Properties

Label 245.4.e.p.116.3
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 116.3
Root \(-1.02943 + 1.78303i\) of defining polynomial
Character \(\chi\) \(=\) 245.116
Dual form 245.4.e.p.226.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.322324 - 0.558282i) q^{2} +(2.09344 - 3.62594i) q^{3} +(3.79221 - 6.56831i) q^{4} +(2.50000 + 4.33013i) q^{5} -2.69906 q^{6} -10.0465 q^{8} +(4.73504 + 8.20133i) q^{9} +O(q^{10})\) \(q+(-0.322324 - 0.558282i) q^{2} +(2.09344 - 3.62594i) q^{3} +(3.79221 - 6.56831i) q^{4} +(2.50000 + 4.33013i) q^{5} -2.69906 q^{6} -10.0465 q^{8} +(4.73504 + 8.20133i) q^{9} +(1.61162 - 2.79141i) q^{10} +(23.8507 - 41.3106i) q^{11} +(-15.8775 - 27.5007i) q^{12} +57.2256 q^{13} +20.9344 q^{15} +(-27.0995 - 46.9377i) q^{16} +(18.4843 - 32.0157i) q^{17} +(3.05244 - 5.28697i) q^{18} +(-15.3830 - 26.6441i) q^{19} +37.9221 q^{20} -30.7506 q^{22} +(-26.5641 - 46.0104i) q^{23} +(-21.0317 + 36.4279i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-18.4452 - 31.9480i) q^{26} +152.696 q^{27} -195.663 q^{29} +(-6.74765 - 11.6873i) q^{30} +(-128.935 + 223.322i) q^{31} +(-57.6555 + 99.8623i) q^{32} +(-99.8597 - 172.962i) q^{33} -23.8317 q^{34} +71.8252 q^{36} +(-173.212 - 300.011i) q^{37} +(-9.91660 + 17.1760i) q^{38} +(119.798 - 207.497i) q^{39} +(-25.1162 - 43.5025i) q^{40} +267.050 q^{41} -176.859 q^{43} +(-180.894 - 313.317i) q^{44} +(-23.6752 + 41.0067i) q^{45} +(-17.1245 + 29.6605i) q^{46} +(155.799 + 269.852i) q^{47} -226.924 q^{48} +16.1162 q^{50} +(-77.3914 - 134.046i) q^{51} +(217.012 - 375.875i) q^{52} +(246.135 - 426.318i) q^{53} +(-49.2175 - 85.2472i) q^{54} +238.507 q^{55} -128.813 q^{57} +(63.0668 + 109.235i) q^{58} +(-49.3827 + 85.5333i) q^{59} +(79.3876 - 137.503i) q^{60} +(-41.0841 - 71.1597i) q^{61} +166.235 q^{62} -359.257 q^{64} +(143.064 + 247.794i) q^{65} +(-64.3744 + 111.500i) q^{66} +(-327.334 + 566.959i) q^{67} +(-140.193 - 242.821i) q^{68} -222.441 q^{69} +779.658 q^{71} +(-47.5705 - 82.3945i) q^{72} +(414.836 - 718.518i) q^{73} +(-111.660 + 193.402i) q^{74} +(52.3359 + 90.6485i) q^{75} -233.342 q^{76} -154.455 q^{78} +(384.713 + 666.343i) q^{79} +(135.497 - 234.689i) q^{80} +(191.813 - 332.229i) q^{81} +(-86.0765 - 149.089i) q^{82} +613.203 q^{83} +184.843 q^{85} +(57.0059 + 98.7372i) q^{86} +(-409.608 + 709.461i) q^{87} +(-239.615 + 415.025i) q^{88} +(228.833 + 396.350i) q^{89} +30.5244 q^{90} -402.947 q^{92} +(539.835 + 935.022i) q^{93} +(100.436 - 173.960i) q^{94} +(76.9148 - 133.220i) q^{95} +(241.396 + 418.111i) q^{96} -1412.11 q^{97} +451.736 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.322324 0.558282i −0.113959 0.197382i 0.803404 0.595434i \(-0.203020\pi\)
−0.917363 + 0.398052i \(0.869687\pi\)
\(3\) 2.09344 3.62594i 0.402882 0.697812i −0.591190 0.806532i \(-0.701342\pi\)
0.994072 + 0.108720i \(0.0346751\pi\)
\(4\) 3.79221 6.56831i 0.474027 0.821039i
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) −2.69906 −0.183648
\(7\) 0 0
\(8\) −10.0465 −0.443995
\(9\) 4.73504 + 8.20133i 0.175372 + 0.303753i
\(10\) 1.61162 2.79141i 0.0509639 0.0882721i
\(11\) 23.8507 41.3106i 0.653750 1.13233i −0.328456 0.944519i \(-0.606528\pi\)
0.982206 0.187808i \(-0.0601383\pi\)
\(12\) −15.8775 27.5007i −0.381954 0.661564i
\(13\) 57.2256 1.22089 0.610443 0.792060i \(-0.290991\pi\)
0.610443 + 0.792060i \(0.290991\pi\)
\(14\) 0 0
\(15\) 20.9344 0.360349
\(16\) −27.0995 46.9377i −0.423430 0.733402i
\(17\) 18.4843 32.0157i 0.263712 0.456762i −0.703514 0.710682i \(-0.748387\pi\)
0.967225 + 0.253920i \(0.0817199\pi\)
\(18\) 3.05244 5.28697i 0.0399703 0.0692306i
\(19\) −15.3830 26.6441i −0.185742 0.321714i 0.758084 0.652156i \(-0.226135\pi\)
−0.943826 + 0.330442i \(0.892802\pi\)
\(20\) 37.9221 0.423982
\(21\) 0 0
\(22\) −30.7506 −0.298002
\(23\) −26.5641 46.0104i −0.240826 0.417123i 0.720124 0.693846i \(-0.244085\pi\)
−0.960950 + 0.276723i \(0.910752\pi\)
\(24\) −21.0317 + 36.4279i −0.178878 + 0.309826i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −18.4452 31.9480i −0.139131 0.240981i
\(27\) 152.696 1.08838
\(28\) 0 0
\(29\) −195.663 −1.25288 −0.626442 0.779468i \(-0.715490\pi\)
−0.626442 + 0.779468i \(0.715490\pi\)
\(30\) −6.74765 11.6873i −0.0410649 0.0711265i
\(31\) −128.935 + 223.322i −0.747014 + 1.29387i 0.202234 + 0.979337i \(0.435180\pi\)
−0.949248 + 0.314529i \(0.898154\pi\)
\(32\) −57.6555 + 99.8623i −0.318505 + 0.551666i
\(33\) −99.8597 172.962i −0.526768 0.912389i
\(34\) −23.8317 −0.120209
\(35\) 0 0
\(36\) 71.8252 0.332524
\(37\) −173.212 300.011i −0.769616 1.33301i −0.937771 0.347254i \(-0.887114\pi\)
0.168155 0.985761i \(-0.446219\pi\)
\(38\) −9.91660 + 17.1760i −0.0423338 + 0.0733243i
\(39\) 119.798 207.497i 0.491873 0.851950i
\(40\) −25.1162 43.5025i −0.0992804 0.171959i
\(41\) 267.050 1.01722 0.508611 0.860996i \(-0.330159\pi\)
0.508611 + 0.860996i \(0.330159\pi\)
\(42\) 0 0
\(43\) −176.859 −0.627227 −0.313614 0.949551i \(-0.601540\pi\)
−0.313614 + 0.949551i \(0.601540\pi\)
\(44\) −180.894 313.317i −0.619790 1.07351i
\(45\) −23.6752 + 41.0067i −0.0784287 + 0.135843i
\(46\) −17.1245 + 29.6605i −0.0548884 + 0.0950696i
\(47\) 155.799 + 269.852i 0.483524 + 0.837489i 0.999821 0.0189211i \(-0.00602314\pi\)
−0.516297 + 0.856410i \(0.672690\pi\)
\(48\) −226.924 −0.682369
\(49\) 0 0
\(50\) 16.1162 0.0455835
\(51\) −77.3914 134.046i −0.212489 0.368042i
\(52\) 217.012 375.875i 0.578733 1.00240i
\(53\) 246.135 426.318i 0.637910 1.10489i −0.347980 0.937502i \(-0.613132\pi\)
0.985891 0.167391i \(-0.0535343\pi\)
\(54\) −49.2175 85.2472i −0.124031 0.214827i
\(55\) 238.507 0.584731
\(56\) 0 0
\(57\) −128.813 −0.299328
\(58\) 63.0668 + 109.235i 0.142777 + 0.247297i
\(59\) −49.3827 + 85.5333i −0.108967 + 0.188737i −0.915352 0.402654i \(-0.868088\pi\)
0.806385 + 0.591391i \(0.201421\pi\)
\(60\) 79.3876 137.503i 0.170815 0.295860i
\(61\) −41.0841 71.1597i −0.0862340 0.149362i 0.819682 0.572818i \(-0.194150\pi\)
−0.905916 + 0.423457i \(0.860817\pi\)
\(62\) 166.235 0.340515
\(63\) 0 0
\(64\) −359.257 −0.701674
\(65\) 143.064 + 247.794i 0.272999 + 0.472847i
\(66\) −64.3744 + 111.500i −0.120060 + 0.207949i
\(67\) −327.334 + 566.959i −0.596869 + 1.03381i 0.396411 + 0.918073i \(0.370255\pi\)
−0.993280 + 0.115734i \(0.963078\pi\)
\(68\) −140.193 242.821i −0.250013 0.433035i
\(69\) −222.441 −0.388098
\(70\) 0 0
\(71\) 779.658 1.30322 0.651608 0.758556i \(-0.274095\pi\)
0.651608 + 0.758556i \(0.274095\pi\)
\(72\) −47.5705 82.3945i −0.0778643 0.134865i
\(73\) 414.836 718.518i 0.665109 1.15200i −0.314147 0.949374i \(-0.601719\pi\)
