Properties

Label 1155.2.l.e.1121.8
Level $1155$
Weight $2$
Character 1155.1121
Analytic conductor $9.223$
Analytic rank $0$
Dimension $40$
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] = [1155,2,Mod(1121,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.1121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.l (of order \(2\), degree \(1\), 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: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1121.8
Character \(\chi\) \(=\) 1155.1121
Dual form 1155.2.l.e.1121.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.04560 q^{2} +(-1.22443 + 1.22506i) q^{3} +2.18447 q^{4} -1.00000i q^{5} +(2.50470 - 2.50597i) q^{6} +1.00000i q^{7} -0.377355 q^{8} +(-0.00153018 - 3.00000i) q^{9} +O(q^{10})\) \(q-2.04560 q^{2} +(-1.22443 + 1.22506i) q^{3} +2.18447 q^{4} -1.00000i q^{5} +(2.50470 - 2.50597i) q^{6} +1.00000i q^{7} -0.377355 q^{8} +(-0.00153018 - 3.00000i) q^{9} +2.04560i q^{10} +(-0.566637 - 3.26786i) q^{11} +(-2.67474 + 2.67610i) q^{12} +2.37539i q^{13} -2.04560i q^{14} +(1.22506 + 1.22443i) q^{15} -3.59703 q^{16} -4.73436 q^{17} +(0.00313014 + 6.13679i) q^{18} +0.636972i q^{19} -2.18447i q^{20} +(-1.22506 - 1.22443i) q^{21} +(1.15911 + 6.68473i) q^{22} -4.83595i q^{23} +(0.462046 - 0.462281i) q^{24} -1.00000 q^{25} -4.85909i q^{26} +(3.67704 + 3.67142i) q^{27} +2.18447i q^{28} +4.70001 q^{29} +(-2.50597 - 2.50470i) q^{30} +1.83079 q^{31} +8.11278 q^{32} +(4.69713 + 3.30711i) q^{33} +9.68459 q^{34} +1.00000 q^{35} +(-0.00334264 - 6.55341i) q^{36} +5.92338 q^{37} -1.30299i q^{38} +(-2.90999 - 2.90850i) q^{39} +0.377355i q^{40} -6.62936 q^{41} +(2.50597 + 2.50470i) q^{42} +10.1301i q^{43} +(-1.23780 - 7.13855i) q^{44} +(-3.00000 + 0.00153018i) q^{45} +9.89242i q^{46} +11.3883i q^{47} +(4.40432 - 4.40656i) q^{48} -1.00000 q^{49} +2.04560 q^{50} +(5.79690 - 5.79986i) q^{51} +5.18897i q^{52} -6.88591i q^{53} +(-7.52176 - 7.51025i) q^{54} +(-3.26786 + 0.566637i) q^{55} -0.377355i q^{56} +(-0.780327 - 0.779929i) q^{57} -9.61432 q^{58} -1.96672i q^{59} +(2.67610 + 2.67474i) q^{60} -3.95587i q^{61} -3.74507 q^{62} +(3.00000 - 0.00153018i) q^{63} -9.40144 q^{64} +2.37539 q^{65} +(-9.60843 - 6.76503i) q^{66} +0.542784 q^{67} -10.3421 q^{68} +(5.92432 + 5.92130i) q^{69} -2.04560 q^{70} +6.29497i q^{71} +(0.000577422 + 1.13206i) q^{72} +6.85940i q^{73} -12.1169 q^{74} +(1.22443 - 1.22506i) q^{75} +1.39145i q^{76} +(3.26786 - 0.566637i) q^{77} +(5.95266 + 5.94963i) q^{78} -6.24475i q^{79} +3.59703i q^{80} +(-9.00000 + 0.00918110i) q^{81} +13.5610 q^{82} +2.16097 q^{83} +(-2.67610 - 2.67474i) q^{84} +4.73436i q^{85} -20.7221i q^{86} +(-5.75484 + 5.75778i) q^{87} +(0.213823 + 1.23314i) q^{88} +12.4798i q^{89} +(6.13679 - 0.00313014i) q^{90} -2.37539 q^{91} -10.5640i q^{92} +(-2.24168 + 2.24283i) q^{93} -23.2958i q^{94} +0.636972 q^{95} +(-9.93355 + 9.93862i) q^{96} -14.6880 q^{97} +2.04560 q^{98} +(-9.80272 + 1.70491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9} - 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} + 40 q^{18} - 2 q^{21} - 4 q^{22} - 12 q^{24} - 40 q^{25} + 32 q^{27} - 24 q^{29} - 8 q^{31} + 52 q^{32} - 16 q^{33} + 32 q^{34} + 40 q^{35} - 48 q^{37} + 66 q^{39} - 16 q^{41} + 32 q^{44} + 32 q^{48} - 40 q^{49} + 4 q^{50} - 14 q^{51} - 72 q^{54} + 8 q^{55} - 24 q^{57} - 80 q^{58} + 24 q^{60} + 48 q^{62} + 76 q^{64} + 4 q^{65} - 76 q^{66} - 48 q^{67} - 32 q^{68} - 20 q^{69} - 4 q^{70} + 128 q^{72} + 4 q^{75} - 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} - 24 q^{83} - 24 q^{84} - 32 q^{87} - 16 q^{88} + 8 q^{90} - 4 q^{91} - 20 q^{93} - 12 q^{95} + 12 q^{96} + 100 q^{97} + 4 q^{98} - 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.04560 −1.44646 −0.723228 0.690609i \(-0.757342\pi\)
−0.723228 + 0.690609i \(0.757342\pi\)
\(3\) −1.22443 + 1.22506i −0.706926 + 0.707287i
\(4\) 2.18447 1.09224
\(5\) 1.00000i 0.447214i
\(6\) 2.50470 2.50597i 1.02254 1.02306i
\(7\) 1.00000i 0.377964i
\(8\) −0.377355 −0.133415
\(9\) −0.00153018 3.00000i −0.000510061 1.00000i
\(10\) 2.04560i 0.646875i
\(11\) −0.566637 3.26786i −0.170847 0.985298i
\(12\) −2.67474 + 2.67610i −0.772130 + 0.772524i
\(13\) 2.37539i 0.658814i 0.944188 + 0.329407i \(0.106849\pi\)
−0.944188 + 0.329407i \(0.893151\pi\)
\(14\) 2.04560i 0.546709i
\(15\) 1.22506 + 1.22443i 0.316308 + 0.316147i
\(16\) −3.59703 −0.899257
\(17\) −4.73436 −1.14825 −0.574125 0.818768i \(-0.694658\pi\)
−0.574125 + 0.818768i \(0.694658\pi\)
\(18\) 0.00313014 + 6.13679i 0.000737781 + 1.44646i
\(19\) 0.636972i 0.146131i 0.997327 + 0.0730657i \(0.0232783\pi\)
−0.997327 + 0.0730657i \(0.976722\pi\)
\(20\) 2.18447i 0.488463i
\(21\) −1.22506 1.22443i −0.267329 0.267193i
\(22\) 1.15911 + 6.68473i 0.247123 + 1.42519i
\(23\) 4.83595i 1.00837i −0.863597 0.504183i \(-0.831794\pi\)
0.863597 0.504183i \(-0.168206\pi\)
\(24\) 0.462046 0.462281i 0.0943147 0.0943628i
\(25\) −1.00000 −0.200000
\(26\) 4.85909i 0.952946i
\(27\) 3.67704 + 3.67142i 0.707648 + 0.706566i
\(28\) 2.18447i 0.412826i
\(29\) 4.70001 0.872769 0.436385 0.899760i \(-0.356259\pi\)
0.436385 + 0.899760i \(0.356259\pi\)
\(30\) −2.50597 2.50470i −0.457526 0.457293i
\(31\) 1.83079 0.328820 0.164410 0.986392i \(-0.447428\pi\)
0.164410 + 0.986392i \(0.447428\pi\)
\(32\) 8.11278 1.43415
\(33\) 4.69713 + 3.30711i 0.817665 + 0.575695i
\(34\) 9.68459 1.66089
\(35\) 1.00000 0.169031
\(36\) −0.00334264 6.55341i −0.000557107 1.09224i
\(37\) 5.92338 0.973798 0.486899 0.873458i \(-0.338128\pi\)
0.486899 + 0.873458i \(0.338128\pi\)
\(38\) 1.30299i 0.211373i
\(39\) −2.90999 2.90850i −0.465971 0.465733i
\(40\) 0.377355i 0.0596650i
\(41\) −6.62936 −1.03533 −0.517666 0.855583i \(-0.673199\pi\)
−0.517666 + 0.855583i \(0.673199\pi\)
\(42\) 2.50597 + 2.50470i 0.386680 + 0.386483i
\(43\) 10.1301i 1.54482i 0.635123 + 0.772411i \(0.280949\pi\)
−0.635123 + 0.772411i \(0.719051\pi\)
\(44\) −1.23780 7.13855i −0.186606 1.07618i
\(45\) −3.00000 + 0.00153018i −0.447214 + 0.000228106i
\(46\) 9.89242i 1.45856i
\(47\) 11.3883i 1.66115i 0.556909 + 0.830574i \(0.311987\pi\)
−0.556909 + 0.830574i \(0.688013\pi\)
\(48\) 4.40432 4.40656i 0.635708 0.636033i
\(49\) −1.00000 −0.142857
\(50\) 2.04560 0.289291
\(51\) 5.79690 5.79986i 0.811728 0.812142i
\(52\) 5.18897i 0.719580i
\(53\) 6.88591i 0.945852i −0.881102 0.472926i \(-0.843198\pi\)
0.881102 0.472926i \(-0.156802\pi\)
\(54\) −7.52176 7.51025i −1.02358 1.02202i
\(55\) −3.26786 + 0.566637i −0.440638 + 0.0764053i
