Properties

Label 76.5.b.a.39.11
Level $76$
Weight $5$
Character 76.39
Analytic conductor $7.856$
Analytic rank $0$
Dimension $36$
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] = [76,5,Mod(39,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.39");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.b (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: \(7.85611719437\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 39.11
Character \(\chi\) \(=\) 76.39
Dual form 76.5.b.a.39.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.32469 - 3.25512i) q^{2} -7.75287i q^{3} +(-5.19165 + 15.1343i) q^{4} +27.0702 q^{5} +(-25.2365 + 18.0230i) q^{6} +95.4821i q^{7} +(61.3329 - 18.2830i) q^{8} +20.8930 q^{9} +O(q^{10})\) \(q+(-2.32469 - 3.25512i) q^{2} -7.75287i q^{3} +(-5.19165 + 15.1343i) q^{4} +27.0702 q^{5} +(-25.2365 + 18.0230i) q^{6} +95.4821i q^{7} +(61.3329 - 18.2830i) q^{8} +20.8930 q^{9} +(-62.9297 - 88.1167i) q^{10} +138.578i q^{11} +(117.334 + 40.2502i) q^{12} -68.1130 q^{13} +(310.806 - 221.966i) q^{14} -209.872i q^{15} +(-202.094 - 157.144i) q^{16} +261.853 q^{17} +(-48.5697 - 68.0093i) q^{18} -82.8191i q^{19} +(-140.539 + 409.688i) q^{20} +740.260 q^{21} +(451.090 - 322.151i) q^{22} -46.0152i q^{23} +(-141.746 - 475.506i) q^{24} +107.794 q^{25} +(158.341 + 221.716i) q^{26} -789.963i q^{27} +(-1445.05 - 495.710i) q^{28} +508.504 q^{29} +(-683.158 + 487.886i) q^{30} +995.645i q^{31} +(-41.7183 + 1023.15i) q^{32} +1074.38 q^{33} +(-608.727 - 852.365i) q^{34} +2584.72i q^{35} +(-108.469 + 316.201i) q^{36} +1035.44 q^{37} +(-269.586 + 192.529i) q^{38} +528.071i q^{39} +(1660.29 - 494.925i) q^{40} -1768.23 q^{41} +(-1720.87 - 2409.64i) q^{42} -249.767i q^{43} +(-2097.28 - 719.450i) q^{44} +565.577 q^{45} +(-149.785 + 106.971i) q^{46} +345.338i q^{47} +(-1218.32 + 1566.81i) q^{48} -6715.83 q^{49} +(-250.588 - 350.883i) q^{50} -2030.11i q^{51} +(353.619 - 1030.84i) q^{52} +2136.43 q^{53} +(-2571.43 + 1836.42i) q^{54} +3751.34i q^{55} +(1745.70 + 5856.20i) q^{56} -642.086 q^{57} +(-1182.11 - 1655.24i) q^{58} -5022.76i q^{59} +(3176.26 + 1089.58i) q^{60} +6478.12 q^{61} +(3240.95 - 2314.57i) q^{62} +1994.91i q^{63} +(3427.46 - 2242.71i) q^{64} -1843.83 q^{65} +(-2497.60 - 3497.24i) q^{66} +3188.74i q^{67} +(-1359.45 + 3962.96i) q^{68} -356.750 q^{69} +(8413.57 - 6008.66i) q^{70} +824.209i q^{71} +(1281.43 - 381.988i) q^{72} +6551.48 q^{73} +(-2407.07 - 3370.48i) q^{74} -835.715i q^{75} +(1253.41 + 429.968i) q^{76} -13231.8 q^{77} +(1718.94 - 1227.60i) q^{78} -11180.3i q^{79} +(-5470.71 - 4253.91i) q^{80} -4432.15 q^{81} +(4110.59 + 5755.82i) q^{82} -1997.06i q^{83} +(-3843.17 + 11203.3i) q^{84} +7088.41 q^{85} +(-813.023 + 580.631i) q^{86} -3942.36i q^{87} +(2533.63 + 8499.42i) q^{88} +8875.25 q^{89} +(-1314.79 - 1841.02i) q^{90} -6503.57i q^{91} +(696.407 + 238.895i) q^{92} +7719.11 q^{93} +(1124.12 - 802.803i) q^{94} -2241.93i q^{95} +(7932.35 + 323.436i) q^{96} -14573.4 q^{97} +(15612.2 + 21860.9i) q^{98} +2895.32i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9} + 152 q^{10} + 160 q^{12} + 120 q^{13} - 60 q^{14} - 38 q^{16} - 600 q^{17} + 286 q^{18} - 600 q^{20} + 608 q^{21} + 1080 q^{22} + 958 q^{24} + 4604 q^{25} - 2766 q^{26} - 2250 q^{28} - 168 q^{29} - 1380 q^{30} + 3576 q^{32} + 1440 q^{33} + 908 q^{34} - 5836 q^{36} - 2248 q^{37} - 1716 q^{40} + 1800 q^{41} - 5006 q^{42} - 2520 q^{44} + 88 q^{45} + 6404 q^{46} + 1064 q^{48} - 12188 q^{49} + 3354 q^{50} + 15492 q^{52} - 6600 q^{53} + 1654 q^{54} + 12924 q^{56} + 5450 q^{58} - 11188 q^{60} + 2200 q^{61} - 9972 q^{62} + 12570 q^{64} - 15792 q^{65} + 10500 q^{66} - 22614 q^{68} + 19904 q^{69} + 900 q^{70} - 11376 q^{72} + 11560 q^{73} + 17304 q^{74} + 1680 q^{77} - 24740 q^{78} + 12900 q^{80} + 13604 q^{81} - 18420 q^{82} + 5644 q^{84} - 11552 q^{85} + 24564 q^{86} - 15304 q^{88} + 13800 q^{89} - 60212 q^{90} - 2142 q^{92} + 34592 q^{93} - 23096 q^{94} - 35770 q^{96} + 8200 q^{97} + 25566 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32469 3.25512i −0.581172 0.813781i
\(3\) 7.75287i 0.861430i −0.902488 0.430715i \(-0.858261\pi\)
0.902488 0.430715i \(-0.141739\pi\)
\(4\) −5.19165 + 15.1343i −0.324478 + 0.945893i
\(5\) 27.0702 1.08281 0.541403 0.840763i \(-0.317893\pi\)
0.541403 + 0.840763i \(0.317893\pi\)
\(6\) −25.2365 + 18.0230i −0.701015 + 0.500639i
\(7\) 95.4821i 1.94861i 0.225223 + 0.974307i \(0.427689\pi\)
−0.225223 + 0.974307i \(0.572311\pi\)
\(8\) 61.3329 18.2830i 0.958327 0.285673i
\(9\) 20.8930 0.257938
\(10\) −62.9297 88.1167i −0.629297 0.881167i
\(11\) 138.578i 1.14528i 0.819809 + 0.572638i \(0.194080\pi\)
−0.819809 + 0.572638i \(0.805920\pi\)
\(12\) 117.334 + 40.2502i 0.814821 + 0.279515i
\(13\) −68.1130 −0.403035 −0.201518 0.979485i \(-0.564587\pi\)
−0.201518 + 0.979485i \(0.564587\pi\)
\(14\) 310.806 221.966i 1.58574 1.13248i
\(15\) 209.872i 0.932762i
\(16\) −202.094 157.144i −0.789428 0.613843i
\(17\) 261.853 0.906067 0.453033 0.891494i \(-0.350342\pi\)
0.453033 + 0.891494i \(0.350342\pi\)
\(18\) −48.5697 68.0093i −0.149906 0.209905i
\(19\) 82.8191i 0.229416i
\(20\) −140.539 + 409.688i −0.351347 + 1.02422i
\(21\) 740.260 1.67860
\(22\) 451.090 322.151i 0.932003 0.665602i
\(23\) 46.0152i 0.0869852i −0.999054 0.0434926i \(-0.986152\pi\)
0.999054 0.0434926i \(-0.0138485\pi\)
\(24\) −141.746 475.506i −0.246087 0.825532i
\(25\) 107.794 0.172471
\(26\) 158.341 + 221.716i 0.234233 + 0.327982i
\(27\) 789.963i 1.08363i
\(28\) −1445.05 495.710i −1.84318 0.632283i
\(29\) 508.504 0.604642 0.302321 0.953206i \(-0.402239\pi\)
0.302321 + 0.953206i \(0.402239\pi\)
\(30\) −683.158 + 487.886i −0.759064 + 0.542095i
\(31\) 995.645i 1.03605i 0.855365 + 0.518026i \(0.173333\pi\)
−0.855365 + 0.518026i \(0.826667\pi\)
\(32\) −41.7183 + 1023.15i −0.0407405 + 0.999170i
\(33\) 1074.38 0.986575
\(34\) −608.727 852.365i −0.526581 0.737340i
\(35\) 2584.72i 2.10997i
\(36\) −108.469 + 316.201i −0.0836953 + 0.243982i
\(37\) 1035.44 0.756346 0.378173 0.925735i \(-0.376552\pi\)
0.378173 + 0.925735i \(0.376552\pi\)
\(38\) −269.586 + 192.529i −0.186694 + 0.133330i
\(39\) 528.071i 0.347187i
\(40\) 1660.29 494.925i 1.03768 0.309328i
\(41\) −1768.23 −1.05189 −0.525947 0.850517i \(-0.676289\pi\)
−0.525947 + 0.850517i \(0.676289\pi\)
\(42\) −1720.87 2409.64i −0.975552 1.36601i
\(43\) 249.767i 0.135082i −0.997716 0.0675411i \(-0.978485\pi\)
0.997716 0.0675411i \(-0.0215154\pi\)
\(44\) −2097.28 719.450i −1.08331 0.371617i
\(45\) 565.577 0.279297
\(46\) −149.785 + 106.971i −0.0707869 + 0.0505534i
\(47\) 345.338i 0.156332i 0.996940 + 0.0781661i \(0.0249065\pi\)
−0.996940 + 0.0781661i \(0.975094\pi\)
\(48\) −1218.32 + 1566.81i −0.528783 + 0.680037i
\(49\) −6715.83 −2.79710
