Properties

Label 1274.2.g.g.295.1
Level $1274$
Weight $2$
Character 1274.295
Analytic conductor $10.173$
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] = [1274,2,Mod(295,1274)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1274, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("1274.295");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1274.g (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: \(10.1729412175\)
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: no (minimal twist has level 182)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1274.295
Dual form 1274.2.g.g.393.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{10} -1.00000 q^{12} +(-2.50000 + 2.59808i) q^{13} +(-1.50000 + 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +2.00000 q^{18} +(-2.00000 - 3.46410i) q^{19} +(1.50000 + 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{24} +4.00000 q^{25} +(1.00000 + 3.46410i) q^{26} +5.00000 q^{27} +(-3.00000 + 5.19615i) q^{29} +(1.50000 + 2.59808i) q^{30} +10.0000 q^{31} +(0.500000 + 0.866025i) q^{32} +6.00000 q^{34} +(1.00000 - 1.73205i) q^{36} +(-4.00000 + 6.92820i) q^{37} -4.00000 q^{38} +(1.00000 + 3.46410i) q^{39} +3.00000 q^{40} +(-4.00000 - 6.92820i) q^{43} +(-3.00000 - 5.19615i) q^{45} +(1.50000 + 2.59808i) q^{46} -6.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(2.00000 - 3.46410i) q^{50} +6.00000 q^{51} +(3.50000 + 0.866025i) q^{52} +12.0000 q^{53} +(2.50000 - 4.33013i) q^{54} -4.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +(1.50000 + 2.59808i) q^{59} +3.00000 q^{60} +(5.50000 + 9.52628i) q^{61} +(5.00000 - 8.66025i) q^{62} +1.00000 q^{64} +(7.50000 - 7.79423i) q^{65} +(-1.00000 + 1.73205i) q^{67} +(3.00000 - 5.19615i) q^{68} +(1.50000 + 2.59808i) q^{69} +(1.50000 + 2.59808i) q^{71} +(-1.00000 - 1.73205i) q^{72} -2.00000 q^{73} +(4.00000 + 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{75} +(-2.00000 + 3.46410i) q^{76} +(3.50000 + 0.866025i) q^{78} -4.00000 q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-9.00000 - 15.5885i) q^{85} -8.00000 q^{86} +(3.00000 + 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{89} -6.00000 q^{90} +3.00000 q^{92} +(5.00000 - 8.66025i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(6.00000 + 10.3923i) q^{95} +1.00000 q^{96} +(1.00000 + 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{3} - q^{4} - 6 q^{5} - q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + q^{3} - q^{4} - 6 q^{5} - q^{6} - 2 q^{8} + 2 q^{9} - 3 q^{10} - 2 q^{12} - 5 q^{13} - 3 q^{15} - q^{16} + 6 q^{17} + 4 q^{18} - 4 q^{19} + 3 q^{20} - 3 q^{23} - q^{24} + 8 q^{25} + 2 q^{26} + 10 q^{27} - 6 q^{29} + 3 q^{30} + 20 q^{31} + q^{32} + 12 q^{34} + 2 q^{36} - 8 q^{37} - 8 q^{38} + 2 q^{39} + 6 q^{40} - 8 q^{43} - 6 q^{45} + 3 q^{46} - 12 q^{47} + q^{48} + 4 q^{50} + 12 q^{51} + 7 q^{52} + 24 q^{53} + 5 q^{54} - 8 q^{57} + 6 q^{58} + 3 q^{59} + 6 q^{60} + 11 q^{61} + 10 q^{62} + 2 q^{64} + 15 q^{65} - 2 q^{67} + 6 q^{68} + 3 q^{69} + 3 q^{71} - 2 q^{72} - 4 q^{73} + 8 q^{74} + 4 q^{75} - 4 q^{76} + 7 q^{78} - 8 q^{79} + 3 q^{80} - q^{81} - 18 q^{85} - 16 q^{86} + 6 q^{87} - 6 q^{89} - 12 q^{90} + 6 q^{92} + 10 q^{93} - 6 q^{94} + 12 q^{95} + 2 q^{96} + 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(885\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) −1.50000 + 2.59808i −0.474342 + 0.821584i
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.50000 + 2.59808i −0.693375 + 0.720577i
\(14\) 0 0
\(15\) −1.50000 + 2.59808i −0.387298 + 0.670820i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i \(0.0927008\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) 2.00000 0.471405
\(19\) −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i \(-0.318398\pi\)
−0.998899 + 0.0469020i \(0.985065\pi\)
\(20\) 1.50000 + 2.59808i 0.335410 + 0.580948i
\(21\) 0 0
\(22\) 0 0
\(23\) −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 4.00000 0.800000
\(26\) 1.00000 + 3.46410i 0.196116 + 0.679366i
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 1.50000 + 2.59808i 0.273861 + 0.474342i
\(31\) 10.0000 1.79605 0.898027 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 1.00000 1.73205i 0.166667 0.288675i
\(37\) −4.00000 + 6.92820i −0.657596 + 1.13899i 0.323640 + 0.946180i \(0.395093\pi\)
−0.981236 + 0.192809i \(0.938240\pi\)
\(38\) −4.00000 −0.648886
\(39\) 1.00000 + 3.46410i 0.160128 + 0.554700i
\(40\) 3.00000 0.474342
\(41\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) 0 0
\(43\) −4.00000 6.92820i −0.609994 1.05654i −0.991241 0.132068i \(-0.957838\pi\)
0.381246 0.924473i \(-0.375495\pi\)
\(44\) 0 0
\(45\) −3.00000 5.19615i −0.447214 0.774597i
\(46\) 1.50000 + 2.59808i 0.221163 + 0.383065i
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 0 0
\(50\) 2.00000 3.46410i 0.282843 0.489898i
\(51\) 6.00000 0.840168
\(52\) 3.50000 + 0.866025i 0.485363 + 0.120096i
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 2.50000 4.33013i 0.340207 0.589256i
\(55\) 0 0
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) 3.00000 + 5.19615i 0.393919 + 0.682288i
\(59\) 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i \(-0.104104\pi\)
−0.751710 + 0.659494i \(0.770771\pi\)
\(60\) 3.00000 0.387298
\(61\) 5.50000 + 9.52628i 0.704203 + 1.21972i 0.966978 + 0.254858i \(0.0820288\pi\)
−0.262776 + 0.964857i \(0.584638\pi\)
\(62\) 5.00000 8.66025i 0.635001 1.09985i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 7.50000 7.79423i 0.930261 0.966755i
\(66\) 0 0
\(67\) −1.00000 + 1.73205i −0.122169 + 0.211604i −0.920623 0.390453i \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) 3.00000 5.19615i 0.363803 0.630126i
\(69\) 1.50000 + 2.59808i 0.180579 + 0.312772i
\(70\) 0 0
\(71\) 1.50000 + 2.59808i 0.178017 + 0.308335i 0.941201 0.337846i \(-0.109698\pi\)
−0.763184 + 0.646181i \(0.776365\pi\)
\(72\) −1.00000 1.73205i −0.117851 0.204124i
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 4.00000 + 6.92820i 0.464991 + 0.805387i
