Properties

Label 35.5.g.a.8.11
Level $35$
Weight $5$
Character 35.8
Analytic conductor $3.618$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 8.11
Character \(\chi\) \(=\) 35.8
Dual form 35.5.g.a.22.11

$q$-expansion

\(f(q)\) \(=\) \(q+(5.01495 - 5.01495i) q^{2} +(-5.80055 - 5.80055i) q^{3} -34.2994i q^{4} +(17.0417 + 18.2915i) q^{5} -58.1789 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-91.7707 - 91.7707i) q^{8} -13.7072i q^{9} +O(q^{10})\) \(q+(5.01495 - 5.01495i) q^{2} +(-5.80055 - 5.80055i) q^{3} -34.2994i q^{4} +(17.0417 + 18.2915i) q^{5} -58.1789 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-91.7707 - 91.7707i) q^{8} -13.7072i q^{9} +(177.194 + 6.26750i) q^{10} +75.9504 q^{11} +(-198.956 + 198.956i) q^{12} +(87.6088 + 87.6088i) q^{13} +131.350i q^{14} +(7.24931 - 204.952i) q^{15} -371.660 q^{16} +(230.654 - 230.654i) q^{17} +(-68.7410 - 68.7410i) q^{18} +527.538i q^{19} +(627.388 - 584.522i) q^{20} +151.926 q^{21} +(380.888 - 380.888i) q^{22} +(-587.599 - 587.599i) q^{23} +1064.64i q^{24} +(-44.1582 + 623.438i) q^{25} +878.707 q^{26} +(-549.354 + 549.354i) q^{27} +(449.178 + 449.178i) q^{28} +1581.66i q^{29} +(-991.470 - 1064.18i) q^{30} -588.270 q^{31} +(-395.524 + 395.524i) q^{32} +(-440.554 - 440.554i) q^{33} -2313.44i q^{34} +(-462.717 - 16.3666i) q^{35} -470.149 q^{36} +(629.670 - 629.670i) q^{37} +(2645.58 + 2645.58i) q^{38} -1016.36i q^{39} +(114.692 - 3242.56i) q^{40} -235.424 q^{41} +(761.900 - 761.900i) q^{42} +(-1361.59 - 1361.59i) q^{43} -2605.06i q^{44} +(250.725 - 233.595i) q^{45} -5893.56 q^{46} +(-1625.74 + 1625.74i) q^{47} +(2155.83 + 2155.83i) q^{48} -343.000i q^{49} +(2905.06 + 3347.96i) q^{50} -2675.84 q^{51} +(3004.93 - 3004.93i) q^{52} +(845.919 + 845.919i) q^{53} +5509.96i q^{54} +(1294.33 + 1389.25i) q^{55} +2403.62 q^{56} +(3060.01 - 3060.01i) q^{57} +(7931.94 + 7931.94i) q^{58} -1607.13i q^{59} +(-7029.75 - 248.647i) q^{60} -2519.75 q^{61} +(-2950.14 + 2950.14i) q^{62} +(179.507 + 179.507i) q^{63} -1979.49i q^{64} +(-109.490 + 3095.50i) q^{65} -4418.72 q^{66} +(3671.67 - 3671.67i) q^{67} +(-7911.31 - 7911.31i) q^{68} +6816.80i q^{69} +(-2402.58 + 2238.42i) q^{70} +6830.43 q^{71} +(-1257.92 + 1257.92i) q^{72} +(-1600.31 - 1600.31i) q^{73} -6315.53i q^{74} +(3872.43 - 3360.14i) q^{75} +18094.3 q^{76} +(-994.632 + 994.632i) q^{77} +(-5096.99 - 5096.99i) q^{78} +3822.06i q^{79} +(-6333.73 - 6798.22i) q^{80} +5262.83 q^{81} +(-1180.64 + 1180.64i) q^{82} +(-4122.84 - 4122.84i) q^{83} -5210.97i q^{84} +(8149.76 + 288.263i) q^{85} -13656.6 q^{86} +(9174.49 - 9174.49i) q^{87} +(-6970.02 - 6970.02i) q^{88} +1140.60i q^{89} +(85.9099 - 2428.84i) q^{90} -2294.61 q^{91} +(-20154.3 + 20154.3i) q^{92} +(3412.29 + 3412.29i) q^{93} +16306.0i q^{94} +(-9649.47 + 8990.17i) q^{95} +4588.52 q^{96} +(1538.00 - 1538.00i) q^{97} +(-1720.13 - 1720.13i) q^{98} -1041.07i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} + O(q^{10}) \) \( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.01495 5.01495i 1.25374 1.25374i 0.299705 0.954032i \(-0.403112\pi\)