\(50\) −250.588 350.883i −0.100235 0.140353i
\(51\) 2030.11i 0.780513i
\(52\) 353.619 1030.84i 0.130776 0.381228i
\(53\) 2136.43 0.760567 0.380284 0.924870i \(-0.375826\pi\)
0.380284 + 0.924870i \(0.375826\pi\)
\(54\) −2571.43 + 1836.42i −0.881834 + 0.629773i
\(55\) 3751.34i 1.24011i
\(56\) 1745.70 + 5856.20i 0.556666 + 1.86741i
\(57\) −642.086 −0.197626
\(58\) −1182.11 1655.24i −0.351401 0.492046i
\(59\) 5022.76i 1.44291i −0.692462 0.721454i \(-0.743474\pi\)
0.692462 0.721454i \(-0.256526\pi\)
\(60\) 3176.26 + 1089.58i 0.882294 + 0.302661i
\(61\) 6478.12 1.74096 0.870481 0.492201i \(-0.163808\pi\)
0.870481 + 0.492201i \(0.163808\pi\)
\(62\) 3240.95 2314.57i 0.843119 0.602124i
\(63\) 1994.91i 0.502622i
\(64\) 3427.46 2242.71i 0.836782 0.547536i
\(65\) −1843.83 −0.436409
\(66\) −2497.60 3497.24i −0.573370 0.802856i
\(67\) 3188.74i 0.710346i 0.934801 + 0.355173i \(0.115578\pi\)
−0.934801 + 0.355173i \(0.884422\pi\)
\(68\) −1359.45 + 3962.96i −0.293999 + 0.857042i
\(69\) −356.750 −0.0749317
\(70\) 8413.57 6008.66i 1.71706 1.22626i
\(71\) 824.209i 0.163501i 0.996653 + 0.0817505i \(0.0260511\pi\)
−0.996653 + 0.0817505i \(0.973949\pi\)
\(72\) 1281.43 381.988i 0.247189 0.0736859i
\(73\) 6551.48 1.22940 0.614701 0.788760i \(-0.289277\pi\)
0.614701 + 0.788760i \(0.289277\pi\)
\(74\) −2407.07 3370.48i −0.439567 0.615500i
\(75\) 835.715i 0.148571i
\(76\) 1253.41 + 429.968i 0.217003 + 0.0744404i
\(77\) −13231.8 −2.23170
\(78\) 1718.94 1227.60i 0.282534 0.201775i
\(79\) 11180.3i 1.79142i −0.444635 0.895712i \(-0.646667\pi\)
0.444635 0.895712i \(-0.353333\pi\)
\(80\) −5470.71 4253.91i −0.854798 0.664674i
\(81\) −4432.15 −0.675530
\(82\) 4110.59 + 5755.82i 0.611332 + 0.856012i
\(83\) 1997.06i 0.289891i −0.989440 0.144945i \(-0.953699\pi\)
0.989440 0.144945i \(-0.0463007\pi\)
\(84\) −3843.17 + 11203.3i −0.544667 + 1.58777i
\(85\) 7088.41 0.981095
\(86\) −813.023 + 580.631i −0.109927 + 0.0785060i
\(87\) 3942.36i 0.520857i
\(88\) 2533.63 + 8499.42i 0.327174 + 1.09755i
\(89\) 8875.25 1.12047 0.560235 0.828333i \(-0.310711\pi\)
0.560235 + 0.828333i \(0.310711\pi\)
\(90\) −1314.79 1841.02i −0.162320 0.227287i
\(91\) 6503.57i 0.785360i
\(92\) 696.407 + 238.895i 0.0822787 + 0.0282248i
\(93\) 7719.11 0.892486
\(94\) 1124.12 802.803i 0.127220 0.0908559i
\(95\) 2241.93i 0.248413i
\(96\) 7932.35 + 323.436i 0.860715 + 0.0350951i
\(97\) −14573.4 −1.54888 −0.774440 0.632647i \(-0.781968\pi\)
−0.774440 + 0.632647i \(0.781968\pi\)
\(98\) 15612.2 + 21860.9i 1.62560 + 2.27622i
\(99\) 2895.32i 0.295410i
\(100\) −559.630 + 1631.39i −0.0559630 + 0.163139i
\(101\) −18606.9 −1.82403 −0.912015 0.410157i \(-0.865474\pi\)
−0.912015 + 0.410157i \(0.865474\pi\)
\(102\) −6608.27 + 4719.38i −0.635167 + 0.453612i
\(103\) 11364.5i 1.07121i −0.844467 0.535607i \(-0.820083\pi\)
0.844467 0.535607i \(-0.179917\pi\)
\(104\) −4177.57 + 1245.31i −0.386240 + 0.115136i
\(105\) 20039.0 1.81759
\(106\) −4966.54 6954.35i −0.442020 0.618935i
\(107\) 19962.5i 1.74360i 0.489863 + 0.871799i \(0.337047\pi\)
−0.489863 + 0.871799i \(0.662953\pi\)
\(108\) 11955.5 + 4101.21i 1.02499 + 0.351613i
\(109\) −6277.28 −0.528346 −0.264173 0.964475i \(-0.585099\pi\)
−0.264173 + 0.964475i \(0.585099\pi\)
\(110\) 12211.1 8720.69i 1.00918 0.720719i
\(111\) 8027.62i 0.651539i
\(112\) 15004.4 19296.3i 1.19614 1.53829i
\(113\) −19344.5 −1.51495 −0.757477 0.652861i \(-0.773568\pi\)
−0.757477 + 0.652861i \(0.773568\pi\)
\(114\) 1492.65 + 2090.07i 0.114854 + 0.160824i
\(115\) 1245.64i 0.0941882i
\(116\) −2639.97 + 7695.84i −0.196193 + 0.571927i
\(117\) −1423.08 −0.103958
\(118\) −16349.7 + 11676.4i −1.17421 + 0.838578i
\(119\) 25002.3i 1.76557i
\(120\) −3837.09 12872.0i −0.266465 0.893892i
\(121\) −4562.96 −0.311656
\(122\) −15059.6 21087.1i −1.01180 1.41676i
\(123\) 13708.9i 0.906134i
\(124\) −15068.4 5169.04i −0.979994 0.336176i
\(125\) −14000.8 −0.896054
\(126\) 6493.67 4637.54i 0.409024 0.292110i
\(127\) 715.835i 0.0443819i 0.999754 + 0.0221909i \(0.00706418\pi\)
−0.999754 + 0.0221909i \(0.992936\pi\)
\(128\) −15268.1 5943.21i −0.931888 0.362745i
\(129\) −1936.41 −0.116364
\(130\) 4286.33 + 6001.89i 0.253629 + 0.355142i
\(131\) 4998.11i 0.291248i −0.989340 0.145624i \(-0.953481\pi\)
0.989340 0.145624i \(-0.0465190\pi\)
\(132\) −5577.81 + 16260.0i −0.320122 + 0.933194i
\(133\) 7907.74 0.447043
\(134\) 10379.7 7412.83i 0.578066 0.412833i
\(135\) 21384.4i 1.17336i
\(136\) 16060.2 4787.48i 0.868308 0.258838i
\(137\) 11383.7 0.606516 0.303258 0.952908i \(-0.401926\pi\)
0.303258 + 0.952908i \(0.401926\pi\)
\(138\) 829.332 + 1161.26i 0.0435482 + 0.0609780i
\(139\) 32382.6i 1.67603i −0.545644 0.838017i \(-0.683715\pi\)
0.545644 0.838017i \(-0.316285\pi\)
\(140\) −39117.9 13418.9i −1.99581 0.684640i
\(141\) 2677.36 0.134669
\(142\) 2682.90 1916.03i 0.133054 0.0950222i
\(143\) 9438.98i 0.461586i
\(144\) −4222.34 3283.21i −0.203624 0.158334i
\(145\) 13765.3 0.654710
\(146\) −15230.2 21325.9i −0.714494 1.00046i
\(147\) 52067.0i 2.40950i
\(148\) −5375.63 + 15670.6i −0.245418 + 0.715423i
\(149\) 21304.2 0.959604 0.479802 0.877377i \(-0.340709\pi\)
0.479802 + 0.877377i \(0.340709\pi\)
\(150\) −2720.35 + 1942.78i −0.120905 + 0.0863456i
\(151\) 5913.44i 0.259350i −0.991557 0.129675i \(-0.958607\pi\)
0.991557 0.129675i \(-0.0413934\pi\)
\(152\) −1514.19 5079.54i −0.0655378 0.219855i
\(153\) 5470.90 0.233709
\(154\) 30759.7 + 43071.0i 1.29700 + 1.81611i
\(155\) 26952.3i 1.12184i
\(156\) −7991.98 2741.56i −0.328402 0.112655i
\(157\) −4806.24 −0.194987 −0.0974936 0.995236i \(-0.531083\pi\)
−0.0974936 + 0.995236i \(0.531083\pi\)
\(158\) −36393.2 + 25990.7i −1.45783 + 1.04113i
\(159\) 16563.5i 0.655175i
\(160\) −1129.32 + 27696.8i −0.0441141 + 1.08191i
\(161\) 4393.63 0.169501
\(162\) 10303.4 + 14427.2i 0.392599 + 0.549733i
\(163\) 39375.3i 1.48200i 0.671504 + 0.741001i \(0.265649\pi\)
−0.671504 + 0.741001i \(0.734351\pi\)
\(164\) 9180.06 26761.0i 0.341317 0.994980i
\(165\) 29083.7 1.06827
\(166\) −6500.67 + 4642.54i −0.235908 + 0.168477i
\(167\) 18655.2i 0.668910i 0.942412 + 0.334455i \(0.108552\pi\)
−0.942412 + 0.334455i \(0.891448\pi\)
\(168\) 45402.4 13534.2i 1.60864 0.479529i
\(169\) −23921.6 −0.837563
\(170\) −16478.3 23073.7i −0.570185 0.798396i
\(171\) 1730.34i 0.0591751i
\(172\) 3780.05 + 1296.70i 0.127773 + 0.0438312i
\(173\) 11613.0 0.388017 0.194008 0.981000i \(-0.437851\pi\)
0.194008 + 0.981000i \(0.437851\pi\)
\(174\) −12832.9 + 9164.77i −0.423863 + 0.302707i
\(175\) 10292.4i 0.336079i
\(176\) 21776.7 28005.8i 0.703020 0.904112i
\(177\) −38940.8 −1.24296
\(178\) −20632.2 28890.0i −0.651186 0.911818i
\(179\) 32946.4i 1.02826i −0.857713 0.514128i \(-0.828116\pi\)
0.857713 0.514128i \(-0.171884\pi\)
