Properties

Label 60.5.c.a.31.4
Level $60$
Weight $5$
Character 60.31
Analytic conductor $6.202$
Analytic rank $0$
Dimension $16$
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] = [60,5,Mod(31,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.31");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 60.c (of order \(2\), degree \(1\), 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: \(6.20219778503\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + 25296 x^{8} - 6656 x^{7} - 110848 x^{6} - 227328 x^{5} + 1077248 x^{4} + \cdots + 16777216 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{4}\cdot 5^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 31.4
Root \(-1.14149 - 2.58786i\) of defining polynomial
Character \(\chi\) \(=\) 60.31
Dual form 60.5.c.a.31.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.40825 + 2.09376i) q^{2} +5.19615i q^{3} +(7.23235 - 14.2721i) q^{4} -11.1803 q^{5} +(-10.8795 - 17.7098i) q^{6} -61.3317i q^{7} +(5.23271 + 63.7857i) q^{8} -27.0000 q^{9} +O(q^{10})\) \(q+(-3.40825 + 2.09376i) q^{2} +5.19615i q^{3} +(7.23235 - 14.2721i) q^{4} -11.1803 q^{5} +(-10.8795 - 17.7098i) q^{6} -61.3317i q^{7} +(5.23271 + 63.7857i) q^{8} -27.0000 q^{9} +(38.1054 - 23.4089i) q^{10} -74.1525i q^{11} +(74.1601 + 37.5804i) q^{12} +181.358 q^{13} +(128.414 + 209.034i) q^{14} -58.0948i q^{15} +(-151.386 - 206.442i) q^{16} +516.182 q^{17} +(92.0228 - 56.5315i) q^{18} -407.870i q^{19} +(-80.8601 + 159.567i) q^{20} +318.689 q^{21} +(155.258 + 252.730i) q^{22} +7.48405i q^{23} +(-331.440 + 27.1900i) q^{24} +125.000 q^{25} +(-618.114 + 379.720i) q^{26} -140.296i q^{27} +(-875.333 - 443.572i) q^{28} -1473.47 q^{29} +(121.636 + 198.001i) q^{30} -1041.01i q^{31} +(948.202 + 386.639i) q^{32} +385.308 q^{33} +(-1759.28 + 1080.76i) q^{34} +685.709i q^{35} +(-195.273 + 385.347i) q^{36} -667.800 q^{37} +(853.982 + 1390.12i) q^{38} +942.365i q^{39} +(-58.5035 - 713.146i) q^{40} +1215.10 q^{41} +(-1086.17 + 667.258i) q^{42} -987.639i q^{43} +(-1058.31 - 536.297i) q^{44} +301.869 q^{45} +(-15.6698 - 25.5075i) q^{46} -2943.18i q^{47} +(1072.70 - 786.626i) q^{48} -1360.58 q^{49} +(-426.031 + 261.720i) q^{50} +2682.16i q^{51} +(1311.64 - 2588.36i) q^{52} -2287.61 q^{53} +(293.746 + 478.164i) q^{54} +829.051i q^{55} +(3912.09 - 320.931i) q^{56} +2119.36 q^{57} +(5021.96 - 3085.09i) q^{58} +390.685i q^{59} +(-829.135 - 420.161i) q^{60} +4108.86 q^{61} +(2179.63 + 3548.03i) q^{62} +1655.96i q^{63} +(-4041.24 + 667.545i) q^{64} -2027.65 q^{65} +(-1313.23 + 806.742i) q^{66} +6166.96i q^{67} +(3733.20 - 7367.00i) q^{68} -38.8883 q^{69} +(-1435.71 - 2337.07i) q^{70} -4462.68i q^{71} +(-141.283 - 1722.21i) q^{72} +3369.06 q^{73} +(2276.03 - 1398.21i) q^{74} +649.519i q^{75} +(-5821.17 - 2949.86i) q^{76} -4547.90 q^{77} +(-1973.08 - 3211.81i) q^{78} +7060.25i q^{79} +(1692.55 + 2308.09i) q^{80} +729.000 q^{81} +(-4141.36 + 2544.12i) q^{82} +4972.33i q^{83} +(2304.87 - 4548.36i) q^{84} -5771.09 q^{85} +(2067.88 + 3366.12i) q^{86} -7656.38i q^{87} +(4729.87 - 388.019i) q^{88} -12370.7 q^{89} +(-1028.85 + 632.041i) q^{90} -11123.0i q^{91} +(106.813 + 54.1273i) q^{92} +5409.26 q^{93} +(6162.30 + 10031.1i) q^{94} +4560.13i q^{95} +(-2009.03 + 4927.00i) q^{96} +2516.32 q^{97} +(4637.19 - 2848.72i) q^{98} +2002.12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 12 q^{2} + 26 q^{4} + 18 q^{6} - 180 q^{8} - 432 q^{9} + 50 q^{10} - 352 q^{13} - 804 q^{14} - 190 q^{16} + 324 q^{18} + 600 q^{20} + 288 q^{21} + 436 q^{22} - 1998 q^{24} + 2000 q^{25} - 852 q^{26} - 1156 q^{28} - 3456 q^{29} + 7668 q^{32} + 4772 q^{34} - 702 q^{36} + 9376 q^{37} - 1320 q^{38} + 550 q^{40} + 1248 q^{41} - 324 q^{42} - 6420 q^{44} - 1112 q^{46} - 4176 q^{48} - 3952 q^{49} - 1500 q^{50} + 12704 q^{52} - 5184 q^{53} - 486 q^{54} - 2604 q^{56} - 11232 q^{57} + 12708 q^{58} + 3150 q^{60} - 3808 q^{61} - 16152 q^{62} - 11902 q^{64} + 2400 q^{65} - 2916 q^{66} - 12312 q^{68} + 9792 q^{69} - 17100 q^{70} + 4860 q^{72} + 11040 q^{73} + 30516 q^{74} - 5160 q^{76} - 27456 q^{77} - 3600 q^{78} + 10800 q^{80} + 11664 q^{81} - 54040 q^{82} - 2052 q^{84} - 11200 q^{85} + 39768 q^{86} - 7220 q^{88} + 7584 q^{89} - 1350 q^{90} + 28848 q^{92} + 19872 q^{93} + 49776 q^{94} + 18882 q^{96} - 14496 q^{97} + 23940 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.40825 + 2.09376i −0.852063 + 0.523440i
\(3\) 5.19615i 0.577350i
\(4\) 7.23235 14.2721i 0.452022 0.892007i
\(5\) −11.1803 −0.447214
\(6\) −10.8795 17.7098i −0.302208 0.491939i
\(7\) 61.3317i 1.25167i −0.779956 0.625834i \(-0.784759\pi\)
0.779956 0.625834i \(-0.215241\pi\)
\(8\) 5.23271 + 63.7857i 0.0817612 + 0.996652i
\(9\) −27.0000 −0.333333
\(10\) 38.1054 23.4089i 0.381054 0.234089i
\(11\) 74.1525i 0.612831i −0.951898 0.306415i \(-0.900870\pi\)
0.951898 0.306415i \(-0.0991297\pi\)
\(12\) 74.1601 + 37.5804i 0.515000 + 0.260975i
\(13\) 181.358 1.07313 0.536563 0.843861i \(-0.319723\pi\)
0.536563 + 0.843861i \(0.319723\pi\)
\(14\) 128.414 + 209.034i 0.655173 + 1.06650i
\(15\) 58.0948i 0.258199i
\(16\) −151.386 206.442i −0.591353 0.806413i
\(17\) 516.182 1.78610 0.893048 0.449962i \(-0.148562\pi\)
0.893048 + 0.449962i \(0.148562\pi\)
\(18\) 92.0228 56.5315i 0.284021 0.174480i
\(19\) 407.870i 1.12983i −0.825147 0.564917i \(-0.808908\pi\)
0.825147 0.564917i \(-0.191092\pi\)
\(20\) −80.8601 + 159.567i −0.202150 + 0.398918i
\(21\) 318.689 0.722651
\(22\) 155.258 + 252.730i 0.320780 + 0.522170i
\(23\) 7.48405i 0.0141475i 0.999975 + 0.00707377i \(0.00225167\pi\)
−0.999975 + 0.00707377i \(0.997748\pi\)
\(24\) −331.440 + 27.1900i −0.575417 + 0.0472048i
\(25\) 125.000 0.200000
\(26\) −618.114 + 379.720i −0.914370 + 0.561716i
\(27\) 140.296i 0.192450i
\(28\) −875.333 443.572i −1.11650 0.565781i
\(29\) −1473.47 −1.75205 −0.876023 0.482270i \(-0.839812\pi\)
−0.876023 + 0.482270i \(0.839812\pi\)
\(30\) 121.636 + 198.001i 0.135152 + 0.220002i
\(31\) 1041.01i 1.08326i −0.840617 0.541630i \(-0.817808\pi\)
0.840617 0.541630i \(-0.182192\pi\)
\(32\) 948.202 + 386.639i 0.925978 + 0.377577i
\(33\) 385.308 0.353818
\(34\) −1759.28 + 1080.76i −1.52187 + 0.934913i
\(35\) 685.709i 0.559763i
\(36\) −195.273 + 385.347i −0.150674 + 0.297336i
\(37\) −667.800 −0.487802 −0.243901 0.969800i \(-0.578427\pi\)
−0.243901 + 0.969800i \(0.578427\pi\)
\(38\) 853.982 + 1390.12i 0.591400 + 0.962690i
\(39\) 942.365i 0.619569i
\(40\) −58.5035 713.146i −0.0365647 0.445716i
\(41\) 1215.10 0.722842 0.361421 0.932403i \(-0.382292\pi\)
0.361421 + 0.932403i \(0.382292\pi\)
\(42\) −1086.17 + 667.258i −0.615744 + 0.378264i
\(43\) 987.639i 0.534148i −0.963676 0.267074i \(-0.913943\pi\)
0.963676 0.267074i \(-0.0860568\pi\)
\(44\) −1058.31 536.297i −0.546649 0.277013i
\(45\) 301.869 0.149071
\(46\) −15.6698 25.5075i −0.00740539 0.0120546i
\(47\) 2943.18i 1.33236i −0.745792 0.666178i \(-0.767929\pi\)