0.954032 0.299705i \(-0.0968884\pi\)
\(3\) −5.80055 5.80055i −0.644506 0.644506i 0.307154 0.951660i \(-0.400623\pi\)
−0.951660 + 0.307154i \(0.900623\pi\)
\(4\) 34.2994i 2.14371i
\(5\) 17.0417 + 18.2915i 0.681670 + 0.731660i
\(6\) −58.1789 −1.61608
\(7\) −13.0958 + 13.0958i −0.267261 + 0.267261i
\(8\) −91.7707 91.7707i −1.43392 1.43392i
\(9\) 13.7072i 0.169225i
\(10\) 177.194 + 6.26750i 1.77194 + 0.0626750i
\(11\) 75.9504 0.627689 0.313845 0.949474i \(-0.398383\pi\)
0.313845 + 0.949474i \(0.398383\pi\)
\(12\) −198.956 + 198.956i −1.38164 + 1.38164i
\(13\) 87.6088 + 87.6088i 0.518395 + 0.518395i 0.917086 0.398690i \(-0.130535\pi\)
−0.398690 + 0.917086i \(0.630535\pi\)
\(14\) 131.350i 0.670151i
\(15\) 7.24931 204.952i 0.0322192 0.910899i
\(16\) −371.660 −1.45180
\(17\) 230.654 230.654i 0.798111 0.798111i −0.184686 0.982798i \(-0.559127\pi\)
0.982798 + 0.184686i \(0.0591269\pi\)
\(18\) −68.7410 68.7410i −0.212163 0.212163i
\(19\) 527.538i 1.46132i 0.682739 + 0.730662i \(0.260789\pi\)
−0.682739 + 0.730662i \(0.739211\pi\)
\(20\) 627.388 584.522i 1.56847 1.46130i
\(21\) 151.926 0.344503
\(22\) 380.888 380.888i 0.786958 0.786958i
\(23\) −587.599 587.599i −1.11077 1.11077i −0.993046 0.117728i \(-0.962439\pi\)
−0.117728 0.993046i \(-0.537561\pi\)
\(24\) 1064.64i 1.84834i
\(25\) −44.1582 + 623.438i −0.0706531 + 0.997501i
\(26\) 878.707 1.29986
\(27\) −549.354 + 549.354i −0.753572 + 0.753572i
\(28\) 449.178 + 449.178i 0.572932 + 0.572932i
\(29\) 1581.66i 1.88069i 0.340226 + 0.940344i \(0.389496\pi\)
−0.340226 + 0.940344i \(0.610504\pi\)
\(30\) −991.470 1064.18i −1.10163 1.18242i
\(31\) −588.270 −0.612144 −0.306072 0.952008i \(-0.599015\pi\)
−0.306072 + 0.952008i \(0.599015\pi\)
\(32\) −395.524 + 395.524i −0.386254 + 0.386254i
\(33\) −440.554 440.554i −0.404549 0.404549i
\(34\) 2313.44i 2.00124i
\(35\) −462.717 16.3666i −0.377728 0.0133605i
\(36\) −470.149 −0.362770
\(37\) 629.670 629.670i 0.459949 0.459949i −0.438690 0.898639i \(-0.644557\pi\)
0.898639 + 0.438690i \(0.144557\pi\)
\(38\) 2645.58 + 2645.58i 1.83212 + 1.83212i
\(39\) 1016.36i 0.668217i
\(40\) 114.692 3242.56i 0.0716823 2.02660i
\(41\) −235.424 −0.140050 −0.0700249 0.997545i \(-0.522308\pi\)
−0.0700249 + 0.997545i \(0.522308\pi\)
\(42\) 761.900 761.900i 0.431916 0.431916i
\(43\) −1361.59 1361.59i −0.736393 0.736393i 0.235485 0.971878i \(-0.424332\pi\)
−0.971878 + 0.235485i \(0.924332\pi\)
\(44\) 2605.06i 1.34559i
\(45\) 250.725 233.595i 0.123815 0.115355i
\(46\) −5893.56 −2.78524
