9.00000 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) −0.500000 2.59808i −0.0771517 0.400892i
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.50000 + 2.59808i 0.221163 + 0.383065i
\(47\) −1.50000 + 2.59808i −0.218797 + 0.378968i −0.954441 0.298401i \(-0.903547\pi\)
0.735643 + 0.677369i \(0.236880\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 0 0
\(51\) −1.50000 + 2.59808i −0.210042 + 0.363803i
\(52\) −2.00000 3.46410i −0.277350 0.480384i
\(53\) −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) 0.500000 + 2.59808i 0.0668153 + 0.347183i
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) 3.00000 + 5.19615i 0.390567 + 0.676481i 0.992524 0.122047i \(-0.0389457\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) −1.00000 −0.127000
\(63\) −2.50000 0.866025i −0.314970 0.109109i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −2.00000 3.46410i −0.244339 0.423207i 0.717607 0.696449i \(-0.245238\pi\)
−0.961946 + 0.273241i \(0.911904\pi\)
\(68\) 1.50000 2.59808i 0.181902 0.315063i
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) 3.00000 0.356034 0.178017 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 7.00000 + 12.1244i 0.819288 + 1.41905i 0.906208 + 0.422833i \(0.138964\pi\)
−0.0869195 + 0.996215i \(0.527702\pi\)
\(74\) −5.00000 8.66025i −0.581238 1.00673i
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) −4.00000 −0.452911
\(79\) −5.50000 + 9.52628i −0.618798 + 1.07179i 0.370907 + 0.928670i \(0.379047\pi\)
−0.989705 + 0.143120i \(0.954286\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 4.50000 7.79423i 0.496942 0.860729i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 2.50000 + 0.866025i 0.272772 + 0.0944911i
\(85\) 0 0
\(86\) −5.00000 + 8.66025i −0.539164 + 0.933859i
\(87\) 0 0
\(88\) 0 0
\(89\) 7.50000 12.9904i 0.794998 1.37698i −0.127842 0.991795i \(-0.540805\pi\)
0.922840 0.385183i \(-0.125862\pi\)
\(90\) 0 0
\(91\) 2.00000 + 10.3923i 0.209657 + 1.08941i
\(92\) −3.00000 −0.312772
\(93\) −0.500000 + 0.866025i −0.0518476 + 0.0898027i
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) 0 0
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 1.00000 6.92820i 0.101015 0.699854i
\(99\) 0 0
\(100\) 0 0
\(101\) −9.00000 15.5885i −0.895533 1.55111i −0.833143 0.553058i \(-0.813461\pi\)
−0.0623905 0.998052i \(-0.519872\pi\)
\(102\) −1.50000 2.59808i −0.148522 0.257248i
\(103\) 2.50000 4.33013i 0.246332 0.426660i −0.716173 0.697923i \(-0.754108\pi\)
0.962505 + 0.271263i \(0.0874412\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −9.00000 + 15.5885i −0.870063 + 1.50699i −0.00813215 + 0.999967i \(0.502589\pi\)
−0.861931 + 0.507026i \(0.830745\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −1.00000 1.73205i −0.0957826 0.165900i 0.814152 0.580651i \(-0.197202\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(110\) 0 0
\(111\) −10.0000 −0.949158
\(112\) −2.50000 0.866025i −0.236228 0.0818317i
\(113\) −21.0000 −1.97551 −0.987757 0.156001i \(-0.950140\pi\)
−0.987757 + 0.156001i \(0.950140\pi\)
\(114\) 1.00000 1.73205i 0.0936586 0.162221i
\(115\) 0 0
\(116\) 0 0
\(117\) −2.00000 + 3.46410i −0.184900 + 0.320256i
\(118\) −6.00000 −0.552345
\(119\) −6.00000 + 5.19615i −0.550019 + 0.476331i
\(120\) 0 0
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) −4.00000 6.92820i −0.362143 0.627250i
\(123\) −4.50000 7.79423i −0.405751 0.702782i
\(124\) 0.500000 0.866025i 0.0449013 0.0777714i
\(125\) 0 0
\(126\) 2.00000 1.73205i 0.178174 0.154303i
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 5.00000 + 8.66025i 0.440225 + 0.762493i
\(130\) 0 0
\(131\) 6.00000 10.3923i 0.524222 0.907980i −0.475380 0.879781i \(-0.657689\pi\)
0.999602 0.0281993i \(-0.00897729\pi\)
\(132\) 0 0
\(133\) −5.00000 1.73205i −0.433555 0.150188i
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 1.50000 + 2.59808i 0.128624 + 0.222783i
\(137\) −4.50000 7.79423i −0.384461 0.665906i 0.607233 0.794524i \(-0.292279\pi\)
−0.991694 + 0.128618i \(0.958946\pi\)
\(138\) −1.50000 + 2.59808i −0.127688 + 0.221163i
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) −1.50000 + 2.59808i −0.125877 + 0.218026i
\(143\) 0 0
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) −14.0000 −1.15865
\(147\) −5.50000 4.33013i −0.453632 0.357143i
\(148\) 10.0000 0.821995
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) −1.00000 + 1.73205i −0.0811107 + 0.140488i
\(153\) −3.00000 −0.242536
\(154\) 0 0
\(155\) 0 0
\(156\) 2.00000 3.46410i 0.160128 0.277350i
\(157\) 4.00000 + 6.92820i 0.319235 + 0.552931i 0.980329 0.197372i \(-0.0632408\pi\)
−0.661094 + 0.750303i \(0.729907\pi\)
\(158\) −5.50000 9.52628i −0.437557 0.757870i
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 0 0
\(161\) 7.50000 + 2.59808i 0.591083 + 0.204757i
\(162\) 1.00000 0.0785674
\(163\) 4.00000 6.92820i 0.313304 0.542659i −0.665771 0.746156i \(-0.731897\pi\)
0.979076 + 0.203497i \(0.0652307\pi\)
\(164\) 4.50000 + 7.79423i 0.351391 + 0.608627i
\(165\) 0 0
\(166\) 0 0
\(167\) 24.0000 1.85718 0.928588 0.371113i \(-0.121024\pi\)
0.928588 + 0.371113i \(0.121024\pi\)
\(168\) −2.00000 + 1.73205i −0.154303 + 0.133631i
