Properties

Label 120.4.m.b.59.17
Level $120$
Weight $4$
Character 120.59
Analytic conductor $7.080$
Analytic rank $0$
Dimension $64$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [120,4,Mod(59,120)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(120, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("120.59");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 120.m (of order \(2\), degree \(1\), 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: \(7.08022920069\)
Analytic rank: \(0\)
Dimension: \(64\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 59.17
Character \(\chi\) \(=\) 120.59
Dual form 120.4.m.b.59.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.65669 - 2.29246i) q^{2} +(-4.82386 - 1.93142i) q^{3} +(-2.51074 + 7.59580i) q^{4} +(7.20740 - 8.54713i) q^{5} +(3.56395 + 14.2583i) q^{6} +30.0545 q^{7} +(21.5726 - 6.82812i) q^{8} +(19.5392 + 18.6338i) q^{9} +O(q^{10})\) \(q+(-1.65669 - 2.29246i) q^{2} +(-4.82386 - 1.93142i) q^{3} +(-2.51074 + 7.59580i) q^{4} +(7.20740 - 8.54713i) q^{5} +(3.56395 + 14.2583i) q^{6} +30.0545 q^{7} +(21.5726 - 6.82812i) q^{8} +(19.5392 + 18.6338i) q^{9} +(-31.5344 - 2.36271i) q^{10} -35.6161i q^{11} +(26.7822 - 31.7918i) q^{12} -58.6475 q^{13} +(-49.7911 - 68.8988i) q^{14} +(-51.2756 + 27.3096i) q^{15} +(-51.3923 - 38.1422i) q^{16} -14.3949 q^{17} +(10.3467 - 75.6634i) q^{18} +106.012 q^{19} +(46.8263 + 76.2056i) q^{20} +(-144.979 - 58.0479i) q^{21} +(-81.6485 + 59.0049i) q^{22} -47.7072i q^{23} +(-117.251 - 8.72786i) q^{24} +(-21.1068 - 123.205i) q^{25} +(97.1608 + 134.447i) q^{26} +(-58.2649 - 127.625i) q^{27} +(-75.4593 + 228.288i) q^{28} -49.5925 q^{29} +(147.554 + 72.3035i) q^{30} -181.017i q^{31} +(-2.29829 + 181.005i) q^{32} +(-68.7896 + 171.807i) q^{33} +(23.8480 + 32.9998i) q^{34} +(216.615 - 256.880i) q^{35} +(-190.597 + 101.631i) q^{36} -113.746 q^{37} +(-175.629 - 243.028i) q^{38} +(282.907 + 113.273i) q^{39} +(97.1215 - 233.597i) q^{40} +53.6178i q^{41} +(107.113 + 428.526i) q^{42} -490.109i q^{43} +(270.533 + 89.4229i) q^{44} +(300.092 - 32.7033i) q^{45} +(-109.367 + 79.0361i) q^{46} +441.575i q^{47} +(174.241 + 283.253i) q^{48} +560.275 q^{49} +(-247.475 + 252.499i) q^{50} +(69.4392 + 27.8027i) q^{51} +(147.249 - 445.475i) q^{52} +65.6784i q^{53} +(-196.049 + 345.006i) q^{54} +(-304.415 - 256.699i) q^{55} +(648.354 - 205.216i) q^{56} +(-511.387 - 204.754i) q^{57} +(82.1595 + 113.689i) q^{58} -406.047i q^{59} +(-78.6987 - 458.046i) q^{60} -213.568i q^{61} +(-414.975 + 299.890i) q^{62} +(587.243 + 560.030i) q^{63} +(418.754 - 294.600i) q^{64} +(-422.696 + 501.268i) q^{65} +(507.824 - 126.934i) q^{66} +825.615i q^{67} +(36.1420 - 109.341i) q^{68} +(-92.1426 + 230.133i) q^{69} +(-947.751 - 71.0102i) q^{70} -157.626 q^{71} +(548.746 + 268.563i) q^{72} +242.743i q^{73} +(188.442 + 260.758i) q^{74} +(-136.144 + 635.090i) q^{75} +(-266.169 + 805.246i) q^{76} -1070.43i q^{77} +(-209.017 - 836.212i) q^{78} -107.503i q^{79} +(-696.411 + 164.351i) q^{80} +(34.5637 + 728.180i) q^{81} +(122.917 - 88.8281i) q^{82} +1158.62 q^{83} +(804.925 - 955.487i) q^{84} +(-103.750 + 123.035i) q^{85} +(-1123.56 + 811.960i) q^{86} +(239.227 + 95.7839i) q^{87} +(-243.191 - 768.331i) q^{88} -750.147i q^{89} +(-572.132 - 633.771i) q^{90} -1762.62 q^{91} +(362.374 + 119.781i) q^{92} +(-349.621 + 873.203i) q^{93} +(1012.29 - 731.554i) q^{94} +(764.070 - 906.098i) q^{95} +(360.683 - 868.702i) q^{96} -83.2231i q^{97} +(-928.203 - 1284.41i) q^{98} +(663.663 - 695.911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9} - 72 q^{10} - 128 q^{16} + 672 q^{19} - 416 q^{24} + 496 q^{25} - 248 q^{30} + 240 q^{34} - 608 q^{36} - 1344 q^{40} + 336 q^{46} + 3520 q^{49} - 544 q^{51} - 952 q^{54} - 2064 q^{60} + 2176 q^{64} - 176 q^{66} + 672 q^{70} - 1600 q^{75} + 2304 q^{76} - 2304 q^{81} - 736 q^{84} - 1432 q^{90} - 2752 q^{91} + 4496 q^{94} + 640 q^{96} + 256 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.65669 2.29246i −0.585729 0.810507i
\(3\) −4.82386 1.93142i −0.928352 0.371702i
\(4\) −2.51074 + 7.59580i −0.313843 + 0.949475i
\(5\) 7.20740 8.54713i 0.644649 0.764478i
\(6\) 3.56395 + 14.2583i 0.242496 + 0.970152i
\(7\) 30.0545 1.62279 0.811396 0.584497i \(-0.198708\pi\)
0.811396 + 0.584497i \(0.198708\pi\)
\(8\) 21.5726 6.82812i 0.953383 0.301763i
\(9\) 19.5392 + 18.6338i 0.723676 + 0.690140i
\(10\) −31.5344 2.36271i −0.997205 0.0747155i
\(11\) 35.6161i 0.976241i −0.872776 0.488121i \(-0.837683\pi\)
0.872776 0.488121i \(-0.162317\pi\)
\(12\) 26.7822 31.7918i 0.644278 0.764791i
\(13\) −58.6475 −1.25122 −0.625611 0.780135i \(-0.715150\pi\)
−0.625611 + 0.780135i \(0.715150\pi\)
\(14\) −49.7911 68.8988i −0.950517 1.31528i
\(15\) −51.2756 + 27.3096i −0.882620 + 0.470088i
\(16\) −51.3923 38.1422i −0.803005 0.595972i
\(17\) −14.3949 −0.205370 −0.102685 0.994714i \(-0.532743\pi\)
−0.102685 + 0.994714i \(0.532743\pi\)
\(18\) 10.3467 75.6634i 0.135486 0.990779i
\(19\) 106.012 1.28004 0.640021 0.768357i \(-0.278925\pi\)
0.640021 + 0.768357i \(0.278925\pi\)
\(20\) 46.8263 + 76.2056i 0.523534 + 0.852005i
\(21\) −144.979 58.0479i −1.50652 0.603195i
\(22\) −81.6485 + 59.0049i −0.791250 + 0.571813i
\(23\) 47.7072i 0.432506i −0.976337 0.216253i \(-0.930616\pi\)
0.976337 0.216253i \(-0.0693836\pi\)
\(24\) −117.251 8.72786i −0.997241 0.0742319i
\(25\) −21.1068 123.205i −0.168855 0.985641i
\(26\) 97.1608 + 134.447i 0.732877 + 1.01412i
\(27\) −58.2649 127.625i −0.415299 0.909685i
\(28\) −75.4593 + 228.288i −0.509302 + 1.54080i
\(29\) −49.5925 −0.317555 −0.158778 0.987314i \(-0.550755\pi\)
−0.158778 + 0.987314i \(0.550755\pi\)
\(30\) 147.554 + 72.3035i 0.897985 + 0.440025i
\(31\) 181.017i 1.04876i −0.851483 0.524382i \(-0.824296\pi\)
0.851483 0.524382i \(-0.175704\pi\)
