Properties

Label 63.4.o.a.41.2
Level $63$
Weight $4$
Character 63.41
Analytic conductor $3.717$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,4,Mod(20,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.20");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.o (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.2
Character \(\chi\) \(=\) 63.41
Dual form 63.4.o.a.20.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.67796 + 2.70082i) q^{2} +(2.75680 - 4.40455i) q^{3} +(10.5889 - 18.3405i) q^{4} +(-3.43953 + 5.95744i) q^{5} +(-1.00030 + 28.0499i) q^{6} +(-17.3445 + 6.49383i) q^{7} +71.1815i q^{8} +(-11.8001 - 24.2849i) q^{9} +O(q^{10})\) \(q+(-4.67796 + 2.70082i) q^{2} +(2.75680 - 4.40455i) q^{3} +(10.5889 - 18.3405i) q^{4} +(-3.43953 + 5.95744i) q^{5} +(-1.00030 + 28.0499i) q^{6} +(-17.3445 + 6.49383i) q^{7} +71.1815i q^{8} +(-11.8001 - 24.2849i) q^{9} -37.1582i q^{10} +(-10.9244 + 6.30723i) q^{11} +(-51.5901 - 97.2002i) q^{12} +(-22.5632 - 13.0269i) q^{13} +(63.5980 - 77.2222i) q^{14} +(16.7577 + 31.5731i) q^{15} +(-107.537 - 186.260i) q^{16} -124.623 q^{17} +(120.790 + 81.7339i) q^{18} +41.3246i q^{19} +(72.8415 + 126.165i) q^{20} +(-19.2128 + 94.2967i) q^{21} +(34.0694 - 59.0099i) q^{22} +(-97.6910 - 56.4019i) q^{23} +(313.522 + 196.233i) q^{24} +(38.8392 + 67.2715i) q^{25} +140.733 q^{26} +(-139.495 - 14.9746i) q^{27} +(-64.5583 + 386.868i) q^{28} +(114.888 - 66.3304i) q^{29} +(-163.665 - 102.438i) q^{30} +(-155.062 - 89.5251i) q^{31} +(512.952 + 296.153i) q^{32} +(-2.33600 + 65.5050i) q^{33} +(582.982 - 336.585i) q^{34} +(20.9702 - 125.664i) q^{35} +(-570.347 - 40.7306i) q^{36} +148.290 q^{37} +(-111.610 - 193.315i) q^{38} +(-119.580 + 63.4683i) q^{39} +(-424.060 - 244.831i) q^{40} +(-93.6165 + 162.149i) q^{41} +(-164.802 - 493.007i) q^{42} +(99.1611 + 171.752i) q^{43} +267.146i q^{44} +(185.263 + 13.2303i) q^{45} +609.326 q^{46} +(92.1405 + 159.592i) q^{47} +(-1116.85 - 39.8286i) q^{48} +(258.660 - 225.264i) q^{49} +(-363.377 - 209.796i) q^{50} +(-343.561 + 548.909i) q^{51} +(-477.838 + 275.880i) q^{52} -359.147i q^{53} +(692.994 - 306.700i) q^{54} -86.7756i q^{55} +(-462.241 - 1234.60i) q^{56} +(182.016 + 113.924i) q^{57} +(-358.293 + 620.582i) q^{58} +(182.287 - 315.730i) q^{59} +(756.510 + 26.9783i) q^{60} +(300.892 - 173.720i) q^{61} +967.165 q^{62} +(362.369 + 344.581i) q^{63} -1478.83 q^{64} +(155.214 - 89.6127i) q^{65} +(-165.990 - 312.739i) q^{66} +(-182.332 + 315.809i) q^{67} +(-1319.62 + 2285.65i) q^{68} +(-517.739 + 274.796i) q^{69} +(241.299 + 644.489i) q^{70} -565.793i q^{71} +(1728.64 - 839.949i) q^{72} +737.140i q^{73} +(-693.694 + 400.504i) q^{74} +(403.373 + 14.3849i) q^{75} +(757.912 + 437.580i) q^{76} +(148.520 - 180.337i) q^{77} +(387.973 - 619.865i) q^{78} +(-451.543 - 782.096i) q^{79} +1479.51 q^{80} +(-450.515 + 573.129i) q^{81} -1011.37i q^{82} +(-382.494 - 662.499i) q^{83} +(1526.00 + 1350.87i) q^{84} +(428.645 - 742.436i) q^{85} +(-927.743 - 535.633i) q^{86} +(24.5667 - 688.887i) q^{87} +(-448.958 - 777.618i) q^{88} -395.916 q^{89} +(-902.385 + 438.471i) q^{90} +(475.941 + 79.4223i) q^{91} +(-2068.87 + 1194.47i) q^{92} +(-821.793 + 436.175i) q^{93} +(-862.059 - 497.710i) q^{94} +(-246.189 - 142.137i) q^{95} +(2718.53 - 1442.89i) q^{96} +(243.773 - 140.742i) q^{97} +(-601.604 + 1752.37i) q^{98} +(282.080 + 190.873i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.67796 + 2.70082i −1.65391 + 0.954885i −0.678466 + 0.734632i \(0.737355\pi\)
−0.975443 + 0.220252i \(0.929312\pi\)
\(3\) 2.75680 4.40455i 0.530546 0.847656i
\(4\) 10.5889 18.3405i 1.32361 2.29256i
\(5\) −3.43953 + 5.95744i −0.307641 + 0.532850i −0.977846 0.209326i \(-0.932873\pi\)
0.670205 + 0.742176i \(0.266206\pi\)
\(6\) −1.00030 + 28.0499i −0.0680619 + 1.90856i
\(7\) −17.3445 + 6.49383i −0.936513 + 0.350634i
\(8\) 71.1815i 3.14581i
\(9\) −11.8001 24.2849i −0.437041 0.899442i
\(10\) 37.1582i 1.17505i
\(11\) −10.9244 + 6.30723i −0.299440 + 0.172882i −0.642191 0.766544i \(-0.721975\pi\)
0.342751 + 0.939426i \(0.388641\pi\)
\(12\) −51.5901 97.2002i −1.24106 2.33827i
\(13\) −22.5632 13.0269i −0.481377 0.277923i 0.239613 0.970869i \(-0.422979\pi\)
−0.720990 + 0.692945i \(0.756313\pi\)
\(14\) 63.5980 77.2222i 1.21409 1.47418i
\(15\) 16.7577 + 31.5731i 0.288455 + 0.543475i
\(16\) −107.537 186.260i −1.68027 2.91032i
\(17\) −124.623 −1.77797 −0.888987 0.457932i \(-0.848590\pi\)
−0.888987 + 0.457932i \(0.848590\pi\)
\(18\) 120.790 + 81.7339i 1.58169 + 1.07027i
\(19\) 41.3246i 0.498974i 0.968378 + 0.249487i \(0.0802620\pi\)
−0.968378 + 0.249487i \(0.919738\pi\)
\(20\) 72.8415 + 126.165i 0.814393 + 1.41057i
\(21\) −19.2128 + 94.2967i −0.199646 + 0.979868i
\(22\) 34.0694 59.0099i 0.330164 0.571862i
\(23\) −97.6910 56.4019i −0.885651 0.511331i −0.0131335 0.999914i \(-0.504181\pi\)
−0.872517 + 0.488583i \(0.837514\pi\)
\(24\) 313.522 + 196.233i 2.66656 + 1.66900i
\(25\) 38.8392 + 67.2715i 0.310714 + 0.538172i
\(26\) 140.733 1.06154
\(27\) −139.495 14.9746i −0.994287 0.106735i
\(28\) −64.5583 + 386.868i −0.435727 + 2.61111i
\(29\) 114.888 66.3304i 0.735658 0.424732i −0.0848304 0.996395i \(-0.527035\pi\)
0.820489 + 0.571663i \(0.193702\pi\)
\(30\) −163.665 102.438i −0.996035 0.623417i
\(31\) −155.062 89.5251i −0.898386 0.518683i −0.0217097 0.999764i \(-0.506911\pi\)
−0.876676 + 0.481081i \(0.840244\pi\)
\(32\) 512.952 + 296.153i 2.83369 + 1.63603i
\(33\) −2.33600 + 65.5050i −0.0123226 + 0.345544i
\(34\) 582.982 336.585i 2.94061 1.69776i
\(35\) 20.9702 125.664i 0.101274 0.606890i
\(36\) −570.347 40.7306i −2.64049 0.188567i
\(37\) 148.290 0.658884 0.329442 0.944176i \(-0.393139\pi\)
0.329442 + 0.944176i \(0.393139\pi\)
\(38\) −111.610 193.315i −0.476462 0.825257i
\(39\) −119.580 + 63.4683i −0.490977 + 0.260591i
\(40\) −424.060 244.831i −1.67624 0.967779i
\(41\) −93.6165 + 162.149i −0.356596 + 0.617643i −0.987390 0.158308i \(-0.949396\pi\)
0.630794 + 0.775951i \(0.282729\pi\)
\(42\) −164.802 493.007i −0.605464 1.81125i
\(43\) 99.1611 + 171.752i 0.351673 + 0.609115i 0.986543 0.163504i \(-0.0522796\pi\)
−0.634870 + 0.772619i \(0.718946\pi\)
\(44\) 267.146i 0.915312i
\(45\) 185.263 + 13.2303i 0.613719 + 0.0438280i
\(46\) 609.326 1.95305
\(47\) 92.1405 + 159.592i 0.285959 + 0.495295i 0.972841 0.231473i \(-0.0743546\pi\)
−0.686882 + 0.726769i \(0.741021\pi\)
\(48\) −1116.85 39.8286i −3.35841 0.119766i
\(49\) 258.660 225.264i 0.754111 0.656746i
\(50\) −363.377 209.796i −1.02779 0.593392i
\(51\) −343.561 + 548.909i −0.943298 + 1.50711i
\(52\) −477.838 + 275.880i −1.27431 + 0.735724i
\(53\) 359.147i 0.930804i −0.885099 0.465402i \(-0.845910\pi\)
0.885099 0.465402i \(-0.154090\pi\)
\(54\) 692.994 306.700i 1.74638 0.772899i
\(55\) 86.7756i 0.212742i
\(56\) −462.241 1234.60i −1.10303 2.94609i
\(57\) 182.016 + 113.924i 0.422958 + 0.264729i
\(58\) −358.293 + 620.582i −0.811141 + 1.40494i
\(59\) 182.287 315.730i 0.402232 0.696687i −0.591763 0.806112i \(-0.701568\pi\)
0.993995 + 0.109425i \(0.0349011\pi\)
\(60\) 756.510 + 26.9783i 1.62775 + 0.0580480i
\(61\) 300.892 173.720i 0.631561 0.364632i −0.149795 0.988717i \(-0.547861\pi\)
0.781356 + 0.624085i \(0.214528\pi\)
\(62\) 967.165 1.98113
\(63\) 362.369 + 344.581i 0.724669 + 0.689097i
\(64\) −1478.83 −2.88833
\(65\) 155.214 89.6127i 0.296183 0.171001i
\(66\) −165.990 312.739i −0.309574 0.583265i
\(67\) −182.332 + 315.809i −0.332469 + 0.575854i −0.982995 0.183630i \(-0.941215\pi\)
0.650526 + 0.759484i \(0.274548\pi\)
