Properties

Label 74.5.d.a.43.1
Level $74$
Weight $5$
Character 74.43
Analytic conductor $7.649$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 43.1
Root \(-14.0996i\) of defining polynomial
Character \(\chi\) \(=\) 74.43
Dual form 74.5.d.a.31.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.00000 + 2.00000i) q^{2} -13.0996i q^{3} -8.00000i q^{4} +(-23.5442 - 23.5442i) q^{5} +(26.1992 + 26.1992i) q^{6} -19.7742 q^{7} +(16.0000 + 16.0000i) q^{8} -90.5991 q^{9} +O(q^{10})\) \(q+(-2.00000 + 2.00000i) q^{2} -13.0996i q^{3} -8.00000i q^{4} +(-23.5442 - 23.5442i) q^{5} +(26.1992 + 26.1992i) q^{6} -19.7742 q^{7} +(16.0000 + 16.0000i) q^{8} -90.5991 q^{9} +94.1766 q^{10} +152.071i q^{11} -104.797 q^{12} +(144.158 + 144.158i) q^{13} +(39.5484 - 39.5484i) q^{14} +(-308.419 + 308.419i) q^{15} -64.0000 q^{16} +(-104.714 - 104.714i) q^{17} +(181.198 - 181.198i) q^{18} +(-227.423 - 227.423i) q^{19} +(-188.353 + 188.353i) q^{20} +259.034i q^{21} +(-304.142 - 304.142i) q^{22} +(-346.188 - 346.188i) q^{23} +(209.593 - 209.593i) q^{24} +483.655i q^{25} -576.631 q^{26} +125.744i q^{27} +158.194i q^{28} +(-831.151 + 831.151i) q^{29} -1233.67i q^{30} +(237.857 - 237.857i) q^{31} +(128.000 - 128.000i) q^{32} +1992.07 q^{33} +418.857 q^{34} +(465.567 + 465.567i) q^{35} +724.792i q^{36} +(-1250.02 - 558.226i) q^{37} +909.692 q^{38} +(1888.41 - 1888.41i) q^{39} -753.413i q^{40} -316.672i q^{41} +(-518.068 - 518.068i) q^{42} +(2172.28 + 2172.28i) q^{43} +1216.57 q^{44} +(2133.08 + 2133.08i) q^{45} +1384.75 q^{46} -613.021 q^{47} +838.373i q^{48} -2009.98 q^{49} +(-967.310 - 967.310i) q^{50} +(-1371.71 + 1371.71i) q^{51} +(1153.26 - 1153.26i) q^{52} -2538.56 q^{53} +(-251.487 - 251.487i) q^{54} +(3580.38 - 3580.38i) q^{55} +(-316.387 - 316.387i) q^{56} +(-2979.15 + 2979.15i) q^{57} -3324.60i q^{58} +(-2732.58 - 2732.58i) q^{59} +(2467.35 + 2467.35i) q^{60} +(1632.21 - 1632.21i) q^{61} +951.430i q^{62} +1791.52 q^{63} +512.000i q^{64} -6788.14i q^{65} +(-3984.13 + 3984.13i) q^{66} -6634.72i q^{67} +(-837.714 + 837.714i) q^{68} +(-4534.92 + 4534.92i) q^{69} -1862.27 q^{70} -9616.78 q^{71} +(-1449.58 - 1449.58i) q^{72} +5989.19i q^{73} +(3616.49 - 1383.58i) q^{74} +6335.68 q^{75} +(-1819.38 + 1819.38i) q^{76} -3007.08i q^{77} +7553.62i q^{78} +(7624.90 + 7624.90i) q^{79} +(1506.83 + 1506.83i) q^{80} -5691.33 q^{81} +(633.345 + 633.345i) q^{82} -2358.53 q^{83} +2072.27 q^{84} +4930.82i q^{85} -8689.13 q^{86} +(10887.7 + 10887.7i) q^{87} +(-2433.13 + 2433.13i) q^{88} +(4769.82 - 4769.82i) q^{89} -8532.31 q^{90} +(-2850.60 - 2850.60i) q^{91} +(-2769.51 + 2769.51i) q^{92} +(-3115.83 - 3115.83i) q^{93} +(1226.04 - 1226.04i) q^{94} +10709.0i q^{95} +(-1676.75 - 1676.75i) q^{96} +(113.114 + 113.114i) q^{97} +(4019.96 - 4019.96i) q^{98} -13777.5i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 28q^{2} - 12q^{5} - 40q^{6} + 48q^{7} + 224q^{8} - 346q^{9} + O(q^{10}) \) \( 14q - 28q^{2} - 12q^{5} - 40q^{6} + 48q^{7} + 224q^{8} - 346q^{9} + 48q^{10} + 160q^{12} - 56q^{13} - 96q^{14} - 378q^{15} - 896q^{16} - 348q^{17} + 692q^{18} - 184q^{19} - 96q^{20} - 320q^{22} - 502q^{23} - 320q^{24} + 224q^{26} - 474q^{29} - 630q^{31} + 1792q^{32} + 632q^{33} + 1392q^{34} + 1826q^{35} - 2544q^{37} + 736q^{38} - 798q^{39} - 224q^{42} + 1936q^{43} + 1280q^{44} + 6162q^{45} + 2008q^{46} + 5716q^{47} + 7862q^{49} - 1372q^{50} - 2422q^{51} - 448q^{52} - 20228q^{53} - 656q^{54} + 14006q^{55} + 768q^{56} - 2270q^{57} - 4502q^{59} + 3024q^{60} - 11906q^{61} - 2588q^{63} - 1264q^{66} - 2784q^{68} + 21440q^{69} - 7304q^{70} - 11224q^{71} - 5536q^{72} + 4924q^{74} - 18652q^{75} - 1472q^{76} + 20488q^{79} + 768q^{80} - 1706q^{81} + 9808q^{82} - 20224q^{83} + 896q^{84} - 7744q^{86} + 19636q^{87} - 2560q^{88} + 13864q^{89} - 24648q^{90} - 6070q^{91} - 4016q^{92} - 13800q^{93} - 11432q^{94} + 2560q^{96} + 16622q^{97} - 15724q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 13.0996i 1.45551i −0.685838 0.727755i \(-0.740564\pi\)
0.685838 0.727755i \(-0.259436\pi\)
\(4\) 8.00000i 0.500000i
\(5\) −23.5442 23.5442i −0.941766 0.941766i 0.0566289 0.998395i \(-0.481965\pi\)
−0.998395 + 0.0566289i \(0.981965\pi\)
\(6\) 26.1992 + 26.1992i 0.727755 + 0.727755i
\(7\) −19.7742 −0.403555 −0.201778 0.979431i \(-0.564672\pi\)
−0.201778 + 0.979431i \(0.564672\pi\)
\(8\) 16.0000 + 16.0000i 0.250000 + 0.250000i
\(9\) −90.5991 −1.11851
\(10\) 94.1766 0.941766
\(11\) 152.071i 1.25678i 0.777897 + 0.628392i \(0.216287\pi\)
−0.777897 + 0.628392i \(0.783713\pi\)
\(12\) −104.797 −0.727755
\(13\) 144.158 + 144.158i 0.853004 + 0.853004i 0.990502 0.137498i \(-0.0439061\pi\)
−0.137498 + 0.990502i \(0.543906\pi\)
\(14\) 39.5484 39.5484i 0.201778 0.201778i
\(15\) −308.419 + 308.419i −1.37075 + 1.37075i
\(16\) −64.0000 −0.250000
\(17\) −104.714 104.714i −0.362333 0.362333i 0.502338 0.864671i \(-0.332473\pi\)
−0.864671 + 0.502338i \(0.832473\pi\)
\(18\) 181.198 181.198i 0.559253 0.559253i
\(19\) −227.423 227.423i −0.629980 0.629980i 0.318083 0.948063i \(-0.396961\pi\)
−0.948063 + 0.318083i \(0.896961\pi\)
\(20\) −188.353 + 188.353i −0.470883 + 0.470883i
\(21\) 259.034i 0.587378i
\(22\) −304.142 304.142i −0.628392 0.628392i
\(23\) −346.188 346.188i −0.654420 0.654420i 0.299634 0.954054i \(-0.403135\pi\)
−0.954054 + 0.299634i \(0.903135\pi\)
\(24\) 209.593 209.593i 0.363877 0.363877i
