Properties

Label 138.6.d.a.137.20
Level $138$
Weight $6$
Character 138.137
Analytic conductor $22.133$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [138,6,Mod(137,138)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(138, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("138.137");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 138.d (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: \(22.1329671342\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 137.20
Character \(\chi\) \(=\) 138.137
Dual form 138.6.d.a.137.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000i q^{2} +(-14.2654 + 6.28478i) q^{3} -16.0000 q^{4} +46.4212 q^{5} +(-25.1391 - 57.0616i) q^{6} +104.982i q^{7} -64.0000i q^{8} +(164.003 - 179.310i) q^{9} +O(q^{10})\) \(q+4.00000i q^{2} +(-14.2654 + 6.28478i) q^{3} -16.0000 q^{4} +46.4212 q^{5} +(-25.1391 - 57.0616i) q^{6} +104.982i q^{7} -64.0000i q^{8} +(164.003 - 179.310i) q^{9} +185.685i q^{10} -578.520 q^{11} +(228.246 - 100.556i) q^{12} -661.326 q^{13} -419.928 q^{14} +(-662.217 + 291.747i) q^{15} +256.000 q^{16} -54.6274 q^{17} +(717.239 + 656.013i) q^{18} -1057.69i q^{19} -742.740 q^{20} +(-659.789 - 1497.61i) q^{21} -2314.08i q^{22} +(2390.00 - 851.011i) q^{23} +(402.226 + 912.985i) q^{24} -970.068 q^{25} -2645.31i q^{26} +(-1212.65 + 3588.65i) q^{27} -1679.71i q^{28} -2907.49i q^{29} +(-1166.99 - 2648.87i) q^{30} +8286.18 q^{31} +1024.00i q^{32} +(8252.82 - 3635.87i) q^{33} -218.510i q^{34} +4873.40i q^{35} +(-2624.05 + 2868.95i) q^{36} -12502.0i q^{37} +4230.77 q^{38} +(9434.08 - 4156.29i) q^{39} -2970.96i q^{40} -7396.71i q^{41} +(5990.45 - 2639.16i) q^{42} -3072.54i q^{43} +9256.32 q^{44} +(7613.23 - 8323.78i) q^{45} +(3404.04 + 9560.02i) q^{46} +22036.7i q^{47} +(-3651.94 + 1608.90i) q^{48} +5785.76 q^{49} -3880.27i q^{50} +(779.281 - 343.321i) q^{51} +10581.2 q^{52} -24688.7 q^{53} +(-14354.6 - 4850.60i) q^{54} -26855.6 q^{55} +6718.85 q^{56} +(6647.35 + 15088.4i) q^{57} +11630.0 q^{58} -8214.34i q^{59} +(10595.5 - 4667.95i) q^{60} -55044.6i q^{61} +33144.7i q^{62} +(18824.3 + 17217.4i) q^{63} -4096.00 q^{64} -30699.6 q^{65} +(14543.5 + 33011.3i) q^{66} -6618.24i q^{67} +874.038 q^{68} +(-28746.0 + 27160.7i) q^{69} -19493.6 q^{70} -20997.9i q^{71} +(-11475.8 - 10496.2i) q^{72} +48703.2 q^{73} +50008.1 q^{74} +(13838.4 - 6096.66i) q^{75} +16923.1i q^{76} -60734.2i q^{77} +(16625.2 + 37736.3i) q^{78} -44636.7i q^{79} +11883.8 q^{80} +(-5254.93 - 58814.7i) q^{81} +29586.8 q^{82} -62926.6 q^{83} +(10556.6 + 23961.8i) q^{84} -2535.87 q^{85} +12290.2 q^{86} +(18272.9 + 41476.5i) q^{87} +37025.3i q^{88} -114278. q^{89} +(33295.1 + 30452.9i) q^{90} -69427.4i q^{91} +(-38240.1 + 13616.2i) q^{92} +(-118206. + 52076.8i) q^{93} -88146.7 q^{94} -49099.4i q^{95} +(-6435.61 - 14607.8i) q^{96} -81715.9i q^{97} +23143.0i q^{98} +(-94879.1 + 103734. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{3} - 640 q^{4} + 80 q^{6} + 504 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 4 q^{3} - 640 q^{4} + 80 q^{6} + 504 q^{9} + 64 q^{12} - 1048 q^{13} + 10240 q^{16} + 1280 q^{18} - 1280 q^{24} + 30480 q^{25} + 1700 q^{27} - 22576 q^{31} - 8064 q^{36} + 55608 q^{39} + 1088 q^{46} - 1024 q^{48} - 23224 q^{49} + 16768 q^{52} + 25456 q^{54} + 210400 q^{55} - 83168 q^{58} - 163840 q^{64} + 99076 q^{69} + 167520 q^{70} - 20480 q^{72} + 241160 q^{73} - 255604 q^{75} - 233440 q^{78} + 78512 q^{81} - 8832 q^{82} - 460296 q^{85} - 4136 q^{87} + 500704 q^{93} - 138272 q^{94} + 20480 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(97\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000i 0.707107i
\(3\) −14.2654 + 6.28478i −0.915126 + 0.403169i
\(4\) −16.0000 −0.500000
\(5\) 46.4212 0.830408 0.415204 0.909728i \(-0.363710\pi\)
0.415204 + 0.909728i \(0.363710\pi\)
\(6\) −25.1391 57.0616i −0.285083 0.647092i
\(7\) 104.982i 0.809786i 0.914364 + 0.404893i \(0.132691\pi\)
−0.914364 + 0.404893i \(0.867309\pi\)
\(8\) 64.0000i 0.353553i
\(9\) 164.003 179.310i 0.674910 0.737900i
\(10\) 185.685i 0.587187i
\(11\) −578.520 −1.44157 −0.720786 0.693157i \(-0.756219\pi\)
−0.720786 + 0.693157i \(0.756219\pi\)
\(12\) 228.246 100.556i 0.457563 0.201584i
\(13\) −661.326 −1.08532 −0.542660 0.839953i \(-0.682583\pi\)
−0.542660 + 0.839953i \(0.682583\pi\)
\(14\) −419.928 −0.572605
\(15\) −662.217 + 291.747i −0.759928 + 0.334795i
\(16\) 256.000 0.250000
\(17\) −54.6274 −0.0458446 −0.0229223 0.999737i \(-0.507297\pi\)
−0.0229223 + 0.999737i \(0.507297\pi\)
\(18\) 717.239 + 656.013i 0.521774 + 0.477234i
\(19\) 1057.69i 0.672164i −0.941833 0.336082i \(-0.890898\pi\)
0.941833 0.336082i \(-0.109102\pi\)
\(20\) −742.740 −0.415204
\(21\) −659.789 1497.61i −0.326480 0.741056i
\(22\) 2314.08i 1.01935i
\(23\) 2390.00 851.011i 0.942061 0.335441i
\(24\) 402.226 + 912.985i 0.142542 + 0.323546i
\(25\) −970.068 −0.310422
\(26\) 2645.31i 0.767436i
\(27\) −1212.65 + 3588.65i −0.320130 + 0.947374i
\(28\) 1679.71i 0.404893i
\(29\) 2907.49i 0.641983i −0.947082 0.320991i \(-0.895984\pi\)
0.947082 0.320991i \(-0.104016\pi\)
\(30\) −1166.99 2648.87i −0.236736 0.537350i
\(31\) 8286.18 1.54864 0.774319 0.632795i \(-0.218093\pi\)
0.774319 + 0.632795i \(0.218093\pi\)
\(32\) 1024.00i 0.176777i
\(33\) 8252.82 3635.87i 1.31922 0.581197i
\(34\) 218.510i 0.0324170i
\(35\) 4873.40i 0.672453i
\(36\) −2624.05 + 2868.95i −0.337455 + 0.368950i
\(37\) 12502.0i 1.50133i −0.660683 0.750665i \(-0.729733\pi\)
0.660683 0.750665i \(-0.270267\pi\)
\(38\) 4230.77 0.475291
\(39\) 9434.08 4156.29i 0.993203 0.437567i
\(40\) 2970.96i 0.293594i
\(41\) 7396.71i 0.687193i −0.939117 0.343597i \(-0.888355\pi\)
0.939117 0.343597i \(-0.111645\pi\)
\(42\) 5990.45 2639.16i 0.524006 0.230856i
\(43\) 3072.54i 0.253412i −0.991940 0.126706i \(-0.959560\pi\)
0.991940 0.126706i \(-0.0404405\pi\)
\(44\) 9256.32 0.720786
\(45\) 7613.23 8323.78i 0.560451 0.612758i
\(46\) 3404.04 + 9560.02i 0.237192 + 0.666138i
\(47\) 22036.7i 1.45513i 0.686039 + 0.727564i \(0.259348\pi\)
−0.686039 + 0.727564i \(0.740652\pi\)
\(48\) −3651.94 + 1608.90i −0.228781 + 0.100792i
\(49\) 5785.76 0.344247
\(50\) 3880.27i 0.219501i
\(51\) 779.281 343.321i 0.0419536 0.0184831i
\(52\) 10581.2 0.542660
\(53\) −24688.7 −1.20728 −0.603642 0.797256i \(-0.706284\pi\)
−0.603642 + 0.797256i \(0.706284\pi\)
\(54\) −14354.6 4850.60i −0.669894 0.226366i
\(55\) −26855.6 −1.19709
\(56\) 6718.85 0.286302
\(57\) 6647.35 + 15088.4i 0.270995 + 0.615114i
\(58\) 11630.0 0.453950
\(59\) 8214.34i 0.307215i −0.988132 0.153608i \(-0.950911\pi\)