\(68\) −1319.62 + 2285.65i −2.35334 + 4.07611i
\(69\) −517.739 + 274.796i −0.903312 + 0.479442i
\(70\) 241.299 + 644.489i 0.412011 + 1.10045i
\(71\) 565.793i 0.945736i −0.881133 0.472868i \(-0.843219\pi\)
0.881133 0.472868i \(-0.156781\pi\)
\(72\) 1728.64 839.949i 2.82947 1.37485i
\(73\) 737.140i 1.18186i 0.806723 + 0.590929i \(0.201239\pi\)
−0.806723 + 0.590929i \(0.798761\pi\)
\(74\) −693.694 + 400.504i −1.08973 + 0.629158i
\(75\) 403.373 + 14.3849i 0.621033 + 0.0221469i
\(76\) 757.912 + 437.580i 1.14393 + 0.660446i
\(77\) 148.520 180.337i 0.219811 0.266900i
\(78\) 387.973 619.865i 0.563196 0.899820i
\(79\) −451.543 782.096i −0.643070 1.11383i −0.984744 0.174012i \(-0.944327\pi\)
0.341673 0.939819i \(-0.389006\pi\)
\(80\) 1479.51 2.06768
\(81\) −450.515 + 573.129i −0.617991 + 0.786186i
\(82\) 1011.37i 1.36203i
\(83\) −382.494 662.499i −0.505833 0.876129i −0.999977 0.00674855i \(-0.997852\pi\)
0.494144 0.869380i \(-0.335481\pi\)
\(84\) 1526.00 + 1350.87i 1.98215 + 1.75466i
\(85\) 428.645 742.436i 0.546978 0.947393i
\(86\) −927.743 535.633i −1.16327 0.671614i
\(87\) 24.5667 688.887i 0.0302739 0.848925i
\(88\) −448.958 777.618i −0.543853 0.941981i
\(89\) −395.916 −0.471539 −0.235770 0.971809i \(-0.575761\pi\)
−0.235770 + 0.971809i \(0.575761\pi\)
\(90\) −902.385 + 438.471i −1.05689 + 0.513543i
\(91\) 475.941 + 79.4223i 0.548265 + 0.0914914i
\(92\) −2068.87 + 1194.47i −2.34451 + 1.35360i
\(93\) −821.793 + 436.175i −0.916300 + 0.486336i
\(94\) −862.059 497.710i −0.945900 0.546115i
\(95\) −246.189 142.137i −0.265878 0.153505i
\(96\) 2718.53 1442.89i 2.89019 1.53400i
\(97\) 243.773 140.742i 0.255169 0.147322i −0.366960 0.930237i \(-0.619601\pi\)
0.622129 + 0.782915i \(0.286268\pi\)
\(98\) −601.604 + 1752.37i −0.620114 + 1.80629i
\(99\) 282.080 + 190.873i 0.286365 + 0.193773i
\(100\) 1645.06 1.64506
\(101\) 552.396 + 956.777i 0.544212 + 0.942603i 0.998656 + 0.0518275i \(0.0165046\pi\)
−0.454444 + 0.890775i \(0.650162\pi\)
\(102\) 124.661 3495.67i 0.121012 3.39336i
\(103\) −1350.73 779.844i −1.29215 0.746023i −0.313114 0.949715i \(-0.601372\pi\)
−0.979035 + 0.203693i \(0.934706\pi\)
\(104\) 927.272 1606.08i 0.874293 1.51432i
\(105\) −495.684 438.796i −0.460703 0.407829i
\(106\) 969.991 + 1680.07i 0.888810 + 1.53946i
\(107\) 741.988i 0.670380i 0.942151 + 0.335190i \(0.108800\pi\)
−0.942151 + 0.335190i \(0.891200\pi\)
\(108\) −1751.73 + 2399.83i −1.56074 + 2.13819i
\(109\) −694.460 −0.610249 −0.305125 0.952312i \(-0.598698\pi\)
−0.305125 + 0.952312i \(0.598698\pi\)
\(110\) 234.365 + 405.933i 0.203144 + 0.351856i
\(111\) 408.806 653.150i 0.349569 0.558507i
\(112\) 3074.72 + 2532.25i 2.59405 + 2.13639i
\(113\) 1407.16 + 812.424i 1.17145 + 0.676340i 0.954022 0.299736i \(-0.0968985\pi\)
0.217432 + 0.976075i \(0.430232\pi\)
\(114\) −1159.15 41.3370i −0.952319 0.0339611i
\(115\) 672.022 387.992i 0.544925 0.314613i
\(116\) 2809.46i 2.24872i
\(117\) −50.1084 + 701.664i −0.0395943 + 0.554435i
\(118\) 1969.30i 1.53634i
\(119\) 2161.52 809.282i 1.66510 0.623418i
\(120\) −2247.42 + 1192.84i −1.70967 + 0.907425i
\(121\) −585.938 + 1014.87i −0.440224 + 0.762490i
\(122\) −938.373 + 1625.31i −0.696363 + 1.20614i
\(123\) 456.109 + 859.350i 0.334358 + 0.629959i
\(124\) −3283.86 + 1895.94i −2.37822 + 1.37307i
\(125\) −1394.24 −0.997636
\(126\) −2625.80 633.242i −1.85654 0.447728i
\(127\) −1099.84 −0.768466 −0.384233 0.923236i \(-0.625534\pi\)
−0.384233 + 0.923236i \(0.625534\pi\)
\(128\) 2814.28 1624.82i 1.94335 1.12200i
\(129\) 1029.86 + 36.7262i 0.702899 + 0.0250664i
\(130\) −484.056 + 838.409i −0.326573 + 0.565641i
\(131\) 597.844 1035.50i 0.398732 0.690624i −0.594838 0.803846i \(-0.702784\pi\)
0.993570 + 0.113222i \(0.0361172\pi\)
\(132\) 1176.66 + 736.467i 0.775870 + 0.485616i
\(133\) −268.355 716.752i −0.174957 0.467295i
\(134\) 1969.79i 1.26988i
\(135\) 569.006 779.526i 0.362758 0.496970i
\(136\) 8870.86i 5.59316i
\(137\) −1175.08 + 678.431i −0.732800 + 0.423082i −0.819446 0.573157i \(-0.805719\pi\)
0.0866457 + 0.996239i \(0.472385\pi\)
\(138\) 1679.79 2683.81i 1.03618 1.65551i
\(139\) 828.064 + 478.083i 0.505291 + 0.291730i 0.730896 0.682489i \(-0.239102\pi\)
−0.225605 + 0.974219i \(0.572436\pi\)
\(140\) −2082.69 1715.25i −1.25728 1.03546i
\(141\) 956.944 + 34.1260i 0.571554 + 0.0203825i
\(142\) 1528.10 + 2646.76i 0.903068 + 1.56416i
\(143\) 328.654 0.192192
\(144\) −3254.37 + 4809.43i −1.88331 + 2.78324i
\(145\) 912.582i 0.522660i
\(146\) −1990.88 3448.31i −1.12854 1.95469i
\(147\) −279.112 1760.29i −0.156604 0.987662i
\(148\) 1570.22 2719.70i 0.872105 1.51053i
\(149\) −166.537 96.1501i −0.0915653 0.0528653i 0.453518 0.891247i \(-0.350169\pi\)
−0.545083 + 0.838382i \(0.683502\pi\)
\(150\) −1925.81 + 1022.15i −1.04828 + 0.556386i
\(151\) −307.926 533.343i −0.165951 0.287436i 0.771041 0.636785i \(-0.219736\pi\)
−0.936993 + 0.349349i \(0.886403\pi\)
\(152\) −2941.54 −1.56968
\(153\) 1470.57 + 3026.46i 0.777047 + 1.59918i
\(154\) −207.714 + 1244.74i −0.108689 + 0.651322i
\(155\) 1066.68 615.849i 0.552761 0.319137i
\(156\) −102.177 + 2865.21i −0.0524406 + 1.47051i
\(157\) −722.630 417.211i −0.367339 0.212083i 0.304956 0.952366i \(-0.401358\pi\)
−0.672295 + 0.740283i \(0.734691\pi\)
\(158\) 4224.60 + 2439.07i 2.12716 + 1.22812i
\(159\) −1581.88 990.096i −0.789001 0.493835i
\(160\) −3528.63 + 2037.26i −1.74352 + 1.00662i
\(161\) 2060.66 + 343.871i 1.00871 + 0.168328i
\(162\) 559.572 3897.84i 0.271383 1.89039i
\(163\) −3304.12 −1.58772 −0.793860 0.608100i \(-0.791932\pi\)
−0.793860 + 0.608100i \(0.791932\pi\)
\(164\) 1982.59 + 3433.94i 0.943988 + 1.63504i
\(165\) −382.207 239.223i −0.180332 0.112870i
\(166\) 3578.58 + 2066.09i 1.67320 + 0.966024i
\(167\) 956.456 1656.63i 0.443190 0.767628i −0.554734 0.832028i \(-0.687180\pi\)
0.997924 + 0.0643998i \(0.0205133\pi\)
\(168\) −6712.18 1367.59i −3.08247 0.628049i
\(169\) −759.101 1314.80i −0.345517 0.598453i
\(170\) 4630.78i 2.08920i
\(171\) 1003.56 487.634i 0.448798 0.218072i
\(172\) 4200.02 1.86191
\(173\) 313.536 + 543.061i 0.137790 + 0.238660i 0.926660 0.375901i \(-0.122667\pi\)
−0.788870 + 0.614561i \(0.789333\pi\)
\(174\) 1745.64 + 3288.94i 0.760555 + 1.43295i
\(175\) −1110.50 914.573i −0.479689 0.395058i
\(176\) 2349.57 + 1356.53i 1.00628 + 0.580977i
\(177\) −888.120 1673.30i −0.377148 0.710579i
\(178\) 1852.08 1069.30i 0.779883 0.450266i
\(179\) 1174.10i 0.490259i 0.969490 + 0.245130i \(0.0788305\pi\)
−0.969490 + 0.245130i \(0.921169\pi\)
\(180\) 2204.38 3257.71i 0.912802 1.34898i
\(181\) 1625.05i 0.667344i 0.942689 + 0.333672i \(0.108288\pi\)
−0.942689 + 0.333672i \(0.891712\pi\)
\(182\) −2440.94 + 913.897i −0.994145 + 0.372212i
\(183\) 64.3405 1804.20i 0.0259901 0.728801i
\(184\) 4014.77 6953.79i 1.60855 2.78609i
\(185\) −510.048 + 883.428i −0.202700 + 0.351086i
\(186\) 2666.28 4259.93i 1.05108 1.67932i
\(187\) 1361.44 786.027i 0.532397 0.307380i
\(188\) 3902.65 1.51399
\(189\) 2516.70 646.130i 0.968588 0.248672i
\(190\) 1535.55 0.586318
\(191\) 113.173 65.3404i 0.0428739 0.0247532i −0.478410 0.878137i \(-0.658787\pi\)
0.521284 + 0.853383i \(0.325453\pi\)
\(192\) −4076.83 + 6513.56i −1.53240 + 2.44831i
\(193\) −570.103 + 987.447i −0.212626 + 0.368280i −0.952536 0.304427i \(-0.901535\pi\)
0.739909 + 0.672707i \(0.234868\pi\)
\(194\) −760.240 + 1316.77i −0.281351 + 0.487314i
\(195\) 33.1898 930.691i 0.0121886 0.341785i
\(196\) −1392.53 7129.24i −0.507481 2.59812i
\(197\) 3462.71i 1.25232i 0.779693 + 0.626162i \(0.215375\pi\)
