Properties

Label 74.5.d.a.31.1
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 31.1
Root \(-15.1052i\) of defining polynomial
Character \(\chi\) \(=\) 74.31
Dual form 74.5.d.a.43.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.00000 - 2.00000i) q^{2} -16.1052i q^{3} +8.00000i q^{4} +(-17.1794 + 17.1794i) q^{5} +(-32.2104 + 32.2104i) q^{6} -18.7264 q^{7} +(16.0000 - 16.0000i) q^{8} -178.377 q^{9} +O(q^{10})\) \(q+(-2.00000 - 2.00000i) q^{2} -16.1052i q^{3} +8.00000i q^{4} +(-17.1794 + 17.1794i) q^{5} +(-32.2104 + 32.2104i) q^{6} -18.7264 q^{7} +(16.0000 - 16.0000i) q^{8} -178.377 q^{9} +68.7178 q^{10} +90.7271i q^{11} +128.842 q^{12} +(49.3596 - 49.3596i) q^{13} +(37.4528 + 37.4528i) q^{14} +(276.678 + 276.678i) q^{15} -64.0000 q^{16} +(208.621 - 208.621i) q^{17} +(356.755 + 356.755i) q^{18} +(-166.028 + 166.028i) q^{19} +(-137.436 - 137.436i) q^{20} +301.592i q^{21} +(181.454 - 181.454i) q^{22} +(-686.354 + 686.354i) q^{23} +(-257.683 - 257.683i) q^{24} +34.7332i q^{25} -197.438 q^{26} +1568.28i q^{27} -149.811i q^{28} +(0.649856 + 0.649856i) q^{29} -1106.71i q^{30} +(-1085.34 - 1085.34i) q^{31} +(128.000 + 128.000i) q^{32} +1461.18 q^{33} -834.484 q^{34} +(321.709 - 321.709i) q^{35} -1427.02i q^{36} +(203.465 - 1353.80i) q^{37} +664.111 q^{38} +(-794.945 - 794.945i) q^{39} +549.742i q^{40} +630.898i q^{41} +(603.184 - 603.184i) q^{42} +(-2018.85 + 2018.85i) q^{43} -725.817 q^{44} +(3064.43 - 3064.43i) q^{45} +2745.41 q^{46} +2159.18 q^{47} +1030.73i q^{48} -2050.32 q^{49} +(69.4665 - 69.4665i) q^{50} +(-3359.88 - 3359.88i) q^{51} +(394.876 + 394.876i) q^{52} -3422.88 q^{53} +(3136.57 - 3136.57i) q^{54} +(-1558.64 - 1558.64i) q^{55} +(-299.622 + 299.622i) q^{56} +(2673.91 + 2673.91i) q^{57} -2.59942i q^{58} +(-2151.08 + 2151.08i) q^{59} +(-2213.43 + 2213.43i) q^{60} +(-4324.19 - 4324.19i) q^{61} +4341.38i q^{62} +3340.36 q^{63} -512.000i q^{64} +1695.94i q^{65} +(-2922.36 - 2922.36i) q^{66} +3386.60i q^{67} +(1668.97 + 1668.97i) q^{68} +(11053.9 + 11053.9i) q^{69} -1286.84 q^{70} -2134.91 q^{71} +(-2854.04 + 2854.04i) q^{72} -9332.10i q^{73} +(-3114.52 + 2300.66i) q^{74} +559.386 q^{75} +(-1328.22 - 1328.22i) q^{76} -1698.99i q^{77} +3179.78i q^{78} +(1614.17 - 1614.17i) q^{79} +(1099.48 - 1099.48i) q^{80} +10808.9 q^{81} +(1261.80 - 1261.80i) q^{82} +8502.87 q^{83} -2412.74 q^{84} +7167.99i q^{85} +8075.38 q^{86} +(10.4661 - 10.4661i) q^{87} +(1451.63 + 1451.63i) q^{88} +(6123.51 + 6123.51i) q^{89} -12257.7 q^{90} +(-924.326 + 924.326i) q^{91} +(-5490.83 - 5490.83i) q^{92} +(-17479.7 + 17479.7i) q^{93} +(-4318.36 - 4318.36i) q^{94} -5704.53i q^{95} +(2061.47 - 2061.47i) q^{96} +(-4623.75 + 4623.75i) q^{97} +(4100.65 + 4100.65i) q^{98} -16183.7i 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
\(3\) 16.1052i 1.78947i −0.446601 0.894733i \(-0.647366\pi\)
0.446601 0.894733i \(-0.352634\pi\)
\(4\) 8.00000i 0.500000i
\(5\) −17.1794 + 17.1794i −0.687178 + 0.687178i −0.961607 0.274429i \(-0.911511\pi\)
0.274429 + 0.961607i \(0.411511\pi\)
\(6\) −32.2104 + 32.2104i −0.894733 + 0.894733i
\(7\) −18.7264 −0.382171 −0.191086 0.981573i \(-0.561201\pi\)
−0.191086 + 0.981573i \(0.561201\pi\)
\(8\) 16.0000 16.0000i 0.250000 0.250000i
\(9\) −178.377 −2.20219
\(10\) 68.7178 0.687178
\(11\) 90.7271i 0.749811i 0.927063 + 0.374905i \(0.122325\pi\)
−0.927063 + 0.374905i \(0.877675\pi\)
\(12\) 128.842 0.894733
\(13\) 49.3596 49.3596i 0.292068 0.292068i −0.545829 0.837897i \(-0.683785\pi\)
0.837897 + 0.545829i \(0.183785\pi\)
\(14\) 37.4528 + 37.4528i 0.191086 + 0.191086i
\(15\) 276.678 + 276.678i 1.22968 + 1.22968i
\(16\) −64.0000 −0.250000
\(17\) 208.621 208.621i 0.721872 0.721872i −0.247114 0.968986i \(-0.579482\pi\)
0.968986 + 0.247114i \(0.0794824\pi\)
\(18\) 356.755 + 356.755i 1.10110 + 1.10110i
\(19\) −166.028 + 166.028i −0.459911 + 0.459911i −0.898626 0.438715i \(-0.855434\pi\)
0.438715 + 0.898626i \(0.355434\pi\)
\(20\) −137.436 137.436i −0.343589 0.343589i
\(21\) 301.592i 0.683882i
\(22\) 181.454 181.454i 0.374905 0.374905i
\(23\) −686.354 + 686.354i −1.29745 + 1.29745i −0.367386 + 0.930068i \(0.619747\pi\)
−0.930068 + 0.367386i \(0.880253\pi\)
\(24\) −257.683 257.683i −0.447367 0.447367i
\(25\) 34.7332i 0.0555732i
\(26\) −197.438 −0.292068
\(27\) 1568.28i 2.15128i
\(28\) 149.811i 0.191086i
\(29\) 0.649856 + 0.649856i 0.000772718 + 0.000772718i 0.707493 0.706720i \(-0.249826\pi\)
−0.706720 + 0.707493i \(0.749826\pi\)
\(30\) 1106.71i 1.22968i
\(31\) −1085.34 1085.34i −1.12939 1.12939i −0.990276 0.139114i \(-0.955575\pi\)
−0.139114 0.990276i \(-0.544425\pi\)
\(32\) 128.000 + 128.000i 0.125000 + 0.125000i
\(33\) 1461.18 1.34176
\(34\) −834.484 −0.721872
\(35\) 321.709 321.709i 0.262620 0.262620i
\(36\) 1427.02i 1.10110i
\(37\) 203.465 1353.80i 0.148623 0.988894i
\(38\) 664.111 0.459911
\(39\) −794.945 794.945i −0.522647 0.522647i
\(40\) 549.742i 0.343589i
\(41\) 630.898i 0.375311i 0.982235 + 0.187656i \(0.0600889\pi\)
−0.982235 + 0.187656i \(0.939911\pi\)
\(42\) 603.184 603.184i 0.341941 0.341941i
\(43\) −2018.85 + 2018.85i −1.09186 + 1.09186i −0.0965281 + 0.995330i \(0.530774\pi\)
−0.995330 + 0.0965281i \(0.969226\pi\)
\(44\) −725.817 −0.374905
\(45\) 3064.43 3064.43i 1.51330 1.51330i
