Properties

Label 201.3.g.b.29.11
Level $201$
Weight $3$
Character 201.29
Analytic conductor $5.477$
Analytic rank $0$
Dimension $84$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [201,3,Mod(29,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.29");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.g (of order \(6\), 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: \(5.47685331364\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(42\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 29.11
Character \(\chi\) \(=\) 201.29
Dual form 201.3.g.b.104.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.19394 - 1.26667i) q^{2} +(-1.19967 - 2.74969i) q^{3} +(1.20891 + 2.09389i) q^{4} -2.77685i q^{5} +(-0.850943 + 7.55223i) q^{6} +(5.01703 + 8.68975i) q^{7} +4.00822i q^{8} +(-6.12157 + 6.59745i) q^{9} +O(q^{10})\) \(q+(-2.19394 - 1.26667i) q^{2} +(-1.19967 - 2.74969i) q^{3} +(1.20891 + 2.09389i) q^{4} -2.77685i q^{5} +(-0.850943 + 7.55223i) q^{6} +(5.01703 + 8.68975i) q^{7} +4.00822i q^{8} +(-6.12157 + 6.59745i) q^{9} +(-3.51736 + 6.09224i) q^{10} +(-1.08300 + 0.625270i) q^{11} +(4.30725 - 5.83610i) q^{12} +(-7.44610 + 12.8970i) q^{13} -25.4197i q^{14} +(-7.63548 + 3.33131i) q^{15} +(9.91272 - 17.1693i) q^{16} +(16.3077 + 9.41524i) q^{17} +(21.7871 - 6.72037i) q^{18} +(-4.57594 + 7.92577i) q^{19} +(5.81442 - 3.35695i) q^{20} +(17.8753 - 24.2201i) q^{21} +3.16805 q^{22} +(-18.7825 - 10.8441i) q^{23} +(11.0213 - 4.80855i) q^{24} +17.2891 q^{25} +(32.6725 - 18.8635i) q^{26} +(25.4848 + 8.91765i) q^{27} +(-12.1302 + 21.0102i) q^{28} +(-26.7578 + 15.4486i) q^{29} +(20.9714 + 2.36294i) q^{30} +(16.2900 + 28.2151i) q^{31} +(-29.6109 + 17.0958i) q^{32} +(3.01854 + 2.22779i) q^{33} +(-23.8520 - 41.3129i) q^{34} +(24.1302 - 13.9316i) q^{35} +(-21.2147 - 4.84219i) q^{36} +(19.7928 - 34.2821i) q^{37} +(20.0787 - 11.5924i) q^{38} +(44.3957 + 5.00226i) q^{39} +11.1302 q^{40} +(-11.4380 + 6.60376i) q^{41} +(-69.8962 + 30.4953i) q^{42} +16.8077 q^{43} +(-2.61849 - 1.51179i) q^{44} +(18.3201 + 16.9987i) q^{45} +(27.4718 + 47.5825i) q^{46} +(-10.7896 + 6.22939i) q^{47} +(-59.1023 - 6.65932i) q^{48} +(-25.8412 + 44.7583i) q^{49} +(-37.9312 - 21.8996i) q^{50} +(6.32512 - 56.1362i) q^{51} -36.0065 q^{52} -16.9415i q^{53} +(-44.6164 - 51.8456i) q^{54} +(1.73628 + 3.00733i) q^{55} +(-34.8304 + 20.1093i) q^{56} +(27.2830 + 3.07410i) q^{57} +78.2733 q^{58} +65.1807i q^{59} +(-16.2060 - 11.9606i) q^{60} +(-45.2012 + 78.2908i) q^{61} -82.5362i q^{62} +(-88.0423 - 20.0954i) q^{63} +7.31748 q^{64} +(35.8131 + 20.6767i) q^{65} +(-3.80062 - 8.71114i) q^{66} +(-18.1078 - 64.5066i) q^{67} +45.5286i q^{68} +(-7.28501 + 64.6554i) q^{69} -70.5867 q^{70} +(-54.8245 + 31.6529i) q^{71} +(-26.4440 - 24.5366i) q^{72} +(-27.6669 + 47.9204i) q^{73} +(-86.8483 + 50.1419i) q^{74} +(-20.7412 - 47.5396i) q^{75} -22.1276 q^{76} +(-10.8669 - 6.27400i) q^{77} +(-91.0651 - 67.2093i) q^{78} +(56.8153 + 98.4069i) q^{79} +(-47.6767 - 27.5261i) q^{80} +(-6.05267 - 80.7735i) q^{81} +33.4591 q^{82} +(110.147 + 63.5935i) q^{83} +(72.3238 + 8.14904i) q^{84} +(26.1447 - 45.2840i) q^{85} +(-36.8751 - 21.2899i) q^{86} +(74.5795 + 55.0424i) q^{87} +(-2.50622 - 4.34090i) q^{88} +59.3003i q^{89} +(-18.6615 - 60.4997i) q^{90} -149.429 q^{91} -52.4380i q^{92} +(58.0401 - 78.6413i) q^{93} +31.5623 q^{94} +(22.0087 + 12.7067i) q^{95} +(82.5316 + 60.9113i) q^{96} +(84.9987 - 147.222i) q^{97} +(113.388 - 65.4645i) q^{98} +(2.50448 - 10.9727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q - 6 q^{3} + 82 q^{4} + 3 q^{6} - 10 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q - 6 q^{3} + 82 q^{4} + 3 q^{6} - 10 q^{7} + 2 q^{9} + 6 q^{10} - 58 q^{12} - 6 q^{13} + 78 q^{15} - 130 q^{16} + 11 q^{18} + 72 q^{19} - 36 q^{21} + 140 q^{22} + 72 q^{24} - 428 q^{25} + 138 q^{27} - 8 q^{28} + 29 q^{30} - 28 q^{31} - 30 q^{33} - 54 q^{34} + 105 q^{36} - 24 q^{37} - 103 q^{39} + 128 q^{40} + 252 q^{42} + 148 q^{43} + 276 q^{45} - 146 q^{46} + 137 q^{48} - 176 q^{49} + 15 q^{51} - 792 q^{52} + 72 q^{54} + 28 q^{55} - 205 q^{57} - 120 q^{58} - 64 q^{60} + 162 q^{61} - 106 q^{63} - 604 q^{64} - 462 q^{66} - 460 q^{67} + 101 q^{69} + 636 q^{70} + 212 q^{72} + 238 q^{73} + 628 q^{75} + 40 q^{76} + 96 q^{78} + 462 q^{79} - 726 q^{81} - 344 q^{82} + 385 q^{84} - 94 q^{85} - 91 q^{87} + 234 q^{88} + 482 q^{90} - 536 q^{91} + 281 q^{93} + 580 q^{94} + 40 q^{96} + 68 q^{97} + 379 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.19394 1.26667i −1.09697 0.633335i −0.161545 0.986865i \(-0.551648\pi\)
−0.935423 + 0.353530i \(0.884981\pi\)
\(3\) −1.19967 2.74969i −0.399891 0.916563i
\(4\) 1.20891 + 2.09389i 0.302227 + 0.523472i
\(5\) 2.77685i 0.555370i −0.960672 0.277685i \(-0.910433\pi\)
0.960672 0.277685i \(-0.0895672\pi\)
\(6\) −0.850943 + 7.55223i −0.141824 + 1.25871i
\(7\) 5.01703 + 8.68975i 0.716719 + 1.24139i 0.962293 + 0.272015i \(0.0876902\pi\)
−0.245574 + 0.969378i \(0.578977\pi\)
\(8\) 4.00822i 0.501027i
\(9\) −6.12157 + 6.59745i −0.680175 + 0.733050i
\(10\) −3.51736 + 6.09224i −0.351736 + 0.609224i
\(11\) −1.08300 + 0.625270i −0.0984546 + 0.0568428i −0.548419 0.836204i \(-0.684770\pi\)
0.449964 + 0.893047i \(0.351437\pi\)
\(12\) 4.30725 5.83610i 0.358937 0.486341i
\(13\) −7.44610 + 12.8970i −0.572777 + 0.992078i 0.423503 + 0.905895i \(0.360800\pi\)
−0.996279 + 0.0861835i \(0.972533\pi\)
\(14\) 25.4197i 1.81569i
\(15\) −7.63548 + 3.33131i −0.509032 + 0.222087i
\(16\) 9.91272 17.1693i 0.619545 1.07308i
\(17\) 16.3077 + 9.41524i 0.959275 + 0.553838i 0.895950 0.444155i \(-0.146496\pi\)
0.0633251 + 0.997993i \(0.479830\pi\)
\(18\) 21.7871 6.72037i 1.21040 0.373354i
\(19\) −4.57594 + 7.92577i −0.240839 + 0.417146i −0.960954 0.276710i \(-0.910756\pi\)
0.720114 + 0.693855i \(0.244089\pi\)
\(20\) 5.81442 3.35695i 0.290721 0.167848i
\(21\) 17.8753 24.2201i 0.851206 1.15334i
\(22\) 3.16805 0.144002
\(23\) −18.7825 10.8441i −0.816631 0.471482i 0.0326224 0.999468i \(-0.489614\pi\)
−0.849253 + 0.527986i \(0.822947\pi\)
\(24\) 11.0213 4.80855i 0.459223 0.200356i
\(25\) 17.2891 0.691564
\(26\) 32.6725 18.8635i 1.25664 0.725519i
\(27\) 25.4848 + 8.91765i 0.943882 + 0.330283i
\(28\) −12.1302 + 21.0102i −0.433223 + 0.750364i
\(29\) −26.7578 + 15.4486i −0.922683 + 0.532711i −0.884490 0.466559i \(-0.845494\pi\)
−0.0381931 + 0.999270i \(0.512160\pi\)
\(30\) 20.9714 + 2.36294i 0.699048 + 0.0787648i
\(31\) 16.2900 + 28.2151i 0.525484 + 0.910165i 0.999559 + 0.0296807i \(0.00944903\pi\)
−0.474076 + 0.880484i \(0.657218\pi\)
\(32\) −29.6109 + 17.0958i −0.925340 + 0.534245i
\(33\) 3.01854 + 2.22779i 0.0914710 + 0.0675089i
\(34\) −23.8520 41.3129i −0.701530 1.21508i
\(35\) 24.1302 13.9316i 0.689433 0.398044i
\(36\) −21.2147 4.84219i −0.589298 0.134505i
\(37\) 19.7928 34.2821i 0.534941 0.926544i −0.464226 0.885717i \(-0.653667\pi\)
0.999166 0.0408274i \(-0.0129994\pi\)
\(38\) 20.0787 11.5924i 0.528386 0.305064i
\(39\) 44.3957 + 5.00226i 1.13835 + 0.128263i
\(40\) 11.1302 0.278256
\(41\) −11.4380 + 6.60376i −0.278977 + 0.161067i −0.632960 0.774184i \(-0.718160\pi\)
0.353983 + 0.935252i \(0.384827\pi\)
\(42\) −69.8962 + 30.4953i −1.66420 + 0.726078i
\(43\) 16.8077 0.390878 0.195439 0.980716i \(-0.437387\pi\)
0.195439 + 0.980716i \(0.437387\pi\)
\(44\) −2.61849 1.51179i −0.0595112 0.0343588i
\(45\) 18.3201 + 16.9987i 0.407114 + 0.377749i
\(46\) 27.4718 + 47.5825i 0.597212 + 1.03440i
\(47\) −10.7896 + 6.22939i −0.229566 + 0.132540i −0.610372 0.792115i \(-0.708980\pi\)
0.380806 + 0.924655i \(0.375647\pi\)