\(56\) 0.377355i 0.0504262i
\(57\) −0.780327 0.779929i −0.103357 0.103304i
\(58\) −9.61432 −1.26242
\(59\) 1.96672i 0.256045i −0.991771 0.128023i \(-0.959137\pi\)
0.991771 0.128023i \(-0.0408630\pi\)
\(60\) 2.67610 + 2.67474i 0.345483 + 0.345307i
\(61\) 3.95587i 0.506497i −0.967401 0.253248i \(-0.918501\pi\)
0.967401 0.253248i \(-0.0814990\pi\)
\(62\) −3.74507 −0.475624
\(63\) 3.00000 0.00153018i 0.377964 0.000192785i
\(64\) −9.40144 −1.17518
\(65\) 2.37539 0.294631
\(66\) −9.60843 6.76503i −1.18272 0.832717i
\(67\) 0.542784 0.0663116 0.0331558 0.999450i \(-0.489444\pi\)
0.0331558 + 0.999450i \(0.489444\pi\)
\(68\) −10.3421 −1.25416
\(69\) 5.92432 + 5.92130i 0.713204 + 0.712840i
\(70\) −2.04560 −0.244496
\(71\) 6.29497i 0.747076i 0.927615 + 0.373538i \(0.121855\pi\)
−0.927615 + 0.373538i \(0.878145\pi\)
\(72\) 0.000577422 1.13206i 6.80499e−5 0.133415i
\(73\) 6.85940i 0.802832i 0.915896 + 0.401416i \(0.131482\pi\)
−0.915896 + 0.401416i \(0.868518\pi\)
\(74\) −12.1169 −1.40856
\(75\) 1.22443 1.22506i 0.141385 0.141457i
\(76\) 1.39145i 0.159610i
\(77\) 3.26786 0.566637i 0.372407 0.0645742i
\(78\) 5.95266 + 5.94963i 0.674006 + 0.673662i
\(79\) 6.24475i 0.702590i −0.936265 0.351295i \(-0.885741\pi\)
0.936265 0.351295i \(-0.114259\pi\)
\(80\) 3.59703i 0.402160i
\(81\) −9.00000 + 0.00918110i −0.999999 + 0.00102012i
\(82\) 13.5610 1.49756
\(83\) 2.16097 0.237197 0.118599 0.992942i \(-0.462160\pi\)
0.118599 + 0.992942i \(0.462160\pi\)
\(84\) −2.67610 2.67474i −0.291987 0.291838i
\(85\) 4.73436i 0.513513i
\(86\) 20.7221i 2.23452i
\(87\) −5.75484 + 5.75778i −0.616984 + 0.617298i
\(88\) 0.213823 + 1.23314i 0.0227936 + 0.131454i
\(89\) 12.4798i 1.32286i 0.750008 + 0.661428i \(0.230049\pi\)
−0.750008 + 0.661428i \(0.769951\pi\)
\(90\) 6.13679 0.00313014i 0.646875 0.000329946i
\(91\) −2.37539 −0.249008
\(92\) 10.5640i 1.10137i
\(93\) −2.24168 + 2.24283i −0.232452 + 0.232570i
\(94\) 23.2958i 2.40278i
\(95\) 0.636972 0.0653519
\(96\) −9.93355 + 9.93862i −1.01384 + 1.01436i
\(97\) −14.6880 −1.49134 −0.745668 0.666318i \(-0.767869\pi\)
−0.745668 + 0.666318i \(0.767869\pi\)
\(98\) 2.04560 0.206637
\(99\) −9.80272 + 1.70491i −0.985210 + 0.171350i
\(100\) −2.18447 −0.218447
\(101\) −17.4470 −1.73604 −0.868019 0.496531i \(-0.834607\pi\)
−0.868019 + 0.496531i \(0.834607\pi\)
\(102\) −11.8581 + 11.8642i −1.17413 + 1.17473i
\(103\) −14.0733 −1.38668 −0.693340 0.720611i \(-0.743861\pi\)
−0.693340 + 0.720611i \(0.743861\pi\)
\(104\) 0.896364i 0.0878957i
\(105\) −1.22443 + 1.22506i −0.119492 + 0.119553i
\(106\) 14.0858i 1.36813i
\(107\) −4.73757 −0.457998 −0.228999 0.973427i \(-0.573545\pi\)
−0.228999 + 0.973427i \(0.573545\pi\)
\(108\) 8.03240 + 8.02012i 0.772918 + 0.771736i
\(109\) 7.36247i 0.705197i 0.935775 + 0.352598i \(0.114702\pi\)
−0.935775 + 0.352598i \(0.885298\pi\)
\(110\) 6.68473 1.15911i 0.637364 0.110517i
\(111\) −7.25278 + 7.25648i −0.688404 + 0.688755i
\(112\) 3.59703i 0.339887i
\(113\) 2.79872i 0.263281i −0.991298 0.131641i \(-0.957976\pi\)
0.991298 0.131641i \(-0.0420245\pi\)
\(114\) 1.59624 + 1.59542i 0.149501 + 0.149425i
\(115\) −4.83595 −0.450955
\(116\) 10.2670 0.953270
\(117\) 7.12616 0.00363478i 0.658814 0.000336035i
\(118\) 4.02312i 0.370359i
\(119\) 4.73436i 0.433998i
\(120\) −0.462281 0.462046i −0.0422003 0.0421788i
\(121\) −10.3578 + 3.70338i −0.941622 + 0.336671i
\(122\) 8.09211i 0.732625i
\(123\) 8.11721 8.12135i 0.731904 0.732277i
\(124\) 3.99931 0.359149
\(125\) 1.00000i 0.0894427i
\(126\) −6.13679 + 0.00313014i −0.546709 + 0.000278855i
\(127\) 13.1403i 1.16601i 0.812467 + 0.583007i \(0.198124\pi\)
−0.812467 + 0.583007i \(0.801876\pi\)
\(128\) 3.00600 0.265695
\(129\) −12.4099 12.4036i −1.09263 1.09208i
\(130\) −4.85909 −0.426170
\(131\) 6.43379 0.562123 0.281061 0.959690i \(-0.409314\pi\)
0.281061 + 0.959690i \(0.409314\pi\)
\(132\) 10.2607 + 7.22430i 0.893083 + 0.628794i
\(133\) −0.636972 −0.0552325
\(134\) −1.11032 −0.0959168
\(135\) 3.67142 3.67704i 0.315986 0.316470i
\(136\) 1.78653 0.153194
\(137\) 16.6169i 1.41968i 0.704363 + 0.709840i \(0.251233\pi\)
−0.704363 + 0.709840i \(0.748767\pi\)
\(138\) −12.1188 12.1126i −1.03162 1.03109i
\(139\) 9.29709i 0.788569i 0.918988 + 0.394285i \(0.129008\pi\)
−0.918988 + 0.394285i \(0.870992\pi\)
\(140\) 2.18447 0.184622
\(141\) −13.9513 13.9441i −1.17491 1.17431i
\(142\) 12.8770i 1.08061i
\(143\) 7.76244 1.34598i 0.649128 0.112557i
\(144\) 0.00550411 + 10.7911i 0.000458676 + 0.899257i
\(145\) 4.70001i 0.390314i
\(146\) 14.0316i 1.16126i
\(147\) 1.22443 1.22506i 0.100989 0.101041i
\(148\) 12.9395 1.06362
\(149\) −15.5271 −1.27203 −0.636014 0.771678i \(-0.719418\pi\)
−0.636014 + 0.771678i \(0.719418\pi\)
\(150\) −2.50470 + 2.50597i −0.204508 + 0.204612i
\(151\) 4.91642i 0.400092i −0.979786 0.200046i \(-0.935891\pi\)
0.979786 0.200046i \(-0.0641092\pi\)
\(152\) 0.240364i 0.0194961i
\(153\) 0.00724443 + 14.2031i 0.000585678 + 1.14825i
\(154\) −6.68473 + 1.15911i −0.538671 + 0.0934038i
\(155\) 1.83079i 0.147053i
\(156\) −6.35678 6.35354i −0.508950 0.508690i
\(157\) 6.37551 0.508821 0.254410 0.967096i \(-0.418119\pi\)
0.254410 + 0.967096i \(0.418119\pi\)
\(158\) 12.7743i 1.01627i
\(159\) 8.43563 + 8.43133i 0.668989 + 0.668648i
\(160\) 8.11278i 0.641372i
\(161\) 4.83595 0.381126
\(162\) 18.4104 0.0187808i 1.44646 0.00147556i
\(163\) −17.0281 −1.33374 −0.666872 0.745173i \(-0.732367\pi\)
−0.666872 + 0.745173i \(0.732367\pi\)
\(164\) −14.4817 −1.13083
\(165\) 3.30711 4.69713i 0.257459 0.365671i
\(166\) −4.42047 −0.343095
\(167\) 17.5347 1.35687 0.678437 0.734659i \(-0.262658\pi\)
0.678437 + 0.734659i \(0.262658\pi\)
\(168\) 0.462281 + 0.462046i 0.0356658 + 0.0356476i
\(169\) 7.35753 0.565964
\(170\) 9.68459i 0.742774i
\(171\) 1.91092 0.000974684i 0.146131 7.45359e-5i
\(172\) 22.1289i 1.68731i
\(173\) −21.7187 −1.65124 −0.825620 0.564227i \(-0.809174\pi\)
−0.825620 + 0.564227i \(0.809174\pi\)
\(174\) 11.7721 11.7781i 0.892440 0.892895i
\(175\) 1.00000i 0.0755929i
\(176\) 2.03821 + 11.7546i 0.153636 + 0.886035i
\(177\) 2.40935 + 2.40812i 0.181098 + 0.181005i
\(178\) 25.5287i 1.91345i
\(179\) 22.4731i 1.67972i 0.542804 + 0.839859i \(0.317363\pi\)
−0.542804 + 0.839859i \(0.682637\pi\)
\(180\) −6.55341 + 0.00334264i −0.488463 + 0.000249146i
\(181\) −2.04960 −0.152346 −0.0761728 0.997095i \(-0.524270\pi\)
−0.0761728 + 0.997095i \(0.524270\pi\)
\(182\) 4.85909 0.360180
\(183\) 4.84616 + 4.84369i 0.358239 + 0.358056i