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −1.00000 1.73205i −0.0764719 0.132453i
\(172\) −5.00000 8.66025i −0.381246 0.660338i
\(173\) −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i \(0.406540\pi\)
−0.973670 + 0.227964i \(0.926793\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −3.00000 + 5.19615i −0.225494 + 0.390567i
\(178\) 7.50000 + 12.9904i 0.562149 + 0.973670i
\(179\) 3.00000 + 5.19615i 0.224231 + 0.388379i 0.956088 0.293079i \(-0.0946798\pi\)
−0.731858 + 0.681457i \(0.761346\pi\)
\(180\) 0 0
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) −10.0000 3.46410i −0.741249 0.256776i
\(183\) −8.00000 −0.591377
\(184\) 1.50000 2.59808i 0.110581 0.191533i
\(185\) 0 0
\(186\) −0.500000 0.866025i −0.0366618 0.0635001i
\(187\) 0 0
\(188\) 3.00000 0.218797
\(189\) −0.500000 2.59808i −0.0363696 0.188982i
\(190\) 0 0
\(191\) 10.5000 18.1865i 0.759753 1.31593i −0.183223 0.983071i \(-0.558653\pi\)
0.942976 0.332860i \(-0.108014\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 8.50000 + 14.7224i 0.611843 + 1.05974i 0.990930 + 0.134382i \(0.0429051\pi\)
−0.379086 + 0.925361i \(0.623762\pi\)
\(194\) −3.50000 + 6.06218i −0.251285 + 0.435239i
\(195\) 0 0
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) −5.50000 9.52628i −0.389885 0.675300i 0.602549 0.798082i \(-0.294152\pi\)
−0.992434 + 0.122782i \(0.960818\pi\)
\(200\) 0 0
\(201\) 2.00000 3.46410i 0.141069 0.244339i
\(202\) 18.0000 1.26648
\(203\) 0 0
\(204\) 3.00000 0.210042
\(205\) 0 0
\(206\) 2.50000 + 4.33013i 0.174183 + 0.301694i
\(207\) 1.50000 + 2.59808i 0.104257 + 0.180579i
\(208\) −2.00000 + 3.46410i −0.138675 + 0.240192i
\(209\) 0 0
\(210\) 0 0
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 1.50000 + 2.59808i 0.102778 + 0.178017i
\(214\) −9.00000 15.5885i −0.615227 1.06561i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −2.00000 + 1.73205i −0.135769 + 0.117579i
\(218\) 2.00000 0.135457
\(219\) −7.00000 + 12.1244i −0.473016 + 0.819288i
\(220\) 0 0
\(221\) 6.00000 + 10.3923i 0.403604 + 0.699062i
\(222\) 5.00000 8.66025i 0.335578 0.581238i
\(223\) 19.0000 1.27233 0.636167 0.771551i \(-0.280519\pi\)
0.636167 + 0.771551i \(0.280519\pi\)
\(224\) 2.00000 1.73205i 0.133631 0.115728i
\(225\) 0 0
\(226\) 10.5000 18.1865i 0.698450 1.20975i
\(227\) −3.00000 5.19615i −0.199117 0.344881i 0.749125 0.662428i \(-0.230474\pi\)
−0.948242 + 0.317547i \(0.897141\pi\)
\(228\) 1.00000 + 1.73205i 0.0662266 + 0.114708i
\(229\) 2.00000 3.46410i 0.132164 0.228914i −0.792347 0.610071i \(-0.791141\pi\)
0.924510 + 0.381157i \(0.124474\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −15.0000 + 25.9808i −0.982683 + 1.70206i −0.330870 + 0.943676i \(0.607342\pi\)
−0.651813 + 0.758380i \(0.725991\pi\)
\(234\) −2.00000 3.46410i −0.130744 0.226455i
\(235\) 0 0
\(236\) 3.00000 5.19615i 0.195283 0.338241i
\(237\) −11.0000 −0.714527
\(238\) −1.50000 7.79423i −0.0972306 0.505225i
\(239\) 15.0000 0.970269 0.485135 0.874439i \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(240\) 0 0
\(241\) −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i \(-0.315567\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) 5.50000 + 9.52628i 0.353553 + 0.612372i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) 9.00000 0.573819
\(247\) −4.00000 + 6.92820i −0.254514 + 0.440831i
\(248\) 0.500000 + 0.866025i 0.0317500 + 0.0549927i
\(249\) 0 0
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0.500000 + 2.59808i 0.0314970 + 0.163663i
\(253\) 0 0
\(254\) −8.00000 + 13.8564i −0.501965 + 0.869428i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 15.0000 25.9808i 0.935674 1.62064i 0.162247 0.986750i \(-0.448126\pi\)
0.773427 0.633885i \(-0.218541\pi\)
\(258\) −10.0000 −0.622573
\(259\) −25.0000 8.66025i −1.55342 0.538122i
\(260\) 0 0
\(261\) 0 0
\(262\) 6.00000 + 10.3923i 0.370681 + 0.642039i
\(263\) 4.50000 + 7.79423i 0.277482 + 0.480613i 0.970758 0.240059i \(-0.0771668\pi\)
−0.693276 + 0.720672i \(0.743833\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.00000 3.46410i 0.245256 0.212398i
\(267\) 15.0000 0.917985
\(268\) −2.00000 + 3.46410i −0.122169 + 0.211604i
\(269\) 3.00000 + 5.19615i 0.182913 + 0.316815i 0.942871 0.333157i \(-0.108114\pi\)
−0.759958 + 0.649972i \(0.774781\pi\)
\(270\) 0 0
\(271\) 3.50000 6.06218i 0.212610 0.368251i −0.739921 0.672694i \(-0.765137\pi\)
0.952531 + 0.304443i \(0.0984703\pi\)
\(272\) −3.00000 −0.181902
\(273\) −8.00000 + 6.92820i −0.484182 + 0.419314i
\(274\) 9.00000 0.543710
\(275\) 0 0
\(276\) −1.50000 2.59808i −0.0902894 0.156386i
\(277\) −14.0000 24.2487i −0.841178 1.45696i −0.888899 0.458103i \(-0.848529\pi\)
0.0477206 0.998861i \(-0.484804\pi\)
\(278\) −1.00000 + 1.73205i −0.0599760 + 0.103882i
\(279\) −1.00000 −0.0598684
\(280\) 0 0
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) 1.50000 2.59808i 0.0893237 0.154713i
\(283\) −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i \(-0.204600\pi\)
−0.919327 + 0.393494i \(0.871266\pi\)
\(284\) −1.50000 2.59808i −0.0890086 0.154167i
\(285\) 0 0
\(286\) 0 0
\(287\) −4.50000 23.3827i −0.265627 1.38024i
\(288\) 1.00000 0.0589256
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 3.50000 + 6.06218i 0.205174 + 0.355371i
