Properties

Label 690.2.j.b.367.8
Level $690$
Weight $2$
Character 690.367
Analytic conductor $5.510$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [690,2,Mod(367,690)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(690, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("690.367");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.j (of order \(4\), 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: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 367.8
Character \(\chi\) \(=\) 690.367
Dual form 690.2.j.b.643.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-1.52094 - 1.63913i) q^{5} +1.00000 q^{6} +(2.68754 - 2.68754i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-1.52094 - 1.63913i) q^{5} +1.00000 q^{6} +(2.68754 - 2.68754i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(0.0835670 - 2.23451i) q^{10} -0.403497i q^{11} +(0.707107 + 0.707107i) q^{12} +(-2.12629 + 2.12629i) q^{13} +3.80076 q^{14} +(-2.23451 - 0.0835670i) q^{15} -1.00000 q^{16} +(4.95666 - 4.95666i) q^{17} +(0.707107 - 0.707107i) q^{18} -5.20795 q^{19} +(1.63913 - 1.52094i) q^{20} -3.80076i q^{21} +(0.285316 - 0.285316i) q^{22} +(2.47384 - 4.10854i) q^{23} +1.00000i q^{24} +(-0.373462 + 4.98603i) q^{25} -3.00703 q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.68754 + 2.68754i) q^{28} -9.42076i q^{29} +(-1.52094 - 1.63913i) q^{30} +3.33683 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.285316 - 0.285316i) q^{33} +7.00978 q^{34} +(-8.49282 - 0.317618i) q^{35} +1.00000 q^{36} +(-2.17130 + 2.17130i) q^{37} +(-3.68258 - 3.68258i) q^{38} +3.00703i q^{39} +(2.23451 + 0.0835670i) q^{40} +5.69885 q^{41} +(2.68754 - 2.68754i) q^{42} +(2.56936 + 2.56936i) q^{43} +0.403497 q^{44} +(-1.63913 + 1.52094i) q^{45} +(4.65445 - 1.15590i) q^{46} +(8.64413 + 8.64413i) q^{47} +(-0.707107 + 0.707107i) q^{48} -7.44578i q^{49} +(-3.78974 + 3.26158i) q^{50} -7.00978i q^{51} +(-2.12629 - 2.12629i) q^{52} +(1.47608 + 1.47608i) q^{53} -1.00000i q^{54} +(-0.661382 + 0.613696i) q^{55} +3.80076i q^{56} +(-3.68258 + 3.68258i) q^{57} +(6.66148 - 6.66148i) q^{58} +13.4003i q^{59} +(0.0835670 - 2.23451i) q^{60} +7.51118i q^{61} +(2.35950 + 2.35950i) q^{62} +(-2.68754 - 2.68754i) q^{63} -1.00000i q^{64} +(6.71923 + 0.251289i) q^{65} -0.403497i q^{66} +(-4.60755 + 4.60755i) q^{67} +(4.95666 + 4.95666i) q^{68} +(-1.15590 - 4.65445i) q^{69} +(-5.78074 - 6.22992i) q^{70} -5.45281 q^{71} +(0.707107 + 0.707107i) q^{72} +(1.06175 - 1.06175i) q^{73} -3.07068 q^{74} +(3.26158 + 3.78974i) q^{75} -5.20795i q^{76} +(-1.08442 - 1.08442i) q^{77} +(-2.12629 + 2.12629i) q^{78} -0.383565 q^{79} +(1.52094 + 1.63913i) q^{80} -1.00000 q^{81} +(4.02970 + 4.02970i) q^{82} +(-12.3708 - 12.3708i) q^{83} +3.80076 q^{84} +(-15.6634 - 0.585786i) q^{85} +3.63363i q^{86} +(-6.66148 - 6.66148i) q^{87} +(0.285316 + 0.285316i) q^{88} -6.23158 q^{89} +(-2.23451 - 0.0835670i) q^{90} +11.4290i q^{91} +(4.10854 + 2.47384i) q^{92} +(2.35950 - 2.35950i) q^{93} +12.2247i q^{94} +(7.92100 + 8.53649i) q^{95} -1.00000 q^{96} +(-8.25631 + 8.25631i) q^{97} +(5.26496 - 5.26496i) q^{98} -0.403497 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 24 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 24 q^{6} + 16 q^{13} - 24 q^{16} + 16 q^{23} - 16 q^{25} + 16 q^{31} + 24 q^{36} + 8 q^{46} + 40 q^{47} - 8 q^{50} + 16 q^{52} - 56 q^{55} - 16 q^{58} - 8 q^{62} + 32 q^{70} + 64 q^{71} - 16 q^{73} + 32 q^{75} + 16 q^{77} + 16 q^{78} - 24 q^{81} + 24 q^{82} - 48 q^{85} + 16 q^{87} + 16 q^{92} - 8 q^{93} + 24 q^{95} - 24 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) −1.52094 1.63913i −0.680187 0.733039i
\(6\) 1.00000 0.408248
\(7\) 2.68754 2.68754i 1.01580 1.01580i 0.0159226 0.999873i \(-0.494931\pi\)
0.999873 0.0159226i \(-0.00506854\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 0.0835670 2.23451i 0.0264262 0.706613i
\(11\) 0.403497i 0.121659i −0.998148 0.0608295i \(-0.980625\pi\)
0.998148 0.0608295i \(-0.0193746\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) −2.12629 + 2.12629i −0.589728 + 0.589728i −0.937558 0.347830i \(-0.886919\pi\)
0.347830 + 0.937558i \(0.386919\pi\)
\(14\) 3.80076 1.01580
\(15\) −2.23451 0.0835670i −0.576947 0.0215769i
\(16\) −1.00000 −0.250000
\(17\) 4.95666 4.95666i 1.20217 1.20217i 0.228662 0.973506i \(-0.426565\pi\)
0.973506 0.228662i \(-0.0734349\pi\)
\(18\) 0.707107 0.707107i 0.166667 0.166667i
\(19\) −5.20795 −1.19479 −0.597393 0.801949i \(-0.703797\pi\)
−0.597393 + 0.801949i \(0.703797\pi\)
\(20\) 1.63913 1.52094i 0.366520 0.340093i
\(21\) 3.80076i 0.829394i
\(22\) 0.285316 0.285316i 0.0608295 0.0608295i
\(23\) 2.47384 4.10854i 0.515832 0.856690i
\(24\) 1.00000i 0.204124i
\(25\) −0.373462 + 4.98603i −0.0746924 + 0.997207i
\(26\) −3.00703 −0.589728
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 2.68754 + 2.68754i 0.507898 + 0.507898i
\(29\) 9.42076i 1.74939i −0.484673 0.874695i \(-0.661061\pi\)
0.484673 0.874695i \(-0.338939\pi\)
\(30\) −1.52094 1.63913i −0.277685 0.299262i
\(31\) 3.33683 0.599312 0.299656 0.954047i \(-0.403128\pi\)
0.299656 + 0.954047i \(0.403128\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −0.285316 0.285316i −0.0496671 0.0496671i
\(34\) 7.00978 1.20217
\(35\) −8.49282 0.317618i −1.43555 0.0536873i
\(36\) 1.00000 0.166667
\(37\) −2.17130 + 2.17130i −0.356959 + 0.356959i −0.862691 0.505732i \(-0.831223\pi\)
0.505732 + 0.862691i \(0.331223\pi\)
\(38\) −3.68258 3.68258i −0.597393 0.597393i
\(39\) 3.00703i 0.481511i
\(40\) 2.23451 + 0.0835670i 0.353306 + 0.0132131i
\(41\) 5.69885 0.890011 0.445006 0.895528i \(-0.353202\pi\)
0.445006 + 0.895528i \(0.353202\pi\)
\(42\) 2.68754 2.68754i 0.414697 0.414697i
\(43\) 2.56936 + 2.56936i 0.391824 + 0.391824i 0.875337 0.483513i \(-0.160639\pi\)
−0.483513 + 0.875337i \(0.660639\pi\)
\(44\) 0.403497 0.0608295
\(45\) −1.63913 + 1.52094i −0.244346 + 0.226729i
\(46\) 4.65445 1.15590i 0.686261 0.170429i
\(47\) 8.64413 + 8.64413i 1.26088 + 1.26088i 0.950669 + 0.310208i \(0.100399\pi\)
0.310208 + 0.950669i \(0.399601\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 7.44578i 1.06368i
\(50\) −3.78974 + 3.26158i −0.535950 + 0.461257i
\(51\) 7.00978i 0.981566i
\(52\) −2.12629 2.12629i −0.294864 0.294864i
\(53\) 1.47608 + 1.47608i 0.202755 + 0.202755i 0.801179 0.598424i \(-0.204206\pi\)
−0.598424 + 0.801179i \(0.704206\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −0.661382 + 0.613696i −0.0891808 + 0.0827508i
\(56\) 3.80076i 0.507898i
\(57\) −3.68258 + 3.68258i −0.487769 + 0.487769i
\(58\) 6.66148 6.66148i 0.874695 0.874695i
\(59\) 13.4003i 1.74458i 0.488992 + 0.872288i \(0.337365\pi\)
−0.488992 + 0.872288i \(0.662635\pi\)
\(60\) 0.0835670 2.23451i 0.0107885 0.288473i
\(61\) 7.51118i 0.961708i 0.876801 + 0.480854i \(0.159673\pi\)
−0.876801 + 0.480854i \(0.840327\pi\)
\(62\) 2.35950 + 2.35950i 0.299656 + 0.299656i
\(63\) −2.68754 2.68754i −0.338599 0.338599i
\(64\) 1.00000i 0.125000i
\(65\) 6.71923 + 0.251289i 0.833418 + 0.0311685i
