Properties

Label 197.3.c.a.14.1
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 14.1
Character \(\chi\) \(=\) 197.14
Dual form 197.3.c.a.183.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.75292 + 2.75292i) q^{2} +(-0.348601 + 0.348601i) q^{3} -11.1571i q^{4} +(-4.86430 + 4.86430i) q^{5} -1.91934i q^{6} +12.7739i q^{7} +(19.7030 + 19.7030i) q^{8} +8.75696i q^{9} +O(q^{10})\) \(q+(-2.75292 + 2.75292i) q^{2} +(-0.348601 + 0.348601i) q^{3} -11.1571i q^{4} +(-4.86430 + 4.86430i) q^{5} -1.91934i q^{6} +12.7739i q^{7} +(19.7030 + 19.7030i) q^{8} +8.75696i q^{9} -26.7821i q^{10} +(-8.10908 + 8.10908i) q^{11} +(3.88938 + 3.88938i) q^{12} +(14.5821 - 14.5821i) q^{13} +(-35.1656 - 35.1656i) q^{14} -3.39140i q^{15} -63.8530 q^{16} +(-2.34315 - 2.34315i) q^{17} +(-24.1072 - 24.1072i) q^{18} -13.1965i q^{19} +(54.2717 + 54.2717i) q^{20} +(-4.45300 - 4.45300i) q^{21} -44.6473i q^{22} -9.51805 q^{23} -13.7370 q^{24} -22.3229i q^{25} +80.2865i q^{26} +(-6.19008 - 6.19008i) q^{27} +142.520 q^{28} -6.71745 q^{29} +(9.33625 + 9.33625i) q^{30} +(-3.29799 + 3.29799i) q^{31} +(96.9702 - 96.9702i) q^{32} -5.65366i q^{33} +12.9010 q^{34} +(-62.1363 - 62.1363i) q^{35} +97.7025 q^{36} +3.35893 q^{37} +(36.3288 + 36.3288i) q^{38} +10.1666i q^{39} -191.683 q^{40} +2.04618i q^{41} +24.5175 q^{42} +38.3292i q^{43} +(90.4741 + 90.4741i) q^{44} +(-42.5965 - 42.5965i) q^{45} +(26.2024 - 26.2024i) q^{46} -21.6000i q^{47} +(22.2592 - 22.2592i) q^{48} -114.173 q^{49} +(61.4532 + 61.4532i) q^{50} +1.63365 q^{51} +(-162.694 - 162.694i) q^{52} +34.4098 q^{53} +34.0816 q^{54} -78.8901i q^{55} +(-251.685 + 251.685i) q^{56} +(4.60029 + 4.60029i) q^{57} +(18.4926 - 18.4926i) q^{58} +40.7776 q^{59} -37.8383 q^{60} +74.2387 q^{61} -18.1582i q^{62} -111.861 q^{63} +278.490i q^{64} +141.863i q^{65} +(15.5641 + 15.5641i) q^{66} +(-29.7634 + 29.7634i) q^{67} +(-26.1428 + 26.1428i) q^{68} +(3.31800 - 3.31800i) q^{69} +342.112 q^{70} +(85.7680 + 85.7680i) q^{71} +(-172.538 + 172.538i) q^{72} +(19.3531 - 19.3531i) q^{73} +(-9.24686 + 9.24686i) q^{74} +(7.78178 + 7.78178i) q^{75} -147.235 q^{76} +(-103.585 - 103.585i) q^{77} +(-27.9879 - 27.9879i) q^{78} +(-61.9554 - 61.9554i) q^{79} +(310.601 - 310.601i) q^{80} -74.4969 q^{81} +(-5.63298 - 5.63298i) q^{82} -78.7914i q^{83} +(-49.6827 + 49.6827i) q^{84} +22.7956 q^{85} +(-105.517 - 105.517i) q^{86} +(2.34171 - 2.34171i) q^{87} -319.547 q^{88} +(15.5211 + 15.5211i) q^{89} +234.529 q^{90} +(186.270 + 186.270i) q^{91} +106.194i q^{92} -2.29936i q^{93} +(59.4631 + 59.4631i) q^{94} +(64.1916 + 64.1916i) q^{95} +67.6077i q^{96} -38.3936i q^{97} +(314.310 - 314.310i) q^{98} +(-71.0109 - 71.0109i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75292 + 2.75292i −1.37646 + 1.37646i −0.525935 + 0.850525i \(0.676284\pi\)
−0.850525 + 0.525935i \(0.823716\pi\)
\(3\) −0.348601 + 0.348601i −0.116200 + 0.116200i −0.762816 0.646616i \(-0.776184\pi\)
0.646616 + 0.762816i \(0.276184\pi\)
\(4\) 11.1571i 2.78928i
\(5\) −4.86430 + 4.86430i −0.972861 + 0.972861i −0.999641 0.0267804i \(-0.991475\pi\)
0.0267804 + 0.999641i \(0.491475\pi\)
\(6\) 1.91934i 0.319890i
\(7\) 12.7739i 1.82485i 0.409247 + 0.912424i \(0.365792\pi\)
−0.409247 + 0.912424i \(0.634208\pi\)
\(8\) 19.7030 + 19.7030i 2.46287 + 2.46287i
\(9\) 8.75696i 0.972995i
\(10\) 26.7821i 2.67821i
\(11\) −8.10908 + 8.10908i −0.737189 + 0.737189i −0.972033 0.234844i \(-0.924542\pi\)
0.234844 + 0.972033i \(0.424542\pi\)
\(12\) 3.88938 + 3.88938i 0.324115 + 0.324115i
\(13\) 14.5821 14.5821i 1.12170 1.12170i 0.130210 0.991486i \(-0.458435\pi\)
0.991486 0.130210i \(-0.0415653\pi\)
\(14\) −35.1656 35.1656i −2.51183 2.51183i
\(15\) 3.39140i 0.226093i
\(16\) −63.8530 −3.99081
\(17\) −2.34315 2.34315i −0.137832 0.137832i 0.634824 0.772657i \(-0.281072\pi\)
−0.772657 + 0.634824i \(0.781072\pi\)
\(18\) −24.1072 24.1072i −1.33929 1.33929i
\(19\) 13.1965i 0.694551i −0.937763 0.347275i \(-0.887107\pi\)
0.937763 0.347275i \(-0.112893\pi\)
\(20\) 54.2717 + 54.2717i 2.71358 + 2.71358i
\(21\) −4.45300 4.45300i −0.212048 0.212048i
\(22\) 44.6473i 2.02942i
\(23\) −9.51805 −0.413828 −0.206914 0.978359i \(-0.566342\pi\)
−0.206914 + 0.978359i \(0.566342\pi\)
\(24\) −13.7370 −0.572373
\(25\) 22.3229i 0.892917i
\(26\) 80.2865i 3.08794i
\(27\) −6.19008 6.19008i −0.229262 0.229262i
\(28\) 142.520 5.09001
\(29\) −6.71745 −0.231636 −0.115818 0.993270i \(-0.536949\pi\)
−0.115818 + 0.993270i \(0.536949\pi\)
\(30\) 9.33625 + 9.33625i 0.311208 + 0.311208i
\(31\) −3.29799 + 3.29799i −0.106387 + 0.106387i −0.758297 0.651910i \(-0.773968\pi\)
0.651910 + 0.758297i \(0.273968\pi\)
\(32\) 96.9702 96.9702i 3.03032 3.03032i
\(33\) 5.65366i 0.171323i
\(34\) 12.9010 0.379441
\(35\) −62.1363 62.1363i −1.77532 1.77532i
\(36\) 97.7025 2.71396
\(37\) 3.35893 0.0907819 0.0453909 0.998969i \(-0.485547\pi\)
0.0453909 + 0.998969i \(0.485547\pi\)
\(38\) 36.3288 + 36.3288i 0.956021 + 0.956021i
\(39\) 10.1666i 0.260683i
\(40\) −191.683 −4.79207
\(41\) 2.04618i 0.0499069i 0.999689 + 0.0249535i \(0.00794376\pi\)
−0.999689 + 0.0249535i \(0.992056\pi\)
\(42\) 24.5175 0.583750
\(43\) 38.3292i 0.891376i 0.895188 + 0.445688i \(0.147041\pi\)
