Properties

Label 74.5.d.a.31.6
Level $74$
Weight $5$
Character 74.31
Analytic conductor $7.649$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 74.d (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.64937726820\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} + \cdots)\)
Defining polynomial: \(x^{14} + 727 x^{12} + 198453 x^{10} + 24875201 x^{8} + 1392846203 x^{6} + 29089700589 x^{4} + 220261242916 x^{2} + 446074380544\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.6
Root \(13.3074i\) of defining polynomial
Character \(\chi\) \(=\) 74.31
Dual form 74.5.d.a.43.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.00000 - 2.00000i) q^{2} +12.3074i q^{3} +8.00000i q^{4} +(10.7621 - 10.7621i) q^{5} +(24.6148 - 24.6148i) q^{6} +35.0611 q^{7} +(16.0000 - 16.0000i) q^{8} -70.4723 q^{9} +O(q^{10})\) \(q+(-2.00000 - 2.00000i) q^{2} +12.3074i q^{3} +8.00000i q^{4} +(10.7621 - 10.7621i) q^{5} +(24.6148 - 24.6148i) q^{6} +35.0611 q^{7} +(16.0000 - 16.0000i) q^{8} -70.4723 q^{9} -43.0483 q^{10} +142.240i q^{11} -98.4593 q^{12} +(-181.910 + 181.910i) q^{13} +(-70.1223 - 70.1223i) q^{14} +(132.453 + 132.453i) q^{15} -64.0000 q^{16} +(-88.0634 + 88.0634i) q^{17} +(140.945 + 140.945i) q^{18} +(13.8864 - 13.8864i) q^{19} +(86.0967 + 86.0967i) q^{20} +431.512i q^{21} +(284.479 - 284.479i) q^{22} +(79.7242 - 79.7242i) q^{23} +(196.919 + 196.919i) q^{24} +393.355i q^{25} +727.640 q^{26} +129.569i q^{27} +280.489i q^{28} +(420.383 + 420.383i) q^{29} -529.813i q^{30} +(-624.657 - 624.657i) q^{31} +(128.000 + 128.000i) q^{32} -1750.60 q^{33} +352.253 q^{34} +(377.331 - 377.331i) q^{35} -563.778i q^{36} +(-7.65345 - 1368.98i) q^{37} -55.5457 q^{38} +(-2238.84 - 2238.84i) q^{39} -344.387i q^{40} +1239.16i q^{41} +(863.024 - 863.024i) q^{42} +(607.562 - 607.562i) q^{43} -1137.92 q^{44} +(-758.428 + 758.428i) q^{45} -318.897 q^{46} +2971.58 q^{47} -787.674i q^{48} -1171.72 q^{49} +(786.710 - 786.710i) q^{50} +(-1083.83 - 1083.83i) q^{51} +(-1455.28 - 1455.28i) q^{52} +1041.64 q^{53} +(259.138 - 259.138i) q^{54} +(1530.80 + 1530.80i) q^{55} +(560.978 - 560.978i) q^{56} +(170.906 + 170.906i) q^{57} -1681.53i q^{58} +(1896.67 - 1896.67i) q^{59} +(-1059.63 + 1059.63i) q^{60} +(4012.39 + 4012.39i) q^{61} +2498.63i q^{62} -2470.84 q^{63} -512.000i q^{64} +3915.46i q^{65} +(3501.20 + 3501.20i) q^{66} +2338.93i q^{67} +(-704.507 - 704.507i) q^{68} +(981.198 + 981.198i) q^{69} -1509.32 q^{70} +3648.82 q^{71} +(-1127.56 + 1127.56i) q^{72} -9943.51i q^{73} +(-2722.65 + 2753.26i) q^{74} -4841.18 q^{75} +(111.091 + 111.091i) q^{76} +4987.09i q^{77} +8955.36i q^{78} +(6403.03 - 6403.03i) q^{79} +(-688.773 + 688.773i) q^{80} -7302.91 q^{81} +(2478.31 - 2478.31i) q^{82} -7154.52 q^{83} -3452.09 q^{84} +1895.49i q^{85} -2430.25 q^{86} +(-5173.82 + 5173.82i) q^{87} +(2275.84 + 2275.84i) q^{88} +(2259.76 + 2259.76i) q^{89} +3033.71 q^{90} +(-6377.97 + 6377.97i) q^{91} +(637.794 + 637.794i) q^{92} +(7687.91 - 7687.91i) q^{93} +(-5943.15 - 5943.15i) q^{94} -298.893i q^{95} +(-1575.35 + 1575.35i) q^{96} +(8558.26 - 8558.26i) q^{97} +(2343.43 + 2343.43i) q^{98} -10024.0i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + O(q^{10}) \) \( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 2.00000i −0.500000 0.500000i
\(3\) 12.3074i 1.36749i 0.729721 + 0.683745i \(0.239650\pi\)
−0.729721 + 0.683745i \(0.760350\pi\)
\(4\) 8.00000i 0.500000i
\(5\) 10.7621 10.7621i 0.430483 0.430483i −0.458309 0.888793i \(-0.651545\pi\)
0.888793 + 0.458309i \(0.151545\pi\)
\(6\) 24.6148 24.6148i 0.683745 0.683745i
\(7\) 35.0611 0.715534 0.357767 0.933811i \(-0.383538\pi\)
0.357767 + 0.933811i \(0.383538\pi\)
\(8\) 16.0000 16.0000i 0.250000 0.250000i
\(9\) −70.4723 −0.870028
\(10\) −43.0483 −0.430483
\(11\) 142.240i 1.17553i 0.809030 + 0.587767i \(0.199993\pi\)
−0.809030 + 0.587767i \(0.800007\pi\)
\(12\) −98.4593 −0.683745
\(13\) −181.910 + 181.910i −1.07639 + 1.07639i −0.0795603 + 0.996830i \(0.525352\pi\)
−0.996830 + 0.0795603i \(0.974648\pi\)
\(14\) −70.1223 70.1223i −0.357767 0.357767i
\(15\) 132.453 + 132.453i 0.588681 + 0.588681i
\(16\) −64.0000 −0.250000
\(17\) −88.0634 + 88.0634i −0.304718 + 0.304718i −0.842856 0.538139i \(-0.819128\pi\)
0.538139 + 0.842856i \(0.319128\pi\)
\(18\) 140.945 + 140.945i 0.435014 + 0.435014i
\(19\) 13.8864 13.8864i 0.0384665 0.0384665i −0.687612 0.726078i \(-0.741341\pi\)
0.726078 + 0.687612i \(0.241341\pi\)
\(20\) 86.0967 + 86.0967i 0.215242 + 0.215242i
\(21\) 431.512i 0.978485i
\(22\) 284.479 284.479i 0.587767 0.587767i
\(23\) 79.7242 79.7242i 0.150707 0.150707i −0.627727 0.778434i \(-0.716014\pi\)
0.778434 + 0.627727i \(0.216014\pi\)
\(24\) 196.919 + 196.919i 0.341872 + 0.341872i
\(25\) 393.355i 0.629368i
\(26\) 727.640 1.07639
\(27\) 129.569i 0.177735i
\(28\) 280.489i 0.357767i
\(29\) 420.383 + 420.383i 0.499861 + 0.499861i 0.911395 0.411534i \(-0.135007\pi\)
−0.411534 + 0.911395i \(0.635007\pi\)
\(30\) 529.813i 0.588681i
\(31\) −624.657 624.657i −0.650007 0.650007i 0.302987 0.952995i \(-0.402016\pi\)
−0.952995 + 0.302987i \(0.902016\pi\)
\(32\) 128.000 + 128.000i 0.125000 + 0.125000i
\(33\) −1750.60 −1.60753
\(34\) 352.253 0.304718
\(35\) 377.331 377.331i 0.308025 0.308025i
\(36\) 563.778i 0.435014i
\(37\) −7.65345 1368.98i −0.00559054 0.999984i
