Properties

Label 245.4.e.q.116.6
Level $245$
Weight $4$
Character 245.116
Analytic conductor $14.455$
Analytic rank $0$
Dimension $12$
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] = [245,4,Mod(116,245)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(245, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("245.116");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.e (of order \(3\), degree \(2\), not 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: \(14.4554679514\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} + 27 x^{10} + 22 x^{9} + 399 x^{8} + 492 x^{7} + 4046 x^{6} + 8784 x^{5} + 22536 x^{4} + 22736 x^{3} + 18792 x^{2} + 4256 x + 784 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 116.6
Root \(2.05188 - 3.55396i\) of defining polynomial
Character \(\chi\) \(=\) 245.116
Dual form 245.4.e.q.226.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.75899 + 4.77871i) q^{2} +(1.93020 - 3.34320i) q^{3} +(-11.2240 + 19.4406i) q^{4} +(-2.50000 - 4.33013i) q^{5} +21.3015 q^{6} -79.7239 q^{8} +(6.04869 + 10.4766i) q^{9} +O(q^{10})\) \(q+(2.75899 + 4.77871i) q^{2} +(1.93020 - 3.34320i) q^{3} +(-11.2240 + 19.4406i) q^{4} +(-2.50000 - 4.33013i) q^{5} +21.3015 q^{6} -79.7239 q^{8} +(6.04869 + 10.4766i) q^{9} +(13.7949 - 23.8935i) q^{10} +(-17.2605 + 29.8961i) q^{11} +(43.3291 + 75.0482i) q^{12} -68.8935 q^{13} -19.3020 q^{15} +(-130.165 - 225.452i) q^{16} +(-45.7173 + 79.1847i) q^{17} +(-33.3765 + 57.8098i) q^{18} +(5.91392 + 10.2432i) q^{19} +112.240 q^{20} -190.486 q^{22} +(0.0520827 + 0.0902099i) q^{23} +(-153.883 + 266.533i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-190.076 - 329.222i) q^{26} +150.931 q^{27} +190.863 q^{29} +(-53.2538 - 92.2384i) q^{30} +(79.9010 - 138.393i) q^{31} +(399.352 - 691.697i) q^{32} +(66.6324 + 115.411i) q^{33} -504.534 q^{34} -271.562 q^{36} +(88.9538 + 154.073i) q^{37} +(-32.6328 + 56.5217i) q^{38} +(-132.978 + 230.324i) q^{39} +(199.310 + 345.215i) q^{40} -145.247 q^{41} +8.25729 q^{43} +(-387.465 - 671.109i) q^{44} +(30.2435 - 52.3832i) q^{45} +(-0.287391 + 0.497776i) q^{46} +(130.264 + 225.624i) q^{47} -1004.98 q^{48} -137.949 q^{50} +(176.487 + 305.684i) q^{51} +(773.262 - 1339.33i) q^{52} +(-176.554 + 305.800i) q^{53} +(416.417 + 721.256i) q^{54} +172.605 q^{55} +45.6601 q^{57} +(526.589 + 912.079i) q^{58} +(120.247 - 208.274i) q^{59} +(216.645 - 375.241i) q^{60} +(389.094 + 673.931i) q^{61} +881.783 q^{62} +2324.58 q^{64} +(172.234 + 298.318i) q^{65} +(-367.676 + 636.833i) q^{66} +(-75.9723 + 131.588i) q^{67} +(-1026.26 - 1777.54i) q^{68} +0.402119 q^{69} -311.449 q^{71} +(-482.225 - 835.238i) q^{72} +(319.944 - 554.159i) q^{73} +(-490.845 + 850.168i) q^{74} +(48.2549 + 83.5799i) q^{75} -265.512 q^{76} -1467.54 q^{78} +(-195.593 - 338.777i) q^{79} +(-650.825 + 1127.26i) q^{80} +(128.012 - 221.723i) q^{81} +(-400.736 - 694.095i) q^{82} -493.205 q^{83} +457.173 q^{85} +(22.7817 + 39.4591i) q^{86} +(368.403 - 638.093i) q^{87} +(1376.08 - 2383.44i) q^{88} +(236.925 + 410.366i) q^{89} +333.765 q^{90} -2.33831 q^{92} +(-308.449 - 534.249i) q^{93} +(-718.795 + 1244.99i) q^{94} +(29.5696 - 51.2160i) q^{95} +(-1541.65 - 2670.22i) q^{96} -839.005 q^{97} -417.615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} + 16 q^{3} - 14 q^{4} - 30 q^{5} - 48 q^{6} - 132 q^{8} - 70 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{2} + 16 q^{3} - 14 q^{4} - 30 q^{5} - 48 q^{6} - 132 q^{8} - 70 q^{9} + 10 q^{10} + 16 q^{11} + 160 q^{12} - 336 q^{13} - 160 q^{15} - 298 q^{16} - 4 q^{17} - 354 q^{18} + 308 q^{19} + 140 q^{20} - 472 q^{22} + 336 q^{23} - 92 q^{24} - 150 q^{25} + 56 q^{26} - 1928 q^{27} + 352 q^{29} + 120 q^{30} + 392 q^{31} + 770 q^{32} + 188 q^{33} - 1624 q^{34} + 460 q^{36} + 140 q^{37} + 20 q^{38} - 140 q^{39} + 330 q^{40} - 1312 q^{41} - 776 q^{43} + 160 q^{44} - 350 q^{45} + 388 q^{46} + 628 q^{47} - 2792 q^{48} - 100 q^{50} - 744 q^{51} + 1520 q^{52} + 676 q^{53} + 2284 q^{54} - 160 q^{55} + 2936 q^{57} + 2012 q^{58} + 996 q^{59} + 800 q^{60} + 740 q^{61} + 728 q^{62} + 2852 q^{64} + 840 q^{65} - 3620 q^{66} - 1768 q^{67} - 2940 q^{68} + 2096 q^{69} - 448 q^{71} - 2858 q^{72} + 2640 q^{73} - 928 q^{74} + 400 q^{75} + 2680 q^{76} + 16 q^{78} - 1636 q^{79} - 1490 q^{80} - 4442 q^{81} - 1756 q^{82} - 280 q^{83} + 40 q^{85} - 1180 q^{86} + 1940 q^{87} + 5652 q^{88} - 1904 q^{89} + 3540 q^{90} - 3904 q^{92} + 1592 q^{93} - 3332 q^{94} + 1540 q^{95} - 6460 q^{96} - 1032 q^{97} - 5608 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.75899 + 4.77871i 0.975449 + 1.68953i 0.678445 + 0.734651i \(0.262654\pi\)
0.297004 + 0.954876i \(0.404012\pi\)
\(3\) 1.93020 3.34320i 0.371466 0.643398i −0.618325 0.785922i \(-0.712188\pi\)
0.989791 + 0.142524i \(0.0455218\pi\)
\(4\) −11.2240 + 19.4406i −1.40300 + 2.43007i
\(5\) −2.50000 4.33013i −0.223607 0.387298i
\(6\) 21.3015 1.44939
\(7\) 0 0
\(8\) −79.7239 −3.52333
\(9\) 6.04869 + 10.4766i 0.224026 + 0.388024i
\(10\) 13.7949 23.8935i 0.436234 0.755580i
\(11\) −17.2605 + 29.8961i −0.473113 + 0.819456i −0.999526 0.0307725i \(-0.990203\pi\)
0.526413 + 0.850229i \(0.323537\pi\)
\(12\) 43.3291 + 75.0482i 1.04234 + 1.80538i
\(13\) −68.8935 −1.46982 −0.734908 0.678167i \(-0.762775\pi\)
−0.734908 + 0.678167i \(0.762775\pi\)
\(14\) 0 0
\(15\) −19.3020 −0.332250
\(16\) −130.165 225.452i −2.03383 3.52269i
\(17\) −45.7173 + 79.1847i −0.652239 + 1.12971i 0.330339 + 0.943862i \(0.392837\pi\)
−0.982578 + 0.185849i \(0.940496\pi\)
\(18\) −33.3765 + 57.8098i −0.437051 + 0.756995i
\(19\) 5.91392 + 10.2432i 0.0714077 + 0.123682i 0.899518 0.436883i \(-0.143918\pi\)
−0.828111 + 0.560564i \(0.810584\pi\)
\(20\) 112.240 1.25488
\(21\) 0 0
\(22\) −190.486 −1.84599
\(23\) 0.0520827 + 0.0902099i 0.000472174 + 0.000817829i 0.866261 0.499591i \(-0.166516\pi\)
−0.865789 + 0.500409i \(0.833183\pi\)
\(24\) −153.883 + 266.533i −1.30880 + 2.26691i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −190.076 329.222i −1.43373 2.48330i
\(27\) 150.931 1.07580
\(28\) 0 0
\(29\) 190.863 1.22215 0.611076 0.791572i \(-0.290737\pi\)
0.611076 + 0.791572i \(0.290737\pi\)
\(30\) −53.2538 92.2384i −0.324093 0.561345i
\(31\) 79.9010 138.393i 0.462924 0.801807i −0.536181 0.844103i \(-0.680134\pi\)
0.999105 + 0.0422954i \(0.0134671\pi\)
\(32\) 399.352 691.697i 2.20613 3.82112i
\(33\) 66.6324 + 115.411i 0.351491 + 0.608801i
\(34\) −504.534 −2.54491
\(35\) 0 0
\(36\) −271.562 −1.25723
\(37\) 88.9538 + 154.073i 0.395241 + 0.684577i 0.993132 0.117000i \(-0.0373277\pi\)
−0.597891 + 0.801577i \(0.703994\pi\)
\(38\) −32.6328 + 56.5217i −0.139309 + 0.241290i
\(39\) −132.978 + 230.324i −0.545987 + 0.945678i
\(40\) 199.310 + 345.215i 0.787841 + 1.36458i