\(47\) −1625.74 + 1625.74i −0.735963 + 0.735963i −0.971794 0.235831i \(-0.924219\pi\)
0.235831 + 0.971794i \(0.424219\pi\)
\(48\) 2155.83 + 2155.83i 0.935691 + 0.935691i
\(49\) 343.000i 0.142857i
\(50\) 2905.06 + 3347.96i 1.16202 + 1.33918i
\(51\) −2675.84 −1.02877
\(52\) 3004.93 3004.93i 1.11129 1.11129i
\(53\) 845.919 + 845.919i 0.301146 + 0.301146i 0.841462 0.540316i \(-0.181695\pi\)
−0.540316 + 0.841462i \(0.681695\pi\)
\(54\) 5509.96i 1.88956i
\(55\) 1294.33 + 1389.25i 0.427877 + 0.459255i
\(56\) 2403.62 0.766461
\(57\) 3060.01 3060.01i 0.941832 0.941832i
\(58\) 7931.94 + 7931.94i 2.35789 + 2.35789i
\(59\) 1607.13i 0.461686i −0.972991 0.230843i \(-0.925852\pi\)
0.972991 0.230843i \(-0.0741485\pi\)
\(60\) −7029.75 248.647i −1.95271 0.0690687i
\(61\) −2519.75 −0.677170 −0.338585 0.940936i \(-0.609948\pi\)
−0.338585 + 0.940936i \(0.609948\pi\)
\(62\) −2950.14 + 2950.14i −0.767467 + 0.767467i
\(63\) 179.507 + 179.507i 0.0452272 + 0.0452272i
\(64\) 1979.49i 0.483274i
\(65\) −109.490 + 3095.50i −0.0259148 + 0.732663i
\(66\) −4418.72 −1.01440
\(67\) 3671.67 3671.67i 0.817926 0.817926i −0.167881 0.985807i \(-0.553692\pi\)
0.985807 + 0.167881i \(0.0536924\pi\)
\(68\) −7911.31 7911.31i −1.71092 1.71092i
\(69\) 6816.80i 1.43180i
\(70\) −2402.58 + 2238.42i −0.490323 + 0.456821i
\(71\) 6830.43 1.35498 0.677488 0.735534i \(-0.263069\pi\)
0.677488 + 0.735534i \(0.263069\pi\)
\(72\) −1257.92 + 1257.92i −0.242654 + 0.242654i
\(73\) −1600.31 1600.31i −0.300302 0.300302i 0.540830 0.841132i \(-0.318110\pi\)
−0.841132 + 0.540830i \(0.818110\pi\)
\(74\) 6315.53i 1.15331i
\(75\) 3872.43 3360.14i 0.688431 0.597359i
\(76\) 18094.3 3.13266
\(77\) −994.632 + 994.632i −0.167757 + 0.167757i
\(78\) −5096.99 5096.99i −0.837769 0.837769i
\(79\) 3822.06i 0.612412i 0.951965 + 0.306206i \(0.0990596\pi\)
−0.951965 + 0.306206i \(0.900940\pi\)
\(80\) −6333.73 6798.22i −0.989646 1.06222i
\(81\) 5262.83 0.802138
\(82\) −1180.64 + 1180.64i −0.175586 + 0.175586i
\(83\) −4122.84 4122.84i −0.598467 0.598467i 0.341437 0.939905i \(-0.389086\pi\)
−0.939905 + 0.341437i \(0.889086\pi\)
\(84\) 5210.97i 0.738516i
\(85\) 8149.76 + 288.263i 1.12799 + 0.0398980i
\(86\) −13656.6 −1.84649
\(87\) 9174.49 9174.49i 1.21211 1.21211i
\(88\) −6970.02 6970.02i −0.900055 0.900055i
\(89\) 1140.60i 0.143997i 0.997405 + 0.0719984i \(0.0229377\pi\)
−0.997405 + 0.0719984i \(0.977062\pi\)
\(90\) 85.9099 2428.84i 0.0106062 0.299857i
\(91\) −2294.61 −0.277094
\(92\) −20154.3 + 20154.3i −2.38118 + 2.38118i
\(93\) 3412.29 + 3412.29i 0.394530 + 0.394530i
\(94\) 16306.0i 1.84541i
\(95\) −9649.47 + 8990.17i −1.06919 + 0.996141i
\(96\) 4588.52 0.497886
\(97\) 1538.00 1538.00i 0.163460 0.163460i −0.620637 0.784098i \(-0.713126\pi\)
0.784098 + 0.620637i \(0.213126\pi\)