\(25\) 483.655i 0.773848i
\(26\) −576.631 −0.853004
\(27\) 125.744i 0.172488i
\(28\) 158.194i 0.201778i
\(29\) −831.151 + 831.151i −0.988289 + 0.988289i −0.999932 0.0116431i \(-0.996294\pi\)
0.0116431 + 0.999932i \(0.496294\pi\)
\(30\) 1233.67i 1.37075i
\(31\) 237.857 237.857i 0.247510 0.247510i −0.572438 0.819948i \(-0.694002\pi\)
0.819948 + 0.572438i \(0.194002\pi\)
\(32\) 128.000 128.000i 0.125000 0.125000i
\(33\) 1992.07 1.82926
\(34\) 418.857 0.362333
\(35\) 465.567 + 465.567i 0.380055 + 0.380055i
\(36\) 724.792i 0.559253i
\(37\) −1250.02 558.226i −0.913088 0.407762i
\(38\) 909.692 0.629980
\(39\) 1888.41 1888.41i 1.24156 1.24156i
\(40\) 753.413i 0.470883i
\(41\) 316.672i 0.188383i −0.995554 0.0941916i \(-0.969973\pi\)
0.995554 0.0941916i \(-0.0300266\pi\)
\(42\) −518.068 518.068i −0.293689 0.293689i
\(43\) 2172.28 + 2172.28i 1.17484 + 1.17484i 0.981041 + 0.193801i \(0.0620815\pi\)
0.193801 + 0.981041i \(0.437919\pi\)
\(44\) 1216.57 0.628392
\(45\) 2133.08 + 2133.08i 1.05337 + 1.05337i
\(46\) 1384.75 0.654420
\(47\) −613.021 −0.277511 −0.138755 0.990327i \(-0.544310\pi\)
−0.138755 + 0.990327i \(0.544310\pi\)
\(48\) 838.373i 0.363877i
\(49\) −2009.98 −0.837143
\(50\) −967.310 967.310i −0.386924 0.386924i
\(51\) −1371.71 + 1371.71i −0.527379 + 0.527379i
\(52\) 1153.26 1153.26i 0.426502 0.426502i
\(53\) −2538.56 −0.903723 −0.451861 0.892088i \(-0.649240\pi\)
−0.451861 + 0.892088i \(0.649240\pi\)
\(54\) −251.487 251.487i −0.0862439 0.0862439i
\(55\) 3580.38 3580.38i 1.18360 1.18360i
\(56\) −316.387 316.387i −0.100889 0.100889i
\(57\) −2979.15 + 2979.15i −0.916942 + 0.916942i
\(58\) 3324.60i 0.988289i
\(59\) −2732.58 2732.58i −0.784998 0.784998i 0.195672 0.980669i \(-0.437311\pi\)
−0.980669 + 0.195672i \(0.937311\pi\)
\(60\) 2467.35 + 2467.35i 0.685375 + 0.685375i
\(61\) 1632.21 1632.21i 0.438649 0.438649i −0.452908 0.891557i \(-0.649613\pi\)
0.891557 + 0.452908i \(0.149613\pi\)
\(62\) 951.430i 0.247510i
\(63\) 1791.52 0.451379
\(64\) 512.000i 0.125000i
\(65\) 6788.14i 1.60666i
\(66\) −3984.13 + 3984.13i −0.914631 + 0.914631i
\(67\) 6634.72i 1.47800i −0.673708 0.738998i \(-0.735299\pi\)
0.673708 0.738998i \(-0.264701\pi\)
\(68\) −837.714 + 837.714i −0.181167 + 0.181167i
\(69\) −4534.92 + 4534.92i −0.952514 + 0.952514i
\(70\) −1862.27 −0.380055
\(71\) −9616.78 −1.90771 −0.953856 0.300265i \(-0.902925\pi\)
−0.953856 + 0.300265i \(0.902925\pi\)
\(72\) −1449.58 1449.58i −0.279627 0.279627i
\(73\) 5989.19i 1.12389i 0.827176 + 0.561943i \(0.189946\pi\)
−0.827176 + 0.561943i \(0.810054\pi\)
\(74\) 3616.49 1383.58i 0.660425 0.252663i
\(75\) 6335.68 1.12634
\(76\) −1819.38 + 1819.38i −0.314990 + 0.314990i
\(77\) 3007.08i 0.507182i
\(78\) 7553.62i 1.24156i
\(79\) 7624.90 + 7624.90i 1.22174 + 1.22174i 0.967012 + 0.254732i \(0.0819873\pi\)
0.254732 + 0.967012i \(0.418013\pi\)
\(80\) 1506.83 + 1506.83i 0.235442 + 0.235442i
\(81\) −5691.33 −0.867449
\(82\) 633.345 + 633.345i 0.0941916 + 0.0941916i
\(83\) −2358.53 −0.342362 −0.171181 0.985240i \(-0.554758\pi\)
−0.171181 + 0.985240i \(0.554758\pi\)
\(84\) 2072.27 0.293689
\(85\) 4930.82i 0.682466i
\(86\) −8689.13 −1.17484
\(87\) 10887.7 + 10887.7i 1.43846 + 1.43846i
\(88\) −2433.13 + 2433.13i −0.314196 + 0.314196i
\(89\) 4769.82 4769.82i 0.602174 0.602174i −0.338715 0.940889i \(-0.609992\pi\)
0.940889 + 0.338715i \(0.109992\pi\)
\(90\) −8532.31 −1.05337
\(91\) −2850.60 2850.60i −0.344234 0.344234i
\(92\) −2769.51 + 2769.51i −0.327210 + 0.327210i
\(93\) −3115.83 3115.83i −0.360254 0.360254i
\(94\) 1226.04 1226.04i 0.138755 0.138755i
\(95\) 10709.0i 1.18659i
\(96\) −1676.75 1676.75i −0.181939 0.181939i
\(97\) 113.114 + 113.114i 0.0120219 + 0.0120219i 0.713092 0.701070i \(-0.247294\pi\)
−0.701070 + 0.713092i \(0.747294\pi\)
\(98\) 4019.96 4019.96i 0.418572 0.418572i
\(99\) 13777.5i 1.40572i
\(100\) 3869.24 0.386924
\(101\) 13533.1i 1.32665i −0.748333 0.663323i \(-0.769146\pi\)
0.748333 0.663323i \(-0.230854\pi\)
\(102\) 5486.85i 0.527379i
\(103\) 13459.1 13459.1i 1.26865 1.26865i 0.321870 0.946784i \(-0.395689\pi\)
0.946784 0.321870i \(-0.104311\pi\)
\(104\) 4613.05i 0.426502i
\(105\) 6098.73 6098.73i 0.553173 0.553173i
\(106\) 5077.11 5077.11i 0.451861 0.451861i
\(107\) 6141.07 0.536385 0.268193 0.963365i \(-0.413574\pi\)
0.268193 + 0.963365i \(0.413574\pi\)
\(108\) 1005.95 0.0862439
\(109\) −14823.0 14823.0i −1.24762 1.24762i −0.956768 0.290853i \(-0.906061\pi\)
−0.290853 0.956768i \(-0.593939\pi\)
\(110\) 14321.5i 1.18360i
\(111\) −7312.53 + 16374.7i −0.593501 + 1.32901i
\(112\) 1265.55 0.100889
\(113\) −10121.6 + 10121.6i −0.792673 + 0.792673i −0.981928 0.189255i \(-0.939393\pi\)
0.189255 + 0.981928i \(0.439393\pi\)
\(114\) 11916.6i 0.916942i
\(115\) 16301.4i 1.23262i
\(116\) 6649.21 + 6649.21i 0.494145 + 0.494145i
\(117\) −13060.6 13060.6i −0.954091 0.954091i
\(118\) 10930.3 0.784998
\(119\) 2070.64 + 2070.64i 0.146221 + 0.146221i
\(120\) −9869.40 −0.685375
\(121\) −8484.56 −0.579507
\(122\) 6528.86i 0.438649i
\(123\) −4148.27 −0.274194
\(124\) −1902.86 1902.86i −0.123755 0.123755i
\(125\) −3327.85 + 3327.85i −0.212983 + 0.212983i
\(126\) −3583.05 + 3583.05i −0.225690 + 0.225690i
\(127\) 12910.8 0.800472 0.400236 0.916412i \(-0.368928\pi\)
0.400236 + 0.916412i \(0.368928\pi\)
\(128\) −1024.00 1024.00i −0.0625000 0.0625000i