0.988132 0.153608i \(-0.0490892\pi\)
\(60\) 10595.5 4667.95i 0.379964 0.167397i
\(61\) 55044.6i 1.89404i −0.321170 0.947021i \(-0.604076\pi\)
0.321170 0.947021i \(-0.395924\pi\)
\(62\) 33144.7i 1.09505i
\(63\) 18824.3 + 17217.4i 0.597541 + 0.546533i
\(64\) −4096.00 −0.125000
\(65\) −30699.6 −0.901258
\(66\) 14543.5 + 33011.3i 0.410968 + 0.932830i
\(67\) 6618.24i 0.180117i −0.995936 0.0900587i \(-0.971295\pi\)
0.995936 0.0900587i \(-0.0287055\pi\)
\(68\) 874.038 0.0229223
\(69\) −28746.0 + 27160.7i −0.726866 + 0.686780i
\(70\) −19493.6 −0.475496
\(71\) 20997.9i 0.494345i −0.968971 0.247173i \(-0.920498\pi\)
0.968971 0.247173i \(-0.0795015\pi\)
\(72\) −11475.8 10496.2i −0.260887 0.238617i
\(73\) 48703.2 1.06967 0.534835 0.844956i \(-0.320374\pi\)
0.534835 + 0.844956i \(0.320374\pi\)
\(74\) 50008.1 1.06160
\(75\) 13838.4 6096.66i 0.284075 0.125152i
\(76\) 16923.1i 0.336082i
\(77\) 60734.2i 1.16737i
\(78\) 16625.2 + 37736.3i 0.309406 + 0.702301i
\(79\) 44636.7i 0.804683i −0.915490 0.402341i \(-0.868196\pi\)
0.915490 0.402341i \(-0.131804\pi\)
\(80\) 11883.8 0.207602
\(81\) −5254.93 58814.7i −0.0889926 0.996032i
\(82\) 29586.8 0.485919
\(83\) −62926.6 −1.00263 −0.501313 0.865266i \(-0.667150\pi\)
−0.501313 + 0.865266i \(0.667150\pi\)
\(84\) 10556.6 + 23961.8i 0.163240 + 0.370528i
\(85\) −2535.87 −0.0380697
\(86\) 12290.2 0.179189
\(87\) 18272.9 + 41476.5i 0.258827 + 0.587495i
\(88\) 37025.3i 0.509673i
\(89\) −114278. −1.52928 −0.764640 0.644458i \(-0.777083\pi\)
−0.764640 + 0.644458i \(0.777083\pi\)
\(90\) 33295.1 + 30452.9i 0.433286 + 0.396299i
\(91\) 69427.4i 0.878876i
\(92\) −38240.1 + 13616.2i −0.471031 + 0.167720i
\(93\) −118206. + 52076.8i −1.41720 + 0.624362i
\(94\) −88146.7 −1.02893
\(95\) 49099.4i 0.558170i
\(96\) −6435.61 14607.8i −0.0712708 0.161773i
\(97\) 81715.9i 0.881815i −0.897553 0.440907i \(-0.854657\pi\)
0.897553 0.440907i \(-0.145343\pi\)
\(98\) 23143.0i 0.243419i
\(99\) −94879.1 + 103734.i −0.972932 + 1.06374i
\(100\) 15521.1 0.155211
\(101\) 36061.1i 0.351751i 0.984412 + 0.175876i \(0.0562756\pi\)
−0.984412 + 0.175876i \(0.943724\pi\)
\(102\) 1373.28 + 3117.13i 0.0130695 + 0.0296657i
\(103\) 151498.i 1.40707i 0.710662 + 0.703534i \(0.248396\pi\)
−0.710662 + 0.703534i \(0.751604\pi\)
\(104\) 42324.9i 0.383718i
\(105\) −30628.2 69521.0i −0.271112 0.615379i
\(106\) 98755.0i 0.853679i
\(107\) 19393.7 0.163757 0.0818786 0.996642i \(-0.473908\pi\)
0.0818786 + 0.996642i \(0.473908\pi\)
\(108\) 19402.4 57418.4i 0.160065 0.473687i
\(109\) 134089.i 1.08100i 0.841342 + 0.540502i \(0.181766\pi\)
−0.841342 + 0.540502i \(0.818234\pi\)
\(110\) 107422.i 0.846474i
\(111\) 78572.5 + 178346.i 0.605289 + 1.37391i
\(112\) 26875.4i 0.202446i
\(113\) −27811.4 −0.204893 −0.102446 0.994739i \(-0.532667\pi\)
−0.102446 + 0.994739i \(0.532667\pi\)
\(114\) −60353.6 + 26589.4i −0.434951 + 0.191623i
\(115\) 110947. 39505.0i 0.782296 0.278553i
\(116\) 46519.8i 0.320991i
\(117\) −108460. + 118582.i −0.732493 + 0.800857i
\(118\) 32857.4 0.217234
\(119\) 5734.90i 0.0371243i
\(120\) 18671.8 + 42381.9i 0.118368 + 0.268675i
\(121\) 173634. 1.07813
\(122\) 220178. 1.33929
\(123\) 46486.7 + 105517.i 0.277055 + 0.628868i
\(124\) −132579. −0.774319
\(125\) −190098. −1.08819
\(126\) −68869.6 + 75297.2i −0.386457 + 0.422525i
\(127\) −266793. −1.46779 −0.733897 0.679261i \(-0.762300\pi\)
−0.733897 + 0.679261i \(0.762300\pi\)
\(128\) 16384.0i 0.0883883i
\(129\) 19310.3 + 43831.1i 0.102168 + 0.231904i
\(130\) 122798.i 0.637286i
\(131\) 159200.i 0.810520i −0.914202 0.405260i \(-0.867181\pi\)
0.914202 0.405260i \(-0.132819\pi\)
\(132\) −132045. + 58173.9i −0.659610 + 0.290598i
\(133\) 111039. 0.544309
\(134\) 26473.0 0.127362
\(135\) −56292.7 + 166589.i −0.265838 + 0.786707i
\(136\) 3496.15i 0.0162085i
\(137\) −1507.05 −0.00686003 −0.00343001 0.999994i \(-0.501092\pi\)
−0.00343001 + 0.999994i \(0.501092\pi\)
\(138\) −108643. 114984.i −0.485627 0.513972i
\(139\) 87208.8 0.382845 0.191423 0.981508i \(-0.438690\pi\)
0.191423 + 0.981508i \(0.438690\pi\)
\(140\) 77974.4i 0.336226i
\(141\) −138496. 314362.i −0.586662 1.33163i
\(142\) 83991.7 0.349555
\(143\) 382590. 1.56457
\(144\) 41984.8 45903.3i 0.168728 0.184475i
\(145\) 134969.i 0.533108i
\(146\) 194813.i 0.756372i
\(147\) −82536.2 + 36362.2i −0.315029 + 0.138790i
\(148\) 200032.i 0.750665i
\(149\) −172655. −0.637107 −0.318553 0.947905i \(-0.603197\pi\)
−0.318553 + 0.947905i \(0.603197\pi\)
\(150\) 24386.7 + 55353.6i 0.0884961 + 0.200871i
\(151\) −218207. −0.778802 −0.389401 0.921068i \(-0.627318\pi\)
−0.389401 + 0.921068i \(0.627318\pi\)
\(152\) −67692.3 −0.237646
\(153\) −8959.06 + 9795.22i −0.0309410 + 0.0338287i
\(154\) 242937. 0.825452
\(155\) 384655. 1.28600
\(156\) −150945. + 66500.6i −0.496602 + 0.218783i
\(157\) 495612.i 1.60470i −0.596856 0.802348i \(-0.703584\pi\)
0.596856 0.802348i \(-0.296416\pi\)
\(158\) 178547. 0.568997
\(159\) 352195. 155163.i 1.10482 0.486739i
\(160\) 47535.4i 0.146797i
\(161\) 89340.9 + 250908.i 0.271635 + 0.762868i
\(162\) 235259. 21019.7i 0.704301 0.0629273i
\(163\) −5266.61 −0.0155261 −0.00776304 0.999970i \(-0.502471\pi\)
−0.00776304 + 0.999970i \(0.502471\pi\)
\(164\) 118347.i 0.343597i
\(165\) 383106. 168782.i 1.09549 0.482631i
\(166\) 251706.i 0.708964i
\(167\) 307465.i 0.853109i 0.904462 + 0.426554i \(0.140273\pi\)
−0.904462 + 0.426554i \(0.859727\pi\)
\(168\) −95847.1 + 42226.5i −0.262003 + 0.115428i
\(169\) 66059.5 0.177917
\(170\) 10143.5i 0.0269194i
\(171\) −189654. 173465.i −0.495989 0.453650i
\(172\) 49160.7i 0.126706i
\(173\) 678994.i 1.72485i 0.506186 + 0.862424i \(0.331055\pi\)
−0.506186 + 0.862424i \(0.668945\pi\)
\(174\) −165906. + 73091.7i −0.415422 + 0.183019i
\(175\) 101840.i 0.251375i
\(176\) −148101. −0.360393
\(177\) 51625.3 + 117181.i 0.123860 + 0.281141i
\(178\) 457111.i 1.08136i
\(179\) 86085.4i 0.200815i 0.994946 + 0.100408i \(0.0320147\pi\)
−0.994946 + 0.100408i \(0.967985\pi\)
\(180\) −121812. + 133180.i −0.280226 + 0.306379i
\(181\) 716990.i 1.62673i −0.581751 0.813367i \(-0.697632\pi\)
0.581751 0.813367i \(-0.302368\pi\)
\(182\) 277710. 0.621459
\(183\) 345943. + 785233.i 0.763619 + 1.73329i
\(184\) −54464.7 152960.i −0.118596 0.333069i
\(185\) 580360.i 1.24672i
\(186\) −208307. 472822.i −0.441491 1.00211i
\(187\) 31603.0 0.0660883
\(188\) 352587.i 0.727564i
\(189\) −376744. 127306.i −0.767170 0.259236i
\(190\) 196397. 0.394686
\(191\) −598502. −1.18709 −0.593543 0.804802i \(-0.702271\pi\)
−0.593543 + 0.804802i \(0.702271\pi\)