\(32\) −2.29829 + 181.005i −0.0126964 + 0.999919i
\(33\) −68.7896 + 171.807i −0.362871 + 0.906296i
\(34\) 23.8480 + 32.9998i 0.120291 + 0.166454i
\(35\) 216.615 256.880i 1.04613 1.24059i
\(36\) −190.597 + 101.631i −0.882392 + 0.470516i
\(37\) −113.746 −0.505397 −0.252699 0.967545i \(-0.581318\pi\)
−0.252699 + 0.967545i \(0.581318\pi\)
\(38\) −175.629 243.028i −0.749758 1.03748i
\(39\) 282.907 + 113.273i 1.16158 + 0.465082i
\(40\) 97.1215 233.597i 0.383906 0.923372i
\(41\) 53.6178i 0.204236i 0.994772 + 0.102118i \(0.0325620\pi\)
−0.994772 + 0.102118i \(0.967438\pi\)
\(42\) 107.113 + 428.526i 0.393520 + 1.57436i
\(43\) 490.109i 1.73816i −0.494669 0.869081i \(-0.664711\pi\)
0.494669 0.869081i \(-0.335289\pi\)
\(44\) 270.533 + 89.4229i 0.926917 + 0.306387i
\(45\) 300.092 32.7033i 0.994114 0.108336i
\(46\) −109.367 + 79.0361i −0.350549 + 0.253331i
\(47\) 441.575i 1.37043i 0.728339 + 0.685217i \(0.240293\pi\)
−0.728339 + 0.685217i \(0.759707\pi\)
\(48\) 174.241 + 283.253i 0.523947 + 0.851751i
\(49\) 560.275 1.63346
\(50\) −247.475 + 252.499i −0.699966 + 0.714176i
\(51\) 69.4392 + 27.8027i 0.190655 + 0.0763363i
\(52\) 147.249 445.475i 0.392688 1.18800i
\(53\) 65.6784i 0.170219i 0.996372 + 0.0851097i \(0.0271241\pi\)
−0.996372 + 0.0851097i \(0.972876\pi\)
\(54\) −196.049 + 345.006i −0.494053 + 0.869432i
\(55\) −304.415 256.699i −0.746316 0.629333i
\(56\) 648.354 205.216i 1.54714 0.489699i
\(57\) −511.387 204.754i −1.18833 0.475794i
\(58\) 82.1595 + 113.689i 0.186001 + 0.257381i
\(59\) 406.047i 0.895979i −0.894039 0.447989i \(-0.852140\pi\)
0.894039 0.447989i \(-0.147860\pi\)
\(60\) −78.6987 458.046i −0.169333 0.985559i
\(61\) 213.568i 0.448271i −0.974558 0.224135i \(-0.928044\pi\)
0.974558 0.224135i \(-0.0719558\pi\)
\(62\) −414.975 + 299.890i −0.850031 + 0.614292i
\(63\) 587.243 + 560.030i 1.17438 + 1.11995i
\(64\) 418.754 294.600i 0.817878 0.575391i
\(65\) −422.696 + 501.268i −0.806600 + 0.956533i
\(66\) 507.824 126.934i 0.947103 0.236735i
\(67\) 825.615i 1.50545i 0.658337 + 0.752723i \(0.271260\pi\)
−0.658337 + 0.752723i \(0.728740\pi\)
\(68\) 36.1420 109.341i 0.0644539 0.194993i
\(69\) −92.1426 + 230.133i −0.160763 + 0.401518i
\(70\) −947.751 71.0102i −1.61826 0.121248i
\(71\) −157.626 −0.263476 −0.131738 0.991285i \(-0.542056\pi\)
−0.131738 + 0.991285i \(0.542056\pi\)
\(72\) 548.746 + 268.563i 0.898199 + 0.439590i
\(73\) 242.743i 0.389190i 0.980884 + 0.194595i \(0.0623393\pi\)
−0.980884 + 0.194595i \(0.937661\pi\)
\(74\) 188.442 + 260.758i 0.296026 + 0.409628i
\(75\) −136.144 + 635.090i −0.209608 + 0.977786i
\(76\) −266.169 + 805.246i −0.401733 + 1.21537i
\(77\) 1070.43i 1.58424i
\(78\) −209.017 836.212i −0.303416 1.21388i
\(79\) 107.503i 0.153101i −0.997066 0.0765506i \(-0.975609\pi\)
0.997066 0.0765506i \(-0.0243907\pi\)
\(80\) −696.411 + 164.351i −0.973265 + 0.229687i
\(81\) 34.5637 + 728.180i 0.0474125 + 0.998875i
\(82\) 122.917 88.8281i 0.165535 0.119627i
\(83\) 1158.62 1.53223 0.766113 0.642706i \(-0.222188\pi\)
0.766113 + 0.642706i \(0.222188\pi\)
\(84\) 804.925 955.487i 1.04553 1.24110i
\(85\) −103.750 + 123.035i −0.132391 + 0.157001i
\(86\) −1123.56 + 811.960i −1.40879 + 1.01809i
\(87\) 239.227 + 95.7839i 0.294803 + 0.118036i
\(88\) −243.191 768.331i −0.294593 0.930732i
\(89\) 750.147i 0.893431i −0.894676 0.446716i \(-0.852594\pi\)
0.894676 0.446716i \(-0.147406\pi\)
\(90\) −572.132 633.771i −0.670089 0.742281i
\(91\) −1762.62 −2.03047
\(92\) 362.374 + 119.781i 0.410654 + 0.135739i
\(93\) −349.621 + 873.203i −0.389828 + 0.973623i
\(94\) 1012.29 731.554i 1.11075 0.802703i
\(95\) 764.070 906.098i 0.825179 0.978565i
\(96\) 360.683 868.702i 0.383459 0.923558i
\(97\) 83.2231i 0.0871136i −0.999051 0.0435568i \(-0.986131\pi\)
0.999051 0.0435568i \(-0.0138690\pi\)
\(98\) −928.203 1284.41i −0.956762 1.32393i
\(99\) 663.663 695.911i 0.673744 0.706482i
\(100\) 988.835 + 149.013i 0.988835 + 0.149013i
\(101\) −978.565 −0.964068 −0.482034 0.876153i \(-0.660102\pi\)
−0.482034 + 0.876153i \(0.660102\pi\)
\(102\) −51.3028 205.247i −0.0498013 0.199240i
\(103\) −484.228 −0.463228 −0.231614 0.972808i \(-0.574401\pi\)
−0.231614 + 0.972808i \(0.574401\pi\)
\(104\) −1265.18 + 400.452i −1.19289 + 0.377573i
\(105\) −1541.06 + 820.779i −1.43231 + 0.762855i
\(106\) 150.565 108.809i 0.137964 0.0997024i
\(107\) 912.615 0.824541 0.412270 0.911062i \(-0.364736\pi\)
0.412270 + 0.911062i \(0.364736\pi\)
\(108\) 1115.70 122.134i 0.994062 0.108818i
\(109\) 1290.42i 1.13395i 0.823736 + 0.566973i \(0.191886\pi\)
−0.823736 + 0.566973i \(0.808114\pi\)
\(110\) −84.1505 + 1123.13i −0.0729404 + 0.973513i
\(111\) 548.694 + 219.691i 0.469187 + 0.187857i
\(112\) −1544.57 1146.35i −1.30311 0.967139i
\(113\) 24.0806 0.0200470 0.0100235 0.999950i \(-0.496809\pi\)
0.0100235 + 0.999950i \(0.496809\pi\)
\(114\) 377.821 + 1511.55i 0.310405 + 1.24184i
\(115\) −407.760 343.845i −0.330642 0.278815i
\(116\) 124.514 376.695i 0.0996625 0.301511i
\(117\) −1145.93 1092.83i −0.905479 0.863519i
\(118\) −930.845 + 672.694i −0.726197 + 0.524801i
\(119\) −432.633 −0.333273
\(120\) −919.674 + 939.255i −0.699619 + 0.714516i
\(121\) 62.4941 0.0469527
\(122\) −489.595 + 353.816i −0.363327 + 0.262565i
\(123\) 103.558 258.645i 0.0759150 0.189603i
\(124\) 1374.97 + 454.489i 0.995775 + 0.329147i
\(125\) −1205.18 707.585i −0.862353 0.506307i
\(126\) 310.966 2274.03i 0.219865 1.60783i
\(127\) 1018.44 0.711593 0.355797 0.934563i \(-0.384210\pi\)
0.355797 + 0.934563i \(0.384210\pi\)
\(128\) −1369.11 471.914i −0.945414 0.325873i
\(129\) −946.607 + 2364.22i −0.646078 + 1.61363i
\(130\) 1849.41 + 138.567i 1.24773 + 0.0934857i
\(131\) 422.320i 0.281666i −0.990033 0.140833i \(-0.955022\pi\)
0.990033 0.140833i \(-0.0449781\pi\)
