Properties

Label 105.4.i.d.46.1
Level $105$
Weight $4$
Character 105.46
Analytic conductor $6.195$
Analytic rank $0$
Dimension $10$
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] = [105,4,Mod(16,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.16");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2 x^{9} + 34 x^{8} + 16 x^{7} + 791 x^{6} - 132 x^{5} + 4906 x^{4} - 1674 x^{3} + 25257 x^{2} - 12852 x + 7056 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 46.1
Root \(-2.05285 - 3.55565i\) of defining polynomial
Character \(\chi\) \(=\) 105.46
Dual form 105.4.i.d.16.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.55285 - 4.42167i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-9.03412 + 15.6476i) q^{4} +(-2.50000 - 4.33013i) q^{5} +15.3171 q^{6} +(-2.74187 + 18.3162i) q^{7} +51.4055 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-2.55285 - 4.42167i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-9.03412 + 15.6476i) q^{4} +(-2.50000 - 4.33013i) q^{5} +15.3171 q^{6} +(-2.74187 + 18.3162i) q^{7} +51.4055 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-12.7643 + 22.1084i) q^{10} +(20.3677 - 35.2779i) q^{11} +(-27.1024 - 46.9427i) q^{12} +70.9263 q^{13} +(87.9877 - 34.6349i) q^{14} +15.0000 q^{15} +(-58.9577 - 102.118i) q^{16} +(-11.3350 + 19.6329i) q^{17} +(-22.9757 + 39.7950i) q^{18} +(-38.8294 - 67.2545i) q^{19} +90.3412 q^{20} +(-43.4740 - 34.5978i) q^{21} -207.983 q^{22} +(45.0311 + 77.9962i) q^{23} +(-77.1083 + 133.555i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-181.064 - 313.613i) q^{26} +27.0000 q^{27} +(-261.833 - 208.374i) q^{28} +213.332 q^{29} +(-38.2928 - 66.3251i) q^{30} +(87.8644 - 152.186i) q^{31} +(-95.3990 + 165.236i) q^{32} +(61.1031 + 105.834i) q^{33} +115.747 q^{34} +(86.1660 - 33.9178i) q^{35} +162.614 q^{36} +(177.466 + 307.381i) q^{37} +(-198.251 + 343.382i) q^{38} +(-106.389 + 184.272i) q^{39} +(-128.514 - 222.592i) q^{40} +249.001 q^{41} +(-41.9975 + 280.551i) q^{42} +297.920 q^{43} +(368.009 + 637.410i) q^{44} +(-22.5000 + 38.9711i) q^{45} +(229.916 - 398.226i) q^{46} +(-84.3854 - 146.160i) q^{47} +353.746 q^{48} +(-327.964 - 100.441i) q^{49} +127.643 q^{50} +(-34.0051 - 58.8986i) q^{51} +(-640.757 + 1109.82i) q^{52} +(51.2366 - 88.7444i) q^{53} +(-68.9270 - 119.385i) q^{54} -203.677 q^{55} +(-140.947 + 941.552i) q^{56} +232.976 q^{57} +(-544.605 - 943.284i) q^{58} +(11.7399 - 20.3340i) q^{59} +(-135.512 + 234.713i) q^{60} +(437.314 + 757.450i) q^{61} -897.220 q^{62} +(155.099 - 61.0521i) q^{63} +30.8343 q^{64} +(-177.316 - 307.120i) q^{65} +(311.975 - 540.356i) q^{66} +(405.386 - 702.149i) q^{67} +(-204.804 - 354.731i) q^{68} -270.187 q^{69} +(-369.943 - 294.411i) q^{70} -632.487 q^{71} +(-231.325 - 400.666i) q^{72} +(-457.436 + 792.302i) q^{73} +(906.091 - 1569.40i) q^{74} +(-37.5000 - 64.9519i) q^{75} +1403.16 q^{76} +(590.311 + 469.786i) q^{77} +1086.39 q^{78} +(260.443 + 451.101i) q^{79} +(-294.789 + 510.589i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-635.664 - 1101.00i) q^{82} -1027.67 q^{83} +(934.121 - 367.701i) q^{84} +113.350 q^{85} +(-760.546 - 1317.30i) q^{86} +(-319.998 + 554.253i) q^{87} +(1047.01 - 1813.48i) q^{88} +(-501.875 - 869.273i) q^{89} +229.757 q^{90} +(-194.470 + 1299.10i) q^{91} -1627.27 q^{92} +(263.593 + 456.557i) q^{93} +(-430.847 + 746.249i) q^{94} +(-194.147 + 336.272i) q^{95} +(-286.197 - 495.708i) q^{96} -639.620 q^{97} +(393.128 + 1706.56i) q^{98} -366.619 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 3 q^{2} - 15 q^{3} - 25 q^{4} - 25 q^{5} + 18 q^{6} - 32 q^{7} + 42 q^{8} - 45 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 3 q^{2} - 15 q^{3} - 25 q^{4} - 25 q^{5} + 18 q^{6} - 32 q^{7} + 42 q^{8} - 45 q^{9} - 15 q^{10} - 43 q^{11} - 75 q^{12} + 246 q^{13} - 23 q^{14} + 150 q^{15} - 161 q^{16} - 124 q^{17} - 27 q^{18} - 37 q^{19} + 250 q^{20} + 3 q^{21} - 442 q^{22} - 77 q^{23} - 63 q^{24} - 125 q^{25} + 79 q^{26} + 270 q^{27} - 71 q^{28} + 720 q^{29} - 45 q^{30} - 314 q^{31} + 59 q^{32} - 129 q^{33} + 352 q^{34} + 155 q^{35} + 450 q^{36} - 225 q^{37} - 759 q^{38} - 369 q^{39} - 105 q^{40} + 682 q^{41} + 354 q^{42} + 64 q^{43} - 679 q^{44} - 225 q^{45} + 331 q^{46} - 25 q^{47} + 966 q^{48} + 710 q^{49} + 150 q^{50} - 372 q^{51} - 2299 q^{52} + 317 q^{53} - 81 q^{54} + 430 q^{55} + 1884 q^{56} + 222 q^{57} - 8 q^{58} - 676 q^{59} - 375 q^{60} + 188 q^{61} - 696 q^{62} + 279 q^{63} - 2206 q^{64} - 615 q^{65} + 663 q^{66} + 1776 q^{67} - 1280 q^{68} + 462 q^{69} - 475 q^{70} - 12 q^{71} - 189 q^{72} - 2006 q^{73} + 2729 q^{74} - 375 q^{75} + 2834 q^{76} + 3731 q^{77} - 474 q^{78} - 200 q^{79} - 805 q^{80} - 405 q^{81} + 539 q^{82} - 664 q^{83} + 1821 q^{84} + 1240 q^{85} - 4262 q^{86} - 1080 q^{87} + 4529 q^{88} - 894 q^{89} + 270 q^{90} + 2016 q^{91} - 7374 q^{92} - 942 q^{93} - 4233 q^{94} - 185 q^{95} + 177 q^{96} - 1152 q^{97} + 2539 q^{98} + 774 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55285 4.42167i −0.902570 1.56330i −0.824146 0.566377i \(-0.808345\pi\)
−0.0784237 0.996920i \(-0.524989\pi\)
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i
\(4\) −9.03412 + 15.6476i −1.12927 + 1.95594i
\(5\) −2.50000 4.33013i −0.223607 0.387298i
\(6\) 15.3171 1.04220
\(7\) −2.74187 + 18.3162i −0.148047 + 0.988980i
\(8\) 51.4055 2.27182
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) −12.7643 + 22.1084i −0.403642 + 0.699128i
\(11\) 20.3677 35.2779i 0.558281 0.966972i −0.439359 0.898312i \(-0.644794\pi\)
0.997640 0.0686601i \(-0.0218724\pi\)
\(12\) −27.1024 46.9427i −0.651982 1.12927i
\(13\) 70.9263 1.51319 0.756593 0.653887i \(-0.226863\pi\)
0.756593 + 0.653887i \(0.226863\pi\)
\(14\) 87.9877 34.6349i 1.67969 0.661183i
\(15\) 15.0000 0.258199
\(16\) −58.9577 102.118i −0.921215 1.59559i
\(17\) −11.3350 + 19.6329i −0.161715 + 0.280098i −0.935484 0.353370i \(-0.885036\pi\)
0.773769 + 0.633468i \(0.218369\pi\)
\(18\) −22.9757 + 39.7950i −0.300857 + 0.521099i
\(19\) −38.8294 67.2545i −0.468846 0.812065i 0.530520 0.847672i \(-0.321997\pi\)
−0.999366 + 0.0356075i \(0.988663\pi\)
\(20\) 90.3412 1.01005
\(21\) −43.4740 34.5978i −0.451753 0.359517i
\(22\) −207.983 −2.01555
\(23\) 45.0311 + 77.9962i 0.408245 + 0.707101i 0.994693 0.102886i \(-0.0328076\pi\)
−0.586448 + 0.809987i \(0.699474\pi\)
\(24\) −77.1083 + 133.555i −0.655819 + 1.13591i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −181.064 313.613i −1.36576 2.36556i
\(27\) 27.0000 0.192450
\(28\) −261.833 208.374i −1.76721 1.40639i
\(29\) 213.332 1.36603 0.683013 0.730406i \(-0.260669\pi\)
0.683013 + 0.730406i \(0.260669\pi\)
\(30\) −38.2928 66.3251i −0.233043 0.403642i
\(31\) 87.8644 152.186i 0.509062 0.881721i −0.490883 0.871225i \(-0.663326\pi\)
0.999945 0.0104956i \(-0.00334091\pi\)
\(32\) −95.3990 + 165.236i −0.527010 + 0.912808i
\(33\) 61.1031 + 105.834i 0.322324 + 0.558281i
\(34\) 115.747 0.583836
\(35\) 86.1660 33.9178i 0.416135 0.163804i
\(36\) 162.614 0.752844
\(37\) 177.466 + 307.381i 0.788521 + 1.36576i 0.926873 + 0.375376i \(0.122486\pi\)
−0.138351 + 0.990383i \(0.544180\pi\)
\(38\) −198.251 + 343.382i −0.846333 + 1.46589i
\(39\) −106.389 + 184.272i −0.436819 + 0.756593i
\(40\) −128.514 222.592i −0.507995 0.879874i
\(41\) 249.001 0.948475 0.474238 0.880397i \(-0.342724\pi\)
0.474238 + 0.880397i \(0.342724\pi\)
\(42\) −41.9975 + 280.551i −0.154294 + 1.03071i