\(38\) −55.5457 −0.0384665
\(39\) −2238.84 2238.84i −1.47195 1.47195i
\(40\) 344.387i 0.215242i
\(41\) 1239.16i 0.737154i 0.929597 + 0.368577i \(0.120155\pi\)
−0.929597 + 0.368577i \(0.879845\pi\)
\(42\) 863.024 863.024i 0.489242 0.489242i
\(43\) 607.562 607.562i 0.328590 0.328590i −0.523460 0.852050i \(-0.675359\pi\)
0.852050 + 0.523460i \(0.175359\pi\)
\(44\) −1137.92 −0.587767
\(45\) −758.428 + 758.428i −0.374533 + 0.374533i
\(46\) −318.897 −0.150707
\(47\) 2971.58 1.34521 0.672607 0.740000i \(-0.265175\pi\)
0.672607 + 0.740000i \(0.265175\pi\)
\(48\) 787.674i 0.341872i
\(49\) −1171.72 −0.488012
\(50\) 786.710 786.710i 0.314684 0.314684i
\(51\) −1083.83 1083.83i −0.416698 0.416698i
\(52\) −1455.28 1455.28i −0.538195 0.538195i
\(53\) 1041.64 0.370822 0.185411 0.982661i \(-0.440638\pi\)
0.185411 + 0.982661i \(0.440638\pi\)
\(54\) 259.138 259.138i 0.0888676 0.0888676i
\(55\) 1530.80 + 1530.80i 0.506048 + 0.506048i
\(56\) 560.978 560.978i 0.178883 0.178883i
\(57\) 170.906 + 170.906i 0.0526026 + 0.0526026i
\(58\) 1681.53i 0.499861i
\(59\) 1896.67 1896.67i 0.544863 0.544863i −0.380087 0.924951i \(-0.624106\pi\)
0.924951 + 0.380087i \(0.124106\pi\)
\(60\) −1059.63 + 1059.63i −0.294341 + 0.294341i
\(61\) 4012.39 + 4012.39i 1.07831 + 1.07831i 0.996661 + 0.0816497i \(0.0260189\pi\)
0.0816497 + 0.996661i \(0.473981\pi\)
\(62\) 2498.63i 0.650007i
\(63\) −2470.84 −0.622534
\(64\) 512.000i 0.125000i
\(65\) 3915.46i 0.926736i
\(66\) 3501.20 + 3501.20i 0.803766 + 0.803766i
\(67\) 2338.93i 0.521037i 0.965469 + 0.260518i \(0.0838934\pi\)
−0.965469 + 0.260518i \(0.916107\pi\)
\(68\) −704.507 704.507i −0.152359 0.152359i
\(69\) 981.198 + 981.198i 0.206091 + 0.206091i
\(70\) −1509.32 −0.308025
\(71\) 3648.82 0.723830 0.361915 0.932211i \(-0.382123\pi\)
0.361915 + 0.932211i \(0.382123\pi\)
\(72\) −1127.56 + 1127.56i −0.217507 + 0.217507i
\(73\) 9943.51i 1.86592i −0.359976 0.932962i \(-0.617215\pi\)
0.359976 0.932962i \(-0.382785\pi\)
\(74\) −2722.65 + 2753.26i −0.497197 + 0.502787i
\(75\) −4841.18 −0.860655
\(76\) 111.091 + 111.091i 0.0192333 + 0.0192333i
\(77\) 4987.09i 0.841135i
\(78\) 8955.36i 1.47195i
\(79\) 6403.03 6403.03i 1.02596 1.02596i 0.0263085 0.999654i \(-0.491625\pi\)
0.999654 0.0263085i \(-0.00837522\pi\)
\(80\) −688.773 + 688.773i −0.107621 + 0.107621i
\(81\) −7302.91 −1.11308
\(82\) 2478.31 2478.31i 0.368577 0.368577i
\(83\) −7154.52 −1.03854 −0.519271 0.854610i \(-0.673797\pi\)
−0.519271 + 0.854610i \(0.673797\pi\)
\(84\) −3452.09 −0.489242
\(85\) 1895.49i 0.262352i
\(86\) −2430.25 −0.328590
\(87\) −5173.82 + 5173.82i −0.683555 + 0.683555i
\(88\) 2275.84 + 2275.84i 0.293884 + 0.293884i
\(89\) 2259.76 + 2259.76i 0.285287 + 0.285287i 0.835213 0.549926i \(-0.185344\pi\)
−0.549926 + 0.835213i \(0.685344\pi\)
\(90\) 3033.71 0.374533
\(91\) −6377.97 + 6377.97i −0.770193 + 0.770193i
\(92\) 637.794 + 637.794i 0.0753537 + 0.0753537i
\(93\) 7687.91 7687.91i 0.888878 0.888878i
\(94\) −5943.15 5943.15i −0.672607 0.672607i
\(95\) 298.893i 0.0331184i
\(96\) −1575.35 + 1575.35i −0.170936 + 0.170936i
\(97\) 8558.26 8558.26i 0.909583 0.909583i −0.0866556 0.996238i \(-0.527618\pi\)
0.996238 + 0.0866556i \(0.0276180\pi\)
\(98\) 2343.43 + 2343.43i 0.244006 + 0.244006i
\(99\) 10024.0i 1.02275i
\(100\) −3146.84 −0.314684
\(101\) 12369.2i 1.21255i 0.795256 + 0.606274i \(0.207336\pi\)
−0.795256 + 0.606274i \(0.792664\pi\)
\(102\) 4335.33i 0.416698i
\(103\) −5805.26 5805.26i −0.547202 0.547202i 0.378429 0.925630i \(-0.376465\pi\)
−0.925630 + 0.378429i \(0.876465\pi\)
\(104\) 5821.12i 0.538195i
\(105\) 4643.97 + 4643.97i 0.421221 + 0.421221i
\(106\) −2083.28 2083.28i −0.185411 0.185411i
\(107\) 3685.46 0.321903 0.160951 0.986962i \(-0.448544\pi\)
0.160951 + 0.986962i \(0.448544\pi\)
\(108\) −1036.55 −0.0888676
\(109\) 9605.82 9605.82i 0.808502 0.808502i −0.175905 0.984407i \(-0.556285\pi\)
0.984407 + 0.175905i \(0.0562851\pi\)
\(110\) 6123.18i 0.506048i
\(111\) 16848.6 94.1941i 1.36747 0.00764500i
\(112\) −2243.91 −0.178883
\(113\) 4922.36 + 4922.36i 0.385493 + 0.385493i 0.873076 0.487583i \(-0.162121\pi\)
−0.487583 + 0.873076i \(0.662121\pi\)
\(114\) 683.623i 0.0526026i
\(115\) 1716.00i 0.129754i
\(116\) −3363.06 + 3363.06i −0.249930 + 0.249930i
\(117\) 12819.6 12819.6i 0.936490 0.936490i
\(118\) −7586.67 −0.544863
\(119\) −3087.60 + 3087.60i −0.218036 + 0.218036i
\(120\) 4238.51 0.294341
\(121\) −5591.14 −0.381882
\(122\) 16049.6i 1.07831i
\(123\) −15250.8 −1.00805
\(124\) 4997.26 4997.26i 0.325004 0.325004i
\(125\) 10959.6 + 10959.6i 0.701416 + 0.701416i
\(126\) 4941.68 + 4941.68i 0.311267 + 0.311267i
\(127\) −23426.1 −1.45242 −0.726211 0.687472i \(-0.758721\pi\)
−0.726211 + 0.687472i \(0.758721\pi\)
\(128\) −1024.00 + 1024.00i −0.0625000 + 0.0625000i
\(129\) 7477.51 + 7477.51i 0.449343 + 0.449343i
\(130\) 7830.92 7830.92i 0.463368 0.463368i
\(131\) −4160.42 4160.42i −0.242435 0.242435i 0.575422 0.817857i \(-0.304838\pi\)
−0.817857 + 0.575422i \(0.804838\pi\)
\(132\) 14004.8i 0.803766i
\(133\) 486.874 486.874i 0.0275241 0.0275241i
\(134\) 4677.87 4677.87i 0.260518 0.260518i
\(135\) 1394.43 + 1394.43i 0.0765121 + 0.0765121i
\(136\) 2818.03i 0.152359i
\(137\) −22901.6 −1.22018 −0.610092 0.792331i \(-0.708867\pi\)
−0.610092 + 0.792331i \(0.708867\pi\)
\(138\) 3924.79i 0.206091i