\(41\) −145.247 −0.553264 −0.276632 0.960976i \(-0.589218\pi\)
−0.276632 + 0.960976i \(0.589218\pi\)
\(42\) 0 0
\(43\) 8.25729 0.0292843 0.0146421 0.999893i \(-0.495339\pi\)
0.0146421 + 0.999893i \(0.495339\pi\)
\(44\) −387.465 671.109i −1.32756 2.29940i
\(45\) 30.2435 52.3832i 0.100187 0.173529i
\(46\) −0.287391 + 0.497776i −0.000921163 + 0.00159550i
\(47\) 130.264 + 225.624i 0.404277 + 0.700228i 0.994237 0.107204i \(-0.0341899\pi\)
−0.589960 + 0.807432i \(0.700857\pi\)
\(48\) −1004.98 −3.02199
\(49\) 0 0
\(50\) −137.949 −0.390180
\(51\) 176.487 + 305.684i 0.484570 + 0.839300i
\(52\) 773.262 1339.33i 2.06216 3.57176i
\(53\) −176.554 + 305.800i −0.457576 + 0.792544i −0.998832 0.0483132i \(-0.984615\pi\)
0.541257 + 0.840857i \(0.317949\pi\)
\(54\) 416.417 + 721.256i 1.04939 + 1.81760i
\(55\) 172.605 0.423165
\(56\) 0 0
\(57\) 45.6601 0.106102
\(58\) 526.589 + 912.079i 1.19215 + 2.06486i
\(59\) 120.247 208.274i 0.265337 0.459576i −0.702315 0.711866i \(-0.747850\pi\)
0.967652 + 0.252290i \(0.0811836\pi\)
\(60\) 216.645 375.241i 0.466147 0.807390i
\(61\) 389.094 + 673.931i 0.816695 + 1.41456i 0.908104 + 0.418744i \(0.137530\pi\)
−0.0914091 + 0.995813i \(0.529137\pi\)
\(62\) 881.783 1.80623
\(63\) 0 0
\(64\) 2324.58 4.54020
\(65\) 172.234 + 298.318i 0.328661 + 0.569257i
\(66\) −367.676 + 636.833i −0.685724 + 1.18771i
\(67\) −75.9723 + 131.588i −0.138530 + 0.239940i −0.926940 0.375209i \(-0.877571\pi\)
0.788411 + 0.615149i \(0.210904\pi\)
\(68\) −1026.26 1777.54i −1.83019 3.16998i
\(69\) 0.402119 0.000701587
\(70\) 0 0
\(71\) −311.449 −0.520594 −0.260297 0.965529i \(-0.583820\pi\)
−0.260297 + 0.965529i \(0.583820\pi\)
\(72\) −482.225 835.238i −0.789316 1.36714i
\(73\) 319.944 554.159i 0.512967 0.888485i −0.486920 0.873447i \(-0.661880\pi\)
0.999887 0.0150383i \(-0.00478701\pi\)
\(74\) −490.845 + 850.168i −0.771075 + 1.33554i
\(75\) 48.2549 + 83.5799i 0.0742933 + 0.128680i
\(76\) −265.512 −0.400740
\(77\) 0 0
\(78\) −1467.54 −2.13033
\(79\) −195.593 338.777i −0.278556 0.482473i 0.692470 0.721447i \(-0.256522\pi\)
−0.971026 + 0.238973i \(0.923189\pi\)
\(80\) −650.825 + 1127.26i −0.909556 + 1.57540i
\(81\) 128.012 221.723i 0.175599 0.304147i
\(82\) −400.736 694.095i −0.539681 0.934755i
\(83\) −493.205 −0.652245 −0.326122 0.945328i \(-0.605742\pi\)
−0.326122 + 0.945328i \(0.605742\pi\)
\(84\) 0 0
\(85\) 457.173 0.583381
\(86\) 22.7817 + 39.4591i 0.0285653 + 0.0494766i
\(87\) 368.403 638.093i 0.453988 0.786331i
\(88\) 1376.08 2383.44i 1.66694 2.88722i
\(89\) 236.925 + 410.366i 0.282180 + 0.488749i 0.971921 0.235306i \(-0.0756092\pi\)
−0.689742 + 0.724056i \(0.742276\pi\)
\(90\) 333.765 0.390910
\(91\) 0 0
\(92\) −2.33831 −0.00264984
\(93\) −308.449 534.249i −0.343921 0.595689i
\(94\) −718.795 + 1244.99i −0.788703 + 1.36607i
\(95\) 29.5696 51.2160i 0.0319345 0.0553121i
\(96\) −1541.65 2670.22i −1.63900 2.83884i
\(97\) −839.005 −0.878227 −0.439114 0.898431i \(-0.644707\pi\)
−0.439114 + 0.898431i \(0.644707\pi\)
\(98\) 0 0
\(99\) −417.615 −0.423958
\(100\) −280.600 486.014i −0.280600 0.486014i
\(101\) 443.720 768.546i 0.437146 0.757160i −0.560322 0.828275i \(-0.689322\pi\)
0.997468 + 0.0711152i \(0.0226558\pi\)
\(102\) −973.848 + 1686.75i −0.945347 + 1.63739i
\(103\) 309.544 + 536.145i 0.296119 + 0.512893i 0.975245 0.221129i \(-0.0709742\pi\)
−0.679126 + 0.734022i \(0.737641\pi\)
\(104\) 5492.46 5.17865
\(105\) 0 0
\(106\) −1948.44 −1.78537
\(107\) 1075.65 + 1863.08i 0.971841 + 1.68328i 0.689990 + 0.723819i \(0.257615\pi\)
0.281851 + 0.959458i \(0.409052\pi\)
\(108\) −1694.05 + 2934.19i −1.50936 + 2.61428i
\(109\) 203.538 352.539i 0.178857 0.309790i −0.762632 0.646832i \(-0.776093\pi\)
0.941489 + 0.337043i \(0.109427\pi\)
\(110\) 476.216 + 824.830i 0.412776 + 0.714950i
\(111\) 686.793 0.587275
\(112\) 0 0
\(113\) −349.581 −0.291025 −0.145513 0.989356i \(-0.546483\pi\)
−0.145513 + 0.989356i \(0.546483\pi\)
\(114\) 125.976 + 218.196i 0.103497 + 0.179263i
\(115\) 0.260414 0.451050i 0.000211163 0.000365744i
\(116\) −2142.25 + 3710.49i −1.71468 + 2.96992i
\(117\) −416.715 721.772i −0.329277 0.570324i
\(118\) 1327.04 1.03529
\(119\) 0 0
\(120\) 1538.83 1.17063
\(121\) 69.6478 + 120.633i 0.0523274 + 0.0906337i
\(122\) −2147.01 + 3718.73i −1.59329 + 2.75966i
\(123\) −280.356 + 485.591i −0.205519 + 0.355969i
\(124\) 1793.62 + 3106.64i 1.29897 + 2.24987i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 1183.78 0.827114 0.413557 0.910478i \(-0.364286\pi\)
0.413557 + 0.910478i \(0.364286\pi\)
\(128\) 3218.68 + 5574.92i 2.22261 + 3.84967i
\(129\) 15.9382 27.6057i 0.0108781 0.0188415i
\(130\) −950.381 + 1646.11i −0.641184 + 1.11056i
\(131\) 111.679 + 193.433i 0.0744840 + 0.129010i 0.900862 0.434106i \(-0.142936\pi\)
−0.826378 + 0.563116i \(0.809602\pi\)
\(132\) −2991.53 −1.97257
\(133\) 0 0
\(134\) −838.426 −0.540515
\(135\) −377.328 653.551i −0.240557 0.416657i
\(136\) 3644.76 6312.91i 2.29806 3.98035i
\(137\) −1018.33 + 1763.80i −0.635050 + 1.09994i 0.351454 + 0.936205i \(0.385687\pi\)
−0.986504 + 0.163734i \(0.947646\pi\)
\(138\) 1.10944 + 1.92161i 0.000684362 + 0.00118535i
\(139\) −2687.00 −1.63963 −0.819815 0.572629i \(-0.805924\pi\)
−0.819815 + 0.572629i \(0.805924\pi\)
\(140\) 0 0
\(141\) 1005.74 0.600701
\(142\) −859.283 1488.32i −0.507813 0.879557i
\(143\) 1189.14 2059.65i 0.695390 1.20445i
\(144\) 1574.66 2727.38i 0.911259 1.57835i
\(145\) −477.158 826.462i −0.273282 0.473337i
\(146\) 3530.88 2.00149
\(147\) 0 0
\(148\) −3993.68 −2.21810
\(149\) −336.750 583.268i −0.185152 0.320693i 0.758476 0.651701i \(-0.225944\pi\)
−0.943628 + 0.331009i \(0.892611\pi\)
\(150\) −266.269 + 461.192i −0.144939 + 0.251041i
\(151\) 1062.59 1840.46i 0.572664 0.991884i −0.423627 0.905837i \(-0.639243\pi\)
0.996291 0.0860467i \(-0.0274234\pi\)
\(152\) −471.480 816.628i −0.251593 0.435772i
\(153\) −1106.12 −0.584473
\(154\) 0 0
\(155\) −799.010 −0.414052
\(156\) −2985.09 5170.33i −1.53204 2.65358i
\(157\) −1406.52 + 2436.16i −0.714983 + 1.23839i 0.247984 + 0.968764i \(0.420232\pi\)
−0.962966 + 0.269622i \(0.913101\pi\)
\(158\) 1079.28 1869.36i 0.543435 0.941257i
\(159\) 681.566 + 1180.51i 0.339948 + 0.588807i
\(160\) −3993.52 −1.97322
\(161\) 0 0
\(162\) 1412.73 0.685153
\(163\) 672.210 + 1164.30i 0.323016 + 0.559480i 0.981109 0.193457i \(-0.0619699\pi\)
−0.658093 + 0.752937i \(0.728637\pi\)
\(164\) 1630.26 2823.69i 0.776231 1.34447i
\(165\) 333.162 577.054i 0.157192 0.272264i
\(166\) −1360.75 2356.88i −0.636232 1.10199i
\(167\) −1451.24 −0.672456 −0.336228 0.941781i \(-0.609151\pi\)
−0.336228 + 0.941781i \(0.609151\pi\)
\(168\) 0 0
\(169\) 2549.31 1.16036
\(170\) 1261.33 + 2184.69i 0.569058 + 0.985638i
\(171\) −71.5429 + 123.916i −0.0319943 + 0.0554157i
\(172\) −92.6799 + 160.526i −0.0410859 + 0.0711629i