\(184\) 1.82487i 0.134531i
\(185\) 5.92338i 0.435496i
\(186\) 4.58558 4.58792i 0.336231 0.336403i
\(187\) 2.68266 + 15.4712i 0.196175 + 1.13137i
\(188\) 24.8773i 1.81436i
\(189\) −3.67142 + 3.67704i −0.267057 + 0.267466i
\(190\) −1.30299 −0.0945287
\(191\) 2.33032i 0.168616i −0.996440 0.0843080i \(-0.973132\pi\)
0.996440 0.0843080i \(-0.0268680\pi\)
\(192\) 11.5114 11.5173i 0.830765 0.831189i
\(193\) 5.98755i 0.430993i −0.976505 0.215497i \(-0.930863\pi\)
0.976505 0.215497i \(-0.0691371\pi\)
\(194\) 30.0456 2.15715
\(195\) −2.90850 + 2.90999i −0.208282 + 0.208388i
\(196\) −2.18447 −0.156034
\(197\) −15.4447 −1.10039 −0.550194 0.835037i \(-0.685446\pi\)
−0.550194 + 0.835037i \(0.685446\pi\)
\(198\) 20.0524 3.48756i 1.42506 0.247850i
\(199\) 20.7622 1.47179 0.735896 0.677095i \(-0.236761\pi\)
0.735896 + 0.677095i \(0.236761\pi\)
\(200\) 0.377355 0.0266830
\(201\) −0.664602 + 0.664941i −0.0468774 + 0.0469013i
\(202\) 35.6895 2.51110
\(203\) 4.70001i 0.329876i
\(204\) 12.6632 12.6696i 0.886599 0.887051i
\(205\) 6.62936i 0.463015i
\(206\) 28.7882 2.00577
\(207\) −14.5079 + 0.00739989i −1.00837 + 0.000514328i
\(208\) 8.54433i 0.592443i
\(209\) 2.08154 0.360932i 0.143983 0.0249662i
\(210\) 2.50470 2.50597i 0.172840 0.172929i
\(211\) 17.1746i 1.18235i −0.806545 0.591173i \(-0.798665\pi\)
0.806545 0.591173i \(-0.201335\pi\)
\(212\) 15.0421i 1.03309i
\(213\) −7.71170 7.70777i −0.528397 0.528128i
\(214\) 9.69117 0.662475
\(215\) 10.1301 0.690865
\(216\) −1.38755 1.38543i −0.0944109 0.0942665i
\(217\) 1.83079i 0.124282i
\(218\) 15.0607i 1.02004i
\(219\) −8.40316 8.39887i −0.567833 0.567543i
\(220\) −7.13855 + 1.23780i −0.481281 + 0.0834526i
\(221\) 11.2459i 0.756483i
\(222\) 14.8363 14.8438i 0.995746 0.996254i
\(223\) 4.43349 0.296889 0.148444 0.988921i \(-0.452573\pi\)
0.148444 + 0.988921i \(0.452573\pi\)
\(224\) 8.11278i 0.542058i
\(225\) 0.00153018 + 3.00000i 0.000102012 + 0.200000i
\(226\) 5.72505i 0.380825i
\(227\) −6.23302 −0.413700 −0.206850 0.978373i \(-0.566321\pi\)
−0.206850 + 0.978373i \(0.566321\pi\)
\(228\) −1.70460 1.70373i −0.112890 0.112832i
\(229\) 0.909472 0.0600996 0.0300498 0.999548i \(-0.490433\pi\)
0.0300498 + 0.999548i \(0.490433\pi\)
\(230\) 9.89242 0.652287
\(231\) −3.30711 + 4.69713i −0.217592 + 0.309048i
\(232\) −1.77357 −0.116441
\(233\) −27.6897 −1.81401 −0.907005 0.421120i \(-0.861637\pi\)
−0.907005 + 0.421120i \(0.861637\pi\)
\(234\) −14.5773 + 0.00743530i −0.952946 + 0.000486061i
\(235\) 11.3883 0.742888
\(236\) 4.29625i 0.279662i
\(237\) 7.65018 + 7.64628i 0.496933 + 0.496679i
\(238\) 9.68459i 0.627759i
\(239\) 23.6267 1.52829 0.764143 0.645047i \(-0.223162\pi\)
0.764143 + 0.645047i \(0.223162\pi\)
\(240\) −4.40656 4.40432i −0.284442 0.284297i
\(241\) 11.4547i 0.737865i −0.929456 0.368932i \(-0.879723\pi\)
0.929456 0.368932i \(-0.120277\pi\)
\(242\) 21.1880 7.57563i 1.36202 0.486980i
\(243\) 11.0086 11.0368i 0.706205 0.708008i
\(244\) 8.64148i 0.553214i
\(245\) 1.00000i 0.0638877i
\(246\) −16.6045 + 16.6130i −1.05867 + 1.05921i
\(247\) −1.51306 −0.0962734
\(248\) −0.690858 −0.0438696
\(249\) −2.64596 + 2.64731i −0.167681 + 0.167766i
\(250\) 2.04560i 0.129375i
\(251\) 22.5704i 1.42463i 0.701860 + 0.712315i \(0.252353\pi\)
−0.701860 + 0.712315i \(0.747647\pi\)
\(252\) 6.55341 0.00334264i 0.412826 0.000210567i
\(253\) −15.8032 + 2.74023i −0.993540 + 0.172277i
\(254\) 26.8798i 1.68659i
\(255\) −5.79986 5.79690i −0.363201 0.363016i
\(256\) 12.6538 0.790863
\(257\) 3.44901i 0.215143i −0.994197 0.107572i \(-0.965692\pi\)
0.994197 0.107572i \(-0.0343075\pi\)
\(258\) 25.3857 + 25.3728i 1.58045 + 1.57964i
\(259\) 5.92338i 0.368061i
\(260\) 5.18897 0.321806
\(261\) −0.00719187 14.1000i −0.000445166 0.872769i
\(262\) −13.1609 −0.813086
\(263\) 21.1738 1.30563 0.652816 0.757516i \(-0.273587\pi\)
0.652816 + 0.757516i \(0.273587\pi\)
\(264\) −1.77248 1.24796i −0.109089 0.0768064i
\(265\) −6.88591 −0.422998
\(266\) 1.30299 0.0798913
\(267\) −15.2885 15.2807i −0.935640 0.935163i
\(268\) 1.18570 0.0724279
\(269\) 24.0947i 1.46908i 0.678564 + 0.734541i \(0.262603\pi\)
−0.678564 + 0.734541i \(0.737397\pi\)
\(270\) −7.51025 + 7.52176i −0.457060 + 0.457759i
\(271\) 2.95183i 0.179311i −0.995973 0.0896553i \(-0.971423\pi\)
0.995973 0.0896553i \(-0.0285765\pi\)
\(272\) 17.0296 1.03257
\(273\) 2.90850 2.90999i 0.176031 0.176120i
\(274\) 33.9916i 2.05351i
\(275\) 0.566637 + 3.26786i 0.0341695 + 0.197060i
\(276\) 12.9415 + 12.9349i 0.778987 + 0.778590i
\(277\) 4.92236i 0.295756i 0.989006 + 0.147878i \(0.0472443\pi\)
−0.989006 + 0.147878i \(0.952756\pi\)
\(278\) 19.0181i 1.14063i
\(279\) −0.00280145 5.49238i −0.000167718 0.328820i
\(280\) −0.377355 −0.0225513
\(281\) 10.4955 0.626109 0.313054 0.949735i \(-0.398648\pi\)
0.313054 + 0.949735i \(0.398648\pi\)
\(282\) 28.5387 + 28.5241i 1.69945 + 1.69859i
\(283\) 9.10112i 0.541006i −0.962719 0.270503i \(-0.912810\pi\)
0.962719 0.270503i \(-0.0871899\pi\)
\(284\) 13.7512i 0.815983i
\(285\) −0.779929 + 0.780327i −0.0461990 + 0.0462226i
\(286\) −15.8788 + 2.75334i −0.938935 + 0.162808i
\(287\) 6.62936i 0.391319i
\(288\) −0.0124140 24.3383i −0.000731504 1.43415i
\(289\) 5.41413 0.318478
\(290\) 9.61432i 0.564573i
\(291\) 17.9844 17.9936i 1.05426 1.05480i
\(292\) 14.9842i 0.876882i
\(293\) −27.1116 −1.58388 −0.791939 0.610600i \(-0.790928\pi\)
−0.791939 + 0.610600i \(0.790928\pi\)
\(294\) −2.50470 + 2.50597i −0.146077 + 0.146151i
\(295\) −1.96672 −0.114507
\(296\) −2.23522 −0.129919
\(297\) 9.91415 14.0964i 0.575278 0.817958i
\(298\) 31.7621 1.83993
\(299\) 11.4873 0.664326
\(300\) 2.67474 2.67610i 0.154426 0.154505i
\(301\) −10.1301 −0.583888
\(302\) 10.0570i 0.578716i
\(303\) 21.3626 21.3735i 1.22725 1.22788i
\(304\) 2.29120i 0.131410i
\(305\) −3.95587 −0.226512
\(306\) −0.0148192 29.0538i −0.000847157 1.66089i
\(307\) 5.75870i 0.328666i 0.986405 + 0.164333i \(0.0525472\pi\)
−0.986405 + 0.164333i \(0.947453\pi\)
\(308\) 7.13855 1.23780i 0.406757 0.0705303i
\(309\) 17.2318 17.2405i 0.980280 0.980780i
\(310\) 3.74507i 0.212705i
\(311\) 8.05967i 0.457022i −0.973541 0.228511i \(-0.926614\pi\)
0.973541 0.228511i \(-0.0733857\pi\)
\(312\) 1.09810 + 1.09754i 0.0621675 + 0.0621358i
\(313\) −15.4684 −0.874327 −0.437164 0.899382i \(-0.644017\pi\)
−0.437164 + 0.899382i \(0.644017\pi\)
\(314\) −13.0417 −0.735987
\(315\) −0.00153018 3.00000i −8.62161e−5 0.169031i
\(316\) 13.6415i 0.767394i