\(66\) 0.403497i 0.0496671i
\(67\) −4.60755 + 4.60755i −0.562902 + 0.562902i −0.930131 0.367229i \(-0.880307\pi\)
0.367229 + 0.930131i \(0.380307\pi\)
\(68\) 4.95666 + 4.95666i 0.601084 + 0.601084i
\(69\) −1.15590 4.65445i −0.139154 0.560330i
\(70\) −5.78074 6.22992i −0.690931 0.744618i
\(71\) −5.45281 −0.647129 −0.323565 0.946206i \(-0.604881\pi\)
−0.323565 + 0.946206i \(0.604881\pi\)
\(72\) 0.707107 + 0.707107i 0.0833333 + 0.0833333i
\(73\) 1.06175 1.06175i 0.124269 0.124269i −0.642237 0.766506i \(-0.721994\pi\)
0.766506 + 0.642237i \(0.221994\pi\)
\(74\) −3.07068 −0.356959
\(75\) 3.26158 + 3.78974i 0.376615 + 0.437601i
\(76\) 5.20795i 0.597393i
\(77\) −1.08442 1.08442i −0.123581 0.123581i
\(78\) −2.12629 + 2.12629i −0.240755 + 0.240755i
\(79\) −0.383565 −0.0431544 −0.0215772 0.999767i \(-0.506869\pi\)
−0.0215772 + 0.999767i \(0.506869\pi\)
\(80\) 1.52094 + 1.63913i 0.170047 + 0.183260i
\(81\) −1.00000 −0.111111
\(82\) 4.02970 + 4.02970i 0.445006 + 0.445006i
\(83\) −12.3708 12.3708i −1.35787 1.35787i −0.876540 0.481328i \(-0.840154\pi\)
−0.481328 0.876540i \(-0.659846\pi\)
\(84\) 3.80076 0.414697
\(85\) −15.6634 0.585786i −1.69893 0.0635375i
\(86\) 3.63363i 0.391824i
\(87\) −6.66148 6.66148i −0.714186 0.714186i
\(88\) 0.285316 + 0.285316i 0.0304147 + 0.0304147i
\(89\) −6.23158 −0.660546 −0.330273 0.943885i \(-0.607141\pi\)
−0.330273 + 0.943885i \(0.607141\pi\)
\(90\) −2.23451 0.0835670i −0.235538 0.00880874i
\(91\) 11.4290i 1.19809i
\(92\) 4.10854 + 2.47384i 0.428345 + 0.257916i
\(93\) 2.35950 2.35950i 0.244668 0.244668i
\(94\) 12.2247i 1.26088i
\(95\) 7.92100 + 8.53649i 0.812678 + 0.875825i
\(96\) −1.00000 −0.102062
\(97\) −8.25631 + 8.25631i −0.838301 + 0.838301i −0.988635 0.150334i \(-0.951965\pi\)
0.150334 + 0.988635i \(0.451965\pi\)
\(98\) 5.26496 5.26496i 0.531841 0.531841i
\(99\) −0.403497 −0.0405530
\(100\) −4.98603 0.373462i −0.498603 0.0373462i
\(101\) −7.08442 −0.704926 −0.352463 0.935826i \(-0.614656\pi\)
−0.352463 + 0.935826i \(0.614656\pi\)
\(102\) 4.95666 4.95666i 0.490783 0.490783i
\(103\) 6.87041 + 6.87041i 0.676961 + 0.676961i 0.959311 0.282350i \(-0.0911140\pi\)
−0.282350 + 0.959311i \(0.591114\pi\)
\(104\) 3.00703i 0.294864i
\(105\) −6.22992 + 5.78074i −0.607978 + 0.564143i
\(106\) 2.08749i 0.202755i
\(107\) 3.14660 3.14660i 0.304194 0.304194i −0.538458 0.842652i \(-0.680993\pi\)
0.842652 + 0.538458i \(0.180993\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) 12.6901 1.21549 0.607744 0.794133i \(-0.292075\pi\)
0.607744 + 0.794133i \(0.292075\pi\)
\(110\) −0.901617 0.0337191i −0.0859658 0.00321499i
\(111\) 3.07068i 0.291456i
\(112\) −2.68754 + 2.68754i −0.253949 + 0.253949i
\(113\) 8.96499 + 8.96499i 0.843356 + 0.843356i 0.989294 0.145938i \(-0.0466200\pi\)
−0.145938 + 0.989294i \(0.546620\pi\)
\(114\) −5.20795 −0.487769
\(115\) −10.4970 + 2.19392i −0.978849 + 0.204584i
\(116\) 9.42076 0.874695
\(117\) 2.12629 + 2.12629i 0.196576 + 0.196576i
\(118\) −9.47547 + 9.47547i −0.872288 + 0.872288i
\(119\) 26.6425i 2.44231i
\(120\) 1.63913 1.52094i 0.149631 0.138843i
\(121\) 10.8372 0.985199
\(122\) −5.31121 + 5.31121i −0.480854 + 0.480854i
\(123\) 4.02970 4.02970i 0.363346 0.363346i
\(124\) 3.33683i 0.299656i
\(125\) 8.74075 6.97132i 0.781796 0.623534i
\(126\) 3.80076i 0.338599i
\(127\) −9.84286 9.84286i −0.873413 0.873413i 0.119430 0.992843i \(-0.461893\pi\)
−0.992843 + 0.119430i \(0.961893\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 3.63363 0.319923
\(130\) 4.57353 + 4.92890i 0.401125 + 0.432293i
\(131\) −1.09419 −0.0955998 −0.0477999 0.998857i \(-0.515221\pi\)
−0.0477999 + 0.998857i \(0.515221\pi\)
\(132\) 0.285316 0.285316i 0.0248335 0.0248335i
\(133\) −13.9966 + 13.9966i −1.21366 + 1.21366i
\(134\) −6.51606 −0.562902
\(135\) −0.0835670 + 2.23451i −0.00719230 + 0.192316i
\(136\) 7.00978i 0.601084i
\(137\) −13.9152 + 13.9152i −1.18885 + 1.18885i −0.211471 + 0.977384i \(0.567825\pi\)
−0.977384 + 0.211471i \(0.932175\pi\)
\(138\) 2.47384 4.10854i 0.210588 0.349742i
\(139\) 19.8141i 1.68061i −0.542116 0.840304i \(-0.682377\pi\)
0.542116 0.840304i \(-0.317623\pi\)
\(140\) 0.317618 8.49282i 0.0268436 0.717774i
\(141\) 12.2247 1.02950
\(142\) −3.85572 3.85572i −0.323565 0.323565i
\(143\) 0.857953 + 0.857953i 0.0717457 + 0.0717457i
\(144\) 1.00000i 0.0833333i
\(145\) −15.4418 + 14.3284i −1.28237 + 1.18991i
\(146\) 1.50154 0.124269
\(147\) −5.26496 5.26496i −0.434247 0.434247i
\(148\) −2.17130 2.17130i −0.178480 0.178480i
\(149\) 11.1431 0.912875 0.456438 0.889755i \(-0.349125\pi\)
0.456438 + 0.889755i \(0.349125\pi\)
\(150\) −0.373462 + 4.98603i −0.0304930 + 0.407108i
\(151\) 19.9653 1.62475 0.812375 0.583135i \(-0.198174\pi\)
0.812375 + 0.583135i \(0.198174\pi\)
\(152\) 3.68258 3.68258i 0.298697 0.298697i
\(153\) −4.95666 4.95666i −0.400723 0.400723i
\(154\) 1.53360i 0.123581i
\(155\) −5.07513 5.46948i −0.407644 0.439319i
\(156\) −3.00703 −0.240755
\(157\) 2.44491 2.44491i 0.195125 0.195125i −0.602781 0.797907i \(-0.705941\pi\)
0.797907 + 0.602781i \(0.205941\pi\)
\(158\) −0.271221 0.271221i −0.0215772 0.0215772i
\(159\) 2.08749 0.165549
\(160\) −0.0835670 + 2.23451i −0.00660655 + 0.176653i
\(161\) −4.39331 17.6904i −0.346242 1.39420i
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) 0.238521 0.238521i 0.0186824 0.0186824i −0.697704 0.716386i \(-0.745795\pi\)
0.716386 + 0.697704i \(0.245795\pi\)
\(164\) 5.69885i 0.445006i
\(165\) −0.0337191 + 0.901617i −0.00262502 + 0.0701908i
\(166\) 17.4949i 1.35787i
\(167\) 6.43688 + 6.43688i 0.498101 + 0.498101i 0.910846 0.412746i \(-0.135430\pi\)
−0.412746 + 0.910846i \(0.635430\pi\)
\(168\) 2.68754 + 2.68754i 0.207348 + 0.207348i
\(169\) 3.95776i 0.304443i
\(170\) −10.6615 11.4899i −0.817698 0.881236i
\(171\) 5.20795i 0.398262i
\(172\) −2.56936 + 2.56936i −0.195912 + 0.195912i
\(173\) −5.89468 + 5.89468i −0.448164 + 0.448164i −0.894744 0.446580i \(-0.852642\pi\)
0.446580 + 0.894744i \(0.352642\pi\)
\(174\) 9.42076i 0.714186i
\(175\) 12.3965 + 14.4039i 0.937086 + 1.08883i
\(176\) 0.403497i 0.0304147i
\(177\) 9.47547 + 9.47547i 0.712220 + 0.712220i
\(178\) −4.40639 4.40639i −0.330273 0.330273i
\(179\) 2.77575i 0.207469i 0.994605 + 0.103735i \(0.0330792\pi\)
−0.994605 + 0.103735i \(0.966921\pi\)
\(180\) −1.52094 1.63913i −0.113364 0.122173i
\(181\) 21.2640i 1.58054i 0.612760 + 0.790269i \(0.290059\pi\)
−0.612760 + 0.790269i \(0.709941\pi\)
\(182\) −8.08153 + 8.08153i −0.599043 + 0.599043i
\(183\) 5.31121 + 5.31121i 0.392616 + 0.392616i
\(184\) 1.15590 + 4.65445i 0.0852143 + 0.343130i
\(185\) 6.86145 + 0.256608i 0.504464 + 0.0188662i
\(186\) 3.33683 0.244668
\(187\) −2.00000 2.00000i −0.146254 0.146254i
\(188\) −8.64413 + 8.64413i −0.630438 + 0.630438i
\(189\) −3.80076 −0.276465
\(190\) −0.435213 + 11.6372i −0.0315737 + 0.844251i
\(191\) 15.5937i 1.12832i −0.825666 0.564160i \(-0.809200\pi\)
0.825666 0.564160i \(-0.190800\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) −6.99660 + 6.99660i −0.503626 + 0.503626i −0.912563 0.408937i \(-0.865900\pi\)