−0.779693 + 0.626162i \(0.784625\pi\)
\(198\) −1835.07 131.049i −0.658651 0.0470368i
\(199\) 2522.77i 0.898667i 0.893364 + 0.449333i \(0.148338\pi\)
−0.893364 + 0.449333i \(0.851662\pi\)
\(200\) −4788.49 + 2764.63i −1.69299 + 0.977446i
\(201\) 888.342 + 1673.71i 0.311735 + 0.587337i
\(202\) −5168.17 2983.84i −1.80015 1.03932i
\(203\) −1561.92 + 1896.52i −0.540027 + 0.655714i
\(204\) 6429.32 + 12113.4i 2.20658 + 4.15739i
\(205\) −643.994 1115.43i −0.219407 0.380025i
\(206\) 8424.88 2.84946
\(207\) −216.952 + 3037.97i −0.0728466 + 1.02006i
\(208\) 5603.51i 1.86795i
\(209\) −260.643 451.447i −0.0862635 0.149413i
\(210\) 3503.90 + 713.913i 1.15139 + 0.234594i
\(211\) −1033.33 + 1789.77i −0.337143 + 0.583948i −0.983894 0.178753i \(-0.942794\pi\)
0.646751 + 0.762701i \(0.276127\pi\)
\(212\) −6586.92 3802.96i −2.13392 1.23202i
\(213\) −2492.06 1559.78i −0.801658 0.501757i
\(214\) −2003.98 3470.99i −0.640135 1.10875i
\(215\) −1364.27 −0.432756
\(216\) 1065.91 9929.44i 0.335769 3.12784i
\(217\) 3270.83 + 545.817i 1.02322 + 0.170749i
\(218\) 3248.65 1875.61i 1.00930 0.582718i
\(219\) 3246.77 + 2032.15i 1.00181 + 0.627031i
\(220\) −1591.51 918.856i −0.487724 0.281588i
\(221\) 2811.90 + 1623.45i 0.855877 + 0.494141i
\(222\) −148.335 + 4159.52i −0.0448449 + 1.25752i
\(223\) 5321.42 3072.32i 1.59797 0.922591i 0.606097 0.795390i \(-0.292734\pi\)
0.991877 0.127201i \(-0.0405992\pi\)
\(224\) −10820.0 1805.59i −3.22743 0.538575i
\(225\) 1175.38 1737.02i 0.348260 0.514672i
\(226\) −8776.84 −2.58331
\(227\) −455.878 789.603i −0.133294 0.230871i 0.791651 0.610974i \(-0.209222\pi\)
−0.924944 + 0.380103i \(0.875889\pi\)
\(228\) 4016.76 2131.94i 1.16674 0.619259i
\(229\) −2305.74 1331.22i −0.665360 0.384146i 0.128956 0.991650i \(-0.458837\pi\)
−0.794316 + 0.607504i \(0.792171\pi\)
\(230\) −2095.80 + 3630.02i −0.600838 + 1.04068i
\(231\) −384.862 1151.32i −0.109619 0.327927i
\(232\) 4721.49 + 8177.87i 1.33613 + 2.31424i
\(233\) 1984.29i 0.557918i −0.960303 0.278959i \(-0.910011\pi\)
0.960303 0.278959i \(-0.0899894\pi\)
\(234\) −1660.66 3417.69i −0.463936 0.954792i
\(235\) −1267.68 −0.351891
\(236\) −3860.42 6686.45i −1.06480 1.84428i
\(237\) −4689.59 167.238i −1.28532 0.0458365i
\(238\) −7925.78 + 9623.67i −2.15862 + 2.62105i
\(239\) −1544.98 891.996i −0.418145 0.241416i 0.276138 0.961118i \(-0.410945\pi\)
−0.694283 + 0.719702i \(0.744278\pi\)
\(240\) 4078.72 6516.59i 1.09700 1.75268i
\(241\) −5182.09 + 2991.88i −1.38510 + 0.799685i −0.992757 0.120136i \(-0.961667\pi\)
−0.392338 + 0.919821i \(0.628334\pi\)
\(242\) 6330.05i 1.68145i
\(243\) 1282.40 + 3564.32i 0.338542 + 0.940951i
\(244\) 7357.99i 1.93052i
\(245\) 452.328 + 2315.76i 0.117952 + 0.603870i
\(246\) −4454.61 2788.13i −1.15454 0.722622i
\(247\) 538.330 932.414i 0.138677 0.240195i
\(248\) 6372.53 11037.5i 1.63168 2.82615i
\(249\) −3972.47 141.664i −1.01102 0.0360546i
\(250\) 6522.19 3765.59i 1.65000 0.952627i
\(251\) −6093.37 −1.53231 −0.766155 0.642656i \(-0.777833\pi\)
−0.766155 + 0.642656i \(0.777833\pi\)
\(252\) 10156.8 2997.29i 2.53897 0.749251i
\(253\) 1422.96 0.353599
\(254\) 5145.02 2970.48i 1.27097 0.733797i
\(255\) −2088.40 3934.74i −0.512866 0.966285i
\(256\) −2861.40 + 4956.10i −0.698585 + 1.20998i
\(257\) 2276.03 3942.19i 0.552431 0.956838i −0.445668 0.895198i \(-0.647034\pi\)
0.998098 0.0616394i \(-0.0196329\pi\)
\(258\) −4916.83 + 2609.66i −1.18647 + 0.629730i
\(259\) −2572.01 + 962.970i −0.617053 + 0.231027i
\(260\) 3795.59i 0.905355i
\(261\) −2966.51 2007.33i −0.703535 0.476056i
\(262\) 6458.68i 1.52297i
\(263\) −773.268 + 446.447i −0.181300 + 0.104673i −0.587903 0.808931i \(-0.700046\pi\)
0.406604 + 0.913605i \(0.366713\pi\)
\(264\) −4662.74 166.280i −1.08701 0.0387645i
\(265\) 2139.60 + 1235.30i 0.495979 + 0.286353i
\(266\) 3191.17 + 2628.16i 0.735576 + 0.605800i
\(267\) −1091.46 + 1743.83i −0.250174 + 0.399703i
\(268\) 3861.39 + 6688.12i 0.880119 + 1.52441i
\(269\) −1159.42 −0.262792 −0.131396 0.991330i \(-0.541946\pi\)
−0.131396 + 0.991330i \(0.541946\pi\)
\(270\) −556.428 + 5183.38i −0.125419 + 1.16833i
\(271\) 2122.71i 0.475813i 0.971288 + 0.237907i \(0.0764612\pi\)
−0.971288 + 0.237907i \(0.923539\pi\)
\(272\) 13401.7 + 23212.4i 2.98748 + 5.17447i
\(273\) 1661.89 1877.35i 0.368434 0.416200i
\(274\) 3664.64 6347.35i 0.807989 1.39948i
\(275\) −848.594 489.936i −0.186080 0.107434i
\(276\) −442.393 + 12405.4i −0.0964817 + 2.70549i
\(277\) 1721.64 + 2981.97i 0.373442 + 0.646821i 0.990093 0.140416i \(-0.0448440\pi\)
−0.616650 + 0.787237i \(0.711511\pi\)
\(278\) −5164.87 −1.11427
\(279\) −344.362 + 4822.08i −0.0738940 + 1.03473i
\(280\) 8944.97 + 1492.69i 1.90916 + 0.318590i
\(281\) −3015.50 + 1741.00i −0.640178 + 0.369607i −0.784683 0.619897i \(-0.787174\pi\)
0.144505 + 0.989504i \(0.453841\pi\)
\(282\) −4568.71 + 2424.89i −0.964762 + 0.512058i
\(283\) −3071.99 1773.61i −0.645268 0.372546i 0.141373 0.989956i \(-0.454848\pi\)
−0.786641 + 0.617411i \(0.788182\pi\)
\(284\) −10376.9 5991.11i −2.16815 1.25178i
\(285\) −1304.74 + 692.507i −0.271180 + 0.143932i
\(286\) −1537.43 + 887.635i −0.317867 + 0.183521i
\(287\) 570.762 3420.31i 0.117390 0.703465i
\(288\) 1139.17 15951.6i 0.233076 3.26375i
\(289\) 10617.9 2.16119
\(290\) −2464.72 4269.02i −0.499080 0.864433i
\(291\) 52.1267 1461.71i 0.0105008 0.294457i
\(292\) 13519.5 + 7805.48i 2.70948 + 1.56432i
\(293\) −1203.25 + 2084.09i −0.239914 + 0.415542i −0.960689 0.277626i \(-0.910452\pi\)
0.720776 + 0.693168i \(0.243786\pi\)
\(294\) 6059.90 + 7480.73i 1.20211 + 1.48396i
\(295\) 1253.96 + 2171.93i 0.247486 + 0.428659i
\(296\) 10555.5i 2.07272i
\(297\) 1618.35 716.236i 0.316182 0.139933i
\(298\) 1038.74 0.201921
\(299\) 1469.48 + 2545.22i 0.284222 + 0.492286i
\(300\) 4535.09 7245.73i 0.872778 1.39444i
\(301\) −2835.23 2335.01i −0.542922 0.447135i
\(302\) 2880.93 + 1663.30i 0.548936 + 0.316929i
\(303\) 5737.02 + 204.590i 1.08773 + 0.0387901i
\(304\) 7697.13 4443.94i 1.45217 0.838412i
\(305\) 2390.06i 0.448703i
\(306\) −15053.2 10185.9i −2.81220 1.90291i
\(307\) 7862.81i 1.46174i −0.682517 0.730870i \(-0.739114\pi\)
0.682517 0.730870i \(-0.260886\pi\)
\(308\) −1734.80 4633.50i −0.320940 0.857201i
\(309\) −7158.55 + 3799.48i −1.31792 + 0.699498i
\(310\) −3326.60 + 5761.83i −0.609477 + 1.05565i
\(311\) 1367.04 2367.77i 0.249252 0.431718i −0.714066 0.700078i \(-0.753148\pi\)
0.963319 + 0.268360i \(0.0864818\pi\)
\(312\) −4517.76 8511.86i −0.819769 1.54452i
\(313\) 3509.53 2026.23i 0.633771 0.365908i −0.148440 0.988921i \(-0.547425\pi\)
0.782211 + 0.623014i \(0.214092\pi\)
\(314\) 4507.25 0.810060
\(315\) −3299.20 + 973.594i −0.590123 + 0.174145i
\(316\) −19125.3 −3.40470
\(317\) −968.686 + 559.271i −0.171630 + 0.0990909i −0.583354 0.812218i \(-0.698260\pi\)
0.411724 + 0.911309i \(0.364927\pi\)
\(318\) 10074.0 + 359.255i 1.77649 + 0.0633523i
\(319\) −836.721 + 1449.24i −0.146857 + 0.254364i
\(320\) 5086.47 8810.03i 0.888570 1.53905i
\(321\) 3268.12 + 2045.51i 0.568251 + 0.355668i
\(322\) −10568.4 + 3956.86i −1.82905 + 0.684805i
\(323\) 5150.00i 0.887163i
\(324\) 5741.01 + 14331.4i 0.984398 + 2.45738i
\(325\) 2023.82i 0.345419i
\(326\) 15456.5 8923.83i 2.62594 1.51609i
\(327\) −1914.49 + 3058.78i −0.323766 + 0.517281i
\(328\) −11542.0 6663.76i −1.94298 1.12178i
\(329\) −2634.49 2169.69i −0.441472 0.363583i
\(330\) 2434.05 + 86.8018i 0.406030 + 0.0144796i
\(331\) 3521.44 + 6099.32i 0.584761 + 1.01284i 0.994905 + 0.100815i \(0.0321452\pi\)
−0.410144 + 0.912021i \(0.634521\pi\)
