Properties

Label 35.5.g.a.22.1
Level $35$
Weight $5$
Character 35.22
Analytic conductor $3.618$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 35.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.61794870793\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 22.1
Character \(\chi\) \(=\) 35.22
Dual form 35.5.g.a.8.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.44757 - 5.44757i) q^{2} +(1.36639 - 1.36639i) q^{3} +43.3520i q^{4} +(7.20796 + 23.9384i) q^{5} -14.8870 q^{6} +(-13.0958 - 13.0958i) q^{7} +(149.002 - 149.002i) q^{8} +77.2660i q^{9} +O(q^{10})\) \(q+(-5.44757 - 5.44757i) q^{2} +(1.36639 - 1.36639i) q^{3} +43.3520i q^{4} +(7.20796 + 23.9384i) q^{5} -14.8870 q^{6} +(-13.0958 - 13.0958i) q^{7} +(149.002 - 149.002i) q^{8} +77.2660i q^{9} +(91.1401 - 169.672i) q^{10} +81.6042 q^{11} +(59.2358 + 59.2358i) q^{12} +(-66.7280 + 66.7280i) q^{13} +142.681i q^{14} +(42.5580 + 22.8603i) q^{15} -929.763 q^{16} +(347.598 + 347.598i) q^{17} +(420.912 - 420.912i) q^{18} +69.2205i q^{19} +(-1037.78 + 312.479i) q^{20} -35.7880 q^{21} +(-444.544 - 444.544i) q^{22} +(40.2630 - 40.2630i) q^{23} -407.189i q^{24} +(-521.091 + 345.093i) q^{25} +727.010 q^{26} +(216.253 + 216.253i) q^{27} +(567.729 - 567.729i) q^{28} +586.403i q^{29} +(-107.305 - 356.371i) q^{30} +538.834 q^{31} +(2680.92 + 2680.92i) q^{32} +(111.503 - 111.503i) q^{33} -3787.13i q^{34} +(219.098 - 407.886i) q^{35} -3349.63 q^{36} +(-1084.74 - 1084.74i) q^{37} +(377.083 - 377.083i) q^{38} +182.353i q^{39} +(4640.86 + 2492.86i) q^{40} +80.0417 q^{41} +(194.957 + 194.957i) q^{42} +(-1323.31 + 1323.31i) q^{43} +3537.70i q^{44} +(-1849.62 + 556.930i) q^{45} -438.671 q^{46} +(-2670.09 - 2670.09i) q^{47} +(-1270.42 + 1270.42i) q^{48} +343.000i q^{49} +(4718.60 + 958.758i) q^{50} +949.909 q^{51} +(-2892.79 - 2892.79i) q^{52} +(1863.94 - 1863.94i) q^{53} -2356.11i q^{54} +(588.199 + 1953.47i) q^{55} -3902.60 q^{56} +(94.5822 + 94.5822i) q^{57} +(3194.47 - 3194.47i) q^{58} +1139.50i q^{59} +(-991.039 + 1844.98i) q^{60} +3393.50 q^{61} +(-2935.33 - 2935.33i) q^{62} +(1011.86 - 1011.86i) q^{63} -14332.8i q^{64} +(-2078.33 - 1116.39i) q^{65} -1214.84 q^{66} +(1840.20 + 1840.20i) q^{67} +(-15069.1 + 15069.1i) q^{68} -110.030i q^{69} +(-3415.54 + 1028.43i) q^{70} +6930.24 q^{71} +(11512.8 + 11512.8i) q^{72} +(-823.082 + 823.082i) q^{73} +11818.3i q^{74} +(-240.481 + 1183.55i) q^{75} -3000.85 q^{76} +(-1068.67 - 1068.67i) q^{77} +(993.380 - 993.380i) q^{78} +86.0479i q^{79} +(-6701.69 - 22257.0i) q^{80} -5667.57 q^{81} +(-436.033 - 436.033i) q^{82} +(7100.46 - 7100.46i) q^{83} -1551.48i q^{84} +(-5815.46 + 10826.4i) q^{85} +14417.6 q^{86} +(801.255 + 801.255i) q^{87} +(12159.2 - 12159.2i) q^{88} -12171.5i q^{89} +(13109.8 + 7042.02i) q^{90} +1747.71 q^{91} +(1745.48 + 1745.48i) q^{92} +(736.258 - 736.258i) q^{93} +29091.0i q^{94} +(-1657.02 + 498.938i) q^{95} +7326.37 q^{96} +(-7968.92 - 7968.92i) q^{97} +(1868.52 - 1868.52i) q^{98} +6305.23i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} + O(q^{10}) \) \( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.44757 5.44757i −1.36189 1.36189i −0.871505 0.490387i \(-0.836855\pi\)
−0.490387 0.871505i \(-0.663145\pi\)
\(3\) 1.36639 1.36639i 0.151821 0.151821i −0.627110 0.778931i \(-0.715762\pi\)
0.778931 + 0.627110i \(0.215762\pi\)
\(4\) 43.3520i 2.70950i
\(5\) 7.20796 + 23.9384i 0.288318 + 0.957535i
\(6\) −14.8870 −0.413528
\(7\) −13.0958 13.0958i −0.267261 0.267261i
\(8\) 149.002 149.002i 2.32815 2.32815i
\(9\) 77.2660i 0.953901i
\(10\) 91.1401 169.672i 0.911401 1.69672i
\(11\) 81.6042 0.674415 0.337207 0.941430i \(-0.390518\pi\)
0.337207 + 0.941430i \(0.390518\pi\)
\(12\) 59.2358 + 59.2358i 0.411359 + 0.411359i
\(13\) −66.7280 + 66.7280i −0.394840 + 0.394840i −0.876408 0.481568i \(-0.840067\pi\)
0.481568 + 0.876408i \(0.340067\pi\)
\(14\) 142.681i 0.727962i
\(15\) 42.5580 + 22.8603i 0.189147 + 0.101601i
\(16\) −929.763 −3.63189
\(17\) 347.598 + 347.598i 1.20276 + 1.20276i 0.973323 + 0.229438i \(0.0736889\pi\)
0.229438 + 0.973323i \(0.426311\pi\)
\(18\) 420.912 420.912i 1.29911 1.29911i
\(19\) 69.2205i 0.191746i 0.995394 + 0.0958732i \(0.0305643\pi\)
−0.995394 + 0.0958732i \(0.969436\pi\)
\(20\) −1037.78 + 312.479i −2.59444 + 0.781198i
\(21\) −35.7880 −0.0811518
\(22\) −444.544 444.544i −0.918480 0.918480i
\(23\) 40.2630 40.2630i 0.0761115 0.0761115i −0.668026 0.744138i \(-0.732861\pi\)
0.744138 + 0.668026i \(0.232861\pi\)
\(24\) 407.189i 0.706926i
\(25\) −521.091 + 345.093i −0.833745 + 0.552149i
\(26\) 727.010 1.07546
\(27\) 216.253 + 216.253i 0.296644 + 0.296644i
\(28\) 567.729 567.729i 0.724144 0.724144i
\(29\) 586.403i 0.697268i 0.937259 + 0.348634i \(0.113354\pi\)
−0.937259 + 0.348634i \(0.886646\pi\)
\(30\) −107.305 356.371i −0.119228 0.395967i
\(31\) 538.834 0.560701 0.280351 0.959898i \(-0.409549\pi\)
0.280351 + 0.959898i \(0.409549\pi\)
\(32\) 2680.92 + 2680.92i 2.61809 + 2.61809i
\(33\) 111.503 111.503i 0.102390 0.102390i
\(34\) 3787.13i 3.27606i
\(35\) 219.098 407.886i 0.178856 0.332968i
\(36\) −3349.63 −2.58459
\(37\) −1084.74 1084.74i −0.792356 0.792356i 0.189521 0.981877i \(-0.439307\pi\)
−0.981877 + 0.189521i \(0.939307\pi\)
\(38\) 377.083 377.083i 0.261138 0.261138i
\(39\) 182.353i 0.119890i
\(40\) 4640.86 + 2492.86i 2.90054 + 1.55804i
\(41\) 80.0417 0.0476155 0.0238078 0.999717i \(-0.492421\pi\)
0.0238078 + 0.999717i \(0.492421\pi\)
\(42\) 194.957 + 194.957i 0.110520 + 0.110520i