0.408937 + 0.912563i \(0.365900\pi\)
\(194\) −11.6762 −0.838301
\(195\) 4.92890 4.57353i 0.352966 0.327517i
\(196\) 7.44578 0.531841
\(197\) 4.96503 + 4.96503i 0.353744 + 0.353744i 0.861501 0.507757i \(-0.169525\pi\)
−0.507757 + 0.861501i \(0.669525\pi\)
\(198\) −0.285316 0.285316i −0.0202765 0.0202765i
\(199\) −13.2209 −0.937202 −0.468601 0.883410i \(-0.655242\pi\)
−0.468601 + 0.883410i \(0.655242\pi\)
\(200\) −3.26158 3.78974i −0.230629 0.267975i
\(201\) 6.51606i 0.459608i
\(202\) −5.00944 5.00944i −0.352463 0.352463i
\(203\) −25.3187 25.3187i −1.77702 1.77702i
\(204\) 7.00978 0.490783
\(205\) −8.66763 9.34113i −0.605374 0.652413i
\(206\) 9.71622i 0.676961i
\(207\) −4.10854 2.47384i −0.285563 0.171944i
\(208\) 2.12629 2.12629i 0.147432 0.147432i
\(209\) 2.10139i 0.145356i
\(210\) −8.49282 0.317618i −0.586060 0.0219177i
\(211\) 14.3412 0.987286 0.493643 0.869665i \(-0.335665\pi\)
0.493643 + 0.869665i \(0.335665\pi\)
\(212\) −1.47608 + 1.47608i −0.101377 + 0.101377i
\(213\) −3.85572 + 3.85572i −0.264189 + 0.264189i
\(214\) 4.44997 0.304194
\(215\) 0.303651 8.11936i 0.0207088 0.553736i
\(216\) 1.00000 0.0680414
\(217\) 8.96787 8.96787i 0.608779 0.608779i
\(218\) 8.97323 + 8.97323i 0.607744 + 0.607744i
\(219\) 1.50154i 0.101465i
\(220\) −0.613696 0.661382i −0.0413754 0.0445904i
\(221\) 21.0786i 1.41790i
\(222\) −2.17130 + 2.17130i −0.145728 + 0.145728i
\(223\) −10.4795 + 10.4795i −0.701757 + 0.701757i −0.964788 0.263030i \(-0.915278\pi\)
0.263030 + 0.964788i \(0.415278\pi\)
\(224\) −3.80076 −0.253949
\(225\) 4.98603 + 0.373462i 0.332402 + 0.0248975i
\(226\) 12.6784i 0.843356i
\(227\) 0.390578 0.390578i 0.0259236 0.0259236i −0.694026 0.719950i \(-0.744165\pi\)
0.719950 + 0.694026i \(0.244165\pi\)
\(228\) −3.68258 3.68258i −0.243885 0.243885i
\(229\) 16.0170 1.05844 0.529218 0.848486i \(-0.322485\pi\)
0.529218 + 0.848486i \(0.322485\pi\)
\(230\) −8.97382 5.87116i −0.591716 0.387133i
\(231\) −1.53360 −0.100903
\(232\) 6.66148 + 6.66148i 0.437348 + 0.437348i
\(233\) −13.0826 + 13.0826i −0.857070 + 0.857070i −0.990992 0.133922i \(-0.957243\pi\)
0.133922 + 0.990992i \(0.457243\pi\)
\(234\) 3.00703i 0.196576i
\(235\) 1.02158 27.3161i 0.0666404 1.78190i
\(236\) −13.4003 −0.872288
\(237\) −0.271221 + 0.271221i −0.0176177 + 0.0176177i
\(238\) 18.8391 18.8391i 1.22116 1.22116i
\(239\) 14.8384i 0.959816i −0.877319 0.479908i \(-0.840670\pi\)
0.877319 0.479908i \(-0.159330\pi\)
\(240\) 2.23451 + 0.0835670i 0.144237 + 0.00539423i
\(241\) 9.52147i 0.613332i 0.951817 + 0.306666i \(0.0992135\pi\)
−0.951817 + 0.306666i \(0.900787\pi\)
\(242\) 7.66305 + 7.66305i 0.492600 + 0.492600i
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) −7.51118 −0.480854
\(245\) −12.2046 + 11.3246i −0.779721 + 0.723503i
\(246\) 5.69885 0.363346
\(247\) 11.0736 11.0736i 0.704598 0.704598i
\(248\) −2.35950 + 2.35950i −0.149828 + 0.149828i
\(249\) −17.4949 −1.10870
\(250\) 11.1101 + 1.25117i 0.702665 + 0.0791310i
\(251\) 2.75797i 0.174082i 0.996205 + 0.0870409i \(0.0277411\pi\)
−0.996205 + 0.0870409i \(0.972259\pi\)
\(252\) 2.68754 2.68754i 0.169299 0.169299i
\(253\) −1.65778 0.998189i −0.104224 0.0627556i
\(254\) 13.9199i 0.873413i
\(255\) −11.4899 + 10.6615i −0.719526 + 0.667648i
\(256\) 1.00000 0.0625000
\(257\) 4.31593 + 4.31593i 0.269220 + 0.269220i 0.828786 0.559566i \(-0.189032\pi\)
−0.559566 + 0.828786i \(0.689032\pi\)
\(258\) 2.56936 + 2.56936i 0.159961 + 0.159961i
\(259\) 11.6709i 0.725196i
\(260\) −0.251289 + 6.71923i −0.0155843 + 0.416709i
\(261\) −9.42076 −0.583130
\(262\) −0.773709 0.773709i −0.0477999 0.0477999i
\(263\) −4.09411 4.09411i −0.252453 0.252453i 0.569522 0.821976i \(-0.307128\pi\)
−0.821976 + 0.569522i \(0.807128\pi\)
\(264\) 0.403497 0.0248335
\(265\) 0.174445 4.66451i 0.0107161 0.286538i
\(266\) −19.7942 −1.21366
\(267\) −4.40639 + 4.40639i −0.269667 + 0.269667i
\(268\) −4.60755 4.60755i −0.281451 0.281451i
\(269\) 30.5379i 1.86193i −0.365111 0.930964i \(-0.618969\pi\)
0.365111 0.930964i \(-0.381031\pi\)
\(270\) −1.63913 + 1.52094i −0.0997540 + 0.0925617i
\(271\) −14.3414 −0.871178 −0.435589 0.900146i \(-0.643460\pi\)
−0.435589 + 0.900146i \(0.643460\pi\)
\(272\) −4.95666 + 4.95666i −0.300542 + 0.300542i
\(273\) 8.08153 + 8.08153i 0.489116 + 0.489116i
\(274\) −19.6791 −1.18885
\(275\) 2.01185 + 0.150691i 0.121319 + 0.00908700i
\(276\) 4.65445 1.15590i 0.280165 0.0695772i
\(277\) 2.49148 + 2.49148i 0.149698 + 0.149698i 0.777983 0.628285i \(-0.216243\pi\)
−0.628285 + 0.777983i \(0.716243\pi\)
\(278\) 14.0107 14.0107i 0.840304 0.840304i
\(279\) 3.33683i 0.199771i
\(280\) 6.22992 5.78074i 0.372309 0.345465i
\(281\) 24.3745i 1.45406i −0.686604 0.727031i \(-0.740900\pi\)
0.686604 0.727031i \(-0.259100\pi\)
\(282\) 8.64413 + 8.64413i 0.514751 + 0.514751i
\(283\) −1.55632 1.55632i −0.0925135 0.0925135i 0.659335 0.751849i \(-0.270838\pi\)
−0.751849 + 0.659335i \(0.770838\pi\)
\(284\) 5.45281i 0.323565i
\(285\) 11.6372 + 0.435213i 0.689328 + 0.0257798i
\(286\) 1.21333i 0.0717457i
\(287\) 15.3159 15.3159i 0.904070 0.904070i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) 32.1370i 1.89041i
\(290\) −21.0507 0.787264i −1.23614 0.0462298i
\(291\) 11.6762i 0.684470i
\(292\) 1.06175 + 1.06175i 0.0621343 + 0.0621343i
\(293\) 16.6999 + 16.6999i 0.975619 + 0.975619i 0.999710 0.0240909i \(-0.00766911\pi\)
−0.0240909 + 0.999710i \(0.507669\pi\)
\(294\) 7.44578i 0.434247i
\(295\) 21.9648 20.3812i 1.27884 1.18664i
\(296\) 3.07068i 0.178480i
\(297\) −0.285316 + 0.285316i −0.0165557 + 0.0165557i
\(298\) 7.87934 + 7.87934i 0.456438 + 0.456438i
\(299\) 3.47584 + 13.9961i 0.201013 + 0.809414i
\(300\) −3.78974 + 3.26158i −0.218800 + 0.188307i
\(301\) 13.8105 0.796026
\(302\) 14.1176 + 14.1176i 0.812375 + 0.812375i
\(303\) −5.00944 + 5.00944i −0.287785 + 0.287785i
\(304\) 5.20795 0.298697
\(305\) 12.3118 11.4241i 0.704970 0.654141i
\(306\) 7.00978i 0.400723i
\(307\) 2.34796 + 2.34796i 0.134005 + 0.134005i 0.770928 0.636923i \(-0.219793\pi\)
−0.636923 + 0.770928i \(0.719793\pi\)
\(308\) 1.08442 1.08442i 0.0617903 0.0617903i
\(309\) 9.71622 0.552737
\(310\) 0.278849 7.45617i 0.0158376 0.423482i
\(311\) 12.8558 0.728988 0.364494 0.931206i \(-0.381242\pi\)
0.364494 + 0.931206i \(0.381242\pi\)
\(312\) −2.12629 2.12629i −0.120378 0.120378i
\(313\) 3.38173 + 3.38173i 0.191147 + 0.191147i 0.796192 0.605045i \(-0.206845\pi\)
−0.605045 + 0.796192i \(0.706845\pi\)
\(314\) 3.45763 0.195125
\(315\) −0.317618 + 8.49282i −0.0178958 + 0.478516i
\(316\) 0.383565i 0.0215772i
\(317\) 16.1019 + 16.1019i 0.904375 + 0.904375i 0.995811 0.0914360i \(-0.0291457\pi\)
−0.0914360 + 0.995811i \(0.529146\pi\)
\(318\) 1.47608 + 1.47608i 0.0827743 + 0.0827743i
\(319\) −3.80125 −0.212829
\(320\) −1.63913 + 1.52094i −0.0916299 + 0.0850233i
\(321\) 4.44997i 0.248373i
\(322\) 9.40249 15.6156i 0.523980 0.870222i
\(323\) −25.8141 + 25.8141i −1.43633 + 1.43633i
\(324\) 1.00000i 0.0555556i
\(325\) −9.80768 11.3959i −0.544032 0.632128i
\(326\) 0.337320 0.0186824