0.745792 0.666178i \(-0.232071\pi\)
\(48\) 1072.70 786.626i 0.465583 0.341418i
\(49\) −1360.58 −0.566672
\(50\) −426.031 + 261.720i −0.170413 + 0.104688i
\(51\) 2682.16i 1.03120i
\(52\) 1311.64 2588.36i 0.485076 0.957235i
\(53\) −2287.61 −0.814384 −0.407192 0.913343i \(-0.633492\pi\)
−0.407192 + 0.913343i \(0.633492\pi\)
\(54\) 293.746 + 478.164i 0.100736 + 0.163980i
\(55\) 829.051i 0.274066i
\(56\) 3912.09 320.931i 1.24748 0.102338i
\(57\) 2119.36 0.652310
\(58\) 5021.96 3085.09i 1.49285 0.917090i
\(59\) 390.685i 0.112234i 0.998424 + 0.0561168i \(0.0178719\pi\)
−0.998424 + 0.0561168i \(0.982128\pi\)
\(60\) −829.135 420.161i −0.230315 0.116711i
\(61\) 4108.86 1.10424 0.552118 0.833766i \(-0.313820\pi\)
0.552118 + 0.833766i \(0.313820\pi\)
\(62\) 2179.63 + 3548.03i 0.567021 + 0.923005i
\(63\) 1655.96i 0.417223i
\(64\) −4041.24 + 667.545i −0.986630 + 0.162975i
\(65\) −2027.65 −0.479916
\(66\) −1313.23 + 806.742i −0.301475 + 0.185202i
\(67\) 6166.96i 1.37379i 0.726755 + 0.686897i \(0.241028\pi\)
−0.726755 + 0.686897i \(0.758972\pi\)
\(68\) 3733.20 7367.00i 0.807354 1.59321i
\(69\) −38.8883 −0.00816809
\(70\) −1435.71 2337.07i −0.293002 0.476953i
\(71\) 4462.68i 0.885276i −0.896700 0.442638i \(-0.854043\pi\)
0.896700 0.442638i \(-0.145957\pi\)
\(72\) −141.283 1722.21i −0.0272537 0.332217i
\(73\) 3369.06 0.632213 0.316106 0.948724i \(-0.397624\pi\)
0.316106 + 0.948724i \(0.397624\pi\)
\(74\) 2276.03 1398.21i 0.415638 0.255335i
\(75\) 649.519i 0.115470i
\(76\) −5821.17 2949.86i −1.00782 0.510710i
\(77\) −4547.90 −0.767061
\(78\) −1973.08 3211.81i −0.324307 0.527912i
\(79\) 7060.25i 1.13127i 0.824656 + 0.565635i \(0.191369\pi\)
−0.824656 + 0.565635i \(0.808631\pi\)
\(80\) 1692.55 + 2308.09i 0.264461 + 0.360639i
\(81\) 729.000 0.111111
\(82\) −4141.36 + 2544.12i −0.615907 + 0.378364i
\(83\) 4972.33i 0.721777i 0.932609 + 0.360889i \(0.117527\pi\)
−0.932609 + 0.360889i \(0.882473\pi\)
\(84\) 2304.87 4548.36i 0.326654 0.644609i
\(85\) −5771.09 −0.798766
\(86\) 2067.88 + 3366.12i 0.279594 + 0.455127i
\(87\) 7656.38i 1.01154i
\(88\) 4729.87 388.019i 0.610779 0.0501058i
\(89\) −12370.7 −1.56175 −0.780877 0.624685i \(-0.785227\pi\)
−0.780877 + 0.624685i \(0.785227\pi\)
\(90\) −1028.85 + 632.041i −0.127018 + 0.0780298i
\(91\) 11123.0i 1.34320i
\(92\) 106.813 + 54.1273i 0.0126197 + 0.00639500i
\(93\) 5409.26 0.625420
\(94\) 6162.30 + 10031.1i 0.697408 + 1.13525i
\(95\) 4560.13i 0.505277i
\(96\) −2009.03 + 4927.00i −0.217994 + 0.534614i
\(97\) 2516.32 0.267438 0.133719 0.991019i \(-0.457308\pi\)
0.133719 + 0.991019i \(0.457308\pi\)
\(98\) 4637.19 2848.72i 0.482840 0.296619i
\(99\) 2002.12i 0.204277i
\(100\) 904.043 1784.01i 0.0904043 0.178401i
\(101\) −2974.94 −0.291632 −0.145816 0.989312i \(-0.546581\pi\)
−0.145816 + 0.989312i \(0.546581\pi\)
\(102\) −5615.79 9141.47i −0.539773 0.878649i
\(103\) 17963.5i 1.69323i 0.532202 + 0.846617i \(0.321365\pi\)
−0.532202 + 0.846617i \(0.678635\pi\)
\(104\) 948.995 + 11568.1i 0.0877399 + 1.06953i
\(105\) −3563.05 −0.323179
\(106\) 7796.73 4789.69i 0.693906 0.426281i
\(107\) 1200.48i 0.104854i 0.998625 + 0.0524272i \(0.0166958\pi\)
−0.998625 + 0.0524272i \(0.983304\pi\)
\(108\) −2002.32 1014.67i −0.171667 0.0869916i
\(109\) 16500.9 1.38884 0.694422 0.719568i \(-0.255660\pi\)
0.694422 + 0.719568i \(0.255660\pi\)
\(110\) −1735.83 2825.61i −0.143457 0.233522i
\(111\) 3469.99i 0.281632i
\(112\) −12661.4 + 9284.78i −1.00936 + 0.740177i
\(113\) −6037.80 −0.472849 −0.236424 0.971650i \(-0.575976\pi\)
−0.236424 + 0.971650i \(0.575976\pi\)
\(114\) −7223.30 + 4437.42i −0.555809 + 0.341445i
\(115\) 83.6742i 0.00632697i
\(116\) −10656.6 + 21029.5i −0.791962 + 1.56284i
\(117\) −4896.67 −0.357708
\(118\) −818.000 1331.55i −0.0587475 0.0956300i
\(119\) 31658.3i 2.23560i
\(120\) 3705.62 303.993i 0.257334 0.0211106i
\(121\) 9142.40 0.624438
\(122\) −14004.0 + 8602.97i −0.940878 + 0.578001i
\(123\) 6313.83i 0.417333i
\(124\) −14857.4 7528.96i −0.966275 0.489657i
\(125\) −1397.54 −0.0894427
\(126\) −3467.17 5643.91i −0.218391 0.355500i
\(127\) 17483.7i 1.08399i −0.840382 0.541995i \(-0.817669\pi\)
0.840382 0.541995i \(-0.182331\pi\)
\(128\) 12375.9 10736.5i 0.755363 0.655306i
\(129\) 5131.92 0.308390
\(130\) 6910.72 4245.40i 0.408919 0.251207i
\(131\) 10698.3i 0.623408i −0.950179 0.311704i \(-0.899100\pi\)
0.950179 0.311704i \(-0.100900\pi\)
\(132\) 2786.68 5499.16i 0.159933 0.315608i
\(133\) −25015.4 −1.41418
\(134\) −12912.1 21018.6i −0.719099 1.17056i
\(135\) 1568.56i 0.0860663i
\(136\) 2701.03 + 32925.0i 0.146033 + 1.78012i
\(137\) 31259.4 1.66548 0.832740 0.553665i \(-0.186771\pi\)
0.832740 + 0.553665i \(0.186771\pi\)
\(138\) 132.541 81.4227i 0.00695972 0.00427550i
\(139\) 22483.1i 1.16366i 0.813310 + 0.581831i \(0.197663\pi\)
−0.813310 + 0.581831i \(0.802337\pi\)
\(140\) 9786.52 + 4959.29i 0.499312 + 0.253025i
\(141\) 15293.2 0.769236
\(142\) 9343.77 + 15209.9i 0.463389 + 0.754311i
\(143\) 13448.2i 0.657644i
\(144\) 4087.43 + 5573.93i 0.197118 + 0.268804i
\(145\) 16473.9 0.783539
\(146\) −11482.6 + 7054.01i −0.538685 + 0.330925i
\(147\) 7069.78i 0.327168i
\(148\) −4829.76 + 9530.92i −0.220497 + 0.435122i
\(149\) 19244.0 0.866808 0.433404 0.901200i \(-0.357312\pi\)
0.433404 + 0.901200i \(0.357312\pi\)
\(150\) −1359.94 2213.72i −0.0604416 0.0983877i
\(151\) 42406.7i 1.85986i −0.367735 0.929931i \(-0.619867\pi\)
0.367735 0.929931i \(-0.380133\pi\)
\(152\) 26016.3 2134.27i 1.12605 0.0923766i
\(153\) −13936.9 −0.595365
\(154\) 15500.4 9522.21i 0.653584 0.401510i
\(155\) 11638.9i 0.484448i
\(156\) 13449.5 + 6815.51i 0.552660 + 0.280059i
\(157\) 13979.2 0.567129 0.283565 0.958953i \(-0.408483\pi\)
0.283565 + 0.958953i \(0.408483\pi\)
\(158\) −14782.5 24063.1i −0.592151 0.963913i
\(159\) 11886.7i 0.470185i
\(160\) −10601.2 4322.75i −0.414110 0.168857i
\(161\) 459.010 0.0177080
\(162\) −2484.61 + 1526.35i −0.0946736 + 0.0581600i
\(163\) 31094.2i 1.17032i 0.810919 + 0.585159i \(0.198968\pi\)
−0.810919 + 0.585159i \(0.801032\pi\)
\(164\) 8788.00 17342.0i 0.326740 0.644780i
\(165\) −4307.87 −0.158232
\(166\) −10410.9 16946.9i −0.377807 0.615000i
\(167\) 30204.9i 1.08304i 0.840687 + 0.541521i \(0.182151\pi\)
−0.840687 + 0.541521i \(0.817849\pi\)
\(168\) 1667.61 + 20327.8i 0.0590847 + 0.720231i
\(169\) 4329.78 0.151598
\(170\) 19669.3 12083.3i 0.680599 0.418106i
\(171\) 11012.5i 0.376612i
\(172\) −14095.7 7142.95i −0.476463 0.241446i
\(173\) −22061.5 −0.737128 −0.368564 0.929602i \(-0.620150\pi\)
−0.368564 + 0.929602i \(0.620150\pi\)
\(174\) 16030.6 + 26094.8i 0.529482 + 0.861899i
\(175\) 7666.46i 0.250334i
\(176\) −15308.2 + 11225.7i −0.494195 + 0.362399i
\(177\) −2030.06 −0.0647981
\(178\) 42162.3 25901.2i 1.33071 0.817484i
\(179\) 4300.24i 0.134210i −0.997746 0.0671052i \(-0.978624\pi\)
0.997746 0.0671052i \(-0.0213763\pi\)