\(43\) −1323.31 + 1323.31i −0.715689 + 0.715689i −0.967719 0.252030i \(-0.918902\pi\)
0.252030 + 0.967719i \(0.418902\pi\)
\(44\) 3537.70i 1.82733i
\(45\) −1849.62 + 556.930i −0.913393 + 0.275027i
\(46\) −438.671 −0.207311
\(47\) −2670.09 2670.09i −1.20873 1.20873i −0.971438 0.237294i \(-0.923740\pi\)
−0.237294 0.971438i \(-0.576260\pi\)
\(48\) −1270.42 + 1270.42i −0.551398 + 0.551398i
\(49\) 343.000i 0.142857i
\(50\) 4718.60 + 958.758i 1.88744 + 0.383503i
\(51\) 949.909 0.365209
\(52\) −2892.79 2892.79i −1.06982 1.06982i
\(53\) 1863.94 1863.94i 0.663560 0.663560i −0.292658 0.956217i \(-0.594540\pi\)
0.956217 + 0.292658i \(0.0945396\pi\)
\(54\) 2356.11i 0.807993i
\(55\) 588.199 + 1953.47i 0.194446 + 0.645776i
\(56\) −3902.60 −1.24445
\(57\) 94.5822 + 94.5822i 0.0291112 + 0.0291112i
\(58\) 3194.47 3194.47i 0.949604 0.949604i
\(59\) 1139.50i 0.327350i 0.986514 + 0.163675i \(0.0523348\pi\)
−0.986514 + 0.163675i \(0.947665\pi\)
\(60\) −991.039 + 1844.98i −0.275288 + 0.512493i
\(61\) 3393.50 0.911985 0.455993 0.889984i \(-0.349284\pi\)
0.455993 + 0.889984i \(0.349284\pi\)
\(62\) −2935.33 2935.33i −0.763615 0.763615i
\(63\) 1011.86 1011.86i 0.254941 0.254941i
\(64\) 14332.8i 3.49921i
\(65\) −2078.33 1116.39i −0.491912 0.264233i
\(66\) −1214.84 −0.278889
\(67\) 1840.20 + 1840.20i 0.409935 + 0.409935i 0.881716 0.471781i \(-0.156389\pi\)
−0.471781 + 0.881716i \(0.656389\pi\)
\(68\) −15069.1 + 15069.1i −3.25888 + 3.25888i
\(69\) 110.030i 0.0231107i
\(70\) −3415.54 + 1028.43i −0.697049 + 0.209885i
\(71\) 6930.24 1.37477 0.687387 0.726291i \(-0.258757\pi\)
0.687387 + 0.726291i \(0.258757\pi\)
\(72\) 11512.8 + 11512.8i 2.22083 + 2.22083i
\(73\) −823.082 + 823.082i −0.154453 + 0.154453i −0.780104 0.625650i \(-0.784834\pi\)
0.625650 + 0.780104i \(0.284834\pi\)
\(74\) 11818.3i 2.15821i
\(75\) −240.481 + 1183.55i −0.0427522 + 0.210408i
\(76\) −3000.85 −0.519537
\(77\) −1068.67 1068.67i −0.180245 0.180245i
\(78\) 993.380 993.380i 0.163277 0.163277i
\(79\) 86.0479i 0.0137875i 0.999976 + 0.00689376i \(0.00219437\pi\)
−0.999976 + 0.00689376i \(0.997806\pi\)
\(80\) −6701.69 22257.0i −1.04714 3.47766i
\(81\) −5667.57 −0.863827
\(82\) −436.033 436.033i −0.0648472 0.0648472i
\(83\) 7100.46 7100.46i 1.03070 1.03070i 0.0311822 0.999514i \(-0.490073\pi\)
0.999514 0.0311822i \(-0.00992720\pi\)
\(84\) 1551.48i 0.219881i
\(85\) −5815.46 + 10826.4i −0.804908 + 1.49846i
\(86\) 14417.6 1.94938
\(87\) 801.255 + 801.255i 0.105860 + 0.105860i
\(88\) 12159.2 12159.2i 1.57014 1.57014i
\(89\) 12171.5i 1.53662i −0.640080 0.768309i \(-0.721099\pi\)
0.640080 0.768309i \(-0.278901\pi\)
\(90\) 13109.8 + 7042.02i 1.61850 + 0.869386i
\(91\) 1747.71 0.211051
\(92\) 1745.48 + 1745.48i 0.206224 + 0.206224i
\(93\) 736.258 736.258i 0.0851263 0.0851263i
\(94\) 29091.0i 3.29232i
\(95\) −1657.02 + 498.938i −0.183604 + 0.0552840i
\(96\) 7326.37 0.794962
\(97\) −7968.92 7968.92i −0.846947 0.846947i 0.142804 0.989751i \(-0.454388\pi\)
−0.989751 + 0.142804i \(0.954388\pi\)
\(98\) 1868.52 1868.52i 0.194556 0.194556i
\(99\) 6305.23i 0.643325i
\(100\) −14960.5 22590.3i −1.49605 2.25903i
\(101\) 7550.77 0.740199 0.370100 0.928992i \(-0.379324\pi\)
0.370100 + 0.928992i \(0.379324\pi\)
\(102\) −5174.70 5174.70i −0.497376 0.497376i
\(103\) 6641.76 6641.76i 0.626049 0.626049i −0.321022 0.947072i \(-0.604026\pi\)
0.947072 + 0.321022i \(0.104026\pi\)
\(104\) 19885.2i 1.83850i
\(105\) −257.958 856.705i −0.0233976 0.0777057i
\(106\) −20307.9 −1.80739
\(107\) −863.078 863.078i −0.0753845 0.0753845i 0.668409 0.743794i \(-0.266976\pi\)
−0.743794 + 0.668409i \(0.766976\pi\)
\(108\) −9375.00 + 9375.00i −0.803755 + 0.803755i
\(109\) 930.380i 0.0783083i −0.999233 0.0391541i \(-0.987534\pi\)
0.999233 0.0391541i \(-0.0124663\pi\)
\(110\) 7437.41 13845.9i 0.614662 1.14429i
\(111\) −2964.34 −0.240593
\(112\) 12176.0 + 12176.0i 0.970663 + 0.970663i
\(113\) −10907.2 + 10907.2i −0.854196 + 0.854196i −0.990647 0.136451i \(-0.956430\pi\)
0.136451 + 0.990647i \(0.456430\pi\)
\(114\) 1030.49i 0.0792925i
\(115\) 1254.04 + 673.616i 0.0948237 + 0.0509351i
\(116\) −25421.7 −1.88925
\(117\) −5155.80 5155.80i −0.376638 0.376638i
\(118\) 6207.53 6207.53i 0.445815 0.445815i
\(119\) 9104.15i 0.642903i
\(120\) 9747.45 2935.00i 0.676906 0.203820i
\(121\) −7981.76 −0.545165
\(122\) −18486.3 18486.3i −1.24203 1.24203i
\(123\) 109.368 109.368i 0.00722905 0.00722905i
\(124\) 23359.5i 1.51922i
\(125\) −12017.0 9986.64i −0.769086 0.639145i
\(126\) −11024.3 −0.694403
\(127\) 9555.32 + 9555.32i 0.592431 + 0.592431i 0.938287 0.345856i \(-0.112412\pi\)
−0.345856 + 0.938287i \(0.612412\pi\)
\(128\) −35184.0 + 35184.0i −2.14746 + 2.14746i
\(129\) 3616.31i 0.217314i
\(130\) 5240.26 + 17403.4i 0.310074 + 1.02979i
\(131\) 17236.3 1.00439 0.502194 0.864755i \(-0.332526\pi\)
0.502194 + 0.864755i \(0.332526\pi\)
\(132\) 4833.89 + 4833.89i 0.277427 + 0.277427i
\(133\) 906.497 906.497i 0.0512464 0.0512464i
\(134\) 20049.2i 1.11657i
\(135\) −3618.00 + 6735.49i −0.198519 + 0.369574i
\(136\) 103585. 5.60043
\(137\) 9441.41 + 9441.41i 0.503032 + 0.503032i 0.912379 0.409347i \(-0.134243\pi\)
−0.409347 + 0.912379i \(0.634243\pi\)
\(138\) −599.396 + 599.396i −0.0314742 + 0.0314742i
\(139\) 26127.4i 1.35228i −0.736772 0.676141i \(-0.763651\pi\)
0.736772 0.676141i \(-0.236349\pi\)
\(140\) 17682.7 + 9498.34i 0.902177 + 0.484609i
\(141\) −7296.77 −0.367022
\(142\) −37753.0 37753.0i −1.87229 1.87229i