\(129\) 28456.0 28456.0i 1.70999 1.70999i
\(130\) 13576.3 + 13576.3i 0.803331 + 0.803331i
\(131\) −3703.95 + 3703.95i −0.215836 + 0.215836i −0.806741 0.590905i \(-0.798771\pi\)
0.590905 + 0.806741i \(0.298771\pi\)
\(132\) 15936.5i 0.914631i
\(133\) 4497.11 + 4497.11i 0.254232 + 0.254232i
\(134\) 13269.4 + 13269.4i 0.738998 + 0.738998i
\(135\) 2960.53 2960.53i 0.162443 0.162443i
\(136\) 3350.86i 0.181167i
\(137\) 10380.8 0.553083 0.276541 0.961002i \(-0.410812\pi\)
0.276541 + 0.961002i \(0.410812\pi\)
\(138\) 18139.7i 0.952514i
\(139\) 28719.5i 1.48644i −0.669049 0.743219i \(-0.733298\pi\)
0.669049 0.743219i \(-0.266702\pi\)
\(140\) 3724.54 3724.54i 0.190027 0.190027i
\(141\) 8030.32i 0.403919i
\(142\) 19233.6 19233.6i 0.953856 0.953856i
\(143\) −21922.2 + 21922.2i −1.07204 + 1.07204i
\(144\) 5798.34 0.279627
\(145\) 39137.5 1.86147
\(146\) −11978.4 11978.4i −0.561943 0.561943i
\(147\) 26329.9i 1.21847i
\(148\) −4465.81 + 10000.1i −0.203881 + 0.456544i
\(149\) −11007.7 −0.495819 −0.247909 0.968783i \(-0.579744\pi\)
−0.247909 + 0.968783i \(0.579744\pi\)
\(150\) −12671.4 + 12671.4i −0.563171 + 0.563171i
\(151\) 23264.9i 1.02034i 0.860072 + 0.510172i \(0.170418\pi\)
−0.860072 + 0.510172i \(0.829582\pi\)
\(152\) 7277.53i 0.314990i
\(153\) 9487.01 + 9487.01i 0.405272 + 0.405272i
\(154\) 6014.16 + 6014.16i 0.253591 + 0.253591i
\(155\) −11200.3 −0.466194
\(156\) −15107.2 15107.2i −0.620778 0.620778i
\(157\) −17848.9 −0.724123 −0.362062 0.932154i \(-0.617927\pi\)
−0.362062 + 0.932154i \(0.617927\pi\)
\(158\) −30499.6 −1.22174
\(159\) 33254.0i 1.31538i
\(160\) −6027.30 −0.235442
\(161\) 6845.59 + 6845.59i 0.264095 + 0.264095i
\(162\) 11382.7 11382.7i 0.433725 0.433725i
\(163\) 26691.5 26691.5i 1.00461 1.00461i 0.00462291 0.999989i \(-0.498528\pi\)
0.999989 0.00462291i \(-0.00147152\pi\)
\(164\) −2533.38 −0.0941916
\(165\) −46901.5 46901.5i −1.72274 1.72274i
\(166\) 4717.07 4717.07i 0.171181 0.171181i
\(167\) 12387.3 + 12387.3i 0.444163 + 0.444163i 0.893408 0.449246i \(-0.148307\pi\)
−0.449246 + 0.893408i \(0.648307\pi\)
\(168\) −4144.54 + 4144.54i −0.146845 + 0.146845i
\(169\) 13001.9i 0.455232i
\(170\) −9861.64 9861.64i −0.341233 0.341233i
\(171\) 20604.3 + 20604.3i 0.704637 + 0.704637i
\(172\) 17378.3 17378.3i 0.587421 0.587421i
\(173\) 31584.6i 1.05532i 0.849457 + 0.527658i \(0.176930\pi\)
−0.849457 + 0.527658i \(0.823070\pi\)
\(174\) −43550.9 −1.43846
\(175\) 9563.89i 0.312290i
\(176\) 9732.54i 0.314196i
\(177\) −35795.6 + 35795.6i −1.14257 + 1.14257i
\(178\) 19079.3i 0.602174i
\(179\) 33482.1 33482.1i 1.04498 1.04498i 0.0460373 0.998940i \(-0.485341\pi\)
0.998940 0.0460373i \(-0.0146593\pi\)
\(180\) 17064.6 17064.6i 0.526686 0.526686i
\(181\) −47551.7 −1.45147 −0.725737 0.687972i \(-0.758501\pi\)
−0.725737 + 0.687972i \(0.758501\pi\)
\(182\) 11402.4 0.344234
\(183\) −21381.3 21381.3i −0.638458 0.638458i
\(184\) 11078.0i 0.327210i
\(185\) 16287.7 + 42573.6i 0.475899 + 1.24393i
\(186\) 12463.3 0.360254
\(187\) 15924.0 15924.0i 0.455375 0.455375i
\(188\) 4904.17i 0.138755i
\(189\) 2486.48i 0.0696084i
\(190\) −21417.9 21417.9i −0.593294 0.593294i
\(191\) 4475.00 + 4475.00i 0.122666 + 0.122666i 0.765775 0.643109i \(-0.222356\pi\)
−0.643109 + 0.765775i \(0.722356\pi\)
\(192\) 6706.99 0.181939
\(193\) 12085.4 + 12085.4i 0.324448 + 0.324448i 0.850470 0.526023i \(-0.176317\pi\)
−0.526023 + 0.850470i \(0.676317\pi\)
\(194\) −452.456 −0.0120219
\(195\) −88921.8 −2.33851
\(196\) 16079.8i 0.418572i
\(197\) −43196.6 −1.11306 −0.556528 0.830829i \(-0.687867\pi\)
−0.556528 + 0.830829i \(0.687867\pi\)
\(198\) 27555.0 + 27555.0i 0.702861 + 0.702861i
\(199\) 14458.4 14458.4i 0.365101 0.365101i −0.500586 0.865687i \(-0.666882\pi\)
0.865687 + 0.500586i \(0.166882\pi\)
\(200\) −7738.48 + 7738.48i −0.193462 + 0.193462i
\(201\) −86912.1 −2.15124
\(202\) 27066.2 + 27066.2i 0.663323 + 0.663323i
\(203\) 16435.3 16435.3i 0.398829 0.398829i
\(204\) 10973.7 + 10973.7i 0.263690 + 0.263690i
\(205\) −7455.78 + 7455.78i −0.177413 + 0.177413i
\(206\) 53836.6i 1.26865i
\(207\) 31364.3 + 31364.3i 0.731973 + 0.731973i
\(208\) −9226.09 9226.09i −0.213251 0.213251i
\(209\) 34584.4 34584.4i 0.791749 0.791749i
\(210\) 24394.9i 0.553173i
\(211\) 38389.4 0.862276 0.431138 0.902286i \(-0.358112\pi\)
0.431138 + 0.902286i \(0.358112\pi\)
\(212\) 20308.5i 0.451861i
\(213\) 125976.i 2.77669i
\(214\) −12282.1 + 12282.1i −0.268193 + 0.268193i
\(215\) 102289.i 2.21285i
\(216\) −2011.90 + 2011.90i −0.0431220 + 0.0431220i
\(217\) −4703.44 + 4703.44i −0.0998841 + 0.0998841i
\(218\) 59291.9 1.24762
\(219\) 78455.9 1.63583
\(220\) −28643.1 28643.1i −0.591799 0.591799i
\(221\) 30190.7i 0.618143i
\(222\) −18124.4 47374.5i −0.367754 0.961255i
\(223\) −6647.07 −0.133666 −0.0668329 0.997764i \(-0.521289\pi\)
−0.0668329 + 0.997764i \(0.521289\pi\)
\(224\) −2531.10 + 2531.10i −0.0504444 + 0.0504444i
\(225\) 43818.7i 0.865554i
\(226\) 40486.5i 0.792673i
\(227\) −17341.3 17341.3i −0.336535 0.336535i 0.518527 0.855061i \(-0.326481\pi\)
−0.855061 + 0.518527i \(0.826481\pi\)
\(228\) 23833.2 + 23833.2i 0.458471 + 0.458471i
\(229\) −74769.8 −1.42579 −0.712895 0.701271i \(-0.752616\pi\)
−0.712895 + 0.701271i \(0.752616\pi\)
\(230\) −32602.8 32602.8i −0.616311 0.616311i
\(231\) −39391.5 −0.738208
\(232\) −26596.8 −0.494145
\(233\) 85523.8i 1.57534i −0.616096 0.787671i \(-0.711287\pi\)