\(139\) 30870.3i 1.59776i −0.601492 0.798879i \(-0.705427\pi\)
0.601492 0.798879i \(-0.294573\pi\)
\(140\) 3018.65 + 3018.65i 0.154013 + 0.154013i
\(141\) 36572.4i 1.83957i
\(142\) −7297.65 7297.65i −0.361915 0.361915i
\(143\) −25874.8 25874.8i −1.26533 1.26533i
\(144\) 4510.23 0.217507
\(145\) 9048.39 0.430364
\(146\) −19887.0 + 19887.0i −0.932962 + 0.932962i
\(147\) 14420.8i 0.667351i
\(148\) 10951.8 61.2276i 0.499992 0.00279527i
\(149\) 23301.1 1.04955 0.524776 0.851240i \(-0.324149\pi\)
0.524776 + 0.851240i \(0.324149\pi\)
\(150\) 9682.37 + 9682.37i 0.430327 + 0.430327i
\(151\) 20776.6i 0.911214i 0.890181 + 0.455607i \(0.150578\pi\)
−0.890181 + 0.455607i \(0.849422\pi\)
\(152\) 444.365i 0.0192333i
\(153\) 6206.03 6206.03i 0.265113 0.265113i
\(154\) 9974.17 9974.17i 0.420567 0.420567i
\(155\) −13445.2 −0.559635
\(156\) 17910.7 17910.7i 0.735976 0.735976i
\(157\) −44450.2 −1.80333 −0.901663 0.432440i \(-0.857653\pi\)
−0.901663 + 0.432440i \(0.857653\pi\)
\(158\) −25612.1 −1.02596
\(159\) 12819.9i 0.507096i
\(160\) 2755.09 0.107621
\(161\) 2795.22 2795.22i 0.107836 0.107836i
\(162\) 14605.8 + 14605.8i 0.556540 + 0.556540i
\(163\) 9806.05 + 9806.05i 0.369079 + 0.369079i 0.867141 0.498063i \(-0.165955\pi\)
−0.498063 + 0.867141i \(0.665955\pi\)
\(164\) −9913.25 −0.368577
\(165\) −18840.1 + 18840.1i −0.692016 + 0.692016i
\(166\) 14309.0 + 14309.0i 0.519271 + 0.519271i
\(167\) 25412.6 25412.6i 0.911207 0.911207i −0.0851606 0.996367i \(-0.527140\pi\)
0.996367 + 0.0851606i \(0.0271403\pi\)
\(168\) 6904.19 + 6904.19i 0.244621 + 0.244621i
\(169\) 37621.5i 1.31723i
\(170\) 3790.98 3790.98i 0.131176 0.131176i
\(171\) −978.607 + 978.607i −0.0334669 + 0.0334669i
\(172\) 4860.50 + 4860.50i 0.164295 + 0.164295i
\(173\) 26725.9i 0.892977i 0.894789 + 0.446489i \(0.147326\pi\)
−0.894789 + 0.446489i \(0.852674\pi\)
\(174\) 20695.3 0.683555
\(175\) 13791.5i 0.450334i
\(176\) 9103.34i 0.293884i
\(177\) 23343.1 + 23343.1i 0.745095 + 0.745095i
\(178\) 9039.02i 0.285287i
\(179\) 29943.6 + 29943.6i 0.934542 + 0.934542i 0.997985 0.0634438i \(-0.0202084\pi\)
−0.0634438 + 0.997985i \(0.520208\pi\)
\(180\) −6067.43 6067.43i −0.187266 0.187266i
\(181\) 36299.1 1.10800 0.553999 0.832518i \(-0.313101\pi\)
0.553999 + 0.832518i \(0.313101\pi\)
\(182\) 25511.9 0.770193
\(183\) −49382.2 + 49382.2i −1.47458 + 1.47458i
\(184\) 2551.18i 0.0753537i
\(185\) −14815.4 14650.7i −0.432883 0.428070i
\(186\) −30751.6 −0.888878
\(187\) −12526.1 12526.1i −0.358206 0.358206i
\(188\) 23772.6i 0.672607i
\(189\) 4542.84i 0.127176i
\(190\) −597.787 + 597.787i −0.0165592 + 0.0165592i
\(191\) 1331.07 1331.07i 0.0364867 0.0364867i −0.688628 0.725115i \(-0.741787\pi\)
0.725115 + 0.688628i \(0.241787\pi\)
\(192\) 6301.39 0.170936
\(193\) −47495.0 + 47495.0i −1.27507 + 1.27507i −0.331675 + 0.943394i \(0.607614\pi\)
−0.943394 + 0.331675i \(0.892386\pi\)
\(194\) −34233.1 −0.909583
\(195\) −48189.2 −1.26730
\(196\) 9373.73i 0.244006i
\(197\) 22672.3 0.584202 0.292101 0.956388i \(-0.405646\pi\)
0.292101 + 0.956388i \(0.405646\pi\)
\(198\) −20047.9 + 20047.9i −0.511374 + 0.511374i
\(199\) −26429.3 26429.3i −0.667389 0.667389i 0.289722 0.957111i \(-0.406437\pi\)
−0.957111 + 0.289722i \(0.906437\pi\)
\(200\) 6293.68 + 6293.68i 0.157342 + 0.157342i
\(201\) −28786.2 −0.712512
\(202\) 24738.4 24738.4i 0.606274 0.606274i
\(203\) 14739.1 + 14739.1i 0.357667 + 0.357667i
\(204\) 8670.65 8670.65i 0.208349 0.208349i
\(205\) 13335.9 + 13335.9i 0.317333 + 0.317333i
\(206\) 23221.1i 0.547202i
\(207\) −5618.35 + 5618.35i −0.131120 + 0.131120i
\(208\) 11642.2 11642.2i 0.269098 0.269098i
\(209\) 1975.20 + 1975.20i 0.0452187 + 0.0452187i
\(210\) 18575.9i 0.421221i
\(211\) 48508.7 1.08957 0.544784 0.838576i \(-0.316612\pi\)
0.544784 + 0.838576i \(0.316612\pi\)
\(212\) 8333.12i 0.185411i
\(213\) 44907.6i 0.989829i
\(214\) −7370.93 7370.93i −0.160951 0.160951i
\(215\) 13077.3i 0.282905i
\(216\) 2073.10 + 2073.10i 0.0444338 + 0.0444338i
\(217\) −21901.2 21901.2i −0.465102 0.465102i
\(218\) −38423.3 −0.808502
\(219\) 122379. 2.55163
\(220\) −12246.4 + 12246.4i −0.253024 + 0.253024i
\(221\) 32039.2i 0.655990i
\(222\) −33885.5 33508.8i −0.687557 0.679912i
\(223\) 37090.7 0.745856 0.372928 0.927860i \(-0.378354\pi\)
0.372928 + 0.927860i \(0.378354\pi\)
\(224\) 4487.83 + 4487.83i 0.0894417 + 0.0894417i
\(225\) 27720.6i 0.547568i
\(226\) 19689.4i 0.385493i
\(227\) 38853.5 38853.5i 0.754012 0.754012i −0.221214 0.975225i \(-0.571002\pi\)
0.975225 + 0.221214i \(0.0710018\pi\)
\(228\) −1367.25 + 1367.25i −0.0263013 + 0.0263013i
\(229\) −22098.2 −0.421391 −0.210695 0.977552i \(-0.567573\pi\)
−0.210695 + 0.977552i \(0.567573\pi\)
\(230\) −3431.99 + 3431.99i −0.0648770 + 0.0648770i
\(231\) −61378.1 −1.15024
\(232\) 13452.3 0.249930
\(233\) 45800.4i 0.843641i −0.906679 0.421821i \(-0.861391\pi\)
0.906679 0.421821i \(-0.138609\pi\)
\(234\) −51278.4 −0.936490
\(235\) 31980.3 31980.3i 0.579092 0.579092i
\(236\) 15173.3 + 15173.3i 0.272432 + 0.272432i
\(237\) 78804.7 + 78804.7i 1.40299 + 1.40299i
\(238\) 12350.4 0.218036
\(239\) 36004.7 36004.7i 0.630323 0.630323i −0.317826 0.948149i \(-0.602953\pi\)
0.948149 + 0.317826i \(0.102953\pi\)
\(240\) −8477.01 8477.01i −0.147170 0.147170i
\(241\) 34717.3 34717.3i 0.597739 0.597739i −0.341971 0.939710i \(-0.611095\pi\)