\(143\) −5445.28 + 5445.28i −0.266286 + 0.266286i
\(144\) 71839.0i 3.46446i
\(145\) −14037.5 + 4226.76i −0.667658 + 0.201035i
\(146\) 8967.59 0.420697
\(147\) 468.672 + 468.672i 0.0216887 + 0.0216887i
\(148\) 47025.4 47025.4i 2.14689 2.14689i
\(149\) 3703.79i 0.166830i 0.996515 + 0.0834149i \(0.0265827\pi\)
−0.996515 + 0.0834149i \(0.973417\pi\)
\(150\) 7757.48 5137.41i 0.344777 0.228329i
\(151\) 22789.3 0.999488 0.499744 0.866173i \(-0.333427\pi\)
0.499744 + 0.866173i \(0.333427\pi\)
\(152\) 10314.0 + 10314.0i 0.446415 + 0.446415i
\(153\) −26857.5 + 26857.5i −1.14731 + 1.14731i
\(154\) 11643.3i 0.490948i
\(155\) 3883.89 + 12898.8i 0.161660 + 0.536891i
\(156\) −7905.36 −0.324842
\(157\) 5151.18 + 5151.18i 0.208981 + 0.208981i 0.803834 0.594853i \(-0.202790\pi\)
−0.594853 + 0.803834i \(0.702790\pi\)
\(158\) 468.752 468.752i 0.0187771 0.0187771i
\(159\) 5093.74i 0.201485i
\(160\) −44852.9 + 83500.8i −1.75207 + 3.26175i
\(161\) −1054.55 −0.0406833
\(162\) 30874.5 + 30874.5i 1.17644 + 1.17644i
\(163\) −20400.5 + 20400.5i −0.767831 + 0.767831i −0.977724 0.209893i \(-0.932688\pi\)
0.209893 + 0.977724i \(0.432688\pi\)
\(164\) 3469.97i 0.129014i
\(165\) 3472.91 + 1865.49i 0.127563 + 0.0685214i
\(166\) −77360.5 −2.80739
\(167\) 31137.0 + 31137.0i 1.11646 + 1.11646i 0.992257 + 0.124204i \(0.0396376\pi\)
0.124204 + 0.992257i \(0.460362\pi\)
\(168\) −5332.47 + 5332.47i −0.188934 + 0.188934i
\(169\) 19655.8i 0.688203i
\(170\) 90657.7 27297.4i 3.13694 0.944548i
\(171\) −5348.39 −0.182907
\(172\) −57368.1 57368.1i −1.93916 1.93916i
\(173\) 17298.0 17298.0i 0.577969 0.577969i −0.356374 0.934343i \(-0.615987\pi\)
0.934343 + 0.356374i \(0.115987\pi\)
\(174\) 8729.78i 0.288340i
\(175\) 11343.4 + 2304.83i 0.370396 + 0.0752597i
\(176\) −75872.6 −2.44940
\(177\) 1557.01 + 1557.01i 0.0496986 + 0.0496986i
\(178\) −66305.3 + 66305.3i −2.09271 + 2.09271i
\(179\) 1332.58i 0.0415897i −0.999784 0.0207949i \(-0.993380\pi\)
0.999784 0.0207949i \(-0.00661969\pi\)
\(180\) −24144.0 80184.7i −0.745185 2.47484i
\(181\) 12567.7 0.383618 0.191809 0.981432i \(-0.438565\pi\)
0.191809 + 0.981432i \(0.438565\pi\)
\(182\) −9520.78 9520.78i −0.287428 0.287428i
\(183\) 4636.84 4636.84i 0.138459 0.138459i
\(184\) 11998.5i 0.354399i
\(185\) 18148.1 33785.5i 0.530258 0.987159i
\(186\) −8021.63 −0.231866
\(187\) 28365.5 + 28365.5i 0.811160 + 0.811160i
\(188\) 115754. 115754.i 3.27506 3.27506i
\(189\) 5664.02i 0.158563i
\(190\) 11744.8 + 6308.76i 0.325339 + 0.174758i
\(191\) −12088.8 −0.331373 −0.165686 0.986179i \(-0.552984\pi\)
−0.165686 + 0.986179i \(0.552984\pi\)
\(192\) −19584.2 19584.2i −0.531254 0.531254i
\(193\) −10539.9 + 10539.9i −0.282957 + 0.282957i −0.834287 0.551330i \(-0.814121\pi\)
0.551330 + 0.834287i \(0.314121\pi\)
\(194\) 86822.5i 2.30690i
\(195\) −4365.23 + 1314.39i −0.114799 + 0.0345665i
\(196\) −14869.7 −0.387071
\(197\) −6811.78 6811.78i −0.175521 0.175521i 0.613879 0.789400i \(-0.289608\pi\)
−0.789400 + 0.613879i \(0.789608\pi\)
\(198\) 34348.1 34348.1i 0.876139 0.876139i
\(199\) 18221.4i 0.460125i −0.973176 0.230063i \(-0.926107\pi\)
0.973176 0.230063i \(-0.0738931\pi\)
\(200\) −26223.9 + 129063.i −0.655598 + 3.22658i
\(201\) 5028.86 0.124474
\(202\) −41133.3 41133.3i −1.00807 1.00807i
\(203\) 7679.41 7679.41i 0.186353 0.186353i
\(204\) 41180.5i 0.989535i
\(205\) 576.937 + 1916.07i 0.0137284 + 0.0455935i
\(206\) −72362.9 −1.70522
\(207\) 3110.96 + 3110.96i 0.0726028 + 0.0726028i
\(208\) 62041.2 62041.2i 1.43401 1.43401i
\(209\) 5648.68i 0.129317i
\(210\) −3261.72 + 6072.20i −0.0739618 + 0.137692i
\(211\) −31576.9 −0.709259 −0.354630 0.935007i \(-0.615393\pi\)
−0.354630 + 0.935007i \(0.615393\pi\)
\(212\) 80805.5 + 80805.5i 1.79791 + 1.79791i
\(213\) 9469.41 9469.41i 0.208720 0.208720i
\(214\) 9403.35i 0.205331i
\(215\) −41216.2 22139.5i −0.891643 0.478951i
\(216\) 64444.2 1.38126
\(217\) −7056.46 7056.46i −0.149854 0.149854i
\(218\) −5068.31 + 5068.31i −0.106647 + 0.106647i
\(219\) 2249.30i 0.0468986i
\(220\) −84686.9 + 25499.6i −1.74973 + 0.526852i
\(221\) −46389.0 −0.949797
\(222\) 16148.5 + 16148.5i 0.327661 + 0.327661i
\(223\) −21493.1 + 21493.1i −0.432204 + 0.432204i −0.889378 0.457174i \(-0.848862\pi\)
0.457174 + 0.889378i \(0.348862\pi\)
\(224\) 70217.6i 1.39943i
\(225\) −26664.0 40262.6i −0.526696 0.795310i
\(226\) 118836. 2.32665
\(227\) −1.06812 1.06812i −2.07285e−5 2.07285e-5i 0.707096 0.707117i \(-0.250005\pi\)
−0.707117 + 0.707096i \(0.750005\pi\)
\(228\) −4100.33 + 4100.33i −0.0788767 + 0.0788767i
\(229\) 61585.7i 1.17438i −0.809449 0.587191i \(-0.800234\pi\)
0.809449 0.587191i \(-0.199766\pi\)
\(230\) −3161.92 10501.1i −0.0597716 0.198508i
\(231\) −2920.45 −0.0547300
\(232\) 87375.1 + 87375.1i 1.62335 + 1.62335i
\(233\) −18979.4 + 18979.4i −0.349599 + 0.349599i −0.859960 0.510361i \(-0.829512\pi\)
0.510361 + 0.859960i \(0.329512\pi\)
\(234\) 56173.1i 1.02588i
\(235\) 44671.7 83163.4i 0.808903 1.50590i
\(236\) −49399.8 −0.886954
\(237\) 117.575 + 117.575i 0.00209324 + 0.00209324i
\(238\) −49595.5 + 49595.5i −0.875565 + 0.875565i
\(239\) 105134.i 1.84055i −0.391269 0.920276i \(-0.627964\pi\)
0.391269 0.920276i \(-0.372036\pi\)
\(240\) −39568.9 21254.6i −0.686960 0.369004i
\(241\) 63055.2 1.08564 0.542821 0.839848i \(-0.317356\pi\)
0.542821 + 0.839848i \(0.317356\pi\)
\(242\) 43481.2 + 43481.2i 0.742455 + 0.742455i
\(243\) −25260.6 + 25260.6i −0.427791 + 0.427791i
\(244\) 147115.i 2.47102i