\(180\) 2183.22 4308.31i 0.0673834 0.132973i
\(181\) −32288.1 −0.985566 −0.492783 0.870152i \(-0.664020\pi\)
−0.492783 + 0.870152i \(0.664020\pi\)
\(182\) 23288.9 + 37910.0i 0.703082 + 1.14449i
\(183\) 21350.3i 0.637531i
\(184\) −477.376 + 39.1619i −0.0141002 + 0.00115672i
\(185\) 7466.24 0.218152
\(186\) −18436.1 + 11325.7i −0.532897 + 0.327370i
\(187\) 38276.2i 1.09457i
\(188\) −42005.3 21286.1i −1.18847 0.602254i
\(189\) −8604.60 −0.240884
\(190\) −9547.81 15542.1i −0.264482 0.430528i
\(191\) 23139.2i 0.634279i 0.948379 + 0.317140i \(0.102722\pi\)
−0.948379 + 0.317140i \(0.897278\pi\)
\(192\) −3468.66 20998.9i −0.0940936 0.569631i
\(193\) −64774.6 −1.73896 −0.869481 0.493966i \(-0.835547\pi\)
−0.869481 + 0.493966i \(0.835547\pi\)
\(194\) −8576.25 + 5268.57i −0.227874 + 0.139988i
\(195\) 10536.0i 0.277080i
\(196\) −9840.18 + 19418.3i −0.256148 + 0.505475i
\(197\) 317.341 0.00817699 0.00408850 0.999992i \(-0.498699\pi\)
0.00408850 + 0.999992i \(0.498699\pi\)
\(198\) −4191.95 6823.72i −0.106927 0.174057i
\(199\) 18051.2i 0.455828i −0.973681 0.227914i \(-0.926810\pi\)
0.973681 0.227914i \(-0.0731905\pi\)
\(200\) 654.089 + 7973.22i 0.0163522 + 0.199330i
\(201\) −32044.5 −0.793161
\(202\) 10139.3 6228.80i 0.248489 0.152652i
\(203\) 90370.5i 2.19298i
\(204\) 38280.1 + 19398.3i 0.919840 + 0.466126i
\(205\) −13585.2 −0.323265
\(206\) −37611.3 61224.2i −0.886306 1.44274i
\(207\) 202.069i 0.00471585i
\(208\) −27455.1 37439.9i −0.634596 0.865382i
\(209\) −30244.6 −0.692398
\(210\) 12143.8 7460.17i 0.275369 0.169165i
\(211\) 62848.8i 1.41167i 0.708378 + 0.705833i \(0.249427\pi\)
−0.708378 + 0.705833i \(0.750573\pi\)
\(212\) −16544.8 + 32649.0i −0.368119 + 0.726436i
\(213\) 23188.8 0.511115
\(214\) −2513.51 4091.53i −0.0548850 0.0893426i
\(215\) 11042.1i 0.238878i
\(216\) 8948.89 734.129i 0.191806 0.0157349i
\(217\) −63847.1 −1.35588
\(218\) −56239.1 + 34548.8i −1.18338 + 0.726976i
\(219\) 17506.2i 0.365008i
\(220\) 11832.3 + 5995.98i 0.244469 + 0.123884i
\(221\) 93613.7 1.91670
\(222\) 7265.33 + 11826.6i 0.147418 + 0.239968i
\(223\) 60726.4i 1.22115i −0.791960 0.610573i \(-0.790939\pi\)
0.791960 0.610573i \(-0.209061\pi\)
\(224\) 23713.2 58154.8i 0.472601 1.15902i
\(225\) −3375.00 −0.0666667
\(226\) 20578.4 12641.7i 0.402897 0.247508i
\(227\) 98629.1i 1.91405i 0.290006 + 0.957025i \(0.406343\pi\)
−0.290006 + 0.957025i \(0.593657\pi\)
\(228\) 15327.9 30247.7i 0.294858 0.581865i
\(229\) 56329.9 1.07416 0.537079 0.843532i \(-0.319528\pi\)
0.537079 + 0.843532i \(0.319528\pi\)
\(230\) 175.194 + 285.183i 0.00331179 + 0.00539098i
\(231\) 23631.6i 0.442863i
\(232\) −7710.25 93986.4i −0.143249 1.74618i
\(233\) 52509.1 0.967215 0.483608 0.875285i \(-0.339326\pi\)
0.483608 + 0.875285i \(0.339326\pi\)
\(234\) 16689.1 10252.4i 0.304790 0.187239i
\(235\) 32905.7i 0.595848i
\(236\) 5575.90 + 2825.57i 0.100113 + 0.0507320i
\(237\) −36686.2 −0.653139
\(238\) 66284.9 + 107899.i 1.17020 + 1.90487i
\(239\) 51142.5i 0.895336i −0.894200 0.447668i \(-0.852255\pi\)
0.894200 0.447668i \(-0.147745\pi\)
\(240\) −11993.2 + 8794.75i −0.208215 + 0.152687i
\(241\) 7.06147 0.000121580 6.07899e−5 1.00000i \(-0.499981\pi\)
6.07899e−5 1.00000i \(0.499981\pi\)
\(242\) −31159.6 + 19142.0i −0.532061 + 0.326856i
\(243\) 3788.00i 0.0641500i
\(244\) 29716.7 58642.1i 0.499139 0.984986i
\(245\) 15211.7 0.253423
\(246\) −13219.6 21519.1i −0.218449 0.355594i
\(247\) 73970.6i 1.21245i
\(248\) 66401.7 5447.32i 1.07963 0.0885685i
\(249\) −25837.0 −0.416718
\(250\) 4763.18 2926.12i 0.0762108 0.0468179i
\(251\) 60466.9i 0.959776i −0.877330 0.479888i \(-0.840677\pi\)
0.877330 0.479888i \(-0.159323\pi\)
\(252\) 23634.0 + 11976.4i 0.372165 + 0.188594i
\(253\) 554.961 0.00867005
\(254\) 36606.6 + 59588.7i 0.567403 + 0.923627i
\(255\) 29987.4i 0.461168i
\(256\) −19700.4 + 62504.9i −0.300604 + 0.953749i
\(257\) 38335.4 0.580408 0.290204 0.956965i \(-0.406277\pi\)
0.290204 + 0.956965i \(0.406277\pi\)
\(258\) −17490.9 + 10745.0i −0.262768 + 0.161424i
\(259\) 40957.3i 0.610566i
\(260\) −14664.6 + 28938.8i −0.216932 + 0.428089i
\(261\) 39783.7 0.584015
\(262\) 22399.7 + 36462.5i 0.326316 + 0.531183i
\(263\) 38851.9i 0.561696i −0.959752 0.280848i \(-0.909384\pi\)
0.959752 0.280848i \(-0.0906156\pi\)
\(264\) 2016.21 + 24577.1i 0.0289286 + 0.352634i
\(265\) 25576.2 0.364204
\(266\) 85258.7 52376.2i 1.20497 0.740237i
\(267\) 64279.8i 0.901679i
\(268\) 88015.6 + 44601.6i 1.22543 + 0.620985i
\(269\) −18724.5 −0.258765 −0.129382 0.991595i \(-0.541299\pi\)
−0.129382 + 0.991595i \(0.541299\pi\)
\(270\) −3284.18 5346.04i −0.0450505 0.0733339i
\(271\) 25639.5i 0.349117i 0.984647 + 0.174559i \(0.0558499\pi\)
−0.984647 + 0.174559i \(0.944150\pi\)
\(272\) −78142.8 106561.i −1.05621 1.44033i
\(273\) 57796.8 0.775495
\(274\) −106540. + 65449.6i −1.41909 + 0.871778i
\(275\) 9269.07i 0.122566i
\(276\) −281.253 + 555.018i −0.00369215 + 0.00728599i
\(277\) −69695.7 −0.908335 −0.454168 0.890916i \(-0.650063\pi\)
−0.454168 + 0.890916i \(0.650063\pi\)
\(278\) −47074.2 76628.1i −0.609107 0.991513i
\(279\) 28107.3i 0.361086i
\(280\) −43738.5 + 3588.12i −0.557889 + 0.0457668i
\(281\) −69900.0 −0.885248 −0.442624 0.896707i \(-0.645952\pi\)
−0.442624 + 0.896707i \(0.645952\pi\)
\(282\) −52123.0 + 32020.3i −0.655438 + 0.402649i
\(283\) 107624.i 1.34381i −0.740637 0.671905i \(-0.765476\pi\)
0.740637 0.671905i \(-0.234524\pi\)
\(284\) −63691.8 32275.6i −0.789673 0.400164i
\(285\) −23695.1 −0.291722
\(286\) 28157.2 + 45834.7i 0.344237 + 0.560354i
\(287\) 74524.0i 0.904758i
\(288\) −25601.4 10439.2i −0.308659 0.125859i
\(289\) 182922. 2.19014
\(290\) −56147.2 + 34492.4i −0.667624 + 0.410135i
\(291\) 13075.2i 0.154405i
\(292\) 24366.2 48083.6i 0.285774 0.563938i
\(293\) 21779.0 0.253689 0.126845 0.991923i \(-0.459515\pi\)
0.126845 + 0.991923i \(0.459515\pi\)
\(294\) 14802.4 + 24095.6i 0.171253 + 0.278768i
\(295\) 4367.99i 0.0501924i
\(296\) −3494.41 42596.1i −0.0398832 0.486168i
\(297\) −10403.3 −0.117939
\(298\) −65588.4 + 40292.3i −0.738574 + 0.453722i
\(299\) 1357.29i 0.0151821i
\(300\) 9270.01 + 4697.55i 0.103000 + 0.0521950i
\(301\) −60573.6 −0.668575
\(302\) 88789.4 + 144533.i 0.973525 + 1.58472i
\(303\) 15458.2i 0.168374i
\(304\) −84201.5 + 61746.0i −0.911113 + 0.668131i
\(305\) −45938.5 −0.493829
\(306\) 47500.5 29180.5i 0.507288 0.311638i
\(307\) 129208.i 1.37092i 0.728111 + 0.685460i \(0.240399\pi\)
−0.728111 + 0.685460i \(0.759601\pi\)
\(308\) −32892.0 + 64908.2i −0.346728 + 0.684223i
\(309\) −93341.2 −0.977590
\(310\) −24369.0 39668.2i −0.253580 0.412780i
\(311\) 39962.2i 0.413170i 0.978429 + 0.206585i \(0.0662351\pi\)
−0.978429 + 0.206585i \(0.933765\pi\)
\(312\) −60109.4 + 4931.12i −0.617495 + 0.0506567i
\(313\) 99259.1 1.01317 0.506584 0.862191i \(-0.330908\pi\)
0.506584 + 0.862191i \(0.330908\pi\)
\(314\) −47644.5 + 29269.0i −0.483230 + 0.296858i