0.616096 0.787671i \(-0.288713\pi\)
\(234\) 52242.2 0.954091
\(235\) 14433.1 + 14433.1i 0.261350 + 0.261350i
\(236\) −21860.6 + 21860.6i −0.392499 + 0.392499i
\(237\) 99883.0 99883.0i 1.77826 1.77826i
\(238\) −8282.56 −0.146221
\(239\) −14535.0 14535.0i −0.254459 0.254459i 0.568337 0.822796i \(-0.307587\pi\)
−0.822796 + 0.568337i \(0.807587\pi\)
\(240\) 19738.8 19738.8i 0.342687 0.342687i
\(241\) 37780.9 + 37780.9i 0.650486 + 0.650486i 0.953110 0.302624i \(-0.0978626\pi\)
−0.302624 + 0.953110i \(0.597863\pi\)
\(242\) 16969.1 16969.1i 0.289753 0.289753i
\(243\) 84739.3i 1.43507i
\(244\) −13057.7 13057.7i −0.219325 0.219325i
\(245\) 47323.3 + 47323.3i 0.788393 + 0.788393i
\(246\) 8296.55 8296.55i 0.137097 0.137097i
\(247\) 65569.5i 1.07475i
\(248\) 7611.44 0.123755
\(249\) 30895.8i 0.498312i
\(250\) 13311.4i 0.212983i
\(251\) 40564.8 40564.8i 0.643876 0.643876i −0.307630 0.951506i \(-0.599536\pi\)
0.951506 + 0.307630i \(0.0995359\pi\)
\(252\) 14332.2i 0.225690i
\(253\) 52645.1 52645.1i 0.822465 0.822465i
\(254\) −25821.6 + 25821.6i −0.400236 + 0.400236i
\(255\) 64591.7 0.993336
\(256\) 4096.00 0.0625000
\(257\) 15552.2 + 15552.2i 0.235464 + 0.235464i 0.814969 0.579505i \(-0.196754\pi\)
−0.579505 + 0.814969i \(0.696754\pi\)
\(258\) 113824.i 1.70999i
\(259\) 24718.1 + 11038.5i 0.368481 + 0.164554i
\(260\) −54305.1 −0.803331
\(261\) 75301.5 75301.5i 1.10541 1.10541i
\(262\) 14815.8i 0.215836i
\(263\) 7873.27i 0.113827i 0.998379 + 0.0569133i \(0.0181259\pi\)
−0.998379 + 0.0569133i \(0.981874\pi\)
\(264\) 31873.0 + 31873.0i 0.457315 + 0.457315i
\(265\) 59768.2 + 59768.2i 0.851096 + 0.851096i
\(266\) −17988.4 −0.254232
\(267\) −62482.7 62482.7i −0.876470 0.876470i
\(268\) −53077.8 −0.738998
\(269\) 49063.4 0.678037 0.339018 0.940780i \(-0.389905\pi\)
0.339018 + 0.940780i \(0.389905\pi\)
\(270\) 11842.1i 0.162443i
\(271\) −21218.5 −0.288919 −0.144460 0.989511i \(-0.546144\pi\)
−0.144460 + 0.989511i \(0.546144\pi\)
\(272\) 6701.71 + 6701.71i 0.0905833 + 0.0905833i
\(273\) −37341.7 + 37341.7i −0.501036 + 0.501036i
\(274\) −20761.6 + 20761.6i −0.276541 + 0.276541i
\(275\) −73549.8 −0.972560
\(276\) 36279.4 + 36279.4i 0.476257 + 0.476257i
\(277\) −48467.9 + 48467.9i −0.631676 + 0.631676i −0.948488 0.316812i \(-0.897388\pi\)
0.316812 + 0.948488i \(0.397388\pi\)
\(278\) 57438.9 + 57438.9i 0.743219 + 0.743219i
\(279\) −21549.7 + 21549.7i −0.276842 + 0.276842i
\(280\) 14898.1i 0.190027i
\(281\) −4510.08 4510.08i −0.0571178 0.0571178i 0.677971 0.735089i \(-0.262860\pi\)
−0.735089 + 0.677971i \(0.762860\pi\)
\(282\) −16060.6 16060.6i −0.201960 0.201960i
\(283\) −72880.9 + 72880.9i −0.909999 + 0.909999i −0.996272 0.0862730i \(-0.972504\pi\)
0.0862730 + 0.996272i \(0.472504\pi\)
\(284\) 76934.2i 0.953856i
\(285\) 140283. 1.72709
\(286\) 87688.8i 1.07204i
\(287\) 6261.94i 0.0760230i
\(288\) −11596.7 + 11596.7i −0.139813 + 0.139813i
\(289\) 61590.8i 0.737429i
\(290\) −78275.0 + 78275.0i −0.930737 + 0.930737i
\(291\) 1481.75 1481.75i 0.0174980 0.0174980i
\(292\) 47913.5 0.561943
\(293\) 23239.5 0.270702 0.135351 0.990798i \(-0.456784\pi\)
0.135351 + 0.990798i \(0.456784\pi\)
\(294\) −52659.8 52659.8i −0.609235 0.609235i
\(295\) 128672.i 1.47857i
\(296\) −11068.7 28931.9i −0.126332 0.330213i
\(297\) −19122.0 −0.216780
\(298\) 22015.3 22015.3i 0.247909 0.247909i
\(299\) 99811.4i 1.11645i
\(300\) 50685.4i 0.563171i
\(301\) −42955.1 42955.1i −0.474113 0.474113i
\(302\) −46529.7 46529.7i −0.510172 0.510172i
\(303\) −177278. −1.93094
\(304\) 14555.1 + 14555.1i 0.157495 + 0.157495i
\(305\) −76858.2 −0.826211
\(306\) −37948.1 −0.405272
\(307\) 8792.55i 0.0932907i −0.998912 0.0466453i \(-0.985147\pi\)
0.998912 0.0466453i \(-0.0148531\pi\)
\(308\) −24056.6 −0.253591
\(309\) −176309. 176309.i −1.84654 1.84654i
\(310\) 22400.6 22400.6i 0.233097 0.233097i
\(311\) 87685.1 87685.1i 0.906577 0.906577i −0.0894171 0.995994i \(-0.528500\pi\)
0.995994 + 0.0894171i \(0.0285004\pi\)
\(312\) 60429.0 0.620778
\(313\) 121488. + 121488.i 1.24006 + 1.24006i 0.959974 + 0.280091i \(0.0903646\pi\)
0.280091 + 0.959974i \(0.409635\pi\)
\(314\) 35697.8 35697.8i 0.362062 0.362062i
\(315\) −42179.9 42179.9i −0.425094 0.425094i
\(316\) 60999.2 60999.2i 0.610872 0.610872i
\(317\) 164919.i 1.64116i 0.571532 + 0.820580i \(0.306349\pi\)
−0.571532 + 0.820580i \(0.693651\pi\)
\(318\) −66508.1 66508.1i −0.657688 0.657688i
\(319\) −126394. 126394.i −1.24207 1.24207i
\(320\) 12054.6 12054.6i 0.117721 0.117721i
\(321\) 80445.5i 0.780714i
\(322\) −27382.4 −0.264095
\(323\) 47628.8i 0.456525i
\(324\) 45530.7i 0.433725i
\(325\) −69722.6 + 69722.6i −0.660095 + 0.660095i
\(326\) 106766.i 1.00461i
\(327\) −194175. + 194175.i −1.81592 + 1.81592i
\(328\) 5066.76 5066.76i 0.0470958 0.0470958i
\(329\) 12122.0 0.111991
\(330\) 187606. 1.72274
\(331\) −125950. 125950.i −1.14958 1.14958i −0.986634 0.162950i \(-0.947899\pi\)
−0.162950 0.986634i \(-0.552101\pi\)
\(332\) 18868.3i 0.171181i
\(333\) 113250. + 50574.8i 1.02130 + 0.456085i
\(334\) −49549.0 −0.444163
\(335\) −156209. + 156209.i −1.39193 + 1.39193i
\(336\) 16578.2i 0.146845i
\(337\) 7186.65i 0.0632800i −0.999499 0.0316400i \(-0.989927\pi\)
0.999499 0.0316400i \(-0.0100730\pi\)
\(338\) −26003.8 26003.8i −0.227616 0.227616i
\(339\) 132589. + 132589.i 1.15374 + 1.15374i
\(340\) 39446.5 0.341233