\(98\) −1720.13 1720.13i −0.179105 0.179105i
\(99\) 1041.07i 0.106221i
\(100\) 21383.6 + 1514.60i 2.13836 + 0.151460i
\(101\) −3238.10 −0.317430 −0.158715 0.987324i \(-0.550735\pi\)
−0.158715 + 0.987324i \(0.550735\pi\)
\(102\) −13419.2 + 13419.2i −1.28981 + 1.28981i
\(103\) −9096.24 9096.24i −0.857407 0.857407i 0.133625 0.991032i \(-0.457338\pi\)
−0.991032 + 0.133625i \(0.957338\pi\)
\(104\) 16079.8i 1.48667i
\(105\) 2589.08 + 2778.95i 0.234837 + 0.252059i
\(106\) 8484.48 0.755116
\(107\) −2177.73 + 2177.73i −0.190211 + 0.190211i −0.795787 0.605576i \(-0.792943\pi\)
0.605576 + 0.795787i \(0.292943\pi\)
\(108\) 18842.5 + 18842.5i 1.61544 + 1.61544i
\(109\) 2560.05i 0.215474i −0.994179 0.107737i \(-0.965640\pi\)
0.994179 0.107737i \(-0.0343605\pi\)
\(110\) 13458.0 + 476.019i 1.11223 + 0.0393404i
\(111\) −7304.87 −0.592880
\(112\) 4867.18 4867.18i 0.388009 0.388009i
\(113\) −491.079 491.079i −0.0384587 0.0384587i 0.687616 0.726075i \(-0.258657\pi\)
−0.726075 + 0.687616i \(0.758657\pi\)
\(114\) 30691.6i 2.36162i
\(115\) 734.360 20761.8i 0.0555282 1.56989i
\(116\) 54250.0 4.03166
\(117\) 1200.87 1200.87i 0.0877253 0.0877253i
\(118\) −8059.68 8059.68i −0.578834 0.578834i
\(119\) 6041.20i 0.426608i
\(120\) −19473.9 + 18143.3i −1.35235 + 1.25995i
\(121\) −8872.53 −0.606006
\(122\) −12636.4 + 12636.4i −0.848993 + 0.848993i
\(123\) 1365.59 + 1365.59i 0.0902629 + 0.0902629i
\(124\) 20177.3i 1.31226i
\(125\) −12156.2 + 9816.75i −0.777994 + 0.628272i
\(126\) 1800.44 0.113406
\(127\) 6070.58 6070.58i 0.376377 0.376377i −0.493417 0.869793i \(-0.664252\pi\)
0.869793 + 0.493417i \(0.164252\pi\)
\(128\) −16255.4 16255.4i −0.992153 0.992153i
\(129\) 15796.0i 0.949219i
\(130\) 14974.7 + 16072.9i 0.886077 + 0.951058i
\(131\) 2199.94 0.128194 0.0640970 0.997944i \(-0.479583\pi\)
0.0640970 + 0.997944i \(0.479583\pi\)
\(132\) −15110.8 + 15110.8i −0.867238 + 0.867238i
\(133\) −6908.53 6908.53i −0.390555 0.390555i
\(134\) 36826.5i 2.05093i
\(135\) −19410.5 686.562i −1.06505 0.0376715i
\(136\) −42334.6 −2.28885
\(137\) 16433.0 16433.0i 0.875541 0.875541i −0.117528 0.993070i \(-0.537497\pi\)
0.993070 + 0.117528i \(0.0374970\pi\)
\(138\) 34185.9 + 34185.9i 1.79510 + 1.79510i
\(139\) 2459.25i 0.127284i −0.997973 0.0636419i \(-0.979728\pi\)
0.997973 0.0636419i \(-0.0202715\pi\)
\(140\) −561.367 + 15870.9i −0.0286412 + 0.809741i
\(141\) 18860.4 0.948665
\(142\) 34254.3 34254.3i 1.69878 1.69878i
\(143\) 6653.92 + 6653.92i 0.325391 + 0.325391i
\(144\) 5094.42i 0.245680i
\(145\) −28930.9 + 26954.2i −1.37602 + 1.28201i
\(146\) −16050.9 −0.753000
\(147\) −1989.59 + 1989.59i −0.0920722 + 0.0920722i
\(148\) −21597.3 21597.3i −0.986000 0.986000i
\(149\) 40002.9i 1.80185i 0.433973 + 0.900926i \(0.357111\pi\)
−0.433973 + 0.900926i \(0.642889\pi\)