\(48\) −59.1023 6.65932i −1.23130 0.138736i
\(49\) −25.8412 + 44.7583i −0.527371 + 0.913434i
\(50\) −37.9312 21.8996i −0.758624 0.437992i
\(51\) 6.32512 56.1362i 0.124022 1.10071i
\(52\) −36.0065 −0.692434
\(53\) 16.9415i 0.319650i −0.987145 0.159825i \(-0.948907\pi\)
0.987145 0.159825i \(-0.0510930\pi\)
\(54\) −44.6164 51.8456i −0.826229 0.960104i
\(55\) 1.73628 + 3.00733i 0.0315688 + 0.0546788i
\(56\) −34.8304 + 20.1093i −0.621972 + 0.359096i
\(57\) 27.2830 + 3.07410i 0.478650 + 0.0539316i
\(58\) 78.2733 1.34954
\(59\) 65.1807i 1.10476i 0.833593 + 0.552379i \(0.186280\pi\)
−0.833593 + 0.552379i \(0.813720\pi\)
\(60\) −16.2060 11.9606i −0.270100 0.199343i
\(61\) −45.2012 + 78.2908i −0.741004 + 1.28346i 0.211035 + 0.977478i \(0.432317\pi\)
−0.952039 + 0.305977i \(0.901017\pi\)
\(62\) 82.5362i 1.33123i
\(63\) −88.0423 20.0954i −1.39750 0.318974i
\(64\) 7.31748 0.114336
\(65\) 35.8131 + 20.6767i 0.550971 + 0.318103i
\(66\) −3.80062 8.71114i −0.0575851 0.131987i
\(67\) −18.1078 64.5066i −0.270266 0.962786i
\(68\) 45.5286i 0.669538i
\(69\) −7.28501 + 64.6554i −0.105580 + 0.937035i
\(70\) −70.5867 −1.00838
\(71\) −54.8245 + 31.6529i −0.772176 + 0.445816i −0.833650 0.552293i \(-0.813753\pi\)
0.0614745 + 0.998109i \(0.480420\pi\)
\(72\) −26.4440 24.5366i −0.367278 0.340786i
\(73\) −27.6669 + 47.9204i −0.378998 + 0.656444i −0.990917 0.134477i \(-0.957065\pi\)
0.611919 + 0.790921i \(0.290398\pi\)
\(74\) −86.8483 + 50.1419i −1.17363 + 0.677593i
\(75\) −20.7412 47.5396i −0.276550 0.633862i
\(76\) −22.1276 −0.291152
\(77\) −10.8669 6.27400i −0.141128 0.0814805i
\(78\) −91.0651 67.2093i −1.16750 0.861658i
\(79\) 56.8153 + 98.4069i 0.719181 + 1.24566i 0.961325 + 0.275417i \(0.0888159\pi\)
−0.242144 + 0.970240i \(0.577851\pi\)
\(80\) −47.6767 27.5261i −0.595959 0.344077i
\(81\) −6.05267 80.7735i −0.0747243 0.997204i
\(82\) 33.4591 0.408038
\(83\) 110.147 + 63.5935i 1.32707 + 0.766186i 0.984846 0.173431i \(-0.0554853\pi\)
0.342228 + 0.939617i \(0.388819\pi\)
\(84\) 72.3238 + 8.14904i 0.860998 + 0.0970124i
\(85\) 26.1447 45.2840i 0.307585 0.532753i
\(86\) −36.8751 21.2899i −0.428780 0.247556i
\(87\) 74.5795 + 55.0424i 0.857236 + 0.632671i
\(88\) −2.50622 4.34090i −0.0284798 0.0493284i
\(89\) 59.3003i 0.666295i 0.942875 + 0.333148i \(0.108111\pi\)
−0.942875 + 0.333148i \(0.891889\pi\)
\(90\) −18.6615 60.4997i −0.207350 0.672218i
\(91\) −149.429 −1.64208
\(92\) 52.4380i 0.569978i
\(93\) 58.0401 78.6413i 0.624087 0.845605i
\(94\) 31.5623 0.335769
\(95\) 22.0087 + 12.7067i 0.231670 + 0.133755i
\(96\) 82.5316 + 60.9113i 0.859704 + 0.634493i
\(97\) 84.9987 147.222i 0.876275 1.51775i 0.0208771 0.999782i \(-0.493354\pi\)
0.855398 0.517971i \(-0.173313\pi\)
\(98\) 113.388 65.4645i 1.15702 0.668005i
\(99\) 2.50448 10.9727i 0.0252977 0.110835i
\(100\) 20.9009 + 36.2014i 0.209009 + 0.362014i
\(101\) 169.624 97.9327i 1.67945 0.969631i 0.717439 0.696621i \(-0.245314\pi\)
0.962011 0.273010i \(-0.0880192\pi\)
\(102\) −84.9830 + 115.147i −0.833166 + 1.12890i
\(103\) −31.8431 55.1539i −0.309156 0.535475i 0.669022 0.743243i \(-0.266713\pi\)
−0.978178 + 0.207768i \(0.933380\pi\)
\(104\) −51.6941 29.8456i −0.497058 0.286977i
\(105\) −67.2557 49.6371i −0.640531 0.472734i
\(106\) −21.4592 + 37.1685i −0.202446 + 0.350646i
\(107\) 172.192i 1.60927i 0.593769 + 0.804635i \(0.297639\pi\)
−0.593769 + 0.804635i \(0.702361\pi\)
\(108\) 12.1362 + 64.1429i 0.112372 + 0.593916i
\(109\) 83.3060 0.764275 0.382138 0.924105i \(-0.375188\pi\)
0.382138 + 0.924105i \(0.375188\pi\)
\(110\) 8.79719i 0.0799745i
\(111\) −118.010 13.2967i −1.06315 0.119790i
\(112\) 198.930 1.77616
\(113\) −4.47920 + 2.58607i −0.0396390 + 0.0228856i −0.519689 0.854356i \(-0.673952\pi\)
0.480050 + 0.877241i \(0.340619\pi\)
\(114\) −55.9634 41.3030i −0.490907 0.362307i
\(115\) −30.1124 + 52.1563i −0.261847 + 0.453533i
\(116\) −64.6954 37.3519i −0.557719 0.321999i
\(117\) −39.5056 128.075i −0.337655 1.09466i
\(118\) 82.5624 143.002i 0.699681 1.21188i
\(119\) 188.946i 1.58778i
\(120\) −13.3526 30.6047i −0.111272 0.255039i
\(121\) −59.7181 + 103.435i −0.493538 + 0.854833i
\(122\) 198.337 114.510i 1.62572 0.938607i
\(123\) 31.8802 + 23.5287i 0.259188 + 0.191290i
\(124\) −39.3862 + 68.2189i −0.317631 + 0.550152i
\(125\) 117.431i 0.939444i
\(126\) 167.705 + 155.609i 1.33099 + 1.23499i
\(127\) −28.0620 48.6048i −0.220960 0.382715i 0.734139 0.678999i \(-0.237586\pi\)
−0.955100 + 0.296284i \(0.904252\pi\)
\(128\) 102.389 + 59.1146i 0.799917 + 0.461833i
\(129\) −20.1638 46.2160i −0.156308 0.358264i
\(130\) −52.3811 90.7268i −0.402932 0.697899i
\(131\) 145.127i 1.10784i 0.832570 + 0.553919i \(0.186868\pi\)
−0.832570 + 0.553919i \(0.813132\pi\)
\(132\) −1.01561 + 9.01369i −0.00769403 + 0.0682855i
\(133\) −91.8306 −0.690456
\(134\) −41.9812 + 164.460i −0.313293 + 1.22731i
\(135\) 24.7630 70.7676i 0.183430 0.524204i
\(136\) −37.7383 + 65.3647i −0.277488 + 0.480623i
\(137\) 128.963i 0.941339i 0.882310 + 0.470670i \(0.155988\pi\)
−0.882310 + 0.470670i \(0.844012\pi\)
\(138\) 97.8799 132.622i 0.709275 0.961030i
\(139\) −45.3889 −0.326539 −0.163269 0.986582i \(-0.552204\pi\)
−0.163269 + 0.986582i \(0.552204\pi\)
\(140\) 58.3422 + 33.6839i 0.416730 + 0.240599i
\(141\) 30.0729 + 22.1949i 0.213283 + 0.157410i
\(142\) 160.375 1.12940
\(143\) 18.6233i 0.130233i
\(144\) 52.5923 + 170.502i 0.365225 + 1.18404i
\(145\) 42.8986 + 74.3025i 0.295852 + 0.512431i
\(146\) 121.399 70.0896i 0.831498 0.480066i
\(147\) 154.072 + 17.3600i 1.04811 + 0.118095i
\(148\) 95.7106 0.646693
\(149\) 266.822i 1.79075i −0.445309 0.895377i \(-0.646906\pi\)
0.445309 0.895377i \(-0.353094\pi\)
\(150\) −14.7120 + 130.571i −0.0980803 + 0.870475i
\(151\) −92.5843 + 160.361i −0.613141 + 1.06199i 0.377566 + 0.925983i \(0.376761\pi\)
−0.990708 + 0.136009i \(0.956572\pi\)
\(152\) −31.7682 18.3414i −0.209001 0.120667i
\(153\) −161.945 + 49.9530i −1.05847 + 0.326490i
\(154\) 15.8942 + 27.5295i 0.103209 + 0.178763i
\(155\) 78.3492 45.2349i 0.505479 0.291838i
\(156\) 43.1961 + 99.0068i 0.276898 + 0.634659i
\(157\) 51.8928 89.8810i 0.330528 0.572490i −0.652088 0.758143i \(-0.726107\pi\)
0.982615 + 0.185653i \(0.0594400\pi\)
\(158\) 287.865i 1.82193i
\(159\) −46.5837 + 20.3242i −0.292980 + 0.127825i
\(160\) 47.4726 + 82.2250i 0.296704 + 0.513906i
\(161\) 217.620i 1.35168i
\(162\) −89.0343 + 184.879i −0.549594 + 1.14123i
\(163\) −61.1178 105.859i −0.374956 0.649443i 0.615365 0.788243i \(-0.289009\pi\)
−0.990320 + 0.138800i \(0.955675\pi\)
\(164\) −27.6551 15.9667i −0.168628 0.0973577i
\(165\) 6.18625 8.38205i 0.0374924 0.0508003i
\(166\) −161.104 279.040i −0.970505 1.68096i
\(167\) 10.5432 6.08710i 0.0631327 0.0364497i −0.468101 0.883675i \(-0.655062\pi\)
0.531234 + 0.847225i \(0.321728\pi\)
\(168\) 97.0795 + 71.6482i 0.577854 + 0.426477i
\(169\) −26.3887 45.7066i −0.156146 0.270454i
\(170\) −114.720 + 66.2335i −0.674822 + 0.389609i
\(171\) −24.2779 78.7077i −0.141976 0.460279i
\(172\) 20.3190 + 35.1935i 0.118134 + 0.204613i
\(173\) −144.428 83.3855i −0.834843 0.481997i 0.0206648 0.999786i \(-0.493422\pi\)
−0.855508 + 0.517789i \(0.826755\pi\)
\(174\) −93.9023 215.227i −0.539668 1.23694i
\(175\) 86.7399 + 150.238i 0.495657 + 0.858502i
\(176\) 24.7925i 0.140867i
\(177\) 179.227 78.1954i 1.01258 0.441782i
\(178\) 75.1139 130.101i 0.421988 0.730905i
\(179\) 60.5265i 0.338137i 0.985604 + 0.169068i \(0.0540759\pi\)
−0.985604 + 0.169068i \(0.945924\pi\)
\(180\) −13.4460 + 58.9102i −0.0747002 + 0.327279i