\(292\) 7.00000 12.1244i 0.409644 0.709524i
\(293\) 24.0000 1.40209 0.701047 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 6.50000 2.59808i 0.379088 0.151523i
\(295\) 0 0
\(296\) −5.00000 + 8.66025i −0.290619 + 0.503367i
\(297\) 0 0
\(298\) 3.00000 + 5.19615i 0.173785 + 0.301005i
\(299\) 6.00000 10.3923i 0.346989 0.601003i
\(300\) 0 0
\(301\) 5.00000 + 25.9808i 0.288195 + 1.49751i
\(302\) 8.00000 0.460348
\(303\) 9.00000 15.5885i 0.517036 0.895533i
\(304\) −1.00000 1.73205i −0.0573539 0.0993399i
\(305\) 0 0
\(306\) 1.50000 2.59808i 0.0857493 0.148522i
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 5.00000 0.284440
\(310\) 0 0
\(311\) −4.50000 7.79423i −0.255172 0.441970i 0.709771 0.704433i \(-0.248799\pi\)
−0.964942 + 0.262463i \(0.915465\pi\)
\(312\) 2.00000 + 3.46410i 0.113228 + 0.196116i
\(313\) 2.50000 4.33013i 0.141308 0.244753i −0.786681 0.617359i \(-0.788202\pi\)
0.927990 + 0.372606i \(0.121536\pi\)
\(314\) −8.00000 −0.451466
\(315\) 0 0
\(316\) 11.0000 0.618798
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 3.00000 + 5.19615i 0.168232 + 0.291386i
\(319\) 0 0
\(320\) 0 0
\(321\) −18.0000 −1.00466
\(322\) −6.00000 + 5.19615i −0.334367 + 0.289570i
\(323\) −6.00000 −0.333849
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) 4.00000 + 6.92820i 0.221540 + 0.383718i
\(327\) 1.00000 1.73205i 0.0553001 0.0957826i
\(328\) −9.00000 −0.496942
\(329\) −7.50000 2.59808i −0.413488 0.143237i
\(330\) 0 0
\(331\) 5.00000 8.66025i 0.274825 0.476011i −0.695266 0.718752i \(-0.744713\pi\)
0.970091 + 0.242742i \(0.0780468\pi\)
\(332\) 0 0
\(333\) −5.00000 8.66025i −0.273998 0.474579i
\(334\) −12.0000 + 20.7846i −0.656611 + 1.13728i
\(335\) 0 0
\(336\) −0.500000 2.59808i −0.0272772 0.141737i
\(337\) −11.0000 −0.599208 −0.299604 0.954064i \(-0.596855\pi\)
−0.299604 + 0.954064i \(0.596855\pi\)
\(338\) −1.50000 + 2.59808i −0.0815892 + 0.141317i
\(339\) −10.5000 18.1865i −0.570282 0.987757i
\(340\) 0 0
\(341\) 0 0
\(342\) 2.00000 0.108148
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 10.0000 0.539164
\(345\) 0 0
\(346\) −9.00000 15.5885i −0.483843 0.838041i
\(347\) −18.0000 31.1769i −0.966291 1.67366i −0.706107 0.708105i \(-0.749550\pi\)
−0.260184 0.965559i \(-0.583783\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) 0 0
\(353\) −7.50000 12.9904i −0.399185 0.691408i 0.594441 0.804139i \(-0.297373\pi\)
−0.993626 + 0.112731i \(0.964040\pi\)
\(354\) −3.00000 5.19615i −0.159448 0.276172i
\(355\) 0 0
\(356\) −15.0000 −0.794998
\(357\) −7.50000 2.59808i −0.396942 0.137505i
\(358\) −6.00000 −0.317110
\(359\) −6.00000 + 10.3923i −0.316668 + 0.548485i −0.979791 0.200026i \(-0.935897\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) −4.00000 + 6.92820i −0.210235 + 0.364138i
\(363\) 11.0000 0.577350
\(364\) 8.00000 6.92820i 0.419314 0.363137i
\(365\) 0 0
\(366\) 4.00000 6.92820i 0.209083 0.362143i
\(367\) 4.00000 + 6.92820i 0.208798 + 0.361649i 0.951336 0.308155i \(-0.0997115\pi\)
−0.742538 + 0.669804i \(0.766378\pi\)
\(368\) 1.50000 + 2.59808i 0.0781929 + 0.135434i
\(369\) 4.50000 7.79423i 0.234261 0.405751i
\(370\) 0 0
\(371\) 12.0000 10.3923i 0.623009 0.539542i
\(372\) 1.00000 0.0518476
\(373\) −2.00000 + 3.46410i −0.103556 + 0.179364i −0.913147 0.407630i \(-0.866355\pi\)
0.809591 + 0.586994i \(0.199689\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −1.50000 + 2.59808i −0.0773566 + 0.133986i
\(377\) 0 0
\(378\) 2.50000 + 0.866025i 0.128586 + 0.0445435i
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) 8.00000 + 13.8564i 0.409852 + 0.709885i
\(382\) 10.5000 + 18.1865i 0.537227 + 0.930504i
\(383\) 10.5000 18.1865i 0.536525 0.929288i −0.462563 0.886586i \(-0.653070\pi\)
0.999088 0.0427020i \(-0.0135966\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −17.0000 −0.865277
\(387\) −5.00000 + 8.66025i −0.254164 + 0.440225i
\(388\) −3.50000 6.06218i −0.177686 0.307760i
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 0 0
\(391\) 9.00000 0.455150
\(392\) −6.50000 + 2.59808i −0.328300 + 0.131223i
\(393\) 12.0000 0.605320
\(394\) −6.00000 + 10.3923i −0.302276 + 0.523557i
\(395\) 0 0
\(396\) 0 0
\(397\) −11.0000 + 19.0526i −0.552074 + 0.956221i 0.446051 + 0.895008i \(0.352830\pi\)
−0.998125 + 0.0612128i \(0.980503\pi\)
\(398\) 11.0000 0.551380
\(399\) −1.00000 5.19615i −0.0500626 0.260133i
\(400\) 0 0
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 2.00000 + 3.46410i 0.0997509 + 0.172774i
\(403\) 2.00000 + 3.46410i 0.0996271 + 0.172559i
\(404\) −9.00000 + 15.5885i −0.447767 + 0.775555i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −1.50000 + 2.59808i −0.0742611 + 0.128624i
\(409\) −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i \(-0.206116\pi\)
−0.921192 + 0.389109i \(0.872783\pi\)
\(410\) 0 0
\(411\) 4.50000 7.79423i 0.221969 0.384461i
\(412\) −5.00000 −0.246332
\(413\) −12.0000 + 10.3923i −0.590481 + 0.511372i
\(414\) −3.00000 −0.147442
\(415\) 0 0
\(416\) −2.00000 3.46410i −0.0980581 0.169842i
\(417\) 1.00000 + 1.73205i 0.0489702 + 0.0848189i
\(418\) 0 0
\(419\) 18.0000 0.879358 0.439679 0.898155i \(-0.355092\pi\)
0.439679 + 0.898155i \(0.355092\pi\)