\(192\) 58431.1 25742.4i 0.114391 0.0503961i
\(193\) 698278. 1.34938 0.674691 0.738100i \(-0.264277\pi\)
0.674691 + 0.738100i \(0.264277\pi\)
\(194\) 326864. 0.623537
\(195\) 437942. 192940.i 0.824764 0.363359i
\(196\) −92572.2 −0.172124
\(197\) 774477.i 1.42181i −0.703286 0.710907i \(-0.748285\pi\)
0.703286 0.710907i \(-0.251715\pi\)
\(198\) −414937. 379516.i −0.752175 0.687967i
\(199\) 830422.i 1.48650i −0.669011 0.743252i \(-0.733282\pi\)
0.669011 0.743252i \(-0.266718\pi\)
\(200\) 62084.4i 0.109751i
\(201\) 41594.2 + 94411.8i 0.0726177 + 0.164830i
\(202\) −144244. −0.248726
\(203\) 305234. 0.519868
\(204\) −12468.5 + 5493.14i −0.0209768 + 0.00924155i
\(205\) 343364.i 0.570651i
\(206\) −605993. −0.994947
\(207\) 239374. 568120.i 0.388285 0.921539i
\(208\) −169300. −0.271330
\(209\) 611896.i 0.968973i
\(210\) 278084. 122513.i 0.435139 0.191705i
\(211\) 336475. 0.520291 0.260146 0.965569i \(-0.416229\pi\)
0.260146 + 0.965569i \(0.416229\pi\)
\(212\) 395020. 0.603642
\(213\) 131967. + 299544.i 0.199305 + 0.452388i
\(214\) 77574.6i 0.115794i
\(215\) 142631.i 0.210435i
\(216\) 229673. + 77609.5i 0.334947 + 0.113183i
\(217\) 869900.i 1.25406i
\(218\) −536357. −0.764386
\(219\) −694770. + 306089.i −0.978883 + 0.431258i
\(220\) 429690. 0.598547
\(221\) 36126.5 0.0497560
\(222\) −713386. + 314290.i −0.971498 + 0.428004i
\(223\) −748144. −1.00745 −0.503724 0.863864i \(-0.668037\pi\)
−0.503724 + 0.863864i \(0.668037\pi\)
\(224\) −107502. −0.143151
\(225\) −159094. + 173943.i −0.209507 + 0.229060i
\(226\) 111246.i 0.144881i
\(227\) −204240. −0.263073 −0.131536 0.991311i \(-0.541991\pi\)
−0.131536 + 0.991311i \(0.541991\pi\)
\(228\) −106358. 241414.i −0.135498 0.307557i
\(229\) 868528.i 1.09445i 0.836986 + 0.547224i \(0.184315\pi\)
−0.836986 + 0.547224i \(0.815685\pi\)
\(230\) 158020. + 443788.i 0.196966 + 0.553167i
\(231\) 381701. + 866398.i 0.470645 + 1.06829i
\(232\) −186079. −0.226975
\(233\) 1.37882e6i 1.66387i −0.554874 0.831934i \(-0.687234\pi\)
0.554874 0.831934i \(-0.312766\pi\)
\(234\) −474329. 433838.i −0.566291 0.517951i
\(235\) 1.02297e6i 1.20835i
\(236\) 131429.i 0.153608i
\(237\) 280532. + 636761.i 0.324423 + 0.736386i
\(238\) 22939.6 0.0262508
\(239\) 440130.i 0.498410i −0.968451 0.249205i \(-0.919831\pi\)
0.968451 0.249205i \(-0.0801692\pi\)
\(240\) −169528. + 74687.3i −0.189982 + 0.0836987i
\(241\) 632523.i 0.701510i 0.936467 + 0.350755i \(0.114075\pi\)
−0.936467 + 0.350755i \(0.885925\pi\)
\(242\) 694537.i 0.762355i
\(243\) 444601. + 805989.i 0.483008 + 0.875616i
\(244\) 880713.i 0.947021i
\(245\) 268582. 0.285866
\(246\) −422068. + 185947.i −0.444677 + 0.195907i
\(247\) 699479.i 0.729512i
\(248\) 530315.i 0.547526i
\(249\) 897673. 395480.i 0.917529 0.404227i
\(250\) 760393.i 0.769463i
\(251\) −373263. −0.373965 −0.186983 0.982363i \(-0.559871\pi\)
−0.186983 + 0.982363i \(0.559871\pi\)
\(252\) −301189. 275478.i −0.298770 0.273266i
\(253\) −1.38267e6 + 492327.i −1.35805 + 0.483562i
\(254\) 1.06717e6i 1.03789i
\(255\) 36175.2 15937.4i 0.0348386 0.0153485i
\(256\) 65536.0 0.0625000
\(257\) 850287.i 0.803032i 0.915852 + 0.401516i \(0.131517\pi\)
−0.915852 + 0.401516i \(0.868483\pi\)
\(258\) −175324. + 77241.0i −0.163981 + 0.0722435i
\(259\) 1.31249e6 1.21576
\(260\) 491193. 0.450629
\(261\) −521341. 476838.i −0.473719 0.433281i
\(262\) 636798. 0.573124
\(263\) −150995. −0.134609 −0.0673046 0.997732i \(-0.521440\pi\)
−0.0673046 + 0.997732i \(0.521440\pi\)
\(264\) −232696. 528180.i −0.205484 0.466415i
\(265\) −1.14608e6 −1.00254
\(266\) 444155.i 0.384884i
\(267\) 1.63022e6 718211.i 1.39948 0.616558i
\(268\) 105892.i 0.0900587i
\(269\) 643301.i 0.542043i 0.962573 + 0.271021i \(0.0873614\pi\)
−0.962573 + 0.271021i \(0.912639\pi\)
\(270\) −666358. 225171.i −0.556286 0.187976i
\(271\) −1.65146e6 −1.36598 −0.682992 0.730426i \(-0.739322\pi\)
−0.682992 + 0.730426i \(0.739322\pi\)
\(272\) −13984.6 −0.0114611
\(273\) 436336. + 990410.i 0.354335 + 0.804282i
\(274\) 6028.19i 0.00485077i
\(275\) 561204. 0.447496
\(276\) 459935. 434571.i 0.363433 0.343390i
\(277\) 396745. 0.310679 0.155340 0.987861i \(-0.450353\pi\)
0.155340 + 0.987861i \(0.450353\pi\)
\(278\) 348835.i 0.270712i
\(279\) 1.35896e6 1.48579e6i 1.04519 1.14274i
\(280\) 311898. 0.237748
\(281\) −1.45610e6 −1.10008 −0.550040 0.835138i \(-0.685388\pi\)
−0.550040 + 0.835138i \(0.685388\pi\)
\(282\) 1.25745e6 553982.i 0.941602 0.414833i
\(283\) 1.56195e6i 1.15931i 0.814860 + 0.579657i \(0.196814\pi\)
−0.814860 + 0.579657i \(0.803186\pi\)
\(284\) 335967.i 0.247173i
\(285\) 308578. + 700422.i 0.225037 + 0.510796i
\(286\) 1.53036e6i 1.10632i
\(287\) 776522. 0.556479
\(288\) 183613. + 167939.i 0.130444 + 0.119308i
\(289\) −1.41687e6 −0.997898
\(290\) 539877. 0.376964
\(291\) 513566. + 1.16571e6i 0.355520 + 0.806971i
\(292\) −779251. −0.534835
\(293\) −2.07699e6 −1.41340 −0.706699 0.707514i \(-0.749817\pi\)
−0.706699 + 0.707514i \(0.749817\pi\)
\(294\) −145449. 330145.i −0.0981391 0.222759i
\(295\) 381320.i 0.255114i
\(296\) −800130. −0.530800
\(297\) 701542. 2.07610e6i 0.461490 1.36571i
\(298\) 690618.i 0.450503i
\(299\) −1.58057e6 + 562796.i −1.02244 + 0.364060i
\(300\) −221415. + 97546.6i −0.142038 + 0.0625762i
\(301\) 322562. 0.205209
\(302\) 872829.i 0.550696i
\(303\) −226636. 514426.i −0.141815 0.321896i
\(304\) 270769.i 0.168041i
\(305\) 2.55524e6i 1.57283i
\(306\) −39180.9 35836.3i −0.0239205 0.0218786i
\(307\) 280461. 0.169835 0.0849173 0.996388i \(-0.472937\pi\)
0.0849173 + 0.996388i \(0.472937\pi\)
\(308\) 971748.i 0.583683i
\(309\) −952133. 2.16118e6i −0.567285 1.28764i
\(310\) 1.53862e6i 0.909341i
\(311\) 903873.i 0.529915i 0.964260 + 0.264958i \(0.0853580\pi\)
−0.964260 + 0.264958i \(0.914642\pi\)
\(312\) −266002. 603781.i −0.154703 0.351150i
\(313\) 1.86380e6i 1.07532i 0.843160 + 0.537662i \(0.180692\pi\)
−0.843160 + 0.537662i \(0.819308\pi\)
\(314\) 1.98245e6 1.13469
\(315\) 873848. + 799253.i 0.496203 + 0.453845i
\(316\) 714188.i 0.402341i
\(317\) 361175.i 0.201869i −0.994893 0.100935i \(-0.967817\pi\)
0.994893 0.100935i \(-0.0321833\pi\)
\(318\) 620653. + 1.40878e6i 0.344176 + 0.781223i
\(319\) 1.68204e6i 0.925465i
\(320\) −190141. −0.103801
\(321\) −276658. + 121885.i −0.149858 + 0.0660217i
\(322\) −1.00363e6 + 357364.i −0.539429 + 0.192075i
\(323\) 57778.9i 0.0308151i
\(324\) 84078.8 + 941035.i 0.0444963 + 0.498016i
\(325\) 641532. 0.336907
\(326\) 21066.4i 0.0109786i
\(327\) −842721. 1.91284e6i −0.435827 0.989255i
\(328\) −473389. −0.242960