\(132\) −1132.30 953.876i −0.746621 0.628971i
\(133\) 3186.14 2.07724
\(134\) 1892.69 1367.79i 1.22017 0.881783i
\(135\) −1510.77 421.848i −0.963157 0.268940i
\(136\) −310.536 + 98.2903i −0.195796 + 0.0619730i
\(137\) 2962.29 1.84734 0.923671 0.383186i \(-0.125173\pi\)
0.923671 + 0.383186i \(0.125173\pi\)
\(138\) 680.222 170.026i 0.419597 0.104881i
\(139\) 724.141 0.441877 0.220938 0.975288i \(-0.429088\pi\)
0.220938 + 0.975288i \(0.429088\pi\)
\(140\) 1407.34 + 2290.32i 0.849588 + 1.38263i
\(141\) 852.867 2130.10i 0.509393 1.27225i
\(142\) 261.138 + 361.352i 0.154325 + 0.213549i
\(143\) 2088.80i 1.22150i
\(144\) −293.433 1702.90i −0.169811 0.985477i
\(145\) −357.433 + 423.874i −0.204712 + 0.242764i
\(146\) 556.478 402.150i 0.315441 0.227960i
\(147\) −2702.69 1082.13i −1.51642 0.607158i
\(148\) 285.587 863.990i 0.158615 0.479862i
\(149\) 1917.06 1.05404 0.527019 0.849854i \(-0.323310\pi\)
0.527019 + 0.849854i \(0.323310\pi\)
\(150\) 1681.47 740.044i 0.915275 0.402829i
\(151\) 2586.17i 1.39377i 0.717182 + 0.696886i \(0.245432\pi\)
−0.717182 + 0.696886i \(0.754568\pi\)
\(152\) 2286.95 723.862i 1.22037 0.386269i
\(153\) −281.266 268.232i −0.148621 0.141734i
\(154\) −2453.91 + 1773.36i −1.28404 + 0.927934i
\(155\) −1547.18 1304.66i −0.801758 0.676085i
\(156\) −1570.71 + 1864.51i −0.806136 + 0.956924i
\(157\) −1527.70 −0.776586 −0.388293 0.921536i \(-0.626935\pi\)
−0.388293 + 0.921536i \(0.626935\pi\)
\(158\) −246.446 + 178.099i −0.124090 + 0.0896758i
\(159\) 126.853 316.823i 0.0632708 0.158023i
\(160\) 1530.51 + 1324.22i 0.756232 + 0.654303i
\(161\) 1433.82i 0.701868i
\(162\) 1612.06 1285.61i 0.781825 0.623498i
\(163\) 2775.55i 1.33373i 0.745179 + 0.666865i \(0.232364\pi\)
−0.745179 + 0.666865i \(0.767636\pi\)
\(164\) −407.270 134.621i −0.193917 0.0640981i
\(165\) 972.663 + 1826.24i 0.458919 + 0.861650i
\(166\) −1919.47 2656.08i −0.897470 1.24188i
\(167\) 1484.84i 0.688025i −0.938965 0.344013i \(-0.888214\pi\)
0.938965 0.344013i \(-0.111786\pi\)
\(168\) −3523.93 262.312i −1.61832 0.120463i
\(169\) 1242.53 0.565558
\(170\) 453.936 + 34.0111i 0.204796 + 0.0153443i
\(171\) 2071.39 + 1975.40i 0.926336 + 0.883409i
\(172\) 3722.77 + 1230.54i 1.65034 + 0.545510i
\(173\) 4487.55i 1.97215i 0.166292 + 0.986077i \(0.446821\pi\)
−0.166292 + 0.986077i \(0.553179\pi\)
\(174\) −176.745 707.103i −0.0770058 0.308077i
\(175\) −634.356 3702.87i −0.274016 1.59949i
\(176\) −1358.48 + 1830.39i −0.581813 + 0.783927i
\(177\) −784.246 + 1958.71i −0.333037 + 0.831784i
\(178\) −1719.68 + 1242.76i −0.724132 + 0.523309i
\(179\) 2713.96i 1.13325i 0.823977 + 0.566623i \(0.191750\pi\)
−0.823977 + 0.566623i \(0.808250\pi\)
\(180\) −505.048 + 2361.55i −0.209134 + 0.977887i
\(181\) 913.737i 0.375235i 0.982242 + 0.187618i \(0.0600765\pi\)
−0.982242 + 0.187618i \(0.939923\pi\)
\(182\) 2920.12 + 4040.74i 1.18931 + 1.64571i
\(183\) −412.489 + 1030.22i −0.166623 + 0.416153i
\(184\) −325.750 1029.17i −0.130514 0.412344i
\(185\) −819.811 + 972.200i −0.325804 + 0.386365i
\(186\) 2581.00 645.137i 1.01746 0.254321i
\(187\) 512.692i 0.200490i
\(188\) −3354.12 1108.68i −1.30119 0.430101i
\(189\) −1751.12 3835.72i −0.673945 1.47623i
\(190\) −3343.02 250.476i −1.27646 0.0956390i
\(191\) 3419.83 1.29555 0.647776 0.761831i \(-0.275699\pi\)
0.647776 + 0.761831i \(0.275699\pi\)
\(192\) −2589.01 + 612.322i −0.973153 + 0.230159i
\(193\) 3786.04i 1.41205i −0.708189 0.706023i \(-0.750487\pi\)
0.708189 0.706023i \(-0.249513\pi\)
\(194\) −190.786 + 137.875i −0.0706062 + 0.0510250i
\(195\) 3007.18 1601.64i 1.10435 0.588185i
\(196\) −1406.71 + 4255.74i −0.512649 + 1.55092i
\(197\) 12.8824i 0.00465904i 0.999997 + 0.00232952i \(0.000741510\pi\)
−0.999997 + 0.00232952i \(0.999258\pi\)
\(198\) −2694.83 368.510i −0.967240 0.132267i
\(199\) 1630.96i 0.580983i −0.956878 0.290491i \(-0.906181\pi\)
0.956878 0.290491i \(-0.0938187\pi\)
\(200\) −1296.59 2513.73i −0.458413 0.888739i
\(201\) 1594.61 3982.65i 0.559577 1.39758i
\(202\) 1621.18 + 2243.32i 0.564683 + 0.781384i
\(203\) −1490.48 −0.515326
\(204\) −385.528 + 457.641i −0.132315 + 0.157065i
\(205\) 458.278 + 386.445i 0.156134 + 0.131661i
\(206\) 802.217 + 1110.07i 0.271326 + 0.375449i
\(207\) 888.966 932.163i 0.298490 0.312994i
\(208\) 3014.03 + 2236.95i 1.00474 + 0.745694i
\(209\) 3775.73i 1.24963i
\(210\) 4434.67 + 2173.05i 1.45724 + 0.714069i
\(211\) −2482.49 −0.809960 −0.404980 0.914326i \(-0.632721\pi\)
−0.404980 + 0.914326i \(0.632721\pi\)
\(212\) −498.880 164.902i −0.161619 0.0534222i
\(213\) 760.367 + 304.442i 0.244598 + 0.0979345i
\(214\) −1511.92 2092.13i −0.482957 0.668296i
\(215\) −4189.03 3532.41i −1.32879 1.12051i
\(216\) −2128.36 2355.37i −0.670448 0.741956i
\(217\) 5440.40i 1.70193i
\(218\) 2958.24 2137.83i 0.919072 0.664185i
\(219\) 468.838 1170.96i 0.144663 0.361306i
\(220\) 2714.15 1667.77i 0.831762 0.511096i
\(221\) 844.228 0.256963
\(222\) −405.384 1621.82i −0.122557 0.490312i
\(223\) 220.601 0.0662444 0.0331222 0.999451i \(-0.489455\pi\)
0.0331222 + 0.999451i \(0.489455\pi\)
\(224\) −69.0740 + 5440.01i −0.0206036 + 1.62266i
\(225\) 1883.37 2800.63i 0.558035 0.829818i
\(226\) −39.8941 55.2038i −0.0117421 0.0162482i
\(227\) −1286.28 −0.376094 −0.188047 0.982160i \(-0.560216\pi\)
−0.188047 + 0.982160i \(0.560216\pi\)
\(228\) 2839.23 3370.31i 0.824704 0.978965i
\(229\) 3473.66i 1.00238i 0.865336 + 0.501192i \(0.167105\pi\)
−0.865336 + 0.501192i \(0.832895\pi\)
\(230\) −112.718 + 1504.42i −0.0323149 + 0.431297i
\(231\) −2067.44 + 5163.58i −0.588864 + 1.47073i
\(232\) −1069.84 + 338.623i −0.302752 + 0.0958264i
\(233\) 1374.39 0.386435 0.193218 0.981156i \(-0.438108\pi\)
0.193218 + 0.981156i \(0.438108\pi\)
\(234\) −606.809 + 4437.47i −0.169523 + 1.23969i
\(235\) 3774.20 + 3182.61i 1.04767 + 0.883449i
