Properties

Label 114.4.e.e.49.2
Level $114$
Weight $4$
Character 114.49
Analytic conductor $6.726$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [114,4,Mod(7,114)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(114, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("114.7");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 114.e (of order \(3\), 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: \(6.72621774065\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.6967728.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.2
Root \(-1.13654 - 1.96854i\) of defining polynomial
Character \(\chi\) \(=\) 114.49
Dual form 114.4.e.e.7.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.60679 - 4.51510i) q^{5} +(-3.00000 - 5.19615i) q^{6} +31.4905 q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.60679 - 4.51510i) q^{5} +(-3.00000 - 5.19615i) q^{6} +31.4905 q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-5.21359 - 9.03020i) q^{10} -21.2113 q^{11} -12.0000 q^{12} +(-28.1384 - 48.7372i) q^{13} +(31.4905 - 54.5431i) q^{14} +(-7.82038 - 13.5453i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-8.63960 + 14.9642i) q^{17} -18.0000 q^{18} +(-42.3436 - 71.1759i) q^{19} -20.8543 q^{20} +(47.2357 - 81.8146i) q^{21} +(-21.2113 + 36.7390i) q^{22} +(103.158 + 178.675i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(48.9093 + 84.7133i) q^{25} -112.554 q^{26} -27.0000 q^{27} +(-62.9809 - 109.086i) q^{28} +(-103.257 - 178.846i) q^{29} -31.2815 q^{30} +129.624 q^{31} +(16.0000 + 27.7128i) q^{32} +(-31.8169 + 55.1085i) q^{33} +(17.2792 + 29.9284i) q^{34} +(82.0891 - 142.183i) q^{35} +(-18.0000 + 31.1769i) q^{36} +440.212 q^{37} +(-165.624 + 2.16540i) q^{38} -168.831 q^{39} +(-20.8543 + 36.1208i) q^{40} +(-217.727 + 377.114i) q^{41} +(-94.4714 - 163.629i) q^{42} +(-64.9984 + 112.580i) q^{43} +(42.4225 + 73.4780i) q^{44} -46.9223 q^{45} +412.633 q^{46} +(-54.2410 - 93.9482i) q^{47} +(24.0000 + 41.5692i) q^{48} +648.649 q^{49} +195.637 q^{50} +(25.9188 + 44.8927i) q^{51} +(-112.554 + 194.949i) q^{52} +(203.640 + 352.715i) q^{53} +(-27.0000 + 46.7654i) q^{54} +(-55.2934 + 95.7709i) q^{55} -251.924 q^{56} +(-248.436 + 3.24810i) q^{57} -413.027 q^{58} +(58.1224 - 100.671i) q^{59} +(-31.2815 + 54.1812i) q^{60} +(170.342 + 295.041i) q^{61} +(129.624 - 224.515i) q^{62} +(-141.707 - 245.444i) q^{63} +64.0000 q^{64} -293.404 q^{65} +(63.6338 + 110.217i) q^{66} +(105.373 + 182.511i) q^{67} +69.1168 q^{68} +618.949 q^{69} +(-164.178 - 284.365i) q^{70} +(-79.0086 + 136.847i) q^{71} +(36.0000 + 62.3538i) q^{72} +(-286.774 + 496.707i) q^{73} +(440.212 - 762.470i) q^{74} +293.456 q^{75} +(-161.873 + 289.035i) q^{76} -667.952 q^{77} +(-168.831 + 292.423i) q^{78} +(442.649 - 766.690i) q^{79} +(41.7087 + 72.2416i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(435.454 + 754.228i) q^{82} -573.632 q^{83} -377.886 q^{84} +(45.0433 + 78.0173i) q^{85} +(129.997 + 225.161i) q^{86} -619.540 q^{87} +169.690 q^{88} +(-107.618 - 186.399i) q^{89} +(-46.9223 + 81.2718i) q^{90} +(-886.092 - 1534.76i) q^{91} +(412.633 - 714.701i) q^{92} +(194.436 - 336.773i) q^{93} -216.964 q^{94} +(-431.748 + 5.64475i) q^{95} +96.0000 q^{96} +(-264.487 + 458.105i) q^{97} +(648.649 - 1123.49i) q^{98} +(95.4507 + 165.325i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} - 34 q^{7} - 48 q^{8} - 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} - 34 q^{7} - 48 q^{8} - 27 q^{9} + 4 q^{10} - 104 q^{11} - 72 q^{12} - 75 q^{13} - 34 q^{14} + 6 q^{15} - 48 q^{16} + 48 q^{17} - 108 q^{18} + 104 q^{19} + 16 q^{20} - 51 q^{21} - 104 q^{22} + 238 q^{23} - 72 q^{24} - 229 q^{25} - 300 q^{26} - 162 q^{27} + 68 q^{28} + 8 q^{29} + 24 q^{30} + 214 q^{31} + 96 q^{32} - 156 q^{33} - 96 q^{34} + 294 q^{35} - 108 q^{36} + 610 q^{37} - 430 q^{38} - 450 q^{39} + 16 q^{40} - 16 q^{41} + 102 q^{42} + 331 q^{43} + 208 q^{44} + 36 q^{45} + 952 q^{46} + 766 q^{47} + 144 q^{48} + 2284 q^{49} - 916 q^{50} - 144 q^{51} - 300 q^{52} + 118 q^{53} - 162 q^{54} + 1400 q^{55} + 272 q^{56} - 645 q^{57} + 32 q^{58} - 936 q^{59} + 24 q^{60} + 399 q^{61} + 214 q^{62} + 153 q^{63} + 384 q^{64} + 740 q^{65} + 312 q^{66} - 61 q^{67} - 384 q^{68} + 1428 q^{69} - 588 q^{70} - 974 q^{71} + 216 q^{72} - 91 q^{73} + 610 q^{74} - 1374 q^{75} - 1276 q^{76} - 72 q^{77} - 450 q^{78} + 321 q^{79} - 32 q^{80} - 243 q^{81} + 32 q^{82} - 4296 q^{83} + 408 q^{84} + 1680 q^{85} - 662 q^{86} + 48 q^{87} + 832 q^{88} - 1116 q^{89} + 36 q^{90} - 1367 q^{91} + 952 q^{92} + 321 q^{93} + 3064 q^{94} - 4198 q^{95} + 576 q^{96} - 1382 q^{97} + 2284 q^{98} + 468 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(97\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.353553 0.612372i
\(3\) 1.50000 2.59808i 0.288675 0.500000i
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) 2.60679 4.51510i 0.233159 0.403843i −0.725577 0.688141i \(-0.758427\pi\)
0.958736 + 0.284298i \(0.0917605\pi\)
\(6\) −3.00000 5.19615i −0.204124 0.353553i
\(7\) 31.4905 1.70033 0.850163 0.526520i \(-0.176504\pi\)
0.850163 + 0.526520i \(0.176504\pi\)
\(8\) −8.00000 −0.353553
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) −5.21359 9.03020i −0.164868 0.285560i
\(11\) −21.2113 −0.581403 −0.290702 0.956814i \(-0.593889\pi\)
−0.290702 + 0.956814i \(0.593889\pi\)
\(12\) −12.0000 −0.288675
\(13\) −28.1384 48.7372i −0.600323 1.03979i −0.992772 0.120016i \(-0.961705\pi\)
0.392449 0.919774i \(-0.371628\pi\)
\(14\) 31.4905 54.5431i 0.601156 1.04123i
\(15\) −7.82038 13.5453i −0.134614 0.233159i
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −8.63960 + 14.9642i −0.123259 + 0.213492i −0.921051 0.389441i \(-0.872668\pi\)
0.797792 + 0.602933i \(0.206001\pi\)
\(18\) −18.0000 −0.235702
\(19\) −42.3436 71.1759i −0.511279 0.859415i
\(20\) −20.8543 −0.233159
\(21\) 47.2357 81.8146i 0.490842 0.850163i
\(22\) −21.2113 + 36.7390i −0.205557 + 0.356035i
\(23\) 103.158 + 178.675i 0.935216 + 1.61984i 0.774248 + 0.632883i \(0.218128\pi\)
0.160969 + 0.986960i \(0.448538\pi\)
\(24\) −12.0000 + 20.7846i −0.102062 + 0.176777i
\(25\) 48.9093 + 84.7133i 0.391274 + 0.677707i
\(26\) −112.554 −0.848985
\(27\) −27.0000 −0.192450
\(28\) −62.9809 109.086i −0.425081 0.736262i
\(29\) −103.257 178.846i −0.661182 1.14520i −0.980305 0.197488i \(-0.936722\pi\)
0.319123 0.947713i \(-0.396612\pi\)
\(30\) −31.2815 −0.190373
\(31\) 129.624 0.751005 0.375503 0.926821i \(-0.377470\pi\)
0.375503 + 0.926821i \(0.377470\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) −31.8169 + 55.1085i −0.167837 + 0.290702i
\(34\) 17.2792 + 29.9284i 0.0871576 + 0.150961i
\(35\) 82.0891 142.183i 0.396446 0.686664i
\(36\) −18.0000 + 31.1769i −0.0833333 + 0.144338i
\(37\) 440.212 1.95596 0.977979 0.208704i \(-0.0669245\pi\)
0.977979 + 0.208704i \(0.0669245\pi\)
\(38\) −165.624 + 2.16540i −0.707046 + 0.00924405i
\(39\) −168.831 −0.693193
\(40\) −20.8543 + 36.1208i −0.0824340 + 0.142780i
\(41\) −217.727 + 377.114i −0.829347 + 1.43647i 0.0692044 + 0.997602i \(0.477954\pi\)
−0.898551 + 0.438868i \(0.855379\pi\)
\(42\) −94.4714 163.629i −0.347077 0.601156i
\(43\) −64.9984 + 112.580i −0.230515 + 0.399264i −0.957960 0.286902i \(-0.907375\pi\)
0.727445 + 0.686166i \(0.240708\pi\)
\(44\) 42.4225 + 73.4780i 0.145351 + 0.251755i
\(45\) −46.9223 −0.155439