\(181\) −148.745 257.635i −0.821798 1.42340i −0.904342 0.426809i \(-0.859638\pi\)
0.0825436 0.996587i \(-0.473696\pi\)
\(182\) 327.838 + 189.278i 1.80131 + 1.03999i
\(183\) 269.502 + 30.3660i 1.47269 + 0.165934i
\(184\) 43.4655 75.2844i 0.236225 0.409154i
\(185\) −95.1964 54.9617i −0.514575 0.297090i
\(186\) −226.949 + 99.0164i −1.22016 + 0.532346i
\(187\) −23.5483 −0.125927
\(188\) −26.0873 15.0615i −0.138762 0.0801143i
\(189\) 50.3659 + 266.197i 0.266486 + 1.40845i
\(190\) −32.1904 55.7555i −0.169423 0.293450i
\(191\) −90.2232 52.0904i −0.472373 0.272725i 0.244860 0.969559i \(-0.421258\pi\)
−0.717232 + 0.696834i \(0.754591\pi\)
\(192\) −8.77857 20.1208i −0.0457217 0.104796i
\(193\) −232.941 −1.20695 −0.603474 0.797382i \(-0.706217\pi\)
−0.603474 + 0.797382i \(0.706217\pi\)
\(194\) −372.964 + 215.331i −1.92249 + 1.10995i
\(195\) 13.8905 123.280i 0.0712335 0.632206i
\(196\) −124.958 −0.637543
\(197\) 180.905 104.446i 0.918300 0.530181i 0.0352074 0.999380i \(-0.488791\pi\)
0.883092 + 0.469199i \(0.155457\pi\)
\(198\) −19.3934 + 20.9010i −0.0979466 + 0.105561i
\(199\) −75.9392 + 131.531i −0.381604 + 0.660958i −0.991292 0.131684i \(-0.957962\pi\)
0.609687 + 0.792642i \(0.291295\pi\)
\(200\) 69.2984i 0.346492i
\(201\) −155.650 + 127.178i −0.774377 + 0.632725i
\(202\) −496.194 −2.45641
\(203\) −268.490 155.013i −1.32261 0.763608i
\(204\) 125.189 54.6194i 0.613674 0.267742i
\(205\) 18.3377 + 31.7618i 0.0894520 + 0.154935i
\(206\) 161.339i 0.783199i
\(207\) 186.522 57.5338i 0.901072 0.277941i
\(208\) 147.622 + 255.689i 0.709722 + 1.22927i
\(209\) 11.4448i 0.0547599i
\(210\) 84.6809 + 194.092i 0.403242 + 0.924245i
\(211\) −72.2837 + 125.199i −0.342577 + 0.593360i −0.984910 0.173065i \(-0.944633\pi\)
0.642334 + 0.766425i \(0.277966\pi\)
\(212\) 35.4735 20.4806i 0.167328 0.0966068i
\(213\) 152.807 + 112.777i 0.717404 + 0.529470i
\(214\) 218.110 377.778i 1.01921 1.76532i
\(215\) 46.6726i 0.217082i
\(216\) −35.7439 + 102.149i −0.165481 + 0.472910i
\(217\) −163.455 + 283.112i −0.753248 + 1.30466i
\(218\) −182.768 105.521i −0.838386 0.484042i
\(219\) 164.957 + 18.5865i 0.753230 + 0.0848698i
\(220\) −4.19801 + 7.27117i −0.0190819 + 0.0330508i
\(221\) −242.857 + 140.214i −1.09890 + 0.634451i
\(222\) 242.064 + 178.652i 1.09038 + 0.804739i
\(223\) 201.882 0.905299 0.452649 0.891689i \(-0.350479\pi\)
0.452649 + 0.891689i \(0.350479\pi\)
\(224\) −297.117 171.541i −1.32642 0.765807i
\(225\) −105.836 + 114.064i −0.470384 + 0.506951i
\(226\) 13.1028 0.0579769
\(227\) −131.863 + 76.1310i −0.580894 + 0.335379i −0.761488 0.648179i \(-0.775531\pi\)
0.180595 + 0.983558i \(0.442198\pi\)
\(228\) 26.5458 + 60.8439i 0.116429 + 0.266859i
\(229\) 176.561 305.813i 0.771010 1.33543i −0.166001 0.986126i \(-0.553085\pi\)
0.937010 0.349302i \(-0.113581\pi\)
\(230\) 132.130 76.2850i 0.574476 0.331674i
\(231\) −4.21485 + 37.4073i −0.0182461 + 0.161936i
\(232\) −61.9215 107.251i −0.266903 0.462289i
\(233\) −179.719 + 103.761i −0.771325 + 0.445325i −0.833347 0.552750i \(-0.813578\pi\)
0.0620219 + 0.998075i \(0.480245\pi\)
\(234\) −75.5564 + 331.030i −0.322891 + 1.41466i
\(235\) 17.2981 + 29.9612i 0.0736089 + 0.127494i
\(236\) −136.481 + 78.7973i −0.578309 + 0.333887i
\(237\) 202.429 274.280i 0.854130 1.15730i
\(238\) 239.332 414.536i 1.00560 1.74175i
\(239\) −99.6248 + 57.5184i −0.416840 + 0.240663i −0.693725 0.720240i \(-0.744031\pi\)
0.276884 + 0.960903i \(0.410698\pi\)
\(240\) −18.4919 + 164.118i −0.0770498 + 0.683827i
\(241\) 75.6578 0.313933 0.156966 0.987604i \(-0.449829\pi\)
0.156966 + 0.987604i \(0.449829\pi\)
\(242\) 262.035 151.286i 1.08279 0.625150i
\(243\) −214.841 + 113.545i −0.884119 + 0.467262i
\(244\) −218.576 −0.895804
\(245\) 124.287 + 71.7572i 0.507294 + 0.292886i
\(246\) −40.1400 92.0022i −0.163171 0.373993i
\(247\) −68.1459 118.032i −0.275894 0.477863i
\(248\) −113.092 + 65.2939i −0.456017 + 0.263282i
\(249\) 42.7218 379.162i 0.171574 1.52274i
\(250\) −148.746 + 257.635i −0.594983 + 1.03054i
\(251\) −167.194 96.5293i −0.666110 0.384579i 0.128491 0.991711i \(-0.458987\pi\)
−0.794601 + 0.607132i \(0.792320\pi\)
\(252\) −64.3575 208.644i −0.255387 0.827953i
\(253\) 27.1219 0.107201
\(254\) 142.181i 0.559768i
\(255\) −155.882 17.5639i −0.611302 0.0688781i
\(256\) −164.392 284.736i −0.642157 1.11225i
\(257\) −114.397 + 66.0469i −0.445123 + 0.256992i −0.705768 0.708443i \(-0.749398\pi\)
0.260645 + 0.965435i \(0.416065\pi\)
\(258\) −14.3024 + 126.936i −0.0554358 + 0.492000i
\(259\) 397.204 1.53361
\(260\) 99.9849i 0.384557i
\(261\) 61.8784 271.103i 0.237082 1.03871i
\(262\) 183.828 318.399i 0.701633 1.21526i
\(263\) 415.049i 1.57813i 0.614309 + 0.789066i \(0.289435\pi\)
−0.614309 + 0.789066i \(0.710565\pi\)
\(264\) −8.92948 + 12.0990i −0.0338238 + 0.0458295i
\(265\) −47.0439 −0.177524
\(266\) 201.471 + 116.319i 0.757408 + 0.437290i
\(267\) 163.057 71.1409i 0.610701 0.266445i
\(268\) 113.179 115.898i 0.422310 0.432456i
\(269\) 292.937i 1.08898i −0.838766 0.544492i \(-0.816722\pi\)
0.838766 0.544492i \(-0.183278\pi\)
\(270\) −143.968 + 123.893i −0.533213 + 0.458863i
\(271\) 32.6499 0.120479 0.0602397 0.998184i \(-0.480813\pi\)
0.0602397 + 0.998184i \(0.480813\pi\)
\(272\) 323.307 186.661i 1.18863 0.686254i
\(273\) 179.266 + 410.884i 0.656652 + 1.50507i
\(274\) 163.354 282.938i 0.596183 1.03262i
\(275\) −18.7241 + 10.8104i −0.0680876 + 0.0393104i
\(276\) −144.188 + 62.9084i −0.522420 + 0.227929i
\(277\) 315.387 1.13858 0.569290 0.822137i \(-0.307218\pi\)
0.569290 + 0.822137i \(0.307218\pi\)
\(278\) 99.5804 + 57.4928i 0.358203 + 0.206808i
\(279\) −285.868 65.2484i −1.02462 0.233865i
\(280\) 55.8407 + 96.7189i 0.199431 + 0.345425i
\(281\) 219.504 + 126.731i 0.781152 + 0.450999i 0.836839 0.547450i \(-0.184401\pi\)
−0.0556861 + 0.998448i \(0.517735\pi\)
\(282\) −37.8644 86.7865i −0.134271 0.307754i
\(283\) −265.254 −0.937294 −0.468647 0.883385i \(-0.655258\pi\)
−0.468647 + 0.883385i \(0.655258\pi\)
\(284\) −132.555 76.5309i −0.466744 0.269475i
\(285\) 8.53632 75.7609i 0.0299520 0.265828i
\(286\) −23.5896 + 40.8583i −0.0824810 + 0.142861i
\(287\) −114.770 66.2625i −0.399896 0.230880i
\(288\) 68.4762 300.010i 0.237765 1.04170i
\(289\) 32.7934 + 56.7999i 0.113472 + 0.196540i
\(290\) 217.353i 0.749494i
\(291\) −506.785 57.1017i −1.74153 0.196226i
\(292\) −133.787 −0.458173
\(293\) 520.418i 1.77617i −0.459680 0.888085i \(-0.652036\pi\)
0.459680 0.888085i \(-0.347964\pi\)
\(294\) −316.035 233.245i −1.07495 0.793352i
\(295\) 180.997 0.613549
\(296\) 137.410 + 79.3339i 0.464224 + 0.268020i
\(297\) −33.1760 + 6.27709i −0.111704 + 0.0211350i
\(298\) −337.976 + 585.392i −1.13415 + 1.96440i
\(299\) 279.713 161.492i 0.935494 0.540108i
\(300\) 74.4684 100.901i 0.248228 0.336336i
\(301\) 84.3249 + 146.055i 0.280149 + 0.485233i
\(302\) 406.248 234.548i 1.34519 0.776648i
\(303\) −472.778 348.927i −1.56032 1.15158i
\(304\) 90.7201 + 157.132i 0.298421 + 0.516881i
\(305\) 217.402 + 125.517i 0.712793 + 0.411531i
\(306\) 418.571 + 95.5375i 1.36788 + 0.312214i
\(307\) 230.654 399.504i 0.751315 1.30131i −0.195871 0.980630i \(-0.562753\pi\)
0.947186 0.320685i \(-0.103913\pi\)
\(308\) 30.3387i 0.0985024i
\(309\) −113.455 + 153.725i −0.367167 + 0.497493i
\(310\) −229.191 −0.739326
\(311\) 100.844i 0.324259i 0.986770 + 0.162129i \(0.0518362\pi\)
−0.986770 + 0.162129i \(0.948164\pi\)
\(312\) −20.0501 + 177.947i −0.0642632 + 0.570344i
\(313\) 212.866 0.680084 0.340042 0.940410i \(-0.389559\pi\)
0.340042 + 0.940410i \(0.389559\pi\)
\(314\) −227.699 + 131.462i −0.725157 + 0.418669i