\(341\) 36171.2 + 36171.2i 0.311067 + 0.311067i
\(342\) −82417.2 −0.704637
\(343\) 87223.6 0.741389
\(344\) 69513.0i 0.587421i
\(345\) 213542. 1.79409
\(346\) −63169.2 63169.2i −0.527658 0.527658i
\(347\) −43965.3 + 43965.3i −0.365133 + 0.365133i −0.865699 0.500566i \(-0.833125\pi\)
0.500566 + 0.865699i \(0.333125\pi\)
\(348\) 87101.9 87101.9i 0.719232 0.719232i
\(349\) −197535. −1.62178 −0.810891 0.585197i \(-0.801017\pi\)
−0.810891 + 0.585197i \(0.801017\pi\)
\(350\) 19127.8 + 19127.8i 0.156145 + 0.156145i
\(351\) −18126.9 + 18126.9i −0.147133 + 0.147133i
\(352\) 19465.1 + 19465.1i 0.157098 + 0.157098i
\(353\) 140884. 140884.i 1.13061 1.13061i 0.140536 0.990076i \(-0.455117\pi\)
0.990076 0.140536i \(-0.0448826\pi\)
\(354\) 143182.i 1.14257i
\(355\) 226419. + 226419.i 1.79662 + 1.79662i
\(356\) −38158.6 38158.6i −0.301087 0.301087i
\(357\) 27124.5 27124.5i 0.212827 0.212827i
\(358\) 133928.i 1.04498i
\(359\) −36497.2 −0.283186 −0.141593 0.989925i \(-0.545222\pi\)
−0.141593 + 0.989925i \(0.545222\pi\)
\(360\) 68258.5i 0.526686i
\(361\) 26878.6i 0.206249i
\(362\) 95103.5 95103.5i 0.725737 0.725737i
\(363\) 111144.i 0.843478i
\(364\) −22804.8 + 22804.8i −0.172117 + 0.172117i
\(365\) 141011. 141011.i 1.05844 1.05844i
\(366\) 85525.3 0.638458
\(367\) 91669.0 0.680598 0.340299 0.940317i \(-0.389472\pi\)
0.340299 + 0.940317i \(0.389472\pi\)
\(368\) 22156.0 + 22156.0i 0.163605 + 0.163605i
\(369\) 28690.2i 0.210708i
\(370\) −117722. 52571.9i −0.859916 0.384016i
\(371\) 50197.9 0.364702
\(372\) −24926.7 + 24926.7i −0.180127 + 0.180127i
\(373\) 83737.2i 0.601867i 0.953645 + 0.300934i \(0.0972983\pi\)
−0.953645 + 0.300934i \(0.902702\pi\)
\(374\) 63696.0i 0.455375i
\(375\) 43593.5 + 43593.5i 0.309998 + 0.309998i
\(376\) −9808.34 9808.34i −0.0693777 0.0693777i
\(377\) −239634. −1.68603
\(378\) 4972.96 + 4972.96i 0.0348042 + 0.0348042i
\(379\) −19315.2 −0.134469 −0.0672343 0.997737i \(-0.521417\pi\)
−0.0672343 + 0.997737i \(0.521417\pi\)
\(380\) 85671.7 0.593294
\(381\) 169126.i 1.16509i
\(382\) −17900.0 −0.122666
\(383\) 107304. + 107304.i 0.731505 + 0.731505i 0.970918 0.239413i \(-0.0769549\pi\)
−0.239413 + 0.970918i \(0.576955\pi\)
\(384\) −13414.0 + 13414.0i −0.0909693 + 0.0909693i
\(385\) −70799.2 + 70799.2i −0.477647 + 0.477647i
\(386\) −48341.4 −0.324448
\(387\) −196807. 196807.i −1.31407 1.31407i
\(388\) 904.912 904.912i 0.00601094 0.00601094i
\(389\) −45020.2 45020.2i −0.297515 0.297515i 0.542525 0.840040i \(-0.317468\pi\)
−0.840040 + 0.542525i \(0.817468\pi\)
\(390\) 177844. 177844.i 1.16925 1.16925i
\(391\) 72501.7i 0.474236i
\(392\) −32159.7 32159.7i −0.209286 0.209286i
\(393\) 48520.2 + 48520.2i 0.314151 + 0.314151i
\(394\) 86393.2 86393.2i 0.556528 0.556528i
\(395\) 359044.i 2.30119i
\(396\) −110220. −0.702861
\(397\) 259119.i 1.64406i 0.569441 + 0.822032i \(0.307160\pi\)
−0.569441 + 0.822032i \(0.692840\pi\)
\(398\) 57833.4i 0.365101i
\(399\) 58910.2 58910.2i 0.370037 0.370037i
\(400\) 30953.9i 0.193462i
\(401\) 193875. 193875.i 1.20568 1.20568i 0.233271 0.972412i \(-0.425057\pi\)
0.972412 0.233271i \(-0.0749431\pi\)
\(402\) 173824. 173824.i 1.07562 1.07562i
\(403\) 68578.0 0.422255
\(404\) −108265. −0.663323
\(405\) 133998. + 133998.i 0.816934 + 0.816934i
\(406\) 65741.4i 0.398829i
\(407\) 84890.0 190091.i 0.512469 1.14756i
\(408\) −43894.8 −0.263690
\(409\) 12139.7 12139.7i 0.0725706 0.0725706i −0.669890 0.742460i \(-0.733659\pi\)
0.742460 + 0.669890i \(0.233659\pi\)
\(410\) 29823.1i 0.177413i
\(411\) 135984.i 0.805017i
\(412\) −107673. 107673.i −0.634327 0.634327i
\(413\) 54034.5 + 54034.5i 0.316790 + 0.316790i
\(414\) −125457. −0.731973
\(415\) 55529.7 + 55529.7i 0.322425 + 0.322425i
\(416\) 36904.4 0.213251
\(417\) −376213. −2.16352
\(418\) 138338.i 0.791749i
\(419\) −87917.3 −0.500779 −0.250390 0.968145i \(-0.580559\pi\)
−0.250390 + 0.968145i \(0.580559\pi\)
\(420\) −48789.9 48789.9i −0.276586 0.276586i
\(421\) 35067.3 35067.3i 0.197851 0.197851i −0.601227 0.799078i \(-0.705321\pi\)
0.799078 + 0.601227i \(0.205321\pi\)
\(422\) −76778.8 + 76778.8i −0.431138 + 0.431138i
\(423\) 55539.1 0.310398
\(424\) −40616.9 40616.9i −0.225931 0.225931i
\(425\) 50645.6 50645.6i 0.280391 0.280391i
\(426\) −251951. 251951.i −1.38835 1.38835i
\(427\) −32275.7 + 32275.7i −0.177019 + 0.177019i
\(428\) 49128.6i 0.268193i
\(429\) 287172. + 287172.i 1.56037 + 1.56037i
\(430\) 204578. + 204578.i 1.10643 + 1.10643i
\(431\) −98575.3 + 98575.3i −0.530656 + 0.530656i −0.920768 0.390111i \(-0.872437\pi\)
0.390111 + 0.920768i \(0.372437\pi\)
\(432\) 8047.59i 0.0431220i
\(433\) −66346.3 −0.353867 −0.176934 0.984223i \(-0.556618\pi\)
−0.176934 + 0.984223i \(0.556618\pi\)
\(434\) 18813.8i 0.0998841i
\(435\) 512685.i 2.70939i
\(436\) −118584. + 118584.i −0.623810 + 0.623810i
\(437\) 157462.i 0.824543i
\(438\) −156912. + 156912.i −0.817914 + 0.817914i
\(439\) −194833. + 194833.i −1.01096 + 1.01096i −0.0110175 + 0.999939i \(0.503507\pi\)
−0.999939 + 0.0110175i \(0.996493\pi\)
\(440\) 114572. 0.591799
\(441\) 182102. 0.936351
\(442\) 60381.5 + 60381.5i 0.309072 + 0.309072i
\(443\) 282981.i 1.44195i −0.692962 0.720974i \(-0.743694\pi\)
0.692962 0.720974i \(-0.256306\pi\)
\(444\) 130998. + 58500.2i 0.664504 + 0.296751i
\(445\) −224603. −1.13422
\(446\) 13294.1 13294.1i 0.0668329 0.0668329i
\(447\) 144196.i 0.721669i