\(43\) 297.920 1.05657 0.528284 0.849068i \(-0.322836\pi\)
0.528284 + 0.849068i \(0.322836\pi\)
\(44\) 368.009 + 637.410i 1.26090 + 2.18394i
\(45\) −22.5000 + 38.9711i −0.0745356 + 0.129099i
\(46\) 229.916 398.226i 0.736939 1.27642i
\(47\) −84.3854 146.160i −0.261891 0.453608i 0.704853 0.709353i \(-0.251013\pi\)
−0.966744 + 0.255745i \(0.917679\pi\)
\(48\) 353.746 1.06373
\(49\) −327.964 100.441i −0.956164 0.292831i
\(50\) 127.643 0.361028
\(51\) −34.0051 58.8986i −0.0933661 0.161715i
\(52\) −640.757 + 1109.82i −1.70879 + 2.95971i
\(53\) 51.2366 88.7444i 0.132790 0.230000i −0.791961 0.610572i \(-0.790940\pi\)
0.924751 + 0.380572i \(0.124273\pi\)
\(54\) −68.9270 119.385i −0.173700 0.300857i
\(55\) −203.677 −0.499342
\(56\) −140.947 + 941.552i −0.336336 + 2.24679i
\(57\) 232.976 0.541377
\(58\) −544.605 943.284i −1.23293 2.13551i
\(59\) 11.7399 20.3340i 0.0259051 0.0448689i −0.852782 0.522267i \(-0.825087\pi\)
0.878687 + 0.477398i \(0.158420\pi\)
\(60\) −135.512 + 234.713i −0.291575 + 0.505023i
\(61\) 437.314 + 757.450i 0.917907 + 1.58986i 0.802589 + 0.596533i \(0.203455\pi\)
0.115318 + 0.993329i \(0.463211\pi\)
\(62\) −897.220 −1.83786
\(63\) 155.099 61.0521i 0.310169 0.122093i
\(64\) 30.8343 0.0602232
\(65\) −177.316 307.120i −0.338358 0.586054i
\(66\) 311.975 540.356i 0.581840 1.00778i
\(67\) 405.386 702.149i 0.739190 1.28032i −0.213670 0.976906i \(-0.568542\pi\)
0.952860 0.303409i \(-0.0981249\pi\)
\(68\) −204.804 354.731i −0.365238 0.632610i
\(69\) −270.187 −0.471401
\(70\) −369.943 294.411i −0.631666 0.502697i
\(71\) −632.487 −1.05722 −0.528608 0.848866i \(-0.677286\pi\)
−0.528608 + 0.848866i \(0.677286\pi\)
\(72\) −231.325 400.666i −0.378637 0.655819i
\(73\) −457.436 + 792.302i −0.733409 + 1.27030i 0.222010 + 0.975045i \(0.428738\pi\)
−0.955418 + 0.295256i \(0.904595\pi\)
\(74\) 906.091 1569.40i 1.42339 2.46539i
\(75\) −37.5000 64.9519i −0.0577350 0.100000i
\(76\) 1403.16 2.11781
\(77\) 590.311 + 469.786i 0.873664 + 0.695286i
\(78\) 1086.39 1.57704
\(79\) 260.443 + 451.101i 0.370913 + 0.642441i 0.989706 0.143113i \(-0.0457114\pi\)
−0.618793 + 0.785554i \(0.712378\pi\)
\(80\) −294.789 + 510.589i −0.411980 + 0.713570i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) −635.664 1101.00i −0.856065 1.48275i
\(83\) −1027.67 −1.35905 −0.679527 0.733651i \(-0.737815\pi\)
−0.679527 + 0.733651i \(0.737815\pi\)
\(84\) 934.121 367.701i 1.21334 0.477613i
\(85\) 113.350 0.144642
\(86\) −760.546 1317.30i −0.953626 1.65173i
\(87\) −319.998 + 554.253i −0.394338 + 0.683013i
\(88\) 1047.01 1813.48i 1.26832 2.19679i
\(89\) −501.875 869.273i −0.597738 1.03531i −0.993154 0.116810i \(-0.962733\pi\)
0.395416 0.918502i \(-0.370600\pi\)
\(90\) 229.757 0.269094
\(91\) −194.470 + 1299.10i −0.224022 + 1.49651i
\(92\) −1627.27 −1.84407
\(93\) 263.593 + 456.557i 0.293907 + 0.509062i
\(94\) −430.847 + 746.249i −0.472750 + 0.818827i
\(95\) −194.147 + 336.272i −0.209674 + 0.363166i
\(96\) −286.197 495.708i −0.304269 0.527010i
\(97\) −639.620 −0.669522 −0.334761 0.942303i \(-0.608656\pi\)
−0.334761 + 0.942303i \(0.608656\pi\)
\(98\) 393.128 + 1706.56i 0.405224 + 1.75907i
\(99\) −366.619 −0.372188
\(100\) −225.853 391.189i −0.225853 0.391189i
\(101\) 316.935 548.947i 0.312239 0.540814i −0.666608 0.745409i \(-0.732254\pi\)
0.978847 + 0.204595i \(0.0655876\pi\)
\(102\) −173.620 + 300.719i −0.168539 + 0.291918i
\(103\) 193.789 + 335.653i 0.185385 + 0.321096i 0.943706 0.330785i \(-0.107314\pi\)
−0.758321 + 0.651881i \(0.773980\pi\)
\(104\) 3646.00 3.43769
\(105\) −41.1280 + 274.743i −0.0382255 + 0.255354i
\(106\) −523.198 −0.479410
\(107\) −69.3650 120.144i −0.0626707 0.108549i 0.832988 0.553292i \(-0.186628\pi\)
−0.895658 + 0.444743i \(0.853295\pi\)
\(108\) −243.921 + 422.484i −0.217327 + 0.376422i
\(109\) 856.485 1483.48i 0.752628 1.30359i −0.193918 0.981018i \(-0.562119\pi\)
0.946545 0.322571i \(-0.104547\pi\)
\(110\) 519.958 + 900.593i 0.450691 + 0.780620i
\(111\) −1064.80 −0.910506
\(112\) 2032.06 799.887i 1.71439 0.674841i
\(113\) 2083.35 1.73438 0.867192 0.497975i \(-0.165923\pi\)
0.867192 + 0.497975i \(0.165923\pi\)
\(114\) −594.754 1030.14i −0.488630 0.846333i
\(115\) 225.156 389.981i 0.182573 0.316225i
\(116\) −1927.27 + 3338.13i −1.54261 + 2.67187i
\(117\) −319.168 552.816i −0.252198 0.436819i
\(118\) −119.881 −0.0935246
\(119\) −328.520 261.445i −0.253070 0.201400i
\(120\) 771.083 0.586582
\(121\) −164.187 284.381i −0.123356 0.213660i
\(122\) 2232.80 3867.32i 1.65695 2.86992i
\(123\) −373.502 + 646.925i −0.273801 + 0.474238i
\(124\) 1587.56 + 2749.73i 1.14973 + 1.99139i
\(125\) 125.000 0.0894427
\(126\) −665.897 529.939i −0.470816 0.374688i
\(127\) 432.085 0.301900 0.150950 0.988541i \(-0.451767\pi\)
0.150950 + 0.988541i \(0.451767\pi\)
\(128\) 684.476 + 1185.55i 0.472654 + 0.818661i
\(129\) −446.880 + 774.019i −0.305005 + 0.528284i
\(130\) −905.322 + 1568.06i −0.610784 + 1.05791i
\(131\) 328.750 + 569.411i 0.219259 + 0.379769i 0.954582 0.297949i \(-0.0963025\pi\)
−0.735322 + 0.677718i \(0.762969\pi\)
\(132\) −2208.05 −1.45596
\(133\) 1338.31 526.803i 0.872527 0.343456i
\(134\) −4139.56 −2.66868
\(135\) −67.5000 116.913i −0.0430331 0.0745356i
\(136\) −582.683 + 1009.24i −0.367387 + 0.636334i
\(137\) −146.258 + 253.326i −0.0912090 + 0.157979i −0.908020 0.418927i \(-0.862406\pi\)
0.816811 + 0.576905i \(0.195740\pi\)
\(138\) 689.747 + 1194.68i 0.425472 + 0.736939i
\(139\) −1673.02 −1.02089 −0.510445 0.859910i \(-0.670519\pi\)
−0.510445 + 0.859910i \(0.670519\pi\)
\(140\) −247.703 + 1654.71i −0.149534 + 0.998915i
\(141\) 506.312 0.302406
\(142\) 1614.65 + 2796.65i 0.954212 + 1.65274i
\(143\) 1444.61 2502.13i 0.844783 1.46321i
\(144\) −530.620 + 919.060i −0.307072 + 0.531864i
\(145\) −533.330 923.755i −0.305453 0.529060i
\(146\) 4671.07 2.64781
\(147\) 752.900 701.415i 0.422436 0.393549i
\(148\) −6413.01 −3.56180
\(149\) −1260.50 2183.26i −0.693050 1.20040i −0.970834 0.239754i \(-0.922933\pi\)
0.277784 0.960644i \(-0.410400\pi\)
\(150\) −191.464 + 331.625i −0.104220 + 0.180514i
\(151\) −689.660 + 1194.53i −0.371680 + 0.643769i −0.989824 0.142296i \(-0.954552\pi\)
0.618144 + 0.786065i \(0.287885\pi\)
\(152\) −1996.04 3457.25i −1.06514 1.84487i
\(153\) 204.031 0.107810
\(154\) 570.262 3809.45i 0.298396 1.99334i
\(155\) −878.644 −0.455319
\(156\) −1922.27 3329.47i −0.986569 1.70879i
\(157\) −996.365 + 1725.76i −0.506488 + 0.877263i 0.493484 + 0.869755i \(0.335723\pi\)
−0.999972 + 0.00750789i \(0.997610\pi\)
\(158\) 1329.75 2303.19i 0.669550 1.15970i
\(159\) 153.710 + 266.233i 0.0766666 + 0.132790i
\(160\) 953.990 0.471372
\(161\) −1552.06 + 610.943i −0.759749 + 0.299062i
\(162\) 413.562 0.200571
\(163\) −951.472 1648.00i −0.457209 0.791909i 0.541603 0.840634i \(-0.317817\pi\)
−0.998812 + 0.0487253i \(0.984484\pi\)
\(164\) −2249.51 + 3896.26i −1.07108 + 1.85516i
\(165\) 305.516 529.169i 0.144148 0.249671i
\(166\) 2623.49 + 4544.02i 1.22664 + 2.12460i
\(167\) −378.184 −0.175238 −0.0876189 0.996154i \(-0.527926\pi\)
−0.0876189 + 0.996154i \(0.527926\pi\)
\(168\) −2234.80 1778.52i −1.02630 0.816760i
\(169\) 2833.54 1.28973
\(170\) −289.367 501.198i −0.130550 0.226119i
\(171\) −349.464 + 605.290i −0.156282 + 0.270688i
\(172\) −2691.45 + 4661.72i −1.19314 + 2.06659i
\(173\) 332.018 + 575.073i 0.145913 + 0.252728i 0.929713 0.368285i \(-0.120055\pi\)
−0.783800 + 0.621013i \(0.786722\pi\)