\(332\) −16200.7 −2.67810
\(333\) −1749.84 3601.21i −0.287959 0.592628i
\(334\) 10332.9i 1.69278i
\(335\) −1254.28 2172.47i −0.204562 0.354313i
\(336\) 19629.8 6561.85i 3.18719 1.06541i
\(337\) 1296.20 2245.08i 0.209520 0.362900i −0.742043 0.670352i \(-0.766143\pi\)
0.951564 + 0.307452i \(0.0994764\pi\)
\(338\) 7102.09 + 4100.39i 1.14291 + 0.659858i
\(339\) 7457.62 3958.21i 1.19481 0.634161i
\(340\) −9077.74 15723.1i −1.44797 2.50796i
\(341\) 2258.62 0.358684
\(342\) −3377.62 + 4991.58i −0.534037 + 0.789221i
\(343\) −3023.49 + 5586.78i −0.475957 + 0.879468i
\(344\) −12225.6 + 7058.43i −1.91616 + 1.10629i
\(345\) 143.700 4029.57i 0.0224248 0.628826i
\(346\) −2933.42 1693.61i −0.455785 0.263148i
\(347\) −7226.45 4172.19i −1.11797 0.645462i −0.177090 0.984195i \(-0.556668\pi\)
−0.940882 + 0.338733i \(0.890002\pi\)
\(348\) −12374.4 7745.11i −1.90614 1.19305i
\(349\) 9981.26 5762.68i 1.53090 0.883866i 0.531581 0.847008i \(-0.321598\pi\)
0.999320 0.0368588i \(-0.0117352\pi\)
\(350\) 7664.95 + 1279.08i 1.17060 + 0.195343i
\(351\) 2952.38 + 2155.05i 0.448963 + 0.327716i
\(352\) −7471.62 −1.13136
\(353\) 5107.82 + 8847.00i 0.770146 + 1.33393i 0.937482 + 0.348033i \(0.113150\pi\)
−0.167336 + 0.985900i \(0.553516\pi\)
\(354\) 8673.86 + 5428.95i 1.30229 + 0.815101i
\(355\) 3370.68 + 1946.06i 0.503935 + 0.290947i
\(356\) −4192.30 + 7261.28i −0.624134 + 1.08103i
\(357\) 2394.36 11751.6i 0.354966 1.74218i
\(358\) −3171.04 5492.40i −0.468141 0.810844i
\(359\) 6593.91i 0.969396i −0.874682 0.484698i \(-0.838930\pi\)
0.874682 0.484698i \(-0.161070\pi\)
\(360\) −941.753 + 13187.3i −0.137874 + 1.93064i
\(361\) 5151.28 0.751025
\(362\) −4388.98 7601.93i −0.637236 1.10373i
\(363\) 2854.75 + 5378.60i 0.412770 + 0.777695i
\(364\) 6496.32 7887.98i 0.935438 1.13583i
\(365\) −4391.47 2535.41i −0.629753 0.363588i
\(366\) 4571.85 + 8613.76i 0.652935 + 1.23019i
\(367\) −4531.96 + 2616.53i −0.644595 + 0.372157i −0.786382 0.617740i \(-0.788048\pi\)
0.141787 + 0.989897i \(0.454715\pi\)
\(368\) 24261.3i 3.43670i
\(369\) 5042.45 + 360.100i 0.711381 + 0.0508023i
\(370\) 5510.19i 0.774219i
\(371\) 2332.24 + 6229.21i 0.326372 + 0.871710i
\(372\) −702.198 + 19690.7i −0.0978690 + 2.74439i
\(373\) 4889.02 8468.04i 0.678670 1.17549i −0.296711 0.954967i \(-0.595890\pi\)
0.975381 0.220524i \(-0.0707768\pi\)
\(374\) −4245.84 + 7354.00i −0.587024 + 1.01676i
\(375\) −3843.64 + 6140.99i −0.529292 + 0.845652i
\(376\) −11360.0 + 6558.69i −1.55810 + 0.899571i
\(377\) −3456.31 −0.472172
\(378\) −10027.9 + 9819.73i −1.36450 + 1.33617i
\(379\) −3637.54 −0.493002 −0.246501 0.969143i \(-0.579281\pi\)
−0.246501 + 0.969143i \(0.579281\pi\)
\(380\) −5213.72 + 3010.14i −0.703837 + 0.406361i
\(381\) −3032.05 + 4844.31i −0.407707 + 0.651395i
\(382\) −352.946 + 611.320i −0.0472730 + 0.0818792i
\(383\) 4495.26 7786.02i 0.599731 1.03876i −0.393129 0.919483i \(-0.628608\pi\)
0.992860 0.119281i \(-0.0380591\pi\)
\(384\) 601.784 16874.9i 0.0799731 2.24256i
\(385\) 563.506 + 1505.08i 0.0745947 + 0.199236i
\(386\) 6158.98i 0.812134i
\(387\) 3000.88 4434.81i 0.394168 0.582517i
\(388\) 5961.21i 0.779987i
\(389\) −4843.12 + 2796.17i −0.631249 + 0.364452i −0.781236 0.624236i \(-0.785410\pi\)
0.149987 + 0.988688i \(0.452077\pi\)
\(390\) 2358.37 + 4443.37i 0.306207 + 0.576920i
\(391\) 12174.6 + 7028.99i 1.57466 + 0.909133i
\(392\) 16034.6 + 18411.8i 2.06600 + 2.37229i
\(393\) −2912.76 5487.89i −0.373865 0.704395i
\(394\) −9352.16 16198.4i −1.19583 2.07123i
\(395\) 6212.39 0.791339
\(396\) 6487.61 3152.35i 0.823270 0.400029i
\(397\) 11561.7i 1.46163i −0.682575 0.730815i \(-0.739140\pi\)
0.682575 0.730815i \(-0.260860\pi\)
\(398\) −6813.56 11801.4i −0.858123 1.48631i
\(399\) −3896.77 793.960i −0.488928 0.0996183i
\(400\) 8353.35 14468.4i 1.04417 1.80855i
\(401\) 3685.19 + 2127.65i 0.458927 + 0.264962i 0.711593 0.702592i \(-0.247974\pi\)
−0.252666 + 0.967554i \(0.581307\pi\)
\(402\) −8676.03 5430.32i −1.07642 0.673730i
\(403\) 2332.46 + 4039.95i 0.288308 + 0.499365i
\(404\) 23397.0 2.88130
\(405\) −1864.82 4655.21i −0.228800 0.571159i
\(406\) 2184.44 13090.3i 0.267025 1.60015i
\(407\) −1619.98 + 935.298i −0.197296 + 0.113909i
\(408\) −39072.1 24455.2i −4.74108 2.96743i
\(409\) 4853.21 + 2802.00i 0.586738 + 0.338753i 0.763807 0.645445i \(-0.223328\pi\)
−0.177068 + 0.984199i \(0.556661\pi\)
\(410\) 6025.16 + 3478.63i 0.725759 + 0.419017i
\(411\) −251.270 + 7045.98i −0.0301563 + 0.845627i
\(412\) −28605.4 + 16515.3i −3.42060 + 1.97488i
\(413\) −1111.37 + 6659.90i −0.132413 + 0.793492i
\(414\) −7190.11 14797.4i −0.853562 1.75665i
\(415\) 5262.40 0.622460
\(416\) −7715.90 13364.3i −0.909382 1.57510i
\(417\) 4388.55 2329.27i 0.515367 0.273537i
\(418\) 2438.56 + 1407.90i 0.285344 + 0.164743i
\(419\) −2039.72 + 3532.89i −0.237820 + 0.411917i −0.960089 0.279696i \(-0.909766\pi\)
0.722268 + 0.691613i \(0.243100\pi\)
\(420\) −13296.5 + 4444.73i −1.54476 + 0.516382i
\(421\) 8228.54 + 14252.3i 0.952576 + 1.64991i 0.739820 + 0.672805i \(0.234911\pi\)
0.212756 + 0.977105i \(0.431756\pi\)
\(422\) 11163.3i 1.28773i
\(423\) 2788.41 4120.83i 0.320514 0.473668i
\(424\) 25564.6 2.92813
\(425\) −4840.27 8383.60i −0.552441 0.956857i
\(426\) 15870.4 + 565.963i 1.80499 + 0.0643685i
\(427\) −4090.69 + 4967.02i −0.463612 + 0.562929i
\(428\) 13608.4 + 7856.81i 1.53688 + 0.887321i
\(429\) 906.033 1447.57i 0.101967 0.162912i
\(430\) 6382.01 3684.65i 0.715739 0.413232i
\(431\) 354.675i 0.0396382i −0.999804 0.0198191i \(-0.993691\pi\)
0.999804 0.0198191i \(-0.00630903\pi\)
\(432\) 12211.7 + 27592.7i 1.36004 + 3.07304i
\(433\) 3100.88i 0.344155i 0.985083 + 0.172077i \(0.0550479\pi\)
−0.985083 + 0.172077i \(0.944952\pi\)
\(434\) −16775.0 + 6280.61i −1.85535 + 0.694652i
\(435\) 4019.51 + 2515.81i 0.443036 + 0.277296i
\(436\) −7353.55 + 12736.7i −0.807732 + 1.39903i
\(437\) 2330.78 4037.04i 0.255141 0.441917i
\(438\) −20676.7 737.362i −2.25564 0.0804395i
\(439\) −13194.9 + 7618.07i −1.43453 + 0.828224i −0.997462 0.0712055i \(-0.977315\pi\)
−0.437065 + 0.899430i \(0.643982\pi\)
\(440\) 6176.82 0.669246
\(441\) −8522.74 3623.41i −0.920283 0.391254i
\(442\) −17538.6 −1.88739
\(443\) 9086.84 5246.29i 0.974557 0.562661i 0.0739349 0.997263i \(-0.476444\pi\)
0.900623 + 0.434602i \(0.143111\pi\)
\(444\) −7650.28 14413.8i −0.817717 1.54065i
\(445\) 1361.77 2358.65i 0.145065 0.251260i
\(446\) −16595.6 + 28744.4i −1.76194 + 3.05176i
\(447\) −882.607 + 468.453i −0.0933912 + 0.0495684i
\(448\) 25649.4 9603.26i 2.70496 1.01275i
\(449\) 13387.2i 1.40708i 0.710656 + 0.703540i \(0.248398\pi\)
−0.710656 + 0.703540i \(0.751602\pi\)
\(450\) −806.989 + 11300.2i −0.0845374 + 1.18377i
\(451\) 2361.84i 0.246596i
\(452\) 29800.5 17205.3i 3.10110 1.79042i
\(453\) −3198.02 114.046i −0.331692 0.0118286i
\(454\) 4265.16 + 2462.49i 0.440911 + 0.254560i
\(455\) −2110.17 + 2562.21i −0.217420 + 0.263997i
\(456\) −8109.25 + 12956.2i −0.832786 + 1.33054i
\(457\) −8043.99 13932.6i −0.823374 1.42613i −0.903156 0.429313i \(-0.858756\pi\)
0.0797820 0.996812i \(-0.474578\pi\)
\(458\) 14381.5 1.46726
\(459\) 17384.3 + 1866.18i 1.76782 + 0.189773i
\(460\) 16433.6i 1.66570i
\(461\) −9398.54 16278.7i −0.949530 1.64463i −0.746416 0.665480i \(-0.768227\pi\)
−0.203115 0.979155i \(-0.565106\pi\)
\(462\) 4909.87 + 4346.38i 0.494433 + 0.437688i
\(463\) −108.245 + 187.487i −0.0108652 + 0.0188191i −0.871407 0.490561i \(-0.836792\pi\)
0.860542 + 0.509380i \(0.170125\pi\)
\(464\) −24709.4 14266.0i −2.47221 1.42733i