\(46\) 2745.41 1.29745
\(47\) 2159.18 0.977447 0.488724 0.872439i \(-0.337463\pi\)
0.488724 + 0.872439i \(0.337463\pi\)
\(48\) 1030.73i 0.447367i
\(49\) −2050.32 −0.853945
\(50\) 69.4665 69.4665i 0.0277866 0.0277866i
\(51\) −3359.88 3359.88i −1.29177 1.29177i
\(52\) 394.876 + 394.876i 0.146034 + 0.146034i
\(53\) −3422.88 −1.21854 −0.609270 0.792963i \(-0.708537\pi\)
−0.609270 + 0.792963i \(0.708537\pi\)
\(54\) 3136.57 3136.57i 1.07564 1.07564i
\(55\) −1558.64 1558.64i −0.515253 0.515253i
\(56\) −299.622 + 299.622i −0.0955428 + 0.0955428i
\(57\) 2673.91 + 2673.91i 0.822995 + 0.822995i
\(58\) 2.59942i 0.000772718i
\(59\) −2151.08 + 2151.08i −0.617949 + 0.617949i −0.945005 0.327056i \(-0.893943\pi\)
0.327056 + 0.945005i \(0.393943\pi\)
\(60\) −2213.43 + 2213.43i −0.614841 + 0.614841i
\(61\) −4324.19 4324.19i −1.16210 1.16210i −0.984014 0.178090i \(-0.943008\pi\)
−0.178090 0.984014i \(-0.556992\pi\)
\(62\) 4341.38i 1.12939i
\(63\) 3340.36 0.841614
\(64\) 512.000i 0.125000i
\(65\) 1695.94i 0.401406i
\(66\) −2922.36 2922.36i −0.670880 0.670880i
\(67\) 3386.60i 0.754423i 0.926127 + 0.377211i \(0.123117\pi\)
−0.926127 + 0.377211i \(0.876883\pi\)
\(68\) 1668.97 + 1668.97i 0.360936 + 0.360936i
\(69\) 11053.9 + 11053.9i 2.32175 + 2.32175i
\(70\) −1286.84 −0.262620
\(71\) −2134.91 −0.423509 −0.211754 0.977323i \(-0.567918\pi\)
−0.211754 + 0.977323i \(0.567918\pi\)
\(72\) −2854.04 + 2854.04i −0.550548 + 0.550548i
\(73\) 9332.10i 1.75119i −0.483044 0.875596i \(-0.660469\pi\)
0.483044 0.875596i \(-0.339531\pi\)
\(74\) −3114.52 + 2300.66i −0.568759 + 0.420135i
\(75\) 559.386 0.0994463
\(76\) −1328.22 1328.22i −0.229955 0.229955i
\(77\) 1698.99i 0.286556i
\(78\) 3179.78i 0.522647i
\(79\) 1614.17 1614.17i 0.258639 0.258639i −0.565861 0.824500i \(-0.691456\pi\)
0.824500 + 0.565861i \(0.191456\pi\)
\(80\) 1099.48 1099.48i 0.171794 0.171794i
\(81\) 10808.9 1.64745
\(82\) 1261.80 1261.80i 0.187656 0.187656i
\(83\) 8502.87 1.23427 0.617134 0.786858i \(-0.288294\pi\)
0.617134 + 0.786858i \(0.288294\pi\)
\(84\) −2412.74 −0.341941
\(85\) 7167.99i 0.992109i
\(86\) 8075.38 1.09186
\(87\) 10.4661 10.4661i 0.00138275 0.00138275i
\(88\) 1451.63 + 1451.63i 0.187453 + 0.187453i
\(89\) 6123.51 + 6123.51i 0.773073 + 0.773073i 0.978642 0.205570i \(-0.0659047\pi\)
−0.205570 + 0.978642i \(0.565905\pi\)
\(90\) −12257.7 −1.51330
\(91\) −924.326 + 924.326i −0.111620 + 0.111620i
\(92\) −5490.83 5490.83i −0.648727 0.648727i
\(93\) −17479.7 + 17479.7i −2.02101 + 2.02101i
\(94\) −4318.36 4318.36i −0.488724 0.488724i
\(95\) 5704.53i 0.632081i
\(96\) 2061.47 2061.47i 0.223683 0.223683i
\(97\) −4623.75 + 4623.75i −0.491417 + 0.491417i −0.908753 0.417335i \(-0.862964\pi\)
0.417335 + 0.908753i \(0.362964\pi\)
\(98\) 4100.65 + 4100.65i 0.426973 + 0.426973i
\(99\) 16183.7i 1.65123i
\(100\) −277.866 −0.0277866
\(101\) 12029.1i 1.17921i −0.807693 0.589604i \(-0.799284\pi\)
0.807693 0.589604i \(-0.200716\pi\)
\(102\) 13439.5i 1.29177i
\(103\) −6308.95 6308.95i −0.594679 0.594679i 0.344213 0.938892i \(-0.388146\pi\)
−0.938892 + 0.344213i \(0.888146\pi\)
\(104\) 1579.51i 0.146034i
\(105\) −5181.19 5181.19i −0.469949 0.469949i
\(106\) 6845.75 + 6845.75i 0.609270 + 0.609270i
\(107\) 800.878 0.0699518 0.0349759 0.999388i \(-0.488865\pi\)
0.0349759 + 0.999388i \(0.488865\pi\)
\(108\) −12546.3 −1.07564
\(109\) 10116.3 10116.3i 0.851468 0.851468i −0.138846 0.990314i \(-0.544339\pi\)
0.990314 + 0.138846i \(0.0443392\pi\)
\(110\) 6234.56i 0.515253i
\(111\) −21803.1 3276.85i −1.76959 0.265956i
\(112\) 1198.49 0.0955428
\(113\) 12960.3 + 12960.3i 1.01498 + 1.01498i 0.999886 + 0.0150957i \(0.00480529\pi\)
0.0150957 + 0.999886i \(0.495195\pi\)
\(114\) 10695.6i 0.822995i
\(115\) 23582.3i 1.78316i
\(116\) −5.19885 + 5.19885i −0.000386359 + 0.000386359i
\(117\) −8804.63 + 8804.63i −0.643190 + 0.643190i
\(118\) 8604.32 0.617949
\(119\) −3906.72 + 3906.72i −0.275879 + 0.275879i
\(120\) 8853.71 0.614841
\(121\) 6409.60 0.437784
\(122\) 17296.8i 1.16210i
\(123\) 10160.7 0.671607
\(124\) 8682.75 8682.75i 0.564695 0.564695i
\(125\) −11333.9 11333.9i −0.725367 0.725367i
\(126\) −6680.73 6680.73i −0.420807 0.420807i
\(127\) 11444.2 0.709544 0.354772 0.934953i \(-0.384559\pi\)
0.354772 + 0.934953i \(0.384559\pi\)
\(128\) −1024.00 + 1024.00i −0.0625000 + 0.0625000i
\(129\) 32513.9 + 32513.9i 1.95384 + 1.95384i
\(130\) 3391.88 3391.88i 0.200703 0.200703i
\(131\) 8345.03 + 8345.03i 0.486279 + 0.486279i 0.907130 0.420851i \(-0.138269\pi\)
−0.420851 + 0.907130i \(0.638269\pi\)
\(132\) 11689.4i 0.670880i
\(133\) 3109.10 3109.10i 0.175765 0.175765i
\(134\) 6773.21 6773.21i 0.377211 0.377211i
\(135\) −26942.2 26942.2i −1.47831 1.47831i
\(136\) 6675.87i 0.360936i
\(137\) 1141.42 0.0608141 0.0304070 0.999538i \(-0.490320\pi\)
0.0304070 + 0.999538i \(0.490320\pi\)
\(138\) 44215.4i 2.32175i
\(139\) 25300.6i 1.30948i −0.755852 0.654742i \(-0.772777\pi\)
0.755852 0.654742i \(-0.227223\pi\)
\(140\) 2573.67 + 2573.67i 0.131310 + 0.131310i
\(141\) 34774.0i 1.74911i
\(142\) 4269.82 + 4269.82i 0.211754 + 0.211754i
\(143\) 4478.25 + 4478.25i 0.218996 + 0.218996i
\(144\) 11416.2 0.550548
\(145\) −22.3283 −0.00106199
\(146\) −18664.2 + 18664.2i −0.875596 + 0.875596i