0.979256 0.202628i \(-0.0649481\pi\)
\(74\) −111.660 + 193.402i −0.175409 + 0.303817i
\(75\) 52.3359 + 90.6485i 0.0805764 + 0.139562i
\(76\) −233.342 −0.352186
\(77\) 0 0
\(78\) −154.455 −0.224213
\(79\) 384.713 + 666.343i 0.547894 + 0.948980i 0.998419 + 0.0562159i \(0.0179035\pi\)
−0.450525 + 0.892764i \(0.648763\pi\)
\(80\) 135.497 234.689i 0.189363 0.327987i
\(81\) 191.813 332.229i 0.263117 0.455733i
\(82\) −86.0765 149.089i −0.115921 0.200782i
\(83\) 613.203 0.810937 0.405469 0.914109i \(-0.367108\pi\)
0.405469 + 0.914109i \(0.367108\pi\)
\(84\) 0 0
\(85\) 184.843 0.235871
\(86\) 57.0059 + 98.7372i 0.0714780 + 0.123804i
\(87\) −409.608 + 709.461i −0.504765 + 0.874278i
\(88\) −239.615 + 415.025i −0.290262 + 0.502748i
\(89\) 228.833 + 396.350i 0.272542 + 0.472057i 0.969512 0.245043i \(-0.0788022\pi\)
−0.696970 + 0.717100i \(0.745469\pi\)
\(90\) 30.5244 0.0357506
\(91\) 0 0
\(92\) −402.947 −0.456632
\(93\) 539.835 + 935.022i 0.601917 + 1.04255i
\(94\) 100.436 173.960i 0.110204 0.190878i
\(95\) 76.9148 133.220i 0.0830662 0.143875i
\(96\) 241.396 + 418.111i 0.256640 + 0.444513i
\(97\) −1412.11 −1.47813 −0.739063 0.673636i \(-0.764732\pi\)
−0.739063 + 0.673636i \(0.764732\pi\)
\(98\) 0 0
\(99\) 451.736 0.458597
\(100\) 94.8054 + 164.208i 0.0948054 + 0.164208i
\(101\) −911.895 + 1579.45i −0.898386 + 1.55605i −0.0688279 + 0.997629i \(0.521926\pi\)
−0.829558 + 0.558421i \(0.811407\pi\)
\(102\) −49.8902 + 86.4124i −0.0484301 + 0.0838833i
\(103\) −203.887 353.143i −0.195045 0.337828i 0.751870 0.659311i \(-0.229152\pi\)
−0.946915 + 0.321483i \(0.895819\pi\)
\(104\) −574.915 −0.542068
\(105\) 0 0
\(106\) −317.341 −0.290782
\(107\) 185.054 + 320.524i 0.167195 + 0.289591i 0.937433 0.348167i \(-0.113196\pi\)
−0.770237 + 0.637757i \(0.779862\pi\)
\(108\) 579.055 1002.95i 0.515922 0.893603i
\(109\) −487.785 + 844.869i −0.428636 + 0.742420i −0.996752 0.0805287i \(-0.974339\pi\)
0.568116 + 0.822948i \(0.307672\pi\)
\(110\) −76.8764 133.154i −0.0666352 0.115416i
\(111\) −1450.43 −1.24026
\(112\) 0 0
\(113\) 1978.85 1.64739 0.823693 0.567036i \(-0.191910\pi\)
0.823693 + 0.567036i \(0.191910\pi\)
\(114\) 41.5195 + 71.9139i 0.0341111 + 0.0590821i
\(115\) 132.820 230.052i 0.107701 0.186543i
\(116\) −741.995 + 1285.17i −0.593901 + 1.02867i
\(117\) 270.966 + 469.326i 0.214109 + 0.370848i
\(118\) 63.6689 0.0496711
\(119\) 0 0
\(120\) −210.317 −0.159993
\(121\) −472.208 817.888i −0.354777 0.614492i
\(122\) −26.4848 + 45.8730i −0.0196542 + 0.0340422i
\(123\) 559.052 968.306i 0.409821 0.709831i
\(124\) 977.899 + 1693.77i 0.708209 + 1.22665i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 1392.38 0.972867 0.486433 0.873718i \(-0.338298\pi\)
0.486433 + 0.873718i \(0.338298\pi\)
\(128\) 577.041 + 999.465i 0.398467 + 0.690164i
\(129\) −370.243 + 641.280i −0.252699 + 0.437687i
\(130\) 92.2259 159.740i 0.0622211 0.107770i
\(131\) 888.509 + 1538.94i 0.592591 + 1.02640i 0.993882 + 0.110447i \(0.0352282\pi\)
−0.401291 + 0.915951i \(0.631438\pi\)
\(132\) −1514.76 −0.998809
\(133\) 0 0
\(134\) 422.031 0.272074
\(135\) 381.739 + 661.192i 0.243369 + 0.421528i
\(136\) −185.702 + 321.645i −0.117087 + 0.202800i
\(137\) 990.240 1715.15i 0.617532 1.06960i −0.372402 0.928071i \(-0.621466\pi\)
0.989935 0.141526i \(-0.0452009\pi\)
\(138\) 71.6981 + 124.185i 0.0442271 + 0.0766037i
\(139\) 2182.09 1.33153 0.665763 0.746163i \(-0.268106\pi\)
0.665763 + 0.746163i \(0.268106\pi\)
\(140\) 0 0
\(141\) 1304.62 0.779213
\(142\) −251.302 435.268i −0.148513 0.257232i
\(143\) 1364.87 2364.02i 0.798154 1.38244i
\(144\) 256.635 444.504i 0.148515 0.257236i
\(145\) −489.157 847.244i −0.280153 0.485240i
\(146\) −534.847 −0.303180
\(147\) 0 0
\(148\) −2627.42 −1.45928
\(149\) −335.077 580.370i −0.184232 0.319099i 0.759085 0.650991i \(-0.225646\pi\)
−0.943317 + 0.331892i \(0.892313\pi\)
\(150\) 33.7383 58.4364i 0.0183648 0.0318087i
\(151\) −1674.42 + 2900.18i −0.902401 + 1.56300i −0.0780315 + 0.996951i \(0.524863\pi\)
−0.824369 + 0.566053i \(0.808470\pi\)
\(152\) 154.544 + 267.679i 0.0824685 + 0.142840i
\(153\) 350.096 0.184990
\(154\) 0 0
\(155\) −1289.35 −0.668149
\(156\) −908.601 1573.74i −0.466322 0.807694i
\(157\) −1204.20 + 2085.74i −0.612140 + 1.06026i 0.378739 + 0.925504i \(0.376358\pi\)
−0.990879 + 0.134754i \(0.956975\pi\)
\(158\) 248.005 429.556i 0.124875 0.216289i
\(159\) −1030.54 1784.94i −0.514005 0.890284i
\(160\) −576.555 −0.284879
\(161\) 0 0
\(162\) −247.303 −0.119938
\(163\) 1905.52 + 3300.45i 0.915654 + 1.58596i 0.805942 + 0.591995i \(0.201659\pi\)
0.109712 + 0.993963i \(0.465007\pi\)
\(164\) 1012.71 1754.06i 0.482191 0.835179i
\(165\) 499.299 864.810i 0.235578 0.408033i
\(166\) −197.650 342.340i −0.0924134 0.160065i
\(167\) 1207.15 0.559354 0.279677 0.960094i \(-0.409773\pi\)
0.279677 + 0.960094i \(0.409773\pi\)
\(168\) 0 0
\(169\) 1077.77 0.490564
\(170\) −59.5793 103.194i −0.0268795 0.0465567i
\(171\) 145.678 252.322i 0.0651478 0.112839i
\(172\) −670.688 + 1161.67i −0.297322 + 0.514978i
\(173\) −1621.64 2808.76i −0.712665 1.23437i −0.963853 0.266434i \(-0.914155\pi\)
0.251188 0.967938i \(-0.419179\pi\)
\(174\) 528.105 0.230089
\(175\) 0 0
\(176\) −2585.36 −1.10727
\(177\) 206.759 + 358.117i 0.0878020 + 0.152078i
\(178\) 147.517 255.507i 0.0621171 0.107590i
\(179\) −429.864 + 744.546i −0.179495 + 0.310894i −0.941708 0.336433i \(-0.890780\pi\)
0.762213 + 0.647326i \(0.224113\pi\)
\(180\) 179.563 + 311.012i 0.0743546 + 0.128786i
\(181\) −290.504 −0.119298 −0.0596491 0.998219i \(-0.518998\pi\)
−0.0596491 + 0.998219i \(0.518998\pi\)
\(182\) 0 0
\(183\) −344.028 −0.138969
\(184\) 266.875 + 462.242i 0.106926 + 0.185201i
\(185\) 866.058 1500.06i 0.344183 0.596142i
\(186\) 348.004 602.760i 0.137187 0.237616i
\(187\) −881.725 1527.19i −0.344803 0.597216i
\(188\) 2363.30 0.916814
\(189\) 0 0
\(190\) −99.1660 −0.0378645
\(191\) −2447.81 4239.73i −0.927315 1.60616i −0.787795 0.615937i \(-0.788778\pi\)
−0.139519 0.990219i \(-0.544556\pi\)
\(192\) −752.082 + 1302.64i −0.282692 + 0.489637i
\(193\) 1774.36 3073.29i 0.661770 1.14622i −0.318381 0.947963i \(-0.603139\pi\)
0.980150 0.198256i \(-0.0635276\pi\)
\(194\) 455.158 + 788.356i 0.168445 + 0.291756i
\(195\) 1197.98 0.439945
\(196\) 0 0
\(197\) −650.107 −0.235118 −0.117559 0.993066i \(-0.537507\pi\)
−0.117559 + 0.993066i \(0.537507\pi\)
\(198\) −145.605 252.196i −0.0522612 0.0905190i
\(199\) −2027.55 + 3511.81i −0.722256 + 1.25098i 0.237838 + 0.971305i \(0.423561\pi\)
−0.960094 + 0.279679i \(0.909772\pi\)