\(465\) 228.091 6396.02i 0.0227473 0.637868i
\(466\) 5359.20 + 9282.42i 0.532748 + 0.922746i
\(467\) −15356.4 −1.52165 −0.760826 0.648956i \(-0.775206\pi\)
−0.760826 + 0.648956i \(0.775206\pi\)
\(468\) 12338.3 + 8348.84i 1.21867 + 0.824627i
\(469\) 1111.65 6661.57i 0.109448 0.655869i
\(470\) 5930.16 3423.78i 0.581995 0.336015i
\(471\) −3829.77 + 2032.69i −0.374664 + 0.198857i
\(472\) 22474.1 + 12975.4i 2.19164 + 1.26535i
\(473\) −2166.56 1250.86i −0.210610 0.121596i
\(474\) 22389.4 11883.4i 2.16958 1.15153i
\(475\) −2779.97 + 1605.01i −0.268534 + 0.155038i
\(476\) 8045.46 48212.7i 0.774712 4.64249i
\(477\) −8721.85 + 4237.97i −0.837204 + 0.406799i
\(478\) 9636.49 0.922098
\(479\) 8696.60 + 15063.0i 0.829557 + 1.43683i 0.898386 + 0.439206i \(0.144740\pi\)
−0.0688295 + 0.997628i \(0.521926\pi\)
\(480\) −754.537 + 21158.3i −0.0717494 + 2.01196i
\(481\) −3345.89 1931.75i −0.317172 0.183119i
\(482\) 16161.1 27991.8i 1.52721 2.64521i
\(483\) 7195.43 8128.30i 0.677854 0.765736i
\(484\) 12408.8 + 21492.7i 1.16537 + 2.01848i
\(485\) 1936.35i 0.181289i
\(486\) −15625.6 13210.2i −1.45842 1.23298i
\(487\) −14133.8 −1.31512 −0.657560 0.753402i \(-0.728412\pi\)
−0.657560 + 0.753402i \(0.728412\pi\)
\(488\) 12365.6 + 21417.9i 1.14706 + 1.98677i
\(489\) −9108.79 + 14553.1i −0.842359 + 1.34584i
\(490\) −8370.41 9611.36i −0.771708 0.886116i
\(491\) −7929.45 4578.07i −0.728821 0.420785i 0.0891699 0.996016i \(-0.471579\pi\)
−0.817991 + 0.575232i \(0.804912\pi\)
\(492\) 20590.6 + 734.289i 1.88678 + 0.0672852i
\(493\) −14317.7 + 8266.30i −1.30798 + 0.755163i
\(494\) 5815.73i 0.529680i
\(495\) −2107.34 + 1023.96i −0.191349 + 0.0929770i
\(496\) 38509.2i 3.48612i
\(497\) 3674.16 + 9813.36i 0.331607 + 0.885693i
\(498\) 18965.6 10066.2i 1.70657 0.905780i
\(499\) −7528.00 + 13038.9i −0.675349 + 1.16974i 0.301017 + 0.953619i \(0.402674\pi\)
−0.976367 + 0.216121i \(0.930659\pi\)
\(500\) −14763.4 + 25571.0i −1.32048 + 2.28714i
\(501\) −4659.95 8779.75i −0.415551 0.782935i
\(502\) 28504.5 16457.1i 2.53430 1.46318i
\(503\) −13644.2 −1.20948 −0.604739 0.796424i \(-0.706722\pi\)
−0.604739 + 0.796424i \(0.706722\pi\)
\(504\) −24527.8 + 25793.9i −2.16777 + 2.27967i
\(505\) −7599.93 −0.669688
\(506\) −6656.54 + 3843.16i −0.584821 + 0.337647i
\(507\) −7883.80 281.148i −0.690595 0.0246276i
\(508\) −11646.1 + 20171.6i −1.01715 + 1.76175i
\(509\) 442.839 767.020i 0.0385629 0.0667929i −0.846100 0.533025i \(-0.821055\pi\)
0.884663 + 0.466232i \(0.154389\pi\)
\(510\) 20396.5 + 12766.1i 1.77093 + 1.10842i
\(511\) −4786.86 12785.3i −0.414400 1.10683i
\(512\) 4915.40i 0.424281i
\(513\) 618.817 5764.55i 0.0532581 0.496123i
\(514\) 24588.6i 2.11003i
\(515\) 9291.75 5364.60i 0.795036 0.459014i
\(516\) 11578.6 18499.2i 0.987829 1.57826i
\(517\) −2013.17 1162.30i −0.171255 0.0988742i
\(518\) 9430.94 11451.3i 0.799945 0.971312i
\(519\) 3256.30 + 116.124i 0.275406 + 0.00982137i
\(520\) 6378.76 + 11048.3i 0.537937 + 0.931734i
\(521\) 8268.31 0.695281 0.347641 0.937628i \(-0.386983\pi\)
0.347641 + 0.937628i \(0.386983\pi\)
\(522\) 19298.7 + 1378.19i 1.61816 + 0.115559i
\(523\) 1489.91i 0.124568i 0.998058 + 0.0622841i \(0.0198385\pi\)
−0.998058 + 0.0622841i \(0.980162\pi\)
\(524\) −12661.0 21929.5i −1.05553 1.82823i
\(525\) −7089.70 + 2369.94i −0.589371 + 0.197015i
\(526\) 2411.55 4176.92i 0.199902 0.346240i
\(527\) 19324.3 + 11156.9i 1.59731 + 0.922206i
\(528\) 12452.2 6609.14i 1.02635 0.544746i
\(529\) 278.849 + 482.981i 0.0229185 + 0.0396960i
\(530\) −13345.3 −1.09374
\(531\) −9818.48 701.174i −0.802421 0.0573039i
\(532\) −15987.1 2667.84i −1.30288 0.217417i
\(533\) 4224.58 2439.06i 0.343315 0.198213i
\(534\) 396.035 11105.4i 0.0320939 0.899959i
\(535\) −4420.35 2552.09i −0.357212 0.206236i
\(536\) −22479.7 12978.7i −1.81152 1.04588i
\(537\) 5171.39 + 3236.76i 0.415571 + 0.260105i
\(538\) 5423.72 3131.39i 0.434634 0.250936i
\(539\) −1404.93 + 4092.31i −0.112272 + 0.327028i
\(540\) −8271.74 18690.1i −0.659183 1.48944i
\(541\) 668.496 0.0531255 0.0265628 0.999647i \(-0.491544\pi\)
0.0265628 + 0.999647i \(0.491544\pi\)
\(542\) −5733.06 9929.95i −0.454347 0.786952i
\(543\) 7157.62 + 4479.95i 0.565678 + 0.354057i
\(544\) −63925.7 36907.5i −5.03822 2.90882i
\(545\) 2388.62 4137.20i 0.187738 0.325171i
\(546\) −2703.87 + 13270.7i −0.211932 + 1.04017i
\(547\) −10234.9 17727.3i −0.800022 1.38568i −0.919601 0.392855i \(-0.871488\pi\)
0.119578 0.992825i \(-0.461846\pi\)
\(548\) 28735.3i 2.23998i
\(549\) −7769.33 5257.22i −0.603983 0.408693i
\(550\) 5292.92 0.410347
\(551\) 2741.07 + 4747.68i 0.211930 + 0.367074i
\(552\) −19560.4 36853.5i −1.50823 2.84164i
\(553\) 12910.6 + 10632.8i 0.992790 + 0.817634i
\(554\) −16107.6 9299.70i −1.23528 0.713189i
\(555\) 2485.00 + 4681.97i 0.190059 + 0.358087i
\(556\) 17536.5 10124.7i 1.33762 0.772273i
\(557\) 18144.3i 1.38025i 0.723692 + 0.690123i \(0.242444\pi\)
−0.723692 + 0.690123i \(0.757556\pi\)
\(558\) −11412.7 23487.5i −0.865835 1.78191i
\(559\) 5167.04i 0.390952i
\(560\) −25661.4 + 9607.72i −1.93641 + 0.725000i
\(561\) 291.120 8163.44i 0.0219093 0.614368i
\(562\) 9404.27 16288.7i 0.705864 1.22259i
\(563\) 2055.50 3560.22i 0.153870 0.266511i −0.778777 0.627301i \(-0.784160\pi\)
0.932647 + 0.360790i \(0.117493\pi\)
\(564\) 10758.8 17189.4i 0.803243 1.28334i
\(565\) −9679.93 + 5588.71i −0.720775 + 0.416140i
\(566\) 19160.9 1.42295
\(567\) 4092.13 12866.2i 0.303092 0.952961i
\(568\) 40274.0 2.97510
\(569\) −16501.7 + 9527.28i −1.21580 + 0.701941i −0.964016 0.265843i \(-0.914350\pi\)
−0.251781 + 0.967784i \(0.581016\pi\)
\(570\) 4233.20 6763.40i 0.311069 0.496996i
\(571\) 4482.05 7763.14i 0.328491 0.568962i −0.653722 0.756735i \(-0.726793\pi\)
0.982213 + 0.187772i \(0.0601268\pi\)
\(572\) 3480.07 6027.66i 0.254387 0.440611i
\(573\) 24.2001 678.606i 0.00176435 0.0494750i
\(574\) 6567.64 + 17541.6i 0.477575 + 1.27556i
\(575\) 8762.43i 0.635511i
\(576\) 17450.3 + 35913.2i 1.26232 + 2.59789i
\(577\) 13608.3i 0.981840i −0.871205 0.490920i \(-0.836661\pi\)
0.871205 0.490920i \(-0.163339\pi\)
\(578\) −49670.3 + 28677.2i −3.57442 + 2.06369i
\(579\) 2777.60 + 5233.24i 0.199366 + 0.375623i
\(580\) 16737.2 + 9663.21i 1.19823 + 0.691798i
\(581\) 10936.3 + 9006.83i 0.780919 + 0.643143i
\(582\) 3703.97 + 6978.60i 0.263805 + 0.497032i
\(583\) 2265.22 + 3923.48i 0.160919 + 0.278720i
\(584\) −52470.7 −3.71790
\(585\) −4007.77 2711.91i −0.283250 0.191665i
\(586\) 12999.1i 0.916359i
\(587\) 4471.37 + 7744.64i 0.314401 + 0.544558i 0.979310 0.202366i \(-0.0648631\pi\)
−0.664909 + 0.746924i \(0.731530\pi\)
\(588\) −35240.0 13520.4i −2.47155 0.948254i
\(589\) 3699.59 6407.87i 0.258809 0.448271i
\(590\) −11732.0 6773.45i −0.818640 0.472642i
\(591\) 15251.7 + 9546.00i 1.06154 + 0.664416i
\(592\) −15946.7 27620.5i −1.10710 1.91756i
\(593\) 19338.8 1.33921 0.669604 0.742719i \(-0.266464\pi\)
0.669604 + 0.742719i \(0.266464\pi\)
\(594\) −5636.14 + 7721.39i −0.389316 + 0.533355i
\(595\) −2613.37 + 15660.7i −0.180063 + 1.07903i
\(596\) −3526.88 + 2036.24i −0.242393 + 0.139946i
\(597\) 11111.7 + 6954.78i 0.761760 + 0.476784i
\(598\) −13748.3 7937.61i −0.940153 0.542798i
\(599\) 7181.37 + 4146.16i 0.489854 + 0.282817i 0.724514 0.689260i \(-0.242064\pi\)
−0.234660 + 0.972078i \(0.575398\pi\)
\(600\) −1023.94 + 28712.7i −0.0696700 + 1.95365i
\(601\) 16063.4 9274.20i 1.09025 0.629455i 0.156606 0.987661i \(-0.449945\pi\)
0.933643 + 0.358206i \(0.116611\pi\)
\(602\) 19569.5 + 3265.65i 1.32491 + 0.221093i