\(329\) −2.31346e6 −1.17834
\(330\) 675126. + 1.53242e6i 0.341272 + 0.774630i
\(331\) 1.10475e6 0.554237 0.277118 0.960836i \(-0.410621\pi\)
0.277118 + 0.960836i \(0.410621\pi\)
\(332\) 1.00683e6 0.501313
\(333\) −2.24174e6 2.05037e6i −1.10783 1.01326i
\(334\) −1.22986e6 −0.603239
\(335\) 307227.i 0.149571i
\(336\) −168906. 383388.i −0.0816200 0.185264i
\(337\) 1.82818e6i 0.876888i −0.898758 0.438444i \(-0.855530\pi\)
0.898758 0.438444i \(-0.144470\pi\)
\(338\) 264238.i 0.125807i
\(339\) 396741. 174789.i 0.187503 0.0826064i
\(340\) 40573.9 0.0190349
\(341\) −4.79372e6 −2.23247
\(342\) 693859. 758617.i 0.320779 0.350718i
\(343\) 2.37184e6i 1.08855i
\(344\) −196643. −0.0895946
\(345\) −1.33442e6 + 1.26083e6i −0.603595 + 0.570308i
\(346\) −2.71598e6 −1.21965
\(347\) 1.53933e6i 0.686289i 0.939283 + 0.343145i \(0.111492\pi\)
−0.939283 + 0.343145i \(0.888508\pi\)
\(348\) −292367. 663624.i −0.129414 0.293747i
\(349\) 2.65317e6 1.16601 0.583005 0.812469i \(-0.301877\pi\)
0.583005 + 0.812469i \(0.301877\pi\)
\(350\) 407359. 0.177749
\(351\) 801957. 2.37327e6i 0.347443 1.02820i
\(352\) 592404.i 0.254837i
\(353\) 2.13691e6i 0.912745i −0.889789 0.456372i \(-0.849148\pi\)
0.889789 0.456372i \(-0.150852\pi\)
\(354\) −468723. + 206501.i −0.198796 + 0.0875819i
\(355\) 974750.i 0.410509i
\(356\) 1.82845e6 0.764640
\(357\) 36042.6 + 81810.6i 0.0149674 + 0.0339734i
\(358\) −344342. −0.141998
\(359\) −904914. −0.370571 −0.185285 0.982685i \(-0.559321\pi\)
−0.185285 + 0.982685i \(0.559321\pi\)
\(360\) −532722. 487247.i −0.216643 0.198149i
\(361\) 1.35739e6 0.548196
\(362\) 2.86796e6 1.15027
\(363\) −2.47696e6 + 1.09125e6i −0.986627 + 0.434669i
\(364\) 1.11084e6i 0.439438i
\(365\) 2.26086e6 0.888264
\(366\) −3.14093e6 + 1.38377e6i −1.22562 + 0.539960i
\(367\) 4.85024e6i 1.87974i −0.341533 0.939870i \(-0.610946\pi\)
0.341533 0.939870i \(-0.389054\pi\)
\(368\) 611841. 217859.i 0.235515 0.0838601i
\(369\) −1.32630e6 1.21308e6i −0.507080 0.463794i
\(370\) 2.32144e6 0.881562
\(371\) 2.59188e6i 0.977641i
\(372\) 1.89129e6 833228.i 0.708599 0.312181i
\(373\) 773061.i 0.287701i −0.989599 0.143851i \(-0.954052\pi\)
0.989599 0.143851i \(-0.0459485\pi\)
\(374\) 126412.i 0.0467315i
\(375\) 2.71183e6 1.19472e6i 0.995826 0.438722i
\(376\) 1.41035e6 0.514466
\(377\) 1.92280e6i 0.696756i
\(378\) 509226. 1.50697e6i 0.183308 0.542471i
\(379\) 554583.i 0.198321i 0.995071 + 0.0991605i \(0.0316157\pi\)
−0.995071 + 0.0991605i \(0.968384\pi\)
\(380\) 785590.i 0.279085i
\(381\) 3.80591e6 1.67673e6i 1.34322 0.591768i
\(382\) 2.39401e6i 0.839397i
\(383\) 3.81249e6 1.32804 0.664021 0.747714i \(-0.268848\pi\)
0.664021 + 0.747714i \(0.268848\pi\)
\(384\) 102970. + 233724.i 0.0356354 + 0.0808864i
\(385\) 2.81936e6i 0.969390i
\(386\) 2.79311e6i 0.954157i
\(387\) −550937. 503907.i −0.186993 0.171030i
\(388\) 1.30745e6i 0.440907i
\(389\) −328921. −0.110209 −0.0551046 0.998481i \(-0.517549\pi\)
−0.0551046 + 0.998481i \(0.517549\pi\)
\(390\) 771760. + 1.75177e6i 0.256934 + 0.583197i
\(391\) −130560. + 46488.5i −0.0431884 + 0.0153781i
\(392\) 370289.i 0.121710i
\(393\) 1.00053e6 + 2.27104e6i 0.326776 + 0.741727i
\(394\) 3.09791e6 1.00537
\(395\) 2.07209e6i 0.668215i
\(396\) 1.51807e6 1.65975e6i 0.486466 0.531868i
\(397\) 3.79002e6 1.20688 0.603442 0.797407i \(-0.293795\pi\)
0.603442 + 0.797407i \(0.293795\pi\)
\(398\) 3.32169e6 1.05112
\(399\) −1.58401e6 + 697853.i −0.498111 + 0.219448i
\(400\) −248337. −0.0776055
\(401\) 3.33202e6 1.03478 0.517388 0.855751i \(-0.326904\pi\)
0.517388 + 0.855751i \(0.326904\pi\)
\(402\) −377647. + 166377.i −0.116552 + 0.0513484i
\(403\) −5.47987e6 −1.68077
\(404\) 576977.i 0.175876i
\(405\) −243940. 2.73025e6i −0.0739002 0.827114i
\(406\) 1.22094e6i 0.367602i
\(407\) 7.23267e6i 2.16428i
\(408\) −21972.5 49874.0i −0.00653476 0.0148328i
\(409\) −633448. −0.187242 −0.0936209 0.995608i \(-0.529844\pi\)
−0.0936209 + 0.995608i \(0.529844\pi\)
\(410\) 1.37346e6 0.403511
\(411\) 21498.6 9471.46i 0.00627779 0.00276575i
\(412\) 2.42397e6i 0.703534i
\(413\) 862359. 0.248778
\(414\) 2.27248e6 + 957495.i 0.651627 + 0.274559i
\(415\) −2.92113e6 −0.832589
\(416\) 677198.i 0.191859i
\(417\) −1.24407e6 + 548088.i −0.350351 + 0.154351i
\(418\) −2.44758e6 −0.685167
\(419\) 4.56704e6 1.27086 0.635432 0.772157i \(-0.280822\pi\)
0.635432 + 0.772157i \(0.280822\pi\)
\(420\) 490052. + 1.11234e6i 0.135556 + 0.307689i
\(421\) 4.87938e6i 1.34171i −0.741588 0.670856i \(-0.765927\pi\)
0.741588 0.670856i \(-0.234073\pi\)
\(422\) 1.34590e6i 0.367902i
\(423\) 3.95139e6 + 3.61408e6i 1.07374 + 0.982081i
\(424\) 1.58008e6i 0.426839i
\(425\) 52992.3 0.0142312
\(426\) −1.19818e6 + 527869.i −0.319887 + 0.140930i
\(427\) 5.77869e6 1.53377
\(428\) −310299. −0.0818786
\(429\) −5.45781e6 + 2.40450e6i −1.43178 + 0.630784i
\(430\) 570525. 0.148800
\(431\) 1.78523e6 0.462916 0.231458 0.972845i \(-0.425650\pi\)
0.231458 + 0.972845i \(0.425650\pi\)
\(432\) −310438. + 918694.i −0.0800324 + 0.236843i
\(433\) 862750.i 0.221139i −0.993868 0.110570i \(-0.964733\pi\)
0.993868 0.110570i \(-0.0352675\pi\)
\(434\) −3.47960e6 −0.886758
\(435\) 848252. + 1.92539e6i 0.214932 + 0.487861i
\(436\) 2.14543e6i 0.540502i
\(437\) −900107. 2.52789e6i −0.225471 0.633219i
\(438\) −1.22435e6 2.77908e6i −0.304945 0.692175i
\(439\) −2.38229e6 −0.589974 −0.294987 0.955501i \(-0.595315\pi\)
−0.294987 + 0.955501i \(0.595315\pi\)
\(440\) 1.71876e6i 0.423237i
\(441\) 948883. 1.03744e6i 0.232336 0.254020i
\(442\) 144506.i 0.0351828i
\(443\) 3.65237e6i 0.884231i −0.896958 0.442115i \(-0.854228\pi\)
0.896958 0.442115i \(-0.145772\pi\)
\(444\) −1.25716e6 2.85354e6i −0.302645 0.686953i
\(445\) −5.30492e6 −1.26993
\(446\) 2.99258e6i 0.712374i
\(447\) 2.46299e6 1.08509e6i 0.583033 0.256861i
\(448\) 430007.i 0.101223i
\(449\) 3.44781e6i 0.807099i 0.914958 + 0.403550i \(0.132224\pi\)
−0.914958 + 0.403550i \(0.867776\pi\)
\(450\) −695771. 636377.i −0.161970 0.148144i
\(451\) 4.27914e6i 0.990639i
\(452\) 444983. 0.102446
\(453\) 3.11281e6 1.37138e6i 0.712702 0.313988i
\(454\) 816959.i 0.186020i
\(455\) 3.22291e6i 0.729826i
\(456\) 965657. 425431.i 0.217476 0.0958113i
\(457\) 2.09933e6i 0.470208i 0.971970 + 0.235104i \(0.0755431\pi\)
−0.971970 + 0.235104i \(0.924457\pi\)
\(458\) −3.47411e6 −0.773891
\(459\) 66243.9 196038.i 0.0146762 0.0434320i
\(460\) −1.77515e6 + 632080.i −0.391148 + 0.139276i
\(461\) 1.55911e6i 0.341684i −0.985298 0.170842i \(-0.945351\pi\)
0.985298 0.170842i \(-0.0546487\pi\)
\(462\) −3.46559e6 + 1.52680e6i −0.755392 + 0.332796i