\(147\) 33020.9i 1.52811i
\(148\) 10830.4 + 1627.72i 0.494447 + 0.0743117i
\(149\) −28257.3 −1.27280 −0.636398 0.771361i \(-0.719576\pi\)
−0.636398 + 0.771361i \(0.719576\pi\)
\(150\) −1118.77 1118.77i −0.0497232 0.0497232i
\(151\) 9514.32i 0.417277i −0.977993 0.208638i \(-0.933097\pi\)
0.977993 0.208638i \(-0.0669031\pi\)
\(152\) 5312.89i 0.229955i
\(153\) −37213.3 + 37213.3i −1.58970 + 1.58970i
\(154\) −3397.98 + 3397.98i −0.143278 + 0.143278i
\(155\) 37291.2 1.55218
\(156\) 6359.56 6359.56i 0.261323 0.261323i
\(157\) −9431.87 −0.382647 −0.191324 0.981527i \(-0.561278\pi\)
−0.191324 + 0.981527i \(0.561278\pi\)
\(158\) −6456.67 −0.258639
\(159\) 55126.1i 2.18054i
\(160\) −4397.94 −0.171794
\(161\) 12852.9 12852.9i 0.495850 0.495850i
\(162\) −21617.9 21617.9i −0.823726 0.823726i
\(163\) −28498.0 28498.0i −1.07261 1.07261i −0.997149 0.0754561i \(-0.975959\pi\)
−0.0754561 0.997149i \(-0.524041\pi\)
\(164\) −5047.19 −0.187656
\(165\) −25102.2 + 25102.2i −0.922028 + 0.922028i
\(166\) −17005.7 17005.7i −0.617134 0.617134i
\(167\) −33862.6 + 33862.6i −1.21419 + 1.21419i −0.244557 + 0.969635i \(0.578643\pi\)
−0.969635 + 0.244557i \(0.921357\pi\)
\(168\) 4825.47 + 4825.47i 0.170971 + 0.170971i
\(169\) 23688.3i 0.829392i
\(170\) 14336.0 14336.0i 0.496054 0.496054i
\(171\) 29615.6 29615.6i 1.01281 1.01281i
\(172\) −16150.8 16150.8i −0.545929 0.545929i
\(173\) 21307.1i 0.711923i −0.934501 0.355961i \(-0.884153\pi\)
0.934501 0.355961i \(-0.115847\pi\)
\(174\) −41.8642 −0.00138275
\(175\) 650.428i 0.0212385i
\(176\) 5806.53i 0.187453i
\(177\) 34643.6 + 34643.6i 1.10580 + 1.10580i
\(178\) 24494.0i 0.773073i
\(179\) −19967.8 19967.8i −0.623194 0.623194i 0.323153 0.946347i \(-0.395257\pi\)
−0.946347 + 0.323153i \(0.895257\pi\)
\(180\) 24515.4 + 24515.4i 0.756648 + 0.756648i
\(181\) 41375.7 1.26296 0.631478 0.775394i \(-0.282449\pi\)
0.631478 + 0.775394i \(0.282449\pi\)
\(182\) 3697.30 0.111620
\(183\) −69641.9 + 69641.9i −2.07955 + 2.07955i
\(184\) 21963.3i 0.648727i
\(185\) 19762.0 + 26752.9i 0.577415 + 0.781677i
\(186\) 69918.7 2.02101
\(187\) 18927.6 + 18927.6i 0.541267 + 0.541267i
\(188\) 17273.5i 0.488724i
\(189\) 29368.3i 0.822157i
\(190\) −11409.1 + 11409.1i −0.316041 + 0.316041i
\(191\) −38258.9 + 38258.9i −1.04873 + 1.04873i −0.0499838 + 0.998750i \(0.515917\pi\)
−0.998750 + 0.0499838i \(0.984083\pi\)
\(192\) −8245.86 −0.223683
\(193\) 11383.2 11383.2i 0.305599 0.305599i −0.537601 0.843199i \(-0.680669\pi\)
0.843199 + 0.537601i \(0.180669\pi\)
\(194\) 18495.0 0.491417
\(195\) 27313.4 0.718302
\(196\) 16402.6i 0.426973i
\(197\) 26633.2 0.686264 0.343132 0.939287i \(-0.388512\pi\)
0.343132 + 0.939287i \(0.388512\pi\)
\(198\) −32367.3 + 32367.3i −0.825613 + 0.825613i
\(199\) 15275.4 + 15275.4i 0.385732 + 0.385732i 0.873162 0.487430i \(-0.162066\pi\)
−0.487430 + 0.873162i \(0.662066\pi\)
\(200\) 555.732 + 555.732i 0.0138933 + 0.0138933i
\(201\) 54541.9 1.35001
\(202\) −24058.2 + 24058.2i −0.589604 + 0.589604i
\(203\) −12.1695 12.1695i −0.000295311 0.000295311i
\(204\) 26879.1 26879.1i 0.645883 0.645883i
\(205\) −10838.5 10838.5i −0.257906 0.257906i
\(206\) 25235.8i 0.594679i
\(207\) 122430. 122430.i 2.85724 2.85724i
\(208\) −3159.01 + 3159.01i −0.0730171 + 0.0730171i
\(209\) −15063.2 15063.2i −0.344846 0.344846i
\(210\) 20724.7i 0.469949i
\(211\) −39950.0 −0.897329 −0.448665 0.893700i \(-0.648100\pi\)
−0.448665 + 0.893700i \(0.648100\pi\)
\(212\) 27383.0i 0.609270i
\(213\) 34383.1i 0.757855i
\(214\) −1601.76 1601.76i −0.0349759 0.0349759i
\(215\) 69365.3i 1.50060i
\(216\) 25092.5 + 25092.5i 0.537820 + 0.537820i
\(217\) 20324.6 + 20324.6i 0.431620 + 0.431620i
\(218\) −40465.2 −0.851468
\(219\) −150295. −3.13370
\(220\) 12469.1 12469.1i 0.257627 0.257627i
\(221\) 20594.9i 0.421672i
\(222\) 37052.6 + 50160.0i 0.751818 + 1.01777i
\(223\) −79047.8 −1.58957 −0.794785 0.606891i \(-0.792417\pi\)
−0.794785 + 0.606891i \(0.792417\pi\)
\(224\) −2396.98 2396.98i −0.0477714 0.0477714i
\(225\) 6195.62i 0.122383i
\(226\) 51841.2i 1.01498i
\(227\) −1601.08 + 1601.08i −0.0310714 + 0.0310714i −0.722472 0.691400i \(-0.756994\pi\)
0.691400 + 0.722472i \(0.256994\pi\)
\(228\) −21391.3 + 21391.3i −0.411498 + 0.411498i
\(229\) 39765.1 0.758283 0.379142 0.925339i \(-0.376219\pi\)
0.379142 + 0.925339i \(0.376219\pi\)
\(230\) −47164.7 + 47164.7i −0.891582 + 0.891582i
\(231\) −27362.6 −0.512782
\(232\) 20.7954 0.000386359
\(233\) 3585.54i 0.0660454i −0.999455 0.0330227i \(-0.989487\pi\)
0.999455 0.0330227i \(-0.0105134\pi\)
\(234\) 35218.5 0.643190
\(235\) −37093.5 + 37093.5i −0.671680 + 0.671680i
\(236\) −17208.6 17208.6i −0.308974 0.308974i
\(237\) −25996.5 25996.5i −0.462826 0.462826i
\(238\) 15626.9 0.275879
\(239\) 30124.4 30124.4i 0.527379 0.527379i −0.392411 0.919790i \(-0.628359\pi\)
0.919790 + 0.392411i \(0.128359\pi\)
\(240\) −17707.4 17707.4i −0.307420 0.307420i
\(241\) −63589.9 + 63589.9i −1.09485 + 1.09485i −0.0998453 + 0.995003i \(0.531835\pi\)
−0.995003 + 0.0998453i \(0.968165\pi\)
\(242\) −12819.2 12819.2i −0.218892 0.218892i
\(243\) 47049.1i 0.796781i
\(244\) 34593.5 34593.5i 0.581052 0.581052i
\(245\) 35223.4 35223.4i 0.586812 0.586812i
\(246\) −20321.5 20321.5i −0.335804 0.335804i
\(247\) 16390.1i 0.268651i