\(315\) −55.8018 + 244.480i −0.177149 + 0.776129i
\(316\) −137.369 + 237.930i −0.434711 + 0.752942i
\(317\) 426.934 + 246.490i 1.34679 + 0.777572i 0.987794 0.155765i \(-0.0497843\pi\)
0.359000 + 0.933337i \(0.383118\pi\)
\(318\) 127.946 + 14.4162i 0.402345 + 0.0453340i
\(319\) 19.3191 33.4617i 0.0605616 0.104896i
\(320\) 20.3196i 0.0634986i
\(321\) 473.474 206.574i 1.47500 0.643532i
\(322\) −275.653 + 477.446i −0.856066 + 1.48275i
\(323\) −149.246 + 86.1672i −0.462062 + 0.266772i
\(324\) 161.814 110.321i 0.499425 0.340498i
\(325\) −128.736 + 222.978i −0.396112 + 0.686085i
\(326\) 309.664i 0.949891i
\(327\) −99.9399 229.066i −0.305627 0.700506i
\(328\) −26.4693 45.8462i −0.0806991 0.139775i
\(329\) −108.264 62.5060i −0.329069 0.189988i
\(330\) −24.1895 + 10.5537i −0.0733016 + 0.0319811i
\(331\) 20.7061 + 35.8641i 0.0625563 + 0.108351i 0.895607 0.444845i \(-0.146741\pi\)
−0.833051 + 0.553196i \(0.813408\pi\)
\(332\) 307.514i 0.926248i
\(333\) 105.012 + 340.443i 0.315350 + 1.02235i
\(334\) −30.8414 −0.0923395
\(335\) −179.125 + 50.2828i −0.534703 + 0.150098i
\(336\) −238.650 546.994i −0.710269 1.62796i
\(337\) −157.282 + 272.420i −0.466712 + 0.808368i −0.999277 0.0380207i \(-0.987895\pi\)
0.532565 + 0.846389i \(0.321228\pi\)
\(338\) 133.703i 0.395572i
\(339\) 12.4845 + 9.21398i 0.0368273 + 0.0271799i
\(340\) 126.426 0.371842
\(341\) −35.2841 20.3713i −0.103473 0.0597399i
\(342\) −46.4326 + 203.432i −0.135768 + 0.594830i
\(343\) −26.9152 −0.0784701
\(344\) 67.3690i 0.195840i
\(345\) 179.538 + 20.2294i 0.520401 + 0.0586359i
\(346\) 211.244 + 365.885i 0.610531 + 1.05747i
\(347\) 484.345 279.636i 1.39581 0.805869i 0.401856 0.915703i \(-0.368365\pi\)
0.993950 + 0.109834i \(0.0350320\pi\)
\(348\) −25.0928 + 222.702i −0.0721059 + 0.639949i
\(349\) −460.213 −1.31866 −0.659331 0.751853i \(-0.729160\pi\)
−0.659331 + 0.751853i \(0.729160\pi\)
\(350\) 439.483i 1.25567i
\(351\) −304.773 + 262.276i −0.868300 + 0.747226i
\(352\) 21.3791 37.0296i 0.0607360 0.105198i
\(353\) −106.133 61.2760i −0.300660 0.173586i 0.342079 0.939671i \(-0.388869\pi\)
−0.642740 + 0.766085i \(0.722202\pi\)
\(354\) −492.260 55.4651i −1.39056 0.156681i
\(355\) 87.8955 + 152.239i 0.247593 + 0.428844i
\(356\) −124.168 + 71.6885i −0.348787 + 0.201372i
\(357\) 519.543 226.673i 1.45530 0.634940i
\(358\) 76.6671 132.791i 0.214154 0.370925i
\(359\) 285.915i 0.796421i −0.917294 0.398211i \(-0.869631\pi\)
0.917294 0.398211i \(-0.130369\pi\)
\(360\) −68.1345 + 73.4311i −0.189263 + 0.203975i
\(361\) 138.621 + 240.099i 0.383993 + 0.665095i
\(362\) 753.646i 2.08189i
\(363\) 356.055 + 40.1183i 0.980869 + 0.110519i
\(364\) −180.646 312.888i −0.496280 0.859582i
\(365\) 133.068 + 76.8268i 0.364570 + 0.210484i
\(366\) −552.807 407.991i −1.51040 1.11473i
\(367\) 191.800 + 332.208i 0.522617 + 0.905199i 0.999654 + 0.0263155i \(0.00837745\pi\)
−0.477037 + 0.878883i \(0.658289\pi\)
\(368\) −372.371 + 214.989i −1.01188 + 0.584208i
\(369\) 26.4509 115.887i 0.0716826 0.314058i
\(370\) 139.237 + 241.165i 0.376315 + 0.651797i
\(371\) 147.217 84.9958i 0.396812 0.229099i
\(372\) 234.831 + 26.4595i 0.631267 + 0.0711276i
\(373\) −282.493 489.293i −0.757355 1.31178i −0.944195 0.329387i \(-0.893158\pi\)
0.186840 0.982390i \(-0.440175\pi\)
\(374\) 51.6635 + 29.8279i 0.138138 + 0.0797538i
\(375\) −322.897 + 140.878i −0.861060 + 0.375675i
\(376\) −24.9687 43.2471i −0.0664062 0.115019i
\(377\) 460.128i 1.22050i
\(378\) 226.684 647.816i 0.599693 1.71380i
\(379\) −133.340 + 230.951i −0.351820 + 0.609370i −0.986568 0.163349i \(-0.947770\pi\)
0.634748 + 0.772719i \(0.281104\pi\)
\(380\) 61.4450i 0.161697i
\(381\) −99.9828 + 135.471i −0.262422 + 0.355568i
\(382\) 131.963 + 228.566i 0.345452 + 0.598340i
\(383\) −74.0808 42.7706i −0.193422 0.111673i 0.400161 0.916445i \(-0.368954\pi\)
−0.593584 + 0.804772i \(0.702287\pi\)
\(384\) 39.7129 352.457i 0.103419 0.917857i
\(385\) −17.4220 + 30.1757i −0.0452519 + 0.0783786i
\(386\) 511.058 + 295.060i 1.32398 + 0.764403i
\(387\) −102.890 + 110.888i −0.265865 + 0.286533i
\(388\) 411.022 1.05933
\(389\) −103.918 59.9970i −0.267141 0.154234i 0.360447 0.932780i \(-0.382624\pi\)
−0.627588 + 0.778546i \(0.715958\pi\)
\(390\) −186.630 + 252.874i −0.478539 + 0.648396i
\(391\) −204.199 353.684i −0.522249 0.904562i
\(392\) −179.401 103.577i −0.457655 0.264227i
\(393\) 399.054 174.105i 1.01540 0.443014i
\(394\) −529.192 −1.34313
\(395\) 273.261 157.768i 0.691801 0.399412i
\(396\) 26.0032 8.02085i 0.0656647 0.0202547i
\(397\) 514.327 1.29553 0.647767 0.761839i \(-0.275703\pi\)
0.647767 + 0.761839i \(0.275703\pi\)
\(398\) 333.212 192.380i 0.837216 0.483367i
\(399\) 110.167 + 252.506i 0.276107 + 0.632846i
\(400\) 171.382 296.842i 0.428455 0.742105i
\(401\) 98.9815i 0.246837i −0.992355 0.123418i \(-0.960614\pi\)
0.992355 0.123418i \(-0.0393857\pi\)
\(402\) 502.578 81.8630i 1.25019 0.203639i
\(403\) −485.188 −1.20394
\(404\) 410.120 + 236.783i 1.01515 + 0.586097i
\(405\) −224.296 + 16.8074i −0.553818 + 0.0414996i
\(406\) 392.699 + 680.175i 0.967240 + 1.67531i
\(407\) 49.5034i 0.121630i
\(408\) 225.006 + 25.3524i 0.551486 + 0.0621383i
\(409\) 148.753 + 257.649i 0.363700 + 0.629948i 0.988567 0.150784i \(-0.0481798\pi\)
−0.624866 + 0.780732i \(0.714847\pi\)
\(410\) 92.9111i 0.226612i
\(411\) 354.609 154.714i 0.862797 0.376433i
\(412\) 76.9907 133.352i 0.186871 0.323669i
\(413\) −566.404 + 327.013i −1.37144 + 0.791800i
\(414\) −482.093 110.036i −1.16448 0.265788i
\(415\) 176.590 305.862i 0.425517 0.737017i
\(416\) 509.189i 1.22401i
\(417\) 54.4518 + 124.805i 0.130580 + 0.299293i
\(418\) −14.4968 + 25.1092i −0.0346813 + 0.0600698i
\(419\) 543.436 + 313.753i 1.29698 + 0.748813i 0.979882 0.199579i \(-0.0639573\pi\)
0.317101 + 0.948392i \(0.397291\pi\)
\(420\) 22.6287 200.833i 0.0538778 0.478173i
\(421\) −305.913 + 529.857i −0.726634 + 1.25857i 0.231664 + 0.972796i \(0.425583\pi\)
−0.958298 + 0.285771i \(0.907750\pi\)
\(422\) 317.172 183.119i 0.751592 0.433932i
\(423\) 24.9514 109.318i 0.0589867 0.258434i
\(424\) 67.9051 0.160153
\(425\) 281.945 + 162.781i 0.663400 + 0.383014i
\(426\) −192.398 440.982i −0.451638 1.03517i
\(427\) −907.104 −2.12436
\(428\) −360.551 + 208.164i −0.842408 + 0.486364i
\(429\) −51.2083 + 22.3419i −0.119367 + 0.0520789i
\(430\) −59.1188 + 102.397i −0.137486 + 0.238132i
\(431\) −220.871 + 127.520i −0.512462 + 0.295870i −0.733845 0.679317i \(-0.762276\pi\)
0.221383 + 0.975187i \(0.428943\pi\)
\(432\) 405.734 349.159i 0.939198 0.808238i
\(433\) −28.0102 48.5152i −0.0646888 0.112044i 0.831867 0.554975i \(-0.187272\pi\)
−0.896556 + 0.442931i \(0.853939\pi\)
\(434\) 717.219 414.087i 1.65258 0.954117i
\(435\) 152.844 207.096i 0.351367 0.476083i
\(436\) 100.709 + 174.433i 0.230984 + 0.400077i
\(437\) 171.895 99.2439i 0.393353 0.227103i
\(438\) −338.363 249.724i −0.772519 0.570146i
\(439\) 97.0820 168.151i 0.221144 0.383032i −0.734012 0.679137i \(-0.762354\pi\)
0.955155 + 0.296105i \(0.0956877\pi\)
\(440\) −12.0540 + 6.95940i −0.0273955 + 0.0158168i
\(441\) −137.102 444.477i −0.310888 1.00788i
\(442\) 710.417 1.60728
\(443\) 158.030 91.2386i 0.356727 0.205956i −0.310917 0.950437i \(-0.600636\pi\)
0.667644 + 0.744481i \(0.267303\pi\)
\(444\) −114.821 263.174i −0.258607 0.592735i
\(445\) 164.668 0.370041
\(446\) −442.916 255.717i −0.993084 0.573358i
\(447\) −733.678 + 320.099i −1.64134 + 0.716106i
\(448\) 36.7120 + 63.5871i 0.0819465 + 0.141935i
\(449\) 84.3847 48.7195i 0.187939 0.108507i −0.403078 0.915166i \(-0.632060\pi\)
0.591017 + 0.806659i \(0.298726\pi\)