−0.895188 + 0.445688i \(0.852959\pi\)
\(44\) 90.4741 + 90.4741i 2.05623 + 2.05623i
\(45\) −42.5965 42.5965i −0.946589 0.946589i
\(46\) 26.2024 26.2024i 0.569618 0.569618i
\(47\) 21.6000i 0.459575i −0.973241 0.229787i \(-0.926197\pi\)
0.973241 0.229787i \(-0.0738031\pi\)
\(48\) 22.2592 22.2592i 0.463733 0.463733i
\(49\) −114.173 −2.33007
\(50\) 61.4532 + 61.4532i 1.22906 + 1.22906i
\(51\) 1.63365 0.0320323
\(52\) −162.694 162.694i −3.12873 3.12873i
\(53\) 34.4098 0.649241 0.324620 0.945844i \(-0.394763\pi\)
0.324620 + 0.945844i \(0.394763\pi\)
\(54\) 34.0816 0.631141
\(55\) 78.8901i 1.43437i
\(56\) −251.685 + 251.685i −4.49437 + 4.49437i
\(57\) 4.60029 + 4.60029i 0.0807069 + 0.0807069i
\(58\) 18.4926 18.4926i 0.318838 0.318838i
\(59\) 40.7776 0.691146 0.345573 0.938392i \(-0.387685\pi\)
0.345573 + 0.938392i \(0.387685\pi\)
\(60\) −37.8383 −0.630638
\(61\) 74.2387 1.21703 0.608514 0.793543i \(-0.291766\pi\)
0.608514 + 0.793543i \(0.291766\pi\)
\(62\) 18.1582i 0.292874i
\(63\) −111.861 −1.77557
\(64\) 278.490i 4.35141i
\(65\) 141.863i 2.18251i
\(66\) 15.5641 + 15.5641i 0.235819 + 0.235819i
\(67\) −29.7634 + 29.7634i −0.444229 + 0.444229i −0.893431 0.449201i \(-0.851709\pi\)
0.449201 + 0.893431i \(0.351709\pi\)
\(68\) −26.1428 + 26.1428i −0.384453 + 0.384453i
\(69\) 3.31800 3.31800i 0.0480869 0.0480869i
\(70\) 342.112 4.88732
\(71\) 85.7680 + 85.7680i 1.20800 + 1.20800i 0.971674 + 0.236326i \(0.0759433\pi\)
0.236326 + 0.971674i \(0.424057\pi\)
\(72\) −172.538 + 172.538i −2.39636 + 2.39636i
\(73\) 19.3531 19.3531i 0.265111 0.265111i −0.562015 0.827127i \(-0.689974\pi\)
0.827127 + 0.562015i \(0.189974\pi\)
\(74\) −9.24686 + 9.24686i −0.124958 + 0.124958i
\(75\) 7.78178 + 7.78178i 0.103757 + 0.103757i
\(76\) −147.235 −1.93730
\(77\) −103.585 103.585i −1.34526 1.34526i
\(78\) −27.9879 27.9879i −0.358819 0.358819i
\(79\) −61.9554 61.9554i −0.784245 0.784245i 0.196299 0.980544i \(-0.437108\pi\)
−0.980544 + 0.196299i \(0.937108\pi\)
\(80\) 310.601 310.601i 3.88251 3.88251i
\(81\) −74.4969 −0.919714
\(82\) −5.63298 5.63298i −0.0686949 0.0686949i
\(83\) 78.7914i 0.949294i −0.880176 0.474647i \(-0.842576\pi\)
0.880176 0.474647i \(-0.157424\pi\)
\(84\) −49.6827 + 49.6827i −0.591461 + 0.591461i
\(85\) 22.7956 0.268183
\(86\) −105.517 105.517i −1.22694 1.22694i
\(87\) 2.34171 2.34171i 0.0269162 0.0269162i
\(88\) −319.547 −3.63121
\(89\) 15.5211 + 15.5211i 0.174394 + 0.174394i 0.788907 0.614513i \(-0.210647\pi\)
−0.614513 + 0.788907i \(0.710647\pi\)
\(90\) 234.529 2.60588
\(91\) 186.270 + 186.270i 2.04693 + 2.04693i
\(92\) 106.194i 1.15428i
\(93\) 2.29936i 0.0247243i
\(94\) 59.4631 + 59.4631i 0.632586 + 0.632586i
\(95\) 64.1916 + 64.1916i 0.675701 + 0.675701i
\(96\) 67.6077i 0.704247i
\(97\) 38.3936i 0.395811i −0.980221 0.197905i \(-0.936586\pi\)
0.980221 0.197905i \(-0.0634138\pi\)
\(98\) 314.310 314.310i 3.20725 3.20725i
\(99\) −71.0109 71.0109i −0.717282 0.717282i
\(100\) −249.060 −2.49060
\(101\) −180.718 −1.78929 −0.894644 0.446780i \(-0.852571\pi\)
−0.894644 + 0.446780i \(0.852571\pi\)
\(102\) −4.49729 + 4.49729i −0.0440911 + 0.0440911i
\(103\) −64.9125 + 64.9125i −0.630218 + 0.630218i −0.948123 0.317905i \(-0.897021\pi\)
0.317905 + 0.948123i \(0.397021\pi\)
\(104\) 574.621 5.52520
\(105\) 43.3215 0.412586
\(106\) −94.7273 + 94.7273i −0.893654 + 0.893654i
\(107\) 169.430i 1.58346i −0.610870 0.791731i \(-0.709180\pi\)
0.610870 0.791731i \(-0.290820\pi\)
\(108\) −69.0636 + 69.0636i −0.639477 + 0.639477i
\(109\) 75.4895i 0.692564i 0.938130 + 0.346282i \(0.112556\pi\)
−0.938130 + 0.346282i \(0.887444\pi\)
\(110\) 217.178 + 217.178i 1.97435 + 1.97435i
\(111\) −1.17092 + 1.17092i −0.0105489 + 0.0105489i
\(112\) 815.654i 7.28263i
\(113\) 71.3001 + 71.3001i 0.630974 + 0.630974i 0.948312 0.317338i \(-0.102789\pi\)
−0.317338 + 0.948312i \(0.602789\pi\)
\(114\) −25.3285 −0.222180
\(115\) 46.2987 46.2987i 0.402598 0.402598i
\(116\) 74.9474i 0.646098i
\(117\) 127.694 + 127.694i 1.09141 + 1.09141i
\(118\) −112.257 + 112.257i −0.951334 + 0.951334i
\(119\) 29.9312 29.9312i 0.251523 0.251523i
\(120\) 66.8207 66.8207i 0.556839 0.556839i
\(121\) 10.5145i 0.0868967i
\(122\) −204.373 + 204.373i −1.67519 + 1.67519i
\(123\) −0.713301 0.713301i −0.00579919 0.00579919i
\(124\) 36.7961 + 36.7961i 0.296743 + 0.296743i
\(125\) −13.0221 13.0221i −0.104177 0.104177i
\(126\) 307.944 307.944i 2.44400 2.44400i
\(127\) 102.805i 0.809489i 0.914430 + 0.404745i \(0.132640\pi\)
−0.914430 + 0.404745i \(0.867360\pi\)
\(128\) −378.780 378.780i −2.95922 2.95922i
\(129\) −13.3616 13.3616i −0.103578 0.103578i
\(130\) −390.538 390.538i −3.00414 3.00414i
\(131\) −94.8251 + 94.8251i −0.723856 + 0.723856i −0.969388 0.245532i \(-0.921037\pi\)
0.245532 + 0.969388i \(0.421037\pi\)
\(132\) −63.0786 −0.477868
\(133\) 168.571 1.26745
\(134\) 163.872i 1.22293i
\(135\) 60.2209 0.446081
\(136\) 92.3341i 0.678927i
\(137\) 13.6465i 0.0996091i 0.998759 + 0.0498046i \(0.0158598\pi\)
−0.998759 + 0.0498046i \(0.984140\pi\)
\(138\) 18.2684i 0.132379i
\(139\) 61.9444 + 61.9444i 0.445643 + 0.445643i 0.893903 0.448260i \(-0.147956\pi\)
−0.448260 + 0.893903i \(0.647956\pi\)
\(140\) −693.263 + 693.263i −4.95188 + 4.95188i