\(248\) −34731.0 −0.564695
\(249\) 136940.i 2.20868i
\(250\) 45335.4i 0.725367i
\(251\) 24224.8 + 24224.8i 0.384515 + 0.384515i 0.872726 0.488211i \(-0.162350\pi\)
−0.488211 + 0.872726i \(0.662350\pi\)
\(252\) 26722.9i 0.420807i
\(253\) −62270.9 62270.9i −0.972845 0.972845i
\(254\) −22888.5 22888.5i −0.354772 0.354772i
\(255\) 115442. 1.77535
\(256\) 4096.00 0.0625000
\(257\) 64397.4 64397.4i 0.974994 0.974994i −0.0247010 0.999695i \(-0.507863\pi\)
0.999695 + 0.0247010i \(0.00786337\pi\)
\(258\) 130056.i 1.95384i
\(259\) −3810.17 + 25351.7i −0.0567995 + 0.377927i
\(260\) −13567.5 −0.200703
\(261\) −115.920 115.920i −0.00170167 0.00170167i
\(262\) 33380.1i 0.486279i
\(263\) 55482.7i 0.802132i 0.916049 + 0.401066i \(0.131360\pi\)
−0.916049 + 0.401066i \(0.868640\pi\)
\(264\) 23378.8 23378.8i 0.335440 0.335440i
\(265\) 58803.1 58803.1i 0.837353 0.837353i
\(266\) −12436.4 −0.175765
\(267\) 98620.4 98620.4i 1.38339 1.38339i
\(268\) −27092.8 −0.377211
\(269\) −83804.2 −1.15814 −0.579070 0.815278i \(-0.696584\pi\)
−0.579070 + 0.815278i \(0.696584\pi\)
\(270\) 107769.i 1.47831i
\(271\) 28151.9 0.383327 0.191663 0.981461i \(-0.438612\pi\)
0.191663 + 0.981461i \(0.438612\pi\)
\(272\) −13351.7 + 13351.7i −0.180468 + 0.180468i
\(273\) 14886.5 + 14886.5i 0.199740 + 0.199740i
\(274\) −2282.84 2282.84i −0.0304070 0.0304070i
\(275\) −3151.24 −0.0416693
\(276\) −88430.9 + 88430.9i −1.16088 + 1.16088i
\(277\) 31671.3 + 31671.3i 0.412768 + 0.412768i 0.882702 0.469933i \(-0.155722\pi\)
−0.469933 + 0.882702i \(0.655722\pi\)
\(278\) −50601.1 + 50601.1i −0.654742 + 0.654742i
\(279\) 193601. + 193601.i 2.48713 + 2.48713i
\(280\) 10294.7i 0.131310i
\(281\) −5298.31 + 5298.31i −0.0671004 + 0.0671004i −0.739861 0.672760i \(-0.765109\pi\)
0.672760 + 0.739861i \(0.265109\pi\)
\(282\) −69548.1 + 69548.1i −0.874555 + 0.874555i
\(283\) 67798.9 + 67798.9i 0.846545 + 0.846545i 0.989700 0.143155i \(-0.0457249\pi\)
−0.143155 + 0.989700i \(0.545725\pi\)
\(284\) 17079.3i 0.211754i
\(285\) −91872.6 −1.13109
\(286\) 17913.0i 0.218996i
\(287\) 11814.4i 0.143433i
\(288\) −22832.3 22832.3i −0.275274 0.275274i
\(289\) 3524.42i 0.0421981i
\(290\) 44.6567 + 44.6567i 0.000530995 + 0.000530995i
\(291\) 74466.4 + 74466.4i 0.879375 + 0.879375i
\(292\) 74656.8 0.875596
\(293\) −4879.11 −0.0568337 −0.0284168 0.999596i \(-0.509047\pi\)
−0.0284168 + 0.999596i \(0.509047\pi\)
\(294\) 66041.7 66041.7i 0.764053 0.764053i
\(295\) 73908.7i 0.849281i
\(296\) −18405.3 24916.2i −0.210068 0.284379i
\(297\) −142286. −1.61305
\(298\) 56514.7 + 56514.7i 0.636398 + 0.636398i
\(299\) 67756.2i 0.757891i
\(300\) 4475.08i 0.0497232i
\(301\) 37805.7 37805.7i 0.417277 0.417277i
\(302\) −19028.6 + 19028.6i −0.208638 + 0.208638i
\(303\) −193731. −2.11015
\(304\) 10625.8 10625.8i 0.114978 0.114978i
\(305\) 148574. 1.59714
\(306\) 148853. 1.58970
\(307\) 63026.6i 0.668724i −0.942445 0.334362i \(-0.891479\pi\)
0.942445 0.334362i \(-0.108521\pi\)
\(308\) 13591.9 0.143278
\(309\) −101607. + 101607.i −1.06416 + 1.06416i
\(310\) −74582.4 74582.4i −0.776092 0.776092i
\(311\) 67733.9 + 67733.9i 0.700302 + 0.700302i 0.964475 0.264173i \(-0.0850991\pi\)
−0.264173 + 0.964475i \(0.585099\pi\)
\(312\) −25438.3 −0.261323
\(313\) −94660.2 + 94660.2i −0.966227 + 0.966227i −0.999448 0.0332215i \(-0.989423\pi\)
0.0332215 + 0.999448i \(0.489423\pi\)
\(314\) 18863.7 + 18863.7i 0.191324 + 0.191324i
\(315\) −57385.6 + 57385.6i −0.578338 + 0.578338i
\(316\) 12913.3 + 12913.3i 0.129320 + 0.129320i
\(317\) 123083.i 1.22484i −0.790534 0.612418i \(-0.790197\pi\)
0.790534 0.612418i \(-0.209803\pi\)
\(318\) 110252. 110252.i 1.09027 1.09027i
\(319\) −58.9595 + 58.9595i −0.000579392 + 0.000579392i
\(320\) 8795.88 + 8795.88i 0.0858972 + 0.0858972i
\(321\) 12898.3i 0.125176i
\(322\) −51411.7 −0.495850
\(323\) 69273.8i 0.663993i
\(324\) 86471.5i 0.823726i
\(325\) 1714.42 + 1714.42i 0.0162312 + 0.0162312i
\(326\) 113992.i 1.07261i
\(327\) −162925. 162925.i −1.52367 1.52367i
\(328\) 10094.4 + 10094.4i 0.0938279 + 0.0938279i
\(329\) −40433.7 −0.373552
\(330\) 100409. 0.922028
\(331\) −104158. + 104158.i −0.950685 + 0.950685i −0.998840 0.0481548i \(-0.984666\pi\)
0.0481548 + 0.998840i \(0.484666\pi\)
\(332\) 68023.0i 0.617134i
\(333\) −36293.6 + 241487.i −0.327297 + 2.17773i
\(334\) 135450. 1.21419
\(335\) −58180.0 58180.0i −0.518423 0.518423i
\(336\) 19301.9i 0.170971i
\(337\) 143471.i 1.26329i 0.775256 + 0.631647i \(0.217621\pi\)
−0.775256 + 0.631647i \(0.782379\pi\)
\(338\) 47376.5 47376.5i 0.414696 0.414696i
\(339\) 208728. 208728.i 1.81628 1.81628i
\(340\) −57343.9 −0.496054
\(341\) 98470.1 98470.1i 0.846829 0.846829i
\(342\) −118462. −1.01281
\(343\) 83357.2 0.708524
\(344\) 64603.1i 0.545929i
\(345\) −379798. −3.19091
\(346\) −42614.3 + 42614.3i −0.355961 + 0.355961i
\(347\) −56881.4 56881.4i −0.472401 0.472401i 0.430290 0.902691i \(-0.358411\pi\)
−0.902691 + 0.430290i \(0.858411\pi\)
\(348\) 83.7285 + 83.7285i 0.000691377 + 0.000691377i
\(349\) −94152.4 −0.773002 −0.386501 0.922289i \(-0.626316\pi\)
−0.386501 + 0.922289i \(0.626316\pi\)
\(350\) −1300.86 + 1300.86i −0.0106192 + 0.0106192i
\(351\) 77409.7 + 77409.7i 0.628321 + 0.628321i
\(352\) −11613.1 + 11613.1i −0.0937263 + 0.0937263i