\(150\) 2569.08 36271.0i 0.114181 1.61204i
\(151\) −11343.6 −0.497503 −0.248751 0.968567i \(-0.580020\pi\)
−0.248751 + 0.968567i \(0.580020\pi\)
\(152\) 48412.5 48412.5i 2.09542 2.09542i
\(153\) −3161.63 3161.63i −0.135060 0.135060i
\(154\) 9976.05i 0.420647i
\(155\) −10025.1 10760.3i −0.417280 0.447881i
\(156\) −34860.5 −1.43247
\(157\) 8858.33 8858.33i 0.359379 0.359379i −0.504205 0.863584i \(-0.668214\pi\)
0.863584 + 0.504205i \(0.168214\pi\)
\(158\) 19167.4 + 19167.4i 0.767804 + 0.767804i
\(159\) 9813.59i 0.388181i
\(160\) −13975.2 494.312i −0.545905 0.0193090i
\(161\) 15390.2 0.593734
\(162\) 26392.8 26392.8i 1.00567 1.00567i
\(163\) 4388.99 + 4388.99i 0.165192 + 0.165192i 0.784862 0.619670i \(-0.212734\pi\)
−0.619670 + 0.784862i \(0.712734\pi\)
\(164\) 8074.90i 0.300227i
\(165\) 550.589 15566.2i 0.0202236 0.571762i
\(166\) −41351.7 −1.50064
\(167\) −36986.7 + 36986.7i −1.32621 + 1.32621i −0.417560 + 0.908649i \(0.637115\pi\)
−0.908649 + 0.417560i \(0.862885\pi\)
\(168\) −13942.3 13942.3i −0.493988 0.493988i
\(169\) 13210.4i 0.462533i
\(170\) 42316.3 39425.0i 1.46423 1.36419i
\(171\) 7231.08 0.247292
\(172\) −46701.8 + 46701.8i −1.57862 + 1.57862i
\(173\) 35346.5 + 35346.5i 1.18101 + 1.18101i 0.979483 + 0.201528i \(0.0645907\pi\)
0.201528 + 0.979483i \(0.435409\pi\)
\(174\) 92019.2i 3.03934i
\(175\) −7586.13 8742.71i −0.247711 0.285476i
\(176\) −28227.7 −0.911277
\(177\) −9322.24 + 9322.24i −0.297560 + 0.297560i
\(178\) 5720.05 + 5720.05i 0.180534 + 0.180534i
\(179\) 30171.1i 0.941640i −0.882229 0.470820i \(-0.843958\pi\)
0.882229 0.470820i \(-0.156042\pi\)
\(180\) −8012.16 8599.74i −0.247289 0.265424i
\(181\) 35744.0 1.09105 0.545526 0.838094i \(-0.316330\pi\)
0.545526 + 0.838094i \(0.316330\pi\)
\(182\) −11507.4 + 11507.4i −0.347403 + 0.347403i
\(183\) 14615.9 + 14615.9i 0.436440 + 0.436440i
\(184\) 107849.i 3.18552i
\(185\) 22248.3 + 786.939i 0.650060 + 0.0229931i
\(186\) 34224.9 0.989274
\(187\) 17518.3 17518.3i 0.500966 0.500966i
\(188\) 55762.0 + 55762.0i 1.57769 + 1.57769i
\(189\) 14388.5i 0.402801i
\(190\) −3306.34 + 93476.8i −0.0915885 + 2.58939i
\(191\) 36695.0 1.00587 0.502933 0.864325i \(-0.332254\pi\)
0.502933 + 0.864325i \(0.332254\pi\)
\(192\) −11482.1 + 11482.1i −0.311473 + 0.311473i
\(193\) −5739.33 5739.33i −0.154080 0.154080i 0.625857 0.779938i \(-0.284749\pi\)
−0.779938 + 0.625857i \(0.784749\pi\)
\(194\) 15426.0i 0.409873i
\(195\) 18590.7 17320.5i 0.488908 0.455503i
\(196\) −11764.7 −0.306245
\(197\) −33650.6 + 33650.6i −0.867082 + 0.867082i −0.992148 0.125066i \(-0.960086\pi\)
0.125066 + 0.992148i \(0.460086\pi\)
\(198\) −5220.90 5220.90i −0.133173 0.133173i
\(199\) 8221.91i 0.207619i 0.994597 + 0.103809i \(0.0331032\pi\)
−0.994597 + 0.103809i \(0.966897\pi\)
\(200\) 61265.8 53160.9i 1.53164 1.32902i