\(173\) −989.579 1714.00i −0.434892 0.753255i 0.562395 0.826869i \(-0.309880\pi\)
−0.997287 + 0.0736139i \(0.976547\pi\)
\(174\) 4065.68 1.77137
\(175\) 0 0
\(176\) 8986.87 3.84893
\(177\) −464.201 804.020i −0.197127 0.341434i
\(178\) −1307.35 + 2264.39i −0.550504 + 0.953501i
\(179\) 2179.33 3774.71i 0.910005 1.57617i 0.0959500 0.995386i \(-0.469411\pi\)
0.814055 0.580788i \(-0.197256\pi\)
\(180\) 678.906 + 1175.90i 0.281126 + 0.486924i
\(181\) 377.923 0.155198 0.0775988 0.996985i \(-0.475275\pi\)
0.0775988 + 0.996985i \(0.475275\pi\)
\(182\) 0 0
\(183\) 3004.11 1.21350
\(184\) −4.15224 7.19189i −0.00166362 0.00288148i
\(185\) 444.769 770.363i 0.176757 0.306152i
\(186\) 1702.01 2947.97i 0.670955 1.16213i
\(187\) −1578.21 2733.54i −0.617166 1.06896i
\(188\) −5848.36 −2.26880
\(189\) 0 0
\(190\) 326.328 0.124602
\(191\) 1212.97 + 2100.93i 0.459517 + 0.795906i 0.998935 0.0461315i \(-0.0146893\pi\)
−0.539419 + 0.842038i \(0.681356\pi\)
\(192\) 4486.90 7771.54i 1.68653 2.92116i
\(193\) 311.461 539.467i 0.116163 0.201200i −0.802081 0.597215i \(-0.796274\pi\)
0.918244 + 0.396015i \(0.129607\pi\)
\(194\) −2314.80 4009.36i −0.856666 1.48379i
\(195\) 1329.78 0.488346
\(196\) 0 0
\(197\) 2842.29 1.02794 0.513971 0.857807i \(-0.328174\pi\)
0.513971 + 0.857807i \(0.328174\pi\)
\(198\) −1152.19 1995.66i −0.413550 0.716289i
\(199\) −433.682 + 751.159i −0.154487 + 0.267579i −0.932872 0.360208i \(-0.882706\pi\)
0.778385 + 0.627787i \(0.216039\pi\)
\(200\) 996.549 1726.07i 0.352333 0.610259i
\(201\) 293.283 + 507.980i 0.102918 + 0.178260i
\(202\) 4896.87 1.70566
\(203\) 0 0
\(204\) −7923.55 −2.71941
\(205\) 363.119 + 628.940i 0.123714 + 0.214278i
\(206\) −1708.05 + 2958.44i −0.577698 + 1.00060i
\(207\) −0.630065 + 1.09130i −0.000211558 + 0.000366429i
\(208\) 8967.52 + 15532.2i 2.98935 + 5.17771i
\(209\) −408.309 −0.135136
\(210\) 0 0
\(211\) −5975.92 −1.94976 −0.974880 0.222730i \(-0.928503\pi\)
−0.974880 + 0.222730i \(0.928503\pi\)
\(212\) −3963.28 6864.61i −1.28396 2.22388i
\(213\) −601.157 + 1041.23i −0.193383 + 0.334949i
\(214\) −5935.40 + 10280.4i −1.89596 + 3.28390i
\(215\) −20.6432 35.7551i −0.00654817 0.0113418i
\(216\) −12032.8 −3.79042
\(217\) 0 0
\(218\) 2246.24 0.697864
\(219\) −1235.11 2139.27i −0.381100 0.660084i
\(220\) −1937.33 + 3355.55i −0.593702 + 1.02832i
\(221\) 3149.62 5455.31i 0.958672 1.66047i
\(222\) 1894.85 + 3281.98i 0.572857 + 0.992217i
\(223\) 5181.58 1.55598 0.777992 0.628274i \(-0.216238\pi\)
0.777992 + 0.628274i \(0.216238\pi\)
\(224\) 0 0
\(225\) −302.435 −0.0896102
\(226\) −964.491 1670.55i −0.283880 0.491695i
\(227\) 1876.53 3250.24i 0.548677 0.950336i −0.449689 0.893185i \(-0.648465\pi\)
0.998366 0.0571507i \(-0.0182016\pi\)
\(228\) −512.489 + 887.658i −0.148862 + 0.257836i
\(229\) −3129.07 5419.71i −0.902947 1.56395i −0.823650 0.567099i \(-0.808066\pi\)
−0.0792969 0.996851i \(-0.525268\pi\)
\(230\) 2.87391 0.000823913
\(231\) 0 0
\(232\) −15216.4 −4.30605
\(233\) −889.981 1541.49i −0.250234 0.433419i 0.713356 0.700802i \(-0.247174\pi\)
−0.963590 + 0.267383i \(0.913841\pi\)
\(234\) 2299.42 3982.72i 0.642385 1.11264i
\(235\) 651.322 1128.12i 0.180798 0.313151i
\(236\) 2699.31 + 4675.35i 0.744536 + 1.28957i
\(237\) −1510.13 −0.413897
\(238\) 0 0
\(239\) 3519.46 0.952532 0.476266 0.879301i \(-0.341990\pi\)
0.476266 + 0.879301i \(0.341990\pi\)
\(240\) 2512.44 + 4351.67i 0.675739 + 1.17041i
\(241\) 181.465 314.307i 0.0485029 0.0840095i −0.840755 0.541416i \(-0.817888\pi\)
0.889258 + 0.457407i \(0.151222\pi\)
\(242\) −384.315 + 665.652i −0.102085 + 0.176817i
\(243\) 1543.39 + 2673.24i 0.407444 + 0.705713i
\(244\) −17468.8 −4.58330
\(245\) 0 0
\(246\) −3093.99 −0.801894
\(247\) −407.430 705.690i −0.104956 0.181789i
\(248\) −6370.01 + 11033.2i −1.63103 + 2.82503i
\(249\) −951.983 + 1648.88i −0.242287 + 0.419653i
\(250\) 344.873 + 597.338i 0.0872468 + 0.151116i
\(251\) 5333.85 1.34131 0.670656 0.741768i \(-0.266012\pi\)
0.670656 + 0.741768i \(0.266012\pi\)
\(252\) 0 0
\(253\) −3.59590 −0.000893567
\(254\) 3266.03 + 5656.93i 0.806807 + 1.39743i
\(255\) 882.433 1528.42i 0.216706 0.375346i
\(256\) −8462.27 + 14657.1i −2.06598 + 3.57839i
\(257\) −1219.39 2112.04i −0.295966 0.512629i 0.679243 0.733914i \(-0.262308\pi\)
−0.975209 + 0.221285i \(0.928975\pi\)
\(258\) 175.893 0.0424442
\(259\) 0 0
\(260\) −7732.62 −1.84445
\(261\) 1154.47 + 1999.61i 0.273793 + 0.474224i
\(262\) −616.239 + 1067.36i −0.145311 + 0.251685i
\(263\) −763.126 + 1321.77i −0.178921 + 0.309901i −0.941511 0.336981i \(-0.890594\pi\)
0.762590 + 0.646882i \(0.223927\pi\)
\(264\) −5312.19 9200.99i −1.23842 2.14501i
\(265\) 1765.54 0.409268
\(266\) 0 0
\(267\) 1829.25 0.419281
\(268\) −1705.43 2953.89i −0.388715 0.673274i
\(269\) −3782.06 + 6550.72i −0.857235 + 1.48478i 0.0173203 + 0.999850i \(0.494487\pi\)
−0.874556 + 0.484925i \(0.838847\pi\)
\(270\) 2082.09 3606.28i 0.469303 0.812856i
\(271\) 2141.34 + 3708.91i 0.479990 + 0.831367i 0.999737 0.0229535i \(-0.00730696\pi\)
−0.519747 + 0.854320i \(0.673974\pi\)
\(272\) 23803.2 5.30617
\(273\) 0 0
\(274\) −11238.2 −2.47784
\(275\) −431.513 747.403i −0.0946227 0.163891i
\(276\) −4.51339 + 7.81743i −0.000984328 + 0.00170491i
\(277\) 2004.20 3471.38i 0.434732 0.752979i −0.562541 0.826769i \(-0.690176\pi\)
0.997274 + 0.0737905i \(0.0235096\pi\)
\(278\) −7413.40 12840.4i −1.59937 2.77020i
\(279\) 1933.18 0.414827
\(280\) 0 0
\(281\) 6935.44 1.47236 0.736181 0.676785i \(-0.236627\pi\)
0.736181 + 0.676785i \(0.236627\pi\)
\(282\) 2774.83 + 4806.15i 0.585953 + 1.01490i
\(283\) −1333.32 + 2309.38i −0.280062 + 0.485082i −0.971400 0.237450i \(-0.923688\pi\)
0.691338 + 0.722532i \(0.257022\pi\)
\(284\) 3495.71 6054.74i 0.730394 1.26508i
\(285\) −114.150 197.714i −0.0237252 0.0410932i
\(286\) 13123.3 2.71327
\(287\) 0 0
\(288\) 9662.22 1.97692
\(289\) −1723.64 2985.43i −0.350832 0.607660i
\(290\) 2632.95 4560.40i 0.533144 0.923433i
\(291\) −1619.44 + 2804.96i −0.326232 + 0.565050i
\(292\) 7182.11 + 12439.8i 1.43939 + 2.49309i
\(293\) −5939.10 −1.18418 −0.592092 0.805870i \(-0.701698\pi\)
−0.592092 + 0.805870i \(0.701698\pi\)
\(294\) 0 0
\(295\) −1202.47 −0.237324
\(296\) −7091.74 12283.3i −1.39256 2.41199i
\(297\) −2605.15 + 4512.26i −0.508977 + 0.881575i
\(298\) 1858.18 3218.46i 0.361213 0.625639i
\(299\) −3.58816 6.21488i −0.000694009 0.00120206i
\(300\) −2166.45 −0.416934
\(301\) 0 0
\(302\) 11726.7 2.23442
\(303\) −1712.93 2966.89i −0.324770 0.562519i
\(304\) 1539.57 2666.61i 0.290462 0.503095i
\(305\) 1945.47 3369.65i 0.365237 0.632609i
\(306\) −3051.77 5285.82i −0.570124 0.987484i
\(307\) −10381.5 −1.92998 −0.964992 0.262278i \(-0.915526\pi\)
−0.964992 + 0.262278i \(0.915526\pi\)
\(308\) 0 0
\(309\) 2389.92 0.439993