\(46\) 412.633 1.32260
\(47\) −54.2410 93.9482i −0.168338 0.291569i 0.769498 0.638649i \(-0.220507\pi\)
−0.937836 + 0.347080i \(0.887173\pi\)
\(48\) 24.0000 + 41.5692i 0.0721688 + 0.125000i
\(49\) 648.649 1.89111
\(50\) 195.637 0.553345
\(51\) 25.9188 + 44.8927i 0.0711639 + 0.123259i
\(52\) −112.554 + 194.949i −0.300161 + 0.519895i
\(53\) 203.640 + 352.715i 0.527776 + 0.914134i 0.999476 + 0.0323753i \(0.0103072\pi\)
−0.471700 + 0.881759i \(0.656359\pi\)
\(54\) −27.0000 + 46.7654i −0.0680414 + 0.117851i
\(55\) −55.2934 + 95.7709i −0.135559 + 0.234795i
\(56\) −251.924 −0.601156
\(57\) −248.436 + 3.24810i −0.577301 + 0.00754774i
\(58\) −413.027 −0.935052
\(59\) 58.1224 100.671i 0.128252 0.222140i −0.794747 0.606941i \(-0.792397\pi\)
0.923000 + 0.384801i \(0.125730\pi\)
\(60\) −31.2815 + 54.1812i −0.0673071 + 0.116579i
\(61\) 170.342 + 295.041i 0.357542 + 0.619282i 0.987550 0.157308i \(-0.0502814\pi\)
−0.630007 + 0.776589i \(0.716948\pi\)
\(62\) 129.624 224.515i 0.265520 0.459895i
\(63\) −141.707 245.444i −0.283388 0.490842i
\(64\) 64.0000 0.125000
\(65\) −293.404 −0.559882
\(66\) 63.6338 + 110.217i 0.118678 + 0.205557i
\(67\) 105.373 + 182.511i 0.192139 + 0.332795i 0.945959 0.324286i \(-0.105124\pi\)
−0.753820 + 0.657081i \(0.771791\pi\)
\(68\) 69.1168 0.123259
\(69\) 618.949 1.07989
\(70\) −164.178 284.365i −0.280329 0.485545i
\(71\) −79.0086 + 136.847i −0.132065 + 0.228743i −0.924472 0.381249i \(-0.875494\pi\)
0.792408 + 0.609992i \(0.208827\pi\)
\(72\) 36.0000 + 62.3538i 0.0589256 + 0.102062i
\(73\) −286.774 + 496.707i −0.459785 + 0.796371i −0.998949 0.0458295i \(-0.985407\pi\)
0.539164 + 0.842201i \(0.318740\pi\)
\(74\) 440.212 762.470i 0.691535 1.19777i
\(75\) 293.456 0.451804
\(76\) −161.873 + 289.035i −0.244318 + 0.436244i
\(77\) −667.952 −0.988575
\(78\) −168.831 + 292.423i −0.245081 + 0.424492i
\(79\) 442.649 766.690i 0.630403 1.09189i −0.357066 0.934079i \(-0.616223\pi\)
0.987469 0.157811i \(-0.0504438\pi\)
\(80\) 41.7087 + 72.2416i 0.0582897 + 0.100961i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 435.454 + 754.228i 0.586437 + 1.01574i
\(83\) −573.632 −0.758606 −0.379303 0.925273i \(-0.623836\pi\)
−0.379303 + 0.925273i \(0.623836\pi\)
\(84\) −377.886 −0.490842
\(85\) 45.0433 + 78.0173i 0.0574780 + 0.0995548i
\(86\) 129.997 + 225.161i 0.162999 + 0.282322i
\(87\) −619.540 −0.763467
\(88\) 169.690 0.205557
\(89\) −107.618 186.399i −0.128174 0.222003i 0.794795 0.606878i \(-0.207578\pi\)
−0.922969 + 0.384874i \(0.874245\pi\)
\(90\) −46.9223 + 81.2718i −0.0549560 + 0.0951866i
\(91\) −886.092 1534.76i −1.02074 1.76798i
\(92\) 412.633 714.701i 0.467608 0.809921i
\(93\) 194.436 336.773i 0.216797 0.375503i
\(94\) −216.964 −0.238065
\(95\) −431.748 + 5.64475i −0.466278 + 0.00609620i
\(96\) 96.0000 0.102062
\(97\) −264.487 + 458.105i −0.276851 + 0.479521i −0.970601 0.240696i \(-0.922624\pi\)
0.693749 + 0.720217i \(0.255958\pi\)
\(98\) 648.649 1123.49i 0.668607 1.15806i
\(99\) 95.4507 + 165.325i 0.0969006 + 0.167837i
\(100\) 195.637 338.853i 0.195637 0.338853i
\(101\) −514.368 890.911i −0.506748 0.877713i −0.999970 0.00780915i \(-0.997514\pi\)
0.493222 0.869904i \(-0.335819\pi\)
\(102\) 103.675 0.100641
\(103\) 108.300 0.103603 0.0518016 0.998657i \(-0.483504\pi\)
0.0518016 + 0.998657i \(0.483504\pi\)
\(104\) 225.107 + 389.898i 0.212246 + 0.367621i
\(105\) −246.267 426.548i −0.228888 0.396446i
\(106\) 814.560 0.746388
\(107\) −1820.02 −1.64438 −0.822188 0.569215i \(-0.807247\pi\)
−0.822188 + 0.569215i \(0.807247\pi\)
\(108\) 54.0000 + 93.5307i 0.0481125 + 0.0833333i
\(109\) 59.5717 103.181i 0.0523480 0.0906694i −0.838664 0.544649i \(-0.816663\pi\)
0.891012 + 0.453980i \(0.149996\pi\)
\(110\) 110.587 + 191.542i 0.0958549 + 0.166025i
\(111\) 660.318 1143.70i 0.564636 0.977979i
\(112\) −251.924 + 436.345i −0.212541 + 0.368131i
\(113\) 1014.96 0.844949 0.422474 0.906375i \(-0.361162\pi\)
0.422474 + 0.906375i \(0.361162\pi\)
\(114\) −242.810 + 433.552i −0.199485 + 0.356192i
\(115\) 1075.65 0.872215
\(116\) −413.027 + 715.383i −0.330591 + 0.572600i
\(117\) −253.246 + 438.635i −0.200108 + 0.346597i
\(118\) −116.245 201.342i −0.0906881 0.157076i
\(119\) −272.065 + 471.230i −0.209581 + 0.363005i
\(120\) 62.5630 + 108.362i 0.0475933 + 0.0824340i
\(121\) −881.082 −0.661970
\(122\) 681.369 0.505641
\(123\) 653.181 + 1131.34i 0.478824 + 0.829347i
\(124\) −259.248 449.031i −0.187751 0.325195i
\(125\) 1161.68 0.831233
\(126\) −566.828 −0.400770
\(127\) −514.100 890.448i −0.359205 0.622161i 0.628623 0.777710i \(-0.283619\pi\)
−0.987828 + 0.155549i \(0.950285\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 194.995 + 337.741i 0.133088 + 0.230515i
\(130\) −293.404 + 508.191i −0.197948 + 0.342856i
\(131\) 794.584 1376.26i 0.529948 0.917896i −0.469442 0.882963i \(-0.655545\pi\)
0.999390 0.0349330i \(-0.0111218\pi\)
\(132\) 254.535 0.167837
\(133\) −1333.42 2241.36i −0.869340 1.46128i
\(134\) 421.491 0.271726
\(135\) −70.3834 + 121.908i −0.0448714 + 0.0777196i
\(136\) 69.1168 119.714i 0.0435788 0.0754807i
\(137\) 1162.53 + 2013.57i 0.724977 + 1.25570i 0.958983 + 0.283462i \(0.0914831\pi\)
−0.234006 + 0.972235i \(0.575184\pi\)
\(138\) 618.949 1072.05i 0.381800 0.661298i
\(139\) −317.528 549.974i −0.193758 0.335599i 0.752735 0.658324i \(-0.228734\pi\)
−0.946493 + 0.322725i \(0.895401\pi\)
\(140\) −656.713 −0.396446
\(141\) −325.446 −0.194380
\(142\) 158.017 + 273.694i 0.0933839 + 0.161746i
\(143\) 596.852 + 1033.78i 0.349030 + 0.604537i
\(144\) 144.000 0.0833333
\(145\) −1076.67 −0.616641
\(146\) 573.547 + 993.413i 0.325117 + 0.563119i
\(147\) 972.974 1685.24i 0.545915 0.945553i
\(148\) −880.424 1524.94i −0.488989 0.846955i
\(149\) −849.157 + 1470.78i −0.466883 + 0.808666i −0.999284 0.0378265i \(-0.987957\pi\)
0.532401 + 0.846492i \(0.321290\pi\)
\(150\) 293.456 508.280i 0.159737 0.276673i
\(151\) −1632.38 −0.879745 −0.439873 0.898060i \(-0.644976\pi\)
−0.439873 + 0.898060i \(0.644976\pi\)
\(152\) 338.749 + 569.408i 0.180764 + 0.303849i
\(153\) 155.513 0.0821730
\(154\) −667.952 + 1156.93i −0.349514 + 0.605376i
\(155\) 337.903 585.265i 0.175103 0.303288i
\(156\) 337.661 + 584.846i 0.173298 + 0.300161i
\(157\) −1481.29 + 2565.66i −0.752990 + 1.30422i 0.193377 + 0.981124i \(0.438056\pi\)
−0.946367 + 0.323092i \(0.895278\pi\)
\(158\) −885.297 1533.38i −0.445763 0.772083i
\(159\) 1221.84 0.609423
\(160\) 166.835 0.0824340
\(161\) 3248.50 + 5626.57i 1.59017 + 2.75426i
\(162\) 81.0000 + 140.296i 0.0392837 + 0.0680414i
\(163\) 626.972 0.301277 0.150639 0.988589i \(-0.451867\pi\)
0.150639 + 0.988589i \(0.451867\pi\)
\(164\) 1741.81 0.829347
\(165\) 165.880 + 287.313i 0.0782652 + 0.135559i
\(166\) −573.632 + 993.560i −0.268208 + 0.464549i
\(167\) −801.078 1387.51i −0.371193 0.642926i 0.618556 0.785741i \(-0.287718\pi\)
−0.989749 + 0.142815i \(0.954385\pi\)
\(168\) −377.886 + 654.517i −0.173539 + 0.300578i
\(169\) −485.043 + 840.120i −0.220775 + 0.382394i
\(170\) 180.173 0.0812862
\(171\) −364.215 + 650.328i −0.162879 + 0.290829i
\(172\) 519.987 0.230515
\(173\) −1145.34 + 1983.79i −0.503346 + 0.871821i 0.496646 + 0.867953i \(0.334565\pi\)
−0.999993 + 0.00386803i \(0.998769\pi\)
\(174\) −619.540 + 1073.07i −0.269926 + 0.467526i
\(175\) 1540.18 + 2667.66i 0.665293 + 1.15232i
\(176\) 169.690 293.912i 0.0726754 0.125878i