\(200\) 125.581 217.512i 0.0443995 0.0769023i
\(201\) 1370.51 + 2373.79i 0.480936 + 0.833005i
\(202\) 1175.70 0.409516
\(203\) 0 0
\(204\) −1173.94 −0.402903
\(205\) 667.624 + 1156.36i 0.227458 + 0.393969i
\(206\) −131.436 + 227.653i −0.0444541 + 0.0769968i
\(207\) 251.564 435.722i 0.0844682 0.146303i
\(208\) −1550.79 2686.04i −0.516960 0.895400i
\(209\) −1467.58 −0.485714
\(210\) 0 0
\(211\) −1569.67 −0.512134 −0.256067 0.966659i \(-0.582427\pi\)
−0.256067 + 0.966659i \(0.582427\pi\)
\(212\) −1866.79 3233.38i −0.604773 1.04750i
\(213\) 1632.16 2826.99i 0.525042 0.909400i
\(214\) 119.295 206.625i 0.0381067 0.0660027i
\(215\) −442.148 765.822i −0.140252 0.242924i
\(216\) −1534.05 −0.483236
\(217\) 0 0
\(218\) 628.900 0.195387
\(219\) −1736.87 3008.34i −0.535921 0.928242i
\(220\) 904.468 1566.58i 0.277178 0.480087i
\(221\) 1057.77 1832.12i 0.321962 0.557655i
\(222\) 467.508 + 809.748i 0.141338 + 0.244805i
\(223\) 4723.86 1.41853 0.709267 0.704940i \(-0.249026\pi\)
0.709267 + 0.704940i \(0.249026\pi\)
\(224\) 0 0
\(225\) −236.752 −0.0701488
\(226\) −637.831 1104.76i −0.187734 0.325165i
\(227\) −1842.51 + 3191.32i −0.538730 + 0.933108i 0.460243 + 0.887793i \(0.347762\pi\)
−0.998973 + 0.0453145i \(0.985571\pi\)
\(228\) −488.487 + 846.084i −0.141890 + 0.245760i
\(229\) −1678.39 2907.05i −0.484328 0.838880i 0.515510 0.856883i \(-0.327602\pi\)
−0.999838 + 0.0180032i \(0.994269\pi\)
\(230\) −171.245 −0.0490937
\(231\) 0 0
\(232\) 1965.72 0.556275
\(233\) −1157.01 2004.00i −0.325314 0.563460i 0.656262 0.754533i \(-0.272137\pi\)
−0.981576 + 0.191073i \(0.938803\pi\)
\(234\) 174.677 302.550i 0.0487992 0.0845228i
\(235\) −778.996 + 1349.26i −0.216239 + 0.374536i
\(236\) 374.539 + 648.721i 0.103307 + 0.178933i
\(237\) 3221.49 0.882946
\(238\) 0 0
\(239\) 941.179 0.254727 0.127364 0.991856i \(-0.459348\pi\)
0.127364 + 0.991856i \(0.459348\pi\)
\(240\) −567.311 982.611i −0.152582 0.264280i
\(241\) −2819.12 + 4882.86i −0.753509 + 1.30512i 0.192604 + 0.981277i \(0.438307\pi\)
−0.946112 + 0.323838i \(0.895027\pi\)
\(242\) −304.408 + 527.250i −0.0808599 + 0.140053i
\(243\) 1258.30 + 2179.43i 0.332180 + 0.575353i
\(244\) −623.199 −0.163509
\(245\) 0 0
\(246\) −720.783 −0.186811
\(247\) −880.299 1524.72i −0.226770 0.392777i
\(248\) 1295.34 2243.60i 0.331671 0.574471i
\(249\) 1283.70 2223.44i 0.326712 0.565882i
\(250\) 40.2905 + 69.7852i 0.0101928 + 0.0176544i
\(251\) 365.822 0.0919940 0.0459970 0.998942i \(-0.485354\pi\)
0.0459970 + 0.998942i \(0.485354\pi\)
\(252\) 0 0
\(253\) −2534.28 −0.629759
\(254\) −448.799 777.342i −0.110867 0.192027i
\(255\) 386.957 670.229i 0.0950282 0.164594i
\(256\) −1065.04 + 1844.70i −0.260019 + 0.450367i
\(257\) 3138.23 + 5435.57i 0.761702 + 1.31931i 0.941973 + 0.335689i \(0.108969\pi\)
−0.180271 + 0.983617i \(0.557697\pi\)
\(258\) 477.353 0.115189
\(259\) 0 0
\(260\) 2170.12 0.517635
\(261\) −926.471 1604.69i −0.219721 0.380568i
\(262\) 572.776 992.076i 0.135062 0.233934i
\(263\) 2112.99 3659.80i 0.495408 0.858072i −0.504578 0.863366i \(-0.668352\pi\)
0.999986 + 0.00529397i \(0.00168513\pi\)
\(264\) 1003.24 + 1737.66i 0.233883 + 0.405097i
\(265\) 2461.35 0.570564
\(266\) 0 0
\(267\) 1916.19 0.439210
\(268\) 2482.64 + 4300.06i 0.565864 + 0.980105i
\(269\) −490.796 + 850.083i −0.111243 + 0.192678i −0.916272 0.400557i \(-0.868816\pi\)
0.805029 + 0.593236i \(0.202150\pi\)
\(270\) 246.087 426.236i 0.0554681 0.0960737i
\(271\) −1942.21 3364.01i −0.435354 0.754055i 0.561971 0.827157i \(-0.310043\pi\)
−0.997324 + 0.0731021i \(0.976710\pi\)
\(272\) −2003.66 −0.446653
\(273\) 0 0
\(274\) −1276.71 −0.281493
\(275\) 596.267 + 1032.76i 0.130750 + 0.226465i
\(276\) −843.544 + 1461.06i −0.183969 + 0.318643i
\(277\) −1807.46 + 3130.62i −0.392058 + 0.679064i −0.992721 0.120438i \(-0.961570\pi\)
0.600663 + 0.799502i \(0.294903\pi\)
\(278\) −703.339 1218.22i −0.151739 0.262820i
\(279\) −2442.05 −0.524021
\(280\) 0 0
\(281\) 72.6835 0.0154304 0.00771518 0.999970i \(-0.497544\pi\)
0.00771518 + 0.999970i \(0.497544\pi\)
\(282\) −420.511 728.347i −0.0887982 0.153803i
\(283\) −871.522 + 1509.52i −0.183062 + 0.317073i −0.942922 0.333014i \(-0.891934\pi\)
0.759860 + 0.650087i \(0.225268\pi\)
\(284\) 2956.63 5121.03i 0.617759 1.06999i
\(285\) −322.033 557.777i −0.0669318 0.115929i
\(286\) −1759.72 −0.363827
\(287\) 0 0
\(288\) −1092.01 −0.223427
\(289\) 1773.16 + 3071.21i 0.360912 + 0.625119i
\(290\) −315.334 + 546.174i −0.0638519 + 0.110595i
\(291\) −2956.17 + 5120.23i −0.595511 + 1.03145i
\(292\) −3146.30 5449.55i −0.630559 1.09216i
\(293\) −4989.29 −0.994804 −0.497402 0.867520i \(-0.665713\pi\)
−0.497402 + 0.867520i \(0.665713\pi\)
\(294\) 0 0
\(295\) −493.827 −0.0974634
\(296\) 1740.17 + 3014.05i 0.341706 + 0.591853i
\(297\) 3641.89 6307.94i 0.711529 1.23240i
\(298\) −216.007 + 374.135i −0.0419897 + 0.0727283i
\(299\) −1520.15 2632.97i −0.294021 0.509260i
\(300\) 793.876 0.152782
\(301\) 0 0
\(302\) 2158.82 0.411346
\(303\) 3817.99 + 6612.95i 0.723887 + 1.25381i
\(304\) −833.741 + 1444.08i −0.157297 + 0.272447i
\(305\) 205.420 355.799i 0.0385650 0.0667966i
\(306\) −112.844 195.452i −0.0210813 0.0365139i
\(307\) 1664.61 0.309461 0.154731 0.987957i \(-0.450549\pi\)
0.154731 + 0.987957i \(0.450549\pi\)
\(308\) 0 0
\(309\) −1707.30 −0.314320
\(310\) 415.589 + 719.821i 0.0761415 + 0.131881i
\(311\) −272.812 + 472.524i −0.0497419 + 0.0861555i −0.889824 0.456303i \(-0.849173\pi\)
0.840082 + 0.542459i \(0.182507\pi\)
\(312\) −1203.55 + 2084.61i −0.218390 + 0.378262i
\(313\) −106.782 184.952i −0.0192833 0.0333997i 0.856223 0.516607i \(-0.172805\pi\)
−0.875506 + 0.483207i \(0.839472\pi\)
\(314\) 1552.58 0.279035
\(315\) 0 0
\(316\) 5835.66 1.03887
\(317\) 1341.97 + 2324.35i 0.237767 + 0.411825i 0.960073 0.279748i \(-0.0902511\pi\)
−0.722306 + 0.691574i \(0.756918\pi\)
\(318\) −664.333 + 1150.66i −0.117151 + 0.202911i
\(319\) −4666.68 + 8082.93i −0.819073 + 1.41868i
\(320\) −898.142 1555.63i −0.156899 0.271757i
\(321\) 1549.60 0.269440
\(322\) 0 0
\(323\) −1137.37 −0.195929
\(324\) −1454.79 2519.77i −0.249449 0.432059i
\(325\) −715.320 + 1238.97i −0.122089 + 0.211464i
\(326\) 1228.39 2127.63i 0.208693 0.361468i
\(327\) 2042.30 + 3537.36i 0.345380 + 0.598215i
\(328\) −2682.91 −0.451642
\(329\) 0 0
\(330\) −643.744 −0.107385
\(331\) 2533.76 + 4388.61i 0.420750 + 0.728760i 0.996013 0.0892084i \(-0.0284337\pi\)
−0.575263 + 0.817968i \(0.695100\pi\)
\(332\) 2325.40 4027.71i 0.384406 0.665811i
\(333\) 1640.33 2841.13i 0.269938 0.467547i
\(334\) −389.093 673.930i −0.0637433 0.110407i
