Properties

Label 35.5.g.a.22.8
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 22.8
Character \(\chi\) \(=\) 35.22
Dual form 35.5.g.a.8.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.48373 + 1.48373i) q^{2} +(2.63880 - 2.63880i) q^{3} -11.5971i q^{4} +(8.51221 - 23.5062i) q^{5} +7.83054 q^{6} +(13.0958 + 13.0958i) q^{7} +(40.9466 - 40.9466i) q^{8} +67.0734i q^{9} +O(q^{10})\) \(q+(1.48373 + 1.48373i) q^{2} +(2.63880 - 2.63880i) q^{3} -11.5971i q^{4} +(8.51221 - 23.5062i) q^{5} +7.83054 q^{6} +(13.0958 + 13.0958i) q^{7} +(40.9466 - 40.9466i) q^{8} +67.0734i q^{9} +(47.5067 - 22.2471i) q^{10} +18.0812 q^{11} +(-30.6025 - 30.6025i) q^{12} +(-1.78021 + 1.78021i) q^{13} +38.8613i q^{14} +(-39.5662 - 84.4904i) q^{15} -64.0460 q^{16} +(8.06293 + 8.06293i) q^{17} +(-99.5188 + 99.5188i) q^{18} +201.172i q^{19} +(-272.604 - 98.7169i) q^{20} +69.1145 q^{21} +(26.8275 + 26.8275i) q^{22} +(-414.713 + 414.713i) q^{23} -216.100i q^{24} +(-480.085 - 400.180i) q^{25} -5.28271 q^{26} +(390.737 + 390.737i) q^{27} +(151.873 - 151.873i) q^{28} +1065.57i q^{29} +(66.6552 - 184.066i) q^{30} +1360.48 q^{31} +(-750.173 - 750.173i) q^{32} +(47.7126 - 47.7126i) q^{33} +23.9264i q^{34} +(419.307 - 196.359i) q^{35} +777.857 q^{36} +(-848.868 - 848.868i) q^{37} +(-298.484 + 298.484i) q^{38} +9.39527i q^{39} +(-613.954 - 1311.05i) q^{40} +2808.50 q^{41} +(102.547 + 102.547i) q^{42} +(322.020 - 322.020i) q^{43} -209.689i q^{44} +(1576.64 + 570.943i) q^{45} -1230.64 q^{46} +(-907.451 - 907.451i) q^{47} +(-169.005 + 169.005i) q^{48} +343.000i q^{49} +(-118.557 - 1306.07i) q^{50} +42.5530 q^{51} +(20.6453 + 20.6453i) q^{52} +(-3087.31 + 3087.31i) q^{53} +1159.50i q^{54} +(153.911 - 425.020i) q^{55} +1072.46 q^{56} +(530.853 + 530.853i) q^{57} +(-1581.02 + 1581.02i) q^{58} +1711.53i q^{59} +(-979.843 + 458.853i) q^{60} -4951.60 q^{61} +(2018.58 + 2018.58i) q^{62} +(-878.380 + 878.380i) q^{63} -1201.37i q^{64} +(26.6925 + 56.9996i) q^{65} +141.585 q^{66} +(-5329.83 - 5329.83i) q^{67} +(93.5065 - 93.5065i) q^{68} +2188.69i q^{69} +(913.481 + 330.795i) q^{70} +3843.45 q^{71} +(2746.43 + 2746.43i) q^{72} +(3299.35 - 3299.35i) q^{73} -2518.98i q^{74} +(-2322.85 + 210.853i) q^{75} +2333.01 q^{76} +(236.787 + 236.787i) q^{77} +(-13.9400 + 13.9400i) q^{78} -9899.41i q^{79} +(-545.173 + 1505.48i) q^{80} -3370.79 q^{81} +(4167.06 + 4167.06i) q^{82} +(5254.07 - 5254.07i) q^{83} -801.527i q^{84} +(258.162 - 120.896i) q^{85} +955.582 q^{86} +(2811.84 + 2811.84i) q^{87} +(740.362 - 740.362i) q^{88} +3691.22i q^{89} +(1492.19 + 3186.44i) q^{90} -46.6266 q^{91} +(4809.46 + 4809.46i) q^{92} +(3590.03 - 3590.03i) q^{93} -2692.82i q^{94} +(4728.79 + 1712.42i) q^{95} -3959.12 q^{96} +(-9933.45 - 9933.45i) q^{97} +(-508.919 + 508.919i) q^{98} +1212.77i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.48373 + 1.48373i 0.370932 + 0.370932i 0.867817 0.496884i \(-0.165523\pi\)
−0.496884 + 0.867817i \(0.665523\pi\)
\(3\) 2.63880 2.63880i 0.293200 0.293200i −0.545143 0.838343i \(-0.683525\pi\)
0.838343 + 0.545143i \(0.183525\pi\)
\(4\) 11.5971i 0.724818i
\(5\) 8.51221 23.5062i 0.340488 0.940249i
\(6\) 7.83054 0.217515
\(7\) 13.0958 + 13.0958i 0.267261 + 0.267261i
\(8\) 40.9466 40.9466i 0.639791 0.639791i
\(9\) 67.0734i 0.828067i
\(10\) 47.5067 22.2471i 0.475067 0.222471i
\(11\) 18.0812 0.149431 0.0747155 0.997205i \(-0.476195\pi\)
0.0747155 + 0.997205i \(0.476195\pi\)
\(12\) −30.6025 30.6025i −0.212517 0.212517i
\(13\) −1.78021 + 1.78021i −0.0105338 + 0.0105338i −0.712354 0.701820i \(-0.752371\pi\)
0.701820 + 0.712354i \(0.252371\pi\)
\(14\) 38.8613i 0.198272i
\(15\) −39.5662 84.4904i −0.175850 0.375513i
\(16\) −64.0460 −0.250180
\(17\) 8.06293 + 8.06293i 0.0278994 + 0.0278994i 0.720919 0.693019i \(-0.243720\pi\)
−0.693019 + 0.720919i \(0.743720\pi\)
\(18\) −99.5188 + 99.5188i −0.307157 + 0.307157i
\(19\) 201.172i 0.557262i 0.960398 + 0.278631i \(0.0898807\pi\)
−0.960398 + 0.278631i \(0.910119\pi\)
\(20\) −272.604 98.7169i −0.681509 0.246792i
\(21\) 69.1145 0.156722
\(22\) 26.8275 + 26.8275i 0.0554288 + 0.0554288i
\(23\) −414.713 + 414.713i −0.783956 + 0.783956i −0.980496 0.196540i \(-0.937030\pi\)
0.196540 + 0.980496i \(0.437030\pi\)
\(24\) 216.100i 0.375174i
\(25\) −480.085 400.180i −0.768135 0.640288i
\(26\) −5.28271 −0.00781466
\(27\) 390.737 + 390.737i 0.535990 + 0.535990i
\(28\) 151.873 151.873i 0.193716 0.193716i
\(29\) 1065.57i 1.26703i 0.773729 + 0.633516i \(0.218389\pi\)
−0.773729 + 0.633516i \(0.781611\pi\)
\(30\) 66.6552 184.066i 0.0740614 0.204518i
\(31\) 1360.48 1.41569 0.707845 0.706368i \(-0.249668\pi\)
0.707845 + 0.706368i \(0.249668\pi\)
\(32\) −750.173 750.173i −0.732591 0.732591i
\(33\) 47.7126 47.7126i 0.0438133 0.0438133i
\(34\) 23.9264i 0.0206976i
\(35\) 419.307 196.359i 0.342291 0.160293i
\(36\) 777.857 0.600198
\(37\) −848.868 848.868i −0.620065 0.620065i 0.325483 0.945548i \(-0.394473\pi\)
−0.945548 + 0.325483i \(0.894473\pi\)
\(38\) −298.484 + 298.484i −0.206707 + 0.206707i
\(39\) 9.39527i 0.00617704i
\(40\) −613.954 1311.05i −0.383721 0.819404i
\(41\) 2808.50 1.67073 0.835366 0.549694i \(-0.185256\pi\)
0.835366 + 0.549694i \(0.185256\pi\)
\(42\) 102.547 + 102.547i 0.0581334 + 0.0581334i
\(43\) 322.020 322.020i 0.174159 0.174159i −0.614645 0.788804i \(-0.710701\pi\)
0.788804 + 0.614645i \(0.210701\pi\)
\(44\) 209.689i 0.108310i
\(45\) 1576.64 + 570.943i 0.778589 + 0.281947i
\(46\) −1230.64 −0.581590