\(177\) −174.367 302.013i −0.0740465 0.128252i
\(178\) −430.471 −0.181265
\(179\) −218.545 −0.0912558 −0.0456279 0.998959i \(-0.514529\pi\)
−0.0456279 + 0.998959i \(0.514529\pi\)
\(180\) 93.8446 + 162.544i 0.0388598 + 0.0673071i
\(181\) 1874.22 + 3246.24i 0.769667 + 1.33310i 0.937744 + 0.347328i \(0.112911\pi\)
−0.168077 + 0.985774i \(0.553756\pi\)
\(182\) −3544.37 −1.44355
\(183\) 1022.05 0.412854
\(184\) −825.266 1429.40i −0.330649 0.572701i
\(185\) 1147.54 1987.60i 0.456049 0.789899i
\(186\) −388.872 673.546i −0.153298 0.265520i
\(187\) 183.257 317.410i 0.0716634 0.124125i
\(188\) −216.964 + 375.793i −0.0841688 + 0.145785i
\(189\) −850.242 −0.327228
\(190\) −421.971 + 753.453i −0.161121 + 0.287691i
\(191\) −141.733 −0.0536935 −0.0268467 0.999640i \(-0.508547\pi\)
−0.0268467 + 0.999640i \(0.508547\pi\)
\(192\) 96.0000 166.277i 0.0360844 0.0625000i
\(193\) 1954.95 3386.07i 0.729120 1.26287i −0.228135 0.973629i \(-0.573263\pi\)
0.957255 0.289244i \(-0.0934038\pi\)
\(194\) 528.974 + 916.210i 0.195763 + 0.339072i
\(195\) −440.107 + 762.287i −0.161624 + 0.279941i
\(196\) −1297.30 2246.99i −0.472776 0.818873i
\(197\) 1203.16 0.435134 0.217567 0.976045i \(-0.430188\pi\)
0.217567 + 0.976045i \(0.430188\pi\)
\(198\) 381.803 0.137038
\(199\) −1851.73 3207.29i −0.659626 1.14251i −0.980712 0.195456i \(-0.937381\pi\)
0.321086 0.947050i \(-0.395952\pi\)
\(200\) −391.274 677.707i −0.138336 0.239605i
\(201\) 632.236 0.221863
\(202\) −2057.47 −0.716649
\(203\) −3251.60 5631.93i −1.12422 1.94721i
\(204\) 103.675 179.571i 0.0355819 0.0616297i
\(205\) 1135.14 + 1966.12i 0.386739 + 0.669851i
\(206\) 108.300 187.581i 0.0366293 0.0634438i
\(207\) 928.424 1608.08i 0.311739 0.539947i
\(208\) 900.430 0.300161
\(209\) 898.162 + 1509.73i 0.297259 + 0.499667i
\(210\) −985.069 −0.323696
\(211\) 12.8499 22.2567i 0.00419253 0.00726168i −0.863922 0.503626i \(-0.831999\pi\)
0.868114 + 0.496365i \(0.165332\pi\)
\(212\) 814.560 1410.86i 0.263888 0.457067i
\(213\) 237.026 + 410.541i 0.0762476 + 0.132065i
\(214\) −1820.02 + 3152.37i −0.581375 + 1.00697i
\(215\) 338.875 + 586.948i 0.107493 + 0.186184i
\(216\) 216.000 0.0680414
\(217\) 4081.92 1.27695
\(218\) −119.143 206.362i −0.0370156 0.0641129i
\(219\) 860.321 + 1490.12i 0.265457 + 0.459785i
\(220\) 442.347 0.135559
\(221\) 972.419 0.295982
\(222\) −1320.64 2287.41i −0.399258 0.691535i
\(223\) 1552.59 2689.17i 0.466230 0.807535i −0.533026 0.846099i \(-0.678945\pi\)
0.999256 + 0.0385642i \(0.0122784\pi\)
\(224\) 503.847 + 872.689i 0.150289 + 0.260308i
\(225\) 440.183 762.420i 0.130425 0.225902i
\(226\) 1014.96 1757.96i 0.298735 0.517423i
\(227\) 664.566 0.194312 0.0971560 0.995269i \(-0.469025\pi\)
0.0971560 + 0.995269i \(0.469025\pi\)
\(228\) 508.124 + 854.111i 0.147593 + 0.248092i
\(229\) −6031.99 −1.74063 −0.870317 0.492492i \(-0.836086\pi\)
−0.870317 + 0.492492i \(0.836086\pi\)
\(230\) 1075.65 1863.08i 0.308375 0.534121i
\(231\) −1001.93 + 1735.39i −0.285377 + 0.494287i
\(232\) 826.053 + 1430.77i 0.233763 + 0.404890i
\(233\) 2879.08 4986.71i 0.809506 1.40211i −0.103701 0.994609i \(-0.533068\pi\)
0.913207 0.407497i \(-0.133598\pi\)
\(234\) 506.492 + 877.270i 0.141497 + 0.245081i
\(235\) −565.581 −0.156998
\(236\) −464.979 −0.128252
\(237\) −1327.95 2300.07i −0.363964 0.630403i
\(238\) 544.130 + 942.461i 0.148196 + 0.256683i
\(239\) −741.406 −0.200659 −0.100330 0.994954i \(-0.531990\pi\)
−0.100330 + 0.994954i \(0.531990\pi\)
\(240\) 250.252 0.0673071
\(241\) −2637.03 4567.48i −0.704840 1.22082i −0.966749 0.255726i \(-0.917686\pi\)
0.261910 0.965092i \(-0.415648\pi\)
\(242\) −881.082 + 1526.08i −0.234042 + 0.405372i
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) 681.369 1180.17i 0.178771 0.309641i
\(245\) 1690.89 2928.71i 0.440928 0.763709i
\(246\) 2612.72 0.677159
\(247\) −2277.43 + 4066.49i −0.586678 + 1.04755i
\(248\) −1036.99 −0.265520
\(249\) −860.448 + 1490.34i −0.218991 + 0.379303i
\(250\) 1161.68 2012.10i 0.293885 0.509024i
\(251\) −1423.18 2465.02i −0.357889 0.619882i 0.629719 0.776823i \(-0.283170\pi\)
−0.987608 + 0.156941i \(0.949837\pi\)
\(252\) −566.828 + 981.775i −0.141694 + 0.245421i
\(253\) −2188.12 3789.93i −0.543738 0.941782i
\(254\) −2056.40 −0.507993
\(255\) 270.260 0.0663699
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −3220.36 5577.82i −0.781635 1.35383i −0.930989 0.365048i \(-0.881053\pi\)
0.149353 0.988784i \(-0.452281\pi\)
\(258\) 779.981 0.188215
\(259\) 13862.5 3.32576
\(260\) 586.809 + 1016.38i 0.139971 + 0.242436i
\(261\) −929.310 + 1609.61i −0.220394 + 0.381734i
\(262\) −1589.17 2752.52i −0.374730 0.649051i
\(263\) −2070.20 + 3585.70i −0.485377 + 0.840698i −0.999859 0.0168037i \(-0.994651\pi\)
0.514482 + 0.857501i \(0.327984\pi\)
\(264\) 254.535 440.868i 0.0593392 0.102779i
\(265\) 2123.39 0.492222
\(266\) −5215.58 + 68.1894i −1.20221 + 0.0157179i
\(267\) −645.706 −0.148002
\(268\) 421.491 730.044i 0.0960696 0.166397i
\(269\) −1583.00 + 2741.83i −0.358799 + 0.621459i −0.987761 0.155978i \(-0.950147\pi\)
0.628961 + 0.777437i \(0.283480\pi\)
\(270\) 140.767 + 243.815i 0.0317289 + 0.0549560i
\(271\) −3222.11 + 5580.86i −0.722249 + 1.25097i 0.237847 + 0.971303i \(0.423558\pi\)
−0.960096 + 0.279669i \(0.909775\pi\)
\(272\) −138.234 239.428i −0.0308149 0.0533729i
\(273\) −5316.55 −1.17865
\(274\) 4650.13 1.02527
\(275\) −1037.43 1796.88i −0.227488 0.394021i
\(276\) −1237.90 2144.10i −0.269974 0.467608i
\(277\) 399.738 0.0867073 0.0433537 0.999060i \(-0.486196\pi\)
0.0433537 + 0.999060i \(0.486196\pi\)
\(278\) −1270.11 −0.274015
\(279\) −583.308 1010.32i −0.125168 0.216797i
\(280\) −656.713 + 1137.46i −0.140165 + 0.242772i
\(281\) −315.183 545.914i −0.0669120 0.115895i 0.830629 0.556827i \(-0.187981\pi\)
−0.897541 + 0.440932i \(0.854648\pi\)
\(282\) −325.446 + 563.689i −0.0687236 + 0.119033i
\(283\) −998.317 + 1729.13i −0.209695 + 0.363203i −0.951619 0.307282i \(-0.900581\pi\)
0.741923 + 0.670485i \(0.233914\pi\)
\(284\) 632.069 0.132065
\(285\) −632.956 + 1130.18i −0.131555 + 0.234899i
\(286\) 2387.41 0.493603
\(287\) −6856.32 + 11875.5i −1.41016 + 2.44247i
\(288\) 144.000 249.415i 0.0294628 0.0510310i
\(289\) 2307.21 + 3996.21i 0.469614 + 0.813396i
\(290\) −1076.67 + 1864.86i −0.218016 + 0.377614i
\(291\) 793.461 + 1374.31i 0.159840 + 0.276851i
\(292\) 2294.19 0.459785
\(293\) 9676.85 1.92945 0.964723 0.263268i \(-0.0848004\pi\)
0.964723 + 0.263268i \(0.0848004\pi\)
\(294\) −1945.95 3370.48i −0.386020 0.668607i
\(295\) −303.026 524.857i −0.0598063 0.103588i
\(296\) −3521.70 −0.691535
\(297\) 572.704 0.111891
\(298\) 1698.31 + 2941.57i 0.330136 + 0.571813i
\(299\) 5805.42 10055.3i 1.12286 1.94486i
\(300\) −586.911 1016.56i −0.112951 0.195637i
\(301\) −2046.83 + 3545.21i −0.391951 + 0.678879i
\(302\) −1632.38 + 2827.37i −0.311037 + 0.538732i
\(303\) −3086.21 −0.585142
\(304\) 1324.99 17.3232i 0.249979 0.00326827i
\(305\) 1776.19 0.333456
\(306\) 155.513 269.356i 0.0290525 0.0503205i
\(307\) −3397.76 + 5885.09i −0.631662 + 1.09407i 0.355550 + 0.934657i \(0.384294\pi\)
−0.987212 + 0.159414i \(0.949040\pi\)
\(308\) 1335.90 + 2313.86i 0.247144 + 0.428065i
\(309\) 162.450 281.372i 0.0299077 0.0518016i
\(310\) −675.806 1170.53i −0.123817 0.214457i
\(311\) −4418.47 −0.805622 −0.402811 0.915283i \(-0.631967\pi\)
