Properties

Label 197.3.c.a.14.13
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 14.13
Character \(\chi\) \(=\) 197.14
Dual form 197.3.c.a.183.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.770755 + 0.770755i) q^{2} +(4.07862 - 4.07862i) q^{3} +2.81187i q^{4} +(-1.79164 + 1.79164i) q^{5} +6.28722i q^{6} -12.4564i q^{7} +(-5.25028 - 5.25028i) q^{8} -24.2702i q^{9} +O(q^{10})\) \(q+(-0.770755 + 0.770755i) q^{2} +(4.07862 - 4.07862i) q^{3} +2.81187i q^{4} +(-1.79164 + 1.79164i) q^{5} +6.28722i q^{6} -12.4564i q^{7} +(-5.25028 - 5.25028i) q^{8} -24.2702i q^{9} -2.76183i q^{10} +(-3.64909 + 3.64909i) q^{11} +(11.4686 + 11.4686i) q^{12} +(7.29392 - 7.29392i) q^{13} +(9.60079 + 9.60079i) q^{14} +14.6148i q^{15} -3.15414 q^{16} +(20.8492 + 20.8492i) q^{17} +(18.7064 + 18.7064i) q^{18} -18.2804i q^{19} +(-5.03787 - 5.03787i) q^{20} +(-50.8047 - 50.8047i) q^{21} -5.62510i q^{22} +13.8824 q^{23} -42.8278 q^{24} +18.5800i q^{25} +11.2436i q^{26} +(-62.2814 - 62.2814i) q^{27} +35.0257 q^{28} +16.1967 q^{29} +(-11.2645 - 11.2645i) q^{30} +(-18.8855 + 18.8855i) q^{31} +(23.4322 - 23.4322i) q^{32} +29.7665i q^{33} -32.1392 q^{34} +(22.3173 + 22.3173i) q^{35} +68.2448 q^{36} +3.02209 q^{37} +(14.0897 + 14.0897i) q^{38} -59.4982i q^{39} +18.8133 q^{40} -5.69712i q^{41} +78.3159 q^{42} +29.5375i q^{43} +(-10.2608 - 10.2608i) q^{44} +(43.4836 + 43.4836i) q^{45} +(-10.6999 + 10.6999i) q^{46} +22.9806i q^{47} +(-12.8645 + 12.8645i) q^{48} -106.161 q^{49} +(-14.3206 - 14.3206i) q^{50} +170.072 q^{51} +(20.5096 + 20.5096i) q^{52} -41.2966 q^{53} +96.0073 q^{54} -13.0757i q^{55} +(-65.3994 + 65.3994i) q^{56} +(-74.5589 - 74.5589i) q^{57} +(-12.4837 + 12.4837i) q^{58} +88.3938 q^{59} -41.0951 q^{60} -31.4183 q^{61} -29.1122i q^{62} -302.318 q^{63} +23.5044i q^{64} +26.1362i q^{65} +(-22.9426 - 22.9426i) q^{66} +(16.9321 - 16.9321i) q^{67} +(-58.6254 + 58.6254i) q^{68} +(56.6210 - 56.6210i) q^{69} -34.4024 q^{70} +(41.9412 + 41.9412i) q^{71} +(-127.426 + 127.426i) q^{72} +(-30.0329 + 30.0329i) q^{73} +(-2.32929 + 2.32929i) q^{74} +(75.7808 + 75.7808i) q^{75} +51.4023 q^{76} +(45.4543 + 45.4543i) q^{77} +(45.8585 + 45.8585i) q^{78} +(99.8739 + 99.8739i) q^{79} +(5.65109 - 5.65109i) q^{80} -289.612 q^{81} +(4.39108 + 4.39108i) q^{82} +64.8005i q^{83} +(142.856 - 142.856i) q^{84} -74.7087 q^{85} +(-22.7661 - 22.7661i) q^{86} +(66.0601 - 66.0601i) q^{87} +38.3175 q^{88} +(-91.0809 - 91.0809i) q^{89} -67.0303 q^{90} +(-90.8556 - 90.8556i) q^{91} +39.0356i q^{92} +154.054i q^{93} +(-17.7124 - 17.7124i) q^{94} +(32.7520 + 32.7520i) q^{95} -191.142i q^{96} -43.2796i q^{97} +(81.8238 - 81.8238i) q^{98} +(88.5642 + 88.5642i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.770755 + 0.770755i −0.385377 + 0.385377i −0.873035 0.487658i \(-0.837851\pi\)
0.487658 + 0.873035i \(0.337851\pi\)
\(3\) 4.07862 4.07862i 1.35954 1.35954i 0.485055 0.874484i \(-0.338800\pi\)
0.874484 0.485055i \(-0.161200\pi\)
\(4\) 2.81187i 0.702969i
\(5\) −1.79164 + 1.79164i −0.358328 + 0.358328i −0.863197 0.504868i \(-0.831541\pi\)
0.504868 + 0.863197i \(0.331541\pi\)
\(6\) 6.28722i 1.04787i
\(7\) 12.4564i 1.77948i −0.456469 0.889739i \(-0.650886\pi\)
0.456469 0.889739i \(-0.349114\pi\)
\(8\) −5.25028 5.25028i −0.656285 0.656285i
\(9\) 24.2702i 2.69669i
\(10\) 2.76183i 0.276183i
\(11\) −3.64909 + 3.64909i −0.331735 + 0.331735i −0.853245 0.521510i \(-0.825369\pi\)
0.521510 + 0.853245i \(0.325369\pi\)
\(12\) 11.4686 + 11.4686i 0.955713 + 0.955713i
\(13\) 7.29392 7.29392i 0.561071 0.561071i −0.368541 0.929612i \(-0.620142\pi\)
0.929612 + 0.368541i \(0.120142\pi\)
\(14\) 9.60079 + 9.60079i 0.685771 + 0.685771i
\(15\) 14.6148i 0.974323i
\(16\) −3.15414 −0.197134
\(17\) 20.8492 + 20.8492i 1.22642 + 1.22642i 0.965307 + 0.261117i \(0.0840908\pi\)
0.261117 + 0.965307i \(0.415909\pi\)
\(18\) 18.7064 + 18.7064i 1.03924 + 1.03924i
\(19\) 18.2804i 0.962129i −0.876685 0.481064i \(-0.840250\pi\)
0.876685 0.481064i \(-0.159750\pi\)
\(20\) −5.03787 5.03787i −0.251894 0.251894i
\(21\) −50.8047 50.8047i −2.41927 2.41927i
\(22\) 5.62510i 0.255686i
\(23\) 13.8824 0.603582 0.301791 0.953374i \(-0.402415\pi\)
0.301791 + 0.953374i \(0.402415\pi\)
\(24\) −42.8278 −1.78449
\(25\) 18.5800i 0.743201i
\(26\) 11.2436i 0.432448i
\(27\) −62.2814 62.2814i −2.30672 2.30672i
\(28\) 35.0257 1.25092
\(29\) 16.1967 0.558507 0.279254 0.960217i \(-0.409913\pi\)
0.279254 + 0.960217i \(0.409913\pi\)
\(30\) −11.2645 11.2645i −0.375482 0.375482i
\(31\) −18.8855 + 18.8855i −0.609211 + 0.609211i −0.942740 0.333529i \(-0.891760\pi\)
0.333529 + 0.942740i \(0.391760\pi\)
\(32\) 23.4322 23.4322i 0.732256 0.732256i
\(33\) 29.7665i 0.902014i
\(34\) −32.1392 −0.945272
\(35\) 22.3173 + 22.3173i 0.637638 + 0.637638i
\(36\) 68.2448 1.89569
\(37\) 3.02209 0.0816781 0.0408391 0.999166i \(-0.486997\pi\)
0.0408391 + 0.999166i \(0.486997\pi\)
\(38\) 14.0897 + 14.0897i 0.370783 + 0.370783i
\(39\) 59.4982i 1.52560i
\(40\) 18.8133 0.470332
\(41\) 5.69712i 0.138954i −0.997584 0.0694771i \(-0.977867\pi\)
0.997584 0.0694771i \(-0.0221331\pi\)
\(42\) 78.3159 1.86466
\(43\) 29.5375i 0.686918i 0.939168 + 0.343459i \(0.111599\pi\)
−0.939168 + 0.343459i \(0.888401\pi\)