\(310\) −2204.46 3818.23i −0.403886 0.699551i
\(311\) 2120.27 3672.42i 0.386590 0.669594i −0.605398 0.795923i \(-0.706986\pi\)
0.991988 + 0.126329i \(0.0403194\pi\)
\(312\) 10601.5 18362.4i 1.92369 3.33194i
\(313\) −141.951 245.867i −0.0256344 0.0444001i 0.852924 0.522036i \(-0.174827\pi\)
−0.878558 + 0.477636i \(0.841494\pi\)
\(314\) −15522.2 −2.78972
\(315\) 0 0
\(316\) 8781.36 1.56326
\(317\) −869.746 1506.44i −0.154100 0.266910i 0.778631 0.627482i \(-0.215915\pi\)
−0.932731 + 0.360573i \(0.882581\pi\)
\(318\) −3760.86 + 6514.01i −0.663204 + 1.14870i
\(319\) −3294.40 + 5706.07i −0.578217 + 1.00150i
\(320\) −5811.46 10065.7i −1.01522 1.75841i
\(321\) 8304.85 1.44402
\(322\) 0 0
\(323\) −1081.47 −0.186300
\(324\) 2873.62 + 4977.25i 0.492733 + 0.853438i
\(325\) 861.169 1491.59i 0.146982 0.254580i
\(326\) −3709.24 + 6424.59i −0.630171 + 1.09149i
\(327\) −785.737 1360.94i −0.132879 0.230153i
\(328\) 11579.7 1.94933
\(329\) 0 0
\(330\) 3676.76 0.613330
\(331\) −2803.48 4855.77i −0.465538 0.806336i 0.533687 0.845682i \(-0.320806\pi\)
−0.999226 + 0.0393458i \(0.987473\pi\)
\(332\) 5535.75 9588.19i 0.915101 1.58500i
\(333\) −1076.11 + 1863.87i −0.177088 + 0.306726i
\(334\) −4003.94 6935.04i −0.655946 1.13613i
\(335\) 759.723 0.123905
\(336\) 0 0
\(337\) −9427.44 −1.52387 −0.761937 0.647652i \(-0.775751\pi\)
−0.761937 + 0.647652i \(0.775751\pi\)
\(338\) 7033.52 + 12182.4i 1.13187 + 1.96046i
\(339\) −674.760 + 1168.72i −0.108106 + 0.187245i
\(340\) −5131.32 + 8887.70i −0.818484 + 1.41766i
\(341\) 2758.27 + 4777.46i 0.438031 + 0.758692i
\(342\) −789.544 −0.124835
\(343\) 0 0
\(344\) −658.303 −0.103178
\(345\) −1.00530 1.74123i −0.000156880 0.000271723i
\(346\) 5460.47 9457.81i 0.848430 1.46952i
\(347\) −5817.11 + 10075.5i −0.899939 + 1.55874i −0.0723679 + 0.997378i \(0.523056\pi\)
−0.827571 + 0.561361i \(0.810278\pi\)
\(348\) 8269.93 + 14323.9i 1.27389 + 2.20645i
\(349\) 1317.10 0.202013 0.101006 0.994886i \(-0.467794\pi\)
0.101006 + 0.994886i \(0.467794\pi\)
\(350\) 0 0
\(351\) −10398.2 −1.58124
\(352\) 13786.0 + 23878.1i 2.08750 + 3.61565i
\(353\) 2924.41 5065.23i 0.440937 0.763725i −0.556822 0.830632i \(-0.687980\pi\)
0.997759 + 0.0669064i \(0.0213129\pi\)
\(354\) 2561.45 4436.56i 0.384575 0.666104i
\(355\) 778.622 + 1348.61i 0.116408 + 0.201625i
\(356\) −10637.0 −1.58359
\(357\) 0 0
\(358\) 24051.0 3.55065
\(359\) 6211.00 + 10757.8i 0.913104 + 1.58154i 0.809654 + 0.586907i \(0.199655\pi\)
0.103450 + 0.994635i \(0.467012\pi\)
\(360\) −2411.13 + 4176.19i −0.352993 + 0.611402i
\(361\) 3359.55 5818.91i 0.489802 0.848362i
\(362\) 1042.68 + 1805.98i 0.151387 + 0.262211i
\(363\) 537.735 0.0777515
\(364\) 0 0
\(365\) −3199.44 −0.458812
\(366\) 8288.30 + 14355.8i 1.18371 + 2.05024i
\(367\) −3295.39 + 5707.78i −0.468713 + 0.811836i −0.999361 0.0357573i \(-0.988616\pi\)
0.530647 + 0.847593i \(0.321949\pi\)
\(368\) 13.5587 23.4844i 0.00192064 0.00332665i
\(369\) −878.557 1521.71i −0.123945 0.214680i
\(370\) 4908.45 0.689670
\(371\) 0 0
\(372\) 13848.1 1.93009
\(373\) −172.139 298.154i −0.0238955 0.0413882i 0.853830 0.520551i \(-0.174274\pi\)
−0.877726 + 0.479163i \(0.840940\pi\)
\(374\) 8708.52 15083.6i 1.20403 2.08544i
\(375\) 241.274 417.900i 0.0332250 0.0575473i
\(376\) −10385.2 17987.7i −1.42440 2.46713i
\(377\) −13149.2 −1.79634
\(378\) 0 0
\(379\) 5241.23 0.710353 0.355177 0.934799i \(-0.384421\pi\)
0.355177 + 0.934799i \(0.384421\pi\)
\(380\) 663.779 + 1149.70i 0.0896083 + 0.155206i
\(381\) 2284.93 3957.61i 0.307245 0.532164i
\(382\) −6693.16 + 11592.9i −0.896470 + 1.55273i
\(383\) 3798.69 + 6579.52i 0.506798 + 0.877801i 0.999969 + 0.00786802i \(0.00250450\pi\)
−0.493171 + 0.869933i \(0.664162\pi\)
\(384\) 24850.7 3.30250
\(385\) 0 0
\(386\) 3437.27 0.453245
\(387\) 49.9458 + 86.5086i 0.00656043 + 0.0113630i
\(388\) 9417.01 16310.7i 1.23216 2.13416i
\(389\) −1550.92 + 2686.27i −0.202146 + 0.350127i −0.949220 0.314614i \(-0.898125\pi\)
0.747074 + 0.664741i \(0.231458\pi\)
\(390\) 3668.84 + 6354.62i 0.476357 + 0.825074i
\(391\) −9.52432 −0.00123188
\(392\) 0 0
\(393\) 862.246 0.110673
\(394\) 7841.84 + 13582.5i 1.00271 + 1.73674i
\(395\) −977.965 + 1693.89i −0.124574 + 0.215769i
\(396\) 4687.31 8118.67i 0.594814 1.03025i
\(397\) −1466.03 2539.24i −0.185335 0.321009i 0.758355 0.651842i \(-0.226004\pi\)
−0.943689 + 0.330833i \(0.892670\pi\)
\(398\) −4786.09 −0.602777
\(399\) 0 0
\(400\) 6508.25 0.813531
\(401\) −44.6187 77.2819i −0.00555649 0.00962413i 0.863234 0.504804i \(-0.168435\pi\)
−0.868790 + 0.495180i \(0.835102\pi\)
\(402\) −1618.33 + 2803.02i −0.200783 + 0.347766i
\(403\) −5504.65 + 9534.34i −0.680413 + 1.17851i
\(404\) 9960.64 + 17252.3i 1.22663 + 2.12459i
\(405\) −1280.12 −0.157061
\(406\) 0 0
\(407\) −6141.56 −0.747975
\(408\) −14070.2 24370.3i −1.70730 2.95713i
\(409\) 73.6942 127.642i 0.00890940 0.0154315i −0.861536 0.507696i \(-0.830497\pi\)
0.870446 + 0.492264i \(0.163831\pi\)
\(410\) −2003.68 + 3470.47i −0.241353 + 0.418035i
\(411\) 3931.16 + 6808.96i 0.471800 + 0.817181i
\(412\) −13897.3 −1.66182
\(413\) 0 0
\(414\) −6.95336 −0.000825457
\(415\) 1233.01 + 2135.64i 0.145846 + 0.252613i
\(416\) −27512.7 + 47653.4i −3.24260 + 5.61635i
\(417\) −5186.44 + 8983.17i −0.609067 + 1.05493i
\(418\) −1126.52 1951.19i −0.131818 0.228315i
\(419\) 3781.67 0.440923 0.220462 0.975396i \(-0.429244\pi\)
0.220462 + 0.975396i \(0.429244\pi\)
\(420\) 0 0
\(421\) −10899.2 −1.26175 −0.630874 0.775885i \(-0.717304\pi\)
−0.630874 + 0.775885i \(0.717304\pi\)
\(422\) −16487.5 28557.2i −1.90189 3.29417i
\(423\) −1575.86 + 2729.47i −0.181137 + 0.313738i
\(424\) 14075.5 24379.6i 1.61219 2.79240i
\(425\) −1142.93 1979.62i −0.130448 0.225942i
\(426\) −6634.33 −0.754541
\(427\) 0 0
\(428\) −48292.4 −5.45398
\(429\) −4590.54 7951.05i −0.516628 0.894826i
\(430\) 113.909 197.296i 0.0127748 0.0221266i
\(431\) 5641.69 9771.69i 0.630512 1.09208i −0.356936 0.934129i \(-0.616178\pi\)
0.987447 0.157949i \(-0.0504882\pi\)
\(432\) −19646.0 34027.8i −2.18800 3.78973i
\(433\) 8906.19 0.988462 0.494231 0.869331i \(-0.335450\pi\)
0.494231 + 0.869331i \(0.335450\pi\)
\(434\) 0 0
\(435\) −3684.03 −0.406059
\(436\) 4569.03 + 7913.80i 0.501874 + 0.869271i
\(437\) −0.616026 + 1.06699i −6.74337e−5 + 0.000116799i
\(438\) 6815.29 11804.4i 0.743487 1.28776i
\(439\) 4074.74 + 7057.67i 0.443000 + 0.767298i 0.997910 0.0646116i \(-0.0205809\pi\)
−0.554911 + 0.831910i \(0.687248\pi\)
\(440\) −13760.8 −1.49095
\(441\) 0 0
\(442\) 34759.1 3.74054
\(443\) 5736.39 + 9935.71i 0.615223 + 1.06560i 0.990345 + 0.138623i \(0.0442675\pi\)
−0.375122 + 0.926975i \(0.622399\pi\)
\(444\) −7708.58 + 13351.6i −0.823948 + 1.42712i
\(445\) 1184.62 2051.83i 0.126195 0.218575i
\(446\) 14295.9 + 24761.3i 1.51778 + 2.62888i