−0.402811 + 0.915283i \(0.631967\pi\)
\(312\) 1350.64 0.245081
\(313\) 695.780 + 1205.13i 0.125648 + 0.217629i 0.921986 0.387223i \(-0.126566\pi\)
−0.796338 + 0.604852i \(0.793232\pi\)
\(314\) 2962.57 + 5131.32i 0.532444 + 0.922221i
\(315\) −1477.60 −0.264297
\(316\) −3541.19 −0.630403
\(317\) −2999.34 5195.01i −0.531419 0.920444i −0.999328 0.0366675i \(-0.988326\pi\)
0.467909 0.883777i \(-0.345008\pi\)
\(318\) 1221.84 2116.29i 0.215464 0.373194i
\(319\) 2190.20 + 3793.54i 0.384413 + 0.665823i
\(320\) 166.835 288.966i 0.0291448 0.0504803i
\(321\) −2730.04 + 4728.56i −0.474691 + 0.822188i
\(322\) 12994.0 2.24884
\(323\) 1430.92 18.7082i 0.246498 0.00322276i
\(324\) 324.000 0.0555556
\(325\) 2752.46 4767.40i 0.469782 0.813686i
\(326\) 626.972 1085.95i 0.106518 0.184494i
\(327\) −178.715 309.543i −0.0302231 0.0523480i
\(328\) 1741.81 3016.91i 0.293218 0.507869i
\(329\) −1708.08 2958.47i −0.286229 0.495763i
\(330\) 663.521 0.110684
\(331\) −6604.73 −1.09676 −0.548382 0.836228i \(-0.684756\pi\)
−0.548382 + 0.836228i \(0.684756\pi\)
\(332\) 1147.26 + 1987.12i 0.189651 + 0.328486i
\(333\) −1980.95 3431.11i −0.325993 0.564636i
\(334\) −3204.31 −0.524947
\(335\) 1098.74 0.179196
\(336\) 755.771 + 1309.03i 0.122710 + 0.212541i
\(337\) 2396.45 4150.77i 0.387367 0.670940i −0.604727 0.796433i \(-0.706718\pi\)
0.992095 + 0.125493i \(0.0400511\pi\)
\(338\) 970.087 + 1680.24i 0.156112 + 0.270393i
\(339\) 1522.44 2636.94i 0.243916 0.422474i
\(340\) 180.173 312.069i 0.0287390 0.0497774i
\(341\) −2749.49 −0.436637
\(342\) 762.186 + 1281.17i 0.120510 + 0.202566i
\(343\) 9625.03 1.51517
\(344\) 519.987 900.644i 0.0814995 0.141161i
\(345\) 1613.47 2794.62i 0.251787 0.436108i
\(346\) 2290.69 + 3967.59i 0.355919 + 0.616471i
\(347\) −2435.68 + 4218.72i −0.376813 + 0.652660i −0.990597 0.136815i \(-0.956314\pi\)
0.613783 + 0.789475i \(0.289647\pi\)
\(348\) 1239.08 + 2146.15i 0.190867 + 0.330591i
\(349\) −2676.44 −0.410506 −0.205253 0.978709i \(-0.565802\pi\)
−0.205253 + 0.978709i \(0.565802\pi\)
\(350\) 6160.70 0.940867
\(351\) 759.738 + 1315.90i 0.115532 + 0.200108i
\(352\) −339.380 587.824i −0.0513893 0.0890088i
\(353\) 3111.41 0.469132 0.234566 0.972100i \(-0.424633\pi\)
0.234566 + 0.972100i \(0.424633\pi\)
\(354\) −697.469 −0.104718
\(355\) 411.918 + 713.463i 0.0615841 + 0.106667i
\(356\) −430.471 + 745.598i −0.0640868 + 0.111002i
\(357\) 816.195 + 1413.69i 0.121002 + 0.209581i
\(358\) −218.545 + 378.530i −0.0322638 + 0.0558826i
\(359\) 467.879 810.391i 0.0687847 0.119139i −0.829582 0.558385i \(-0.811421\pi\)
0.898367 + 0.439246i \(0.144755\pi\)
\(360\) 375.378 0.0549560
\(361\) −3273.03 + 6027.70i −0.477188 + 0.878801i
\(362\) 7496.88 1.08847
\(363\) −1321.62 + 2289.12i −0.191094 + 0.330985i
\(364\) −3544.37 + 6139.03i −0.510372 + 0.883990i
\(365\) 1495.12 + 2589.62i 0.214406 + 0.371362i
\(366\) 1022.05 1770.25i 0.145966 0.252821i
\(367\) −5504.62 9534.29i −0.782940 1.35609i −0.930222 0.366997i \(-0.880386\pi\)
0.147282 0.989095i \(-0.452947\pi\)
\(368\) −3301.06 −0.467608
\(369\) 3919.08 0.552898
\(370\) −2295.08 3975.20i −0.322475 0.558543i
\(371\) 6412.72 + 11107.2i 0.897390 + 1.55433i
\(372\) −1555.49 −0.216797
\(373\) −6151.39 −0.853906 −0.426953 0.904274i \(-0.640413\pi\)
−0.426953 + 0.904274i \(0.640413\pi\)
\(374\) −366.514 634.820i −0.0506737 0.0877694i
\(375\) 1742.53 3018.14i 0.239956 0.415617i
\(376\) 433.928 + 751.586i 0.0595163 + 0.103085i
\(377\) −5810.96 + 10064.9i −0.793845 + 1.37498i
\(378\) −850.242 + 1472.66i −0.115692 + 0.200385i
\(379\) 13458.6 1.82407 0.912037 0.410109i \(-0.134509\pi\)
0.912037 + 0.410109i \(0.134509\pi\)
\(380\) 883.049 + 1484.33i 0.119209 + 0.200380i
\(381\) −3084.60 −0.414774
\(382\) −141.733 + 245.489i −0.0189835 + 0.0328804i
\(383\) 5545.19 9604.56i 0.739807 1.28138i −0.212775 0.977101i \(-0.568250\pi\)
0.952582 0.304282i \(-0.0984166\pi\)
\(384\) −192.000 332.554i −0.0255155 0.0441942i
\(385\) −1741.21 + 3015.87i −0.230495 + 0.399229i
\(386\) −3909.89 6772.14i −0.515566 0.892986i
\(387\) 1169.97 0.153677
\(388\) 2115.90 0.276851
\(389\) −636.543 1102.53i −0.0829667 0.143702i 0.821556 0.570127i \(-0.193106\pi\)
−0.904523 + 0.426425i \(0.859773\pi\)
\(390\) 880.213 + 1524.57i 0.114285 + 0.197948i
\(391\) −3564.98 −0.461097
\(392\) −5189.19 −0.668607
\(393\) −2383.75 4128.78i −0.305965 0.529948i
\(394\) 1203.16 2083.93i 0.153843 0.266464i
\(395\) −2307.79 3997.20i −0.293968 0.509168i
\(396\) 381.803 661.302i 0.0484503 0.0839183i
\(397\) 6164.46 10677.2i 0.779309 1.34980i −0.153032 0.988221i \(-0.548904\pi\)
0.932341 0.361581i \(-0.117763\pi\)
\(398\) −7406.92 −0.932853
\(399\) −7823.36 + 102.284i −0.981599 + 0.0128336i
\(400\) −1565.10 −0.195637
\(401\) −4899.77 + 8486.65i −0.610181 + 1.05687i 0.381028 + 0.924563i \(0.375570\pi\)
−0.991209 + 0.132302i \(0.957763\pi\)
\(402\) 632.236 1095.07i 0.0784405 0.135863i
\(403\) −3647.42 6317.51i −0.450846 0.780887i
\(404\) −2057.47 + 3563.65i −0.253374 + 0.438856i
\(405\) 211.150 + 365.723i 0.0259065 + 0.0448714i
\(406\) −13006.4 −1.58989
\(407\) −9337.46 −1.13720
\(408\) −207.350 359.141i −0.0251602 0.0435788i
\(409\) −4042.33 7001.52i −0.488705 0.846461i 0.511211 0.859455i \(-0.329197\pi\)
−0.999916 + 0.0129939i \(0.995864\pi\)
\(410\) 4540.55 0.546931
\(411\) 6975.20 0.837132
\(412\) −216.600 375.163i −0.0259008 0.0448615i
\(413\) 1830.30 3170.17i 0.218071 0.377710i
\(414\) −1856.85 3216.15i −0.220433 0.381800i
\(415\) −1495.34 + 2590.00i −0.176876 + 0.306357i
\(416\) 900.430 1559.59i 0.106123 0.183811i
\(417\) −1905.17 −0.223733
\(418\) 3513.09 45.9308i 0.411079 0.00537452i
\(419\) −78.3882 −0.00913965 −0.00456983 0.999990i \(-0.501455\pi\)
−0.00456983 + 0.999990i \(0.501455\pi\)
\(420\) −985.069 + 1706.19i −0.114444 + 0.198223i
\(421\) −3542.60 + 6135.95i −0.410108 + 0.710328i −0.994901 0.100854i \(-0.967842\pi\)
0.584793 + 0.811183i \(0.301176\pi\)
\(422\) −25.6998 44.5134i −0.00296457 0.00513478i
\(423\) −488.169 + 845.534i −0.0561125 + 0.0971898i
\(424\) −1629.12 2821.72i −0.186597 0.323195i
\(425\) −1690.23 −0.192913
\(426\) 948.103 0.107830
\(427\) 5364.16 + 9290.99i 0.607938 + 1.05298i
\(428\) 3640.05 + 6304.75i 0.411094 + 0.712036i
\(429\) 3581.11 0.403025
\(430\) 1355.50 0.152019
\(431\) 7450.70 + 12905.0i 0.832686 + 1.44225i 0.895900 + 0.444255i \(0.146532\pi\)
−0.0632142 + 0.998000i \(0.520135\pi\)
\(432\) 216.000 374.123i 0.0240563 0.0416667i
\(433\) −2114.74 3662.84i −0.234707 0.406524i 0.724481 0.689295i \(-0.242080\pi\)
−0.959187 + 0.282771i \(0.908746\pi\)
\(434\) 4081.92 7070.09i 0.451471 0.781971i
\(435\) −1615.01 + 2797.28i −0.178009 + 0.308321i
\(436\) −476.573 −0.0523480
\(437\) 8349.29 14908.1i 0.913960 1.63193i
\(438\) 3441.28 0.375413
\(439\) −5260.77 + 9111.93i −0.571943 + 0.990634i 0.424423 + 0.905464i \(0.360477\pi\)
−0.996366 + 0.0851705i \(0.972857\pi\)
\(440\) 442.347 766.168i 0.0479274 0.0830127i
\(441\) −2918.92 5055.72i −0.315184 0.545915i
\(442\) 972.419 1684.28i 0.104645 0.181251i
\(443\) −6933.71 12009.5i −0.743636 1.28801i −0.950829 0.309715i \(-0.899766\pi\)
0.207194 0.978300i \(-0.433567\pi\)
\(444\) −5282.55 −0.564636
\(445\) −1122.15 −0.119539
\(446\) −3105.19 5378.34i −0.329675 0.571013i
\(447\) 2547.47 + 4412.35i 0.269555 + 0.466883i
\(448\) 2015.39 0.212541
\(449\) 9599.89 1.00901 0.504507 0.863408i \(-0.331674\pi\)