\(236\) 3084.25 + 1019.48i 0.850709 + 0.281197i
\(237\) −207.633 + 518.578i −0.0569080 + 0.142132i
\(238\) 716.740 + 991.795i 0.195207 + 0.270120i
\(239\) −6110.81 −1.65387 −0.826936 0.562296i \(-0.809918\pi\)
−0.826936 + 0.562296i \(0.809918\pi\)
\(240\) 3676.82 + 552.258i 0.988907 + 0.148534i
\(241\) 7359.10 1.96698 0.983488 0.180975i \(-0.0579253\pi\)
0.983488 + 0.180975i \(0.0579253\pi\)
\(242\) −103.533 143.265i −0.0275016 0.0380555i
\(243\) 1239.69 3579.40i 0.327268 0.944931i
\(244\) 1622.22 + 536.214i 0.425622 + 0.140687i
\(245\) 4038.13 4788.74i 1.05301 1.24874i
\(246\) −764.497 + 191.091i −0.198140 + 0.0495265i
\(247\) −6217.34 −1.60162
\(248\) −1236.01 3905.02i −0.316478 0.999874i
\(249\) −5589.01 2237.78i −1.42245 0.569531i
\(250\) 374.493 + 3935.07i 0.0947401 + 0.995502i
\(251\) 1602.46i 0.402973i 0.979491 + 0.201486i \(0.0645772\pi\)
−0.979491 + 0.201486i \(0.935423\pi\)
\(252\) −5728.29 + 3054.49i −1.43194 + 0.763550i
\(253\) −1699.14 −0.422230
\(254\) −1687.25 2334.74i −0.416801 0.576751i
\(255\) 738.109 393.121i 0.181263 0.0965419i
\(256\) 1186.34 + 3920.43i 0.289634 + 0.957137i
\(257\) −1317.48 −0.319775 −0.159887 0.987135i \(-0.551113\pi\)
−0.159887 + 0.987135i \(0.551113\pi\)
\(258\) 6988.11 1746.72i 1.68628 0.421497i
\(259\) −3418.58 −0.820155
\(260\) −2746.25 4469.27i −0.655058 1.06605i
\(261\) −969.000 924.096i −0.229807 0.219158i
\(262\) −968.151 + 699.654i −0.228292 + 0.164980i
\(263\) 621.813i 0.145789i −0.997340 0.0728947i \(-0.976776\pi\)
0.997340 0.0728947i \(-0.0232237\pi\)
\(264\) −310.852 + 4176.03i −0.0724683 + 0.973548i
\(265\) 561.362 + 473.371i 0.130129 + 0.109732i
\(266\) −5278.45 7304.10i −1.21670 1.68362i
\(267\) −1448.85 + 3618.60i −0.332090 + 0.829419i
\(268\) −6271.20 2072.91i −1.42938 0.472474i
\(269\) −105.003 −0.0237998 −0.0118999 0.999929i \(-0.503788\pi\)
−0.0118999 + 0.999929i \(0.503788\pi\)
\(270\) 1535.81 + 4162.25i 0.346171 + 0.938171i
\(271\) 979.683i 0.219600i 0.993954 + 0.109800i \(0.0350210\pi\)
−0.993954 + 0.109800i \(0.964979\pi\)
\(272\) 739.789 + 549.055i 0.164913 + 0.122395i
\(273\) 8502.65 + 3404.37i 1.88500 + 0.754731i
\(274\) −4907.61 6790.94i −1.08204 1.49728i
\(275\) −4388.08 + 751.743i −0.962224 + 0.164843i
\(276\) −1516.70 1277.70i −0.330777 0.278654i
\(277\) 7385.36 1.60196 0.800981 0.598690i \(-0.204312\pi\)
0.800981 + 0.598690i \(0.204312\pi\)
\(278\) −1199.68 1660.06i −0.258820 0.358144i
\(279\) 3373.04 3536.94i 0.723795 0.758965i
\(280\) 2918.94 7020.64i 0.623000 1.49844i
\(281\) 2837.82i 0.602457i 0.953552 + 0.301229i \(0.0973967\pi\)
−0.953552 + 0.301229i \(0.902603\pi\)
\(282\) −6296.10 + 1573.75i −1.32953 + 0.332324i
\(283\) 3418.04i 0.717955i −0.933346 0.358977i \(-0.883126\pi\)
0.933346 0.358977i \(-0.116874\pi\)
\(284\) 395.759 1197.30i 0.0826901 0.250164i
\(285\) −5435.82 + 2895.15i −1.12979 + 0.601733i
\(286\) 4788.48 3460.49i 0.990030 0.715465i
\(287\) 1611.46i 0.331433i
\(288\) −3417.71 + 3493.87i −0.699273 + 0.714855i
\(289\) −4705.79 −0.957823
\(290\) 1563.87 + 117.173i 0.316667 + 0.0237263i
\(291\) −160.739 + 401.456i −0.0323803 + 0.0808721i
\(292\) −1843.82 609.465i −0.369526 0.122145i
\(293\) 3323.01i 0.662569i 0.943531 + 0.331284i \(0.107482\pi\)
−0.943531 + 0.331284i \(0.892518\pi\)
\(294\) 1996.79 + 7988.56i 0.396106 + 1.58470i
\(295\) −3470.53 2926.54i −0.684957 0.577592i
\(296\) −2453.79 + 776.669i −0.481837 + 0.152510i
\(297\) −4545.51 + 2075.17i −0.888072 + 0.405432i
\(298\) −3175.98 4394.78i −0.617381 0.854305i
\(299\) 2797.91i 0.541161i
\(300\) −4482.19 2628.67i −0.862599 0.505889i
\(301\) 14730.0i 2.82068i
\(302\) 5928.69 4284.49i 1.12966 0.816372i
\(303\) 4720.46 + 1890.02i 0.894995 + 0.358346i
\(304\) −5448.20 4043.53i −1.02788 0.762870i
\(305\) −1825.39 1539.27i −0.342694 0.288978i
\(306\) −148.940 + 1089.17i −0.0278247 + 0.203476i
\(307\) 455.313i 0.0846452i 0.999104 + 0.0423226i \(0.0134757\pi\)
−0.999104 + 0.0423226i \(0.986524\pi\)
\(308\) 8130.73 + 2687.56i 1.50419 + 0.497202i
\(309\) 2335.85 + 935.248i 0.430038 + 0.172183i
\(310\) −427.692 + 5708.27i −0.0783589 + 1.04583i
\(311\) −1672.37 −0.304923 −0.152462 0.988309i \(-0.548720\pi\)
−0.152462 + 0.988309i \(0.548720\pi\)
\(312\) 6876.49 + 511.867i 1.24777 + 0.0928807i
\(313\) 3116.09i 0.562721i 0.959602 + 0.281361i \(0.0907857\pi\)
−0.959602 + 0.281361i \(0.909214\pi\)
\(314\) 2530.93 + 3502.20i 0.454869 + 0.629428i
\(315\) 9019.14 982.882i 1.61324 0.175807i
\(316\) 816.569 + 269.912i 0.145366 + 0.0480498i
\(317\) 4710.18i 0.834543i 0.908782 + 0.417272i \(0.137014\pi\)
−0.908782 + 0.417272i \(0.862986\pi\)
\(318\) −936.461 + 234.074i −0.165139 + 0.0412775i
\(319\) 1766.29i 0.310010i
\(320\) 500.137 5702.44i 0.0873704 0.996176i
\(321\) −4402.33 1762.64i −0.765464 0.306483i
\(322\) −3286.97 + 2375.39i −0.568869 + 0.411104i
\(323\) −1526.04 −0.262882
\(324\) −5617.89 1565.74i −0.963287 0.268473i
\(325\) 1237.86 + 7225.67i 0.211275 + 1.23326i
\(326\) 6362.84 4598.23i 1.08100 0.781204i
\(327\) 2492.35 6224.82i 0.421490 1.05270i
\(328\) 366.108 + 1156.67i 0.0616309 + 0.194715i
\(329\) 13271.3i 2.22393i
\(330\) 2575.17 5255.30i 0.429571 0.876651i
\(331\) −7743.80 −1.28592 −0.642958 0.765902i \(-0.722293\pi\)
−0.642958 + 0.765902i \(0.722293\pi\)
\(332\) −2908.99 + 8800.63i −0.480879 + 1.45481i
\(333\) −2222.51 2119.52i −0.365744 0.348795i
\(334\) −3403.93 + 2459.92i −0.557649 + 0.402996i
\(335\) 7056.64 + 5950.53i 1.15088 + 0.970485i
\(336\) 5236.72 + 8513.03i 0.850258 + 1.38221i
\(337\) 8409.42i 1.35932i 0.733528 + 0.679659i \(0.237872\pi\)
−0.733528 + 0.679659i \(0.762128\pi\)
\(338\) −2058.49 2848.45i −0.331264 0.458389i
\(339\) −116.161 46.5098i −0.0186107 0.00745151i
\(340\) −674.062 1096.98i −0.107518 0.174976i