0.939710 + 0.341971i \(0.111095\pi\)
\(242\) 11182.3 + 11182.3i 0.190941 + 0.190941i
\(243\) 79384.8i 1.34439i
\(244\) −32099.2 + 32099.2i −0.539155 + 0.539155i
\(245\) −12610.1 + 12610.1i −0.210081 + 0.210081i
\(246\) 30501.6 + 30501.6i 0.504025 + 0.504025i
\(247\) 5052.15i 0.0828100i
\(248\) −19989.0 −0.325004
\(249\) 88053.6i 1.42020i
\(250\) 43838.5i 0.701416i
\(251\) −43521.6 43521.6i −0.690807 0.690807i 0.271602 0.962410i \(-0.412447\pi\)
−0.962410 + 0.271602i \(0.912447\pi\)
\(252\) 19766.7i 0.311267i
\(253\) 11340.0 + 11340.0i 0.177162 + 0.177162i
\(254\) 46852.2 + 46852.2i 0.726211 + 0.726211i
\(255\) −23328.6 −0.358763
\(256\) 4096.00 0.0625000
\(257\) −53578.0 + 53578.0i −0.811185 + 0.811185i −0.984812 0.173627i \(-0.944451\pi\)
0.173627 + 0.984812i \(0.444451\pi\)
\(258\) 29910.1i 0.449343i
\(259\) −268.339 47998.0i −0.00400022 0.715522i
\(260\) −31323.7 −0.463368
\(261\) −29625.3 29625.3i −0.434893 0.434893i
\(262\) 16641.7i 0.242435i
\(263\) 26433.1i 0.382153i −0.981575 0.191077i \(-0.938802\pi\)
0.981575 0.191077i \(-0.0611979\pi\)
\(264\) −28009.6 + 28009.6i −0.401883 + 0.401883i
\(265\) 11210.2 11210.2i 0.159633 0.159633i
\(266\) −1947.49 −0.0275241
\(267\) −27811.7 + 27811.7i −0.390127 + 0.390127i
\(268\) −18711.5 −0.260518
\(269\) −120348. −1.66316 −0.831578 0.555408i \(-0.812562\pi\)
−0.831578 + 0.555408i \(0.812562\pi\)
\(270\) 5577.73i 0.0765121i
\(271\) 12124.6 0.165093 0.0825464 0.996587i \(-0.473695\pi\)
0.0825464 + 0.996587i \(0.473695\pi\)
\(272\) 5636.06 5636.06i 0.0761794 0.0761794i
\(273\) −78496.3 78496.3i −1.05323 1.05323i
\(274\) 45803.2 + 45803.2i 0.610092 + 0.610092i
\(275\) −55950.7 −0.739844
\(276\) −7849.59 + 7849.59i −0.103045 + 0.103045i
\(277\) 4822.15 + 4822.15i 0.0628465 + 0.0628465i 0.737831 0.674985i \(-0.235850\pi\)
−0.674985 + 0.737831i \(0.735850\pi\)
\(278\) −61740.6 + 61740.6i −0.798879 + 0.798879i
\(279\) 44021.0 + 44021.0i 0.565525 + 0.565525i
\(280\) 12074.6i 0.154013i
\(281\) 75002.5 75002.5i 0.949868 0.949868i −0.0489341 0.998802i \(-0.515582\pi\)
0.998802 + 0.0489341i \(0.0155824\pi\)
\(282\) 73144.8 73144.8i 0.919783 0.919783i
\(283\) 23758.4 + 23758.4i 0.296650 + 0.296650i 0.839700 0.543050i \(-0.182731\pi\)
−0.543050 + 0.839700i \(0.682731\pi\)
\(284\) 29190.6i 0.361915i
\(285\) 3678.60 0.0452890
\(286\) 103499.i 1.26533i
\(287\) 43446.2i 0.527459i
\(288\) −9020.45 9020.45i −0.108754 0.108754i
\(289\) 68010.7i 0.814294i
\(290\) −18096.8 18096.8i −0.215182 0.215182i
\(291\) 105330. + 105330.i 1.24384 + 1.24384i
\(292\) 79548.0 0.932962
\(293\) 108751. 1.26677 0.633384 0.773837i \(-0.281665\pi\)
0.633384 + 0.773837i \(0.281665\pi\)
\(294\) −28841.6 + 28841.6i −0.333675 + 0.333675i
\(295\) 40824.2i 0.469109i
\(296\) −22026.1 21781.2i −0.251394 0.248598i
\(297\) −18429.9 −0.208934
\(298\) −46602.2 46602.2i −0.524776 0.524776i
\(299\) 29005.3i 0.324440i
\(300\) 38729.5i 0.430327i
\(301\) 21301.8 21301.8i 0.235117 0.235117i
\(302\) 41553.2 41553.2i 0.455607 0.455607i
\(303\) −152233. −1.65815
\(304\) −888.730 + 888.730i −0.00961663 + 0.00961663i
\(305\) 86363.4 0.928389
\(306\) −24824.1 −0.265113
\(307\) 162258.i 1.72159i 0.508952 + 0.860795i \(0.330033\pi\)
−0.508952 + 0.860795i \(0.669967\pi\)
\(308\) −39896.7 −0.420567
\(309\) 71447.7 71447.7i 0.748293 0.748293i
\(310\) 26890.4 + 26890.4i 0.279817 + 0.279817i
\(311\) 88112.7 + 88112.7i 0.910999 + 0.910999i 0.996351 0.0853518i \(-0.0272014\pi\)
−0.0853518 + 0.996351i \(0.527201\pi\)
\(312\) −71642.9 −0.735976
\(313\) −88253.8 + 88253.8i −0.900834 + 0.900834i −0.995508 0.0946740i \(-0.969819\pi\)
0.0946740 + 0.995508i \(0.469819\pi\)
\(314\) 88900.3 + 88900.3i 0.901663 + 0.901663i
\(315\) −26591.4 + 26591.4i −0.267991 + 0.267991i
\(316\) 51224.2 + 51224.2i 0.512981 + 0.512981i
\(317\) 34320.2i 0.341532i −0.985312 0.170766i \(-0.945376\pi\)
0.985312 0.170766i \(-0.0546242\pi\)
\(318\) 25639.8 25639.8i 0.253548 0.253548i
\(319\) −59795.2 + 59795.2i −0.587604 + 0.587604i
\(320\) −5510.19 5510.19i −0.0538104 0.0538104i
\(321\) 45358.5i 0.440199i
\(322\) −11180.9 −0.107836
\(323\) 2445.77i 0.0234428i
\(324\) 58423.3i 0.556540i
\(325\) −71555.2 71555.2i −0.677446 0.677446i
\(326\) 39224.2i 0.369079i
\(327\) 118223. + 118223.i 1.10562 + 1.10562i
\(328\) 19826.5 + 19826.5i 0.184289 + 0.184289i
\(329\) 104187. 0.962545
\(330\) 75360.5 0.692016
\(331\) 27326.2 27326.2i 0.249415 0.249415i −0.571316 0.820731i \(-0.693567\pi\)
0.820731 + 0.571316i \(0.193567\pi\)
\(332\) 57236.1i 0.519271i
\(333\) 539.356 + 96475.0i 0.00486393 + 0.870014i
\(334\) −101651. −0.911207
\(335\) 25171.8 + 25171.8i 0.224298 + 0.224298i
\(336\) 27616.8i 0.244621i
\(337\) 129267.i 1.13822i 0.822261 + 0.569110i \(0.192712\pi\)
−0.822261 + 0.569110i \(0.807288\pi\)
\(338\) −75242.9 + 75242.9i −0.658616 + 0.658616i
\(339\) −60581.5 + 60581.5i −0.527158 + 0.527158i
\(340\) −15163.9 −0.131176
\(341\) 88851.0 88851.0i 0.764106 0.764106i
\(342\) 3914.43 0.0334669
\(343\) −125264. −1.06472
\(344\) 19442.0i 0.164295i
\(345\) 21119.5 0.177437
\(346\) 53451.8 53451.8i 0.446489 0.446489i
\(347\) −58943.9 58943.9i −0.489531 0.489531i 0.418627 0.908158i \(-0.362511\pi\)
−0.908158 + 0.418627i \(0.862511\pi\)
\(348\) −41390.6 41390.6i −0.341777 0.341777i