\(420\) 0 0
\(421\) −40.0000 −1.94948 −0.974740 0.223341i \(-0.928304\pi\)
−0.974740 + 0.223341i \(0.928304\pi\)
\(422\) −7.00000 + 12.1244i −0.340755 + 0.590204i
\(423\) −1.50000 2.59808i −0.0729325 0.126323i
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) 0 0
\(426\) −3.00000 −0.145350
\(427\) −20.0000 6.92820i −0.967868 0.335279i
\(428\) 18.0000 0.870063
\(429\) 0 0
\(430\) 0 0
\(431\) 13.5000 + 23.3827i 0.650272 + 1.12630i 0.983057 + 0.183301i \(0.0586785\pi\)
−0.332785 + 0.943003i \(0.607988\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −29.0000 −1.39365 −0.696826 0.717241i \(-0.745405\pi\)
−0.696826 + 0.717241i \(0.745405\pi\)
\(434\) −0.500000 2.59808i −0.0240008 0.124712i
\(435\) 0 0
\(436\) −1.00000 + 1.73205i −0.0478913 + 0.0829502i
\(437\) 3.00000 + 5.19615i 0.143509 + 0.248566i
\(438\) −7.00000 12.1244i −0.334473 0.579324i
\(439\) −2.50000 + 4.33013i −0.119318 + 0.206666i −0.919498 0.393095i \(-0.871404\pi\)
0.800179 + 0.599761i \(0.204738\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) −12.0000 −0.570782
\(443\) −3.00000 + 5.19615i −0.142534 + 0.246877i −0.928450 0.371457i \(-0.878858\pi\)
0.785916 + 0.618333i \(0.212192\pi\)
\(444\) 5.00000 + 8.66025i 0.237289 + 0.410997i
\(445\) 0 0
\(446\) −9.50000 + 16.4545i −0.449838 + 0.779142i
\(447\) 6.00000 0.283790
\(448\) 0.500000 + 2.59808i 0.0236228 + 0.122748i
\(449\) −21.0000 −0.991051 −0.495526 0.868593i \(-0.665025\pi\)
−0.495526 + 0.868593i \(0.665025\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 10.5000 + 18.1865i 0.493878 + 0.855423i
\(453\) 4.00000 6.92820i 0.187936 0.325515i
\(454\) 6.00000 0.281594
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) 1.00000 1.73205i 0.0467780 0.0810219i −0.841688 0.539964i \(-0.818438\pi\)
0.888466 + 0.458942i \(0.151771\pi\)
\(458\) 2.00000 + 3.46410i 0.0934539 + 0.161867i
\(459\) −1.50000 2.59808i −0.0700140 0.121268i
\(460\) 0 0
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) −5.00000 −0.232370 −0.116185 0.993228i \(-0.537067\pi\)
−0.116185 + 0.993228i \(0.537067\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −15.0000 25.9808i −0.694862 1.20354i
\(467\) 6.00000 10.3923i 0.277647 0.480899i −0.693153 0.720791i \(-0.743779\pi\)
0.970799 + 0.239892i \(0.0771121\pi\)
\(468\) 4.00000 0.184900
\(469\) 8.00000 6.92820i 0.369406 0.319915i
\(470\) 0 0
\(471\) −4.00000 + 6.92820i −0.184310 + 0.319235i
\(472\) 3.00000 + 5.19615i 0.138086 + 0.239172i
\(473\) 0 0
\(474\) 5.50000 9.52628i 0.252623 0.437557i
\(475\) 0 0
\(476\) 7.50000 + 2.59808i 0.343762 + 0.119083i
\(477\) 6.00000 0.274721
\(478\) −7.50000 + 12.9904i −0.343042 + 0.594166i
\(479\) 13.5000 + 23.3827i 0.616831 + 1.06838i 0.990060 + 0.140643i \(0.0449170\pi\)
−0.373230 + 0.927739i \(0.621750\pi\)
\(480\) 0 0
\(481\) −20.0000 + 34.6410i −0.911922 + 1.57949i
\(482\) 14.0000 0.637683
\(483\) 1.50000 + 7.79423i 0.0682524 + 0.354650i
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) −15.5000 26.8468i −0.702372 1.21654i −0.967632 0.252367i \(-0.918791\pi\)
0.265260 0.964177i \(-0.414542\pi\)
\(488\) −4.00000 + 6.92820i −0.181071 + 0.313625i
\(489\) 8.00000 0.361773
\(490\) 0 0
\(491\) −6.00000 −0.270776 −0.135388 0.990793i \(-0.543228\pi\)
−0.135388 + 0.990793i \(0.543228\pi\)
\(492\) −4.50000 + 7.79423i −0.202876 + 0.351391i
\(493\) 0 0
\(494\) −4.00000 6.92820i −0.179969 0.311715i
\(495\) 0 0
\(496\) −1.00000 −0.0449013
\(497\) 1.50000 + 7.79423i 0.0672842 + 0.349619i
\(498\) 0 0
\(499\) −16.0000 + 27.7128i −0.716258 + 1.24060i 0.246214 + 0.969216i \(0.420813\pi\)
−0.962472 + 0.271380i \(0.912520\pi\)
\(500\) 0 0
\(501\) 12.0000 + 20.7846i 0.536120 + 0.928588i
\(502\) −6.00000 + 10.3923i −0.267793 + 0.463831i
\(503\) 36.0000 1.60516 0.802580 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) −2.50000 0.866025i −0.111359 0.0385758i
\(505\) 0 0
\(506\) 0 0
\(507\) 1.50000 + 2.59808i 0.0666173 + 0.115385i
\(508\) −8.00000 13.8564i −0.354943 0.614779i
\(509\) 18.0000 31.1769i 0.797836 1.38189i −0.123187 0.992384i \(-0.539311\pi\)
0.921023 0.389509i \(-0.127355\pi\)
\(510\) 0 0
\(511\) −28.0000 + 24.2487i −1.23865 + 1.07270i
\(512\) 1.00000 0.0441942
\(513\) 1.00000 1.73205i 0.0441511 0.0764719i
\(514\) 15.0000 + 25.9808i 0.661622 + 1.14596i
\(515\) 0 0
\(516\) 5.00000 8.66025i 0.220113 0.381246i
\(517\) 0 0
\(518\) 20.0000 17.3205i 0.878750 0.761019i
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) −7.50000 12.9904i −0.328581 0.569119i 0.653650 0.756797i \(-0.273237\pi\)
−0.982231 + 0.187678i \(0.939904\pi\)
\(522\) 0 0
\(523\) 16.0000 27.7128i 0.699631 1.21180i −0.268963 0.963150i \(-0.586681\pi\)
0.968594 0.248646i \(-0.0799857\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) −9.00000 −0.392419
\(527\) −1.50000 + 2.59808i −0.0653410 + 0.113174i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 1.00000 + 5.19615i 0.0433555 + 0.225282i
\(533\) −36.0000 −1.55933
\(534\) −7.50000 + 12.9904i −0.324557 + 0.562149i
\(535\) 0 0
\(536\) −2.00000 3.46410i −0.0863868 0.149626i
\(537\) −3.00000 + 5.19615i −0.129460 + 0.224231i
\(538\) −6.00000 −0.258678
\(539\) 0 0
\(540\) 0 0
\(541\) 8.00000 13.8564i 0.343947 0.595733i −0.641215 0.767361i \(-0.721569\pi\)