\(317\) 1.78189i 0.100081i 0.998747 + 0.0500403i \(0.0159350\pi\)
−0.998747 + 0.0500403i \(0.984065\pi\)
\(318\) −17.2559 17.2471i −0.967663 0.967170i
\(319\) −2.66320 15.3590i −0.149110 0.859937i
\(320\) 9.40144i 0.525556i
\(321\) 5.80084 5.80380i 0.323771 0.323936i
\(322\) −9.89242 −0.551283
\(323\) 3.01565i 0.167795i
\(324\) −19.6602 + 0.0200558i −1.09224 + 0.00111421i
\(325\) 2.37539i 0.131763i
\(326\) 34.8326 1.92920
\(327\) −9.01944 9.01485i −0.498776 0.498522i
\(328\) 2.50162 0.138129
\(329\) −11.3883 −0.627855
\(330\) −6.76503 + 9.60843i −0.372402 + 0.528927i
\(331\) 26.3766 1.44979 0.724894 0.688861i \(-0.241889\pi\)
0.724894 + 0.688861i \(0.241889\pi\)
\(332\) 4.72058 0.259075
\(333\) −0.00906386 17.7701i −0.000496697 0.973798i
\(334\) −35.8689 −1.96266
\(335\) 0.542784i 0.0296554i
\(336\) 4.40656 + 4.40432i 0.240398 + 0.240275i
\(337\) 26.0748i 1.42038i 0.704008 + 0.710192i \(0.251392\pi\)
−0.704008 + 0.710192i \(0.748608\pi\)
\(338\) −15.0506 −0.818642
\(339\) 3.42859 + 3.42684i 0.186215 + 0.186120i
\(340\) 10.3421i 0.560877i
\(341\) −1.03739 5.98278i −0.0561780 0.323986i
\(342\) −3.90896 + 0.00199381i −0.211373 + 0.000107813i
\(343\) 1.00000i 0.0539949i
\(344\) 3.82263i 0.206103i
\(345\) 5.92130 5.92432i 0.318792 0.318955i
\(346\) 44.4277 2.38845
\(347\) −32.5968 −1.74989 −0.874944 0.484225i \(-0.839102\pi\)
−0.874944 + 0.484225i \(0.839102\pi\)
\(348\) −12.5713 + 12.5777i −0.673892 + 0.674235i
\(349\) 23.6094i 1.26378i 0.775057 + 0.631891i \(0.217721\pi\)
−0.775057 + 0.631891i \(0.782279\pi\)
\(350\) 2.04560i 0.109342i
\(351\) −8.72105 + 8.73441i −0.465495 + 0.466208i
\(352\) −4.59700 26.5115i −0.245021 1.41307i
\(353\) 1.54586i 0.0822778i 0.999153 + 0.0411389i \(0.0130986\pi\)
−0.999153 + 0.0411389i \(0.986901\pi\)
\(354\) −4.92856 4.92604i −0.261950 0.261816i
\(355\) 6.29497 0.334102
\(356\) 27.2618i 1.44487i
\(357\) 5.79986 + 5.79690i 0.306961 + 0.306804i
\(358\) 45.9709i 2.42964i
\(359\) −29.4604 −1.55486 −0.777430 0.628969i \(-0.783477\pi\)
−0.777430 + 0.628969i \(0.783477\pi\)
\(360\) 1.13206 0.000577422i 0.0596650 3.04328e-5i
\(361\) 18.5943 0.978646
\(362\) 4.19266 0.220361
\(363\) 8.14563 17.2235i 0.427535 0.903999i
\(364\) −5.18897 −0.271976
\(365\) 6.85940 0.359037
\(366\) −9.91330 9.90824i −0.518176 0.517912i
\(367\) 16.8829 0.881280 0.440640 0.897684i \(-0.354751\pi\)
0.440640 + 0.897684i \(0.354751\pi\)
\(368\) 17.3951i 0.906780i
\(369\) 0.0101441 + 19.8881i 0.000528083 + 1.03533i
\(370\) 12.1169i 0.629926i
\(371\) 6.88591 0.357498
\(372\) −4.89689 + 4.89939i −0.253892 + 0.254021i
\(373\) 7.88226i 0.408128i −0.978958 0.204064i \(-0.934585\pi\)
0.978958 0.204064i \(-0.0654150\pi\)
\(374\) −5.48764 31.6479i −0.283759 1.63647i
\(375\) −1.22506 1.22443i −0.0632617 0.0632294i
\(376\) 4.29741i 0.221622i
\(377\) 11.1643i 0.574993i
\(378\) 7.51025 7.52176i 0.386286 0.386877i
\(379\) −4.34576 −0.223227 −0.111613 0.993752i \(-0.535602\pi\)
−0.111613 + 0.993752i \(0.535602\pi\)
\(380\) 1.39145 0.0713797
\(381\) −16.0976 16.0894i −0.824706 0.824286i
\(382\) 4.76690i 0.243896i
\(383\) 20.1719i 1.03073i −0.856970 0.515367i \(-0.827656\pi\)
0.856970 0.515367i \(-0.172344\pi\)
\(384\) −3.68064 + 3.68252i −0.187827 + 0.187923i
\(385\) −0.566637 3.26786i −0.0288785 0.166546i
\(386\) 12.2481i 0.623413i
\(387\) 30.3902 0.0155009i 1.54482 0.000787954i
\(388\) −32.0854 −1.62889
\(389\) 20.0116i 1.01463i −0.861762 0.507313i \(-0.830639\pi\)
0.861762 0.507313i \(-0.169361\pi\)
\(390\) 5.94963 5.95266i 0.301271 0.301425i
\(391\) 22.8951i 1.15786i
\(392\) 0.377355 0.0190593
\(393\) −7.87774 + 7.88176i −0.397379 + 0.397582i
\(394\) 31.5936 1.59166
\(395\) −6.24475 −0.314208
\(396\) −21.4138 + 3.72433i −1.07608 + 0.187154i
\(397\) −5.93402 −0.297820 −0.148910 0.988851i \(-0.547576\pi\)
−0.148910 + 0.988851i \(0.547576\pi\)
\(398\) −42.4711 −2.12888
\(399\) 0.779929 0.780327i 0.0390453 0.0390652i
\(400\) 3.59703 0.179851
\(401\) 6.75438i 0.337297i 0.985676 + 0.168649i \(0.0539403\pi\)
−0.985676 + 0.168649i \(0.946060\pi\)
\(402\) 1.35951 1.36020i 0.0678061 0.0678407i
\(403\) 4.34884i 0.216631i
\(404\) −38.1124 −1.89616
\(405\) 0.00918110 + 9.00000i 0.000456212 + 0.447213i
\(406\) 9.61432i 0.477151i
\(407\) −3.35641 19.3568i −0.166371 0.959481i
\(408\) −2.18749 + 2.18860i −0.108297 + 0.108352i
\(409\) 16.1388i 0.798014i 0.916948 + 0.399007i \(0.130645\pi\)
−0.916948 + 0.399007i \(0.869355\pi\)
\(410\) 13.5610i 0.669731i
\(411\) −20.3567 20.3463i −1.00412 1.00361i
\(412\) −30.7426 −1.51458
\(413\) 1.96672 0.0967761
\(414\) 29.6772 0.0151372i 1.45856 0.000743953i
\(415\) 2.16097i 0.106078i
\(416\) 19.2710i 0.944839i
\(417\) −11.3895 11.3837i −0.557745 0.557460i
\(418\) −4.25799 + 0.738321i −0.208265 + 0.0361125i
\(419\) 25.6930i 1.25519i 0.778542 + 0.627593i \(0.215960\pi\)
−0.778542 + 0.627593i \(0.784040\pi\)
\(420\) −2.67474 + 2.67610i −0.130514 + 0.130580i
\(421\) 18.9921 0.925619 0.462810 0.886458i \(-0.346841\pi\)
0.462810 + 0.886458i \(0.346841\pi\)
\(422\) 35.1323i 1.71021i
\(423\) 34.1648 0.0174261i 1.66115 0.000847287i
\(424\) 2.59843i 0.126191i
\(425\) 4.73436 0.229650
\(426\) 15.7750 + 15.7670i 0.764303 + 0.763913i
\(427\) 3.95587 0.191438
\(428\) −10.3491 −0.500242
\(429\) −7.85568 + 11.1575i −0.379276 + 0.538689i
\(430\) −20.7221 −0.999307
\(431\) −21.6210 −1.04145 −0.520723 0.853725i \(-0.674338\pi\)
−0.520723 + 0.853725i \(0.674338\pi\)
\(432\) −13.2264 13.2062i −0.636357 0.635384i
\(433\) 10.2110 0.490711 0.245355 0.969433i \(-0.421095\pi\)
0.245355 + 0.969433i \(0.421095\pi\)
\(434\) 3.74507i 0.179769i
\(435\) 5.75778 + 5.75484i 0.276064 + 0.275923i
\(436\) 16.0831i 0.770241i
\(437\) 3.08037 0.147354
\(438\) 17.1895 + 17.1807i 0.821345 + 0.820927i
\(439\) 18.4912i 0.882536i 0.897375 + 0.441268i \(0.145471\pi\)
−0.897375 + 0.441268i \(0.854529\pi\)
\(440\) 1.23314 0.213823i 0.0587878 0.0101936i
\(441\) 0.00153018 + 3.00000i 7.28659e−5 + 0.142857i
\(442\) 23.0047i 1.09422i
\(443\) 8.61282i 0.409207i 0.978845 + 0.204604i \(0.0655906\pi\)
−0.978845 + 0.204604i \(0.934409\pi\)
\(444\) −15.8435 + 15.8516i −0.751899 + 0.752283i
\(445\) 12.4798 0.591600
\(446\) −9.06914 −0.429436
\(447\) 19.0118 19.0215i 0.899230 0.899688i
\(448\) 9.40144i 0.444176i
\(449\) 16.6872i 0.787516i −0.919214 0.393758i \(-0.871175\pi\)
0.919214 0.393758i \(-0.128825\pi\)
\(450\) −0.00313014 6.13679i −0.000147556 0.289291i
\(451\) 3.75644 + 21.6638i 0.176884 + 1.02011i
\(452\) 6.11372i 0.287565i