\(75\) 2.00000 3.46410i 0.230940 0.400000i
\(76\) −2.00000 + 3.46410i −0.229416 + 0.397360i
\(77\) 0 0
\(78\) 3.50000 + 0.866025i 0.396297 + 0.0980581i
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 1.50000 2.59808i 0.167705 0.290474i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −9.00000 15.5885i −0.976187 1.69081i
\(86\) −8.00000 −0.862662
\(87\) 3.00000 + 5.19615i 0.321634 + 0.557086i
\(88\) 0 0
\(89\) −3.00000 + 5.19615i −0.317999 + 0.550791i −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) −6.00000 −0.632456
\(91\) 0 0
\(92\) 3.00000 0.312772
\(93\) 5.00000 8.66025i 0.518476 0.898027i
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) 6.00000 + 10.3923i 0.615587 + 1.06623i
\(96\) 1.00000 0.102062
\(97\) 1.00000 + 1.73205i 0.101535 + 0.175863i 0.912317 0.409484i \(-0.134291\pi\)
−0.810782 + 0.585348i \(0.800958\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 3.00000 5.19615i 0.297044 0.514496i
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 2.50000 2.59808i 0.245145 0.254762i
\(105\) 0 0
\(106\) 6.00000 10.3923i 0.582772 1.00939i
\(107\) 9.00000 15.5885i 0.870063 1.50699i 0.00813215 0.999967i \(-0.497411\pi\)
0.861931 0.507026i \(-0.169255\pi\)
\(108\) −2.50000 4.33013i −0.240563 0.416667i
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) 4.00000 + 6.92820i 0.379663 + 0.657596i
\(112\) 0 0
\(113\) 9.00000 + 15.5885i 0.846649 + 1.46644i 0.884182 + 0.467143i \(0.154717\pi\)
−0.0375328 + 0.999295i \(0.511950\pi\)
\(114\) −2.00000 + 3.46410i −0.187317 + 0.324443i
\(115\) 4.50000 7.79423i 0.419627 0.726816i
\(116\) 6.00000 0.557086
\(117\) −7.00000 1.73205i −0.647150 0.160128i
\(118\) 3.00000 0.276172
\(119\) 0 0
\(120\) 1.50000 2.59808i 0.136931 0.237171i
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) 11.0000 0.995893
\(123\) 0 0
\(124\) −5.00000 8.66025i −0.449013 0.777714i
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) −5.50000 + 9.52628i −0.488046 + 0.845321i −0.999905 0.0137486i \(-0.995624\pi\)
0.511859 + 0.859069i \(0.328957\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −8.00000 −0.704361
\(130\) −3.00000 10.3923i −0.263117 0.911465i
\(131\) −15.0000 −1.31056 −0.655278 0.755388i \(-0.727449\pi\)
−0.655278 + 0.755388i \(0.727449\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1.00000 + 1.73205i 0.0863868 + 0.149626i
\(135\) −15.0000 −1.29099
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) −1.50000 2.59808i −0.128154 0.221969i 0.794808 0.606861i \(-0.207572\pi\)
−0.922961 + 0.384893i \(0.874238\pi\)
\(138\) 3.00000 0.255377
\(139\) −8.00000 13.8564i −0.678551 1.17529i −0.975417 0.220366i \(-0.929275\pi\)
0.296866 0.954919i \(-0.404058\pi\)
\(140\) 0 0
\(141\) −3.00000 + 5.19615i −0.252646 + 0.437595i
\(142\) 3.00000 0.251754
\(143\) 0 0
\(144\) −2.00000 −0.166667
\(145\) 9.00000 15.5885i 0.747409 1.29455i
\(146\) −1.00000 + 1.73205i −0.0827606 + 0.143346i
\(147\) 0 0
\(148\) 8.00000 0.657596
\(149\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) −2.00000 3.46410i −0.163299 0.282843i
\(151\) −1.00000 −0.0813788 −0.0406894 0.999172i \(-0.512955\pi\)
−0.0406894 + 0.999172i \(0.512955\pi\)
\(152\) 2.00000 + 3.46410i 0.162221 + 0.280976i
\(153\) −6.00000 + 10.3923i −0.485071 + 0.840168i
\(154\) 0 0
\(155\) −30.0000 −2.40966
\(156\) 2.50000 2.59808i 0.200160 0.208013i
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) −2.00000 + 3.46410i −0.159111 + 0.275589i
\(159\) 6.00000 10.3923i 0.475831 0.824163i
\(160\) −1.50000 2.59808i −0.118585 0.205396i
\(161\) 0 0
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −10.0000 17.3205i −0.783260 1.35665i −0.930033 0.367477i \(-0.880222\pi\)
0.146772 0.989170i \(-0.453112\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 0 0
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) −18.0000 −1.38054
\(171\) 4.00000 6.92820i 0.305888 0.529813i
\(172\) −4.00000 + 6.92820i −0.304997 + 0.528271i
\(173\) 4.50000 + 7.79423i 0.342129 + 0.592584i 0.984828 0.173534i \(-0.0555188\pi\)
−0.642699 + 0.766119i \(0.722185\pi\)
\(174\) 6.00000 0.454859
\(175\) 0 0
\(176\) 0 0
\(177\) 3.00000 0.225494
\(178\) 3.00000 + 5.19615i 0.224860 + 0.389468i
\(179\) −3.00000 + 5.19615i −0.224231 + 0.388379i −0.956088 0.293079i \(-0.905320\pi\)
0.731858 + 0.681457i \(0.238654\pi\)
\(180\) −3.00000 + 5.19615i −0.223607 + 0.387298i
\(181\) −5.00000 −0.371647 −0.185824 0.982583i \(-0.559495\pi\)
−0.185824 + 0.982583i \(0.559495\pi\)
\(182\) 0 0
\(183\) 11.0000 0.813143
\(184\) 1.50000 2.59808i 0.110581 0.191533i
\(185\) 12.0000 20.7846i 0.882258 1.52811i
\(186\) −5.00000 8.66025i −0.366618 0.635001i
\(187\) 0 0
\(188\) 3.00000 + 5.19615i 0.218797 + 0.378968i
\(189\) 0 0
\(190\) 12.0000 0.870572
\(191\) 12.0000 + 20.7846i 0.868290 + 1.50392i 0.863743 + 0.503932i \(0.168114\pi\)
0.00454614 + 0.999990i \(0.498553\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i \(-0.890928\pi\)
0.761911 + 0.647682i \(0.224262\pi\)
\(194\) 2.00000 0.143592
\(195\) −3.00000 10.3923i −0.214834 0.744208i
\(196\) 0 0
\(197\) −6.00000 + 10.3923i −0.427482 + 0.740421i −0.996649 0.0818013i \(-0.973933\pi\)
0.569166 + 0.822222i \(0.307266\pi\)
\(198\) 0 0
\(199\) 7.00000 + 12.1244i 0.496217 + 0.859473i 0.999990 0.00436292i \(-0.00138876\pi\)
−0.503774 + 0.863836i \(0.668055\pi\)
\(200\) −4.00000 −0.282843
\(201\) 1.00000 + 1.73205i 0.0705346 + 0.122169i
\(202\) 3.00000 + 5.19615i 0.211079 + 0.365600i
\(203\) 0 0
\(204\) −3.00000 5.19615i −0.210042 0.363803i
\(205\) 0 0
\(206\) −7.00000 + 12.1244i −0.487713 + 0.844744i
\(207\) −6.00000 −0.417029
\(208\) −1.00000 3.46410i −0.0693375 0.240192i
\(209\) 0 0
\(210\) 0 0
\(211\) 2.00000 3.46410i 0.137686 0.238479i −0.788935 0.614477i \(-0.789367\pi\)
0.926620 + 0.375999i \(0.122700\pi\)
\(212\) −6.00000 10.3923i −0.412082 0.713746i
\(213\) 3.00000 0.205557
\(214\) −9.00000 15.5885i −0.615227 1.06561i
\(215\) 12.0000 + 20.7846i 0.818393 + 1.41750i
\(216\) −5.00000 −0.340207
\(217\) 0 0
\(218\) −8.00000 + 13.8564i −0.541828 + 0.938474i