\(315\) 18514.2i 0.186588i
\(316\) 100765. + 51062.2i 1.00910 + 0.511358i
\(317\) 92350.2 0.919008 0.459504 0.888176i \(-0.348027\pi\)
0.459504 + 0.888176i \(0.348027\pi\)
\(318\) 24888.0 + 40513.0i 0.246114 + 0.400627i
\(319\) 109262.i 1.07371i
\(320\) 45182.4 7463.38i 0.441234 0.0728846i
\(321\) −6237.87 −0.0605378
\(322\) −1564.42 + 961.056i −0.0150883 + 0.00926908i
\(323\) 210535.i 2.01799i
\(324\) 5272.38 10404.4i 0.0502246 0.0991119i
\(325\) 22669.8 0.214625
\(326\) −65103.7 105977.i −0.612591 0.997184i
\(327\) 85741.0i 0.801850i
\(328\) 6358.25 + 77505.8i 0.0591004 + 0.720422i
\(329\) −180510. −1.66767
\(330\) 14682.3 9019.65i 0.134824 0.0828251i
\(331\) 37376.0i 0.341143i 0.985345 + 0.170572i \(0.0545614\pi\)
−0.985345 + 0.170572i \(0.945439\pi\)
\(332\) 70965.6 + 35961.6i 0.643831 + 0.326259i
\(333\) 18030.6 0.162601
\(334\) −63241.9 102946.i −0.566907 0.922819i
\(335\) 68948.7i 0.614380i
\(336\) −48245.2 65790.7i −0.427342 0.582755i
\(337\) 119047. 1.04824 0.524118 0.851645i \(-0.324395\pi\)
0.524118 + 0.851645i \(0.324395\pi\)
\(338\) −14757.0 + 9065.51i −0.129171 + 0.0793522i
\(339\) 31373.4i 0.272999i
\(340\) −41738.5 + 82365.6i −0.361060 + 0.712505i
\(341\) −77193.7 −0.663855
\(342\) −23057.5 37533.4i −0.197133 0.320897i
\(343\) 63810.8i 0.542383i
\(344\) 62997.3 5168.03i 0.532359 0.0436725i
\(345\) 434.784 0.00365288
\(346\) 75191.1 46191.5i 0.628079 0.385842i
\(347\) 84780.6i 0.704105i 0.935980 + 0.352052i \(0.114516\pi\)
−0.935980 + 0.352052i \(0.885484\pi\)
\(348\) −109273. 55373.6i −0.902304 0.457240i
\(349\) −171629. −1.40909 −0.704545 0.709659i \(-0.748849\pi\)
−0.704545 + 0.709659i \(0.748849\pi\)
\(350\) 16051.7 + 26129.2i 0.131035 + 0.213300i
\(351\) 25443.8i 0.206523i
\(352\) 28670.2 70311.6i 0.231391 0.567468i
\(353\) 195140. 1.56602 0.783010 0.622009i \(-0.213683\pi\)
0.783010 + 0.622009i \(0.213683\pi\)
\(354\) 6918.95 4250.45i 0.0552120 0.0339179i
\(355\) 49894.3i 0.395908i
\(356\) −89468.9 + 176555.i −0.705947 + 1.39310i
\(357\) 164501. 1.29072
\(358\) 9003.66 + 14656.3i 0.0702511 + 0.114356i
\(359\) 50318.4i 0.390426i −0.980761 0.195213i \(-0.937460\pi\)
0.980761 0.195213i \(-0.0625398\pi\)
\(360\) 1579.59 + 19254.9i 0.0121882 + 0.148572i
\(361\) −36037.2 −0.276527
\(362\) 110046. 67603.6i 0.839764 0.515884i
\(363\) 47505.3i 0.360520i
\(364\) −158749. 80445.4i −1.19814 0.607154i
\(365\) −37667.3 −0.282734
\(366\) −44702.3 72767.1i −0.333709 0.543216i
\(367\) 50718.2i 0.376558i 0.982116 + 0.188279i \(0.0602909\pi\)
−0.982116 + 0.188279i \(0.939709\pi\)
\(368\) 1545.02 1132.98i 0.0114088 0.00836619i
\(369\) −32807.6 −0.240947
\(370\) −25446.8 + 15632.5i −0.185879 + 0.114189i
\(371\) 140303.i 1.01934i
\(372\) 39121.6 77201.5i 0.282703 0.557879i
\(373\) −119570. −0.859417 −0.429709 0.902968i \(-0.641384\pi\)
−0.429709 + 0.902968i \(0.641384\pi\)
\(374\) 80141.1 + 130455.i 0.572944 + 0.932646i
\(375\) 7261.84i 0.0516398i
\(376\) 187733. 15400.8i 1.32790 0.108935i
\(377\) −267226. −1.88016
\(378\) 29326.6 18016.0i 0.205248 0.126088i
\(379\) 104060.i 0.724447i 0.932091 + 0.362223i \(0.117982\pi\)
−0.932091 + 0.362223i \(0.882018\pi\)
\(380\) 65082.7 + 32980.4i 0.450711 + 0.228396i
\(381\) 90847.8 0.625842
\(382\) −48447.8 78864.0i −0.332007 0.540446i
\(383\) 72442.8i 0.493853i 0.969034 + 0.246926i \(0.0794206\pi\)
−0.969034 + 0.246926i \(0.920579\pi\)
\(384\) 55788.7 + 64306.9i 0.378341 + 0.436109i
\(385\) 50847.1 0.343040
\(386\) 220768. 135622.i 1.48171 0.910242i
\(387\) 26666.3i 0.178049i
\(388\) 18198.9 35913.2i 0.120888 0.238556i
\(389\) −162511. −1.07395 −0.536975 0.843598i \(-0.680433\pi\)
−0.536975 + 0.843598i \(0.680433\pi\)
\(390\) 22059.8 + 35909.2i 0.145035 + 0.236089i
\(391\) 3863.13i 0.0252689i
\(392\) −7119.52 86785.5i −0.0463317 0.564775i
\(393\) 55590.0 0.359925
\(394\) −1081.58 + 664.435i −0.00696731 + 0.00428016i
\(395\) 78936.0i 0.505919i
\(396\) 28574.5 + 14480.0i 0.182216 + 0.0923376i
\(397\) 53291.6 0.338125 0.169063 0.985605i \(-0.445926\pi\)
0.169063 + 0.985605i \(0.445926\pi\)
\(398\) 37794.9 + 61523.1i 0.238598 + 0.388394i
\(399\) 129984.i 0.816476i
\(400\) −18923.3 25805.2i −0.118271 0.161283i
\(401\) −33793.7 −0.210159 −0.105079 0.994464i \(-0.533510\pi\)
−0.105079 + 0.994464i \(0.533510\pi\)
\(402\) 109216. 67093.4i 0.675823 0.415172i
\(403\) 188796.i 1.16247i
\(404\) −21515.8 + 42458.6i −0.131824 + 0.260138i
\(405\) −8150.47 −0.0496904
\(406\) −189214. 308005.i −1.14789 1.86856i
\(407\) 49519.1i 0.298940i
\(408\) −171083. + 14035.0i −1.02775 + 0.0843123i
\(409\) 192978. 1.15361 0.576807 0.816881i \(-0.304299\pi\)
0.576807 + 0.816881i \(0.304299\pi\)
\(410\) 46301.8 28444.1i 0.275442 0.169210i
\(411\) 162429.i 0.961565i
\(412\) 256377. + 129918.i 1.51038 + 0.765379i
\(413\) 23961.4 0.140479
\(414\) 423.085 + 688.703i 0.00246846 + 0.00401820i
\(415\) 55592.3i 0.322789i
\(416\) 171964. + 70120.1i 0.993691 + 0.405187i
\(417\) −116826. −0.671840
\(418\) 103081. 63325.0i 0.589966 0.362428i
\(419\) 207731.i 1.18324i 0.806216 + 0.591621i \(0.201512\pi\)
−0.806216 + 0.591621i \(0.798488\pi\)
\(420\) −25769.2 + 50852.3i −0.146084 + 0.288278i
\(421\) −135957. −0.767075 −0.383538 0.923525i \(-0.625294\pi\)
−0.383538 + 0.923525i \(0.625294\pi\)
\(422\) −131590. 214204.i −0.738922 1.20283i
\(423\) 79465.8i 0.444119i
\(424\) −11970.4 145917.i −0.0665850 0.811658i
\(425\) 64522.7 0.357219
\(426\) −79033.1 + 48551.7i −0.435502 + 0.267538i
\(427\) 252004.i 1.38214i
\(428\) 17133.4 + 8682.28i 0.0935309 + 0.0473965i
\(429\) 69878.7 0.379691
\(430\) −23119.6 37634.4i −0.125038 0.203539i
\(431\) 151994.i 0.818222i 0.912485 + 0.409111i \(0.134161\pi\)
−0.912485 + 0.409111i \(0.865839\pi\)
\(432\) −28963.0 + 21238.9i −0.155194 + 0.113806i
\(433\) −36457.2 −0.194450 −0.0972249 0.995262i \(-0.530997\pi\)
−0.0972249 + 0.995262i \(0.530997\pi\)
\(434\) 217607. 133680.i 1.15530 0.709722i
\(435\) 85600.9i 0.452376i
\(436\) 119340. 235502.i 0.627788 1.23886i
\(437\) 3052.52 0.0159844
\(438\) −36653.7 59665.4i −0.191060 0.311010i
\(439\) 118065.i 0.612620i 0.951932 + 0.306310i \(0.0990944\pi\)
−0.951932 + 0.306310i \(0.900906\pi\)
\(440\) −52881.6 + 4338.18i −0.273149 + 0.0224080i
\(441\) 36735.6 0.188891
\(442\) −319059. + 196005.i −1.63315 + 1.00328i
\(443\) 113592.i 0.578817i −0.957206 0.289409i \(-0.906541\pi\)
0.957206 0.289409i \(-0.0934587\pi\)
\(444\) −49524.1 25096.2i −0.251218 0.127304i
\(445\) 138308. 0.698438
\(446\) 127146. + 206971.i 0.639196 + 1.04049i
\(447\) 99994.7i 0.500452i
\(448\) 40941.7 + 247856.i 0.203990 + 1.23493i
\(449\) −1745.18 −0.00865662 −0.00432831 0.999991i \(-0.501378\pi\)
−0.00432831 + 0.999991i \(0.501378\pi\)
\(450\) 11502.8 7066.44i 0.0568042 0.0348960i
\(451\) 90102.5i 0.442980i
\(452\) −43667.5 + 86172.2i −0.213738 + 0.421784i
\(453\) 220352. 1.07379