0.985162 + 0.171628i \(0.0549027\pi\)
\(542\) 3.50000 + 6.06218i 0.150338 + 0.260393i
\(543\) 4.00000 + 6.92820i 0.171656 + 0.297318i
\(544\) 1.50000 2.59808i 0.0643120 0.111392i
\(545\) 0 0
\(546\) −2.00000 10.3923i −0.0855921 0.444750i
\(547\) −26.0000 −1.11168 −0.555840 0.831289i \(-0.687603\pi\)
−0.555840 + 0.831289i \(0.687603\pi\)
\(548\) −4.50000 + 7.79423i −0.192230 + 0.332953i
\(549\) −4.00000 6.92820i −0.170716 0.295689i
\(550\) 0 0
\(551\) 0 0
\(552\) 3.00000 0.127688
\(553\) −27.5000 9.52628i −1.16942 0.405099i
\(554\) 28.0000 1.18961
\(555\) 0 0
\(556\) −1.00000 1.73205i −0.0424094 0.0734553i
\(557\) 3.00000 + 5.19615i 0.127114 + 0.220168i 0.922557 0.385860i \(-0.126095\pi\)
−0.795443 + 0.606028i \(0.792762\pi\)
\(558\) 0.500000 0.866025i 0.0211667 0.0366618i
\(559\) 40.0000 1.69182
\(560\) 0 0
\(561\) 0 0
\(562\) −4.50000 + 7.79423i −0.189821 + 0.328780i
\(563\) −15.0000 25.9808i −0.632175 1.09496i −0.987106 0.160066i \(-0.948829\pi\)
0.354932 0.934892i \(-0.384504\pi\)
\(564\) 1.50000 + 2.59808i 0.0631614 + 0.109399i
\(565\) 0 0
\(566\) 4.00000 0.168133
\(567\) 2.00000 1.73205i 0.0839921 0.0727393i
\(568\) 3.00000 0.125877
\(569\) −13.5000 + 23.3827i −0.565949 + 0.980253i 0.431011 + 0.902347i \(0.358157\pi\)
−0.996961 + 0.0779066i \(0.975176\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) 0 0
\(573\) 21.0000 0.877288
\(574\) 22.5000 + 7.79423i 0.939132 + 0.325325i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 7.00000 + 12.1244i 0.291414 + 0.504744i 0.974144 0.225927i \(-0.0725410\pi\)
−0.682730 + 0.730670i \(0.739208\pi\)
\(578\) 4.00000 + 6.92820i 0.166378 + 0.288175i
\(579\) −8.50000 + 14.7224i −0.353248 + 0.611843i
\(580\) 0 0
\(581\) 0 0
\(582\) −7.00000 −0.290159
\(583\) 0 0
\(584\) 7.00000 + 12.1244i 0.289662 + 0.501709i
\(585\) 0 0
\(586\) −12.0000 + 20.7846i −0.495715 + 0.858604i
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) −1.00000 + 6.92820i −0.0412393 + 0.285714i
\(589\) −2.00000 −0.0824086
\(590\) 0 0
\(591\) 6.00000 + 10.3923i 0.246807 + 0.427482i
\(592\) −5.00000 8.66025i −0.205499 0.355934i
\(593\) 10.5000 18.1865i 0.431183 0.746831i −0.565792 0.824548i \(-0.691430\pi\)
0.996976 + 0.0777165i \(0.0247629\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 5.50000 9.52628i 0.225100 0.389885i
\(598\) 6.00000 + 10.3923i 0.245358 + 0.424973i
\(599\) 1.50000 + 2.59808i 0.0612883 + 0.106155i 0.895042 0.445983i \(-0.147146\pi\)
−0.833753 + 0.552137i \(0.813812\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) −25.0000 8.66025i −1.01892 0.352966i
\(603\) 4.00000 0.162893
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) 0 0
\(606\) 9.00000 + 15.5885i 0.365600 + 0.633238i
\(607\) −3.50000 + 6.06218i −0.142061 + 0.246056i −0.928272 0.371901i \(-0.878706\pi\)
0.786212 + 0.617957i \(0.212039\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) −6.00000 + 10.3923i −0.242734 + 0.420428i
\(612\) 1.50000 + 2.59808i 0.0606339 + 0.105021i
\(613\) −8.00000 13.8564i −0.323117 0.559655i 0.658012 0.753007i \(-0.271397\pi\)
−0.981129 + 0.193352i \(0.938064\pi\)
\(614\) −14.0000 + 24.2487i −0.564994 + 0.978598i
\(615\) 0 0
\(616\) 0 0
\(617\) 15.0000 0.603877 0.301939 0.953327i \(-0.402366\pi\)
0.301939 + 0.953327i \(0.402366\pi\)
\(618\) −2.50000 + 4.33013i −0.100565 + 0.174183i
\(619\) −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i \(-0.298329\pi\)
−0.993959 + 0.109749i \(0.964995\pi\)
\(620\) 0 0
\(621\) −1.50000 + 2.59808i −0.0601929 + 0.104257i
\(622\) 9.00000 0.360867
\(623\) 37.5000 + 12.9904i 1.50241 + 0.520449i
\(624\) −4.00000 −0.160128
\(625\) 0 0
\(626\) 2.50000 + 4.33013i 0.0999201 + 0.173067i
\(627\) 0 0
\(628\) 4.00000 6.92820i 0.159617 0.276465i
\(629\) −30.0000 −1.19618
\(630\) 0 0
\(631\) −37.0000 −1.47295 −0.736473 0.676467i \(-0.763510\pi\)
−0.736473 + 0.676467i \(0.763510\pi\)
\(632\) −5.50000 + 9.52628i −0.218778 + 0.378935i
\(633\) 7.00000 + 12.1244i 0.278225 + 0.481900i
\(634\) −9.00000 15.5885i −0.357436 0.619097i
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) −26.0000 + 10.3923i −1.03016 + 0.411758i
\(638\) 0 0
\(639\) −1.50000 + 2.59808i −0.0593391 + 0.102778i
\(640\) 0 0
\(641\) 16.5000 + 28.5788i 0.651711 + 1.12880i 0.982708 + 0.185164i \(0.0592817\pi\)
−0.330997 + 0.943632i \(0.607385\pi\)
\(642\) 9.00000 15.5885i 0.355202 0.615227i
\(643\) −38.0000 −1.49857 −0.749287 0.662246i \(-0.769604\pi\)
−0.749287 + 0.662246i \(0.769604\pi\)
\(644\) −1.50000 7.79423i −0.0591083 0.307136i
\(645\) 0 0
\(646\) 3.00000 5.19615i 0.118033 0.204440i
\(647\) 12.0000 + 20.7846i 0.471769 + 0.817127i 0.999478 0.0322975i \(-0.0102824\pi\)
−0.527710 + 0.849425i \(0.676949\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 0 0
\(650\) 0 0
\(651\) −2.50000 0.866025i −0.0979827 0.0339422i
\(652\) −8.00000 −0.313304
\(653\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(654\) 1.00000 + 1.73205i 0.0391031 + 0.0677285i
\(655\) 0 0
\(656\) 4.50000 7.79423i 0.175695 0.304314i
\(657\) −14.0000 −0.546192
\(658\) 6.00000 5.19615i 0.233904 0.202567i
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) 5.00000 + 8.66025i 0.194477 + 0.336845i 0.946729 0.322031i \(-0.104366\pi\)
