Properties

Label 197.3.c.a.14.3
Level $197$
Weight $3$
Character 197.14
Analytic conductor $5.368$
Analytic rank $0$
Dimension $64$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [197,3,Mod(14,197)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(197, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("197.14");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 197.c (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: \(5.36786120790\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 14.3
Character \(\chi\) \(=\) 197.14
Dual form 197.3.c.a.183.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.37240 + 2.37240i) q^{2} +(3.08237 - 3.08237i) q^{3} -7.25653i q^{4} +(3.27580 - 3.27580i) q^{5} +14.6252i q^{6} -0.819881i q^{7} +(7.72579 + 7.72579i) q^{8} -10.0021i q^{9} +O(q^{10})\) \(q+(-2.37240 + 2.37240i) q^{2} +(3.08237 - 3.08237i) q^{3} -7.25653i q^{4} +(3.27580 - 3.27580i) q^{5} +14.6252i q^{6} -0.819881i q^{7} +(7.72579 + 7.72579i) q^{8} -10.0021i q^{9} +15.5430i q^{10} +(-4.39521 + 4.39521i) q^{11} +(-22.3674 - 22.3674i) q^{12} +(5.48761 - 5.48761i) q^{13} +(1.94508 + 1.94508i) q^{14} -20.1945i q^{15} -7.63115 q^{16} +(-18.6785 - 18.6785i) q^{17} +(23.7289 + 23.7289i) q^{18} -22.4970i q^{19} +(-23.7710 - 23.7710i) q^{20} +(-2.52718 - 2.52718i) q^{21} -20.8544i q^{22} -3.81214 q^{23} +47.6276 q^{24} +3.53825i q^{25} +26.0376i q^{26} +(-3.08872 - 3.08872i) q^{27} -5.94949 q^{28} +23.0467 q^{29} +(47.9093 + 47.9093i) q^{30} +(5.47013 - 5.47013i) q^{31} +(-12.7990 + 12.7990i) q^{32} +27.0954i q^{33} +88.6256 q^{34} +(-2.68577 - 2.68577i) q^{35} -72.5803 q^{36} +24.8800 q^{37} +(53.3718 + 53.3718i) q^{38} -33.8297i q^{39} +50.6163 q^{40} +0.125150i q^{41} +11.9909 q^{42} -48.0131i q^{43} +(31.8940 + 31.8940i) q^{44} +(-32.7648 - 32.7648i) q^{45} +(9.04390 - 9.04390i) q^{46} +61.5091i q^{47} +(-23.5221 + 23.5221i) q^{48} +48.3278 q^{49} +(-8.39413 - 8.39413i) q^{50} -115.148 q^{51} +(-39.8210 - 39.8210i) q^{52} +32.8032 q^{53} +14.6553 q^{54} +28.7957i q^{55} +(6.33423 - 6.33423i) q^{56} +(-69.3442 - 69.3442i) q^{57} +(-54.6758 + 54.6758i) q^{58} -56.0504 q^{59} -146.542 q^{60} -108.466 q^{61} +25.9547i q^{62} -8.20050 q^{63} -91.2534i q^{64} -35.9527i q^{65} +(-64.2810 - 64.2810i) q^{66} +(68.6798 - 68.6798i) q^{67} +(-135.541 + 135.541i) q^{68} +(-11.7504 + 11.7504i) q^{69} +12.7434 q^{70} +(70.0898 + 70.0898i) q^{71} +(77.2738 - 77.2738i) q^{72} +(4.47833 - 4.47833i) q^{73} +(-59.0253 + 59.0253i) q^{74} +(10.9062 + 10.9062i) q^{75} -163.250 q^{76} +(3.60355 + 3.60355i) q^{77} +(80.2576 + 80.2576i) q^{78} +(43.2246 + 43.2246i) q^{79} +(-24.9981 + 24.9981i) q^{80} +70.9774 q^{81} +(-0.296905 - 0.296905i) q^{82} +58.1466i q^{83} +(-18.3386 + 18.3386i) q^{84} -122.374 q^{85} +(113.906 + 113.906i) q^{86} +(71.0385 - 71.0385i) q^{87} -67.9130 q^{88} +(106.620 + 106.620i) q^{89} +155.462 q^{90} +(-4.49919 - 4.49919i) q^{91} +27.6629i q^{92} -33.7220i q^{93} +(-145.924 - 145.924i) q^{94} +(-73.6957 - 73.6957i) q^{95} +78.9029i q^{96} +12.2502i q^{97} +(-114.653 + 114.653i) q^{98} +(43.9612 + 43.9612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8} + 10 q^{11} + 68 q^{12} + 2 q^{13} - 2 q^{14} - 280 q^{16} - 30 q^{17} - 68 q^{18} + 114 q^{20} - 20 q^{21} + 48 q^{23} + 60 q^{24} + 22 q^{27} + 392 q^{28} + 56 q^{29} - 70 q^{30} - 64 q^{31} - 156 q^{32} - 52 q^{34} - 92 q^{35} - 36 q^{36} - 160 q^{37} + 40 q^{38} + 52 q^{40} + 80 q^{42} + 140 q^{44} + 324 q^{45} + 214 q^{46} + 216 q^{48} - 836 q^{49} + 126 q^{50} + 124 q^{51} - 10 q^{52} - 16 q^{53} + 400 q^{54} - 40 q^{56} + 68 q^{57} - 266 q^{58} - 364 q^{59} - 68 q^{60} - 168 q^{61} - 12 q^{63} + 238 q^{66} - 112 q^{67} - 148 q^{68} - 48 q^{69} + 48 q^{70} + 150 q^{71} - 474 q^{72} + 18 q^{73} + 236 q^{74} + 64 q^{75} - 260 q^{76} - 388 q^{77} - 782 q^{78} + 202 q^{79} + 796 q^{80} - 516 q^{81} + 72 q^{82} - 294 q^{84} - 696 q^{85} + 618 q^{86} + 464 q^{87} - 244 q^{88} - 536 q^{89} + 1484 q^{90} + 212 q^{91} + 132 q^{94} + 370 q^{95} - 530 q^{98} - 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/197\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37240 + 2.37240i −1.18620 + 1.18620i −0.208088 + 0.978110i \(0.566724\pi\)
−0.978110 + 0.208088i \(0.933276\pi\)
\(3\) 3.08237 3.08237i 1.02746 1.02746i 0.0278458 0.999612i \(-0.491135\pi\)
0.999612 0.0278458i \(-0.00886472\pi\)
\(4\) 7.25653i 1.81413i
\(5\) 3.27580 3.27580i 0.655160 0.655160i −0.299071 0.954231i \(-0.596677\pi\)
0.954231 + 0.299071i \(0.0966766\pi\)
\(6\) 14.6252i 2.43754i
\(7\) 0.819881i 0.117126i −0.998284 0.0585629i \(-0.981348\pi\)
0.998284 0.0585629i \(-0.0186518\pi\)
\(8\) 7.72579 + 7.72579i 0.965724 + 0.965724i
\(9\) 10.0021i 1.11134i
\(10\) 15.5430i 1.55430i
\(11\) −4.39521 + 4.39521i −0.399565 + 0.399565i −0.878080 0.478515i \(-0.841175\pi\)
0.478515 + 0.878080i \(0.341175\pi\)
\(12\) −22.3674 22.3674i −1.86395 1.86395i
\(13\) 5.48761 5.48761i 0.422124 0.422124i −0.463810 0.885934i \(-0.653518\pi\)
0.885934 + 0.463810i \(0.153518\pi\)
\(14\) 1.94508 + 1.94508i 0.138934 + 0.138934i
\(15\) 20.1945i 1.34630i
\(16\) −7.63115 −0.476947
\(17\) −18.6785 18.6785i −1.09873 1.09873i −0.994559 0.104176i \(-0.966780\pi\)
−0.104176 0.994559i \(-0.533220\pi\)
\(18\) 23.7289 + 23.7289i 1.31827 + 1.31827i
\(19\) 22.4970i 1.18405i −0.805919 0.592026i \(-0.798328\pi\)