\(353\) −65406.7 65406.7i −0.524896 0.524896i 0.394150 0.919046i \(-0.371039\pi\)
−0.919046 + 0.394150i \(0.871039\pi\)
\(354\) 138574.i 1.10580i
\(355\) 36676.5 36676.5i 0.291026 0.291026i
\(356\) −48988.1 + 48988.1i −0.386536 + 0.386536i
\(357\) 62918.4 + 62918.4i 0.493675 + 0.493675i
\(358\) 79871.0i 0.623194i
\(359\) 98394.7 0.763454 0.381727 0.924275i \(-0.375330\pi\)
0.381727 + 0.924275i \(0.375330\pi\)
\(360\) 98061.6i 0.756648i
\(361\) 75190.5i 0.576964i
\(362\) −82751.3 82751.3i −0.631478 0.631478i
\(363\) 103228.i 0.783400i
\(364\) −7394.61 7394.61i −0.0558100 0.0558100i
\(365\) 160320. + 160320.i 1.20338 + 1.20338i
\(366\) 278568. 2.07955
\(367\) 192551. 1.42960 0.714800 0.699329i \(-0.246518\pi\)
0.714800 + 0.699329i \(0.246518\pi\)
\(368\) 43926.6 43926.6i 0.324364 0.324364i
\(369\) 112538.i 0.826507i
\(370\) 13981.7 93029.8i 0.102131 0.679546i
\(371\) 64098.1 0.465690
\(372\) −139837. 139837.i −1.01050 1.01050i
\(373\) 58181.1i 0.418181i 0.977896 + 0.209091i \(0.0670503\pi\)
−0.977896 + 0.209091i \(0.932950\pi\)
\(374\) 75710.3i 0.541267i
\(375\) −182534. + 182534.i −1.29802 + 1.29802i
\(376\) 34546.9 34546.9i 0.244362 0.244362i
\(377\) 64.1532 0.000451373
\(378\) −58736.5 + 58736.5i −0.411078 + 0.411078i
\(379\) −148456. −1.03352 −0.516759 0.856131i \(-0.672862\pi\)
−0.516759 + 0.856131i \(0.672862\pi\)
\(380\) 45636.3 0.316041
\(381\) 184312.i 1.26970i
\(382\) 153035. 1.04873
\(383\) −1840.77 + 1840.77i −0.0125488 + 0.0125488i −0.713353 0.700805i \(-0.752825\pi\)
0.700805 + 0.713353i \(0.252825\pi\)
\(384\) 16491.7 + 16491.7i 0.111842 + 0.111842i
\(385\) 29187.7 + 29187.7i 0.196915 + 0.196915i
\(386\) −45533.0 −0.305599
\(387\) 360117. 360117.i 2.40448 2.40448i
\(388\) −36990.0 36990.0i −0.245709 0.245709i
\(389\) 17200.6 17200.6i 0.113669 0.113669i −0.647984 0.761654i \(-0.724388\pi\)
0.761654 + 0.647984i \(0.224388\pi\)
\(390\) −54626.9 54626.9i −0.359151 0.359151i
\(391\) 286376.i 1.87319i
\(392\) −32805.2 + 32805.2i −0.213486 + 0.213486i
\(393\) 134398. 134398.i 0.870179 0.870179i
\(394\) −53266.5 53266.5i −0.343132 0.343132i
\(395\) 55461.0i 0.355462i
\(396\) 129469. 0.825613
\(397\) 39243.2i 0.248991i −0.992220 0.124496i \(-0.960269\pi\)
0.992220 0.124496i \(-0.0397312\pi\)
\(398\) 61101.5i 0.385732i
\(399\) −50072.7 50072.7i −0.314525 0.314525i
\(400\) 2222.93i 0.0138933i
\(401\) −120450. 120450.i −0.749064 0.749064i 0.225239 0.974304i \(-0.427684\pi\)
−0.974304 + 0.225239i \(0.927684\pi\)
\(402\) −109084. 109084.i −0.675007 0.675007i
\(403\) −107144. −0.659718
\(404\) 96232.7 0.589604
\(405\) −185692. + 185692.i −1.13209 + 1.13209i
\(406\) 48.6778i 0.000295311i
\(407\) 122826. + 18459.8i 0.741483 + 0.111439i
\(408\) −107516. −0.645883
\(409\) 94473.8 + 94473.8i 0.564761 + 0.564761i 0.930656 0.365895i \(-0.119237\pi\)
−0.365895 + 0.930656i \(0.619237\pi\)
\(410\) 43353.9i 0.257906i
\(411\) 18382.8i 0.108825i
\(412\) 50471.6 50471.6i 0.297339 0.297339i
\(413\) 40281.9 40281.9i 0.236162 0.236162i
\(414\) −489720. −2.85724
\(415\) −146075. + 146075.i −0.848162 + 0.848162i
\(416\) 12636.0 0.0730171
\(417\) −407470. −2.34328
\(418\) 60252.9i 0.344846i
\(419\) 299736. 1.70730 0.853651 0.520846i \(-0.174383\pi\)
0.853651 + 0.520846i \(0.174383\pi\)
\(420\) 41449.5 41449.5i 0.234974 0.234974i
\(421\) −4982.01 4982.01i −0.0281087 0.0281087i 0.692913 0.721021i \(-0.256327\pi\)
−0.721021 + 0.692913i \(0.756327\pi\)
\(422\) 79900.0 + 79900.0i 0.448665 + 0.448665i
\(423\) −385149. −2.15253
\(424\) −54766.0 + 54766.0i −0.304635 + 0.304635i
\(425\) 7246.08 + 7246.08i 0.0401167 + 0.0401167i
\(426\) 68766.2 68766.2i 0.378928 0.378928i
\(427\) 80976.4 + 80976.4i 0.444123 + 0.444123i
\(428\) 6407.03i 0.0349759i
\(429\) 72123.1 72123.1i 0.391886 0.391886i
\(430\) −138731. + 138731.i −0.750301 + 0.750301i
\(431\) −100084. 100084.i −0.538780 0.538780i 0.384391 0.923170i \(-0.374412\pi\)
−0.923170 + 0.384391i \(0.874412\pi\)
\(432\) 100370.i 0.537820i
\(433\) 195739. 1.04400 0.522001 0.852945i \(-0.325186\pi\)
0.522001 + 0.852945i \(0.325186\pi\)
\(434\) 81298.3i 0.431620i
\(435\) 359.602i 0.00190039i
\(436\) 80930.4 + 80930.4i 0.425734 + 0.425734i
\(437\) 227908.i 1.19343i
\(438\) 300591. + 300591.i 1.56685 + 1.56685i
\(439\) −108866. 108866.i −0.564890 0.564890i 0.365803 0.930692i \(-0.380794\pi\)
−0.930692 + 0.365803i \(0.880794\pi\)
\(440\) −49876.5 −0.257627
\(441\) 365731. 1.88055
\(442\) −41189.8 + 41189.8i −0.210836 + 0.210836i
\(443\) 170934.i 0.871004i −0.900188 0.435502i \(-0.856571\pi\)
0.900188 0.435502i \(-0.143429\pi\)
\(444\) 26214.8 174425.i 0.132978 0.884796i
\(445\) −210397. −1.06248
\(446\) 158096. + 158096.i 0.794785 + 0.794785i
\(447\) 455090.i 2.27763i
\(448\) 9587.91i 0.0477714i
\(449\) −72459.7 + 72459.7i −0.359421 + 0.359421i −0.863600 0.504178i \(-0.831795\pi\)
0.504178 + 0.863600i \(0.331795\pi\)
\(450\) −12391.2 + 12391.2i −0.0611914 + 0.0611914i
\(451\) −57239.6 −0.281412
\(452\) −103682. + 103682.i −0.507491 + 0.507491i
\(453\) −153230. −0.746702
\(454\) 6404.31 0.0310714
\(455\) 31758.8i 0.153406i
\(456\) 85565.2 0.411498
\(457\) 238333. 238333.i 1.14117 1.14117i 0.152939 0.988236i \(-0.451126\pi\)
0.988236 0.152939i \(-0.0488739\pi\)