\(335\) −3273.34 −0.533856
\(336\) 0 0
\(337\) −9353.21 −1.51187 −0.755937 0.654644i \(-0.772818\pi\)
−0.755937 + 0.654644i \(0.772818\pi\)
\(338\) −347.391 601.699i −0.0559041 0.0968287i
\(339\) 4142.60 7175.19i 0.663703 1.14957i
\(340\) 700.964 1214.10i 0.111809 0.193659i
\(341\) 6150.37 + 10652.8i 0.976720 + 1.69173i
\(342\) −187.822 −0.0296966
\(343\) 0 0
\(344\) 1776.81 0.278486
\(345\) −556.103 963.198i −0.0867813 0.150310i
\(346\) −1045.39 + 1810.66i −0.162429 + 0.281335i
\(347\) −1174.67 + 2034.59i −0.181728 + 0.314762i −0.942469 0.334293i \(-0.891502\pi\)
0.760741 + 0.649055i \(0.224836\pi\)
\(348\) 3106.64 + 5380.86i 0.478544 + 0.828863i
\(349\) −10472.6 −1.60626 −0.803128 0.595806i \(-0.796833\pi\)
−0.803128 + 0.595806i \(0.796833\pi\)
\(350\) 0 0
\(351\) 8738.10 1.32879
\(352\) 2750.24 + 4763.56i 0.416445 + 0.721303i
\(353\) 3587.31 6213.41i 0.540888 0.936845i −0.457966 0.888970i \(-0.651422\pi\)
0.998853 0.0478752i \(-0.0152450\pi\)
\(354\) 133.287 230.859i 0.0200116 0.0346611i
\(355\) 1949.14 + 3376.02i 0.291408 + 0.504733i
\(356\) 3471.14 0.516769
\(357\) 0 0
\(358\) 554.222 0.0818199
\(359\) 3767.06 + 6524.74i 0.553811 + 0.959228i 0.997995 + 0.0632926i \(0.0201601\pi\)
−0.444185 + 0.895935i \(0.646507\pi\)
\(360\) 237.852 411.972i 0.0348220 0.0603135i
\(361\) 2956.23 5120.34i 0.431000 0.746514i
\(362\) 93.6364 + 162.183i 0.0135951 + 0.0235474i
\(363\) −3954.15 −0.571733
\(364\) 0 0
\(365\) 4148.36 0.594891
\(366\) 110.888 + 192.064i 0.0158367 + 0.0274300i
\(367\) −2726.53 + 4722.49i −0.387803 + 0.671694i −0.992154 0.125024i \(-0.960099\pi\)
0.604351 + 0.796718i \(0.293433\pi\)
\(368\) −1439.75 + 2493.71i −0.203946 + 0.353244i
\(369\) 1264.49 + 2190.16i 0.178392 + 0.308985i
\(370\) −1116.60 −0.156891
\(371\) 0 0
\(372\) 8188.68 1.14130
\(373\) −4115.65 7128.51i −0.571314 0.989545i −0.996431 0.0844067i \(-0.973101\pi\)
0.425117 0.905138i \(-0.360233\pi\)
\(374\) −568.402 + 984.501i −0.0785866 + 0.136116i
\(375\) −261.680 + 453.242i −0.0360349 + 0.0624142i
\(376\) −1565.23 2711.06i −0.214683 0.371841i
\(377\) −11196.9 −1.52963
\(378\) 0 0
\(379\) 1670.06 0.226346 0.113173 0.993575i \(-0.463898\pi\)
0.113173 + 0.993575i \(0.463898\pi\)
\(380\) −583.355 1010.40i −0.0787512 0.136401i
\(381\) 2914.87 5048.70i 0.391951 0.678879i
\(382\) −1577.97 + 2733.13i −0.211351 + 0.366071i
\(383\) −1610.07 2788.72i −0.214806 0.372055i 0.738407 0.674356i \(-0.235579\pi\)
−0.953213 + 0.302301i \(0.902245\pi\)
\(384\) 4832.00 0.642140
\(385\) 0 0
\(386\) −2287.68 −0.301658
\(387\) −837.435 1450.48i −0.109998 0.190522i
\(388\) −5355.03 + 9275.19i −0.700672 + 1.21360i
\(389\) −1761.11 + 3050.34i −0.229543 + 0.397579i −0.957673 0.287860i \(-0.907056\pi\)
0.728130 + 0.685439i \(0.240390\pi\)
\(390\) −386.138 668.811i −0.0501356 0.0868374i
\(391\) −1964.07 −0.254034
\(392\) 0 0
\(393\) 7440.15 0.954977
\(394\) 209.545 + 362.943i 0.0267937 + 0.0464081i
\(395\) −1923.57 + 3331.71i −0.245026 + 0.424397i
\(396\) 1713.08 2967.14i 0.217387 0.376526i
\(397\) 2727.58 + 4724.31i 0.344819 + 0.597245i 0.985321 0.170712i \(-0.0546068\pi\)
−0.640502 + 0.767957i \(0.721274\pi\)
\(398\) 2614.11 0.329229
\(399\) 0 0
\(400\) 1354.97 0.169372
\(401\) 580.899 + 1006.15i 0.0723409 + 0.125298i 0.899927 0.436041i \(-0.143620\pi\)
−0.827586 + 0.561339i \(0.810286\pi\)
\(402\) 883.494 1530.26i 0.109614 0.189856i
\(403\) −7378.39 + 12779.7i −0.912019 + 1.57966i
\(404\) 6916.20 + 11979.2i 0.851718 + 1.47522i
\(405\) 1918.13 0.235339
\(406\) 0 0
\(407\) −16524.8 −2.01255
\(408\) 777.510 + 1346.69i 0.0943443 + 0.163409i
\(409\) 3699.32 6407.42i 0.447237 0.774637i −0.550968 0.834526i \(-0.685742\pi\)
0.998205 + 0.0598896i \(0.0190749\pi\)
\(410\) 430.382 745.444i 0.0518416 0.0897924i
\(411\) −4146.01 7181.10i −0.497586 0.861843i
\(412\) −3092.74 −0.369826
\(413\) 0 0
\(414\) −324.341 −0.0385036
\(415\) 1533.01 + 2655.25i 0.181331 + 0.314075i
\(416\) −3299.37 + 5714.68i −0.388858 + 0.673522i
\(417\) 4568.06 7912.11i 0.536448 0.929155i
\(418\) 473.035 + 819.320i 0.0553514 + 0.0958714i
\(419\) 2134.46 0.248867 0.124433 0.992228i \(-0.460289\pi\)
0.124433 + 0.992228i \(0.460289\pi\)
\(420\) 0 0
\(421\) −3902.36 −0.451756 −0.225878 0.974156i \(-0.572525\pi\)
−0.225878 + 0.974156i \(0.572525\pi\)
\(422\) 505.941 + 876.316i 0.0583621 + 0.101086i
\(423\) −1475.43 + 2555.52i −0.169593 + 0.293744i
\(424\) −2472.79 + 4283.00i −0.283229 + 0.490568i
\(425\) 462.107 + 800.393i 0.0527423 + 0.0913524i
\(426\) −2104.34 −0.239333
\(427\) 0 0
\(428\) 2807.06 0.317020
\(429\) −5714.53 9897.86i −0.643124 1.11392i
\(430\) −285.030 + 493.686i −0.0319659 + 0.0553666i
\(431\) 1809.07 3133.39i 0.202180 0.350186i −0.747050 0.664767i \(-0.768531\pi\)
0.949231 + 0.314581i \(0.101864\pi\)
\(432\) −4137.98 7167.18i −0.460853 0.798221i
\(433\) 4222.37 0.468624 0.234312 0.972161i \(-0.424716\pi\)
0.234312 + 0.972161i \(0.424716\pi\)
\(434\) 0 0
\(435\) −4096.08 −0.451475
\(436\) 3699.57 + 6407.85i 0.406370 + 0.703854i
\(437\) −817.269 + 1415.55i −0.0894629 + 0.154954i
\(438\) −1119.67 + 1939.32i −0.122146 + 0.211563i
\(439\) −6758.98 11706.9i −0.734826 1.27276i −0.954800 0.297250i \(-0.903931\pi\)
0.219974 0.975506i \(-0.429403\pi\)
\(440\) −2396.15 −0.259618
\(441\) 0 0
\(442\) −1363.78 −0.146762
\(443\) −8295.58 14368.4i −0.889695 1.54100i −0.840236 0.542222i \(-0.817583\pi\)
−0.0494599 0.998776i \(-0.515750\pi\)
\(444\) −5500.34 + 9526.87i −0.587916 + 1.01830i
\(445\) −1144.17 + 1981.75i −0.121885 + 0.211110i
\(446\) −1522.61 2637.24i −0.161654 0.279993i
\(447\) −2805.85 −0.296895
\(448\) 0 0
\(449\) 8354.32 0.878095 0.439048 0.898464i \(-0.355316\pi\)
0.439048 + 0.898464i \(0.355316\pi\)
\(450\) 76.3109 + 132.174i 0.00799407 + 0.0138461i
\(451\) 6369.31 11032.0i 0.665009 1.15183i
\(452\) 7504.23 12997.7i 0.780905 1.35257i
\(453\) 7010.59 + 12142.7i 0.727122 + 1.25941i
\(454\) 2375.54 0.245572
\(455\) 0 0
\(456\) 1294.12 0.132900
\(457\) 640.168 + 1108.80i 0.0655269 + 0.113496i 0.896928 0.442177i \(-0.145794\pi\)
−0.831401 + 0.555673i \(0.812461\pi\)
\(458\) −1081.97 + 1874.03i −0.110387 + 0.191195i
\(459\) 2822.47 4888.66i 0.287019 0.497131i
\(460\) −1007.37 1744.81i −0.102106 0.176853i
\(461\) 6986.72 0.705865 0.352932 0.935649i \(-0.385185\pi\)
0.352932 + 0.935649i \(0.385185\pi\)
\(462\) 0 0
\(463\) −5587.32 −0.560831 −0.280416 0.959879i \(-0.590472\pi\)
−0.280416 + 0.959879i \(0.590472\pi\)
\(464\) 5302.36 + 9183.96i 0.530508 + 0.918867i
\(465\) −2699.18 + 4675.11i −0.269185 + 0.466243i