\(603\) 9820.94 + 701.350i 0.663250 + 0.0473651i
\(604\) −13042.3 −0.878618
\(605\) −4030.70 6981.38i −0.270862 0.469146i
\(606\) −27390.1 + 14537.6i −1.83605 + 0.974504i
\(607\) −4155.60 2399.24i −0.277876 0.160432i 0.354586 0.935024i \(-0.384622\pi\)
−0.632461 + 0.774592i \(0.717955\pi\)
\(608\) −12238.4 + 21197.5i −0.816336 + 1.41394i
\(609\) 4047.42 + 12107.9i 0.269310 + 0.805644i
\(610\) −6455.12 11180.6i −0.428460 0.742114i
\(611\) 4801.21i 0.317899i
\(612\) 71078.4 + 5075.97i 4.69473 + 0.335268i
\(613\) −19326.3 −1.27338 −0.636690 0.771120i \(-0.719697\pi\)
−0.636690 + 0.771120i \(0.719697\pi\)
\(614\) 21236.0 + 36781.9i 1.39579 + 2.41758i
\(615\) −6688.33 238.516i −0.438536 0.0156388i
\(616\) 12836.6 + 10571.9i 0.839616 + 0.691483i
\(617\) 18359.9 + 10600.1i 1.19796 + 0.691642i 0.960100 0.279658i \(-0.0902211\pi\)
0.237859 + 0.971300i \(0.423554\pi\)
\(618\) 23225.7 37107.8i 1.51177 2.41536i
\(619\) −3393.65 + 1959.33i −0.220359 + 0.127224i −0.606117 0.795376i \(-0.707274\pi\)
0.385757 + 0.922600i \(0.373940\pi\)
\(620\) 26084.6i 1.68965i
\(621\) 12782.8 + 9330.64i 0.826015 + 0.602940i
\(622\) 14768.5i 0.952029i
\(623\) 6866.95 2571.01i 0.441603 0.165338i
\(624\) 24680.9 + 15447.7i 1.58338 + 0.991034i
\(625\) −59.3801 + 102.849i −0.00380033 + 0.00658236i
\(626\) −10945.0 + 18957.2i −0.698799 + 1.21036i
\(627\) −2706.96 96.5343i −0.172417 0.00614866i
\(628\) −15303.7 + 8835.58i −0.972426 + 0.561430i
\(629\) −18480.4 −1.17148
\(630\) 12804.0 13465.0i 0.809721 0.851520i
\(631\) −5823.13 −0.367378 −0.183689 0.982984i \(-0.558804\pi\)
−0.183689 + 0.982984i \(0.558804\pi\)
\(632\) 55670.7 32141.5i 3.50390 2.02297i
\(633\) 5034.47 + 9485.39i 0.316117 + 0.595593i
\(634\) 3020.98 5232.50i 0.189241 0.327774i
\(635\) 3782.94 6552.25i 0.236412 0.409477i
\(636\) −34909.1 + 18528.4i −2.17647 + 1.15519i
\(637\) −8770.69 + 1713.14i −0.545537 + 0.106558i
\(638\) 9039.34i 0.560926i
\(639\) −13740.2 + 6676.41i −0.850634 + 0.413325i
\(640\) 22354.5i 1.38069i
\(641\) 18914.5 10920.3i 1.16549 0.672894i 0.212874 0.977080i \(-0.431718\pi\)
0.952613 + 0.304186i \(0.0983844\pi\)
\(642\) −20812.7 742.211i −1.27946 0.0456273i
\(643\) 21222.1 + 12252.6i 1.30158 + 0.751470i 0.980676 0.195640i \(-0.0626783\pi\)
0.320909 + 0.947110i \(0.396012\pi\)
\(644\) 28126.8 34152.3i 1.72104 2.08973i
\(645\) −3761.02 + 6009.00i −0.229597 + 0.366828i
\(646\) 13909.2 + 24091.5i 0.847138 + 1.46729i
\(647\) −1181.15 −0.0717709 −0.0358855 0.999356i \(-0.511425\pi\)
−0.0358855 + 0.999356i \(0.511425\pi\)
\(648\) −40796.2 32068.3i −2.47319 1.94408i
\(649\) 4598.89i 0.278155i
\(650\) 5465.96 + 9467.33i 0.329835 + 0.571291i
\(651\) 11421.1 12901.8i 0.687601 0.776746i
\(652\) −34986.9 + 60599.0i −2.10152 + 3.63994i
\(653\) −19828.3 11447.9i −1.18827 0.686050i −0.230360 0.973106i \(-0.573990\pi\)
−0.957914 + 0.287056i \(0.907324\pi\)
\(654\) 694.669 19479.5i 0.0415347 1.16470i
\(655\) 4112.60 + 7123.24i 0.245332 + 0.424928i
\(656\) 40269.1 2.39672
\(657\) 17901.4 8698.32i 1.06301 0.516520i
\(658\) 18184.0 + 3034.44i 1.07733 + 0.179779i
\(659\) −27.2112 + 15.7104i −0.00160849 + 0.000928663i −0.500804 0.865561i \(-0.666962\pi\)
0.499196 + 0.866489i \(0.333629\pi\)
\(660\) −8434.61 + 4476.76i −0.497450 + 0.264027i
\(661\) −9789.93 5652.22i −0.576073 0.332596i 0.183498 0.983020i \(-0.441258\pi\)
−0.759571 + 0.650424i \(0.774591\pi\)
\(662\) −32946.3 19021.6i −1.93428 1.11676i
\(663\) 14902.4 7909.62i 0.872944 0.463324i
\(664\) 47157.6 27226.5i 2.75613 1.59125i
\(665\) 5193.02 + 866.582i 0.302822 + 0.0505333i
\(666\) 17911.9 + 12120.3i 1.04215 + 0.705184i
\(667\) −14964.6 −0.868715
\(668\) −20255.6 35083.7i −1.17322 2.03208i
\(669\) 1137.89 31908.2i 0.0657601 1.84401i
\(670\) 11734.9 + 6775.15i 0.676655 + 0.390667i
\(671\) −2191.38 + 3795.58i −0.126076 + 0.218371i
\(672\) −37781.5 + 42679.8i −2.16883 + 2.45001i
\(673\) 4328.66 + 7497.46i 0.247931 + 0.429429i 0.962952 0.269674i \(-0.0869161\pi\)
−0.715021 + 0.699103i \(0.753583\pi\)
\(674\) 14003.2i 0.800271i
\(675\) −4410.51 9965.62i −0.251497 0.568262i
\(676\) −32152.1 −1.82932
\(677\) −10348.5 17924.2i −0.587483 1.01755i −0.994561 0.104156i \(-0.966786\pi\)
0.407078 0.913393i \(-0.366548\pi\)
\(678\) −24196.0 + 38658.0i −1.37056 + 2.18975i
\(679\) −3314.15 + 4024.12i −0.187313 + 0.227440i
\(680\) 52847.7 + 30511.6i 2.98032 + 1.72069i
\(681\) −4734.61 168.843i −0.266418 0.00950085i
\(682\) −10565.7 + 6100.13i −0.593230 + 0.342502i
\(683\) 20058.0i 1.12372i −0.827233 0.561859i \(-0.810086\pi\)
0.827233 0.561859i \(-0.189914\pi\)
\(684\) 1683.17 23569.3i 0.0940902 1.31754i
\(685\) 9333.94i 0.520630i
\(686\) −945.108 34300.6i −0.0526012 1.90904i
\(687\) −12219.9 + 6485.83i −0.678628 + 0.360189i
\(688\) 21327.1 36939.6i 1.18181 2.04696i
\(689\) −4678.56 + 8103.50i −0.258692 + 0.448068i
\(690\) 10210.9 + 19238.3i 0.563367 + 1.06143i
\(691\) 4672.42 2697.62i 0.257232 0.148513i −0.365839 0.930678i \(-0.619218\pi\)
0.623071 + 0.782165i \(0.285885\pi\)
\(692\) 13280.0 0.729522
\(693\) −6132.02 1478.81i −0.336127 0.0810612i
\(694\) 45073.4 2.46537
\(695\) −5696.30 + 3288.76i −0.310897 + 0.179496i
\(696\) 49036.0 + 1748.70i 2.67055 + 0.0952358i
\(697\) 11666.8 20207.5i 0.634019 1.09815i
\(698\) −31128.0 + 53915.2i −1.68798 + 2.92367i
\(699\) −8739.89 5470.28i −0.472923 0.296002i
\(700\) −28532.6 + 10682.7i −1.54061 + 0.576812i
\(701\) 18702.4i 1.00767i −0.863799 0.503837i \(-0.831921\pi\)
0.863799 0.503837i \(-0.168079\pi\)
\(702\) −19631.5 2107.41i −1.05547 0.113304i
\(703\) 6128.01i 0.328766i
\(704\) 16155.4 9327.30i 0.864883 0.499340i
\(705\) −3494.74 + 5583.56i −0.186694 + 0.298282i
\(706\) −47788.3 27590.6i −2.54750 1.47080i
\(707\) −15794.2 13007.6i −0.840170 0.691940i
\(708\) −40093.2 1429.78i −2.12824 0.0758962i
\(709\) −9346.71 16189.0i −0.495096 0.857531i 0.504888 0.863185i \(-0.331534\pi\)
−0.999984 + 0.00565368i \(0.998200\pi\)
\(710\) −21023.9 −1.11128
\(711\) −13664.9 + 20194.5i −0.720778 + 1.06519i
\(712\) 28181.9i 1.48337i
\(713\) 10098.8 + 17491.6i 0.530438 + 0.918745i
\(714\) 20538.1 + 61440.0i 1.07650 + 3.22036i
\(715\) −1130.41 + 1957.94i −0.0591260 + 0.102409i
\(716\) 21533.6 + 12432.4i 1.12395 + 0.648912i
\(717\) −8188.05 + 4345.90i −0.426483 + 0.226360i
\(718\) 17809.0 + 30846.0i 0.925661 + 1.60329i
\(719\) 18386.7 0.953697 0.476848 0.878986i \(-0.341779\pi\)
0.476848 + 0.878986i \(0.341779\pi\)
\(720\) −17458.4 35929.9i −0.903662 1.85976i
\(721\) 28491.8 + 4754.56i 1.47169 + 0.245588i
\(722\) −24097.5 + 13912.7i −1.24213 + 0.717142i
\(723\) −1108.10 + 31072.8i −0.0569996 + 1.59835i
\(724\) 29804.2 + 17207.5i 1.52992 + 0.883302i
\(725\) 8924.29 + 5152.44i 0.457159 + 0.263941i
\(726\) −27881.0 17450.7i −1.42529 0.892088i
\(727\) 1268.25 732.227i 0.0647000 0.0373546i −0.467301 0.884098i \(-0.654774\pi\)
0.532001 + 0.846744i \(0.321440\pi\)
\(728\) −5653.40 + 33878.2i −0.287814 + 1.72474i
\(729\) 19234.5 + 4177.74i 0.977215 + 0.212251i
\(730\) 27390.8 1.38874
\(731\) −12357.8 21404.3i −0.625265 1.08299i
\(732\) −32408.6 20284.5i −1.63642 1.02423i
\(733\) −5272.89 3044.31i −0.265701 0.153402i 0.361231 0.932476i \(-0.382356\pi\)
−0.626932 + 0.779074i \(0.715690\pi\)
\(734\) 14133.5 24480.0i 0.710734 1.23103i
\(735\) 11446.8 + 4391.78i 0.574453 + 0.220399i
\(736\) −33407.2 57863.0i −1.67311 2.89790i
\(737\) 4600.05i 0.229912i
\(738\) −24560.9 + 11934.2i −1.22507 + 0.595264i
\(739\) 239.229 0.0119082 0.00595412 0.999982i \(-0.498105\pi\)