\(201\) −42595.4 −1.05432
\(202\) −16238.9 + 16238.9i −0.397974 + 0.397974i
\(203\) −20713.1 20713.1i −0.502635 0.502635i
\(204\) 91779.9i 2.20540i
\(205\) −4012.03 4306.25i −0.0954677 0.102469i
\(206\) −91234.3 −2.14993
\(207\) −8054.35 + 8054.35i −0.187970 + 0.187970i
\(208\) −32560.7 32560.7i −0.752604 0.752604i
\(209\) 40066.7i 0.917258i
\(210\) 26920.4 + 952.194i 0.610440 + 0.0215917i
\(211\) −30204.5 −0.678432 −0.339216 0.940708i \(-0.610162\pi\)
−0.339216 + 0.940708i \(0.610162\pi\)
\(212\) 29014.5 29014.5i 0.645571 0.645571i
\(213\) −39620.3 39620.3i −0.873289 0.873289i
\(214\) 21842.4i 0.476950i
\(215\) 1701.67 48109.4i 0.0368127 1.04077i
\(216\) 100829. 2.16112
\(217\) 7703.87 7703.87i 0.163602 0.163602i
\(218\) −12838.5 12838.5i −0.270148 0.270148i
\(219\) 18565.4i 0.387093i
\(220\) 47650.4 44394.7i 0.984512 0.917246i
\(221\) 40414.7 0.827474
\(222\) −36633.6 + 36633.6i −0.743315 + 0.743315i
\(223\) −1152.95 1152.95i −0.0231846 0.0231846i 0.695419 0.718604i \(-0.255219\pi\)
−0.718604 + 0.695419i \(0.755219\pi\)
\(224\) 10359.4i 0.206462i
\(225\) 8545.60 + 605.285i 0.168802 + 0.0119563i
\(226\) −4925.47 −0.0964341
\(227\) 5784.04 5784.04i 0.112248 0.112248i −0.648752 0.761000i \(-0.724709\pi\)
0.761000 + 0.648752i \(0.224709\pi\)
\(228\) −104957. 104957.i −2.01902 2.01902i
\(229\) 102632.i 1.95710i −0.206001 0.978552i \(-0.566045\pi\)
0.206001 0.978552i \(-0.433955\pi\)
\(230\) −100437. 107802.i −1.89861 2.03785i
\(231\) 11538.8 0.216241
\(232\) 145150. 145150.i 2.69675 2.69675i
\(233\) 16734.1 + 16734.1i 0.308241 + 0.308241i 0.844227 0.535986i \(-0.180060\pi\)
−0.535986 + 0.844227i \(0.680060\pi\)
\(234\) 12044.6i 0.219969i
\(235\) −57442.8 2031.79i −1.04016 0.0367912i
\(236\) −55123.7 −0.989724
\(237\) 22170.1 22170.1i 0.394703 0.394703i
\(238\) 30296.3 + 30296.3i 0.534855 + 0.534855i
\(239\) 40418.5i 0.707594i 0.935322 + 0.353797i \(0.115110\pi\)
−0.935322 + 0.353797i \(0.884890\pi\)
\(240\) −2694.28 + 76172.5i −0.0467757 + 1.32244i
\(241\) 27952.5 0.481268 0.240634 0.970616i \(-0.422645\pi\)
0.240634 + 0.970616i \(0.422645\pi\)
\(242\) −44495.3 + 44495.3i −0.759772 + 0.759772i
\(243\) 13970.4 + 13970.4i 0.236589 + 0.236589i
\(244\) 86425.9i 1.45166i
\(245\) 6273.99 5845.32i 0.104523 0.0973814i
\(246\) 13696.7 0.226332
\(247\) −46217.0 + 46217.0i −0.757543 + 0.757543i
\(248\) 53986.0 + 53986.0i 0.877763 + 0.877763i
\(249\) 47829.5i 0.771431i
\(250\) −11732.0 + 110193.i −0.187712 + 1.76309i
\(251\) 32087.2 0.509312 0.254656 0.967032i \(-0.418038\pi\)
0.254656 + 0.967032i \(0.418038\pi\)
\(252\) 6156.98 6156.98i 0.0969543 0.0969543i
\(253\) −44628.4 44628.4i −0.697221 0.697221i
\(254\) 60887.3i 0.943755i
\(255\) −45601.0 48945.2i −0.701284 0.752713i
\(256\) −131368. −2.00452