\(219\) −1.00000 + 1.73205i −0.0675737 + 0.117041i
\(220\) 0 0
\(221\) −21.0000 5.19615i −1.41261 0.349531i
\(222\) 8.00000 0.536925
\(223\) 4.00000 6.92820i 0.267860 0.463947i −0.700449 0.713702i \(-0.747017\pi\)
0.968309 + 0.249756i \(0.0803503\pi\)
\(224\) 0 0
\(225\) 4.00000 + 6.92820i 0.266667 + 0.461880i
\(226\) 18.0000 1.19734
\(227\) −7.50000 12.9904i −0.497792 0.862202i 0.502204 0.864749i \(-0.332523\pi\)
−0.999997 + 0.00254715i \(0.999189\pi\)
\(228\) 2.00000 + 3.46410i 0.132453 + 0.229416i
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) −4.50000 7.79423i −0.296721 0.513936i
\(231\) 0 0
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) −3.00000 −0.196537 −0.0982683 0.995160i \(-0.531330\pi\)
−0.0982683 + 0.995160i \(0.531330\pi\)
\(234\) −5.00000 + 5.19615i −0.326860 + 0.339683i
\(235\) 18.0000 1.17419
\(236\) 1.50000 2.59808i 0.0976417 0.169120i
\(237\) −2.00000 + 3.46410i −0.129914 + 0.225018i
\(238\) 0 0
\(239\) 21.0000 1.35838 0.679189 0.733964i \(-0.262332\pi\)
0.679189 + 0.733964i \(0.262332\pi\)
\(240\) −1.50000 2.59808i −0.0968246 0.167705i
\(241\) −14.0000 24.2487i −0.901819 1.56200i −0.825131 0.564942i \(-0.808899\pi\)
−0.0766885 0.997055i \(-0.524435\pi\)
\(242\) 11.0000 0.707107
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 5.50000 9.52628i 0.352101 0.609858i
\(245\) 0 0
\(246\) 0 0
\(247\) 14.0000 + 3.46410i 0.890799 + 0.220416i
\(248\) −10.0000 −0.635001
\(249\) 0 0
\(250\) 1.50000 2.59808i 0.0948683 0.164317i
\(251\) 1.50000 + 2.59808i 0.0946792 + 0.163989i 0.909475 0.415759i \(-0.136484\pi\)
−0.814795 + 0.579748i \(0.803151\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 5.50000 + 9.52628i 0.345101 + 0.597732i
\(255\) −18.0000 −1.12720
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) −4.00000 + 6.92820i −0.249029 + 0.431331i
\(259\) 0 0
\(260\) −10.5000 2.59808i −0.651182 0.161126i
\(261\) −12.0000 −0.742781
\(262\) −7.50000 + 12.9904i −0.463352 + 0.802548i
\(263\) 13.5000 23.3827i 0.832446 1.44184i −0.0636476 0.997972i \(-0.520273\pi\)
0.896093 0.443866i \(-0.146393\pi\)
\(264\) 0 0
\(265\) −36.0000 −2.21146
\(266\) 0 0
\(267\) 3.00000 + 5.19615i 0.183597 + 0.317999i
\(268\) 2.00000 0.122169
\(269\) 4.50000 + 7.79423i 0.274370 + 0.475223i 0.969976 0.243201i \(-0.0781974\pi\)
−0.695606 + 0.718423i \(0.744864\pi\)
\(270\) −7.50000 + 12.9904i −0.456435 + 0.790569i
\(271\) 1.00000 1.73205i 0.0607457 0.105215i −0.834053 0.551684i \(-0.813985\pi\)
0.894799 + 0.446469i \(0.147319\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) −3.00000 −0.181237
\(275\) 0 0
\(276\) 1.50000 2.59808i 0.0902894 0.156386i
\(277\) −13.0000 22.5167i −0.781094 1.35290i −0.931305 0.364241i \(-0.881328\pi\)
0.150210 0.988654i \(-0.452005\pi\)
\(278\) −16.0000 −0.959616
\(279\) 10.0000 + 17.3205i 0.598684 + 1.03695i
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 3.00000 + 5.19615i 0.178647 + 0.309426i
\(283\) −15.5000 + 26.8468i −0.921379 + 1.59588i −0.124096 + 0.992270i \(0.539603\pi\)
−0.797283 + 0.603606i \(0.793730\pi\)
\(284\) 1.50000 2.59808i 0.0890086 0.154167i
\(285\) 12.0000 0.710819
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 + 1.73205i −0.0589256 + 0.102062i
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) −9.00000 15.5885i −0.528498 0.915386i
\(291\) 2.00000 0.117242
\(292\) 1.00000 + 1.73205i 0.0585206 + 0.101361i
\(293\) −3.00000 5.19615i −0.175262 0.303562i 0.764990 0.644042i \(-0.222744\pi\)
−0.940252 + 0.340480i \(0.889411\pi\)
\(294\) 0 0
\(295\) −4.50000 7.79423i −0.262000 0.453798i
\(296\) 4.00000 6.92820i 0.232495 0.402694i
\(297\) 0 0
\(298\) 0 0
\(299\) −3.00000 10.3923i −0.173494 0.601003i
\(300\) −4.00000 −0.230940
\(301\) 0 0
\(302\) −0.500000 + 0.866025i −0.0287718 + 0.0498342i
\(303\) 3.00000 + 5.19615i 0.172345 + 0.298511i
\(304\) 4.00000 0.229416
\(305\) −16.5000 28.5788i −0.944787 1.63642i
\(306\) 6.00000 + 10.3923i 0.342997 + 0.594089i
\(307\) 13.0000 0.741949 0.370975 0.928643i \(-0.379024\pi\)
0.370975 + 0.928643i \(0.379024\pi\)
\(308\) 0 0
\(309\) −7.00000 + 12.1244i −0.398216 + 0.689730i
\(310\) −15.0000 + 25.9808i −0.851943 + 1.47561i
\(311\) 6.00000 0.340229 0.170114 0.985424i \(-0.445586\pi\)
0.170114 + 0.985424i \(0.445586\pi\)
\(312\) −1.00000 3.46410i −0.0566139 0.196116i
\(313\) −8.00000 −0.452187 −0.226093 0.974106i \(-0.572595\pi\)
−0.226093 + 0.974106i \(0.572595\pi\)
\(314\) −1.00000 + 1.73205i −0.0564333 + 0.0977453i
\(315\) 0 0
\(316\) 2.00000 + 3.46410i 0.112509 + 0.194871i
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) −6.00000 10.3923i −0.336463 0.582772i
\(319\) 0 0
\(320\) −3.00000 −0.167705
\(321\) −9.00000 15.5885i −0.502331 0.870063i
\(322\) 0 0
\(323\) 12.0000 20.7846i 0.667698 1.15649i
\(324\) 1.00000 0.0555556
\(325\) −10.0000 + 10.3923i −0.554700 + 0.576461i
\(326\) −20.0000 −1.10770
\(327\) −8.00000 + 13.8564i −0.442401 + 0.766261i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 5.00000 + 8.66025i 0.274825 + 0.476011i 0.970091 0.242742i \(-0.0780468\pi\)
−0.695266 + 0.718752i \(0.744713\pi\)
\(332\) 0 0
\(333\) −16.0000 −0.876795
\(334\) 6.00000 + 10.3923i 0.328305 + 0.568642i
\(335\) 3.00000 5.19615i 0.163908 0.283896i
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −11.5000 6.06218i −0.625518 0.329739i
\(339\) 18.0000 0.977626
\(340\) −9.00000 + 15.5885i −0.488094 + 0.845403i
\(341\) 0 0
\(342\) −4.00000 6.92820i −0.216295 0.374634i
\(343\) 0 0
\(344\) 4.00000 + 6.92820i 0.215666 + 0.373544i
\(345\) −4.50000 7.79423i −0.242272 0.419627i
\(346\) 9.00000 0.483843
\(347\) 12.0000 + 20.7846i 0.644194 + 1.11578i 0.984487 + 0.175457i \(0.0561403\pi\)
−0.340293 + 0.940319i \(0.610526\pi\)
\(348\) 3.00000 5.19615i 0.160817 0.278543i
\(349\) 14.5000 25.1147i 0.776167 1.34436i −0.157969 0.987444i \(-0.550495\pi\)
0.934136 0.356917i \(-0.116172\pi\)
\(350\) 0 0
\(351\) −12.5000 + 12.9904i −0.667201 + 0.693375i
\(352\) 0 0