\(47\) −907.451 907.451i −0.410797 0.410797i 0.471219 0.882016i \(-0.343814\pi\)
−0.882016 + 0.471219i \(0.843814\pi\)
\(48\) −169.005 + 169.005i −0.0733528 + 0.0733528i
\(49\) 343.000i 0.142857i
\(50\) −118.557 1306.07i −0.0474229 0.522430i
\(51\) 42.5530 0.0163602
\(52\) 20.6453 + 20.6453i 0.00763510 + 0.00763510i
\(53\) −3087.31 + 3087.31i −1.09908 + 1.09908i −0.104558 + 0.994519i \(0.533343\pi\)
−0.994519 + 0.104558i \(0.966657\pi\)
\(54\) 1159.50i 0.397632i
\(55\) 153.911 425.020i 0.0508795 0.140502i
\(56\) 1072.46 0.341983
\(57\) 530.853 + 530.853i 0.163390 + 0.163390i
\(58\) −1581.02 + 1581.02i −0.469983 + 0.469983i
\(59\) 1711.53i 0.491678i 0.969311 + 0.245839i \(0.0790635\pi\)
−0.969311 + 0.245839i \(0.920936\pi\)
\(60\) −979.843 + 458.853i −0.272178 + 0.127459i
\(61\) −4951.60 −1.33072 −0.665358 0.746524i \(-0.731721\pi\)
−0.665358 + 0.746524i \(0.731721\pi\)
\(62\) 2018.58 + 2018.58i 0.525125 + 0.525125i
\(63\) −878.380 + 878.380i −0.221310 + 0.221310i
\(64\) 1201.37i 0.293304i
\(65\) 26.6925 + 56.9996i 0.00631776 + 0.0134910i
\(66\) 141.585 0.0325035
\(67\) −5329.83 5329.83i −1.18731 1.18731i −0.977808 0.209502i \(-0.932816\pi\)
−0.209502 0.977808i \(-0.567184\pi\)
\(68\) 93.5065 93.5065i 0.0202220 0.0202220i
\(69\) 2188.69i 0.459713i
\(70\) 913.481 + 330.795i 0.186425 + 0.0675092i
\(71\) 3843.45 0.762439 0.381219 0.924485i \(-0.375504\pi\)
0.381219 + 0.924485i \(0.375504\pi\)
\(72\) 2746.43 + 2746.43i 0.529790 + 0.529790i
\(73\) 3299.35 3299.35i 0.619132 0.619132i −0.326177 0.945309i \(-0.605761\pi\)
0.945309 + 0.326177i \(0.105761\pi\)
\(74\) 2518.98i 0.460004i
\(75\) −2322.85 + 210.853i −0.412950 + 0.0374850i
\(76\) 2333.01 0.403914
\(77\) 236.787 + 236.787i 0.0399371 + 0.0399371i
\(78\) −13.9400 + 13.9400i −0.00229126 + 0.00229126i
\(79\) 9899.41i 1.58619i −0.609099 0.793094i \(-0.708469\pi\)
0.609099 0.793094i \(-0.291531\pi\)
\(80\) −545.173 + 1505.48i −0.0851833 + 0.235231i
\(81\) −3370.79 −0.513762
\(82\) 4167.06 + 4167.06i 0.619729 + 0.619729i
\(83\) 5254.07 5254.07i 0.762676 0.762676i −0.214130 0.976805i \(-0.568692\pi\)
0.976805 + 0.214130i \(0.0686915\pi\)
\(84\) 801.527i 0.113595i
\(85\) 258.162 120.896i 0.0357318 0.0167330i
\(86\) 955.582 0.129203
\(87\) 2811.84 + 2811.84i 0.371495 + 0.371495i
\(88\) 740.362 740.362i 0.0956046 0.0956046i
\(89\) 3691.22i 0.466004i 0.972476 + 0.233002i \(0.0748548\pi\)
−0.972476 + 0.233002i \(0.925145\pi\)
\(90\) 1492.19 + 3186.44i 0.184221 + 0.393387i
\(91\) −46.6266 −0.00563056
\(92\) 4809.46 + 4809.46i 0.568226 + 0.568226i
\(93\) 3590.03 3590.03i 0.415081 0.415081i
\(94\) 2692.82i 0.304756i
\(95\) 4728.79 + 1712.42i 0.523965 + 0.189741i
\(96\) −3959.12 −0.429592
\(97\) −9933.45 9933.45i −1.05574 1.05574i −0.998352 0.0573876i \(-0.981723\pi\)
−0.0573876 0.998352i \(-0.518277\pi\)
\(98\) −508.919 + 508.919i −0.0529903 + 0.0529903i
\(99\) 1212.77i 0.123739i
\(100\) −4640.92 + 5567.58i −0.464092 + 0.556758i
\(101\) −16631.2 −1.63035 −0.815174 0.579217i \(-0.803358\pi\)
−0.815174 + 0.579217i \(0.803358\pi\)
\(102\) 63.1371 + 63.1371i 0.00606854 + 0.00606854i
\(103\) 7782.56 7782.56i 0.733581 0.733581i −0.237747 0.971327i \(-0.576409\pi\)
0.971327 + 0.237747i \(0.0764088\pi\)
\(104\) 145.787i 0.0134789i
\(105\) 588.317 1624.62i 0.0533621 0.147358i
\(106\) −9161.46 −0.815367
\(107\) 6893.44 + 6893.44i 0.602100 + 0.602100i 0.940869 0.338770i \(-0.110011\pi\)
−0.338770 + 0.940869i \(0.610011\pi\)
\(108\) 4531.41 4531.41i 0.388495 0.388495i
\(109\) 12312.6i 1.03632i 0.855283 + 0.518162i \(0.173383\pi\)
−0.855283 + 0.518162i \(0.826617\pi\)
\(110\) 858.976 402.252i 0.0709897 0.0332440i
\(111\) −4480.00 −0.363606
\(112\) −838.734 838.734i −0.0668634 0.0668634i
\(113\) −4571.88 + 4571.88i −0.358045 + 0.358045i −0.863092 0.505047i \(-0.831475\pi\)
0.505047 + 0.863092i \(0.331475\pi\)
\(114\) 1575.28i 0.121213i
\(115\) 6218.21 + 13278.5i 0.470186 + 1.00404i
\(116\) 12357.6 0.918368
\(117\) −119.405 119.405i −0.00872270 0.00872270i
\(118\) −2539.45 + 2539.45i −0.182379 + 0.182379i
\(119\) 211.181i 0.0149129i
\(120\) −5079.70 1839.49i −0.352757 0.127742i
\(121\) −14314.1 −0.977670
\(122\) −7346.83 7346.83i −0.493606 0.493606i
\(123\) 7411.09 7411.09i 0.489860 0.489860i
\(124\) 15777.6i 1.02612i
\(125\) −13493.3 + 7878.56i −0.863571 + 0.504228i
\(126\) −2606.56 −0.164182
\(127\) −756.980 756.980i −0.0469328 0.0469328i 0.683251 0.730184i \(-0.260566\pi\)
−0.730184 + 0.683251i \(0.760566\pi\)
\(128\) −10220.3 + 10220.3i −0.623795 + 0.623795i
\(129\) 1699.50i 0.102127i
\(130\) −44.9676 + 124.177i −0.00266080 + 0.00734773i
\(131\) 4951.67 0.288542 0.144271 0.989538i \(-0.453916\pi\)
0.144271 + 0.989538i \(0.453916\pi\)
\(132\) −553.328 553.328i −0.0317566 0.0317566i
\(133\) −2634.50 + 2634.50i −0.148935 + 0.148935i
\(134\) 15816.1i 0.880824i
\(135\) 12510.8 5858.71i 0.686462 0.321466i
\(136\) 660.299 0.0356996
\(137\) 13415.6 + 13415.6i 0.714774 + 0.714774i 0.967530 0.252756i \(-0.0813369\pi\)
−0.252756 + 0.967530i \(0.581337\pi\)
\(138\) −3247.43 + 3247.43i −0.170522 + 0.170522i
\(139\) 6023.08i 0.311738i 0.987778 + 0.155869i \(0.0498177\pi\)
−0.987778 + 0.155869i \(0.950182\pi\)
\(140\) −2277.19 4862.74i −0.116183 0.248099i
\(141\) −4789.17 −0.240892
\(142\) 5702.65 + 5702.65i 0.282813 + 0.282813i
\(143\) −32.1883 + 32.1883i −0.00157408 + 0.00157408i
\(144\) 4295.79i 0.207166i
\(145\) 25047.6 + 9070.39i 1.19133 + 0.431410i
\(146\) 9790.70 0.459312