\(458\) −79530.3 79530.3i −0.379142 0.379142i
\(459\) 327177. + 327177.i 1.55295 + 1.55295i
\(460\) 188659. 0.891582
\(461\) −35237.3 + 35237.3i −0.165806 + 0.165806i −0.785133 0.619327i \(-0.787406\pi\)
0.619327 + 0.785133i \(0.287406\pi\)
\(462\) 54725.1 + 54725.1i 0.256391 + 0.256391i
\(463\) 186902. 186902.i 0.871870 0.871870i −0.120806 0.992676i \(-0.538548\pi\)
0.992676 + 0.120806i \(0.0385478\pi\)
\(464\) −41.5908 41.5908i −0.000193180 0.000193180i
\(465\) 600583.i 2.77758i
\(466\) −7171.08 + 7171.08i −0.0330227 + 0.0330227i
\(467\) 206870. 206870.i 0.948556 0.948556i −0.0501835 0.998740i \(-0.515981\pi\)
0.998740 + 0.0501835i \(0.0159806\pi\)
\(468\) −70437.0 70437.0i −0.321595 0.321595i
\(469\) 63418.8i 0.288319i
\(470\) 148374. 0.671680
\(471\) 151902.i 0.684734i
\(472\) 68834.5i 0.308974i
\(473\) −183164. 183164.i −0.818687 0.818687i
\(474\) 103986.i 0.462826i
\(475\) −5766.68 5766.68i −0.0255587 0.0255587i
\(476\) −31253.7 31253.7i −0.137939 0.137939i
\(477\) 610564. 2.68346
\(478\) −120498. −0.527379
\(479\) −224838. + 224838.i −0.979940 + 0.979940i −0.999803 0.0198625i \(-0.993677\pi\)
0.0198625 + 0.999803i \(0.493677\pi\)
\(480\) 70829.7i 0.307420i
\(481\) −56779.8 76865.7i −0.245416 0.332233i
\(482\) 254360. 1.09485
\(483\) −206999. 206999.i −0.887307 0.887307i
\(484\) 51276.8i 0.218892i
\(485\) 158867.i 0.675382i
\(486\) −94098.3 + 94098.3i −0.398391 + 0.398391i
\(487\) −198378. + 198378.i −0.836440 + 0.836440i −0.988388 0.151949i \(-0.951445\pi\)
0.151949 + 0.988388i \(0.451445\pi\)
\(488\) −138374. −0.581052
\(489\) −458967. + 458967.i −1.91939 + 1.91939i
\(490\) −140894. −0.586812
\(491\) −303671. −1.25962 −0.629812 0.776748i \(-0.716868\pi\)
−0.629812 + 0.776748i \(0.716868\pi\)
\(492\) 81286.0i 0.335804i
\(493\) 271.147 0.00111561
\(494\) 32780.2 32780.2i 0.134325 0.134325i
\(495\) 278026. + 278026.i 1.13469 + 1.13469i
\(496\) 69462.0 + 69462.0i 0.282348 + 0.282348i
\(497\) 39979.1 0.161853
\(498\) −273881. + 273881.i −1.10434 + 1.10434i
\(499\) −131685. 131685.i −0.528855 0.528855i 0.391376 0.920231i \(-0.371999\pi\)
−0.920231 + 0.391376i \(0.871999\pi\)
\(500\) 90670.8 90670.8i 0.362683 0.362683i
\(501\) 545364. + 545364.i 2.17276 + 2.17276i
\(502\) 96899.2i 0.384515i
\(503\) −215652. + 215652.i −0.852349 + 0.852349i −0.990422 0.138073i \(-0.955909\pi\)
0.138073 + 0.990422i \(0.455909\pi\)
\(504\) 53445.8 53445.8i 0.210403 0.210403i
\(505\) 206653. + 206653.i 0.810325 + 0.810325i
\(506\) 249083.i 0.972845i
\(507\) 381504. 1.48417
\(508\) 91553.9i 0.354772i
\(509\) 14522.4i 0.0560534i 0.999607 + 0.0280267i \(0.00892234\pi\)
−0.999607 + 0.0280267i \(0.991078\pi\)
\(510\) −230884. 230884.i −0.887673 0.887673i
\(511\) 174756.i 0.669255i
\(512\) −8192.00 8192.00i −0.0312500 0.0312500i
\(513\) −260379. 260379.i −0.989397 0.989397i
\(514\) −257589. −0.974994
\(515\) 216768. 0.817300
\(516\) −260111. + 260111.i −0.976922 + 0.976922i
\(517\) 195896.i 0.732900i
\(518\) 58323.7 43083.1i 0.217363 0.160564i
\(519\) −343156. −1.27396
\(520\) 27135.0 + 27135.0i 0.100351 + 0.100351i
\(521\) 438916.i 1.61699i −0.588506 0.808493i \(-0.700284\pi\)
0.588506 0.808493i \(-0.299716\pi\)
\(522\) 463.679i 0.00170167i
\(523\) −200303. + 200303.i −0.732290 + 0.732290i −0.971073 0.238783i \(-0.923252\pi\)
0.238783 + 0.971073i \(0.423252\pi\)
\(524\) −66760.2 + 66760.2i −0.243139 + 0.243139i
\(525\) −10475.3 −0.0380055
\(526\) 110965. 110965.i 0.401066 0.401066i
\(527\) −452851. −1.63055
\(528\) −93515.4 −0.335440
\(529\) 662321.i 2.36678i
\(530\) −235213. −0.837353
\(531\) 383704. 383704.i 1.36084 1.36084i
\(532\) 24872.8 + 24872.8i 0.0878823 + 0.0878823i
\(533\) 31140.9 + 31140.9i 0.109617 + 0.109617i
\(534\) −394481. −1.38339
\(535\) −13758.6 + 13758.6i −0.0480693 + 0.0480693i
\(536\) 54185.7 + 54185.7i 0.188606 + 0.188606i
\(537\) −321585. + 321585.i −1.11518 + 1.11518i
\(538\) 167608. + 167608.i 0.579070 + 0.579070i
\(539\) 186020.i 0.640297i
\(540\) 215538. 215538.i 0.739156 0.739156i
\(541\) 243047. 243047.i 0.830418 0.830418i −0.157156 0.987574i \(-0.550233\pi\)
0.987574 + 0.157156i \(0.0502326\pi\)
\(542\) −56303.8 56303.8i −0.191663 0.191663i
\(543\) 666363.i 2.26002i
\(544\) 53407.0 0.180468
\(545\) 347585.i 1.17022i
\(546\) 59545.8i 0.199740i
\(547\) 229291. + 229291.i 0.766325 + 0.766325i 0.977458 0.211132i \(-0.0677150\pi\)
−0.211132 + 0.977458i \(0.567715\pi\)
\(548\) 9131.36i 0.0304070i
\(549\) 771338. + 771338.i 2.55917 + 2.55917i
\(550\) 6302.49 + 6302.49i 0.0208347 + 0.0208347i
\(551\) −215.788 −0.000710763
\(552\) 353724. 1.16088
\(553\) −30227.5 + 30227.5i −0.0988444 + 0.0988444i
\(554\) 126685.i 0.412768i
\(555\) 430861. 318272.i 1.39878 1.03327i
\(556\) 202404. 0.654742
\(557\) 130650. + 130650.i 0.421113 + 0.421113i 0.885587 0.464474i \(-0.153757\pi\)
−0.464474 + 0.885587i \(0.653757\pi\)
\(558\) 774404.i 2.48713i
\(559\) 199299.i 0.637795i
\(560\) −20589.4 + 20589.4i −0.0656549 + 0.0656549i
\(561\) 304832. 304832.i 0.968579 0.968579i
\(562\) 21193.2 0.0671004
\(563\) −414380. + 414380.i −1.30732 + 1.30732i −0.383976 + 0.923343i \(0.625445\pi\)
−0.923343 + 0.383976i \(0.874555\pi\)
\(564\) 278192. 0.874555
\(565\) −445302. −1.39495
\(566\) 271196.i 0.846545i