\(245\) −8210.86 + 2472.33i −0.136791 + 0.0411883i
\(246\) −1191.58 −0.0196904
\(247\) −4618.94 4618.94i −0.0757092 0.0757092i
\(248\) 80287.2 80287.2i 1.30540 1.30540i
\(249\) 19404.0i 0.312963i
\(250\) 11060.3 + 119866.i 0.176965 + 1.91786i
\(251\) −82573.8 −1.31067 −0.655337 0.755337i \(-0.727473\pi\)
−0.655337 + 0.755337i \(0.727473\pi\)
\(252\) 43866.1 + 43866.1i 0.690762 + 0.690762i
\(253\) 3285.63 3285.63i 0.0513307 0.0513307i
\(254\) 104107.i 1.61365i
\(255\) 6846.90 + 22739.3i 0.105297 + 0.349701i
\(256\) 154010. 2.35001
\(257\) 52953.5 + 52953.5i 0.801730 + 0.801730i 0.983366 0.181636i \(-0.0581391\pi\)
−0.181636 + 0.983366i \(0.558139\pi\)
\(258\) 19700.1 19700.1i 0.295958 0.295958i
\(259\) 28411.0i 0.423532i
\(260\) 48397.6 90099.8i 0.715940 1.33284i
\(261\) −45309.0 −0.665125
\(262\) −93895.9 93895.9i −1.36787 1.36787i
\(263\) 24595.0 24595.0i 0.355578 0.355578i −0.506602 0.862180i \(-0.669099\pi\)
0.862180 + 0.506602i \(0.169099\pi\)
\(264\) 33228.4i 0.476761i
\(265\) 58054.9 + 31184.5i 0.826698 + 0.444065i
\(266\) −9876.41 −0.139584
\(267\) −16631.1 16631.1i −0.233291 0.233291i
\(268\) −79776.2 + 79776.2i −1.11072 + 1.11072i
\(269\) 49771.6i 0.687823i −0.939002 0.343912i \(-0.888248\pi\)
0.939002 0.343912i \(-0.111752\pi\)
\(270\) 56401.4 16982.7i 0.773681 0.232959i
\(271\) 39084.7 0.532192 0.266096 0.963947i \(-0.414266\pi\)
0.266096 + 0.963947i \(0.414266\pi\)
\(272\) −323184. 323184.i −4.36829 4.36829i
\(273\) 2388.06 2388.06i 0.0320420 0.0320420i
\(274\) 102865.i 1.37015i
\(275\) −42523.2 + 28161.1i −0.562290 + 0.372378i
\(276\) 4770.02 0.0626184
\(277\) −29445.9 29445.9i −0.383765 0.383765i 0.488692 0.872456i \(-0.337474\pi\)
−0.872456 + 0.488692i \(0.837474\pi\)
\(278\) −142331. + 142331.i −1.84166 + 1.84166i
\(279\) 41633.5i 0.534853i
\(280\) −28129.7 93421.8i −0.358798 1.19160i
\(281\) 151923. 1.92402 0.962010 0.273013i \(-0.0880203\pi\)
0.962010 + 0.273013i \(0.0880203\pi\)
\(282\) 39749.6 + 39749.6i 0.499844 + 0.499844i
\(283\) 76183.3 76183.3i 0.951234 0.951234i −0.0476314 0.998865i \(-0.515167\pi\)
0.998865 + 0.0476314i \(0.0151673\pi\)
\(284\) 300440.i 3.72495i
\(285\) −1582.40 + 2945.89i −0.0194817 + 0.0362682i
\(286\) 59327.1 0.725305
\(287\) −1048.21 1048.21i −0.0127258 0.0127258i
\(288\) −207144. + 207144.i −2.49739 + 2.49739i
\(289\) 158128.i 1.89327i
\(290\) 99495.9 + 53444.8i 1.18307 + 0.635491i
\(291\) −21777.3 −0.257169
\(292\) −35682.2 35682.2i −0.418491 0.418491i
\(293\) −35656.3 + 35656.3i −0.415337 + 0.415337i −0.883593 0.468256i \(-0.844883\pi\)
0.468256 + 0.883593i \(0.344883\pi\)
\(294\) 5106.24i 0.0590754i
\(295\) −27277.9 + 8213.50i −0.313449 + 0.0943809i
\(296\) −323255. −3.68945
\(297\) 17647.2 + 17647.2i 0.200061 + 0.200061i
\(298\) 20176.6 20176.6i 0.227204 0.227204i
\(299\) 5373.33i 0.0601037i
\(300\) −51309.1 10425.3i −0.570101 0.115837i
\(301\) 34659.6 0.382552
\(302\) −124146. 124146.i −1.36120 1.36120i
\(303\) 10317.3 10317.3i 0.112378 0.112378i
\(304\) 64358.6i 0.696402i
\(305\) 24460.2 + 81234.8i 0.262942 + 0.873258i
\(306\) 292616. 3.12504
\(307\) 61183.2 + 61183.2i 0.649165 + 0.649165i 0.952791 0.303626i \(-0.0981974\pi\)
−0.303626 + 0.952791i \(0.598197\pi\)
\(308\) 46329.1 46329.1i 0.488374 0.488374i
\(309\) 18150.5i 0.190095i
\(310\) 49109.4 91424.9i 0.511023 0.951351i
\(311\) −143150. −1.48003 −0.740015 0.672591i \(-0.765181\pi\)
−0.740015 + 0.672591i \(0.765181\pi\)
\(312\) 27170.9 + 27170.9i 0.279123 + 0.279123i
\(313\) −34807.0 + 34807.0i −0.355285 + 0.355285i −0.862072 0.506786i \(-0.830833\pi\)
0.506786 + 0.862072i \(0.330833\pi\)
\(314\) 56122.8i 0.569220i
\(315\) 31515.7 + 16928.8i 0.317619 + 0.170610i
\(316\) −3730.35 −0.0373573
\(317\) −19515.0 19515.0i −0.194200 0.194200i 0.603308 0.797508i \(-0.293849\pi\)
−0.797508 + 0.603308i \(0.793849\pi\)
\(318\) −27748.5 + 27748.5i −0.274401 + 0.274401i
\(319\) 47852.9i 0.470248i
\(320\) 343103. 103310.i 3.35062 1.00889i
\(321\) −2358.60 −0.0228899
\(322\) 5744.74 + 5744.74i 0.0554063 + 0.0554063i
\(323\) −24060.9 + 24060.9i −0.230625 + 0.230625i
\(324\) 245700.i 2.34054i
\(325\) 11743.9 57798.7i 0.111185 0.547207i
\(326\) 222266. 2.09141
\(327\) −1271.26 1271.26i −0.0118889 0.0118889i
\(328\) 11926.4 11926.4i 0.110856 0.110856i
\(329\) 69933.9i 0.646094i
\(330\) −8756.53 29081.3i −0.0804089 0.267046i
\(331\) −42277.0 −0.385876 −0.192938 0.981211i \(-0.561802\pi\)
−0.192938 + 0.981211i \(0.561802\pi\)
\(332\) 307819. + 307819.i 2.79267 + 2.79267i
\(333\) 83813.1 83813.1i 0.755829 0.755829i
\(334\) 339241.i 3.04100i
\(335\) −30787.3 + 57315.4i −0.274335 + 0.510718i
\(336\) 33274.3 0.294734
\(337\) −7458.03 7458.03i −0.0656696 0.0656696i 0.673509 0.739179i \(-0.264786\pi\)
−0.739179 + 0.673509i \(0.764786\pi\)
\(338\) 107076. 107076.i 0.937258 0.937258i
\(339\) 29807.1i 0.259370i
\(340\) −469346. 252112.i −4.06009 2.18090i
\(341\) 43971.1 0.378145
\(342\) 29135.7 + 29135.7i 0.249100 + 0.249100i
\(343\) 4491.86 4491.86i 0.0381802 0.0381802i
\(344\) 394351.i 3.33247i
\(345\) 2633.94 793.091i 0.0221293 0.00666323i
\(346\) −188464. −1.57426
\(347\) −97115.7 97115.7i −0.806548 0.806548i 0.177561 0.984110i \(-0.443179\pi\)
−0.984110 + 0.177561i \(0.943179\pi\)
\(348\) −34736.0 + 34736.0i −0.286828 + 0.286828i
\(349\) 92436.0i 0.758910i −0.925210 0.379455i \(-0.876111\pi\)
0.925210 0.379455i \(-0.123889\pi\)
\(350\) −49238.1 74349.5i −0.401944 0.606935i
\(351\) −28860.3 −0.234253