\(174\) 3267.63 1.42367
\(175\) −362.283 288.315i −0.156492 0.124540i
\(176\) −4803.34 −2.05719
\(177\) 35.2196 + 61.0021i 0.0149563 + 0.0259051i
\(178\) −2562.43 + 4438.26i −1.07900 + 1.86888i
\(179\) 167.500 290.118i 0.0699414 0.121142i −0.828934 0.559347i \(-0.811052\pi\)
0.898875 + 0.438204i \(0.144385\pi\)
\(180\) −406.535 704.140i −0.168341 0.291575i
\(181\) 1225.58 0.503298 0.251649 0.967819i \(-0.419027\pi\)
0.251649 + 0.967819i \(0.419027\pi\)
\(182\) 6240.64 2456.52i 2.54169 1.00049i
\(183\) −2623.88 −1.05991
\(184\) 2314.85 + 4009.43i 0.927461 + 1.60641i
\(185\) 887.332 1536.90i 0.352637 0.610786i
\(186\) 1345.83 2331.05i 0.530543 0.918928i
\(187\) 461.738 + 799.753i 0.180565 + 0.312747i
\(188\) 3049.39 1.18298
\(189\) −74.0304 + 494.537i −0.0284916 + 0.190329i
\(190\) 1982.51 0.756983
\(191\) 790.698 + 1369.53i 0.299544 + 0.518826i 0.976032 0.217628i \(-0.0698321\pi\)
−0.676488 + 0.736454i \(0.736499\pi\)
\(192\) −46.2515 + 80.1099i −0.0173850 + 0.0301116i
\(193\) 1947.31 3372.85i 0.726273 1.25794i −0.232175 0.972674i \(-0.574584\pi\)
0.958448 0.285268i \(-0.0920825\pi\)
\(194\) 1632.86 + 2828.19i 0.604290 + 1.04666i
\(195\) 1063.89 0.390703
\(196\) 4534.53 4224.45i 1.65252 1.53952i
\(197\) 993.858 0.359439 0.179719 0.983718i \(-0.442481\pi\)
0.179719 + 0.983718i \(0.442481\pi\)
\(198\) 935.924 + 1621.07i 0.335925 + 0.581840i
\(199\) 1539.94 2667.26i 0.548560 0.950134i −0.449813 0.893123i \(-0.648509\pi\)
0.998374 0.0570118i \(-0.0181572\pi\)
\(200\) −642.569 + 1112.96i −0.227182 + 0.393491i
\(201\) 1216.16 + 2106.45i 0.426772 + 0.739190i
\(202\) −3236.35 −1.12727
\(203\) −584.928 + 3907.43i −0.202236 + 1.35097i
\(204\) 1228.83 0.421740
\(205\) −622.503 1078.21i −0.212085 0.367343i
\(206\) 989.431 1713.74i 0.334645 0.579622i
\(207\) 405.280 701.966i 0.136082 0.235700i
\(208\) −4181.65 7242.83i −1.39397 2.41442i
\(209\) −3163.46 −1.04699
\(210\) 1319.82 519.523i 0.433695 0.170717i
\(211\) 2114.72 0.689968 0.344984 0.938609i \(-0.387884\pi\)
0.344984 + 0.938609i \(0.387884\pi\)
\(212\) 925.756 + 1603.46i 0.299911 + 0.519461i
\(213\) 948.730 1643.25i 0.305192 0.528608i
\(214\) −354.157 + 613.419i −0.113129 + 0.195946i
\(215\) −744.800 1290.03i −0.236256 0.409207i
\(216\) 1387.95 0.437213
\(217\) 2546.55 + 2026.61i 0.796640 + 0.633988i
\(218\) −8745.92 −2.71720
\(219\) −1372.31 2376.91i −0.423434 0.733409i
\(220\) 1840.04 3187.05i 0.563890 0.976686i
\(221\) −803.952 + 1392.49i −0.244704 + 0.423840i
\(222\) 2718.27 + 4708.19i 0.821795 + 1.42339i
\(223\) 2578.44 0.774282 0.387141 0.922021i \(-0.373463\pi\)
0.387141 + 0.922021i \(0.373463\pi\)
\(224\) −2764.92 2200.40i −0.824727 0.656341i
\(225\) 225.000 0.0666667
\(226\) −5318.49 9211.90i −1.56540 2.71136i
\(227\) −1462.96 + 2533.93i −0.427754 + 0.740892i −0.996673 0.0815014i \(-0.974028\pi\)
0.568919 + 0.822394i \(0.307362\pi\)
\(228\) −2104.74 + 3645.51i −0.611358 + 1.05890i
\(229\) 523.938 + 907.488i 0.151191 + 0.261871i 0.931666 0.363317i \(-0.118356\pi\)
−0.780474 + 0.625188i \(0.785022\pi\)
\(230\) −2299.16 −0.659139
\(231\) −2106.01 + 828.994i −0.599848 + 0.236120i
\(232\) 10966.4 3.10337
\(233\) 1934.99 + 3351.51i 0.544058 + 0.942337i 0.998666 + 0.0516447i \(0.0164463\pi\)
−0.454607 + 0.890692i \(0.650220\pi\)
\(234\) −1629.58 + 2822.51i −0.455252 + 0.788519i
\(235\) −421.927 + 730.799i −0.117121 + 0.202860i
\(236\) 212.119 + 367.400i 0.0585074 + 0.101338i
\(237\) −1562.66 −0.428294
\(238\) −317.362 + 2120.04i −0.0864350 + 0.577402i
\(239\) −6060.77 −1.64033 −0.820164 0.572128i \(-0.806118\pi\)
−0.820164 + 0.572128i \(0.806118\pi\)
\(240\) −884.366 1531.77i −0.237857 0.411980i
\(241\) 2092.06 3623.55i 0.559176 0.968521i −0.438390 0.898785i \(-0.644451\pi\)
0.997565 0.0697357i \(-0.0222156\pi\)
\(242\) −838.292 + 1451.97i −0.222676 + 0.385685i
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) −15803.0 −4.14624
\(245\) 384.989 + 1671.23i 0.100392 + 0.435800i
\(246\) 3813.98 0.988499
\(247\) −2754.02 4770.11i −0.709451 1.22880i
\(248\) 4516.72 7823.18i 1.15650 2.00311i
\(249\) 1541.50 2669.96i 0.392325 0.679527i
\(250\) −319.107 552.709i −0.0807283 0.139826i
\(251\) −2631.65 −0.661786 −0.330893 0.943668i \(-0.607350\pi\)
−0.330893 + 0.943668i \(0.607350\pi\)
\(252\) −445.866 + 2978.47i −0.111456 + 0.744547i
\(253\) 3668.72 0.911663
\(254\) −1103.05 1910.54i −0.272486 0.471959i
\(255\) −170.026 + 294.493i −0.0417546 + 0.0723210i
\(256\) 3618.07 6266.68i 0.883318 1.52995i
\(257\) −1644.38 2848.15i −0.399120 0.691296i 0.594498 0.804097i \(-0.297351\pi\)
−0.993618 + 0.112802i \(0.964018\pi\)
\(258\) 4563.28 1.10115
\(259\) −6116.63 + 2407.71i −1.46745 + 0.577636i
\(260\) 6407.57 1.52839
\(261\) −959.994 1662.76i −0.227671 0.394338i
\(262\) 1678.50 2907.25i 0.395794 0.685535i
\(263\) 2704.45 4684.24i 0.634081 1.09826i −0.352627 0.935764i \(-0.614712\pi\)
0.986709 0.162498i \(-0.0519550\pi\)
\(264\) 3141.04 + 5440.44i 0.732263 + 1.26832i
\(265\) −512.366 −0.118771
\(266\) −5745.86 4572.71i −1.32444 1.05403i
\(267\) 3011.25 0.690208
\(268\) 7324.61 + 12686.6i 1.66948 + 2.89163i
\(269\) −269.894 + 467.470i −0.0611738 + 0.105956i −0.894990 0.446086i \(-0.852818\pi\)
0.833817 + 0.552042i \(0.186151\pi\)
\(270\) −344.635 + 596.926i −0.0776809 + 0.134547i
\(271\) −2045.57 3543.03i −0.458522 0.794184i 0.540361 0.841433i \(-0.318288\pi\)
−0.998883 + 0.0472494i \(0.984954\pi\)
\(272\) 2673.15 0.595896
\(273\) −3083.45 2453.90i −0.683586 0.544016i
\(274\) 1493.50 0.329290
\(275\) 509.193 + 881.948i 0.111656 + 0.193394i
\(276\) 2440.90 4227.76i 0.532336 0.922034i
\(277\) −1545.67 + 2677.18i −0.335271 + 0.580707i −0.983537 0.180707i \(-0.942161\pi\)
0.648265 + 0.761414i \(0.275495\pi\)
\(278\) 4270.97 + 7397.55i 0.921425 + 1.59595i
\(279\) −1581.56 −0.339375
\(280\) 4429.41 1743.56i 0.945385 0.372135i
\(281\) 7215.73 1.53187 0.765933 0.642920i \(-0.222277\pi\)
0.765933 + 0.642920i \(0.222277\pi\)
\(282\) −1292.54 2238.75i −0.272942 0.472750i
\(283\) −1482.36 + 2567.52i −0.311368 + 0.539305i −0.978659 0.205492i \(-0.934120\pi\)
0.667291 + 0.744797i \(0.267454\pi\)
\(284\) 5713.96 9896.87i 1.19388 2.06786i
\(285\) −582.441 1008.82i −0.121055 0.209674i
\(286\) −14751.5 −3.04990
\(287\) −682.728 + 4560.75i −0.140419 + 0.938023i
\(288\) 1717.18 0.351340
\(289\) 2199.53 + 3809.70i 0.447697 + 0.775433i
\(290\) −2723.03 + 4716.42i −0.551385 + 0.955027i
\(291\) 959.430 1661.78i 0.193274 0.334761i
\(292\) −8265.06 14315.5i −1.65643 2.86901i
\(293\) −7924.10 −1.57997 −0.789984 0.613127i \(-0.789911\pi\)
−0.789984 + 0.613127i \(0.789911\pi\)
\(294\) −5023.47 1538.47i −0.996513 0.305188i
\(295\) −117.399 −0.0231702
\(296\) 9122.75 + 15801.1i 1.79138 + 3.10276i
\(297\) 549.928 952.504i 0.107441 0.186094i
\(298\) −6435.76 + 11147.1i −1.25105 + 2.16689i
\(299\) 3193.89 + 5531.98i 0.617750 + 1.06997i
\(300\) 1355.12 0.260793
\(301\) −816.857 + 5456.76i −0.156421 + 1.04492i
\(302\) 7042.41 1.34187
\(303\) 950.804 + 1646.84i 0.180271 + 0.312239i
\(304\) −4578.59 + 7930.34i −0.863816 + 1.49617i
\(305\) 2186.57 3787.25i 0.410500 0.711008i
\(306\) −520.861 902.157i −0.0973059 0.168539i
\(307\) −4067.00 −0.756079 −0.378039 0.925790i \(-0.623402\pi\)
−0.378039 + 0.925790i \(0.623402\pi\)
\(308\) −12683.9 + 4992.82i −2.34654 + 0.923676i
\(309\) −1162.73 −0.214064
\(310\) 2243.05 + 3885.08i 0.410957 + 0.711799i