\(353\) −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i \(-0.884378\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(354\) 1.50000 2.59808i 0.0797241 0.138086i
\(355\) −4.50000 7.79423i −0.238835 0.413675i
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 3.00000 + 5.19615i 0.158555 + 0.274625i
\(359\) −9.00000 −0.475002 −0.237501 0.971387i \(-0.576328\pi\)
−0.237501 + 0.971387i \(0.576328\pi\)
\(360\) 3.00000 + 5.19615i 0.158114 + 0.273861i
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) −2.50000 + 4.33013i −0.131397 + 0.227586i
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 5.50000 9.52628i 0.287490 0.497947i
\(367\) −5.00000 + 8.66025i −0.260998 + 0.452062i −0.966507 0.256639i \(-0.917385\pi\)
0.705509 + 0.708700i \(0.250718\pi\)
\(368\) −1.50000 2.59808i −0.0781929 0.135434i
\(369\) 0 0
\(370\) −12.0000 20.7846i −0.623850 1.08054i
\(371\) 0 0
\(372\) −10.0000 −0.518476
\(373\) −16.0000 27.7128i −0.828449 1.43492i −0.899255 0.437425i \(-0.855891\pi\)
0.0708063 0.997490i \(-0.477443\pi\)
\(374\) 0 0
\(375\) 1.50000 2.59808i 0.0774597 0.134164i
\(376\) 6.00000 0.309426
\(377\) −6.00000 20.7846i −0.309016 1.07046i
\(378\) 0 0
\(379\) 14.0000 24.2487i 0.719132 1.24557i −0.242213 0.970223i \(-0.577873\pi\)
0.961344 0.275349i \(-0.0887935\pi\)
\(380\) 6.00000 10.3923i 0.307794 0.533114i
\(381\) 5.50000 + 9.52628i 0.281774 + 0.488046i
\(382\) 24.0000 1.22795
\(383\) −3.00000 5.19615i −0.153293 0.265511i 0.779143 0.626846i \(-0.215654\pi\)
−0.932436 + 0.361335i \(0.882321\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 0 0
\(386\) 2.50000 + 4.33013i 0.127247 + 0.220398i
\(387\) 8.00000 13.8564i 0.406663 0.704361i
\(388\) 1.00000 1.73205i 0.0507673 0.0879316i
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) −10.5000 2.59808i −0.531688 0.131559i
\(391\) −18.0000 −0.910299
\(392\) 0 0
\(393\) −7.50000 + 12.9904i −0.378325 + 0.655278i
\(394\) 6.00000 + 10.3923i 0.302276 + 0.523557i
\(395\) 12.0000 0.603786
\(396\) 0 0
\(397\) −3.50000 6.06218i −0.175660 0.304252i 0.764730 0.644351i \(-0.222873\pi\)
−0.940389 + 0.340099i \(0.889539\pi\)
\(398\) 14.0000 0.701757
\(399\) 0 0
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) −3.00000 + 5.19615i −0.149813 + 0.259483i −0.931158 0.364615i \(-0.881200\pi\)
0.781345 + 0.624099i \(0.214534\pi\)
\(402\) 2.00000 0.0997509
\(403\) −25.0000 + 25.9808i −1.24534 + 1.29419i
\(404\) 6.00000 0.298511
\(405\) 1.50000 2.59808i 0.0745356 0.129099i
\(406\) 0 0
\(407\) 0 0
\(408\) −6.00000 −0.297044
\(409\) −11.0000 19.0526i −0.543915 0.942088i −0.998674 0.0514740i \(-0.983608\pi\)
0.454759 0.890614i \(-0.349725\pi\)
\(410\) 0 0
\(411\) −3.00000 −0.147979
\(412\) 7.00000 + 12.1244i 0.344865 + 0.597324i
\(413\) 0 0
\(414\) −3.00000 + 5.19615i −0.147442 + 0.255377i
\(415\) 0 0
\(416\) −3.50000 0.866025i −0.171602 0.0424604i
\(417\) −16.0000 −0.783523
\(418\) 0 0
\(419\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(420\) 0 0
\(421\) 26.0000 1.26716 0.633581 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) −2.00000 3.46410i −0.0973585 0.168630i
\(423\) −6.00000 10.3923i −0.291730 0.505291i
\(424\) −12.0000 −0.582772
\(425\) 12.0000 + 20.7846i 0.582086 + 1.00820i
\(426\) 1.50000 2.59808i 0.0726752 0.125877i
\(427\) 0 0
\(428\) −18.0000 −0.870063
\(429\) 0 0
\(430\) 24.0000 1.15738
\(431\) 16.5000 28.5788i 0.794777 1.37659i −0.128204 0.991748i \(-0.540921\pi\)
0.922981 0.384846i \(-0.125746\pi\)
\(432\) −2.50000 + 4.33013i −0.120281 + 0.208333i
\(433\) −2.00000 3.46410i −0.0961139 0.166474i 0.813959 0.580922i \(-0.197308\pi\)
−0.910073 + 0.414448i \(0.863975\pi\)
\(434\) 0 0
\(435\) −9.00000 15.5885i −0.431517 0.747409i
\(436\) 8.00000 + 13.8564i 0.383131 + 0.663602i
\(437\) 12.0000 0.574038
\(438\) 1.00000 + 1.73205i 0.0477818 + 0.0827606i
\(439\) 7.00000 12.1244i 0.334092 0.578664i −0.649218 0.760602i \(-0.724904\pi\)
0.983310 + 0.181938i \(0.0582371\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −15.0000 + 15.5885i −0.713477 + 0.741467i
\(443\) 18.0000 0.855206 0.427603 0.903967i \(-0.359358\pi\)
0.427603 + 0.903967i \(0.359358\pi\)
\(444\) 4.00000 6.92820i 0.189832 0.328798i
\(445\) 9.00000 15.5885i 0.426641 0.738964i
\(446\) −4.00000 6.92820i −0.189405 0.328060i
\(447\) 0 0
\(448\) 0 0
\(449\) −4.50000 7.79423i −0.212368 0.367832i 0.740087 0.672511i \(-0.234784\pi\)
−0.952455 + 0.304679i \(0.901451\pi\)
\(450\) 8.00000 0.377124
\(451\) 0 0
\(452\) 9.00000 15.5885i 0.423324 0.733219i
\(453\) −0.500000 + 0.866025i −0.0234920 + 0.0406894i
\(454\) −15.0000 −0.703985
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −14.5000 + 25.1147i −0.678281 + 1.17482i 0.297217 + 0.954810i \(0.403942\pi\)
−0.975498 + 0.220008i \(0.929392\pi\)
\(458\) 11.0000 19.0526i 0.513996 0.890268i
\(459\) 15.0000 + 25.9808i 0.700140 + 1.21268i
\(460\) −9.00000 −0.419627
\(461\) 10.5000 + 18.1865i 0.489034 + 0.847031i 0.999920 0.0126168i \(-0.00401615\pi\)
−0.510887 + 0.859648i \(0.670683\pi\)
\(462\) 0 0
\(463\) −31.0000 −1.44069 −0.720346 0.693615i \(-0.756017\pi\)
−0.720346 + 0.693615i \(0.756017\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) −15.0000 + 25.9808i −0.695608 + 1.20483i
\(466\) −1.50000 + 2.59808i −0.0694862 + 0.120354i
\(467\) 3.00000 0.138823 0.0694117 0.997588i \(-0.477888\pi\)
0.0694117 + 0.997588i \(0.477888\pi\)
\(468\) 2.00000 + 6.92820i 0.0924500 + 0.320256i
\(469\) 0 0
\(470\) 9.00000 15.5885i 0.415139 0.719042i
\(471\) −1.00000 + 1.73205i −0.0460776 + 0.0798087i
\(472\) −1.50000 2.59808i −0.0690431 0.119586i
\(473\) 0 0
\(474\) 2.00000 + 3.46410i 0.0918630 + 0.159111i
\(475\) −8.00000 13.8564i −0.367065 0.635776i
\(476\) 0 0
\(477\) 12.0000 + 20.7846i 0.549442 + 0.951662i
\(478\) 10.5000 18.1865i 0.480259 0.831833i
\(479\) 15.0000 25.9808i 0.685367 1.18709i −0.287954 0.957644i \(-0.592975\pi\)
0.973321 0.229447i \(-0.0736918\pi\)
\(480\) −3.00000 −0.136931
\(481\) −8.00000 27.7128i −0.364769 1.26360i
\(482\) −28.0000 −1.27537
\(483\) 0 0
\(484\) 5.50000 9.52628i 0.250000 0.433013i
\(485\) −3.00000 5.19615i −0.136223 0.235945i