\(352\) 218774. + 218774.i 1.76568 + 1.76568i
\(353\) −7000.38 + 7000.38i −0.0561787 + 0.0561787i −0.734638 0.678459i \(-0.762648\pi\)
0.678459 + 0.734638i \(0.262648\pi\)
\(354\) 16963.8i 0.135368i
\(355\) 49952.9 + 165899.i 0.396373 + 1.31639i
\(356\) 527661. 4.16346
\(357\) −12439.8 12439.8i −0.0976063 0.0976063i
\(358\) −7259.30 + 7259.30i −0.0566407 + 0.0566407i
\(359\) 202042.i 1.56766i 0.620973 + 0.783832i \(0.286738\pi\)
−0.620973 + 0.783832i \(0.713262\pi\)
\(360\) −192613. + 358580.i −1.48621 + 2.76682i
\(361\) 125530. 0.963233
\(362\) −68463.5 68463.5i −0.522446 0.522446i
\(363\) −10906.2 + 10906.2i −0.0827675 + 0.0827675i
\(364\) 75766.8i 0.571842i
\(365\) −25636.0 13770.5i −0.192426 0.103363i
\(366\) −50519.0 −0.377132
\(367\) −126698. 126698.i −0.940671 0.940671i 0.0576654 0.998336i \(-0.481634\pi\)
−0.998336 + 0.0576654i \(0.981634\pi\)
\(368\) −37435.0 + 37435.0i −0.276428 + 0.276428i
\(369\) 6184.50i 0.0454205i
\(370\) −282912. + 85186.1i −2.06656 + 0.622250i
\(371\) −48819.6 −0.354688
\(372\) 31918.2 + 31918.2i 0.230650 + 0.230650i
\(373\) 110870. 110870.i 0.796889 0.796889i −0.185714 0.982604i \(-0.559460\pi\)
0.982604 + 0.185714i \(0.0594599\pi\)
\(374\) 309046.i 2.20943i
\(375\) −30065.5 + 2774.22i −0.213799 + 0.0197278i
\(376\) −795696. −5.62823
\(377\) −39129.4 39129.4i −0.275309 0.275309i
\(378\) −30855.1 + 30855.1i −0.215945 + 0.215945i
\(379\) 143098.i 0.996219i −0.867114 0.498110i \(-0.834028\pi\)
0.867114 0.498110i \(-0.165972\pi\)
\(380\) −21630.0 71835.3i −0.149792 0.497475i
\(381\) 26112.6 0.179887
\(382\) 65854.6 + 65854.6i 0.451294 + 0.451294i
\(383\) −48897.7 + 48897.7i −0.333343 + 0.333343i −0.853854 0.520512i \(-0.825741\pi\)
0.520512 + 0.853854i \(0.325741\pi\)
\(384\) 96150.2i 0.652060i
\(385\) 17879.3 33285.2i 0.120623 0.224559i
\(386\) 114833. 0.770715
\(387\) −102247. 102247.i −0.682696 0.682696i
\(388\) 345469. 345469.i 2.29480 2.29480i
\(389\) 116811.i 0.771943i 0.922511 + 0.385971i \(0.126134\pi\)
−0.922511 + 0.385971i \(0.873866\pi\)
\(390\) 30940.1 + 16619.7i 0.203420 + 0.109268i
\(391\) 27990.7 0.183088
\(392\) 51107.6 + 51107.6i 0.332593 + 0.332593i
\(393\) 23551.5 23551.5i 0.152487 0.152487i
\(394\) 74215.3i 0.478080i
\(395\) −2059.85 + 620.229i −0.0132020 + 0.00397519i
\(396\) −273344. −1.74309
\(397\) −3607.04 3607.04i −0.0228860 0.0228860i 0.695571 0.718457i \(-0.255151\pi\)
−0.718457 + 0.695571i \(0.755151\pi\)
\(398\) −99262.4 + 99262.4i −0.626641 + 0.626641i
\(399\) 2477.26i 0.0155606i
\(400\) 484491. 320855.i 3.02807 2.00534i
\(401\) −19377.6 −0.120506 −0.0602532 0.998183i \(-0.519191\pi\)
−0.0602532 + 0.998183i \(0.519191\pi\)
\(402\) −27395.0 27395.0i −0.169520 0.169520i
\(403\) −35955.3 + 35955.3i −0.221387 + 0.221387i
\(404\) 327341.i 2.00557i
\(405\) −40851.6 135672.i −0.249057 0.827144i
\(406\) −83668.2 −0.507585
\(407\) −88519.0 88519.0i −0.534377 0.534377i
\(408\) 141538. 141538.i 0.850263 0.850263i
\(409\) 287642.i 1.71952i 0.510701 + 0.859758i \(0.329386\pi\)
−0.510701 + 0.859758i \(0.670614\pi\)
\(410\) 7295.01 13580.8i 0.0433968 0.0807901i
\(411\) 25801.3 0.152742
\(412\) 287933. + 287933.i 1.69628 + 1.69628i
\(413\) 14922.7 14922.7i 0.0874879 0.0874879i
\(414\) 33894.3i 0.197754i
\(415\) 221153. + 118794.i 1.28410 + 0.689759i
\(416\) −357785. −2.06745
\(417\) −35700.3 35700.3i −0.205305 0.205305i
\(418\) 30771.6 30771.6i 0.176115 0.176115i
\(419\) 10754.6i 0.0612585i 0.999531 + 0.0306293i \(0.00975113\pi\)
−0.999531 + 0.0306293i \(0.990249\pi\)
\(420\) 37139.9 11183.0i 0.210544 0.0633957i
\(421\) 131257. 0.740556 0.370278 0.928921i \(-0.379262\pi\)
0.370278 + 0.928921i \(0.379262\pi\)
\(422\) 172017. + 172017.i 0.965934 + 0.965934i
\(423\) 206307. 206307.i 1.15301 1.15301i
\(424\) 555461.i 3.08974i
\(425\) −301084. 61176.4i −1.66690 0.338693i
\(426\) −103171. −0.568508
\(427\) −44440.6 44440.6i −0.243738 0.243738i
\(428\) 37416.1 37416.1i 0.204254 0.204254i
\(429\) 14880.8i 0.0808557i
\(430\) 103922. + 345135.i 0.562042 + 1.86660i
\(431\) −233112. −1.25490 −0.627452 0.778655i \(-0.715902\pi\)
−0.627452 + 0.778655i \(0.715902\pi\)
\(432\) −201064. 201064.i −1.07738 1.07738i
\(433\) −71663.4 + 71663.4i −0.382227 + 0.382227i −0.871904 0.489677i \(-0.837115\pi\)
0.489677 + 0.871904i \(0.337115\pi\)
\(434\) 76881.1i 0.408169i
\(435\) −13405.3 + 24956.1i −0.0708433 + 0.131886i
\(436\) 40333.8 0.212176
\(437\) 2787.02 + 2787.02i 0.0145941 + 0.0145941i
\(438\) 12253.2 12253.2i 0.0638708 0.0638708i
\(439\) 299601.i 1.55459i −0.629139 0.777293i \(-0.716592\pi\)
0.629139 0.777293i \(-0.283408\pi\)
\(440\) 378714. + 203428.i 1.95616 + 1.05076i
\(441\) −26502.2 −0.136272
\(442\) 252707. + 252707.i 1.29352 + 1.29352i
\(443\) 129039. 129039.i 0.657528 0.657528i −0.297267 0.954795i \(-0.596075\pi\)
0.954795 + 0.297267i \(0.0960750\pi\)
\(444\) 128510.i 0.651886i
\(445\) 291367. 87732.0i 1.47136 0.443035i
\(446\) 234170. 1.17723
\(447\) 5060.82 + 5060.82i 0.0253283 + 0.0253283i
\(448\) −187699. + 187699.i −0.935203 + 0.935203i
\(449\) 241835.i 1.19957i 0.800161 + 0.599786i \(0.204748\pi\)
−0.800161 + 0.599786i \(0.795252\pi\)
\(450\) −74079.3 + 364587.i −0.365824 + 1.80043i
\(451\) 6531.74 0.0321126
\(452\) −472850. 472850.i −2.31444 2.31444i
\(453\) 31139.1 31139.1i 0.151744 0.151744i
\(454\) 11.6373i 5.64600e-5i
\(455\) 12597.4 + 41837.4i 0.0608498 + 0.202088i
\(456\) 28185.8 0.135551