\(327\) 8.97323 8.97323i 0.496221 0.496221i
\(328\) −4.02970 + 4.02970i −0.222503 + 0.222503i
\(329\) 46.4630 2.56159
\(330\) −0.661382 + 0.613696i −0.0364079 + 0.0337829i
\(331\) 11.6757 0.641756 0.320878 0.947120i \(-0.396022\pi\)
0.320878 + 0.947120i \(0.396022\pi\)
\(332\) 12.3708 12.3708i 0.678934 0.678934i
\(333\) 2.17130 + 2.17130i 0.118986 + 0.118986i
\(334\) 9.10312i 0.498101i
\(335\) 14.5602 + 0.544528i 0.795508 + 0.0297507i
\(336\) 3.80076i 0.207348i
\(337\) 10.5109 10.5109i 0.572567 0.572567i −0.360278 0.932845i \(-0.617318\pi\)
0.932845 + 0.360278i \(0.117318\pi\)
\(338\) −2.79856 + 2.79856i −0.152221 + 0.152221i
\(339\) 12.6784 0.688597
\(340\) 0.585786 15.6634i 0.0317687 0.849467i
\(341\) 1.34640i 0.0729117i
\(342\) −3.68258 + 3.68258i −0.199131 + 0.199131i
\(343\) −1.19805 1.19805i −0.0646884 0.0646884i
\(344\) −3.63363 −0.195912
\(345\) −5.87116 + 8.97382i −0.316093 + 0.483134i
\(346\) −8.33634 −0.448164
\(347\) −17.9614 17.9614i −0.964218 0.964218i 0.0351639 0.999382i \(-0.488805\pi\)
−0.999382 + 0.0351639i \(0.988805\pi\)
\(348\) 6.66148 6.66148i 0.357093 0.357093i
\(349\) 18.2166i 0.975113i 0.873092 + 0.487556i \(0.162112\pi\)
−0.873092 + 0.487556i \(0.837888\pi\)
\(350\) −1.41944 + 18.9507i −0.0758722 + 1.01296i
\(351\) 3.00703 0.160504
\(352\) −0.285316 + 0.285316i −0.0152074 + 0.0152074i
\(353\) −13.3386 + 13.3386i −0.709942 + 0.709942i −0.966523 0.256581i \(-0.917404\pi\)
0.256581 + 0.966523i \(0.417404\pi\)
\(354\) 13.4003i 0.712220i
\(355\) 8.29342 + 8.93784i 0.440169 + 0.474371i
\(356\) 6.23158i 0.330273i
\(357\) −18.8391 18.8391i −0.997070 0.997070i
\(358\) −1.96275 + 1.96275i −0.103735 + 0.103735i
\(359\) 23.6679 1.24915 0.624573 0.780967i \(-0.285273\pi\)
0.624573 + 0.780967i \(0.285273\pi\)
\(360\) 0.0835670 2.23451i 0.00440437 0.117769i
\(361\) 8.12277 0.427514
\(362\) −15.0359 + 15.0359i −0.790269 + 0.790269i
\(363\) 7.66305 7.66305i 0.402206 0.402206i
\(364\) −11.4290 −0.599043
\(365\) −3.35521 0.125479i −0.175620 0.00656789i
\(366\) 7.51118i 0.392616i
\(367\) 1.82999 1.82999i 0.0955248 0.0955248i −0.657729 0.753254i \(-0.728483\pi\)
0.753254 + 0.657729i \(0.228483\pi\)
\(368\) −2.47384 + 4.10854i −0.128958 + 0.214172i
\(369\) 5.69885i 0.296670i
\(370\) 4.67033 + 5.03323i 0.242799 + 0.261665i
\(371\) 7.93404 0.411915
\(372\) 2.35950 + 2.35950i 0.122334 + 0.122334i
\(373\) −4.97536 4.97536i −0.257615 0.257615i 0.566469 0.824083i \(-0.308309\pi\)
−0.824083 + 0.566469i \(0.808309\pi\)
\(374\) 2.82843i 0.146254i
\(375\) 1.25117 11.1101i 0.0646102 0.573724i
\(376\) −12.2247 −0.630438
\(377\) 20.0313 + 20.0313i 1.03166 + 1.03166i
\(378\) −2.68754 2.68754i −0.138232 0.138232i
\(379\) 3.53426 0.181543 0.0907714 0.995872i \(-0.471067\pi\)
0.0907714 + 0.995872i \(0.471067\pi\)
\(380\) −8.53649 + 7.92100i −0.437912 + 0.406339i
\(381\) −13.9199 −0.713138
\(382\) 11.0264 11.0264i 0.564160 0.564160i
\(383\) −13.8129 13.8129i −0.705805 0.705805i 0.259845 0.965650i \(-0.416329\pi\)
−0.965650 + 0.259845i \(0.916329\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −0.128158 + 3.42683i −0.00653154 + 0.174647i
\(386\) −9.89468 −0.503626
\(387\) 2.56936 2.56936i 0.130608 0.130608i
\(388\) −8.25631 8.25631i −0.419150 0.419150i
\(389\) 6.63285 0.336299 0.168149 0.985762i \(-0.446221\pi\)
0.168149 + 0.985762i \(0.446221\pi\)
\(390\) 6.71923 + 0.251289i 0.340242 + 0.0127245i
\(391\) −8.10263 32.6267i −0.409768 1.65000i
\(392\) 5.26496 + 5.26496i 0.265921 + 0.265921i
\(393\) −0.773709 + 0.773709i −0.0390284 + 0.0390284i
\(394\) 7.02162i 0.353744i
\(395\) 0.583380 + 0.628711i 0.0293530 + 0.0316339i
\(396\) 0.403497i 0.0202765i
\(397\) −6.61498 6.61498i −0.331996 0.331996i 0.521348 0.853344i \(-0.325429\pi\)
−0.853344 + 0.521348i \(0.825429\pi\)
\(398\) −9.34856 9.34856i −0.468601 0.468601i
\(399\) 19.7942i 0.990948i
\(400\) 0.373462 4.98603i 0.0186731 0.249302i
\(401\) 9.81654i 0.490215i −0.969496 0.245107i \(-0.921177\pi\)
0.969496 0.245107i \(-0.0788232\pi\)
\(402\) −4.60755 + 4.60755i −0.229804 + 0.229804i
\(403\) −7.09508 + 7.09508i −0.353431 + 0.353431i
\(404\) 7.08442i 0.352463i
\(405\) 1.52094 + 1.63913i 0.0755763 + 0.0814488i
\(406\) 35.8060i 1.77702i
\(407\) 0.876113 + 0.876113i 0.0434273 + 0.0434273i
\(408\) 4.95666 + 4.95666i 0.245391 + 0.245391i
\(409\) 1.62998i 0.0805974i −0.999188 0.0402987i \(-0.987169\pi\)
0.999188 0.0402987i \(-0.0128309\pi\)
\(410\) 0.476236 12.7341i 0.0235196 0.628893i
\(411\) 19.6791i 0.970696i
\(412\) −6.87041 + 6.87041i −0.338481 + 0.338481i
\(413\) 36.0140 + 36.0140i 1.77213 + 1.77213i
\(414\) −1.15590 4.65445i −0.0568096 0.228754i
\(415\) −1.46200 + 39.0925i −0.0717666 + 1.91897i
\(416\) 3.00703 0.147432
\(417\) −14.0107 14.0107i −0.686105 0.686105i
\(418\) −1.48591 + 1.48591i −0.0726782 + 0.0726782i
\(419\) −11.2744 −0.550791 −0.275395 0.961331i \(-0.588809\pi\)
−0.275395 + 0.961331i \(0.588809\pi\)
\(420\) −5.78074 6.22992i −0.282071 0.303989i
\(421\) 16.1033i 0.784825i −0.919789 0.392412i \(-0.871641\pi\)
0.919789 0.392412i \(-0.128359\pi\)
\(422\) 10.1407 + 10.1407i 0.493643 + 0.493643i
\(423\) 8.64413 8.64413i 0.420292 0.420292i
\(424\) −2.08749 −0.101377
\(425\) 22.8630 + 26.5652i 1.10902 + 1.28860i
\(426\) −5.45281 −0.264189
\(427\) 20.1866 + 20.1866i 0.976899 + 0.976899i
\(428\) 3.14660 + 3.14660i 0.152097 + 0.152097i
\(429\) 1.21333 0.0585801
\(430\) 5.95597 5.52654i 0.287222 0.266513i
\(431\) 37.5672i 1.80955i −0.425894 0.904773i \(-0.640040\pi\)
0.425894 0.904773i \(-0.359960\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) −19.4771 19.4771i −0.936012 0.936012i 0.0620607 0.998072i \(-0.480233\pi\)
−0.998072 + 0.0620607i \(0.980233\pi\)
\(434\) 12.6825 0.608779
\(435\) −0.787264 + 21.0507i −0.0377464 + 1.00931i
\(436\) 12.6901i 0.607744i
\(437\) −12.8837 + 21.3971i −0.616309 + 1.02356i
\(438\) 1.06175 1.06175i 0.0507324 0.0507324i
\(439\) 27.5197i 1.31344i −0.754133 0.656721i \(-0.771943\pi\)
0.754133 0.656721i \(-0.228057\pi\)
\(440\) 0.0337191 0.901617i 0.00160749 0.0429829i
\(441\) −7.44578 −0.354561
\(442\) −14.9048 + 14.9048i −0.708951 + 0.708951i
\(443\) 21.8369 21.8369i 1.03750 1.03750i 0.0382321 0.999269i \(-0.487827\pi\)
0.999269 0.0382321i \(-0.0121726\pi\)
\(444\) −3.07068 −0.145728
\(445\) 9.47788 + 10.2143i 0.449295 + 0.484206i
\(446\) −14.8202 −0.701757
\(447\) 7.87934 7.87934i 0.372680 0.372680i
\(448\) −2.68754 2.68754i −0.126974 0.126974i
\(449\) 3.81966i 0.180261i 0.995930 + 0.0901306i \(0.0287284\pi\)
−0.995930 + 0.0901306i \(0.971272\pi\)
\(450\) 3.26158 + 3.78974i 0.153752 + 0.178650i
\(451\) 2.29947i 0.108278i
\(452\) −8.96499 + 8.96499i −0.421678 + 0.421678i
\(453\) 14.1176 14.1176i 0.663301 0.663301i
\(454\) 0.552361 0.0259236
\(455\) 18.7336 17.3829i 0.878244 0.814922i
\(456\) 5.20795i 0.243885i
\(457\) −19.1698 + 19.1698i −0.896726 + 0.896726i −0.995145 0.0984194i \(-0.968621\pi\)
0.0984194 + 0.995145i \(0.468621\pi\)
\(458\) 11.3258 + 11.3258i 0.529218 + 0.529218i
\(459\) −7.00978 −0.327189