\(486\) 16.0000 0.725775
\(487\) 6.50000 + 11.2583i 0.294543 + 0.510164i 0.974879 0.222737i \(-0.0714992\pi\)
−0.680335 + 0.732901i \(0.738166\pi\)
\(488\) −5.50000 9.52628i −0.248973 0.431234i
\(489\) −20.0000 −0.904431
\(490\) 0 0
\(491\) −6.00000 + 10.3923i −0.270776 + 0.468998i −0.969061 0.246822i \(-0.920614\pi\)
0.698285 + 0.715820i \(0.253947\pi\)
\(492\) 0 0
\(493\) −36.0000 −1.62136
\(494\) 10.0000 10.3923i 0.449921 0.467572i
\(495\) 0 0
\(496\) −5.00000 + 8.66025i −0.224507 + 0.388857i
\(497\) 0 0
\(498\) 0 0
\(499\) −22.0000 −0.984855 −0.492428 0.870353i \(-0.663890\pi\)
−0.492428 + 0.870353i \(0.663890\pi\)
\(500\) −1.50000 2.59808i −0.0670820 0.116190i
\(501\) 6.00000 + 10.3923i 0.268060 + 0.464294i
\(502\) 3.00000 0.133897
\(503\) 21.0000 + 36.3731i 0.936344 + 1.62179i 0.772220 + 0.635355i \(0.219146\pi\)
0.164124 + 0.986440i \(0.447520\pi\)
\(504\) 0 0
\(505\) 9.00000 15.5885i 0.400495 0.693677i
\(506\) 0 0
\(507\) −11.5000 6.06218i −0.510733 0.269231i
\(508\) 11.0000 0.488046
\(509\) −7.50000 + 12.9904i −0.332432 + 0.575789i −0.982988 0.183669i \(-0.941202\pi\)
0.650556 + 0.759458i \(0.274536\pi\)
\(510\) −9.00000 + 15.5885i −0.398527 + 0.690268i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −10.0000 17.3205i −0.441511 0.764719i
\(514\) 3.00000 + 5.19615i 0.132324 + 0.229192i
\(515\) 42.0000 1.85074
\(516\) 4.00000 + 6.92820i 0.176090 + 0.304997i
\(517\) 0 0
\(518\) 0 0
\(519\) 9.00000 0.395056
\(520\) −7.50000 + 7.79423i −0.328897 + 0.341800i
\(521\) 36.0000 1.57719 0.788594 0.614914i \(-0.210809\pi\)
0.788594 + 0.614914i \(0.210809\pi\)
\(522\) −6.00000 + 10.3923i −0.262613 + 0.454859i
\(523\) −0.500000 + 0.866025i −0.0218635 + 0.0378686i −0.876750 0.480946i \(-0.840293\pi\)
0.854887 + 0.518815i \(0.173627\pi\)
\(524\) 7.50000 + 12.9904i 0.327639 + 0.567487i
\(525\) 0 0
\(526\) −13.5000 23.3827i −0.588628 1.01953i
\(527\) 30.0000 + 51.9615i 1.30682 + 2.26348i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) −18.0000 + 31.1769i −0.781870 + 1.35424i
\(531\) −3.00000 + 5.19615i −0.130189 + 0.225494i
\(532\) 0 0
\(533\) 0 0
\(534\) 6.00000 0.259645
\(535\) −27.0000 + 46.7654i −1.16731 + 2.02184i
\(536\) 1.00000 1.73205i 0.0431934 0.0748132i
\(537\) 3.00000 + 5.19615i 0.129460 + 0.224231i
\(538\) 9.00000 0.388018
\(539\) 0 0
\(540\) 7.50000 + 12.9904i 0.322749 + 0.559017i
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) −1.00000 1.73205i −0.0429537 0.0743980i
\(543\) −2.50000 + 4.33013i −0.107285 + 0.185824i
\(544\) −3.00000 + 5.19615i −0.128624 + 0.222783i
\(545\) 48.0000 2.05609
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) −1.50000 + 2.59808i −0.0640768 + 0.110984i
\(549\) −11.0000 + 19.0526i −0.469469 + 0.813143i
\(550\) 0 0
\(551\) 24.0000 1.02243
\(552\) −1.50000 2.59808i −0.0638442 0.110581i
\(553\) 0 0
\(554\) −26.0000 −1.10463
\(555\) −12.0000 20.7846i −0.509372 0.882258i
\(556\) −8.00000 + 13.8564i −0.339276 + 0.587643i
\(557\) −12.0000 + 20.7846i −0.508456 + 0.880672i 0.491496 + 0.870880i \(0.336450\pi\)
−0.999952 + 0.00979220i \(0.996883\pi\)
\(558\) 20.0000 0.846668
\(559\) 28.0000 + 6.92820i 1.18427 + 0.293032i
\(560\) 0 0
\(561\) 0 0
\(562\) 9.00000 15.5885i 0.379642 0.657559i
\(563\) −18.0000 31.1769i −0.758610 1.31395i −0.943560 0.331202i \(-0.892546\pi\)
0.184950 0.982748i \(-0.440788\pi\)
\(564\) 6.00000 0.252646
\(565\) −27.0000 46.7654i −1.13590 1.96743i
\(566\) 15.5000 + 26.8468i 0.651514 + 1.12845i
\(567\) 0 0
\(568\) −1.50000 2.59808i −0.0629386 0.109013i
\(569\) 22.5000 38.9711i 0.943249 1.63376i 0.184030 0.982921i \(-0.441086\pi\)
0.759220 0.650835i \(-0.225581\pi\)
\(570\) 6.00000 10.3923i 0.251312 0.435286i
\(571\) 8.00000 0.334790 0.167395 0.985890i \(-0.446465\pi\)
0.167395 + 0.985890i \(0.446465\pi\)
\(572\) 0 0
\(573\) 24.0000 1.00261
\(574\) 0 0
\(575\) −6.00000 + 10.3923i −0.250217 + 0.433389i
\(576\) 1.00000 + 1.73205i 0.0416667 + 0.0721688i
\(577\) 28.0000 1.16566 0.582828 0.812596i \(-0.301946\pi\)
0.582828 + 0.812596i \(0.301946\pi\)
\(578\) 9.50000 + 16.4545i 0.395148 + 0.684416i
\(579\) 2.50000 + 4.33013i 0.103896 + 0.179954i
\(580\) −18.0000 −0.747409
\(581\) 0 0
\(582\) 1.00000 1.73205i 0.0414513 0.0717958i
\(583\) 0 0
\(584\) 2.00000 0.0827606
\(585\) 21.0000 + 5.19615i 0.868243 + 0.214834i
\(586\) −6.00000 −0.247858
\(587\) 1.50000 2.59808i 0.0619116 0.107234i −0.833408 0.552658i \(-0.813614\pi\)
0.895320 + 0.445424i \(0.146947\pi\)
\(588\) 0 0
\(589\) −20.0000 34.6410i −0.824086 1.42736i
\(590\) −9.00000 −0.370524
\(591\) 6.00000 + 10.3923i 0.246807 + 0.427482i
\(592\) −4.00000 6.92820i −0.164399 0.284747i
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 14.0000 0.572982
\(598\) −10.5000 2.59808i −0.429377 0.106243i
\(599\) 3.00000 0.122577 0.0612883 0.998120i \(-0.480479\pi\)
0.0612883 + 0.998120i \(0.480479\pi\)
\(600\) −2.00000 + 3.46410i −0.0816497 + 0.141421i
\(601\) 13.0000 22.5167i 0.530281 0.918474i −0.469095 0.883148i \(-0.655420\pi\)
0.999376 0.0353259i \(-0.0112469\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 0.500000 + 0.866025i 0.0203447 + 0.0352381i
\(605\) −16.5000 28.5788i −0.670820 1.16190i
\(606\) 6.00000 0.243733
\(607\) −5.00000 8.66025i −0.202944 0.351509i 0.746532 0.665350i \(-0.231718\pi\)
−0.949476 + 0.313841i \(0.898384\pi\)
\(608\) 2.00000 3.46410i 0.0811107 0.140488i
\(609\) 0 0
\(610\) −33.0000 −1.33613
\(611\) 15.0000 15.5885i 0.606835 0.630641i
\(612\) 12.0000 0.485071
\(613\) 11.0000 19.0526i 0.444286 0.769526i −0.553716 0.832705i \(-0.686791\pi\)
0.998002 + 0.0631797i \(0.0201241\pi\)
\(614\) 6.50000 11.2583i 0.262319 0.454349i
\(615\) 0 0
\(616\) 0 0
\(617\) 1.50000 + 2.59808i 0.0603877 + 0.104595i 0.894639 0.446790i \(-0.147433\pi\)
−0.834251 + 0.551385i \(0.814100\pi\)
\(618\) 7.00000 + 12.1244i 0.281581 + 0.487713i
\(619\) 37.0000 1.48716 0.743578 0.668649i \(-0.233127\pi\)
0.743578 + 0.668649i \(0.233127\pi\)
\(620\) 15.0000 + 25.9808i 0.602414 + 1.04341i
\(621\) −7.50000 + 12.9904i −0.300965 + 0.521286i