\(349\) −199349. −1.63668 −0.818340 0.574734i \(-0.805105\pi\)
−0.818340 + 0.574734i \(0.805105\pi\)
\(350\) 27583.0 27583.0i 0.225167 0.225167i
\(351\) −23569.9 23569.9i −0.191313 0.191313i
\(352\) −18206.7 + 18206.7i −0.146942 + 0.146942i
\(353\) −134420. 134420.i −1.07873 1.07873i −0.996623 0.0821094i \(-0.973834\pi\)
−0.0821094 0.996623i \(-0.526166\pi\)
\(354\) 93372.3i 0.745095i
\(355\) 39268.9 39268.9i 0.311596 0.311596i
\(356\) −18078.0 + 18078.0i −0.142643 + 0.142643i
\(357\) −38000.4 38000.4i −0.298161 0.298161i
\(358\) 119775.i 0.934542i
\(359\) 237450. 1.84240 0.921199 0.389091i \(-0.127211\pi\)
0.921199 + 0.389091i \(0.127211\pi\)
\(360\) 24269.7i 0.187266i
\(361\) 129935.i 0.997041i
\(362\) −72598.2 72598.2i −0.553999 0.553999i
\(363\) 68812.4i 0.522220i
\(364\) −51023.8 51023.8i −0.385097 0.385097i
\(365\) −107013. 107013.i −0.803249 0.803249i
\(366\) 197529. 1.47458
\(367\) −204541. −1.51862 −0.759309 0.650730i \(-0.774463\pi\)
−0.759309 + 0.650730i \(0.774463\pi\)
\(368\) −5102.35 + 5102.35i −0.0376769 + 0.0376769i
\(369\) 87326.2i 0.641345i
\(370\) 329.468 + 58932.2i 0.00240663 + 0.430477i
\(371\) 36521.1 0.265336
\(372\) 61503.3 + 61503.3i 0.444439 + 0.444439i
\(373\) 10556.7i 0.0758767i −0.999280 0.0379384i \(-0.987921\pi\)
0.999280 0.0379384i \(-0.0120791\pi\)
\(374\) 50104.4i 0.358206i
\(375\) −134885. + 134885.i −0.959179 + 0.959179i
\(376\) 47545.2 47545.2i 0.336303 0.336303i
\(377\) −152944. −1.07609
\(378\) 9085.68 9085.68i 0.0635878 0.0635878i
\(379\) 130955. 0.911682 0.455841 0.890061i \(-0.349339\pi\)
0.455841 + 0.890061i \(0.349339\pi\)
\(380\) 2391.15 0.0165592
\(381\) 288315.i 1.98617i
\(382\) −5324.29 −0.0364867
\(383\) −152787. + 152787.i −1.04157 + 1.04157i −0.0424733 + 0.999098i \(0.513524\pi\)
−0.999098 + 0.0424733i \(0.986476\pi\)
\(384\) −12602.8 12602.8i −0.0854681 0.0854681i
\(385\) 53671.4 + 53671.4i 0.362094 + 0.362094i
\(386\) 189980. 1.27507
\(387\) −42816.3 + 42816.3i −0.285882 + 0.285882i
\(388\) 68466.1 + 68466.1i 0.454791 + 0.454791i
\(389\) −112269. + 112269.i −0.741929 + 0.741929i −0.972949 0.231020i \(-0.925794\pi\)
0.231020 + 0.972949i \(0.425794\pi\)
\(390\) 96378.3 + 96378.3i 0.633651 + 0.633651i
\(391\) 14041.6i 0.0918464i
\(392\) −18747.5 + 18747.5i −0.122003 + 0.122003i
\(393\) 51204.0 51204.0i 0.331527 0.331527i
\(394\) −45344.6 45344.6i −0.292101 0.292101i
\(395\) 137820.i 0.883319i
\(396\) 80191.6 0.511374
\(397\) 157029.i 0.996319i −0.867085 0.498160i \(-0.834009\pi\)
0.867085 0.498160i \(-0.165991\pi\)
\(398\) 105717.i 0.667389i
\(399\) 5992.15 + 5992.15i 0.0376389 + 0.0376389i
\(400\) 25174.7i 0.157342i
\(401\) 15819.3 + 15819.3i 0.0983779 + 0.0983779i 0.754583 0.656205i \(-0.227839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(402\) 57572.4 + 57572.4i 0.356256 + 0.356256i
\(403\) 227263. 1.39932
\(404\) −98953.6 −0.606274
\(405\) −78594.5 + 78594.5i −0.479162 + 0.479162i
\(406\) 58956.4i 0.357667i
\(407\) 194723. 1088.62i 1.17552 0.00657187i
\(408\) −34682.6 −0.208349
\(409\) 38105.9 + 38105.9i 0.227795 + 0.227795i 0.811771 0.583976i \(-0.198504\pi\)
−0.583976 + 0.811771i \(0.698504\pi\)
\(410\) 53343.6i 0.317333i
\(411\) 281860.i 1.66859i
\(412\) 46442.1 46442.1i 0.273601 0.273601i
\(413\) 66499.4 66499.4i 0.389868 0.389868i
\(414\) 22473.4 0.131120
\(415\) −76997.5 + 76997.5i −0.447075 + 0.447075i
\(416\) −46569.0 −0.269098
\(417\) 379933. 2.18492
\(418\) 7900.80i 0.0452187i
\(419\) 260486. 1.48374 0.741868 0.670546i \(-0.233940\pi\)
0.741868 + 0.670546i \(0.233940\pi\)
\(420\) −37151.7 + 37151.7i −0.210611 + 0.210611i
\(421\) −94783.8 94783.8i −0.534774 0.534774i 0.387216 0.921989i \(-0.373437\pi\)
−0.921989 + 0.387216i \(0.873437\pi\)
\(422\) −97017.3 97017.3i −0.544784 0.544784i
\(423\) −209414. −1.17037
\(424\) 16666.2 16666.2i 0.0927056 0.0927056i
\(425\) −34640.2 34640.2i −0.191780 0.191780i
\(426\) 89815.1 89815.1i 0.494915 0.494915i
\(427\) 140679. + 140679.i 0.771568 + 0.771568i
\(428\) 29483.7i 0.160951i
\(429\) 318452. 318452.i 1.73033 1.73033i
\(430\) −26154.5 + 26154.5i −0.141452 + 0.141452i
\(431\) −67577.5 67577.5i −0.363788 0.363788i 0.501418 0.865205i \(-0.332812\pi\)
−0.865205 + 0.501418i \(0.832812\pi\)
\(432\) 8292.42i 0.0444338i
\(433\) −236655. −1.26224 −0.631118 0.775687i \(-0.717404\pi\)
−0.631118 + 0.775687i \(0.717404\pi\)
\(434\) 87604.8i 0.465102i
\(435\) 111362.i 0.588518i
\(436\) 76846.5 + 76846.5i 0.404251 + 0.404251i
\(437\) 2214.17i 0.0115944i
\(438\) −244758. 244758.i −1.27582 1.27582i
\(439\) 131517. + 131517.i 0.682424 + 0.682424i 0.960546 0.278122i \(-0.0897120\pi\)
−0.278122 + 0.960546i \(0.589712\pi\)
\(440\) 48985.5 0.253024
\(441\) 82573.5 0.424584
\(442\) −64078.4 + 64078.4i −0.327995 + 0.327995i
\(443\) 190133.i 0.968835i −0.874837 0.484418i \(-0.839032\pi\)
0.874837 0.484418i \(-0.160968\pi\)
\(444\) 753.553 + 134789.i 0.00382250 + 0.683734i
\(445\) 48639.4 0.245622
\(446\) −74181.4 74181.4i −0.372928 0.372928i
\(447\) 286776.i 1.43525i
\(448\) 17951.3i 0.0894417i
\(449\) −201365. + 201365.i −0.998831 + 0.998831i −0.999999 0.00116876i \(-0.999628\pi\)
0.00116876 + 0.999999i \(0.499628\pi\)
\(450\) −55441.3 + 55441.3i −0.273784 + 0.273784i
\(451\) −176257. −0.866550
\(452\) −39378.9 + 39378.9i −0.192747 + 0.192747i
\(453\) −255706. −1.24608