−0.752252 + 0.658876i \(0.771032\pi\)
\(662\) 5.00000 + 8.66025i 0.194331 + 0.336590i
\(663\) −6.00000 + 10.3923i −0.233021 + 0.403604i
\(664\) 0 0
\(665\) 0 0
\(666\) 10.0000 0.387492
\(667\) 0 0
\(668\) −12.0000 20.7846i −0.464294 0.804181i
\(669\) 9.50000 + 16.4545i 0.367291 + 0.636167i
\(670\) 0 0
\(671\) 0 0
\(672\) 2.50000 + 0.866025i 0.0964396 + 0.0334077i
\(673\) 19.0000 0.732396 0.366198 0.930537i \(-0.380659\pi\)
0.366198 + 0.930537i \(0.380659\pi\)
\(674\) 5.50000 9.52628i 0.211852 0.366939i
\(675\) 0 0
\(676\) −1.50000 2.59808i −0.0576923 0.0999260i
\(677\) −6.00000 + 10.3923i −0.230599 + 0.399409i −0.957984 0.286820i \(-0.907402\pi\)
0.727386 + 0.686229i \(0.240735\pi\)
\(678\) 21.0000 0.806500
\(679\) 3.50000 + 18.1865i 0.134318 + 0.697935i
\(680\) 0 0
\(681\) 3.00000 5.19615i 0.114960 0.199117i
\(682\) 0 0
\(683\) 3.00000 + 5.19615i 0.114792 + 0.198825i 0.917697 0.397282i \(-0.130047\pi\)
−0.802905 + 0.596107i \(0.796713\pi\)
\(684\) −1.00000 + 1.73205i −0.0382360 + 0.0662266i
\(685\) 0 0
\(686\) 18.5000 0.866025i 0.706333 0.0330650i
\(687\) 4.00000 0.152610
\(688\) −5.00000 + 8.66025i −0.190623 + 0.330169i
\(689\) −12.0000 20.7846i −0.457164 0.791831i
\(690\) 0 0
\(691\) −10.0000 + 17.3205i −0.380418 + 0.658903i −0.991122 0.132956i \(-0.957553\pi\)
0.610704 + 0.791859i \(0.290887\pi\)
\(692\) 18.0000 0.684257
\(693\) 0 0
\(694\) 36.0000 1.36654
\(695\) 0 0
\(696\) 0 0
\(697\) −13.5000 23.3827i −0.511349 0.885682i
\(698\) −13.0000 + 22.5167i −0.492057 + 0.852268i
\(699\) −30.0000 −1.13470
\(700\) 0 0
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) 2.00000 3.46410i 0.0754851 0.130744i
\(703\) −10.0000 17.3205i −0.377157 0.653255i
\(704\) 0 0
\(705\) 0 0
\(706\) 15.0000 0.564532
\(707\) 36.0000 31.1769i 1.35392 1.17253i
\(708\) 6.00000 0.225494
\(709\) 17.0000 29.4449i 0.638448 1.10583i −0.347325 0.937745i \(-0.612910\pi\)
0.985773 0.168080i \(-0.0537568\pi\)
\(710\) 0 0
\(711\) −5.50000 9.52628i −0.206266 0.357263i
\(712\) 7.50000 12.9904i 0.281074 0.486835i
\(713\) 3.00000 0.112351
\(714\) 6.00000 5.19615i 0.224544 0.194461i
\(715\) 0 0
\(716\) 3.00000 5.19615i 0.112115 0.194189i
\(717\) 7.50000 + 12.9904i 0.280093 + 0.485135i
\(718\) −6.00000 10.3923i −0.223918 0.387837i
\(719\) 13.5000 23.3827i 0.503465 0.872027i −0.496527 0.868021i \(-0.665392\pi\)
0.999992 0.00400572i \(-0.00127506\pi\)
\(720\) 0 0
\(721\) 12.5000 + 4.33013i 0.465524 + 0.161262i
\(722\) −15.0000 −0.558242
\(723\) 7.00000 12.1244i 0.260333 0.450910i
\(724\) −4.00000 6.92820i −0.148659 0.257485i
\(725\) 0 0
\(726\) −5.50000 + 9.52628i −0.204124 + 0.353553i
\(727\) 37.0000 1.37225 0.686127 0.727482i \(-0.259309\pi\)
0.686127 + 0.727482i \(0.259309\pi\)
\(728\) 2.00000 + 10.3923i 0.0741249 + 0.385164i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 15.0000 + 25.9808i 0.554795 + 0.960933i
\(732\) 4.00000 + 6.92820i 0.147844 + 0.256074i
\(733\) 7.00000 12.1244i 0.258551 0.447823i −0.707303 0.706910i \(-0.750088\pi\)
0.965854 + 0.259087i \(0.0834217\pi\)
\(734\) −8.00000 −0.295285
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) 0 0
\(738\) 4.50000 + 7.79423i 0.165647 + 0.286910i
\(739\) −1.00000 1.73205i −0.0367856 0.0637145i 0.847046 0.531519i \(-0.178379\pi\)
−0.883832 + 0.467804i \(0.845045\pi\)
\(740\) 0 0
\(741\) −8.00000 −0.293887
\(742\) 3.00000 + 15.5885i 0.110133 + 0.572270i
\(743\) 51.0000 1.87101 0.935504 0.353315i \(-0.114946\pi\)
0.935504 + 0.353315i \(0.114946\pi\)
\(744\) −0.500000 + 0.866025i −0.0183309 + 0.0317500i
\(745\) 0 0
\(746\) −2.00000 3.46410i −0.0732252 0.126830i
\(747\) 0 0
\(748\) 0 0
\(749\) −45.0000 15.5885i −1.64426 0.569590i
\(750\) 0 0
\(751\) 8.00000 13.8564i 0.291924 0.505627i −0.682341 0.731034i \(-0.739038\pi\)
0.974265 + 0.225407i \(0.0723712\pi\)
\(752\) −1.50000 2.59808i −0.0546994 0.0947421i
\(753\) 6.00000 + 10.3923i 0.218652 + 0.378717i
\(754\) 0 0
\(755\) 0 0
\(756\) −2.00000 + 1.73205i −0.0727393 + 0.0629941i
\(757\) 16.0000 0.581530 0.290765 0.956795i \(-0.406090\pi\)
0.290765 + 0.956795i \(0.406090\pi\)
\(758\) 8.00000 13.8564i 0.290573 0.503287i
\(759\) 0 0
\(760\) 0 0
\(761\) −13.5000 + 23.3827i −0.489375 + 0.847622i −0.999925 0.0122260i \(-0.996108\pi\)
0.510551 + 0.859848i \(0.329442\pi\)
\(762\) −16.0000 −0.579619
\(763\) 4.00000 3.46410i 0.144810 0.125409i
\(764\) −21.0000 −0.759753
\(765\) 0 0
\(766\) 10.5000 + 18.1865i 0.379380 + 0.657106i
\(767\) 12.0000 + 20.7846i 0.433295 + 0.750489i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) 26.0000 0.937584 0.468792 0.883309i \(-0.344689\pi\)
0.468792 + 0.883309i \(0.344689\pi\)
\(770\) 0 0
\(771\) 30.0000 1.08042
\(772\) 8.50000 14.7224i 0.305922 0.529872i
\(773\) 9.00000 + 15.5885i 0.323708 + 0.560678i 0.981250 0.192740i \(-0.0617373\pi\)
−0.657542 + 0.753418i \(0.728404\pi\)
\(774\) −5.00000 8.66025i −0.179721 0.311286i
\(775\) 0 0
\(776\) 7.00000 0.251285
\(777\) −5.00000 25.9808i −0.179374 0.932055i
\(778\) 6.00000 0.215110
\(779\) 9.00000 15.5885i 0.322458 0.558514i
\(780\) 0 0
\(781\) 0 0
\(782\) −4.50000 + 7.79423i −0.160920 + 0.278721i
\(783\) 0 0