\(450\) 376.680 116.189i 0.837066 0.258198i
\(451\) 8.25827 14.3037i 0.0183110 0.0317156i
\(452\) −10.8299 6.25263i −0.0239599 0.0138333i
\(453\) 552.013 + 62.1977i 1.21857 + 0.137302i
\(454\) 385.732 0.849629
\(455\) 414.943i 0.911962i
\(456\) −12.3217 + 109.356i −0.0270212 + 0.239816i
\(457\) −176.621 305.917i −0.386479 0.669402i 0.605494 0.795850i \(-0.292976\pi\)
−0.991973 + 0.126448i \(0.959642\pi\)
\(458\) −774.728 + 447.290i −1.69155 + 0.976615i
\(459\) 331.636 + 385.372i 0.722519 + 0.839590i
\(460\) −145.612 −0.316549
\(461\) 165.690i 0.359414i 0.983720 + 0.179707i \(0.0575150\pi\)
−0.983720 + 0.179707i \(0.942485\pi\)
\(462\) 56.6298 76.7305i 0.122575 0.166083i
\(463\) 354.700 614.359i 0.766091 1.32691i −0.173577 0.984820i \(-0.555532\pi\)
0.939668 0.342088i \(-0.111134\pi\)
\(464\) 612.552i 1.32015i
\(465\) −218.375 161.169i −0.469624 0.346600i
\(466\) 525.722 1.12816
\(467\) −481.494 277.991i −1.03104 0.595269i −0.113755 0.993509i \(-0.536288\pi\)
−0.917281 + 0.398240i \(0.869621\pi\)
\(468\) 220.417 237.551i 0.470976 0.507588i
\(469\) 469.699 480.984i 1.00149 1.02555i
\(470\) 87.6439i 0.186476i
\(471\) −309.399 34.8614i −0.656898 0.0740156i
\(472\) −261.258 −0.553513
\(473\) −18.2028 + 10.5094i −0.0384837 + 0.0222186i
\(474\) −791.539 + 345.343i −1.66991 + 0.728572i
\(475\) −79.1139 + 137.029i −0.166556 + 0.288483i
\(476\) −395.632 + 228.418i −0.831160 + 0.479870i
\(477\) 111.770 + 103.708i 0.234320 + 0.217418i
\(478\) 291.428 0.609681
\(479\) 5.43996 + 3.14076i 0.0113569 + 0.00655691i 0.505668 0.862728i \(-0.331246\pi\)
−0.494311 + 0.869285i \(0.664580\pi\)
\(480\) 169.142 229.178i 0.352378 0.477454i
\(481\) 294.758 + 510.536i 0.612803 + 1.06141i
\(482\) −165.989 95.8335i −0.344375 0.198825i
\(483\) −598.389 + 261.073i −1.23890 + 0.540524i
\(484\) −288.774 −0.596641
\(485\) −408.814 236.029i −0.842915 0.486657i
\(486\) 615.171 + 23.0226i 1.26578 + 0.0473716i
\(487\) −318.294 + 551.302i −0.653581 + 1.13204i 0.328666 + 0.944446i \(0.393401\pi\)
−0.982247 + 0.187590i \(0.939932\pi\)
\(488\) −313.807 181.176i −0.643046 0.371263i
\(489\) −217.758 + 295.051i −0.445314 + 0.603377i
\(490\) −181.785 314.861i −0.370990 0.642574i
\(491\) 395.028i 0.804538i −0.915522 0.402269i \(-0.868222\pi\)
0.915522 0.402269i \(-0.131778\pi\)
\(492\) −10.7263 + 95.1975i −0.0218015 + 0.193491i
\(493\) −581.810 −1.18014
\(494\) 345.273i 0.698934i
\(495\) −30.4695 6.95456i −0.0615546 0.0140496i
\(496\) 645.913 1.30224
\(497\) −550.112 317.607i −1.10687 0.639049i
\(498\) −574.002 + 777.742i −1.15261 + 1.56173i
\(499\) 443.847 768.765i 0.889472 1.54061i 0.0489713 0.998800i \(-0.484406\pi\)
0.840501 0.541810i \(-0.182261\pi\)
\(500\) 245.886 141.963i 0.491773 0.283925i
\(501\) −29.3860 21.6879i −0.0586546 0.0432892i
\(502\) 244.542 + 423.558i 0.487135 + 0.843742i
\(503\) 21.8411 12.6099i 0.0434216 0.0250695i −0.478132 0.878288i \(-0.658686\pi\)
0.521554 + 0.853218i \(0.325353\pi\)
\(504\) 80.5466 352.893i 0.159815 0.700184i
\(505\) −271.945 471.022i −0.538504 0.932717i
\(506\) −59.5038 34.3546i −0.117597 0.0678944i
\(507\) −94.0212 + 127.394i −0.185446 + 0.251270i
\(508\) 67.8486 117.517i 0.133560 0.231333i
\(509\) 468.439i 0.920311i 0.887838 + 0.460156i \(0.152206\pi\)
−0.887838 + 0.460156i \(0.847794\pi\)
\(510\) 319.748 + 235.985i 0.626956 + 0.462716i
\(511\) −555.222 −1.08654
\(512\) 360.007i 0.703138i
\(513\) −187.296 + 161.180i −0.365100 + 0.314191i
\(514\) 334.639 0.651048
\(515\) −153.154 + 88.4236i −0.297387 + 0.171696i
\(516\) 72.3951 98.0915i 0.140301 0.190100i
\(517\) 7.79010 13.4929i 0.0150679 0.0260984i
\(518\) −871.442 503.127i −1.68232 0.971288i
\(519\) −56.0180 + 497.167i −0.107934 + 0.957932i
\(520\) −82.8768 + 143.547i −0.159378 + 0.276051i
\(521\) 618.338i 1.18683i −0.804897 0.593414i \(-0.797780\pi\)
0.804897 0.593414i \(-0.202220\pi\)
\(522\) −479.156 + 516.404i −0.917923 + 0.989280i
\(523\) −204.530 + 354.256i −0.391070 + 0.677354i −0.992591 0.121503i \(-0.961228\pi\)
0.601521 + 0.798857i \(0.294562\pi\)
\(524\) −303.879 + 175.445i −0.579922 + 0.334818i
\(525\) 309.048 418.744i 0.588663 0.797608i
\(526\) 525.730 910.591i 0.999486 1.73116i
\(527\) 613.497i 1.16413i
\(528\) 68.1717 29.7429i 0.129113 0.0563312i
\(529\) −29.3116 50.7691i −0.0554094 0.0959718i
\(530\) 103.211 + 59.5891i 0.194739 + 0.112432i
\(531\) −430.026 399.008i −0.809842 0.751428i
\(532\) −111.015 192.283i −0.208674 0.361434i
\(533\) 196.689i 0.369022i
\(534\) −447.850 50.4612i −0.838669 0.0944966i
\(535\) 478.152 0.893741
\(536\) 258.557 72.5801i 0.482382 0.135411i
\(537\) 166.429 72.6119i 0.309924 0.135218i
\(538\) −371.054 + 642.685i −0.689692 + 1.19458i
\(539\) 64.6309i 0.119909i
\(540\) 178.115 33.7005i 0.329843 0.0624082i
\(541\) −776.475 −1.43526 −0.717629 0.696425i \(-0.754773\pi\)
−0.717629 + 0.696425i \(0.754773\pi\)
\(542\) −71.6319 41.3567i −0.132162 0.0763039i
\(543\) −529.969 + 718.081i −0.976003 + 1.32243i
\(544\) −643.846 −1.18354
\(545\) 231.328i 0.424456i
\(546\) 127.156 1128.52i 0.232886 2.06689i
\(547\) 510.885 + 884.879i 0.933976 + 1.61769i 0.776449 + 0.630180i \(0.217019\pi\)
0.157527 + 0.987515i \(0.449648\pi\)
\(548\) −270.035 + 155.905i −0.492765 + 0.284498i
\(549\) −239.817 777.476i −0.436825 1.41617i
\(550\) 54.7726 0.0995866
\(551\) 282.768i 0.513191i
\(552\) −259.153 29.1999i −0.469480 0.0528984i
\(553\) −570.088 + 987.421i −1.03090 + 1.78557i
\(554\) −691.939 399.491i −1.24899 0.721103i
\(555\) −36.9230 + 327.697i −0.0665280 + 0.590444i
\(556\) −54.8709 95.0393i −0.0986887 0.170934i
\(557\) 605.962 349.852i 1.08790 0.628101i 0.154885 0.987932i \(-0.450499\pi\)
0.933017 + 0.359832i \(0.117166\pi\)
\(558\) 544.529 + 505.252i 0.975858 + 0.905469i
\(559\) −125.152 + 216.770i −0.223886 + 0.387781i
\(560\) 552.398i 0.986425i
\(561\) 28.2502 + 64.7504i 0.0503569 + 0.115420i
\(562\) −321.052 556.078i −0.571266 0.989463i
\(563\) 315.468i 0.560333i −0.959951 0.280167i \(-0.909610\pi\)
0.959951 0.280167i \(-0.0903897\pi\)
\(564\) −10.1182 + 89.8007i −0.0179402 + 0.159221i
\(565\) 7.18113 + 12.4381i 0.0127100 + 0.0220143i
\(566\) 581.951 + 335.990i 1.02818 + 0.593621i
\(567\) 671.536 457.840i 1.18437 0.807477i
\(568\) −126.872 219.748i −0.223366 0.386881i
\(569\) −488.395 + 281.975i −0.858339 + 0.495562i −0.863456 0.504425i \(-0.831705\pi\)
0.00511664 + 0.999987i \(0.498371\pi\)
\(570\) −114.692 + 155.402i −0.201214 + 0.272635i
\(571\) 300.627 + 520.701i 0.526492 + 0.911910i 0.999524 + 0.0308649i \(0.00982616\pi\)
−0.473032 + 0.881045i \(0.656841\pi\)
\(572\) 38.9951 22.5138i 0.0681732 0.0393598i
\(573\) −34.9941 + 310.577i −0.0610717 + 0.542019i
\(574\) 167.866 + 290.752i 0.292449 + 0.506536i
\(575\) −324.733 187.484i −0.564752 0.326060i
\(576\) −44.7945 + 48.2767i −0.0777682 + 0.0838137i
\(577\) 487.957 + 845.166i 0.845679 + 1.46476i 0.885030 + 0.465534i \(0.154138\pi\)
−0.0393509 + 0.999225i \(0.512529\pi\)
\(578\) 166.154i 0.287464i
\(579\) 279.453 + 640.516i 0.482648 + 1.10624i
\(580\) −103.721 + 179.650i −0.178829 + 0.309741i
\(581\) 1276.20i 2.19656i
\(582\) 1039.53 + 767.208i 1.78613 + 1.31823i
\(583\) 10.5930 + 18.3476i 0.0181698 + 0.0314710i
\(584\) −192.075 110.895i −0.328896 0.189888i
\(585\) −355.646 + 109.701i −0.607942 + 0.187523i
\(586\) −659.198 + 1141.76i −1.12491 + 1.94840i
\(587\) 409.456 + 236.400i 0.697541 + 0.402725i 0.806431 0.591329i \(-0.201396\pi\)
−0.108890 + 0.994054i \(0.534730\pi\)
\(588\) 149.909 + 343.597i 0.254947 + 0.584348i
\(589\) −298.169 −0.506228
\(590\) −397.096 229.264i −0.673044 0.388582i