\(311\) −3826.29 + 6627.33i −0.697650 + 1.20836i 0.271630 + 0.962402i \(0.412437\pi\)
−0.969279 + 0.245963i \(0.920896\pi\)
\(312\) −5469.00 + 9472.59i −0.992376 + 1.71884i
\(313\) −911.061 1578.00i −0.164525 0.284965i 0.771962 0.635669i \(-0.219276\pi\)
−0.936486 + 0.350704i \(0.885942\pi\)
\(314\) 10174.3 1.82856
\(315\) −652.110 518.968i −0.116642 0.0928270i
\(316\) −9411.50 −1.67544
\(317\) −1574.43 2726.99i −0.278955 0.483164i 0.692170 0.721734i \(-0.256655\pi\)
−0.971125 + 0.238570i \(0.923321\pi\)
\(318\) 784.797 1359.31i 0.138394 0.239705i
\(319\) 4345.09 7525.91i 0.762627 1.32091i
\(320\) −77.0858 133.516i −0.0134663 0.0233244i
\(321\) 416.190 0.0723659
\(322\) 6663.57 + 5303.06i 1.15325 + 0.917788i
\(323\) 1760.53 0.303277
\(324\) −731.764 1267.45i −0.125474 0.217327i
\(325\) −886.578 + 1535.60i −0.151319 + 0.262091i
\(326\) −4857.94 + 8414.19i −0.825326 + 1.42951i
\(327\) 2569.46 + 4450.43i 0.434530 + 0.752628i
\(328\) 12800.0 2.15477
\(329\) 2908.46 1144.87i 0.487382 0.191850i
\(330\) −3119.75 −0.520413
\(331\) 2928.06 + 5071.55i 0.486226 + 0.842168i 0.999875 0.0158326i \(-0.00503989\pi\)
−0.513649 + 0.858001i \(0.671707\pi\)
\(332\) 9284.10 16080.5i 1.53473 2.65823i
\(333\) 1597.20 2766.43i 0.262840 0.455253i
\(334\) 965.447 + 1672.20i 0.158164 + 0.273949i
\(335\) −4053.86 −0.661152
\(336\) −969.925 + 6479.28i −0.157481 + 1.05201i
\(337\) −7065.69 −1.14212 −0.571058 0.820910i \(-0.693467\pi\)
−0.571058 + 0.820910i \(0.693467\pi\)
\(338\) −7233.60 12529.0i −1.16407 2.01623i
\(339\) −3125.03 + 5412.71i −0.500673 + 0.867192i
\(340\) −1024.02 + 1773.66i −0.163339 + 0.282912i
\(341\) −3579.20 6199.35i −0.568400 0.984497i
\(342\) 3568.53 0.564222
\(343\) 2738.93 5731.66i 0.431161 0.902275i
\(344\) 15314.7 2.40033
\(345\) 675.467 + 1169.94i 0.105408 + 0.182573i
\(346\) 1695.19 2936.15i 0.263393 0.456210i
\(347\) −4948.72 + 8571.44i −0.765595 + 1.32605i 0.174337 + 0.984686i \(0.444222\pi\)
−0.939932 + 0.341363i \(0.889111\pi\)
\(348\) −5781.80 10014.4i −0.890624 1.54261i
\(349\) 11832.6 1.81486 0.907431 0.420201i \(-0.138040\pi\)
0.907431 + 0.420201i \(0.138040\pi\)
\(350\) −349.979 + 2337.93i −0.0534490 + 0.357050i
\(351\) 1915.01 0.291213
\(352\) 3886.12 + 6730.95i 0.588440 + 1.01921i
\(353\) −3503.69 + 6068.57i −0.528279 + 0.915007i 0.471177 + 0.882039i \(0.343829\pi\)
−0.999456 + 0.0329681i \(0.989504\pi\)
\(354\) 179.821 311.459i 0.0269982 0.0467623i
\(355\) 1581.22 + 2738.75i 0.236401 + 0.409458i
\(356\) 18136.0 2.70002
\(357\) 1172.03 461.352i 0.173755 0.0683959i
\(358\) −1710.41 −0.252508
\(359\) −1407.19 2437.33i −0.206877 0.358322i 0.743852 0.668344i \(-0.232997\pi\)
−0.950729 + 0.310023i \(0.899663\pi\)
\(360\) −1156.62 + 2003.33i −0.169332 + 0.293291i
\(361\) 414.057 717.169i 0.0603670 0.104559i
\(362\) −3128.73 5419.13i −0.454261 0.786804i
\(363\) 985.124 0.142440
\(364\) −18570.8 14779.2i −2.67411 2.12813i
\(365\) 4574.36 0.655981
\(366\) 6698.39 + 11602.0i 0.956641 + 1.65695i
\(367\) −1174.93 + 2035.03i −0.167114 + 0.289449i −0.937404 0.348244i \(-0.886778\pi\)
0.770290 + 0.637694i \(0.220111\pi\)
\(368\) 5309.87 9196.96i 0.752163 1.30278i
\(369\) −1120.51 1940.77i −0.158079 0.273801i
\(370\) −9060.91 −1.27312
\(371\) 1484.97 + 1181.78i 0.207806 + 0.165378i
\(372\) −9525.34 −1.32760
\(373\) 829.650 + 1437.00i 0.115168 + 0.199477i 0.917847 0.396935i \(-0.129926\pi\)
−0.802679 + 0.596411i \(0.796593\pi\)
\(374\) 2357.50 4083.31i 0.325945 0.564553i
\(375\) −187.500 + 324.760i −0.0258199 + 0.0447214i
\(376\) −4337.87 7513.42i −0.594970 1.03052i
\(377\) 15130.8 2.06705
\(378\) 2375.67 935.142i 0.323257 0.127245i
\(379\) 5327.80 0.722087 0.361043 0.932549i \(-0.382421\pi\)
0.361043 + 0.932549i \(0.382421\pi\)
\(380\) −3507.89 6075.85i −0.473556 0.820223i
\(381\) −648.127 + 1122.59i −0.0871510 + 0.150950i
\(382\) 4037.07 6992.42i 0.540719 0.936553i
\(383\) −3119.88 5403.78i −0.416235 0.720941i 0.579322 0.815099i \(-0.303317\pi\)
−0.995557 + 0.0941580i \(0.969984\pi\)
\(384\) −4106.86 −0.545774
\(385\) 558.455 3730.59i 0.0739260 0.493840i
\(386\) −19884.8 −2.62205
\(387\) −1340.64 2322.06i −0.176095 0.305005i
\(388\) 5778.41 10008.5i 0.756067 1.30955i
\(389\) −4742.61 + 8214.43i −0.618148 + 1.07066i 0.371675 + 0.928363i \(0.378784\pi\)
−0.989823 + 0.142301i \(0.954550\pi\)
\(390\) −2715.97 4704.19i −0.352637 0.610784i
\(391\) −2041.72 −0.264077
\(392\) −16859.2 5163.22i −2.17224 0.665260i
\(393\) −1972.50 −0.253179
\(394\) −2537.17 4394.51i −0.324419 0.561910i
\(395\) 1302.22 2255.50i 0.165877 0.287308i
\(396\) 3312.08 5736.69i 0.420299 0.727978i
\(397\) −3946.37 6835.31i −0.498898 0.864117i 0.501101 0.865389i \(-0.332928\pi\)
−0.999999 + 0.00127185i \(0.999595\pi\)
\(398\) −15725.0 −1.98046
\(399\) −638.790 + 4267.23i −0.0801491 + 0.535411i
\(400\) 2947.89 0.368486
\(401\) 6229.83 + 10790.4i 0.775817 + 1.34375i 0.934334 + 0.356398i \(0.115995\pi\)
−0.158517 + 0.987356i \(0.550671\pi\)
\(402\) 6209.34 10754.9i 0.770383 1.33434i
\(403\) 6231.90 10794.0i 0.770305 1.33421i
\(404\) 5726.45 + 9918.50i 0.705202 + 1.22145i
\(405\) 405.000 0.0496904
\(406\) 18770.6 7388.73i 2.29450 0.903193i
\(407\) 14458.3 1.76087
\(408\) −1748.05 3027.71i −0.212111 0.367387i
\(409\) −1701.81 + 2947.62i −0.205744 + 0.356358i −0.950369 0.311124i \(-0.899295\pi\)
0.744626 + 0.667482i \(0.232628\pi\)
\(410\) −3178.32 + 5505.01i −0.382844 + 0.663105i
\(411\) −438.773 759.977i −0.0526595 0.0912090i
\(412\) −7002.86 −0.837393
\(413\) 340.253 + 270.783i 0.0405393 + 0.0322623i
\(414\) −4138.48 −0.491293
\(415\) 2569.17 + 4449.94i 0.303894 + 0.526359i
\(416\) −6766.29 + 11719.6i −0.797463 + 1.38125i
\(417\) 2509.53 4346.63i 0.294706 0.510445i
\(418\) 8075.86 + 13987.8i 0.944983 + 1.63676i
\(419\) −1376.83 −0.160532 −0.0802658 0.996773i \(-0.525577\pi\)
−0.0802658 + 0.996773i \(0.525577\pi\)
\(420\) −3927.50 3125.61i −0.456291 0.363129i
\(421\) −15757.3 −1.82414 −0.912069 0.410036i \(-0.865516\pi\)
−0.912069 + 0.410036i \(0.865516\pi\)
\(422\) −5398.57 9350.60i −0.622745 1.07863i
\(423\) −759.469 + 1315.44i −0.0872970 + 0.151203i
\(424\) 2633.84 4561.95i 0.301676 0.522519i
\(425\) −283.376 490.822i −0.0323430 0.0560196i
\(426\) −9687.88 −1.10183
\(427\) −15072.6 + 5933.09i −1.70823 + 0.672418i
\(428\) 2506.61 0.283088
\(429\) 4333.82 + 7506.39i 0.487736 + 0.844783i
\(430\) −3802.73 + 6586.52i −0.426474 + 0.738675i
\(431\) −2541.85 + 4402.62i −0.284076 + 0.492034i −0.972385 0.233384i \(-0.925020\pi\)
0.688309 + 0.725418i \(0.258353\pi\)
\(432\) −1591.86 2757.18i −0.177288 0.307072i
\(433\) 4631.44 0.514025 0.257013 0.966408i \(-0.417262\pi\)
0.257013 + 0.966408i \(0.417262\pi\)
\(434\) 2460.06 16433.6i 0.272089 1.81760i
\(435\) 3199.98 0.352706
\(436\) 15475.2 + 26803.8i 1.69983 + 2.94420i
\(437\) 3497.06 6057.09i 0.382808 0.663043i
\(438\) −7006.60 + 12135.8i −0.764357 + 1.32391i
\(439\) 1169.44 + 2025.52i 0.127139 + 0.220212i 0.922567 0.385837i \(-0.126087\pi\)
−0.795428 + 0.606048i \(0.792754\pi\)
\(440\) −10470.1 −1.13442
\(441\) 692.980 + 3008.21i 0.0748277 + 0.324826i
\(442\) 8209.49 0.883451
\(443\) −5905.74 10229.0i −0.633387 1.09706i −0.986854 0.161612i \(-0.948331\pi\)
0.353468 0.935447i \(-0.385002\pi\)
\(444\) 9619.52 16661.5i 1.02820 1.78090i
\(445\) −2509.38 + 4346.37i −0.267316 + 0.463006i
\(446\) −6582.37 11401.0i −0.698844 1.21043i
\(447\) 7563.02 0.800265