\(341\) −6447.13 −1.02385
\(342\) 1096.88 8021.22i 0.173428 1.26824i
\(343\) 6530.10 1.02797
\(344\) −3346.52 10572.9i −0.524513 1.65713i
\(345\) 1302.87 + 2446.21i 0.203316 + 0.381738i
\(346\) 10287.5 7434.50i 1.59844 1.15515i
\(347\) 4830.70 0.747336 0.373668 0.927562i \(-0.378100\pi\)
0.373668 + 0.927562i \(0.378100\pi\)
\(348\) −1328.19 + 1576.63i −0.204594 + 0.242863i
\(349\) 6202.35i 0.951301i 0.879634 + 0.475650i \(0.157787\pi\)
−0.879634 + 0.475650i \(0.842213\pi\)
\(350\) −7437.75 + 7588.76i −1.13590 + 1.15896i
\(351\) 3417.09 + 7484.90i 0.519632 + 1.13822i
\(352\) 6446.68 + 81.8561i 0.976163 + 0.0123947i
\(353\) −7678.75 −1.15779 −0.578893 0.815404i \(-0.696515\pi\)
−0.578893 + 0.815404i \(0.696515\pi\)
\(354\) 5789.52 1447.13i 0.869236 0.217271i
\(355\) −1136.07 + 1347.25i −0.169850 + 0.201422i
\(356\) 5697.96 + 1883.43i 0.848291 + 0.280397i
\(357\) 2086.96 + 835.596i 0.309394 + 0.123878i
\(358\) 6221.64 4496.19i 0.918503 0.663775i
\(359\) 12403.8 1.82352 0.911762 0.410719i \(-0.134722\pi\)
0.911762 + 0.410719i \(0.134722\pi\)
\(360\) 6250.47 2754.56i 0.915080 0.403272i
\(361\) 4379.54 0.638509
\(362\) 2094.71 1513.78i 0.304131 0.219786i
\(363\) −301.463 120.702i −0.0435887 0.0174524i
\(364\) 4425.50 13388.5i 0.637250 1.92788i
\(365\) 2074.75 + 1749.54i 0.297528 + 0.250891i
\(366\) 3045.10 761.144i 0.434891 0.108704i
\(367\) −1231.21 −0.175119 −0.0875597 0.996159i \(-0.527907\pi\)
−0.0875597 + 0.996159i \(0.527907\pi\)
\(368\) −1819.66 + 2451.78i −0.257762 + 0.347305i
\(369\) −999.102 + 1047.65i −0.140952 + 0.147801i
\(370\) 3586.90 + 268.748i 0.503985 + 0.0377610i
\(371\) 1973.93i 0.276231i
\(372\) −5754.86 4848.04i −0.802086 0.675696i
\(373\) −5114.70 −0.709998 −0.354999 0.934867i \(-0.615519\pi\)
−0.354999 + 0.934867i \(0.615519\pi\)
\(374\) 1175.32 849.372i 0.162499 0.117433i
\(375\) 4446.95 + 5740.99i 0.612372 + 0.790569i
\(376\) 3015.13 + 9525.93i 0.413546 + 1.30655i
\(377\) 2908.48 0.397332
\(378\) −5892.16 + 10369.0i −0.801746 + 1.41091i
\(379\) 2973.78 0.403041 0.201521 0.979484i \(-0.435412\pi\)
0.201521 + 0.979484i \(0.435412\pi\)
\(380\) 4964.15 + 8078.71i 0.670146 + 1.09060i
\(381\) −4912.83 1967.04i −0.660609 0.264500i
\(382\) −5665.61 7839.83i −0.758843 1.05005i
\(383\) 4239.61i 0.565623i −0.959175 0.282812i \(-0.908733\pi\)
0.959175 0.282812i \(-0.0912671\pi\)
\(384\) 5692.91 + 4920.76i 0.756549 + 0.653937i
\(385\) −9149.06 7714.98i −1.21112 1.02128i
\(386\) −8679.34 + 6272.30i −1.14447 + 0.827076i
\(387\) 9132.60 9576.37i 1.19958 1.25787i
\(388\) 632.146 + 208.952i 0.0827122 + 0.0273400i
\(389\) 1866.70 0.243304 0.121652 0.992573i \(-0.461181\pi\)
0.121652 + 0.992573i \(0.461181\pi\)
\(390\) −8653.68 4240.42i −1.12358 0.550569i
\(391\) 686.742i 0.0888237i
\(392\) 12086.6 3825.62i 1.55731 0.492916i
\(393\) −815.677 + 2037.21i −0.104696 + 0.261485i
\(394\) 29.5323 21.3421i 0.00377619 0.00272894i
\(395\) −918.839 774.815i −0.117043 0.0986966i
\(396\) 3619.71 + 6788.30i 0.459337 + 0.861427i
\(397\) −7085.75 −0.895778 −0.447889 0.894089i \(-0.647824\pi\)
−0.447889 + 0.894089i \(0.647824\pi\)
\(398\) −3738.91 + 2701.99i −0.470890 + 0.340298i
\(399\) −15369.5 6153.77i −1.92841 0.772115i
\(400\) −3614.59 + 7136.86i −0.451823 + 0.892107i
\(401\) 4052.17i 0.504628i −0.967645 0.252314i \(-0.918808\pi\)
0.967645 0.252314i \(-0.0811915\pi\)
\(402\) −11771.8 + 2942.45i −1.46051 + 0.365064i
\(403\) 10616.2i 1.31224i
\(404\) 2456.93 7432.98i 0.302566 0.915358i
\(405\) 6472.96 + 4952.86i 0.794183 + 0.607678i
\(406\) 2469.27 + 3416.87i 0.301841 + 0.417675i
\(407\) 4051.18i 0.493390i
\(408\) 1687.82 + 125.637i 0.204803 + 0.0152450i
\(409\) 3577.29 0.432483 0.216242 0.976340i \(-0.430620\pi\)
0.216242 + 0.976340i \(0.430620\pi\)
\(410\) 126.683 1690.80i 0.0152596 0.203665i
\(411\) −14289.7 5721.43i −1.71498 0.686660i
\(412\) 1215.77 3678.10i 0.145381 0.439823i
\(413\) 12203.5i 1.45399i
\(414\) −3609.69 493.613i −0.428518 0.0585985i
\(415\) 8350.62 9902.85i 0.987749 1.17135i
\(416\) 134.789 10615.5i 0.0158860 1.25112i
\(417\) −3493.16 1398.62i −0.410217 0.164246i
\(418\) −8655.71 + 6255.22i −1.01283 + 0.731945i
\(419\) 13722.4i 1.59996i −0.600028 0.799979i \(-0.704844\pi\)
0.600028 0.799979i \(-0.295156\pi\)
\(420\) −2365.25 13766.4i −0.274792 1.59936i
\(421\) 3588.59i 0.415433i −0.978189 0.207717i \(-0.933397\pi\)
0.978189 0.207717i \(-0.0666032\pi\)
\(422\) 4112.72 + 5691.00i 0.474417 + 0.656478i
\(423\) −8228.22 + 8628.05i −0.945792 + 0.991749i
\(424\) 448.460 + 1416.85i 0.0513659 + 0.162284i
\(425\) 303.832 + 1773.53i 0.0346777 + 0.202421i
\(426\) −561.771 2247.48i −0.0638918 0.255612i
\(427\) 6418.68i 0.727451i
\(428\) −2291.34 + 6932.04i −0.258776 + 0.782881i
\(429\) 4034.34 10076.1i 0.454032 1.13398i
\(430\) −1157.99 + 15455.3i −0.129868 + 1.73330i
\(431\) 8138.32 0.909534 0.454767 0.890610i \(-0.349723\pi\)
0.454767 + 0.890610i \(0.349723\pi\)
\(432\) −1873.54 + 8781.31i −0.208659 + 0.977988i
\(433\) 2624.71i 0.291306i −0.989336 0.145653i \(-0.953472\pi\)
0.989336 0.145653i \(-0.0465284\pi\)
\(434\) −12471.9 + 9013.06i −1.37942 + 0.996868i
\(435\) 2542.88 1354.35i 0.280280 0.149279i
\(436\) −9801.80 3239.92i −1.07665 0.355881i
\(437\) 5057.53i 0.553626i
\(438\) −3461.09 + 865.122i −0.377574 + 0.0943770i
\(439\) 1733.88i 0.188504i 0.995548 + 0.0942522i \(0.0300460\pi\)
−0.995548 + 0.0942522i \(0.969954\pi\)
\(440\) −8319.80 3459.09i −0.901434 0.374785i
\(441\) 10947.4 + 10440.1i 1.18209 + 1.12731i
\(442\) −1398.62 1935.36i −0.150511 0.208271i
\(443\) 3608.99 0.387061 0.193531 0.981094i \(-0.438006\pi\)
0.193531 + 0.981094i \(0.438006\pi\)
\(444\) −3046.36 + 3616.18i −0.325617 + 0.386523i
\(445\) −6411.60 5406.61i −0.683009 0.575950i
\(446\) −365.467 505.718i −0.0388013 0.0536916i