\(591\) −504.219 372.132i −0.853163 0.629665i
\(592\) −392.401 679.658i −0.662839 1.14807i
\(593\) 211.037 + 121.842i 0.355880 + 0.205468i 0.667272 0.744814i \(-0.267462\pi\)
−0.311392 + 0.950282i \(0.600795\pi\)
\(594\) 80.7370 + 28.2515i 0.135921 + 0.0475615i
\(595\) 524.676 0.881808
\(596\) 558.696 322.563i 0.937410 0.541214i
\(597\) 452.770 + 51.0157i 0.758410 + 0.0854534i
\(598\) −818.230 −1.36828
\(599\) 162.805 93.9954i 0.271794 0.156921i −0.357908 0.933757i \(-0.616510\pi\)
0.629703 + 0.776836i \(0.283177\pi\)
\(600\) 190.549 83.1354i 0.317582 0.138559i
\(601\) 529.729 917.517i 0.881412 1.52665i 0.0316409 0.999499i \(-0.489927\pi\)
0.849771 0.527151i \(-0.176740\pi\)
\(602\) 427.247i 0.709713i
\(603\) 536.428 + 275.417i 0.889598 + 0.456744i
\(604\) −447.703 −0.741230
\(605\) 287.223 + 165.828i 0.474749 + 0.274096i
\(606\) 595.270 + 1364.38i 0.982294 + 2.25145i
\(607\) −470.870 815.570i −0.775733 1.34361i −0.934382 0.356274i \(-0.884047\pi\)
0.158649 0.987335i \(-0.449286\pi\)
\(608\) 312.919i 0.514669i
\(609\) −104.137 + 924.227i −0.170996 + 1.51761i
\(610\) −317.978 550.753i −0.521275 0.902874i
\(611\) 185.538i 0.303664i
\(612\) −300.372 278.707i −0.490805 0.455403i
\(613\) −105.365 + 182.497i −0.171883 + 0.297711i −0.939078 0.343703i \(-0.888319\pi\)
0.767195 + 0.641414i \(0.221652\pi\)
\(614\) −1012.08 + 584.324i −1.64834 + 0.951668i
\(615\) 65.3358 88.5266i 0.106237 0.143946i
\(616\) 25.1476 43.5569i 0.0408240 0.0707092i
\(617\) 642.960i 1.04208i −0.853534 0.521038i \(-0.825545\pi\)
0.853534 0.521038i \(-0.174455\pi\)
\(618\) 443.632 193.554i 0.717851 0.313194i
\(619\) 286.851 496.840i 0.463410 0.802649i −0.535718 0.844397i \(-0.679959\pi\)
0.999128 + 0.0417475i \(0.0132925\pi\)
\(620\) 189.434 + 109.370i 0.305538 + 0.176403i
\(621\) −381.965 443.855i −0.615080 0.714743i
\(622\) 127.737 221.246i 0.205364 0.355702i
\(623\) −515.305 + 297.511i −0.827134 + 0.477546i
\(624\) 525.967 712.658i 0.842896 1.14208i
\(625\) 106.140 0.169824
\(626\) −467.015 269.631i −0.746031 0.430721i
\(627\) −31.4697 + 13.7300i −0.0501909 + 0.0218980i
\(628\) 250.934 0.399577
\(629\) 645.549 372.708i 1.02631 0.592541i
\(630\) 432.102 465.692i 0.685876 0.739194i
\(631\) 231.410 400.813i 0.366735 0.635203i −0.622318 0.782764i \(-0.713809\pi\)
0.989053 + 0.147561i \(0.0471423\pi\)
\(632\) −394.436 + 227.728i −0.624108 + 0.360329i
\(633\) 430.975 + 48.5599i 0.680845 + 0.0767139i
\(634\) −624.444 1081.57i −0.984928 1.70594i
\(635\) −134.968 + 77.9239i −0.212548 + 0.122715i
\(636\) −98.8720 72.9711i −0.155459 0.114734i
\(637\) −384.832 666.549i −0.604132 1.04639i
\(638\) −84.7700 + 48.9420i −0.132868 + 0.0767115i
\(639\) 126.784 555.467i 0.198409 0.869276i
\(640\) 164.152 284.320i 0.256488 0.444250i
\(641\) 619.718 357.795i 0.966799 0.558182i 0.0685403 0.997648i \(-0.478166\pi\)
0.898259 + 0.439467i \(0.144833\pi\)
\(642\) −1300.43 146.526i −2.02560 0.228233i
\(643\) 418.620 0.651042 0.325521 0.945535i \(-0.394460\pi\)
0.325521 + 0.945535i \(0.394460\pi\)
\(644\) 455.673 263.083i 0.707567 0.408514i
\(645\) −128.335 + 55.9918i −0.198969 + 0.0868090i
\(646\) 436.582 0.675823
\(647\) 686.744 + 396.492i 1.06143 + 0.612816i 0.925827 0.377948i \(-0.123370\pi\)
0.135601 + 0.990764i \(0.456703\pi\)
\(648\) 323.758 24.2604i 0.499626 0.0374389i
\(649\) −40.7555 70.5907i −0.0627975 0.108768i
\(650\) 564.879 326.133i 0.869044 0.501743i
\(651\) 974.562 + 109.808i 1.49702 + 0.168676i
\(652\) 147.771 255.948i 0.226643 0.392558i
\(653\) 1049.22 + 605.770i 1.60677 + 0.927672i 0.990086 + 0.140464i \(0.0448595\pi\)
0.616689 + 0.787207i \(0.288474\pi\)
\(654\) −70.8887 + 629.146i −0.108392 + 0.961997i
\(655\) 402.996 0.615261
\(656\) 261.845i 0.399154i
\(657\) −146.788 475.879i −0.223421 0.724321i
\(658\) 158.349 + 274.269i 0.240652 + 0.416822i
\(659\) −741.569 + 428.145i −1.12529 + 0.649689i −0.942747 0.333508i \(-0.891768\pi\)
−0.182548 + 0.983197i \(0.558434\pi\)
\(660\) 25.0297 + 2.82020i 0.0379238 + 0.00427304i
\(661\) −506.976 −0.766983 −0.383492 0.923544i \(-0.625278\pi\)
−0.383492 + 0.923544i \(0.625278\pi\)
\(662\) 104.911i 0.158476i
\(663\) 676.892 + 499.571i 1.02095 + 0.753501i
\(664\) −254.896 + 441.494i −0.383880 + 0.664900i
\(665\) 255.000i 0.383459i
\(666\) 200.840 879.925i 0.301561 1.32121i
\(667\) 670.105 1.00466
\(668\) 25.4914 + 14.7175i 0.0381608 + 0.0220321i
\(669\) −242.192 555.112i −0.362021 0.829763i
\(670\) 456.682 + 116.576i 0.681614 + 0.173993i
\(671\) 113.052i 0.168483i
\(672\) −115.240 + 1022.77i −0.171489 + 1.52198i
\(673\) −65.6191 −0.0975023 −0.0487512 0.998811i \(-0.515524\pi\)
−0.0487512 + 0.998811i \(0.515524\pi\)
\(674\) 690.133 398.448i 1.02394 0.591170i
\(675\) 440.609 + 154.178i 0.652754 + 0.228412i
\(676\) 63.8031 110.510i 0.0943832 0.163477i
\(677\) −930.170 + 537.034i −1.37396 + 0.793255i −0.991424 0.130686i \(-0.958282\pi\)
−0.382534 + 0.923941i \(0.624949\pi\)
\(678\) −15.7190 36.0286i −0.0231844 0.0531395i
\(679\) 1705.76 2.51217
\(680\) 181.508 + 104.794i 0.266924 + 0.154108i
\(681\) 367.529 + 271.249i 0.539690 + 0.398310i
\(682\) 51.6075 + 89.3868i 0.0756708 + 0.131066i
\(683\) 764.934 + 441.635i 1.11996 + 0.646610i 0.941391 0.337317i \(-0.109519\pi\)
0.178570 + 0.983927i \(0.442853\pi\)
\(684\) 135.455 145.985i 0.198034 0.213429i
\(685\) 358.112 0.522792
\(686\) 59.0503 + 34.0927i 0.0860792 + 0.0496979i
\(687\) −1052.71 118.613i −1.53232 0.172654i
\(688\) 166.610 288.577i 0.242166 0.419444i
\(689\) 218.494 + 126.148i 0.317118 + 0.183088i
\(690\) −368.272 271.798i −0.533728 0.393910i
\(691\) −337.699 584.912i −0.488711 0.846472i 0.511205 0.859459i \(-0.329199\pi\)
−0.999916 + 0.0129872i \(0.995866\pi\)
\(692\) 403.221i 0.582689i
\(693\) 107.915 33.2870i 0.155721 0.0480332i
\(694\) −1416.83 −2.04154
\(695\) 126.038i 0.181350i
\(696\) −220.622 + 298.931i −0.316985 + 0.429498i
\(697\) −248.704 −0.356820
\(698\) 1009.68 + 582.938i 1.44653 + 0.835155i
\(699\) 500.913 + 369.692i 0.716614 + 0.528887i
\(700\) −209.721 + 363.247i −0.299601 + 0.518925i
\(701\) 511.193 295.137i 0.729233 0.421023i −0.0889082 0.996040i \(-0.528338\pi\)
0.818142 + 0.575017i \(0.195004\pi\)
\(702\) 1000.87 189.371i 1.42574 0.269759i
\(703\) 181.142 + 313.746i 0.257669 + 0.446296i
\(704\) −7.92483 + 4.57540i −0.0112569 + 0.00649915i
\(705\) 61.6318 83.5079i 0.0874210 0.118451i
\(706\) 155.233 + 268.871i 0.219877 + 0.380838i
\(707\) 1702.02 + 982.663i 2.40739 + 1.38991i
\(708\) 380.401 + 280.749i 0.537289 + 0.396539i
\(709\) 178.511 309.190i 0.251778 0.436093i −0.712237 0.701939i \(-0.752318\pi\)
0.964016 + 0.265846i \(0.0856512\pi\)
\(710\) 445.338i 0.627237i
\(711\) −997.033 227.569i −1.40230 0.320070i
\(712\) −237.688 −0.333832
\(713\) 706.601i 0.991025i
\(714\) −1426.97 160.782i −1.99855 0.225186i
\(715\) −51.7141 −0.0723275
\(716\) −126.736 + 73.1709i −0.177005 + 0.102194i
\(717\) 277.675 + 204.934i 0.387273 + 0.285822i
\(718\) −362.160 + 627.280i −0.504401 + 0.873649i
\(719\) 68.5709 + 39.5894i 0.0953699 + 0.0550618i 0.546926 0.837181i \(-0.315798\pi\)
−0.451557 + 0.892243i \(0.649131\pi\)
\(720\) 473.459 146.041i 0.657582 0.202835i
\(721\) 319.516 553.418i 0.443156 0.767569i
\(722\) 702.351i 0.972785i
\(723\) −90.7646 208.036i −0.125539 0.287739i
\(724\) 359.639 622.913i 0.496739 0.860377i
\(725\) −462.618 + 267.093i −0.638094 + 0.368404i
\(726\) −730.346 539.022i −1.00599 0.742454i
\(727\) 481.814 834.527i 0.662743 1.14790i −0.317149 0.948376i \(-0.602725\pi\)
0.979892 0.199529i \(-0.0639412\pi\)
\(728\) 598.945i 0.822726i