\(448\) −84.5435 + 564.766i −0.00891586 + 0.0595596i
\(449\) 9582.29 1.00716 0.503582 0.863948i \(-0.332015\pi\)
0.503582 + 0.863948i \(0.332015\pi\)
\(450\) −574.392 994.876i −0.0601713 0.104220i
\(451\) 5071.59 8784.25i 0.529516 0.917149i
\(452\) −18821.3 + 32599.4i −1.95858 + 3.39236i
\(453\) −2068.98 3583.58i −0.214590 0.371680i
\(454\) 14938.9 1.54431
\(455\) 6111.43 2405.66i 0.629689 0.247866i
\(456\) 11976.3 1.22991
\(457\) 3285.97 + 5691.47i 0.336349 + 0.582573i 0.983743 0.179582i \(-0.0574746\pi\)
−0.647394 + 0.762155i \(0.724141\pi\)
\(458\) 2675.08 4633.37i 0.272922 0.472714i
\(459\) −306.046 + 530.087i −0.0311220 + 0.0539049i
\(460\) 4068.17 + 7046.27i 0.412346 + 0.714204i
\(461\) −4197.59 −0.424081 −0.212041 0.977261i \(-0.568011\pi\)
−0.212041 + 0.977261i \(0.568011\pi\)
\(462\) 9041.86 + 7195.77i 0.910531 + 0.724626i
\(463\) −6125.75 −0.614876 −0.307438 0.951568i \(-0.599472\pi\)
−0.307438 + 0.951568i \(0.599472\pi\)
\(464\) −12577.6 21785.0i −1.25840 2.17962i
\(465\) 1317.97 2282.79i 0.131439 0.227659i
\(466\) 9879.51 17111.8i 0.982101 1.70105i
\(467\) −1614.04 2795.60i −0.159934 0.277013i 0.774911 0.632070i \(-0.217795\pi\)
−0.934845 + 0.355057i \(0.884461\pi\)
\(468\) 11533.6 1.13919
\(469\) 11749.2 + 9350.31i 1.15677 + 0.920591i
\(470\) 4308.47 0.422840
\(471\) −2989.10 5177.27i −0.292421 0.506488i
\(472\) 603.494 1045.28i 0.0588518 0.101934i
\(473\) 6067.95 10510.0i 0.589862 1.02167i
\(474\) 3989.24 + 6909.57i 0.386565 + 0.669550i
\(475\) 1941.47 0.187538
\(476\) 7058.87 2778.60i 0.679711 0.267557i
\(477\) −922.259 −0.0885269
\(478\) 15472.3 + 26798.7i 1.48051 + 2.56432i
\(479\) −1563.15 + 2707.46i −0.149107 + 0.258261i −0.930898 0.365280i \(-0.880973\pi\)
0.781791 + 0.623541i \(0.214307\pi\)
\(480\) −1430.98 + 2478.54i −0.136073 + 0.235686i
\(481\) 12587.0 + 21801.4i 1.19318 + 2.06665i
\(482\) −21362.9 −2.01878
\(483\) 740.815 4948.79i 0.0697894 0.466206i
\(484\) 5933.15 0.557208
\(485\) 1599.05 + 2769.64i 0.149710 + 0.259305i
\(486\) −620.343 + 1074.47i −0.0578999 + 0.100286i
\(487\) 434.519 752.609i 0.0404311 0.0700286i −0.845102 0.534605i \(-0.820460\pi\)
0.885533 + 0.464577i \(0.153794\pi\)
\(488\) 22480.3 + 38937.1i 2.08532 + 3.61188i
\(489\) 5708.83 0.527939
\(490\) 6406.81 5968.70i 0.590674 0.550282i
\(491\) 6617.71 0.608254 0.304127 0.952631i \(-0.401635\pi\)
0.304127 + 0.952631i \(0.401635\pi\)
\(492\) −6748.53 11688.8i −0.618388 1.07108i
\(493\) −2418.13 + 4188.32i −0.220907 + 0.382622i
\(494\) −14061.2 + 24354.8i −1.28066 + 2.21816i
\(495\) 916.547 + 1587.51i 0.0832237 + 0.144148i
\(496\) −20721.2 −1.87582
\(497\) 1734.19 11584.7i 0.156518 1.04557i
\(498\) −15740.9 −1.41640
\(499\) 444.077 + 769.164i 0.0398389 + 0.0690030i 0.885257 0.465102i \(-0.153982\pi\)
−0.845418 + 0.534105i \(0.820649\pi\)
\(500\) −1129.27 + 1955.94i −0.101005 + 0.174945i
\(501\) 567.275 982.550i 0.0505868 0.0876189i
\(502\) 6718.21 + 11636.3i 0.597308 + 1.03457i
\(503\) −10757.4 −0.953572 −0.476786 0.879019i \(-0.658198\pi\)
−0.476786 + 0.879019i \(0.658198\pi\)
\(504\) 7972.93 3138.41i 0.704648 0.277373i
\(505\) −3169.35 −0.279275
\(506\) −9365.71 16221.9i −0.822839 1.42520i
\(507\) −4250.30 + 7361.74i −0.372313 + 0.644865i
\(508\) −3903.50 + 6761.07i −0.340925 + 0.590500i
\(509\) −4430.01 7673.01i −0.385770 0.668173i 0.606106 0.795384i \(-0.292731\pi\)
−0.991876 + 0.127211i \(0.959397\pi\)
\(510\) 1736.20 0.150746
\(511\) −13257.7 10550.9i −1.14772 0.913391i
\(512\) −25994.0 −2.24372
\(513\) −1048.39 1815.87i −0.0902294 0.156282i
\(514\) −8395.74 + 14541.8i −0.720467 + 1.24789i
\(515\) 968.946 1678.26i 0.0829065 0.143598i
\(516\) −8074.34 13985.2i −0.688862 1.19314i
\(517\) −6874.95 −0.584835
\(518\) 26261.0 + 20899.2i 2.22749 + 1.77270i
\(519\) −1992.11 −0.168485
\(520\) −9115.00 15787.6i −0.768691 1.33141i
\(521\) 37.6937 65.2875i 0.00316966 0.00549001i −0.864436 0.502742i \(-0.832324\pi\)
0.867606 + 0.497252i \(0.165658\pi\)
\(522\) −4901.45 + 8489.56i −0.410978 + 0.711835i
\(523\) −4333.30 7505.49i −0.362298 0.627518i 0.626041 0.779790i \(-0.284674\pi\)
−0.988339 + 0.152272i \(0.951341\pi\)
\(524\) −11879.9 −0.990408
\(525\) 1292.49 508.767i 0.107446 0.0422941i
\(526\) −27616.2 −2.28921
\(527\) 1991.89 + 3450.06i 0.164646 + 0.285175i
\(528\) 7205.01 12479.4i 0.593859 1.02859i
\(529\) 2027.90 3512.42i 0.166672 0.288684i
\(530\) 1308.00 + 2265.51i 0.107199 + 0.185675i
\(531\) −211.318 −0.0172701
\(532\) −3847.27 + 25700.5i −0.313534 + 2.09447i
\(533\) 17660.7 1.43522
\(534\) −7687.28 13314.8i −0.622961 1.07900i
\(535\) −346.825 + 600.719i −0.0280272 + 0.0485445i
\(536\) 20839.1 36094.3i 1.67931 2.90865i
\(537\) 502.499 + 870.354i 0.0403807 + 0.0699414i
\(538\) 2756.00 0.220854
\(539\) −10223.2 + 9524.14i −0.816968 + 0.761102i
\(540\) 2439.21 0.194383
\(541\) −6142.38 10638.9i −0.488136 0.845477i 0.511771 0.859122i \(-0.328990\pi\)
−0.999907 + 0.0136455i \(0.995656\pi\)
\(542\) −10444.1 + 18089.7i −0.827697 + 1.43361i
\(543\) −1838.37 + 3184.16i −0.145290 + 0.251649i
\(544\) −2162.70 3745.91i −0.170451 0.295229i
\(545\) −8564.85 −0.673171
\(546\) −2978.72 + 19898.4i −0.233476 + 1.55966i
\(547\) −2906.85 −0.227218 −0.113609 0.993526i \(-0.536241\pi\)
−0.113609 + 0.993526i \(0.536241\pi\)
\(548\) −2642.62 4577.15i −0.205998 0.356800i
\(549\) 3935.83 6817.05i 0.305969 0.529954i
\(550\) 2599.79 4502.97i 0.201555 0.349104i
\(551\) −8283.55 14347.5i −0.640456 1.10930i
\(552\) −13889.1 −1.07094
\(553\) −8976.54 + 3533.46i −0.690274 + 0.271715i
\(554\) 15783.5 1.21042
\(555\) 2662.00 + 4610.71i 0.203595 + 0.352637i
\(556\) 15114.3 26178.7i 1.15286 1.99680i
\(557\) −1936.91 + 3354.83i −0.147342 + 0.255204i −0.930244 0.366941i \(-0.880405\pi\)
0.782902 + 0.622145i \(0.213738\pi\)
\(558\) 4037.49 + 6993.14i 0.306309 + 0.530543i
\(559\) 21130.4 1.59878
\(560\) −8543.77 6799.37i −0.644714 0.513082i
\(561\) −2770.43 −0.208498
\(562\) −18420.7 31905.6i −1.38262 2.39476i
\(563\) 2730.54 4729.44i 0.204403 0.354036i −0.745540 0.666461i \(-0.767808\pi\)
0.949942 + 0.312426i \(0.101141\pi\)
\(564\) −4574.09 + 7922.55i −0.341496 + 0.591489i
\(565\) −5208.38 9021.18i −0.387820 0.671724i
\(566\) 15137.0 1.12412
\(567\) −1173.80 934.142i −0.0869399 0.0691892i
\(568\) −32513.3 −2.40181
\(569\) −6552.48 11349.2i −0.482767 0.836177i 0.517037 0.855963i \(-0.327035\pi\)
−0.999804 + 0.0197860i \(0.993701\pi\)
\(570\) −2973.77 + 5150.72i −0.218522 + 0.378491i
\(571\) −1719.63 + 2978.49i −0.126032 + 0.218294i −0.922136 0.386866i \(-0.873558\pi\)
0.796104 + 0.605160i \(0.206891\pi\)
\(572\) 26101.5 + 45209.1i 1.90797 + 3.30470i
\(573\) −4744.19 −0.345884
\(574\) 21909.1 8624.13i 1.59315 0.627115i
\(575\) −2251.56 −0.163298
\(576\) −138.754 240.330i −0.0100372 0.0173850i
\(577\) −8896.09 + 15408.5i −0.641853 + 1.11172i 0.343166 + 0.939275i \(0.388501\pi\)
−0.985019 + 0.172447i \(0.944833\pi\)
\(578\) 11230.2 19451.2i 0.808155 1.39977i
\(579\) 5841.94 + 10118.5i 0.419314 + 0.726273i
\(580\) 19272.7 1.37975
\(581\) 2817.73 18823.0i 0.201204 1.34408i
\(582\) −9797.14 −0.697774
\(583\) −2087.15 3615.04i −0.148269 0.256809i
\(584\) −23514.7 + 40728.7i −1.66617 + 2.88590i
\(585\) −1595.84 + 2764.08i −0.112786 + 0.195351i
\(586\) 20229.1 + 35037.8i 1.42603 + 2.46996i
\(587\) 14416.6 1.01369 0.506846 0.862037i \(-0.330811\pi\)
0.506846 + 0.862037i \(0.330811\pi\)
\(588\) 4173.64 + 18117.7i 0.292718 + 1.27068i