\(180\) −2936.28 + 8559.61i −0.0906258 + 0.264185i
\(181\) 15644.6 0.477538 0.238769 0.971076i \(-0.423256\pi\)
0.238769 + 0.971076i \(0.423256\pi\)
\(182\) −21169.9 + 15118.8i −0.639111 + 0.456429i
\(183\) 50224.0i 1.49972i
\(184\) −841.298 2822.25i −0.0248493 0.0833603i
\(185\) 28029.5 0.818977
\(186\) −17944.5 25126.7i −0.518688 0.726288i
\(187\) 36287.2i 1.03770i
\(188\) −5226.45 1792.87i −0.147874 0.0507264i
\(189\) 75427.3 2.11157
\(190\) −7297.75 + 5211.78i −0.202154 + 0.144371i
\(191\) 38399.7i 1.05259i −0.850301 0.526297i \(-0.823580\pi\)
0.850301 0.526297i \(-0.176420\pi\)
\(192\) −17387.4 26572.7i −0.471664 0.720829i
\(193\) 23655.4 0.635062 0.317531 0.948248i \(-0.397146\pi\)
0.317531 + 0.948248i \(0.397146\pi\)
\(194\) 33878.6 + 47438.2i 0.900166 + 1.26045i
\(195\) 14295.0i 0.375936i
\(196\) 34866.3 101639.i 0.907597 2.64576i
\(197\) 32656.2 0.841460 0.420730 0.907186i \(-0.361774\pi\)
0.420730 + 0.907186i \(0.361774\pi\)
\(198\) 9424.61 6730.71i 0.240399 0.171684i
\(199\) 17582.4i 0.443989i −0.975048 0.221995i \(-0.928743\pi\)
0.975048 0.221995i \(-0.0712568\pi\)
\(200\) 6611.34 1970.81i 0.165283 0.0492702i
\(201\) 24721.9 0.611913
\(202\) 43255.3 + 60567.8i 1.06008 + 1.48436i
\(203\) 48553.0i 1.17821i
\(204\) 30724.3 + 10539.6i 0.738282 + 0.253259i
\(205\) −47866.4 −1.13900
\(206\) −36992.9 + 26418.9i −0.871733 + 0.622559i
\(207\) 961.395i 0.0224368i
\(208\) 13765.2 + 10703.5i 0.318167 + 0.247401i
\(209\) 11476.9 0.262744
\(210\) −46584.4 65229.3i −1.05633 1.47912i
\(211\) 8226.23i 0.184772i −0.995723 0.0923860i \(-0.970551\pi\)
0.995723 0.0923860i \(-0.0294494\pi\)
\(212\) −11091.6 + 32333.4i −0.246787 + 0.719415i
\(213\) 6389.98 0.140845
\(214\) 64980.3 46406.5i 1.41891 1.01333i
\(215\) 6761.24i 0.146268i
\(216\) −14442.9 48450.8i −0.309562 1.03847i
\(217\) −95066.3 −2.01886
\(218\) 14592.7 + 20433.3i 0.307060 + 0.429958i
\(219\) 50792.8i 1.05904i
\(220\) −56773.9 19475.6i −1.17301 0.402389i
\(221\) −17835.6 −0.365177
\(222\) −26130.9 + 18661.7i −0.530210 + 0.378656i
\(223\) 48097.4i 0.967189i −0.875292 0.483595i \(-0.839331\pi\)
0.875292 0.483595i \(-0.160669\pi\)
\(224\) −97692.5 3983.35i −1.94700 0.0793875i
\(225\) 2252.14 0.0444868
\(226\) 44969.8 + 62968.6i 0.880449 + 1.23284i
\(227\) 31760.4i 0.616359i 0.951328 + 0.308180i \(0.0997198\pi\)
−0.951328 + 0.308180i \(0.900280\pi\)
\(228\) 3333.48 9717.51i 0.0641252 0.186933i
\(229\) −54243.4 −1.03437 −0.517185 0.855874i \(-0.673020\pi\)
−0.517185 + 0.855874i \(0.673020\pi\)
\(230\) −4054.71 + 2895.72i −0.0766485 + 0.0547396i
\(231\) 102584.i 1.92245i
\(232\) 31188.0 9297.00i 0.579445 0.172730i
\(233\) 108192. 1.99289 0.996447 0.0842239i \(-0.0268411\pi\)
0.996447 + 0.0842239i \(0.0268411\pi\)
\(234\) 3308.23 + 4632.31i 0.0604176 + 0.0845992i
\(235\) 9348.36i 0.169278i
\(236\) 76016.0 + 26076.4i 1.36484 + 0.468192i
\(237\) −86679.2 −1.54319
\(238\) 81385.6 58122.6i 1.43679 1.02610i
\(239\) 2954.27i 0.0517195i 0.999666 + 0.0258598i \(0.00823233\pi\)
−0.999666 + 0.0258598i \(0.991768\pi\)
\(240\) −32980.0 + 42413.7i −0.572570 + 0.736349i
\(241\) −42725.9 −0.735627 −0.367813 0.929900i \(-0.619893\pi\)
−0.367813 + 0.929900i \(0.619893\pi\)
\(242\) 10607.4 + 14853.0i 0.181126 + 0.253620i
\(243\) 29625.1i 0.501704i
\(244\) −33632.1 + 98041.8i −0.564904 + 1.64676i
\(245\) −181799. −3.02872
\(246\) 44624.1 31868.9i 0.737394 0.526620i
\(247\) 5641.05i 0.0924626i
\(248\) 18203.4 + 61065.9i 0.295972 + 0.992876i
\(249\) −15482.9 −0.249721
\(250\) 32547.6 + 45574.5i 0.520762 + 0.729192i
\(251\) 23355.5i 0.370717i −0.982671 0.185359i \(-0.940655\pi\)
0.982671 0.185359i \(-0.0593446\pi\)
\(252\) −30191.5 10356.9i −0.475427 0.163090i
\(253\) 6376.71 0.0996221
\(254\) 2330.13 1664.09i 0.0361171 0.0257935i
\(255\) 54955.6i 0.845145i
\(256\) 16147.6 + 63515.5i 0.246393 + 0.969170i
\(257\) −72635.4 −1.09972 −0.549860 0.835257i \(-0.685319\pi\)
−0.549860 + 0.835257i \(0.685319\pi\)
\(258\) 4501.55 + 6303.26i 0.0676275 + 0.0946947i
\(259\) 98865.8i 1.47383i
\(260\) 9572.52 27905.1i 0.141605 0.412797i
\(261\) 10624.2 0.155960
\(262\) −16269.5 + 11619.0i −0.237012 + 0.169265i
\(263\) 26045.0i 0.376542i 0.982117 + 0.188271i \(0.0602884\pi\)
−0.982117 + 0.188271i \(0.939712\pi\)
\(264\) 65894.9 19642.9i 0.945462 0.281837i
\(265\) 57833.6 0.823547
\(266\) −18383.0 25740.7i −0.259809 0.363795i
\(267\) 68808.7i 0.965207i
\(268\) −48259.3 16554.8i −0.671911 0.230492i
\(269\) −1823.60 −0.0252014 −0.0126007 0.999921i \(-0.504011\pi\)
−0.0126007 + 0.999921i \(0.504011\pi\)
\(270\) −69609.0 + 49712.2i −0.954856 + 0.681923i
\(271\) 51451.6i 0.700585i −0.936640 0.350292i \(-0.886082\pi\)
0.936640 0.350292i \(-0.113918\pi\)
\(272\) −52918.9 41148.6i −0.715274 0.556183i
\(273\) −50421.3 −0.676533
\(274\) −26463.6 37055.4i −0.352490 0.493571i
\(275\) 14937.9i 0.197526i
\(276\) 1852.12 5399.16i 0.0243137 0.0708774i
\(277\) 72997.4 0.951367 0.475683 0.879617i \(-0.342201\pi\)
0.475683 + 0.879617i \(0.342201\pi\)
\(278\) −105410. + 75279.6i −1.36392 + 0.974064i
\(279\) 20802.0i 0.267237i
\(280\) 47256.5 + 158528.i 0.602761 + 2.02204i
\(281\) 66784.4 0.845790 0.422895 0.906179i \(-0.361014\pi\)
0.422895 + 0.906179i \(0.361014\pi\)
\(282\) −6224.03 8715.14i −0.0782660 0.109591i
\(283\) 152009.i 1.89800i −0.315277 0.949000i \(-0.602098\pi\)
0.315277 0.949000i \(-0.397902\pi\)
\(284\) −12473.8 4279.00i −0.154654 0.0530525i
\(285\) −17381.4 −0.213990
\(286\) −30725.0 + 21942.7i −0.375630 + 0.268261i
\(287\) 168835.i 2.04974i
\(288\) −871.619 + 21376.7i −0.0105085 + 0.257724i
\(289\) −14953.9 −0.179043
\(290\) −32000.0 44807.7i −0.380499 0.532791i
\(291\) 112986.i 1.33425i
\(292\) −34013.0 + 99152.1i −0.398914 + 1.16288i
\(293\) −33912.7 −0.395027 −0.197514 0.980300i \(-0.563287\pi\)
−0.197514 + 0.980300i \(0.563287\pi\)
\(294\) 169484. 121039.i 1.96081 1.40034i
\(295\) 135967.i 1.56239i
\(296\) 63506.5 18931.0i 0.724827 0.216067i
\(297\) 109472. 1.24105
\(298\) −49525.5 69347.7i −0.557695 0.780907i
\(299\) 3134.23i 0.0350581i
\(300\) 12647.9 + 4338.74i 0.140533 + 0.0482082i
\(301\) 23848.3 0.263223
\(302\) −19249.0 + 13746.9i −0.211054 + 0.150727i
\(303\) 144257.i 1.57127i
\(304\) −13014.5 + 16737.2i −0.140825 + 0.181107i
\(305\) 175364. 1.88513
\(306\) −12718.1 17808.4i −0.135825 0.190188i
\(307\) 38139.5i 0.404667i 0.979317 + 0.202334i \(0.0648525\pi\)
−0.979317 + 0.202334i \(0.935147\pi\)
\(308\) 68694.6 200253.i 0.724138 2.11095i
\(309\) −88107.5 −0.922776
\(310\) 87733.0 62655.7i 0.912935 0.651984i
\(311\) 69149.4i 0.714937i −0.933925 0.357468i \(-0.883640\pi\)
0.933925 0.357468i \(-0.116360\pi\)
\(312\) 9654.75 + 32388.1i 0.0991817 + 0.332718i
\(313\) −114540. −1.16915 −0.584575 0.811340i \(-0.698739\pi\)