\(466\) −745.863 + 1291.87i −0.0741447 + 0.128422i
\(467\) −4966.92 8602.95i −0.492166 0.852456i 0.507793 0.861479i \(-0.330461\pi\)
−0.999959 + 0.00902263i \(0.997128\pi\)
\(468\) 4110.24 0.405974
\(469\) 0 0
\(470\) 1004.36 0.0985691
\(471\) 5041.85 + 8732.75i 0.493241 + 0.854318i
\(472\) 496.121 859.308i 0.0483810 0.0837984i
\(473\) −4218.21 + 7306.15i −0.410049 + 0.710226i
\(474\) −1038.36 1798.50i −0.100619 0.174278i
\(475\) 769.148 0.0742967
\(476\) 0 0
\(477\) 4661.84 0.447486
\(478\) −303.365 525.443i −0.0290284 0.0502787i
\(479\) 2534.31 4389.55i 0.241744 0.418714i −0.719467 0.694527i \(-0.755614\pi\)
0.961211 + 0.275813i \(0.0889471\pi\)
\(480\) −1206.98 + 2090.55i −0.114773 + 0.198792i
\(481\) −9912.14 17168.3i −0.939614 1.62746i
\(482\) 3634.68 0.343476
\(483\) 0 0
\(484\) −7162.86 −0.672695
\(485\) −3530.28 6114.62i −0.330519 0.572476i
\(486\) 811.158 1404.97i 0.0757096 0.131133i
\(487\) −132.177 + 228.937i −0.0122988 + 0.0213021i −0.872109 0.489311i \(-0.837248\pi\)
0.859811 + 0.510613i \(0.170582\pi\)
\(488\) 412.750 + 714.904i 0.0382875 + 0.0663159i
\(489\) 15956.3 1.47560
\(490\) 0 0
\(491\) −7459.47 −0.685623 −0.342812 0.939404i \(-0.611379\pi\)
−0.342812 + 0.939404i \(0.611379\pi\)
\(492\) −4240.09 7344.05i −0.388532 0.672958i
\(493\) −3616.68 + 6264.28i −0.330400 + 0.572270i
\(494\) −567.483 + 982.910i −0.0516848 + 0.0895206i
\(495\) 1129.34 + 1956.07i 0.102545 + 0.177614i
\(496\) 13976.3 1.26523
\(497\) 0 0
\(498\) −1655.07 −0.148927
\(499\) −3603.34 6241.16i −0.323261 0.559905i 0.657897 0.753108i \(-0.271446\pi\)
−0.981159 + 0.193202i \(0.938113\pi\)
\(500\) −474.027 + 821.039i −0.0423982 + 0.0734359i
\(501\) 2527.09 4377.05i 0.225354 0.390324i
\(502\) −117.913 204.232i −0.0104835 0.0181580i
\(503\) −10886.7 −0.965037 −0.482519 0.875886i \(-0.660278\pi\)
−0.482519 + 0.875886i \(0.660278\pi\)
\(504\) 0 0
\(505\) −9118.95 −0.803541
\(506\) 816.861 + 1414.84i 0.0717666 + 0.124303i
\(507\) 2256.24 3907.93i 0.197640 0.342322i
\(508\) 5280.22 9145.61i 0.461165 0.798761i
\(509\) 3752.48 + 6499.49i 0.326770 + 0.565982i 0.981869 0.189561i \(-0.0607064\pi\)
−0.655099 + 0.755543i \(0.727373\pi\)
\(510\) −498.902 −0.0433172
\(511\) 0 0
\(512\) 10605.8 0.915459
\(513\) −2348.91 4068.43i −0.202158 0.350148i
\(514\) 2023.05 3504.03i 0.173605 0.300693i
\(515\) 1019.44 1765.72i 0.0872267 0.151081i
\(516\) 2808.09 + 4863.75i 0.239572 + 0.414951i
\(517\) 14863.7 1.26442
\(518\) 0 0
\(519\) −13579.2 −1.14848
\(520\) −1437.29 2489.46i −0.121210 0.209942i
\(521\) 11132.4 19281.8i 0.936120 1.62141i 0.163495 0.986544i \(-0.447723\pi\)
0.772625 0.634863i \(-0.218944\pi\)
\(522\) −597.248 + 1034.46i −0.0500782 + 0.0867380i
\(523\) −5643.33 9774.54i −0.471828 0.817229i 0.527653 0.849460i \(-0.323072\pi\)
−0.999480 + 0.0322308i \(0.989739\pi\)
\(524\) 13477.7 1.12362
\(525\) 0 0
\(526\) −2724.27 −0.225824
\(527\) 4766.55 + 8255.90i 0.393992 + 0.682415i
\(528\) −5412.30 + 9374.37i −0.446098 + 0.772665i
\(529\) 4672.20 8092.48i 0.384006 0.665118i
\(530\) −793.352 1374.13i −0.0650208 0.112619i
\(531\) −935.316 −0.0764393
\(532\) 0 0
\(533\) 15282.1 1.24191
\(534\) −617.634 1069.77i −0.0500518 0.0866922i
\(535\) −925.272 + 1602.62i −0.0747720 + 0.129509i
\(536\) 3288.55 5695.94i 0.265007 0.459006i
\(537\) 1799.79 + 3117.32i 0.144630 + 0.250507i
\(538\) 632.781 0.0507084
\(539\) 0 0
\(540\) 5790.55 0.461455
\(541\) −8203.38 14208.7i −0.651924 1.12917i −0.982655 0.185440i \(-0.940629\pi\)
0.330732 0.943725i \(-0.392705\pi\)
\(542\) −1252.04 + 2168.60i −0.0992248 + 0.171862i
\(543\) −608.152 + 1053.35i −0.0480631 + 0.0832478i
\(544\) 2131.44 + 3691.77i 0.167987 + 0.290962i
\(545\) −4877.85 −0.383384
\(546\) 0 0
\(547\) −8692.48 −0.679458 −0.339729 0.940523i \(-0.610335\pi\)
−0.339729 + 0.940523i \(0.610335\pi\)
\(548\) −7510.41 13008.4i −0.585454 1.01404i
\(549\) 389.070 673.888i 0.0302461 0.0523877i
\(550\) 384.382 665.769i 0.0298002 0.0516154i
\(551\) 3009.87 + 5213.25i 0.232713 + 0.403071i
\(552\) 2234.75 0.172314
\(553\) 0 0
\(554\) 2330.36 0.178714
\(555\) −3626.08 6280.55i −0.277330 0.480350i
\(556\) 8274.94 14332.6i 0.631179 1.09323i
\(557\) 6967.85 12068.7i 0.530049 0.918071i −0.469337 0.883019i \(-0.655507\pi\)
0.999385 0.0350521i \(-0.0111597\pi\)
\(558\) 787.132 + 1363.35i 0.0597168 + 0.103432i
\(559\) −10120.9 −0.765773
\(560\) 0 0
\(561\) −7383.34 −0.555659
\(562\) −23.4276 40.5778i −0.00175843 0.00304568i
\(563\) −11131.8 + 19280.9i −0.833304 + 1.44332i 0.0621002 + 0.998070i \(0.480220\pi\)
−0.895404 + 0.445255i \(0.853113\pi\)
\(564\) 4947.41 8569.17i 0.369368 0.639764i
\(565\) 4947.13 + 8568.68i 0.368367 + 0.638030i
\(566\) 1123.65 0.0834462
\(567\) 0 0
\(568\) −7832.81 −0.578622
\(569\) −4762.83 8249.47i −0.350911 0.607795i 0.635498 0.772102i \(-0.280795\pi\)
−0.986409 + 0.164307i \(0.947461\pi\)
\(570\) −207.598 + 359.570i −0.0152549 + 0.0264223i
\(571\) −3835.00 + 6642.41i −0.281068 + 0.486823i −0.971648 0.236432i \(-0.924022\pi\)
0.690580 + 0.723256i \(0.257355\pi\)
\(572\) −10351.7 17929.8i −0.756693 1.31063i
\(573\) −20497.3 −1.49439
\(574\) 0 0
\(575\) 1328.20 0.0963304
\(576\) −1701.10 2946.39i −0.123054 0.213136i
\(577\) 1953.57 3383.69i 0.140950 0.244133i −0.786904 0.617075i \(-0.788318\pi\)
0.927855 + 0.372942i \(0.121651\pi\)
\(578\) 1143.07 1979.85i 0.0822582 0.142475i
\(579\) −7429.04 12867.5i −0.533230 0.923582i
\(580\) −7419.95 −0.531201
\(581\) 0 0
\(582\) 3811.38 0.271455
\(583\) −11741.0 20336.0i −0.834067 1.44465i
\(584\) −4167.64 + 7218.57i −0.295305 + 0.511484i
\(585\) −1354.83 + 2346.63i −0.0957526 + 0.165848i
\(586\) 1608.17 + 2785.43i 0.113367 + 0.196357i
\(587\) 19891.6 1.39866 0.699331 0.714798i \(-0.253481\pi\)
0.699331 + 0.714798i \(0.253481\pi\)
\(588\) 0 0
\(589\) 7933.61 0.555007
\(590\) 159.172 + 275.694i 0.0111068 + 0.0192375i
\(591\) −1360.96 + 2357.25i −0.0947248 + 0.164068i
\(592\) −9387.89 + 16260.3i −0.651757 + 1.12888i
\(593\) 2390.18 + 4139.91i 0.165519 + 0.286688i 0.936840 0.349759i \(-0.113737\pi\)
−0.771320 + 0.636447i \(0.780403\pi\)
\(594\) −4695.48 −0.324340
\(595\) 0 0
\(596\) −5082.74 −0.349324
\(597\) 8489.08 + 14703.5i 0.581968 + 1.00800i
\(598\) −979.959 + 1697.34i −0.0670126 + 0.116069i
\(599\) −5542.80 + 9600.42i −0.378085 + 0.654862i −0.990784 0.135454i \(-0.956751\pi\)
0.612699 + 0.790317i \(0.290084\pi\)
\(600\) −525.791 910.697i −0.0357756 0.0619651i
\(601\) 1573.44 0.106792 0.0533958 0.998573i \(-0.482995\pi\)
0.0533958 + 0.998573i \(0.482995\pi\)
\(602\) 0 0
\(603\) −6199.76 −0.418696