\(447\) −2599.97 −0.275111
\(448\) 0 0
\(449\) 1963.80 0.206409 0.103204 0.994660i \(-0.467090\pi\)
0.103204 + 0.994660i \(0.467090\pi\)
\(450\) −834.413 1445.25i −0.0874102 0.151399i
\(451\) 2507.05 4342.34i 0.261757 0.453376i
\(452\) 3923.71 6796.06i 0.408309 0.707212i
\(453\) −4102.01 7104.89i −0.425451 0.736903i
\(454\) 20709.3 2.14083
\(455\) 0 0
\(456\) −3640.20 −0.373833
\(457\) −2794.93 4840.96i −0.286086 0.495515i 0.686786 0.726860i \(-0.259021\pi\)
−0.972872 + 0.231344i \(0.925688\pi\)
\(458\) 17266.1 29905.8i 1.76156 3.05111i
\(459\) −6900.16 + 11951.4i −0.701682 + 1.21535i
\(460\) 5.84577 + 10.1252i 0.000592523 + 0.00102628i
\(461\) 18790.9 1.89844 0.949219 0.314618i \(-0.101876\pi\)
0.949219 + 0.314618i \(0.101876\pi\)
\(462\) 0 0
\(463\) −7892.22 −0.792187 −0.396094 0.918210i \(-0.629634\pi\)
−0.396094 + 0.918210i \(0.629634\pi\)
\(464\) −24843.7 43030.6i −2.48565 4.30527i
\(465\) −1542.24 + 2671.25i −0.153806 + 0.266400i
\(466\) 4910.89 8505.91i 0.488182 0.845556i
\(467\) 192.755 + 333.862i 0.0190999 + 0.0330820i 0.875417 0.483368i \(-0.160587\pi\)
−0.856317 + 0.516450i \(0.827253\pi\)
\(468\) 18708.9 1.84790
\(469\) 0 0
\(470\) 7187.95 0.705437
\(471\) 5429.71 + 9404.53i 0.531184 + 0.920038i
\(472\) −9586.58 + 16604.4i −0.934869 + 1.61924i
\(473\) −142.525 + 246.861i −0.0138548 + 0.0239972i
\(474\) −4166.43 7216.47i −0.403735 0.699290i
\(475\) −295.696 −0.0285631
\(476\) 0 0
\(477\) −4271.67 −0.410035
\(478\) 9710.15 + 16818.5i 0.929146 + 1.60933i
\(479\) 847.229 1467.44i 0.0808160 0.139977i −0.822785 0.568353i \(-0.807581\pi\)
0.903601 + 0.428376i \(0.140914\pi\)
\(480\) −7708.27 + 13351.1i −0.732985 + 1.26957i
\(481\) −6128.34 10614.6i −0.580932 1.00620i
\(482\) 2002.64 0.189248
\(483\) 0 0
\(484\) −3126.91 −0.293662
\(485\) 2097.51 + 3633.00i 0.196378 + 0.340136i
\(486\) −8516.41 + 14750.9i −0.794881 + 1.37677i
\(487\) −7855.58 + 13606.3i −0.730945 + 1.26603i 0.225534 + 0.974235i \(0.427587\pi\)
−0.956480 + 0.291799i \(0.905746\pi\)
\(488\) −31020.1 53728.4i −2.87749 4.98395i
\(489\) 5189.99 0.479958
\(490\) 0 0
\(491\) −2716.34 −0.249667 −0.124834 0.992178i \(-0.539840\pi\)
−0.124834 + 0.992178i \(0.539840\pi\)
\(492\) −6293.44 10900.6i −0.576687 0.998852i
\(493\) −8725.75 + 15113.4i −0.797136 + 1.38068i
\(494\) 2248.19 3893.98i 0.204759 0.354653i
\(495\) 1044.04 + 1808.32i 0.0947999 + 0.164198i
\(496\) −41601.2 −3.76603
\(497\) 0 0
\(498\) −10506.0 −0.945355
\(499\) −2147.67 3719.87i −0.192671 0.333716i 0.753463 0.657490i \(-0.228382\pi\)
−0.946135 + 0.323774i \(0.895048\pi\)
\(500\) −1403.00 + 2430.07i −0.125488 + 0.217352i
\(501\) −2801.17 + 4851.77i −0.249795 + 0.432657i
\(502\) 14716.0 + 25488.9i 1.30838 + 2.26619i
\(503\) −6515.26 −0.577537 −0.288769 0.957399i \(-0.593246\pi\)
−0.288769 + 0.957399i \(0.593246\pi\)
\(504\) 0 0
\(505\) −4437.20 −0.390996
\(506\) −9.92105 17.1838i −0.000871629 0.00150971i
\(507\) 4920.67 8522.85i 0.431035 0.746574i
\(508\) −13286.8 + 23013.3i −1.16044 + 2.00994i
\(509\) 7195.88 + 12463.6i 0.626624 + 1.08535i 0.988224 + 0.153012i \(0.0488973\pi\)
−0.361600 + 0.932333i \(0.617769\pi\)
\(510\) 9738.48 0.845544
\(511\) 0 0
\(512\) −41890.2 −3.61583
\(513\) 892.594 + 1546.02i 0.0768207 + 0.133057i
\(514\) 6728.56 11654.2i 0.577401 1.00009i
\(515\) 1547.72 2680.73i 0.132428 0.229373i
\(516\) 357.781 + 619.695i 0.0305241 + 0.0528692i
\(517\) −8993.73 −0.765075
\(518\) 0 0
\(519\) −7640.32 −0.646191
\(520\) −13731.1 23783.0i −1.15798 2.00568i
\(521\) 1456.68 2523.05i 0.122492 0.212163i −0.798258 0.602316i \(-0.794245\pi\)
0.920750 + 0.390153i \(0.127578\pi\)
\(522\) −6370.35 + 11033.8i −0.534143 + 0.925163i
\(523\) 8435.11 + 14610.0i 0.705242 + 1.22151i 0.966604 + 0.256274i \(0.0824949\pi\)
−0.261362 + 0.965241i \(0.584172\pi\)
\(524\) −5013.93 −0.418005
\(525\) 0 0
\(526\) −8421.82 −0.698115
\(527\) 7305.71 + 12653.9i 0.603874 + 1.04594i
\(528\) 17346.4 30044.9i 1.42975 2.47639i
\(529\) 6083.49 10536.9i 0.500000 0.866025i
\(530\) 4871.09 + 8436.98i 0.399220 + 0.691470i
\(531\) 2909.35 0.237769
\(532\) 0 0
\(533\) 10006.6 0.813197
\(534\) 5046.86 + 8741.43i 0.408987 + 0.708387i
\(535\) 5378.25 9315.40i 0.434620 0.752785i
\(536\) 6056.80 10490.7i 0.488086 0.845390i
\(537\) −8413.07 14571.9i −0.676072 1.17099i
\(538\) −41738.6 −3.34476
\(539\) 0 0
\(540\) 16940.5 1.35001
\(541\) 1114.79 + 1930.88i 0.0885929 + 0.153447i 0.906917 0.421310i \(-0.138430\pi\)
−0.818324 + 0.574758i \(0.805096\pi\)
\(542\) −11815.9 + 20465.7i −0.936412 + 1.62191i
\(543\) 729.465 1263.47i 0.0576507 0.0998539i
\(544\) 36514.5 + 63245.0i 2.87785 + 4.98457i
\(545\) −2035.38 −0.159975
\(546\) 0 0
\(547\) −1218.73 −0.0952639 −0.0476319 0.998865i \(-0.515167\pi\)
−0.0476319 + 0.998865i \(0.515167\pi\)
\(548\) −22859.5 39593.9i −1.78195 3.08643i
\(549\) −4707.02 + 8152.80i −0.365921 + 0.633794i
\(550\) 2381.08 4124.15i 0.184599 0.319735i
\(551\) 1128.75 + 1955.05i 0.0872710 + 0.151158i
\(552\) −32.0585 −0.00247192
\(553\) 0 0
\(554\) 22118.3 1.69624
\(555\) −1716.98 2973.90i −0.131319 0.227451i
\(556\) 30158.9 52236.8i 2.30040 3.98442i
\(557\) 11367.3 19688.7i 0.864714 1.49773i −0.00261590 0.999997i \(-0.500833\pi\)
0.867330 0.497733i \(-0.165834\pi\)
\(558\) 5333.63 + 9238.12i 0.404643 + 0.700862i
\(559\) −568.873 −0.0430425
\(560\) 0 0
\(561\) −12185.0 −0.917026
\(562\) 19134.8 + 33142.4i 1.43621 + 2.48759i
\(563\) 2151.06 3725.74i 0.161023 0.278901i −0.774213 0.632926i \(-0.781854\pi\)
0.935236 + 0.354025i \(0.115187\pi\)
\(564\) −11288.5 + 19552.2i −0.842784 + 1.45975i
\(565\) 873.954 + 1513.73i 0.0650752 + 0.112714i
\(566\) −14714.4 −1.09275
\(567\) 0 0
\(568\) 24829.9 1.83422
\(569\) −7433.46 12875.1i −0.547675 0.948601i −0.998433 0.0559547i \(-0.982180\pi\)
0.450759 0.892646i \(-0.351154\pi\)
\(570\) 629.878 1090.98i 0.0462854 0.0801686i
\(571\) −8257.24 + 14302.0i −0.605174 + 1.04819i 0.386850 + 0.922143i \(0.373563\pi\)
−0.992024 + 0.126050i \(0.959770\pi\)
\(572\) 26693.8 + 46235.1i 1.95127 + 3.37969i
\(573\) 9365.10 0.682780
\(574\) 0 0
\(575\) −2.60414 −0.000188870
\(576\) 14060.7 + 24353.8i 1.01712 + 1.76171i
\(577\) 933.984 1617.71i 0.0673870 0.116718i −0.830363 0.557222i \(-0.811867\pi\)
0.897750 + 0.440505i \(0.145200\pi\)
\(578\) 9511.00 16473.5i 0.684438 1.18548i
\(579\) −1202.36 2082.55i −0.0863014 0.149478i
\(580\) 21422.5 1.53366
\(581\) 0 0
\(582\) −17872.1 −1.27289
\(583\) −6094.82 10556.5i −0.432970 0.749927i
\(584\) −25507.2 + 44179.7i −1.80735 + 3.13043i
\(585\) −2083.58 + 3608.86i −0.147257 + 0.255056i
\(586\) −16385.9 28381.2i −1.15511 2.00071i
\(587\) −3926.15 −0.276064 −0.138032 0.990428i \(-0.544078\pi\)
−0.138032 + 0.990428i \(0.544078\pi\)
\(588\) 0 0
\(589\) 1890.11 0.132225