0.504507 + 0.863408i \(0.331674\pi\)
\(450\) −880.367 1524.84i −0.0922242 0.159737i
\(451\) 4618.26 7999.06i 0.482185 0.835169i
\(452\) −2029.92 3515.92i −0.211237 0.365874i
\(453\) −2448.58 + 4241.06i −0.253961 + 0.439873i
\(454\) 664.566 1151.06i 0.0686996 0.118991i
\(455\) −9239.44 −0.951981
\(456\) 1987.49 25.9848i 0.204107 0.00266853i
\(457\) −6261.10 −0.640880 −0.320440 0.947269i \(-0.603831\pi\)
−0.320440 + 0.947269i \(0.603831\pi\)
\(458\) −6031.99 + 10447.7i −0.615407 + 1.06592i
\(459\) 233.269 404.034i 0.0237213 0.0410865i
\(460\) −2151.30 3726.16i −0.218054 0.377680i
\(461\) 4912.78 8509.18i 0.496336 0.859679i −0.503655 0.863905i \(-0.668012\pi\)
0.999991 + 0.00422602i \(0.00134519\pi\)
\(462\) 2003.86 + 3470.78i 0.201792 + 0.349514i
\(463\) 9276.57 0.931142 0.465571 0.885011i \(-0.345849\pi\)
0.465571 + 0.885011i \(0.345849\pi\)
\(464\) 3304.21 0.330591
\(465\) −1013.71 1755.80i −0.101096 0.175103i
\(466\) −5758.16 9973.43i −0.572407 0.991438i
\(467\) 18209.4 1.80435 0.902174 0.431372i \(-0.141970\pi\)
0.902174 + 0.431372i \(0.141970\pi\)
\(468\) 2025.97 0.200108
\(469\) 3318.24 + 5747.35i 0.326699 + 0.565859i
\(470\) −565.581 + 979.615i −0.0555070 + 0.0961410i
\(471\) 4443.86 + 7696.98i 0.434739 + 0.752990i
\(472\) −464.979 + 805.367i −0.0453441 + 0.0785382i
\(473\) 1378.70 2387.97i 0.134022 0.232134i
\(474\) −5311.78 −0.514722
\(475\) 3958.55 7068.23i 0.382381 0.682764i
\(476\) 2176.52 0.209581
\(477\) 1832.76 3174.43i 0.175925 0.304711i
\(478\) −741.406 + 1284.15i −0.0709437 + 0.122878i
\(479\) −6370.84 11034.6i −0.607706 1.05258i −0.991618 0.129208i \(-0.958757\pi\)
0.383912 0.923370i \(-0.374577\pi\)
\(480\) 250.252 433.449i 0.0237967 0.0412170i
\(481\) −12386.9 21454.7i −1.17421 2.03378i
\(482\) −10548.1 −0.996794
\(483\) 19491.0 1.83617
\(484\) 1762.16 + 3052.16i 0.165493 + 0.286641i
\(485\) 1378.93 + 2388.37i 0.129101 + 0.223609i
\(486\) 486.000 0.0453609
\(487\) −5006.72 −0.465864 −0.232932 0.972493i \(-0.574832\pi\)
−0.232932 + 0.972493i \(0.574832\pi\)
\(488\) −1362.74 2360.33i −0.126410 0.218949i
\(489\) 940.458 1628.92i 0.0869713 0.150639i
\(490\) −3381.79 5857.43i −0.311783 0.540024i
\(491\) −481.656 + 834.253i −0.0442705 + 0.0766788i −0.887312 0.461170i \(-0.847430\pi\)
0.843041 + 0.537849i \(0.180763\pi\)
\(492\) 2612.72 4525.37i 0.239412 0.414673i
\(493\) 3568.38 0.325988
\(494\) 4765.94 + 8011.12i 0.434068 + 0.729630i
\(495\) 995.281 0.0903728
\(496\) −1036.99 + 1796.12i −0.0938756 + 0.162597i
\(497\) −2488.02 + 4309.37i −0.224553 + 0.388937i
\(498\) 1720.90 + 2980.68i 0.154850 + 0.268208i
\(499\) −2482.42 + 4299.68i −0.222702 + 0.385732i −0.955628 0.294577i \(-0.904821\pi\)
0.732925 + 0.680309i \(0.238154\pi\)
\(500\) −2323.37 4024.19i −0.207808 0.359935i
\(501\) −4806.47 −0.428617
\(502\) −5692.71 −0.506132
\(503\) 7384.24 + 12789.9i 0.654567 + 1.13374i 0.982002 + 0.188869i \(0.0604823\pi\)
−0.327435 + 0.944874i \(0.606184\pi\)
\(504\) 1133.66 + 1963.55i 0.100193 + 0.173539i
\(505\) −5363.40 −0.472610
\(506\) −8752.46 −0.768962
\(507\) 1455.13 + 2520.36i 0.127465 + 0.220775i
\(508\) −2056.40 + 3561.79i −0.179603 + 0.311081i
\(509\) −3007.96 5209.94i −0.261936 0.453686i 0.704820 0.709386i \(-0.251028\pi\)
−0.966756 + 0.255699i \(0.917694\pi\)
\(510\) 270.260 468.104i 0.0234653 0.0406431i
\(511\) −9030.63 + 15641.5i −0.781784 + 1.35409i
\(512\) −512.000 −0.0441942
\(513\) 1143.28 + 1921.75i 0.0983957 + 0.165394i
\(514\) −12881.4 −1.10540
\(515\) 282.316 488.986i 0.0241560 0.0418394i
\(516\) 779.981 1350.97i 0.0665441 0.115258i
\(517\) 1150.52 + 1992.76i 0.0978721 + 0.169519i
\(518\) 13862.5 24010.5i 1.17584 2.03661i
\(519\) 3436.03 + 5951.38i 0.290607 + 0.503346i
\(520\) 2347.23 0.197948
\(521\) 10009.4 0.841685 0.420842 0.907134i \(-0.361735\pi\)
0.420842 + 0.907134i \(0.361735\pi\)
\(522\) 1858.62 + 3219.22i 0.155842 + 0.269926i
\(523\) −1244.04 2154.75i −0.104012 0.180154i 0.809322 0.587365i \(-0.199835\pi\)
−0.913334 + 0.407211i \(0.866501\pi\)
\(524\) −6356.67 −0.529948
\(525\) 9241.05 0.768214
\(526\) 4140.40 + 7171.39i 0.343213 + 0.594463i
\(527\) −1119.90 + 1939.72i −0.0925685 + 0.160333i
\(528\) −509.070 881.736i −0.0419592 0.0726754i
\(529\) −15199.7 + 26326.7i −1.24926 + 2.16378i
\(530\) 2123.39 3677.82i 0.174027 0.301423i
\(531\) −1046.20 −0.0855016
\(532\) −5097.47 + 9101.83i −0.415420 + 0.741757i
\(533\) 24506.0 1.99150
\(534\) −645.706 + 1118.40i −0.0523267 + 0.0906325i
\(535\) −4744.43 + 8217.59i −0.383401 + 0.664070i
\(536\) −842.982 1460.09i −0.0679315 0.117661i
\(537\) −327.817 + 567.796i −0.0263433 + 0.0456279i
\(538\) 3165.99 + 5483.66i 0.253709 + 0.439438i
\(539\) −13758.7 −1.09949
\(540\) 563.067 0.0448714
\(541\) 4866.02 + 8428.19i 0.386703 + 0.669790i 0.992004 0.126207i \(-0.0402804\pi\)
−0.605301 + 0.795997i \(0.706947\pi\)
\(542\) 6444.23 + 11161.7i 0.510707 + 0.884571i
\(543\) 11245.3 0.888735
\(544\) −552.934 −0.0435788
\(545\) −310.582 537.944i −0.0244108 0.0422807i
\(546\) −5316.55 + 9208.54i −0.416717 + 0.721775i
\(547\) −6216.18 10766.7i −0.485895 0.841596i 0.513973 0.857806i \(-0.328173\pi\)
−0.999869 + 0.0162107i \(0.994840\pi\)
\(548\) 4650.13 8054.26i 0.362489 0.627849i
\(549\) 1533.08 2655.37i 0.119181 0.206427i
\(550\) −4149.71 −0.321717
\(551\) −8357.25 + 14922.4i −0.646154 + 1.15375i
\(552\) −4951.59 −0.381800
\(553\) 13939.2 24143.4i 1.07189 1.85657i
\(554\) 399.738 692.367i 0.0306557 0.0530972i
\(555\) −3442.63 5962.80i −0.263300 0.456049i
\(556\) −1270.11 + 2199.90i −0.0968790 + 0.167799i
\(557\) 8952.74 + 15506.6i 0.681041 + 1.17960i 0.974664 + 0.223676i \(0.0718058\pi\)
−0.293623 + 0.955921i \(0.594861\pi\)
\(558\) −2333.23 −0.177014
\(559\) 7315.81 0.553535
\(560\) 1313.43 + 2274.92i 0.0991114 + 0.171666i
\(561\) −549.770 952.230i −0.0413749 0.0716634i
\(562\) −1260.73 −0.0946278
\(563\) −1825.07 −0.136621 −0.0683106 0.997664i \(-0.521761\pi\)
−0.0683106 + 0.997664i \(0.521761\pi\)
\(564\) 650.892 + 1127.38i 0.0485949 + 0.0841688i
\(565\) 2645.79 4582.64i 0.197007 0.341226i
\(566\) 1996.63 + 3458.27i 0.148277 + 0.256823i
\(567\) −1275.36 + 2208.99i −0.0944625 + 0.163614i
\(568\) 632.069 1094.78i 0.0466919 0.0808728i
\(569\) −4974.94 −0.366538 −0.183269 0.983063i \(-0.558668\pi\)
−0.183269 + 0.983063i \(0.558668\pi\)
\(570\) 1324.57 + 2226.49i 0.0973338 + 0.163610i
\(571\) 14203.4 1.04097 0.520485 0.853871i \(-0.325751\pi\)
0.520485 + 0.853871i \(0.325751\pi\)
\(572\) 2387.41 4135.11i 0.174515 0.302269i
\(573\) −212.600 + 368.234i −0.0155000 + 0.0268467i
\(574\) 13712.6 + 23751.0i 0.997133 + 1.72709i
\(575\) −10090.8 + 17477.8i −0.731852 + 1.26760i
\(576\) −288.000 498.831i −0.0208333 0.0360844i
\(577\) 5279.89 0.380944 0.190472 0.981693i \(-0.438998\pi\)
0.190472 + 0.981693i \(0.438998\pi\)
\(578\) 9228.86 0.664135
\(579\) −5864.84 10158.2i −0.420958 0.729120i
\(580\) 2153.35 + 3729.71i 0.154160 + 0.267013i
\(581\) −18063.9 −1.28988
\(582\) 3173.84 0.226048
\(583\) −4319.46 7481.53i −0.306851 0.531481i
\(584\) 2294.19 3973.65i 0.162559 0.281560i
\(585\) 1320.32 + 2286.86i 0.0933137 + 0.161624i
\(586\) 9676.85 16760.8i 0.682162 1.18154i
\(587\) −6614.29 + 11456.3i −0.465078 + 0.805539i −0.999205 0.0398654i \(-0.987307\pi\)
0.534127 + 0.845404i \(0.320640\pi\)
\(588\) −7783.79 −0.545915