\(604\) 12699.5 + 21996.2i 0.855524 + 1.48181i
\(605\) 2361.04 4089.44i 0.158661 0.274809i
\(606\) 2461.26 4263.03i 0.164987 0.285765i
\(607\) 4271.36 + 7398.22i 0.285617 + 0.494702i 0.972759 0.231821i \(-0.0744683\pi\)
−0.687142 + 0.726523i \(0.741135\pi\)
\(608\) 3547.65 0.236639
\(609\) 0 0
\(610\) −264.848 −0.0175793
\(611\) 8915.70 + 15442.4i 0.590328 + 1.02248i
\(612\) 1327.64 2299.54i 0.0876904 0.151884i
\(613\) −7534.08 + 13049.4i −0.496409 + 0.859805i −0.999991 0.00414209i \(-0.998682\pi\)
0.503583 + 0.863947i \(0.332015\pi\)
\(614\) −536.545 929.323i −0.0352658 0.0610822i
\(615\) 5590.52 0.366555
\(616\) 0 0
\(617\) 2524.58 0.164725 0.0823627 0.996602i \(-0.473753\pi\)
0.0823627 + 0.996602i \(0.473753\pi\)
\(618\) 550.304 + 953.155i 0.0358196 + 0.0620413i
\(619\) −10619.5 + 18393.4i −0.689551 + 1.19434i 0.282433 + 0.959287i \(0.408859\pi\)
−0.971983 + 0.235050i \(0.924475\pi\)
\(620\) −4889.50 + 8468.85i −0.316721 + 0.548576i
\(621\) −4056.22 7025.58i −0.262110 0.453988i
\(622\) 351.735 0.0226741
\(623\) 0 0
\(624\) −12985.9 −0.833095
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −68.8369 + 119.229i −0.00439501 + 0.00761238i
\(627\) −3072.28 + 5321.34i −0.195686 + 0.338937i
\(628\) 9133.21 + 15819.2i 0.580342 + 1.00518i
\(629\) −12806.8 −0.811827
\(630\) 0 0
\(631\) −8885.83 −0.560601 −0.280300 0.959912i \(-0.590434\pi\)
−0.280300 + 0.959912i \(0.590434\pi\)
\(632\) −3865.01 6694.39i −0.243262 0.421343i
\(633\) −3286.00 + 5691.51i −0.206330 + 0.357373i
\(634\) 865.095 1498.39i 0.0541914 0.0938622i
\(635\) 3480.96 + 6029.20i 0.217540 + 0.376790i
\(636\) −15632.1 −0.974609
\(637\) 0 0
\(638\) 6016.74 0.373362
\(639\) 3691.71 + 6394.23i 0.228547 + 0.395856i
\(640\) −2885.21 + 4997.32i −0.178200 + 0.308651i
\(641\) −1827.82 + 3165.87i −0.112628 + 0.195077i −0.916829 0.399280i \(-0.869260\pi\)
0.804201 + 0.594357i \(0.202593\pi\)
\(642\) −499.473 865.112i −0.0307050 0.0531827i
\(643\) −4221.22 −0.258894 −0.129447 0.991586i \(-0.541320\pi\)
−0.129447 + 0.991586i \(0.541320\pi\)
\(644\) 0 0
\(645\) −3702.43 −0.226020
\(646\) 366.602 + 634.974i 0.0223278 + 0.0386729i
\(647\) 51.8393 89.7884i 0.00314995 0.00545587i −0.864446 0.502725i \(-0.832331\pi\)
0.867596 + 0.497270i \(0.165664\pi\)
\(648\) −1927.04 + 3337.73i −0.116823 + 0.202343i
\(649\) 2355.62 + 4080.05i 0.142475 + 0.246773i
\(650\) 922.259 0.0556523
\(651\) 0 0
\(652\) 28904.5 1.73618
\(653\) −2238.05 3876.42i −0.134122 0.232307i 0.791140 0.611636i \(-0.209488\pi\)
−0.925262 + 0.379329i \(0.876155\pi\)
\(654\) 1316.56 2280.35i 0.0787181 0.136344i
\(655\) −4442.55 + 7694.71i −0.265015 + 0.459019i
\(656\) −7236.91 12534.7i −0.430722 0.746033i
\(657\) 7857.07 0.466566
\(658\) 0 0
\(659\) 12022.0 0.710641 0.355321 0.934745i \(-0.384372\pi\)
0.355321 + 0.934745i \(0.384372\pi\)
\(660\) −3786.89 6559.09i −0.223340 0.386837i
\(661\) 6725.51 11648.9i 0.395752 0.685462i −0.597445 0.801910i \(-0.703817\pi\)
0.993197 + 0.116448i \(0.0371507\pi\)
\(662\) 1633.38 2829.11i 0.0958962 0.166097i
\(663\) −4428.77 7670.85i −0.259426 0.449338i
\(664\) −6160.53 −0.360053
\(665\) 0 0
\(666\) −2114.87 −0.123047
\(667\) 5197.60 + 9002.51i 0.301727 + 0.522606i
\(668\) 4577.77 7928.93i 0.265149 0.459251i
\(669\) 9889.10 17128.4i 0.571502 0.989870i
\(670\) 1055.08 + 1827.45i 0.0608375 + 0.105374i
\(671\) −3919.53 −0.225502
\(672\) 0 0
\(673\) 9774.83 0.559869 0.279935 0.960019i \(-0.409687\pi\)
0.279935 + 0.960019i \(0.409687\pi\)
\(674\) 3014.76 + 5221.72i 0.172291 + 0.298417i
\(675\) −1908.70 + 3305.96i −0.108838 + 0.188513i
\(676\) 4087.13 7079.13i 0.232541 0.402772i
\(677\) 11928.7 + 20661.1i 0.677190 + 1.17293i 0.975824 + 0.218560i \(0.0701358\pi\)
−0.298634 + 0.954368i \(0.596531\pi\)
\(678\) −5341.04 −0.302539
\(679\) 0 0
\(680\) −1857.02 −0.104726
\(681\) 7714.36 + 13361.7i 0.434089 + 0.751865i
\(682\) 3964.83 6867.28i 0.222612 0.385574i
\(683\) −5959.68 + 10322.5i −0.333881 + 0.578299i −0.983269 0.182158i \(-0.941692\pi\)
0.649388 + 0.760457i \(0.275025\pi\)
\(684\) −1104.88 1913.72i −0.0617636 0.106978i
\(685\) 9902.40 0.552338
\(686\) 0 0
\(687\) −14054.4 −0.780508
\(688\) 4792.79 + 8301.36i 0.265587 + 0.460009i
\(689\) 14085.2 24396.3i 0.778816 1.34895i
\(690\) −358.490 + 620.924i −0.0197790 + 0.0342582i
\(691\) −4101.79 7104.51i −0.225817 0.391126i 0.730747 0.682648i \(-0.239172\pi\)
−0.956564 + 0.291522i \(0.905838\pi\)
\(692\) −24598.4 −1.35129
\(693\) 0 0
\(694\) 1514.50 0.0828380
\(695\) 5455.21 + 9448.71i 0.297738 + 0.515698i
\(696\) 4115.11 7127.58i 0.224113 0.388176i
\(697\) 4936.22 8549.79i 0.268254 0.464629i
\(698\) 3375.56 + 5846.64i 0.183047 + 0.317047i
\(699\) −9688.49 −0.524252
\(700\) 0 0
\(701\) 449.084 0.0241964 0.0120982 0.999927i \(-0.496149\pi\)
0.0120982 + 0.999927i \(0.496149\pi\)
\(702\) −2816.50 4878.32i −0.151427 0.262280i
\(703\) −5329.01 + 9230.12i −0.285900 + 0.495193i
\(704\) −8568.51 + 14841.1i −0.458719 + 0.794524i
\(705\) 3261.56 + 5649.18i 0.174237 + 0.301788i
\(706\) −4625.11 −0.246556
\(707\) 0 0
\(708\) 3136.30 0.166482
\(709\) −948.819 1643.40i −0.0502590 0.0870512i 0.839801 0.542894i \(-0.182671\pi\)
−0.890060 + 0.455843i \(0.849338\pi\)
\(710\) 1256.51 2176.34i 0.0664170 0.115038i
\(711\) −3643.27 + 6310.32i −0.192170 + 0.332849i
\(712\) −2298.96 3981.92i −0.121007 0.209591i
\(713\) 13700.2 0.719601
\(714\) 0 0
\(715\) 13648.7 0.713891
\(716\) 3260.27 + 5646.96i 0.170171 + 0.294744i
\(717\) 1970.30 3412.66i 0.102625 0.177752i
\(718\) 2428.43 4206.16i 0.126223 0.218625i
\(719\) 3247.35 + 5624.58i 0.168436 + 0.291740i 0.937870 0.346986i \(-0.112795\pi\)
−0.769434 + 0.638726i \(0.779462\pi\)
\(720\) 2566.35 0.132836
\(721\) 0 0
\(722\) −3811.45 −0.196465
\(723\) 11803.3 + 20443.9i 0.607150 + 1.05162i
\(724\) −1101.65 + 1908.12i −0.0565506 + 0.0979485i
\(725\) 2445.78 4236.22i 0.125288 0.217006i
\(726\) 1274.52 + 2207.53i 0.0651540 + 0.112850i
\(727\) 18311.2 0.934148 0.467074 0.884218i \(-0.345308\pi\)
0.467074 + 0.884218i \(0.345308\pi\)
\(728\) 0 0
\(729\) 20894.5 1.06155
\(730\) −1337.12 2315.96i −0.0677931 0.117421i
\(731\) −3269.11 + 5662.27i −0.165407 + 0.286493i
\(732\) −1304.63 + 2259.68i −0.0658749 + 0.114099i
\(733\) 10616.6 + 18388.5i 0.534972 + 0.926598i 0.999165 + 0.0408640i \(0.0130111\pi\)
−0.464193 + 0.885734i \(0.653656\pi\)
\(734\) 3515.30 0.176774
\(735\) 0 0
\(736\) 6126.27 0.306817
\(737\) 15614.3 + 27044.7i 0.780406 + 1.35170i
\(738\) 815.152 1411.88i 0.0406587 0.0704230i
\(739\) 11011.8 19072.9i 0.548138 0.949404i −0.450264 0.892896i \(-0.648670\pi\)