\(44\) −10.2608 10.2608i −0.233199 0.233199i
\(45\) 43.4836 + 43.4836i 0.966301 + 0.966301i
\(46\) −10.6999 + 10.6999i −0.232607 + 0.232607i
\(47\) 22.9806i 0.488948i 0.969656 + 0.244474i \(0.0786153\pi\)
−0.969656 + 0.244474i \(0.921385\pi\)
\(48\) −12.8645 + 12.8645i −0.268011 + 0.268011i
\(49\) −106.161 −2.16654
\(50\) −14.3206 14.3206i −0.286413 0.286413i
\(51\) 170.072 3.33474
\(52\) 20.5096 + 20.5096i 0.394415 + 0.394415i
\(53\) −41.2966 −0.779180 −0.389590 0.920988i \(-0.627383\pi\)
−0.389590 + 0.920988i \(0.627383\pi\)
\(54\) 96.0073 1.77791
\(55\) 13.0757i 0.237740i
\(56\) −65.3994 + 65.3994i −1.16785 + 1.16785i
\(57\) −74.5589 74.5589i −1.30805 1.30805i
\(58\) −12.4837 + 12.4837i −0.215236 + 0.215236i
\(59\) 88.3938 1.49820 0.749100 0.662457i \(-0.230486\pi\)
0.749100 + 0.662457i \(0.230486\pi\)
\(60\) −41.0951 −0.684919
\(61\) −31.4183 −0.515054 −0.257527 0.966271i \(-0.582908\pi\)
−0.257527 + 0.966271i \(0.582908\pi\)
\(62\) 29.1122i 0.469552i
\(63\) −302.318 −4.79870
\(64\) 23.5044i 0.367256i
\(65\) 26.1362i 0.402095i
\(66\) −22.9426 22.9426i −0.347616 0.347616i
\(67\) 16.9321 16.9321i 0.252717 0.252717i −0.569366 0.822084i \(-0.692811\pi\)
0.822084 + 0.569366i \(0.192811\pi\)
\(68\) −58.6254 + 58.6254i −0.862138 + 0.862138i
\(69\) 56.6210 56.6210i 0.820594 0.820594i
\(70\) −34.4024 −0.491462
\(71\) 41.9412 + 41.9412i 0.590721 + 0.590721i 0.937826 0.347105i \(-0.112835\pi\)
−0.347105 + 0.937826i \(0.612835\pi\)
\(72\) −127.426 + 127.426i −1.76980 + 1.76980i
\(73\) −30.0329 + 30.0329i −0.411410 + 0.411410i −0.882230 0.470819i \(-0.843958\pi\)
0.470819 + 0.882230i \(0.343958\pi\)
\(74\) −2.32929 + 2.32929i −0.0314769 + 0.0314769i
\(75\) 75.7808 + 75.7808i 1.01041 + 1.01041i
\(76\) 51.4023 0.676346
\(77\) 45.4543 + 45.4543i 0.590316 + 0.590316i
\(78\) 45.8585 + 45.8585i 0.587930 + 0.587930i
\(79\) 99.8739 + 99.8739i 1.26423 + 1.26423i 0.949024 + 0.315203i \(0.102072\pi\)
0.315203 + 0.949024i \(0.397928\pi\)
\(80\) 5.65109 5.65109i 0.0706386 0.0706386i
\(81\) −289.612 −3.57545
\(82\) 4.39108 + 4.39108i 0.0535498 + 0.0535498i
\(83\) 64.8005i 0.780729i 0.920660 + 0.390364i \(0.127651\pi\)
−0.920660 + 0.390364i \(0.872349\pi\)
\(84\) 142.856 142.856i 1.70067 1.70067i
\(85\) −74.7087 −0.878925
\(86\) −22.7661 22.7661i −0.264722 0.264722i
\(87\) 66.0601 66.0601i 0.759312 0.759312i
\(88\) 38.3175 0.435426
\(89\) −91.0809 91.0809i −1.02338 1.02338i −0.999720 0.0236614i \(-0.992468\pi\)
−0.0236614 0.999720i \(-0.507532\pi\)
\(90\) −67.0303 −0.744781
\(91\) −90.8556 90.8556i −0.998414 0.998414i
\(92\) 39.0356i 0.424299i
\(93\) 154.054i 1.65649i
\(94\) −17.7124 17.7124i −0.188430 0.188430i
\(95\) 32.7520 + 32.7520i 0.344758 + 0.344758i
\(96\) 191.142i 1.99106i
\(97\) 43.2796i 0.446181i −0.974798 0.223091i \(-0.928385\pi\)
0.974798 0.223091i \(-0.0716146\pi\)
\(98\) 81.8238 81.8238i 0.834937 0.834937i
\(99\) 88.5642 + 88.5642i 0.894587 + 0.894587i
\(100\) −52.2447 −0.522447
\(101\) 24.0889 0.238504 0.119252 0.992864i \(-0.461950\pi\)
0.119252 + 0.992864i \(0.461950\pi\)
\(102\) −131.084 + 131.084i −1.28513 + 1.28513i
\(103\) 56.5935 56.5935i 0.549451 0.549451i −0.376831 0.926282i \(-0.622986\pi\)
0.926282 + 0.376831i \(0.122986\pi\)
\(104\) −76.5903 −0.736445
\(105\) 182.048 1.73379
\(106\) 31.8295 31.8295i 0.300278 0.300278i
\(107\) 37.4639i 0.350130i 0.984557 + 0.175065i \(0.0560136\pi\)
−0.984557 + 0.175065i \(0.943986\pi\)
\(108\) 175.127 175.127i 1.62155 1.62155i
\(109\) 10.0860i 0.0925321i 0.998929 + 0.0462661i \(0.0147322\pi\)
−0.998929 + 0.0462661i \(0.985268\pi\)
\(110\) 10.0782 + 10.0782i 0.0916197 + 0.0916197i
\(111\) 12.3260 12.3260i 0.111045 0.111045i
\(112\) 39.2891i 0.350795i
\(113\) 144.737 + 144.737i 1.28086 + 1.28086i 0.940181 + 0.340677i \(0.110656\pi\)
0.340677 + 0.940181i \(0.389344\pi\)
\(114\) 114.933 1.00819
\(115\) −24.8723 + 24.8723i −0.216281 + 0.216281i
\(116\) 45.5431i 0.392613i
\(117\) −177.025 177.025i −1.51303 1.51303i
\(118\) −68.1299 + 68.1299i −0.577372 + 0.577372i
\(119\) 259.705 259.705i 2.18240 2.18240i
\(120\) 76.7321 76.7321i 0.639434 0.639434i
\(121\) 94.3683i 0.779903i
\(122\) 24.2158 24.2158i 0.198490 0.198490i
\(123\) −23.2364 23.2364i −0.188914 0.188914i
\(124\) −53.1037 53.1037i −0.428256 0.428256i
\(125\) −78.0798 78.0798i −0.624639 0.624639i
\(126\) 233.013 233.013i 1.84931 1.84931i
\(127\) 190.593i 1.50073i −0.661023 0.750365i \(-0.729878\pi\)
0.661023 0.750365i \(-0.270122\pi\)
\(128\) 75.6127 + 75.6127i 0.590724 + 0.590724i
\(129\) 120.472 + 120.472i 0.933891 + 0.933891i
\(130\) −20.1446 20.1446i −0.154958 0.154958i
\(131\) 56.6884 56.6884i 0.432736 0.432736i −0.456822 0.889558i \(-0.651013\pi\)
0.889558 + 0.456822i \(0.151013\pi\)
\(132\) −83.6995 −0.634087
\(133\) −227.708 −1.71209
\(134\) 26.1009i 0.194783i
\(135\) 223.172 1.65313
\(136\) 218.929i 1.60977i
\(137\) 176.470i 1.28810i 0.764983 + 0.644050i \(0.222747\pi\)
−0.764983 + 0.644050i \(0.777253\pi\)
\(138\) 87.2817i 0.632476i
\(139\) 111.899 + 111.899i 0.805028 + 0.805028i 0.983877 0.178849i \(-0.0572374\pi\)
−0.178849 + 0.983877i \(0.557237\pi\)
\(140\) −62.7535 + 62.7535i −0.448240 + 0.448240i