\(147\) 905.110 + 905.110i 0.0418858 + 0.0418858i
\(148\) −9844.41 + 9844.41i −0.449434 + 0.449434i
\(149\) 15207.8i 0.685003i −0.939517 0.342502i \(-0.888726\pi\)
0.939517 0.342502i \(-0.111274\pi\)
\(150\) −3759.32 3133.63i −0.167081 0.139272i
\(151\) 38369.4 1.68279 0.841397 0.540417i \(-0.181734\pi\)
0.841397 + 0.540417i \(0.181734\pi\)
\(152\) 8237.30 + 8237.30i 0.356531 + 0.356531i
\(153\) −540.808 + 540.808i −0.0231026 + 0.0231026i
\(154\) 702.656i 0.0296280i
\(155\) 11580.7 31979.7i 0.482026 1.33110i
\(156\) 108.958 0.00447723
\(157\) −4024.99 4024.99i −0.163292 0.163292i 0.620731 0.784023i \(-0.286836\pi\)
−0.784023 + 0.620731i \(0.786836\pi\)
\(158\) 14688.0 14688.0i 0.588369 0.588369i
\(159\) 16293.6i 0.644500i
\(160\) −24019.4 + 11248.1i −0.938256 + 0.439379i
\(161\) −10862.0 −0.419042
\(162\) −5001.34 5001.34i −0.190571 0.190571i
\(163\) 7525.01 7525.01i 0.283225 0.283225i −0.551169 0.834394i \(-0.685818\pi\)
0.834394 + 0.551169i \(0.185818\pi\)
\(164\) 32570.5i 1.21098i
\(165\) −715.404 1527.68i −0.0262774 0.0561133i
\(166\) 15591.2 0.565802
\(167\) −34535.2 34535.2i −1.23831 1.23831i −0.960692 0.277615i \(-0.910456\pi\)
−0.277615 0.960692i \(-0.589544\pi\)
\(168\) 2830.01 2830.01i 0.100269 0.100269i
\(169\) 28554.7i 0.999778i
\(170\) 562.419 + 203.667i 0.0194609 + 0.00704729i
\(171\) −13493.3 −0.461451
\(172\) −3734.50 3734.50i −0.126234 0.126234i
\(173\) −23342.7 + 23342.7i −0.779937 + 0.779937i −0.979820 0.199883i \(-0.935944\pi\)
0.199883 + 0.979820i \(0.435944\pi\)
\(174\) 8344.03i 0.275599i
\(175\) −1046.42 11527.8i −0.0341687 0.376417i
\(176\) −1158.03 −0.0373846
\(177\) 4516.40 + 4516.40i 0.144160 + 0.144160i
\(178\) −5476.77 + 5476.77i −0.172856 + 0.172856i
\(179\) 28472.1i 0.888614i 0.895875 + 0.444307i \(0.146550\pi\)
−0.895875 + 0.444307i \(0.853450\pi\)
\(180\) 6621.28 18284.5i 0.204360 0.564335i
\(181\) 40886.7 1.24803 0.624015 0.781412i \(-0.285500\pi\)
0.624015 + 0.781412i \(0.285500\pi\)
\(182\) −69.1813 69.1813i −0.00208856 0.00208856i
\(183\) −13066.3 + 13066.3i −0.390167 + 0.390167i
\(184\) 33962.2i 1.00314i
\(185\) −27179.4 + 12727.9i −0.794140 + 0.371890i
\(186\) 10653.3 0.307934
\(187\) 145.787 + 145.787i 0.00416904 + 0.00416904i
\(188\) −10523.8 + 10523.8i −0.297753 + 0.297753i
\(189\) 10234.0i 0.286499i
\(190\) 4475.48 + 9557.00i 0.123974 + 0.264737i
\(191\) −15424.7 −0.422814 −0.211407 0.977398i \(-0.567804\pi\)
−0.211407 + 0.977398i \(0.567804\pi\)
\(192\) −3170.18 3170.18i −0.0859968 0.0859968i
\(193\) −6739.80 + 6739.80i −0.180939 + 0.180939i −0.791765 0.610826i \(-0.790838\pi\)
0.610826 + 0.791765i \(0.290838\pi\)
\(194\) 29477.1i 0.783216i
\(195\) 220.847 + 79.9745i 0.00580795 + 0.00210321i
\(196\) 3977.80 0.103545
\(197\) −21.4403 21.4403i −0.000552458 0.000552458i 0.706830 0.707383i \(-0.250124\pi\)
−0.707383 + 0.706830i \(0.750124\pi\)
\(198\) −1799.42 + 1799.42i −0.0458988 + 0.0458988i
\(199\) 61587.1i 1.55519i 0.628765 + 0.777596i \(0.283561\pi\)
−0.628765 + 0.777596i \(0.716439\pi\)
\(200\) −36043.9 + 3271.83i −0.901096 + 0.0817958i
\(201\) −28128.8 −0.696240
\(202\) −24676.2 24676.2i −0.604749 0.604749i
\(203\) −13954.5 + 13954.5i −0.338629 + 0.338629i
\(204\) 493.491i 0.0118582i
\(205\) 23906.6 66017.3i 0.568865 1.57090i
\(206\) 23094.4 0.544218
\(207\) −27816.2 27816.2i −0.649168 0.649168i
\(208\) 114.016 114.016i 0.00263535 0.00263535i
\(209\) 3637.42i 0.0832723i
\(210\) 3283.40 1537.59i 0.0744536 0.0348661i
\(211\) 7989.99 0.179466 0.0897328 0.995966i \(-0.471399\pi\)
0.0897328 + 0.995966i \(0.471399\pi\)
\(212\) 35803.8 + 35803.8i 0.796631 + 0.796631i
\(213\) 10142.1 10142.1i 0.223547 0.223547i
\(214\) 20456.0i 0.446676i
\(215\) −4828.37 10310.6i −0.104454 0.223052i
\(216\) 31998.7 0.685843
\(217\) 17816.5 + 17816.5i 0.378359 + 0.378359i
\(218\) −18268.5 + 18268.5i −0.384406 + 0.384406i
\(219\) 17412.7i 0.363059i
\(220\) −4928.99 1784.92i −0.101839 0.0368784i
\(221\) −28.7075 −0.000587774
\(222\) −6647.10 6647.10i −0.134873 0.134873i
\(223\) 68789.7 68789.7i 1.38329 1.38329i 0.544589 0.838703i \(-0.316686\pi\)
0.838703 0.544589i \(-0.183314\pi\)
\(224\) 19648.2i 0.391586i
\(225\) 26841.4 32200.9i 0.530201 0.636067i
\(226\) −13566.9 −0.265621
\(227\) 10650.0 + 10650.0i 0.206680 + 0.206680i 0.802855 0.596175i \(-0.203314\pi\)
−0.596175 + 0.802855i \(0.703314\pi\)
\(228\) 6156.35 6156.35i 0.118428 0.118428i
\(229\) 21675.8i 0.413336i −0.978411 0.206668i \(-0.933738\pi\)
0.978411 0.206668i \(-0.0662620\pi\)
\(230\) −10475.5 + 28927.8i −0.198025 + 0.546839i
\(231\) 1249.67 0.0234192
\(232\) 43631.7 + 43631.7i 0.810636 + 0.810636i
\(233\) 14316.4 14316.4i 0.263707 0.263707i −0.562851 0.826558i \(-0.690296\pi\)
0.826558 + 0.562851i \(0.190296\pi\)
\(234\) 354.330i 0.00647106i
\(235\) −29055.1 + 13606.3i −0.526123 + 0.246380i
\(236\) 19848.8 0.356377
\(237\) −26122.6 26122.6i −0.465071 0.465071i
\(238\) −313.336 + 313.336i −0.00553166 + 0.00553166i
\(239\) 80312.5i 1.40601i −0.711187 0.703003i \(-0.751842\pi\)
0.711187 0.703003i \(-0.248158\pi\)
\(240\) 2534.06 + 5411.27i 0.0439941 + 0.0939457i
\(241\) 14965.1 0.257659 0.128829 0.991667i \(-0.458878\pi\)
0.128829 + 0.991667i \(0.458878\pi\)
\(242\) −21238.2 21238.2i −0.362650 0.362650i
\(243\) −40544.5 + 40544.5i −0.686625 + 0.686625i
\(244\) 57424.1i 0.964528i
\(245\) 8062.63 + 2919.69i 0.134321 + 0.0486412i
\(246\) 21992.1 0.363410
\(247\) −358.129 358.129i −0.00587009 0.00587009i