\(141\) 7.52978 + 7.52978i 0.0534027 + 0.0534027i
\(142\) −472.225 −3.32553
\(143\) 236.494i 1.65381i
\(144\) 559.158i 3.88304i
\(145\) 32.6757 32.6757i 0.225350 0.225350i
\(146\) 106.555i 0.729830i
\(147\) 39.8009 39.8009i 0.270754 0.270754i
\(148\) 37.4760i 0.253216i
\(149\) −126.863 126.863i −0.851430 0.851430i 0.138880 0.990309i \(-0.455650\pi\)
−0.990309 + 0.138880i \(0.955650\pi\)
\(150\) −42.8452 −0.285635
\(151\) 115.455 + 115.455i 0.764605 + 0.764605i 0.977151 0.212546i \(-0.0681756\pi\)
−0.212546 + 0.977151i \(0.568176\pi\)
\(152\) 260.010 260.010i 1.71059 1.71059i
\(153\) 20.5188 20.5188i 0.134110 0.134110i
\(154\) 570.322 3.70339
\(155\) 32.0848i 0.206999i
\(156\) 113.430 0.727118
\(157\) 94.8677i 0.604253i −0.953268 0.302126i \(-0.902304\pi\)
0.953268 0.302126i \(-0.0976965\pi\)
\(158\) 341.116 2.15896
\(159\) −11.9953 + 11.9953i −0.0754419 + 0.0754419i
\(160\) 943.385i 5.89616i
\(161\) 121.583i 0.755174i
\(162\) 205.084 205.084i 1.26595 1.26595i
\(163\) 296.256i 1.81752i 0.417317 + 0.908761i \(0.362970\pi\)
−0.417317 + 0.908761i \(0.637030\pi\)
\(164\) 22.8295 0.139205
\(165\) 27.5011 + 27.5011i 0.166674 + 0.166674i
\(166\) 216.906 + 216.906i 1.30666 + 1.30666i
\(167\) −77.6643 + 77.6643i −0.465056 + 0.465056i −0.900308 0.435253i \(-0.856659\pi\)
0.435253 + 0.900308i \(0.356659\pi\)
\(168\) 175.475i 1.04449i
\(169\) 256.273i 1.51641i
\(170\) −62.7544 + 62.7544i −0.369143 + 0.369143i
\(171\) 115.561 0.675794
\(172\) 427.643 2.48630
\(173\) 41.2422i 0.238394i 0.992871 + 0.119197i \(0.0380321\pi\)
−0.992871 + 0.119197i \(0.961968\pi\)
\(174\) 12.8931i 0.0740980i
\(175\) 285.152 1.62944
\(176\) 517.789 517.789i 2.94199 2.94199i
\(177\) −14.2151 + 14.2151i −0.0803113 + 0.0803113i
\(178\) −85.4567 −0.480094
\(179\) −201.036 + 201.036i −1.12311 + 1.12311i −0.131838 + 0.991271i \(0.542088\pi\)
−0.991271 + 0.131838i \(0.957912\pi\)
\(180\) −475.255 + 475.255i −2.64030 + 2.64030i
\(181\) 268.261i 1.48210i −0.671448 0.741051i \(-0.734327\pi\)
0.671448 0.741051i \(-0.265673\pi\)
\(182\) −1025.57 −5.63502
\(183\) −25.8796 + 25.8796i −0.141419 + 0.141419i
\(184\) −187.534 187.534i −1.01921 1.01921i
\(185\) −16.3389 + 16.3389i −0.0883181 + 0.0883181i
\(186\) 6.32995 + 6.32995i 0.0340320 + 0.0340320i
\(187\) 38.0016 0.203217
\(188\) −240.994 −1.28188
\(189\) 79.0717 79.0717i 0.418369 0.418369i
\(190\) −353.429 −1.86015
\(191\) −272.235 −1.42531 −0.712656 0.701513i \(-0.752508\pi\)
−0.712656 + 0.701513i \(0.752508\pi\)
\(192\) −97.0818 97.0818i −0.505634 0.505634i
\(193\) −219.804 −1.13888 −0.569441 0.822032i \(-0.692840\pi\)
−0.569441 + 0.822032i \(0.692840\pi\)
\(194\) 105.695 + 105.695i 0.544817 + 0.544817i
\(195\) −49.4536 49.4536i −0.253608 0.253608i
\(196\) 1273.85i 6.49922i
\(197\) 132.361 145.909i 0.671883 0.740657i
\(198\) 390.974 1.97462
\(199\) −212.090 + 212.090i −1.06578 + 1.06578i −0.0681023 + 0.997678i \(0.521694\pi\)
−0.997678 + 0.0681023i \(0.978306\pi\)
\(200\) 439.829 439.829i 2.19914 2.19914i
\(201\) 20.7510i 0.103239i
\(202\) 497.502 497.502i 2.46288 2.46288i
\(203\) 85.8082i 0.422701i
\(204\) 18.2268i 0.0893470i
\(205\) −9.95326 9.95326i −0.0485525 0.0485525i
\(206\) 357.398i 1.73494i
\(207\) 83.3492i 0.402653i
\(208\) −931.108 + 931.108i −4.47648 + 4.47648i
\(209\) 107.011 + 107.011i 0.512015 + 0.512015i
\(210\) −119.261 + 119.261i −0.567907 + 0.567907i
\(211\) 122.733 + 122.733i 0.581671 + 0.581671i 0.935362 0.353691i \(-0.115074\pi\)
−0.353691 + 0.935362i \(0.615074\pi\)
\(212\) 383.914i 1.81092i
\(213\) −59.7975 −0.280740
\(214\) 466.428 + 466.428i 2.17957 + 2.17957i
\(215\) −186.445 186.445i −0.867185 0.867185i
\(216\) 243.926i 1.12929i
\(217\) −42.1283 42.1283i −0.194140 0.194140i
\(218\) −207.817 207.817i −0.953287 0.953287i
\(219\) 13.4930i 0.0616119i
\(220\) −880.187 −4.00085
\(221\) −68.3358 −0.309212
\(222\) 6.44692i 0.0290402i
\(223\) 365.088i 1.63716i −0.574390 0.818582i \(-0.694761\pi\)
0.574390 0.818582i \(-0.305239\pi\)
\(224\) 1238.69 + 1238.69i 5.52987 + 5.52987i
\(225\) 195.481 0.868804
\(226\) −392.567 −1.73702
\(227\) 173.151 + 173.151i 0.762781 + 0.762781i 0.976824 0.214044i \(-0.0686635\pi\)
−0.214044 + 0.976824i \(0.568663\pi\)
\(228\) 51.3261 51.3261i 0.225114 0.225114i
\(229\) 24.2459 24.2459i 0.105877 0.105877i −0.652184 0.758061i \(-0.726147\pi\)
0.758061 + 0.652184i \(0.226147\pi\)
\(230\) 254.913i 1.10832i
\(231\) 72.2195 0.312639
\(232\) −132.354 132.354i −0.570491 0.570491i
\(233\) 13.3801 0.0574253 0.0287126 0.999588i \(-0.490859\pi\)
0.0287126 + 0.999588i \(0.490859\pi\)
\(234\) −703.065 −3.00455
\(235\) 105.069 + 105.069i 0.447102 + 0.447102i
\(236\) 454.961i 1.92780i
\(237\) 43.1953 0.182259
\(238\) 164.796i 0.692422i
\(239\) −300.679 −1.25807 −0.629036 0.777376i \(-0.716550\pi\)
−0.629036 + 0.777376i \(0.716550\pi\)
\(240\) 216.551i 0.902296i
\(241\) 12.1894 + 12.1894i 0.0505784 + 0.0505784i 0.731944 0.681365i \(-0.238613\pi\)
−0.681365 + 0.731944i \(0.738613\pi\)
\(242\) 28.9456 + 28.9456i 0.119610 + 0.119610i
\(243\) 81.6804 81.6804i 0.336133 0.336133i
\(244\) 828.291i 3.39463i
\(245\) 555.374 555.374i 2.26683 2.26683i
\(246\) 3.92732 0.0159647
\(247\) −192.432 192.432i −0.779075 0.779075i