\(257\) −14697.1 + 14697.1i −0.222518 + 0.222518i −0.809558 0.587040i \(-0.800293\pi\)
0.587040 + 0.809558i \(0.300293\pi\)
\(258\) 79215.9 + 79215.9i 1.19007 + 1.19007i
\(259\) 16492.1i 0.245853i
\(260\) 106174. + 3755.45i 1.57062 + 0.0555540i
\(261\) 21680.1 0.318259
\(262\) 11032.6 11032.6i 0.160722 0.160722i
\(263\) 17788.8 + 17788.8i 0.257179 + 0.257179i 0.823906 0.566727i \(-0.191791\pi\)
−0.566727 + 0.823906i \(0.691791\pi\)
\(264\) 80860.0i 1.16018i
\(265\) −1057.20 + 29889.1i −0.0150544 + 0.425619i
\(266\) −69291.9 −0.979308
\(267\) 6616.10 6616.10i 0.0928068 0.0928068i
\(268\) −125936. 125936.i −1.75340 1.75340i
\(269\) 2894.86i 0.0400058i −0.999800 0.0200029i \(-0.993632\pi\)
0.999800 0.0200029i \(-0.00636755\pi\)
\(270\) −100786. + 93899.4i −1.38252 + 1.28806i
\(271\) 120397. 1.63937 0.819685 0.572814i \(-0.194148\pi\)
0.819685 + 0.572814i \(0.194148\pi\)
\(272\) −85724.9 + 85724.9i −1.15870 + 1.15870i
\(273\) 13310.0 + 13310.0i 0.178589 + 0.178589i
\(274\) 164822.i 2.19540i
\(275\) −3353.83 + 47350.4i −0.0443482 + 0.626121i
\(276\) 233812. 3.06937
\(277\) 53882.9 53882.9i 0.702249 0.702249i −0.262644 0.964893i \(-0.584594\pi\)
0.964893 + 0.262644i \(0.0845944\pi\)
\(278\) −12333.0 12333.0i −0.159580 0.159580i
\(279\) 8063.54i 0.103590i
\(280\) 40961.9 + 43965.9i 0.522473 + 0.560789i
\(281\) −131983. −1.67150 −0.835748 0.549113i \(-0.814966\pi\)
−0.835748 + 0.549113i \(0.814966\pi\)
\(282\) 94584.0 94584.0i 1.18938 1.18938i
\(283\) 61319.2 + 61319.2i 0.765639 + 0.765639i 0.977335 0.211697i \(-0.0678989\pi\)
−0.211697 + 0.977335i \(0.567899\pi\)
\(284\) 234280.i 2.90468i
\(285\) 108120. + 3824.29i 1.33112 + 0.0470827i
\(286\) 66738.2 0.815910
\(287\) 3083.06 3083.06i 0.0374299 0.0374299i
\(288\) 5421.53 + 5421.53i 0.0653638 + 0.0653638i
\(289\) 22881.7i 0.273964i
\(290\) −9913.04 + 280261.i −0.117872 + 3.33247i
\(291\) −17842.5 −0.210702
\(292\) −54889.7 + 54889.7i −0.643762 + 0.643762i
\(293\) −66889.0 66889.0i −0.779147 0.779147i 0.200539 0.979686i \(-0.435731\pi\)
−0.979686 + 0.200539i \(0.935731\pi\)
\(294\) 19955.4i 0.230869i
\(295\) 29396.8 27388.3i 0.337798 0.314718i
\(296\) −115571. −1.31906
\(297\) −41723.7 + 41723.7i −0.473009 + 0.473009i
\(298\) 200613. + 200613.i 2.25905 + 2.25905i
\(299\) 102958.i 1.15164i
\(300\) −115251. 132822.i −1.28057 1.47580i
\(301\) 35662.3 0.393619
\(302\) −56887.4 + 56887.4i −0.623737 + 0.623737i
\(303\) 18782.8 + 18782.8i 0.204585 + 0.204585i
\(304\) 196065.i 2.12155i
\(305\) −42940.9 46090.0i −0.461606 0.495458i
\(306\) −31710.8 −0.338660
\(307\) 13072.6 13072.6i 0.138703 0.138703i −0.634346 0.773049i \(-0.718731\pi\)
0.773049 + 0.634346i \(0.218731\pi\)
\(308\) 34115.3 + 34115.3i 0.359623 + 0.359623i
\(309\) 105526.i 1.10521i
\(310\) −104238. 3686.98i −1.08468 0.0383661i