\(248\) 55707.0 55707.0i 0.905745 0.905745i
\(249\) 27728.9i 0.447234i
\(250\) −31710.1 8330.75i −0.507361 0.133292i
\(251\) 49620.5 0.787614 0.393807 0.919193i \(-0.371158\pi\)
0.393807 + 0.919193i \(0.371158\pi\)
\(252\) 10186.7 + 10186.7i 0.160410 + 0.160410i
\(253\) −7498.49 + 7498.49i −0.117147 + 0.117147i
\(254\) 2246.31i 0.0348178i
\(255\) 362.220 1000.26i 0.00557047 0.0153827i
\(256\) −49550.1 −0.756075
\(257\) 61440.3 + 61440.3i 0.930222 + 0.930222i 0.997719 0.0674972i \(-0.0215014\pi\)
−0.0674972 + 0.997719i \(0.521501\pi\)
\(258\) 2521.59 2521.59i 0.0378822 0.0378822i
\(259\) 22233.2i 0.331438i
\(260\) 661.030 309.556i 0.00977855 0.00457923i
\(261\) −71471.7 −1.04919
\(262\) 7346.94 + 7346.94i 0.107030 + 0.107030i
\(263\) −30152.4 + 30152.4i −0.435924 + 0.435924i −0.890638 0.454713i \(-0.849742\pi\)
0.454713 + 0.890638i \(0.349742\pi\)
\(264\) 3907.34i 0.0560627i
\(265\) 46291.1 + 98850.7i 0.659183 + 1.40763i
\(266\) −7817.79 −0.110489
\(267\) 9740.40 + 9740.40i 0.136633 + 0.136633i
\(268\) −61810.6 + 61810.6i −0.860584 + 0.860584i
\(269\) 27372.8i 0.378282i −0.981950 0.189141i \(-0.939430\pi\)
0.981950 0.189141i \(-0.0605703\pi\)
\(270\) 27255.4 + 9869.87i 0.373873 + 0.135389i
\(271\) −107491. −1.46364 −0.731821 0.681497i \(-0.761329\pi\)
−0.731821 + 0.681497i \(0.761329\pi\)
\(272\) −516.398 516.398i −0.00697987 0.00697987i
\(273\) −123.039 + 123.039i −0.00165088 + 0.00165088i
\(274\) 39810.3i 0.530266i
\(275\) −8680.48 7235.71i −0.114783 0.0956788i
\(276\) 25382.5 0.333208
\(277\) −90987.9 90987.9i −1.18583 1.18583i −0.978208 0.207626i \(-0.933426\pi\)
−0.207626 0.978208i \(-0.566574\pi\)
\(278\) −8936.62 + 8936.62i −0.115634 + 0.115634i
\(279\) 91251.9i 1.17229i
\(280\) 9128.99 25209.4i 0.116441 0.321549i
\(281\) −81617.1 −1.03364 −0.516819 0.856095i \(-0.672884\pi\)
−0.516819 + 0.856095i \(0.672884\pi\)
\(282\) −7105.83 7105.83i −0.0893546 0.0893546i
\(283\) −25062.7 + 25062.7i −0.312936 + 0.312936i −0.846046 0.533110i \(-0.821023\pi\)
0.533110 + 0.846046i \(0.321023\pi\)
\(284\) 44572.9i 0.552629i
\(285\) 16997.1 7959.61i 0.209259 0.0979946i
\(286\) −95.5175 −0.00116775
\(287\) 36779.6 + 36779.6i 0.446522 + 0.446522i
\(288\) 50316.7 50316.7i 0.606634 0.606634i
\(289\) 83391.0i 0.998443i
\(290\) 23705.9 + 50621.9i 0.281877 + 0.601925i
\(291\) −52424.9 −0.619087
\(292\) −38262.9 38262.9i −0.448758 0.448758i
\(293\) 53618.1 53618.1i 0.624562 0.624562i −0.322132 0.946695i \(-0.604400\pi\)
0.946695 + 0.322132i \(0.104400\pi\)
\(294\) 2685.88i 0.0310736i
\(295\) 40231.7 + 14568.9i 0.462300 + 0.167411i
\(296\) −69516.6 −0.793424
\(297\) 7064.97 + 7064.97i 0.0800936 + 0.0800936i
\(298\) 22564.2 22564.2i 0.254090 0.254090i
\(299\) 1476.56i 0.0165161i
\(300\) 2445.28 + 26938.2i 0.0271698 + 0.299314i
\(301\) 8434.23 0.0930920
\(302\) 56929.8 + 56929.8i 0.624203 + 0.624203i
\(303\) −43886.4 + 43886.4i −0.478019 + 0.478019i
\(304\) 12884.2i 0.139416i
\(305\) −42149.0 + 116393.i −0.453094 + 1.25120i
\(306\) −1604.83 −0.0171390
\(307\) −76759.5 76759.5i −0.814433 0.814433i 0.170862 0.985295i \(-0.445345\pi\)
−0.985295 + 0.170862i \(0.945345\pi\)
\(308\) 2746.04 2746.04i 0.0289472 0.0289472i
\(309\) 41073.3i 0.430172i
\(310\) 64631.8 30266.6i 0.672547 0.314949i
\(311\) 157851. 1.63203 0.816014 0.578033i \(-0.196179\pi\)
0.816014 + 0.578033i \(0.196179\pi\)
\(312\) 384.705 + 384.705i 0.00395201 + 0.00395201i
\(313\) 75579.4 75579.4i 0.771463 0.771463i −0.206899 0.978362i \(-0.566337\pi\)
0.978362 + 0.206899i \(0.0663373\pi\)
\(314\) 11944.0i 0.121141i
\(315\) 13170.4 + 28124.4i 0.132733 + 0.283440i
\(316\) −114804. −1.14970
\(317\) 51889.2 + 51889.2i 0.516367 + 0.516367i 0.916470 0.400103i \(-0.131026\pi\)
−0.400103 + 0.916470i \(0.631026\pi\)
\(318\) −24175.3 + 24175.3i −0.239066 + 0.239066i
\(319\) 19266.8i 0.189334i
\(320\) −28239.7 10226.3i −0.275778 0.0998665i
\(321\) 36380.9 0.353072
\(322\) −16116.3 16116.3i −0.155436 0.155436i
\(323\) −1622.03 + 1622.03i −0.0155473 + 0.0155473i
\(324\) 39091.4i 0.372384i
\(325\) 1567.06 142.248i 0.0148361 0.00134672i
\(326\) 22330.2 0.210115
\(327\) 32490.4 + 32490.4i 0.303851 + 0.303851i
\(328\) 114999. 114999.i 1.06892 1.06892i
\(329\) 23767.6i 0.219580i
\(330\) 1205.20 3328.13i 0.0110671 0.0305614i
\(331\) 53202.6 0.485598 0.242799 0.970077i \(-0.421935\pi\)
0.242799 + 0.970077i \(0.421935\pi\)
\(332\) −60932.0 60932.0i −0.552801 0.552801i
\(333\) 56936.5 56936.5i 0.513455 0.513455i
\(334\) 102482.i 0.918657i
\(335\) −170653. + 79915.6i −1.52063 + 0.712101i
\(336\) −4426.51 −0.0392087
\(337\) 95083.4 + 95083.4i 0.837231 + 0.837231i 0.988494 0.151263i \(-0.0483340\pi\)
−0.151263 + 0.988494i \(0.548334\pi\)
\(338\) −42367.4 + 42367.4i −0.370850 + 0.370850i
\(339\) 24128.6i 0.209958i
\(340\) −1402.04 2993.93i −0.0121284 0.0258991i
\(341\) 24599.0 0.211548
\(342\) −20020.4 20020.4i −0.171167 0.171167i
\(343\) −4491.86 + 4491.86i −0.0381802 + 0.0381802i
\(344\) 26371.3i 0.222851i
\(345\) 51447.9 + 18630.6i 0.432244 + 0.156527i
\(346\) −69268.6 −0.578608
\(347\) 74352.3 + 74352.3i 0.617498 + 0.617498i 0.944889 0.327391i \(-0.106169\pi\)
−0.327391 + 0.944889i \(0.606169\pi\)
\(348\) 32609.2 32609.2i 0.269266 0.269266i
\(349\) 100857.i 0.828045i −0.910267 0.414022i \(-0.864124\pi\)
0.910267 0.414022i \(-0.135876\pi\)
\(350\) 15551.5 18656.7i 0.126951 0.152300i
\(351\) −1391.19 −0.0112920
\(352\) −13564.0 13564.0i −0.109472 0.109472i