0.00595412 + 0.999982i \(0.498105\pi\)
\(740\) 10801.7 + 18709.0i 0.536590 + 0.929402i
\(741\) −2622.80 4941.58i −0.130028 0.244984i
\(742\) −27734.1 22841.0i −1.37217 1.13008i
\(743\) 5720.45 + 3302.70i 0.282454 + 0.163075i 0.634534 0.772895i \(-0.281192\pi\)
−0.352080 + 0.935970i \(0.614526\pi\)
\(744\) −31047.6 58496.4i −1.52992 2.88250i
\(745\) 1145.62 661.423i 0.0563385 0.0325271i
\(746\) 52817.5i 2.59221i
\(747\) −11575.3 + 17106.4i −0.566957 + 0.837871i
\(748\) 33292.5i 1.62740i
\(749\) −4818.34 12869.4i −0.235058 0.627819i
\(750\) 1394.66 39108.3i 0.0679009 1.90404i
\(751\) −16064.2 + 27824.1i −0.780549 + 1.35195i 0.151073 + 0.988523i \(0.451727\pi\)
−0.931622 + 0.363428i \(0.881606\pi\)
\(752\) 19817.1 34324.2i 0.960978 1.66446i
\(753\) −16798.2 + 26838.5i −0.812962 + 1.29887i
\(754\) 16168.5 9334.87i 0.780930 0.450870i
\(755\) 4236.48 0.204214
\(756\) 14798.7 52999.3i 0.711936 2.54969i
\(757\) 37994.5 1.82422 0.912109 0.409948i \(-0.134453\pi\)
0.912109 + 0.409948i \(0.134453\pi\)
\(758\) 17016.3 9824.34i 0.815380 0.470760i
\(759\) 3922.81 6267.49i 0.187601 0.299731i
\(760\) 10117.5 17524.1i 0.482896 0.836401i
\(761\) −2352.30 + 4074.31i −0.112051 + 0.194078i −0.916597 0.399812i \(-0.869075\pi\)
0.804546 + 0.593890i \(0.202409\pi\)
\(762\) 1100.17 30850.5i 0.0523033 1.46666i
\(763\) 12045.0 4509.71i 0.571506 0.213974i
\(764\) 2767.53i 0.131054i
\(765\) −23088.1 1648.80i −1.09118 0.0779250i
\(766\) 48563.6i 2.29070i
\(767\) −8225.95 + 4749.25i −0.387251 + 0.223580i
\(768\) 13941.1 + 26266.2i 0.655019 + 1.23411i
\(769\) 9940.18 + 5738.97i 0.466128 + 0.269119i 0.714617 0.699516i \(-0.246601\pi\)
−0.248490 + 0.968635i \(0.579934\pi\)
\(770\) −6701.00 5518.75i −0.313620 0.258288i
\(771\) −11089.0 20892.7i −0.517979 0.975918i
\(772\) 12073.5 + 20911.9i 0.562868 + 0.974916i
\(773\) 22568.8 1.05012 0.525059 0.851066i \(-0.324043\pi\)
0.525059 + 0.851066i \(0.324043\pi\)
\(774\) −2060.34 + 28850.7i −0.0956812 + 1.33982i
\(775\) 13908.4i 0.644649i
\(776\) 10018.3 + 17352.1i 0.463446 + 0.802713i
\(777\) −2849.06 + 13983.2i −0.131544 + 0.645619i
\(778\) 15103.9 26160.8i 0.696018 1.20554i
\(779\) −6700.72 3868.66i −0.308188 0.177932i
\(780\) −16717.9 10463.7i −0.767430 0.480333i
\(781\) 3568.58 + 6180.97i 0.163501 + 0.283191i
\(782\) −75936.1 −3.47247
\(783\) −17019.5 + 7532.34i −0.776790 + 0.343785i
\(784\) −69773.4 23953.8i −3.17845 1.09119i
\(785\) 4971.02 2870.02i 0.226017 0.130491i
\(786\) 28447.6 + 17805.3i 1.29096 + 0.808007i
\(787\) 1440.47 + 831.659i 0.0652445 + 0.0376689i 0.532267 0.846576i \(-0.321340\pi\)
−0.467023 + 0.884245i \(0.654673\pi\)
\(788\) 63507.7 + 36666.2i 2.87103 + 1.65759i
\(789\) −165.350 + 4636.66i −0.00746086 + 0.209214i
\(790\) −29061.3 + 16778.5i −1.30880 + 0.755638i
\(791\) −29682.1 4953.19i −1.33423 0.222649i
\(792\) −13586.6 + 20078.9i −0.609571 + 0.900848i
\(793\) −9052.11 −0.405359
\(794\) 31226.2 + 54085.4i 1.39569 + 2.41740i
\(795\) 11339.4 6018.49i 0.505869 0.268495i
\(796\) 46268.8 + 26713.3i 2.06025 + 1.18948i
\(797\) −5493.37 + 9514.80i −0.244147 + 0.422875i −0.961891 0.273432i \(-0.911841\pi\)
0.717744 + 0.696307i \(0.245175\pi\)
\(798\) 20373.3 6810.37i 0.903767 0.302111i
\(799\) −11482.8 19888.9i −0.508428 0.880622i
\(800\) 46009.4i 2.03335i
\(801\) 4671.85 + 9614.79i 0.206082 + 0.424122i
\(802\) −22985.6 −1.01203
\(803\) −4649.31 8052.84i −0.204322 0.353896i
\(804\) 40103.2 + 1430.14i 1.75912 + 0.0627328i
\(805\) −9136.30 + 11093.5i −0.400015 + 0.485708i
\(806\) −21822.3 12599.1i −0.953672 0.550603i
\(807\) −3196.29 + 5106.72i −0.139423 + 0.222757i
\(808\) −68104.8 + 39320.3i −2.96525 + 1.71199i
\(809\) 29805.7i 1.29532i −0.761930 0.647659i \(-0.775748\pi\)
0.761930 0.647659i \(-0.224252\pi\)
\(810\) 21296.5 + 16740.3i 0.923805 + 0.726168i
\(811\) 12409.9i 0.537323i −0.963235 0.268662i \(-0.913419\pi\)
0.963235 0.268662i \(-0.0865813\pi\)
\(812\) 18244.1 + 48728.5i 0.788477 + 2.10595i
\(813\) 9349.58 + 5851.88i 0.403326 + 0.252441i
\(814\) 5052.14 8750.57i 0.217540 0.376790i
\(815\) 11364.6 19684.1i 0.488448 0.846017i
\(816\) 139186. + 4963.56i 5.97117 + 0.212941i
\(817\) −7097.58 + 4097.79i −0.303932 + 0.175476i
\(818\) −30270.8 −1.29388
\(819\) −3687.39 12495.4i −0.157323 0.533118i
\(820\) −27276.7 −1.16164
\(821\) −3158.37 + 1823.49i −0.134261 + 0.0775154i −0.565626 0.824662i \(-0.691365\pi\)
0.431365 + 0.902177i \(0.358032\pi\)
\(822\) −17854.5 33639.5i −0.757600 1.42739i
\(823\) 20305.8 35170.6i 0.860042 1.48964i −0.0118459 0.999930i \(-0.503771\pi\)
0.871888 0.489706i \(-0.162896\pi\)
\(824\) 55510.5 96146.9i 2.34684 4.06485i
\(825\) −4497.35 + 2387.02i −0.189791 + 0.100734i
\(826\) −12788.3 34156.4i −0.538694 1.43880i
\(827\) 15836.6i 0.665891i −0.942946 0.332945i \(-0.891958\pi\)
0.942946 0.332945i \(-0.108042\pi\)
\(828\) 53420.4 + 36147.6i 2.24214 + 1.51717i
\(829\) 8427.35i 0.353069i 0.984294 + 0.176534i \(0.0564886\pi\)
−0.984294 + 0.176534i \(0.943511\pi\)
\(830\) −24617.3 + 14212.8i −1.02949 + 0.594377i
\(831\) 17880.5 + 637.644i 0.746410 + 0.0266181i
\(832\) 33367.1 + 19264.5i 1.39038 + 0.802735i
\(833\) −32235.1 + 28073.1i −1.34079 + 1.16768i
\(834\) −14238.5 + 22748.9i −0.591174 + 0.944521i
\(835\) 6579.52 + 11396.1i 0.272687 + 0.472308i
\(836\) −11039.7 −0.456717
\(837\) 20289.7 + 14810.3i 0.837892 + 0.611610i
\(838\) 22035.6i 0.908363i
\(839\) 1249.78 + 2164.69i 0.0514270 + 0.0890742i 0.890593 0.454801i \(-0.150290\pi\)
−0.839166 + 0.543875i \(0.816956\pi\)
\(840\) 31234.1 35283.5i 1.28295 1.44928i
\(841\) −3395.06 + 5880.42i −0.139205 + 0.241110i
\(842\) −76985.6 44447.6i −3.15095 1.81920i
\(843\) −644.814 + 18081.5i −0.0263447 + 0.738744i
\(844\) 21883.5 + 37903.4i 0.892491 + 1.54584i
\(845\) 10443.8 0.425181
\(846\) −1914.46 + 26808.1i −0.0778021 + 1.08946i
\(847\) 3572.35 21407.4i 0.144920 0.868439i
\(848\) −66894.8 + 38621.7i −2.70894 + 1.56400i
\(849\) −16280.8 + 8641.23i −0.658135 + 0.349312i
\(850\) 45285.2 + 26145.4i 1.82738 + 1.05504i
\(851\) −14486.6 8363.83i −0.583541 0.336908i
\(852\) −54995.2 + 29189.3i −2.21139 + 1.17372i
\(853\) −14523.6 + 8385.18i −0.582974 + 0.336580i −0.762314 0.647207i \(-0.775937\pi\)
0.179340 + 0.983787i \(0.442604\pi\)
\(854\) 5721.07 34283.7i 0.229240 1.37373i
\(855\) −546.737 + 7655.91i −0.0218690 + 0.306230i
\(856\) −52815.8 −2.10889
\(857\) 5953.98 + 10312.6i 0.237321 + 0.411052i 0.959945 0.280190i \(-0.0903974\pi\)
−0.722624 + 0.691242i \(0.757064\pi\)
\(858\) −328.753 + 9218.71i −0.0130809 + 0.366809i
\(859\) −40304.1 23269.6i −1.60088 0.924270i −0.991311 0.131538i \(-0.958009\pi\)
−0.609571 0.792732i \(-0.708658\pi\)
\(860\) −14446.1 + 25021.4i −0.572800 + 0.992118i
\(861\) −13491.4 11943.1i −0.534015 0.472727i
\(862\) 957.913 + 1659.15i 0.0378499 + 0.0655580i
\(863\) 33359.8i 1.31585i 0.753083 + 0.657926i \(0.228566\pi\)
−0.753083 + 0.657926i \(0.771434\pi\)
\(864\) −67119.3 48993.0i −2.64288 1.92914i
\(865\) −4313.67 −0.169560
\(866\) −8374.93 14505.8i −0.328628 0.569200i
\(867\) 29271.5 46767.2i 1.14661 1.83195i
\(868\) 44644.9 54208.9i 1.74579 2.11978i
\(869\) 9865.71 + 5695.97i 0.385122 + 0.222350i
\(870\) −25597.8 912.856i −0.997527 0.0355733i
\(871\) 8228.01 4750.44i 0.320087 0.184802i
\(872\) 49432.7i 1.91973i
\(873\) −6294.47 4259.23i −0.244027 0.165124i
\(874\) 25180.1i 0.974520i
\(875\) 24182.3 9053.95i 0.934298 0.349805i
\(876\) 71650.1 38029.1i 2.76351 1.46676i
\(877\) −2221.72 + 3848.13i −0.0855441 + 0.148167i −0.905623 0.424084i \(-0.860596\pi\)