0.998402 0.0565080i \(-0.0179966\pi\)
\(740\) −6568.55 11377.1i −0.326304 0.565175i
\(741\) −7371.40 −0.365446
\(742\) 0 0
\(743\) 9436.77 0.465951 0.232975 0.972483i \(-0.425154\pi\)
0.232975 + 0.972483i \(0.425154\pi\)
\(744\) −5423.44 9393.67i −0.267248 0.462888i
\(745\) 1675.38 2901.85i 0.0823911 0.142706i
\(746\) −2653.14 + 4595.38i −0.130212 + 0.225535i
\(747\) 2903.54 + 5029.08i 0.142216 + 0.246325i
\(748\) −13374.8 −0.653783
\(749\) 0 0
\(750\) 337.383 0.0164260
\(751\) 19580.9 + 33915.1i 0.951421 + 1.64791i 0.742354 + 0.670008i \(0.233709\pi\)
0.209067 + 0.977901i \(0.432957\pi\)
\(752\) 8444.16 14625.7i 0.409477 0.709235i
\(753\) 765.826 1326.45i 0.0370627 0.0641946i
\(754\) 3609.03 + 6251.03i 0.174315 + 0.301922i
\(755\) −16744.2 −0.807132
\(756\) 0 0
\(757\) 20340.6 0.976607 0.488303 0.872674i \(-0.337616\pi\)
0.488303 + 0.872674i \(0.337616\pi\)
\(758\) −538.301 932.365i −0.0257942 0.0446768i
\(759\) −5305.36 + 9189.16i −0.253719 + 0.439454i
\(760\) −772.722 + 1338.39i −0.0368810 + 0.0638798i
\(761\) 1653.95 + 2864.72i 0.0787852 + 0.136460i 0.902726 0.430216i \(-0.141563\pi\)
−0.823941 + 0.566676i \(0.808229\pi\)
\(762\) −3758.13 −0.178665
\(763\) 0 0
\(764\) −37130.4 −1.75829
\(765\) 875.239 + 1515.96i 0.0413651 + 0.0716465i
\(766\) −1037.93 + 1797.74i −0.0489580 + 0.0847978i
\(767\) −2825.95 + 4894.69i −0.133037 + 0.230427i
\(768\) 4459.19 + 7723.54i 0.209514 + 0.362889i
\(769\) −17234.0 −0.808159 −0.404079 0.914724i \(-0.632408\pi\)
−0.404079 + 0.914724i \(0.632408\pi\)
\(770\) 0 0
\(771\) 26278.7 1.22750
\(772\) −13457.5 23309.1i −0.627393 1.08668i
\(773\) −4363.17 + 7557.23i −0.203017 + 0.351636i −0.949499 0.313770i \(-0.898408\pi\)
0.746482 + 0.665406i \(0.231741\pi\)
\(774\) −539.851 + 935.049i −0.0250705 + 0.0434233i
\(775\) −3223.38 5583.05i −0.149403 0.258773i
\(776\) 14186.7 0.656281
\(777\) 0 0
\(778\) 2270.60 0.104634
\(779\) −4108.01 7115.29i −0.188941 0.327255i
\(780\) 4543.00 7868.72i 0.208546 0.361212i
\(781\) 18595.3 32208.1i 0.851977 1.47567i
\(782\) 633.068 + 1096.51i 0.0289494 + 0.0501419i
\(783\) −29876.8 −1.36362
\(784\) 0 0
\(785\) −12042.0 −0.547515
\(786\) −2398.14 4153.70i −0.108828 0.188496i
\(787\) −5321.03 + 9216.30i −0.241009 + 0.417440i −0.961002 0.276541i \(-0.910812\pi\)
0.719993 + 0.693982i \(0.244145\pi\)
\(788\) −2465.35 + 4270.11i −0.111452 + 0.193041i
\(789\) −8846.81 15323.1i −0.399182 0.691404i
\(790\) 2480.05 0.111691
\(791\) 0 0
\(792\) −4538.35 −0.203615
\(793\) −2351.06 4072.16i −0.105282 0.182354i
\(794\) 1758.33 3045.51i 0.0785904 0.136123i
\(795\) 5152.68 8924.71i 0.229870 0.398147i
\(796\) 15377.8 + 26635.1i 0.684737 + 1.18600i
\(797\) −29234.1 −1.29928 −0.649640 0.760242i \(-0.725080\pi\)
−0.649640 + 0.760242i \(0.725080\pi\)
\(798\) 0 0
\(799\) 11519.3 0.510044
\(800\) −1441.39 2496.56i −0.0637010 0.110333i
\(801\) −2167.07 + 3753.47i −0.0955925 + 0.165571i
\(802\) 374.475 648.610i 0.0164878 0.0285576i
\(803\) −19788.2 34274.2i −0.869629 1.50624i
\(804\) 20789.0 0.911906
\(805\) 0 0
\(806\) 9512.93 0.415730
\(807\) 2054.90 + 3559.19i 0.0896355 + 0.155253i
\(808\) 9161.33 15867.9i 0.398879 0.690879i
\(809\) −18105.6 + 31359.8i −0.786846 + 1.36286i 0.141045 + 0.990003i \(0.454954\pi\)
−0.927890 + 0.372853i \(0.878379\pi\)
\(810\) −618.258 1070.85i −0.0268190 0.0464518i
\(811\) 27995.2 1.21214 0.606069 0.795412i \(-0.292746\pi\)
0.606069 + 0.795412i \(0.292746\pi\)
\(812\) 0 0
\(813\) −16263.6 −0.701585
\(814\) 5326.35 + 9225.51i 0.229347 + 0.397241i
\(815\) −9527.58 + 16502.3i −0.409493 + 0.709262i
\(816\) −4194.53 + 7265.15i −0.179949 + 0.311680i
\(817\) 2720.62 + 4712.25i 0.116502 + 0.201788i
\(818\) −4769.52 −0.203866
\(819\) 0 0
\(820\) 10127.1 0.431285
\(821\) −22402.9 38802.9i −0.952333 1.64949i −0.740356 0.672215i \(-0.765343\pi\)
−0.211977 0.977275i \(-0.567990\pi\)
\(822\) −2672.72 + 4629.28i −0.113408 + 0.196429i
\(823\) 7925.47 13727.3i 0.335680 0.581415i −0.647935 0.761695i \(-0.724367\pi\)
0.983615 + 0.180281i \(0.0577007\pi\)
\(824\) 2048.35 + 3547.85i 0.0865991 + 0.149994i
\(825\) 4992.99 0.210707
\(826\) 0 0
\(827\) −45013.9 −1.89273 −0.946363 0.323104i \(-0.895274\pi\)
−0.946363 + 0.323104i \(0.895274\pi\)
\(828\) −1907.97 3304.70i −0.0800804 0.138703i
\(829\) 2827.91 4898.09i 0.118477 0.205208i −0.800687 0.599083i \(-0.795532\pi\)
0.919164 + 0.393874i \(0.128865\pi\)
\(830\) 988.251 1711.70i 0.0413285 0.0715831i
\(831\) 7567.63 + 13107.5i 0.315906 + 0.547166i
\(832\) −20558.7 −0.856664
\(833\) 0 0
\(834\) −5889.58 −0.244532
\(835\) 3017.88 + 5227.11i 0.125075 + 0.216637i
\(836\) −5565.36 + 9639.49i −0.230242 + 0.398790i
\(837\) −19687.8 + 34100.3i −0.813036 + 1.40822i
\(838\) −687.987 1191.63i −0.0283605 0.0491219i
\(839\) 22037.0 0.906797 0.453398 0.891308i \(-0.350211\pi\)
0.453398 + 0.891308i \(0.350211\pi\)
\(840\) 0 0
\(841\) 13894.9 0.569719
\(842\) 1257.82 + 2178.62i 0.0514816 + 0.0891687i
\(843\) 152.158 263.546i 0.00621662 0.0107675i
\(844\) −5952.51 + 10310.1i −0.242765 + 0.420482i
\(845\) 2694.42 + 4666.88i 0.109694 + 0.189995i
\(846\) 1902.27 0.0773065
\(847\) 0 0
\(848\) −26680.5 −1.08044
\(849\) 3648.95 + 6320.17i 0.147505 + 0.255486i
\(850\) 297.896 515.972i 0.0120209 0.0208208i
\(851\) −9202.42 + 15939.1i −0.370687 + 0.642049i
\(852\) −12379.0 21441.1i −0.497768 0.862160i
\(853\) 44486.7 1.78569 0.892846 0.450362i \(-0.148705\pi\)
0.892846 + 0.450362i \(0.148705\pi\)
\(854\) 0 0
\(855\) 1456.78 0.0582699
\(856\) −1859.14 3220.13i −0.0742339 0.128577i
\(857\) −19279.8 + 33393.6i −0.768478 + 1.33104i 0.169910 + 0.985460i \(0.445652\pi\)
−0.938388 + 0.345583i \(0.887681\pi\)
\(858\) −3683.86 + 6380.64i −0.146579 + 0.253883i
\(859\) 4213.01 + 7297.14i 0.167341 + 0.289843i 0.937484 0.348028i \(-0.113149\pi\)
−0.770143 + 0.637871i \(0.779815\pi\)
\(860\) −6706.88 −0.265933
\(861\) 0 0
\(862\) −2332.42 −0.0921608
\(863\) 10027.2 + 17367.6i 0.395514 + 0.685051i 0.993167 0.116704i \(-0.0372330\pi\)
−0.597652 + 0.801755i \(0.703900\pi\)
\(864\) −8803.75 + 15248.5i −0.346655 + 0.600423i
\(865\) 8108.20 14043.8i 0.318713 0.552028i
\(866\) −1360.97 2357.27i −0.0534038 0.0924981i
\(867\) 14848.0 0.581621
\(868\) 0 0
\(869\) 36702.6 1.43274
\(870\) 1320.26 + 2286.76i 0.0514496 + 0.0891133i
\(871\) −18731.9 + 32444.6i −0.728709 + 1.26216i
\(872\) 4900.52 8487.95i 0.190313 0.329631i
\(873\) −6686.41 11581.2i −0.259222 0.448985i
\(874\) 1053.70 0.0407803
\(875\) 0 0
\(876\) −26346.3 −1.01616
\(877\) −23541.1 40774.3i −0.906414 1.56995i −0.819008 0.573782i \(-0.805476\pi\)