\(353\) −30072.1 + 30072.1i −0.241332 + 0.241332i −0.817401 0.576069i \(-0.804586\pi\)
0.576069 + 0.817401i \(0.304586\pi\)
\(354\) 13402.2i 0.106947i
\(355\) 32716.3 90345.1i 0.259602 0.716882i
\(356\) 42807.4 0.337768
\(357\) 557.265 + 557.265i 0.00437246 + 0.00437246i
\(358\) −42244.9 + 42244.9i −0.329616 + 0.329616i
\(359\) 12797.6i 0.0992974i −0.998767 0.0496487i \(-0.984190\pi\)
0.998767 0.0496487i \(-0.0158102\pi\)
\(360\) 87936.4 41180.0i 0.678522 0.317747i
\(361\) 89850.9 0.689459
\(362\) 60664.8 + 60664.8i 0.462935 + 0.462935i
\(363\) −37772.0 + 37772.0i −0.286653 + 0.286653i
\(364\) 540.734i 0.00408113i
\(365\) −49470.5 105640.i −0.371331 0.792945i
\(366\) −38773.7 −0.289451
\(367\) −62216.0 62216.0i −0.461924 0.461924i 0.437362 0.899286i \(-0.355913\pi\)
−0.899286 + 0.437362i \(0.855913\pi\)
\(368\) 26560.7 26560.7i 0.196130 0.196130i
\(369\) 188376.i 1.38348i
\(370\) −59211.8 21442.1i −0.432518 0.156626i
\(371\) −80861.5 −0.587481
\(372\) −41634.0 41634.0i −0.300858 0.300858i
\(373\) 47558.2 47558.2i 0.341828 0.341828i −0.515226 0.857054i \(-0.672292\pi\)
0.857054 + 0.515226i \(0.172292\pi\)
\(374\) 432.617i 0.00309286i
\(375\) −14816.2 + 56396.1i −0.105360 + 0.401039i
\(376\) −74314.1 −0.525649
\(377\) −1896.95 1896.95i −0.0133467 0.0133467i
\(378\) −15184.5 + 15184.5i −0.106272 + 0.106272i
\(379\) 109716.i 0.763817i 0.924200 + 0.381909i \(0.124733\pi\)
−0.924200 + 0.381909i \(0.875267\pi\)
\(380\) 19859.0 54840.2i 0.137528 0.379780i
\(381\) −3995.04 −0.0275215
\(382\) −22886.0 22886.0i −0.156835 0.156835i
\(383\) −93866.2 + 93866.2i −0.639899 + 0.639899i −0.950530 0.310631i \(-0.899460\pi\)
0.310631 + 0.950530i \(0.399460\pi\)
\(384\) 53938.5i 0.365794i
\(385\) 7581.55 3550.39i 0.0511490 0.0239527i
\(386\) −20000.1 −0.134232
\(387\) 21599.0 + 21599.0i 0.144215 + 0.144215i
\(388\) −115199. + 115199.i −0.765219 + 0.765219i
\(389\) 111194.i 0.734821i −0.930059 0.367410i \(-0.880244\pi\)
0.930059 0.367410i \(-0.119756\pi\)
\(390\) 209.017 + 446.338i 0.00137421 + 0.00293451i
\(391\) −6687.60 −0.0437438
\(392\) 14044.7 + 14044.7i 0.0913987 + 0.0913987i
\(393\) 13066.5 13066.5i 0.0846007 0.0846007i
\(394\) 63.6233i 0.000409849i
\(395\) −232698. 84265.8i −1.49141 0.540079i
\(396\) 14064.5 0.0896882
\(397\) 56827.1 + 56827.1i 0.360557 + 0.360557i 0.864018 0.503461i \(-0.167940\pi\)
−0.503461 + 0.864018i \(0.667940\pi\)
\(398\) −91378.7 + 91378.7i −0.576871 + 0.576871i
\(399\) 13903.9i 0.0873354i
\(400\) 30747.5 + 25629.9i 0.192172 + 0.160187i
\(401\) 160496. 0.998104 0.499052 0.866572i \(-0.333682\pi\)
0.499052 + 0.866572i \(0.333682\pi\)
\(402\) −41735.5 41735.5i −0.258258 0.258258i
\(403\) −2421.94 + 2421.94i −0.0149126 + 0.0149126i
\(404\) 192873.i 1.18171i
\(405\) −28692.9 + 79234.6i −0.174930 + 0.483064i
\(406\) −41409.6 −0.251217
\(407\) −15348.5 15348.5i −0.0926569 0.0926569i
\(408\) 1742.40 1742.40i 0.0104671 0.0104671i
\(409\) 135898.i 0.812396i 0.913785 + 0.406198i \(0.133146\pi\)
−0.913785 + 0.406198i \(0.866854\pi\)
\(410\) 133423. 62480.9i 0.793710 0.371689i
\(411\) 70802.3 0.419144
\(412\) −90255.0 90255.0i −0.531713 0.531713i
\(413\) −22413.9 + 22413.9i −0.131407 + 0.131407i
\(414\) 82543.5i 0.481595i
\(415\) −78779.6 168227.i −0.457423 0.976787i
\(416\) 2670.94 0.0154339
\(417\) 15893.7 + 15893.7i 0.0914016 + 0.0914016i
\(418\) −5396.94 + 5396.94i −0.0308884 + 0.0308884i
\(419\) 16910.3i 0.0963216i −0.998840 0.0481608i \(-0.984664\pi\)
0.998840 0.0481608i \(-0.0153360\pi\)
\(420\) −18840.9 6822.77i −0.106808 0.0386778i
\(421\) −169177. −0.954500 −0.477250 0.878768i \(-0.658366\pi\)
−0.477250 + 0.878768i \(0.658366\pi\)
\(422\) 11855.0 + 11855.0i 0.0665696 + 0.0665696i
\(423\) 60865.8 60865.8i 0.340168 0.340168i
\(424\) 252830.i 1.40636i
\(425\) −644.267 7097.51i −0.00356687 0.0392942i
\(426\) 30096.3 0.165842
\(427\) −64845.1 64845.1i −0.355649 0.355649i
\(428\) 79943.8 79943.8i 0.436413 0.436413i
\(429\) 169.877i 0.000923041i
\(430\) 8134.12 22462.1i 0.0439920 0.121483i
\(431\) 317161. 1.70736 0.853680 0.520797i \(-0.174365\pi\)
0.853680 + 0.520797i \(0.174365\pi\)
\(432\) −25025.1 25025.1i −0.134094 0.134094i
\(433\) 32567.7 32567.7i 0.173704 0.173704i −0.614900 0.788605i \(-0.710804\pi\)
0.788605 + 0.614900i \(0.210804\pi\)
\(434\) 52869.9i 0.280691i
\(435\) 90030.8 42160.8i 0.475787 0.222808i
\(436\) 142790. 0.751146
\(437\) −83428.5 83428.5i −0.436869 0.436869i
\(438\) 25835.7 25835.7i 0.134671 0.134671i
\(439\) 144941.i 0.752078i −0.926604 0.376039i \(-0.877286\pi\)
0.926604 0.376039i \(-0.122714\pi\)
\(440\) −11101.0 23705.2i −0.0573399 0.122444i
\(441\) −23006.2 −0.118295
\(442\) −42.5941 42.5941i −0.000218024 0.000218024i
\(443\) −122190. + 122190.i −0.622625 + 0.622625i −0.946202 0.323577i \(-0.895115\pi\)
0.323577 + 0.946202i \(0.395115\pi\)
\(444\) 51954.9i 0.263549i
\(445\) 86766.5 + 31420.4i 0.438160 + 0.158669i
\(446\) 204131. 1.02622
\(447\) −40130.3 40130.3i −0.200843 0.200843i
\(448\) 15732.9 15732.9i 0.0783887 0.0783887i
\(449\) 256403.i 1.27184i −0.771757 0.635918i \(-0.780622\pi\)
0.771757 0.635918i \(-0.219378\pi\)
\(450\) 87602.9 7952.03i 0.432607 0.0392693i
\(451\) 50781.0 0.249659
\(452\) 53020.5 + 53020.5i 0.259517 + 0.259517i
\(453\) 101249. 101249.i 0.493396 0.493396i
\(454\) 31603.4i 0.153328i
\(455\) −396.896 + 1096.02i −0.00191714 + 0.00529412i
\(456\) 43473.3 0.209070
\(457\) 161721. + 161721.i 0.774344 + 0.774344i 0.978863 0.204519i \(-0.0655629\pi\)
−0.204519 + 0.978863i \(0.565563\pi\)