\(460\) −2.19392 10.4970i −0.102292 0.489425i
\(461\) −23.5334 −1.09606 −0.548029 0.836459i \(-0.684622\pi\)
−0.548029 + 0.836459i \(0.684622\pi\)
\(462\) −1.08442 1.08442i −0.0504516 0.0504516i
\(463\) 20.0945 20.0945i 0.933869 0.933869i −0.0640760 0.997945i \(-0.520410\pi\)
0.997945 + 0.0640760i \(0.0204100\pi\)
\(464\) 9.42076i 0.437348i
\(465\) −7.45617 0.278849i −0.345771 0.0129313i
\(466\) −18.5016 −0.857070
\(467\) −8.34291 + 8.34291i −0.386064 + 0.386064i −0.873281 0.487217i \(-0.838012\pi\)
0.487217 + 0.873281i \(0.338012\pi\)
\(468\) −2.12629 + 2.12629i −0.0982879 + 0.0982879i
\(469\) 24.7660i 1.14359i
\(470\) 20.0377 18.5930i 0.924272 0.857631i
\(471\) 3.45763i 0.159319i
\(472\) −9.47547 9.47547i −0.436144 0.436144i
\(473\) 1.03673 1.03673i 0.0476689 0.0476689i
\(474\) −0.383565 −0.0176177
\(475\) 1.94497 25.9670i 0.0892414 1.19145i
\(476\) 26.6425 1.22116
\(477\) 1.47608 1.47608i 0.0675849 0.0675849i
\(478\) 10.4923 10.4923i 0.479908 0.479908i
\(479\) −21.0887 −0.963565 −0.481783 0.876291i \(-0.660011\pi\)
−0.481783 + 0.876291i \(0.660011\pi\)
\(480\) 1.52094 + 1.63913i 0.0694213 + 0.0748155i
\(481\) 9.23364i 0.421018i
\(482\) −6.73270 + 6.73270i −0.306666 + 0.306666i
\(483\) −15.6156 9.40249i −0.710533 0.427828i
\(484\) 10.8372i 0.492600i
\(485\) 26.0905 + 0.975743i 1.18471 + 0.0443062i
\(486\) −1.00000 −0.0453609
\(487\) −0.859666 0.859666i −0.0389552 0.0389552i 0.687361 0.726316i \(-0.258769\pi\)
−0.726316 + 0.687361i \(0.758769\pi\)
\(488\) −5.31121 5.31121i −0.240427 0.240427i
\(489\) 0.337320i 0.0152541i
\(490\) −16.6376 0.622221i −0.751612 0.0281091i
\(491\) −27.6182 −1.24639 −0.623197 0.782065i \(-0.714166\pi\)
−0.623197 + 0.782065i \(0.714166\pi\)
\(492\) 4.02970 + 4.02970i 0.181673 + 0.181673i
\(493\) −46.6955 46.6955i −2.10306 2.10306i
\(494\) 15.6605 0.704598
\(495\) 0.613696 + 0.661382i 0.0275836 + 0.0297269i
\(496\) −3.33683 −0.149828
\(497\) −14.6547 + 14.6547i −0.657351 + 0.657351i
\(498\) −12.3708 12.3708i −0.554348 0.554348i
\(499\) 18.6771i 0.836101i 0.908424 + 0.418051i \(0.137287\pi\)
−0.908424 + 0.418051i \(0.862713\pi\)
\(500\) 6.97132 + 8.74075i 0.311767 + 0.390898i
\(501\) 9.10312 0.406697
\(502\) −1.95018 + 1.95018i −0.0870409 + 0.0870409i
\(503\) 2.24840 + 2.24840i 0.100251 + 0.100251i 0.755453 0.655202i \(-0.227417\pi\)
−0.655202 + 0.755453i \(0.727417\pi\)
\(504\) 3.80076 0.169299
\(505\) 10.7750 + 11.6122i 0.479481 + 0.516738i
\(506\) −0.466404 1.87806i −0.0207342 0.0834898i
\(507\) 2.79856 + 2.79856i 0.124288 + 0.124288i
\(508\) 9.84286 9.84286i 0.436706 0.436706i
\(509\) 10.9101i 0.483582i −0.970328 0.241791i \(-0.922265\pi\)
0.970328 0.241791i \(-0.0777348\pi\)
\(510\) −15.6634 0.585786i −0.693587 0.0259391i
\(511\) 5.70700i 0.252463i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 3.68258 + 3.68258i 0.162590 + 0.162590i
\(514\) 6.10364i 0.269220i
\(515\) 0.811956 21.7110i 0.0357790 0.956699i
\(516\) 3.63363i 0.159961i
\(517\) 3.48788 3.48788i 0.153397 0.153397i
\(518\) −8.25259 + 8.25259i −0.362598 + 0.362598i
\(519\) 8.33634i 0.365925i
\(520\) −4.92890 + 4.57353i −0.216147 + 0.200562i
\(521\) 31.7519i 1.39108i 0.718489 + 0.695539i \(0.244834\pi\)
−0.718489 + 0.695539i \(0.755166\pi\)
\(522\) −6.66148 6.66148i −0.291565 0.291565i
\(523\) 17.6479 + 17.6479i 0.771687 + 0.771687i 0.978401 0.206714i \(-0.0662771\pi\)
−0.206714 + 0.978401i \(0.566277\pi\)
\(524\) 1.09419i 0.0477999i
\(525\) 18.9507 + 1.41944i 0.827077 + 0.0619494i
\(526\) 5.78994i 0.252453i
\(527\) 16.5395 16.5395i 0.720474 0.720474i
\(528\) 0.285316 + 0.285316i 0.0124168 + 0.0124168i
\(529\) −10.7602 20.3278i −0.467834 0.883816i
\(530\) 3.42165 3.17495i 0.148627 0.137911i
\(531\) 13.4003 0.581525
\(532\) −13.9966 13.9966i −0.606829 0.606829i
\(533\) −12.1174 + 12.1174i −0.524864 + 0.524864i
\(534\) −6.23158 −0.269667
\(535\) −9.94348 0.371871i −0.429894 0.0160774i
\(536\) 6.51606i 0.281451i
\(537\) 1.96275 + 1.96275i 0.0846989 + 0.0846989i
\(538\) 21.5936 21.5936i 0.930964 0.930964i
\(539\) −3.00435 −0.129407
\(540\) −2.23451 0.0835670i −0.0961578 0.00359615i
\(541\) 33.4617 1.43863 0.719315 0.694684i \(-0.244456\pi\)
0.719315 + 0.694684i \(0.244456\pi\)
\(542\) −10.1409 10.1409i −0.435589 0.435589i
\(543\) 15.0359 + 15.0359i 0.645252 + 0.645252i
\(544\) −7.00978 −0.300542
\(545\) −19.3009 20.8006i −0.826758 0.890999i
\(546\) 11.4290i 0.489116i
\(547\) −12.8216 12.8216i −0.548213 0.548213i 0.377711 0.925924i \(-0.376711\pi\)
−0.925924 + 0.377711i \(0.876711\pi\)
\(548\) −13.9152 13.9152i −0.594427 0.594427i
\(549\) 7.51118 0.320569
\(550\) 1.31604 + 1.52915i 0.0561161 + 0.0652031i
\(551\) 49.0629i 2.09015i
\(552\) 4.10854 + 2.47384i 0.174871 + 0.105294i
\(553\) −1.03085 + 1.03085i −0.0438361 + 0.0438361i
\(554\) 3.52348i 0.149698i
\(555\) 5.03323 4.67033i 0.213649 0.198245i
\(556\) 19.8141 0.840304
\(557\) 14.8590 14.8590i 0.629594 0.629594i −0.318372 0.947966i \(-0.603136\pi\)
0.947966 + 0.318372i \(0.103136\pi\)
\(558\) 2.35950 2.35950i 0.0998854 0.0998854i
\(559\) −10.9264 −0.462139
\(560\) 8.49282 + 0.317618i 0.358887 + 0.0134218i
\(561\) −2.82843 −0.119416
\(562\) 17.2354 17.2354i 0.727031 0.727031i
\(563\) 2.14137 + 2.14137i 0.0902478 + 0.0902478i 0.750789 0.660542i \(-0.229673\pi\)
−0.660542 + 0.750789i \(0.729673\pi\)
\(564\) 12.2247i 0.514751i
\(565\) 1.05950 28.3300i 0.0445734 1.19185i
\(566\) 2.20097i 0.0925135i
\(567\) −2.68754 + 2.68754i −0.112866 + 0.112866i
\(568\) 3.85572 3.85572i 0.161782 0.161782i
\(569\) −44.6987 −1.87387 −0.936934 0.349506i \(-0.886350\pi\)
−0.936934 + 0.349506i \(0.886350\pi\)
\(570\) 7.92100 + 8.53649i 0.331774 + 0.357554i
\(571\) 26.7672i 1.12017i −0.828435 0.560085i \(-0.810768\pi\)
0.828435 0.560085i \(-0.189232\pi\)
\(572\) −0.857953 + 0.857953i −0.0358728 + 0.0358728i
\(573\) −11.0264 11.0264i −0.460635 0.460635i
\(574\) 21.6600 0.904070
\(575\) 19.5614 + 13.8691i 0.815768 + 0.578380i
\(576\) −1.00000 −0.0416667
\(577\) −14.2226 14.2226i −0.592095 0.592095i 0.346102 0.938197i \(-0.387505\pi\)
−0.938197 + 0.346102i \(0.887505\pi\)
\(578\) 22.7243 22.7243i 0.945207 0.945207i
\(579\) 9.89468i 0.411209i
\(580\) −14.3284 15.4418i −0.594956 0.641186i
\(581\) −66.4940 −2.75863
\(582\) −8.25631 + 8.25631i −0.342235 + 0.342235i
\(583\) 0.595593 0.595593i 0.0246669 0.0246669i
\(584\) 1.50154i 0.0621343i
\(585\) 0.251289 6.71923i 0.0103895 0.277806i
\(586\) 23.6172i 0.975619i
\(587\) −7.01819 7.01819i −0.289672 0.289672i 0.547279 0.836950i \(-0.315664\pi\)
−0.836950 + 0.547279i \(0.815664\pi\)
\(588\) 5.26496 5.26496i 0.217123 0.217123i
\(589\) −17.3781 −0.716050
\(590\) 29.9431 + 1.11983i 1.23274 + 0.0461025i
\(591\) 7.02162 0.288831
\(592\) 2.17130 2.17130i 0.0892398 0.0892398i
\(593\) −22.3974 + 22.3974i −0.919752 + 0.919752i −0.997011 0.0772588i \(-0.975383\pi\)
0.0772588 + 0.997011i \(0.475383\pi\)
\(594\) −0.403497 −0.0165557
\(595\) −43.6704 + 40.5217i −1.79031 + 1.66123i
\(596\) 11.1431i 0.456438i
\(597\) −9.34856 + 9.34856i −0.382611 + 0.382611i