\(729\) 569.951 + 454.529i 0.781826 + 0.623497i
\(730\) −194.628 337.106i −0.266614 0.461789i
\(731\) 274.095 + 158.249i 0.374959 + 0.216483i
\(732\) 262.220 + 601.017i 0.358224 + 0.821061i
\(733\) −275.546 477.260i −0.375915 0.651104i 0.614548 0.788879i \(-0.289338\pi\)
−0.990464 + 0.137775i \(0.956005\pi\)
\(734\) 971.791i 1.32397i
\(735\) 48.2061 427.836i 0.0655866 0.582090i
\(736\) 741.555 1.00755
\(737\) 59.9449 + 58.5384i 0.0813363 + 0.0794280i
\(738\) −204.823 + 220.745i −0.277537 + 0.299112i
\(739\) −432.695 + 749.449i −0.585514 + 1.01414i 0.409297 + 0.912401i \(0.365774\pi\)
−0.994811 + 0.101739i \(0.967559\pi\)
\(740\) 265.774i 0.359154i
\(741\) −242.799 + 328.980i −0.327664 + 0.443967i
\(742\) −430.647 −0.580386
\(743\) −1171.82 676.549i −1.57714 0.910563i −0.995256 0.0972931i \(-0.968982\pi\)
−0.581886 0.813270i \(-0.697685\pi\)
\(744\) 315.211 + 232.637i 0.423671 + 0.312685i
\(745\) −740.926 −0.994532
\(746\) 1431.30i 1.91864i
\(747\) −1093.83 + 337.398i −1.46429 + 0.451670i
\(748\) −28.4677 49.3075i −0.0380584 0.0659191i
\(749\) −1496.31 + 863.892i −1.99774 + 1.15339i
\(750\) 886.863 + 99.9268i 1.18248 + 0.133236i
\(751\) 188.319 0.250758 0.125379 0.992109i \(-0.459985\pi\)
0.125379 + 0.992109i \(0.459985\pi\)
\(752\) 247.001i 0.328458i
\(753\) −64.8480 + 575.534i −0.0861195 + 0.764321i
\(754\) −582.830 + 1009.49i −0.772985 + 1.33885i
\(755\) 445.298 + 257.093i 0.589799 + 0.340520i
\(756\) −496.498 + 427.268i −0.656744 + 0.565169i
\(757\) 327.545 + 567.325i 0.432688 + 0.749438i 0.997104 0.0760527i \(-0.0242317\pi\)
−0.564415 + 0.825491i \(0.690898\pi\)
\(758\) 585.079 337.795i 0.771871 0.445640i
\(759\) −32.5374 74.5769i −0.0428688 0.0982568i
\(760\) −50.9313 + 88.2156i −0.0670149 + 0.116073i
\(761\) 1124.03i 1.47705i 0.674228 + 0.738523i \(0.264476\pi\)
−0.674228 + 0.738523i \(0.735524\pi\)
\(762\) 390.954 170.571i 0.513062 0.223846i
\(763\) 417.949 + 723.908i 0.547770 + 0.948766i
\(764\) 251.890i 0.329698i
\(765\) 138.712 + 449.698i 0.181323 + 0.587840i
\(766\) 108.352 + 187.672i 0.141452 + 0.245002i
\(767\) −840.636 485.342i −1.09601 0.632779i
\(768\) −585.718 + 793.617i −0.762653 + 1.03336i
\(769\) −117.913 204.231i −0.153332 0.265580i 0.779118 0.626877i \(-0.215667\pi\)
−0.932451 + 0.361298i \(0.882334\pi\)
\(770\) 76.4454 44.1358i 0.0992798 0.0573192i
\(771\) 318.847 + 235.321i 0.413550 + 0.305215i
\(772\) −281.604 487.753i −0.364772 0.631804i
\(773\) 210.844 121.731i 0.272761 0.157478i −0.357381 0.933959i \(-0.616330\pi\)
0.630142 + 0.776480i \(0.282997\pi\)
\(774\) 366.192 112.954i 0.473117 0.145936i
\(775\) 281.639 + 487.814i 0.363406 + 0.629437i
\(776\) 590.098 + 340.693i 0.760436 + 0.439038i
\(777\) −476.515 1092.19i −0.613276 1.40565i
\(778\) 151.993 + 263.259i 0.195363 + 0.338379i
\(779\) 120.874i 0.155165i
\(780\) 274.927 119.949i 0.352471 0.153781i
\(781\) 39.5833 68.5603i 0.0506828 0.0877852i
\(782\) 1034.61i 1.32303i
\(783\) −819.683 + 155.089i −1.04685 + 0.198070i
\(784\) 512.313 + 887.352i 0.653460 + 1.13183i
\(785\) −249.586 144.099i −0.317944 0.183565i
\(786\) −1096.03 123.495i −1.39444 0.157118i
\(787\) 343.929 595.703i 0.437013 0.756928i −0.560445 0.828192i \(-0.689370\pi\)
0.997458 + 0.0712635i \(0.0227031\pi\)
\(788\) 437.395 + 252.530i 0.555069 + 0.320469i
\(789\) 1141.25 497.922i 1.44646 0.631080i
\(790\) −799.358 −1.01185
\(791\) −44.9446 25.9488i −0.0568200 0.0328050i
\(792\) 43.9809 + 10.0385i 0.0555314 + 0.0126749i
\(793\) −673.145 1165.92i −0.848859 1.47027i
\(794\) −1128.40 651.483i −1.42116 0.820507i
\(795\) 56.4373 + 129.356i 0.0709903 + 0.162712i
\(796\) −367.214 −0.461324
\(797\) 475.968 274.800i 0.597199 0.344793i −0.170740 0.985316i \(-0.554616\pi\)
0.767939 + 0.640523i \(0.221282\pi\)
\(798\) 78.1426 693.526i 0.0979231 0.869080i
\(799\) −234.605 −0.293623
\(800\) −511.945 + 295.572i −0.639932 + 0.369465i
\(801\) −391.231 363.011i −0.488428 0.453197i
\(802\) −125.377 + 217.159i −0.156330 + 0.270772i
\(803\) 69.1971i 0.0861732i
\(804\) −454.462 172.167i −0.565251 0.214138i
\(805\) −604.300 −0.750683
\(806\) 1064.47 + 614.573i 1.32068 + 0.762497i
\(807\) −805.485 + 351.428i −0.998122 + 0.435475i
\(808\) 392.536 + 679.892i 0.485812 + 0.841450i
\(809\) 18.8249i 0.0232693i 0.999932 + 0.0116347i \(0.00370351\pi\)
−0.999932 + 0.0116347i \(0.996296\pi\)
\(810\) 513.381 + 247.235i 0.633804 + 0.305228i
\(811\) 287.889 + 498.638i 0.354980 + 0.614844i 0.987115 0.160015i \(-0.0511542\pi\)
−0.632134 + 0.774859i \(0.717821\pi\)
\(812\) 749.583i 0.923131i
\(813\) −39.1692 89.7772i −0.0481786 0.110427i
\(814\) 62.7045 108.607i 0.0770326 0.133424i
\(815\) −293.955 + 169.715i −0.360681 + 0.208239i
\(816\) −901.122 665.060i −1.10432 0.815025i
\(817\) −76.9112 + 133.214i −0.0941386 + 0.163053i
\(818\) 753.686i 0.921377i
\(819\) 914.742 985.852i 1.11690 1.20373i
\(820\) −44.3370 + 76.7940i −0.0540696 + 0.0936512i
\(821\) −40.8231 23.5692i −0.0497236 0.0287079i 0.474932 0.880022i \(-0.342473\pi\)
−0.524656 + 0.851314i \(0.675806\pi\)
\(822\) −973.962 109.741i −1.18487 0.133504i
\(823\) 392.202 679.314i 0.476552 0.825411i −0.523087 0.852279i \(-0.675220\pi\)
0.999639 + 0.0268675i \(0.00855323\pi\)
\(824\) 221.069 127.634i 0.268287 0.154896i
\(825\) 52.1879 + 38.5165i 0.0632580 + 0.0466867i
\(826\) 1656.87 2.00590
\(827\) −1043.69 602.574i −1.26202 0.728627i −0.288554 0.957464i \(-0.593174\pi\)
−0.973465 + 0.228837i \(0.926508\pi\)
\(828\) 345.957 + 321.003i 0.417822 + 0.387685i
\(829\) −1605.08 −1.93616 −0.968080 0.250643i \(-0.919358\pi\)
−0.968080 + 0.250643i \(0.919358\pi\)
\(830\) −774.853 + 447.362i −0.933558 + 0.538990i
\(831\) −378.361 867.216i −0.455308 1.04358i
\(832\) −54.4867 + 94.3737i −0.0654888 + 0.113430i
\(833\) −842.819 + 486.602i −1.01179 + 0.584156i
\(834\) 38.6234 342.787i 0.0463110 0.411016i
\(835\) −16.9030 29.2768i −0.0202431 0.0350620i
\(836\) 23.9641 13.8357i 0.0286652 0.0165499i
\(837\) 163.535 + 864.325i 0.195383 + 1.03265i
\(838\) −794.843 1376.71i −0.948499 1.64285i
\(839\) −219.329 + 126.630i −0.261417 + 0.150929i −0.624981 0.780640i \(-0.714893\pi\)
0.363564 + 0.931569i \(0.381560\pi\)
\(840\) 198.956 269.575i 0.236853 0.320923i
\(841\) 56.8204 98.4158i 0.0675629 0.117022i
\(842\) 1342.31 774.982i 1.59419 0.920406i
\(843\) 85.1371 755.602i 0.100993 0.896325i
\(844\) −349.537 −0.414143
\(845\) −126.921 + 73.2776i −0.150202 + 0.0867191i
\(846\) −193.211 + 208.231i −0.228382 + 0.246136i
\(847\) −1198.43 −1.41491
\(848\) −290.874 167.936i −0.343011 0.198038i
\(849\) 318.218 + 729.367i 0.374815 + 0.859089i
\(850\) −412.380 714.262i −0.485152 0.840309i
\(851\) −743.517 + 429.270i −0.873698 + 0.504430i
\(852\) −51.4131 + 456.298i −0.0603440 + 0.535561i
\(853\) 432.342 748.837i 0.506848 0.877887i −0.493120 0.869961i \(-0.664144\pi\)
0.999969 0.00792577i \(-0.00252288\pi\)
\(854\) 1990.13 + 1149.00i 2.33036 + 1.34543i
\(855\) −218.560 + 67.4160i −0.255625 + 0.0788492i
\(856\) −690.183 −0.806288
\(857\) 394.298i 0.460091i 0.973180 + 0.230045i \(0.0738874\pi\)
−0.973180 + 0.230045i \(0.926113\pi\)
\(858\) 140.647 + 15.8474i 0.163925 + 0.0184701i
\(859\) −122.946 212.949i −0.143127 0.247903i 0.785546 0.618804i \(-0.212382\pi\)
−0.928673 + 0.370900i \(0.879049\pi\)
\(860\) 97.7272 56.4228i 0.113636 0.0656079i
\(861\) −44.5149 + 395.075i −0.0517014 + 0.458856i
\(862\) 646.103 0.749539
\(863\) 1091.27i 1.26451i −0.774762 0.632253i \(-0.782130\pi\)
0.774762 0.632253i \(-0.217870\pi\)
\(864\) −907.082 + 171.625i −1.04986 + 0.198640i