\(453\) 6.02289 + 6.01982i 0.282980 + 0.282836i
\(454\) 12.7503 0.598399
\(455\) 2.37539i 0.111360i
\(456\) 0.294460 + 0.294310i 0.0137894 + 0.0137823i
\(457\) 24.2227i 1.13309i 0.824031 + 0.566544i \(0.191720\pi\)
−0.824031 + 0.566544i \(0.808280\pi\)
\(458\) −1.86041 −0.0869315
\(459\) −17.4084 17.3818i −0.812556 0.811314i
\(460\) −10.5640 −0.492549
\(461\) −23.5724 −1.09788 −0.548938 0.835863i \(-0.684968\pi\)
−0.548938 + 0.835863i \(0.684968\pi\)
\(462\) 6.76503 9.60843i 0.314738 0.447025i
\(463\) −6.36147 −0.295643 −0.147821 0.989014i \(-0.547226\pi\)
−0.147821 + 0.989014i \(0.547226\pi\)
\(464\) −16.9060 −0.784844
\(465\) 2.24283 + 2.24168i 0.104009 + 0.103955i
\(466\) 56.6419 2.62389
\(467\) 38.5449i 1.78364i 0.452386 + 0.891822i \(0.350573\pi\)
−0.452386 + 0.891822i \(0.649427\pi\)
\(468\) 15.5669 0.00794007i 0.719580 0.000367030i
\(469\) 0.542784i 0.0250634i
\(470\) −23.2958 −1.07455
\(471\) −7.80638 + 7.81036i −0.359699 + 0.359882i
\(472\) 0.742152i 0.0341603i
\(473\) 33.1037 5.74007i 1.52211 0.263929i
\(474\) −15.6492 15.6412i −0.718791 0.718425i
\(475\) 0.636972i 0.0292263i
\(476\) 10.3421i 0.474028i
\(477\) −20.6577 + 0.0105367i −0.945852 + 0.000482442i
\(478\) −48.3308 −2.21060
\(479\) 24.8867 1.13710 0.568550 0.822648i \(-0.307504\pi\)
0.568550 + 0.822648i \(0.307504\pi\)
\(480\) 9.93862 + 9.93355i 0.453634 + 0.453403i
\(481\) 14.0703i 0.641552i
\(482\) 23.4318i 1.06729i
\(483\) −5.92130 + 5.92432i −0.269428 + 0.269566i
\(484\) −22.6264 + 8.08993i −1.02847 + 0.367724i
\(485\) 14.6880i 0.666946i
\(486\) −22.5193 + 22.5768i −1.02149 + 1.02410i
\(487\) −12.5901 −0.570514 −0.285257 0.958451i \(-0.592079\pi\)
−0.285257 + 0.958451i \(0.592079\pi\)
\(488\) 1.49276i 0.0675743i
\(489\) 20.8497 20.8604i 0.942858 0.943339i
\(490\) 2.04560i 0.0924107i
\(491\) 18.3662 0.828854 0.414427 0.910082i \(-0.363982\pi\)
0.414427 + 0.910082i \(0.363982\pi\)
\(492\) 17.7318 17.7409i 0.799412 0.799820i
\(493\) −22.2515 −1.00216
\(494\) 3.09510 0.139255
\(495\) 1.70491 + 9.80272i 0.0766300 + 0.440599i
\(496\) −6.58541 −0.295694
\(497\) −6.29497 −0.282368
\(498\) 5.41257 5.41533i 0.242543 0.242667i
\(499\) 11.3997 0.510321 0.255160 0.966899i \(-0.417872\pi\)
0.255160 + 0.966899i \(0.417872\pi\)
\(500\) 2.18447i 0.0976925i
\(501\) −21.4700 + 21.4810i −0.959210 + 0.959699i
\(502\) 46.1699i 2.06066i
\(503\) 16.3592 0.729421 0.364710 0.931121i \(-0.381168\pi\)
0.364710 + 0.931121i \(0.381168\pi\)
\(504\) −1.13206 0.000577422i −0.0504262 2.57204e-5i
\(505\) 17.4470i 0.776380i
\(506\) 32.3271 5.60540i 1.43711 0.249191i
\(507\) −9.00880 + 9.01340i −0.400095 + 0.400299i
\(508\) 28.7046i 1.27356i
\(509\) 4.04066i 0.179099i −0.995982 0.0895496i \(-0.971457\pi\)
0.995982 0.0895496i \(-0.0285428\pi\)
\(510\) 11.8642 + 11.8581i 0.525355 + 0.525087i
\(511\) −6.85940 −0.303442
\(512\) −31.8966 −1.40964
\(513\) −2.33859 + 2.34217i −0.103251 + 0.103410i
\(514\) 7.05529i 0.311196i
\(515\) 14.0733i 0.620142i
\(516\) −27.1091 27.0953i −1.19341 1.19280i
\(517\) 37.2152 6.45300i 1.63672 0.283803i
\(518\) 12.1169i 0.532384i
\(519\) 26.5930 26.6066i 1.16731 1.16790i
\(520\) −0.896364 −0.0393082
\(521\) 41.5493i 1.82031i 0.414269 + 0.910154i \(0.364037\pi\)
−0.414269 + 0.910154i \(0.635963\pi\)
\(522\) 0.0147117 + 28.8430i 0.000643913 + 1.26242i
\(523\) 14.3063i 0.625571i 0.949824 + 0.312785i \(0.101262\pi\)
−0.949824 + 0.312785i \(0.898738\pi\)
\(524\) 14.0544 0.613971
\(525\) 1.22506 + 1.22443i 0.0534659 + 0.0534386i
\(526\) −43.3131 −1.88854
\(527\) −8.66762 −0.377568
\(528\) −16.8957 11.8958i −0.735290 0.517697i
\(529\) −0.386438 −0.0168016
\(530\) 14.0858 0.611848
\(531\) −5.90017 + 0.00300945i −0.256045 + 0.000130599i
\(532\) −1.39145 −0.0603269
\(533\) 15.7473i 0.682092i
\(534\) 31.2741 + 31.2581i 1.35336 + 1.35267i
\(535\) 4.73757i 0.204823i
\(536\) −0.204822 −0.00884697
\(537\) −27.5308 27.5168i −1.18804 1.18744i
\(538\) 49.2882i 2.12496i
\(539\) 0.566637 + 3.26786i 0.0244068 + 0.140757i
\(540\) 8.02012 8.03240i 0.345131 0.345659i
\(541\) 5.57042i 0.239491i 0.992805 + 0.119746i \(0.0382079\pi\)
−0.992805 + 0.119746i \(0.961792\pi\)
\(542\) 6.03825i 0.259365i
\(543\) 2.50960 2.51088i 0.107697 0.107752i
\(544\) −38.4088 −1.64676
\(545\) 7.36247 0.315373
\(546\) −5.94963 + 5.95266i −0.254620 + 0.254750i
\(547\) 17.6879i 0.756282i 0.925748 + 0.378141i \(0.123436\pi\)
−0.925748 + 0.378141i \(0.876564\pi\)
\(548\) 36.2992i 1.55063i
\(549\) −11.8676 + 0.00605320i −0.506497 + 0.000258344i
\(550\) −1.15911 6.68473i −0.0494246 0.285038i
\(551\) 2.99377i 0.127539i
\(552\) −2.23557 2.23443i −0.0951522 0.0951037i
\(553\) 6.24475 0.265554
\(554\) 10.0692i 0.427798i
\(555\) 7.25648 + 7.25278i 0.308021 + 0.307863i
\(556\) 20.3092i 0.861304i
\(557\) 15.1992 0.644009 0.322005 0.946738i \(-0.395643\pi\)
0.322005 + 0.946738i \(0.395643\pi\)
\(558\) 0.00573064 + 11.2352i 0.000242597 + 0.475624i
\(559\) −24.0629 −1.01775
\(560\) −3.59703 −0.152002
\(561\) −22.2379 15.6571i −0.938884 0.661042i
\(562\) −21.4696 −0.905639
\(563\) 9.08289 0.382798 0.191399 0.981512i \(-0.438698\pi\)
0.191399 + 0.981512i \(0.438698\pi\)
\(564\) −30.4761 30.4606i −1.28328 1.28262i
\(565\) −2.79872 −0.117743
\(566\) 18.6172i 0.782541i
\(567\) −0.00918110 9.00000i −0.000385570 0.377964i
\(568\) 2.37544i 0.0996712i
\(569\) −22.4721 −0.942079 −0.471040 0.882112i \(-0.656121\pi\)
−0.471040 + 0.882112i \(0.656121\pi\)
\(570\) 1.59542 1.59624i 0.0668248 0.0668589i
\(571\) 31.0553i 1.29962i −0.760096 0.649811i \(-0.774848\pi\)
0.760096 0.649811i \(-0.225152\pi\)
\(572\) 16.9568 2.94026i 0.709001 0.122938i
\(573\) 2.85478 + 2.85332i 0.119260 + 0.119199i
\(574\) 13.5610i 0.566026i
\(575\) 4.83595i 0.201673i
\(576\) 0.0143859 + 28.2043i 0.000599413 + 1.17518i
\(577\) 30.2733 1.26030 0.630148 0.776475i \(-0.282994\pi\)
0.630148 + 0.776475i \(0.282994\pi\)
\(578\) −11.0751 −0.460665
\(579\) 7.33509 + 7.33135i 0.304836 + 0.304681i
\(580\) 10.2670i 0.426315i
\(581\) 2.16097i 0.0896521i
\(582\) −36.7889 + 36.8076i −1.52495 + 1.52573i
\(583\) −22.5022 + 3.90181i −0.931945 + 0.161596i
\(584\) 2.58843i 0.107110i
\(585\) −0.00363478 7.12616i −0.000150280 0.294631i
\(586\) 55.4595 2.29101
\(587\) 32.4208i 1.33815i −0.743195 0.669075i \(-0.766690\pi\)
0.743195 0.669075i \(-0.233310\pi\)
\(588\) 2.67474 2.67610i 0.110304 0.110361i
\(589\) 1.16616i 0.0480509i
\(590\) 4.02312 0.165629
\(591\) 18.9110 18.9206i 0.777893 0.778290i
\(592\) −21.3066 −0.875695