\(598\) −7.43893 + 12.3545i −0.304201 + 0.505214i
\(599\) 2.54190i 0.103859i 0.998651 + 0.0519296i \(0.0165371\pi\)
−0.998651 + 0.0519296i \(0.983463\pi\)
\(600\) −4.98603 0.373462i −0.203554 0.0152465i
\(601\) −15.8155 −0.645130 −0.322565 0.946547i \(-0.604545\pi\)
−0.322565 + 0.946547i \(0.604545\pi\)
\(602\) 9.76553 + 9.76553i 0.398013 + 0.398013i
\(603\) 4.60755 + 4.60755i 0.187634 + 0.187634i
\(604\) 19.9653i 0.812375i
\(605\) −16.4828 17.7635i −0.670119 0.722189i
\(606\) −7.08442 −0.287785
\(607\) −3.60929 3.60929i −0.146497 0.146497i 0.630054 0.776551i \(-0.283033\pi\)
−0.776551 + 0.630054i \(0.783033\pi\)
\(608\) 3.68258 + 3.68258i 0.149348 + 0.149348i
\(609\) −35.8060 −1.45093
\(610\) 16.7838 + 0.627687i 0.679556 + 0.0254143i
\(611\) −36.7599 −1.48715
\(612\) 4.95666 4.95666i 0.200361 0.200361i
\(613\) 14.0673 + 14.0673i 0.568173 + 0.568173i 0.931616 0.363444i \(-0.118399\pi\)
−0.363444 + 0.931616i \(0.618399\pi\)
\(614\) 3.32051i 0.134005i
\(615\) −12.7341 0.476236i −0.513489 0.0192037i
\(616\) 1.53360 0.0617903
\(617\) 31.3443 31.3443i 1.26187 1.26187i 0.311688 0.950185i \(-0.399106\pi\)
0.950185 0.311688i \(-0.100894\pi\)
\(618\) 6.87041 + 6.87041i 0.276368 + 0.276368i
\(619\) −20.0495 −0.805857 −0.402928 0.915232i \(-0.632008\pi\)
−0.402928 + 0.915232i \(0.632008\pi\)
\(620\) 5.46948 5.07513i 0.219660 0.203822i
\(621\) −4.65445 + 1.15590i −0.186777 + 0.0463848i
\(622\) 9.09045 + 9.09045i 0.364494 + 0.364494i
\(623\) −16.7476 + 16.7476i −0.670980 + 0.670980i
\(624\) 3.00703i 0.120378i
\(625\) −24.7211 3.72419i −0.988842 0.148967i
\(626\) 4.78249i 0.191147i
\(627\) 1.48591 + 1.48591i 0.0593415 + 0.0593415i
\(628\) 2.44491 + 2.44491i 0.0975627 + 0.0975627i
\(629\) 21.5248i 0.858250i
\(630\) −6.22992 + 5.78074i −0.248206 + 0.230310i
\(631\) 13.0006i 0.517544i 0.965938 + 0.258772i \(0.0833178\pi\)
−0.965938 + 0.258772i \(0.916682\pi\)
\(632\) 0.271221 0.271221i 0.0107886 0.0107886i
\(633\) 10.1407 10.1407i 0.403058 0.403058i
\(634\) 22.7716i 0.904375i
\(635\) −1.16324 + 31.1041i −0.0461620 + 1.23433i
\(636\) 2.08749i 0.0827743i
\(637\) 15.8319 + 15.8319i 0.627283 + 0.627283i
\(638\) −2.68789 2.68789i −0.106415 0.106415i
\(639\) 5.45281i 0.215710i
\(640\) −2.23451 0.0835670i −0.0883266 0.00330328i
\(641\) 14.0108i 0.553393i 0.960957 + 0.276696i \(0.0892396\pi\)
−0.960957 + 0.276696i \(0.910760\pi\)
\(642\) 3.14660 3.14660i 0.124187 0.124187i
\(643\) −10.2908 10.2908i −0.405829 0.405829i 0.474452 0.880281i \(-0.342646\pi\)
−0.880281 + 0.474452i \(0.842646\pi\)
\(644\) 17.6904 4.39331i 0.697101 0.173121i
\(645\) −5.52654 5.95597i −0.217607 0.234516i
\(646\) −36.5066 −1.43633
\(647\) −11.8108 11.8108i −0.464329 0.464329i 0.435743 0.900071i \(-0.356486\pi\)
−0.900071 + 0.435743i \(0.856486\pi\)
\(648\) 0.707107 0.707107i 0.0277778 0.0277778i
\(649\) 5.40700 0.212243
\(650\) 1.12301 14.9932i 0.0440482 0.588080i
\(651\) 12.6825i 0.497066i
\(652\) 0.238521 + 0.238521i 0.00934121 + 0.00934121i
\(653\) −7.33870 + 7.33870i −0.287185 + 0.287185i −0.835966 0.548781i \(-0.815092\pi\)
0.548781 + 0.835966i \(0.315092\pi\)
\(654\) 12.6901 0.496221
\(655\) 1.66420 + 1.79351i 0.0650257 + 0.0700784i
\(656\) −5.69885 −0.222503
\(657\) −1.06175 1.06175i −0.0414229 0.0414229i
\(658\) 32.8543 + 32.8543i 1.28079 + 1.28079i
\(659\) −29.6115 −1.15350 −0.576750 0.816921i \(-0.695679\pi\)
−0.576750 + 0.816921i \(0.695679\pi\)
\(660\) −0.901617 0.0337191i −0.0350954 0.00131251i
\(661\) 0.177775i 0.00691465i −0.999994 0.00345732i \(-0.998899\pi\)
0.999994 0.00345732i \(-0.00110050\pi\)
\(662\) 8.25599 + 8.25599i 0.320878 + 0.320878i
\(663\) 14.9048 + 14.9048i 0.578856 + 0.578856i
\(664\) 17.4949 0.678934
\(665\) 44.2302 + 1.65414i 1.71517 + 0.0641448i
\(666\) 3.07068i 0.118986i
\(667\) −38.7055 23.3055i −1.49868 0.902392i
\(668\) −6.43688 + 6.43688i −0.249050 + 0.249050i
\(669\) 14.8202i 0.572982i
\(670\) 9.91057 + 10.6806i 0.382879 + 0.412629i
\(671\) 3.03074 0.117000
\(672\) −2.68754 + 2.68754i −0.103674 + 0.103674i
\(673\) 3.91098 3.91098i 0.150757 0.150757i −0.627699 0.778456i \(-0.716003\pi\)
0.778456 + 0.627699i \(0.216003\pi\)
\(674\) 14.8647 0.572567
\(675\) 3.78974 3.26158i 0.145867 0.125538i
\(676\) −3.95776 −0.152221
\(677\) −31.1105 + 31.1105i −1.19567 + 1.19567i −0.220223 + 0.975450i \(0.570678\pi\)
−0.975450 + 0.220223i \(0.929322\pi\)
\(678\) 8.96499 + 8.96499i 0.344299 + 0.344299i
\(679\) 44.3784i 1.70309i
\(680\) 11.4899 10.6615i 0.440618 0.408849i
\(681\) 0.552361i 0.0211665i
\(682\) 0.952050 0.952050i 0.0364559 0.0364559i
\(683\) 27.1997 27.1997i 1.04077 1.04077i 0.0416348 0.999133i \(-0.486743\pi\)
0.999133 0.0416348i \(-0.0132566\pi\)
\(684\) −5.20795 −0.199131
\(685\) 43.9730 + 1.64452i 1.68012 + 0.0628339i
\(686\) 1.69429i 0.0646884i
\(687\) 11.3258 11.3258i 0.432104 0.432104i
\(688\) −2.56936 2.56936i −0.0979560 0.0979560i
\(689\) −6.27715 −0.239140
\(690\) −10.4970 + 2.19392i −0.399613 + 0.0835209i
\(691\) 31.8947 1.21333 0.606666 0.794957i \(-0.292507\pi\)
0.606666 + 0.794957i \(0.292507\pi\)
\(692\) −5.89468 5.89468i −0.224082 0.224082i
\(693\) −1.08442 + 1.08442i −0.0411936 + 0.0411936i
\(694\) 25.4012i 0.964218i
\(695\) −32.4777 + 30.1361i −1.23195 + 1.14313i
\(696\) 9.42076 0.357093
\(697\) 28.2473 28.2473i 1.06994 1.06994i
\(698\) −12.8811 + 12.8811i −0.487556 + 0.487556i
\(699\) 18.5016i 0.699795i
\(700\) −14.4039 + 12.3965i −0.544415 + 0.468543i
\(701\) 39.2405i 1.48209i 0.671454 + 0.741046i \(0.265670\pi\)
−0.671454 + 0.741046i \(0.734330\pi\)
\(702\) 2.12629 + 2.12629i 0.0802518 + 0.0802518i
\(703\) 11.3080 11.3080i 0.426490 0.426490i
\(704\) −0.403497 −0.0152074
\(705\) −18.5930 20.0377i −0.700253 0.754665i
\(706\) −18.8636 −0.709942
\(707\) −19.0397 + 19.0397i −0.716061 + 0.716061i
\(708\) −9.47547 + 9.47547i −0.356110 + 0.356110i
\(709\) 19.6493 0.737944 0.368972 0.929440i \(-0.379710\pi\)
0.368972 + 0.929440i \(0.379710\pi\)
\(710\) −0.455675 + 12.1843i −0.0171012 + 0.457270i
\(711\) 0.383565i 0.0143848i
\(712\) 4.40639 4.40639i 0.165137 0.165137i
\(713\) 8.25480 13.7095i 0.309145 0.513425i
\(714\) 26.6425i 0.997070i
\(715\) 0.101394 2.71119i 0.00379193 0.101393i
\(716\) −2.77575 −0.103735
\(717\) −10.4923 10.4923i −0.391843 0.391843i
\(718\) 16.7358 + 16.7358i 0.624573 + 0.624573i
\(719\) 42.4908i 1.58464i 0.610105 + 0.792321i \(0.291127\pi\)
−0.610105 + 0.792321i \(0.708873\pi\)
\(720\) 1.63913 1.52094i 0.0610866 0.0566822i
\(721\) 36.9290 1.37531
\(722\) 5.74366 + 5.74366i 0.213757 + 0.213757i
\(723\) 6.73270 + 6.73270i 0.250392 + 0.250392i
\(724\) −21.2640 −0.790269
\(725\) 46.9722 + 3.51829i 1.74450 + 0.130666i
\(726\) 10.8372 0.402206
\(727\) −28.3443 + 28.3443i −1.05123 + 1.05123i −0.0526167 + 0.998615i \(0.516756\pi\)
−0.998615 + 0.0526167i \(0.983244\pi\)
\(728\) −8.08153 8.08153i −0.299521 0.299521i
\(729\) 1.00000i 0.0370370i
\(730\) −2.28376 2.46122i −0.0845258 0.0910937i
\(731\) 25.4709 0.942076
\(732\) −5.31121 + 5.31121i −0.196308 + 0.196308i