\(248\) −129.961 −0.524034
\(249\) 27.4667 + 27.4667i 0.110308 + 0.110308i
\(250\) 71.6976 0.286791
\(251\) 80.9798 0.322629 0.161314 0.986903i \(-0.448427\pi\)
0.161314 + 0.986903i \(0.448427\pi\)
\(252\) 1248.04i 4.95256i
\(253\) 77.1827 77.1827i 0.305070 0.305070i
\(254\) −283.014 283.014i −1.11423 1.11423i
\(255\) −7.94655 + 7.94655i −0.0311629 + 0.0311629i
\(256\) 971.542 3.79509
\(257\) 191.905 0.746712 0.373356 0.927688i \(-0.378207\pi\)
0.373356 + 0.927688i \(0.378207\pi\)
\(258\) 73.5666 0.285142
\(259\) 42.9067i 0.165663i
\(260\) 1582.79 6.08764
\(261\) 58.8244i 0.225381i
\(262\) 522.092i 1.99272i
\(263\) 4.98614 + 4.98614i 0.0189587 + 0.0189587i 0.716523 0.697564i \(-0.245733\pi\)
−0.697564 + 0.716523i \(0.745733\pi\)
\(264\) 111.394 111.394i 0.421947 0.421947i
\(265\) −167.380 + 167.380i −0.631621 + 0.631621i
\(266\) −464.062 + 464.062i −1.74459 + 1.74459i
\(267\) −10.8213 −0.0405293
\(268\) 332.074 + 332.074i 1.23908 + 1.23908i
\(269\) −136.358 + 136.358i −0.506906 + 0.506906i −0.913575 0.406669i \(-0.866690\pi\)
0.406669 + 0.913575i \(0.366690\pi\)
\(270\) −165.783 + 165.783i −0.614012 + 0.614012i
\(271\) −150.728 + 150.728i −0.556192 + 0.556192i −0.928221 0.372029i \(-0.878662\pi\)
0.372029 + 0.928221i \(0.378662\pi\)
\(272\) 149.617 + 149.617i 0.550063 + 0.550063i
\(273\) −129.868 −0.475706
\(274\) −37.5676 37.5676i −0.137108 0.137108i
\(275\) 181.018 + 181.018i 0.658249 + 0.658249i
\(276\) −37.0193 37.0193i −0.134128 0.134128i
\(277\) 186.722 186.722i 0.674086 0.674086i −0.284570 0.958655i \(-0.591851\pi\)
0.958655 + 0.284570i \(0.0918507\pi\)
\(278\) −341.056 −1.22682
\(279\) −28.8803 28.8803i −0.103514 0.103514i
\(280\) 2448.54i 8.74480i
\(281\) −85.8791 + 85.8791i −0.305620 + 0.305620i −0.843208 0.537588i \(-0.819336\pi\)
0.537588 + 0.843208i \(0.319336\pi\)
\(282\) −41.4577 −0.147013
\(283\) 380.810 + 380.810i 1.34562 + 1.34562i 0.890359 + 0.455260i \(0.150454\pi\)
0.455260 + 0.890359i \(0.349546\pi\)
\(284\) 956.924 956.924i 3.36945 3.36945i
\(285\) −44.7545 −0.157033
\(286\) −651.050 651.050i −2.27640 2.27640i
\(287\) −26.1378 −0.0910725
\(288\) 849.164 + 849.164i 2.94848 + 2.94848i
\(289\) 278.019i 0.962005i
\(290\) 179.907i 0.620370i
\(291\) 13.3840 + 13.3840i 0.0459932 + 0.0459932i
\(292\) −215.925 215.925i −0.739470 0.739470i
\(293\) 15.3937i 0.0525381i −0.999655 0.0262690i \(-0.991637\pi\)
0.999655 0.0262690i \(-0.00836266\pi\)
\(294\) 219.137i 0.745365i
\(295\) −198.355 + 198.355i −0.672389 + 0.672389i
\(296\) 66.1810 + 66.1810i 0.223584 + 0.223584i
\(297\) 100.392 0.338020
\(298\) 698.487 2.34392
\(299\) −138.793 + 138.793i −0.464190 + 0.464190i
\(300\) 86.8224 86.8224i 0.289408 0.289408i
\(301\) −489.614 −1.62662
\(302\) −635.678 −2.10490
\(303\) 62.9984 62.9984i 0.207915 0.207915i
\(304\) 842.634i 2.77182i
\(305\) −361.120 + 361.120i −1.18400 + 1.18400i
\(306\) 112.973i 0.369194i
\(307\) 334.742 + 334.742i 1.09037 + 1.09037i 0.995489 + 0.0948771i \(0.0302458\pi\)
0.0948771 + 0.995489i \(0.469754\pi\)
\(308\) −1155.71 + 1155.71i −3.75231 + 3.75231i
\(309\) 45.2570i 0.146463i
\(310\) 88.3270 + 88.3270i 0.284926 + 0.284926i
\(311\) −136.771 −0.439778 −0.219889 0.975525i \(-0.570570\pi\)
−0.219889 + 0.975525i \(0.570570\pi\)
\(312\) −200.313 + 200.313i −0.642029 + 0.642029i
\(313\) 489.795i 1.56484i −0.622751 0.782420i \(-0.713985\pi\)
0.622751 0.782420i \(-0.286015\pi\)
\(314\) 261.163 + 261.163i 0.831730 + 0.831730i
\(315\) 544.125 544.125i 1.72738 1.72738i
\(316\) −691.244 + 691.244i −2.18748 + 2.18748i
\(317\) 18.2212 18.2212i 0.0574802 0.0574802i −0.677782 0.735263i \(-0.737059\pi\)
0.735263 + 0.677782i \(0.237059\pi\)
\(318\) 66.0440i 0.207685i
\(319\) 54.4723 54.4723i 0.170760 0.170760i
\(320\) −1354.66 1354.66i −4.23332 4.23332i
\(321\) 59.0636 + 59.0636i 0.183999 + 0.183999i
\(322\) 334.708 + 334.708i 1.03947 + 1.03947i
\(323\) −30.9213 + 30.9213i −0.0957315 + 0.0957315i
\(324\) 831.171i 2.56534i
\(325\) −325.514 325.514i −1.00158 1.00158i
\(326\) −815.569 815.569i −2.50175 2.50175i
\(327\) −26.3157 26.3157i −0.0804761 0.0804761i
\(328\) −40.3160 + 40.3160i −0.122915 + 0.122915i
\(329\) 275.917 0.838654
\(330\) −151.417 −0.458839
\(331\) 111.798i 0.337759i −0.985637 0.168880i \(-0.945985\pi\)
0.985637 0.168880i \(-0.0540149\pi\)
\(332\) −879.086 −2.64785
\(333\) 29.4140i 0.0883303i
\(334\) 427.607i 1.28026i
\(335\) 289.556i 0.864346i
\(336\) 284.337 + 284.337i 0.846242 + 0.846242i
\(337\) −403.163 + 403.163i −1.19633 + 1.19633i −0.221073 + 0.975257i \(0.570956\pi\)
−0.975257 + 0.221073i \(0.929044\pi\)
\(338\) 705.499 + 705.499i 2.08727 + 2.08727i
\(339\) −49.7105 −0.146639
\(340\) 254.333i 0.748039i
\(341\) 53.4873i 0.156854i
\(342\) −318.130 + 318.130i −0.930203 + 0.930203i
\(343\) 832.520i 2.42717i
\(344\) −755.199 + 755.199i −2.19535 + 2.19535i
\(345\) 32.2795i 0.0935638i
\(346\) −113.537 113.537i −0.328140 0.328140i
\(347\) −25.5663 −0.0736781 −0.0368390 0.999321i \(-0.511729\pi\)
−0.0368390 + 0.999321i \(0.511729\pi\)
\(348\) −26.1267 26.1267i −0.0750767 0.0750767i
\(349\) 24.3550 24.3550i 0.0697850 0.0697850i −0.671353 0.741138i \(-0.734286\pi\)
0.741138 + 0.671353i \(0.234286\pi\)