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) 0 0
\(786\) −6.00000 + 10.3923i −0.214013 + 0.370681i
\(787\) −11.0000 19.0526i −0.392108 0.679150i 0.600620 0.799535i \(-0.294921\pi\)
−0.992727 + 0.120384i \(0.961587\pi\)
\(788\) −6.00000 10.3923i −0.213741 0.370211i
\(789\) −4.50000 + 7.79423i −0.160204 + 0.277482i
\(790\) 0 0
\(791\) −10.5000 54.5596i −0.373337 1.93992i
\(792\) 0 0
\(793\) −16.0000 + 27.7128i −0.568177 + 0.984111i
\(794\) −11.0000 19.0526i −0.390375 0.676150i
\(795\) 0 0
\(796\) −5.50000 + 9.52628i −0.194942 + 0.337650i
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 5.00000 + 1.73205i 0.176998 + 0.0613139i
\(799\) −9.00000 −0.318397
\(800\) 0 0
\(801\) 7.50000 + 12.9904i 0.264999 + 0.458993i
\(802\) −9.00000 15.5885i −0.317801 0.550448i
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) −4.00000 −0.140894
\(807\) −3.00000 + 5.19615i −0.105605 + 0.182913i
\(808\) −9.00000 15.5885i −0.316619 0.548400i
\(809\) −3.00000 5.19615i −0.105474 0.182687i 0.808458 0.588555i \(-0.200303\pi\)
−0.913932 + 0.405868i \(0.866969\pi\)
\(810\) 0 0
\(811\) 56.0000 1.96643 0.983213 0.182462i \(-0.0584065\pi\)
0.983213 + 0.182462i \(0.0584065\pi\)
\(812\) 0 0
\(813\) 7.00000 0.245501
\(814\) 0 0
\(815\) 0 0
\(816\) −1.50000 2.59808i −0.0525105 0.0909509i
\(817\) −10.0000 + 17.3205i −0.349856 + 0.605968i
\(818\) 5.00000 0.174821
\(819\) −10.0000 3.46410i −0.349428 0.121046i
\(820\) 0 0
\(821\) 27.0000 46.7654i 0.942306 1.63212i 0.181250 0.983437i \(-0.441986\pi\)
0.761056 0.648686i \(-0.224681\pi\)
\(822\) 4.50000 + 7.79423i 0.156956 + 0.271855i
\(823\) 16.0000 + 27.7128i 0.557725 + 0.966008i 0.997686 + 0.0679910i \(0.0216589\pi\)
−0.439961 + 0.898017i \(0.645008\pi\)
\(824\) 2.50000 4.33013i 0.0870916 0.150847i
\(825\) 0 0
\(826\) −3.00000 15.5885i −0.104383 0.542392i
\(827\) −48.0000 −1.66912 −0.834562 0.550914i \(-0.814279\pi\)
−0.834562 + 0.550914i \(0.814279\pi\)
\(828\) 1.50000 2.59808i 0.0521286 0.0902894i
\(829\) −1.00000 1.73205i −0.0347314 0.0601566i 0.848137 0.529777i \(-0.177724\pi\)
−0.882869 + 0.469620i \(0.844391\pi\)
\(830\) 0 0
\(831\) 14.0000 24.2487i 0.485655 0.841178i
\(832\) 4.00000 0.138675
\(833\) −16.5000 12.9904i −0.571691 0.450090i
\(834\) −2.00000 −0.0692543
\(835\) 0 0
\(836\) 0 0
\(837\) −0.500000 0.866025i −0.0172825 0.0299342i
\(838\) −9.00000 + 15.5885i −0.310900 + 0.538494i
\(839\) 27.0000 0.932144 0.466072 0.884747i \(-0.345669\pi\)
0.466072 + 0.884747i \(0.345669\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 20.0000 34.6410i 0.689246 1.19381i
\(843\) 4.50000 + 7.79423i 0.154988 + 0.268447i
\(844\) −7.00000 12.1244i −0.240950 0.417338i
\(845\) 0 0
\(846\) 3.00000 0.103142
\(847\) 27.5000 + 9.52628i 0.944911 + 0.327327i
\(848\) 6.00000 0.206041
\(849\) 2.00000 3.46410i 0.0686398 0.118888i
\(850\) 0 0
\(851\) 15.0000 + 25.9808i 0.514193 + 0.890609i
\(852\) 1.50000 2.59808i 0.0513892 0.0890086i
\(853\) −26.0000 −0.890223 −0.445112 0.895475i \(-0.646836\pi\)
−0.445112 + 0.895475i \(0.646836\pi\)
\(854\) 16.0000 13.8564i 0.547509 0.474156i
\(855\) 0 0
\(856\) −9.00000 + 15.5885i −0.307614 + 0.532803i
\(857\) 27.0000 + 46.7654i 0.922302 + 1.59747i 0.795843 + 0.605503i \(0.207028\pi\)
0.126459 + 0.991972i \(0.459639\pi\)
\(858\) 0 0
\(859\) 2.00000 3.46410i 0.0682391 0.118194i −0.829887 0.557931i \(-0.811595\pi\)
0.898126 + 0.439738i \(0.144929\pi\)
\(860\) 0 0
\(861\) 18.0000 15.5885i 0.613438 0.531253i
\(862\) −27.0000 −0.919624
\(863\) −7.50000 + 12.9904i −0.255303 + 0.442198i −0.964978 0.262332i \(-0.915509\pi\)
0.709675 + 0.704529i \(0.248842\pi\)
\(864\) 0.500000 + 0.866025i 0.0170103 + 0.0294628i
\(865\) 0 0
\(866\) 14.5000 25.1147i 0.492730 0.853433i
\(867\) 8.00000 0.271694
\(868\) 2.50000 + 0.866025i 0.0848555 + 0.0293948i
\(869\) 0 0
\(870\) 0 0
\(871\) −8.00000 13.8564i −0.271070 0.469506i
\(872\) −1.00000 1.73205i −0.0338643 0.0586546i
\(873\) −3.50000 + 6.06218i −0.118457 + 0.205174i
\(874\) −6.00000 −0.202953
\(875\) 0 0
\(876\) 14.0000 0.473016
\(877\) 19.0000 32.9090i 0.641584 1.11126i −0.343495 0.939155i \(-0.611611\pi\)
0.985079 0.172102i \(-0.0550559\pi\)
\(878\) −2.50000 4.33013i −0.0843709 0.146135i
\(879\) 12.0000 + 20.7846i 0.404750 + 0.701047i
\(880\) 0 0
\(881\) −3.00000 −0.101073 −0.0505363 0.998722i \(-0.516093\pi\)
−0.0505363 + 0.998722i \(0.516093\pi\)
\(882\) 5.50000 + 4.33013i 0.185195 + 0.145803i
\(883\) −38.0000 −1.27880 −0.639401 0.768874i \(-0.720818\pi\)
−0.639401 + 0.768874i \(0.720818\pi\)
\(884\) 6.00000 10.3923i 0.201802 0.349531i
\(885\) 0 0
\(886\) −3.00000 5.19615i −0.100787 0.174568i
\(887\) 24.0000 41.5692i 0.805841 1.39576i −0.109881 0.993945i \(-0.535047\pi\)
0.915722 0.401813i \(-0.131620\pi\)
\(888\) −10.0000 −0.335578
\(889\) 8.00000 + 41.5692i 0.268311 + 1.39419i
\(890\) 0 0
\(891\) 0 0
\(892\) −9.50000 16.4545i −0.318084 0.550937i
\(893\) −3.00000 5.19615i −0.100391 0.173883i
\(894\) −3.00000 + 5.19615i −0.100335 + 0.173785i
\(895\) 0 0
\(896\) −2.50000 0.866025i −0.0835191 0.0289319i
\(897\) 12.0000 0.400668
\(898\) 10.5000 18.1865i 0.350390 0.606892i
\(899\) 0 0
\(900\) 0 0
\(901\) 9.00000 15.5885i 0.299833 0.519327i
\(902\) 0 0