\(590\) −3317.61 5746.26i −0.231498 0.400966i
\(591\) 5486.17 9502.33i 0.381846 0.661377i
\(592\) 23157.3 40109.7i 1.60770 2.78463i
\(593\) −3777.09 6542.11i −0.261562 0.453039i 0.705095 0.709113i \(-0.250904\pi\)
−0.966657 + 0.256074i \(0.917571\pi\)
\(594\) −28750.3 −1.98593
\(595\) 0 0
\(596\) 15118.8 1.03907
\(597\) 1674.18 + 2899.77i 0.114773 + 0.198793i
\(598\) 19.7994 34.2935i 0.00135394 0.00234509i
\(599\) −14105.5 + 24431.4i −0.962160 + 1.66651i −0.245099 + 0.969498i \(0.578821\pi\)
−0.717060 + 0.697011i \(0.754513\pi\)
\(600\) −3847.07 6663.32i −0.261760 0.453381i
\(601\) 23181.4 1.57336 0.786679 0.617363i \(-0.211799\pi\)
0.786679 + 0.617363i \(0.211799\pi\)
\(602\) 0 0
\(603\) −1838.13 −0.124137
\(604\) 23853.0 + 41314.7i 1.60690 + 2.78323i
\(605\) 348.239 603.167i 0.0234015 0.0405326i
\(606\) 9451.92 16371.2i 0.633594 1.09742i
\(607\) −12431.8 21532.5i −0.831287 1.43983i −0.897018 0.441994i \(-0.854271\pi\)
0.0657313 0.997837i \(-0.479062\pi\)
\(608\) 9446.93 0.630137
\(609\) 0 0
\(610\) 21470.1 1.42508
\(611\) −8974.36 15544.1i −0.594213 1.02921i
\(612\) 12415.1 21503.6i 0.820017 1.42031i
\(613\) 6396.36 11078.8i 0.421446 0.729966i −0.574635 0.818410i \(-0.694856\pi\)
0.996081 + 0.0884435i \(0.0281893\pi\)
\(614\) −28642.5 49610.3i −1.88260 3.26076i
\(615\) 2803.56 0.183822
\(616\) 0 0
\(617\) 19793.3 1.29149 0.645744 0.763554i \(-0.276547\pi\)
0.645744 + 0.763554i \(0.276547\pi\)
\(618\) 6593.76 + 11420.7i 0.429191 + 0.743380i
\(619\) −10475.8 + 18144.7i −0.680226 + 1.17819i 0.294686 + 0.955594i \(0.404785\pi\)
−0.974912 + 0.222592i \(0.928548\pi\)
\(620\) 8968.10 15533.2i 0.580915 1.00617i
\(621\) 7.86091 + 13.6155i 0.000507967 + 0.000879824i
\(622\) 23399.2 1.50840
\(623\) 0 0
\(624\) 69236.3 4.44178
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) 783.284 1356.69i 0.0500101 0.0866200i
\(627\) −788.117 + 1365.06i −0.0501984 + 0.0869461i
\(628\) −31573.5 54687.0i −2.00624 3.47492i
\(629\) −16266.9 −1.03117
\(630\) 0 0
\(631\) 23273.5 1.46831 0.734156 0.678981i \(-0.237578\pi\)
0.734156 + 0.678981i \(0.237578\pi\)
\(632\) 15593.4 + 27008.6i 0.981446 + 1.69991i
\(633\) −11534.7 + 19978.7i −0.724270 + 1.25447i
\(634\) 4799.24 8312.52i 0.300634 0.520713i
\(635\) −2959.45 5125.91i −0.184948 0.320340i
\(636\) −30599.6 −1.90779
\(637\) 0 0
\(638\) −36356.8 −2.25608
\(639\) −1883.86 3262.94i −0.116626 0.202003i
\(640\) 16093.4 27874.6i 0.993981 1.72163i
\(641\) 11058.9 19154.5i 0.681434 1.18028i −0.293110 0.956079i \(-0.594690\pi\)
0.974543 0.224199i \(-0.0719765\pi\)
\(642\) 22913.0 + 39686.5i 1.40857 + 2.43972i
\(643\) −20269.9 −1.24318 −0.621591 0.783342i \(-0.713513\pi\)
−0.621591 + 0.783342i \(0.713513\pi\)
\(644\) 0 0
\(645\) −159.382 −0.00972969
\(646\) −2983.77 5168.04i −0.181726 0.314758i
\(647\) −1572.62 + 2723.87i −0.0955583 + 0.165512i −0.909841 0.414956i \(-0.863797\pi\)
0.814283 + 0.580468i \(0.197130\pi\)
\(648\) −10205.6 + 17676.6i −0.618695 + 1.07161i
\(649\) 4151.06 + 7189.85i 0.251069 + 0.434864i
\(650\) 9503.81 0.573493
\(651\) 0 0
\(652\) −30179.6 −1.81277
\(653\) 2976.67 + 5155.75i 0.178386 + 0.308974i 0.941328 0.337493i \(-0.109579\pi\)
−0.762942 + 0.646467i \(0.776246\pi\)
\(654\) 4335.68 7509.61i 0.259233 0.449005i
\(655\) 558.393 967.165i 0.0333102 0.0576950i
\(656\) 18906.1 + 32746.4i 1.12524 + 1.94898i
\(657\) 7740.96 0.459671
\(658\) 0 0
\(659\) 26277.5 1.55330 0.776652 0.629930i \(-0.216916\pi\)
0.776652 + 0.629930i \(0.216916\pi\)
\(660\) 7478.83 + 12953.7i 0.441081 + 0.763974i
\(661\) −12002.2 + 20788.4i −0.706248 + 1.22326i 0.259991 + 0.965611i \(0.416280\pi\)
−0.966239 + 0.257647i \(0.917053\pi\)
\(662\) 15469.5 26794.0i 0.908218 1.57308i
\(663\) −12158.8 21059.6i −0.712229 1.23362i
\(664\) 39320.3 2.29808
\(665\) 0 0
\(666\) −11875.9 −0.690962
\(667\) 9.94068 + 17.2178i 0.000577068 + 0.000999512i
\(668\) 16288.7 28212.9i 0.943457 1.63412i
\(669\) 10001.5 17323.1i 0.577996 1.00112i
\(670\) 2096.06 + 3630.49i 0.120863 + 0.209340i
\(671\) −26863.9 −1.54556
\(672\) 0 0
\(673\) 9205.36 0.527252 0.263626 0.964625i \(-0.415082\pi\)
0.263626 + 0.964625i \(0.415082\pi\)
\(674\) −26010.2 45050.9i −1.48646 2.57463i
\(675\) −1886.64 + 3267.76i −0.107580 + 0.186335i
\(676\) −28613.5 + 49560.1i −1.62799 + 2.81976i
\(677\) −9386.57 16258.0i −0.532873 0.922964i −0.999263 0.0383843i \(-0.987779\pi\)
0.466390 0.884579i \(-0.345554\pi\)
\(678\) −7446.62 −0.421808
\(679\) 0 0
\(680\) −36447.6 −2.05544
\(681\) −7244.14 12547.2i −0.407630 0.706036i
\(682\) −15220.0 + 26361.9i −0.854554 + 1.48013i
\(683\) 5111.12 8852.73i 0.286342 0.495959i −0.686592 0.727043i \(-0.740894\pi\)
0.972934 + 0.231084i \(0.0742272\pi\)
\(684\) −1606.00 2781.67i −0.0897761 0.155497i
\(685\) 10183.3 0.568006
\(686\) 0 0
\(687\) −24158.9 −1.34166
\(688\) −1074.81 1861.63i −0.0595592 0.103160i
\(689\) 12163.4 21067.6i 0.672552 1.16489i
\(690\) 5.54721 9.60805i 0.000306056 0.000530105i
\(691\) 11177.6 + 19360.1i 0.615361 + 1.06584i 0.990321 + 0.138795i \(0.0443229\pi\)
−0.374961 + 0.927041i \(0.622344\pi\)
\(692\) 44428.2 2.44062
\(693\) 0 0
\(694\) −64197.3 −3.51138
\(695\) 6717.50 + 11635.1i 0.366632 + 0.635026i
\(696\) −29370.5 + 50871.3i −1.59955 + 2.77050i
\(697\) 6640.32 11501.4i 0.360861 0.625029i
\(698\) 3633.85 + 6294.01i 0.197053 + 0.341307i
\(699\) −6871.35 −0.371814
\(700\) 0 0
\(701\) 16217.3 0.873779 0.436890 0.899515i \(-0.356080\pi\)
0.436890 + 0.899515i \(0.356080\pi\)
\(702\) −28688.4 49689.8i −1.54241 2.67154i
\(703\) −1052.13 + 1822.34i −0.0564465 + 0.0977682i
\(704\) −40123.5 + 69496.0i −2.14803 + 3.72050i
\(705\) −2514.36 4354.99i −0.134321 0.232650i
\(706\) 32273.7 1.72045
\(707\) 0 0
\(708\) 20840.8 1.10628
\(709\) −1961.46 3397.35i −0.103899 0.179958i 0.809389 0.587273i \(-0.199798\pi\)
−0.913288 + 0.407315i \(0.866465\pi\)
\(710\) −4296.41 + 7441.61i −0.227101 + 0.393350i
\(711\) 2366.16 4098.32i 0.124807 0.216173i
\(712\) −18888.6 32716.0i −0.994212 1.72203i
\(713\) 16.6458 0.000874322
\(714\) 0 0
\(715\) −11891.4 −0.621976
\(716\) 48921.7 + 84734.9i 2.55348 + 4.42275i
\(717\) 6793.25 11766.3i 0.353833 0.612857i
\(718\) −34272.2 + 59361.1i −1.78137 + 3.08543i
\(719\) 11954.3 + 20705.4i 0.620055 + 1.07397i 0.989475 + 0.144705i \(0.0462232\pi\)
−0.369420 + 0.929263i \(0.620444\pi\)
\(720\) −15746.6 −0.815055
\(721\) 0 0
\(722\) 37075.8 1.91111
\(723\) −700.527 1213.35i −0.0360344 0.0624134i
\(724\) −4241.81 + 7347.03i −0.217743 + 0.377141i
\(725\) −2385.79 + 4132.31i −0.122215 + 0.211683i
\(726\) 1483.60 + 2569.68i 0.0758426 + 0.131363i
\(727\) 26906.4 1.37263 0.686315 0.727305i \(-0.259227\pi\)
0.686315 + 0.727305i \(0.259227\pi\)
\(728\) 0 0
\(729\) 18828.9 0.956605
\(730\) −8827.21 15289.2i −0.447547 0.775175i