\(454\) −206506. 336153.i −1.00189 1.63089i
\(455\) 124359.i 0.600696i
\(456\) 11090.0 + 135185.i 0.0533337 + 0.650126i
\(457\) −74606.1 −0.357225 −0.178613 0.983919i \(-0.557161\pi\)
−0.178613 + 0.983919i \(0.557161\pi\)
\(458\) −191987. + 117941.i −0.915250 + 0.562257i
\(459\) 72418.3i 0.343734i
\(460\) −1194.21 605.161i −0.00564371 0.00285993i
\(461\) 17305.9 0.0814314 0.0407157 0.999171i \(-0.487036\pi\)
0.0407157 + 0.999171i \(0.487036\pi\)
\(462\) 49478.9 + 80542.4i 0.231812 + 0.377347i
\(463\) 124639.i 0.581422i 0.956811 + 0.290711i \(0.0938918\pi\)
−0.956811 + 0.290711i \(0.906108\pi\)
\(464\) 223063. + 304186.i 1.03608 + 1.41287i
\(465\) −60477.3 −0.279696
\(466\) −178964. + 109941.i −0.824128 + 0.506279i
\(467\) 208541.i 0.956219i −0.878300 0.478110i \(-0.841322\pi\)
0.878300 0.478110i \(-0.158678\pi\)
\(468\) −35414.4 + 69885.8i −0.161692 + 0.319078i
\(469\) 378230. 1.71953
\(470\) −68896.6 112151.i −0.311891 0.507700i
\(471\) 72637.9i 0.327432i
\(472\) −24920.1 + 2044.34i −0.111858 + 0.00917634i
\(473\) −73235.9 −0.327342
\(474\) 125036. 76812.0i 0.556515 0.341879i
\(475\) 50983.8i 0.225967i
\(476\) −451831. 228964.i −1.99417 1.01054i
\(477\) 61765.3 0.271461
\(478\) 107080. + 174306.i 0.468654 + 0.762882i
\(479\) 399291.i 1.74028i −0.492805 0.870140i \(-0.664028\pi\)
0.492805 0.870140i \(-0.335972\pi\)
\(480\) 22461.7 55085.5i 0.0974899 0.239087i
\(481\) −121111. −0.523472
\(482\) −24.0673 + 14.7850i −0.000103594 + 6.36397e-5i
\(483\) 2385.08i 0.0102237i
\(484\) 66121.0 130481.i 0.282260 0.557003i
\(485\) −28133.3 −0.119602
\(486\) −7931.15 12910.4i −0.0335787 0.0546598i
\(487\) 432403.i 1.82318i 0.411097 + 0.911592i \(0.365146\pi\)
−0.411097 + 0.911592i \(0.634854\pi\)
\(488\) 21500.5 + 262087.i 0.0902836 + 1.10054i
\(489\) −161570. −0.675683
\(490\) −51845.4 + 31849.7i −0.215933 + 0.132652i
\(491\) 266902.i 1.10710i −0.832814 0.553552i \(-0.813272\pi\)
0.832814 0.553552i \(-0.186728\pi\)
\(492\) 90111.7 + 45663.8i 0.372264 + 0.188643i
\(493\) −760578. −3.12932
\(494\) 154877. + 252110.i 0.634647 + 1.03309i
\(495\) 22384.4i 0.0913554i
\(496\) −214908. + 157595.i −0.873554 + 0.640589i
\(497\) −273704. −1.10807
\(498\) 88058.8 54096.4i 0.355070 0.218127i
\(499\) 21287.2i 0.0854905i 0.999086 + 0.0427452i \(0.0136104\pi\)
−0.999086 + 0.0427452i \(0.986390\pi\)
\(500\) −10107.5 + 19945.9i −0.0404300 + 0.0797835i
\(501\) −156949. −0.625294
\(502\) 126603. + 206086.i 0.502385 + 0.817790i
\(503\) 267207.i 1.05612i 0.849208 + 0.528058i \(0.177080\pi\)
−0.849208 + 0.528058i \(0.822920\pi\)
\(504\) −105626. + 8665.15i −0.415826 + 0.0341126i
\(505\) 33260.8 0.130422
\(506\) −1891.45 + 1161.96i −0.00738743 + 0.00453825i
\(507\) 22498.2i 0.0875249i
\(508\) −249529. 126448.i −0.966926 0.489987i
\(509\) 449991. 1.73687 0.868437 0.495800i \(-0.165125\pi\)
0.868437 + 0.495800i \(0.165125\pi\)
\(510\) 62786.5 + 102205.i 0.241394 + 0.392944i
\(511\) 206630.i 0.791320i
\(512\) −63726.5 254280.i −0.243097 0.970002i
\(513\) −57222.6 −0.217437
\(514\) −130657. + 80265.0i −0.494544 + 0.303809i
\(515\) 200838.i 0.757238i
\(516\) 37115.8 73243.4i 0.139399 0.275086i
\(517\) −218244. −0.816509
\(518\) −85754.8 139593.i −0.319594 0.520240i
\(519\) 114635.i 0.425581i
\(520\) −10610.1 129335.i −0.0392385 0.478309i
\(521\) 147922. 0.544951 0.272475 0.962163i \(-0.412158\pi\)
0.272475 + 0.962163i \(0.412158\pi\)
\(522\) −135593. + 83297.5i −0.497618 + 0.305697i
\(523\) 329638.i 1.20513i −0.798070 0.602565i \(-0.794145\pi\)
0.798070 0.602565i \(-0.205855\pi\)
\(524\) −152687. 77373.8i −0.556084 0.281794i
\(525\) 39836.1 0.144530
\(526\) 81346.6 + 132417.i 0.294014 + 0.478600i
\(527\) 537351.i 1.93480i
\(528\) −58330.4 79543.6i −0.209231 0.285323i
\(529\) 279785. 0.999800
\(530\) −87170.1 + 53550.4i −0.310324 + 0.190639i
\(531\) 10548.5i 0.0374112i
\(532\) −180920. + 357022.i −0.639239 + 1.26146i
\(533\) 220368. 0.775700
\(534\) 134586. + 219082.i 0.471975 + 0.768287i
\(535\) 13421.8i 0.0468923i
\(536\) −393364. + 32270.0i −1.36919 + 0.112323i
\(537\) 22344.7 0.0774865
\(538\) 63817.7 39204.6i 0.220484 0.135448i
\(539\) 100890.i 0.347274i
\(540\) 22386.6 + 11344.4i 0.0767717 + 0.0389038i
\(541\) 412276. 1.40862 0.704309 0.709894i \(-0.251257\pi\)
0.704309 + 0.709894i \(0.251257\pi\)
\(542\) −53683.0 87385.9i −0.182742 0.297470i
\(543\) 167774.i 0.569017i
\(544\) 489444. + 199576.i 1.65389 + 0.674388i
\(545\) −184485. −0.621110
\(546\) −196986. + 121013.i −0.660770 + 0.405925i
\(547\) 37918.1i 0.126728i 0.997990 + 0.0633638i \(0.0201829\pi\)
−0.997990 + 0.0633638i \(0.979817\pi\)
\(548\) 226079. 446137.i 0.752833 1.48562i
\(549\) −110939. −0.368079
\(550\) 19407.2 + 31591.3i 0.0641560 + 0.104434i
\(551\) 600985.i 1.97952i
\(552\) −203.491 2480.52i −0.000667832 0.00814074i
\(553\) 433017. 1.41597
\(554\) 237540. 145926.i 0.773959 0.475459i
\(555\) 38795.7i 0.125950i
\(556\) 320881. + 162606.i 1.03799 + 0.526000i
\(557\) 229026. 0.738200 0.369100 0.929390i \(-0.379666\pi\)
0.369100 + 0.929390i \(0.379666\pi\)
\(558\) −58850.0 95796.8i −0.189007 0.307668i
\(559\) 179116.i 0.573207i
\(560\) 141559. 103807.i 0.451400 0.331017i
\(561\) 198889. 0.631953
\(562\) 238237. 146354.i 0.754286 0.463374i
\(563\) 529561.i 1.67070i 0.549717 + 0.835351i \(0.314735\pi\)
−0.549717 + 0.835351i \(0.685265\pi\)
\(564\) 110606. 218266.i 0.347712 0.686164i
\(565\) 67504.7 0.211464
\(566\) 225340. + 366811.i 0.703403 + 1.14501i
\(567\) 44710.8i 0.139074i
\(568\) 284655. 23351.9i 0.882312 0.0723812i
\(569\) 273177. 0.843760 0.421880 0.906652i \(-0.361370\pi\)
0.421880 + 0.906652i \(0.361370\pi\)
\(570\) 80758.9 49611.9i 0.248566 0.152699i
\(571\) 465596.i 1.42803i −0.700132 0.714014i \(-0.746875\pi\)
0.700132 0.714014i \(-0.253125\pi\)
\(572\) −191934. 97261.8i −0.586623 0.297269i
\(573\) −120235. −0.366201
\(574\) 156035. + 253996.i 0.473586 + 0.770910i
\(575\) 935.506i 0.00282951i
\(576\) 109113. 18023.7i 0.328877 0.0543249i
\(577\) 292168. 0.877570 0.438785 0.898592i \(-0.355409\pi\)
0.438785 + 0.898592i \(0.355409\pi\)
\(578\) −623446. + 382996.i −1.86613 + 1.14641i
\(579\) 336579.i 1.00399i
\(580\) 119145. 235117.i 0.354176 0.698922i
\(581\) 304961. 0.903426
\(582\) −27376.3 44563.5i −0.0808218 0.131563i
\(583\) 169632.i 0.499080i
\(584\) 17629.3 + 214898.i 0.0516905 + 0.630096i
\(585\) 54746.4 0.159972
\(586\) −74228.2 + 45599.9i −0.216159 + 0.132791i
\(587\) 184222.i 0.534644i −0.963607 0.267322i \(-0.913861\pi\)
0.963607 0.267322i \(-0.0861387\pi\)
\(588\) −100901. 51131.1i −0.291836 0.147887i
\(589\) −424598. −1.22390
\(590\) 9145.52 + 14887.2i 0.0262727 + 0.0427670i
\(591\) 1648.95i 0.00472099i
\(592\) 101096. + 137862.i 0.288463 + 0.393370i
\(593\) −385641. −1.09666 −0.548332 0.836261i \(-0.684737\pi\)
−0.548332 + 0.836261i \(0.684737\pi\)
\(594\) 35457.1 21782.0i 0.100492 0.0617342i