\(454\) −155414. −0.754012
\(455\) 137281.i 0.663111i
\(456\) 5468.98 0.0263013
\(457\) −88971.9 + 88971.9i −0.426011 + 0.426011i −0.887267 0.461256i \(-0.847399\pi\)
0.461256 + 0.887267i \(0.347399\pi\)
\(458\) 44196.3 + 44196.3i 0.210695 + 0.210695i
\(459\) −11410.3 11410.3i −0.0541591 0.0541591i
\(460\) 13728.0 0.0648770
\(461\) −222424. + 222424.i −1.04660 + 1.04660i −0.0477366 + 0.998860i \(0.515201\pi\)
−0.998860 + 0.0477366i \(0.984799\pi\)
\(462\) 122756. + 122756.i 0.575121 + 0.575121i
\(463\) −164606. + 164606.i −0.767861 + 0.767861i −0.977730 0.209868i \(-0.932696\pi\)
0.209868 + 0.977730i \(0.432696\pi\)
\(464\) −26904.5 26904.5i −0.124965 0.124965i
\(465\) 165476.i 0.765295i
\(466\) −91600.9 + 91600.9i −0.421821 + 0.421821i
\(467\) 209613. 209613.i 0.961134 0.961134i −0.0381387 0.999272i \(-0.512143\pi\)
0.999272 + 0.0381387i \(0.0121429\pi\)
\(468\) 102557. + 102557.i 0.468245 + 0.468245i
\(469\) 82005.7i 0.372819i
\(470\) −127921. −0.579092
\(471\) 547066.i 2.46603i
\(472\) 60693.4i 0.272432i
\(473\) 86419.4 + 86419.4i 0.386268 + 0.386268i
\(474\) 315219.i 1.40299i
\(475\) 5462.29 + 5462.29i 0.0242096 + 0.0242096i
\(476\) −24700.8 24700.8i −0.109018 0.109018i
\(477\) −73406.7 −0.322626
\(478\) −144019. −0.630323
\(479\) −157711. + 157711.i −0.687373 + 0.687373i −0.961650 0.274278i \(-0.911561\pi\)
0.274278 + 0.961650i \(0.411561\pi\)
\(480\) 33908.1i 0.147170i
\(481\) 250423. + 247639.i 1.08239 + 1.07036i
\(482\) −138869. −0.597739
\(483\) 34401.9 + 34401.9i 0.147465 + 0.147465i
\(484\) 44729.1i 0.190941i
\(485\) 184209.i 0.783120i
\(486\) −158770. + 158770.i −0.672195 + 0.672195i
\(487\) 13375.5 13375.5i 0.0563966 0.0563966i −0.678346 0.734743i \(-0.737303\pi\)
0.734743 + 0.678346i \(0.237303\pi\)
\(488\) 128397. 0.539155
\(489\) −120687. + 120687.i −0.504711 + 0.504711i
\(490\) 50440.4 0.210081
\(491\) 386204. 1.60197 0.800984 0.598686i \(-0.204310\pi\)
0.800984 + 0.598686i \(0.204310\pi\)
\(492\) 122006.i 0.504025i
\(493\) −74040.7 −0.304633
\(494\) 10104.3 10104.3i 0.0414050 0.0414050i
\(495\) −107879. 107879.i −0.440276 0.440276i
\(496\) 39978.1 + 39978.1i 0.162502 + 0.162502i
\(497\) 127932. 0.517924
\(498\) −176107. + 176107.i −0.710098 + 0.710098i
\(499\) −22816.0 22816.0i −0.0916303 0.0916303i 0.659806 0.751436i \(-0.270639\pi\)
−0.751436 + 0.659806i \(0.770639\pi\)
\(500\) −87677.0 + 87677.0i −0.350708 + 0.350708i
\(501\) 312764. + 312764.i 1.24607 + 1.24607i
\(502\) 174086.i 0.690807i
\(503\) 310068. 310068.i 1.22552 1.22552i 0.259882 0.965640i \(-0.416316\pi\)
0.965640 0.259882i \(-0.0836837\pi\)
\(504\) −39533.4 + 39533.4i −0.155634 + 0.155634i
\(505\) 133118. + 133118.i 0.521981 + 0.521981i
\(506\) 45359.8i 0.177162i
\(507\) 463023. 1.80130
\(508\) 187409.i 0.726211i
\(509\) 308422.i 1.19045i 0.803560 + 0.595224i \(0.202937\pi\)
−0.803560 + 0.595224i \(0.797063\pi\)
\(510\) 46657.1 + 46657.1i 0.179382 + 0.179382i
\(511\) 348631.i 1.33513i
\(512\) −8192.00 8192.00i −0.0312500 0.0312500i
\(513\) 1799.25 + 1799.25i 0.00683686 + 0.00683686i
\(514\) 214312. 0.811185
\(515\) −124953. −0.471122
\(516\) −59820.1 + 59820.1i −0.224671 + 0.224671i
\(517\) 422676.i 1.58135i
\(518\) −95459.2 + 96532.6i −0.355761 + 0.359761i
\(519\) −328927. −1.22114
\(520\) 62647.4 + 62647.4i 0.231684 + 0.231684i
\(521\) 312647.i 1.15181i −0.817518 0.575903i \(-0.804651\pi\)
0.817518 0.575903i \(-0.195349\pi\)
\(522\) 118501.i 0.434893i
\(523\) 206955. 206955.i 0.756611 0.756611i −0.219093 0.975704i \(-0.570310\pi\)
0.975704 + 0.219093i \(0.0703098\pi\)
\(524\) 33283.4 33283.4i 0.121217 0.121217i
\(525\) −169737. −0.615827
\(526\) −52866.3 + 52866.3i −0.191077 + 0.191077i
\(527\) 110019. 0.396137
\(528\) 112039. 0.401883
\(529\) 267129.i 0.954575i
\(530\) −44840.8 −0.159633
\(531\) −133663. + 133663.i −0.474046 + 0.474046i
\(532\) 3894.99 + 3894.99i 0.0137620 + 0.0137620i
\(533\) −225415. 225415.i −0.793466 0.793466i
\(534\) 111247. 0.390127
\(535\) 39663.3 39663.3i 0.138574 0.138574i
\(536\) 37422.9 + 37422.9i 0.130259 + 0.130259i
\(537\) −368529. + 368529.i −1.27798 + 1.27798i
\(538\) 240695. + 240695.i 0.831578 + 0.831578i
\(539\) 166665.i 0.573675i
\(540\) −11155.5 + 11155.5i −0.0382560 + 0.0382560i
\(541\) 52416.1 52416.1i 0.179089 0.179089i −0.611869 0.790959i \(-0.709582\pi\)
0.790959 + 0.611869i \(0.209582\pi\)
\(542\) −24249.2 24249.2i −0.0825464 0.0825464i
\(543\) 446748.i 1.51517i
\(544\) −22544.2 −0.0761794
\(545\) 206757.i 0.696093i
\(546\) 313985.i 1.05323i
\(547\) −270647. 270647.i −0.904543 0.904543i 0.0912822 0.995825i \(-0.470903\pi\)
−0.995825 + 0.0912822i \(0.970903\pi\)
\(548\) 183213.i 0.610092i
\(549\) −282763. 282763.i −0.938161 0.938161i
\(550\) 111901. + 111901.i 0.369922 + 0.369922i
\(551\) 11675.2 0.0384558
\(552\) 31398.4 0.103045
\(553\) 224498. 224498.i 0.734111 0.734111i
\(554\) 19288.6i 0.0628465i
\(555\) 180312. 182339.i 0.585381 0.591963i
\(556\) 246962. 0.798879
\(557\) 312727. + 312727.i 1.00799 + 1.00799i 0.999968 + 0.00801789i \(0.00255220\pi\)
0.00801789 + 0.999968i \(0.497448\pi\)
\(558\) 176084.i 0.565525i
\(559\) 221043.i 0.707381i
\(560\) −24149.2 + 24149.2i −0.0770063 + 0.0770063i
\(561\) 154164. 154164.i 0.489843 0.489843i
\(562\) −300010. −0.949868