\(350\) −784.999 + 784.999i −2.24285 + 2.24285i
\(351\) −180.528 −0.514326
\(352\) 1572.68i 4.46784i
\(353\) 264.398 0.749003 0.374501 0.927226i \(-0.377814\pi\)
0.374501 + 0.927226i \(0.377814\pi\)
\(354\) 78.2660i 0.221090i
\(355\) −834.403 −2.35043
\(356\) 173.171 173.171i 0.486435 0.486435i
\(357\) 20.8681i 0.0584540i
\(358\) 1106.87i 3.09183i
\(359\) −43.8889 + 43.8889i −0.122253 + 0.122253i −0.765586 0.643333i \(-0.777551\pi\)
0.643333 + 0.765586i \(0.277551\pi\)
\(360\) 1678.56i 4.66266i
\(361\) 186.853 0.517600
\(362\) 738.500 + 738.500i 2.04005 + 2.04005i
\(363\) 3.66536 + 3.66536i 0.0100974 + 0.0100974i
\(364\) 2078.24 2078.24i 5.70945 5.70945i
\(365\) 188.279i 0.515833i
\(366\) 142.489i 0.389315i
\(367\) −183.908 + 183.908i −0.501111 + 0.501111i −0.911783 0.410672i \(-0.865294\pi\)
0.410672 + 0.911783i \(0.365294\pi\)
\(368\) 607.756 1.65151
\(369\) −17.9183 −0.0485592
\(370\) 89.9591i 0.243133i
\(371\) 439.548i 1.18477i
\(372\) −25.6543 −0.0689631
\(373\) 61.4692 61.4692i 0.164797 0.164797i −0.619891 0.784688i \(-0.712823\pi\)
0.784688 + 0.619891i \(0.212823\pi\)
\(374\) −104.615 + 104.615i −0.279720 + 0.279720i
\(375\) 9.07903 0.0242107
\(376\) 425.585 425.585i 1.13188 1.13188i
\(377\) −97.9542 + 97.9542i −0.259825 + 0.259825i
\(378\) 435.356i 1.15174i
\(379\) 458.816 1.21059 0.605297 0.795999i \(-0.293054\pi\)
0.605297 + 0.795999i \(0.293054\pi\)
\(380\) 716.194 716.194i 1.88472 1.88472i
\(381\) −35.8379 35.8379i −0.0940628 0.0940628i
\(382\) 749.440 749.440i 1.96189 1.96189i
\(383\) −201.542 201.542i −0.526220 0.526220i 0.393223 0.919443i \(-0.371360\pi\)
−0.919443 + 0.393223i \(0.871360\pi\)
\(384\) 264.086 0.687724
\(385\) 1007.74 2.61750
\(386\) 605.104 605.104i 1.56763 1.56763i
\(387\) −335.647 −0.867304
\(388\) −428.363 −1.10403
\(389\) 459.084 + 459.084i 1.18017 + 1.18017i 0.979701 + 0.200464i \(0.0642451\pi\)
0.200464 + 0.979701i \(0.435755\pi\)
\(390\) 272.283 0.698162
\(391\) 22.3022 + 22.3022i 0.0570389 + 0.0570389i
\(392\) −2249.56 2249.56i −5.73867 5.73867i
\(393\) 66.1122i 0.168224i
\(394\) 37.2978 + 766.056i 0.0946645 + 1.94430i
\(395\) 602.739 1.52592
\(396\) −792.278 + 792.278i −2.00070 + 2.00070i
\(397\) −409.777 + 409.777i −1.03218 + 1.03218i −0.0327196 + 0.999465i \(0.510417\pi\)
−0.999465 + 0.0327196i \(0.989583\pi\)
\(398\) 1167.74i 2.93401i
\(399\) −58.7638 + 58.7638i −0.147278 + 0.147278i
\(400\) 1425.39i 3.56346i
\(401\) 451.222i 1.12524i −0.826715 0.562621i \(-0.809793\pi\)
0.826715 0.562621i \(-0.190207\pi\)
\(402\) 57.1259 + 57.1259i 0.142104 + 0.142104i
\(403\) 96.1829i 0.238667i
\(404\) 2016.29i 4.99083i
\(405\) 362.375 362.375i 0.894754 0.894754i
\(406\) 236.223 + 236.223i 0.581830 + 0.581830i
\(407\) −27.2378 + 27.2378i −0.0669234 + 0.0669234i
\(408\) 32.1877 + 32.1877i 0.0788914 + 0.0788914i
\(409\) 560.947i 1.37151i 0.727833 + 0.685755i \(0.240528\pi\)
−0.727833 + 0.685755i \(0.759472\pi\)
\(410\) 54.8011 0.133661
\(411\) −4.75716 4.75716i −0.0115746 0.0115746i
\(412\) 724.237 + 724.237i 1.75786 + 1.75786i
\(413\) 520.890i 1.26124i
\(414\) 229.454 + 229.454i 0.554236 + 0.554236i
\(415\) 383.265 + 383.265i 0.923531 + 0.923531i
\(416\) 2828.05i 6.79820i
\(417\) −43.1877 −0.103568
\(418\) −589.186 −1.40954
\(419\) 407.368i 0.972238i 0.873893 + 0.486119i \(0.161588\pi\)
−0.873893 + 0.486119i \(0.838412\pi\)
\(420\) 483.343i 1.15082i
\(421\) −234.508 234.508i −0.557026 0.557026i 0.371434 0.928460i \(-0.378866\pi\)
−0.928460 + 0.371434i \(0.878866\pi\)
\(422\) −675.746 −1.60129
\(423\) 189.150 0.447164
\(424\) 677.975 + 677.975i 1.59900 + 1.59900i
\(425\) −52.3059 + 52.3059i −0.123073 + 0.123073i
\(426\) 164.618 164.618i 0.386427 0.386427i
\(427\) 948.320i 2.22089i
\(428\) −1890.36 −4.41672
\(429\) −82.4420 82.4420i −0.192173 0.192173i
\(430\) 1026.53 2.38729
\(431\) 402.633 0.934183 0.467091 0.884209i \(-0.345302\pi\)
0.467091 + 0.884209i \(0.345302\pi\)
\(432\) 395.255 + 395.255i 0.914943 + 0.914943i
\(433\) 136.747i 0.315814i −0.987454 0.157907i \(-0.949525\pi\)
0.987454 0.157907i \(-0.0504746\pi\)
\(434\) 231.952 0.534450
\(435\) 22.7815i 0.0523713i
\(436\) 842.246 1.93176
\(437\) 125.605i 0.287425i
\(438\) −37.1452 37.1452i −0.0848064 0.0848064i
\(439\) −78.3867 78.3867i −0.178557 0.178557i 0.612169 0.790727i \(-0.290297\pi\)
−0.790727 + 0.612169i \(0.790297\pi\)
\(440\) 1554.37 1554.37i 3.53266 3.53266i
\(441\) 999.811i 2.26715i
\(442\) 188.123 188.123i 0.425618 0.425618i
\(443\) 152.649 0.344580 0.172290 0.985046i \(-0.444883\pi\)
0.172290 + 0.985046i \(0.444883\pi\)
\(444\) 13.0642 + 13.0642i 0.0294238 + 0.0294238i
\(445\) −150.999 −0.339323
\(446\) 1005.06 + 1005.06i 2.25349 + 2.25349i
\(447\) 88.4490 0.197873
\(448\) −3557.41 −7.94066
\(449\) 320.599i 0.714029i −0.934099 0.357014i \(-0.883795\pi\)
0.934099 0.357014i \(-0.116205\pi\)
\(450\) −538.143 + 538.143i −1.19587 + 1.19587i
\(451\) −16.5927 16.5927i −0.0367909 0.0367909i
\(452\) 795.504 795.504i 1.75997 1.75997i
\(453\) −80.4956 −0.177694
\(454\) −953.342 −2.09987
\(455\) −1812.15 −3.98275
\(456\) 181.279i 0.397542i
\(457\) 576.633 1.26178 0.630890 0.775873i \(-0.282690\pi\)
0.630890 + 0.775873i \(0.282690\pi\)