\(589\) −5488.75 9226.11i −0.383973 0.645425i
\(590\) −1212.10 −0.0845789
\(591\) 1804.74 3125.90i 0.125612 0.217567i
\(592\) −3521.70 + 6099.76i −0.244495 + 0.423477i
\(593\) 348.240 + 603.169i 0.0241155 + 0.0417693i 0.877831 0.478970i \(-0.158990\pi\)
−0.853716 + 0.520739i \(0.825656\pi\)
\(594\) 572.704 991.953i 0.0395595 0.0685190i
\(595\) 1418.43 + 2456.80i 0.0977313 + 0.169276i
\(596\) 6793.25 0.466883
\(597\) −11110.4 −0.761671
\(598\) −11610.8 20110.6i −0.793985 1.37522i
\(599\) −11348.5 19656.2i −0.774105 1.34079i −0.935296 0.353865i \(-0.884867\pi\)
0.161192 0.986923i \(-0.448466\pi\)
\(600\) −2347.64 −0.159737
\(601\) 15591.5 1.05822 0.529110 0.848553i \(-0.322526\pi\)
0.529110 + 0.848553i \(0.322526\pi\)
\(602\) 4093.66 + 7090.42i 0.277151 + 0.480040i
\(603\) 948.354 1642.60i 0.0640464 0.110932i
\(604\) 3264.77 + 5654.75i 0.219936 + 0.380941i
\(605\) −2296.80 + 3978.17i −0.154344 + 0.267332i
\(606\) −3086.21 + 5345.47i −0.206879 + 0.358325i
\(607\) 13728.2 0.917975 0.458988 0.888443i \(-0.348212\pi\)
0.458988 + 0.888443i \(0.348212\pi\)
\(608\) 1294.99 2312.28i 0.0863794 0.154236i
\(609\) −19509.6 −1.29814
\(610\) 1776.19 3076.45i 0.117895 0.204200i
\(611\) −3052.52 + 5287.11i −0.202114 + 0.350072i
\(612\) −311.026 538.712i −0.0205432 0.0355819i
\(613\) −10985.7 + 19027.7i −0.723829 + 1.25371i 0.235625 + 0.971844i \(0.424286\pi\)
−0.959454 + 0.281864i \(0.909047\pi\)
\(614\) 6795.52 + 11770.2i 0.446653 + 0.773625i
\(615\) 6810.83 0.446568
\(616\) 5343.62 0.349514
\(617\) 9259.34 + 16037.6i 0.604160 + 1.04644i 0.992184 + 0.124787i \(0.0398247\pi\)
−0.388023 + 0.921650i \(0.626842\pi\)
\(618\) −324.901 562.744i −0.0211479 0.0366293i
\(619\) −7363.53 −0.478134 −0.239067 0.971003i \(-0.576842\pi\)
−0.239067 + 0.971003i \(0.576842\pi\)
\(620\) −2703.22 −0.175103
\(621\) −2785.27 4824.23i −0.179982 0.311739i
\(622\) −4418.47 + 7653.02i −0.284831 + 0.493341i
\(623\) −3388.93 5869.80i −0.217937 0.377478i
\(624\) 1350.64 2339.39i 0.0866492 0.150081i
\(625\) −3085.39 + 5344.05i −0.197465 + 0.342019i
\(626\) 2783.12 0.177693
\(627\) 5269.64 68.8963i 0.335645 0.00438828i
\(628\) 11850.3 0.752990
\(629\) −3803.26 + 6587.43i −0.241090 + 0.417581i
\(630\) −1477.60 + 2559.29i −0.0934431 + 0.161848i
\(631\) 10189.5 + 17648.7i 0.642848 + 1.11345i 0.984794 + 0.173726i \(0.0555808\pi\)
−0.341946 + 0.939720i \(0.611086\pi\)
\(632\) −3541.19 + 6133.52i −0.222881 + 0.386042i
\(633\) −38.5497 66.7701i −0.00242056 0.00419253i
\(634\) −11997.4 −0.751540
\(635\) −5360.61 −0.335007
\(636\) −2443.68 4232.58i −0.152356 0.263888i
\(637\) −18252.0 31613.3i −1.13527 1.96635i
\(638\) 8760.81 0.543643
\(639\) 1422.16 0.0880432
\(640\) −333.670 577.933i −0.0206085 0.0356950i
\(641\) −993.124 + 1720.14i −0.0611951 + 0.105993i −0.895000 0.446066i \(-0.852825\pi\)
0.833805 + 0.552059i \(0.186158\pi\)
\(642\) 5460.07 + 9457.12i 0.335657 + 0.581375i
\(643\) 5578.32 9661.94i 0.342127 0.592581i −0.642701 0.766117i \(-0.722186\pi\)
0.984827 + 0.173536i \(0.0555194\pi\)
\(644\) 12994.0 22506.3i 0.795086 1.37713i
\(645\) 2033.25 0.124123
\(646\) 1398.52 2497.14i 0.0851766 0.152088i
\(647\) −18657.7 −1.13371 −0.566854 0.823818i \(-0.691840\pi\)
−0.566854 + 0.823818i \(0.691840\pi\)
\(648\) 324.000 561.184i 0.0196419 0.0340207i
\(649\) −1232.85 + 2135.36i −0.0745664 + 0.129153i
\(650\) −5504.92 9534.80i −0.332186 0.575363i
\(651\) 6122.88 10605.1i 0.368625 0.638476i
\(652\) −1253.94 2171.89i −0.0753193 0.130457i
\(653\) 7972.68 0.477787 0.238894 0.971046i \(-0.423215\pi\)
0.238894 + 0.971046i \(0.423215\pi\)
\(654\) −714.860 −0.0427420
\(655\) −4142.63 7175.25i −0.247124 0.428031i
\(656\) −3483.63 6033.82i −0.207337 0.359118i
\(657\) 5161.93 0.306523
\(658\) −6832.30 −0.404789
\(659\) −2663.80 4613.84i −0.157461 0.272731i 0.776491 0.630128i \(-0.216998\pi\)
−0.933953 + 0.357397i \(0.883664\pi\)
\(660\) 663.521 1149.25i 0.0391326 0.0677796i
\(661\) 3472.53 + 6014.60i 0.204336 + 0.353920i 0.949921 0.312491i \(-0.101163\pi\)
−0.745585 + 0.666410i \(0.767830\pi\)
\(662\) −6604.73 + 11439.7i −0.387765 + 0.671628i
\(663\) 1458.63 2526.42i 0.0854426 0.147991i
\(664\) 4589.06 0.268208
\(665\) −13595.9 + 177.756i −0.792823 + 0.0103655i
\(666\) −7923.82 −0.461024
\(667\) 21303.5 36898.8i 1.23670 2.14202i
\(668\) −3204.31 + 5550.03i −0.185597 + 0.321463i
\(669\) −4657.78 8067.52i −0.269178 0.466230i
\(670\) 1098.74 1903.07i 0.0633552 0.109735i
\(671\) −3613.17 6258.20i −0.207876 0.360052i
\(672\) 3023.08 0.173539
\(673\) −8261.87 −0.473212 −0.236606 0.971606i \(-0.576035\pi\)
−0.236606 + 0.971606i \(0.576035\pi\)
\(674\) −4792.90 8301.54i −0.273910 0.474426i
\(675\) −1320.55 2287.26i −0.0753007 0.130425i
\(676\) 3880.35 0.220775
\(677\) 12128.3 0.688523 0.344261 0.938874i \(-0.388129\pi\)
0.344261 + 0.938874i \(0.388129\pi\)
\(678\) −3044.87 5273.88i −0.172474 0.298735i
\(679\) −8328.82 + 14425.9i −0.470737 + 0.815341i
\(680\) −360.346 624.138i −0.0203215 0.0351980i
\(681\) 996.849 1726.59i 0.0560930 0.0971560i
\(682\) −2749.49 + 4762.25i −0.154374 + 0.267384i
\(683\) 3609.67 0.202226 0.101113 0.994875i \(-0.467760\pi\)
0.101113 + 0.994875i \(0.467760\pi\)
\(684\) 2981.23 38.9772i 0.166652 0.00217884i
\(685\) 12121.9 0.676139
\(686\) 9625.03 16671.0i 0.535693 0.927848i
\(687\) −9047.99 + 15671.6i −0.502478 + 0.870317i
\(688\) −1039.97 1801.29i −0.0576288 0.0998161i
\(689\) 11460.2 19849.7i 0.633672 1.09755i
\(690\) −3226.95 5589.23i −0.178040 0.308375i
\(691\) −375.152 −0.0206534 −0.0103267 0.999947i \(-0.503287\pi\)
−0.0103267 + 0.999947i \(0.503287\pi\)
\(692\) 9162.75 0.503346
\(693\) 3005.79 + 5206.17i 0.164762 + 0.285377i
\(694\) 4871.36 + 8437.45i 0.266447 + 0.461500i
\(695\) −3310.92 −0.180705
\(696\) 4956.32 0.269926
\(697\) −3762.15 6516.23i −0.204450 0.354117i
\(698\) −2676.44 + 4635.73i −0.145136 + 0.251382i
\(699\) −8637.24 14960.1i −0.467368 0.809506i
\(700\) 6160.70 10670.6i 0.332647 0.576161i
\(701\) −6900.20 + 11951.5i −0.371779 + 0.643940i −0.989839 0.142191i \(-0.954585\pi\)
0.618060 + 0.786131i \(0.287919\pi\)
\(702\) 3038.95 0.163387
\(703\) −18640.2 31332.5i −1.00004 1.68098i
\(704\) −1357.52 −0.0726754
\(705\) −848.371 + 1469.42i −0.0453213 + 0.0784988i
\(706\) 3111.41 5389.12i 0.165863 0.287284i
\(707\) −16197.7 28055.2i −0.861636 1.49240i
\(708\) −697.469 + 1208.05i −0.0370233 + 0.0641262i
\(709\) 12672.6 + 21949.6i 0.671270 + 1.16267i 0.977544 + 0.210730i \(0.0675841\pi\)
−0.306275 + 0.951943i \(0.599083\pi\)
\(710\) 1647.67 0.0870931
\(711\) −7967.68 −0.420269
\(712\) 860.942 + 1491.20i 0.0453162 + 0.0784900i
\(713\) 13371.8 + 23160.6i 0.702352 + 1.21651i
\(714\) 3264.78 0.171122
\(715\) 6223.48 0.325517
\(716\) 437.089 + 757.061i 0.0228140 + 0.0395149i
\(717\) −1112.11 + 1926.23i −0.0579253 + 0.100330i
\(718\) −935.758 1620.78i −0.0486382 0.0842438i
\(719\) 9963.90 17258.0i 0.516816 0.895151i −0.482993 0.875624i \(-0.660450\pi\)
0.999809 0.0195275i \(-0.00621618\pi\)
\(720\) 375.378 650.174i 0.0194299 0.0336536i
\(721\) 3410.42 0.176159
\(722\) 7167.25 + 11696.8i 0.369442 + 0.602920i
\(723\) −15822.2 −0.813879
\(724\) 7496.88 12985.0i 0.384833 0.666551i
\(725\) 10100.4 17494.4i 0.517407 0.896175i
\(726\) 2643.25 + 4578.24i 0.135124 + 0.234042i
\(727\) −3329.24 + 5766.41i −0.169841 + 0.294174i −0.938364 0.345649i \(-0.887659\pi\)