\(563\) −262229. + 262229.i −0.827303 + 0.827303i −0.987143 0.159840i \(-0.948902\pi\)
0.159840 + 0.987143i \(0.448902\pi\)
\(564\) −292579. −0.919783
\(565\) 105950. 0.331897
\(566\) 95033.6i 0.296650i
\(567\) −256048. −0.796446
\(568\) 58381.2 58381.2i 0.180957 0.180957i
\(569\) 72427.4 + 72427.4i 0.223706 + 0.223706i 0.810057 0.586351i \(-0.199436\pi\)
−0.586351 + 0.810057i \(0.699436\pi\)
\(570\) −7357.21 7357.21i −0.0226445 0.0226445i
\(571\) 187442. 0.574902 0.287451 0.957795i \(-0.407192\pi\)
0.287451 + 0.957795i \(0.407192\pi\)
\(572\) 206999. 206999.i 0.632667 0.632667i
\(573\) 16382.0 + 16382.0i 0.0498952 + 0.0498952i
\(574\) 86892.5 86892.5i 0.263729 0.263729i
\(575\) 31359.9 + 31359.9i 0.0948505 + 0.0948505i
\(576\) 36081.8i 0.108754i
\(577\) 440676. 440676.i 1.32363 1.32363i 0.412820 0.910813i \(-0.364544\pi\)
0.910813 0.412820i \(-0.135456\pi\)
\(578\) 136021. 136021.i 0.407147 0.407147i
\(579\) −584541. 584541.i −1.74364 1.74364i
\(580\) 72387.1i 0.215182i
\(581\) −250846. −0.743112
\(582\) 421320.i 1.24384i
\(583\) 148163.i 0.435914i
\(584\) −159096. 159096.i −0.466481 0.466481i
\(585\) 275931.i 0.806286i
\(586\) −217502. 217502.i −0.633384 0.633384i
\(587\) −254904. 254904.i −0.739777 0.739777i 0.232758 0.972535i \(-0.425225\pi\)
−0.972535 + 0.232758i \(0.925225\pi\)
\(588\) 115366. 0.333675
\(589\) −17348.5 −0.0500070
\(590\) −81648.4 + 81648.4i −0.234554 + 0.234554i
\(591\) 279037.i 0.798890i
\(592\) 489.821 + 87614.6i 0.00139763 + 0.249996i
\(593\) −67949.6 −0.193231 −0.0966156 0.995322i \(-0.530802\pi\)
−0.0966156 + 0.995322i \(0.530802\pi\)
\(594\) 36859.7 + 36859.7i 0.104467 + 0.104467i
\(595\) 66458.1i 0.187721i
\(596\) 186409.i 0.524776i
\(597\) 325276. 325276.i 0.912648 0.912648i
\(598\) 58010.5 58010.5i 0.162220 0.162220i
\(599\) 288040. 0.802785 0.401393 0.915906i \(-0.368526\pi\)
0.401393 + 0.915906i \(0.368526\pi\)
\(600\) −77458.9 + 77458.9i −0.215164 + 0.215164i
\(601\) 117937. 0.326513 0.163257 0.986584i \(-0.447800\pi\)
0.163257 + 0.986584i \(0.447800\pi\)
\(602\) −85207.3 −0.235117
\(603\) 164830.i 0.453316i
\(604\) −166213. −0.455607
\(605\) −60172.3 + 60172.3i −0.164394 + 0.164394i
\(606\) 304465. + 304465.i 0.829073 + 0.829073i
\(607\) −93551.7 93551.7i −0.253907 0.253907i 0.568663 0.822570i \(-0.307461\pi\)
−0.822570 + 0.568663i \(0.807461\pi\)
\(608\) 3554.92 0.00961663
\(609\) −181400. + 181400.i −0.489106 + 0.489106i
\(610\) −172727. 172727.i −0.464195 0.464195i
\(611\) −540559. + 540559.i −1.44797 + 1.44797i
\(612\) 49648.2 + 49648.2i 0.132556 + 0.132556i
\(613\) 268669.i 0.714983i −0.933916 0.357492i \(-0.883632\pi\)
0.933916 0.357492i \(-0.116368\pi\)
\(614\) 324516. 324516.i 0.860795 0.860795i
\(615\) −164130. + 164130.i −0.433949 + 0.433949i
\(616\) 79793.4 + 79793.4i 0.210284 + 0.210284i
\(617\) 484519.i 1.27274i −0.771383 0.636371i \(-0.780435\pi\)
0.771383 0.636371i \(-0.219565\pi\)
\(618\) −285791. −0.748293
\(619\) 172756.i 0.450870i −0.974258 0.225435i \(-0.927620\pi\)
0.974258 0.225435i \(-0.0723804\pi\)
\(620\) 107562.i 0.279817i
\(621\) 10329.8 + 10329.8i 0.0267860 + 0.0267860i
\(622\) 352451.i 0.910999i
\(623\) 79229.6 + 79229.6i 0.204132 + 0.204132i
\(624\) 143286. + 143286.i 0.367988 + 0.367988i
\(625\) −9950.31 −0.0254728
\(626\) 353015. 0.900834
\(627\) −24309.6 + 24309.6i −0.0618361 + 0.0618361i
\(628\) 355601.i 0.901663i
\(629\) 121231. + 119883.i 0.306416 + 0.303009i
\(630\) 106365. 0.267991
\(631\) −170631. 170631.i −0.428549 0.428549i 0.459585 0.888134i \(-0.347998\pi\)
−0.888134 + 0.459585i \(0.847998\pi\)
\(632\) 204897.i 0.512981i
\(633\) 597016.i 1.48997i
\(634\) −68640.4 + 68640.4i −0.170766 + 0.170766i
\(635\) −252114. + 252114.i −0.625243 + 0.625243i
\(636\) −102559. −0.253548
\(637\) 213147. 213147.i 0.525291 0.525291i
\(638\) 239181. 0.587604
\(639\) −257141. −0.629752
\(640\) 22040.7i 0.0538104i
\(641\) 300030. 0.730211 0.365105 0.930966i \(-0.381033\pi\)
0.365105 + 0.930966i \(0.381033\pi\)
\(642\) 90717.0 90717.0i 0.220099 0.220099i
\(643\) −131810. 131810.i −0.318806 0.318806i 0.529502 0.848309i \(-0.322379\pi\)
−0.848309 + 0.529502i \(0.822379\pi\)
\(644\) 22361.8 + 22361.8i 0.0539181 + 0.0539181i
\(645\) 160947. 0.386869
\(646\) 4891.54 4891.54i 0.0117214 0.0117214i
\(647\) 164840. + 164840.i 0.393780 + 0.393780i 0.876032 0.482253i \(-0.160181\pi\)
−0.482253 + 0.876032i \(0.660181\pi\)
\(648\) −116847. + 116847.i −0.278270 + 0.278270i
\(649\) 269782. + 269782.i 0.640505 + 0.640505i
\(650\) 286221.i 0.677446i
\(651\) 269547. 269547.i 0.636022 0.636022i
\(652\) −78448.4 + 78448.4i −0.184539 + 0.184539i
\(653\) −398531. 398531.i −0.934622 0.934622i 0.0633679 0.997990i \(-0.479816\pi\)
−0.997990 + 0.0633679i \(0.979816\pi\)
\(654\) 472891.i 1.10562i
\(655\) −89549.5 −0.208728
\(656\) 79306.0i 0.184289i
\(657\) 700741.i 1.62341i
\(658\) −208374. 208374.i −0.481273 0.481273i
\(659\) 282645.i 0.650833i 0.945571 + 0.325417i \(0.105505\pi\)
−0.945571 + 0.325417i \(0.894495\pi\)
\(660\) −150721. 150721.i −0.346008 0.346008i
\(661\) 411076. + 411076.i 0.940848 + 0.940848i 0.998346 0.0574980i \(-0.0183123\pi\)
−0.0574980 + 0.998346i \(0.518312\pi\)
\(662\) −109305. −0.249415
\(663\) 394320. 0.897060
\(664\) −114472. + 114472.i −0.259636 + 0.259636i
\(665\) 10479.5i 0.0236973i
\(666\) 191871. 194029.i 0.432575 0.437439i