\(622\) 3.00000 5.19615i 0.120289 0.208347i
\(623\) 0 0
\(624\) −3.50000 0.866025i −0.140112 0.0346688i
\(625\) −29.0000 −1.16000
\(626\) −4.00000 + 6.92820i −0.159872 + 0.276907i
\(627\) 0 0
\(628\) 1.00000 + 1.73205i 0.0399043 + 0.0691164i
\(629\) −48.0000 −1.91389
\(630\) 0 0
\(631\) −2.50000 4.33013i −0.0995234 0.172380i 0.811964 0.583707i \(-0.198398\pi\)
−0.911487 + 0.411328i \(0.865065\pi\)
\(632\) 4.00000 0.159111
\(633\) −2.00000 3.46410i −0.0794929 0.137686i
\(634\) −6.00000 + 10.3923i −0.238290 + 0.412731i
\(635\) 16.5000 28.5788i 0.654783 1.13412i
\(636\) −12.0000 −0.475831
\(637\) 0 0
\(638\) 0 0
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) −1.50000 + 2.59808i −0.0592927 + 0.102698i
\(641\) 4.50000 + 7.79423i 0.177739 + 0.307854i 0.941106 0.338112i \(-0.109788\pi\)
−0.763367 + 0.645966i \(0.776455\pi\)
\(642\) −18.0000 −0.710403
\(643\) 20.5000 + 35.5070i 0.808441 + 1.40026i 0.913943 + 0.405842i \(0.133022\pi\)
−0.105502 + 0.994419i \(0.533645\pi\)
\(644\) 0 0
\(645\) 24.0000 0.944999
\(646\) −12.0000 20.7846i −0.472134 0.817760i
\(647\) −18.0000 + 31.1769i −0.707653 + 1.22569i 0.258073 + 0.966126i \(0.416913\pi\)
−0.965726 + 0.259565i \(0.916421\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 0 0
\(650\) 4.00000 + 13.8564i 0.156893 + 0.543493i
\(651\) 0 0
\(652\) −10.0000 + 17.3205i −0.391630 + 0.678323i
\(653\) −15.0000 + 25.9808i −0.586995 + 1.01671i 0.407628 + 0.913148i \(0.366356\pi\)
−0.994623 + 0.103558i \(0.966977\pi\)
\(654\) 8.00000 + 13.8564i 0.312825 + 0.541828i
\(655\) 45.0000 1.75830
\(656\) 0 0
\(657\) −2.00000 3.46410i −0.0780274 0.135147i
\(658\) 0 0
\(659\) −3.00000 5.19615i −0.116863 0.202413i 0.801660 0.597781i \(-0.203951\pi\)
−0.918523 + 0.395367i \(0.870617\pi\)
\(660\) 0 0
\(661\) 11.5000 19.9186i 0.447298 0.774743i −0.550911 0.834564i \(-0.685720\pi\)
0.998209 + 0.0598209i \(0.0190530\pi\)
\(662\) 10.0000 0.388661
\(663\) −15.0000 + 15.5885i −0.582552 + 0.605406i
\(664\) 0 0
\(665\) 0 0
\(666\) −8.00000 + 13.8564i −0.309994 + 0.536925i
\(667\) −9.00000 15.5885i −0.348481 0.603587i
\(668\) 12.0000 0.464294
\(669\) −4.00000 6.92820i −0.154649 0.267860i
\(670\) −3.00000 5.19615i −0.115900 0.200745i
\(671\) 0 0
\(672\) 0 0
\(673\) 5.00000 8.66025i 0.192736 0.333828i −0.753420 0.657539i \(-0.771597\pi\)
0.946156 + 0.323711i \(0.104931\pi\)
\(674\) 7.00000 12.1244i 0.269630 0.467013i
\(675\) 20.0000 0.769800
\(676\) −11.0000 + 6.92820i −0.423077 + 0.266469i
\(677\) 51.0000 1.96009 0.980045 0.198778i \(-0.0636972\pi\)
0.980045 + 0.198778i \(0.0636972\pi\)
\(678\) 9.00000 15.5885i 0.345643 0.598671i
\(679\) 0 0
\(680\) 9.00000 + 15.5885i 0.345134 + 0.597790i
\(681\) −15.0000 −0.574801
\(682\) 0 0
\(683\) 12.0000 + 20.7846i 0.459167 + 0.795301i 0.998917 0.0465244i \(-0.0148145\pi\)
−0.539750 + 0.841825i \(0.681481\pi\)
\(684\) −8.00000 −0.305888
\(685\) 4.50000 + 7.79423i 0.171936 + 0.297802i
\(686\) 0 0
\(687\) 11.0000 19.0526i 0.419676 0.726900i
\(688\) 8.00000 0.304997
\(689\) −30.0000 + 31.1769i −1.14291 + 1.18775i
\(690\) −9.00000 −0.342624
\(691\) −0.500000 + 0.866025i −0.0190209 + 0.0329452i −0.875379 0.483437i \(-0.839388\pi\)
0.856358 + 0.516382i \(0.172722\pi\)
\(692\) 4.50000 7.79423i 0.171064 0.296292i
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) 24.0000 + 41.5692i 0.910372 + 1.57681i
\(696\) −3.00000 5.19615i −0.113715 0.196960i
\(697\) 0 0
\(698\) −14.5000 25.1147i −0.548833 0.950607i
\(699\) −1.50000 + 2.59808i −0.0567352 + 0.0982683i
\(700\) 0 0
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) 5.00000 + 17.3205i 0.188713 + 0.653720i
\(703\) 32.0000 1.20690
\(704\) 0 0
\(705\) 9.00000 15.5885i 0.338960 0.587095i
\(706\) 3.00000 + 5.19615i 0.112906 + 0.195560i
\(707\) 0 0
\(708\) −1.50000 2.59808i −0.0563735 0.0976417i
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) −9.00000 −0.337764
\(711\) −4.00000 6.92820i −0.150012 0.259828i
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) −15.0000 + 25.9808i −0.561754 + 0.972987i
\(714\) 0 0
\(715\) 0 0
\(716\) 6.00000 0.224231
\(717\) 10.5000 18.1865i 0.392130 0.679189i
\(718\) −4.50000 + 7.79423i −0.167939 + 0.290878i
\(719\) −24.0000 41.5692i −0.895049 1.55027i −0.833744 0.552151i \(-0.813807\pi\)
−0.0613050 0.998119i \(-0.519526\pi\)
\(720\) 6.00000 0.223607
\(721\) 0 0
\(722\) −1.50000 2.59808i −0.0558242 0.0966904i
\(723\) −28.0000 −1.04133
\(724\) 2.50000 + 4.33013i 0.0929118 + 0.160928i
\(725\) −12.0000 + 20.7846i −0.445669 + 0.771921i
\(726\) 5.50000 9.52628i 0.204124 0.353553i
\(727\) 52.0000 1.92857 0.964287 0.264861i \(-0.0853260\pi\)
0.964287 + 0.264861i \(0.0853260\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 3.00000 5.19615i 0.111035 0.192318i
\(731\) 24.0000 41.5692i 0.887672 1.53749i
\(732\) −5.50000 9.52628i −0.203286 0.352101i
\(733\) −35.0000 −1.29275 −0.646377 0.763018i \(-0.723717\pi\)
−0.646377 + 0.763018i \(0.723717\pi\)
\(734\) 5.00000 + 8.66025i 0.184553 + 0.319656i
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) 0 0
\(738\) 0 0
\(739\) 8.00000 13.8564i 0.294285 0.509716i −0.680534 0.732717i \(-0.738252\pi\)
0.974818 + 0.223001i \(0.0715853\pi\)
\(740\) −24.0000 −0.882258
\(741\) 10.0000 10.3923i 0.367359 0.381771i
\(742\) 0 0
\(743\) −24.0000 + 41.5692i −0.880475 + 1.52503i −0.0296605 + 0.999560i \(0.509443\pi\)
−0.850814 + 0.525467i \(0.823891\pi\)
\(744\) −5.00000 + 8.66025i −0.183309 + 0.317500i
\(745\) 0 0
\(746\) −32.0000 −1.17160
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) −1.50000 2.59808i −0.0547723 0.0948683i
\(751\) −8.50000 + 14.7224i −0.310169 + 0.537229i −0.978399 0.206726i \(-0.933719\pi\)
0.668229 + 0.743955i \(0.267052\pi\)
\(752\) 3.00000 5.19615i 0.109399 0.189484i
\(753\) 3.00000 0.109326
\(754\) −21.0000 5.19615i −0.764775 0.189233i
\(755\) 3.00000 0.109181
\(756\) 0 0
\(757\) 26.0000 45.0333i 0.944986 1.63676i 0.189207 0.981937i \(-0.439408\pi\)
0.755779 0.654827i \(-0.227258\pi\)
\(758\) −14.0000 24.2487i −0.508503 0.880753i
\(759\) 0 0