\(457\) −146983. 146983.i −0.703778 0.703778i 0.261441 0.965219i \(-0.415802\pi\)
−0.965219 + 0.261441i \(0.915802\pi\)
\(458\) −335492. + 335492.i −1.59938 + 1.59938i
\(459\) 150338.i 0.713583i
\(460\) −29202.6 + 54365.3i −0.138009 + 0.256925i
\(461\) 248662. 1.17006 0.585030 0.811012i \(-0.301083\pi\)
0.585030 + 0.811012i \(0.301083\pi\)
\(462\) 15909.3 + 15909.3i 0.0745363 + 0.0745363i
\(463\) −155970. + 155970.i −0.727575 + 0.727575i −0.970136 0.242561i \(-0.922013\pi\)
0.242561 + 0.970136i \(0.422013\pi\)
\(464\) 545216.i 2.53240i
\(465\) 22931.7 + 12317.9i 0.106055 + 0.0569679i
\(466\) 206783. 0.952233
\(467\) 210168. + 210168.i 0.963678 + 0.963678i 0.999363 0.0356846i \(-0.0113612\pi\)
−0.0356846 + 0.999363i \(0.511361\pi\)
\(468\) 223514. 223514.i 1.02050 1.02050i
\(469\) 48197.7i 0.219119i
\(470\) −696390. + 209686.i −3.15251 + 0.949237i
\(471\) 14077.0 0.0634555
\(472\) 169788. + 169788.i 0.762120 + 0.762120i
\(473\) −107988. + 107988.i −0.482671 + 0.482671i
\(474\) 1281.00i 0.00570153i
\(475\) −23887.5 36070.1i −0.105873 0.159868i
\(476\) 394683. 1.74195
\(477\) 144019. + 144019.i 0.632970 + 0.632970i
\(478\) −572726. + 572726.i −2.50663 + 2.50663i
\(479\) 208148.i 0.907196i 0.891206 + 0.453598i \(0.149860\pi\)
−0.891206 + 0.453598i \(0.850140\pi\)
\(480\) 52808.1 + 175381.i 0.229202 + 0.761203i
\(481\) 144764. 0.625708
\(482\) −343497. 343497.i −1.47853 1.47853i
\(483\) −1440.93 + 1440.93i −0.00617659 + 0.00617659i
\(484\) 346025.i 1.47712i
\(485\) 133323. 248203.i 0.566791 1.05517i
\(486\) 275218. 1.16521
\(487\) 39534.4 + 39534.4i 0.166693 + 0.166693i 0.785524 0.618831i \(-0.212393\pi\)
−0.618831 + 0.785524i \(0.712393\pi\)
\(488\) 505637. 505637.i 2.12324 2.12324i
\(489\) 55750.1i 0.233146i
\(490\) 58197.4 + 31261.0i 0.242388 + 0.130200i
\(491\) −46929.8 −0.194664 −0.0973319 0.995252i \(-0.531031\pi\)
−0.0973319 + 0.995252i \(0.531031\pi\)
\(492\) 4741.33 + 4741.33i 0.0195871 + 0.0195871i
\(493\) −203832. + 203832.i −0.838647 + 0.838647i
\(494\) 50324.0i 0.206215i
\(495\) −150937. + 45447.8i −0.616006 + 0.185482i
\(496\) −500988. −2.03640
\(497\) −90757.0 90757.0i −0.367424 0.367424i
\(498\) −105705. + 105705.i −0.426222 + 0.426222i
\(499\) 474425.i 1.90532i −0.304045 0.952658i \(-0.598337\pi\)
0.304045 0.952658i \(-0.401663\pi\)
\(500\) 432941. 520960.i 1.73176 2.08384i
\(501\) 85090.5 0.339005
\(502\) 449826. + 449826.i 1.78500 + 1.78500i
\(503\) 309798. 309798.i 1.22445 1.22445i 0.258422 0.966032i \(-0.416798\pi\)
0.966032 0.258422i \(-0.0832024\pi\)
\(504\) 301538.i 1.18708i
\(505\) 54425.6 + 180753.i 0.213413 + 0.708766i
\(506\) −35797.4 −0.139814
\(507\) 26857.4 + 26857.4i 0.104484 + 0.104484i
\(508\) −414242. + 414242.i −1.60519 + 1.60519i
\(509\) 436300.i 1.68403i −0.539455 0.842015i \(-0.681370\pi\)
0.539455 0.842015i \(-0.318630\pi\)
\(510\) 86574.8 161173.i 0.332852 0.619657i
\(511\) 21557.8 0.0825588
\(512\) −276038. 276038.i −1.05300 1.05300i
\(513\) −14969.1 + 14969.1i −0.0568803 + 0.0568803i
\(514\) 576935.i 2.18374i
\(515\) 206866. + 111119.i 0.779965 + 0.418963i
\(516\) −156774. −0.588811
\(517\) −217890. 217890.i −0.815186 0.815186i
\(518\) 154771. 154771.i 0.576805 0.576805i
\(519\) 47271.7i 0.175496i
\(520\) −476019. + 143331.i −1.76042 + 0.530072i
\(521\) −468198. −1.72486 −0.862431 0.506174i \(-0.831059\pi\)
−0.862431 + 0.506174i \(0.831059\pi\)
\(522\) 246824. + 246824.i 0.905828 + 0.905828i
\(523\) 55782.4 55782.4i 0.203936 0.203936i −0.597748 0.801684i \(-0.703938\pi\)
0.801684 + 0.597748i \(0.203938\pi\)
\(524\) 747228.i 2.72139i
\(525\) 18648.8 12350.2i 0.0676600 0.0448079i
\(526\) −267966. −0.968518
\(527\) 187298. + 187298.i 0.674390 + 0.674390i
\(528\) −103672. + 103672.i −0.371871 + 0.371871i
\(529\) 276599.i 0.988414i
\(530\) −146378. 486137.i −0.521104 1.73064i
\(531\) −88044.9 −0.312259
\(532\) 39298.5 + 39298.5i 0.138852 + 0.138852i
\(533\) −5341.02 + 5341.02i −0.0188005 + 0.0188005i
\(534\) 181198.i 0.635434i
\(535\) 14439.6 26881.7i 0.0504486 0.0939180i
\(536\) 548385. 1.90878
\(537\) −1820.82 1820.82i −0.00631420 0.00631420i
\(538\) −271134. + 271134.i −0.936741 + 0.936741i
\(539\) 27990.2i 0.0963450i
\(540\) −291997. 156848.i −1.00136 0.537886i
\(541\) −272065. −0.929561 −0.464780 0.885426i \(-0.653867\pi\)
−0.464780 + 0.885426i \(0.653867\pi\)
\(542\) −212917. 212917.i −0.724788 0.724788i
\(543\) 17172.4 17172.4i 0.0582413 0.0582413i
\(544\) 1.86376e6i 6.29786i
\(545\) 22271.8 6706.14i 0.0749829 0.0225777i
\(546\) −26018.2 −0.0872755
\(547\) 6581.91 + 6581.91i 0.0219977 + 0.0219977i 0.718020 0.696022i \(-0.245049\pi\)
−0.696022 + 0.718020i \(0.745049\pi\)
\(548\) −409304. + 409304.i −1.36297 + 1.36297i
\(549\) 262202.i 0.869943i
\(550\) 385057. + 78238.7i 1.27292 + 0.258640i
\(551\) −40591.1 −0.133699
\(552\) −16394.7 16394.7i −0.0538052 0.0538052i
\(553\) 1126.87 1126.87i 0.00368487 0.00368487i
\(554\) 320817.i 1.04529i
\(555\) −21366.9 70961.6i −0.0693673 0.230376i
\(556\) 1.13268e6 3.66401
\(557\) −313808. 313808.i −1.01147 1.01147i −0.999933 0.0115379i \(-0.996327\pi\)
−0.0115379 0.999933i \(-0.503673\pi\)
\(558\) 226801. 226801.i 0.728412 0.728412i
\(559\) 176603.i 0.565165i
\(560\) −203709. + 379237.i −0.649584 + 1.20930i
\(561\) 77516.6 0.246303
\(562\) −827609. 827609.i −2.62031 2.62031i
\(563\) 15752.0 15752.0i 0.0496957 0.0496957i −0.681822 0.731518i \(-0.738812\pi\)
0.731518 + 0.681822i \(0.238812\pi\)
\(564\) 316329.i 0.994446i