\(595\) 353951.i 0.999790i
\(596\) 139179. 274652.i 0.391816 0.773198i
\(597\) 93797.0 0.263172
\(598\) −2841.85 4626.00i −0.00794691 0.0129361i
\(599\) 316862.i 0.883115i 0.897233 + 0.441557i \(0.145574\pi\)
−0.897233 + 0.441557i \(0.854426\pi\)
\(600\) −41430.0 + 3398.75i −0.115083 + 0.00944096i
\(601\) −388882. −1.07663 −0.538317 0.842742i \(-0.680940\pi\)
−0.538317 + 0.842742i \(0.680940\pi\)
\(602\) 206450. 126827.i 0.569668 0.349959i
\(603\) 166508.i 0.457931i
\(604\) −605233. 306700.i −1.65901 0.840698i
\(605\) −102215. −0.279257
\(606\) 32365.8 + 52685.5i 0.0881335 + 0.143465i
\(607\) 235572.i 0.639362i 0.947525 + 0.319681i \(0.103576\pi\)
−0.947525 + 0.319681i \(0.896424\pi\)
\(608\) 157698. 386743.i 0.426599 1.04620i
\(609\) −469579. −1.26612
\(610\) 156570. 96184.1i 0.420774 0.258490i
\(611\) 533769.i 1.42979i
\(612\) −100797. + 198909.i −0.269118 + 0.531070i
\(613\) −74819.9 −0.199111 −0.0995557 0.995032i \(-0.531742\pi\)
−0.0995557 + 0.995032i \(0.531742\pi\)
\(614\) −270530. 440372.i −0.717594 1.16811i
\(615\) 70590.8i 0.186637i
\(616\) −23797.9 290091.i −0.0627158 0.764493i
\(617\) 476184. 1.25085 0.625424 0.780285i \(-0.284926\pi\)
0.625424 + 0.780285i \(0.284926\pi\)
\(618\) 318130. 195434.i 0.832968 0.511709i
\(619\) 95751.1i 0.249898i −0.992163 0.124949i \(-0.960123\pi\)
0.992163 0.124949i \(-0.0398767\pi\)
\(620\) 166111. + 84176.3i 0.432131 + 0.218981i
\(621\) 1049.98 0.00272270
\(622\) −83671.3 136201.i −0.216270 0.352047i
\(623\) 758713.i 1.95480i
\(624\) 194543. 142661.i 0.499628 0.366384i
\(625\) 15625.0 0.0400000
\(626\) −338300. + 207825.i −0.863283 + 0.530332i
\(627\) 157156.i 0.399756i
\(628\) 101102. 199512.i 0.256355 0.505883i
\(629\) −344706. −0.871260
\(630\) 38764.2 + 63100.9i 0.0976674 + 0.158984i
\(631\) 363696.i 0.913439i 0.889611 + 0.456720i \(0.150976\pi\)
−0.889611 + 0.456720i \(0.849024\pi\)
\(632\) −450343. + 36944.3i −1.12748 + 0.0924939i
\(633\) −326572. −0.815026
\(634\) −314753. + 193359.i −0.783053 + 0.481045i
\(635\) 195473.i 0.484775i
\(636\) −169649. 85969.1i −0.419408 0.212534i
\(637\) −246752. −0.608110
\(638\) −228767. 372391.i −0.562021 0.914866i
\(639\) 120492.i 0.295092i
\(640\) −138366. + 120038.i −0.337809 + 0.293062i
\(641\) 11650.4 0.0283547 0.0141773 0.999899i \(-0.495487\pi\)
0.0141773 + 0.999899i \(0.495487\pi\)
\(642\) 21260.2 13060.6i 0.0515820 0.0316879i
\(643\) 477647.i 1.15527i 0.816294 + 0.577637i \(0.196025\pi\)
−0.816294 + 0.577637i \(0.803975\pi\)
\(644\) 3319.72 6551.04i 0.00800441 0.0157957i
\(645\) −57376.6 −0.137916
\(646\) 440810. + 717557.i 1.05630 + 1.71946i
\(647\) 184457.i 0.440642i 0.975427 + 0.220321i \(0.0707105\pi\)
−0.975427 + 0.220321i \(0.929289\pi\)
\(648\) 3814.65 + 46499.8i 0.00908457 + 0.110739i
\(649\) 28970.3 0.0687802
\(650\) −77264.3 + 47465.0i −0.182874 + 0.112343i
\(651\) 331759.i 0.782818i
\(652\) 443779. + 224884.i 1.04393 + 0.529009i
\(653\) 105463. 0.247329 0.123664 0.992324i \(-0.460535\pi\)
0.123664 + 0.992324i \(0.460535\pi\)
\(654\) −179521. 292227.i −0.419720 0.683226i
\(655\) 119611.i 0.278796i
\(656\) −183949. 250847.i −0.427455 0.582909i
\(657\) −90964.7 −0.210738
\(658\) 615223. 377944.i 1.42096 0.872924i
\(659\) 434371.i 1.00021i 0.865966 + 0.500103i \(0.166705\pi\)
−0.865966 + 0.500103i \(0.833295\pi\)
\(660\) −31156.0 + 61482.5i −0.0715244 + 0.141144i
\(661\) −474718. −1.08651 −0.543254 0.839568i \(-0.682808\pi\)
−0.543254 + 0.839568i \(0.682808\pi\)
\(662\) −78256.3 127387.i −0.178568 0.290675i
\(663\) 486431.i 1.10661i
\(664\) −317163. + 26018.8i −0.719361 + 0.0590134i
\(665\) 279681. 0.632439
\(666\) −61452.8 + 37751.8i −0.138546 + 0.0851116i
\(667\) 11027.5i 0.0247871i
\(668\) 431088. + 218453.i 0.966080 + 0.489558i
\(669\) 315544. 0.705029
\(670\) 144362. + 234995.i 0.321591 + 0.523490i
\(671\) 304683.i 0.676710i
\(672\) 302181. + 123217.i 0.669159 + 0.272856i
\(673\) −701401. −1.54859 −0.774295 0.632825i \(-0.781895\pi\)
−0.774295 + 0.632825i \(0.781895\pi\)
\(674\) −405743. + 249256.i −0.893164 + 0.548689i
\(675\) 17537.0i 0.0384900i
\(676\) 31314.4 61795.1i 0.0685254 0.135226i
\(677\) −284255. −0.620199 −0.310100 0.950704i \(-0.600362\pi\)
−0.310100 + 0.950704i \(0.600362\pi\)
\(678\) 65688.2 + 106928.i 0.142899 + 0.232613i
\(679\) 154330.i 0.334743i
\(680\) −30198.4 368113.i −0.0653080 0.796092i
\(681\) −512492. −1.10508
\(682\) 263096. 161625.i 0.565646 0.347488i
\(683\) 659478.i 1.41371i −0.707361 0.706853i \(-0.750114\pi\)
0.707361 0.706853i \(-0.249886\pi\)
\(684\) 157172. + 79646.2i 0.335940 + 0.170237i
\(685\) −349491. −0.744825
\(686\) 133604. + 217483.i 0.283905 + 0.462144i
\(687\) 292699.i 0.620166i
\(688\) −203890. + 149515.i −0.430744 + 0.315870i
\(689\) −414876. −0.873936
\(690\) −1481.85 + 910.333i −0.00311248 + 0.00191206i
\(691\) 163007.i 0.341390i −0.985324 0.170695i \(-0.945399\pi\)
0.985324 0.170695i \(-0.0546012\pi\)
\(692\) −159556. + 314864.i −0.333198 + 0.657523i
\(693\) 122793. 0.255687
\(694\) −177510. 288953.i −0.368556 0.599941i
\(695\) 251369.i 0.520405i
\(696\) 488367. 40063.6i 1.00816 0.0827050i
\(697\) 627211. 1.29106
\(698\) 584953. 359349.i 1.20063 0.737574i
\(699\) 272846.i 0.558422i
\(700\) −109417. 55446.5i −0.223299 0.113156i
\(701\) 270195. 0.549847 0.274924 0.961466i \(-0.411347\pi\)
0.274924 + 0.961466i \(0.411347\pi\)
\(702\) 53273.3 + 86719.0i 0.108102 + 0.175971i
\(703\) 272376.i 0.551135i
\(704\) 49500.2 + 299668.i 0.0998760 + 0.604638i
\(705\) −170983. −0.344013
\(706\) −665087. + 408577.i −1.33435 + 0.819717i
\(707\) 182458.i 0.365026i
\(708\) −14682.1 + 28973.2i −0.0292901 + 0.0578003i
\(709\) 40040.3 0.0796534 0.0398267 0.999207i \(-0.487319\pi\)
0.0398267 + 0.999207i \(0.487319\pi\)
\(710\) −104467. 170052.i −0.207234 0.337338i
\(711\) 190627.i 0.377090i
\(712\) −64732.1 789071.i −0.127691 1.55653i
\(713\) 7790.99 0.0153255
\(714\) −560662. + 344426.i −1.09978 + 0.675616i
\(715\) 150355.i 0.294107i
\(716\) −61373.5 31100.8i −0.119717 0.0606660i
\(717\) 265744. 0.516922
\(718\) 105355. + 171498.i 0.204364 + 0.332667i
\(719\) 388789.i 0.752066i 0.926606 + 0.376033i \(0.122712\pi\)
−0.926606 + 0.376033i \(0.877288\pi\)
\(720\) −45698.9 62318.4i −0.0881537 0.120213i
\(721\) 1.10173e6 2.11937
\(722\) 122824. 75453.3i 0.235618 0.144745i
\(723\) 36.6925i 7.01941e-5i
\(724\) −233519. + 460820.i −0.445497 + 0.879132i
\(725\) −184184. −0.350409
\(726\) −99464.7 161910.i −0.188710 0.307185i
\(727\) 569739.i 1.07797i −0.842315 0.538985i \(-0.818808\pi\)
0.842315 0.538985i \(-0.181192\pi\)
\(728\) 709489. 58203.5i 1.33870 0.109821i
\(729\) −19683.0 −0.0370370
\(730\) 128379. 78866.2i 0.240907 0.147994i
\(731\) 509801.i 0.954039i
\(732\) 304714. + 154413.i 0.568682 + 0.288178i
\(733\) 119853. 0.223070 0.111535 0.993760i \(-0.464423\pi\)
0.111535 + 0.993760i \(0.464423\pi\)
\(734\) −106192. 172860.i −0.197105 0.320851i