\(731\) −377.501 + 653.850i −0.0191004 + 0.0330828i
\(732\) −33718.2 + 58401.6i −1.70254 + 2.94889i
\(733\) 13818.7 + 23934.7i 0.696325 + 1.20607i 0.969732 + 0.244172i \(0.0785162\pi\)
−0.273407 + 0.961899i \(0.588150\pi\)
\(734\) −36367.7 −1.82882
\(735\) 0 0
\(736\) 83.1973 0.00416670
\(737\) −2622.64 4542.55i −0.131080 0.227038i
\(738\) 4847.85 8396.73i 0.241805 0.418818i
\(739\) 7019.44 12158.0i 0.349410 0.605197i −0.636734 0.771083i \(-0.719715\pi\)
0.986145 + 0.165887i \(0.0530486\pi\)
\(740\) 9984.19 + 17293.1i 0.495981 + 0.859065i
\(741\) −3145.68 −0.155951
\(742\) 0 0
\(743\) 17698.7 0.873893 0.436946 0.899488i \(-0.356060\pi\)
0.436946 + 0.899488i \(0.356060\pi\)
\(744\) 24590.7 + 42592.4i 1.21175 + 2.09881i
\(745\) −1683.75 + 2916.34i −0.0828025 + 0.143418i
\(746\) 949.859 1645.20i 0.0466177 0.0807442i
\(747\) −2983.25 5167.14i −0.146120 0.253087i
\(748\) 70855.4 3.46354
\(749\) 0 0
\(750\) 2662.69 0.129637
\(751\) −8599.83 14895.3i −0.417859 0.723754i 0.577865 0.816133i \(-0.303886\pi\)
−0.995724 + 0.0923791i \(0.970553\pi\)
\(752\) 33911.7 58736.8i 1.64446 2.84829i
\(753\) 10295.4 17832.1i 0.498253 0.862999i
\(754\) −36278.6 62836.3i −1.75224 3.03496i
\(755\) −10625.9 −0.512206
\(756\) 0 0
\(757\) −19200.7 −0.921879 −0.460939 0.887432i \(-0.652487\pi\)
−0.460939 + 0.887432i \(0.652487\pi\)
\(758\) 14460.5 + 25046.3i 0.692914 + 1.20016i
\(759\) −6.94080 + 12.0218i −0.000331930 + 0.000574920i
\(760\) −2357.40 + 4083.14i −0.112516 + 0.194883i
\(761\) −13959.4 24178.3i −0.664949 1.15173i −0.979299 0.202419i \(-0.935120\pi\)
0.314350 0.949307i \(-0.398213\pi\)
\(762\) 25216.3 1.19881
\(763\) 0 0
\(764\) −54457.7 −2.57881
\(765\) 2765.30 + 4789.64i 0.130692 + 0.226366i
\(766\) −20961.1 + 36305.6i −0.988712 + 1.71250i
\(767\) −8284.25 + 14348.7i −0.389996 + 0.675493i
\(768\) 32667.7 + 56582.1i 1.53489 + 2.65850i
\(769\) 7436.29 0.348712 0.174356 0.984683i \(-0.444216\pi\)
0.174356 + 0.984683i \(0.444216\pi\)
\(770\) 0 0
\(771\) −9414.64 −0.439766
\(772\) 6991.70 + 12110.0i 0.325954 + 0.564569i
\(773\) 2494.92 4321.33i 0.116088 0.201070i −0.802126 0.597155i \(-0.796298\pi\)
0.918214 + 0.396084i \(0.129631\pi\)
\(774\) −275.600 + 477.352i −0.0127987 + 0.0221681i
\(775\) 1997.52 + 3459.81i 0.0925847 + 0.160361i
\(776\) 66888.7 3.09429
\(777\) 0 0
\(778\) −17115.9 −0.788731
\(779\) −858.981 1487.80i −0.0395073 0.0684287i
\(780\) −14925.5 + 25851.7i −0.685150 + 1.18672i
\(781\) 5375.77 9311.11i 0.246300 0.426604i
\(782\) −26.2775 45.5139i −0.00120164 0.00208130i
\(783\) 28807.2 1.31480
\(784\) 0 0
\(785\) 14065.2 0.639500
\(786\) 2378.92 + 4120.42i 0.107956 + 0.186985i
\(787\) −1435.35 + 2486.09i −0.0650122 + 0.112604i −0.896699 0.442640i \(-0.854042\pi\)
0.831687 + 0.555244i \(0.187375\pi\)
\(788\) −31901.9 + 55255.7i −1.44221 + 2.49797i
\(789\) 2945.96 + 5102.56i 0.132927 + 0.230236i
\(790\) −10792.8 −0.486063
\(791\) 0 0
\(792\) 33293.9 1.49374
\(793\) −26806.1 46429.4i −1.20039 2.07914i
\(794\) 8089.50 14011.4i 0.361569 0.626256i
\(795\) 3407.83 5902.54i 0.152029 0.263322i
\(796\) −9735.31 16862.0i −0.433491 0.750828i
\(797\) −4676.61 −0.207847 −0.103923 0.994585i \(-0.533140\pi\)
−0.103923 + 0.994585i \(0.533140\pi\)
\(798\) 0 0
\(799\) −23821.3 −1.05474
\(800\) 9983.79 + 17292.4i 0.441225 + 0.764225i
\(801\) −2866.17 + 4964.35i −0.126431 + 0.218985i
\(802\) 246.205 426.440i 0.0108402 0.0187757i
\(803\) 11044.8 + 19130.2i 0.485383 + 0.840708i
\(804\) −13167.2 −0.577578
\(805\) 0 0
\(806\) −60749.1 −2.65483
\(807\) 14600.2 + 25288.3i 0.636868 + 1.10309i
\(808\) −35375.1 + 61271.4i −1.54021 + 2.66772i
\(809\) 7688.45 13316.8i 0.334131 0.578731i −0.649187 0.760629i \(-0.724891\pi\)
0.983317 + 0.181898i \(0.0582240\pi\)
\(810\) −3531.83 6117.32i −0.153205 0.265359i
\(811\) −36422.9 −1.57704 −0.788522 0.615007i \(-0.789153\pi\)
−0.788522 + 0.615007i \(0.789153\pi\)
\(812\) 0 0
\(813\) 16532.8 0.713200
\(814\) −16944.5 29348.7i −0.729612 1.26372i
\(815\) 3361.05 5821.51i 0.144457 0.250207i
\(816\) 45944.8 79578.6i 1.97106 3.41398i
\(817\) 48.8329 + 84.5811i 0.00209112 + 0.00362193i
\(818\) 813.285 0.0347627
\(819\) 0 0
\(820\) −16302.6 −0.694282
\(821\) 12739.5 + 22065.5i 0.541550 + 0.937991i 0.998815 + 0.0486612i \(0.0154955\pi\)
−0.457266 + 0.889330i \(0.651171\pi\)
\(822\) −21692.0 + 37571.7i −0.920433 + 1.59424i
\(823\) 8966.65 15530.7i 0.379779 0.657796i −0.611251 0.791437i \(-0.709334\pi\)
0.991030 + 0.133641i \(0.0426668\pi\)
\(824\) −24678.0 42743.6i −1.04333 1.80709i
\(825\) −3331.62 −0.140597
\(826\) 0 0
\(827\) 13021.6 0.547529 0.273764 0.961797i \(-0.411731\pi\)
0.273764 + 0.961797i \(0.411731\pi\)
\(828\) −14.1437 24.4976i −0.000593633 0.00102820i
\(829\) −5698.80 + 9870.61i −0.238754 + 0.413535i −0.960357 0.278773i \(-0.910072\pi\)
0.721603 + 0.692307i \(0.243406\pi\)
\(830\) −6803.74 + 11784.4i −0.284532 + 0.492823i
\(831\) −7737.01 13400.9i −0.322977 0.559412i
\(832\) −160149. −6.67326
\(833\) 0 0
\(834\) −57237.2 −2.37646
\(835\) 3628.09 + 6284.04i 0.150366 + 0.260441i
\(836\) 4582.87 7937.77i 0.189596 0.328389i
\(837\) 12059.5 20887.7i 0.498015 0.862588i
\(838\) 10433.6 + 18071.5i 0.430098 + 0.744952i
\(839\) 37681.2 1.55053 0.775267 0.631633i \(-0.217615\pi\)
0.775267 + 0.631633i \(0.217615\pi\)
\(840\) 0 0
\(841\) 12039.8 0.493656
\(842\) −30070.8 52084.2i −1.23077 2.13176i
\(843\) 13386.7 23186.5i 0.546932 0.947315i
\(844\) 67073.9 116175.i 2.73552 4.73806i
\(845\) −6373.28 11038.8i −0.259465 0.449406i
\(846\) −17391.1 −0.706758
\(847\) 0 0
\(848\) 91924.4 3.72252
\(849\) 5147.13 + 8915.09i 0.208067 + 0.360383i
\(850\) 6306.67 10923.5i 0.254491 0.440791i
\(851\) −9.26591 + 16.0490i −0.000373245 + 0.000646479i
\(852\) −13494.8 23373.7i −0.542634 0.939869i
\(853\) −21771.6 −0.873911 −0.436956 0.899483i \(-0.643943\pi\)
−0.436956 + 0.899483i \(0.643943\pi\)
\(854\) 0 0
\(855\) 715.429 0.0286166
\(856\) −85754.9 148532.i −3.42412 5.93074i
\(857\) 14930.1 25859.7i 0.595103 1.03075i −0.398429 0.917199i \(-0.630445\pi\)
0.993532 0.113550i \(-0.0362221\pi\)
\(858\) 25330.5 43873.7i 1.00789 1.74571i
\(859\) 9265.32 + 16048.0i 0.368019 + 0.637428i 0.989256 0.146195i \(-0.0467027\pi\)
−0.621236 + 0.783623i \(0.713369\pi\)
\(860\) 926.799 0.0367484
\(861\) 0 0
\(862\) 62261.4 2.46013
\(863\) 10648.2 + 18443.3i 0.420012 + 0.727482i 0.995940 0.0900182i \(-0.0286925\pi\)
−0.575928 + 0.817500i \(0.695359\pi\)
\(864\) 60274.6 104399.i 2.37336 4.11078i
\(865\) −4947.90 + 8570.01i −0.194490 + 0.336866i
\(866\) 24572.1 + 42560.1i 0.964195 + 1.67003i
\(867\) −13307.8 −0.521290
\(868\) 0 0
\(869\) 13504.2 0.527155
\(870\) −10164.2 17604.9i −0.396090 0.686049i
\(871\) 5233.99 9065.54i 0.203613 0.352668i
\(872\) −16226.9 + 28105.7i −0.630173 + 1.09149i