\(565\) −339720. 182482.i −1.06420 0.571642i
\(566\) −830028. −2.59095
\(567\) 74221.4 + 74221.4i 0.230868 + 0.230868i
\(568\) 1.03262e6 1.03262e6i 3.20069 3.20069i
\(569\) 91745.8i 0.283375i 0.989911 + 0.141688i \(0.0452528\pi\)
−0.989911 + 0.141688i \(0.954747\pi\)
\(570\) 24668.1 7427.70i 0.0759254 0.0228615i
\(571\) −441760. −1.35492 −0.677461 0.735558i \(-0.736920\pi\)
−0.677461 + 0.735558i \(0.736920\pi\)
\(572\) −236064. 236064.i −0.721502 0.721502i
\(573\) −16518.0 + 16518.0i −0.0503094 + 0.0503094i
\(574\) 11420.4i 0.0346623i
\(575\) −7086.18 + 34875.2i −0.0214327 + 0.105483i
\(576\) 1.10743e6 3.33790
\(577\) 215875. + 215875.i 0.648412 + 0.648412i 0.952609 0.304197i \(-0.0983883\pi\)
−0.304197 + 0.952609i \(0.598388\pi\)
\(578\) 861412. 861412.i 2.57843 2.57843i
\(579\) 28803.2i 0.0859178i
\(580\) −183239. 608554.i −0.544705 1.80902i
\(581\) −185973. −0.550930
\(582\) 118633. + 118633.i 0.350236 + 0.350236i
\(583\) 152105. 152105.i 0.447515 0.447515i
\(584\) 245281.i 0.719182i
\(585\) 86258.6 160584.i 0.252052 0.469236i
\(586\) 388480. 1.13129
\(587\) 415527. + 415527.i 1.20593 + 1.20593i 0.972333 + 0.233601i \(0.0750509\pi\)
0.233601 + 0.972333i \(0.424949\pi\)
\(588\) −20317.9 + 20317.9i −0.0587656 + 0.0587656i
\(589\) 37298.3i 0.107512i
\(590\) 193342. + 103854.i 0.555420 + 0.298347i
\(591\) −18615.1 −0.0532955
\(592\) 1.00855e6 + 1.00855e6i 2.87775 + 2.87775i
\(593\) −186492. + 186492.i −0.530337 + 0.530337i −0.920673 0.390336i \(-0.872359\pi\)
0.390336 + 0.920673i \(0.372359\pi\)
\(594\) 192268.i 0.544922i
\(595\) 217938. 65622.3i 0.615602 0.185361i
\(596\) −160567. −0.452025
\(597\) −24897.6 24897.6i −0.0698568 0.0698568i
\(598\) 29271.6 29271.6i 0.0818548 0.0818548i
\(599\) 135461.i 0.377538i −0.982022 0.188769i \(-0.939550\pi\)
0.982022 0.188769i \(-0.0604498\pi\)
\(600\) 140518. + 212183.i 0.390329 + 0.589396i
\(601\) −68623.2 −0.189986 −0.0949931 0.995478i \(-0.530283\pi\)
−0.0949931 + 0.995478i \(0.530283\pi\)
\(602\) −188810. 188810.i −0.520994 0.520994i
\(603\) −142185. + 142185.i −0.391037 + 0.391037i
\(604\) 987963.i 2.70811i
\(605\) −57532.1 191070.i −0.157181 0.522014i
\(606\) −112408. −0.306093
\(607\) 166899. + 166899.i 0.452978 + 0.452978i 0.896342 0.443364i \(-0.146215\pi\)
−0.443364 + 0.896342i \(0.646215\pi\)
\(608\) −185574. + 185574.i −0.502009 + 0.502009i
\(609\) 20986.2i 0.0565846i
\(610\) 309284. 575780.i 0.831184 1.54738i
\(611\) 356339. 0.954511
\(612\) −1.16433e6 1.16433e6i −3.10865 3.10865i
\(613\) −415920. + 415920.i −1.10685 + 1.10685i −0.113290 + 0.993562i \(0.536139\pi\)
−0.993562 + 0.113290i \(0.963861\pi\)
\(614\) 666599.i 1.76819i
\(615\) 3406.42 + 1829.78i 0.00900633 + 0.00483780i
\(616\) −318468. −0.839276
\(617\) 477043. + 477043.i 1.25310 + 1.25310i 0.954321 + 0.298783i \(0.0965808\pi\)
0.298783 + 0.954321i \(0.403419\pi\)
\(618\) −98875.9 + 98875.9i −0.258889 + 0.258889i
\(619\) 96183.1i 0.251025i 0.992092 + 0.125513i \(0.0400575\pi\)
−0.992092 + 0.125513i \(0.959942\pi\)
\(620\) −559189. + 168374.i −1.45471 + 0.438019i
\(621\) 17414.0 0.0451560
\(622\) 779819. + 779819.i 2.01564 + 2.01564i
\(623\) −159396. + 159396.i −0.410678 + 0.410678i
\(624\) 169545.i 0.435428i
\(625\) 152446. 359650.i 0.390262 0.920704i
\(626\) 379226. 0.967721
\(627\) 7718.30 + 7718.30i 0.0196330 + 0.0196330i
\(628\) −223314. + 223314.i −0.566234 + 0.566234i
\(629\) 754104.i 1.90603i
\(630\) −79463.0 263905.i −0.200209 0.664915i
\(631\) −204909. −0.514637 −0.257319 0.966327i \(-0.582839\pi\)
−0.257319 + 0.966327i \(0.582839\pi\)
\(632\) 12821.3 + 12821.3i 0.0320995 + 0.0320995i
\(633\) −43146.4 + 43146.4i −0.107681 + 0.107681i
\(634\) 212618.i 0.528959i
\(635\) −159864. + 297613.i −0.396465 + 0.738082i
\(636\) 220824. 0.545923
\(637\) −22887.7 22887.7i −0.0564057 0.0564057i
\(638\) 260682. 260682.i 0.640427 0.640427i
\(639\) 535472.i 1.31140i
\(640\) −1.09585e6 588643.i −2.67542 1.43712i
\(641\) −32846.1 −0.0799408 −0.0399704 0.999201i \(-0.512726\pi\)
−0.0399704 + 0.999201i \(0.512726\pi\)
\(642\) 12848.6 + 12848.6i 0.0311736 + 0.0311736i
\(643\) −78540.8 + 78540.8i −0.189965 + 0.189965i −0.795681 0.605716i \(-0.792887\pi\)
0.605716 + 0.795681i \(0.292887\pi\)
\(644\) 45716.9i 0.110231i
\(645\) −86568.7 + 26066.2i −0.208085 + 0.0626554i
\(646\) 262147. 0.628173
\(647\) 303680. + 303680.i 0.725449 + 0.725449i 0.969710 0.244260i \(-0.0785452\pi\)
−0.244260 + 0.969710i \(0.578545\pi\)
\(648\) −844478. + 844478.i −2.01112 + 2.01112i
\(649\) 92988.3i 0.220769i
\(650\) −378838. + 250886.i −0.896659 + 0.593814i
\(651\) −19283.8 −0.0455019
\(652\) −884402. 884402.i −2.08044 2.08044i
\(653\) 290141. 290141.i 0.680429 0.680429i −0.279668 0.960097i \(-0.590224\pi\)
0.960097 + 0.279668i \(0.0902245\pi\)
\(654\) 13850.6i 0.0323827i
\(655\) 124238. + 412609.i 0.289583 + 0.961736i
\(656\) −74419.9 −0.172934
\(657\) −63596.2 63596.2i −0.147333 0.147333i
\(658\) 380970. 380970.i 0.879910 0.879910i
\(659\) 495743.i 1.14153i −0.821115 0.570763i \(-0.806647\pi\)
0.821115 0.570763i \(-0.193353\pi\)
\(660\) −80872.9 + 150558.i −0.185659 + 0.345633i
\(661\) 182581. 0.417882 0.208941 0.977928i \(-0.432998\pi\)
0.208941 + 0.977928i \(0.432998\pi\)
\(662\) 230307. + 230307.i 0.525522 + 0.525522i
\(663\) −63385.5 + 63385.5i −0.144199 + 0.144199i
\(664\) 2.11596e6i 4.79924i
\(665\) 28234.1 + 15166.1i 0.0638455 + 0.0342949i
\(666\) −913155. −2.05871
\(667\) 23610.3 + 23610.3i 0.0530701 + 0.0530701i