−0.584575 + 0.811340i \(0.698739\pi\)
\(314\) 11173.0 + 15644.9i 0.113321 + 0.158677i
\(315\) 54002.5i 0.544243i
\(316\) 169206. + 58044.1i 1.69450 + 0.581278i
\(317\) −58663.2 −0.583778 −0.291889 0.956452i \(-0.594284\pi\)
−0.291889 + 0.956452i \(0.594284\pi\)
\(318\) −53916.2 + 38504.9i −0.533169 + 0.380770i
\(319\) 70467.6i 0.692482i
\(320\) 92781.9 60710.4i 0.906074 0.592875i
\(321\) 154766. 1.50199
\(322\) −10213.8 14301.8i −0.0985090 0.137936i
\(323\) 21686.4i 0.207866i
\(324\) 23010.2 67077.5i 0.219195 0.638979i
\(325\) −7342.18 −0.0695118
\(326\) 128172. 91535.3i 1.20603 0.861298i
\(327\) 48666.9i 0.455133i
\(328\) −108451. + 32328.7i −1.00806 + 0.300497i
\(329\) −32973.6 −0.304631
\(330\) −67610.4 94670.9i −0.620849 0.869338i
\(331\) 110676.i 1.01018i 0.863067 + 0.505090i \(0.168541\pi\)
−0.863067 + 0.505090i \(0.831459\pi\)
\(332\) 30224.1 + 10368.0i 0.274206 + 0.0940633i
\(333\) 21633.4 0.195091
\(334\) 60725.1 43367.6i 0.544346 0.388752i
\(335\) 86319.8i 0.769167i
\(336\) −149602. 116327.i −1.32513 1.03039i
\(337\) −52549.8 −0.462712 −0.231356 0.972869i \(-0.574316\pi\)
−0.231356 + 0.972869i \(0.574316\pi\)
\(338\) 55610.3 + 77867.8i 0.486768 + 0.681592i
\(339\) 149975.i 1.30503i
\(340\) −36800.6 + 107278.i −0.318344 + 0.928011i
\(341\) −137975. −1.18656
\(342\) −5632.46 + 4022.50i −0.0481555 + 0.0343909i
\(343\) 411989.i 3.50185i
\(344\) −4566.50 15319.0i −0.0385893 0.129453i
\(345\) −9657.28 −0.0811366
\(346\) −26996.5 37801.6i −0.225504 0.315761i
\(347\) 58173.0i 0.483128i 0.970385 + 0.241564i \(0.0776604\pi\)
−0.970385 + 0.241564i \(0.922340\pi\)
\(348\) 59664.9 + 20467.4i 0.492675 + 0.169007i
\(349\) 93243.7 0.765542 0.382771 0.923843i \(-0.374970\pi\)
0.382771 + 0.923843i \(0.374970\pi\)
\(350\) 33503.1 23926.7i 0.273495 0.195320i
\(351\) 53806.7i 0.436739i
\(352\) −141786. 5781.25i −1.14432 0.0466591i
\(353\) 204758. 1.64320 0.821601 0.570063i \(-0.193081\pi\)
0.821601 + 0.570063i \(0.193081\pi\)
\(354\) 90525.3 + 126757.i 0.722376 + 1.01150i
\(355\) 22311.5i 0.177040i
\(356\) −46077.2 + 134321.i −0.363568 + 1.05985i
\(357\) 193840. 1.52092
\(358\) −107244. + 76590.0i −0.836775 + 0.597594i
\(359\) 34342.6i 0.266468i 0.991085 + 0.133234i \(0.0425362\pi\)
−0.991085 + 0.133234i \(0.957464\pi\)
\(360\) 34688.5 10340.5i 0.267658 0.0797876i
\(361\) −6859.00 −0.0526316
\(362\) −36368.9 50925.2i −0.277532 0.388611i
\(363\) 35376.0i 0.268470i
\(364\) 98426.9 + 33764.3i 0.742867 + 0.254832i
\(365\) 177350. 1.33121
\(366\) −163485. + 116755.i −1.22044 + 0.871594i
\(367\) 149381.i 1.10908i −0.832157 0.554540i \(-0.812894\pi\)
0.832157 0.554540i \(-0.187106\pi\)
\(368\) −7231.01 + 9299.37i −0.0533953 + 0.0686686i
\(369\) −36943.7 −0.271324
\(370\) −65159.8 91239.4i −0.475966 0.666468i
\(371\) 203991.i 1.48205i
\(372\) −40074.9 + 116823.i −0.289592 + 0.844196i
\(373\) 46484.3 0.334110 0.167055 0.985948i \(-0.446574\pi\)
0.167055 + 0.985948i \(0.446574\pi\)
\(374\) 118119. 84356.4i 0.844457 0.603080i
\(375\) 108547.i 0.771888i
\(376\) 6313.83 + 21180.6i 0.0446598 + 0.149817i
\(377\) −34635.7 −0.243692
\(378\) −175345. 245525.i −1.22718 1.71835i
\(379\) 30244.9i 0.210559i 0.994443 + 0.105279i \(0.0335737\pi\)
−0.994443 + 0.105279i \(0.966426\pi\)
\(380\) 33930.0 + 11639.3i 0.234972 + 0.0806046i
\(381\) 5549.78 0.0382319
\(382\) −124996. + 89267.2i −0.856580 + 0.611738i
\(383\) 243104.i 1.65728i 0.559785 + 0.828638i \(0.310884\pi\)
−0.559785 + 0.828638i \(0.689116\pi\)
\(384\) −46077.0 + 118371.i −0.312479 + 0.802757i
\(385\) −358186. −2.41650
\(386\) −54991.5 77001.4i −0.369080 0.516802i
\(387\) 5218.38i 0.0348429i
\(388\) 75660.1 220558.i 0.502578 1.46508i
\(389\) 142045. 0.938700 0.469350 0.883012i \(-0.344488\pi\)
0.469350 + 0.883012i \(0.344488\pi\)
\(390\) 46531.9 33231.4i 0.305930 0.218484i
\(391\) 12049.2i 0.0788144i
\(392\) −411902. + 122786.i −2.68054 + 0.799054i
\(393\) −38749.7 −0.250890
\(394\) −75915.6 106300.i −0.489033 0.684764i
\(395\) 302652.i 1.93977i
\(396\) −43818.6 15031.5i −0.279427 0.0958542i
\(397\) 106459. 0.675464 0.337732 0.941242i \(-0.390340\pi\)
0.337732 + 0.941242i \(0.390340\pi\)
\(398\) −57233.0 + 40873.7i −0.361310 + 0.258034i
\(399\) 61307.7i 0.385096i
\(400\) −21784.5 16939.2i −0.136153 0.105870i
\(401\) 10549.6 0.0656063 0.0328031 0.999462i \(-0.489557\pi\)
0.0328031 + 0.999462i \(0.489557\pi\)
\(402\) −57470.7 80472.8i −0.355627 0.497963i
\(403\) 67816.4i 0.417565i
\(404\) 96600.7 281603.i 0.591858 1.72534i
\(405\) −119979. −0.731468
\(406\) 158046. 112871.i 0.958808 0.684745i
\(407\) 143489.i 0.866225i
\(408\) −37116.7 124513.i −0.222971 0.747987i
\(409\) −2759.57 −0.0164966 −0.00824830 0.999966i \(-0.502626\pi\)
−0.00824830 + 0.999966i \(0.502626\pi\)
\(410\) 111275. + 155811.i 0.661954 + 0.926895i
\(411\) 88256.4i 0.522472i
\(412\) 171994. + 59000.5i 1.01325 + 0.347585i
\(413\) 479584. 2.81167
\(414\) −3129.46 + 2234.94i −0.0182586 + 0.0130396i
\(415\) 54060.7i 0.313896i
\(416\) 2841.55 69689.8i 0.0164199 0.402701i
\(417\) −251058. −1.44379
\(418\) −26680.3 37358.8i −0.152700 0.213816i
\(419\) 36994.3i 0.210720i −0.994434 0.105360i \(-0.966400\pi\)
0.994434 0.105360i \(-0.0335996\pi\)
\(420\) −104035. + 303276.i −0.589770 + 1.71925i
\(421\) −197130. −1.11221 −0.556107 0.831111i \(-0.687705\pi\)
−0.556107 + 0.831111i \(0.687705\pi\)
\(422\) −26777.4 + 19123.4i −0.150364 + 0.107384i
\(423\) 7215.14i 0.0403241i
\(424\) 131034. 39060.5i 0.728872 0.217273i
\(425\) 28226.3 0.156270
\(426\) −14854.7 20800.2i −0.0818550 0.114617i
\(427\) 618545.i 3.39247i
\(428\) −302118. 103638.i −1.64926 0.565760i
\(429\) −73179.2 −0.397624
\(430\) −22008.7 + 15717.8i −0.119030 + 0.0850069i
\(431\) 179901.i 0.968455i −0.874942 0.484227i \(-0.839101\pi\)
0.874942 0.484227i \(-0.160899\pi\)
\(432\) −124138. + 159646.i −0.665176 + 0.855444i
\(433\) −79092.9 −0.421853 −0.210927 0.977502i \(-0.567648\pi\)
−0.210927 + 0.977502i \(0.567648\pi\)
\(434\) 221000. + 309453.i 1.17331 + 1.64291i
\(435\) 106720.i 0.563987i
\(436\) 32589.4 95002.2i 0.171437 0.499759i
\(437\) −3810.94 −0.0199558
\(438\) −165337. + 118077.i −0.861830 + 0.615487i
\(439\) 178466.i 0.926035i −0.886349 0.463017i \(-0.846767\pi\)
0.886349 0.463017i \(-0.153233\pi\)
\(440\) 68585.9 + 230081.i 0.354266 + 1.18843i
\(441\) −140314. −0.721478
\(442\) 41462.2 + 58057.1i 0.212231 + 0.297174i
\(443\) 308460.i 1.57178i 0.618366 + 0.785890i \(0.287795\pi\)
−0.618366 + 0.785890i \(0.712205\pi\)
\(444\) 121492. + 41676.6i 0.616287 + 0.211410i
\(445\) 240255. 1.21325
\(446\) −156563. + 111811.i −0.787080 + 0.562103i
\(447\) 165168.i 0.826632i
\(448\) 214138. + 327261.i 1.06694 + 1.63057i
\(449\) 26812.0 0.132995 0.0664977 0.997787i \(-0.478817\pi\)
0.0664977 + 0.997787i \(0.478817\pi\)