0.805919 0.592026i \(-0.201672\pi\)
\(20\) −23.7710 23.7710i −1.18855 1.18855i
\(21\) −2.52718 2.52718i −0.120342 0.120342i
\(22\) 20.8544i 0.947927i
\(23\) −3.81214 −0.165745 −0.0828725 0.996560i \(-0.526409\pi\)
−0.0828725 + 0.996560i \(0.526409\pi\)
\(24\) 47.6276 1.98448
\(25\) 3.53825i 0.141530i
\(26\) 26.0376i 1.00145i
\(27\) −3.08872 3.08872i −0.114397 0.114397i
\(28\) −5.94949 −0.212482
\(29\) 23.0467 0.794713 0.397356 0.917664i \(-0.369928\pi\)
0.397356 + 0.917664i \(0.369928\pi\)
\(30\) 47.9093 + 47.9093i 1.59698 + 1.59698i
\(31\) 5.47013 5.47013i 0.176456 0.176456i −0.613353 0.789809i \(-0.710180\pi\)
0.789809 + 0.613353i \(0.210180\pi\)
\(32\) −12.7990 + 12.7990i −0.399970 + 0.399970i
\(33\) 27.0954i 0.821072i
\(34\) 88.6256 2.60663
\(35\) −2.68577 2.68577i −0.0767362 0.0767362i
\(36\) −72.5803 −2.01612
\(37\) 24.8800 0.672434 0.336217 0.941785i \(-0.390853\pi\)
0.336217 + 0.941785i \(0.390853\pi\)
\(38\) 53.3718 + 53.3718i 1.40452 + 1.40452i
\(39\) 33.8297i 0.867429i
\(40\) 50.6163 1.26541
\(41\) 0.125150i 0.00305243i 0.999999 + 0.00152622i \(0.000485810\pi\)
−0.999999 + 0.00152622i \(0.999514\pi\)
\(42\) 11.9909 0.285499
\(43\) 48.0131i 1.11658i −0.829645 0.558292i \(-0.811457\pi\)
0.829645 0.558292i \(-0.188543\pi\)
\(44\) 31.8940 + 31.8940i 0.724864 + 0.724864i
\(45\) −32.7648 32.7648i −0.728106 0.728106i
\(46\) 9.04390 9.04390i 0.196607 0.196607i
\(47\) 61.5091i 1.30870i 0.756190 + 0.654352i \(0.227059\pi\)
−0.756190 + 0.654352i \(0.772941\pi\)
\(48\) −23.5221 + 23.5221i −0.490043 + 0.490043i
\(49\) 48.3278 0.986282
\(50\) −8.39413 8.39413i −0.167883 0.167883i
\(51\) −115.148 −2.25781
\(52\) −39.8210 39.8210i −0.765789 0.765789i
\(53\) 32.8032 0.618929 0.309465 0.950911i \(-0.399850\pi\)
0.309465 + 0.950911i \(0.399850\pi\)
\(54\) 14.6553 0.271395
\(55\) 28.7957i 0.523558i
\(56\) 6.33423 6.33423i 0.113111 0.113111i
\(57\) −69.3442 69.3442i −1.21656 1.21656i
\(58\) −54.6758 + 54.6758i −0.942687 + 0.942687i
\(59\) −56.0504 −0.950006 −0.475003 0.879984i \(-0.657553\pi\)
−0.475003 + 0.879984i \(0.657553\pi\)
\(60\) −146.542 −2.44237
\(61\) −108.466 −1.77813 −0.889065 0.457781i \(-0.848644\pi\)
−0.889065 + 0.457781i \(0.848644\pi\)
\(62\) 25.9547i 0.418624i
\(63\) −8.20050 −0.130167
\(64\) 91.2534i 1.42584i
\(65\) 35.9527i 0.553118i
\(66\) −64.2810 64.2810i −0.973955 0.973955i
\(67\) 68.6798 68.6798i 1.02507 1.02507i 0.0253934 0.999678i \(-0.491916\pi\)
0.999678 0.0253934i \(-0.00808383\pi\)
\(68\) −135.541 + 135.541i −1.99325 + 1.99325i
\(69\) −11.7504 + 11.7504i −0.170296 + 0.170296i
\(70\) 12.7434 0.182049
\(71\) 70.0898 + 70.0898i 0.987180 + 0.987180i 0.999919 0.0127390i \(-0.00405505\pi\)
−0.0127390 + 0.999919i \(0.504055\pi\)
\(72\) 77.2738 77.2738i 1.07325 1.07325i
\(73\) 4.47833 4.47833i 0.0613470 0.0613470i −0.675768 0.737115i \(-0.736188\pi\)
0.737115 + 0.675768i \(0.236188\pi\)
\(74\) −59.0253 + 59.0253i −0.797640 + 0.797640i
\(75\) 10.9062 + 10.9062i 0.145416 + 0.145416i
\(76\) −163.250 −2.14803
\(77\) 3.60355 + 3.60355i 0.0467994 + 0.0467994i
\(78\) 80.2576 + 80.2576i 1.02894 + 1.02894i
\(79\) 43.2246 + 43.2246i 0.547147 + 0.547147i 0.925615 0.378467i \(-0.123549\pi\)
−0.378467 + 0.925615i \(0.623549\pi\)
\(80\) −24.9981 + 24.9981i −0.312477 + 0.312477i
\(81\) 70.9774 0.876264
\(82\) −0.296905 0.296905i −0.00362079 0.00362079i
\(83\) 58.1466i 0.700561i 0.936645 + 0.350281i \(0.113914\pi\)
−0.936645 + 0.350281i \(0.886086\pi\)
\(84\) −18.3386 + 18.3386i −0.218316 + 0.218316i
\(85\) −122.374 −1.43969
\(86\) 113.906 + 113.906i 1.32449 + 1.32449i
\(87\) 71.0385 71.0385i 0.816534 0.816534i
\(88\) −67.9130 −0.771739
\(89\) 106.620 + 106.620i 1.19797 + 1.19797i 0.974772 + 0.223202i \(0.0716509\pi\)
0.223202 + 0.974772i \(0.428349\pi\)
\(90\) 155.462 1.72736
\(91\) −4.49919 4.49919i −0.0494416 0.0494416i
\(92\) 27.6629i 0.300684i
\(93\) 33.7220i 0.362602i
\(94\) −145.924 145.924i −1.55238 1.55238i
\(95\) −73.6957 73.6957i −0.775744 0.775744i
\(96\) 78.9029i 0.821905i
\(97\) 12.2502i 0.126291i 0.998004 + 0.0631455i \(0.0201132\pi\)
−0.998004 + 0.0631455i \(0.979887\pi\)
\(98\) −114.653 + 114.653i −1.16993 + 1.16993i
\(99\) 43.9612 + 43.9612i 0.444052 + 0.444052i
\(100\) 25.6754 0.256754
\(101\) −31.6367 −0.313234 −0.156617 0.987659i \(-0.550059\pi\)
−0.156617 + 0.987659i \(0.550059\pi\)
\(102\) 273.177 273.177i 2.67821 2.67821i
\(103\) −42.9539 + 42.9539i −0.417028 + 0.417028i −0.884178 0.467150i \(-0.845281\pi\)
0.467150 + 0.884178i \(0.345281\pi\)
\(104\) 84.7923 0.815310
\(105\) −16.5571 −0.157686
\(106\) −77.8223 + 77.8223i −0.734173 + 0.734173i
\(107\) 116.722i 1.09086i 0.838157 + 0.545429i \(0.183633\pi\)
−0.838157 + 0.545429i \(0.816367\pi\)
\(108\) −22.4134 + 22.4134i −0.207531 + 0.207531i
\(109\) 48.5873i 0.445755i −0.974846 0.222878i \(-0.928455\pi\)
0.974846 0.222878i \(-0.0715450\pi\)
\(110\) −68.3148 68.3148i −0.621044 0.621044i
\(111\) 76.6896 76.6896i 0.690897 0.690897i
\(112\) 6.25663i 0.0558628i
\(113\) −122.345 122.345i −1.08270 1.08270i −0.996257 0.0864404i \(-0.972451\pi\)
−0.0864404 0.996257i \(-0.527549\pi\)
\(114\) 329.024 2.88617
\(115\) −12.4878 + 12.4878i −0.108590 + 0.108590i
\(116\) 167.239i 1.44172i
\(117\) −54.8874 54.8874i −0.469123 0.469123i
\(118\) 132.974 132.974i 1.12690 1.12690i
\(119\) −15.3141 + 15.3141i −0.128690 + 0.128690i
\(120\) 156.018 156.018i 1.30015 1.30015i