\(141\) 93.7289 + 93.7289i 0.664744 + 0.664744i
\(142\) −64.6527 −0.455301
\(143\) 53.2323i 0.372254i
\(144\) 76.5517i 0.531609i
\(145\) −29.0187 + 29.0187i −0.200129 + 0.200129i
\(146\) 46.2961i 0.317096i
\(147\) −432.989 + 432.989i −2.94550 + 2.94550i
\(148\) 8.49774i 0.0574172i
\(149\) −64.1689 64.1689i −0.430664 0.430664i 0.458190 0.888854i \(-0.348498\pi\)
−0.888854 + 0.458190i \(0.848498\pi\)
\(150\) −116.817 −0.778779
\(151\) −189.569 189.569i −1.25543 1.25543i −0.953253 0.302173i \(-0.902288\pi\)
−0.302173 0.953253i \(-0.597712\pi\)
\(152\) −95.9775 + 95.9775i −0.631431 + 0.631431i
\(153\) 506.015 506.015i 3.30729 3.30729i
\(154\) −70.0682 −0.454989
\(155\) 67.6722i 0.436595i
\(156\) 167.302 1.07245
\(157\) 299.212i 1.90581i −0.303271 0.952904i \(-0.598079\pi\)
0.303271 0.952904i \(-0.401921\pi\)
\(158\) −153.957 −0.974409
\(159\) −168.433 + 168.433i −1.05933 + 1.05933i
\(160\) 83.9643i 0.524777i
\(161\) 172.924i 1.07406i
\(162\) 223.219 223.219i 1.37790 1.37790i
\(163\) 82.0498i 0.503373i 0.967809 + 0.251687i \(0.0809852\pi\)
−0.967809 + 0.251687i \(0.919015\pi\)
\(164\) 16.0196 0.0976805
\(165\) −53.3308 53.3308i −0.323217 0.323217i
\(166\) −49.9453 49.9453i −0.300875 0.300875i
\(167\) −106.878 + 106.878i −0.639985 + 0.639985i −0.950552 0.310567i \(-0.899481\pi\)
0.310567 + 0.950552i \(0.399481\pi\)
\(168\) 533.478i 3.17546i
\(169\) 62.5974i 0.370399i
\(170\) 57.5820 57.5820i 0.338718 0.338718i
\(171\) −443.670 −2.59456
\(172\) −83.0556 −0.482882
\(173\) 58.2207i 0.336536i 0.985741 + 0.168268i \(0.0538174\pi\)
−0.985741 + 0.168268i \(0.946183\pi\)
\(174\) 101.832i 0.585243i
\(175\) 231.439 1.32251
\(176\) 11.5097 11.5097i 0.0653962 0.0653962i
\(177\) 360.525 360.525i 2.03686 2.03686i
\(178\) 140.402 0.788776
\(179\) −58.9171 + 58.9171i −0.329146 + 0.329146i −0.852262 0.523116i \(-0.824770\pi\)
0.523116 + 0.852262i \(0.324770\pi\)
\(180\) −122.270 + 122.270i −0.679280 + 0.679280i
\(181\) 252.074i 1.39268i −0.717714 0.696338i \(-0.754812\pi\)
0.717714 0.696338i \(-0.245188\pi\)
\(182\) 140.055 0.769532
\(183\) −128.143 + 128.143i −0.700235 + 0.700235i
\(184\) −72.8865 72.8865i −0.396122 0.396122i
\(185\) −5.41451 + 5.41451i −0.0292676 + 0.0292676i
\(186\) −118.738 118.738i −0.638374 0.638374i
\(187\) −152.161 −0.813696
\(188\) −64.6185 −0.343715
\(189\) −775.799 + 775.799i −4.10475 + 4.10475i
\(190\) −50.4875 −0.265724
\(191\) −158.693 −0.830854 −0.415427 0.909627i \(-0.636368\pi\)
−0.415427 + 0.909627i \(0.636368\pi\)
\(192\) 95.8654 + 95.8654i 0.499299 + 0.499299i
\(193\) 121.453 0.629292 0.314646 0.949209i \(-0.398114\pi\)
0.314646 + 0.949209i \(0.398114\pi\)
\(194\) 33.3579 + 33.3579i 0.171948 + 0.171948i
\(195\) 106.600 + 106.600i 0.546664 + 0.546664i
\(196\) 298.511i 1.52301i
\(197\) 59.2912 187.866i 0.300971 0.953633i
\(198\) −136.522 −0.689507
\(199\) 217.422 217.422i 1.09257 1.09257i 0.0973196 0.995253i \(-0.468973\pi\)
0.995253 0.0973196i \(-0.0310269\pi\)
\(200\) 97.5505 97.5505i 0.487752 0.487752i
\(201\) 138.119i 0.687158i
\(202\) −18.5667 + 18.5667i −0.0919142 + 0.0919142i
\(203\) 201.752i 0.993852i
\(204\) 478.221i 2.34422i
\(205\) 10.2072 + 10.2072i 0.0497913 + 0.0497913i
\(206\) 87.2393i 0.423492i
\(207\) 336.929i 1.62768i
\(208\) −23.0060 + 23.0060i −0.110606 + 0.110606i
\(209\) 66.7069 + 66.7069i 0.319172 + 0.319172i
\(210\) −140.314 + 140.314i −0.668162 + 0.668162i
\(211\) 49.2757 + 49.2757i 0.233534 + 0.233534i 0.814166 0.580632i \(-0.197194\pi\)
−0.580632 + 0.814166i \(0.697194\pi\)
\(212\) 116.121i 0.547739i
\(213\) 342.124 1.60622
\(214\) −28.8755 28.8755i −0.134932 0.134932i
\(215\) −52.9206 52.9206i −0.246142 0.246142i
\(216\) 653.990i 3.02773i
\(217\) 235.245 + 235.245i 1.08408 + 1.08408i
\(218\) −7.77383 7.77383i −0.0356598 0.0356598i
\(219\) 244.986i 1.11866i
\(220\) 36.7673 0.167124
\(221\) 304.145 1.37622
\(222\) 19.0006i 0.0855881i
\(223\) 310.528i 1.39250i −0.717797 0.696252i \(-0.754850\pi\)
0.717797 0.696252i \(-0.245150\pi\)
\(224\) −291.880 291.880i −1.30303 1.30303i
\(225\) 450.942 2.00418
\(226\) −223.113 −0.987226
\(227\) 281.201 + 281.201i 1.23877 + 1.23877i 0.960504 + 0.278265i \(0.0897592\pi\)
0.278265 + 0.960504i \(0.410241\pi\)
\(228\) 209.650 209.650i 0.919519 0.919519i
\(229\) −136.786 + 136.786i −0.597320 + 0.597320i −0.939599 0.342278i \(-0.888801\pi\)
0.342278 + 0.939599i \(0.388801\pi\)
\(230\) 38.3409i 0.166699i
\(231\) 370.781 1.60511
\(232\) −85.0373 85.0373i −0.366540 0.366540i
\(233\) −222.823 −0.956323 −0.478162 0.878272i \(-0.658697\pi\)
−0.478162 + 0.878272i \(0.658697\pi\)
\(234\) 272.886 1.16618
\(235\) −41.1730 41.1730i −0.175204 0.175204i
\(236\) 248.552i 1.05319i
\(237\) 814.695 3.43753
\(238\) 400.338i 1.68209i
\(239\) 116.614 0.487925 0.243963 0.969785i \(-0.421553\pi\)
0.243963 + 0.969785i \(0.421553\pi\)
\(240\) 46.0973i 0.192072i
\(241\) −255.305 255.305i −1.05936 1.05936i −0.998123 0.0612340i \(-0.980496\pi\)
−0.0612340 0.998123i \(-0.519504\pi\)
\(242\) −72.7348 72.7348i −0.300557 0.300557i
\(243\) −620.682 + 620.682i −2.55425 + 2.55425i
\(244\) 88.3442i 0.362067i
\(245\) 190.202 190.202i 0.776335 0.776335i
\(246\) 35.8191 0.145606
\(247\) −133.336 133.336i −0.539822 0.539822i