\(567\) −202412. −0.629609
\(568\) −34158.5 + 34158.5i −0.105877 + 0.105877i
\(569\) 33073.8 + 33073.8i 0.102155 + 0.102155i 0.756337 0.654182i \(-0.226987\pi\)
−0.654182 + 0.756337i \(0.726987\pi\)
\(570\) 183745. + 183745.i 0.565544 + 0.565544i
\(571\) −106772. −0.327481 −0.163741 0.986503i \(-0.552356\pi\)
−0.163741 + 0.986503i \(0.552356\pi\)
\(572\) −35826.0 + 35826.0i −0.109498 + 0.109498i
\(573\) 616167. + 616167.i 1.87667 + 1.87667i
\(574\) −23628.9 + 23628.9i −0.0717166 + 0.0717166i
\(575\) −23839.3 23839.3i −0.0721037 0.0721037i
\(576\) 91329.2i 0.275274i
\(577\) −314660. + 314660.i −0.945126 + 0.945126i −0.998571 0.0534445i \(-0.982980\pi\)
0.0534445 + 0.998571i \(0.482980\pi\)
\(578\) −7048.85 + 7048.85i −0.0210990 + 0.0210990i
\(579\) −183329. 183329.i −0.546858 0.546858i
\(580\) 178.627i 0.000530995i
\(581\) −159228. −0.471702
\(582\) 297865.i 0.879375i
\(583\) 310548.i 0.913674i
\(584\) −149314. 149314.i −0.437798 0.437798i
\(585\) 302517.i 0.883972i
\(586\) 9758.23 + 9758.23i 0.0284168 + 0.0284168i
\(587\) 122380. + 122380.i 0.355168 + 0.355168i 0.862028 0.506860i \(-0.169194\pi\)
−0.506860 + 0.862028i \(0.669194\pi\)
\(588\) −264167. −0.764053
\(589\) 360395. 1.03884
\(590\) −147817. + 147817.i −0.424641 + 0.424641i
\(591\) 428934.i 1.22805i
\(592\) −13021.8 + 86642.9i −0.0371558 + 0.247223i
\(593\) −228088. −0.648624 −0.324312 0.945950i \(-0.605133\pi\)
−0.324312 + 0.945950i \(0.605133\pi\)
\(594\) 284571. + 284571.i 0.806526 + 0.806526i
\(595\) 134230.i 0.379155i
\(596\) 226059.i 0.636398i
\(597\) 246013. 246013.i 0.690255 0.690255i
\(598\) 135512. 135512.i 0.378945 0.378945i
\(599\) −143065. −0.398732 −0.199366 0.979925i \(-0.563888\pi\)
−0.199366 + 0.979925i \(0.563888\pi\)
\(600\) 8950.17 8950.17i 0.0248616 0.0248616i
\(601\) 25941.8 0.0718209 0.0359104 0.999355i \(-0.488567\pi\)
0.0359104 + 0.999355i \(0.488567\pi\)
\(602\) −151223. −0.417277
\(603\) 604094.i 1.66138i
\(604\) 76114.6 0.208638
\(605\) −110113. + 110113.i −0.300836 + 0.300836i
\(606\) 387462. + 387462.i 1.05508 + 1.05508i
\(607\) 90425.1 + 90425.1i 0.245421 + 0.245421i 0.819088 0.573667i \(-0.194480\pi\)
−0.573667 + 0.819088i \(0.694480\pi\)
\(608\) −42503.1 −0.114978
\(609\) −195.991 + 195.991i −0.000528448 + 0.000528448i
\(610\) −297149. 297149.i −0.798572 0.798572i
\(611\) 106576. 106576.i 0.285481 0.285481i
\(612\) −297706. 297706.i −0.794850 0.794850i
\(613\) 440270.i 1.17165i −0.810437 0.585826i \(-0.800770\pi\)
0.810437 0.585826i \(-0.199230\pi\)
\(614\) −126053. + 126053.i −0.334362 + 0.334362i
\(615\) −174556. + 174556.i −0.461514 + 0.461514i
\(616\) −27183.8 27183.8i −0.0716390 0.0716390i
\(617\) 160802.i 0.422398i 0.977443 + 0.211199i \(0.0677368\pi\)
−0.977443 + 0.211199i \(0.932263\pi\)
\(618\) 406427. 1.06416
\(619\) 28646.9i 0.0747646i 0.999301 + 0.0373823i \(0.0119019\pi\)
−0.999301 + 0.0373823i \(0.988098\pi\)
\(620\) 298330.i 0.776092i
\(621\) −1.07640e6 1.07640e6i −2.79119 2.79119i
\(622\) 270936.i 0.700302i
\(623\) −114671. 114671.i −0.295446 0.295446i
\(624\) 50876.5 + 50876.5i 0.130662 + 0.130662i
\(625\) 367710. 0.941338
\(626\) 378641. 0.966227
\(627\) −242596. + 242596.i −0.617090 + 0.617090i
\(628\) 75455.0i 0.191324i
\(629\) −239983. 324877.i −0.606568 0.821142i
\(630\) 229542. 0.578338
\(631\) −121496. 121496.i −0.305143 0.305143i 0.537879 0.843022i \(-0.319226\pi\)
−0.843022 + 0.537879i \(0.819226\pi\)
\(632\) 51653.3i 0.129320i
\(633\) 643403.i 1.60574i
\(634\) −246165. + 246165.i −0.612418 + 0.612418i
\(635\) −196606. + 196606.i −0.487583 + 0.487583i
\(636\) −441009. −1.09027
\(637\) −101203. + 101203.i −0.249410 + 0.249410i
\(638\) 235.838 0.000579392
\(639\) 380819. 0.932647
\(640\) 35183.5i 0.0858972i
\(641\) −567299. −1.38069 −0.690345 0.723480i \(-0.742541\pi\)
−0.690345 + 0.723480i \(0.742541\pi\)
\(642\) −25796.6 + 25796.6i −0.0625882 + 0.0625882i
\(643\) −210883. 210883.i −0.510058 0.510058i 0.404486 0.914544i \(-0.367450\pi\)
−0.914544 + 0.404486i \(0.867450\pi\)
\(644\) 102823. + 102823.i 0.247925 + 0.247925i
\(645\) −1.11714e6 −2.68528
\(646\) 138548. 138548.i 0.331997 0.331997i
\(647\) 373004. + 373004.i 0.891055 + 0.891055i 0.994622 0.103567i \(-0.0330257\pi\)
−0.103567 + 0.994622i \(0.533026\pi\)
\(648\) 172943. 172943.i 0.411863 0.411863i
\(649\) −195161. 195161.i −0.463344 0.463344i
\(650\) 6857.67i 0.0162312i
\(651\) 327331. 327331.i 0.772370 0.772370i
\(652\) 227984. 227984.i 0.536303 0.536303i
\(653\) 406883. + 406883.i 0.954209 + 0.954209i 0.998997 0.0447872i \(-0.0142610\pi\)
−0.0447872 + 0.998997i \(0.514261\pi\)
\(654\) 651700.i 1.52367i
\(655\) −286726. −0.668320
\(656\) 40377.5i 0.0938279i
\(657\) 1.66464e6i 3.85646i
\(658\) 80867.3 + 80867.3i 0.186776 + 0.186776i
\(659\) 515331.i 1.18663i −0.804971 0.593315i \(-0.797819\pi\)
0.804971 0.593315i \(-0.202181\pi\)
\(660\) −200818. 200818.i −0.461014 0.461014i
\(661\) −108672. 108672.i −0.248723 0.248723i 0.571723 0.820447i \(-0.306275\pi\)
−0.820447 + 0.571723i \(0.806275\pi\)
\(662\) 416632. 0.950685
\(663\) −331685. −0.754568
\(664\) 136046. 136046.i 0.308567 0.308567i
\(665\) 106825.i 0.241563i
\(666\) 555560. 410386.i 1.25251 0.925218i
\(667\) −892.062 −0.00200513
\(668\) −270901. 270901.i −0.607096 0.607096i