\(450\) −5235.53 7331.00i −0.0258545 0.0362025i
\(451\) 245039.i 1.20471i
\(452\) 100430. 292765.i 0.491570 1.43299i
\(453\) −45846.2 −0.223412
\(454\) 103384. 73833.0i 0.501581 0.358211i
\(455\) 176053.i 0.850394i
\(456\) −39381.0 + 11739.3i −0.189390 + 0.0564562i
\(457\) −305012. −1.46044 −0.730222 0.683209i \(-0.760584\pi\)
−0.730222 + 0.683209i \(0.760584\pi\)
\(458\) 126099. + 176569.i 0.601147 + 0.841750i
\(459\) 206854.i 0.981837i
\(460\) 18851.9 + 6466.92i 0.0890920 + 0.0305620i
\(461\) 48637.0 0.228858 0.114429 0.993431i \(-0.463496\pi\)
0.114429 + 0.993431i \(0.463496\pi\)
\(462\) 333924. 238476.i 1.56446 1.11728i
\(463\) 9810.69i 0.0457654i 0.999738 + 0.0228827i \(0.00728443\pi\)
−0.999738 + 0.0228827i \(0.992716\pi\)
\(464\) −102765. 79908.3i −0.477321 0.371155i
\(465\) 208958. 0.966390
\(466\) −251513. 352179.i −1.15821 1.62178i
\(467\) 139743.i 0.640761i 0.947289 + 0.320381i \(0.103811\pi\)
−0.947289 + 0.320381i \(0.896189\pi\)
\(468\) 7388.15 21537.4i 0.0337322 0.0983333i
\(469\) −304468. −1.38419
\(470\) 30430.1 21732.0i 0.137755 0.0983794i
\(471\) 37262.2i 0.167968i
\(472\) −91831.4 308061.i −0.412199 1.38278i
\(473\) 34612.3 0.154706
\(474\) 201502. + 282152.i 0.896857 + 1.25582i
\(475\) 8927.42i 0.0395675i
\(476\) −378392. 129803.i −1.67004 0.572890i
\(477\) 44636.5 0.196179
\(478\) 9616.51 6867.76i 0.0420883 0.0300579i
\(479\) 19255.8i 0.0839248i 0.999119 + 0.0419624i \(0.0133610\pi\)
−0.999119 + 0.0419624i \(0.986639\pi\)
\(480\) 214730. + 8755.48i 0.931988 + 0.0380012i
\(481\) −70526.8 −0.304834
\(482\) 99324.5 + 139078.i 0.427526 + 0.598639i
\(483\) 34063.2i 0.146013i
\(484\) 23689.3 69057.1i 0.101126 0.294793i
\(485\) −394505. −1.67714
\(486\) −96433.4 + 68869.2i −0.408277 + 0.291576i
\(487\) 421633.i 1.77778i −0.458124 0.888888i \(-0.651479\pi\)
0.458124 0.888888i \(-0.348521\pi\)
\(488\) 397322. 118440.i 1.66841 0.497345i
\(489\) 305272. 1.27664
\(490\) 422625. + 591777.i 1.76021 + 2.46471i
\(491\) 26607.2i 0.110366i 0.998476 + 0.0551830i \(0.0175742\pi\)
−0.998476 + 0.0551830i \(0.982426\pi\)
\(492\) −207474. 71171.8i −0.857106 0.294021i
\(493\) 133153. 0.547846
\(494\) 18362.3 13113.7i 0.0752443 0.0537367i
\(495\) 78376.7i 0.319872i
\(496\) 156460. 201213.i 0.635973 0.817888i
\(497\) −78697.2 −0.318600
\(498\) 35993.0 + 50398.9i 0.145131 + 0.203218i
\(499\) 307129.i 1.23344i 0.787181 + 0.616722i \(0.211540\pi\)
−0.787181 + 0.616722i \(0.788460\pi\)
\(500\) 72687.5 211893.i 0.290750 0.847572i
\(501\) 144632. 0.576219
\(502\) −76025.2 + 54294.4i −0.301682 + 0.215450i
\(503\) 60713.0i 0.239964i 0.992776 + 0.119982i \(0.0382836\pi\)
−0.992776 + 0.119982i \(0.961716\pi\)
\(504\) 36473.0 + 122354.i 0.143585 + 0.481676i
\(505\) −503693. −1.97507
\(506\) −14823.9 20757.0i −0.0578976 0.0810705i
\(507\) 185461.i 0.721502i
\(508\) −10833.7 3716.37i −0.0419805 0.0144010i
\(509\) −50488.9 −0.194877 −0.0974385 0.995242i \(-0.531065\pi\)
−0.0974385 + 0.995242i \(0.531065\pi\)
\(510\) −178887. + 127755.i −0.687763 + 0.491175i
\(511\) 625550.i 2.39563i
\(512\) 169213. 200216.i 0.645495 0.763764i
\(513\) −65424.0 −0.248601
\(514\) 168855. + 236437.i 0.639127 + 0.894931i
\(515\) 307639.i 1.15992i
\(516\) 10053.2 29306.2i 0.0377576 0.110068i
\(517\) −47856.4 −0.179044
\(518\) 321820. 229832.i 1.19937 0.856547i
\(519\) 90033.7i 0.334249i
\(520\) −113087. + 33710.8i −0.418223 + 0.124670i
\(521\) 346352. 1.27598 0.637988 0.770046i \(-0.279767\pi\)
0.637988 + 0.770046i \(0.279767\pi\)
\(522\) −24697.9 34583.0i −0.0906397 0.126917i
\(523\) 218022.i 0.797072i −0.917153 0.398536i \(-0.869518\pi\)
0.917153 0.398536i \(-0.130482\pi\)
\(524\) 75642.8 + 25948.4i 0.275490 + 0.0945037i
\(525\) 79795.8 0.289508
\(526\) 84779.8 60546.6i 0.306423 0.218836i
\(527\) 260713.i 0.938732i
\(528\) −217125. 168832.i −0.778830 0.605602i
\(529\) 277724. 0.992434
\(530\) −134445. 188256.i −0.478623 0.670187i
\(531\) 104941.i 0.372181i
\(532\) −41054.2 + 119678.i −0.145056 + 0.422855i
\(533\) 120440. 0.423951
\(534\) −223981. + 159959.i −0.785467 + 0.560951i
\(535\) 540387.i 1.88798i
\(536\) 58299.9 + 195575.i 0.202926 + 0.680744i
\(537\) −255429. −0.885771
\(538\) 4239.29 + 5936.03i 0.0146463 + 0.0205084i
\(539\) 930669.i 3.20345i
\(540\) 323638. + 111021.i 1.10987 + 0.380729i
\(541\) −206688. −0.706187 −0.353094 0.935588i \(-0.614870\pi\)
−0.353094 + 0.935588i \(0.614870\pi\)
\(542\) −167481. + 119609.i −0.570122 + 0.407160i
\(543\) 121291.i 0.411366i
\(544\) −10924.1 + 267915.i −0.0369136 + 0.905314i
\(545\) −169927. −0.572097
\(546\) 117214. + 164128.i 0.393182 + 0.550550i
\(547\) 393318.i 1.31453i −0.753662 0.657263i \(-0.771714\pi\)
0.753662 0.657263i \(-0.228286\pi\)
\(548\) −59100.2 + 172284.i −0.196801 + 0.573700i
\(549\) 135347. 0.449061
\(550\) 48624.8 34726.1i 0.160743 0.114797i
\(551\) 42113.8i 0.138714i
\(552\) −21880.5 + 6522.47i −0.0718091 + 0.0214059i
\(553\) 1.06752e6 3.49079
\(554\) −169696. 237616.i −0.552908 0.774204i
\(555\) 217309.i 0.705491i
\(556\) 490088. + 168119.i 1.58535 + 0.543836i
\(557\) −179469. −0.578469 −0.289234 0.957258i \(-0.593401\pi\)
−0.289234 + 0.957258i \(0.593401\pi\)
\(558\) 67713.1 48358.2i 0.217472 0.155311i
\(559\) 17012.4i 0.0544429i
\(560\) 406172. 522355.i 1.29519 1.66567i
\(561\) 281330. 0.893903
\(562\) −155253. 217391.i −0.491549 0.688287i
\(563\) 216106.i 0.681791i 0.940101 + 0.340895i \(0.110730\pi\)
−0.940101 + 0.340895i \(0.889270\pi\)
\(564\) −13899.9 + 40520.0i −0.0436973 + 0.127383i
\(565\) −523658. −1.64040
\(566\) −494808. + 353373.i −1.54456 + 1.10306i
\(567\) 423191.i 1.31635i
\(568\) 15069.0 + 50551.1i 0.0467078 + 0.156687i
\(569\) −359240. −1.10959 −0.554793 0.831989i \(-0.687202\pi\)
−0.554793 + 0.831989i \(0.687202\pi\)
\(570\) 40406.3 + 56578.5i 0.124365 + 0.174141i
\(571\) 338881.i 1.03938i −0.854355 0.519691i \(-0.826047\pi\)
0.854355 0.519691i \(-0.173953\pi\)
\(572\) 142852. + 49003.9i 0.436611 + 0.149775i
\(573\) −297708. −0.906736
\(574\) −549578. + 392488.i −1.66804 + 1.19125i
\(575\) 4960.17i 0.0150024i
\(576\) 71609.9 46856.8i 0.215838 0.141230i
\(577\) −173684. −0.521685 −0.260842 0.965381i \(-0.584000\pi\)
−0.260842 + 0.965381i \(0.584000\pi\)
\(578\) 34763.1 + 48676.7i 0.104055 + 0.145702i
\(579\) 183398.i 0.547062i
\(580\) −71464.5 + 208328.i −0.212439 + 0.619286i
\(581\) 190683. 0.564886
\(582\) 367783. 262657.i 1.08579 0.775430i
\(583\) 296063.i 0.871059i
\(584\) 401822. 119781.i 1.17817 0.351207i
\(585\) −38523.1 −0.112567
\(586\) 78836.4 + 110390.i 0.229579 + 0.321465i
\(587\) 11640.3i 0.0337823i 0.999857 + 0.0168911i \(0.00537687\pi\)
−0.999857 + 0.0168911i \(0.994623\pi\)
\(588\) −787997. 270314.i −2.27913 0.781831i
\(589\) 82458.4 0.237686