\(248\) 198.309 0.799632
\(249\) 264.296 + 264.296i 1.06143 + 1.06143i
\(250\) 120.361 0.481443
\(251\) −1.35870 −0.00541316 −0.00270658 0.999996i \(-0.500862\pi\)
−0.00270658 + 0.999996i \(0.500862\pi\)
\(252\) 850.081i 3.37334i
\(253\) −50.6581 + 50.6581i −0.200230 + 0.200230i
\(254\) 146.900 + 146.900i 0.578348 + 0.578348i
\(255\) −304.708 + 304.708i −1.19493 + 1.19493i
\(256\) −210.575 −0.822559
\(257\) −340.463 −1.32476 −0.662379 0.749169i \(-0.730453\pi\)
−0.662379 + 0.749169i \(0.730453\pi\)
\(258\) −185.709 −0.719801
\(259\) 37.6442i 0.145345i
\(260\) −73.4917 −0.282660
\(261\) 393.098i 1.50612i
\(262\) 87.3856i 0.333533i
\(263\) −9.05544 9.05544i −0.0344313 0.0344313i 0.689682 0.724113i \(-0.257751\pi\)
−0.724113 + 0.689682i \(0.757751\pi\)
\(264\) 156.282 156.282i 0.591979 0.591979i
\(265\) 73.9887 73.9887i 0.279202 0.279202i
\(266\) 175.507 175.507i 0.659800 0.659800i
\(267\) −742.968 −2.78265
\(268\) 47.6108 + 47.6108i 0.177652 + 0.177652i
\(269\) −233.819 + 233.819i −0.869216 + 0.869216i −0.992386 0.123170i \(-0.960694\pi\)
0.123170 + 0.992386i \(0.460694\pi\)
\(270\) −172.011 + 172.011i −0.637077 + 0.637077i
\(271\) −115.273 + 115.273i −0.425360 + 0.425360i −0.887044 0.461684i \(-0.847245\pi\)
0.461684 + 0.887044i \(0.347245\pi\)
\(272\) −65.7613 65.7613i −0.241770 0.241770i
\(273\) −741.131 −2.71476
\(274\) −136.015 136.015i −0.496405 0.496405i
\(275\) −67.8002 67.8002i −0.246546 0.246546i
\(276\) 159.211 + 159.211i 0.576852 + 0.576852i
\(277\) −247.116 + 247.116i −0.892115 + 0.892115i −0.994722 0.102607i \(-0.967282\pi\)
0.102607 + 0.994722i \(0.467282\pi\)
\(278\) −172.493 −0.620479
\(279\) 458.356 + 458.356i 1.64285 + 1.64285i
\(280\) 234.345i 0.836945i
\(281\) 176.735 176.735i 0.628949 0.628949i −0.318855 0.947804i \(-0.603298\pi\)
0.947804 + 0.318855i \(0.103298\pi\)
\(282\) −144.484 −0.512355
\(283\) 385.727 + 385.727i 1.36299 + 1.36299i 0.870075 + 0.492919i \(0.164070\pi\)
0.492919 + 0.870075i \(0.335930\pi\)
\(284\) −117.933 + 117.933i −0.415258 + 0.415258i
\(285\) 267.166 0.937424
\(286\) −41.0290 41.0290i −0.143458 0.143458i
\(287\) −70.9654 −0.247266
\(288\) −568.705 568.705i −1.97467 1.97467i
\(289\) 580.379i 2.00823i
\(290\) 44.7326i 0.154250i
\(291\) −176.521 176.521i −0.606601 0.606601i
\(292\) −84.4489 84.4489i −0.289208 0.289208i
\(293\) 46.1505i 0.157510i −0.996894 0.0787551i \(-0.974905\pi\)
0.996894 0.0787551i \(-0.0250945\pi\)
\(294\) 667.456i 2.27026i
\(295\) −158.370 + 158.370i −0.536848 + 0.536848i
\(296\) −15.8668 15.8668i −0.0536042 0.0536042i
\(297\) 454.540 1.53044
\(298\) 98.9169 0.331936
\(299\) 101.257 101.257i 0.338652 0.338652i
\(300\) −213.086 + 213.086i −0.710287 + 0.710287i
\(301\) 367.929 1.22236
\(302\) 292.223 0.967626
\(303\) 98.2495 98.2495i 0.324256 0.324256i
\(304\) 57.6591i 0.189668i
\(305\) 56.2903 56.2903i 0.184558 0.184558i
\(306\) 780.027i 2.54911i
\(307\) −87.1204 87.1204i −0.283780 0.283780i 0.550835 0.834614i \(-0.314310\pi\)
−0.834614 + 0.550835i \(0.814310\pi\)
\(308\) −127.812 + 127.812i −0.414974 + 0.414974i
\(309\) 461.646i 1.49400i
\(310\) 52.1587 + 52.1587i 0.168254 + 0.168254i
\(311\) −292.031 −0.939005 −0.469503 0.882931i \(-0.655567\pi\)
−0.469503 + 0.882931i \(0.655567\pi\)
\(312\) −312.382 + 312.382i −1.00123 + 1.00123i
\(313\) 19.1153i 0.0610713i 0.999534 + 0.0305356i \(0.00972131\pi\)
−0.999534 + 0.0305356i \(0.990279\pi\)
\(314\) 230.619 + 230.619i 0.734455 + 0.734455i
\(315\) 541.646 541.646i 1.71951 1.71951i
\(316\) −280.833 + 280.833i −0.888712 + 0.888712i
\(317\) −132.398 + 132.398i −0.417660 + 0.417660i −0.884396 0.466737i \(-0.845430\pi\)
0.466737 + 0.884396i \(0.345430\pi\)
\(318\) 259.641i 0.816480i
\(319\) −59.1032 + 59.1032i −0.185276 + 0.185276i
\(320\) −42.1115 42.1115i −0.131598 0.131598i
\(321\) 152.801 + 152.801i 0.476016 + 0.476016i
\(322\) 133.282 + 133.282i 0.413919 + 0.413919i
\(323\) 381.133 381.133i 1.17998 1.17998i
\(324\) 814.352i 2.51343i
\(325\) 135.521 + 135.521i 0.416989 + 0.416989i
\(326\) −63.2403 63.2403i −0.193989 0.193989i
\(327\) 41.1369 + 41.1369i 0.125801 + 0.125801i
\(328\) −29.9115 + 29.9115i −0.0911936 + 0.0911936i
\(329\) 286.254 0.870073
\(330\) 82.2100 0.249121
\(331\) 18.3874i 0.0555512i 0.999614 + 0.0277756i \(0.00884239\pi\)
−0.999614 + 0.0277756i \(0.991158\pi\)
\(332\) −182.211 −0.548828
\(333\) 73.3468i 0.220261i
\(334\) 164.753i 0.493271i
\(335\) 60.6724i 0.181112i
\(336\) 160.245 + 160.245i 0.476920 + 0.476920i
\(337\) −217.224 + 217.224i −0.644581 + 0.644581i −0.951678 0.307097i \(-0.900642\pi\)
0.307097 + 0.951678i \(0.400642\pi\)
\(338\) −48.2473 48.2473i −0.142743 0.142743i
\(339\) 1180.65 3.48275
\(340\) 210.071i 0.617857i
\(341\) 137.830i 0.404193i
\(342\) 341.961 341.961i 0.999886 0.999886i
\(343\) 712.014i 2.07584i
\(344\) 155.080 155.080i 0.450814 0.450814i
\(345\) 202.889i 0.588084i
\(346\) −44.8739 44.8739i −0.129693 0.129693i
\(347\) −63.8678 −0.184057 −0.0920286 0.995756i \(-0.529335\pi\)
−0.0920286 + 0.995756i \(0.529335\pi\)
\(348\) 185.753 + 185.753i 0.533773 + 0.533773i
\(349\) 30.8444 30.8444i 0.0883793 0.0883793i −0.661535 0.749914i \(-0.730095\pi\)
0.749914 + 0.661535i \(0.230095\pi\)