\(463\) −4.79193e6 −1.03886 −0.519432 0.854512i \(-0.673856\pi\)
−0.519432 + 0.854512i \(0.673856\pi\)
\(464\) 744318.i 0.160496i
\(465\) −5.48725e6 + 2.41747e6i −1.17685 + 0.518476i
\(466\) 5.51530e6 1.17653
\(467\) −4.43239e6 −0.940473 −0.470236 0.882541i \(-0.655831\pi\)
−0.470236 + 0.882541i \(0.655831\pi\)
\(468\) 1.73535e6 1.89732e6i 0.366246 0.400428i
\(469\) 694797. 0.145856
\(470\) −4.09188e6 −0.854433
\(471\) 3.11481e6 + 7.07011e6i 0.646963 + 1.46850i
\(472\) −525718. −0.108617
\(473\) 1.77753e6i 0.365312i
\(474\) −2.54704e6 + 1.12213e6i −0.520704 + 0.229402i
\(475\) 1.02603e6i 0.208654i
\(476\) 91758.4i 0.0185621i
\(477\) −4.04903e6 + 4.42693e6i −0.814808 + 0.890855i
\(478\) 1.76052e6 0.352429
\(479\) −3.19416e6 −0.636090 −0.318045 0.948076i \(-0.603026\pi\)
−0.318045 + 0.948076i \(0.603026\pi\)
\(480\) −298749. 678111.i −0.0591839 0.134338i
\(481\) 8.26792e6i 1.62942i
\(482\) −2.53009e6 −0.496042
\(483\) −2.85138e6 3.01781e6i −0.556144 0.588605i
\(484\) −2.77815e6 −0.539066
\(485\) 3.79335e6i 0.732266i
\(486\) −3.22396e6 + 1.77840e6i −0.619154 + 0.341539i
\(487\) 4.87872e6 0.932145 0.466072 0.884747i \(-0.345669\pi\)
0.466072 + 0.884747i \(0.345669\pi\)
\(488\) −3.52285e6 −0.669645
\(489\) 75130.2 33099.4i 0.0142083 0.00625963i
\(490\) 1.07433e6i 0.202138i
\(491\) 7.58791e6i 1.42043i 0.703987 + 0.710213i \(0.251401\pi\)
−0.703987 + 0.710213i \(0.748599\pi\)
\(492\) −743787. 1.68827e6i −0.138527 0.314434i
\(493\) 158829.i 0.0294314i
\(494\) −2.79792e6 −0.515843
\(495\) −4.40441e6 + 4.81547e6i −0.807931 + 0.883336i
\(496\) 2.12126e6 0.387159
\(497\) 2.20441e6 0.400314
\(498\) 1.58192e6 + 3.59069e6i 0.285832 + 0.648791i
\(499\) 6.67031e6 1.19921 0.599604 0.800297i \(-0.295325\pi\)
0.599604 + 0.800297i \(0.295325\pi\)
\(500\) 3.04157e6 0.544093
\(501\) −1.93235e6 4.38611e6i −0.343947 0.780702i
\(502\) 1.49305e6i 0.264433i
\(503\) 7.71176e6 1.35904 0.679522 0.733655i \(-0.262187\pi\)
0.679522 + 0.733655i \(0.262187\pi\)
\(504\) 1.10191e6 1.20476e6i 0.193228 0.211263i
\(505\) 1.67400e6i 0.292097i
\(506\) −1.96931e6 5.53066e6i −0.341930 0.960287i
\(507\) −942365. + 415169.i −0.162817 + 0.0717307i
\(508\) 4.26869e6 0.733897
\(509\) 6.01246e6i 1.02863i −0.857602 0.514313i \(-0.828047\pi\)
0.857602 0.514313i \(-0.171953\pi\)
\(510\) 63749.5 + 144701.i 0.0108530 + 0.0246346i
\(511\) 5.11296e6i 0.866204i
\(512\) 262144.i 0.0441942i
\(513\) 3.79568e6 + 1.28261e6i 0.636790 + 0.215179i
\(514\) −3.40115e6 −0.567829
\(515\) 7.03274e6i 1.16844i
\(516\) −308964. 701297.i −0.0510839 0.115952i
\(517\) 1.27487e7i 2.09767i
\(518\) 5.24996e6i 0.859669i
\(519\) −4.26733e6 9.68613e6i −0.695405 1.57845i
\(520\) 1.96477e6i 0.318643i
\(521\) −1.04577e7 −1.68788 −0.843941 0.536436i \(-0.819770\pi\)
−0.843941 + 0.536436i \(0.819770\pi\)
\(522\) 1.90735e6 2.08536e6i 0.306376 0.334970i
\(523\) 3.52422e6i 0.563390i −0.959504 0.281695i \(-0.909103\pi\)
0.959504 0.281695i \(-0.0908966\pi\)
\(524\) 2.54719e6i 0.405260i
\(525\) 640040. + 1.45279e6i 0.101347 + 0.230040i
\(526\) 603982.i 0.0951830i
\(527\) −452652. −0.0709967
\(528\) 2.11272e6 930782.i 0.329805 0.145299i
\(529\) 4.98790e6 4.06784e6i 0.774959 0.632011i
\(530\) 4.58433e6i 0.708902i
\(531\) −1.47291e6 1.34718e6i −0.226694 0.207343i
\(532\) −1.77662e6 −0.272154
\(533\) 4.89164e6i 0.745824i
\(534\) 2.87284e6 + 6.52088e6i 0.435972 + 0.989584i
\(535\) 900278. 0.135985
\(536\) −423567. −0.0636811
\(537\) −541028. 1.22804e6i −0.0809625 0.183771i
\(538\) −2.57320e6 −0.383282
\(539\) −3.34718e6 −0.496257
\(540\) 900683. 2.66543e6i 0.132919 0.393354i
\(541\) −1.09709e7 −1.61157 −0.805786 0.592206i \(-0.798257\pi\)
−0.805786 + 0.592206i \(0.798257\pi\)
\(542\) 6.60585e6i 0.965897i
\(543\) 4.50612e6 + 1.02281e7i 0.655848 + 1.48867i
\(544\) 55938.4i 0.00810426i
\(545\) 6.22459e6i 0.897676i
\(546\) −3.96164e6 + 1.74534e6i −0.568713 + 0.250553i
\(547\) −9.00106e6 −1.28625 −0.643125 0.765761i \(-0.722362\pi\)
−0.643125 + 0.765761i \(0.722362\pi\)
\(548\) 24112.8 0.00343001
\(549\) −9.87002e6 9.02748e6i −1.39761 1.27831i
\(550\) 2.24482e6i 0.316427i
\(551\) −3.07523e6 −0.431517
\(552\) 1.73828e6 + 1.83974e6i 0.242813 + 0.256986i
\(553\) 4.68606e6 0.651621
\(554\) 1.58698e6i 0.219683i
\(555\) 3.64743e6 + 8.27906e6i 0.502637 + 1.14090i
\(556\) −1.39534e6 −0.191423
\(557\) 4.16338e6 0.568601 0.284300 0.958735i \(-0.408239\pi\)
0.284300 + 0.958735i \(0.408239\pi\)
\(558\) 5.94317e6 + 5.43584e6i 0.808039 + 0.739062i
\(559\) 2.03195e6i 0.275033i
\(560\) 1.24759e6i 0.168113i
\(561\) −450830. + 198618.i −0.0604791 + 0.0266447i
\(562\) 5.82439e6i 0.777875i
\(563\) 1.15019e7 1.52932 0.764661 0.644432i \(-0.222906\pi\)
0.764661 + 0.644432i \(0.222906\pi\)
\(564\) 2.21593e6 + 5.02979e6i 0.293331 + 0.665813i
\(565\) −1.29104e6 −0.170145
\(566\) −6.24780e6 −0.819759
\(567\) 6.17449e6 551673.i 0.806573 0.0720650i
\(568\) −1.34387e6 −0.174778
\(569\) 6.25524e6 0.809960 0.404980 0.914326i \(-0.367279\pi\)
0.404980 + 0.914326i \(0.367279\pi\)
\(570\) −2.80169e6 + 1.23431e6i −0.361187 + 0.159125i
\(571\) 507892.i 0.0651900i 0.999469 + 0.0325950i \(0.0103771\pi\)
−0.999469 + 0.0325950i \(0.989623\pi\)
\(572\) −6.12145e6 −0.782283
\(573\) 8.53787e6 3.76145e6i 1.08633 0.478596i
\(574\) 3.10609e6i 0.393490i
\(575\) −2.31847e6 + 825539.i −0.292436 + 0.104128i
\(576\) −671757. + 734452.i −0.0843638 + 0.0922375i
\(577\) 1.06418e7 1.33068 0.665340 0.746540i \(-0.268287\pi\)
0.665340 + 0.746540i \(0.268287\pi\)
\(578\) 5.66749e6i 0.705621i
\(579\) −9.96121e6 + 4.38852e6i −1.23485 + 0.544029i
\(580\) 2.15951e6i 0.266554i
\(581\) 6.60617e6i 0.811912i
\(582\) −4.66284e6 + 2.05427e6i −0.570615 + 0.251391i
\(583\) 1.42829e7 1.74039
\(584\) 3.11700e6i 0.378186i
\(585\) −5.03483e6 + 5.50473e6i −0.608268 + 0.665038i
\(586\) 8.30795e6i 0.999424i
\(587\) 1.39325e7i 1.66892i −0.551070 0.834459i \(-0.685780\pi\)
0.551070 0.834459i \(-0.314220\pi\)
\(588\) 1.32058e6 581795.i 0.157515 0.0693948i
\(589\) 8.76422e6i 1.04094i
\(590\) 1.52528e6 0.180393
\(591\) 4.86741e6 + 1.10482e7i 0.573231 + 1.30114i
\(592\) 3.20052e6i 0.375333i
\(593\) 1.47891e7i 1.72705i 0.504304 + 0.863526i \(0.331749\pi\)
−0.504304 + 0.863526i \(0.668251\pi\)
\(594\) 8.30442e6 + 2.80617e6i 0.965702 + 0.326323i
\(595\) 266221.i 0.0308283i
\(596\) 2.76247e6 0.318553
\(597\) 5.21902e6 + 1.18463e7i 0.599312 + 1.36034i
\(598\) −2.25118e6 6.32229e6i −0.257429 0.722972i
\(599\) 706139.i 0.0804125i −0.999191 0.0402062i \(-0.987199\pi\)
0.999191 0.0402062i \(-0.0128015\pi\)