\(458\) 133.494i 0.291472i
\(459\) 29.0086i 0.0631995i
\(460\) −516.561 516.561i −1.12296 1.12296i
\(461\) −578.481 + 578.481i −1.25484 + 1.25484i −0.301314 + 0.953525i \(0.597425\pi\)
−0.953525 + 0.301314i \(0.902575\pi\)
\(462\) −198.814 + 198.814i −0.430334 + 0.430334i
\(463\) −50.3654 + 50.3654i −0.108781 + 0.108781i −0.759402 0.650622i \(-0.774508\pi\)
0.650622 + 0.759402i \(0.274508\pi\)
\(464\) 428.929 0.924416
\(465\) 11.1848 + 11.1848i 0.0240533 + 0.0240533i
\(466\) −36.8343 + 36.8343i −0.0790436 + 0.0790436i
\(467\) 489.961 489.961i 1.04917 1.04917i 0.0504390 0.998727i \(-0.483938\pi\)
0.998727 0.0504390i \(-0.0160621\pi\)
\(468\) 1424.70 1424.70i 3.04424 3.04424i
\(469\) −380.195 380.195i −0.810650 0.810650i
\(470\) −578.493 −1.23084
\(471\) 33.0709 + 33.0709i 0.0702143 + 0.0702143i
\(472\) 803.441 + 803.441i 1.70221 + 1.70221i
\(473\) −310.814 310.814i −0.657113 0.657113i
\(474\) −118.913 + 118.913i −0.250872 + 0.250872i
\(475\) −294.584 −0.620176
\(476\) −333.946 333.946i −0.701568 0.701568i
\(477\) 301.325i 0.631708i
\(478\) 827.746 827.746i 1.73169 1.73169i
\(479\) 142.337 0.297155 0.148578 0.988901i \(-0.452531\pi\)
0.148578 + 0.988901i \(0.452531\pi\)
\(480\) −328.865 328.865i −0.685134 0.685134i
\(481\) 48.9801 48.9801i 0.101830 0.101830i
\(482\) −67.1128 −0.139238
\(483\) 42.3839 + 42.3839i 0.0877513 + 0.0877513i
\(484\) −117.312 −0.242379
\(485\) 186.758 + 186.758i 0.385069 + 0.385069i
\(486\) 449.719i 0.925348i
\(487\) 126.649i 0.260059i 0.991510 + 0.130029i \(0.0415071\pi\)
−0.991510 + 0.130029i \(0.958493\pi\)
\(488\) 1462.73 + 1462.73i 2.99739 + 2.99739i
\(489\) −103.275 103.275i −0.211196 0.211196i
\(490\) 3057.80i 6.24041i
\(491\) 477.700i 0.972911i 0.873705 + 0.486456i \(0.161711\pi\)
−0.873705 + 0.486456i \(0.838289\pi\)
\(492\) −7.95839 + 7.95839i −0.0161756 + 0.0161756i
\(493\) 15.7400 + 15.7400i 0.0319269 + 0.0319269i
\(494\) 1059.50 2.14473
\(495\) 690.837 1.39563
\(496\) 210.586 210.586i 0.424570 0.424570i
\(497\) −1095.59 + 1095.59i −2.20442 + 2.20442i
\(498\) −151.227 −0.303669
\(499\) −368.876 −0.739230 −0.369615 0.929185i \(-0.620511\pi\)
−0.369615 + 0.929185i \(0.620511\pi\)
\(500\) −145.289 + 145.289i −0.290579 + 0.290579i
\(501\) 54.1476i 0.108079i
\(502\) −222.931 + 222.931i −0.444086 + 0.444086i
\(503\) 557.241i 1.10784i −0.832571 0.553918i \(-0.813132\pi\)
0.832571 0.553918i \(-0.186868\pi\)
\(504\) −2203.99 2203.99i −4.37300 4.37300i
\(505\) 879.068 879.068i 1.74073 1.74073i
\(506\) 424.955i 0.839833i
\(507\) 89.3369 + 89.3369i 0.176207 + 0.176207i
\(508\) 1147.01 2.25789
\(509\) −238.504 + 238.504i −0.468574 + 0.468574i −0.901452 0.432878i \(-0.857498\pi\)
0.432878 + 0.901452i \(0.357498\pi\)
\(510\) 43.7524i 0.0857890i
\(511\) 247.215 + 247.215i 0.483788 + 0.483788i
\(512\) −1159.46 + 1159.46i −2.26456 + 2.26456i
\(513\) −81.6872 + 81.6872i −0.159234 + 0.159234i
\(514\) −528.299 + 528.299i −1.02782 + 1.02782i
\(515\) 631.508i 1.22623i
\(516\) −149.077 + 149.077i −0.288908 + 0.288908i
\(517\) 175.156 + 175.156i 0.338794 + 0.338794i
\(518\) −118.119 118.119i −0.228029 0.228029i
\(519\) −14.3771 14.3771i −0.0277015 0.0277015i
\(520\) −2795.13 + 2795.13i −5.37525 + 5.37525i
\(521\) 19.9161i 0.0382268i 0.999817 + 0.0191134i \(0.00608435\pi\)
−0.999817 + 0.0191134i \(0.993916\pi\)
\(522\) 161.939 + 161.939i 0.310228 + 0.310228i
\(523\) −30.7150 30.7150i −0.0587284 0.0587284i 0.677133 0.735861i \(-0.263222\pi\)
−0.735861 + 0.677133i \(0.763222\pi\)
\(524\) 1057.98 + 1057.98i 2.01904 + 2.01904i
\(525\) −99.4040 + 99.4040i −0.189341 + 0.189341i
\(526\) −27.4529 −0.0521918
\(527\) 15.4553 0.0293270
\(528\) 361.003i 0.683718i
\(529\) −438.407 −0.828746
\(530\) 921.565i 1.73880i
\(531\) 357.088i 0.672481i
\(532\) 1880.77i 3.53527i
\(533\) 29.8376 + 29.8376i 0.0559804 + 0.0559804i
\(534\) 29.7903 29.7903i 0.0557870 0.0557870i
\(535\) 824.162 + 824.162i 1.54049 + 1.54049i
\(536\) −1172.85 −2.18816
\(537\) 140.163i 0.261011i
\(538\) 750.763i 1.39547i
\(539\) 925.841 925.841i 1.71770 1.71770i
\(540\) 671.892i 1.24425i
\(541\) 512.192 512.192i 0.946750 0.946750i −0.0519019 0.998652i \(-0.516528\pi\)
0.998652 + 0.0519019i \(0.0165283\pi\)
\(542\) 829.884i 1.53115i
\(543\) 93.5158 + 93.5158i 0.172221 + 0.172221i
\(544\) −454.431 −0.835351
\(545\) −367.204 367.204i −0.673769 0.673769i
\(546\) 357.516 357.516i 0.654790 0.654790i
\(547\) 330.961 330.961i 0.605047 0.605047i −0.336600 0.941648i \(-0.609277\pi\)
0.941648 + 0.336600i \(0.109277\pi\)
\(548\) 152.255 0.277838
\(549\) 650.105i 1.18416i
\(550\) −996.659 −1.81211
\(551\) 88.6465i 0.160883i
\(552\) 130.749 0.236864
\(553\) 791.414 791.414i 1.43113 1.43113i
\(554\) 1028.06i 1.85570i
\(555\) 11.3915i 0.0205252i
\(556\) 691.122 691.122i 1.24302 1.24302i
\(557\) 261.110i 0.468780i −0.972143 0.234390i \(-0.924691\pi\)
0.972143 0.234390i \(-0.0753092\pi\)
\(558\) 159.010 0.284965
\(559\) 558.918 + 558.918i 0.999853 + 0.999853i
\(560\) 3967.59 + 3967.59i 7.08498 + 7.08498i
\(561\) −13.2474 + 13.2474i −0.0236138 + 0.0236138i
\(562\) 472.837i 0.841346i
\(563\) 175.000i 0.310835i −0.987849 0.155418i \(-0.950328\pi\)
0.987849 0.155418i \(-0.0496723\pi\)