\(350\) −178.383 + 178.383i −0.509666 + 0.509666i
\(351\) −908.551 −2.58846
\(352\) 171.012i 0.485830i
\(353\) 31.9956 0.0906392 0.0453196 0.998973i \(-0.485569\pi\)
0.0453196 + 0.998973i \(0.485569\pi\)
\(354\) 555.752i 1.56992i
\(355\) −150.287 −0.423344
\(356\) 256.108 256.108i 0.719405 0.719405i
\(357\) 2118.47i 5.93410i
\(358\) 90.8213i 0.253691i
\(359\) −304.136 + 304.136i −0.847176 + 0.847176i −0.989780 0.142604i \(-0.954452\pi\)
0.142604 + 0.989780i \(0.454452\pi\)
\(360\) 456.602i 1.26834i
\(361\) 26.8253 0.0743084
\(362\) 194.287 + 194.287i 0.536706 + 0.536706i
\(363\) 384.892 + 384.892i 1.06031 + 1.06031i
\(364\) 255.475 255.475i 0.701854 0.701854i
\(365\) 107.617i 0.294840i
\(366\) 197.534i 0.539710i
\(367\) −40.8840 + 40.8840i −0.111400 + 0.111400i −0.760610 0.649209i \(-0.775100\pi\)
0.649209 + 0.760610i \(0.275100\pi\)
\(368\) −43.7870 −0.118986
\(369\) −138.270 −0.374717
\(370\) 8.34651i 0.0225581i
\(371\) 514.404i 1.38653i
\(372\) −433.180 −1.16446
\(373\) −178.472 + 178.472i −0.478477 + 0.478477i −0.904644 0.426167i \(-0.859864\pi\)
0.426167 + 0.904644i \(0.359864\pi\)
\(374\) 117.279 117.279i 0.313580 0.313580i
\(375\) −636.915 −1.69844
\(376\) 120.655 120.655i 0.320890 0.320890i
\(377\) 118.137 118.137i 0.313362 0.313362i
\(378\) 1195.90i 3.16376i
\(379\) 261.615 0.690277 0.345138 0.938552i \(-0.387832\pi\)
0.345138 + 0.938552i \(0.387832\pi\)
\(380\) −92.0946 + 92.0946i −0.242354 + 0.242354i
\(381\) −777.355 777.355i −2.04030 2.04030i
\(382\) 122.313 122.313i 0.320192 0.320192i
\(383\) −180.772 180.772i −0.471989 0.471989i 0.430569 0.902558i \(-0.358313\pi\)
−0.902558 + 0.430569i \(0.858313\pi\)
\(384\) 616.790 1.60622
\(385\) −162.876 −0.423054
\(386\) −93.6107 + 93.6107i −0.242515 + 0.242515i
\(387\) 716.881 1.85240
\(388\) 121.697 0.313651
\(389\) 45.0851 + 45.0851i 0.115900 + 0.115900i 0.762678 0.646778i \(-0.223884\pi\)
−0.646778 + 0.762678i \(0.723884\pi\)
\(390\) −164.324 −0.421344
\(391\) 289.437 + 289.437i 0.740248 + 0.740248i
\(392\) 557.374 + 557.374i 1.42187 + 1.42187i
\(393\) 462.420i 1.17664i
\(394\) 99.0995 + 190.497i 0.251521 + 0.483496i
\(395\) −357.877 −0.906017
\(396\) −249.031 + 249.031i −0.628867 + 0.628867i
\(397\) 321.228 321.228i 0.809138 0.809138i −0.175365 0.984503i \(-0.556111\pi\)
0.984503 + 0.175365i \(0.0561107\pi\)
\(398\) 335.158i 0.842105i
\(399\) −928.732 + 928.732i −2.32765 + 2.32765i
\(400\) 58.6040i 0.146510i
\(401\) 79.9636i 0.199410i 0.995017 + 0.0997052i \(0.0317900\pi\)
−0.995017 + 0.0997052i \(0.968210\pi\)
\(402\) 106.456 + 106.456i 0.264815 + 0.264815i
\(403\) 275.499i 0.683621i
\(404\) 67.7351i 0.167661i
\(405\) 518.880 518.880i 1.28119 1.28119i
\(406\) 155.501 + 155.501i 0.383008 + 0.383008i
\(407\) −11.0279 + 11.0279i −0.0270955 + 0.0270955i
\(408\) −892.925 892.925i −2.18854 2.18854i
\(409\) 153.074i 0.374264i −0.982335 0.187132i \(-0.940081\pi\)
0.982335 0.187132i \(-0.0599192\pi\)
\(410\) −15.7345 −0.0383768
\(411\) 719.752 + 719.752i 1.75122 + 1.75122i
\(412\) 159.134 + 159.134i 0.386247 + 0.386247i
\(413\) 1101.06i 2.66602i
\(414\) 259.689 + 259.689i 0.627269 + 0.627269i
\(415\) −116.099 116.099i −0.279757 0.279757i
\(416\) 341.825i 0.821695i
\(417\) 912.785 2.18893
\(418\) −102.829 −0.246003
\(419\) 622.087i 1.48470i −0.670015 0.742348i \(-0.733712\pi\)
0.670015 0.742348i \(-0.266288\pi\)
\(420\) 511.895i 1.21880i
\(421\) 129.554 + 129.554i 0.307728 + 0.307728i 0.844028 0.536299i \(-0.180178\pi\)
−0.536299 + 0.844028i \(0.680178\pi\)
\(422\) −75.9590 −0.179998
\(423\) 557.743 1.31854
\(424\) 216.819 + 216.819i 0.511365 + 0.511365i
\(425\) −387.379 + 387.379i −0.911480 + 0.911480i
\(426\) −263.694 + 263.694i −0.618999 + 0.618999i
\(427\) 391.357i 0.916527i
\(428\) −105.344 −0.246131
\(429\) 217.114 + 217.114i 0.506094 + 0.506094i
\(430\) 81.5775 0.189715
\(431\) −226.262 −0.524970 −0.262485 0.964936i \(-0.584542\pi\)
−0.262485 + 0.964936i \(0.584542\pi\)
\(432\) 196.444 + 196.444i 0.454732 + 0.454732i
\(433\) 418.510i 0.966535i −0.875473 0.483268i \(-0.839450\pi\)
0.875473 0.483268i \(-0.160550\pi\)
\(434\) −362.632 −0.835557
\(435\) 236.712i 0.544166i
\(436\) −28.3606 −0.0650472
\(437\) 253.776i 0.580724i
\(438\) −188.824 188.824i −0.431105 0.431105i
\(439\) 114.416 + 114.416i 0.260630 + 0.260630i 0.825310 0.564680i \(-0.191000\pi\)
−0.564680 + 0.825310i \(0.691000\pi\)
\(440\) −68.6512 + 68.6512i −0.156026 + 0.156026i
\(441\) 2576.54i 5.84250i
\(442\) −234.421 + 234.421i −0.530365 + 0.530365i
\(443\) −280.909 −0.634107 −0.317053 0.948408i \(-0.602693\pi\)
−0.317053 + 0.948408i \(0.602693\pi\)
\(444\) 34.6590 + 34.6590i 0.0780609 + 0.0780609i
\(445\) 326.369 0.733413
\(446\) 239.341 + 239.341i 0.536640 + 0.536640i
\(447\) −523.440 −1.17101
\(448\) 292.779 0.653525
\(449\) 307.464i 0.684776i −0.939559 0.342388i \(-0.888764\pi\)
0.939559 0.342388i \(-0.111236\pi\)
\(450\) −347.565 + 347.565i −0.772367 + 0.772367i
\(451\) 20.7893 + 20.7893i 0.0460960 + 0.0460960i
\(452\) −406.982 + 406.982i −0.900402 + 0.900402i
\(453\) −1546.36 −3.41360
\(454\) −433.473 −0.954787
\(455\) 325.562 0.715520
\(456\) 782.911i 1.71691i
\(457\) −124.373 −0.272151 −0.136076 0.990698i \(-0.543449\pi\)