\(448\) 10124.4i 0.0504444i
\(449\) 175892. + 175892.i 0.872475 + 0.872475i 0.992742 0.120266i \(-0.0383748\pi\)
−0.120266 + 0.992742i \(0.538375\pi\)
\(450\) 87637.3 + 87637.3i 0.432777 + 0.432777i
\(451\) 48156.6 0.236757
\(452\) 80973.1 + 80973.1i 0.396336 + 0.396336i
\(453\) 304760. 1.48512
\(454\) 69365.2 0.336535
\(455\) 134230.i 0.648376i
\(456\) −95332.6 −0.458471
\(457\) −116094. 116094.i −0.555873 0.555873i 0.372257 0.928130i \(-0.378584\pi\)
−0.928130 + 0.372257i \(0.878584\pi\)
\(458\) 149540. 149540.i 0.712895 0.712895i
\(459\) 13167.2 13167.2i 0.0624981 0.0624981i
\(460\) 130411. 0.616311
\(461\) −166216. 166216.i −0.782116 0.782116i 0.198072 0.980188i \(-0.436532\pi\)
−0.980188 + 0.198072i \(0.936532\pi\)
\(462\) 78783.0 78783.0i 0.369104 0.369104i
\(463\) −232696. 232696.i −1.08549 1.08549i −0.995986 0.0895072i \(-0.971471\pi\)
−0.0895072 0.995986i \(-0.528529\pi\)
\(464\) 53193.7 53193.7i 0.247072 0.247072i
\(465\) 146719.i 0.678549i
\(466\) 171048. + 171048.i 0.787671 + 0.787671i
\(467\) 13082.1 + 13082.1i 0.0599851 + 0.0599851i 0.736463 0.676478i \(-0.236495\pi\)
−0.676478 + 0.736463i \(0.736495\pi\)
\(468\) −104484. + 104484.i −0.477045 + 0.477045i
\(469\) 131196.i 0.596453i
\(470\) −57732.3 −0.261350
\(471\) 233813.i 1.05397i
\(472\) 87442.5i 0.392499i
\(473\) −330341. + 330341.i −1.47652 + 1.47652i
\(474\) 399532.i 1.77826i
\(475\) 109994. 109994.i 0.487509 0.487509i
\(476\) 16565.1 16565.1i 0.0731107 0.0731107i
\(477\) 229991. 1.01082
\(478\) 58139.9 0.254459
\(479\) −25172.8 25172.8i −0.109714 0.109714i 0.650119 0.759832i \(-0.274719\pi\)
−0.759832 + 0.650119i \(0.774719\pi\)
\(480\) 78955.2i 0.342687i
\(481\) −99727.1 260672.i −0.431045 1.12669i
\(482\) −151124. −0.650486
\(483\) 89674.4 89674.4i 0.384392 0.384392i
\(484\) 67876.5i 0.289753i
\(485\) 5326.35i 0.0226436i
\(486\) −169479. 169479.i −0.717534 0.717534i
\(487\) −264887. 264887.i −1.11687 1.11687i −0.992198 0.124672i \(-0.960212\pi\)
−0.124672 0.992198i \(-0.539788\pi\)
\(488\) 52230.9 0.219325
\(489\) −349648. 349648.i −1.46222 1.46222i
\(490\) −189293. −0.788393
\(491\) 130782. 0.542483 0.271241 0.962511i \(-0.412566\pi\)
0.271241 + 0.962511i \(0.412566\pi\)
\(492\) 33186.2i 0.137097i
\(493\) 174067. 0.716180
\(494\) 131139. + 131139.i 0.537376 + 0.537376i
\(495\) −324379. + 324379.i −1.32386 + 1.32386i
\(496\) −15222.9 + 15222.9i −0.0618776 + 0.0618776i
\(497\) 190164. 0.769867
\(498\) −61791.6 61791.6i −0.249156 0.249156i
\(499\) −63580.0 + 63580.0i −0.255340 + 0.255340i −0.823156 0.567816i \(-0.807789\pi\)
0.567816 + 0.823156i \(0.307789\pi\)
\(500\) 26622.8 + 26622.8i 0.106491 + 0.106491i
\(501\) 162268. 162268.i 0.646483 0.646483i
\(502\) 162259.i 0.643876i
\(503\) 320918. + 320918.i 1.26841 + 1.26841i 0.946911 + 0.321497i \(0.104186\pi\)
0.321497 + 0.946911i \(0.395814\pi\)
\(504\) 28664.4 + 28664.4i 0.112845 + 0.112845i
\(505\) −318626. + 318626.i −1.24939 + 1.24939i
\(506\) 210581.i 0.822465i
\(507\) 170319. 0.662594
\(508\) 103287.i 0.400236i
\(509\) 293144.i 1.13148i −0.824585 0.565738i \(-0.808591\pi\)
0.824585 0.565738i \(-0.191409\pi\)
\(510\) −129183. + 129183.i −0.496668 + 0.496668i
\(511\) 118432.i 0.453550i
\(512\) −8192.00 + 8192.00i −0.0312500 + 0.0312500i
\(513\) 28597.0 28597.0i 0.108664 0.108664i
\(514\) −62208.8 −0.235464
\(515\) −633769. −2.38955
\(516\) −227648. 227648.i −0.854996 0.854996i
\(517\) 93222.7i 0.348771i
\(518\) −71513.2 + 27359.3i −0.266518 + 0.101964i
\(519\) 413745. 1.53602
\(520\) 108610. 108610.i 0.401665 0.401665i
\(521\) 215318.i 0.793242i −0.917982 0.396621i \(-0.870183\pi\)
0.917982 0.396621i \(-0.129817\pi\)
\(522\) 301206.i 1.10541i
\(523\) −308216. 308216.i −1.12681 1.12681i −0.990692 0.136121i \(-0.956536\pi\)
−0.136121 0.990692i \(-0.543464\pi\)
\(524\) 29631.6 + 29631.6i 0.107918 + 0.107918i
\(525\) −125283. −0.454541
\(526\) −15746.5 15746.5i −0.0569133 0.0569133i
\(527\) −49814.1 −0.179362
\(528\) −127492. −0.457315
\(529\) 40148.5i 0.143469i
\(530\) −239073. −0.851096
\(531\) 247569. + 247569.i 0.878025 + 0.878025i
\(532\) 35976.8 35976.8i 0.127116 0.127116i
\(533\) 45650.7 45650.7i 0.160692 0.160692i
\(534\) 249931. 0.876470
\(535\) −144586. 144586.i −0.505150 0.505150i
\(536\) 106156. 106156.i 0.369499 0.369499i
\(537\) −438602. 438602.i −1.52097 1.52097i
\(538\) −98126.8 + 98126.8i −0.339018 + 0.339018i
\(539\) 305660.i 1.05211i
\(540\) −23684.2 23684.2i −0.0812216 0.0812216i
\(541\) 161345. + 161345.i 0.551265 + 0.551265i 0.926806 0.375541i \(-0.122543\pi\)
−0.375541 + 0.926806i \(0.622543\pi\)
\(542\) 42437.1 42437.1i 0.144460 0.144460i
\(543\) 622908.i 2.11263i
\(544\) −26806.9 −0.0905833
\(545\) 697989.i 2.34993i
\(546\) 149367.i 0.501036i
\(547\) 250164. 250164.i 0.836083 0.836083i −0.152258 0.988341i \(-0.548654\pi\)
0.988341 + 0.152258i \(0.0486544\pi\)
\(548\) 83046.5i 0.276541i
\(549\) −147877. + 147877.i −0.490632 + 0.490632i
\(550\) 147100. 147100.i 0.486280 0.486280i
\(551\) 378046. 1.24521
\(552\) −145117. −0.476257
\(553\) −150776. 150776.i −0.493041 0.493041i
\(554\) 193872.i 0.631676i
\(555\) 557696. 213361.i 1.81055 0.692676i
\(556\) −229756. −0.743219
\(557\) 191922. 191922.i 0.618606 0.618606i −0.326567 0.945174i \(-0.605892\pi\)
0.945174 + 0.326567i \(0.105892\pi\)
\(558\) 86198.6i 0.276842i
\(559\) 626302.i 2.00429i