\(121\) 82.3642i 0.680696i
\(122\) 257.324 257.324i 2.10921 2.10921i
\(123\) 0.385758 + 0.385758i 0.00313625 + 0.00313625i
\(124\) −39.6942 39.6942i −0.320115 0.320115i
\(125\) 93.4856 + 93.4856i 0.747885 + 0.747885i
\(126\) 19.4548 19.4548i 0.154403 0.154403i
\(127\) 85.8354i 0.675869i 0.941170 + 0.337935i \(0.109728\pi\)
−0.941170 + 0.337935i \(0.890272\pi\)
\(128\) 165.293 + 165.293i 1.29135 + 1.29135i
\(129\) −147.994 147.994i −1.14724 1.14724i
\(130\) 85.2940 + 85.2940i 0.656107 + 0.656107i
\(131\) −87.7433 + 87.7433i −0.669796 + 0.669796i −0.957669 0.287873i \(-0.907052\pi\)
0.287873 + 0.957669i \(0.407052\pi\)
\(132\) 196.619 1.48953
\(133\) −18.4449 −0.138683
\(134\) 325.871i 2.43188i
\(135\) −20.2361 −0.149897
\(136\) 288.612i 2.12215i
\(137\) 65.1374i 0.475455i 0.971332 + 0.237728i \(0.0764026\pi\)
−0.971332 + 0.237728i \(0.923597\pi\)
\(138\) 55.7534i 0.404010i
\(139\) 107.142 + 107.142i 0.770803 + 0.770803i 0.978247 0.207444i \(-0.0665145\pi\)
−0.207444 + 0.978247i \(0.566515\pi\)
\(140\) −19.4894 + 19.4894i −0.139210 + 0.139210i
\(141\) 189.594 + 189.594i 1.34464 + 1.34464i
\(142\) −332.562 −2.34198
\(143\) 48.2385i 0.337332i
\(144\) 76.3272i 0.530050i
\(145\) 75.4963 75.4963i 0.520664 0.520664i
\(146\) 21.2487i 0.145539i
\(147\) 148.964 148.964i 1.01336 1.01336i
\(148\) 180.543i 1.21988i
\(149\) −142.706 142.706i −0.957757 0.957757i 0.0413859 0.999143i \(-0.486823\pi\)
−0.999143 + 0.0413859i \(0.986823\pi\)
\(150\) −51.7477 −0.344985
\(151\) 143.842 + 143.842i 0.952598 + 0.952598i 0.998926 0.0463279i \(-0.0147519\pi\)
−0.0463279 + 0.998926i \(0.514752\pi\)
\(152\) 173.807 173.807i 1.14347 1.14347i
\(153\) −186.823 + 186.823i −1.22107 + 1.22107i
\(154\) −17.0981 −0.111027
\(155\) 35.8381i 0.231214i
\(156\) −245.487 −1.57363
\(157\) 293.312i 1.86823i −0.356971 0.934116i \(-0.616190\pi\)
0.356971 0.934116i \(-0.383810\pi\)
\(158\) −205.092 −1.29805
\(159\) 101.112 101.112i 0.635924 0.635924i
\(160\) 83.8543i 0.524089i
\(161\) 3.12550i 0.0194130i
\(162\) −168.386 + 168.386i −1.03942 + 1.03942i
\(163\) 85.4023i 0.523941i 0.965076 + 0.261970i \(0.0843723\pi\)
−0.965076 + 0.261970i \(0.915628\pi\)
\(164\) 0.908154 0.00553752
\(165\) 88.7591 + 88.7591i 0.537934 + 0.537934i
\(166\) −137.947 137.947i −0.831005 0.831005i
\(167\) 153.489 153.489i 0.919095 0.919095i −0.0778686 0.996964i \(-0.524811\pi\)
0.996964 + 0.0778686i \(0.0248115\pi\)
\(168\) 39.0489i 0.232434i
\(169\) 108.772i 0.643623i
\(170\) 290.320 290.320i 1.70776 1.70776i
\(171\) −225.016 −1.31588
\(172\) −348.409 −2.02563
\(173\) 98.9897i 0.572195i −0.958201 0.286097i \(-0.907642\pi\)
0.958201 0.286097i \(-0.0923581\pi\)
\(174\) 337.063i 1.93714i
\(175\) 2.90094 0.0165768
\(176\) 33.5405 33.5405i 0.190571 0.190571i
\(177\) −172.768 + 172.768i −0.976091 + 0.976091i
\(178\) −505.888 −2.84207
\(179\) −214.314 + 214.314i −1.19729 + 1.19729i −0.222309 + 0.974976i \(0.571360\pi\)
−0.974976 + 0.222309i \(0.928640\pi\)
\(180\) −237.759 + 237.759i −1.32088 + 1.32088i
\(181\) 72.8828i 0.402667i 0.979523 + 0.201334i \(0.0645276\pi\)
−0.979523 + 0.201334i \(0.935472\pi\)
\(182\) 21.3477 0.117295
\(183\) −334.332 + 334.332i −1.82695 + 1.82695i
\(184\) −29.4518 29.4518i −0.160064 0.160064i
\(185\) 81.5021 81.5021i 0.440552 0.440552i
\(186\) 80.0020 + 80.0020i 0.430118 + 0.430118i
\(187\) 164.192 0.878032
\(188\) 446.343 2.37416
\(189\) −2.53238 + 2.53238i −0.0133988 + 0.0133988i
\(190\) 349.671 1.84037
\(191\) −181.701 −0.951312 −0.475656 0.879632i \(-0.657789\pi\)
−0.475656 + 0.879632i \(0.657789\pi\)
\(192\) −281.277 281.277i −1.46499 1.46499i
\(193\) 281.726 1.45972 0.729861 0.683596i \(-0.239585\pi\)
0.729861 + 0.683596i \(0.239585\pi\)
\(194\) −29.0624 29.0624i −0.149806 0.149806i
\(195\) −110.820 110.820i −0.568305 0.568305i
\(196\) 350.692i 1.78925i
\(197\) −21.2380 195.852i −0.107807 0.994172i
\(198\) −208.587 −1.05347
\(199\) −23.8535 + 23.8535i −0.119867 + 0.119867i −0.764496 0.644629i \(-0.777012\pi\)
0.644629 + 0.764496i \(0.277012\pi\)
\(200\) −27.3358 + 27.3358i −0.136679 + 0.136679i
\(201\) 423.393i 2.10643i
\(202\) 75.0547 75.0547i 0.371558 0.371558i
\(203\) 18.8955i 0.0930814i
\(204\) 835.577i 4.09596i
\(205\) 0.409966 + 0.409966i 0.00199983 + 0.00199983i
\(206\) 203.807i 0.989356i
\(207\) 38.1292i 0.184199i
\(208\) −41.8768 + 41.8768i −0.201331 + 0.201331i
\(209\) 98.8791 + 98.8791i 0.473106 + 0.473106i
\(210\) 39.2800 39.2800i 0.187047 0.187047i
\(211\) −110.556 110.556i −0.523963 0.523963i 0.394803 0.918766i \(-0.370813\pi\)
−0.918766 + 0.394803i \(0.870813\pi\)
\(212\) 238.038i 1.12282i
\(213\) 432.086 2.02857
\(214\) −276.910 276.910i −1.29397 1.29397i
\(215\) −157.281 157.281i −0.731541 0.731541i
\(216\) 47.7256i 0.220952i
\(217\) −4.48486 4.48486i −0.0206675 0.0206675i
\(218\) 115.268 + 115.268i 0.528754 + 0.528754i
\(219\) 27.6078i 0.126063i
\(220\) 208.957 0.949804
\(221\) −205.001 −0.927604
\(222\) 363.876i 1.63908i
\(223\) 73.8097i 0.330985i −0.986211 0.165493i \(-0.947079\pi\)
0.986211 0.165493i \(-0.0529214\pi\)
\(224\) 10.4937 + 10.4937i 0.0468468 + 0.0468468i
\(225\) 35.3898 0.157288
\(226\) 580.501 2.56859
\(227\) −46.4421 46.4421i −0.204591 0.204591i 0.597373 0.801964i \(-0.296211\pi\)
−0.801964 + 0.597373i \(0.796211\pi\)
\(228\) −503.198 + 503.198i −2.20701 + 2.20701i