\(735\) 79042.5i 0.146314i
\(736\) −2893.62 + 7096.39i −0.00534178 + 0.0131003i
\(737\) 457296. 0.841904
\(738\) 111817. 68691.3i 0.205302 0.126121i
\(739\) 543414.i 0.995044i 0.867451 + 0.497522i \(0.165757\pi\)
−0.867451 + 0.497522i \(0.834243\pi\)
\(740\) 53998.4 106559.i 0.0986092 0.194593i
\(741\) 384363. 0.700011
\(742\) −293760. 478187.i −0.533562 0.868540i
\(743\) 33513.7i 0.0607078i −0.999539 0.0303539i \(-0.990337\pi\)
0.999539 0.0303539i \(-0.00966343\pi\)
\(744\) 28305.1 + 345033.i 0.0511351 + 0.623326i
\(745\) −215154. −0.387648
\(746\) 407524. 250351.i 0.732277 0.449853i
\(747\) 134253.i 0.240592i
\(748\) −546282. 276827.i −0.976368 0.494771i
\(749\) 73627.4 0.131243
\(750\) 15204.6 + 24750.2i 0.0270303 + 0.0440003i
\(751\) 483614.i 0.857471i −0.903430 0.428735i \(-0.858959\pi\)
0.903430 0.428735i \(-0.141041\pi\)
\(752\) −607594. + 445557.i −1.07443 + 0.787893i
\(753\) 314195. 0.554127
\(754\) 910773. 559506.i 1.60202 0.984153i
\(755\) 474121.i 0.831755i
\(756\) −62231.5 + 122806.i −0.108885 + 0.214870i
\(757\) −154021. −0.268774 −0.134387 0.990929i \(-0.542906\pi\)
−0.134387 + 0.990929i \(0.542906\pi\)
\(758\) −217877. 354663.i −0.379204 0.617274i
\(759\) 2883.66i 0.00500566i
\(760\) −290871. + 23861.9i −0.503586 + 0.0413121i
\(761\) −242974. −0.419557 −0.209779 0.977749i \(-0.567274\pi\)
−0.209779 + 0.977749i \(0.567274\pi\)
\(762\) −309632. + 190213.i −0.533256 + 0.327590i
\(763\) 1.01203e6i 1.73837i
\(764\) 330245. + 167350.i 0.565782 + 0.286708i
\(765\) 155819. 0.266255
\(766\) −151678. 246903.i −0.258502 0.420794i
\(767\) 70853.9i 0.120441i
\(768\) −324785. 102366.i −0.550647 0.173554i
\(769\) −86574.7 −0.146399 −0.0731995 0.997317i \(-0.523321\pi\)
−0.0731995 + 0.997317i \(0.523321\pi\)
\(770\) −173300. + 106462.i −0.292292 + 0.179561i
\(771\) 199196.i 0.335099i
\(772\) −468473. + 924471.i −0.786049 + 1.55117i
\(773\) 1.07093e6 1.79227 0.896133 0.443785i \(-0.146365\pi\)
0.896133 + 0.443785i \(0.146365\pi\)
\(774\) −55832.7 90885.3i −0.0931980 0.151709i
\(775\) 130127.i 0.216652i
\(776\) 13167.2 + 160505.i 0.0218660 + 0.266542i
\(777\) −212821. −0.352510
\(778\) 553879. 340259.i 0.915073 0.562148i
\(779\) 495602.i 0.816692i
\(780\) −150370. 76199.7i −0.247157 0.125246i
\(781\) −330919. −0.542525
\(782\) −8088.46 13166.5i −0.0132267 0.0215307i
\(783\) 206722.i 0.337181i
\(784\) 205973. + 280880.i 0.335103 + 0.456972i
\(785\) −156292. −0.253628
\(786\) −189465. + 116392.i −0.306678 + 0.188399i
\(787\) 751269.i 1.21296i −0.795099 0.606479i \(-0.792581\pi\)
0.795099 0.606479i \(-0.207419\pi\)
\(788\) 2295.12 4529.12i 0.00369618 0.00729393i
\(789\) 201881. 0.324295
\(790\) 165273. + 269034.i 0.264818 + 0.431075i
\(791\) 370309.i 0.591849i
\(792\) −127707. + 10476.5i −0.203593 + 0.0167019i
\(793\) 745176. 1.18498
\(794\) −181631. + 111580.i −0.288104 + 0.176988i
\(795\) 132898.i 0.210273i
\(796\) −257629. 130553.i −0.406601 0.206044i
\(797\) −410930. −0.646921 −0.323461 0.946242i \(-0.604846\pi\)
−0.323461 + 0.946242i \(0.604846\pi\)
\(798\) 272155. + 443017.i 0.427376 + 0.695689i
\(799\) 1.51921e6i 2.37972i
\(800\) 118525. + 48329.8i 0.185196 + 0.0755153i
\(801\) 334008. 0.520585
\(802\) 115177. 70755.9i 0.179068 0.110005i
\(803\) 249825.i 0.387440i
\(804\) −231757. + 457342.i −0.358526 + 0.707505i
\(805\) −5131.88 −0.00791927
\(806\) 395293. + 643464.i 0.608484 + 0.990500i
\(807\) 97295.3i 0.149398i
\(808\) −15567.0 189758.i −0.0238442 0.290655i
\(809\) −81222.3 −0.124102 −0.0620510 0.998073i \(-0.519764\pi\)
−0.0620510 + 0.998073i \(0.519764\pi\)
\(810\) 27778.8 17065.1i 0.0423393 0.0260099i
\(811\) 665948.i 1.01251i 0.862384 + 0.506254i \(0.168970\pi\)
−0.862384 + 0.506254i \(0.831030\pi\)
\(812\) 1.28978e6 + 653590.i 1.95615 + 0.991274i
\(813\) −133227. −0.201563
\(814\) −103681. 168774.i −0.156477 0.254716i
\(815\) 347643.i 0.523382i
\(816\) 553709. 406042.i 0.831575 0.609805i
\(817\) −402829. −0.603499
\(818\) −657716. + 404049.i −0.982951 + 0.603847i
\(819\) 300321.i 0.447732i
\(820\) −98252.9 + 193889.i −0.146123 + 0.288354i
\(821\) 175974. 0.261074 0.130537 0.991443i \(-0.458330\pi\)
0.130537 + 0.991443i \(0.458330\pi\)
\(822\) −340086. 553597.i −0.503321 0.819314i
\(823\) 825656.i 1.21899i 0.792790 + 0.609494i \(0.208627\pi\)
−0.792790 + 0.609494i \(0.791373\pi\)
\(824\) −1.14582e6 + 93998.0i −1.68757 + 0.138441i
\(825\) 48163.5 0.0707636
\(826\) −81666.4 + 50169.4i −0.119697 + 0.0735324i
\(827\) 184129.i 0.269222i 0.990899 + 0.134611i \(0.0429785\pi\)
−0.990899 + 0.134611i \(0.957022\pi\)
\(828\) −2883.96 1461.44i −0.00420657 0.00213167i
\(829\) −713518. −1.03824 −0.519118 0.854703i \(-0.673739\pi\)
−0.519118 + 0.854703i \(0.673739\pi\)
\(830\) 116397. + 189472.i 0.168960 + 0.275036i
\(831\) 362149.i 0.524428i
\(832\) −732911. + 121065.i −1.05878 + 0.174892i
\(833\) −702306. −1.01213
\(834\) 398171. 244605.i 0.572450 0.351668i
\(835\) 337701.i 0.484351i
\(836\) −218740. + 431655.i −0.312979 + 0.617624i
\(837\) −146050. −0.208473
\(838\) −434939. 708000.i −0.619356 1.00820i
\(839\) 1.30678e6i 1.85643i −0.372047 0.928214i \(-0.621344\pi\)
0.372047 0.928214i \(-0.378656\pi\)
\(840\) −18644.4 227272.i −0.0264235 0.322097i
\(841\) 1.46383e6 2.06966
\(842\) 463376. 284662.i 0.653596 0.401518i
\(843\) 363211.i 0.511098i
\(844\) 896985. + 454544.i 1.25922 + 0.638104i
\(845\) −48408.4 −0.0677965
\(846\) −166382. 270839.i −0.232469 0.378417i
\(847\) 560719.i 0.781589i
\(848\) 346312. + 472257.i 0.481589 + 0.656730i
\(849\) 559233. 0.775849
\(850\) −219910. + 135095.i −0.304373 + 0.186983i
\(851\) 4997.85i 0.00690120i
\(852\) 167709. 330952.i 0.231035 0.455918i
\(853\) 590922. 0.812143 0.406071 0.913841i \(-0.366898\pi\)
0.406071 + 0.913841i \(0.366898\pi\)
\(854\) 527635. + 858891.i 0.723465 + 1.17767i
\(855\) 123123.i 0.168426i
\(856\) −76573.4 + 6281.76i −0.104503 + 0.00857302i
\(857\) −756073. −1.02944 −0.514721 0.857358i \(-0.672105\pi\)
−0.514721 + 0.857358i \(0.672105\pi\)
\(858\) −238164. + 146309.i −0.323521 + 0.198745i
\(859\) 1.02880e6i 1.39426i 0.716945 + 0.697130i \(0.245540\pi\)
−0.716945 + 0.697130i \(0.754460\pi\)
\(860\) 157595. + 79860.6i 0.213081 + 0.107978i
\(861\) 387238. 0.522362
\(862\) −318238. 518033.i −0.428290 0.697176i
\(863\) 520287.i 0.698589i −0.937013 0.349294i \(-0.886421\pi\)
0.937013 0.349294i \(-0.113579\pi\)
\(864\) 54243.9 133029.i 0.0726647 0.178205i
\(865\) 246655. 0.329654
\(866\) 124255. 76332.6i 0.165683 0.101783i
\(867\) 950493.i 1.26448i
\(868\) −461764. + 911232.i −0.612887 + 1.20946i
\(869\) 523536. 0.693277
\(870\) −179228. 291749.i −0.236792 0.385453i
\(871\) 1.11843e6i 1.47425i
\(872\) 86344.3 + 1.05252e6i 0.113554 + 1.38419i
\(873\) −67940.7 −0.0891459
\(874\) −10403.8 + 6391.25i −0.0136197 + 0.00836686i
\(875\) 85713.7i 0.111953i
\(876\) 249850. + 126611.i 0.325590 + 0.164992i