\(593\) 10.4749 0.430154 0.215077 0.976597i \(-0.431000\pi\)
0.215077 + 0.976597i \(0.431000\pi\)
\(594\) −20.2804 + 28.8356i −0.832114 + 1.18314i
\(595\) −4.73436 −0.194090
\(596\) −33.9184 −1.38935
\(597\) −25.4219 + 25.4348i −1.04045 + 1.04098i
\(598\) −23.4983 −0.960918
\(599\) 23.8437i 0.974225i 0.873339 + 0.487113i \(0.161950\pi\)
−0.873339 + 0.487113i \(0.838050\pi\)
\(600\) −0.462046 + 0.462281i −0.0188629 + 0.0188726i
\(601\) 42.7707i 1.74465i −0.488924 0.872327i \(-0.662610\pi\)
0.488924 0.872327i \(-0.337390\pi\)
\(602\) 20.7221 0.844568
\(603\) −0.000830559 1.62835i −3.38230e−5 0.0663116i
\(604\) 10.7398i 0.436995i
\(605\) 3.70338 + 10.3578i 0.150564 + 0.421106i
\(606\) −43.6994 + 43.7217i −1.77517 + 1.77607i
\(607\) 47.0364i 1.90915i −0.297971 0.954575i \(-0.596310\pi\)
0.297971 0.954575i \(-0.403690\pi\)
\(608\) 5.16761i 0.209574i
\(609\) −5.75778 5.75484i −0.233317 0.233198i
\(610\) 8.09211 0.327640
\(611\) −27.0515 −1.09439
\(612\) 0.0158253 + 31.0262i 0.000639698 + 1.25416i
\(613\) 13.1181i 0.529836i −0.964271 0.264918i \(-0.914655\pi\)
0.964271 0.264918i \(-0.0853448\pi\)
\(614\) 11.7800i 0.475401i
\(615\) −8.12135 8.11721i −0.327484 0.327317i
\(616\) −1.23314 + 0.213823i −0.0496848 + 0.00861518i
\(617\) 35.8827i 1.44458i −0.691588 0.722292i \(-0.743089\pi\)
0.691588 0.722292i \(-0.256911\pi\)
\(618\) −35.2492 + 35.2672i −1.41793 + 1.41866i
\(619\) −25.0255 −1.00586 −0.502931 0.864327i \(-0.667745\pi\)
−0.502931 + 0.864327i \(0.667745\pi\)
\(620\) 3.99931i 0.160616i
\(621\) 17.7548 17.7820i 0.712477 0.713568i
\(622\) 16.4869i 0.661063i
\(623\) −12.4798 −0.499993
\(624\) 10.4673 + 10.4620i 0.419027 + 0.418814i
\(625\) 1.00000 0.0400000
\(626\) 31.6422 1.26468
\(627\) −2.10654 + 2.99194i −0.0841271 + 0.119486i
\(628\) 13.9271 0.555752
\(629\) −28.0434 −1.11816
\(630\) 0.00313014 + 6.13679i 0.000124708 + 0.244496i
\(631\) −9.53055 −0.379405 −0.189703 0.981842i \(-0.560752\pi\)
−0.189703 + 0.981842i \(0.560752\pi\)
\(632\) 2.35649i 0.0937361i
\(633\) 21.0398 + 21.0291i 0.836258 + 0.835832i
\(634\) 3.64502i 0.144762i
\(635\) 13.1403 0.521457
\(636\) 18.4274 + 18.4180i 0.730694 + 0.730321i
\(637\) 2.37539i 0.0941163i
\(638\) 5.44783 + 31.4183i 0.215682 + 1.24386i
\(639\) 18.8849 0.00963246i 0.747076 0.000381054i
\(640\) 3.00600i 0.118822i
\(641\) 24.8099i 0.979933i −0.871741 0.489966i \(-0.837009\pi\)
0.871741 0.489966i \(-0.162991\pi\)
\(642\) −11.8662 + 11.8722i −0.468321 + 0.468560i
\(643\) −41.9082 −1.65270 −0.826348 0.563159i \(-0.809586\pi\)
−0.826348 + 0.563159i \(0.809586\pi\)
\(644\) 10.5640 0.416280
\(645\) −12.4036 + 12.4099i −0.488391 + 0.488640i
\(646\) 6.16881i 0.242709i
\(647\) 38.6385i 1.51904i −0.650487 0.759518i \(-0.725435\pi\)
0.650487 0.759518i \(-0.274565\pi\)
\(648\) 3.39619 0.00346453i 0.133415 0.000136100i
\(649\) −6.42698 + 1.11442i −0.252281 + 0.0437447i
\(650\) 4.85909i 0.190589i
\(651\) −2.24283 2.24168i −0.0879032 0.0878584i
\(652\) −37.1974 −1.45676
\(653\) 11.1028i 0.434487i 0.976117 + 0.217244i \(0.0697066\pi\)
−0.976117 + 0.217244i \(0.930293\pi\)
\(654\) 18.4502 + 18.4408i 0.721458 + 0.721090i
\(655\) 6.43379i 0.251389i
\(656\) 23.8460 0.931030
\(657\) 20.5782 0.0104961i 0.802832 0.000409493i
\(658\) 23.2958 0.908164
\(659\) −3.84987 −0.149970 −0.0749848 0.997185i \(-0.523891\pi\)
−0.0749848 + 0.997185i \(0.523891\pi\)
\(660\) 7.22430 10.2607i 0.281205 0.399399i
\(661\) −24.6238 −0.957756 −0.478878 0.877881i \(-0.658956\pi\)
−0.478878 + 0.877881i \(0.658956\pi\)
\(662\) −53.9559 −2.09705
\(663\) 13.7769 + 13.7699i 0.535051 + 0.534778i
\(664\) −0.815452 −0.0316457
\(665\) 0.636972i 0.0247007i
\(666\) 0.0185410 + 36.3506i 0.000718450 + 1.40856i
\(667\) 22.7290i 0.880071i
\(668\) 38.3040 1.48203
\(669\) −5.42851 + 5.43128i −0.209878 + 0.209985i
\(670\) 1.11032i 0.0428953i
\(671\) −12.9272 + 2.24154i −0.499050 + 0.0865336i
\(672\) −9.93862 9.93355i −0.383391 0.383195i
\(673\) 14.6708i 0.565517i −0.959191 0.282759i \(-0.908750\pi\)
0.959191 0.282759i \(-0.0912496\pi\)
\(674\) 53.3385i 2.05452i
\(675\) −3.67704 3.67142i −0.141530 0.141313i
\(676\) 16.0723 0.618166
\(677\) 46.1925 1.77532 0.887661 0.460498i \(-0.152329\pi\)
0.887661 + 0.460498i \(0.152329\pi\)
\(678\) −7.01351 7.00993i −0.269352 0.269215i
\(679\) 14.6880i 0.563672i
\(680\) 1.78653i 0.0685104i
\(681\) 7.63191 7.63581i 0.292455 0.292605i
\(682\) 2.12209 + 12.2384i 0.0812591 + 0.468631i
\(683\) 19.9481i 0.763291i 0.924309 + 0.381645i \(0.124642\pi\)
−0.924309 + 0.381645i \(0.875358\pi\)
\(684\) 4.17434 0.00212917i 0.159610 8.14108e-5i
\(685\) 16.6169 0.634901
\(686\) 2.04560i 0.0781013i
\(687\) −1.11359 + 1.11416i −0.0424860 + 0.0425077i
\(688\) 36.4382i 1.38919i
\(689\) 16.3567 0.623140
\(690\) −12.1126 + 12.1188i −0.461119 + 0.461354i
\(691\) 30.0622 1.14362 0.571810 0.820386i \(-0.306242\pi\)
0.571810 + 0.820386i \(0.306242\pi\)
\(692\) −47.4438 −1.80354
\(693\) −1.70491 9.80272i −0.0647642 0.372374i
\(694\) 66.6799 2.53114
\(695\) 9.29709 0.352659
\(696\) 2.17162 2.17272i 0.0823149 0.0823569i
\(697\) 31.3858 1.18882
\(698\) 48.2953i 1.82801i
\(699\) 33.9041 33.9214i 1.28237 1.28303i
\(700\) 2.18447i 0.0825653i
\(701\) 27.0757 1.02264 0.511318 0.859392i \(-0.329157\pi\)
0.511318 + 0.859392i \(0.329157\pi\)
\(702\) 17.8398 17.8671i 0.673319 0.674350i
\(703\) 3.77303i 0.142302i
\(704\) 5.32720 + 30.7226i 0.200776 + 1.15790i
\(705\) −13.9441 + 13.9513i −0.525167 + 0.525435i
\(706\) 3.16221i 0.119011i
\(707\) 17.4470i 0.656161i
\(708\) 5.26315 + 5.26047i 0.197801 + 0.197700i
\(709\) −7.84277 −0.294541 −0.147271 0.989096i \(-0.547049\pi\)
−0.147271 + 0.989096i \(0.547049\pi\)
\(710\) −12.8770 −0.483265
\(711\) −18.7343 + 0.00955562i −0.702590 + 0.000358364i
\(712\) 4.70932i 0.176489i
\(713\) 8.85362i 0.331571i
\(714\) −11.8642 11.8581i −0.444006 0.443779i
\(715\) −1.34598 7.76244i −0.0503369 0.290299i
\(716\) 49.0919i 1.83465i
\(717\) −28.9293 + 28.9441i −1.08039 + 1.08094i
\(718\) 60.2642 2.24904
\(719\) 9.42161i 0.351367i 0.984447 + 0.175683i \(0.0562135\pi\)
−0.984447 + 0.175683i \(0.943787\pi\)
\(720\) 10.7911 0.00550411i 0.402160 0.000205126i
\(721\) 14.0733i 0.524116i
\(722\) −38.0364 −1.41557
\(723\) 14.0327 + 14.0256i 0.521882 + 0.521616i
\(724\) −4.47729 −0.166397
\(725\) −4.70001 −0.174554
\(726\) −16.6627 + 35.2323i −0.618410 + 1.30759i
\(727\) 4.00681 0.148604 0.0743022 0.997236i \(-0.476327\pi\)
0.0743022 + 0.997236i \(0.476327\pi\)
\(728\) 0.896364 0.0332215