\(229\) −110.329 + 110.329i −0.481785 + 0.481785i −0.905701 0.423917i \(-0.860655\pi\)
0.423917 + 0.905701i \(0.360655\pi\)
\(230\) 59.2520i 0.257618i
\(231\) 22.2150 0.0961688
\(232\) 178.054 + 178.054i 0.767473 + 0.767473i
\(233\) 327.849 1.40708 0.703538 0.710658i \(-0.251603\pi\)
0.703538 + 0.710658i \(0.251603\pi\)
\(234\) 260.429 1.11295
\(235\) 201.492 + 201.492i 0.857411 + 0.857411i
\(236\) 406.731i 1.72344i
\(237\) 266.469 1.12434
\(238\) 72.6624i 0.305304i
\(239\) −51.5982 −0.215892 −0.107946 0.994157i \(-0.534427\pi\)
−0.107946 + 0.994157i \(0.534427\pi\)
\(240\) 154.107i 0.642113i
\(241\) 294.588 + 294.588i 1.22236 + 1.22236i 0.966792 + 0.255565i \(0.0822613\pi\)
0.255565 + 0.966792i \(0.417739\pi\)
\(242\) −195.401 195.401i −0.807440 0.807440i
\(243\) 246.577 246.577i 1.01472 1.01472i
\(244\) 787.087i 3.22576i
\(245\) 158.312 158.312i 0.646172 0.646172i
\(246\) −1.83034 −0.00744042
\(247\) −123.455 123.455i −0.499817 0.499817i
\(248\) 84.5222 0.340815
\(249\) 179.230 + 179.230i 0.719797 + 0.719797i
\(250\) −443.570 −1.77428
\(251\) 214.813 0.855828 0.427914 0.903819i \(-0.359249\pi\)
0.427914 + 0.903819i \(0.359249\pi\)
\(252\) 59.5072i 0.236140i
\(253\) 16.7552 16.7552i 0.0662259 0.0662259i
\(254\) −203.636 203.636i −0.801715 0.801715i
\(255\) −377.203 + 377.203i −1.47923 + 1.47923i
\(256\) −419.268 −1.63777
\(257\) −387.798 −1.50894 −0.754471 0.656334i \(-0.772106\pi\)
−0.754471 + 0.656334i \(0.772106\pi\)
\(258\) 702.203 2.72172
\(259\) 20.3987i 0.0787593i
\(260\) −260.892 −1.00343
\(261\) 230.514i 0.883196i
\(262\) 416.324i 1.58902i
\(263\) 23.2568 + 23.2568i 0.0884288 + 0.0884288i 0.749937 0.661509i \(-0.230084\pi\)
−0.661509 + 0.749937i \(0.730084\pi\)
\(264\) −209.333 + 209.333i −0.792929 + 0.792929i
\(265\) 107.457 107.457i 0.405498 0.405498i
\(266\) 43.7585 43.7585i 0.164506 0.164506i
\(267\) 657.283 2.46174
\(268\) −498.377 498.377i −1.85962 1.85962i
\(269\) 146.130 146.130i 0.543233 0.543233i −0.381242 0.924475i \(-0.624504\pi\)
0.924475 + 0.381242i \(0.124504\pi\)
\(270\) 48.0080 48.0080i 0.177807 0.177807i
\(271\) 19.7746 19.7746i 0.0729691 0.0729691i −0.669680 0.742649i \(-0.733569\pi\)
0.742649 + 0.669680i \(0.233569\pi\)
\(272\) 142.538 + 142.538i 0.524038 + 0.524038i
\(273\) −27.7364 −0.101598
\(274\) −154.532 154.532i −0.563984 0.563984i
\(275\) −15.5514 15.5514i −0.0565504 0.0565504i
\(276\) 85.2674 + 85.2674i 0.308940 + 0.308940i
\(277\) 125.343 125.343i 0.452501 0.452501i −0.443683 0.896184i \(-0.646328\pi\)
0.896184 + 0.443683i \(0.146328\pi\)
\(278\) −508.365 −1.82865
\(279\) −54.7126 54.7126i −0.196103 0.196103i
\(280\) 41.4993i 0.148212i
\(281\) 265.807 265.807i 0.945933 0.945933i −0.0526783 0.998612i \(-0.516776\pi\)
0.998612 + 0.0526783i \(0.0167758\pi\)
\(282\) −899.584 −3.19002
\(283\) −173.693 173.693i −0.613756 0.613756i 0.330167 0.943923i \(-0.392895\pi\)
−0.943923 + 0.330167i \(0.892895\pi\)
\(284\) 508.609 508.609i 1.79088 1.79088i
\(285\) −454.315 −1.59409
\(286\) −114.441 114.441i −0.400143 0.400143i
\(287\) 0.102608 0.000357519
\(288\) 128.017 + 128.017i 0.444503 + 0.444503i
\(289\) 408.772i 1.41443i
\(290\) 358.214i 1.23522i
\(291\) 37.7598 + 37.7598i 0.129759 + 0.129759i
\(292\) −32.4971 32.4971i −0.111292 0.111292i
\(293\) 164.093i 0.560044i −0.959994 0.280022i \(-0.909658\pi\)
0.959994 0.280022i \(-0.0903417\pi\)
\(294\) 706.805i 2.40410i
\(295\) −183.610 + 183.610i −0.622406 + 0.622406i
\(296\) 192.218 + 192.218i 0.649385 + 0.649385i
\(297\) 27.1512 0.0914181
\(298\) 677.110 2.27218
\(299\) −20.9195 + 20.9195i −0.0699650 + 0.0699650i
\(300\) 79.1413 79.1413i 0.263804 0.263804i
\(301\) −39.3650 −0.130781
\(302\) −682.502 −2.25994
\(303\) −97.5161 + 97.5161i −0.321835 + 0.321835i
\(304\) 171.678i 0.564730i
\(305\) −355.313 + 355.313i −1.16496 + 1.16496i
\(306\) 886.438i 2.89686i
\(307\) −224.467 224.467i −0.731162 0.731162i 0.239688 0.970850i \(-0.422955\pi\)
−0.970850 + 0.239688i \(0.922955\pi\)
\(308\) 26.1493 26.1493i 0.0849003 0.0849003i
\(309\) 264.800i 0.856958i
\(310\) 85.0223 + 85.0223i 0.274266 + 0.274266i
\(311\) 306.877 0.986741 0.493371 0.869819i \(-0.335765\pi\)
0.493371 + 0.869819i \(0.335765\pi\)
\(312\) 261.362 261.362i 0.837697 0.837697i
\(313\) 304.924i 0.974198i −0.873347 0.487099i \(-0.838055\pi\)
0.873347 0.487099i \(-0.161945\pi\)
\(314\) 695.853 + 695.853i 2.21609 + 2.21609i
\(315\) −26.8632 + 26.8632i −0.0852800 + 0.0852800i
\(316\) 313.661 313.661i 0.992598 0.992598i
\(317\) 418.763 418.763i 1.32102 1.32102i 0.408068 0.912951i \(-0.366202\pi\)
0.912951 0.408068i \(-0.133798\pi\)
\(318\) 479.755i 1.50866i
\(319\) −101.295 + 101.295i −0.317539 + 0.317539i
\(320\) −298.928 298.928i −0.934150 0.934150i
\(321\) 359.780 + 359.780i 1.12081 + 1.12081i
\(322\) −7.41492 7.41492i −0.0230277 0.0230277i
\(323\) −420.210 + 420.210i −1.30096 + 1.30096i
\(324\) 515.050i 1.58966i
\(325\) 19.4165 + 19.4165i 0.0597432 + 0.0597432i
\(326\) −202.608 202.608i −0.621498 0.621498i
\(327\) −149.764 149.764i −0.457995 0.457995i
\(328\) −0.966881 + 0.966881i −0.00294781 + 0.00294781i
\(329\) 50.4301 0.153283
\(330\) −421.144 −1.27619
\(331\) 462.020i 1.39583i 0.716180 + 0.697915i \(0.245889\pi\)
−0.716180 + 0.697915i \(0.754111\pi\)
\(332\) 421.943 1.27091
\(333\) 248.852i 0.747302i
\(334\) 728.273i 2.18046i
\(335\) 449.962i 1.34317i
\(336\) 19.2853 + 19.2853i 0.0573967 + 0.0573967i