−0.136076 + 0.990698i \(0.543449\pi\)
\(458\) 210.857i 0.460387i
\(459\) 2597.03i 5.65803i
\(460\) −69.9377 69.9377i −0.152039 0.152039i
\(461\) −138.002 + 138.002i −0.299354 + 0.299354i −0.840761 0.541407i \(-0.817892\pi\)
0.541407 + 0.840761i \(0.317892\pi\)
\(462\) −285.781 + 285.781i −0.618575 + 0.618575i
\(463\) 520.943 520.943i 1.12515 1.12515i 0.134192 0.990955i \(-0.457156\pi\)
0.990955 0.134192i \(-0.0428440\pi\)
\(464\) −51.0867 −0.110101
\(465\) −276.009 276.009i −0.593568 0.593568i
\(466\) 171.742 171.742i 0.368545 0.368545i
\(467\) −458.622 + 458.622i −0.982061 + 0.982061i −0.999842 0.0177809i \(-0.994340\pi\)
0.0177809 + 0.999842i \(0.494340\pi\)
\(468\) 497.772 497.772i 1.06362 1.06362i
\(469\) −210.912 210.912i −0.449705 0.449705i
\(470\) 63.4685 0.135039
\(471\) −1220.37 1220.37i −2.59102 2.59102i
\(472\) −464.093 464.093i −0.983247 0.983247i
\(473\) −107.785 107.785i −0.227875 0.227875i
\(474\) −627.930 + 627.930i −1.32475 + 1.32475i
\(475\) 339.651 0.715055
\(476\) 730.258 + 730.258i 1.53416 + 1.53416i
\(477\) 1002.28i 2.10121i
\(478\) −89.8809 + 89.8809i −0.188035 + 0.188035i
\(479\) −37.1360 −0.0775282 −0.0387641 0.999248i \(-0.512342\pi\)
−0.0387641 + 0.999248i \(0.512342\pi\)
\(480\) 342.458 + 342.458i 0.713454 + 0.713454i
\(481\) 22.0429 22.0429i 0.0458272 0.0458272i
\(482\) 393.555 0.816505
\(483\) −705.290 705.290i −1.46023 1.46023i
\(484\) −265.352 −0.548248
\(485\) 77.5415 + 77.5415i 0.159879 + 0.159879i
\(486\) 956.787i 1.96870i
\(487\) 578.917i 1.18874i −0.804191 0.594371i \(-0.797401\pi\)
0.804191 0.594371i \(-0.202599\pi\)
\(488\) 164.955 + 164.955i 0.338022 + 0.338022i
\(489\) 334.650 + 334.650i 0.684355 + 0.684355i
\(490\) 293.198i 0.598363i
\(491\) 566.666i 1.15411i 0.816707 + 0.577053i \(0.195797\pi\)
−0.816707 + 0.577053i \(0.804203\pi\)
\(492\) 65.3378 65.3378i 0.132800 0.132800i
\(493\) 337.689 + 337.689i 0.684967 + 0.684967i
\(494\) 205.539 0.416071
\(495\) −317.351 −0.641112
\(496\) 59.5676 59.5676i 0.120096 0.120096i
\(497\) 522.434 522.434i 1.05118 1.05118i
\(498\) −407.415 −0.818103
\(499\) −522.976 −1.04805 −0.524024 0.851704i \(-0.675570\pi\)
−0.524024 + 0.851704i \(0.675570\pi\)
\(500\) 219.551 219.551i 0.439101 0.439101i
\(501\) 871.825i 1.74017i
\(502\) 1.04723 1.04723i 0.00208611 0.00208611i
\(503\) 680.317i 1.35252i 0.736664 + 0.676259i \(0.236400\pi\)
−0.736664 + 0.676259i \(0.763600\pi\)
\(504\) 1587.26 + 1587.26i 3.14932 + 3.14932i
\(505\) −43.1588 + 43.1588i −0.0854629 + 0.0854629i
\(506\) 78.0899i 0.154328i
\(507\) 255.311 + 255.311i 0.503572 + 0.503572i
\(508\) 535.923 1.05497
\(509\) 252.887 252.887i 0.496831 0.496831i −0.413619 0.910450i \(-0.635735\pi\)
0.910450 + 0.413619i \(0.135735\pi\)
\(510\) 469.710i 0.921000i
\(511\) 374.101 + 374.101i 0.732096 + 0.732096i
\(512\) −140.149 + 140.149i −0.273728 + 0.273728i
\(513\) −1138.53 + 1138.53i −2.21936 + 2.21936i
\(514\) 262.413 262.413i 0.510531 0.510531i
\(515\) 202.791i 0.393768i
\(516\) −338.752 + 338.752i −0.656496 + 0.656496i
\(517\) −83.8581 83.8581i −0.162201 0.162201i
\(518\) 29.0145 + 29.0145i 0.0560125 + 0.0560125i
\(519\) 237.460 + 237.460i 0.457533 + 0.457533i
\(520\) 137.222 137.222i 0.263889 0.263889i
\(521\) 755.345i 1.44980i 0.688855 + 0.724899i \(0.258114\pi\)
−0.688855 + 0.724899i \(0.741886\pi\)
\(522\) 302.982 + 302.982i 0.580425 + 0.580425i
\(523\) 669.892 + 669.892i 1.28086 + 1.28086i 0.940177 + 0.340688i \(0.110660\pi\)
0.340688 + 0.940177i \(0.389340\pi\)
\(524\) 159.401 + 159.401i 0.304200 + 0.304200i
\(525\) 943.953 943.953i 1.79801 1.79801i
\(526\) 13.9590 0.0265381
\(527\) −787.497 −1.49430
\(528\) 93.8875i 0.177817i
\(529\) −336.279 −0.635688
\(530\) 114.054i 0.215197i
\(531\) 2145.34i 4.04018i
\(532\) 640.285i 1.20354i
\(533\) −41.5544 41.5544i −0.0779632 0.0779632i
\(534\) 572.646 572.646i 1.07237 1.07237i
\(535\) −67.1220 67.1220i −0.125462 0.125462i
\(536\) −177.796 −0.331709
\(537\) 480.601i 0.894974i
\(538\) 360.434i 0.669952i
\(539\) 387.390 387.390i 0.718719 0.718719i
\(540\) 627.531i 1.16210i
\(541\) 380.352 380.352i 0.703054 0.703054i −0.262011 0.965065i \(-0.584386\pi\)
0.965065 + 0.262011i \(0.0843858\pi\)
\(542\) 177.694i 0.327848i
\(543\) −1028.11 1028.11i −1.89340 1.89340i
\(544\) 977.086 1.79611
\(545\) −18.0705 18.0705i −0.0331569 0.0331569i
\(546\) 571.230 571.230i 1.04621 1.04621i
\(547\) −48.5591 + 48.5591i −0.0887734 + 0.0887734i −0.750099 0.661326i \(-0.769994\pi\)
0.661326 + 0.750099i \(0.269994\pi\)
\(548\) −496.211 −0.905494
\(549\) 762.528i 1.38894i
\(550\) 104.515 0.190027
\(551\) 296.083i 0.537356i
\(552\) −594.552 −1.07709
\(553\) 1244.06 1244.06i 2.24967 2.24967i
\(554\) 380.931i 0.687602i
\(555\) 44.1674i 0.0795809i
\(556\) −314.645 + 314.645i −0.565909 + 0.565909i
\(557\) 74.4865i 0.133728i −0.997762 0.0668640i \(-0.978701\pi\)
0.997762 0.0668640i \(-0.0212994\pi\)
\(558\) −706.560 −1.26624
\(559\) 215.444 + 215.444i 0.385409 + 0.385409i
\(560\) −70.3920 70.3920i −0.125700 0.125700i
\(561\) −620.607 + 620.607i −1.10625 + 1.10625i
\(562\) 272.438i 0.484765i
\(563\) 204.532i 0.363289i 0.983364 + 0.181644i \(0.0581420\pi\)
−0.983364 + 0.181644i \(0.941858\pi\)