\(458\) 32161.0 32161.0i 0.153320 0.153320i
\(459\) 6300.96i 0.0299076i
\(460\) 153991. 72113.1i 0.727748 0.340799i
\(461\) −15976.3 −0.0751753 −0.0375877 0.999293i \(-0.511967\pi\)
−0.0375877 + 0.999293i \(0.511967\pi\)
\(462\) 1854.17 + 1854.17i 0.00868693 + 0.00868693i
\(463\) −272415. + 272415.i −1.27078 + 1.27078i −0.325094 + 0.945682i \(0.605396\pi\)
−0.945682 + 0.325094i \(0.894604\pi\)
\(464\) 68245.8i 0.316986i
\(465\) −53829.0 114947.i −0.248949 0.531609i
\(466\) 42483.4 0.195635
\(467\) −204044. 204044.i −0.935598 0.935598i 0.0624499 0.998048i \(-0.480109\pi\)
−0.998048 + 0.0624499i \(0.980109\pi\)
\(468\) −1384.75 + 1384.75i −0.00632237 + 0.00632237i
\(469\) 139597.i 0.634644i
\(470\) −63298.1 22921.9i −0.286546 0.103766i
\(471\) −21242.3 −0.0957547
\(472\) 70081.5 + 70081.5i 0.314571 + 0.314571i
\(473\) 5822.50 5822.50i 0.0260248 0.0260248i
\(474\) 77517.7i 0.345020i
\(475\) 80504.8 96579.4i 0.356808 0.428053i
\(476\) 2449.09 0.0108091
\(477\) −207076. 207076.i −0.910109 0.910109i
\(478\) 119162. 119162.i 0.521533 0.521533i
\(479\) 36564.3i 0.159363i 0.996820 + 0.0796813i \(0.0253903\pi\)
−0.996820 + 0.0796813i \(0.974610\pi\)
\(480\) −33700.9 + 93063.9i −0.146271 + 0.403923i
\(481\) 3022.33 0.0130633
\(482\) 22204.2 + 22204.2i 0.0955741 + 0.0955741i
\(483\) −28662.7 + 28662.7i −0.122863 + 0.122863i
\(484\) 166002.i 0.708633i
\(485\) −318054. + 148942.i −1.35212 + 0.633191i
\(486\) −120314. −0.509383
\(487\) 76566.7 + 76566.7i 0.322836 + 0.322836i 0.849854 0.527018i \(-0.176690\pi\)
−0.527018 + 0.849854i \(0.676690\pi\)
\(488\) −202751. + 202751.i −0.851381 + 0.851381i
\(489\) 39714.0i 0.166083i
\(490\) 7630.74 + 16294.8i 0.0317815 + 0.0678667i
\(491\) 399454. 1.65693 0.828464 0.560043i \(-0.189215\pi\)
0.828464 + 0.560043i \(0.189215\pi\)
\(492\) −85947.1 85947.1i −0.355059 0.355059i
\(493\) −8591.65 + 8591.65i −0.0353494 + 0.0353494i
\(494\) 1062.73i 0.00435482i
\(495\) 28507.5 + 10323.3i 0.116345 + 0.0421317i
\(496\) −87133.2 −0.354177
\(497\) 50333.1 + 50333.1i 0.203770 + 0.203770i
\(498\) 41142.2 41142.2i 0.165893 0.165893i
\(499\) 17571.0i 0.0705658i −0.999377 0.0352829i \(-0.988767\pi\)
0.999377 0.0352829i \(-0.0112332\pi\)
\(500\) 91368.4 + 156483.i 0.365473 + 0.625932i
\(501\) −182263. −0.726145
\(502\) 73623.4 + 73623.4i 0.292152 + 0.292152i
\(503\) −131869. + 131869.i −0.521202 + 0.521202i −0.917934 0.396732i \(-0.870144\pi\)
0.396732 + 0.917934i \(0.370144\pi\)
\(504\) 71933.4i 0.283185i
\(505\) −141568. + 390936.i −0.555114 + 1.53293i
\(506\) −22251.5 −0.0869075
\(507\) 75350.2 + 75350.2i 0.293135 + 0.293135i
\(508\) −8778.76 + 8778.76i −0.0340178 + 0.0340178i
\(509\) 127171.i 0.490855i −0.969415 0.245427i \(-0.921072\pi\)
0.969415 0.245427i \(-0.0789283\pi\)
\(510\) 2021.55 946.678i 0.00777221 0.00363967i
\(511\) 86415.4 0.330940
\(512\) 90005.1 + 90005.1i 0.343342 + 0.343342i
\(513\) −78605.2 + 78605.2i −0.298687 + 0.298687i
\(514\) 182321.i 0.690099i
\(515\) −116692. 249185.i −0.439973 0.939524i
\(516\) −19709.2 −0.0740236
\(517\) −16407.8 16407.8i −0.0613858 0.0613858i
\(518\) 32988.1 32988.1i 0.122941 0.122941i
\(519\) 123194.i 0.457356i
\(520\) 3426.91 + 1240.97i 0.0126735 + 0.00458940i
\(521\) −91618.7 −0.337527 −0.168764 0.985657i \(-0.553977\pi\)
−0.168764 + 0.985657i \(0.553977\pi\)
\(522\) −106045. 106045.i −0.389178 0.389178i
\(523\) 103824. 103824.i 0.379573 0.379573i −0.491375 0.870948i \(-0.663506\pi\)
0.870948 + 0.491375i \(0.163506\pi\)
\(524\) 57425.0i 0.209141i
\(525\) −33180.8 27658.2i −0.120384 0.100347i
\(526\) −89476.2 −0.323397
\(527\) 10969.4 + 10969.4i 0.0394969 + 0.0394969i
\(528\) −3055.80 + 3055.80i −0.0109612 + 0.0109612i
\(529\) 64132.6i 0.229175i
\(530\) −77984.3 + 215351.i −0.277623 + 0.766648i
\(531\) −114798. −0.407143
\(532\) 30552.6 + 30552.6i 0.107951 + 0.107951i
\(533\) −4999.73 + 4999.73i −0.0175992 + 0.0175992i
\(534\) 28904.2i 0.101363i
\(535\) 220717. 103360.i 0.771131 0.361115i
\(536\) −436477. −1.51926
\(537\) 75132.2 + 75132.2i 0.260542 + 0.260542i
\(538\) 40613.9 40613.9i 0.140317 0.140317i
\(539\) 6201.84i 0.0213473i
\(540\) −67944.0 145089.i −0.233004 0.497560i
\(541\) −334086. −1.14147 −0.570735 0.821135i \(-0.693342\pi\)
−0.570735 + 0.821135i \(0.693342\pi\)
\(542\) −159488. 159488.i −0.542912 0.542912i
\(543\) 107892. 107892.i 0.365923 0.365923i
\(544\) 12097.2i 0.0408777i
\(545\) 289422. + 104807.i 0.974402 + 0.352856i
\(546\) −365.112 −0.00122473
\(547\) 190383. + 190383.i 0.636287 + 0.636287i 0.949637 0.313351i \(-0.101452\pi\)
−0.313351 + 0.949637i \(0.601452\pi\)
\(548\) 155582. 155582.i 0.518082 0.518082i
\(549\) 332121.i 1.10192i
\(550\) −2143.65 23615.3i −0.00708645 0.0780672i
\(551\) −214363. −0.706069
\(552\) 89619.6 + 89619.6i 0.294120 + 0.294120i
\(553\) 129641. 129641.i 0.423927 0.423927i
\(554\) 270003.i 0.879729i
\(555\) −38134.7 + 105308.i −0.123804 + 0.341880i
\(556\) 69850.2 0.225953
\(557\) −77060.8 77060.8i −0.248384 0.248384i 0.571923 0.820307i \(-0.306197\pi\)
−0.820307 + 0.571923i \(0.806197\pi\)
\(558\) −135393. + 135393.i −0.434839 + 0.434839i
\(559\) 1146.53i 0.00366912i
\(560\) −26854.9 + 12576.0i −0.0856344 + 0.0401020i
\(561\) 769.407 0.00244473
\(562\) −121098. 121098.i −0.383410 0.383410i
\(563\) 285556. 285556.i 0.900897 0.900897i −0.0946167 0.995514i \(-0.530163\pi\)
0.995514 + 0.0946167i \(0.0301625\pi\)
\(564\) 55540.4i 0.174603i
\(565\) 68550.7 + 146384.i 0.214741 + 0.458561i