\(600\) −390186. 885658.i −0.0442480 0.100436i
\(601\) −1.60096e7 −1.80798 −0.903991 0.427551i \(-0.859377\pi\)
−0.903991 + 0.427551i \(0.859377\pi\)
\(602\) 1.29025e6i 0.145105i
\(603\) −1.18671e6 1.08541e6i −0.132909 0.121563i
\(604\) 3.49132e6 0.389401
\(605\) 8.06032e6 0.895290
\(606\) 2.05770e6 906544.i 0.227615 0.100278i
\(607\) 6.76123e6 0.744825 0.372413 0.928067i \(-0.378531\pi\)
0.372413 + 0.928067i \(0.378531\pi\)
\(608\) 1.08308e6 0.118823
\(609\) −4.35429e6 + 1.91833e6i −0.475745 + 0.209595i
\(610\) 1.02209e7 1.11216
\(611\) 1.45734e7i 1.57928i
\(612\) 143345. 156724.i 0.0154705 0.0169144i
\(613\) 3.11552e6i 0.334872i 0.985883 + 0.167436i \(0.0535488\pi\)
−0.985883 + 0.167436i \(0.946451\pi\)
\(614\) 1.12184e6i 0.120091i
\(615\) 2.15797e6 + 4.89823e6i 0.230069 + 0.522218i
\(616\) −3.88699e6 −0.412726
\(617\) 1.74682e7 1.84729 0.923645 0.383248i \(-0.125195\pi\)
0.923645 + 0.383248i \(0.125195\pi\)
\(618\) 8.64474e6 3.80853e6i 0.910501 0.401131i
\(619\) 4.52333e6i 0.474495i −0.971449 0.237247i \(-0.923755\pi\)
0.971449 0.237247i \(-0.0762452\pi\)
\(620\) −6.15447e6 −0.643001
\(621\) 155741. + 9.60886e6i 0.0162059 + 0.999869i
\(622\) −3.61549e6 −0.374707
\(623\) 1.19971e7i 1.23839i
\(624\) 2.41513e6 1.06401e6i 0.248301 0.109392i
\(625\) −5.79313e6 −0.593216
\(626\) −7.45522e6 −0.760369
\(627\) −3.84563e6 8.72893e6i −0.390659 0.886732i
\(628\) 7.92980e6i 0.802348i
\(629\) 682953.i 0.0688279i
\(630\) −3.19701e6 + 3.49539e6i −0.320917 + 0.350868i
\(631\) 7.95471e6i 0.795336i 0.917529 + 0.397668i \(0.130180\pi\)
−0.917529 + 0.397668i \(0.869820\pi\)
\(632\) −2.85675e6 −0.284498
\(633\) −4.79995e6 + 2.11467e6i −0.476132 + 0.209765i
\(634\) 1.44470e6 0.142743
\(635\) −1.23849e7 −1.21887
\(636\) −5.63512e6 + 2.48261e6i −0.552408 + 0.243369i
\(637\) −3.82628e6 −0.373618
\(638\) −6.72816e6 −0.654402
\(639\) −3.76513e6 3.44373e6i −0.364777 0.333639i
\(640\) 760566.i 0.0733984i
\(641\) 2.60477e6 0.250394 0.125197 0.992132i \(-0.460044\pi\)
0.125197 + 0.992132i \(0.460044\pi\)
\(642\) −487539. 1.10663e6i −0.0466844 0.105966i
\(643\) 1.12007e7i 1.06836i −0.845371 0.534179i \(-0.820621\pi\)
0.845371 0.534179i \(-0.179379\pi\)
\(644\) −1.42945e6 4.01452e6i −0.135817 0.381434i
\(645\) 896406. + 2.03469e6i 0.0848409 + 0.192575i
\(646\) −231116. −0.0217895
\(647\) 6.03514e6i 0.566796i 0.959002 + 0.283398i \(0.0914618\pi\)
−0.959002 + 0.283398i \(0.908538\pi\)
\(648\) −3.76414e6 + 336315.i −0.352151 + 0.0314636i
\(649\) 4.75216e6i 0.442873i
\(650\) 2.56613e6i 0.238229i
\(651\) −5.46713e6 1.24095e7i −0.505600 1.14763i
\(652\) 84265.7 0.00776304
\(653\) 2.16366e7i 1.98566i 0.119515 + 0.992832i \(0.461866\pi\)
−0.119515 + 0.992832i \(0.538134\pi\)
\(654\) 7.65134e6 3.37088e6i 0.699509 0.308176i
\(655\) 7.39024e6i 0.673062i
\(656\) 1.89356e6i 0.171798i
\(657\) 7.98748e6 8.73295e6i 0.721932 0.789310i
\(658\) 9.25382e6i 0.833214i
\(659\) −2.95605e6 −0.265154 −0.132577 0.991173i \(-0.542325\pi\)
−0.132577 + 0.991173i \(0.542325\pi\)
\(660\) −6.12970e6 + 2.70050e6i −0.547746 + 0.241315i
\(661\) 9.44325e6i 0.840655i −0.907372 0.420328i \(-0.861915\pi\)
0.907372 0.420328i \(-0.138085\pi\)
\(662\) 4.41901e6i 0.391905i
\(663\) −515359. + 227047.i −0.0455330 + 0.0200601i
\(664\) 4.02730e6i 0.354482i
\(665\) 5.15455e6 0.451998
\(666\) 8.20149e6 8.96694e6i 0.716485 0.783355i
\(667\) −2.47431e6 6.94892e6i −0.215347 0.604787i
\(668\) 4.91944e6i 0.426554i
\(669\) 1.06726e7 4.70192e6i 0.921942 0.406172i
\(670\) 1.22891e6 0.105763
\(671\) 3.18444e7i 2.73040i
\(672\) 1.53355e6 675624.i 0.131001 0.0577141i
\(673\) 1.77229e7 1.50833 0.754165 0.656685i \(-0.228042\pi\)
0.754165 + 0.656685i \(0.228042\pi\)
\(674\) 7.31272e6 0.620053
\(675\) 1.17635e6 3.48123e6i 0.0993752 0.294086i
\(676\) −1.05695e6 −0.0889587
\(677\) −2.80472e6 −0.235189 −0.117595 0.993062i \(-0.537518\pi\)
−0.117595 + 0.993062i \(0.537518\pi\)
\(678\) 699154. + 1.58696e6i 0.0584115 + 0.132585i
\(679\) 8.57871e6 0.714081
\(680\) 162296.i 0.0134597i
\(681\) 2.91356e6 1.28360e6i 0.240744 0.106063i
\(682\) 1.91749e7i 1.57860i
\(683\) 6.08512e6i 0.499135i −0.968357 0.249567i \(-0.919712\pi\)
0.968357 0.249567i \(-0.0802884\pi\)
\(684\) 3.03447e6 + 2.77544e6i 0.247995 + 0.226825i
\(685\) −69959.1 −0.00569662
\(686\) −9.48734e6 −0.769723
\(687\) −5.45850e6 1.23899e7i −0.441247 1.00156i
\(688\) 786571.i 0.0633530i
\(689\) 1.63273e7 1.31029
\(690\) −5.04333e6 5.33769e6i −0.403268 0.426806i
\(691\) 1.21419e7 0.967368 0.483684 0.875243i \(-0.339298\pi\)
0.483684 + 0.875243i \(0.339298\pi\)
\(692\) 1.08639e7i 0.862424i
\(693\) −1.08902e7 9.96061e6i −0.861399 0.787867i
\(694\) −6.15731e6 −0.485280
\(695\) 4.04834e6 0.317918
\(696\) 2.65450e6 1.16947e6i 0.207711 0.0915093i
\(697\) 404063.i 0.0315041i
\(698\) 1.06127e7i 0.824493i
\(699\) 8.66560e6 + 1.96695e7i 0.670820 + 1.52265i
\(700\) 1.62944e6i 0.125688i
\(701\) −1.31040e7 −1.00718 −0.503590 0.863943i \(-0.667988\pi\)
−0.503590 + 0.863943i \(0.667988\pi\)
\(702\) 9.49307e6 + 3.20783e6i 0.727049 + 0.245679i
\(703\) −1.32233e7 −1.00914
\(704\) 2.36962e6 0.180197
\(705\) −6.42914e6 1.45931e7i −0.487169 1.10579i
\(706\) 8.54764e6 0.645408
\(707\) −3.78577e6 −0.284843
\(708\) −826005. 1.87489e6i −0.0619298 0.140570i
\(709\) 151796.i 0.0113408i −0.999984 0.00567040i \(-0.998195\pi\)
0.999984 0.00567040i \(-0.00180495\pi\)
\(710\) 3.89900e6 0.290273
\(711\) −8.00380e6 7.32057e6i −0.593775 0.543089i
\(712\) 7.31378e6i 0.540682i
\(713\) 1.98040e7 7.05163e6i 1.45891 0.519476i
\(714\) −327242. + 144170.i −0.0240228 + 0.0105835i
\(715\) 1.77603e7 1.29923
\(716\) 1.37737e6i 0.100408i
\(717\) 2.76612e6 + 6.27863e6i 0.200943 + 0.456108i
\(718\) 3.61966e6i 0.262033i
\(719\) 2.13306e7i 1.53879i −0.638771 0.769397i \(-0.720557\pi\)
0.638771 0.769397i \(-0.279443\pi\)
\(720\) 1.94899e6 2.13089e6i 0.140113 0.153190i
\(721\) −1.59046e7 −1.13942
\(722\) 5.42955e6i 0.387633i
\(723\) −3.97526e6 9.02319e6i −0.282827 0.641969i
\(724\) 1.14718e7i 0.813367i
\(725\) 2.82046e6i 0.199285i
\(726\) −4.36501e6 9.90785e6i −0.307358 0.697651i
\(727\) 1.67210e7i 1.17335i −0.809824 0.586673i \(-0.800438\pi\)
0.809824 0.586673i \(-0.199562\pi\)
\(728\) −4.44335e6 −0.310730
\(729\) −1.14079e7 8.70354e6i −0.795034 0.606565i
\(730\) 9.04345e6i 0.628097i
\(731\) 167845.i 0.0116176i
\(732\) −5.53508e6 1.25637e7i −0.381809 0.866644i
\(733\) 1.85430e7i 1.27473i 0.770561 + 0.637366i \(0.219976\pi\)
−0.770561 + 0.637366i \(0.780024\pi\)
\(734\) 1.94009e7 1.32918
\(735\) −3.83143e6 + 1.68798e6i −0.261603 + 0.115252i