\(760\) −6.00000 10.3923i −0.217643 0.376969i
\(761\) 6.00000 + 10.3923i 0.217500 + 0.376721i 0.954043 0.299670i \(-0.0968765\pi\)
−0.736543 + 0.676391i \(0.763543\pi\)
\(762\) 11.0000 0.398488
\(763\) 0 0
\(764\) 12.0000 20.7846i 0.434145 0.751961i
\(765\) 18.0000 31.1769i 0.650791 1.12720i
\(766\) −6.00000 −0.216789
\(767\) −10.5000 2.59808i −0.379133 0.0938111i
\(768\) −1.00000 −0.0360844
\(769\) −5.00000 + 8.66025i −0.180305 + 0.312297i −0.941984 0.335657i \(-0.891042\pi\)
0.761680 + 0.647954i \(0.224375\pi\)
\(770\) 0 0
\(771\) 3.00000 + 5.19615i 0.108042 + 0.187135i
\(772\) 5.00000 0.179954
\(773\) −15.0000 25.9808i −0.539513 0.934463i −0.998930 0.0462427i \(-0.985275\pi\)
0.459418 0.888220i \(-0.348058\pi\)
\(774\) −8.00000 13.8564i −0.287554 0.498058i
\(775\) 40.0000 1.43684
\(776\) −1.00000 1.73205i −0.0358979 0.0621770i
\(777\) 0 0
\(778\) −15.0000 + 25.9808i −0.537776 + 0.931455i
\(779\) 0 0
\(780\) −7.50000 + 7.79423i −0.268543 + 0.279078i
\(781\) 0 0
\(782\) −9.00000 + 15.5885i −0.321839 + 0.557442i
\(783\) −15.0000 + 25.9808i −0.536056 + 0.928477i
\(784\) 0 0
\(785\) 6.00000 0.214149
\(786\) 7.50000 + 12.9904i 0.267516 + 0.463352i
\(787\) 26.5000 + 45.8993i 0.944623 + 1.63614i 0.756504 + 0.653989i \(0.226906\pi\)
0.188119 + 0.982146i \(0.439761\pi\)
\(788\) 12.0000 0.427482
\(789\) −13.5000 23.3827i −0.480613 0.832446i
\(790\) 6.00000 10.3923i 0.213470 0.369742i
\(791\) 0 0
\(792\) 0 0
\(793\) −38.5000 9.52628i −1.36718 0.338288i
\(794\) −7.00000 −0.248421
\(795\) −18.0000 + 31.1769i −0.638394 + 1.10573i
\(796\) 7.00000 12.1244i 0.248108 0.429736i
\(797\) −7.50000 12.9904i −0.265664 0.460143i 0.702074 0.712104i \(-0.252258\pi\)
−0.967737 + 0.251961i \(0.918924\pi\)
\(798\) 0 0
\(799\) −18.0000 31.1769i −0.636794 1.10296i
\(800\) 2.00000 + 3.46410i 0.0707107 + 0.122474i
\(801\) −12.0000 −0.423999
\(802\) 3.00000 + 5.19615i 0.105934 + 0.183483i
\(803\) 0 0
\(804\) 1.00000 1.73205i 0.0352673 0.0610847i
\(805\) 0 0
\(806\) 10.0000 + 34.6410i 0.352235 + 1.22018i
\(807\) 9.00000 0.316815
\(808\) 3.00000 5.19615i 0.105540 0.182800i
\(809\) 21.0000 36.3731i 0.738321 1.27881i −0.214930 0.976629i \(-0.568952\pi\)
0.953251 0.302180i \(-0.0977142\pi\)
\(810\) −1.50000 2.59808i −0.0527046 0.0912871i
\(811\) 19.0000 0.667180 0.333590 0.942718i \(-0.391740\pi\)
0.333590 + 0.942718i \(0.391740\pi\)
\(812\) 0 0
\(813\) −1.00000 1.73205i −0.0350715 0.0607457i
\(814\) 0 0
\(815\) 30.0000 + 51.9615i 1.05085 + 1.82013i
\(816\) −3.00000 + 5.19615i −0.105021 + 0.181902i
\(817\) −16.0000 + 27.7128i −0.559769 + 0.969549i
\(818\) −22.0000 −0.769212
\(819\) 0 0
\(820\) 0 0
\(821\) −6.00000 + 10.3923i −0.209401 + 0.362694i −0.951526 0.307568i \(-0.900485\pi\)
0.742125 + 0.670262i \(0.233818\pi\)
\(822\) −1.50000 + 2.59808i −0.0523185 + 0.0906183i
\(823\) 6.50000 + 11.2583i 0.226576 + 0.392441i 0.956791 0.290776i \(-0.0939136\pi\)
−0.730215 + 0.683217i \(0.760580\pi\)
\(824\) 14.0000 0.487713
\(825\) 0 0
\(826\) 0 0
\(827\) 24.0000 0.834562 0.417281 0.908778i \(-0.362983\pi\)
0.417281 + 0.908778i \(0.362983\pi\)
\(828\) 3.00000 + 5.19615i 0.104257 + 0.180579i
\(829\) −12.5000 + 21.6506i −0.434143 + 0.751958i −0.997225 0.0744432i \(-0.976282\pi\)
0.563082 + 0.826401i \(0.309615\pi\)
\(830\) 0 0
\(831\) −26.0000 −0.901930
\(832\) −2.50000 + 2.59808i −0.0866719 + 0.0900721i
\(833\) 0 0
\(834\) −8.00000 + 13.8564i −0.277017 + 0.479808i
\(835\) 18.0000 31.1769i 0.622916 1.07892i
\(836\) 0 0
\(837\) 50.0000 1.72825
\(838\) 0 0
\(839\) −27.0000 46.7654i −0.932144 1.61452i −0.779650 0.626215i \(-0.784603\pi\)
−0.152493 0.988304i \(-0.548730\pi\)
\(840\) 0 0
\(841\) −3.50000 6.06218i −0.120690 0.209041i
\(842\) 13.0000 22.5167i 0.448010 0.775975i
\(843\) 9.00000 15.5885i 0.309976 0.536895i
\(844\) −4.00000 −0.137686
\(845\) 1.50000 + 38.9711i 0.0516016 + 1.34065i
\(846\) −12.0000 −0.412568
\(847\) 0 0
\(848\) −6.00000 + 10.3923i −0.206041 + 0.356873i
\(849\) 15.5000 + 26.8468i 0.531959 + 0.921379i
\(850\) 24.0000 0.823193
\(851\) −12.0000 20.7846i −0.411355 0.712487i
\(852\) −1.50000 2.59808i −0.0513892 0.0890086i
\(853\) −17.0000 −0.582069 −0.291034 0.956713i \(-0.593999\pi\)
−0.291034 + 0.956713i \(0.593999\pi\)
\(854\) 0 0
\(855\) −12.0000 + 20.7846i −0.410391 + 0.710819i
\(856\) −9.00000 + 15.5885i −0.307614 + 0.532803i
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 0 0
\(859\) 4.00000 0.136478 0.0682391 0.997669i \(-0.478262\pi\)
0.0682391 + 0.997669i \(0.478262\pi\)
\(860\) 12.0000 20.7846i 0.409197 0.708749i
\(861\) 0 0
\(862\) −16.5000 28.5788i −0.561992 0.973399i
\(863\) −57.0000 −1.94030 −0.970151 0.242500i \(-0.922032\pi\)
−0.970151 + 0.242500i \(0.922032\pi\)
\(864\) 2.50000 + 4.33013i 0.0850517 + 0.147314i
\(865\) −13.5000 23.3827i −0.459014 0.795035i
\(866\) −4.00000 −0.135926
\(867\) 9.50000 + 16.4545i 0.322637 + 0.558824i
\(868\) 0 0
\(869\) 0 0
\(870\) −18.0000 −0.610257
\(871\) −2.00000 6.92820i −0.0677674 0.234753i
\(872\) 16.0000 0.541828
\(873\) −2.00000 + 3.46410i −0.0676897 + 0.117242i
\(874\) 6.00000 10.3923i 0.202953 0.351525i
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) 11.0000 + 19.0526i 0.371444 + 0.643359i 0.989788 0.142548i \(-0.0455296\pi\)
−0.618344 + 0.785907i \(0.712196\pi\)
\(878\) −7.00000 12.1244i −0.236239 0.409177i
\(879\) −6.00000 −0.202375
\(880\) 0 0
\(881\) −3.00000 + 5.19615i −0.101073 + 0.175063i −0.912127 0.409908i \(-0.865561\pi\)
0.811054 + 0.584971i \(0.198894\pi\)
\(882\) 0 0
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 6.00000 + 20.7846i 0.201802 + 0.699062i
\(885\) −9.00000 −0.302532
\(886\) 9.00000 15.5885i 0.302361 0.523704i
\(887\) 6.00000 10.3923i 0.201460 0.348939i −0.747539 0.664218i \(-0.768765\pi\)
0.948999 + 0.315279i \(0.102098\pi\)
\(888\) −4.00000 6.92820i −0.134231 0.232495i
\(889\) 0 0
\(890\) −9.00000 15.5885i −0.301681 0.522526i
\(891\) 0 0
\(892\) −8.00000 −0.267860
\(893\) 12.0000 + 20.7846i 0.401565 + 0.695530i
\(894\) 0 0
\(895\) 9.00000 15.5885i 0.300837 0.521065i