\(590\) −442590. + 316081.i −1.27144 + 0.908018i
\(591\) 253180.i 0.724859i
\(592\) −209255. 162713.i −0.597081 0.464278i
\(593\) 36753.2 0.104517 0.0522583 0.998634i \(-0.483358\pi\)
0.0522583 + 0.998634i \(0.483358\pi\)
\(594\) −254488. 356344.i −0.721264 1.00994i
\(595\) 676817.i 1.91178i
\(596\) −110604. + 322423.i −0.311371 + 0.907683i
\(597\) −136314. −0.382466
\(598\) 10202.3 7286.11i 0.0285296 0.0203748i
\(599\) 311824.i 0.869073i −0.900654 0.434536i \(-0.856912\pi\)
0.900654 0.434536i \(-0.143088\pi\)
\(600\) −15279.4 51256.8i −0.0424428 0.142380i
\(601\) 200210. 0.554289 0.277145 0.960828i \(-0.410612\pi\)
0.277145 + 0.960828i \(0.410612\pi\)
\(602\) −55439.8 77629.1i −0.152978 0.214206i
\(603\) 66622.3i 0.183225i
\(604\) 89495.8 + 30700.5i 0.245318 + 0.0841535i
\(605\) −123520. −0.337463
\(606\) 469575. 335353.i 1.27867 0.913181i
\(607\) 307693.i 0.835103i 0.908653 + 0.417551i \(0.137112\pi\)
−0.908653 + 0.417551i \(0.862888\pi\)
\(608\) 84736.3 + 3455.07i 0.229225 + 0.00934651i
\(609\) 376425. 1.01495
\(610\) −407666. 570831.i −1.09558 1.53408i
\(611\) 23522.0i 0.0630074i
\(612\) −28403.0 + 82798.2i −0.0758335 + 0.221064i
\(613\) −274260. −0.729862 −0.364931 0.931034i \(-0.618907\pi\)
−0.364931 + 0.931034i \(0.618907\pi\)
\(614\) 124149. 88662.4i 0.329310 0.235181i
\(615\) 371102.i 0.981168i
\(616\) −811542. + 241917.i −2.13870 + 0.637536i
\(617\) −409116. −1.07467 −0.537336 0.843368i \(-0.680569\pi\)
−0.537336 + 0.843368i \(0.680569\pi\)
\(618\) 204823. + 286801.i 0.536291 + 0.750937i
\(619\) 17549.2i 0.0458012i −0.999738 0.0229006i \(-0.992710\pi\)
0.999738 0.0229006i \(-0.00729012\pi\)
\(620\) −407904. 139927.i −1.06114 0.364014i
\(621\) −36350.3 −0.0942594
\(622\) −225090. + 160751.i −0.581802 + 0.415501i
\(623\) 847427.i 2.18337i
\(624\) 82983.1 106720.i 0.213118 0.274079i
\(625\) −446377. −1.14272
\(626\) 266271. + 372843.i 0.679477 + 0.951431i
\(627\) 88979.2i 0.226336i
\(628\) 24952.3 72739.0i 0.0632691 0.184437i
\(629\) 271133. 0.685300
\(630\) 175785. 125539.i 0.442894 0.316299i
\(631\) 494018.i 1.24075i 0.784305 + 0.620375i \(0.213020\pi\)
−0.784305 + 0.620375i \(0.786980\pi\)
\(632\) −204409. 685719.i −0.511761 1.71677i
\(633\) −63776.9 −0.159168
\(634\) 136374. + 190956.i 0.339275 + 0.475067i
\(635\) 19377.8i 0.0480570i
\(636\) 250677. + 85991.8i 0.619726 + 0.212590i
\(637\) 457435. 1.12733
\(638\) 229381. 163815.i 0.563528 0.402451i
\(639\) 17220.2i 0.0421732i
\(640\) −413309. 160884.i −1.00906 0.392783i
\(641\) −541057. −1.31682 −0.658411 0.752659i \(-0.728771\pi\)
−0.658411 + 0.752659i \(0.728771\pi\)
\(642\) −359784. 503784.i −0.872914 1.22229i
\(643\) 19642.5i 0.0475088i 0.999718 + 0.0237544i \(0.00756197\pi\)
−0.999718 + 0.0237544i \(0.992438\pi\)
\(644\) −22810.2 + 66494.4i −0.0549993 + 0.160330i
\(645\) −52419.0 −0.126000
\(646\) −70592.1 + 50414.2i −0.169157 + 0.120806i
\(647\) 645080.i 1.54101i 0.637435 + 0.770504i \(0.279995\pi\)
−0.637435 + 0.770504i \(0.720005\pi\)
\(648\) −271837. + 81033.2i −0.647379 + 0.192980i
\(649\) 696046. 1.65253
\(650\) 17068.3 + 23899.7i 0.0403983 + 0.0565673i
\(651\) 737037.i 1.73911i
\(652\) −595918. 204423.i −1.40182 0.480877i
\(653\) −49027.0 −0.114977 −0.0574883 0.998346i \(-0.518309\pi\)
−0.0574883 + 0.998346i \(0.518309\pi\)
\(654\) 158417. 113135.i 0.370379 0.264511i
\(655\) 135300.i 0.315365i
\(656\) 357349. + 277867.i 0.830395 + 0.645699i
\(657\) 136880. 0.317110
\(658\) 76653.3 + 107333.i 0.177043 + 0.247903i
\(659\) 66084.5i 0.152170i 0.997101 + 0.0760850i \(0.0242420\pi\)
−0.997101 + 0.0760850i \(0.975758\pi\)
\(660\) −150992. + 440160.i −0.346630 + 1.01047i
\(661\) 585427. 1.33989 0.669946 0.742410i \(-0.266317\pi\)
0.669946 + 0.742410i \(0.266317\pi\)
\(662\) 360265. 257288.i 0.822065 0.587088i
\(663\) 138277.i 0.314574i
\(664\) −36512.3 122486.i −0.0828139 0.277810i
\(665\) 214064. 0.484061
\(666\) −50290.9 70419.4i −0.113381 0.158761i
\(667\) 23398.9i 0.0525949i
\(668\) −282334. 96851.4i −0.632717 0.217047i
\(669\) −372893. −0.833166
\(670\) 280981. 200667.i 0.625933 0.447018i
\(671\) 897727.i 1.99388i
\(672\) −30882.4 + 757397.i −0.0683868 + 1.67720i
\(673\) 793279. 1.75144 0.875721 0.482817i \(-0.160386\pi\)
0.875721 + 0.482817i \(0.160386\pi\)
\(674\) 122162. + 171056.i 0.268915 + 0.376546i
\(675\) 85153.5i 0.186894i
\(676\) 124193. 362037.i 0.271771 0.792245i
\(677\) 672510. 1.46731 0.733654 0.679523i \(-0.237813\pi\)
0.733654 + 0.679523i \(0.237813\pi\)
\(678\) 488187. 348645.i 1.06201 0.758446i
\(679\) 1.39150e6i 3.01817i
\(680\) 434753. 129598.i 0.940210 0.280272i
\(681\) 246234. 0.530950
\(682\) 320749. + 449125.i 0.689598 + 0.965603i
\(683\) 197889.i 0.424210i 0.977247 + 0.212105i \(0.0680319\pi\)
−0.977247 + 0.212105i \(0.931968\pi\)
\(684\) 26187.4 + 8983.31i 0.0559733 + 0.0192010i
\(685\) 308159. 0.656740
\(686\) −1.34108e6 + 957746.i −2.84974 + 2.03518i
\(687\) 420542.i 0.891037i
\(688\) −39249.4 + 50476.3i −0.0829194 + 0.106638i
\(689\) −145519. −0.306535
\(690\) 22450.2 + 31435.6i 0.0471543 + 0.0660274i
\(691\) 174133.i 0.364690i 0.983235 + 0.182345i \(0.0583688\pi\)
−0.983235 + 0.182345i \(0.941631\pi\)
\(692\) −60290.4 + 175754.i −0.125903 + 0.367022i
\(693\) −276451. −0.575641
\(694\) 189360. 135234.i 0.393161 0.280781i
\(695\) 876604.i 1.81482i
\(696\) −72078.4 241797.i −0.148794 0.499151i
\(697\) −463018. −0.953087
\(698\) −216763. 303520.i −0.444911 0.622983i
\(699\) 838800.i 1.71674i
\(700\) −155768. 53434.6i −0.317895 0.109050i
\(701\) −669508. −1.36245 −0.681224 0.732075i \(-0.738552\pi\)
−0.681224 + 0.732075i \(0.738552\pi\)
\(702\) 175148. 125084.i 0.355410 0.253821i
\(703\) 85754.0i 0.173518i
\(704\) 310791. + 474972.i 0.627079 + 0.958346i
\(705\) 72476.6 0.145821
\(706\) −475998. 666512.i −0.954983 1.33721i
\(707\) 1.77663e6i 3.55433i
\(708\) 202167. 589342.i 0.403315 1.17571i
\(709\) −94715.2 −0.188420 −0.0942101 0.995552i \(-0.530033\pi\)
−0.0942101 + 0.995552i \(0.530033\pi\)
\(710\) 72626.6 51867.2i 0.144072 0.102891i
\(711\) 233589.i 0.462077i
\(712\) 544345. 162267.i 1.07378 0.320088i
\(713\) 45814.8 0.0901212
\(714\) −450617. 630972.i −0.883916 1.23769i
\(715\) 255515.i 0.499809i
\(716\) 498620. + 171046.i 0.972621 + 0.333647i
\(717\) 22904.1 0.0445527
\(718\) 111790. 79835.9i 0.216846 0.154864i
\(719\) 374829.i 0.725063i −0.931972 0.362531i \(-0.881913\pi\)
0.931972 0.362531i \(-0.118087\pi\)
\(720\) −114299. 88877.0i −0.220485 0.171445i
\(721\) 1.08511e6 2.08738
\(722\) 15945.0 + 22326.9i 0.0305880 + 0.0428306i
\(723\) 331249.i 0.633691i
\(724\) −81221.4 + 236770.i −0.154951 + 0.451700i
\(725\) 54813.8 0.104283
\(726\) 115153. 82238.2i 0.218476 0.156027i
\(727\) 294599.i 0.557394i 0.960379 + 0.278697i \(0.0899025\pi\)