\(877\) −132059. −0.171699 −0.0858496 0.996308i \(-0.527360\pi\)
−0.0858496 + 0.996308i \(0.527360\pi\)
\(878\) −247199. 402394.i −0.320670 0.521990i
\(879\) 113167.i 0.146468i
\(880\) 171151. 125507.i 0.221011 0.162070i
\(881\) −485203. −0.625132 −0.312566 0.949896i \(-0.601189\pi\)
−0.312566 + 0.949896i \(0.601189\pi\)
\(882\) −125204. + 76915.6i −0.160947 + 0.0988729i
\(883\) 454909.i 0.583449i 0.956502 + 0.291725i \(0.0942291\pi\)
−0.956502 + 0.291725i \(0.905771\pi\)
\(884\) 677047. 1.33607e6i 0.866392 1.70971i
\(885\) 22696.7 0.0289786
\(886\) 237835. + 387151.i 0.302976 + 0.493189i
\(887\) 372656.i 0.473654i 0.971552 + 0.236827i \(0.0761075\pi\)
−0.971552 + 0.236827i \(0.923893\pi\)
\(888\) 221336. 18157.5i 0.280689 0.0230266i
\(889\) −1.07230e6 −1.35679
\(890\) −471389. + 289584.i −0.595113 + 0.365590i
\(891\) 54057.2i 0.0680923i
\(892\) −866694. 439194.i −1.08927 0.551985i
\(893\) −1.20043e6 −1.50534
\(894\) −209365. 340807.i −0.261956 0.426416i
\(895\) 48078.1i 0.0600207i
\(896\) −658490. 759033.i −0.820226 0.945464i
\(897\) −7052.71 −0.00876538
\(898\) 5948.02 3653.99i 0.00737598 0.00453122i
\(899\) 1.53390e6i 1.89792i
\(900\) −24409.2 + 48168.4i −0.0301348 + 0.0594671i
\(901\) −1.18082e6 −1.45457
\(902\) 188653. + 307092.i 0.231873 + 0.377447i
\(903\) 314750.i 0.386002i
\(904\) −31594.1 385126.i −0.0386607 0.471266i
\(905\) 360992. 0.440759
\(906\) −751014. + 461363.i −0.914938 + 0.562065i
\(907\) 354962.i 0.431487i −0.976450 0.215743i \(-0.930783\pi\)
0.976450 0.215743i \(-0.0692175\pi\)
\(908\) 1.40765e6 + 713320.i 1.70735 + 0.865192i
\(909\) 80323.3 0.0972106
\(910\) −260378. 423847.i −0.314428 0.511830i
\(911\) 108935.i 0.131260i −0.997844 0.0656298i \(-0.979094\pi\)
0.997844 0.0656298i \(-0.0209056\pi\)
\(912\) −320842. 437524.i −0.385746 0.526032i
\(913\) 368711. 0.442328
\(914\) 254276. 156207.i 0.304378 0.186986i
\(915\) 238703.i 0.285113i
\(916\) 407398. 803947.i 0.485543 0.958157i
\(917\) −656145. −0.780299
\(918\) 151626. + 246820.i 0.179924 + 0.292883i
\(919\) 306482.i 0.362889i 0.983401 + 0.181444i \(0.0580772\pi\)
−0.983401 + 0.181444i \(0.941923\pi\)
\(920\) 5337.22 437.843i 0.00630579 0.000517301i
\(921\) −671383. −0.791500
\(922\) −58982.8 + 36234.3i −0.0693846 + 0.0426244i
\(923\) 809343.i 0.950012i
\(924\) −337273. 170912.i −0.395037 0.200184i
\(925\) −83475.1 −0.0975603
\(926\) −260964. 424800.i −0.304339 0.495408i
\(927\) 485015.i 0.564412i
\(928\) −1.39715e6 569700.i −1.62236 0.661532i
\(929\) 230175. 0.266702 0.133351 0.991069i \(-0.457426\pi\)
0.133351 + 0.991069i \(0.457426\pi\)
\(930\) 206122. 126625.i 0.238319 0.146404i
\(931\) 554940.i 0.640246i
\(932\) 379764. 749416.i 0.437202 0.862763i
\(933\) −207650. −0.238544
\(934\) 436634. + 710760.i 0.500523 + 0.814759i
\(935\) 427941.i 0.489509i
\(936\) −25622.9 312338.i −0.0292466 0.356511i
\(937\) 1.06117e6 1.20867 0.604333 0.796732i \(-0.293440\pi\)
0.604333 + 0.796732i \(0.293440\pi\)
\(938\) −1.28910e6 + 791923.i −1.46515 + 0.900073i
\(939\) 515765.i 0.584953i
\(940\) 469634. + 237985.i 0.531501 + 0.269336i
\(941\) −1.17032e6 −1.32168 −0.660838 0.750529i \(-0.729799\pi\)
−0.660838 + 0.750529i \(0.729799\pi\)
\(942\) −152086. 247568.i −0.171391 0.278993i
\(943\) 9093.85i 0.0102264i
\(944\) 80653.7 59144.4i 0.0905066 0.0663696i
\(945\) 96202.4 0.107726
\(946\) 249606. 153338.i 0.278916 0.171344i
\(947\) 605186.i 0.674822i 0.941357 + 0.337411i \(0.109551\pi\)
−0.941357 + 0.337411i \(0.890449\pi\)
\(948\) −265327. + 523589.i −0.295233 + 0.582604i
\(949\) 611007. 0.678444
\(950\) 106748. + 173766.i 0.118280 + 0.192538i
\(951\) 479866.i 0.530590i
\(952\) 2.01935e6 165659.i 2.22811 0.182785i
\(953\) −1.26323e6 −1.39090 −0.695452 0.718572i \(-0.744796\pi\)
−0.695452 + 0.718572i \(0.744796\pi\)
\(954\) −210512. + 129322.i −0.231302 + 0.142094i
\(955\) 258704.i 0.283658i
\(956\) −729911. 369880.i −0.798646 0.404711i
\(957\) −567740. −0.619905
\(958\) 836020. + 1.36089e6i 0.910931 + 1.48283i
\(959\) 1.91719e6i 2.08463i
\(960\) 38780.9 + 234775.i 0.0420799 + 0.254747i
\(961\) −160185. −0.173451
\(962\) 412777. 253577.i 0.446031 0.274006i
\(963\) 32412.9i 0.0349515i
\(964\) 51.0710 100.782i 5.49567e−5 0.000108450i
\(965\) 724202. 0.777688
\(966\) −4993.79 8128.97i −0.00535151 0.00871126i
\(967\) 1.65602e6i 1.77098i 0.464657 + 0.885491i \(0.346177\pi\)
−0.464657 + 0.885491i \(0.653823\pi\)
\(968\) 47839.6 + 583155.i 0.0510548 + 0.622348i
\(969\) 1.09397e6 1.16509
\(970\) 95885.4 58904.4i 0.101908 0.0626043i
\(971\) 538842.i 0.571508i 0.958303 + 0.285754i \(0.0922441\pi\)
−0.958303 + 0.285754i \(0.907756\pi\)
\(972\) 54062.7 + 27396.1i 0.0572223 + 0.0289972i
\(973\) 1.37893e6 1.45652
\(974\) −905347. 1.47374e6i −0.954327 1.55347i
\(975\) 117796.i 0.123914i
\(976\) −622026. 848241.i −0.652993 0.890470i
\(977\) 962571. 1.00843 0.504213 0.863579i \(-0.331783\pi\)
0.504213 + 0.863579i \(0.331783\pi\)
\(978\) 550671. 338289.i 0.575724 0.353679i
\(979\) 917315.i 0.957091i
\(980\) 110017. 217104.i 0.114553 0.226055i
\(981\) −445523. −0.462948
\(982\) 558828. + 909669.i 0.579503 + 0.943323i
\(983\) 386329.i 0.399807i 0.979816 + 0.199903i \(0.0640628\pi\)
−0.979816 + 0.199903i \(0.935937\pi\)
\(984\) −402732. + 33038.5i −0.415936 + 0.0341216i
\(985\) −3547.98 −0.00365686
\(986\) 2.59224e6 1.59247e6i 2.66638 1.63801i
\(987\) 937958.i 0.962828i
\(988\) −1.05572e6 534981.i −1.08152 0.548055i
\(989\) 7391.54 0.00755688
\(990\) 46867.5 + 76291.5i 0.0478191 + 0.0778406i
\(991\) 18475.3i 0.0188124i 0.999956 + 0.00940620i \(0.00299413\pi\)
−0.999956 + 0.00940620i \(0.997006\pi\)
\(992\) 402495. 987090.i 0.409014 1.00307i
\(993\) −194211. −0.196959
\(994\) 932851. 573070.i 0.944147 0.580009i
\(995\) 201819.i 0.203852i
\(996\) −186862. + 368748.i −0.188366 + 0.371716i
\(997\) 177630. 0.178701 0.0893503 0.996000i \(-0.471521\pi\)
0.0893503 + 0.996000i \(0.471521\pi\)
\(998\) −44570.3 72552.1i −0.0447491 0.0728432i
\(999\) 93689.8i 0.0938775i
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 60.5.c.a.31.4 yes 16
3.2 odd 2 180.5.c.c.91.13 16
4.3 odd 2 inner 60.5.c.a.31.3 16
5.2 odd 4 300.5.f.b.199.11 32
5.3 odd 4 300.5.f.b.199.22 32
5.4 even 2 300.5.c.d.151.13 16
8.3 odd 2 960.5.e.f.511.16 16
8.5 even 2 960.5.e.f.511.5 16
12.11 even 2 180.5.c.c.91.14 16
20.3 even 4 300.5.f.b.199.12 32
20.7 even 4 300.5.f.b.199.21 32
20.19 odd 2 300.5.c.d.151.14 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.5.c.a.31.3 16 4.3 odd 2 inner
60.5.c.a.31.4 yes 16 1.1 even 1 trivial
180.5.c.c.91.13 16 3.2 odd 2
180.5.c.c.91.14 16 12.11 even 2
300.5.c.d.151.13 16 5.4 even 2
300.5.c.d.151.14 16 20.19 odd 2
300.5.f.b.199.11 32 5.2 odd 4
300.5.f.b.199.12 32 20.3 even 4
300.5.f.b.199.21 32 20.7 even 4
300.5.f.b.199.22 32 5.3 odd 4
960.5.e.f.511.5 16 8.5 even 2
960.5.e.f.511.16 16 8.3 odd 2