\(669\) 1.27308e6i 2.84448i
\(670\) 232720.i 0.518423i
\(671\) 392321. 392321.i 0.871358 0.871358i
\(672\) −38603.8 + 38603.8i −0.0854853 + 0.0854853i
\(673\) 538303. 1.18849 0.594247 0.804283i \(-0.297450\pi\)
0.594247 + 0.804283i \(0.297450\pi\)
\(674\) 286942. 286942.i 0.631647 0.631647i
\(675\) −54471.5 −0.119553
\(676\) −189506. −0.414696
\(677\) 79620.7i 0.173720i 0.996221 + 0.0868598i \(0.0276832\pi\)
−0.996221 + 0.0868598i \(0.972317\pi\)
\(678\) −834913. −1.81628
\(679\) 86586.1 86586.1i 0.187806 0.187806i
\(680\) 114688. + 114688.i 0.248027 + 0.248027i
\(681\) 25785.7 + 25785.7i 0.0556012 + 0.0556012i
\(682\) −393880. −0.846829
\(683\) 76616.8 76616.8i 0.164241 0.164241i −0.620201 0.784443i \(-0.712949\pi\)
0.784443 + 0.620201i \(0.212949\pi\)
\(684\) 236925. + 236925.i 0.506406 + 0.506406i
\(685\) −19609.0 + 19609.0i −0.0417901 + 0.0417901i
\(686\) −166714. 166714.i −0.354262 0.354262i
\(687\) 640425.i 1.35692i
\(688\) 129206. 129206.i 0.272965 0.272965i
\(689\) −168952. + 168952.i −0.355897 + 0.355897i
\(690\) 759597. + 759597.i 1.59546 + 1.59546i
\(691\) 109656.i 0.229655i −0.993385 0.114827i \(-0.963369\pi\)
0.993385 0.114827i \(-0.0366315\pi\)
\(692\) 170457. 0.355961
\(693\) 303061.i 0.631051i
\(694\) 227525.i 0.472401i
\(695\) 434650. + 434650.i 0.899849 + 0.899849i
\(696\) 334.914i 0.000691377i
\(697\) 131619. + 131619.i 0.270927 + 0.270927i
\(698\) 188305. + 188305.i 0.386501 + 0.386501i
\(699\) −57745.9 −0.118186
\(700\) 5203.42 0.0106192
\(701\) 41649.9 41649.9i 0.0847574 0.0847574i −0.663457 0.748214i \(-0.730911\pi\)
0.748214 + 0.663457i \(0.230911\pi\)
\(702\) 309639.i 0.628321i
\(703\) 190987. + 258549.i 0.386450 + 0.523157i
\(704\) 46452.3 0.0937263
\(705\) 597399. + 597399.i 1.20195 + 1.20195i
\(706\) 261627.i 0.524896i
\(707\) 225261.i 0.450659i
\(708\) −277148. + 277148.i −0.552899 + 0.552899i
\(709\) 279963. 279963.i 0.556939 0.556939i −0.371496 0.928435i \(-0.621155\pi\)
0.928435 + 0.371496i \(0.121155\pi\)
\(710\) −146706. −0.291026
\(711\) −287931. + 287931.i −0.569573 + 0.569573i
\(712\) 195952. 0.386536
\(713\) 1.48986e6 2.93067
\(714\) 251674.i 0.493675i
\(715\) −153868. −0.300978
\(716\) 159742. 159742.i 0.311597 0.311597i
\(717\) −485160. 485160.i −0.943728 0.943728i
\(718\) −196789. 196789.i −0.381727 0.381727i
\(719\) 612341. 1.18450 0.592250 0.805754i \(-0.298240\pi\)
0.592250 + 0.805754i \(0.298240\pi\)
\(720\) −196123. + 196123.i −0.378324 + 0.378324i
\(721\) 118144. + 118144.i 0.227269 + 0.227269i
\(722\) 150381. 150381.i 0.288482 0.288482i
\(723\) 1.02413e6 + 1.02413e6i 1.95919 + 1.95919i
\(724\) 331005.i 0.631478i
\(725\) −22.5716 + 22.5716i −4.29424e−5 + 4.29424e-5i
\(726\) −206456. + 206456.i −0.391700 + 0.391700i
\(727\) −238127. 238127.i −0.450547 0.450547i 0.444989 0.895536i \(-0.353208\pi\)
−0.895536 + 0.444989i \(0.853208\pi\)
\(728\) 29578.4i 0.0558100i
\(729\) 117788. 0.221639
\(730\) 641281.i 1.20338i
\(731\) 842347.i 1.57636i
\(732\) −557135. 557135.i −1.03977 1.03977i
\(733\) 291296.i 0.542159i 0.962557 + 0.271079i \(0.0873806\pi\)
−0.962557 + 0.271079i \(0.912619\pi\)
\(734\) −385103. 385103.i −0.714800 0.714800i
\(735\) −567280. 567280.i −1.05008 1.05008i
\(736\) −175707. −0.324364
\(737\) −307257. −0.565674
\(738\) −225076. + 225076.i −0.413254 + 0.413254i
\(739\) 1.03614e6i 1.89727i −0.316370 0.948636i \(-0.602464\pi\)
0.316370 0.948636i \(-0.397536\pi\)
\(740\) −214023. + 158096.i −0.390838 + 0.288708i
\(741\) 263966. 0.480742
\(742\) −128196. 128196.i −0.232845 0.232845i
\(743\) 107255.i 0.194284i 0.995271 + 0.0971422i \(0.0309702\pi\)
−0.995271 + 0.0971422i \(0.969030\pi\)
\(744\) 559350.i 1.01050i
\(745\) 485445. 485445.i 0.874637 0.874637i
\(746\) 116362. 116362.i 0.209091 0.209091i
\(747\) −1.51672e6 −2.71809
\(748\) −151421. + 151421.i −0.270634 + 0.270634i
\(749\) −14997.6 −0.0267336
\(750\) 730136. 1.29802
\(751\) 349562.i 0.619790i −0.950771 0.309895i \(-0.899706\pi\)
0.950771 0.309895i \(-0.100294\pi\)
\(752\) −138188. −0.244362
\(753\) 390145. 390145.i 0.688076 0.688076i
\(754\) −128.306 128.306i −0.000225687 0.000225687i
\(755\) 163451. + 163451.i 0.286743 + 0.286743i
\(756\) 234946. 0.411078
\(757\) −247044. + 247044.i −0.431104 + 0.431104i −0.889004 0.457900i \(-0.848602\pi\)
0.457900 + 0.889004i \(0.348602\pi\)
\(758\) 296911. + 296911.i 0.516759 + 0.516759i
\(759\) −1.00288e6 + 1.00288e6i −1.74087 + 1.74087i
\(760\) −91272.5 91272.5i −0.158020 0.158020i
\(761\) 657307.i 1.13501i 0.823371 + 0.567504i \(0.192091\pi\)
−0.823371 + 0.567504i \(0.807909\pi\)
\(762\) −368623. + 368623.i −0.634852 + 0.634852i
\(763\) −189442. + 189442.i −0.325407 + 0.325407i
\(764\) −306071. 306071.i −0.524367 0.524367i
\(765\) 1.27861e6i 2.18481i
\(766\) 7363.08 0.0125488
\(767\) 212353.i 0.360966i
\(768\) 65966.9i 0.111842i
\(769\) 128881. + 128881.i 0.217940 + 0.217940i 0.807630 0.589690i \(-0.200750\pi\)
−0.589690 + 0.807630i \(0.700750\pi\)
\(770\) 116751.i 0.196915i
\(771\) −1.03713e6 1.03713e6i −1.74472 1.74472i
\(772\) 91065.9 + 91065.9i 0.152799 + 0.152799i
\(773\) −385897. −0.645821 −0.322910 0.946430i \(-0.604661\pi\)
−0.322910 + 0.946430i \(0.604661\pi\)
\(774\) −1.44047e6 −2.40448
\(775\) 37697.5 37697.5i