−0.960379 + 0.278697i \(0.910097\pi\)
\(728\) −118905. 398883.i −0.224356 0.752632i
\(729\) −588684. −1.10771
\(730\) −412283. 577295.i −0.773659 1.08331i
\(731\) 65402.3i 0.122394i
\(732\) 760105. + 260746.i 1.41857 + 0.486626i
\(733\) 733723. 1.36560 0.682801 0.730604i \(-0.260761\pi\)
0.682801 + 0.730604i \(0.260761\pi\)
\(734\) −486253. + 347264.i −0.902547 + 0.644566i
\(735\) 1.40946e6i 2.60903i
\(736\) 47080.4 + 1919.67i 0.0869130 + 0.00354382i
\(737\) −441890. −0.813541
\(738\) 85882.6 + 120256.i 0.157686 + 0.220798i
\(739\) 204061.i 0.373655i −0.982393 0.186828i \(-0.940179\pi\)
0.982393 0.186828i \(-0.0598206\pi\)
\(740\) −145519. + 424206.i −0.265740 + 0.774665i
\(741\) 43734.4 0.0796501
\(742\) 664016. 474216.i 1.20607 0.861327i
\(743\) 159993.i 0.289816i 0.989445 + 0.144908i \(0.0462886\pi\)
−0.989445 + 0.144908i \(0.953711\pi\)
\(744\) 473436. 141129.i 0.855294 0.254959i
\(745\) 576707. 1.03907
\(746\) −108062. 151312.i −0.194175 0.271892i
\(747\) 41724.5i 0.0747739i
\(748\) −549181. 188390.i −0.981550 0.336710i
\(749\) −1.90606e6 −3.39760
\(750\) 353333. 252337.i 0.628148 0.448600i
\(751\) 658168.i 1.16696i 0.812127 + 0.583481i \(0.198310\pi\)
−0.812127 + 0.583481i \(0.801690\pi\)
\(752\) 54267.8 69790.6i 0.0959635 0.123413i
\(753\) −181073. −0.319347
\(754\) 80517.2 + 112743.i 0.141627 + 0.198312i
\(755\) 160078.i 0.280826i
\(756\) −391592. + 1.14154e6i −0.685158 + 1.99732i
\(757\) 588857. 1.02759 0.513793 0.857914i \(-0.328240\pi\)
0.513793 + 0.857914i \(0.328240\pi\)
\(758\) 98450.7 70309.8i 0.171349 0.122371i
\(759\) 49437.8i 0.0858174i
\(760\) −40989.3 137504.i −0.0709648 0.238061i
\(761\) 500664. 0.864524 0.432262 0.901748i \(-0.357716\pi\)
0.432262 + 0.901748i \(0.357716\pi\)
\(762\) −12901.5 18065.2i −0.0222193 0.0311124i
\(763\) 599368.i 1.02954i
\(764\) 581152. + 199358.i 0.995641 + 0.341544i
\(765\) 148098. 0.253062
\(766\) 791333. 565141.i 1.34866 0.963162i
\(767\) 342115.i 0.581543i
\(768\) 492428. 125190.i 0.834872 0.212250i
\(769\) −685037. −1.15841 −0.579204 0.815183i \(-0.696637\pi\)
−0.579204 + 0.815183i \(0.696637\pi\)
\(770\) 832670. + 1.16594e6i 1.40440 + 1.96650i
\(771\) 563133.i 0.947332i
\(772\) −122811. + 358008.i −0.206064 + 0.600701i
\(773\) 1.01843e6 1.70440 0.852200 0.523216i \(-0.175268\pi\)
0.852200 + 0.523216i \(0.175268\pi\)
\(774\) −16986.5 + 12131.1i −0.0283545 + 0.0202497i
\(775\) 107325.i 0.178689i
\(776\) −893830. + 266446.i −1.48433 + 0.442473i
\(777\) 766494. 1.26960
\(778\) −330210. 462374.i −0.545546 0.763896i
\(779\) 146444.i 0.241321i
\(780\) −216344. 74214.5i −0.355595 0.121983i
\(781\) −114217. −0.187254
\(782\) −39221.7 + 28010.7i −0.0641377 + 0.0458047i
\(783\) 401699.i 0.655206i
\(784\) 1.35723e6 + 1.05535e6i 2.20811 + 1.71698i
\(785\) −130106. −0.211134
\(786\) 90081.0 + 126135.i 0.145810 + 0.204169i
\(787\) 35708.8i 0.0576535i 0.999584 + 0.0288267i \(0.00917711\pi\)
−0.999584 + 0.0288267i \(0.990823\pi\)
\(788\) −169540. + 494229.i −0.273035 + 0.795932i
\(789\) 201924. 0.324365
\(790\) −985169. + 703571.i −1.57854 + 1.12734i
\(791\) 1.84705e6i 2.95206i
\(792\) 52935.2 + 177578.i 0.0843906 + 0.283100i
\(793\) −441244. −0.701669
\(794\) −247484. 346538.i −0.392561 0.549679i
\(795\) 448377.i 0.709428i
\(796\) 266098. + 91281.8i 0.419967 + 0.144065i
\(797\) −50303.0 −0.0791912 −0.0395956 0.999216i \(-0.512607\pi\)
−0.0395956 + 0.999216i \(0.512607\pi\)
\(798\) −199564. + 142521.i −0.313384 + 0.223807i
\(799\) 90427.9i 0.141647i
\(800\) −4496.99 + 110290.i −0.00702654 + 0.172328i
\(801\) 185431. 0.289012
\(802\) −24524.4 34340.1i −0.0381285 0.0533891i
\(803\) 907894.i 1.40800i
\(804\) −128347. + 374148.i −0.198552 + 0.578804i
\(805\) 118936. 0.183536
\(806\) −220751. + 157652.i −0.339807 + 0.242677i
\(807\) 14138.1i 0.0217092i
\(808\) −1.14122e6 + 340191.i −1.74802 + 0.521075i
\(809\) −1.23431e6 −1.88594 −0.942972 0.332873i \(-0.891982\pi\)
−0.942972 + 0.332873i \(0.891982\pi\)
\(810\) 278914. + 390547.i 0.425109 + 0.595255i
\(811\) 645223.i 0.980998i −0.871442 0.490499i \(-0.836815\pi\)
0.871442 0.490499i \(-0.163185\pi\)
\(812\) −734815. 252070.i −1.11446 0.382305i
\(813\) −398898. −0.603505
\(814\) 467075. 333568.i 0.704917 0.503426i
\(815\) 1.06590e6i 1.60472i
\(816\) −319020. + 410273.i −0.479113 + 0.616159i
\(817\) −20685.5 −0.0309900
\(818\) 6415.14 + 8982.74i 0.00958737 + 0.0134246i
\(819\) 135879.i 0.202574i
\(820\) 248506. 724424.i 0.369580 1.07737i
\(821\) −275509. −0.408742 −0.204371 0.978894i \(-0.565515\pi\)
−0.204371 + 0.978894i \(0.565515\pi\)
\(822\) −287285. + 205169.i −0.425177 + 0.303646i
\(823\) 327870.i 0.484063i 0.970268 + 0.242031i \(0.0778137\pi\)
−0.970268 + 0.242031i \(0.922186\pi\)
\(824\) −207778. 697019.i −0.306016 1.02657i
\(825\) 115812. 0.170155
\(826\) −1.11488e6 1.56110e6i −1.63406 2.28808i
\(827\) 459333.i 0.671609i 0.941932 + 0.335804i \(0.109008\pi\)
−0.941932 + 0.335804i \(0.890992\pi\)
\(828\) 14550.0 + 4991.23i 0.0212228 + 0.00728026i
\(829\) −1.21143e6 −1.76274 −0.881369 0.472429i \(-0.843377\pi\)
−0.881369 + 0.472429i \(0.843377\pi\)
\(830\) −175974. + 125674.i −0.255442 + 0.182428i
\(831\) 565940.i 0.819536i
\(832\) −233454. + 152757.i −0.337253 + 0.220676i
\(833\) −1.75856e6 −2.53436
\(834\) 583633. + 817226.i 0.839088 + 1.17493i
\(835\) 505000.i 0.724300i
\(836\) −59584.2 + 173695.i −0.0852548 + 0.248528i
\(837\) 786523. 1.12269
\(838\) −120421. + 86000.2i −0.171480 + 0.122465i
\(839\) 302017.i 0.429050i 0.976719 + 0.214525i \(0.0688203\pi\)
−0.976719 + 0.214525i \(0.931180\pi\)
\(840\) 1.22905e6 366374.i 1.74185 0.519237i
\(841\) −448705. −0.634408
\(842\) 458265. + 641682.i 0.646387 + 0.905098i
\(843\) 517771.i 0.728589i
\(844\) 124498. + 42707.7i 0.174775 + 0.0599545i
\(845\) −647562. −0.906919
\(846\) 23486.2 16773.0i 0.0328149 0.0234352i
\(847\) 435681.i 0.607297i
\(848\) −431759. 335727.i −0.600413 0.466869i
\(849\) −1.17851e6 −1.63499
\(850\) −65617.3 91880.0i −0.0908197 0.127169i
\(851\) 47645.9i 0.0657910i
\(852\) −33174.6 + 96707.9i −0.0457010 + 0.133224i
\(853\) −359597. −0.494217 −0.247109 0.968988i \(-0.579480\pi\)
−0.247109 + 0.968988i \(0.579480\pi\)
\(854\) 2.01344e6 1.43792e6i 2.76072 1.97161i
\(855\) 46840.6i 0.0640752i
\(856\) 364975. + 1.22436e6i 0.498098 + 1.67094i
\(857\) 132686. 0.180661 0.0903304 0.995912i \(-0.471208\pi\)
0.0903304 + 0.995912i \(0.471208\pi\)
\(858\) 170119. + 238207.i 0.231088 + 0.323579i
\(859\) 621274.i 0.841971i 0.907067 + 0.420986i \(0.138316\pi\)
−0.907067 + 0.420986i \(0.861684\pi\)
\(860\) 102327. + 35102.0i 0.138354 + 0.0474608i
\(861\) −1.30895e6 −1.76571
\(862\) −585600. + 418214.i −0.788110 + 0.562839i
\(863\) 151855.i 0.203896i −0.994790 0.101948i \(-0.967492\pi\)