\(729\) 0.0413149 + 27.0000i 0.00153018 + 0.999999i
\(730\) −14.0316 −0.519332
\(731\) 47.9594i 1.77384i
\(732\) 10.5863 + 10.5809i 0.391281 + 0.391081i
\(733\) 38.1353i 1.40856i 0.709923 + 0.704279i \(0.248730\pi\)
−0.709923 + 0.704279i \(0.751270\pi\)
\(734\) −34.5356 −1.27473
\(735\) −1.22506 1.22443i −0.0451869 0.0451639i
\(736\) 39.2330i 1.44615i
\(737\) −0.307561 1.77374i −0.0113292 0.0653366i
\(738\) −0.0207508 40.6830i −0.000763849 1.49756i
\(739\) 31.1709i 1.14664i 0.819332 + 0.573319i \(0.194345\pi\)
−0.819332 + 0.573319i \(0.805655\pi\)
\(740\) 12.9395i 0.475664i
\(741\) 1.85263 1.85358i 0.0680582 0.0680929i
\(742\) −14.0858 −0.517106
\(743\) 40.4561 1.48419 0.742095 0.670294i \(-0.233832\pi\)
0.742095 + 0.670294i \(0.233832\pi\)
\(744\) 0.845909 0.846341i 0.0310125 0.0310284i
\(745\) 15.5271i 0.568868i
\(746\) 16.1239i 0.590339i
\(747\) −0.00330668 6.48291i −0.000120985 0.237197i
\(748\) 5.86019 + 33.7965i 0.214270 + 1.23572i
\(749\) 4.73757i 0.173107i
\(750\) 2.50597 + 2.50470i 0.0915053 + 0.0914586i
\(751\) 38.5721 1.40752 0.703758 0.710440i \(-0.251504\pi\)
0.703758 + 0.710440i \(0.251504\pi\)
\(752\) 40.9639i 1.49380i
\(753\) −27.6500 27.6359i −1.00762 1.00711i
\(754\) 22.8377i 0.831702i
\(755\) −4.91642 −0.178927
\(756\) −8.02012 + 8.03240i −0.291689 + 0.292136i
\(757\) −35.8603 −1.30337 −0.651683 0.758491i \(-0.725937\pi\)
−0.651683 + 0.758491i \(0.725937\pi\)
\(758\) 8.88968 0.322888
\(759\) 15.9930 22.7151i 0.580511 0.824505i
\(760\) −0.240364 −0.00871893
\(761\) 12.7730 0.463021 0.231510 0.972832i \(-0.425633\pi\)
0.231510 + 0.972832i \(0.425633\pi\)
\(762\) 32.9293 + 32.9125i 1.19290 + 1.19229i
\(763\) −7.36247 −0.266539
\(764\) 5.09052i 0.184168i
\(765\) 14.2031 0.00724443i 0.513513 0.000261923i
\(766\) 41.2635i 1.49091i
\(767\) 4.67173 0.168686
\(768\) −15.4937 + 15.5016i −0.559082 + 0.559367i
\(769\) 1.97553i 0.0712395i 0.999365 + 0.0356197i \(0.0113405\pi\)
−0.999365 + 0.0356197i \(0.988659\pi\)
\(770\) 1.15911 + 6.68473i 0.0417714 + 0.240901i
\(771\) 4.22524 + 4.22308i 0.152168 + 0.152091i
\(772\) 13.0796i 0.470747i
\(773\) 25.8041i 0.928108i 0.885807 + 0.464054i \(0.153606\pi\)
−0.885807 + 0.464054i \(0.846394\pi\)
\(774\) −62.1662 + 0.0317086i −2.23452 + 0.00113974i
\(775\) −1.83079 −0.0657640
\(776\) 5.54257 0.198967
\(777\) −7.25648 7.25278i −0.260325 0.260192i
\(778\) 40.9356i 1.46761i
\(779\) 4.22272i 0.151295i
\(780\) −6.35354 + 6.35678i −0.227493 + 0.227609i
\(781\) 20.5711 3.56696i 0.736092 0.127636i
\(782\) 46.8342i 1.67479i
\(783\) 17.2821 + 17.2557i 0.617613 + 0.616669i
\(784\) 3.59703 0.128465
\(785\) 6.37551i 0.227552i
\(786\) 16.1147 16.1229i 0.574792 0.575085i
\(787\) 15.7483i 0.561367i 0.959800 + 0.280683i \(0.0905611\pi\)
−0.959800 + 0.280683i \(0.909439\pi\)
\(788\) −33.7385 −1.20188
\(789\) −25.9259 + 25.9391i −0.922986 + 0.923457i
\(790\) 12.7743 0.454488
\(791\) 2.79872 0.0995109
\(792\) 3.69910 0.643356i 0.131442 0.0228607i
\(793\) 9.39671 0.333687
\(794\) 12.1386 0.430783
\(795\) 8.43133 8.43563i 0.299028 0.299181i
\(796\) 45.3544 1.60754
\(797\) 30.7765i 1.09016i −0.838384 0.545080i \(-0.816499\pi\)
0.838384 0.545080i \(-0.183501\pi\)
\(798\) −1.59542 + 1.59624i −0.0564773 + 0.0565061i
\(799\) 53.9161i 1.90741i
\(800\) −8.11278 −0.286830
\(801\) 37.4394 0.0190964i 1.32286 0.000674738i
\(802\) 13.8167i 0.487886i
\(803\) 22.4156 3.88679i 0.791029 0.137162i
\(804\) −1.45180 + 1.45255i −0.0512012 + 0.0512273i
\(805\) 4.83595i 0.170445i
\(806\) 8.89598i 0.313348i
\(807\) −29.5174 29.5024i −1.03906 1.03853i
\(808\) 6.58370 0.231614
\(809\) −19.3715 −0.681064 −0.340532 0.940233i \(-0.610607\pi\)
−0.340532 + 0.940233i \(0.610607\pi\)
\(810\) −0.0187808 18.4104i −0.000659891 0.646875i
\(811\) 32.0378i 1.12500i −0.826797 0.562500i \(-0.809840\pi\)
0.826797 0.562500i \(-0.190160\pi\)
\(812\) 10.2670i 0.360302i
\(813\) 3.61615 + 3.61431i 0.126824 + 0.126759i
\(814\) 6.86586 + 39.5962i 0.240648 + 1.38785i
\(815\) 17.0281i 0.596468i
\(816\) −20.8516 + 20.8622i −0.729952 + 0.730325i
\(817\) −6.45257 −0.225747
\(818\) 33.0136i 1.15429i
\(819\) 0.00363478 + 7.12616i 0.000127009 + 0.249008i
\(820\) 14.4817i 0.505721i
\(821\) −46.7599 −1.63193 −0.815966 0.578100i \(-0.803794\pi\)
−0.815966 + 0.578100i \(0.803794\pi\)
\(822\) 41.6416 + 41.6204i 1.45242 + 1.45168i
\(823\) −28.2494 −0.984712 −0.492356 0.870394i \(-0.663864\pi\)
−0.492356 + 0.870394i \(0.663864\pi\)
\(824\) 5.31061 0.185004
\(825\) −4.69713 3.30711i −0.163533 0.115139i
\(826\) −4.02312 −0.139982
\(827\) −23.6293 −0.821670 −0.410835 0.911710i \(-0.634763\pi\)
−0.410835 + 0.911710i \(0.634763\pi\)
\(828\) −31.6920 + 0.0161649i −1.10137 + 0.000561768i
\(829\) 12.1268 0.421180 0.210590 0.977575i \(-0.432462\pi\)
0.210590 + 0.977575i \(0.432462\pi\)
\(830\) 4.42047i 0.153437i
\(831\) −6.03017 6.02710i −0.209184 0.209078i
\(832\) 22.3321i 0.774225i
\(833\) 4.73436 0.164036
\(834\) 23.2983 + 23.2864i 0.806754 + 0.806342i
\(835\) 17.5347i 0.606812i
\(836\) 4.54706 0.788445i 0.157263 0.0272689i
\(837\) 6.73190 + 6.72161i 0.232689 + 0.232333i
\(838\) 52.5576i 1.81557i
\(839\) 2.31556i 0.0799422i 0.999201 + 0.0399711i \(0.0127266\pi\)
−0.999201 + 0.0399711i \(0.987273\pi\)
\(840\) 0.462046 0.462281i 0.0159421 0.0159502i
\(841\) −6.90994 −0.238274
\(842\) −38.8502 −1.33887
\(843\) −12.8510 + 12.8576i −0.442613 + 0.442839i
\(844\) 37.5174i 1.29140i
\(845\) 7.35753i 0.253107i
\(846\) −69.8874 + 0.0356468i −2.40278 + 0.00122556i
\(847\) −3.70338 10.3578i −0.127250 0.355900i
\(848\) 24.7688i 0.850564i
\(849\) 11.1494 + 11.1437i 0.382646 + 0.382451i
\(850\) −9.68459 −0.332179
\(851\) 28.6452i 0.981945i
\(852\) −16.8460 16.8374i −0.577134 0.576840i
\(853\) 47.5073i 1.62662i 0.581831 + 0.813310i \(0.302336\pi\)
−0.581831 + 0.813310i \(0.697664\pi\)
\(854\) −8.09211 −0.276906
\(855\) −0.000974684 1.91092i −3.33335e−5 0.0653519i
\(856\) 1.78775 0.0611039
\(857\) 5.15358 0.176043 0.0880215 0.996119i \(-0.471946\pi\)
0.0880215 + 0.996119i \(0.471946\pi\)
\(858\) 16.0696 22.8238i 0.548606 0.779190i
\(859\) 22.6256 0.771974 0.385987 0.922504i \(-0.373861\pi\)
0.385987 + 0.922504i \(0.373861\pi\)
\(860\) 22.1289 0.754588
\(861\) 8.12135 + 8.11721i 0.276775 + 0.276634i
\(862\) 44.2279 1.50641
\(863\) 11.7358i 0.399490i 0.979848 + 0.199745i \(0.0640114\pi\)
−0.979848 + 0.199745i \(0.935989\pi\)
\(864\) 29.8311 + 29.7854i 1.01487 + 1.01332i
\(865\) 21.7187i 0.738457i
\(866\) −20.8877 −0.709792