\(873\) −5074.88 8789.96i −0.196745 0.340773i
\(874\) −6.79843 −0.000263112
\(875\) 0 0
\(876\) 55451.5 2.13874
\(877\) 9396.72 + 16275.6i 0.361807 + 0.626668i 0.988258 0.152793i \(-0.0488266\pi\)
−0.626451 + 0.779460i \(0.715493\pi\)
\(878\) −22484.3 + 38944.0i −0.864248 + 1.49692i
\(879\) −11463.6 + 19855.6i −0.439885 + 0.761902i
\(880\) −22467.2 38914.3i −0.860646 1.49068i
\(881\) −1638.62 −0.0626634 −0.0313317 0.999509i \(-0.509975\pi\)
−0.0313317 + 0.999509i \(0.509975\pi\)
\(882\) 0 0
\(883\) −35424.1 −1.35008 −0.675038 0.737783i \(-0.735873\pi\)
−0.675038 + 0.737783i \(0.735873\pi\)
\(884\) 70702.8 + 122461.i 2.69004 + 4.65928i
\(885\) −2321.01 + 4020.10i −0.0881580 + 0.152694i
\(886\) −31653.2 + 54825.0i −1.20024 + 2.07887i
\(887\) −2565.71 4443.93i −0.0971229 0.168222i 0.813370 0.581747i \(-0.197631\pi\)
−0.910493 + 0.413525i \(0.864297\pi\)
\(888\) −54753.8 −2.06916
\(889\) 0 0
\(890\) 13073.5 0.492386
\(891\) 4419.11 + 7654.13i 0.166157 + 0.287792i
\(892\) −58158.2 + 100733.i −2.18305 + 3.78115i
\(893\) −1540.74 + 2668.65i −0.0577369 + 0.100003i
\(894\) −7173.30 12424.5i −0.268357 0.464807i
\(895\) −21793.3 −0.813933
\(896\) 0 0
\(897\) −27.7034 −0.00103120
\(898\) 5418.10 + 9384.43i 0.201341 + 0.348733i
\(899\) 15250.2 26414.0i 0.565763 0.979931i
\(900\) 3394.53 5879.50i 0.125723 0.217759i
\(901\) −16143.1 27960.7i −0.596898 1.03386i
\(902\) 27667.7 1.02132
\(903\) 0 0
\(904\) 27870.0 1.02538
\(905\) −944.807 1636.45i −0.0347032 0.0601078i
\(906\) 22634.8 39204.6i 0.830011 1.43762i
\(907\) 9967.28 17263.8i 0.364893 0.632014i −0.623866 0.781532i \(-0.714439\pi\)
0.988759 + 0.149518i \(0.0477721\pi\)
\(908\) 42124.4 + 72961.6i 1.53959 + 2.66665i
\(909\) 10735.7 0.391728
\(910\) 0 0
\(911\) 48387.4 1.75976 0.879882 0.475193i \(-0.157622\pi\)
0.879882 + 0.475193i \(0.157622\pi\)
\(912\) −5943.34 10294.2i −0.215794 0.373765i
\(913\) 8512.99 14744.9i 0.308586 0.534486i
\(914\) 15422.3 26712.3i 0.558124 0.966700i
\(915\) −7510.28 13008.2i −0.271347 0.469986i
\(916\) 140483. 5.06735
\(917\) 0 0
\(918\) −76149.8 −2.73782
\(919\) 7215.87 + 12498.2i 0.259009 + 0.448617i 0.965977 0.258629i \(-0.0832706\pi\)
−0.706968 + 0.707246i \(0.749937\pi\)
\(920\) −20.7612 + 35.9594i −0.000743996 + 0.00128864i
\(921\) −20038.4 + 34707.5i −0.716924 + 1.24175i
\(922\) 51843.8 + 89796.2i 1.85183 + 3.20746i
\(923\) 21456.8 0.765177
\(924\) 0 0
\(925\) −4447.69 −0.158096
\(926\) −21774.5 37714.6i −0.772738 1.33842i
\(927\) −3744.67 + 6485.96i −0.132676 + 0.229802i
\(928\) 76221.5 132020.i 2.69622 4.66999i
\(929\) 2774.91 + 4806.28i 0.0979998 + 0.169741i 0.910857 0.412723i \(-0.135422\pi\)
−0.812857 + 0.582464i \(0.802089\pi\)
\(930\) −17020.1 −0.600120
\(931\) 0 0
\(932\) 39956.7 1.40432
\(933\) −8185.08 14177.0i −0.287211 0.497463i
\(934\) −1063.62 + 1842.24i −0.0372620 + 0.0645396i
\(935\) −7891.05 + 13667.7i −0.276005 + 0.478055i
\(936\) 33222.2 + 57542.5i 1.16015 + 2.00944i
\(937\) −26231.9 −0.914576 −0.457288 0.889319i \(-0.651179\pi\)
−0.457288 + 0.889319i \(0.651179\pi\)
\(938\) 0 0
\(939\) −1095.98 −0.0380893
\(940\) 14620.9 + 25324.1i 0.507320 + 0.878704i
\(941\) 1418.40 2456.74i 0.0491376 0.0851089i −0.840410 0.541950i \(-0.817686\pi\)
0.889548 + 0.456842i \(0.151019\pi\)
\(942\) −29961.0 + 51893.9i −1.03629 + 1.79490i
\(943\) −7.56488 13.1028i −0.000261237 0.000452476i
\(944\) −62607.9 −2.15860
\(945\) 0 0
\(946\) −1572.90 −0.0540586
\(947\) 20136.4 + 34877.3i 0.690967 + 1.19679i 0.971521 + 0.236952i \(0.0761486\pi\)
−0.280554 + 0.959838i \(0.590518\pi\)
\(948\) 16949.7 29357.8i 0.580698 1.00580i
\(949\) −22042.0 + 38177.9i −0.753967 + 1.30591i
\(950\) −815.821 1413.04i −0.0278618 0.0482581i
\(951\) −6715.12 −0.228972
\(952\) 0 0
\(953\) 17770.1 0.604019 0.302010 0.953305i \(-0.402343\pi\)
0.302010 + 0.953305i \(0.402343\pi\)
\(954\) −11785.5 20413.1i −0.399968 0.692765i
\(955\) 6064.87 10504.7i 0.205502 0.355940i
\(956\) −39502.5 + 68420.3i −1.33640 + 2.31472i
\(957\) 12717.7 + 22027.7i 0.429576 + 0.744047i
\(958\) 9349.97 0.315328
\(959\) 0 0
\(960\) −44869.0 −1.50848
\(961\) 2127.18 + 3684.38i 0.0714033 + 0.123674i
\(962\) 33816.0 58571.0i 1.13334 1.96300i
\(963\) −13012.5 + 22538.4i −0.435434 + 0.754194i
\(964\) 4073.54 + 7055.57i 0.136099 + 0.235731i
\(965\) −3114.61 −0.103899
\(966\) 0 0
\(967\) −3530.14 −0.117396 −0.0586978 0.998276i \(-0.518695\pi\)
−0.0586978 + 0.998276i \(0.518695\pi\)
\(968\) −5552.59 9617.37i −0.184367 0.319333i
\(969\) −2087.45 + 3615.58i −0.0692040 + 0.119865i
\(970\) −11574.0 + 20046.8i −0.383113 + 0.663571i
\(971\) 8825.36 + 15286.0i 0.291678 + 0.505201i 0.974207 0.225658i \(-0.0724532\pi\)
−0.682529 + 0.730859i \(0.739120\pi\)
\(972\) −69292.3 −2.28658
\(973\) 0 0
\(974\) −86693.8 −2.85200
\(975\) −3324.45 5758.11i −0.109197 0.189136i
\(976\) 101293. 175444.i 3.32204 5.75393i
\(977\) 7238.82 12538.0i 0.237042 0.410569i −0.722822 0.691034i \(-0.757155\pi\)
0.959864 + 0.280465i \(0.0904886\pi\)
\(978\) 14319.1 + 24801.4i 0.468175 + 0.810902i
\(979\) −16357.8 −0.534012
\(980\) 0 0
\(981\) 4924.56 0.160274
\(982\) −7494.34 12980.6i −0.243538 0.421820i
\(983\) −4382.05 + 7589.93i −0.142183 + 0.246268i −0.928318 0.371786i \(-0.878745\pi\)
0.786136 + 0.618054i \(0.212079\pi\)
\(984\) 22351.1 38713.2i 0.724112 1.25420i
\(985\) −7105.72 12307.5i −0.229855 0.398120i
\(986\) −96296.9 −3.11026
\(987\) 0 0
\(988\) 18292.0 0.589015
\(989\) 0.430062 + 0.744889i 1.38273e−5 + 2.39495e-5i
\(990\) −5760.97 + 9978.29i −0.184945 + 0.320334i
\(991\) −16812.1 + 29119.3i −0.538903 + 0.933407i 0.460061 + 0.887887i \(0.347828\pi\)
−0.998963 + 0.0455192i \(0.985506\pi\)
\(992\) −63817.1 110535.i −2.04254 3.53778i
\(993\) −21645.1 −0.691727
\(994\) 0 0
\(995\) 4336.82 0.138177
\(996\) −21370.1 37014.2i −0.679858 1.17755i
\(997\) 8315.63 14403.1i 0.264151 0.457523i −0.703190 0.711002i \(-0.748242\pi\)
0.967341 + 0.253479i \(0.0815749\pi\)
\(998\) 11850.8 20526.2i 0.375882 0.651046i
\(999\) 13425.9 + 23254.3i 0.425202 + 0.736471i
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 245.4.e.q.116.6 12
7.2 even 3 inner 245.4.e.q.226.6 12
7.3 odd 6 245.4.a.p.1.1 yes 6
7.4 even 3 245.4.a.o.1.1 6
7.5 odd 6 245.4.e.p.226.6 12
7.6 odd 2 245.4.e.p.116.6 12
21.11 odd 6 2205.4.a.bz.1.6 6
21.17 even 6 2205.4.a.ca.1.6 6
35.4 even 6 1225.4.a.bj.1.6 6
35.24 odd 6 1225.4.a.bi.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.4.a.o.1.1 6 7.4 even 3
245.4.a.p.1.1 yes 6 7.3 odd 6
245.4.e.p.116.6 12 7.6 odd 2
245.4.e.p.226.6 12 7.5 odd 6
245.4.e.q.116.6 12 1.1 even 1 trivial
245.4.e.q.226.6 12 7.2 even 3 inner
1225.4.a.bi.1.6 6 35.24 odd 6
1225.4.a.bj.1.6 6 35.4 even 6
2205.4.a.bz.1.6 6 21.11 odd 6
2205.4.a.ca.1.6 6 21.17 even 6