\(566\) −74372.7 −0.232156
\(567\) −44143.2 44143.2i −0.137309 0.137309i
\(568\) 157376. 157376.i 0.487801 0.487801i
\(569\) 281883.i 0.870650i 0.900273 + 0.435325i \(0.143367\pi\)
−0.900273 + 0.435325i \(0.856633\pi\)
\(570\) 37029.0 + 13409.1i 0.113970 + 0.0412716i
\(571\) −191251. −0.586585 −0.293292 0.956023i \(-0.594751\pi\)
−0.293292 + 0.956023i \(0.594751\pi\)
\(572\) 373.291 + 373.291i 0.00114092 + 0.00114092i
\(573\) −40702.7 + 40702.7i −0.123969 + 0.123969i
\(574\) 109142.i 0.331259i
\(575\) 365057. 33137.6i 1.10414 0.100227i
\(576\) 80580.1 0.242875
\(577\) 394966. + 394966.i 1.18634 + 1.18634i 0.978072 + 0.208265i \(0.0667817\pi\)
0.208265 + 0.978072i \(0.433218\pi\)
\(578\) 123730. 123730.i 0.370355 0.370355i
\(579\) 35570.0i 0.106103i
\(580\) 105190. 290480.i 0.312694 0.863495i
\(581\) 137613. 0.407667
\(582\) −77784.4 77784.4i −0.229639 0.229639i
\(583\) −55822.1 + 55822.1i −0.164236 + 0.164236i
\(584\) 270195.i 0.792230i
\(585\) −3823.16 + 1790.36i −0.0111715 + 0.00523153i
\(586\) 159109. 0.463341
\(587\) 434613. + 434613.i 1.26132 + 1.26132i 0.950452 + 0.310871i \(0.100621\pi\)
0.310871 + 0.950452i \(0.399379\pi\)
\(588\) 10496.6 10496.6i 0.0303596 0.0303596i
\(589\) 273690.i 0.788910i
\(590\) 38076.6 + 81309.3i 0.109384 + 0.233580i
\(591\) −113.154 −0.000323962
\(592\) 54366.6 + 54366.6i 0.155128 + 0.155128i
\(593\) 149520. 149520.i 0.425197 0.425197i −0.461792 0.886988i \(-0.652793\pi\)
0.886988 + 0.461792i \(0.152793\pi\)
\(594\) 20965.0i 0.0594186i
\(595\) 4964.07 + 1797.62i 0.0140218 + 0.00507766i
\(596\) −176366. −0.496503
\(597\) 162516. + 162516.i 0.455983 + 0.455983i
\(598\) 2190.81 2190.81i 0.00612635 0.00612635i
\(599\) 251890.i 0.702033i −0.936369 0.351017i \(-0.885836\pi\)
0.936369 0.351017i \(-0.114164\pi\)
\(600\) −86478.9 + 103746.i −0.240219 + 0.288184i
\(601\) −46644.1 −0.129136 −0.0645681 0.997913i \(-0.520567\pi\)
−0.0645681 + 0.997913i \(0.520567\pi\)
\(602\) 12514.1 + 12514.1i 0.0345308 + 0.0345308i
\(603\) 357490. 357490.i 0.983172 0.983172i
\(604\) 444973.i 1.21972i
\(605\) −121844. + 336470.i −0.332885 + 0.919253i
\(606\) −130231. −0.354625
\(607\) −404387. 404387.i −1.09754 1.09754i −0.994698 0.102841i \(-0.967207\pi\)
−0.102841 0.994698i \(-0.532793\pi\)
\(608\) 150914. 150914.i 0.408245 0.408245i
\(609\) 73646.6i 0.198572i
\(610\) −235234. + 110158.i −0.632180 + 0.296045i
\(611\) 3230.91 0.00865452
\(612\) 6271.80 + 6271.80i 0.0167452 + 0.0167452i
\(613\) −425304. + 425304.i −1.13182 + 1.13182i −0.141950 + 0.989874i \(0.545337\pi\)
−0.989874 + 0.141950i \(0.954663\pi\)
\(614\) 227781.i 0.604199i
\(615\) −111122. 237291.i −0.293798 0.627381i
\(616\) 19391.3 0.0511028
\(617\) −249065. 249065.i −0.654247 0.654247i 0.299766 0.954013i \(-0.403092\pi\)
−0.954013 + 0.299766i \(0.903092\pi\)
\(618\) 60941.7 60941.7i 0.159565 0.159565i
\(619\) 63129.3i 0.164759i −0.996601 0.0823796i \(-0.973748\pi\)
0.996601 0.0823796i \(-0.0262520\pi\)
\(620\) −370871. 134302.i −0.964806 0.349381i
\(621\) −324087. −0.840386
\(622\) 234209. + 234209.i 0.605372 + 0.605372i
\(623\) −48339.4 + 48339.4i −0.124545 + 0.124545i
\(624\) 601.730i 0.00154537i
\(625\) 70337.3 + 384240.i 0.180064 + 0.983655i
\(626\) 224279. 0.572321
\(627\) 9598.43 + 9598.43i 0.0244155 + 0.0244155i
\(628\) −46678.2 + 46678.2i −0.118357 + 0.118357i
\(629\) 13688.7i 0.0345989i
\(630\) −22187.6 + 61270.3i −0.0559022 + 0.154372i
\(631\) 603122. 1.51477 0.757385 0.652969i \(-0.226477\pi\)
0.757385 + 0.652969i \(0.226477\pi\)
\(632\) −405347. 405347.i −1.01483 1.01483i
\(633\) 21084.0 21084.0i 0.0526194 0.0526194i
\(634\) 153979.i 0.383075i
\(635\) −24237.3 + 11350.2i −0.0601086 + 0.0281484i
\(636\) 188958. 0.467145
\(637\) −610.613 610.613i −0.00150483 0.00150483i
\(638\) −28586.7 + 28586.7i −0.0702301 + 0.0702301i
\(639\) 257794.i 0.631350i
\(640\) 153243. + 327237.i 0.374127 + 0.798917i
\(641\) −405370. −0.986587 −0.493293 0.869863i \(-0.664207\pi\)
−0.493293 + 0.869863i \(0.664207\pi\)
\(642\) 53979.4 + 53979.4i 0.130966 + 0.130966i
\(643\) −167231. + 167231.i −0.404478 + 0.404478i −0.879808 0.475330i \(-0.842329\pi\)
0.475330 + 0.879808i \(0.342329\pi\)
\(644\) 125968.i 0.303729i
\(645\) −39948.7 14466.5i −0.0960249 0.0347731i
\(646\) −4813.32 −0.0115340
\(647\) 318214. + 318214.i 0.760170 + 0.760170i 0.976353 0.216183i \(-0.0693607\pi\)
−0.216183 + 0.976353i \(0.569361\pi\)
\(648\) −138023. + 138023.i −0.328700 + 0.328700i
\(649\) 30946.5i 0.0734720i
\(650\) 2536.15 + 2114.03i 0.00600272 + 0.00500363i
\(651\) 94028.7 0.221870
\(652\) −87268.2 87268.2i −0.205287 0.205287i
\(653\) 517979. 517979.i 1.21475 1.21475i 0.245300 0.969447i \(-0.421113\pi\)
0.969447 0.245300i \(-0.0788866\pi\)
\(654\) 96414.1i 0.225416i
\(655\) 42149.7 116395.i 0.0982452 0.271301i
\(656\) −179873. −0.417984
\(657\) 221299. + 221299.i 0.512683 + 0.512683i
\(658\) 35264.7 35264.7i 0.0814495 0.0814495i
\(659\) 378556.i 0.871686i 0.900023 + 0.435843i \(0.143550\pi\)
−0.900023 + 0.435843i \(0.856450\pi\)
\(660\) −17716.7 + 8296.60i −0.0406719 + 0.0190464i
\(661\) −793156. −1.81533 −0.907666 0.419694i \(-0.862137\pi\)
−0.907666 + 0.419694i \(0.862137\pi\)
\(662\) 78938.2 + 78938.2i 0.180124 + 0.180124i
\(663\) −75.7534 + 75.7534i −0.000172336 + 0.000172336i
\(664\) 430273.i 0.975906i
\(665\) 39501.8 + 84352.7i 0.0893251 + 0.190746i
\(666\) 168957. 0.380914
\(667\) −441907. 441907.i −0.993298 0.993298i
\(668\) −400507. + 400507.i −0.897548 + 0.897548i