\(564\) 84.0107 84.0107i 0.148955 0.148955i
\(565\) −693.651 −1.22770
\(566\) −2096.68 −3.70438
\(567\) 951.618i 1.67834i
\(568\) 3379.77i 5.95030i
\(569\) −699.493 −1.22934 −0.614669 0.788785i \(-0.710710\pi\)
−0.614669 + 0.788785i \(0.710710\pi\)
\(570\) 123.205 123.205i 0.216150 0.216150i
\(571\) 44.3380 44.3380i 0.0776498 0.0776498i −0.667215 0.744865i \(-0.732514\pi\)
0.744865 + 0.667215i \(0.232514\pi\)
\(572\) 2638.60 4.61293
\(573\) 94.9012 94.9012i 0.165622 0.165622i
\(574\) 71.9553 71.9553i 0.125358 0.125358i
\(575\) 212.471i 0.369514i
\(576\) −2438.73 −4.23390
\(577\) −793.882 + 793.882i −1.37588 + 1.37588i −0.524416 + 0.851462i \(0.675716\pi\)
−0.851462 + 0.524416i \(0.824284\pi\)
\(578\) 765.365 + 765.365i 1.32416 + 1.32416i
\(579\) 76.6239 76.6239i 0.132338 0.132338i
\(580\) −364.567 364.567i −0.628564 0.628564i
\(581\) 1006.48 1.73232
\(582\) −73.6903 −0.126616
\(583\) −279.032 + 279.032i −0.478613 + 0.478613i
\(584\) 762.629 1.30587
\(585\) −1242.29 −2.12357
\(586\) 42.3775 + 42.3775i 0.0723165 + 0.0723165i
\(587\) −478.705 −0.815511 −0.407756 0.913091i \(-0.633688\pi\)
−0.407756 + 0.913091i \(0.633688\pi\)
\(588\) −444.064 444.064i −0.755210 0.755210i
\(589\) 43.5218 + 43.5218i 0.0738910 + 0.0738910i
\(590\) 1092.11i 1.85103i
\(591\) 4.72300 + 97.0052i 0.00799154 + 0.164137i
\(592\) −214.478 −0.362293
\(593\) 258.535 258.535i 0.435978 0.435978i −0.454678 0.890656i \(-0.650246\pi\)
0.890656 + 0.454678i \(0.150246\pi\)
\(594\) −276.371 + 276.371i −0.465270 + 0.465270i
\(595\) 291.189i 0.489393i
\(596\) −1415.43 + 1415.43i −2.37488 + 2.37488i
\(597\) 147.870i 0.247688i
\(598\) 764.171i 1.27788i
\(599\) −556.457 556.457i −0.928976 0.928976i 0.0686640 0.997640i \(-0.478126\pi\)
−0.997640 + 0.0686640i \(0.978126\pi\)
\(600\) 306.649i 0.511082i
\(601\) 45.2934i 0.0753634i 0.999290 + 0.0376817i \(0.0119973\pi\)
−0.999290 + 0.0376817i \(0.988003\pi\)
\(602\) 1347.87 1347.87i 2.23898 2.23898i
\(603\) −260.636 260.636i −0.432233 0.432233i
\(604\) 1288.15 1288.15i 2.13270 2.13270i
\(605\) 51.1457 + 51.1457i 0.0845384 + 0.0845384i
\(606\) 346.859i 0.572375i
\(607\) −56.2260 −0.0926294 −0.0463147 0.998927i \(-0.514748\pi\)
−0.0463147 + 0.998927i \(0.514748\pi\)
\(608\) −1279.66 1279.66i −2.10471 2.10471i
\(609\) 29.9128 + 29.9128i 0.0491179 + 0.0491179i
\(610\) 1988.27i 3.25945i
\(611\) −314.973 314.973i −0.515504 0.515504i
\(612\) −228.931 228.931i −0.374071 0.374071i
\(613\) 543.158i 0.886066i 0.896505 + 0.443033i \(0.146098\pi\)
−0.896505 + 0.443033i \(0.853902\pi\)
\(614\) −1843.04 −3.00169
\(615\) 6.93943 0.0112836
\(616\) 4081.87i 6.62641i
\(617\) 601.854i 0.975452i 0.872997 + 0.487726i \(0.162173\pi\)
−0.872997 + 0.487726i \(0.837827\pi\)
\(618\) 124.589 + 124.589i 0.201600 + 0.201600i
\(619\) 863.396 1.39482 0.697412 0.716671i \(-0.254335\pi\)
0.697412 + 0.716671i \(0.254335\pi\)
\(620\) −357.975 −0.577379
\(621\) 58.9175 + 58.9175i 0.0948753 + 0.0948753i
\(622\) 376.520 376.520i 0.605337 0.605337i
\(623\) −198.266 + 198.266i −0.318243 + 0.318243i
\(624\) 649.170i 1.04034i
\(625\) 684.760 1.09562
\(626\) 1348.37 + 1348.37i 2.15394 + 2.15394i
\(627\) −74.6083 −0.118993
\(628\) −1058.45 −1.68543
\(629\) −7.87047 7.87047i −0.0125127 0.0125127i
\(630\) 2995.86i 4.75534i
\(631\) −683.405 −1.08305 −0.541525 0.840685i \(-0.682153\pi\)
−0.541525 + 0.840685i \(0.682153\pi\)
\(632\) 2441.41i 3.86299i
\(633\) −85.5693 −0.135181
\(634\) 100.323i 0.158238i
\(635\) −500.076 500.076i −0.787520 0.787520i
\(636\) 133.833 + 133.833i 0.210429 + 0.210429i
\(637\) −1664.88 + 1664.88i −2.61363 + 2.61363i
\(638\) 299.916i 0.470088i
\(639\) −751.066 + 751.066i −1.17538 + 1.17538i
\(640\) 3685.00 5.75782
\(641\) 17.8094 + 17.8094i 0.0277838 + 0.0277838i 0.720862 0.693078i \(-0.243746\pi\)
−0.693078 + 0.720862i \(0.743746\pi\)
\(642\) −325.194 −0.506533
\(643\) 623.526 + 623.526i 0.969714 + 0.969714i 0.999555 0.0298402i \(-0.00949984\pi\)
−0.0298402 + 0.999555i \(0.509500\pi\)
\(644\) −1356.52 −2.10639
\(645\) 129.989 0.201534
\(646\) 170.247i 0.263541i
\(647\) −379.254 + 379.254i −0.586173 + 0.586173i −0.936593 0.350419i \(-0.886039\pi\)
0.350419 + 0.936593i \(0.386039\pi\)
\(648\) −1467.81 1467.81i −2.26514 2.26514i
\(649\) −330.669 + 330.669i −0.509505 + 0.509505i
\(650\) 1792.23 2.75727
\(651\) 29.3719 0.0451181
\(652\) 3305.37 5.06958
\(653\) 625.010i 0.957136i −0.878050 0.478568i \(-0.841156\pi\)
0.878050 0.478568i \(-0.158844\pi\)
\(654\) 144.890 0.221544
\(655\) 922.517i 1.40842i
\(656\) 130.655i 0.199169i
\(657\) 169.474 + 169.474i 0.257952 + 0.257952i
\(658\) −759.578 + 759.578i −1.15437 + 1.15437i
\(659\) −68.3569 + 68.3569i −0.103728 + 0.103728i −0.757066 0.653338i \(-0.773368\pi\)
0.653338 + 0.757066i \(0.273368\pi\)
\(660\) 306.834 306.834i 0.464900 0.464900i
\(661\) 873.154 1.32096 0.660479 0.750844i \(-0.270353\pi\)
0.660479 + 0.750844i \(0.270353\pi\)
\(662\) 307.772 + 307.772i 0.464912 + 0.464912i
\(663\) 23.8219 23.8219i 0.0359305 0.0359305i
\(664\) 1552.43 1552.43i 2.33799 2.33799i
\(665\) −819.979 + 819.979i −1.23305 + 1.23305i
\(666\) −80.9743 80.9743i −0.121583 0.121583i
\(667\) 63.9370 0.0958576
\(668\) 866.510 + 866.510i 1.29717 + 1.29717i