\(667\) 67029.4 0.150665
\(668\) 203301. + 203301.i 0.455603 + 0.455603i
\(669\) 456490.i 1.01995i
\(670\) 100687.i 0.224298i
\(671\) −570722. + 570722.i −1.26759 + 1.26759i
\(672\) −55233.5 + 55233.5i −0.122311 + 0.122311i
\(673\) −550661. −1.21578 −0.607889 0.794022i \(-0.707983\pi\)
−0.607889 + 0.794022i \(0.707983\pi\)
\(674\) 258533. 258533.i 0.569110 0.569110i
\(675\) −50966.6 −0.111861
\(676\) 300972. 0.658616
\(677\) 37674.3i 0.0821992i −0.999155 0.0410996i \(-0.986914\pi\)
0.999155 0.0410996i \(-0.0130861\pi\)
\(678\) 242326. 0.527158
\(679\) 300063. 300063.i 0.650837 0.650837i
\(680\) 30327.8 + 30327.8i 0.0655879 + 0.0655879i
\(681\) 478185. + 478185.i 1.03110 + 1.03110i
\(682\) −355404. −0.764106
\(683\) 57341.0 57341.0i 0.122920 0.122920i −0.642971 0.765891i \(-0.722298\pi\)
0.765891 + 0.642971i \(0.222298\pi\)
\(684\) −7828.86 7828.86i −0.0167335 0.0167335i
\(685\) −246469. + 246469.i −0.525269 + 0.525269i
\(686\) 250527. + 250527.i 0.532361 + 0.532361i
\(687\) 271971.i 0.576247i
\(688\) −38884.0 + 38884.0i −0.0821474 + 0.0821474i
\(689\) −189485. + 189485.i −0.399150 + 0.399150i
\(690\) −42239.0 42239.0i −0.0887187 0.0887187i
\(691\) 360431.i 0.754859i −0.926038 0.377429i \(-0.876808\pi\)
0.926038 0.377429i \(-0.123192\pi\)
\(692\) −213807. −0.446489
\(693\) 351451.i 0.731811i
\(694\) 235776.i 0.489531i
\(695\) −332228. 332228.i −0.687808 0.687808i
\(696\) 165562.i 0.341777i
\(697\) −109124. 109124.i −0.224624 0.224624i
\(698\) 398699. + 398699.i 0.818340 + 0.818340i
\(699\) 563685. 1.15367
\(700\) −110332. −0.225167
\(701\) −26111.7 + 26111.7i −0.0531373 + 0.0531373i −0.733176 0.680039i \(-0.761963\pi\)
0.680039 + 0.733176i \(0.261963\pi\)
\(702\) 94279.6i 0.191313i
\(703\) −19116.5 18903.9i −0.0386810 0.0382509i
\(704\) 72826.7 0.146942
\(705\) 393595. + 393595.i 0.791902 + 0.791902i
\(706\) 537679.i 1.07873i
\(707\) 433678.i 0.867618i
\(708\) −186745. + 186745.i −0.372547 + 0.372547i
\(709\) −17996.5 + 17996.5i −0.0358010 + 0.0358010i −0.724781 0.688980i \(-0.758059\pi\)
0.688980 + 0.724781i \(0.258059\pi\)
\(710\) −157076. −0.311596
\(711\) −451236. + 451236.i −0.892616 + 0.892616i
\(712\) 72312.2 0.142643
\(713\) −99600.6 −0.195922
\(714\) 152002.i 0.298161i
\(715\) −556934. −1.08941
\(716\) −239549. + 239549.i −0.467271 + 0.467271i
\(717\) 443124. + 443124.i 0.861960 + 0.861960i
\(718\) −474900. 474900.i −0.921199 0.921199i
\(719\) −838819. −1.62260 −0.811298 0.584633i \(-0.801238\pi\)
−0.811298 + 0.584633i \(0.801238\pi\)
\(720\) 48539.4 48539.4i 0.0936331 0.0936331i
\(721\) −203539. 203539.i −0.391541 0.391541i
\(722\) 259871. 259871.i 0.498520 0.498520i
\(723\) 427280. + 427280.i 0.817402 + 0.817402i
\(724\) 290393.i 0.553999i
\(725\) −165360. + 165360.i −0.314597 + 0.314597i
\(726\) −137625. + 137625.i −0.261110 + 0.261110i
\(727\) −653992. 653992.i −1.23738 1.23738i −0.961068 0.276314i \(-0.910887\pi\)
−0.276314 0.961068i \(-0.589113\pi\)
\(728\) 204095.i 0.385097i
\(729\) 385486. 0.725359
\(730\) 428051.i 0.803249i
\(731\) 107008.i 0.200254i
\(732\) −395057. 395057.i −0.737289 0.737289i
\(733\) 199044.i 0.370460i 0.982695 + 0.185230i \(0.0593029\pi\)
−0.982695 + 0.185230i \(0.940697\pi\)
\(734\) 409082. + 409082.i 0.759309 + 0.759309i
\(735\) −155198. 155198.i −0.287283 0.287283i
\(736\) 20409.4 0.0376769
\(737\) −332689. −0.612497
\(738\) −174652. + 174652.i −0.320672 + 0.320672i
\(739\) 637184.i 1.16674i −0.812205 0.583372i \(-0.801733\pi\)
0.812205 0.583372i \(-0.198267\pi\)
\(740\) 117206. 118523.i 0.214035 0.216442i
\(741\) −62178.9 −0.113242
\(742\) −73042.2 73042.2i −0.132668 0.132668i
\(743\) 296206.i 0.536557i 0.963341 + 0.268279i \(0.0864548\pi\)
−0.963341 + 0.268279i \(0.913545\pi\)
\(744\) 246013.i 0.444439i
\(745\) 250768. 250768.i 0.451815 0.451815i
\(746\) −21113.3 + 21113.3i −0.0379384 + 0.0379384i
\(747\) 504195. 0.903561
\(748\) 100209. 100209.i 0.179103 0.179103i
\(749\) 129217. 0.230332
\(750\) 539538. 0.959179
\(751\) 318219.i 0.564218i −0.959382 0.282109i \(-0.908966\pi\)
0.959382 0.282109i \(-0.0910339\pi\)
\(752\) −190181. −0.336303
\(753\) 535638. 535638.i 0.944672 0.944672i
\(754\) 305887. + 305887.i 0.538045 + 0.538045i
\(755\) 223599. + 223599.i 0.392263 + 0.392263i
\(756\) −36342.7 −0.0635878
\(757\) 690801. 690801.i 1.20548 1.20548i 0.233009 0.972475i \(-0.425143\pi\)
0.972475 0.233009i \(-0.0748570\pi\)
\(758\) −261910. 261910.i −0.455841 0.455841i
\(759\) −139565. + 139565.i −0.242267 + 0.242267i
\(760\) −4782.29 4782.29i −0.00827960 0.00827960i
\(761\) 483055.i 0.834117i −0.908880 0.417059i \(-0.863061\pi\)
0.908880 0.417059i \(-0.136939\pi\)
\(762\) −576630. + 576630.i −0.993086 + 0.993086i
\(763\) 336791. 336791.i 0.578511 0.578511i
\(764\) 10648.6 + 10648.6i 0.0182434 + 0.0182434i
\(765\) 133580.i 0.228253i
\(766\) 611148. 1.04157
\(767\) 690046.i 1.17297i
\(768\) 50411.1i 0.0854681i
\(769\) −346196. 346196.i −0.585422 0.585422i 0.350966 0.936388i \(-0.385853\pi\)
−0.936388 + 0.350966i \(0.885853\pi\)
\(770\) 214686.i 0.362094i
\(771\) −659406. 659406.i −1.10929 1.10929i
\(772\) −379960. 379960.i −0.637534 0.637534i
\(773\) −124294. −0.208014 −0.104007 0.994577i \(-0.533166\pi\)
−0.104007 + 0.994577i \(0.533166\pi\)
\(774\) 171265. 0.285882
\(775\) 245712. 245712.i 0.409094 0.40