0.768523 + 0.639823i \(0.220992\pi\)
\(728\) 7088.74 + 12278.1i 0.360888 + 0.625076i
\(729\) 729.000 0.0370370
\(730\) 5980.48 0.303216
\(731\) −1123.12 1945.30i −0.0568264 0.0984262i
\(732\) −2044.11 3540.50i −0.103214 0.178771i
\(733\) 27502.1 1.38583 0.692914 0.721021i \(-0.256327\pi\)
0.692914 + 0.721021i \(0.256327\pi\)
\(734\) −22018.5 −1.10724
\(735\) −5072.68 8786.14i −0.254570 0.440928i
\(736\) −3301.06 + 5717.61i −0.165324 + 0.286350i
\(737\) −2235.09 3871.29i −0.111710 0.193488i
\(738\) 3919.08 6788.05i 0.195479 0.338579i
\(739\) −6421.84 + 11123.0i −0.319663 + 0.553673i −0.980418 0.196929i \(-0.936903\pi\)
0.660754 + 0.750602i \(0.270237\pi\)
\(740\) −9180.34 −0.456049
\(741\) 7148.90 + 12016.7i 0.354415 + 0.595741i
\(742\) 25650.9 1.26910
\(743\) −2403.24 + 4162.54i −0.118663 + 0.205530i −0.919238 0.393702i \(-0.871194\pi\)
0.800575 + 0.599232i \(0.204527\pi\)
\(744\) −1555.49 + 2694.18i −0.0766491 + 0.132760i
\(745\) 4427.15 + 7668.05i 0.217716 + 0.377095i
\(746\) −6151.39 + 10654.5i −0.301901 + 0.522909i
\(747\) 2581.34 + 4471.02i 0.126434 + 0.218991i
\(748\) −1466.05 −0.0716634
\(749\) −57313.4 −2.79598
\(750\) −3485.05 6036.29i −0.169675 0.293885i
\(751\) 2147.88 + 3720.24i 0.104364 + 0.180764i 0.913478 0.406888i \(-0.133386\pi\)
−0.809114 + 0.587652i \(0.800053\pi\)
\(752\) 1735.71 0.0841688
\(753\) −8539.07 −0.413255
\(754\) 11621.9 + 20129.8i 0.561333 + 0.972258i
\(755\) −4255.29 + 7370.38i −0.205120 + 0.355279i
\(756\) 1700.48 + 2945.33i 0.0818069 + 0.141694i
\(757\) −10412.5 + 18035.0i −0.499933 + 0.865910i −1.00000 7.71784e-5i \(-0.999975\pi\)
0.500067 + 0.865987i \(0.333309\pi\)
\(758\) 13458.6 23311.0i 0.644907 1.11701i
\(759\) −13128.7 −0.627854
\(760\) 3453.98 45.1580i 0.164854 0.00215533i
\(761\) −19534.2 −0.930507 −0.465253 0.885178i \(-0.654037\pi\)
−0.465253 + 0.885178i \(0.654037\pi\)
\(762\) −3084.60 + 5342.69i −0.146645 + 0.253996i
\(763\) 1875.94 3249.22i 0.0890086 0.154167i
\(764\) 283.466 + 490.978i 0.0134234 + 0.0232500i
\(765\) 405.390 702.156i 0.0191593 0.0331849i
\(766\) −11090.4 19209.1i −0.523123 0.906075i
\(767\) −6541.89 −0.307971
\(768\) −768.000 −0.0360844
\(769\) −284.228 492.298i −0.0133284 0.0230855i 0.859284 0.511498i \(-0.170909\pi\)
−0.872613 + 0.488413i \(0.837576\pi\)
\(770\) 3482.43 + 6031.74i 0.162984 + 0.282297i
\(771\) −19322.1 −0.902555
\(772\) −15639.6 −0.729120
\(773\) −48.4982 84.0014i −0.00225661 0.00390857i 0.864895 0.501953i \(-0.167385\pi\)
−0.867152 + 0.498044i \(0.834052\pi\)
\(774\) 1169.97 2026.45i 0.0543330 0.0941075i
\(775\) 6339.81 + 10980.9i 0.293849 + 0.508961i
\(776\) 2115.90 3664.84i 0.0978817 0.169536i
\(777\) 20793.7 36015.8i 0.960065 1.66288i
\(778\) −2546.17 −0.117333
\(779\) 36060.8 471.465i 1.65855 0.0216842i
\(780\) 3520.85 0.161624
\(781\) 1675.87 2902.70i 0.0767829 0.132992i
\(782\) −3564.98 + 6174.73i −0.163022 + 0.282363i
\(783\) 2787.93 + 4828.83i 0.127245 + 0.220394i
\(784\) −5189.19 + 8987.95i −0.236388 + 0.409436i
\(785\) 7722.81 + 13376.3i 0.351132 + 0.608179i
\(786\) −9535.01 −0.432700
\(787\) 4906.36 0.222227 0.111114 0.993808i \(-0.464558\pi\)
0.111114 + 0.993808i \(0.464558\pi\)
\(788\) −2406.32 4167.86i −0.108784 0.188419i
\(789\) 6210.61 + 10757.1i 0.280233 + 0.485377i
\(790\) −9231.15 −0.415734
\(791\) 31961.5 1.43669
\(792\) −763.605 1322.60i −0.0342595 0.0593392i
\(793\) 9586.33 16604.0i 0.429282 0.743538i
\(794\) −12328.9 21354.3i −0.551054 0.954454i
\(795\) 3185.09 5516.73i 0.142092 0.246111i
\(796\) −7406.92 + 12829.2i −0.329813 + 0.571253i
\(797\) −32043.3 −1.42413 −0.712066 0.702113i \(-0.752240\pi\)
−0.712066 + 0.702113i \(0.752240\pi\)
\(798\) −7646.20 + 13652.7i −0.339189 + 0.605642i
\(799\) 1874.48 0.0829968
\(800\) −1565.10 + 2710.83i −0.0691681 + 0.119803i
\(801\) −968.560 + 1677.59i −0.0427246 + 0.0740011i
\(802\) 9799.54 + 16973.3i 0.431463 + 0.747316i
\(803\) 6082.83 10535.8i 0.267321 0.463013i
\(804\) −1264.47 2190.13i −0.0554658 0.0960696i
\(805\) 33872.7 1.48305
\(806\) −14589.7 −0.637592
\(807\) 4748.99 + 8225.49i 0.207153 + 0.358799i
\(808\) 4114.94 + 7127.29i 0.179162 + 0.310318i
\(809\) 18714.9 0.813326 0.406663 0.913578i \(-0.366692\pi\)
0.406663 + 0.913578i \(0.366692\pi\)
\(810\) 844.601 0.0366374
\(811\) 4564.67 + 7906.24i 0.197641 + 0.342325i 0.947763 0.318975i \(-0.103338\pi\)
−0.750122 + 0.661300i \(0.770005\pi\)
\(812\) −13006.4 + 22527.7i −0.562112 + 0.973607i
\(813\) 9666.34 + 16742.6i 0.416991 + 0.722249i
\(814\) −9337.46 + 16172.9i −0.402061 + 0.696390i
\(815\) 1634.39 2830.84i 0.0702454 0.121669i
\(816\) −829.401 −0.0355819
\(817\) 10765.3 140.747i 0.460991 0.00602708i
\(818\) −16169.3 −0.691133
\(819\) −7974.83 + 13812.8i −0.340248 + 0.589327i
\(820\) 4540.55 7864.47i 0.193369 0.334926i
\(821\) −11414.4 19770.2i −0.485218 0.840422i 0.514638 0.857408i \(-0.327926\pi\)
−0.999856 + 0.0169856i \(0.994593\pi\)
\(822\) 6975.20 12081.4i 0.295971 0.512636i
\(823\) 18938.9 + 32803.1i 0.802149 + 1.38936i 0.918199 + 0.396120i \(0.129643\pi\)
−0.116050 + 0.993243i \(0.537023\pi\)
\(824\) −866.401 −0.0366293
\(825\) −6224.56 −0.262681
\(826\) −3660.60 6340.35i −0.154199 0.267081i
\(827\) 2060.45 + 3568.80i 0.0866370 + 0.150060i 0.906088 0.423090i \(-0.139055\pi\)
−0.819451 + 0.573150i \(0.805721\pi\)
\(828\) −7427.39 −0.311739
\(829\) −17959.7 −0.752431 −0.376216 0.926532i \(-0.622775\pi\)
−0.376216 + 0.926532i \(0.622775\pi\)
\(830\) 2990.68 + 5180.01i 0.125070 + 0.216627i
\(831\) 599.607 1038.55i 0.0250303 0.0433537i
\(832\) −1800.86 3119.18i −0.0750404 0.129974i
\(833\) −5604.07 + 9706.53i −0.233097 + 0.403735i
\(834\) −1905.17 + 3299.85i −0.0791014 + 0.137008i
\(835\) −8352.98 −0.346188
\(836\) 3433.54 6130.79i 0.142047 0.253634i
\(837\) −3499.85 −0.144531
\(838\) −78.3882 + 135.772i −0.00323136 + 0.00559687i
\(839\) 24100.4 41743.1i 0.991702 1.71768i 0.384515 0.923119i \(-0.374369\pi\)
0.607187 0.794559i \(-0.292298\pi\)
\(840\) 1970.14 + 3412.38i 0.0809241 + 0.140165i
\(841\) −9129.37 + 15812.5i −0.374323 + 0.648347i
\(842\) 7085.19 + 12271.9i 0.289990 + 0.502278i
\(843\) −1891.10 −0.0772633
\(844\) −102.799 −0.00419253
\(845\) 2528.82 + 4380.04i 0.102951 + 0.178317i
\(846\) 976.339 + 1691.07i 0.0396776 + 0.0687236i
\(847\) −27745.7 −1.12556
\(848\) −6516.48 −0.263888
\(849\) 2994.95 + 5187.40i 0.121068 + 0.209695i
\(850\) −1690.23 + 2927.56i −0.0682050 + 0.118135i
\(851\) 45411.5 + 78655.0i 1.82924 + 3.16834i
\(852\) 948.103 1642.16i 0.0381238 0.0660324i
\(853\) −18435.6 + 31931.4i −0.740004 + 1.28172i 0.212490 + 0.977163i \(0.431843\pi\)
−0.952493 + 0.304560i \(0.901490\pi\)
\(854\) 21456.6 0.859755
\(855\) 1986.86 + 3339.74i 0.0794727 + 0.133587i
\(856\) 14560.2 0.581375
\(857\) −16835.4 + 29159.8i −0.671047 + 1.16229i 0.306560 + 0.951851i \(0.400822\pi\)
−0.977607 + 0.210437i \(0.932511\pi\)
\(858\) 3581.11 6202.67i 0.142491 0.246801i
\(859\) −10423.3 18053.6i −0.414013 0.717091i 0.581312 0.813681i \(-0.302540\pi\)
−0.995324 + 0.0965901i \(0.969206\pi\)
\(860\) 1355.50 2347.79i 0.0537467 0.0930919i
\(861\) 20569.0 + 35626.5i 0.814156 + 1.41016i
\(862\) 29802.8 1.17760
\(863\) −47623.4 −1.87847 −0.939235 0.343275i \(-0.888464\pi\)
−0.939235 + 0.343275i \(0.888464\pi\)
\(864\) −432.000 748.246i −0.0170103 0.0294628i