\(669\) 363045.i 0.811164i
\(670\) −371776. 134630.i −0.828193 0.299910i
\(671\) −89530.6 −0.198850
\(672\) −51847.8 51847.8i −0.114813 0.114813i
\(673\) −277903. + 277903.i −0.613570 + 0.613570i −0.943874 0.330305i \(-0.892848\pi\)
0.330305 + 0.943874i \(0.392848\pi\)
\(674\) 282156.i 0.621112i
\(675\) −31221.7 343952.i −0.0685251 0.754901i
\(676\) 331151. 0.724657
\(677\) −244917. 244917.i −0.534369 0.534369i 0.387501 0.921869i \(-0.373338\pi\)
−0.921869 + 0.387501i \(0.873338\pi\)
\(678\) −35800.3 + 35800.3i −0.0778802 + 0.0778802i
\(679\) 260173.i 0.564317i
\(680\) 5620.61 15521.1i 0.0121553 0.0335665i
\(681\) 56206.5 0.121197
\(682\) 36498.3 + 36498.3i 0.0784700 + 0.0784700i
\(683\) −504443. + 504443.i −1.08136 + 1.08136i −0.0849785 + 0.996383i \(0.527082\pi\)
−0.996383 + 0.0849785i \(0.972918\pi\)
\(684\) 156483.i 0.334468i
\(685\) 429547. 201154.i 0.915438 0.428693i
\(686\) −13329.4 −0.0283245
\(687\) −57198.1 57198.1i −0.121190 0.121190i
\(688\) −20624.1 + 20624.1i −0.0435711 + 0.0435711i
\(689\) 10992.1i 0.0231549i
\(690\) 48692.0 + 103978.i 0.102273 + 0.218394i
\(691\) 452722. 0.948146 0.474073 0.880486i \(-0.342783\pi\)
0.474073 + 0.880486i \(0.342783\pi\)
\(692\) 270708. + 270708.i 0.565312 + 0.565312i
\(693\) −15882.1 + 15882.1i −0.0330706 + 0.0330706i
\(694\) 220638.i 0.458100i
\(695\) 141580. + 51269.7i 0.293111 + 0.106143i
\(696\) 230271. 0.475358
\(697\) 22644.7 + 22644.7i 0.0466124 + 0.0466124i
\(698\) 149644. 149644.i 0.307149 0.307149i
\(699\) 75556.4i 0.154638i
\(700\) −133689. + 12135.4i −0.272834 + 0.0247661i
\(701\) −430640. −0.876352 −0.438176 0.898889i \(-0.644375\pi\)
−0.438176 + 0.898889i \(0.644375\pi\)
\(702\) −2064.15 2064.15i −0.00418858 0.00418858i
\(703\) 170768. 170768.i 0.345539 0.345539i
\(704\) 21722.2i 0.0438287i
\(705\) −40766.4 + 112575.i −0.0820209 + 0.226498i
\(706\) −89237.7 −0.179035
\(707\) −217798. 217798.i −0.435729 0.435729i
\(708\) 52377.1 52377.1i 0.104490 0.104490i
\(709\) 232388.i 0.462298i 0.972918 + 0.231149i \(0.0742484\pi\)
−0.972918 + 0.231149i \(0.925752\pi\)
\(710\) 182590. 85505.5i 0.362209 0.169620i
\(711\) 663987. 1.31347
\(712\) 151143. + 151143.i 0.298145 + 0.298145i
\(713\) −564208. + 564208.i −1.10984 + 1.10984i
\(714\) 1653.66i 0.00324377i
\(715\) 482.632 + 1030.62i 0.000944070 + 0.00201598i
\(716\) 330193. 0.644084
\(717\) −211929. 211929.i −0.412242 0.412242i
\(718\) 18988.1 18988.1i 0.0368326 0.0368326i
\(719\) 684958.i 1.32497i 0.749075 + 0.662485i \(0.230498\pi\)
−0.749075 + 0.662485i \(0.769502\pi\)
\(720\) −100978. 36566.6i −0.194787 0.0705375i
\(721\) 203838. 0.392115
\(722\) 133315. + 133315.i 0.255743 + 0.255743i
\(723\) 39489.9 39489.9i 0.0755457 0.0755457i
\(724\) 474167.i 0.904595i
\(725\) 426421. 511566.i 0.811265 0.973252i
\(726\) −112087. −0.212658
\(727\) −344257. 344257.i −0.651350 0.651350i 0.301968 0.953318i \(-0.402356\pi\)
−0.953318 + 0.301968i \(0.902356\pi\)
\(728\) −1909.20 + 1909.20i −0.00360238 + 0.00360238i
\(729\) 59055.9i 0.111124i
\(730\) 83340.5 230142.i 0.156390 0.431868i
\(731\) 5192.85 0.00971787
\(732\) 151531. + 151531.i 0.282800 + 0.282800i
\(733\) 458945. 458945.i 0.854186 0.854186i −0.136460 0.990646i \(-0.543572\pi\)
0.990646 + 0.136460i \(0.0435724\pi\)
\(734\) 184624.i 0.342685i
\(735\) 28980.2 13571.2i 0.0536447 0.0251214i
\(736\) 622213. 1.14864
\(737\) −96369.6 96369.6i −0.177421 0.177421i
\(738\) −279499. + 279499.i −0.513177 + 0.513177i
\(739\) 61500.0i 0.112612i −0.998414 0.0563062i \(-0.982068\pi\)
0.998414 0.0563062i \(-0.0179323\pi\)
\(740\) 147607. + 315202.i 0.269553 + 0.575607i
\(741\) −1890.06 −0.00344223
\(742\) −119977. 119977.i −0.217916 0.217916i
\(743\) 33421.8 33421.8i 0.0605414 0.0605414i −0.676188 0.736729i \(-0.736369\pi\)
0.736729 + 0.676188i \(0.236369\pi\)
\(744\) 294000.i 0.531130i
\(745\) −357477. 129452.i −0.644073 0.233236i
\(746\) 141127. 0.253590
\(747\) 352409. + 352409.i 0.631546 + 0.631546i
\(748\) 1690.71 1690.71i 0.00302179 0.00302179i
\(749\) 180550.i 0.321836i
\(750\) −105660. + 61693.4i −0.187840 + 0.109677i
\(751\) 257993. 0.457434 0.228717 0.973493i \(-0.426547\pi\)
0.228717 + 0.973493i \(0.426547\pi\)
\(752\) 58118.6 + 58118.6i 0.102773 + 0.102773i
\(753\) 130939. 130939.i 0.230929 0.230929i
\(754\) 5629.12i 0.00990143i
\(755\) 326608. 901919.i 0.572972 1.58225i
\(756\) 118685. 0.207660
\(757\) −783812. 783812.i −1.36779 1.36779i −0.863581 0.504211i \(-0.831783\pi\)
−0.504211 0.863581i \(-0.668217\pi\)
\(758\) −162788. + 162788.i −0.283325 + 0.283325i
\(759\) 39574.1i 0.0686954i
\(760\) 263745. 123510.i 0.456623 0.213833i
\(761\) 614396. 1.06091 0.530456 0.847713i \(-0.322021\pi\)
0.530456 + 0.847713i \(0.322021\pi\)
\(762\) −5927.56 5927.56i −0.0102086 0.0102086i
\(763\) −161243. + 161243.i −0.276969 + 0.276969i
\(764\) 178881.i 0.306463i
\(765\) 8108.88 + 17315.8i 0.0138560 + 0.0295883i
\(766\) −278544. −0.474719
\(767\) −3046.89 3046.89i −0.00517925 0.00517925i
\(768\) −130753. + 130753.i −0.221682 + 0.221682i
\(769\) 232260.i 0.392755i 0.980528 + 0.196377i \(0.0629177\pi\)
−0.980528 + 0.196377i \(0.937082\pi\)
\(770\) 16516.8 + 5981.16i 0.0278576 + 0.0100880i
\(771\) 324258. 0.545483
\(772\) 78162.1 + 78162.1i 0.131148 + 0.131148i
\(773\) 654735. 654735.i 1.09574 1.09574i 0.100834 0.994903i \(-0.467849\pi\)
0.994903 0.100834i \(-0.0321510\pi\)
\(774\) 64094.2i 0.106988i
\(775\) −653144. 544436.i −1.08744 0.906448i