\(668\) −1.34985e6 + 1.34985e6i −3.02505 + 3.02505i
\(669\) 58735.9i 0.131235i
\(670\) 479945. 144514.i 1.06916 0.321928i
\(671\) 276924. 0.615056
\(672\) −95944.6 95944.6i −0.212462 0.212462i
\(673\) −551601. + 551601.i −1.21785 + 1.21785i −0.249470 + 0.968382i \(0.580257\pi\)
−0.968382 + 0.249470i \(0.919743\pi\)
\(674\) 81256.2i 0.178870i
\(675\) −187315. 38060.0i −0.411117 0.0835336i
\(676\) −852116. −1.86469
\(677\) −112272. 112272.i −0.244959 0.244959i 0.573939 0.818898i \(-0.305415\pi\)
−0.818898 + 0.573939i \(0.805415\pi\)
\(678\) 162376. 162376.i 0.353234 0.353234i
\(679\) 208719.i 0.452712i
\(680\) 746640. + 2.47967e6i 1.61471 + 5.36260i
\(681\) −2.91894 −6.29406e−6
\(682\) −239536. 239536.i −0.514993 0.514993i
\(683\) 434268. 434268.i 0.930928 0.930928i −0.0668362 0.997764i \(-0.521291\pi\)
0.997764 + 0.0668362i \(0.0212905\pi\)
\(684\) 231863.i 0.495587i
\(685\) −157959. + 294065.i −0.336637 + 0.626704i
\(686\) −48939.4 −0.103995
\(687\) −84150.1 84150.1i −0.178296 0.178296i
\(688\) 1.23036e6 1.23036e6i 2.59930 2.59930i
\(689\) 248754.i 0.524000i
\(690\) −18669.0 10028.1i −0.0392123 0.0210631i
\(691\) 684956. 1.43452 0.717260 0.696806i \(-0.245396\pi\)
0.717260 + 0.696806i \(0.245396\pi\)
\(692\) 749904. + 749904.i 1.56601 + 1.56601i
\(693\) 82572.0 82572.0i 0.171936 0.171936i
\(694\) 1.05809e6i 2.19686i
\(695\) 625448. 188325.i 1.29486 0.389887i
\(696\) 238777. 0.492917
\(697\) 27822.3 + 27822.3i 0.0572701 + 0.0572701i
\(698\) −503552. + 503552.i −1.03355 + 1.03355i
\(699\) 51866.6i 0.106153i
\(700\) −99918.9 + 491758.i −0.203916 + 1.00359i
\(701\) 809809. 1.64796 0.823980 0.566619i \(-0.191749\pi\)
0.823980 + 0.566619i \(0.191749\pi\)
\(702\) 157218. + 157218.i 0.319028 + 0.319028i
\(703\) 75085.9 75085.9i 0.151931 0.151931i
\(704\) 1.16961e6i 2.35992i
\(705\) −52594.8 174673.i −0.105819 0.351436i
\(706\) 76270.0 0.153019
\(707\) −98883.4 98883.4i −0.197827 0.197827i
\(708\) −67499.4 + 67499.4i −0.134658 + 0.134658i
\(709\) 204474.i 0.406768i 0.979099 + 0.203384i \(0.0651939\pi\)
−0.979099 + 0.203384i \(0.934806\pi\)
\(710\) 631622. 1.17587e6i 1.25297 2.33260i
\(711\) −6648.57 −0.0131519
\(712\) −1.81358e6 1.81358e6i −3.57748 3.57748i
\(713\) 21695.1 21695.1i 0.0426758 0.0426758i
\(714\) 135534.i 0.265858i
\(715\) −169600. 91101.8i −0.331753 0.178203i
\(716\) 57769.9 0.112687
\(717\) −143654. 143654.i −0.279435 0.279435i
\(718\) 1.10064e6 1.10064e6i 2.13499 2.13499i
\(719\) 603232.i 1.16688i −0.812156 0.583441i \(-0.801706\pi\)
0.812156 0.583441i \(-0.198294\pi\)
\(720\) 1.71971e6 517813.i 3.31734 0.998867i
\(721\) −173958. −0.334637
\(722\) −683831. 683831.i −1.31182 1.31182i
\(723\) 86158.0 86158.0i 0.164823 0.164823i
\(724\) 544835.i 1.03941i
\(725\) −202364. 305569.i −0.384996 0.581344i
\(726\) 118824. 0.225441
\(727\) −277495. 277495.i −0.525033 0.525033i 0.394054 0.919087i \(-0.371072\pi\)
−0.919087 + 0.394054i \(0.871072\pi\)
\(728\) 260412. 260412.i 0.491359 0.491359i
\(729\) 390041.i 0.733932i
\(730\) 64638.0 + 214669.i 0.121295 + 0.402832i
\(731\) −919959. −1.72161
\(732\) 201016. + 201016.i 0.375154 + 0.375154i
\(733\) −602150. + 602150.i −1.12072 + 1.12072i −0.129085 + 0.991634i \(0.541204\pi\)
−0.991634 + 0.129085i \(0.958796\pi\)
\(734\) 1.38039e6i 2.56218i
\(735\) −7841.08 + 14597.4i −0.0145145 + 0.0270210i
\(736\) 215884. 0.398533
\(737\) 150168. + 150168.i 0.276466 + 0.276466i
\(738\) 33690.5 33690.5i 0.0618578 0.0618578i
\(739\) 510748.i 0.935228i −0.883933 0.467614i \(-0.845114\pi\)
0.883933 0.467614i \(-0.154886\pi\)
\(740\) 1.46467e6 + 786755.i 2.67471 + 1.43673i
\(741\) −12622.6 −0.0229885
\(742\) 265948. + 265948.i 0.483046 + 0.483046i
\(743\) 483448. 483448.i 0.875735 0.875735i −0.117355 0.993090i \(-0.537442\pi\)
0.993090 + 0.117355i \(0.0374416\pi\)
\(744\) 219407.i 0.396374i
\(745\) −88662.6 + 26696.7i −0.159745 + 0.0481000i
\(746\) −1.20795e6 −2.17055
\(747\) 548624. + 548624.i 0.983181 + 0.983181i
\(748\) −1.22970e6 + 1.22970e6i −2.19784 + 2.19784i
\(749\) 22605.4i 0.0402947i
\(750\) 178897. + 148671.i 0.318039 + 0.264305i
\(751\) −803929. −1.42540 −0.712702 0.701467i \(-0.752529\pi\)
−0.712702 + 0.701467i \(0.752529\pi\)
\(752\) 2.48255e6 + 2.48255e6i 4.38998 + 4.38998i
\(753\) −112828. + 112828.i −0.198988 + 0.198988i
\(754\) 426321.i 0.749883i
\(755\) 164265. + 545539.i 0.288171 + 0.957045i
\(756\) 245546. 0.429625
\(757\) −137325. 137325.i −0.239640 0.239640i 0.577061 0.816701i \(-0.304199\pi\)
−0.816701 + 0.577061i \(0.804199\pi\)
\(758\) −779536. + 779536.i −1.35674 + 1.35674i
\(759\) 8978.90i 0.0155862i
\(760\) −172557. + 321242.i −0.298748 + 0.556168i
\(761\) −410285. −0.708462 −0.354231 0.935158i \(-0.615257\pi\)
−0.354231 + 0.935158i \(0.615257\pi\)
\(762\) −142250. 142250.i −0.244987 0.244987i
\(763\) −12184.1 + 12184.1i −0.0209288 + 0.0209288i
\(764\) 524074.i 0.897854i
\(765\) −836512. 449337.i −1.42939 0.767802i
\(766\) 532747. 0.907954
\(767\) −76036.8 76036.8i −0.129251 0.129251i
\(768\) 210438. 210438.i 0.356781 0.356781i
\(769\) 306046.i 0.517529i −0.965941 0.258764i \(-0.916685\pi\)
0.965941 0.258764i \(-0.0833153\pi\)
\(770\) −278722. + 83924.6i −0.470100 + 0.141549i
\(771\) 144710. 0.243439
\(772\) −456925. 456925.i −0.766673 0.766673i
\(773\) 746945. 746945.i 1.25006 1.25006i 0.294363 0.955694i \(-0.404893\pi\)
0.955694 0.294363i \(-0.0951074\pi\)
\(774\) 1.11399e6i 1.85952i
\(775\) −280781. + 185948.i −0.467482 + 0.309591i