\(337\) −342.994 + 342.994i −1.01779 + 1.01779i −0.0179486 + 0.999839i \(0.505714\pi\)
−0.999839 + 0.0179486i \(0.994286\pi\)
\(338\) −258.051 258.051i −0.763464 0.763464i
\(339\) −754.225 −2.22485
\(340\) 888.011i 2.61180i
\(341\) 48.0848i 0.141011i
\(342\) 533.828 533.828i 1.56090 1.56090i
\(343\) 79.7972i 0.232645i
\(344\) 370.939 370.939i 1.07831 1.07831i
\(345\) 76.9841i 0.223142i
\(346\) 234.843 + 234.843i 0.678737 + 0.678737i
\(347\) −480.723 −1.38537 −0.692684 0.721241i \(-0.743572\pi\)
−0.692684 + 0.721241i \(0.743572\pi\)
\(348\) −515.493 515.493i −1.48130 1.48130i
\(349\) 440.470 440.470i 1.26209 1.26209i 0.312013 0.950078i \(-0.398997\pi\)
0.950078 0.312013i \(-0.101003\pi\)
\(350\) −6.88219 + 6.88219i −0.0196634 + 0.0196634i
\(351\) −33.8994 −0.0965794
\(352\) 112.509i 0.319628i
\(353\) −71.0279 −0.201212 −0.100606 0.994926i \(-0.532078\pi\)
−0.100606 + 0.994926i \(0.532078\pi\)
\(354\) 819.749i 2.31568i
\(355\) 459.200 1.29352
\(356\) 773.689 773.689i 2.17328 2.17328i
\(357\) 94.4078i 0.264448i
\(358\) 1016.88i 2.84044i
\(359\) −422.963 + 422.963i −1.17817 + 1.17817i −0.197961 + 0.980210i \(0.563432\pi\)
−0.980210 + 0.197961i \(0.936568\pi\)
\(360\) 506.267i 1.40630i
\(361\) −145.115 −0.401980
\(362\) −172.907 172.907i −0.477643 0.477643i
\(363\) 253.877 + 253.877i 0.699386 + 0.699386i
\(364\) −32.6485 + 32.6485i −0.0896937 + 0.0896937i
\(365\) 29.3402i 0.0803842i
\(366\) 1586.34i 4.33426i
\(367\) −390.668 + 390.668i −1.06449 + 1.06449i −0.0667195 + 0.997772i \(0.521253\pi\)
−0.997772 + 0.0667195i \(0.978747\pi\)
\(368\) 29.0910 0.0790516
\(369\) 1.25176 0.00339229
\(370\) 386.711i 1.04516i
\(371\) 26.8948i 0.0724926i
\(372\) −244.705 −0.657809
\(373\) 238.146 238.146i 0.638460 0.638460i −0.311715 0.950176i \(-0.600903\pi\)
0.950176 + 0.311715i \(0.100903\pi\)
\(374\) −389.528 + 389.528i −1.04152 + 1.04152i
\(375\) 576.315 1.53684
\(376\) −475.206 + 475.206i −1.26385 + 1.26385i
\(377\) 126.471 126.471i 0.335467 0.335467i
\(378\) 12.0156i 0.0317874i
\(379\) 10.3651 0.0273486 0.0136743 0.999907i \(-0.495647\pi\)
0.0136743 + 0.999907i \(0.495647\pi\)
\(380\) −534.775 + 534.775i −1.40730 + 1.40730i
\(381\) 264.577 + 264.577i 0.694427 + 0.694427i
\(382\) 431.066 431.066i 1.12844 1.12844i
\(383\) −82.7429 82.7429i −0.216039 0.216039i 0.590788 0.806827i \(-0.298817\pi\)
−0.806827 + 0.590788i \(0.798817\pi\)
\(384\) 1018.99 2.65362
\(385\) 23.6090 0.0613222
\(386\) −668.367 + 668.367i −1.73152 + 1.73152i
\(387\) −480.230 −1.24090
\(388\) 88.8942 0.229109
\(389\) −418.355 418.355i −1.07546 1.07546i −0.996910 0.0785540i \(-0.974970\pi\)
−0.0785540 0.996910i \(-0.525030\pi\)
\(390\) 525.816 1.34825
\(391\) 71.2049 + 71.2049i 0.182110 + 0.182110i
\(392\) 373.370 + 373.370i 0.952476 + 0.952476i
\(393\) 540.915i 1.37637i
\(394\) 515.023 + 414.253i 1.30717 + 1.05140i
\(395\) 283.191 0.716938
\(396\) 319.006 319.006i 0.805570 0.805570i
\(397\) −149.873 + 149.873i −0.377513 + 0.377513i −0.870204 0.492691i \(-0.836013\pi\)
0.492691 + 0.870204i \(0.336013\pi\)
\(398\) 113.180i 0.284372i
\(399\) −56.8539 + 56.8539i −0.142491 + 0.142491i
\(400\) 27.0009i 0.0675023i
\(401\) 375.045i 0.935275i 0.883920 + 0.467638i \(0.154895\pi\)
−0.883920 + 0.467638i \(0.845105\pi\)
\(402\) 1004.46 + 1004.46i 2.49865 + 2.49865i
\(403\) 60.0359i 0.148973i
\(404\) 229.573i 0.568249i
\(405\) 232.508 232.508i 0.574093 0.574093i
\(406\) 44.8277 + 44.8277i 0.110413 + 0.110413i
\(407\) −109.353 + 109.353i −0.268681 + 0.268681i
\(408\) −889.611 889.611i −2.18042 2.18042i
\(409\) 380.685i 0.930771i 0.885108 + 0.465385i \(0.154084\pi\)
−0.885108 + 0.465385i \(0.845916\pi\)
\(410\) −1.94520 −0.00474440
\(411\) 200.778 + 200.778i 0.488510 + 0.488510i
\(412\) 311.696 + 311.696i 0.756545 + 0.756545i
\(413\) 45.9546i 0.111270i
\(414\) −90.4576 90.4576i −0.218497 0.218497i
\(415\) 190.477 + 190.477i 0.458980 + 0.458980i
\(416\) 140.472i 0.337674i
\(417\) 660.501 1.58393
\(418\) −469.161 −1.12239
\(419\) 164.676i 0.393022i 0.980502 + 0.196511i \(0.0629611\pi\)
−0.980502 + 0.196511i \(0.937039\pi\)
\(420\) 120.147i 0.286064i
\(421\) −252.148 252.148i −0.598927 0.598927i 0.341100 0.940027i \(-0.389201\pi\)
−0.940027 + 0.341100i \(0.889201\pi\)
\(422\) 524.566 1.24305
\(423\) 615.217 1.45441
\(424\) 253.431 + 253.431i 0.597715 + 0.597715i
\(425\) 66.0892 66.0892i 0.155504 0.155504i
\(426\) −1025.08 + 1025.08i −2.40629 + 2.40629i
\(427\) 88.9291i 0.208265i
\(428\) 846.995 1.97896
\(429\) 148.689 + 148.689i 0.346594 + 0.346594i
\(430\) 746.268 1.73551
\(431\) −362.646 −0.841406 −0.420703 0.907198i \(-0.638217\pi\)
−0.420703 + 0.907198i \(0.638217\pi\)
\(432\) 23.5705 + 23.5705i 0.0545613 + 0.0545613i
\(433\) 338.525i 0.781812i −0.920431 0.390906i \(-0.872162\pi\)
0.920431 0.390906i \(-0.127838\pi\)
\(434\) 21.2797 0.0490316
\(435\) 465.416i 1.06992i
\(436\) −352.575 −0.808659
\(437\) 85.7616i 0.196251i
\(438\) 65.4966 + 65.4966i 0.149536 + 0.149536i
\(439\) −278.041 278.041i −0.633352 0.633352i 0.315555 0.948907i \(-0.397809\pi\)
−0.948907 + 0.315555i \(0.897809\pi\)
\(440\) −222.470 + 222.470i −0.505613 + 0.505613i
\(441\) 483.377i 1.09609i
\(442\) 486.343 486.343i 1.10032 1.10032i
\(443\) 433.756 0.979133 0.489567 0.871966i \(-0.337155\pi\)
0.489567 + 0.871966i \(0.337155\pi\)
\(444\) −556.501 556.501i −1.25338 1.25338i
\(445\) 698.530 1.56973