\(736\) 871435. + 2.44737e6i 0.0592981 + 0.166534i
\(737\) 3.82878e6i 0.259652i
\(738\) 4.85234e6 5.30521e6i 0.327952 0.358560i
\(739\) −7.00315e6 −0.471718 −0.235859 0.971787i \(-0.575790\pi\)
−0.235859 + 0.971787i \(0.575790\pi\)
\(740\) 9.28576e6i 0.623359i
\(741\) −4.39607e6 9.97835e6i −0.294116 0.667595i
\(742\) 1.03675e7 0.691297
\(743\) −1.90312e7 −1.26472 −0.632361 0.774674i \(-0.717914\pi\)
−0.632361 + 0.774674i \(0.717914\pi\)
\(744\) 3.33291e6 + 7.56516e6i 0.220745 + 0.501055i
\(745\) −8.01484e6 −0.529059
\(746\) 3.09224e6 0.203435
\(747\) −1.03202e7 + 1.12833e7i −0.676683 + 0.739838i
\(748\) −505649. −0.0330442
\(749\) 2.03599e6i 0.132608i
\(750\) 4.77890e6 + 1.08473e7i 0.310223 + 0.704156i
\(751\) 2.27683e7i 1.47309i 0.676386 + 0.736547i \(0.263545\pi\)
−0.676386 + 0.736547i \(0.736455\pi\)
\(752\) 5.64139e6i 0.363782i
\(753\) 5.32475e6 2.34588e6i 0.342225 0.150771i
\(754\) −7.69120e6 −0.492681
\(755\) −1.01295e7 −0.646724
\(756\) 6.02790e6 + 2.03690e6i 0.383585 + 0.129618i
\(757\) 1.17215e7i 0.743435i 0.928346 + 0.371717i \(0.121231\pi\)
−0.928346 + 0.371717i \(0.878769\pi\)
\(758\) −2.21833e6 −0.140234
\(759\) 1.66301e7 1.57130e7i 1.04783 0.990043i
\(760\) −3.14236e6 −0.197343
\(761\) 2.42582e7i 1.51844i −0.650834 0.759220i \(-0.725581\pi\)
0.650834 0.759220i \(-0.274419\pi\)
\(762\) 6.70693e6 + 1.52236e7i 0.418443 + 0.949797i
\(763\) −1.40770e7 −0.875382
\(764\) 9.57604e6 0.593543
\(765\) −415891. + 454706.i −0.0256937 + 0.0280917i
\(766\) 1.52500e7i 0.939068i
\(767\) 5.43236e6i 0.333426i
\(768\) −934897. + 411879.i −0.0571954 + 0.0251980i
\(769\) 2.96832e6i 0.181007i −0.995896 0.0905033i \(-0.971152\pi\)
0.995896 0.0905033i \(-0.0288476\pi\)
\(770\) 1.12774e7 0.685462
\(771\) −5.34386e6 1.21297e7i −0.323757 0.734875i
\(772\) −1.11724e7 −0.674691
\(773\) 1.40122e7 0.843448 0.421724 0.906724i \(-0.361425\pi\)
0.421724 + 0.906724i \(0.361425\pi\)
\(774\) 2.01563e6 2.20375e6i 0.120937 0.132224i
\(775\) −8.03816e6 −0.480731
\(776\) −5.22982e6 −0.311769
\(777\) −1.87232e7 + 8.24870e6i −1.11257 + 0.490155i
\(778\) 1.31568e6i 0.0779296i
\(779\) −7.82344e6 −0.461906
\(780\) −7.00707e6 + 3.08704e6i −0.412382 + 0.181679i
\(781\) 1.21477e7i 0.712635i
\(782\) −185954. 522239.i −0.0108740 0.0305388i
\(783\) 1.04340e7 + 3.52577e6i 0.608198 + 0.205518i
\(784\) 1.48115e6 0.0860618
\(785\) 2.30069e7i 1.33255i
\(786\) −9.08418e6 + 4.00213e6i −0.524480 + 0.231066i
\(787\) 2.78881e7i 1.60503i −0.596633 0.802514i \(-0.703495\pi\)
0.596633 0.802514i \(-0.296505\pi\)
\(788\) 1.23916e7i 0.710907i
\(789\) 2.15401e6 948973.i 0.123184 0.0542702i
\(790\) 8.28837e6 0.472500
\(791\) 2.91970e6i 0.165919i
\(792\) 6.63899e6 + 6.07226e6i 0.376088 + 0.343983i
\(793\) 3.64024e7i 2.05564i
\(794\) 1.51601e7i 0.853396i
\(795\) 1.63493e7 7.20287e6i 0.917449 0.404192i
\(796\) 1.32868e7i 0.743252i
\(797\) 1.98565e7 1.10728 0.553640 0.832756i \(-0.313238\pi\)
0.553640 + 0.832756i \(0.313238\pi\)
\(798\) −2.79141e6 6.33604e6i −0.155173 0.352217i
\(799\) 1.20381e6i 0.0667098i
\(800\) 993350.i 0.0548753i
\(801\) −1.87419e7 + 2.04911e7i −1.03213 + 1.12846i
\(802\) 1.33281e7i 0.731697i
\(803\) −2.81758e7 −1.54201
\(804\) −665507. 1.51059e6i −0.0363088 0.0824150i
\(805\) 4.14732e6 + 1.16474e7i 0.225568 + 0.633492i
\(806\) 2.19195e7i 1.18848i
\(807\) −4.04300e6 9.17694e6i −0.218535 0.496037i
\(808\) 2.30791e6 0.124363
\(809\) 2.73543e7i 1.46945i 0.678366 + 0.734724i \(0.262689\pi\)
−0.678366 + 0.734724i \(0.737311\pi\)
\(810\) 1.09210e7 975761.i 0.584858 0.0522553i
\(811\) −1.89733e7 −1.01295 −0.506477 0.862253i \(-0.669053\pi\)
−0.506477 + 0.862253i \(0.669053\pi\)
\(812\) −4.88375e6 −0.259934
\(813\) 2.35588e7 1.03791e7i 1.25005 0.550722i
\(814\) −2.89307e7 −1.53038
\(815\) −244482. −0.0128930
\(816\) 199496. 87890.2i 0.0104884 0.00462078i
\(817\) −3.24980e6 −0.170334
\(818\) 2.53379e6i 0.132400i
\(819\) −1.24490e7 1.13863e7i −0.648522 0.593162i
\(820\) 5.49383e6i 0.285326i
\(821\) 2.29178e7i 1.18663i 0.804971 + 0.593314i \(0.202181\pi\)
−0.804971 + 0.593314i \(0.797819\pi\)
\(822\) 37885.8 + 85994.6i 0.00195568 + 0.00443907i
\(823\) −1.77229e7 −0.912083 −0.456041 0.889959i \(-0.650733\pi\)
−0.456041 + 0.889959i \(0.650733\pi\)
\(824\) 9.69589e6 0.497473
\(825\) −8.00580e6 + 3.52704e6i −0.409515 + 0.180416i
\(826\) 3.44943e6i 0.175913i
\(827\) −3.39229e7 −1.72476 −0.862380 0.506261i \(-0.831027\pi\)
−0.862380 + 0.506261i \(0.831027\pi\)
\(828\) −3.82998e6 + 9.08991e6i −0.194143 + 0.460770i
\(829\) 2.43200e7 1.22907 0.614537 0.788888i \(-0.289343\pi\)
0.614537 + 0.788888i \(0.289343\pi\)
\(830\) 1.16845e7i 0.588730i
\(831\) −5.65973e6 + 2.49345e6i −0.284311 + 0.125256i
\(832\) 2.70879e6 0.135665
\(833\) −316061. −0.0157819
\(834\) −2.19235e6 4.97627e6i −0.109143 0.247736i
\(835\) 1.42729e7i 0.708429i
\(836\) 9.79033e6i 0.484486i
\(837\) −1.00482e7 + 2.97362e7i −0.495765 + 1.46714i
\(838\) 1.82681e7i 0.898637i
\(839\) −1.32599e6 −0.0650334 −0.0325167 0.999471i \(-0.510352\pi\)
−0.0325167 + 0.999471i \(0.510352\pi\)
\(840\) −4.44934e6 + 1.96021e6i −0.217569 + 0.0958525i
\(841\) 1.20576e7 0.587858
\(842\) 1.95175e7 0.948733
\(843\) 2.07718e7 9.15125e6i 1.00671 0.443518i
\(844\) −5.38360e6 −0.260146
\(845\) 3.06656e6 0.147744
\(846\) −1.44563e7 + 1.58056e7i −0.694436 + 0.759248i
\(847\) 1.82285e7i 0.873056i
\(848\) −6.32032e6 −0.301821
\(849\) −9.81651e6 2.22818e7i −0.467399 1.06092i
\(850\) 211969.i 0.0100630i
\(851\) −1.06394e7 2.98799e7i −0.503607 1.41435i
\(852\) −2.11148e6 4.79270e6i −0.0996523 0.226194i
\(853\) 1.55445e7 0.731485 0.365743 0.930716i \(-0.380815\pi\)
0.365743 + 0.930716i \(0.380815\pi\)
\(854\) 2.31148e7i 1.08454i
\(855\) −8.80399e6 8.05245e6i −0.411874 0.376715i
\(856\) 1.24119e6i 0.0578969i
\(857\) 1.41982e6i 0.0660360i 0.999455 + 0.0330180i \(0.0105119\pi\)
−0.999455 + 0.0330180i \(0.989488\pi\)
\(858\) −9.61798e6 2.18312e7i −0.446032 1.01242i
\(859\) −6.46087e6 −0.298750 −0.149375 0.988781i \(-0.547726\pi\)
−0.149375 + 0.988781i \(0.547726\pi\)
\(860\) 2.28210e6i 0.105218i
\(861\) −1.10774e7 + 4.88027e6i −0.509249 + 0.224355i
\(862\) 7.14094e6i 0.327331i
\(863\) 4.23625e7i 1.93622i 0.250523 + 0.968111i \(0.419397\pi\)
−0.250523 + 0.968111i \(0.580603\pi\)
\(864\) −3.67477e6 1.24175e6i −0.167474 0.0565914i
\(865\) 3.15198e7i 1.43233i
\(866\) 3.45100e6 0.156369
\(867\) 2.02123e7 8.90473e6i 0.913202 0.402321i
\(868\) 1.39184e7i 0.627032i
\(869\) 2.58232e7i 1.16001i
\(870\) −7.70156e6 + 3.39301e6i −0.344970 + 0.151980i