−0.0874057 0.996173i \(-0.527858\pi\)
\(878\) −4357.16 + 7546.83i −0.167480 + 0.290083i
\(879\) −10444.8 + 18090.9i −0.400789 + 0.694186i
\(880\) −6463.41 11195.0i −0.247593 0.428843i
\(881\) 9467.24 0.362042 0.181021 0.983479i \(-0.442060\pi\)
0.181021 + 0.983479i \(0.442060\pi\)
\(882\) 0 0
\(883\) −3049.49 −0.116221 −0.0581106 0.998310i \(-0.518508\pi\)
−0.0581106 + 0.998310i \(0.518508\pi\)
\(884\) −8022.62 13895.6i −0.305237 0.528686i
\(885\) −1033.79 + 1790.59i −0.0392663 + 0.0680112i
\(886\) −5347.73 + 9262.54i −0.202777 + 0.351220i
\(887\) −9734.29 16860.3i −0.368484 0.638233i 0.620845 0.783934i \(-0.286790\pi\)
−0.989329 + 0.145700i \(0.953456\pi\)
\(888\) 14571.7 0.550669
\(889\) 0 0
\(890\) 1475.17 0.0555592
\(891\) −9149.71 15847.8i −0.344026 0.595870i
\(892\) 17913.9 31027.8i 0.672423 1.16467i
\(893\) 4793.30 8302.25i 0.179621 0.311113i
\(894\) 904.393 + 1566.45i 0.0338338 + 0.0586019i
\(895\) −4298.64 −0.160545
\(896\) 0 0
\(897\) −12729.3 −0.473823
\(898\) −2692.80 4664.06i −0.100067 0.173321i
\(899\) 25227.8 43695.8i 0.935922 1.62106i
\(900\) −897.815 + 1555.06i −0.0332524 + 0.0575948i
\(901\) −9099.26 15760.4i −0.336449 0.582746i
\(902\) −8211.92 −0.303134
\(903\) 0 0
\(904\) −19880.5 −0.731432
\(905\) −726.260 1257.92i −0.0266759 0.0462040i
\(906\) 4519.36 7827.77i 0.165724 0.287042i
\(907\) 16007.1 27725.1i 0.586006 1.01499i −0.408743 0.912649i \(-0.634033\pi\)
0.994749 0.102343i \(-0.0326339\pi\)
\(908\) 13974.4 + 24204.3i 0.510745 + 0.884636i
\(909\) −17271.4 −0.630206
\(910\) 0 0
\(911\) 20921.1 0.760866 0.380433 0.924809i \(-0.375775\pi\)
0.380433 + 0.924809i \(0.375775\pi\)
\(912\) 3490.77 + 6046.19i 0.126744 + 0.219528i
\(913\) 14625.3 25331.8i 0.530150 0.918247i
\(914\) 412.683 714.788i 0.0149347 0.0258677i
\(915\) −860.069 1489.68i −0.0310743 0.0538223i
\(916\) −25459.2 −0.918337
\(917\) 0 0
\(918\) −3639.00 −0.130833
\(919\) −21733.7 37643.9i −0.780118 1.35120i −0.931872 0.362786i \(-0.881826\pi\)
0.151754 0.988418i \(-0.451508\pi\)
\(920\) −1334.38 + 2311.21i −0.0478186 + 0.0828242i
\(921\) 3484.77 6035.79i 0.124676 0.215946i
\(922\) −2251.99 3900.55i −0.0804395 0.139325i
\(923\) 44616.4 1.59108
\(924\) 0 0
\(925\) 8660.58 0.307847
\(926\) 1800.93 + 3119.30i 0.0639116 + 0.110698i
\(927\) 1930.83 3344.30i 0.0684108 0.118491i
\(928\) 11281.0 19539.3i 0.399050 0.691174i
\(929\) −9271.05 16057.9i −0.327420 0.567108i 0.654579 0.755993i \(-0.272846\pi\)
−0.981999 + 0.188885i \(0.939513\pi\)
\(930\) 3480.04 0.122704
\(931\) 0 0
\(932\) −17550.5 −0.616830
\(933\) 1142.23 + 1978.40i 0.0400803 + 0.0694210i
\(934\) −3201.91 + 5545.87i −0.112173 + 0.194290i
\(935\) 4408.62 7635.96i 0.154200 0.267083i
\(936\) −2722.25 4715.07i −0.0950635 0.164655i
\(937\) −13842.5 −0.482619 −0.241309 0.970448i \(-0.577577\pi\)
−0.241309 + 0.970448i \(0.577577\pi\)
\(938\) 0 0
\(939\) −894.167 −0.0310757
\(940\) 5908.24 + 10233.4i 0.205006 + 0.355081i
\(941\) −26696.6 + 46239.8i −0.924850 + 1.60189i −0.133047 + 0.991110i \(0.542476\pi\)
−0.791803 + 0.610777i \(0.790857\pi\)
\(942\) 3250.22 5629.55i 0.112418 0.194714i
\(943\) −7093.93 12287.0i −0.244974 0.424307i
\(944\) 5352.98 0.184560
\(945\) 0 0
\(946\) 5438.52 0.186915
\(947\) −11172.1 19350.7i −0.383364 0.664005i 0.608177 0.793801i \(-0.291901\pi\)
−0.991541 + 0.129796i \(0.958568\pi\)
\(948\) 12216.6 21159.7i 0.418540 0.724933i
\(949\) 23739.3 41117.6i 0.812022 1.40646i
\(950\) −247.915 429.401i −0.00846676 0.0146649i
\(951\) 11237.3 0.383169
\(952\) 0 0
\(953\) −8902.63 −0.302607 −0.151304 0.988487i \(-0.548347\pi\)
−0.151304 + 0.988487i \(0.548347\pi\)
\(954\) −1502.62 2602.62i −0.0509950 0.0883259i
\(955\) 12239.0 21198.6i 0.414708 0.718295i
\(956\) 3569.15 6181.96i 0.120748 0.209141i
\(957\) 19538.8 + 33842.2i 0.659979 + 1.14312i
\(958\) −3267.48 −0.110196
\(959\) 0 0
\(960\) −7520.82 −0.252847
\(961\) −18353.0 31788.4i −0.616059 1.06705i
\(962\) −6389.84 + 11067.5i −0.214155 + 0.370927i
\(963\) −1752.48 + 3035.39i −0.0586427 + 0.101572i
\(964\) 21381.4 + 37033.7i 0.714366 + 1.23732i
\(965\) 17743.6 0.591905
\(966\) 0 0
\(967\) −2225.57 −0.0740119 −0.0370059 0.999315i \(-0.511782\pi\)
−0.0370059 + 0.999315i \(0.511782\pi\)
\(968\) 4744.02 + 8216.89i 0.157519 + 0.272831i
\(969\) −2381.02 + 4124.04i −0.0789363 + 0.136722i
\(970\) −2275.79 + 3941.78i −0.0753311 + 0.130477i
\(971\) −5662.41 9807.59i −0.187143 0.324141i 0.757154 0.653237i \(-0.226589\pi\)
−0.944296 + 0.329096i \(0.893256\pi\)
\(972\) 19086.9 0.629849
\(973\) 0 0
\(974\) 170.415 0.00560621
\(975\) 2994.96 + 5187.41i 0.0983747 + 0.170390i
\(976\) −2226.72 + 3856.78i −0.0730281 + 0.126488i
\(977\) 28847.9 49966.1i 0.944654 1.63619i 0.188213 0.982128i \(-0.439731\pi\)
0.756442 0.654061i \(-0.226936\pi\)
\(978\) −5143.10 8908.11i −0.168158 0.291258i
\(979\) 21831.3 0.712697
\(980\) 0 0
\(981\) −9238.73 −0.300683
\(982\) 2404.36 + 4164.48i 0.0781328 + 0.135330i
\(983\) 29828.6 51664.7i 0.967839 1.67635i 0.266054 0.963958i \(-0.414280\pi\)
0.701786 0.712388i \(-0.252386\pi\)
\(984\) −5616.49 + 9728.05i −0.181959 + 0.315162i
\(985\) −1625.27 2815.05i −0.0525740 0.0910608i
\(986\) 4662.98 0.150608
\(987\) 0 0
\(988\) −13353.1 −0.429980
\(989\) 4698.10 + 8137.35i 0.151053 + 0.261631i
\(990\) 728.026 1260.98i 0.0233719 0.0404813i
\(991\) −1445.30 + 2503.33i −0.0463284 + 0.0802431i −0.888260 0.459342i \(-0.848085\pi\)
0.841931 + 0.539585i \(0.181419\pi\)
\(992\) −14867.6 25751.5i −0.475855 0.824205i
\(993\) 21217.1 0.678050
\(994\) 0 0
\(995\) −20275.5 −0.646005
\(996\) −9736.15 16863.5i −0.309741 0.536487i
\(997\) −5309.79 + 9196.83i −0.168669 + 0.292143i −0.937952 0.346765i \(-0.887280\pi\)
0.769283 + 0.638908i \(0.220613\pi\)
\(998\) −2322.88 + 4023.35i −0.0736769 + 0.127612i
\(999\) −26448.7 45810.4i −0.837636 1.45083i
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.p.116.3 12
7.2 even 3 inner 245.4.e.p.226.3 12
7.3 odd 6 245.4.a.o.1.4 6
7.4 even 3 245.4.a.p.1.4 yes 6
7.5 odd 6 245.4.e.q.226.3 12
7.6 odd 2 245.4.e.q.116.3 12
21.11 odd 6 2205.4.a.ca.1.3 6
21.17 even 6 2205.4.a.bz.1.3 6
35.4 even 6 1225.4.a.bi.1.3 6
35.24 odd 6 1225.4.a.bj.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.4.a.o.1.4 6 7.3 odd 6
245.4.a.p.1.4 yes 6 7.4 even 3
245.4.e.p.116.3 12 1.1 even 1 trivial
245.4.e.p.226.3 12 7.2 even 3 inner
245.4.e.q.116.3 12 7.6 odd 2
245.4.e.q.226.3 12 7.5 odd 6
1225.4.a.bi.1.3 6 35.4 even 6
1225.4.a.bj.1.3 6 35.24 odd 6
2205.4.a.bz.1.3 6 21.17 even 6
2205.4.a.ca.1.3 6 21.11 odd 6