\(865\) −231.549 + 401.055i −0.267687 + 0.463647i
\(866\) 141.919i 0.163879i
\(867\) 116.841 158.313i 0.134764 0.182599i
\(868\) −790.407 −0.910607
\(869\) −123.062 71.0498i −0.141613 0.0817604i
\(870\) −597.654 + 260.753i −0.686959 + 0.299716i
\(871\) 966.776 + 246.786i 1.10996 + 0.283336i
\(872\) 333.909i 0.382923i
\(873\) 450.964 + 1462.01i 0.516568 + 1.67469i
\(874\) −502.837 −0.575328
\(875\) 1020.44 589.153i 1.16622 0.673317i
\(876\) 160.500 + 367.872i 0.183219 + 0.419945i
\(877\) −340.351 + 589.504i −0.388085 + 0.672183i −0.992192 0.124720i \(-0.960197\pi\)
0.604107 + 0.796903i \(0.293530\pi\)
\(878\) −425.984 + 245.942i −0.485175 + 0.280116i
\(879\) −1430.99 + 624.331i −1.62797 + 0.710274i
\(880\) 68.8451 0.0782331
\(881\) 1400.63 + 808.655i 1.58982 + 0.917884i 0.993335 + 0.115260i \(0.0367700\pi\)
0.596486 + 0.802624i \(0.296563\pi\)
\(882\) −262.213 + 1148.82i −0.297294 + 1.30251i
\(883\) 173.112 + 299.838i 0.196049 + 0.339567i 0.947244 0.320513i \(-0.103855\pi\)
−0.751195 + 0.660081i \(0.770522\pi\)
\(884\) −587.183 339.010i −0.664234 0.383496i
\(885\) −217.137 497.686i −0.245353 0.562357i
\(886\) −462.277 −0.521757
\(887\) 1313.31 + 758.241i 1.48062 + 0.854838i 0.999759 0.0219569i \(-0.00698966\pi\)
0.480864 + 0.876795i \(0.340323\pi\)
\(888\) 53.2961 473.010i 0.0600182 0.532669i
\(889\) 281.576 487.703i 0.316733 0.548597i
\(890\) −361.271 208.580i −0.405923 0.234360i
\(891\) 57.0603 + 83.6932i 0.0640408 + 0.0939318i
\(892\) 244.056 + 422.718i 0.273605 + 0.473899i
\(893\) 114.021i 0.127683i
\(894\) 2015.10 + 227.051i 2.25403 + 0.253972i
\(895\) 168.073 0.187791
\(896\) 1186.32i 1.32402i
\(897\) −779.617 575.385i −0.869138 0.641455i
\(898\) −246.846 −0.274884
\(899\) −871.770 503.316i −0.969710 0.559863i
\(900\) −366.783 83.7170i −0.407537 0.0930189i
\(901\) 159.508 276.276i 0.177034 0.306632i
\(902\) −36.2363 + 20.9210i −0.0401732 + 0.0231940i
\(903\) 300.444 407.085i 0.332717 0.450814i
\(904\) −10.3655 17.9536i −0.0114663 0.0198602i
\(905\) −715.414 + 413.044i −0.790512 + 0.456402i
\(906\) −1132.30 835.676i −1.24978 0.922380i
\(907\) 541.185 + 937.361i 0.596676 + 1.03347i 0.993308 + 0.115496i \(0.0368457\pi\)
−0.396632 + 0.917978i \(0.629821\pi\)
\(908\) −318.820 184.071i −0.351123 0.202721i
\(909\) −392.263 + 1718.59i −0.431532 + 1.89064i
\(910\) 525.596 910.358i 0.577578 1.00039i
\(911\) 792.591i 0.870024i −0.900425 0.435012i \(-0.856744\pi\)
0.900425 0.435012i \(-0.143256\pi\)
\(912\) 323.229 437.959i 0.354418 0.480218i
\(913\) −159.052 −0.174209
\(914\) 894.883i 0.979084i
\(915\) 84.3218 748.367i 0.0921550 0.817888i
\(916\) 853.784 0.932079
\(917\) −1261.12 + 728.106i −1.37526 + 0.794009i
\(918\) −239.450 1265.55i −0.260839 1.37860i
\(919\) 426.192 738.186i 0.463756 0.803249i −0.535388 0.844606i \(-0.679835\pi\)
0.999144 + 0.0413571i \(0.0131681\pi\)
\(920\) −209.054 120.697i −0.227232 0.131193i
\(921\) −1375.22 154.952i −1.49318 0.168243i
\(922\) 209.875 363.513i 0.227630 0.394266i
\(923\) 942.763i 1.02141i
\(924\) −83.4221 + 36.3965i −0.0902836 + 0.0393902i
\(925\) 342.200 592.707i 0.369946 0.640765i
\(926\) −1556.38 + 898.576i −1.68076 + 0.970385i
\(927\) 558.805 + 127.545i 0.602810 + 0.137589i
\(928\) 528.215 914.895i 0.569197 0.985878i
\(929\) 520.241i 0.560001i −0.960000 0.280000i \(-0.909665\pi\)
0.960000 0.280000i \(-0.0903346\pi\)
\(930\) 274.954 + 630.204i 0.295649 + 0.677638i
\(931\) −236.496 409.623i −0.254023 0.439981i
\(932\) −434.526 250.874i −0.466230 0.269178i
\(933\) 277.291 120.980i 0.297203 0.129668i
\(934\) 704.245 + 1219.79i 0.754010 + 1.30598i
\(935\) 65.3901i 0.0699359i
\(936\) 513.354 158.347i 0.548455 0.169174i
\(937\) 1401.85 1.49610 0.748051 0.663642i \(-0.230990\pi\)
0.748051 + 0.663642i \(0.230990\pi\)
\(938\) −1639.74 + 460.295i −1.74812 + 0.490720i
\(939\) −255.370 585.316i −0.271959 0.623340i
\(940\) −41.8235 + 72.4405i −0.0444931 + 0.0770644i
\(941\) 1368.80i 1.45463i −0.686306 0.727313i \(-0.740769\pi\)
0.686306 0.727313i \(-0.259231\pi\)
\(942\) 634.644 + 468.390i 0.673720 + 0.497230i
\(943\) 286.447 0.303761
\(944\) 1119.11 + 646.117i 1.18550 + 0.684446i
\(945\) 739.189 139.859i 0.782211 0.147999i
\(946\) 53.2477 0.0562872
\(947\) 912.803i 0.963890i −0.876202 0.481945i \(-0.839931\pi\)
0.876202 0.481945i \(-0.160069\pi\)
\(948\) 819.030 + 92.2837i 0.863955 + 0.0973457i
\(949\) −412.020 713.640i −0.434163 0.751992i
\(950\) 347.142 200.422i 0.365413 0.210971i
\(951\) 165.591 1469.64i 0.174123 1.54537i
\(952\) −757.337 −0.795522
\(953\) 483.395i 0.507235i −0.967305 0.253618i \(-0.918380\pi\)
0.967305 0.253618i \(-0.0816205\pi\)
\(954\) −113.853 369.106i −0.119343 0.386904i
\(955\) −144.647 + 250.536i −0.151463 + 0.262342i
\(956\) −240.874 139.069i −0.251961 0.145469i
\(957\) −115.186 12.9785i −0.120362 0.0135617i
\(958\) −7.95662 13.7813i −0.00830545 0.0143855i
\(959\) −1120.66 + 647.014i −1.16857 + 0.674675i
\(960\) −55.8724 + 24.3768i −0.0582005 + 0.0253925i
\(961\) −50.2283 + 86.9979i −0.0522667 + 0.0905286i
\(962\) 1493.45i 1.55244i
\(963\) −1136.03 1054.09i −1.17968 1.09459i
\(964\) 91.4633 + 158.419i 0.0948789 + 0.164335i
\(965\) 646.843i 0.670304i
\(966\) 1643.52 + 185.183i 1.70137 + 0.191701i
\(967\) −30.5652 52.9405i −0.0316083 0.0547472i 0.849789 0.527124i \(-0.176730\pi\)
−0.881397 + 0.472377i \(0.843396\pi\)
\(968\) −414.589 239.363i −0.428294 0.247276i
\(969\) 415.979 + 307.008i 0.429287 + 0.316829i
\(970\) 597.941 + 1035.66i 0.616434 + 1.06770i
\(971\) −830.038 + 479.223i −0.854828 + 0.493535i −0.862277 0.506437i \(-0.830962\pi\)
0.00744873 + 0.999972i \(0.497629\pi\)
\(972\) −497.472 312.588i −0.511803 0.321592i
\(973\) −227.717 394.418i −0.234036 0.405363i
\(974\) 1396.63 806.347i 1.43392 0.827872i
\(975\) 767.561 + 86.4845i 0.787242 + 0.0887020i
\(976\) 896.134 + 1552.15i 0.918170 + 1.59032i
\(977\) 829.456 + 478.887i 0.848983 + 0.490160i 0.860307 0.509775i \(-0.170272\pi\)
−0.0113248 + 0.999936i \(0.503605\pi\)
\(978\) 851.481 371.496i 0.870635 0.379852i
\(979\) −37.0787 64.2222i −0.0378741 0.0655998i
\(980\) 346.991i 0.354072i
\(981\) −509.964 + 549.607i −0.519841 + 0.560252i
\(982\) −500.370 + 866.667i −0.509542 + 0.882552i
\(983\) 1650.39i 1.67893i −0.543416 0.839464i \(-0.682869\pi\)
0.543416 0.839464i \(-0.317131\pi\)
\(984\) −94.3082 + 127.783i −0.0958417 + 0.129860i
\(985\) −290.030 502.346i −0.294447 0.509996i
\(986\) 1276.45 + 736.962i 1.29458 + 0.747426i
\(987\) −41.9913 + 372.678i −0.0425444 + 0.377587i
\(988\) 164.764 285.380i 0.166765 0.288846i
\(989\) −315.691 182.265i −0.319203 0.184292i
\(990\) 58.0390 + 53.8527i 0.0586253 + 0.0543966i
\(991\) 1398.10 1.41079 0.705397 0.708812i \(-0.250769\pi\)
0.705397 + 0.708812i \(0.250769\pi\)
\(992\) −964.723 556.983i −0.972503 0.561475i
\(993\) 73.7745 99.9606i 0.0742946 0.100665i
\(994\) 804.608 + 1393.62i 0.809464 + 1.40203i
\(995\) 365.241 + 210.872i 0.367077 + 0.211932i
\(996\) 845.568 368.916i 0.848964 0.370398i
\(997\) 226.817 0.227500 0.113750 0.993509i \(-0.463714\pi\)
0.113750 + 0.993509i \(0.463714\pi\)
\(998\) −1947.54 + 1124.41i −1.95145 + 1.12667i
\(999\) 810.132 697.169i 0.810943 0.697867i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 201.3.g.b.29.11 84
3.2 odd 2 inner 201.3.g.b.29.32 yes 84
67.37 even 3 inner 201.3.g.b.104.32 yes 84
201.104 odd 6 inner 201.3.g.b.104.11 yes 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.3.g.b.29.11 84 1.1 even 1 trivial
201.3.g.b.29.32 yes 84 3.2 odd 2 inner
201.3.g.b.104.11 yes 84 201.104 odd 6 inner
201.3.g.b.104.32 yes 84 67.37 even 3 inner