\(865\) 5971.35 + 10342.7i 0.234719 + 0.406545i
\(866\) −8458.97 −0.331925
\(867\) 13843.3 0.542264
\(868\) −8163.84 14140.2i −0.319238 0.552937i
\(869\) −9389.14 + 16262.5i −0.366519 + 0.634829i
\(870\) 3230.02 + 5594.57i 0.125871 + 0.218016i
\(871\) 5930.05 10271.1i 0.230691 0.399569i
\(872\) −476.573 + 825.449i −0.0185078 + 0.0320565i
\(873\) 4760.77 0.184568
\(874\) −17472.4 29369.5i −0.676215 1.13666i
\(875\) 36582.0 1.41337
\(876\) 3441.28 5960.48i 0.132729 0.229893i
\(877\) 4698.68 8138.35i 0.180916 0.313355i −0.761277 0.648427i \(-0.775427\pi\)
0.942193 + 0.335072i \(0.108761\pi\)
\(878\) 10521.5 + 18223.9i 0.404425 + 0.700484i
\(879\) 14515.3 25141.2i 0.556983 0.964723i
\(880\) −884.694 1532.34i −0.0338898 0.0586989i
\(881\) 49897.4 1.90816 0.954079 0.299555i \(-0.0968384\pi\)
0.954079 + 0.299555i \(0.0968384\pi\)
\(882\) −11675.7 −0.445738
\(883\) 1631.56 + 2825.95i 0.0621818 + 0.107702i 0.895440 0.445181i \(-0.146861\pi\)
−0.833259 + 0.552883i \(0.813527\pi\)
\(884\) −1944.84 3368.56i −0.0739955 0.128164i
\(885\) −1818.16 −0.0690584
\(886\) −27734.8 −1.05166
\(887\) −19308.8 33443.9i −0.730921 1.26599i −0.956490 0.291765i \(-0.905758\pi\)
0.225569 0.974227i \(-0.427576\pi\)
\(888\) −5282.55 + 9149.64i −0.199629 + 0.345768i
\(889\) −16189.3 28040.6i −0.610765 1.05788i
\(890\) −1122.15 + 1943.62i −0.0422635 + 0.0732025i
\(891\) 859.056 1487.93i 0.0323002 0.0559456i
\(892\) −12420.8 −0.466230
\(893\) −4390.09 + 7838.77i −0.164512 + 0.293745i
\(894\) 10189.9 0.381209
\(895\) −569.701 + 986.751i −0.0212771 + 0.0368530i
\(896\) 2015.39 3490.76i 0.0751445 0.130154i
\(897\) −17416.3 30165.9i −0.648286 1.12286i
\(898\) 9599.89 16627.5i 0.356740 0.617892i
\(899\) −13384.5 23182.7i −0.496551 0.860052i
\(900\) −3521.47 −0.130425
\(901\) −7037.47 −0.260213
\(902\) −9236.52 15998.1i −0.340956 0.590554i
\(903\) 6140.49 + 10635.6i 0.226293 + 0.391951i
\(904\) −8119.66 −0.298735
\(905\) 19542.8 0.717818
\(906\) 4897.15 + 8482.12i 0.179577 + 0.311037i
\(907\) −290.222 + 502.680i −0.0106248 + 0.0184027i −0.871289 0.490770i \(-0.836715\pi\)
0.860664 + 0.509173i \(0.170049\pi\)
\(908\) −1329.13 2302.13i −0.0485780 0.0841395i
\(909\) −4629.31 + 8018.20i −0.168916 + 0.292571i
\(910\) −9239.44 + 16003.2i −0.336576 + 0.582967i
\(911\) −16704.1 −0.607498 −0.303749 0.952752i \(-0.598238\pi\)
−0.303749 + 0.952752i \(0.598238\pi\)
\(912\) 1942.48 3468.42i 0.0705285 0.125933i
\(913\) 12167.5 0.441056
\(914\) −6261.10 + 10844.5i −0.226585 + 0.392457i
\(915\) 2664.28 4614.67i 0.0962606 0.166728i
\(916\) 12064.0 + 20895.4i 0.435158 + 0.753717i
\(917\) 25021.8 43339.1i 0.901083 1.56072i
\(918\) −466.538 808.068i −0.0167735 0.0290525i
\(919\) 46725.6 1.67719 0.838594 0.544756i \(-0.183378\pi\)
0.838594 + 0.544756i \(0.183378\pi\)
\(920\) −8605.19 −0.308375
\(921\) 10193.3 + 17655.3i 0.364690 + 0.631662i
\(922\) −9825.55 17018.4i −0.350962 0.607885i
\(923\) 8892.72 0.317126
\(924\) 8015.43 0.285377
\(925\) 21530.5 + 37291.8i 0.765316 + 1.32557i
\(926\) 9276.57 16067.5i 0.329208 0.570206i
\(927\) −487.351 844.116i −0.0172672 0.0299077i
\(928\) 3304.21 5723.06i 0.116882 0.202445i
\(929\) 9098.05 15758.3i 0.321310 0.556526i −0.659448 0.751750i \(-0.729210\pi\)
0.980759 + 0.195224i \(0.0625434\pi\)
\(930\) −4054.84 −0.142971
\(931\) −27466.2 46168.2i −0.966882 1.62524i
\(932\) −23032.6 −0.809506
\(933\) −6627.71 + 11479.5i −0.232563 + 0.402811i
\(934\) 18209.4 31539.6i 0.637933 1.10493i
\(935\) −955.425 1654.85i −0.0334179 0.0578815i
\(936\) 2025.97 3509.08i 0.0707487 0.122540i
\(937\) 14372.3 + 24893.5i 0.501091 + 0.867915i 0.999999 + 0.00126003i \(0.000401079\pi\)
−0.498908 + 0.866655i \(0.666266\pi\)
\(938\) 13272.9 0.462022
\(939\) 4174.68 0.145086
\(940\) 1131.16 + 1959.23i 0.0392494 + 0.0679819i
\(941\) −5551.31 9615.15i −0.192314 0.333098i 0.753703 0.657216i \(-0.228266\pi\)
−0.946017 + 0.324118i \(0.894933\pi\)
\(942\) 17775.4 0.614814
\(943\) −89841.3 −3.10248
\(944\) 929.958 + 1610.73i 0.0320631 + 0.0555349i
\(945\) −2216.41 + 3838.93i −0.0762960 + 0.132149i
\(946\) −2757.40 4775.95i −0.0947681 0.164143i
\(947\) 17405.4 30147.0i 0.597254 1.03447i −0.395971 0.918263i \(-0.629592\pi\)
0.993225 0.116211i \(-0.0370747\pi\)
\(948\) −5311.78 + 9200.28i −0.181982 + 0.315202i
\(949\) 32277.4 1.10408
\(950\) −8283.99 13924.7i −0.282914 0.475553i
\(951\) −17996.0 −0.613629
\(952\) 2176.52 3769.84i 0.0740981 0.128342i
\(953\) −16618.4 + 28783.9i −0.564872 + 0.978387i 0.432189 + 0.901783i \(0.357741\pi\)
−0.997062 + 0.0766045i \(0.975592\pi\)
\(954\) −3665.52 6348.87i −0.124398 0.215464i
\(955\) −369.469 + 639.939i −0.0125191 + 0.0216837i
\(956\) 1482.81 + 2568.30i 0.0501648 + 0.0868880i
\(957\) 13141.2 0.443882
\(958\) −25483.4 −0.859426
\(959\) 36608.7 + 63408.1i 1.23270 + 2.13509i
\(960\) −500.504 866.899i −0.0168268 0.0291448i
\(961\) −12988.6 −0.435991
\(962\) −49547.5 −1.66058
\(963\) 8190.11 + 14185.7i 0.274063 + 0.474691i
\(964\) −10548.1 + 18269.9i −0.352420 + 0.610409i
\(965\) −10192.3 17653.6i −0.340001 0.588900i
\(966\) 19491.0 33759.4i 0.649185 1.12442i
\(967\) 2601.77 4506.40i 0.0865225 0.149861i −0.819516 0.573056i \(-0.805758\pi\)
0.906039 + 0.423194i \(0.139091\pi\)
\(968\) 7048.66 0.234042
\(969\) 2097.78 3745.71i 0.0695464 0.124179i
\(970\) 5515.70 0.182576
\(971\) 18518.2 32074.4i 0.612026 1.06006i −0.378873 0.925449i \(-0.623688\pi\)
0.990899 0.134611i \(-0.0429784\pi\)
\(972\) 486.000 841.777i 0.0160375 0.0277778i
\(973\) −9999.10 17318.9i −0.329452 0.570627i
\(974\) −5006.72 + 8671.89i −0.164708 + 0.285282i
\(975\) −8257.38 14302.2i −0.271229 0.469782i
\(976\) −5450.95 −0.178771
\(977\) 28630.1 0.937520 0.468760 0.883326i \(-0.344701\pi\)
0.468760 + 0.883326i \(0.344701\pi\)
\(978\) −1880.92 3257.84i −0.0614980 0.106518i
\(979\) 2282.71 + 3953.77i 0.0745206 + 0.129073i
\(980\) −13527.2 −0.440928
\(981\) −1072.29 −0.0348987
\(982\) 963.312 + 1668.51i 0.0313040 + 0.0542201i
\(983\) 12831.3 22224.4i 0.416332 0.721108i −0.579235 0.815160i \(-0.696649\pi\)
0.995567 + 0.0940523i \(0.0299821\pi\)
\(984\) −5225.44 9050.74i −0.169290 0.293218i
\(985\) 3136.39 5432.38i 0.101455 0.175726i
\(986\) 3568.38 6180.62i 0.115254 0.199626i
\(987\) −10248.5 −0.330508
\(988\) 18641.6 243.724i 0.600272 0.00784806i
\(989\) −26820.5 −0.862327
\(990\) 995.281 1723.88i 0.0319516 0.0553418i
\(991\) 11814.9 20464.0i 0.378720 0.655963i −0.612156 0.790737i \(-0.709698\pi\)
0.990876 + 0.134774i \(0.0430310\pi\)
\(992\) 2073.98 + 3592.25i 0.0663801 + 0.114974i
\(993\) −9907.10 + 17159.6i −0.316609 + 0.548382i
\(994\) 4976.04 + 8618.75i 0.158783 + 0.275020i
\(995\) −19308.3 −0.615190
\(996\) 6883.58 0.218991
\(997\) −25651.8 44430.2i −0.814845 1.41135i −0.909439 0.415836i \(-0.863489\pi\)
0.0945948 0.995516i \(-0.469844\pi\)
\(998\) 4964.84 + 8599.36i 0.157474 + 0.272754i
\(999\) −11885.7 −0.376424
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 114.4.e.e.49.2 yes 6
3.2 odd 2 342.4.g.g.163.2 6
19.7 even 3 inner 114.4.e.e.7.2 6
19.8 odd 6 2166.4.a.w.1.2 3
19.11 even 3 2166.4.a.s.1.2 3
57.26 odd 6 342.4.g.g.235.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.4.e.e.7.2 6 19.7 even 3 inner
114.4.e.e.49.2 yes 6 1.1 even 1 trivial
342.4.g.g.163.2 6 3.2 odd 2
342.4.g.g.235.2 6 57.26 odd 6
2166.4.a.s.1.2 3 19.11 even 3
2166.4.a.w.1.2 3 19.8 odd 6