\(733\) 35.1881 + 35.1881i 1.29970 + 1.29970i 0.928587 + 0.371114i \(0.121024\pi\)
0.371114 + 0.928587i \(0.378976\pi\)
\(734\) 2.58800 0.0955248
\(735\) −0.622221 + 16.6376i −0.0229510 + 0.613688i
\(736\) −4.65445 + 1.15590i −0.171565 + 0.0426072i
\(737\) 1.85913 + 1.85913i 0.0684821 + 0.0684821i
\(738\) 4.02970 4.02970i 0.148335 0.148335i
\(739\) 7.24476i 0.266503i −0.991082 0.133251i \(-0.957458\pi\)
0.991082 0.133251i \(-0.0425417\pi\)
\(740\) −0.256608 + 6.86145i −0.00943308 + 0.252232i
\(741\) 15.6605i 0.575302i
\(742\) 5.61022 + 5.61022i 0.205957 + 0.205957i
\(743\) 38.2888 + 38.2888i 1.40468 + 1.40468i 0.784309 + 0.620370i \(0.213017\pi\)
0.620370 + 0.784309i \(0.286983\pi\)
\(744\) 3.33683i 0.122334i
\(745\) −16.9480 18.2649i −0.620926 0.669173i
\(746\) 7.03623i 0.257615i
\(747\) −12.3708 + 12.3708i −0.452623 + 0.452623i
\(748\) 2.00000 2.00000i 0.0731272 0.0731272i
\(749\) 16.9133i 0.617997i
\(750\) 8.74075 6.97132i 0.319167 0.254557i
\(751\) 24.3210i 0.887484i 0.896155 + 0.443742i \(0.146349\pi\)
−0.896155 + 0.443742i \(0.853651\pi\)
\(752\) −8.64413 8.64413i −0.315219 0.315219i
\(753\) 1.95018 + 1.95018i 0.0710686 + 0.0710686i
\(754\) 28.3285i 1.03166i
\(755\) −30.3660 32.7256i −1.10513 1.19101i
\(756\) 3.80076i 0.138232i
\(757\) −26.9257 + 26.9257i −0.978630 + 0.978630i −0.999776 0.0211465i \(-0.993268\pi\)
0.0211465 + 0.999776i \(0.493268\pi\)
\(758\) 2.49910 + 2.49910i 0.0907714 + 0.0907714i
\(759\) −1.87806 + 0.466404i −0.0681691 + 0.0169294i
\(760\) −11.6372 0.435213i −0.422126 0.0157868i
\(761\) −6.15795 −0.223226 −0.111613 0.993752i \(-0.535602\pi\)
−0.111613 + 0.993752i \(0.535602\pi\)
\(762\) −9.84286 9.84286i −0.356569 0.356569i
\(763\) 34.1051 34.1051i 1.23469 1.23469i
\(764\) 15.5937 0.564160
\(765\) −0.585786 + 15.6634i −0.0211792 + 0.566311i
\(766\) 19.5344i 0.705805i
\(767\) −28.4931 28.4931i −1.02882 1.02882i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) −23.1519 −0.834877 −0.417439 0.908705i \(-0.637072\pi\)
−0.417439 + 0.908705i \(0.637072\pi\)
\(770\) −2.51376 + 2.33251i −0.0905895 + 0.0840579i
\(771\) 6.10364 0.219817
\(772\) −6.99660 6.99660i −0.251813 0.251813i
\(773\) −7.51233 7.51233i −0.270200 0.270200i 0.558981 0.829181i \(-0.311193\pi\)
−0.829181 + 0.558981i \(0.811193\pi\)
\(774\) 3.63363 0.130608
\(775\) −1.24618 + 16.6375i −0.0447641 + 0.597638i
\(776\) 11.6762i 0.419150i
\(777\) 8.25259 + 8.25259i 0.296060 + 0.296060i
\(778\) 4.69013 + 4.69013i 0.168149 + 0.168149i
\(779\) −29.6794 −1.06337
\(780\) 4.57353 + 4.92890i 0.163759 + 0.176483i
\(781\) 2.20019i 0.0787291i
\(782\) 17.3411 28.8000i 0.620117 1.02988i
\(783\) −6.66148 + 6.66148i −0.238062 + 0.238062i
\(784\) 7.44578i 0.265921i
\(785\) −7.72610 0.288944i −0.275756 0.0103128i
\(786\) −1.09419 −0.0390284
\(787\) −8.97134 + 8.97134i −0.319794 + 0.319794i −0.848688 0.528894i \(-0.822607\pi\)
0.528894 + 0.848688i \(0.322607\pi\)
\(788\) −4.96503 + 4.96503i −0.176872 + 0.176872i
\(789\) −5.78994 −0.206127
\(790\) −0.0320534 + 0.857078i −0.00114041 + 0.0304935i
\(791\) 48.1876 1.71335
\(792\) 0.285316 0.285316i 0.0101382 0.0101382i
\(793\) −15.9710 15.9710i −0.567146 0.567146i
\(794\) 9.35499i 0.331996i
\(795\) −3.17495 3.42165i −0.112604 0.121354i
\(796\) 13.2209i 0.468601i
\(797\) 10.1932 10.1932i 0.361061 0.361061i −0.503142 0.864204i \(-0.667823\pi\)
0.864204 + 0.503142i \(0.167823\pi\)
\(798\) −13.9966 + 13.9966i −0.495474 + 0.495474i
\(799\) 85.6921 3.03157
\(800\) 3.78974 3.26158i 0.133987 0.115314i
\(801\) 6.23158i 0.220182i
\(802\) 6.94134 6.94134i 0.245107 0.245107i
\(803\) −0.428414 0.428414i −0.0151184 0.0151184i
\(804\) −6.51606 −0.229804
\(805\) −22.3149 + 34.1073i −0.786496 + 1.20213i
\(806\) −10.0340 −0.353431
\(807\) −21.5936 21.5936i −0.760129 0.760129i
\(808\) 5.00944 5.00944i 0.176231 0.176231i
\(809\) 20.1026i 0.706771i 0.935478 + 0.353385i \(0.114970\pi\)
−0.935478 + 0.353385i \(0.885030\pi\)
\(810\) −0.0835670 + 2.23451i −0.00293625 + 0.0785125i
\(811\) −48.2332 −1.69370 −0.846849 0.531833i \(-0.821503\pi\)
−0.846849 + 0.531833i \(0.821503\pi\)
\(812\) 25.3187 25.3187i 0.888512 0.888512i
\(813\) −10.1409 + 10.1409i −0.355657 + 0.355657i
\(814\) 1.23901i 0.0434273i
\(815\) −0.753743 0.0281888i −0.0264025 0.000987411i
\(816\) 7.00978i 0.245391i
\(817\) −13.3811 13.3811i −0.468146 0.468146i
\(818\) 1.15257 1.15257i 0.0402987 0.0402987i
\(819\) 11.4290 0.399362
\(820\) 9.34113 8.66763i 0.326207 0.302687i
\(821\) −12.0371 −0.420098 −0.210049 0.977691i \(-0.567362\pi\)
−0.210049 + 0.977691i \(0.567362\pi\)
\(822\) −13.9152 + 13.9152i −0.485348 + 0.485348i
\(823\) −25.7663 + 25.7663i −0.898157 + 0.898157i −0.995273 0.0971160i \(-0.969038\pi\)
0.0971160 + 0.995273i \(0.469038\pi\)
\(824\) −9.71622 −0.338481
\(825\) 1.52915 1.31604i 0.0532381 0.0458186i
\(826\) 50.9315i 1.77213i
\(827\) −7.09270 + 7.09270i −0.246637 + 0.246637i −0.819589 0.572952i \(-0.805798\pi\)
0.572952 + 0.819589i \(0.305798\pi\)
\(828\) 2.47384 4.10854i 0.0859720 0.142782i
\(829\) 18.4503i 0.640807i −0.947281 0.320403i \(-0.896182\pi\)
0.947281 0.320403i \(-0.103818\pi\)
\(830\) −28.6764 + 26.6088i −0.995371 + 0.923604i
\(831\) 3.52348 0.122228
\(832\) 2.12629 + 2.12629i 0.0737160 + 0.0737160i
\(833\) −36.9062 36.9062i −1.27872 1.27872i
\(834\) 19.8141i 0.686105i
\(835\) 0.760721 20.3410i 0.0263258 0.703929i
\(836\) −2.10139 −0.0726782
\(837\) −2.35950 2.35950i −0.0815561 0.0815561i
\(838\) −7.97221 7.97221i −0.275395 0.275395i
\(839\) −8.78459 −0.303278 −0.151639 0.988436i \(-0.548455\pi\)
−0.151639 + 0.988436i \(0.548455\pi\)
\(840\) 0.317618 8.49282i 0.0109589 0.293030i
\(841\) −59.7506 −2.06037
\(842\) 11.3867 11.3867i 0.392412 0.392412i
\(843\) −17.2354 17.2354i −0.593619 0.593619i
\(844\) 14.3412i 0.493643i
\(845\) 6.48726 6.01952i 0.223168 0.207078i
\(846\) 12.2247 0.420292
\(847\) 29.1254 29.1254i 1.00076 1.00076i
\(848\) −1.47608 1.47608i −0.0506887 0.0506887i
\(849\) −2.20097 −0.0755370
\(850\) −2.61789 + 34.9510i −0.0897928 + 1.19881i
\(851\) 3.54941 + 14.2923i 0.121672 + 0.489935i
\(852\) −3.85572 3.85572i −0.132095 0.132095i
\(853\) 24.3103 24.3103i 0.832367 0.832367i −0.155473 0.987840i \(-0.549690\pi\)
0.987840 + 0.155473i \(0.0496901\pi\)
\(854\) 28.5482i 0.976899i
\(855\) 8.53649 7.92100i 0.291942 0.270893i
\(856\) 4.44997i 0.152097i
\(857\) −0.739435 0.739435i −0.0252586 0.0252586i 0.694365 0.719623i \(-0.255685\pi\)
−0.719623 + 0.694365i \(0.755685\pi\)
\(858\) 0.857953 + 0.857953i 0.0292900 + 0.0292900i
\(859\) 30.8003i 1.05089i −0.850827 0.525446i \(-0.823899\pi\)
0.850827 0.525446i \(-0.176101\pi\)
\(860\) 8.11936 + 0.303651i 0.276868 + 0.0103544i
\(861\) 21.6600i 0.738170i
\(862\) 26.5640 26.5640i 0.904773 0.904773i
\(863\) 13.3147 13.3147i 0.453238 0.453238i −0.443190 0.896428i \(-0.646153\pi\)
0.896428 + 0.443190i \(0.146153\pi\)
\(864\) 1.00000i 0.0340207i
\(865\) 18.6276 + 0.696643i 0.633357 + 0.0236866i
\(866\) 27.5448i 0.936012i
\(867\) −22.7243 22.7243i −0.771758 0.771758i
\(868\) 8.96787 + 8.96787i 0.304389 + 0.304389i