\(446\) 175.106 + 175.106i 0.392614 + 0.392614i
\(447\) −879.746 −1.96811
\(448\) −74.8170 −0.167002
\(449\) 670.200i 1.49265i −0.665581 0.746326i \(-0.731816\pi\)
0.665581 0.746326i \(-0.268184\pi\)
\(450\) −83.9586 + 83.9586i −0.186575 + 0.186575i
\(451\) −0.550060 0.550060i −0.00121965 0.00121965i
\(452\) −887.799 + 887.799i −1.96416 + 1.96416i
\(453\) 886.752 1.95751
\(454\) 220.358 0.485371
\(455\) −29.4769 −0.0647844
\(456\) 1071.48i 2.34973i
\(457\) −331.169 −0.724658 −0.362329 0.932050i \(-0.618018\pi\)
−0.362329 + 0.932050i \(0.618018\pi\)
\(458\) 523.487i 1.14298i
\(459\) 115.385i 0.251384i
\(460\) 90.6181 + 90.6181i 0.196996 + 0.196996i
\(461\) 26.1842 26.1842i 0.0567987 0.0567987i −0.678137 0.734936i \(-0.737212\pi\)
0.734936 + 0.678137i \(0.237212\pi\)
\(462\) −52.7028 + 52.7028i −0.114075 + 0.114075i
\(463\) −157.939 + 157.939i −0.341120 + 0.341120i −0.856788 0.515668i \(-0.827544\pi\)
0.515668 + 0.856788i \(0.327544\pi\)
\(464\) −175.873 −0.379036
\(465\) −110.467 110.467i −0.237563 0.237563i
\(466\) −777.787 + 777.787i −1.66907 + 1.66907i
\(467\) 209.253 209.253i 0.448080 0.448080i −0.446636 0.894716i \(-0.647378\pi\)
0.894716 + 0.446636i \(0.147378\pi\)
\(468\) −398.292 + 398.292i −0.851052 + 0.851052i
\(469\) −56.3092 56.3092i −0.120062 0.120062i
\(470\) −956.036 −2.03412
\(471\) −904.098 904.098i −1.91953 1.91953i
\(472\) −433.033 433.033i −0.917444 0.917444i
\(473\) 211.028 + 211.028i 0.446148 + 0.446148i
\(474\) −632.170 + 632.170i −1.33369 + 1.33369i
\(475\) 79.6000 0.167579
\(476\) 111.128 + 111.128i 0.233461 + 0.233461i
\(477\) 328.100i 0.687841i
\(478\) 122.411 122.411i 0.256091 0.256091i
\(479\) −56.8562 −0.118698 −0.0593489 0.998237i \(-0.518902\pi\)
−0.0593489 + 0.998237i \(0.518902\pi\)
\(480\) 258.470 + 258.470i 0.538480 + 0.538480i
\(481\) 136.532 136.532i 0.283850 0.283850i
\(482\) −1397.76 −2.89991
\(483\) 9.63395 + 9.63395i 0.0199461 + 0.0199461i
\(484\) 597.678 1.23487
\(485\) 40.1293 + 40.1293i 0.0827409 + 0.0827409i
\(486\) 1169.96i 2.40732i
\(487\) 358.291i 0.735710i −0.929883 0.367855i \(-0.880092\pi\)
0.929883 0.367855i \(-0.119908\pi\)
\(488\) −837.985 837.985i −1.71718 1.71718i
\(489\) 263.242 + 263.242i 0.538327 + 0.538327i
\(490\) 751.159i 1.53298i
\(491\) 248.740i 0.506599i 0.967388 + 0.253299i \(0.0815157\pi\)
−0.967388 + 0.253299i \(0.918484\pi\)
\(492\) 2.79927 2.79927i 0.00568957 0.00568957i
\(493\) −430.477 430.477i −0.873178 0.873178i
\(494\) 585.767 1.18576
\(495\) 288.016 0.581851
\(496\) −41.7434 + 41.7434i −0.0841601 + 0.0841601i
\(497\) 57.4653 57.4653i 0.115624 0.115624i
\(498\) −850.407 −1.70764
\(499\) −879.371 −1.76227 −0.881133 0.472868i \(-0.843219\pi\)
−0.881133 + 0.472868i \(0.843219\pi\)
\(500\) 678.382 678.382i 1.35676 1.35676i
\(501\) 946.220i 1.88866i
\(502\) −509.621 + 509.621i −1.01518 + 1.01518i
\(503\) 348.017i 0.691882i 0.938256 + 0.345941i \(0.112440\pi\)
−0.938256 + 0.345941i \(0.887560\pi\)
\(504\) −63.3553 63.3553i −0.125705 0.125705i
\(505\) −103.635 + 103.635i −0.205219 + 0.205219i
\(506\) 79.4998i 0.157114i
\(507\) 335.277 + 335.277i 0.661295 + 0.661295i
\(508\) 622.868 1.22612
\(509\) 387.459 387.459i 0.761216 0.761216i −0.215326 0.976542i \(-0.569081\pi\)
0.976542 + 0.215326i \(0.0690814\pi\)
\(510\) 1789.75i 3.50931i
\(511\) −3.67170 3.67170i −0.00718531 0.00718531i
\(512\) 333.498 333.498i 0.651364 0.651364i
\(513\) −69.4869 + 69.4869i −0.135452 + 0.135452i
\(514\) 920.010 920.010i 1.78990 1.78990i
\(515\) 281.417i 0.546440i
\(516\) −1073.93 + 1073.93i −2.08125 + 2.08125i
\(517\) −270.346 270.346i −0.522912 0.522912i
\(518\) 48.3937 + 48.3937i 0.0934242 + 0.0934242i
\(519\) −305.123 305.123i −0.587906 0.587906i
\(520\) 277.763 277.763i 0.534159 0.534159i
\(521\) 615.109i 1.18063i 0.807172 + 0.590316i \(0.200997\pi\)
−0.807172 + 0.590316i \(0.799003\pi\)
\(522\) 546.871 + 546.871i 1.04765 + 1.04765i
\(523\) −102.223 102.223i −0.195456 0.195456i 0.602593 0.798049i \(-0.294134\pi\)
−0.798049 + 0.602593i \(0.794134\pi\)
\(524\) 636.712 + 636.712i 1.21510 + 1.21510i
\(525\) 8.94179 8.94179i 0.0170320 0.0170320i
\(526\) −110.349 −0.209788
\(527\) −204.348 −0.387756
\(528\) 206.769i 0.391608i
\(529\) −514.468 −0.972529
\(530\) 509.861i 0.962002i
\(531\) 560.619i 1.05578i
\(532\) 133.846i 0.251590i
\(533\) 0.686773 + 0.686773i 0.00128851 + 0.00128851i
\(534\) −1559.34 + 1559.34i −2.92011 + 2.92011i
\(535\) 382.357 + 382.357i 0.714687 + 0.714687i
\(536\) 1061.21 1.97987
\(537\) 1321.19i 2.46032i
\(538\) 693.355i 1.28876i
\(539\) −212.411 + 212.411i −0.394084 + 0.394084i
\(540\) 146.844i 0.271933i
\(541\) −367.831 + 367.831i −0.679910 + 0.679910i −0.959980 0.280070i \(-0.909642\pi\)
0.280070 + 0.959980i \(0.409642\pi\)
\(542\) 93.8265i 0.173112i
\(543\) 224.652 + 224.652i 0.413724 + 0.413724i
\(544\) 478.134 0.878922
\(545\) −159.162 159.162i −0.292041 0.292041i
\(546\) 65.8017 65.8017i 0.120516 0.120516i
\(547\) −610.470 + 610.470i −1.11603 + 1.11603i −0.123716 + 0.992318i \(0.539481\pi\)
−0.992318 + 0.123716i \(0.960519\pi\)
\(548\) 472.672 0.862539
\(549\) 1084.88i 1.97611i
\(550\) 73.7880 0.134160
\(551\) 518.481i 0.940982i
\(552\) −181.563 −0.328918
\(553\) 35.4390 35.4390i 0.0640851 0.0640851i
\(554\) 594.726i 1.07351i
\(555\) 502.440i 0.905297i
\(556\) 777.477 777.477i 1.39834 1.39834i
\(557\) 0.989596i 0.00177665i −1.00000 0.000888326i \(-0.999717\pi\)