0.820079 + 0.572251i \(0.193930\pi\)
\(878\) 41150.1 71274.0i 1.58172 2.73961i
\(879\) 5862.36 + 11045.2i 0.224952 + 0.423829i
\(880\) −16162.9 + 9331.63i −0.619147 + 0.357465i
\(881\) 31877.6 1.21905 0.609525 0.792767i \(-0.291360\pi\)
0.609525 + 0.792767i \(0.291360\pi\)
\(882\) 49655.2 6068.25i 1.89567 0.231665i
\(883\) 7852.54 0.299274 0.149637 0.988741i \(-0.452190\pi\)
0.149637 + 0.988741i \(0.452190\pi\)
\(884\) 59549.7 34381.0i 2.26569 1.30810i
\(885\) 13023.3 + 464.429i 0.494658 + 0.0176402i
\(886\) −28338.6 + 49083.9i −1.07455 + 1.86118i
\(887\) 6816.09 11805.8i 0.258018 0.446900i −0.707693 0.706520i \(-0.750264\pi\)
0.965711 + 0.259620i \(0.0835973\pi\)
\(888\) 46492.2 + 29099.4i 1.75695 + 1.09967i
\(889\) 19076.2 7142.19i 0.719678 0.269451i
\(890\) 14711.5i 0.554081i
\(891\) 1306.77 9102.62i 0.0491340 0.342255i
\(892\) 130130.i 4.88460i
\(893\) −6595.07 + 3807.66i −0.247139 + 0.142686i
\(894\) 2863.59 4575.17i 0.107128 0.171159i
\(895\) −6994.64 4038.36i −0.261235 0.150824i
\(896\) −38260.7 + 46457.1i −1.42656 + 1.73217i
\(897\) 15261.6 + 544.250i 0.568082 + 0.0202586i
\(898\) −36156.3 62624.6i −1.34360 2.32718i
\(899\) −23752.9 −0.881207
\(900\) −19411.8 39950.0i −0.718956 1.47963i
\(901\) 44758.0i 1.65495i
\(902\) 6378.91 + 11048.6i 0.235471 + 0.407847i
\(903\) −18100.8 + 6050.73i −0.667063 + 0.222985i
\(904\) −57829.5 + 100164.i −2.12763 + 3.68517i
\(905\) −9681.16 5589.42i −0.355594 0.205302i
\(906\) 15268.2 8103.79i 0.559883 0.297164i
\(907\) 12109.3 + 20974.0i 0.443312 + 0.767840i 0.997933 0.0642638i \(-0.0204699\pi\)
−0.554621 + 0.832103i \(0.687137\pi\)
\(908\) −19308.9 −0.705715
\(909\) 16716.9 24705.0i 0.609973 0.901443i
\(910\) 2951.19 17685.1i 0.107507 0.644238i
\(911\) 23767.6 13722.2i 0.864385 0.499053i −0.00109314 0.999999i \(-0.500348\pi\)
0.865478 + 0.500946i \(0.167015\pi\)
\(912\) 1645.90 46153.4i 0.0597600 1.67576i
\(913\) 8357.06 + 4824.95i 0.302933 + 0.174899i
\(914\) 75258.9 + 43450.7i 2.72357 + 1.57245i
\(915\) 10527.1 + 6588.92i 0.380346 + 0.238058i
\(916\) −48830.3 + 28192.2i −1.76135 + 1.01692i
\(917\) −3644.94 + 21842.4i −0.131261 + 0.786586i
\(918\) −86363.1 + 38221.9i −3.10502 + 1.37420i
\(919\) 34400.6 1.23479 0.617395 0.786653i \(-0.288188\pi\)
0.617395 + 0.786653i \(0.288188\pi\)
\(920\) 27617.9 + 47835.5i 0.989711 + 1.71423i
\(921\) −34632.1 21676.2i −1.23905 0.775521i
\(922\) 87932.0 + 50767.5i 3.14087 + 1.81338i
\(923\) −7370.51 + 12766.1i −0.262842 + 0.455256i
\(924\) −25191.0 5132.61i −0.896885 0.182739i
\(925\) 5759.47 + 9975.69i 0.204724 + 0.354593i
\(926\) 1169.41i 0.0415001i
\(927\) −2999.71 + 42004.6i −0.106282 + 1.48826i
\(928\) 78575.8 2.77950
\(929\) −9180.18 15900.5i −0.324211 0.561550i 0.657141 0.753767i \(-0.271765\pi\)
−0.981352 + 0.192217i \(0.938432\pi\)
\(930\) 16207.5 + 30536.4i 0.571468 + 1.07670i
\(931\) 9308.94 + 10689.0i 0.327699 + 0.376282i
\(932\) −36392.7 21011.4i −1.27906 0.738466i
\(933\) −6660.34 12548.7i −0.233708 0.440326i
\(934\) 71836.8 41475.0i 2.51667 1.45300i
\(935\) 10814.3i 0.378250i
\(936\) −49945.5 3566.79i −1.74414 0.124556i
\(937\) 55153.5i 1.92293i 0.274924 + 0.961466i \(0.411347\pi\)
−0.274924 + 0.961466i \(0.588653\pi\)
\(938\) 12791.5 + 34164.9i 0.445263 + 1.18926i
\(939\) 750.452 21043.8i 0.0260810 0.731351i
\(940\) −13423.3 + 23249.8i −0.465766 + 0.806730i
\(941\) −20322.4 + 35199.5i −0.704029 + 1.21941i 0.263011 + 0.964793i \(0.415284\pi\)
−0.967041 + 0.254622i \(0.918049\pi\)
\(942\) 12425.6 19852.4i 0.429774 0.686652i
\(943\) 18291.0 10560.3i 0.631640 0.364677i
\(944\) −78410.6 −2.70344
\(945\) −4806.99 + 17215.5i −0.165472 + 0.592614i
\(946\) 13513.4 0.464439
\(947\) −30834.2 + 17802.2i −1.05806 + 0.610868i −0.924894 0.380226i \(-0.875846\pi\)
−0.133162 + 0.991094i \(0.542513\pi\)
\(948\) −52724.7 + 84238.4i −1.80635 + 2.88601i
\(949\) 9602.62 16632.2i 0.328466 0.568920i
\(950\) 8669.72 15016.4i 0.296087 0.512838i
\(951\) −207.137 + 5808.43i −0.00706296 + 0.198056i
\(952\) 57605.9 + 153860.i 1.96115 + 5.23807i
\(953\) 28893.7i 0.982118i 0.871126 + 0.491059i \(0.163390\pi\)
−0.871126 + 0.491059i \(0.836610\pi\)
\(954\) 29354.5 43381.2i 0.996212 1.47224i
\(955\) 898.962i 0.0304604i
\(956\) −32719.2 + 18890.5i −1.10692 + 0.639081i
\(957\) 4076.59 + 7680.66i 0.137699 + 0.259436i
\(958\) −81364.7 46975.9i −2.74402 1.58426i
\(959\) 15975.4 19397.8i 0.537929 0.653166i
\(960\) −24781.8 46691.1i −0.833156 1.56974i
\(961\) 1133.99 + 1964.13i 0.0380648 + 0.0659302i
\(962\) 20869.3 0.699431
\(963\) 18019.1 8755.53i 0.602968 0.292983i
\(964\) 126723.i 4.23388i
\(965\) −3921.77 6792.71i −0.130825 0.226596i
\(966\) −11706.8 + 57457.4i −0.389919 + 1.91373i
\(967\) 24894.3 43118.2i 0.827867 1.43391i −0.0718412 0.997416i \(-0.522887\pi\)
0.899708 0.436492i \(-0.143779\pi\)
\(968\) −72240.2 41707.9i −2.39865 1.38486i
\(969\) −22683.4 14197.5i −0.752009 0.470681i
\(970\) −5229.74 9058.18i −0.173110 0.299836i
\(971\) 23098.3 0.763397 0.381698 0.924287i \(-0.375339\pi\)
0.381698 + 0.924287i \(0.375339\pi\)
\(972\) 78950.4 + 14222.4i 2.60528 + 0.469324i
\(973\) −17466.9 2914.78i −0.575502 0.0960365i
\(974\) 66117.4 38172.9i 2.17509 1.25579i
\(975\) −8914.00 5579.26i −0.292796 0.183261i
\(976\) −64714.2 37362.8i −2.12239 1.22536i
\(977\) 3023.09 + 1745.38i 0.0989940 + 0.0571542i 0.548680 0.836033i \(-0.315131\pi\)
−0.449686 + 0.893187i \(0.648464\pi\)
\(978\) 3305.11 92680.2i 0.108063 3.03025i
\(979\) 4325.16 2497.13i 0.141198 0.0815206i
\(980\) 47261.7 + 16225.4i 1.54053 + 0.528877i
\(981\) 8194.70 + 16864.9i 0.266704 + 0.548884i
\(982\) 49458.2 1.60720
\(983\) −7109.05 12313.2i −0.230665 0.399523i 0.727339 0.686278i \(-0.240757\pi\)
−0.958004 + 0.286755i \(0.907423\pi\)
\(984\) −61169.8 + 32466.5i −1.98173 + 1.05182i
\(985\) −20628.9 11910.1i −0.667301 0.385266i
\(986\) 44651.6 77338.9i 1.44219 2.49794i
\(987\) −16819.3 + 5622.34i −0.542415 + 0.181318i
\(988\) −11400.6 19746.4i −0.367107 0.635848i
\(989\) 22371.5i 0.719285i
\(990\) 7092.51 10481.6i 0.227692 0.336492i
\(991\) −263.472 −0.00844549 −0.00422274 0.999991i \(-0.501344\pi\)
−0.00422274 + 0.999991i \(0.501344\pi\)
\(992\) −53026.3 91844.2i −1.69716 2.93957i
\(993\) 36572.7 + 1304.23i 1.16878 + 0.0416804i
\(994\) −43691.7 35983.3i −1.39418 1.14821i
\(995\) −15029.3 8677.16i −0.478854 0.276467i
\(996\) −44662.1 + 71356.8i −1.42086 + 2.27011i
\(997\) 41959.3 24225.2i 1.33286 0.769528i 0.347125 0.937819i \(-0.387158\pi\)
0.985737 + 0.168290i \(0.0538247\pi\)
\(998\) 81327.1i 2.57952i
\(999\) −20685.6 2220.57i −0.655120 0.0703262i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 63.4.o.a.41.2 yes 44
3.2 odd 2 189.4.o.a.125.22 44
7.6 odd 2 inner 63.4.o.a.41.1 yes 44
9.2 odd 6 inner 63.4.o.a.20.1 44
9.4 even 3 567.4.c.c.566.13 44
9.5 odd 6 567.4.c.c.566.32 44
9.7 even 3 189.4.o.a.62.21 44
21.20 even 2 189.4.o.a.125.21 44
63.13 odd 6 567.4.c.c.566.31 44
63.20 even 6 inner 63.4.o.a.20.2 yes 44
63.34 odd 6 189.4.o.a.62.22 44
63.41 even 6 567.4.c.c.566.14 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.o.a.20.1 44 9.2 odd 6 inner
63.4.o.a.20.2 yes 44 63.20 even 6 inner
63.4.o.a.41.1 yes 44 7.6 odd 2 inner
63.4.o.a.41.2 yes 44 1.1 even 1 trivial
189.4.o.a.62.21 44 9.7 even 3
189.4.o.a.62.22 44 63.34 odd 6
189.4.o.a.125.21 44 21.20 even 2
189.4.o.a.125.22 44 3.2 odd 2
567.4.c.c.566.13 44 9.4 even 3
567.4.c.c.566.14 44 63.41 even 6
567.4.c.c.566.31 44 63.13 odd 6
567.4.c.c.566.32 44 9.5 odd 6