\(869\) 0.154767i 0.00525012i
\(870\) −15.4418 + 14.3284i −0.523526 + 0.485780i
\(871\) 19.5940i 0.663918i
\(872\) −8.97323 + 8.97323i −0.303872 + 0.303872i
\(873\) 8.25631 + 8.25631i 0.279434 + 0.279434i
\(874\) −24.2401 + 6.01989i −0.819935 + 0.203626i
\(875\) 4.75540 42.2269i 0.160762 1.42753i
\(876\) 1.50154 0.0507324
\(877\) 28.5210 + 28.5210i 0.963087 + 0.963087i 0.999343 0.0362555i \(-0.0115430\pi\)
−0.0362555 + 0.999343i \(0.511543\pi\)
\(878\) 19.4594 19.4594i 0.656721 0.656721i
\(879\) 23.6172 0.796589
\(880\) 0.661382 0.613696i 0.0222952 0.0206877i
\(881\) 13.8180i 0.465540i −0.972532 0.232770i \(-0.925221\pi\)
0.972532 0.232770i \(-0.0747789\pi\)
\(882\) −5.26496 5.26496i −0.177280 0.177280i
\(883\) −36.0797 + 36.0797i −1.21418 + 1.21418i −0.244539 + 0.969639i \(0.578637\pi\)
−0.969639 + 0.244539i \(0.921363\pi\)
\(884\) −21.0786 −0.708951
\(885\) 1.11983 29.9431i 0.0376426 1.00653i
\(886\) 30.8820 1.03750
\(887\) −0.653908 0.653908i −0.0219561 0.0219561i 0.696044 0.718000i \(-0.254942\pi\)
−0.718000 + 0.696044i \(0.754942\pi\)
\(888\) −2.17130 2.17130i −0.0728640 0.0728640i
\(889\) −52.9062 −1.77442
\(890\) −0.520755 + 13.9245i −0.0174557 + 0.466750i
\(891\) 0.403497i 0.0135177i
\(892\) −10.4795 10.4795i −0.350879 0.350879i
\(893\) −45.0182 45.0182i −1.50648 1.50648i
\(894\) 11.1431 0.372680
\(895\) 4.54980 4.22175i 0.152083 0.141118i
\(896\) 3.80076i 0.126974i
\(897\) 12.3545 + 7.43893i 0.412505 + 0.248379i
\(898\) −2.70091 + 2.70091i −0.0901306 + 0.0901306i
\(899\) 31.4355i 1.04843i
\(900\) −0.373462 + 4.98603i −0.0124487 + 0.166201i
\(901\) 14.6328 0.487490
\(902\) 1.62597 1.62597i 0.0541389 0.0541389i
\(903\) 9.76553 9.76553i 0.324976 0.324976i
\(904\) −12.6784 −0.421678
\(905\) 34.8543 32.3413i 1.15860 1.07506i
\(906\) 19.9653 0.663301
\(907\) −5.71177 + 5.71177i −0.189656 + 0.189656i −0.795547 0.605891i \(-0.792817\pi\)
0.605891 + 0.795547i \(0.292817\pi\)
\(908\) 0.390578 + 0.390578i 0.0129618 + 0.0129618i
\(909\) 7.08442i 0.234975i
\(910\) 25.5382 + 0.955088i 0.846583 + 0.0316609i
\(911\) 40.5977i 1.34506i 0.740069 + 0.672531i \(0.234793\pi\)
−0.740069 + 0.672531i \(0.765207\pi\)
\(912\) 3.68258 3.68258i 0.121942 0.121942i
\(913\) −4.99157 + 4.99157i −0.165197 + 0.165197i
\(914\) −27.1102 −0.896726
\(915\) 0.627687 16.7838i 0.0207507 0.554855i
\(916\) 16.0170i 0.529218i
\(917\) −2.94068 + 2.94068i −0.0971098 + 0.0971098i
\(918\) −4.95666 4.95666i −0.163594 0.163594i
\(919\) 48.2150 1.59047 0.795233 0.606304i \(-0.207349\pi\)
0.795233 + 0.606304i \(0.207349\pi\)
\(920\) 5.87116 8.97382i 0.193566 0.295858i
\(921\) 3.32051 0.109415
\(922\) −16.6406 16.6406i −0.548029 0.548029i
\(923\) 11.5943 11.5943i 0.381630 0.381630i
\(924\) 1.53360i 0.0504516i
\(925\) −10.0153 11.6371i −0.329300 0.382624i
\(926\) 28.4179 0.933869
\(927\) 6.87041 6.87041i 0.225654 0.225654i
\(928\) −6.66148 + 6.66148i −0.218674 + 0.218674i
\(929\) 11.6567i 0.382444i 0.981547 + 0.191222i \(0.0612451\pi\)
−0.981547 + 0.191222i \(0.938755\pi\)
\(930\) −5.07513 5.46948i −0.166420 0.179351i
\(931\) 38.7773i 1.27087i
\(932\) −13.0826 13.0826i −0.428535 0.428535i
\(933\) 9.09045 9.09045i 0.297608 0.297608i
\(934\) −11.7987 −0.386064
\(935\) −0.236363 + 6.32014i −0.00772990 + 0.206691i
\(936\) −3.00703 −0.0982879
\(937\) −17.6289 + 17.6289i −0.575910 + 0.575910i −0.933774 0.357864i \(-0.883505\pi\)
0.357864 + 0.933774i \(0.383505\pi\)
\(938\) −17.5122 + 17.5122i −0.571794 + 0.571794i
\(939\) 4.78249 0.156071
\(940\) 27.3161 + 1.02158i 0.890952 + 0.0333202i
\(941\) 27.4365i 0.894403i 0.894433 + 0.447202i \(0.147579\pi\)
−0.894433 + 0.447202i \(0.852421\pi\)
\(942\) 2.44491 2.44491i 0.0796596 0.0796596i
\(943\) 14.0981 23.4140i 0.459097 0.762463i
\(944\) 13.4003i 0.436144i
\(945\) 5.78074 + 6.22992i 0.188048 + 0.202659i
\(946\) 1.46616 0.0476689
\(947\) −15.9301 15.9301i −0.517658 0.517658i 0.399204 0.916862i \(-0.369286\pi\)
−0.916862 + 0.399204i \(0.869286\pi\)
\(948\) −0.271221 0.271221i −0.00880886 0.00880886i
\(949\) 4.51519i 0.146569i
\(950\) 19.7368 16.9862i 0.640345 0.551104i
\(951\) 22.7716 0.738419
\(952\) 18.8391 + 18.8391i 0.610578 + 0.610578i
\(953\) 2.64543 + 2.64543i 0.0856937 + 0.0856937i 0.748654 0.662961i \(-0.230700\pi\)
−0.662961 + 0.748654i \(0.730700\pi\)
\(954\) 2.08749 0.0675849
\(955\) −25.5600 + 23.7171i −0.827102 + 0.767468i
\(956\) 14.8384 0.479908
\(957\) −2.68789 + 2.68789i −0.0868871 + 0.0868871i
\(958\) −14.9119 14.9119i −0.481783 0.481783i
\(959\) 74.7954i 2.41527i
\(960\) −0.0835670 + 2.23451i −0.00269711 + 0.0721184i
\(961\) −19.8656 −0.640825
\(962\) 6.52917 6.52917i 0.210509 0.210509i
\(963\) −3.14660 3.14660i −0.101398 0.101398i
\(964\) −9.52147 −0.306666
\(965\) 22.1097 + 0.826869i 0.711737 + 0.0266179i
\(966\) −4.39331 17.6904i −0.141353 0.569181i
\(967\) −15.6966 15.6966i −0.504768 0.504768i 0.408148 0.912916i \(-0.366175\pi\)
−0.912916 + 0.408148i \(0.866175\pi\)
\(968\) −7.66305 + 7.66305i −0.246300 + 0.246300i
\(969\) 36.5066i 1.17276i
\(970\) 17.7588 + 19.1387i 0.570201 + 0.614507i
\(971\) 25.6347i 0.822656i −0.911487 0.411328i \(-0.865065\pi\)
0.911487 0.411328i \(-0.134935\pi\)
\(972\) −0.707107 0.707107i −0.0226805 0.0226805i
\(973\) −53.2512 53.2512i −1.70715 1.70715i
\(974\) 1.21575i 0.0389552i
\(975\) −14.9932 1.12301i −0.480166 0.0359652i
\(976\) 7.51118i 0.240427i
\(977\) 7.40750 7.40750i 0.236987 0.236987i −0.578614 0.815601i \(-0.696406\pi\)
0.815601 + 0.578614i \(0.196406\pi\)
\(978\) 0.238521 0.238521i 0.00762706 0.00762706i
\(979\) 2.51443i 0.0803614i
\(980\) −11.3246 12.2046i −0.361751 0.389860i
\(981\) 12.6901i 0.405162i
\(982\) −19.5290 19.5290i −0.623197 0.623197i
\(983\) −13.6949 13.6949i −0.436800 0.436800i 0.454134 0.890933i \(-0.349949\pi\)
−0.890933 + 0.454134i \(0.849949\pi\)
\(984\) 5.69885i 0.181673i
\(985\) 0.586776 15.6898i 0.0186962 0.499920i
\(986\) 66.0374i 2.10306i
\(987\) 32.8543 32.8543i 1.04576 1.04576i
\(988\) 11.0736 + 11.0736i 0.352299 + 0.352299i
\(989\) 16.9125 4.20012i 0.537787 0.133556i
\(990\) −0.0337191 + 0.901617i −0.00107166 + 0.0286553i
\(991\) −5.10343 −0.162116 −0.0810578 0.996709i \(-0.525830\pi\)
−0.0810578 + 0.996709i \(0.525830\pi\)
\(992\) −2.35950 2.35950i −0.0749140 0.0749140i
\(993\) 8.25599 8.25599i 0.261996 0.261996i
\(994\) −20.7248 −0.657351
\(995\) 20.1082 + 21.6706i 0.637472 + 0.687005i
\(996\) 17.4949i 0.554348i
\(997\) 14.7859 + 14.7859i 0.468274 + 0.468274i 0.901355 0.433081i \(-0.142574\pi\)
−0.433081 + 0.901355i \(0.642574\pi\)
\(998\) −13.2067 + 13.2067i −0.418051 + 0.418051i
\(999\) 3.07068 0.0971520
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 690.2.j.b.367.8 24
5.3 odd 4 inner 690.2.j.b.643.11 yes 24
23.22 odd 2 inner 690.2.j.b.367.11 yes 24
115.68 even 4 inner 690.2.j.b.643.8 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.2.j.b.367.8 24 1.1 even 1 trivial
690.2.j.b.367.11 yes 24 23.22 odd 2 inner
690.2.j.b.643.8 yes 24 115.68 even 4 inner
690.2.j.b.643.11 yes 24 5.3 odd 4 inner