\(447\) −9247.63 3702.65i −0.978518 0.391788i
\(448\) 12585.4 8854.08i 1.32725 0.933741i
\(449\) 1133.13i 0.119100i 0.998225 + 0.0595499i \(0.0189665\pi\)
−0.998225 + 0.0595499i \(0.981033\pi\)
\(450\) −9540.50 + 322.246i −0.999430 + 0.0337574i
\(451\) 1909.66 0.199384
\(452\) −60.4603 + 182.911i −0.00629162 + 0.0190341i
\(453\) 4994.98 12475.3i 0.518067 1.29391i
\(454\) 2130.97 + 2948.74i 0.220289 + 0.304827i
\(455\) −12703.9 + 15065.4i −1.30894 + 1.55225i
\(456\) −12430.0 925.257i −1.27651 0.0950200i
\(457\) 2261.32i 0.231466i 0.993280 + 0.115733i \(0.0369217\pi\)
−0.993280 + 0.115733i \(0.963078\pi\)
\(458\) 7963.22 5754.78i 0.812439 0.587125i
\(459\) 838.720 + 1837.16i 0.0852899 + 0.186822i
\(460\) 3635.56 2233.95i 0.368497 0.226432i
\(461\) −9091.77 −0.918538 −0.459269 0.888297i \(-0.651889\pi\)
−0.459269 + 0.888297i \(0.651889\pi\)
\(462\) 15262.4 3814.94i 1.53695 0.384171i
\(463\) −13361.2 −1.34114 −0.670568 0.741848i \(-0.733950\pi\)
−0.670568 + 0.741848i \(0.733950\pi\)
\(464\) 2548.67 + 1891.57i 0.254998 + 0.189254i
\(465\) 4943.52 + 9281.77i 0.493012 + 0.925660i
\(466\) −2276.94 3150.74i −0.226346 0.313208i
\(467\) 11343.7 1.12404 0.562019 0.827124i \(-0.310025\pi\)
0.562019 + 0.827124i \(0.310025\pi\)
\(468\) 11178.0 5960.43i 1.10407 0.588720i
\(469\) 24813.5i 2.44303i
\(470\) 1043.31 13924.8i 0.102393 1.36660i
\(471\) 7369.42 + 2950.63i 0.720945 + 0.288658i
\(472\) −2772.53 8759.48i −0.270373 0.854211i
\(473\) −17455.8 −1.69687
\(474\) 1532.80 383.134i 0.148532 0.0371264i
\(475\) −2237.58 13061.2i −0.216141 1.26166i
\(476\) 1086.23 3286.20i 0.104595 0.316434i
\(477\) −1223.84 + 1283.31i −0.117475 + 0.123184i
\(478\) 10123.7 + 14008.8i 0.968721 + 1.34048i
\(479\) −3825.30 −0.364890 −0.182445 0.983216i \(-0.558401\pi\)
−0.182445 + 0.983216i \(0.558401\pi\)
\(480\) −4825.33 9343.89i −0.458844 0.888517i
\(481\) 6670.91 0.632364
\(482\) −12191.8 16870.4i −1.15211 1.59425i
\(483\) −2769.30 + 6916.54i −0.260885 + 0.651580i
\(484\) −156.907 + 474.692i −0.0147358 + 0.0445804i
\(485\) −711.318 599.822i −0.0665965 0.0561577i
\(486\) −10259.4 + 3088.01i −0.957564 + 0.288221i
\(487\) 11327.9 1.05403 0.527017 0.849855i \(-0.323311\pi\)
0.527017 + 0.849855i \(0.323311\pi\)
\(488\) −1458.26 4607.21i −0.135272 0.427374i
\(489\) 5360.75 13388.9i 0.495750 1.23817i
\(490\) −17667.9 1323.77i −1.62889 0.122044i
\(491\) 17714.2i 1.62817i 0.580747 + 0.814084i \(0.302761\pi\)
−0.580747 + 0.814084i \(0.697239\pi\)
\(492\) 1704.60 + 1436.00i 0.156198 + 0.131585i
\(493\) 713.881 0.0652162
\(494\) 10300.2 + 14253.0i 0.938114 + 1.29812i
\(495\) −1164.76 10688.1i −0.105762 0.970496i
\(496\) −6904.41 + 9302.91i −0.625034 + 0.842163i
\(497\) −4737.38 −0.427567
\(498\) 4129.25 + 16519.9i 0.371559 + 1.48649i
\(499\) 16471.4 1.47768 0.738839 0.673882i \(-0.235374\pi\)
0.738839 + 0.673882i \(0.235374\pi\)
\(500\) 8400.56 7377.70i 0.751369 0.659882i
\(501\) −2867.84 + 7162.65i −0.255740 + 0.638730i
\(502\) 3673.57 2654.78i 0.326612 0.236033i
\(503\) 14790.4i 1.31108i −0.755162 0.655538i \(-0.772442\pi\)
0.755162 0.655538i \(-0.227558\pi\)
\(504\) 16492.3 + 8071.54i 1.45759 + 0.713363i
\(505\) −7052.91 + 8363.92i −0.621486 + 0.737009i
\(506\) 2814.96 + 3895.22i 0.247313 + 0.342221i
\(507\) −5993.79 2399.85i −0.525037 0.210219i
\(508\) −2557.05 + 7735.90i −0.223329 + 0.675640i
\(509\) −14027.9 −1.22157 −0.610783 0.791798i \(-0.709145\pi\)
−0.610783 + 0.791798i \(0.709145\pi\)
\(510\) −2124.03 1040.80i −0.184419 0.0903679i
\(511\) 7295.52i 0.631575i
\(512\) 7022.04 9214.59i 0.606119 0.795374i
\(513\) −6176.77 13529.8i −0.531601 1.16444i
\(514\) 2182.66 + 3020.27i 0.187301 + 0.259180i
\(515\) −3490.03 + 4138.76i −0.298619 + 0.354128i
\(516\) −15581.4 13126.2i −1.32933 1.11986i
\(517\) 15727.2 1.33787
\(518\) 5663.53 + 7836.95i 0.480388 + 0.664741i
\(519\) 8667.35 21647.3i 0.733053 1.83085i
\(520\) −5695.93 + 13699.9i −0.480352 + 1.15534i
\(521\) 13903.0i 1.16910i −0.811356 0.584552i \(-0.801270\pi\)
0.811356 0.584552i \(-0.198730\pi\)
\(522\) −513.120 + 3752.34i −0.0430242 + 0.314627i
\(523\) 11850.7i 0.990813i −0.868661 0.495407i \(-0.835019\pi\)
0.868661 0.495407i \(-0.164981\pi\)
\(524\) 3207.86 + 1060.34i 0.267435 + 0.0883990i
\(525\) −4091.75 + 19087.3i −0.340150 + 1.58674i
\(526\) −1425.48 + 1030.15i −0.118163 + 0.0853931i
\(527\) 2605.74i 0.215384i
\(528\) 10088.4 6205.77i 0.831514 0.511499i
\(529\) 9891.02 0.812938
\(530\) 155.179 2071.13i 0.0127180 0.169744i
\(531\) 7566.19 7933.84i 0.618351 0.648398i
\(532\) −7999.59 + 24201.3i −0.651929 + 1.97229i
\(533\) 3144.55i 0.255545i
\(534\) 10695.8 2673.48i 0.866765 0.216653i
\(535\) 6577.58 7800.24i 0.531540 0.630344i
\(536\) 5637.39 + 17810.6i 0.454288 + 1.43527i
\(537\) 5241.79 13091.8i 0.421229 1.05205i
\(538\) 173.958 + 240.715i 0.0139402 + 0.0192899i
\(539\) 19954.8i 1.59465i
\(540\) 6997.43 10416.3i 0.557632 0.830088i
\(541\) 19263.3i 1.53086i −0.643519 0.765430i \(-0.722526\pi\)
0.643519 0.765430i \(-0.277474\pi\)
\(542\) 2245.88 1623.03i 0.177987 0.128626i
\(543\) 1764.81 4407.74i 0.139476 0.348350i
\(544\) 33.0837 2605.55i 0.00260745 0.205353i
\(545\) 11029.4 + 9300.60i 0.866878 + 0.730998i
\(546\) −6281.90 25132.0i −0.492382 1.96987i
\(547\) 5317.24i 0.415629i 0.978168 + 0.207814i \(0.0666350\pi\)
−0.978168 + 0.207814i \(0.933365\pi\)
\(548\) −7437.56 + 22501.0i −0.579776 + 1.75400i
\(549\) 3979.57 4172.95i 0.309370 0.324403i
\(550\) 8993.04 + 8814.10i 0.697209 + 0.683336i
\(551\) −5257.40 −0.406484
\(552\) −416.382 + 5593.72i −0.0321058 + 0.431313i
\(553\) 3230.94i 0.248452i
\(554\) −12235.3 16930.6i −0.938315 1.29840i
\(555\) 5832.38 3106.36i 0.446073 0.237581i
\(556\) −1818.13 + 5500.43i −0.138680 + 0.419551i