\(564\) −263.554 + 263.554i −0.467294 + 0.467294i
\(565\) −518.633 −0.917935
\(566\) −594.602 −1.05053
\(567\) 3607.50i 6.36244i
\(568\) 440.406i 0.775363i
\(569\) −322.772 −0.567262 −0.283631 0.958934i \(-0.591539\pi\)
−0.283631 + 0.958934i \(0.591539\pi\)
\(570\) −205.919 + 205.919i −0.361262 + 0.361262i
\(571\) −214.664 + 214.664i −0.375944 + 0.375944i −0.869637 0.493692i \(-0.835647\pi\)
0.493692 + 0.869637i \(0.335647\pi\)
\(572\) −149.683 −0.261683
\(573\) −647.248 + 647.248i −1.12958 + 1.12958i
\(574\) 54.6969 54.6969i 0.0952907 0.0952907i
\(575\) 257.935i 0.448583i
\(576\) 570.457 0.990376
\(577\) −116.609 + 116.609i −0.202094 + 0.202094i −0.800897 0.598802i \(-0.795643\pi\)
0.598802 + 0.800897i \(0.295643\pi\)
\(578\) −447.330 447.330i −0.773927 0.773927i
\(579\) 495.361 495.361i 0.855546 0.855546i
\(580\) −81.5970 81.5970i −0.140684 0.140684i
\(581\) 807.177 1.38929
\(582\) 272.108 0.467540
\(583\) 150.695 150.695i 0.258482 0.258482i
\(584\) 315.363 0.540005
\(585\) 634.331 1.08433
\(586\) 35.5707 + 35.5707i 0.0607009 + 0.0607009i
\(587\) −769.607 −1.31108 −0.655542 0.755158i \(-0.727560\pi\)
−0.655542 + 0.755158i \(0.727560\pi\)
\(588\) −1217.51 1217.51i −2.07060 2.07060i
\(589\) 345.236 + 345.236i 0.586139 + 0.586139i
\(590\) 244.129i 0.413778i
\(591\) −524.406 1008.06i −0.887320 1.70568i
\(592\) −9.53210 −0.0161015
\(593\) 137.438 137.438i 0.231767 0.231767i −0.581663 0.813430i \(-0.697598\pi\)
0.813430 + 0.581663i \(0.197598\pi\)
\(594\) −350.339 + 350.339i −0.589796 + 0.589796i
\(595\) 930.597i 1.56403i
\(596\) 180.435 180.435i 0.302743 0.302743i
\(597\) 1773.56i 2.97079i
\(598\) 156.089i 0.261018i
\(599\) −72.5088 72.5088i −0.121050 0.121050i 0.643987 0.765037i \(-0.277279\pi\)
−0.765037 + 0.643987i \(0.777279\pi\)
\(600\) 795.742i 1.32624i
\(601\) 477.333i 0.794231i 0.917769 + 0.397115i \(0.129989\pi\)
−0.917769 + 0.397115i \(0.870011\pi\)
\(602\) −283.583 + 283.583i −0.471068 + 0.471068i
\(603\) −410.945 410.945i −0.681501 0.681501i
\(604\) 533.045 533.045i 0.882525 0.882525i
\(605\) −169.074 169.074i −0.279462 0.279462i
\(606\) 151.453i 0.249922i
\(607\) −1073.67 −1.76882 −0.884410 0.466711i \(-0.845439\pi\)
−0.884410 + 0.466711i \(0.845439\pi\)
\(608\) −428.351 428.351i −0.704525 0.704525i
\(609\) −822.868 822.868i −1.35118 1.35118i
\(610\) 86.7720i 0.142249i
\(611\) 167.618 + 167.618i 0.274335 + 0.274335i
\(612\) 1422.85 + 1422.85i 2.32492 + 2.32492i
\(613\) 520.153i 0.848536i 0.905537 + 0.424268i \(0.139469\pi\)
−0.905537 + 0.424268i \(0.860531\pi\)
\(614\) 134.297 0.218725
\(615\) 83.2626 0.135386
\(616\) 477.296i 0.774831i
\(617\) 41.7746i 0.0677060i 0.999427 + 0.0338530i \(0.0107778\pi\)
−0.999427 + 0.0338530i \(0.989222\pi\)
\(618\) 355.816 + 355.816i 0.575754 + 0.575754i
\(619\) −454.582 −0.734382 −0.367191 0.930146i \(-0.619680\pi\)
−0.367191 + 0.930146i \(0.619680\pi\)
\(620\) 190.286 0.306913
\(621\) −864.614 864.614i −1.39229 1.39229i
\(622\) 225.084 225.084i 0.361871 0.361871i
\(623\) −1134.54 + 1134.54i −1.82109 + 1.82109i
\(624\) 187.666i 0.300746i
\(625\) −184.719 −0.295550
\(626\) −14.7332 14.7332i −0.0235355 0.0235355i
\(627\) 544.144 0.867853
\(628\) 841.347 1.33972
\(629\) 63.0082 + 63.0082i 0.100172 + 0.100172i
\(630\) 834.953i 1.32532i
\(631\) 665.119 1.05407 0.527036 0.849843i \(-0.323303\pi\)
0.527036 + 0.849843i \(0.323303\pi\)
\(632\) 1048.73i 1.65939i
\(633\) 401.954 0.634998
\(634\) 204.093i 0.321913i
\(635\) 341.474 + 341.474i 0.537755 + 0.537755i
\(636\) −473.612 473.612i −0.744673 0.744673i
\(637\) −774.328 + 774.328i −1.21559 + 1.21559i
\(638\) 91.1081i 0.142803i
\(639\) 1017.92 1017.92i 1.59299 1.59299i
\(640\) −270.942 −0.423347
\(641\) 10.7337 + 10.7337i 0.0167452 + 0.0167452i 0.715430 0.698685i \(-0.246231\pi\)
−0.698685 + 0.715430i \(0.746231\pi\)
\(642\) −235.544 −0.366891
\(643\) −95.8475 95.8475i −0.149063 0.149063i 0.628636 0.777699i \(-0.283613\pi\)
−0.777699 + 0.628636i \(0.783613\pi\)
\(644\) 486.241 0.755032
\(645\) −431.685 −0.669280
\(646\) 587.520i 0.909473i
\(647\) 142.445 142.445i 0.220162 0.220162i −0.588404 0.808567i \(-0.700244\pi\)
0.808567 + 0.588404i \(0.200244\pi\)
\(648\) 1520.54 + 1520.54i 2.34652 + 2.34652i
\(649\) −322.557 + 322.557i −0.497006 + 0.497006i
\(650\) −208.907 −0.321396
\(651\) 1918.95 2.94769
\(652\) −230.714 −0.353856
\(653\) 446.322i 0.683495i −0.939792 0.341747i \(-0.888981\pi\)
0.939792 0.341747i \(-0.111019\pi\)
\(654\) −63.4130 −0.0969617
\(655\) 203.131i 0.310123i
\(656\) 17.9695i 0.0273926i
\(657\) 728.906 + 728.906i 1.10945 + 1.10945i
\(658\) −220.632 + 220.632i −0.335306 + 0.335306i
\(659\) 206.775 206.775i 0.313771 0.313771i −0.532598 0.846368i \(-0.678784\pi\)
0.846368 + 0.532598i \(0.178784\pi\)
\(660\) 149.960 149.960i 0.227212 0.227212i
\(661\) −181.862 −0.275132 −0.137566 0.990493i \(-0.543928\pi\)
−0.137566 + 0.990493i \(0.543928\pi\)
\(662\) −14.1722 14.1722i −0.0214082 0.0214082i
\(663\) 1240.49 1240.49i 1.87103 1.87103i
\(664\) 340.221 340.221i 0.512381 0.512381i
\(665\) 407.971 407.971i 0.613490 0.613490i
\(666\) 56.5324 + 56.5324i 0.0848835 + 0.0848835i
\(667\) 224.849 0.337105
\(668\) −300.526 300.526i −0.449890 0.449890i