\(896\) 0 0
\(897\) −10.5000 2.59808i −0.350585 0.0867472i
\(898\) −9.00000 −0.300334
\(899\) −30.0000 + 51.9615i −1.00056 + 1.73301i
\(900\) 4.00000 6.92820i 0.133333 0.230940i
\(901\) 36.0000 + 62.3538i 1.19933 + 2.07731i
\(902\) 0 0
\(903\) 0 0
\(904\) −9.00000 15.5885i −0.299336 0.518464i
\(905\) 15.0000 0.498617
\(906\) 0.500000 + 0.866025i 0.0166114 + 0.0287718i
\(907\) −7.00000 + 12.1244i −0.232431 + 0.402583i −0.958523 0.285015i \(-0.908001\pi\)
0.726092 + 0.687598i \(0.241335\pi\)
\(908\) −7.50000 + 12.9904i −0.248896 + 0.431101i
\(909\) −12.0000 −0.398015
\(910\) 0 0
\(911\) 21.0000 0.695761 0.347881 0.937539i \(-0.386901\pi\)
0.347881 + 0.937539i \(0.386901\pi\)
\(912\) 2.00000 3.46410i 0.0662266 0.114708i
\(913\) 0 0
\(914\) 14.5000 + 25.1147i 0.479617 + 0.830722i
\(915\) −33.0000 −1.09095
\(916\) −11.0000 19.0526i −0.363450 0.629514i
\(917\) 0 0
\(918\) 30.0000 0.990148
\(919\) 3.50000 + 6.06218i 0.115454 + 0.199973i 0.917961 0.396670i \(-0.129834\pi\)
−0.802507 + 0.596643i \(0.796501\pi\)
\(920\) −4.50000 + 7.79423i −0.148361 + 0.256968i
\(921\) 6.50000 11.2583i 0.214182 0.370975i
\(922\) 21.0000 0.691598
\(923\) −10.5000 2.59808i −0.345612 0.0855167i
\(924\) 0 0
\(925\) −16.0000 + 27.7128i −0.526077 + 0.911192i
\(926\) −15.5000 + 26.8468i −0.509362 + 0.882240i
\(927\) −14.0000 24.2487i −0.459820 0.796432i
\(928\) −6.00000 −0.196960
\(929\) 9.00000 + 15.5885i 0.295280 + 0.511441i 0.975050 0.221985i \(-0.0712536\pi\)
−0.679770 + 0.733426i \(0.737920\pi\)
\(930\) 15.0000 + 25.9808i 0.491869 + 0.851943i
\(931\) 0 0
\(932\) 1.50000 + 2.59808i 0.0491341 + 0.0851028i
\(933\) 3.00000 5.19615i 0.0982156 0.170114i
\(934\) 1.50000 2.59808i 0.0490815 0.0850117i
\(935\) 0 0
\(936\) 7.00000 + 1.73205i 0.228802 + 0.0566139i
\(937\) −8.00000 −0.261349 −0.130674 0.991425i \(-0.541714\pi\)
−0.130674 + 0.991425i \(0.541714\pi\)
\(938\) 0 0
\(939\) −4.00000 + 6.92820i −0.130535 + 0.226093i
\(940\) −9.00000 15.5885i −0.293548 0.508439i
\(941\) −15.0000 −0.488986 −0.244493 0.969651i \(-0.578622\pi\)
−0.244493 + 0.969651i \(0.578622\pi\)
\(942\) 1.00000 + 1.73205i 0.0325818 + 0.0564333i
\(943\) 0 0
\(944\) −3.00000 −0.0976417
\(945\) 0 0
\(946\) 0 0
\(947\) 21.0000 36.3731i 0.682408 1.18197i −0.291835 0.956469i \(-0.594266\pi\)
0.974244 0.225497i \(-0.0724007\pi\)
\(948\) 4.00000 0.129914
\(949\) 5.00000 5.19615i 0.162307 0.168674i
\(950\) −16.0000 −0.519109
\(951\) −6.00000 + 10.3923i −0.194563 + 0.336994i
\(952\) 0 0
\(953\) 7.50000 + 12.9904i 0.242949 + 0.420800i 0.961553 0.274620i \(-0.0885520\pi\)
−0.718604 + 0.695419i \(0.755219\pi\)
\(954\) 24.0000 0.777029
\(955\) −36.0000 62.3538i −1.16493 2.01772i
\(956\) −10.5000 18.1865i −0.339594 0.588195i
\(957\) 0 0
\(958\) −15.0000 25.9808i −0.484628 0.839400i
\(959\) 0 0
\(960\) −1.50000 + 2.59808i −0.0484123 + 0.0838525i
\(961\) 69.0000 2.22581
\(962\) −28.0000 6.92820i −0.902756 0.223374i
\(963\) 36.0000 1.16008
\(964\) −14.0000 + 24.2487i −0.450910 + 0.780998i
\(965\) 7.50000 12.9904i 0.241434 0.418175i
\(966\) 0 0
\(967\) −16.0000 −0.514525 −0.257263 0.966342i \(-0.582821\pi\)
−0.257263 + 0.966342i \(0.582821\pi\)
\(968\) −5.50000 9.52628i −0.176777 0.306186i
\(969\) −12.0000 20.7846i −0.385496 0.667698i
\(970\) −6.00000 −0.192648
\(971\) 1.50000 + 2.59808i 0.0481373 + 0.0833762i 0.889090 0.457732i \(-0.151338\pi\)
−0.840953 + 0.541108i \(0.818005\pi\)
\(972\) 8.00000 13.8564i 0.256600 0.444444i
\(973\) 0 0
\(974\) 13.0000 0.416547
\(975\) 4.00000 + 13.8564i 0.128103 + 0.443760i
\(976\) −11.0000 −0.352101
\(977\) −19.5000 + 33.7750i −0.623860 + 1.08056i 0.364900 + 0.931047i \(0.381103\pi\)
−0.988760 + 0.149511i \(0.952230\pi\)
\(978\) −10.0000 + 17.3205i −0.319765 + 0.553849i
\(979\) 0 0
\(980\) 0 0
\(981\) −16.0000 27.7128i −0.510841 0.884802i
\(982\) 6.00000 + 10.3923i 0.191468 + 0.331632i
\(983\) 30.0000 0.956851 0.478426 0.878128i \(-0.341208\pi\)
0.478426 + 0.878128i \(0.341208\pi\)
\(984\) 0 0
\(985\) 18.0000 31.1769i 0.573528 0.993379i
\(986\) −18.0000 + 31.1769i −0.573237 + 0.992875i
\(987\) 0 0
\(988\) −4.00000 13.8564i −0.127257 0.440831i
\(989\) 24.0000 0.763156
\(990\) 0 0
\(991\) −8.50000 + 14.7224i −0.270011 + 0.467673i −0.968864 0.247592i \(-0.920361\pi\)
0.698853 + 0.715265i \(0.253694\pi\)
\(992\) 5.00000 + 8.66025i 0.158750 + 0.274963i
\(993\) 10.0000 0.317340
\(994\) 0 0
\(995\) −21.0000 36.3731i −0.665745 1.15310i
\(996\) 0 0
\(997\) 17.5000 + 30.3109i 0.554231 + 0.959955i 0.997963 + 0.0637961i \(0.0203207\pi\)
−0.443732 + 0.896159i \(0.646346\pi\)
\(998\) −11.0000 + 19.0526i −0.348199 + 0.603098i
\(999\) −20.0000 + 34.6410i −0.632772 + 1.09599i
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 1274.2.g.g.295.1 2
7.2 even 3 1274.2.e.i.165.1 2
7.3 odd 6 1274.2.h.j.373.1 2
7.4 even 3 1274.2.h.i.373.1 2
7.5 odd 6 1274.2.e.d.165.1 2
7.6 odd 2 182.2.g.b.113.1 yes 2
13.3 even 3 inner 1274.2.g.g.393.1 2
21.20 even 2 1638.2.r.c.1387.1 2
28.27 even 2 1456.2.s.e.113.1 2
91.3 odd 6 1274.2.e.d.471.1 2
91.6 even 12 2366.2.d.f.337.2 2
91.16 even 3 1274.2.h.i.263.1 2
91.20 even 12 2366.2.d.f.337.1 2
91.48 odd 6 2366.2.a.f.1.1 1
91.55 odd 6 182.2.g.b.29.1 2
91.68 odd 6 1274.2.h.j.263.1 2
91.69 odd 6 2366.2.a.n.1.1 1
91.81 even 3 1274.2.e.i.471.1 2
273.146 even 6 1638.2.r.c.757.1 2
364.55 even 6 1456.2.s.e.1121.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
182.2.g.b.29.1 2 91.55 odd 6
182.2.g.b.113.1 yes 2 7.6 odd 2
1274.2.e.d.165.1 2 7.5 odd 6
1274.2.e.d.471.1 2 91.3 odd 6
1274.2.e.i.165.1 2 7.2 even 3
1274.2.e.i.471.1 2 91.81 even 3
1274.2.g.g.295.1 2 1.1 even 1 trivial
1274.2.g.g.393.1 2 13.3 even 3 inner
1274.2.h.i.263.1 2 91.16 even 3
1274.2.h.i.373.1 2 7.4 even 3
1274.2.h.j.263.1 2 91.68 odd 6
1274.2.h.j.373.1 2 7.3 odd 6
1456.2.s.e.113.1 2 28.27 even 2
1456.2.s.e.1121.1 2 364.55 even 6
1638.2.r.c.757.1 2 273.146 even 6
1638.2.r.c.1387.1 2 21.20 even 2
2366.2.a.f.1.1 1 91.48 odd 6
2366.2.a.n.1.1 1 91.69 odd 6
2366.2.d.f.337.1 2 91.20 even 12
2366.2.d.f.337.2 2 91.6 even 12