\(557\) 10227.8i 0.778039i 0.921230 + 0.389019i \(0.127186\pi\)
−0.921230 + 0.389019i \(0.872814\pi\)
\(558\) −13696.4 1872.94i −1.03909 0.142093i
\(559\) 28743.7i 2.17483i
\(560\) −20930.3 + 4939.48i −1.57941 + 0.372734i
\(561\) 990.222 2473.15i 0.0745227 0.186126i
\(562\) 6505.60 4701.40i 0.488296 0.352877i
\(563\) 6371.34 0.476945 0.238472 0.971149i \(-0.423353\pi\)
0.238472 + 0.971149i \(0.423353\pi\)
\(564\) 14038.5 + 11826.3i 1.04810 + 0.882941i
\(565\) 173.559 205.820i 0.0129233 0.0153255i
\(566\) −7835.71 + 5662.63i −0.581907 + 0.420527i
\(567\) 1038.80 + 21885.1i 0.0769407 + 1.62097i
\(568\) −3400.41 + 1076.29i −0.251193 + 0.0795073i
\(569\) 3929.11i 0.289485i −0.989469 0.144742i \(-0.953765\pi\)
0.989469 0.144742i \(-0.0462353\pi\)
\(570\) 15642.5 + 7665.04i 1.14946 + 0.563251i
\(571\) −4292.81 −0.314621 −0.157310 0.987549i \(-0.550282\pi\)
−0.157310 + 0.987549i \(0.550282\pi\)
\(572\) −15866.1 5244.43i −1.15978 0.383358i
\(573\) −16496.8 6605.14i −1.20273 0.481559i
\(574\) 3694.20 2669.69i 0.268629 0.194130i
\(575\) −5877.77 + 1006.95i −0.426296 + 0.0730307i
\(576\) 13671.6 + 2046.70i 0.988979 + 0.148054i
\(577\) 1957.65i 0.141244i 0.997503 + 0.0706221i \(0.0224985\pi\)
−0.997503 + 0.0706221i \(0.977502\pi\)
\(578\) 7796.04 + 10787.8i 0.561025 + 0.776322i
\(579\) −7312.42 + 18263.3i −0.524860 + 1.31088i
\(580\) −2322.24 3779.23i −0.166251 0.270558i
\(581\) 34821.7 2.48649
\(582\) 1186.62 296.603i 0.0845135 0.0211247i
\(583\) 2339.21 0.166175
\(584\) 1657.48 + 5236.59i 0.117443 + 0.371047i
\(585\) −17599.7 + 1917.97i −1.24386 + 0.135552i
\(586\) 7617.88 5505.21i 0.537016 0.388086i
\(587\) −17909.4 −1.25928 −0.629642 0.776886i \(-0.716798\pi\)
−0.629642 + 0.776886i \(0.716798\pi\)
\(588\) 15005.4 17812.1i 1.05240 1.24925i
\(589\) 19190.0i 1.34246i
\(590\) −959.371 + 12804.4i −0.0669435 + 0.893475i
\(591\) 24.8813 62.1428i 0.00173177 0.00432523i
\(592\) 5845.66 + 4338.52i 0.405836 + 0.301203i
\(593\) 20213.4 1.39977 0.699887 0.714253i \(-0.253233\pi\)
0.699887 + 0.714253i \(0.253233\pi\)
\(594\) 12287.8 + 6982.49i 0.848775 + 0.482315i
\(595\) −3118.16 + 3697.77i −0.214844 + 0.254780i
\(596\) −4813.25 + 14561.6i −0.330803 + 1.00078i
\(597\) −3150.06 + 7867.51i −0.215952 + 0.539356i
\(598\) 6414.09 4635.27i 0.438615 0.316974i
\(599\) 8469.13 0.577695 0.288848 0.957375i \(-0.406728\pi\)
0.288848 + 0.957375i \(0.406728\pi\)
\(600\) 1399.48 + 14630.2i 0.0952228 + 0.995456i
\(601\) −16288.3 −1.10551 −0.552756 0.833343i \(-0.686424\pi\)
−0.552756 + 0.833343i \(0.686424\pi\)
\(602\) −33768.0 + 24403.1i −2.28618 + 1.65215i
\(603\) −15384.3 + 16131.9i −1.03897 + 1.08945i
\(604\) −19644.0 6493.21i −1.32335 0.437426i
\(605\) 450.420 534.145i 0.0302680 0.0358943i
\(606\) −3487.55 13952.6i −0.233782 0.935293i
\(607\) 6769.57 0.452666 0.226333 0.974050i \(-0.427326\pi\)
0.226333 + 0.974050i \(0.427326\pi\)
\(608\) −243.646 + 19188.7i −0.0162519 + 1.27994i
\(609\) 7189.87 + 2878.74i 0.478404 + 0.191548i
\(610\) −504.599 + 6734.72i −0.0334928 + 0.447018i
\(611\) 25897.3i 1.71472i
\(612\) 2743.63 1462.98i 0.181217 0.0966298i
\(613\) 8543.04 0.562887 0.281444 0.959578i \(-0.409187\pi\)
0.281444 + 0.959578i \(0.409187\pi\)
\(614\) 1043.79 754.313i 0.0686055 0.0495791i
\(615\) −1464.28 2749.28i −0.0960090 0.180263i
\(616\) −7308.99 23091.8i −0.478064 1.51038i
\(617\) 9253.24 0.603763 0.301881 0.953346i \(-0.402385\pi\)
0.301881 + 0.953346i \(0.402385\pi\)
\(618\) −1725.76 6904.26i −0.112331 0.449401i
\(619\) 16231.5 1.05396 0.526980 0.849878i \(-0.323324\pi\)
0.526980 + 0.849878i \(0.323324\pi\)
\(620\) 13794.5 8476.38i 0.893552 0.549064i
\(621\) −6088.64 + 2779.65i −0.393444 + 0.179619i
\(622\) 2770.59 + 3833.83i 0.178602 + 0.247143i
\(623\) 22545.3i 1.44985i
\(624\) −10218.8 16612.1i −0.655575 1.06573i
\(625\) −14734.0 + 5200.94i −0.942976 + 0.332860i
\(626\) 7143.51 5162.40i 0.456090 0.329602i
\(627\) −7292.52 + 18213.6i −0.464490 + 1.16010i
\(628\) 3835.67 11604.1i 0.243726 0.737349i
\(629\) 1637.36 0.103793
\(630\) −17195.2 19047.7i −1.08741 1.20457i
\(631\) 12901.7i 0.813960i 0.913437 + 0.406980i \(0.133418\pi\)
−0.913437 + 0.406980i \(0.866582\pi\)
\(632\) −734.041 2319.11i −0.0462003 0.145964i
\(633\) 11975.2 + 4794.72i 0.751928 + 0.301064i
\(634\) 10797.9 7803.32i 0.676403 0.488816i
\(635\) 7340.33 8704.78i 0.458728 0.543998i
\(636\) 2088.03 + 1759.01i 0.130182 + 0.109669i
\(637\) −32858.7 −2.04382
\(638\) 4049.15 2926.20i 0.251266 0.181582i
\(639\) −3079.90 2937.17i −0.190671 0.181835i
\(640\) −13901.2 + 8300.65i −0.858583 + 0.512675i
\(641\) 13164.5i 0.811182i 0.914055 + 0.405591i \(0.132934\pi\)
−0.914055 + 0.405591i \(0.867066\pi\)
\(642\) 3252.51 + 13012.3i 0.199948 + 0.799930i
\(643\) 22712.5i 1.39299i −0.717561 0.696496i \(-0.754741\pi\)
0.717561 0.696496i \(-0.245259\pi\)
\(644\) 10891.0 + 3599.95i 0.666406 + 0.220276i
\(645\) 13384.7 + 25130.6i 0.817089 + 1.53414i
\(646\) 2528.17 + 3498.38i 0.153978 + 0.213068i
\(647\) 2451.48i 0.148961i 0.997222 + 0.0744803i \(0.0237298\pi\)
−0.997222 + 0.0744803i \(0.976270\pi\)
\(648\) 5717.73 + 15472.7i 0.346626 + 0.938003i
\(649\) −14461.8 −0.874692
\(650\) 14513.8 14808.5i 0.875813 0.893594i
\(651\) −10507.7 + 26243.7i −0.632609 + 1.57999i
\(652\) −21082.5 6968.70i −1.26634 0.418582i
\(653\) 26329.5i 1.57787i 0.614474 + 0.788937i \(0.289368\pi\)
−0.614474 + 0.788937i \(0.710632\pi\)
\(654\) −18399.2 + 4599.00i −1.10010 + 0.274977i
\(655\) −3609.62 3043.83i −0.215328 0.181576i
\(656\) 2045.10 2755.54i 0.121719 0.164003i
\(657\) −4523.22 + 4743.01i −0.268596 + 0.281647i
\(658\) 30424.0 21986.5i 1.80251 1.30262i
\(659\) 29804.9i 1.76181i 0.473292 + 0.880906i \(0.343066\pi\)
−0.473292 + 0.880906i \(0.656934\pi\)
\(660\) −16313.8 + 2802.94i −0.962143 + 0.165310i