\(903\) −20.0000 + 17.3205i −0.665558 + 0.576390i
\(904\) −21.0000 −0.698450
\(905\) 0 0
\(906\) 4.00000 + 6.92820i 0.132891 + 0.230174i
\(907\) −8.00000 13.8564i −0.265636 0.460094i 0.702094 0.712084i \(-0.252248\pi\)
−0.967730 + 0.251990i \(0.918915\pi\)
\(908\) −3.00000 + 5.19615i −0.0995585 + 0.172440i
\(909\) 18.0000 0.597022
\(910\) 0 0
\(911\) 39.0000 1.29213 0.646064 0.763283i \(-0.276414\pi\)
0.646064 + 0.763283i \(0.276414\pi\)
\(912\) 1.00000 1.73205i 0.0331133 0.0573539i
\(913\) 0 0
\(914\) 1.00000 + 1.73205i 0.0330771 + 0.0572911i
\(915\) 0 0
\(916\) −4.00000 −0.132164
\(917\) 30.0000 + 10.3923i 0.990687 + 0.343184i
\(918\) 3.00000 0.0990148
\(919\) 9.50000 16.4545i 0.313376 0.542783i −0.665715 0.746206i \(-0.731873\pi\)
0.979091 + 0.203423i \(0.0652066\pi\)
\(920\) 0 0
\(921\) 14.0000 + 24.2487i 0.461316 + 0.799022i
\(922\) 6.00000 10.3923i 0.197599 0.342252i
\(923\) 12.0000 0.394985
\(924\) 0 0
\(925\) 0 0
\(926\) 2.50000 4.33013i 0.0821551 0.142297i
\(927\) 2.50000 + 4.33013i 0.0821108 + 0.142220i
\(928\) 0 0
\(929\) −9.00000 + 15.5885i −0.295280 + 0.511441i −0.975050 0.221985i \(-0.928746\pi\)
0.679770 + 0.733426i \(0.262080\pi\)
\(930\) 0 0
\(931\) 2.00000 13.8564i 0.0655474 0.454125i
\(932\) 30.0000 0.982683
\(933\) 4.50000 7.79423i 0.147323 0.255172i
\(934\) 6.00000 + 10.3923i 0.196326 + 0.340047i
\(935\) 0 0
\(936\) −2.00000 + 3.46410i −0.0653720 + 0.113228i
\(937\) −26.0000 −0.849383 −0.424691 0.905338i \(-0.639617\pi\)
−0.424691 + 0.905338i \(0.639617\pi\)
\(938\) 2.00000 + 10.3923i 0.0653023 + 0.339321i
\(939\) 5.00000 0.163169
\(940\) 0 0
\(941\) −15.0000 25.9808i −0.488986 0.846949i 0.510934 0.859620i \(-0.329300\pi\)
−0.999920 + 0.0126715i \(0.995966\pi\)
\(942\) −4.00000 6.92820i −0.130327 0.225733i
\(943\) −13.5000 + 23.3827i −0.439620 + 0.761445i
\(944\) −6.00000 −0.195283
\(945\) 0 0
\(946\) 0 0
\(947\) −24.0000 + 41.5692i −0.779895 + 1.35082i 0.152106 + 0.988364i \(0.451394\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(948\) 5.50000 + 9.52628i 0.178632 + 0.309399i
\(949\) 28.0000 + 48.4974i 0.908918 + 1.57429i
\(950\) 0 0
\(951\) −18.0000 −0.583690
\(952\) −6.00000 + 5.19615i −0.194461 + 0.168408i
\(953\) −6.00000 −0.194359 −0.0971795 0.995267i \(-0.530982\pi\)
−0.0971795 + 0.995267i \(0.530982\pi\)
\(954\) −3.00000 + 5.19615i −0.0971286 + 0.168232i
\(955\) 0 0
\(956\) −7.50000 12.9904i −0.242567 0.420139i
\(957\) 0 0
\(958\) −27.0000 −0.872330
\(959\) 18.0000 15.5885i 0.581250 0.503378i
\(960\) 0 0
\(961\) 15.0000 25.9808i 0.483871 0.838089i
\(962\) −20.0000 34.6410i −0.644826 1.11687i
\(963\) −9.00000 15.5885i −0.290021 0.502331i
\(964\) −7.00000 + 12.1244i −0.225455 + 0.390499i
\(965\) 0 0
\(966\) −7.50000 2.59808i −0.241309 0.0835917i
\(967\) 49.0000 1.57573 0.787867 0.615846i \(-0.211185\pi\)
0.787867 + 0.615846i \(0.211185\pi\)
\(968\) 5.50000 9.52628i 0.176777 0.306186i
\(969\) −3.00000 5.19615i −0.0963739 0.166924i
\(970\) 0 0
\(971\) 18.0000 31.1769i 0.577647 1.00051i −0.418101 0.908401i \(-0.637304\pi\)
0.995748 0.0921142i \(-0.0293625\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 1.00000 + 5.19615i 0.0320585 + 0.166581i
\(974\) 31.0000 0.993304
\(975\) 0 0
\(976\) −4.00000 6.92820i −0.128037 0.221766i
\(977\) 13.5000 + 23.3827i 0.431903 + 0.748078i 0.997037 0.0769208i \(-0.0245089\pi\)
−0.565134 + 0.824999i \(0.691176\pi\)
\(978\) −4.00000 + 6.92820i −0.127906 + 0.221540i
\(979\) 0 0
\(980\) 0 0
\(981\) 2.00000 0.0638551
\(982\) 3.00000 5.19615i 0.0957338 0.165816i
\(983\) −6.00000 10.3923i −0.191370 0.331463i 0.754334 0.656490i \(-0.227960\pi\)
−0.945705 + 0.325027i \(0.894626\pi\)
\(984\) −4.50000 7.79423i −0.143455 0.248471i
\(985\) 0 0
\(986\) 0 0
\(987\) −1.50000 7.79423i −0.0477455 0.248093i
\(988\) 8.00000 0.254514
\(989\) 15.0000 25.9808i 0.476972 0.826140i
\(990\) 0 0
\(991\) −29.5000 51.0955i −0.937098 1.62310i −0.770849 0.637018i \(-0.780168\pi\)
−0.166250 0.986084i \(-0.553166\pi\)
\(992\) 0.500000 0.866025i 0.0158750 0.0274963i
\(993\) 10.0000 0.317340
\(994\) −7.50000 2.59808i −0.237886 0.0824060i
\(995\) 0 0
\(996\) 0 0
\(997\) −20.0000 34.6410i −0.633406 1.09709i −0.986850 0.161636i \(-0.948323\pi\)
0.353444 0.935456i \(-0.385010\pi\)
\(998\) −16.0000 27.7128i −0.506471 0.877234i
\(999\) 5.00000 8.66025i 0.158193 0.273998i
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 1050.2.i.h.751.1 yes 2
5.2 odd 4 1050.2.o.e.499.1 4
5.3 odd 4 1050.2.o.e.499.2 4
5.4 even 2 1050.2.i.m.751.1 yes 2
7.2 even 3 7350.2.a.by.1.1 1
7.4 even 3 inner 1050.2.i.h.151.1 2
7.5 odd 6 7350.2.a.cq.1.1 1
35.4 even 6 1050.2.i.m.151.1 yes 2
35.9 even 6 7350.2.a.bb.1.1 1
35.18 odd 12 1050.2.o.e.949.1 4
35.19 odd 6 7350.2.a.n.1.1 1
35.32 odd 12 1050.2.o.e.949.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.i.h.151.1 2 7.4 even 3 inner
1050.2.i.h.751.1 yes 2 1.1 even 1 trivial
1050.2.i.m.151.1 yes 2 35.4 even 6
1050.2.i.m.751.1 yes 2 5.4 even 2
1050.2.o.e.499.1 4 5.2 odd 4
1050.2.o.e.499.2 4 5.3 odd 4
1050.2.o.e.949.1 4 35.18 odd 12
1050.2.o.e.949.2 4 35.32 odd 12
7350.2.a.n.1.1 1 35.19 odd 6
7350.2.a.bb.1.1 1 35.9 even 6
7350.2.a.by.1.1 1 7.2 even 3
7350.2.a.cq.1.1 1 7.5 odd 6