\(867\) −6.62924 + 6.63262i −0.225141 + 0.225256i
\(868\) 3.99931i 0.135746i
\(869\) −20.4070 + 3.53851i −0.692260 + 0.120036i
\(870\) −11.7781 11.7721i −0.399315 0.399111i
\(871\) 1.28932i 0.0436870i
\(872\) 2.77826i 0.0940839i
\(873\) 0.0224753 + 44.0639i 0.000760672 + 1.49134i
\(874\) −6.30119 −0.213141
\(875\) −1.00000 −0.0338062
\(876\) −18.3565 18.3471i −0.620207 0.619891i
\(877\) 34.3823i 1.16101i −0.814258 0.580503i \(-0.802856\pi\)
0.814258 0.580503i \(-0.197144\pi\)
\(878\) 37.8255i 1.27655i
\(879\) 33.1964 33.2133i 1.11969 1.12026i
\(880\) 11.7546 2.03821i 0.396247 0.0687079i
\(881\) 45.6864i 1.53921i 0.638519 + 0.769606i \(0.279548\pi\)
−0.638519 + 0.769606i \(0.720452\pi\)
\(882\) −0.00313014 6.13679i −0.000105397 0.206637i
\(883\) 32.6587 1.09905 0.549527 0.835476i \(-0.314808\pi\)
0.549527 + 0.835476i \(0.314808\pi\)
\(884\) 24.5664i 0.826258i
\(885\) 2.40812 2.40935i 0.0809480 0.0809893i
\(886\) 17.6184i 0.591901i
\(887\) 10.1516 0.340857 0.170429 0.985370i \(-0.445485\pi\)
0.170429 + 0.985370i \(0.445485\pi\)
\(888\) 2.73687 2.73827i 0.0918434 0.0918903i
\(889\) −13.1403 −0.440712
\(890\) −25.5287 −0.855723
\(891\) 5.12973 + 29.4055i 0.171852 + 0.985123i
\(892\) 9.68483 0.324272
\(893\) −7.25400 −0.242746
\(894\) −38.8906 + 38.9104i −1.30070 + 1.30136i
\(895\) 22.4731 0.751193
\(896\) 3.00600i 0.100423i
\(897\) −14.0654 + 14.0726i −0.469629 + 0.469869i
\(898\) 34.1353i 1.13911i
\(899\) 8.60473 0.286984
\(900\) 0.00334264 + 6.55341i 0.000111421 + 0.218447i
\(901\) 32.6003i 1.08607i
\(902\) −7.68417 44.3155i −0.255855 1.47555i
\(903\) 12.4036 12.4099i 0.412766 0.412976i
\(904\) 1.05611i 0.0351257i
\(905\) 2.04960i 0.0681310i
\(906\) −12.3204 12.3141i −0.409319 0.409110i
\(907\) −24.3139 −0.807329 −0.403664 0.914907i \(-0.632264\pi\)
−0.403664 + 0.914907i \(0.632264\pi\)
\(908\) −13.6159 −0.451858
\(909\) 0.0266971 + 52.3409i 0.000885485 + 1.73604i
\(910\) 4.85909i 0.161077i
\(911\) 36.9280i 1.22348i −0.791059 0.611740i \(-0.790470\pi\)
0.791059 0.611740i \(-0.209530\pi\)
\(912\) 2.80686 + 2.80543i 0.0929443 + 0.0928969i
\(913\) −1.22448 7.06175i −0.0405245 0.233710i
\(914\) 49.5498i 1.63896i
\(915\) 4.84369 4.84616i 0.160127 0.160209i
\(916\) 1.98672 0.0656430
\(917\) 6.43379i 0.212462i
\(918\) 35.6107 + 35.5562i 1.17533 + 1.17353i
\(919\) 36.7202i 1.21129i 0.795736 + 0.605644i \(0.207084\pi\)
−0.795736 + 0.605644i \(0.792916\pi\)
\(920\) 1.82487 0.0601642
\(921\) −7.05473 7.05113i −0.232461 0.232343i
\(922\) 48.2196 1.58803
\(923\) −14.9530 −0.492184
\(924\) −7.22430 + 10.2607i −0.237662 + 0.337554i
\(925\) −5.92338 −0.194760
\(926\) 13.0130 0.427634
\(927\) 0.0215347 + 42.2198i 0.000707291 + 1.38668i
\(928\) 38.1301 1.25168
\(929\) 20.9898i 0.688653i 0.938850 + 0.344326i \(0.111893\pi\)
−0.938850 + 0.344326i \(0.888107\pi\)
\(930\) −4.58792 4.58558i −0.150444 0.150367i
\(931\) 0.636972i 0.0208759i
\(932\) −60.4873 −1.98133
\(933\) 9.87356 + 9.86853i 0.323246 + 0.323081i
\(934\) 78.8474i 2.57996i
\(935\) 15.4712 2.68266i 0.505963 0.0877323i
\(936\) −2.68909 + 0.00137160i −0.0878957 + 4.48322e-5i
\(937\) 34.8033i 1.13697i −0.822692 0.568487i \(-0.807529\pi\)
0.822692 0.568487i \(-0.192471\pi\)
\(938\) 1.11032i 0.0362532i
\(939\) 18.9400 18.9497i 0.618085 0.618400i
\(940\) 24.8773 0.811409
\(941\) 58.5246 1.90785 0.953924 0.300049i \(-0.0970030\pi\)
0.953924 + 0.300049i \(0.0970030\pi\)
\(942\) 15.9687 15.9769i 0.520289 0.520554i
\(943\) 32.0593i 1.04399i
\(944\) 7.07435i 0.230251i
\(945\) 3.67704 + 3.67142i 0.119614 + 0.119431i
\(946\) −67.7169 + 11.7419i −2.20166 + 0.381761i
\(947\) 36.3434i 1.18100i −0.807037 0.590500i \(-0.798930\pi\)
0.807037 0.590500i \(-0.201070\pi\)
\(948\) 16.7116 + 16.7031i 0.542768 + 0.542491i
\(949\) −16.2937 −0.528917
\(950\) 1.30299i 0.0422745i
\(951\) −2.18291 2.18180i −0.0707858 0.0707497i
\(952\) 1.78653i 0.0579019i
\(953\) 33.0869 1.07179 0.535896 0.844284i \(-0.319974\pi\)
0.535896 + 0.844284i \(0.319974\pi\)
\(954\) 42.2574 0.0215538i 1.36813 0.000697832i
\(955\) −2.33032 −0.0754074
\(956\) 51.6119 1.66925
\(957\) 22.0765 + 15.5435i 0.713633 + 0.502449i
\(958\) −50.9081 −1.64477
\(959\) −16.6169 −0.536589
\(960\) −11.5173 11.5114i −0.371719 0.371530i
\(961\) −27.6482 −0.891877
\(962\) 28.7822i 0.927977i
\(963\) 0.00724935 + 14.2127i 0.000233607 + 0.457998i
\(964\) 25.0226i 0.805922i
\(965\) −5.98755 −0.192746
\(966\) 12.1126 12.1188i 0.389716 0.389915i
\(967\) 13.2363i 0.425652i −0.977090 0.212826i \(-0.931733\pi\)
0.977090 0.212826i \(-0.0682667\pi\)
\(968\) 3.90858 1.39749i 0.125627 0.0449170i
\(969\) 3.69435 + 3.69246i 0.118679 + 0.118619i
\(970\) 30.0456i 0.964708i
\(971\) 37.3725i 1.19934i 0.800248 + 0.599670i \(0.204701\pi\)
−0.800248 + 0.599670i \(0.795299\pi\)
\(972\) 24.0481 24.1095i 0.771342 0.773312i
\(973\) −9.29709 −0.298051
\(974\) 25.7544 0.825223
\(975\) 2.90999 + 2.90850i 0.0931941 + 0.0931466i
\(976\) 14.2294i 0.455470i
\(977\) 7.28663i 0.233120i −0.993184 0.116560i \(-0.962813\pi\)
0.993184 0.116560i \(-0.0371867\pi\)
\(978\) −42.6502 + 42.6720i −1.36380 + 1.36450i
\(979\) 40.7823 7.07152i 1.30341 0.226007i
\(980\) 2.18447i 0.0697804i
\(981\) 22.0874 0.0112659i 0.705196 0.000359693i
\(982\) −37.5698 −1.19890
\(983\) 3.98229i 0.127015i −0.997981 0.0635076i \(-0.979771\pi\)
0.997981 0.0635076i \(-0.0202287\pi\)
\(984\) −3.06307 + 3.06463i −0.0976470 + 0.0976969i
\(985\) 15.4447i 0.492109i
\(986\) 45.5176 1.44958
\(987\) 13.9441 13.9513i 0.443847 0.444074i
\(988\) −3.30523 −0.105153
\(989\) 48.9886 1.55775
\(990\) −3.48756 20.0524i −0.110842 0.637308i
\(991\) −58.1994 −1.84877 −0.924383 0.381466i \(-0.875419\pi\)
−0.924383 + 0.381466i \(0.875419\pi\)
\(992\) 14.8528 0.471577
\(993\) −32.2963 + 32.3128i −1.02489 + 1.02542i
\(994\) 12.8770 0.408433
\(995\) 20.7622i 0.658205i
\(996\) −5.78003 + 5.78297i −0.183147 + 0.183241i
\(997\) 30.0188i 0.950705i −0.879796 0.475352i \(-0.842321\pi\)
0.879796 0.475352i \(-0.157679\pi\)
\(998\) −23.3192 −0.738156
\(999\) 21.7805 + 21.7472i 0.689106 + 0.688052i
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 1155.2.l.e.1121.8 yes 40
3.2 odd 2 1155.2.l.f.1121.33 yes 40
11.10 odd 2 1155.2.l.f.1121.34 yes 40
33.32 even 2 inner 1155.2.l.e.1121.7 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.l.e.1121.7 40 33.32 even 2 inner
1155.2.l.e.1121.8 yes 40 1.1 even 1 trivial
1155.2.l.f.1121.33 yes 40 3.2 odd 2
1155.2.l.f.1121.34 yes 40 11.10 odd 2