\(669\) −1266.53 1266.53i −1.89316 1.89316i
\(670\) −46.7635 46.7635i −0.0697963 0.0697963i
\(671\) 114.648 114.648i 0.170861 0.170861i
\(672\) −2380.93 −3.54305
\(673\) −580.202 580.202i −0.862113 0.862113i 0.129470 0.991583i \(-0.458672\pi\)
−0.991583 + 0.129470i \(0.958672\pi\)
\(674\) 334.852i 0.496814i
\(675\) 1157.19 1157.19i 1.71436 1.71436i
\(676\) −176.016 −0.260379
\(677\) 71.3075 + 71.3075i 0.105329 + 0.105329i 0.757807 0.652479i \(-0.226271\pi\)
−0.652479 + 0.757807i \(0.726271\pi\)
\(678\) −909.993 + 909.993i −1.34217 + 1.34217i
\(679\) −539.106 −0.793970
\(680\) 392.242 + 392.242i 0.576826 + 0.576826i
\(681\) 2293.82 3.36831
\(682\) 106.233 + 106.233i 0.155767 + 0.155767i
\(683\) 191.450i 0.280307i −0.990130 0.140153i \(-0.955240\pi\)
0.990130 0.140153i \(-0.0447596\pi\)
\(684\) 1247.55i 1.82390i
\(685\) −316.171 316.171i −0.461563 0.461563i
\(686\) −548.788 548.788i −0.799982 0.799982i
\(687\) 1115.80i 1.62416i
\(688\) 93.1653i 0.135415i
\(689\) −301.214 + 301.214i −0.437175 + 0.437175i
\(690\) −156.378 156.378i −0.226634 0.226634i
\(691\) 786.170 1.13773 0.568864 0.822432i \(-0.307383\pi\)
0.568864 + 0.822432i \(0.307383\pi\)
\(692\) −163.709 −0.236574
\(693\) 1103.19 1103.19i 1.59190 1.59190i
\(694\) 49.2264 49.2264i 0.0709315 0.0709315i
\(695\) −400.965 −0.576929
\(696\) −693.669 −0.996651
\(697\) 118.781 118.781i 0.170417 0.170417i
\(698\) 47.5469i 0.0681187i
\(699\) −908.811 + 908.811i −1.30016 + 1.30016i
\(700\) 650.779i 0.929684i
\(701\) 185.025 + 185.025i 0.263944 + 0.263944i 0.826654 0.562710i \(-0.190241\pi\)
−0.562710 + 0.826654i \(0.690241\pi\)
\(702\) 700.270 700.270i 0.997535 0.997535i
\(703\) 55.2452i 0.0785849i
\(704\) −85.7696 85.7696i −0.121832 0.121832i
\(705\) −335.857 −0.476394
\(706\) −24.6608 + 24.6608i −0.0349303 + 0.0349303i
\(707\) 300.060i 0.424413i
\(708\) 1013.75 + 1013.75i 1.43185 + 1.43185i
\(709\) −624.792 + 624.792i −0.881229 + 0.881229i −0.993660 0.112430i \(-0.964136\pi\)
0.112430 + 0.993660i \(0.464136\pi\)
\(710\) 115.835 115.835i 0.163147 0.163147i
\(711\) 2423.96 2423.96i 3.40923 3.40923i
\(712\) 956.402i 1.34326i
\(713\) −262.176 + 262.176i −0.367709 + 0.367709i
\(714\) 1632.82 + 1632.82i 2.28687 + 2.28687i
\(715\) −95.3733 95.3733i −0.133389 0.133389i
\(716\) −165.668 165.668i −0.231379 0.231379i
\(717\) 475.624 475.624i 0.663353 0.663353i
\(718\) 468.829i 0.652965i
\(719\) 243.918 + 243.918i 0.339246 + 0.339246i 0.856083 0.516838i \(-0.172891\pi\)
−0.516838 + 0.856083i \(0.672891\pi\)
\(720\) −137.153 137.153i −0.190491 0.190491i
\(721\) −704.948 704.948i −0.977737 0.977737i
\(722\) −20.6757 + 20.6757i −0.0286368 + 0.0286368i
\(723\) −2082.58 −2.88048
\(724\) 708.801 0.979008
\(725\) 300.935i 0.415083i
\(726\) −593.315 −0.817238
\(727\) 206.541i 0.284101i 0.989859 + 0.142050i \(0.0453695\pi\)
−0.989859 + 0.142050i \(0.954631\pi\)
\(728\) 954.036i 1.31049i
\(729\) 2456.55i 3.36975i
\(730\) 82.9460 + 82.9460i 0.113625 + 0.113625i
\(731\) −615.833 + 615.833i −0.842452 + 0.842452i
\(732\) −360.322 360.322i −0.492243 0.492243i
\(733\) 512.252 0.698843 0.349421 0.936966i \(-0.386378\pi\)
0.349421 + 0.936966i \(0.386378\pi\)
\(734\) 63.0230i 0.0858624i
\(735\) 1551.52i 2.11091i
\(736\) 325.295 325.295i 0.441977 0.441977i
\(737\) 123.573i 0.167670i
\(738\) 106.573 106.573i 0.144407 0.144407i
\(739\) 394.248i 0.533489i 0.963767 + 0.266745i \(0.0859480\pi\)
−0.963767 + 0.266745i \(0.914052\pi\)
\(740\) −15.2249 15.2249i −0.0205742 0.0205742i
\(741\) −1087.65 −1.46782
\(742\) −396.479 396.479i −0.534339 0.534339i
\(743\) 328.638 328.638i 0.442312 0.442312i −0.450477 0.892788i \(-0.648746\pi\)
0.892788 + 0.450477i \(0.148746\pi\)
\(744\) 808.825 808.825i 1.08713 1.08713i
\(745\) 229.935 0.308638
\(746\) 275.116i 0.368789i
\(747\) 1572.72 2.10538
\(748\) 427.858i 0.572003i
\(749\) 466.664 0.623049
\(750\) 490.905 490.905i 0.654541 0.654541i
\(751\) 787.826i 1.04904i −0.851399 0.524518i \(-0.824246\pi\)
0.851399 0.524518i \(-0.175754\pi\)
\(752\) 72.4839i 0.0963882i
\(753\) −5.54163 + 5.54163i −0.00735940 + 0.00735940i
\(754\) 182.110i 0.241525i
\(755\) 679.281 0.899710
\(756\) −2181.45 2181.45i −2.88551 2.88551i
\(757\) −722.305 722.305i −0.954168 0.954168i 0.0448270 0.998995i \(-0.485726\pi\)
−0.998995 + 0.0448270i \(0.985726\pi\)
\(758\) −201.641 + 201.641i −0.266017 + 0.266017i
\(759\) 413.230i 0.544440i
\(760\) 343.915i 0.452519i
\(761\) −346.382 + 346.382i −0.455166 + 0.455166i −0.897065 0.441899i \(-0.854305\pi\)
0.441899 + 0.897065i \(0.354305\pi\)
\(762\) 1198.30 1.57257
\(763\) 125.635 0.164659
\(764\) 446.225i 0.584064i
\(765\) 1813.20i 2.37019i
\(766\) 278.661 0.363788
\(767\) 644.738 644.738i 0.840597 0.840597i
\(768\) −858.856 + 858.856i −1.11830 + 1.11830i
\(769\) −709.265 −0.922321 −0.461161 0.887317i \(-0.652567\pi\)
−0.461161 + 0.887317i \(0.652567\pi\)
\(770\) 125.537 125.537i 0.163035 0.163035i
\(771\) −1388.62 + 1388.62i −1.80106 + 1.80106i
\(772\) 341.511i 0.442372i
\(773\) 823.941 1.06590 0.532950 0.846147i \(-0.321083\pi\)
0.532950 + 0.846147i \(0.321083\pi\)
\(774\) −552.539 + 552.539i −0.713875 + 0.713875i
\(775\) −350.894 350.894i −0.452766 0.452766i