1.00000 0.000888326i \(-0.000282763\pi\)
\(558\) 259.600 0.465233
\(559\) −263.477 263.477i −0.471337 0.471337i
\(560\) 20.4955 + 20.4955i 0.0365991 + 0.0365991i
\(561\) 506.101 506.101i 0.902141 0.902141i
\(562\) 1261.20i 2.24413i
\(563\) 667.879i 1.18629i −0.805097 0.593143i \(-0.797887\pi\)
0.805097 0.593143i \(-0.202113\pi\)
\(564\) 1375.80 1375.80i 2.43935 2.43935i
\(565\) −801.555 −1.41868
\(566\) 824.137 1.45607
\(567\) 58.1930i 0.102633i
\(568\) 1083.00i 1.90669i
\(569\) −761.118 −1.33764 −0.668821 0.743424i \(-0.733201\pi\)
−0.668821 + 0.743424i \(0.733201\pi\)
\(570\) 1077.82 1077.82i 1.89091 1.89091i
\(571\) −112.786 + 112.786i −0.197524 + 0.197524i −0.798938 0.601414i \(-0.794604\pi\)
0.601414 + 0.798938i \(0.294604\pi\)
\(572\) 350.044 0.611965
\(573\) −560.069 + 560.069i −0.977433 + 0.977433i
\(574\) −0.243427 + 0.243427i −0.000424088 + 0.000424088i
\(575\) 13.4883i 0.0234579i
\(576\) −912.722 −1.58459
\(577\) 196.147 196.147i 0.339943 0.339943i −0.516403 0.856346i \(-0.672729\pi\)
0.856346 + 0.516403i \(0.172729\pi\)
\(578\) −969.769 969.769i −1.67780 1.67780i
\(579\) 868.386 868.386i 1.49980 1.49980i
\(580\) −547.842 547.842i −0.944554 0.944554i
\(581\) 47.6733 0.0820538
\(582\) −179.162 −0.307839
\(583\) −144.177 + 144.177i −0.247302 + 0.247302i
\(584\) 69.1973 0.118488
\(585\) −359.601 −0.614702
\(586\) 389.293 + 389.293i 0.664323 + 0.664323i
\(587\) 708.124 1.20634 0.603172 0.797611i \(-0.293903\pi\)
0.603172 + 0.797611i \(0.293903\pi\)
\(588\) −1080.96 1080.96i −1.83838 1.83838i
\(589\) −123.062 123.062i −0.208933 0.208933i
\(590\) 871.191i 1.47659i
\(591\) −669.152 538.225i −1.13224 0.910702i
\(592\) −189.863 −0.320715
\(593\) −76.1146 + 76.1146i −0.128355 + 0.128355i −0.768366 0.640011i \(-0.778930\pi\)
0.640011 + 0.768366i \(0.278930\pi\)
\(594\) −64.4133 + 64.4133i −0.108440 + 0.108440i
\(595\) 100.332i 0.168625i
\(596\) −1035.55 + 1035.55i −1.73750 + 1.73750i
\(597\) 147.051i 0.246316i
\(598\) 99.2588i 0.165985i
\(599\) 252.210 + 252.210i 0.421052 + 0.421052i 0.885566 0.464514i \(-0.153771\pi\)
−0.464514 + 0.885566i \(0.653771\pi\)
\(600\) 168.518i 0.280864i
\(601\) 840.803i 1.39901i 0.714629 + 0.699504i \(0.246595\pi\)
−0.714629 + 0.699504i \(0.753405\pi\)
\(602\) 93.3895 93.3895i 0.155132 0.155132i
\(603\) −686.939 686.939i −1.13920 1.13920i
\(604\) 1043.80 1043.80i 1.72814 1.72814i
\(605\) 269.809 + 269.809i 0.445965 + 0.445965i
\(606\) 462.694i 0.763521i
\(607\) −558.068 −0.919387 −0.459693 0.888078i \(-0.652041\pi\)
−0.459693 + 0.888078i \(0.652041\pi\)
\(608\) 287.940 + 287.940i 0.473586 + 0.473586i
\(609\) −58.2431 58.2431i −0.0956372 0.0956372i
\(610\) 1685.89i 2.76375i
\(611\) 337.538 + 337.538i 0.552435 + 0.552435i
\(612\) 1355.69 + 1355.69i 2.21518 + 2.21518i
\(613\) 382.855i 0.624560i −0.949990 0.312280i \(-0.898907\pi\)
0.949990 0.312280i \(-0.101093\pi\)
\(614\) 1065.05 1.73461
\(615\) 2.52734 0.00410949
\(616\) 55.6806i 0.0903906i
\(617\) 967.644i 1.56831i −0.620568 0.784153i \(-0.713098\pi\)
0.620568 0.784153i \(-0.286902\pi\)
\(618\) −628.211 628.211i −1.01652 1.01652i
\(619\) 272.133 0.439633 0.219816 0.975541i \(-0.429454\pi\)
0.219816 + 0.975541i \(0.429454\pi\)
\(620\) −260.061 −0.419453
\(621\) 11.7746 + 11.7746i 0.0189607 + 0.0189607i
\(622\) −728.033 + 728.033i −1.17047 + 1.17047i
\(623\) 87.4154 87.4154i 0.140314 0.140314i
\(624\) 258.160i 0.413718i
\(625\) 524.025 0.838439
\(626\) 723.401 + 723.401i 1.15559 + 1.15559i
\(627\) 609.565 0.972193
\(628\) −2128.43 −3.38922
\(629\) −464.721 464.721i −0.738826 0.738826i
\(630\) 127.460i 0.202318i
\(631\) 1029.69 1.63184 0.815920 0.578165i \(-0.196231\pi\)
0.815920 + 0.578165i \(0.196231\pi\)
\(632\) 667.889i 1.05679i
\(633\) −681.551 −1.07670
\(634\) 1986.95i 3.13398i
\(635\) 281.180 + 281.180i 0.442803 + 0.442803i
\(636\) −733.722 733.722i −1.15365 1.15365i
\(637\) 265.204 265.204i 0.416333 0.416333i
\(638\) 480.624i 0.753329i
\(639\) 701.042 701.042i 1.09709 1.09709i
\(640\) 1082.94 1.69209
\(641\) −45.9001 45.9001i −0.0716070 0.0716070i 0.670396 0.742003i \(-0.266124\pi\)
−0.742003 + 0.670396i \(0.766124\pi\)
\(642\) −1707.08 −2.65901
\(643\) −286.890 286.890i −0.446174 0.446174i 0.447906 0.894080i \(-0.352170\pi\)
−0.894080 + 0.447906i \(0.852170\pi\)
\(644\) 22.6803 0.0352178
\(645\) −969.600 −1.50326
\(646\) 1993.81i 3.08639i
\(647\) 733.363 733.363i 1.13348 1.13348i 0.143888 0.989594i \(-0.454040\pi\)
0.989594 0.143888i \(-0.0459604\pi\)
\(648\) 548.356 + 548.356i 0.846229 + 0.846229i
\(649\) 246.353 246.353i 0.379589 0.379589i
\(650\) −92.1275 −0.141735
\(651\) −27.6480 −0.0424701
\(652\) 619.725 0.950498
\(653\) 987.389i 1.51208i 0.654524 + 0.756041i \(0.272869\pi\)
−0.654524 + 0.756041i \(0.727131\pi\)
\(654\) 710.601 1.08655
\(655\) 574.859i 0.877648i
\(656\) 0.955037i 0.00145585i
\(657\) −44.7925 44.7925i −0.0681773 0.0681773i
\(658\) −119.640 + 119.640i −0.181824 + 0.181824i
\(659\) −581.166 + 581.166i −0.881891 + 0.881891i −0.993727 0.111835i \(-0.964327\pi\)
0.111835 + 0.993727i \(0.464327\pi\)
\(660\) 644.084 644.084i 0.975884 0.975884i
\(661\) −85.2172 −0.128922 −0.0644608 0.997920i \(-0.520533\pi\)
−0.0644608 + 0.997920i \(0.520533\pi\)
\(662\) −1096.09 1096.09i −1.65573 1.65573i
\(663\) −631.888 + 631.888i −0.953075 + 0.953075i
\(664\) −449.228 + 449.228i −0.676549 + 0.676549i