\(669\) 127.270 + 127.270i 0.190239 + 0.190239i
\(670\) 797.124 + 797.124i 1.18974 + 1.18974i
\(671\) −602.008 + 602.008i −0.897180 + 0.897180i
\(672\) −863.616 −1.28514
\(673\) −810.969 810.969i −1.20501 1.20501i −0.972625 0.232382i \(-0.925348\pi\)
−0.232382 0.972625i \(-0.574652\pi\)
\(674\) 2219.75i 3.29340i
\(675\) −138.181 + 138.181i −0.204712 + 0.204712i
\(676\) −2859.27 −4.22969
\(677\) −515.057 515.057i −0.760793 0.760793i 0.215672 0.976466i \(-0.430806\pi\)
−0.976466 + 0.215672i \(0.930806\pi\)
\(678\) 136.849 136.849i 0.201842 0.201842i
\(679\) 490.438 0.722294
\(680\) 449.141 + 449.141i 0.660502 + 0.660502i
\(681\) −120.721 −0.177270
\(682\) 147.246 + 147.246i 0.215904 + 0.215904i
\(683\) 707.910i 1.03647i 0.855238 + 0.518236i \(0.173411\pi\)
−0.855238 + 0.518236i \(0.826589\pi\)
\(684\) 1289.33i 1.88498i
\(685\) −66.3805 66.3805i −0.0969058 0.0969058i
\(686\) 2291.86 + 2291.86i 3.34090 + 3.34090i
\(687\) 16.9043i 0.0246059i
\(688\) 2447.43i 3.55731i
\(689\) 501.765 501.765i 0.728251 0.728251i
\(690\) −88.8629 88.8629i −0.128787 0.128787i
\(691\) 139.556 0.201962 0.100981 0.994888i \(-0.467802\pi\)
0.100981 + 0.994888i \(0.467802\pi\)
\(692\) 460.145 0.664949
\(693\) 907.088 907.088i 1.30893 1.30893i
\(694\) 70.3819 70.3819i 0.101415 0.101415i
\(695\) −602.633 −0.867098
\(696\) 92.2772 0.132582
\(697\) 4.79451 4.79451i 0.00687878 0.00687878i
\(698\) 134.095i 0.192112i
\(699\) −4.66431 + 4.66431i −0.00667283 + 0.00667283i
\(700\) 3181.47i 4.54496i
\(701\) −640.508 640.508i −0.913706 0.913706i 0.0828559 0.996562i \(-0.473596\pi\)
−0.996562 + 0.0828559i \(0.973596\pi\)
\(702\) 496.980 496.980i 0.707949 0.707949i
\(703\) 44.3260i 0.0630526i
\(704\) −2258.30 2258.30i −3.20781 3.20781i
\(705\) −73.2543 −0.103907
\(706\) −727.866 + 727.866i −1.03097 + 1.03097i
\(707\) 2308.48i 3.26518i
\(708\) 158.600 + 158.600i 0.224011 + 0.224011i
\(709\) −167.271 + 167.271i −0.235925 + 0.235925i −0.815161 0.579235i \(-0.803351\pi\)
0.579235 + 0.815161i \(0.303351\pi\)
\(710\) 2297.04 2297.04i 3.23527 3.23527i
\(711\) 542.540 542.540i 0.763066 0.763066i
\(712\) 611.625i 0.859024i
\(713\) 31.3904 31.3904i 0.0440258 0.0440258i
\(714\) −57.4481 57.4481i −0.0804596 0.0804596i
\(715\) −1150.38 1150.38i −1.60892 1.60892i
\(716\) 2242.99 + 2242.99i 3.13267 + 3.13267i
\(717\) 104.817 104.817i 0.146188 0.146188i
\(718\) 241.645i 0.336553i
\(719\) 627.016 + 627.016i 0.872066 + 0.872066i 0.992697 0.120631i \(-0.0384918\pi\)
−0.120631 + 0.992697i \(0.538492\pi\)
\(720\) 2719.91 + 2719.91i 3.77766 + 3.77766i
\(721\) −829.188 829.188i −1.15005 1.15005i
\(722\) −514.392 + 514.392i −0.712455 + 0.712455i
\(723\) −8.49846 −0.0117544
\(724\) −2993.02 −4.13400
\(725\) 149.953i 0.206832i
\(726\) −20.1809 −0.0277973
\(727\) 374.777i 0.515511i 0.966210 + 0.257756i \(0.0829829\pi\)
−0.966210 + 0.257756i \(0.917017\pi\)
\(728\) 7340.16i 10.0826i
\(729\) 613.524i 0.841597i
\(730\) −518.317 518.317i −0.710023 0.710023i
\(731\) 89.8109 89.8109i 0.122860 0.122860i
\(732\) 288.743 + 288.743i 0.394457 + 0.394457i
\(733\) −984.247 −1.34277 −0.671383 0.741111i \(-0.734299\pi\)
−0.671383 + 0.741111i \(0.734299\pi\)
\(734\) 1012.57i 1.37952i
\(735\) 387.207i 0.526813i
\(736\) −922.968 + 922.968i −1.25403 + 1.25403i
\(737\) 482.707i 0.654962i
\(738\) 49.3278 49.3278i 0.0668398 0.0668398i
\(739\) 695.375i 0.940967i −0.882409 0.470484i \(-0.844079\pi\)
0.882409 0.470484i \(-0.155921\pi\)
\(740\) 182.295 + 182.295i 0.246344 + 0.246344i
\(741\) 134.163 0.181057
\(742\) −1210.04 1210.04i −1.63078 1.63078i
\(743\) 468.037 468.037i 0.629928 0.629928i −0.318122 0.948050i \(-0.603052\pi\)
0.948050 + 0.318122i \(0.103052\pi\)
\(744\) 45.3043 45.3043i 0.0608929 0.0608929i
\(745\) 1234.20 1.65665
\(746\) 338.440i 0.453672i
\(747\) 689.973 0.923658
\(748\) 423.988i 0.566829i
\(749\) 2164.29 2.88958
\(750\) −24.9938 + 24.9938i −0.0333251 + 0.0333251i
\(751\) 34.3867i 0.0457878i −0.999738 0.0228939i \(-0.992712\pi\)
0.999738 0.0228939i \(-0.00728799\pi\)
\(752\) 1379.23i 1.83408i
\(753\) −28.2296 + 28.2296i −0.0374895 + 0.0374895i
\(754\) 539.320i 0.715279i
\(755\) −1123.22 −1.48771
\(756\) −882.213 882.213i −1.16695 1.16695i
\(757\) −269.660 269.660i −0.356222 0.356222i 0.506196 0.862418i \(-0.331051\pi\)
−0.862418 + 0.506196i \(0.831051\pi\)
\(758\) −1263.08 + 1263.08i −1.66634 + 1.66634i
\(759\) 53.8119i 0.0708984i
\(760\) 2529.53i 3.32833i
\(761\) 582.868 582.868i 0.765924 0.765924i −0.211462 0.977386i \(-0.567823\pi\)
0.977386 + 0.211462i \(0.0678226\pi\)
\(762\) 197.318 0.258947
\(763\) −964.298 −1.26382
\(764\) 3037.36i 3.97560i
\(765\) 199.620i 0.260941i
\(766\) 1109.66 1.44864
\(767\) 594.621 594.621i 0.775256 0.775256i
\(768\) −338.680 + 338.680i −0.440990 + 0.440990i
\(769\) 990.557 1.28811 0.644055 0.764979i \(-0.277251\pi\)
0.644055 + 0.764979i \(0.277251\pi\)
\(770\) −2774.22 + 2774.22i −3.60288 + 3.60288i
\(771\) −66.8981 + 66.8981i −0.0867680 + 0.0867680i
\(772\) 2452.39i 3.17667i
\(773\) 1336.28 1.72869 0.864345 0.502899i \(-0.167733\pi\)
0.864345 + 0.502899i \(0.167733\pi\)
\(774\) 924.008 924.008i 1.19381 1.19381i
\(775\) 73.6207 + 73.6207i 0.0949945 + 0.0949945i