\(560\) −29796.3 29796.3i −0.0950137 0.0950137i
\(561\) −208598. 208598.i −0.662802 0.662802i
\(562\) 18040.3 0.0571178
\(563\) −12868.7 12868.7i −0.0405992 0.0405992i 0.686516 0.727115i \(-0.259139\pi\)
−0.727115 + 0.686516i \(0.759139\pi\)
\(564\) 64242.6 0.201960
\(565\) 476611. 1.49302
\(566\) 291523.i 0.909999i
\(567\) 112542. 0.350064
\(568\) −153868. 153868.i −0.476928 0.476928i
\(569\) −196332. + 196332.i −0.606411 + 0.606411i −0.942006 0.335595i \(-0.891063\pi\)
0.335595 + 0.942006i \(0.391063\pi\)
\(570\) −280566. + 280566.i −0.863545 + 0.863545i
\(571\) 30220.9 0.0926906 0.0463453 0.998925i \(-0.485243\pi\)
0.0463453 + 0.998925i \(0.485243\pi\)
\(572\) 175378. + 175378.i 0.536021 + 0.536021i
\(573\) 58620.6 58620.6i 0.178542 0.178542i
\(574\) −12523.9 12523.9i −0.0380115 0.0380115i
\(575\) 167436. 167436.i 0.506421 0.506421i
\(576\) 46386.7i 0.139813i
\(577\) 96144.6 + 96144.6i 0.288784 + 0.288784i 0.836599 0.547815i \(-0.184540\pi\)
−0.547815 + 0.836599i \(0.684540\pi\)
\(578\) 123182. + 123182.i 0.368715 + 0.368715i
\(579\) 158313. 158313.i 0.472237 0.472237i
\(580\) 313100.i 0.930737i
\(581\) 46638.1 0.138162
\(582\) 5926.98i 0.0174980i
\(583\) 386041.i 1.13578i
\(584\) −95827.1 + 95827.1i −0.280972 + 0.280972i
\(585\) 614999.i 1.79706i
\(586\) −46479.1 + 46479.1i −0.135351 + 0.135351i
\(587\) 198548. 198548.i 0.576222 0.576222i −0.357638 0.933860i \(-0.616418\pi\)
0.933860 + 0.357638i \(0.116418\pi\)
\(588\) 210639. 0.609235
\(589\) −108188. −0.311853
\(590\) −257345. 257345.i −0.739284 0.739284i
\(591\) 565858.i 1.62006i
\(592\) 80001.1 + 35726.5i 0.228272 + 0.101940i
\(593\) 118739. 0.337664 0.168832 0.985645i \(-0.446000\pi\)
0.168832 + 0.985645i \(0.446000\pi\)
\(594\) 38243.9 38243.9i 0.108390 0.108390i
\(595\) 97503.0i 0.275413i
\(596\) 88061.4i 0.247909i
\(597\) −189398. 189398.i −0.531407 0.531407i
\(598\) 199623. + 199623.i 0.558223 + 0.558223i
\(599\) −134637. −0.375240 −0.187620 0.982242i \(-0.560077\pi\)
−0.187620 + 0.982242i \(0.560077\pi\)
\(600\) 101371. + 101371.i 0.281586 + 0.281586i
\(601\) 123225. 0.341154 0.170577 0.985344i \(-0.445437\pi\)
0.170577 + 0.985344i \(0.445437\pi\)
\(602\) 171821. 0.474113
\(603\) 601100.i 1.65315i
\(604\) 186119. 0.510172
\(605\) 199762. + 199762.i 0.545760 + 0.545760i
\(606\) 354556. 354556.i 0.965472 0.965472i
\(607\) 758.659 758.659i 0.00205906 0.00205906i −0.706077 0.708136i \(-0.749537\pi\)
0.708136 + 0.706077i \(0.249537\pi\)
\(608\) −58220.3 −0.157495
\(609\) −215296. 215296.i −0.580499 0.580499i
\(610\) 153716. 153716.i 0.413105 0.413105i
\(611\) −88371.7 88371.7i −0.236718 0.236718i
\(612\) 75896.1 75896.1i 0.202636 0.202636i
\(613\) 374042.i 0.995404i −0.867348 0.497702i \(-0.834177\pi\)
0.867348 0.497702i \(-0.165823\pi\)
\(614\) 17585.1 + 17585.1i 0.0466453 + 0.0466453i
\(615\) 97667.6 + 97667.6i 0.258226 + 0.258226i
\(616\) 48113.3 48113.3i 0.126795 0.126795i
\(617\) 300323.i 0.788894i 0.918919 + 0.394447i \(0.129064\pi\)
−0.918919 + 0.394447i \(0.870936\pi\)
\(618\) 705237. 1.84654
\(619\) 62524.1i 0.163180i 0.996666 + 0.0815898i \(0.0259997\pi\)
−0.996666 + 0.0815898i \(0.974000\pi\)
\(620\) 89602.5i 0.233097i
\(621\) 43531.0 43531.0i 0.112880 0.112880i
\(622\) 350740.i 0.906577i
\(623\) −94319.4 + 94319.4i −0.243011 + 0.243011i
\(624\) −120858. + 120858.i −0.310389 + 0.310389i
\(625\) 458987. 1.17501
\(626\) −485951. −1.24006
\(627\) −453041. 453041.i −1.15240 1.15240i
\(628\) 142791.i 0.362062i
\(629\) 72440.5 + 189349.i 0.183096 + 0.478588i
\(630\) 168720. 0.425094
\(631\) 155309. 155309.i 0.390065 0.390065i −0.484645 0.874711i \(-0.661051\pi\)
0.874711 + 0.484645i \(0.161051\pi\)
\(632\) 243997.i 0.610872i
\(633\) 502885.i 1.25505i
\(634\) −329837. 329837.i −0.820580 0.820580i
\(635\) −303974. 303974.i −0.753858 0.753858i
\(636\) 266032. 0.657688
\(637\) −289754. 289754.i −0.714087 0.714087i
\(638\) 505576. 1.24207
\(639\) 871271. 2.13379
\(640\) 48218.4i 0.117721i
\(641\) −602346. −1.46599 −0.732993 0.680236i \(-0.761877\pi\)
−0.732993 + 0.680236i \(0.761877\pi\)
\(642\) 160891. + 160891.i 0.390357 + 0.390357i
\(643\) −203681. + 203681.i −0.492640 + 0.492640i −0.909137 0.416497i \(-0.863258\pi\)
0.416497 + 0.909137i \(0.363258\pi\)
\(644\) 54764.7 54764.7i 0.132047 0.132047i
\(645\) −1.33994e6 −3.22083
\(646\) −95257.7 95257.7i −0.228263 0.228263i
\(647\) 108538. 108538.i 0.259282 0.259282i −0.565480 0.824762i \(-0.691309\pi\)
0.824762 + 0.565480i \(0.191309\pi\)
\(648\) −91061.3 91061.3i −0.216862 0.216862i
\(649\) 415545. 415545.i 0.986573 0.986573i
\(650\) 278890.i 0.660095i
\(651\) 61613.1 + 61613.1i 0.145382 + 0.145382i
\(652\) −213532. 213532.i −0.502306 0.502306i
\(653\) −329684. + 329684.i −0.773165 + 0.773165i −0.978658 0.205494i \(-0.934120\pi\)
0.205494 + 0.978658i \(0.434120\pi\)
\(654\) 776700.i 1.81592i
\(655\) 174413. 0.406533
\(656\) 20267.0i 0.0470958i
\(657\) 542615.i 1.25708i
\(658\) −24244.0 + 24244.0i −0.0559954 + 0.0559954i
\(659\) 685736.i 1.57901i 0.613741 + 0.789507i \(0.289664\pi\)
−0.613741 + 0.789507i \(0.710336\pi\)
\(660\) −375212. + 375212.i −0.861368 + 0.861368i
\(661\) −487186. + 487186.i −1.11504 + 1.11504i −0.122585 + 0.992458i \(0.539118\pi\)
−0.992458 + 0.122585i \(0.960882\pi\)
\(662\) 503798. 1.14958
\(663\) −395486. −0.899713
\(664\) −37736.6 37736.6i −0.0855906 0.0855906i