\(871\) 4.37682e6i 0.195485i
\(872\) 8.58171e6 0.382193
\(873\) −1.46525e7 1.34017e7i −0.650691 0.595146i
\(874\) 1.01116e7 3.60043e6i 0.447754 0.159432i
\(875\) 1.99569e7i 0.881197i
\(876\) 1.11163e7 4.89742e6i 0.489442 0.215629i
\(877\) −2.08726e7 −0.916383 −0.458191 0.888854i \(-0.651503\pi\)
−0.458191 + 0.888854i \(0.651503\pi\)
\(878\) 9.52915e6i 0.417174i
\(879\) 2.96290e7 1.30534e7i 1.29344 0.569838i
\(880\) −6.87504e6 −0.299274
\(881\) 2.34455e7 1.01770 0.508851 0.860855i \(-0.330070\pi\)
0.508851 + 0.860855i \(0.330070\pi\)
\(882\) 4.14977e6 + 3.79553e6i 0.179619 + 0.164286i
\(883\) −3.76556e7 −1.62528 −0.812639 0.582767i \(-0.801970\pi\)
−0.812639 + 0.582767i \(0.801970\pi\)
\(884\) −578025. −0.0248780
\(885\) 2.39651e6 + 5.43968e6i 0.102854 + 0.233461i
\(886\) 1.46095e7 0.625246
\(887\) 3.76988e7i 1.60886i −0.594046 0.804431i \(-0.702470\pi\)
0.594046 0.804431i \(-0.297530\pi\)
\(888\) 1.14142e7 5.02864e6i 0.485749 0.214002i
\(889\) 2.80085e7i 1.18860i
\(890\) 2.12197e7i 0.897974i
\(891\) 3.04008e6 + 3.40255e7i 0.128289 + 1.43585i
\(892\) 1.19703e7 0.503724
\(893\) 2.33080e7 0.978085
\(894\) 4.34038e6 + 9.85194e6i 0.181628 + 0.412266i
\(895\) 3.99619e6i 0.166759i
\(896\) 1.72003e6 0.0715756
\(897\) 1.90105e7 1.79621e7i 0.788881 0.745375i
\(898\) −1.37912e7 −0.570706
\(899\) 2.40920e7i 0.994199i
\(900\) 2.54551e6 2.78308e6i 0.104753 0.114530i
\(901\) 1.34868e6 0.0553474
\(902\) −1.71166e7 −0.700488
\(903\) −4.60148e6 + 2.02723e6i −0.187792 + 0.0827340i
\(904\) 1.77993e6i 0.0724406i
\(905\) 3.32836e7i 1.35085i
\(906\) 5.48554e6 + 1.24513e7i 0.222023 + 0.503956i
\(907\) 7.81724e6i 0.315526i −0.987477 0.157763i \(-0.949572\pi\)
0.987477 0.157763i \(-0.0504282\pi\)
\(908\) 3.26784e6 0.131536
\(909\) 6.46610e6 + 5.91413e6i 0.259557 + 0.237400i
\(910\) 1.28916e7 0.516065
\(911\) −1.13258e7 −0.452140 −0.226070 0.974111i \(-0.572588\pi\)
−0.226070 + 0.974111i \(0.572588\pi\)
\(912\) 1.70172e6 + 3.86263e6i 0.0677488 + 0.153779i
\(913\) 3.64043e7 1.44536
\(914\) −8.39732e6 −0.332487
\(915\) 1.60591e7 + 3.64515e7i 0.634115 + 1.43934i
\(916\) 1.38964e7i 0.547224i
\(917\) 1.67131e7 0.656347
\(918\) 784154. + 264975.i 0.0307110 + 0.0103776i
\(919\) 5.35114e6i 0.209005i −0.994525 0.104503i \(-0.966675\pi\)
0.994525 0.104503i \(-0.0333251\pi\)
\(920\) −2.52832e6 7.10061e6i −0.0984832 0.276583i
\(921\) −4.00089e6 + 1.76263e6i −0.155420 + 0.0684720i
\(922\) 6.23644e6 0.241607
\(923\) 1.38865e7i 0.536523i
\(924\) −6.10722e6 1.38624e7i −0.235323 0.534143i
\(925\) 1.21278e7i 0.466046i
\(926\) 1.91677e7i 0.734587i
\(927\) 2.71651e7 + 2.48462e7i 1.03827 + 0.949644i
\(928\) 2.97727e6 0.113488
\(929\) 3.42386e7i 1.30160i 0.759250 + 0.650799i \(0.225566\pi\)
−0.759250 + 0.650799i \(0.774434\pi\)
\(930\) −9.66987e6 2.19490e7i −0.366618 0.832161i
\(931\) 6.11955e6i 0.231390i
\(932\) 2.20612e7i 0.831934i
\(933\) −5.68064e6 1.28941e7i −0.213645 0.484939i
\(934\) 1.77296e7i 0.665015i
\(935\) 1.46705e6 0.0548803
\(936\) 7.58926e6 + 6.94141e6i 0.283146 + 0.258975i
\(937\) 3.00322e6i 0.111747i −0.998438 0.0558737i \(-0.982206\pi\)
0.998438 0.0558737i \(-0.0177944\pi\)
\(938\) 2.77919e6i 0.103136i
\(939\) −1.17136e7 2.65879e7i −0.433537 0.984057i
\(940\) 1.63675e7i 0.604176i
\(941\) −1.38304e7 −0.509169 −0.254585 0.967050i \(-0.581939\pi\)
−0.254585 + 0.967050i \(0.581939\pi\)
\(942\) −2.82804e7 + 1.24592e7i −1.03839 + 0.457472i
\(943\) −6.29468e6 1.76782e7i −0.230513 0.647378i
\(944\) 2.10287e6i 0.0768038i
\(945\) −1.74889e7 5.90972e6i −0.637064 0.215272i
\(946\) −7.11011e6 −0.258314
\(947\) 2.76242e7i 1.00096i 0.865749 + 0.500478i \(0.166843\pi\)
−0.865749 + 0.500478i \(0.833157\pi\)
\(948\) −4.48851e6 1.01882e7i −0.162211 0.368193i
\(949\) −3.22087e7 −1.16093
\(950\) −4.10413e6 −0.147541
\(951\) 2.26991e6 + 5.15231e6i 0.0813873 + 0.184736i
\(952\) −367033. −0.0131254
\(953\) 1.42475e7 0.508167 0.254083 0.967182i \(-0.418226\pi\)
0.254083 + 0.967182i \(0.418226\pi\)
\(954\) −1.77077e7 1.61961e7i −0.629929 0.576156i
\(955\) −2.77832e7 −0.985767
\(956\) 7.04208e6i 0.249205i
\(957\) −1.05713e7 2.39950e7i −0.373118 0.846917i
\(958\) 1.27767e7i 0.449783i
\(959\) 158213.i 0.00555515i
\(960\) 2.71244e6 1.19500e6i 0.0949910 0.0418493i
\(961\) 4.00316e7 1.39828
\(962\) −3.30717e7 −1.15218
\(963\) 3.18062e6 3.47747e6i 0.110521 0.120836i
\(964\) 1.01204e7i 0.350755i
\(965\) 3.24149e7 1.12054
\(966\) 1.20712e7 1.14055e7i 0.416207 0.393254i
\(967\) 4.31861e7 1.48517 0.742587 0.669749i \(-0.233598\pi\)
0.742587 + 0.669749i \(0.233598\pi\)
\(968\) 1.11126e7i 0.381177i
\(969\) −363128. 824239.i −0.0124237 0.0281997i
\(970\) 1.51734e7 0.517791
\(971\) −5.09861e7 −1.73542 −0.867708 0.497075i \(-0.834407\pi\)
−0.867708 + 0.497075i \(0.834407\pi\)
\(972\) −7.11361e6 1.28958e7i −0.241504 0.437808i
\(973\) 9.15536e6i 0.310023i
\(974\) 1.95149e7i 0.659126i
\(975\) −9.15170e6 + 4.03188e6i −0.308312 + 0.135830i
\(976\) 1.40914e7i 0.473511i
\(977\) −2.83114e7 −0.948909 −0.474455 0.880280i \(-0.657355\pi\)
−0.474455 + 0.880280i \(0.657355\pi\)
\(978\) 132398. + 300521.i 0.00442623 + 0.0100468i
\(979\) 6.61120e7 2.20457
\(980\) −4.29732e6 −0.142933
\(981\) 2.40435e7 + 2.19911e7i 0.797673 + 0.729581i
\(982\) −3.03516e7 −1.00439
\(983\) −1.34774e7 −0.444860 −0.222430 0.974949i \(-0.571399\pi\)
−0.222430 + 0.974949i \(0.571399\pi\)
\(984\) 6.75309e6 2.97515e6i 0.222339 0.0979537i
\(985\) 3.59522e7i 1.18069i
\(986\) −635314. −0.0208112
\(987\) 3.30024e7 1.45396e7i 1.07833 0.475071i
\(988\) 1.11917e7i 0.364756i
\(989\) −2.61477e6 7.34339e6i −0.0850046 0.238730i
\(990\) −1.92619e7 1.76176e7i −0.624613 0.571294i
\(991\) 1.18912e7 0.384630 0.192315 0.981333i \(-0.438400\pi\)
0.192315 + 0.981333i \(0.438400\pi\)
\(992\) 8.48504e6i 0.273763i
\(993\) −1.57598e7 + 6.94313e6i −0.507197 + 0.223451i
\(994\) 8.81762e6i 0.283065i
\(995\) 3.85492e7i 1.23441i
\(996\) −1.43628e7 + 6.32767e6i −0.458765 + 0.202114i
\(997\) −3.41726e7 −1.08878 −0.544390 0.838832i \(-0.683239\pi\)
−0.544390 + 0.838832i \(0.683239\pi\)
\(998\) 2.66812e7i 0.847969i
\(999\) 4.48654e7 + 1.51606e7i 1.42232 + 0.480620i
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 138.6.d.a.137.20 yes 40
3.2 odd 2 inner 138.6.d.a.137.17 40
23.22 odd 2 inner 138.6.d.a.137.19 yes 40
69.68 even 2 inner 138.6.d.a.137.18 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
138.6.d.a.137.17 40 3.2 odd 2 inner
138.6.d.a.137.18 yes 40 69.68 even 2 inner
138.6.d.a.137.19 yes 40 23.22 odd 2 inner
138.6.d.a.137.20 yes 40 1.1 even 1 trivial