0.994790 0.101948i \(-0.0325075\pi\)
\(864\) 808251. + 32955.9i 1.08273 + 0.0441474i
\(865\) 314365. 0.420147
\(866\) 183866. + 257457.i 0.245169 + 0.343296i
\(867\) 115935.i 0.154233i
\(868\) 493551. 1.43876e6i 0.655077 1.90963i
\(869\) 1.54934e6 2.05167
\(870\) −347388. + 248092.i −0.458962 + 0.327774i
\(871\) 217195.i 0.286294i
\(872\) −385004. + 114768.i −0.506328 + 0.150934i
\(873\) −304482. −0.399515
\(874\) 8859.24 + 12405.1i 0.0115977 + 0.0162396i
\(875\) 1.33683e6i 1.74606i
\(876\) 768713. + 263699.i 1.00174 + 0.343637i
\(877\) 76093.6 0.0989347 0.0494674 0.998776i \(-0.484248\pi\)
0.0494674 + 0.998776i \(0.484248\pi\)
\(878\) −580930. + 414878.i −0.753589 + 0.538185i
\(879\) 262921.i 0.340288i
\(880\) 589500. 758121.i 0.761235 0.978979i
\(881\) 1.05655e6 1.36125 0.680624 0.732633i \(-0.261709\pi\)
0.680624 + 0.732633i \(0.261709\pi\)
\(882\) 326186. + 456739.i 0.419303 + 0.587125i
\(883\) 1.42282e6i 1.82485i 0.409242 + 0.912426i \(0.365793\pi\)
−0.409242 + 0.912426i \(0.634207\pi\)
\(884\) 92596.2 269929.i 0.118492 0.345418i
\(885\) −1.05414e6 −1.34589
\(886\) 1.00408e6 717074.i 1.27908 0.913474i
\(887\) 527731.i 0.670757i 0.942083 + 0.335378i \(0.108864\pi\)
−0.942083 + 0.335378i \(0.891136\pi\)
\(888\) −146769. 492357.i −0.186127 0.624388i
\(889\) −68349.5 −0.0864832
\(890\) −558517. 782058.i −0.705109 0.987322i
\(891\) 614200.i 0.773668i
\(892\) 727919. + 249705.i 0.914858 + 0.313832i
\(893\) 28600.6 0.0358651
\(894\) −537644. + 383965.i −0.672697 + 0.480415i
\(895\) 891864.i 1.11340i
\(896\) 567470. 1.45783e6i 0.706850 1.81589i
\(897\) 24299.3 0.0302001
\(898\) −62329.6 87276.4i −0.0772932 0.108229i
\(899\) 506289.i 0.626440i
\(900\) −11692.3 + 34084.6i −0.0144350 + 0.0420797i
\(901\) 559432. 0.689125
\(902\) −797632. + 569639.i −0.980369 + 0.700143i
\(903\) 184893.i 0.226748i
\(904\) −1.18645e6 + 353676.i −1.45182 + 0.432781i
\(905\) 423503. 0.517082
\(906\) 106578. + 149235.i 0.129841 + 0.181808i
\(907\) 559308.i 0.679887i −0.940446 0.339944i \(-0.889592\pi\)
0.940446 0.339944i \(-0.110408\pi\)
\(908\) −480671. 164889.i −0.583010 0.199995i
\(909\) −388754. −0.470487
\(910\) −573073. + 409268.i −0.692034 + 0.494225i
\(911\) 1.29307e6i 1.55807i −0.626983 0.779033i \(-0.715710\pi\)
0.626983 0.779033i \(-0.284290\pi\)
\(912\) 129761. + 100900.i 0.156011 + 0.121311i
\(913\) 276749. 0.332005
\(914\) 709059. + 992853.i 0.848770 + 1.18848i
\(915\) 1.35957e6i 1.62390i
\(916\) 281613. 820935.i 0.335630 0.978403i
\(917\) 477230. 0.567530
\(918\) −673337. + 480872.i −0.799000 + 0.570616i
\(919\) 987271.i 1.16897i 0.811403 + 0.584487i \(0.198704\pi\)
−0.811403 + 0.584487i \(0.801296\pi\)
\(920\) −22774.1 76398.7i −0.0269070 0.0902631i
\(921\) 295690. 0.348593
\(922\) −113066. 158320.i −0.133006 0.186240i
\(923\) 56139.3i 0.0658967i
\(924\) −1.55254e6 532581.i −1.81844 0.623794i
\(925\) 111614. 0.130448
\(926\) 31935.0 22806.8i 0.0372430 0.0265976i
\(927\) 237439.i 0.276307i
\(928\) −21213.9 + 520276.i −0.0246334 + 0.604140i
\(929\) 472888. 0.547933 0.273966 0.961739i \(-0.411664\pi\)
0.273966 + 0.961739i \(0.411664\pi\)
\(930\) −485761. 680183.i −0.561639 0.786429i
\(931\) 556199.i 0.641698i
\(932\) −561696. + 1.63741e6i −0.646650 + 1.88506i
\(933\) −536106. −0.615868
\(934\) 454881. 324859.i 0.521439 0.372392i
\(935\) 982300.i 1.12362i
\(936\) −87281.9 + 26018.3i −0.0996260 + 0.0296980i
\(937\) 183381. 0.208869 0.104435 0.994532i \(-0.466697\pi\)
0.104435 + 0.994532i \(0.466697\pi\)
\(938\) 707793. + 991080.i 0.804452 + 1.12643i
\(939\) 888017.i 1.00714i
\(940\) −141481. 48533.4i −0.160119 0.0549269i
\(941\) 1.15706e6 1.30670 0.653351 0.757055i \(-0.273363\pi\)
0.653351 + 0.757055i \(0.273363\pi\)
\(942\) 121293. 86622.9i 0.136689 0.0976182i
\(943\) 81365.7i 0.0914993i
\(944\) −789297. + 1.01507e6i −0.885720 + 1.13907i
\(945\) 2.04183e6 2.28642
\(946\) −80462.8 112667.i −0.0899110 0.125897i
\(947\) 330922.i 0.369000i −0.982833 0.184500i \(-0.940933\pi\)
0.982833 0.184500i \(-0.0590665\pi\)
\(948\) 450008. 1.31183e6i 0.500730 1.45969i
\(949\) −446241. −0.495492
\(950\) −29059.8 + 20753.5i −0.0321993 + 0.0229955i
\(951\) 454808.i 0.502884i
\(952\) 457118. + 1.53346e6i 0.504376 + 1.69200i
\(953\) −1.14501e6 −1.26073 −0.630366 0.776298i \(-0.717095\pi\)
−0.630366 + 0.776298i \(0.717095\pi\)
\(954\) −103766. 145297.i −0.114014 0.159647i
\(955\) 1.03949e6i 1.13976i
\(956\) −44710.8 15337.5i −0.0489211 0.0167819i
\(957\) 546326. 0.596524
\(958\) 62680.0 44763.7i 0.0682964 0.0487748i
\(959\) 1.08694e6i 1.18187i
\(960\) −470680. 719326.i −0.510721 0.780519i
\(961\) −67788.8 −0.0734025
\(962\) 163953. + 229573.i 0.177161 + 0.248068i
\(963\) 417076.i 0.449741i
\(964\) 221818. 646627.i 0.238695 0.695824i
\(965\) 640357. 0.687650
\(966\) −110880. + 79186.4i −0.118823 + 0.0848587i
\(967\) 1.36604e6i 1.46087i −0.682982 0.730436i \(-0.739317\pi\)
0.682982 0.730436i \(-0.260683\pi\)
\(968\) −279860. + 83424.7i −0.298668 + 0.0890316i
\(969\) −168132. −0.179062
\(970\) 917101. + 1.28416e6i 0.974706 + 1.36482i
\(971\) 52205.0i 0.0553699i −0.999617 0.0276850i \(-0.991186\pi\)
0.999617 0.0276850i \(-0.00881352\pi\)
\(972\) 448355. + 153803.i 0.474559 + 0.162792i
\(973\) 3.09196e6 3.26594
\(974\) −1.37247e6 + 980166.i −1.44672 + 1.03319i
\(975\) 56923.0i 0.0598795i
\(976\) −1.30919e6 1.01800e6i −1.37436 1.06868i
\(977\) −833646. −0.873358 −0.436679 0.899617i \(-0.643845\pi\)
−0.436679 + 0.899617i \(0.643845\pi\)
\(978\) −709662. 993697.i −0.741948 1.03891i
\(979\) 1.22992e6i 1.28325i
\(980\) 943835. 2.75139e6i 0.982752 2.86484i
\(981\) −131151. −0.136281
\(982\) 86609.6 61853.4i 0.0898138 0.0641417i
\(983\) 809453.i 0.837692i 0.908057 + 0.418846i \(0.137565\pi\)
−0.908057 + 0.418846i \(0.862435\pi\)
\(984\) 250640. + 840807.i 0.258858 + 0.868373i
\(985\) 884010. 0.911139
\(986\) −309540. 433431.i −0.318393 0.445826i
\(987\) 255640.i 0.262419i
\(988\) −85373.3 29286.4i −0.0874598 0.0300021i
\(989\) −11493.1 −0.0117502
\(990\) 255126. 182201.i 0.260306 0.185901i
\(991\) 241862.i 0.246275i 0.992390 + 0.123137i \(0.0392956\pi\)
−0.992390 + 0.123137i \(0.960704\pi\)
\(992\) −1.01869e6 41536.6i −1.03519 0.0422092i
\(993\) 858059. 0.870199
\(994\) 182946. + 256169.i 0.185162 + 0.259271i
\(995\) 475959.i 0.480755i
\(996\) 80382.0 234323.i 0.0810289 0.236209i
\(997\) 483196. 0.486108 0.243054 0.970013i \(-0.421851\pi\)
0.243054 + 0.970013i \(0.421851\pi\)
\(998\) 999742. 713979.i 1.00375 0.716843i
\(999\) 817958.i 0.819596i
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 76.5.b.a.39.11 36
4.3 odd 2 inner 76.5.b.a.39.12 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.5.b.a.39.11 36 1.1 even 1 trivial
76.5.b.a.39.12 yes 36 4.3 odd 2 inner