\(661\) 8483.43i 0.499194i 0.968350 + 0.249597i \(0.0802981\pi\)
−0.968350 + 0.249597i \(0.919702\pi\)
\(662\) 12829.1 + 17752.4i 0.753198 + 1.04224i
\(663\) −4072.43 1630.56i −0.238552 0.0955137i
\(664\) 24994.4 7911.17i 1.46080 0.462369i
\(665\) 22963.8 27232.4i 1.33909 1.58801i
\(666\) −1176.90 + 8606.39i −0.0684742 + 0.500737i
\(667\) 2365.92i 0.137345i
\(668\) 11278.5 + 3728.05i 0.653262 + 0.215932i
\(669\) −1064.15 426.072i −0.0614981 0.0246232i
\(670\) 1950.69 26035.3i 0.112480 1.50124i
\(671\) −7606.44 −0.437621
\(672\) 10840.2 26108.5i 0.622274 1.49874i
\(673\) 32692.9i 1.87254i 0.351285 + 0.936268i \(0.385745\pi\)
−0.351285 + 0.936268i \(0.614255\pi\)
\(674\) 19278.3 13931.8i 1.10174 0.796193i
\(675\) −14494.3 + 9872.30i −0.826497 + 0.562941i
\(676\) −3119.68 + 9438.01i −0.177496 + 0.536983i
\(677\) 16192.2i 0.919226i −0.888119 0.459613i \(-0.847988\pi\)
0.888119 0.459613i \(-0.152012\pi\)
\(678\) 85.8220 + 343.348i 0.00486132 + 0.0194487i
\(679\) 2501.23i 0.141367i
\(680\) −1398.06 + 3362.61i −0.0788428 + 0.189633i
\(681\) 6204.82 + 2484.34i 0.349147 + 0.139795i
\(682\) 10680.9 + 14779.8i 0.599697 + 0.829835i
\(683\) 14545.0 0.814862 0.407431 0.913236i \(-0.366425\pi\)
0.407431 + 0.913236i \(0.366425\pi\)
\(684\) −20205.5 + 10774.1i −1.12950 + 0.602281i
\(685\) 21350.4 25319.1i 1.19089 1.41225i
\(686\) −10818.4 14970.0i −0.602110 0.833174i
\(687\) 6709.09 16756.4i 0.372588 0.930565i
\(688\) −18693.9 + 25187.9i −1.03590 + 1.39575i
\(689\) 3851.88i 0.212982i
\(690\) 3449.40 7039.39i 0.190314 0.388384i
\(691\) 8218.62 0.452462 0.226231 0.974074i \(-0.427360\pi\)
0.226231 + 0.974074i \(0.427360\pi\)
\(692\) −34086.6 11267.1i −1.87251 0.618947i
\(693\) 19946.1 20915.3i 1.09335 1.14647i
\(694\) −8002.98 11074.2i −0.437736 0.605721i
\(695\) 5219.17 6189.33i 0.284856 0.337805i
\(696\) 5814.78 + 432.836i 0.316679 + 0.0235727i
\(697\) 771.825i 0.0419440i
\(698\) 14218.6 10275.4i 0.771036 0.557205i
\(699\) −6629.87 2654.53i −0.358748 0.143639i
\(700\) 29719.0 + 4478.53i 1.60467 + 0.241818i
\(701\) −22746.0 −1.22554 −0.612770 0.790261i \(-0.709945\pi\)
−0.612770 + 0.790261i \(0.709945\pi\)
\(702\) 11497.8 20233.7i 0.618170 1.08785i
\(703\) −12058.4 −0.646930
\(704\) −10492.5 14914.4i −0.561721 0.798447i
\(705\) −12059.3 22642.0i −0.644224 1.20957i
\(706\) 12721.3 + 17603.2i 0.678149 + 0.938393i
\(707\) −29410.3 −1.56448
\(708\) −12908.9 10874.8i −0.685237 0.577260i
\(709\) 16822.0i 0.891062i 0.895266 + 0.445531i \(0.146985\pi\)
−0.895266 + 0.445531i \(0.853015\pi\)
\(710\) 4970.65 + 372.425i 0.262739 + 0.0196857i
\(711\) 2003.18 2100.52i 0.105661 0.110796i
\(712\) −5122.09 16182.6i −0.269604 0.851782i
\(713\) −8635.84 −0.453597
\(714\) −1541.88 6168.60i −0.0808172 0.323325i
\(715\) 17853.2 + 15054.8i 0.933807 + 0.787436i
\(716\) −20614.7 6814.06i −1.07599 0.355661i
\(717\) 29477.7 + 11802.5i 1.53538 + 0.614747i
\(718\) −20549.2 28435.1i −1.06809 1.47798i
\(719\) −24046.5 −1.24726 −0.623631 0.781719i \(-0.714343\pi\)
−0.623631 + 0.781719i \(0.714343\pi\)
\(720\) −16669.8 9765.50i −0.862844 0.505470i
\(721\) −14553.3 −0.751722
\(722\) −7255.54 10039.9i −0.373994 0.517516i
\(723\) −35499.2 14213.5i −1.82605 0.731128i
\(724\) −6940.56 2294.16i −0.356276 0.117765i
\(725\) 1046.74 + 6110.05i 0.0536207 + 0.312995i
\(726\) 222.726 + 891.057i 0.0113858 + 0.0455513i
\(727\) 2465.88 0.125797 0.0628986 0.998020i \(-0.479966\pi\)
0.0628986 + 0.998020i \(0.479966\pi\)
\(728\) −38024.4 + 12035.4i −1.93582 + 0.612722i
\(729\) −12893.4 + 14872.1i −0.655053 + 0.755583i
\(730\) 573.531 7654.74i 0.0290785 0.388102i
\(731\) 7055.10i 0.356966i
\(732\) −6789.69 5719.80i −0.342834 0.288811i
\(733\) −31105.2 −1.56739 −0.783696 0.621145i \(-0.786668\pi\)
−0.783696 + 0.621145i \(0.786668\pi\)
\(734\) 2039.74 + 2822.51i 0.102573 + 0.141936i
\(735\) −28728.4 + 15300.9i −1.44172 + 0.767868i
\(736\) 8635.23 + 109.645i 0.432471 + 0.00549126i
\(737\) 29405.2 1.46968
\(738\) 4056.90 + 554.768i 0.202353 + 0.0276711i
\(739\) −12767.8 −0.635548 −0.317774 0.948167i \(-0.602935\pi\)
−0.317774 + 0.948167i \(0.602935\pi\)
\(740\) −5326.30 8668.07i −0.264593 0.430601i
\(741\) 29991.6 + 12008.3i 1.48687 + 0.595324i
\(742\) 4525.17 3270.20i 0.223887 0.161796i
\(743\) 26197.5i 1.29353i −0.762690 0.646764i \(-0.776122\pi\)
0.762690 0.646764i \(-0.223878\pi\)
\(744\) −1579.89 + 21224.5i −0.0778518 + 1.04587i
\(745\) 13817.0 16385.4i 0.679485 0.805789i
\(746\) 8473.48 + 11725.2i 0.415866 + 0.575458i
\(747\) 22638.5 + 21589.4i 1.10883 + 1.05745i
\(748\) −3894.30 1287.24i −0.190361 0.0629226i
\(749\) 27428.2 1.33806
\(750\) 5793.76 19705.5i 0.282078 0.959392i
\(751\) 7833.34i 0.380616i −0.981724 0.190308i \(-0.939051\pi\)
0.981724 0.190308i \(-0.0609486\pi\)
\(752\) 16842.7 22693.6i 0.816740 1.10047i
\(753\) 3095.02 7730.03i 0.149786 0.374101i
\(754\) −4818.45 6667.57i −0.232729 0.322040i
\(755\) 22104.3 + 18639.6i 1.06551 + 0.898494i
\(756\) 33532.0 3670.68i 1.61316 0.176589i
\(757\) 10981.8 0.527266 0.263633 0.964623i \(-0.415079\pi\)
0.263633 + 0.964623i \(0.415079\pi\)
\(758\) −4926.63 6817.26i −0.236073 0.326668i
\(759\) 8196.43 + 3281.76i 0.391978 + 0.156944i
\(760\) 10296.0 24764.0i 0.491417 1.18196i
\(761\) 24605.3i 1.17206i −0.810288 0.586032i \(-0.800689\pi\)
0.810288 0.586032i \(-0.199311\pi\)
\(762\) 3629.68 + 14521.3i 0.172558 + 0.690354i
\(763\) 38783.1i 1.84016i
\(764\) −8586.33 + 25976.4i −0.406600 + 1.23009i
\(765\) −4319.81 + 470.762i −0.204161 + 0.0222489i
\(766\) −9719.13 + 7023.72i −0.458442 + 0.331302i
\(767\) 23813.6i 1.12107i
\(768\) 1849.26 21202.9i 0.0868873 0.996218i
\(769\) −17233.6 −0.808140 −0.404070 0.914728i \(-0.632405\pi\)
−0.404070 + 0.914728i \(0.632405\pi\)
\(770\) −2529.11 + 33755.2i −0.118367 + 1.57981i