\(665\) −60.4217 + 60.4217i −0.0908597 + 0.0908597i
\(666\) 590.375 + 590.375i 0.886449 + 0.886449i
\(667\) −87.8570 −0.131720
\(668\) −1113.80 1113.80i −1.66736 1.66736i
\(669\) −227.509 227.509i −0.340073 0.340073i
\(670\) 1067.49 + 1067.49i 1.59327 + 1.59327i
\(671\) 476.731 476.731i 0.710478 0.710478i
\(672\) 64.6910 0.0962663
\(673\) 332.466 + 332.466i 0.494007 + 0.494007i 0.909566 0.415559i \(-0.136414\pi\)
−0.415559 + 0.909566i \(0.636414\pi\)
\(674\) 1627.44i 2.41460i
\(675\) 10.9287 10.9287i 0.0161906 0.0161906i
\(676\) 789.309 1.16762
\(677\) −40.8547 40.8547i −0.0603466 0.0603466i 0.676289 0.736636i \(-0.263587\pi\)
−0.736636 + 0.676289i \(0.763587\pi\)
\(678\) 1789.32 1789.32i 2.63912 2.63912i
\(679\) 10.0437 0.0147919
\(680\) −945.436 945.436i −1.39035 1.39035i
\(681\) −286.304 −0.420417
\(682\) −114.076 114.076i −0.167267 0.167267i
\(683\) 594.885i 0.870989i 0.900191 + 0.435494i \(0.143426\pi\)
−0.900191 + 0.435494i \(0.856574\pi\)
\(684\) 1632.84i 2.38719i
\(685\) 213.377 + 213.377i 0.311499 + 0.311499i
\(686\) 189.311 + 189.311i 0.275963 + 0.275963i
\(687\) 680.148i 0.990027i
\(688\) 366.395i 0.532551i
\(689\) 180.011 180.011i 0.261265 0.261265i
\(690\) −182.637 182.637i −0.264691 0.264691i
\(691\) 436.690 0.631969 0.315984 0.948764i \(-0.397665\pi\)
0.315984 + 0.948764i \(0.397665\pi\)
\(692\) −718.322 −1.03804
\(693\) 36.0429 36.0429i 0.0520100 0.0520100i
\(694\) 1140.47 1140.47i 1.64332 1.64332i
\(695\) 701.949 1.01000
\(696\) 1097.66 1.57709
\(697\) 2.33761 2.33761i 0.00335381 0.00335381i
\(698\) 2089.94i 2.99418i
\(699\) 1010.55 1010.55i 1.44571 1.44571i
\(700\) 21.0508i 0.0300726i
\(701\) −728.508 728.508i −1.03924 1.03924i −0.999198 0.0400426i \(-0.987251\pi\)
−0.0400426 0.999198i \(-0.512749\pi\)
\(702\) 80.4228 80.4228i 0.114562 0.114562i
\(703\) 559.726i 0.796197i
\(704\) 401.078 + 401.078i 0.569714 + 0.569714i
\(705\) 1242.14 1.76191
\(706\) 168.506 168.506i 0.238678 0.238678i
\(707\) 25.9383i 0.0366878i
\(708\) 1253.70 + 1253.70i 1.77076 + 1.77076i
\(709\) 109.500 109.500i 0.154443 0.154443i −0.625656 0.780099i \(-0.715169\pi\)
0.780099 + 0.625656i \(0.215169\pi\)
\(710\) −1089.41 + 1089.41i −1.53437 + 1.53437i
\(711\) 432.335 432.335i 0.608066 0.608066i
\(712\) 1647.44i 2.31382i
\(713\) −20.8529 + 20.8529i −0.0292467 + 0.0292467i
\(714\) −223.973 223.973i −0.313687 0.313687i
\(715\) 158.020 + 158.020i 0.221006 + 0.221006i
\(716\) 1555.18 + 1555.18i 2.17204 + 2.17204i
\(717\) −159.045 + 159.045i −0.221820 + 0.221820i
\(718\) 2006.87i 2.79509i
\(719\) −303.903 303.903i −0.422675 0.422675i 0.463449 0.886124i \(-0.346612\pi\)
−0.886124 + 0.463449i \(0.846612\pi\)
\(720\) 250.033 + 250.033i 0.347268 + 0.347268i
\(721\) 35.2171 + 35.2171i 0.0488448 + 0.0488448i
\(722\) 344.270 344.270i 0.476828 0.476828i
\(723\) 1816.06 2.51184
\(724\) 528.876 0.730492
\(725\) 81.5449i 0.112476i
\(726\) −1204.59 −1.65922
\(727\) 534.752i 0.735560i 0.929913 + 0.367780i \(0.119882\pi\)
−0.929913 + 0.367780i \(0.880118\pi\)
\(728\) 69.5196i 0.0954939i
\(729\) 881.290i 1.20890i
\(730\) 69.6067 + 69.6067i 0.0953516 + 0.0953516i
\(731\) −896.812 + 896.812i −1.22683 + 1.22683i
\(732\) 2426.09 + 2426.09i 3.31434 + 3.31434i
\(733\) 240.128 0.327596 0.163798 0.986494i \(-0.447625\pi\)
0.163798 + 0.986494i \(0.447625\pi\)
\(734\) 1853.64i 2.52540i
\(735\) 975.955i 1.32783i
\(736\) 48.7917 48.7917i 0.0662931 0.0662931i
\(737\) 603.724i 0.819165i
\(738\) −2.96966 + 2.96966i −0.00402393 + 0.00402393i
\(739\) 627.696i 0.849386i −0.905337 0.424693i \(-0.860382\pi\)
0.905337 0.424693i \(-0.139618\pi\)
\(740\) −591.423 591.423i −0.799220 0.799220i
\(741\) −761.068 −1.02708
\(742\) 63.8050 + 63.8050i 0.0859906 + 0.0859906i
\(743\) 40.1016 40.1016i 0.0539725 0.0539725i −0.679605 0.733578i \(-0.737849\pi\)
0.733578 + 0.679605i \(0.237849\pi\)
\(744\) 260.529 260.529i 0.350174 0.350174i
\(745\) −934.952 −1.25497
\(746\) 1129.95i 1.51468i
\(747\) 581.585 0.778562
\(748\) 1191.46i 1.59287i
\(749\) 95.6979 0.127768
\(750\) −1367.25 + 1367.25i −1.82300 + 1.82300i
\(751\) 496.092i 0.660576i −0.943880 0.330288i \(-0.892854\pi\)
0.943880 0.330288i \(-0.107146\pi\)
\(752\) 469.385i 0.624182i
\(753\) 662.134 662.134i 0.879328 0.879328i
\(754\) 600.080i 0.795862i
\(755\) 942.398 1.24821
\(756\) 18.3763 + 18.3763i 0.0243073 + 0.0243073i
\(757\) −182.576 182.576i −0.241184 0.241184i 0.576156 0.817340i \(-0.304552\pi\)
−0.817340 + 0.576156i \(0.804552\pi\)
\(758\) −24.5902 + 24.5902i −0.0324409 + 0.0324409i
\(759\) 103.291i 0.136089i
\(760\) 1138.72i 1.49831i
\(761\) −596.944 + 596.944i −0.784421 + 0.784421i −0.980573 0.196153i \(-0.937155\pi\)
0.196153 + 0.980573i \(0.437155\pi\)
\(762\) −1255.36 −1.64746
\(763\) −39.8358 −0.0522094
\(764\) 1318.52i 1.72581i
\(765\) 1223.99i 1.59999i
\(766\) 392.598 0.512530
\(767\) −307.583 + 307.583i −0.401020 + 0.401020i
\(768\) −1292.34 + 1292.34i −1.68274 + 1.68274i
\(769\) −349.377 −0.454327 −0.227164 0.973857i \(-0.572945\pi\)
−0.227164 + 0.973857i \(0.572945\pi\)
\(770\) −56.0100 + 56.0100i −0.0727403 + 0.0727403i
\(771\) −1195.34 + 1195.34i −1.55037 + 1.55037i
\(772\) 2044.36i 2.64813i
\(773\) −1025.15 −1.32620 −0.663101 0.748530i \(-0.730760\pi\)
−0.663101 + 0.748530i \(0.730760\pi\)
\(774\) 1139.30 1139.30i 1.47196 1.47196i
\(775\) 19.3547 + 19.3547i 0.0249738 + 0.0249738i