\(589\) −13646.9 −0.954686
\(590\) 299.702 + 519.098i 0.0209127 + 0.0362219i
\(591\) −1490.79 + 2582.12i −0.103761 + 0.179719i
\(592\) 20926.0 36245.0i 1.45280 2.51631i
\(593\) −4086.02 7077.19i −0.282955 0.490093i 0.689156 0.724613i \(-0.257982\pi\)
−0.972111 + 0.234520i \(0.924648\pi\)
\(594\) −5615.54 −0.387893
\(595\) −310.792 + 2076.15i −0.0214138 + 0.143048i
\(596\) 45550.2 3.13055
\(597\) 4619.82 + 8001.77i 0.316711 + 0.548560i
\(598\) 16307.1 28244.7i 1.11513 1.93145i
\(599\) 1246.09 2158.29i 0.0849980 0.147221i −0.820392 0.571801i \(-0.806245\pi\)
0.905390 + 0.424580i \(0.139578\pi\)
\(600\) −1927.71 3338.89i −0.131164 0.227182i
\(601\) −13835.4 −0.939031 −0.469516 0.882924i \(-0.655571\pi\)
−0.469516 + 0.882924i \(0.655571\pi\)
\(602\) 26213.3 10318.4i 1.77471 0.698584i
\(603\) −7296.94 −0.492794
\(604\) −12460.9 21583.0i −0.839452 1.45397i
\(605\) −820.937 + 1421.90i −0.0551666 + 0.0955514i
\(606\) 4854.52 8408.28i 0.325415 0.563636i
\(607\) −3667.95 6353.08i −0.245268 0.424816i 0.716939 0.697136i \(-0.245543\pi\)
−0.962207 + 0.272320i \(0.912209\pi\)
\(608\) 14817.1 0.988345
\(609\) −9274.40 7380.83i −0.617106 0.491110i
\(610\) −22328.0 −1.48202
\(611\) −5985.14 10366.6i −0.396289 0.686394i
\(612\) −1843.24 + 3192.58i −0.121746 + 0.210870i
\(613\) −3006.02 + 5206.58i −0.198062 + 0.343054i −0.947900 0.318568i \(-0.896798\pi\)
0.749838 + 0.661622i \(0.230131\pi\)
\(614\) 10382.5 + 17983.0i 0.682414 + 1.18198i
\(615\) 3735.02 0.244895
\(616\) 30345.2 + 24149.6i 1.98481 + 1.57957i
\(617\) −22927.4 −1.49598 −0.747991 0.663708i \(-0.768982\pi\)
−0.747991 + 0.663708i \(0.768982\pi\)
\(618\) 2968.29 + 5141.23i 0.193207 + 0.334645i
\(619\) −8960.76 + 15520.5i −0.581847 + 1.00779i 0.413413 + 0.910543i \(0.364336\pi\)
−0.995260 + 0.0972452i \(0.968997\pi\)
\(620\) 7937.78 13748.6i 0.514176 0.890578i
\(621\) 1215.84 + 2105.90i 0.0785668 + 0.136082i
\(622\) 39071.8 2.51871
\(623\) 17297.8 6809.00i 1.11240 0.437876i
\(624\) 25089.9 1.60962
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −4651.61 + 8056.82i −0.296990 + 0.514402i
\(627\) 4745.19 8218.92i 0.302241 0.523496i
\(628\) −18002.6 31181.4i −1.14392 1.98132i
\(629\) −8046.35 −0.510062
\(630\) −629.962 + 4208.27i −0.0398386 + 0.266129i
\(631\) 19270.7 1.21578 0.607888 0.794023i \(-0.292017\pi\)
0.607888 + 0.794023i \(0.292017\pi\)
\(632\) 13388.2 + 23189.1i 0.842650 + 1.45951i
\(633\) −3172.08 + 5494.20i −0.199177 + 0.344984i
\(634\) −8038.57 + 13923.2i −0.503553 + 0.872179i
\(635\) −1080.21 1870.98i −0.0675069 0.116925i
\(636\) −5554.53 −0.346308
\(637\) −23261.3 7123.90i −1.44685 0.443107i
\(638\) −44369.5 −2.75330
\(639\) 2846.19 + 4929.75i 0.176203 + 0.305192i
\(640\) 3422.38 5927.74i 0.211377 0.366116i
\(641\) −14119.3 + 24455.3i −0.870013 + 1.50691i −0.00803063 + 0.999968i \(0.502556\pi\)
−0.861982 + 0.506939i \(0.830777\pi\)
\(642\) −1062.47 1840.26i −0.0653153 0.113129i
\(643\) −19055.3 −1.16869 −0.584346 0.811505i \(-0.698649\pi\)
−0.584346 + 0.811505i \(0.698649\pi\)
\(644\) 4461.74 29805.3i 0.273008 1.82375i
\(645\) 4468.80 0.272804
\(646\) −4494.38 7784.49i −0.273729 0.474112i
\(647\) 8105.65 14039.4i 0.492529 0.853084i −0.507434 0.861690i \(-0.669406\pi\)
0.999963 + 0.00860593i \(0.00273939\pi\)
\(648\) −2081.92 + 3606.00i −0.126212 + 0.218606i
\(649\) −478.228 828.316i −0.0289247 0.0500990i
\(650\) 9053.22 0.546302
\(651\) −9085.11 + 3576.20i −0.546964 + 0.215303i
\(652\) 34382.9 2.06524
\(653\) 13266.0 + 22977.4i 0.795007 + 1.37699i 0.922834 + 0.385197i \(0.125866\pi\)
−0.127827 + 0.991796i \(0.540800\pi\)
\(654\) 13118.9 22722.6i 0.784387 1.35860i
\(655\) 1643.75 2847.06i 0.0980558 0.169838i
\(656\) −14680.6 25427.5i −0.873749 1.51338i
\(657\) 8233.85 0.488939
\(658\) −12487.1 9937.58i −0.739814 0.588765i
\(659\) 1883.19 0.111318 0.0556592 0.998450i \(-0.482274\pi\)
0.0556592 + 0.998450i \(0.482274\pi\)
\(660\) 5520.13 + 9561.15i 0.325562 + 0.563890i
\(661\) −2337.13 + 4048.03i −0.137525 + 0.238200i −0.926559 0.376149i \(-0.877248\pi\)
0.789034 + 0.614349i \(0.210581\pi\)
\(662\) 14949.8 25893.8i 0.877706 1.52023i
\(663\) −2411.86 4177.46i −0.141280 0.244704i
\(664\) −52827.9 −3.08753
\(665\) −5626.90 4478.04i −0.328123 0.261129i
\(666\) −16309.6 −0.948928
\(667\) 9606.58 + 16639.1i 0.557673 + 0.965919i
\(668\) 3416.56 5917.65i 0.197890 0.342756i
\(669\) −3867.65 + 6698.97i −0.223516 + 0.387141i
\(670\) 10348.9 + 17924.8i 0.596736 + 1.03358i
\(671\) 35628.3 2.04980
\(672\) 9864.18 3882.87i 0.566248 0.222894i
\(673\) −23344.3 −1.33709 −0.668543 0.743674i \(-0.733082\pi\)
−0.668543 + 0.743674i \(0.733082\pi\)
\(674\) 18037.7 + 31242.2i 1.03084 + 1.78547i
\(675\) −337.500 + 584.567i −0.0192450 + 0.0333333i
\(676\) −25598.5 + 44337.9i −1.45645 + 2.52264i
\(677\) −699.747 1212.00i −0.0397245 0.0688048i 0.845480 0.534008i \(-0.179315\pi\)
−0.885204 + 0.465203i \(0.845981\pi\)
\(678\) 31911.0 1.80757
\(679\) 1753.75 11715.4i 0.0991205 0.662144i
\(680\) 5826.83 0.328601
\(681\) −4388.89 7601.78i −0.246964 0.427754i
\(682\) −18274.3 + 31652.1i −1.02604 + 1.77716i
\(683\) −16510.3 + 28596.8i −0.924964 + 1.60209i −0.133346 + 0.991070i \(0.542572\pi\)
−0.791618 + 0.611016i \(0.790761\pi\)
\(684\) −6314.21 10936.5i −0.352968 0.611358i
\(685\) 1462.58 0.0815798
\(686\) −32335.6 + 2521.44i −1.79968 + 0.140334i
\(687\) −3143.63 −0.174581
\(688\) −17564.7 30422.9i −0.973325 1.68585i
\(689\) 3634.02 6294.31i 0.200936 0.348032i
\(690\) 3448.73 5973.38i 0.190277 0.329569i
\(691\) −360.088 623.691i −0.0198240 0.0343362i 0.855943 0.517070i \(-0.172977\pi\)
−0.875767 + 0.482734i \(0.839644\pi\)
\(692\) −11998.0 −0.659096
\(693\) 1005.22 6715.05i 0.0551012 0.368086i
\(694\) 50533.5 2.76401
\(695\) 4182.55 + 7244.39i 0.228278 + 0.395389i
\(696\) −16449.7 + 28491.6i −0.895866 + 1.55169i
\(697\) −2822.44 + 4888.61i −0.153382 + 0.265666i
\(698\) −30207.0 52320.1i −1.63804 2.83717i
\(699\) −11610.0 −0.628224
\(700\) 7784.34 3064.18i 0.420315 0.165450i
\(701\) 11675.1 0.629048 0.314524 0.949249i \(-0.398155\pi\)
0.314524 + 0.949249i \(0.398155\pi\)
\(702\) −4888.74 8467.54i −0.262840 0.455252i
\(703\) 13781.8 23870.8i 0.739390 1.28066i
\(704\) 628.024 1087.77i 0.0336215 0.0582342i
\(705\) −1265.78 2192.40i −0.0676200 0.117121i
\(706\) 35777.6 1.90724
\(707\) 9185.61 + 7310.17i 0.488629 + 0.388864i
\(708\) −1272.71 −0.0675586
\(709\) 13385.9 + 23185.0i 0.709050 + 1.22811i 0.965210 + 0.261477i \(0.0842095\pi\)
−0.256159 + 0.966635i \(0.582457\pi\)
\(710\) 8073.23 13983.2i 0.426736 0.739129i
\(711\) 2343.99 4059.91i 0.123638 0.214147i
\(712\) −25799.1 44685.4i −1.35796 2.35205i
\(713\) 15826.5 0.831288
\(714\) −5031.98 4004.59i −0.263749 0.209899i
\(715\) −14446.1 −0.755597
\(716\) 3026.43 + 5241.92i 0.157965 + 0.273603i
\(717\) 9091.15 15746.3i 0.473522 0.820164i
\(718\) −7184.72 + 12444.3i −0.373442 + 0.646821i
\(719\) −17391.7 30123.4i −0.902089 1.56246i −0.824778 0.565457i \(-0.808700\pi\)
−0.0773114 0.997007i \(-0.524634\pi\)
\(720\) 5306.20 0.274653
\(721\) −6679.22 + 2629.16i −0.345003 + 0.135805i
\(722\) −4228.11 −0.217942
\(723\) 6276.18 + 10870.7i 0.322840 + 0.559176i
\(724\) −11072.1 + 19177.4i −0.568357 + 0.984422i
\(725\) −2666.65 + 4618.77i −0.136603 + 0.236603i
\(726\) −2514.88 4355.90i −0.128562 0.222676i
\(727\) 25368.1 1.29415 0.647077 0.762425i \(-0.275991\pi\)
0.647077 + 0.762425i \(0.275991\pi\)