\(665\) 211761.i 0.478854i
\(666\) −327650. + 125351.i −0.738690 + 0.282605i
\(667\) 575469. 1.29351
\(668\) 99098.0 99098.0i 0.222081 0.222081i
\(669\) 87073.8i 0.194552i
\(670\) 624836.i 1.39193i
\(671\) 248212. + 248212.i 0.551288 + 0.551288i
\(672\) 33156.3 + 33156.3i 0.0734223 + 0.0734223i
\(673\) 644106. 1.42209 0.711045 0.703146i \(-0.248222\pi\)
0.711045 + 0.703146i \(0.248222\pi\)
\(674\) 14373.3 + 14373.3i 0.0316400 + 0.0316400i
\(675\) −60816.5 −0.133479
\(676\) 104015. 0.227616
\(677\) 380512.i 0.830215i −0.909772 0.415107i \(-0.863744\pi\)
0.909772 0.415107i \(-0.136256\pi\)
\(678\) −530357. −1.15374
\(679\) −2236.74 2236.74i −0.00485149 0.00485149i
\(680\) −78893.1 + 78893.1i −0.170617 + 0.170617i
\(681\) −227164. + 227164.i −0.489829 + 0.489829i
\(682\) −144685. −0.311067
\(683\) 290940. + 290940.i 0.623680 + 0.623680i 0.946470 0.322791i \(-0.104621\pi\)
−0.322791 + 0.946470i \(0.604621\pi\)
\(684\) 164834. 164834.i 0.352319 0.352319i
\(685\) −244407. 244407.i −0.520875 0.520875i
\(686\) −174447. + 174447.i −0.370694 + 0.370694i
\(687\) 979453.i 2.07525i
\(688\) −139026. 139026.i −0.293710 0.293710i
\(689\) −365952. 365952.i −0.770879 0.770879i
\(690\) −427084. + 427084.i −0.897046 + 0.897046i
\(691\) 676751.i 1.41734i 0.705542 + 0.708668i \(0.250704\pi\)
−0.705542 + 0.708668i \(0.749296\pi\)
\(692\) 252677. 0.527658
\(693\) 272439.i 0.567286i
\(694\) 175861.i 0.365133i
\(695\) −676175. + 676175.i −1.39988 + 1.39988i
\(696\) 348407.i 0.719232i
\(697\) −33160.1 + 33160.1i −0.0682575 + 0.0682575i
\(698\) 395069. 395069.i 0.810891 0.810891i
\(699\) −1.12033e6 −2.29293
\(700\) −76511.1 −0.156145
\(701\) 358626. + 358626.i 0.729802 + 0.729802i 0.970580 0.240778i \(-0.0774026\pi\)
−0.240778 + 0.970580i \(0.577403\pi\)
\(702\) 72507.7i 0.147133i
\(703\) 157329. + 411236.i 0.318346 + 0.832110i
\(704\) −77860.3 −0.157098
\(705\) 189067. 189067.i 0.380398 0.380398i
\(706\) 563538.i 1.13061i
\(707\) 267606.i 0.535375i
\(708\) 286365. + 286365.i 0.571286 + 0.571286i
\(709\) 395349. + 395349.i 0.786481 + 0.786481i 0.980916 0.194434i \(-0.0622871\pi\)
−0.194434 + 0.980916i \(0.562287\pi\)
\(710\) −905676. −1.79662
\(711\) −690809. 690809.i −1.36653 1.36653i
\(712\) 152634. 0.301087
\(713\) −164687. −0.323951
\(714\) 108498.i 0.212827i
\(715\) 1.03228e6 2.01923
\(716\) −267857. 267857.i −0.522489 0.522489i
\(717\) −190402. + 190402.i −0.370368 + 0.370368i
\(718\) 72994.5 72994.5i 0.141593 0.141593i
\(719\) −623995. −1.20705 −0.603523 0.797346i \(-0.706237\pi\)
−0.603523 + 0.797346i \(0.706237\pi\)
\(720\) −136517. 136517.i −0.263343 0.263343i
\(721\) −266144. + 266144.i −0.511972 + 0.511972i
\(722\) 53757.3 + 53757.3i 0.103125 + 0.103125i
\(723\) 494914. 494914.i 0.946788 0.946788i
\(724\) 380414.i 0.725737i
\(725\) −401990. 401990.i −0.764785 0.764785i
\(726\) −222288. 222288.i −0.421739 0.421739i
\(727\) −13044.1 + 13044.1i −0.0246800 + 0.0246800i −0.719339 0.694659i \(-0.755555\pi\)
0.694659 + 0.719339i \(0.255555\pi\)
\(728\) 91219.3i 0.172117i
\(729\) 649052. 1.22131
\(730\) 564042.i 1.05844i
\(731\) 454938.i 0.851368i
\(732\) −171051. + 171051.i −0.319229 + 0.319229i
\(733\) 324175.i 0.603354i −0.953410 0.301677i \(-0.902454\pi\)
0.953410 0.301677i \(-0.0975464\pi\)
\(734\) −183338. + 183338.i −0.340299 + 0.340299i
\(735\) 619916. 619916.i 1.14751 1.14751i
\(736\) −88624.2 −0.163605
\(737\) 1.00895e6 1.85752
\(738\) −57380.4 57380.4i −0.105354 0.105354i
\(739\) 412435.i 0.755207i 0.925967 + 0.377604i \(0.123252\pi\)
−0.925967 + 0.377604i \(0.876748\pi\)
\(740\) 340589. 130301.i 0.621966 0.237950i
\(741\) −858933. −1.56431
\(742\) −100396. + 100396.i −0.182351 + 0.182351i
\(743\) 65043.9i 0.117823i 0.998263 + 0.0589114i \(0.0187629\pi\)
−0.998263 + 0.0589114i \(0.981237\pi\)
\(744\) 99706.7i 0.180127i
\(745\) 259166. + 259166.i 0.466945 + 0.466945i
\(746\) −167474. 167474.i −0.300934 0.300934i
\(747\) 213681. 0.382935
\(748\) −127392. 127392.i −0.227687 0.227687i
\(749\) −121435. −0.216461
\(750\) −174374. −0.309998
\(751\) 53025.2i 0.0940161i 0.998895 + 0.0470081i \(0.0149687\pi\)
−0.998895 + 0.0470081i \(0.985031\pi\)
\(752\) 39233.4 0.0693777
\(753\) −531382. 531382.i −0.937167 0.937167i
\(754\) 479267. 479267.i 0.843015 0.843015i
\(755\) 547752. 547752.i 0.960925 0.960925i
\(756\) −19891.8 −0.0348042
\(757\) 139987. + 139987.i 0.244285 + 0.244285i 0.818620 0.574335i \(-0.194739\pi\)
−0.574335 + 0.818620i \(0.694739\pi\)
\(758\) 38630.4 38630.4i 0.0672343 0.0672343i
\(759\) −689629. 689629.i −1.19710 1.19710i
\(760\) −171343. + 171343.i −0.296647 + 0.296647i
\(761\) 996640.i 1.72095i 0.509490 + 0.860477i \(0.329834\pi\)
−0.509490 + 0.860477i \(0.670166\pi\)
\(762\) 338253. + 338253.i 0.582547 + 0.582547i
\(763\) 293113. + 293113.i 0.503484 + 0.503484i
\(764\) 35800.0 35800.0i 0.0613332 0.0613332i
\(765\) 446728.i 0.763343i
\(766\) −429215. −0.731505
\(767\) 787844.i 1.33921i
\(768\) 53655.9i 0.0909693i
\(769\) −401157. + 401157.i −0.678362 + 0.678362i −0.959630 0.281267i \(-0.909245\pi\)
0.281267 + 0.959630i \(0.409245\pi\)
\(770\) 283197.i 0.477647i
\(771\) 203727. 203727.i 0.342721 0.342721i
\(772\) 96682.8 96682.8i 0.162224 0.162224i
\(773\) 176385. 0.295191 0.147595 0.989048i \(-0.452847\pi\)
0.147595 + 0.989048i \(0.452847\pi\)
\(774\) 787227. 1.31407
\(775\) 115041. + 115041.i 0.191535