\(728\) −9996.84 + 66780.8i −0.508939 + 3.39981i
\(729\) 729.000 0.0370370
\(730\) −11677.7 20226.3i −0.592068 1.02549i
\(731\) −3376.94 + 5849.02i −0.170863 + 0.295943i
\(732\) 23704.5 41057.4i 1.19692 2.07312i
\(733\) −15845.8 27445.7i −0.798468 1.38299i −0.920614 0.390474i \(-0.872311\pi\)
0.122146 0.992512i \(-0.461022\pi\)
\(734\) 11997.7 0.603327
\(735\) −4919.47 1506.61i −0.246881 0.0756086i
\(736\) −17183.7 −0.860596
\(737\) −16513.6 28602.3i −0.825352 1.42955i
\(738\) −5720.98 + 9909.02i −0.285355 + 0.494249i
\(739\) 6597.98 11428.0i 0.328431 0.568860i −0.653770 0.756694i \(-0.726813\pi\)
0.982201 + 0.187834i \(0.0601467\pi\)
\(740\) 16032.5 + 27769.2i 0.796443 + 1.37948i
\(741\) 16524.1 0.819203
\(742\) 1434.54 9582.99i 0.0709752 0.474128i
\(743\) 8244.34 0.407073 0.203537 0.979067i \(-0.434756\pi\)
0.203537 + 0.979067i \(0.434756\pi\)
\(744\) 13550.1 + 23469.5i 0.667705 + 1.15650i
\(745\) −6302.52 + 10916.3i −0.309941 + 0.536834i
\(746\) 4235.95 7336.88i 0.207894 0.360083i
\(747\) 4624.51 + 8009.89i 0.226509 + 0.392325i
\(748\) −16685.6 −0.815622
\(749\) 2390.76 941.084i 0.116631 0.0459098i
\(750\) 1914.64 0.0932170
\(751\) −15884.9 27513.4i −0.771834 1.33686i −0.936557 0.350516i \(-0.886006\pi\)
0.164722 0.986340i \(-0.447327\pi\)
\(752\) −9950.35 + 17234.5i −0.482516 + 0.835742i
\(753\) 3947.47 6837.22i 0.191041 0.330893i
\(754\) −38626.8 66903.6i −1.86566 3.23141i
\(755\) 6896.60 0.332441
\(756\) −7069.49 5626.10i −0.340099 0.270660i
\(757\) −3019.09 −0.144954 −0.0724772 0.997370i \(-0.523090\pi\)
−0.0724772 + 0.997370i \(0.523090\pi\)
\(758\) −13601.1 23557.8i −0.651734 1.12884i
\(759\) −5503.08 + 9531.62i −0.263174 + 0.455831i
\(760\) −9980.22 + 17286.2i −0.476343 + 0.825050i
\(761\) −12048.2 20868.0i −0.573910 0.994041i −0.996159 0.0875612i \(-0.972093\pi\)
0.422249 0.906480i \(-0.361241\pi\)
\(762\) 6618.29 0.314640
\(763\) 24823.2 + 19755.0i 1.17780 + 0.937326i
\(764\) −28573.1 −1.35306
\(765\) −510.077 883.479i −0.0241070 0.0417546i
\(766\) −15929.2 + 27590.1i −0.751363 + 1.30140i
\(767\) 832.665 1442.22i 0.0391992 0.0678950i
\(768\) 10854.2 + 18800.1i 0.509984 + 0.883318i
\(769\) 7954.16 0.372996 0.186498 0.982455i \(-0.440286\pi\)
0.186498 + 0.982455i \(0.440286\pi\)
\(770\) −17921.1 + 7054.33i −0.838741 + 0.330156i
\(771\) 9866.30 0.460864
\(772\) 35184.5 + 60941.4i 1.64031 + 2.84110i
\(773\) −18119.7 + 31384.2i −0.843105 + 1.46030i 0.0441523 + 0.999025i \(0.485941\pi\)
−0.887257 + 0.461275i \(0.847392\pi\)
\(774\) −6844.92 + 11855.7i −0.317875 + 0.550576i
\(775\) 2196.61 + 3804.64i 0.101812 + 0.176344i
\(776\) −32880.0 −1.52104
\(777\) 2919.53 19503.0i 0.134798 0.900473i
\(778\) 48428.7 2.23169
\(779\) −9668.57 16746.5i −0.444689 0.770223i
\(780\) −9611.35 + 16647.3i −0.441207 + 0.764193i
\(781\) −12882.3 + 22312.8i −0.590224 + 1.02230i
\(782\) 5212.21 + 9027.81i 0.238348 + 0.412831i
\(783\) 5759.96 0.262892
\(784\) 9079.23 + 39412.8i 0.413595 + 1.79541i
\(785\) 9963.65 0.453017
\(786\) 5035.50 + 8721.74i 0.228512 + 0.395794i
\(787\) 4842.06 8386.70i 0.219315 0.379865i −0.735284 0.677759i \(-0.762951\pi\)
0.954599 + 0.297895i \(0.0962844\pi\)
\(788\) −8978.63 + 15551.4i −0.405902 + 0.703042i
\(789\) 8113.34 + 14052.7i 0.366087 + 0.634081i
\(790\) −13297.5 −0.598864
\(791\) −5712.27 + 38159.0i −0.256770 + 1.71527i
\(792\) −18846.2 −0.845545
\(793\) 31017.0 + 53723.1i 1.38896 + 2.40575i
\(794\) −20149.0 + 34899.1i −0.900581 + 1.55985i
\(795\) 768.549 1331.17i 0.0342863 0.0593857i
\(796\) 27824.0 + 48192.6i 1.23894 + 2.14591i
\(797\) 6717.98 0.298573 0.149287 0.988794i \(-0.452302\pi\)
0.149287 + 0.988794i \(0.452302\pi\)
\(798\) 20499.0 8069.11i 0.909346 0.357949i
\(799\) 3826.05 0.169407
\(800\) −2384.97 4130.90i −0.105402 0.182562i
\(801\) −4516.88 + 7823.46i −0.199246 + 0.345104i
\(802\) 31807.7 55092.5i 1.40046 2.42567i
\(803\) 18633.8 + 32274.8i 0.818897 + 1.41837i
\(804\) −43947.7 −1.92775
\(805\) 6525.61 + 5193.26i 0.285711 + 0.227377i
\(806\) −63636.5 −2.78102
\(807\) −809.683 1402.41i −0.0353187 0.0611738i
\(808\) 16292.2 28218.9i 0.709353 1.22863i
\(809\) 605.364 1048.52i 0.0263083 0.0455674i −0.852571 0.522611i \(-0.824958\pi\)
0.878880 + 0.477043i \(0.158291\pi\)
\(810\) −1033.91 1790.78i −0.0448491 0.0776809i
\(811\) 34825.1 1.50786 0.753930 0.656955i \(-0.228156\pi\)
0.753930 + 0.656955i \(0.228156\pi\)
\(812\) −55857.4 44452.9i −2.41405 1.92117i
\(813\) 12273.4 0.529456
\(814\) −36910.0 63930.0i −1.58931 2.75276i
\(815\) −4757.36 + 8239.99i −0.204470 + 0.354152i
\(816\) −4009.73 + 6945.06i −0.172020 + 0.297948i
\(817\) −11568.1 20036.5i −0.495367 0.858001i
\(818\) 17377.9 0.742792
\(819\) 11000.6 4330.19i 0.469342 0.184749i
\(820\) 22495.1 0.958003
\(821\) −15084.8 26127.7i −0.641247 1.11067i −0.985155 0.171669i \(-0.945084\pi\)
0.343908 0.939003i \(-0.388249\pi\)
\(822\) −2240.25 + 3880.22i −0.0950579 + 0.164645i
\(823\) 13008.2 22530.8i 0.550956 0.954284i −0.447250 0.894409i \(-0.647597\pi\)
0.998206 0.0598746i \(-0.0190701\pi\)
\(824\) 9961.83 + 17254.4i 0.421161 + 0.729472i
\(825\) −3055.16 −0.128930
\(826\) 328.696 2195.75i 0.0138460 0.0924940i
\(827\) 15602.4 0.656045 0.328022 0.944670i \(-0.393618\pi\)
0.328022 + 0.944670i \(0.393618\pi\)
\(828\) 7322.70 + 12683.3i 0.307345 + 0.532336i
\(829\) 9753.00 16892.7i 0.408607 0.707729i −0.586126 0.810220i \(-0.699348\pi\)
0.994734 + 0.102491i \(0.0326812\pi\)
\(830\) 13117.5 22720.1i 0.548570 0.950152i
\(831\) −4637.00 8031.53i −0.193569 0.335271i
\(832\) 2186.96 0.0911289
\(833\) 5689.43 5300.38i 0.236647 0.220465i
\(834\) −25625.8 −1.06397
\(835\) 945.459 + 1637.58i 0.0391844 + 0.0678693i
\(836\) 28579.1 49500.5i 1.18233 2.04786i
\(837\) 2372.34 4109.01i 0.0979690 0.169687i
\(838\) 3514.86 + 6087.91i 0.144891 + 0.250959i
\(839\) −12231.2 −0.503300 −0.251650 0.967818i \(-0.580973\pi\)
−0.251650 + 0.967818i \(0.580973\pi\)
\(840\) −2114.20 + 14123.3i −0.0868417 + 0.580118i
\(841\) 21121.6 0.866028
\(842\) 40226.0 + 69673.5i 1.64641 + 2.85167i
\(843\) −10823.6 + 18747.0i −0.442212 + 0.765933i
\(844\) −19104.6 + 33090.2i −0.779157 + 1.34954i
\(845\) −7083.84 12269.6i −0.288392 0.499510i
\(846\) 7755.25 0.315167
\(847\) 5658.95 2227.55i 0.229568 0.0903654i
\(848\) −12083.2 −0.489314
\(849\) −4447.07 7702.56i −0.179768 0.311368i
\(850\) −1446.83 + 2505.99i −0.0583836 + 0.101123i
\(851\) −15983.0 + 27683.4i −0.643820 + 1.11513i
\(852\) 17141.9 + 29690.6i 0.689286 + 1.19388i
\(853\) 1234.83 0.0495660 0.0247830 0.999693i \(-0.492111\pi\)
0.0247830 + 0.999693i \(0.492111\pi\)
\(854\) 64712.4 + 51500.0i 2.59299 + 2.06357i
\(855\) 3494.64 0.139783
\(856\) −3565.74 6176.05i −0.142377 0.246604i
\(857\) −12050.7 + 20872.4i −0.480331 + 0.831958i −0.999745 0.0225648i \(-0.992817\pi\)
0.519414 + 0.854523i \(0.326150\pi\)
\(858\) 22127.2 38325.4i 0.880431 1.52495i
\(859\) −6681.47 11572.6i −0.265389 0.459666i 0.702277 0.711904i \(-0.252167\pi\)
−0.967665 + 0.252238i \(0.918834\pi\)
\(860\) 26914.5 1.06718
\(861\) −10825.1 8614.91i −0.428476 0.340993i
\(862\) 25955.9 1.02559
\(863\) 10967.0 + 18995.5i 0.432587 + 0.749262i 0.997095 0.0761649i \(-0.0242675\pi\)
−0.564508 + 0.825427i \(0.690934\pi\)
\(864\) −2575.77 + 4461.37i −0.101423 + 0.175670i
\(865\) 1660.09 2875.36i 0.0652541 0.113023i
\(866\) −11823.4 20478.7i −0.463944 0.803574i
\(867\) −13197.2 −0.516956
\(868\) −54717.4 + 21538.6i −2.13966 + 0.842243i
\(869\) 21218.5 0.828296
\(870\) −8169.08 14149.3i −0.318342 0.551385i
\(871\) 28752.5 49800.8i 1.11853 1.93735i
\(872\) 44028.1 76258.8i 1.70984 2.96152i
\(873\) 2878.29 + 4985.35i 0.111587 + 0.193274i
\(874\) −35709.9 −1.38204
\(875\) −342.733 + 2289.52i −0.0132417 + 0.0884571i
\(876\) 49590.4 1.91268
\(877\) 385.159 + 667.115i 0.0148300 + 0.0256863i 0.873345 0.487102i \(-0.161946\pi\)
−0.858515 + 0.512788i \(0.828613\pi\)
\(878\) 5970.80 10341.7i 0.229504 0.397513i
\(879\) 11886.1 20587.4i 0.456097 0.789984i
\(880\) 12008.3 + 20799.1i 0.460001 + 0.796746i
\(881\) 17887.9 0.684064 0.342032 0.939688i \(-0.388885\pi\)
0.342032 + 0.939688i \(0.388885\pi\)
\(882\) 11532.3 10743.7i 0.440262 0.410156i
\(883\) 583.389 0.0222340 0.0111170 0.999938i \(-0.496461\pi\)
0.0111170 + 0.999938i \(0.496461\pi\)
\(884\) −14526.0 25159.8i −0.552672 0.957257i
\(885\) 176.098 305.011i 0.00668866 0.0115851i
\(886\) −30153.0 + 52226.5i −1.14335 + 1.98034i
\(887\) 21221.9 + 36757.4i 0.803340 + 1.39143i 0.917406 + 0.397952i \(0.130279\pi\)
−0.114067 + 0.993473i \(0.536388\pi\)
\(888\) −54736.5 −2.06851
\(889\) −1184.72 + 7914.14i −0.0446953 + 0.298573i
\(890\) 25624.3 0.965087
\(891\) 1649.78 + 2857.51i 0.0620313 + 0.107441i
\(892\) −23293.9 + 40346.2i −0.874370 + 1.51445i
\(893\) −6553.27 + 11350.6i −0.245573 + 0.425345i
\(894\) −19307.3 33441.2i −0.722295 1.25105i
\(895\) −1675.00 −0.0625575
\(896\) −23591.4 + 9286.37i −0.879614 + 0.346245i
\(897\) −19163.3 −0.713317
\(898\) −24462.2 42369.8i −0.909036 1.57450i
\(899\) 18744.3 32466.1i 0.695392 1.20445i
\(900\) −2032.68 + 3520.70i −0.0752844 + 0.130396i
\(901\) 1161.54 + 2011.84i 0.0429483 + 0.0743887i
\(902\) −51788.1 −1.91170
\(903\) −12951.8 10307.4i −0.477307 0.379854i
\(904\) 107096. 3.94021
\(905\) −3063.96 5306.93i −0.112541 0.194926i
\(906\) −10563.6 + 18296.7i −0.387365 + 0.670935i
\(907\) 13858.9 24004.3i 0.507362 0.878777i −0.492602 0.870255i \(-0.663954\pi\)
0.999964 0.00852197i \(-0.00271266\pi\)
\(908\) −26433.2 45783.6i −0.966096 1.67333i
\(909\) −5704.82 −0.208160
\(910\) −26238.6 20881.4i −0.955827 0.760674i
\(911\) 20446.7 0.743609 0.371805 0.928311i \(-0.378739\pi\)
0.371805 + 0.928311i \(0.378739\pi\)
\(912\) −13735.8 23791.0i −0.498724 0.863816i
\(913\) −20931.3 + 36254.0i −0.758734 + 1.31417i
\(914\) 16777.2 29059.0i 0.607156 1.05163i
\(915\) 6559.71 + 11361.8i 0.237003 + 0.410500i
\(916\) −18933.3 −0.682941
\(917\) −11330.8 + 4460.19i −0.408044 + 0.160620i
\(918\) 3125.16 0.112359
\(919\) −8727.76 15116.9i −0.313278 0.542613i 0.665792 0.746137i \(-0.268094\pi\)
−0.979070 + 0.203524i \(0.934760\pi\)
\(920\) 11574.2 20047.2i 0.414773 0.718408i
\(921\) 6100.50 10566.4i 0.218261 0.378039i
\(922\) 10715.8 + 18560.4i 0.382763 + 0.662965i
\(923\) −44859.9 −1.59976
\(924\) 6054.18 40443.1i 0.215550 1.43991i
\(925\) −8873.32 −0.315409
\(926\) 15638.1 + 27086.0i 0.554969 + 0.961234i
\(927\) 1744.10 3020.87i 0.0617949 0.107032i
\(928\) −20351.7 + 35250.1i −0.719909 + 1.24692i
\(929\) −10374.4 17969.0i −0.366387 0.634600i 0.622611 0.782531i \(-0.286072\pi\)
−0.988998 + 0.147931i \(0.952739\pi\)
\(930\) −13458.3 −0.474532
\(931\) 5979.55 + 25957.1i 0.210496 + 0.913760i
\(932\) −69923.8 −2.45754
\(933\) −11478.9 19882.0i −0.402788 0.697650i
\(934\) −8240.83 + 14273.5i −0.288702 + 0.500047i
\(935\) 2308.69 3998.77i 0.0807510 0.139865i
\(936\) −16407.0 28417.8i −0.572948 0.992376i
\(937\) 12135.5 0.423106 0.211553 0.977366i \(-0.432148\pi\)
0.211553 + 0.977366i \(0.432148\pi\)
\(938\) 11350.1 75820.9i 0.395090 2.63928i
\(939\) 5466.36 0.189977
\(940\) −7623.48 13204.3i −0.264522 0.458165i
\(941\) 12633.0 21881.0i 0.437646 0.758025i −0.559862 0.828586i \(-0.689146\pi\)
0.997507 + 0.0705612i \(0.0224790\pi\)
\(942\) −15261.4 + 26433.6i −0.527861 + 0.914282i
\(943\) 11212.8 + 19421.2i 0.387210 + 0.670668i
\(944\) −2768.62 −0.0954566
\(945\) 2326.48 915.781i 0.0800852 0.0315242i
\(946\) −61962.3 −2.12957
\(947\) 21384.4 + 37038.8i 0.733789 + 1.27096i 0.955253 + 0.295791i \(0.0955832\pi\)
−0.221464 + 0.975169i \(0.571083\pi\)
\(948\) 14117.3 24451.8i 0.483657 0.837719i
\(949\) −32444.2 + 56195.0i −1.10978 + 1.92220i
\(950\) −4956.29 8584.54i −0.169267 0.293178i
\(951\) 9446.57 0.322110
\(952\) −16887.7 13439.7i −0.574931 0.457546i
\(953\) −25855.5 −0.878846 −0.439423 0.898280i \(-0.644817\pi\)
−0.439423 + 0.898280i \(0.644817\pi\)
\(954\) 2354.39 + 4077.93i 0.0799017 + 0.138394i
\(955\) 3953.49 6847.65i 0.133960 0.232026i
\(956\) 54753.7 94836.2i 1.85237 3.20839i
\(957\) 13035.3 + 22577.7i 0.440303 + 0.762627i
\(958\) 15962.0 0.538318
\(959\) −4238.94 3373.47i −0.142735 0.113592i
\(960\) 462.515 0.0155496
\(961\) −544.820 943.655i −0.0182881 0.0316758i
\(962\) 64265.7 111311.i 2.15385 3.73059i
\(963\) −624.285 + 1081.29i −0.0208902 + 0.0361830i
\(964\) 37799.8 + 65471.2i 1.26292 + 2.18743i
\(965\) −19473.1 −0.649598
\(966\) −23773.1 + 9357.88i −0.791808 + 0.311682i
\(967\) −20336.0 −0.676278 −0.338139 0.941096i \(-0.609797\pi\)
−0.338139 + 0.941096i \(0.609797\pi\)
\(968\) −8440.13 14618.7i −0.280244 0.485397i
\(969\) −2640.80 + 4573.99i −0.0875486 + 0.151639i
\(970\) 8164.28 14141.0i 0.270247 0.468081i
\(971\) 15561.9 + 26953.9i 0.514319 + 0.890827i 0.999862 + 0.0166139i \(0.00528862\pi\)
−0.485543 + 0.874213i \(0.661378\pi\)
\(972\) 4390.58 0.144885
\(973\) 4587.20 30643.3i 0.151140 1.00964i
\(974\) −4437.05 −0.145967
\(975\) −2659.73 4606.80i −0.0873638 0.151319i
\(976\) 51566.1 89315.1i 1.69118 2.92921i
\(977\) −15658.7 + 27121.6i −0.512758 + 0.888123i 0.487132 + 0.873328i \(0.338043\pi\)
−0.999891 + 0.0147951i \(0.995290\pi\)
\(978\) −14573.8 25242.6i −0.476502 0.825326i
\(979\) −40888.2 −1.33482
\(980\) −29628.7 9073.96i −0.965769 0.295772i
\(981\) −15416.7 −0.501752
\(982\) −16894.0 29261.3i −0.548992 0.950882i
\(983\) 2001.06 3465.94i 0.0649277 0.112458i −0.831734 0.555174i \(-0.812652\pi\)
0.896662 + 0.442716i \(0.145985\pi\)
\(984\) −19200.1 + 33255.5i −0.622028 + 1.07738i
\(985\) −2484.64 4303.53i −0.0803729 0.139210i
\(986\) 24692.5 0.797535
\(987\) −1388.24 + 9273.70i −0.0447702 + 0.299073i
\(988\) 99520.7 3.20463
\(989\) 13415.7 + 23236.6i 0.431338 + 0.747100i
\(990\) 4679.62 8105.34i 0.150230 0.260207i
\(991\) −5021.23 + 8697.02i −0.160953 + 0.278779i −0.935211 0.354091i \(-0.884790\pi\)
0.774258 + 0.632871i \(0.218123\pi\)
\(992\) 16764.4 + 29036.7i 0.536561 + 0.929351i
\(993\) −17568.4 −0.561445
\(994\) −55651.0 + 21906.1i −1.77580 + 0.699013i
\(995\) −15399.4 −0.490647
\(996\) 27852.3 + 48241.6i 0.886078 + 1.53473i
\(997\) 4703.72 8147.08i 0.149417 0.258797i −0.781595 0.623786i \(-0.785594\pi\)
0.931012 + 0.364989i \(0.118927\pi\)
\(998\) 2267.33 3927.13i 0.0719148 0.124560i
\(999\) 4791.59 + 8299.28i 0.151751 + 0.262840i
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 105.4.i.d.46.1 yes 10
3.2 odd 2 315.4.j.h.46.5 10
7.2 even 3 inner 105.4.i.d.16.1 10
7.3 odd 6 735.4.a.z.1.5 5
7.4 even 3 735.4.a.ba.1.5 5
21.2 odd 6 315.4.j.h.226.5 10
21.11 odd 6 2205.4.a.br.1.1 5
21.17 even 6 2205.4.a.bs.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.i.d.16.1 10 7.2 even 3 inner
105.4.i.d.46.1 yes 10 1.1 even 1 trivial
315.4.j.h.46.5 10 3.2 odd 2
315.4.j.h.226.5 10 21.2 odd 6
735.4.a.z.1.5 5 7.3 odd 6
735.4.a.ba.1.5 5 7.4 even 3
2205.4.a.br.1.1 5 21.11 odd 6
2205.4.a.bs.1.1 5 21.17 even 6