\(311\) −34805.2 −0.359851 −0.179926 0.983680i \(-0.557586\pi\)
−0.179926 + 0.983680i \(0.557586\pi\)
\(312\) −93271.9 + 93271.9i −0.958168 + 0.958168i
\(313\) −67248.3 67248.3i −0.686424 0.686424i 0.275016 0.961440i \(-0.411317\pi\)
−0.961440 + 0.275016i \(0.911317\pi\)
\(314\) 88848.1i 0.901133i
\(315\) −224.341 + 6342.56i −0.00226093 + 0.0639210i
\(316\) 131095. 1.31284
\(317\) 126470. 126470.i 1.25854 1.25854i 0.306752 0.951790i \(-0.400758\pi\)
0.951790 0.306752i \(-0.0992422\pi\)
\(318\) −49214.7 49214.7i −0.486676 0.486676i
\(319\) 120128.i 1.18049i
\(320\) 36207.8 33734.0i 0.353592 0.329433i
\(321\) 25264.0 0.245184
\(322\) 77180.9 77180.9i 0.744386 0.744386i
\(323\) 121679. + 121679.i 1.16630 + 1.16630i
\(324\) 180512.i 1.71955i
\(325\) −58487.3 + 50750.0i −0.553726 + 0.480473i
\(326\) 44021.1 0.414215
\(327\) −14849.7 + 14849.7i −0.138874 + 0.138874i
\(328\) 21605.0 + 21605.0i 0.200820 + 0.200820i
\(329\) 42580.8i 0.393389i
\(330\) −75302.6 80824.9i −0.691484 0.742194i
\(331\) −81352.0 −0.742527 −0.371264 0.928527i \(-0.621075\pi\)
−0.371264 + 0.928527i \(0.621075\pi\)
\(332\) −141411. + 141411.i −1.28294 + 1.28294i
\(333\) −8631.02 8631.02i −0.0778348 0.0778348i
\(334\) 370972.i 3.32544i
\(335\) 129732. + 4588.72i 1.15600 + 0.0408886i
\(336\) −56464.7 −0.500148
\(337\) −111373. + 111373.i −0.980661 + 0.980661i −0.999817 0.0191559i \(-0.993902\pi\)
0.0191559 + 0.999817i \(0.493902\pi\)
\(338\) −66249.5 66249.5i −0.579895 0.579895i
\(339\) 5697.05i 0.0495736i
\(340\) 9887.26 279532.i 0.0855299 2.41810i
\(341\) −44679.4 −0.384236
\(342\) 36263.5 36263.5i 0.310040 0.310040i
\(343\) 4491.86 + 4491.86i 0.0381802 + 0.0381802i
\(344\) 249908.i 2.11185i
\(345\) −124690. + 116170.i −1.04759 + 0.976015i
\(346\) 354522. 2.96135
\(347\) 9505.40 9505.40i 0.0789426 0.0789426i −0.666533 0.745476i \(-0.732222\pi\)
0.745476 + 0.666533i \(0.232222\pi\)
\(348\) −314680. 314680.i −2.59843 2.59843i
\(349\) 187256.i 1.53739i −0.639615 0.768696i \(-0.720906\pi\)
0.639615 0.768696i \(-0.279094\pi\)
\(350\) −81888.3 5800.16i −0.668476 0.0473482i
\(351\) −96256.5 −0.781296
\(352\) −30040.2 + 30040.2i −0.242448 + 0.242448i
\(353\) −109193. 109193.i −0.876284 0.876284i 0.116864 0.993148i \(-0.462716\pi\)
−0.993148 + 0.116864i \(0.962716\pi\)
\(354\) 93501.2i 0.746123i
\(355\) 116402. + 124939.i 0.923646 + 0.991382i
\(356\) 39121.9 0.308688
\(357\) 35042.3 35042.3i 0.274952 0.274952i
\(358\) −151307. 151307.i −1.18057 1.18057i
\(359\) 56473.7i 0.438185i 0.975704 + 0.219092i \(0.0703096\pi\)
−0.975704 + 0.219092i \(0.929690\pi\)
\(360\) −44446.4 1572.10i −0.342951 0.0121304i
\(361\) −147976. −1.13547
\(362\) 179254. 179254.i 1.36789 1.36789i
\(363\) 51465.6 + 51465.6i 0.390574 + 0.390574i
\(364\) 78704.0i 0.594010i
\(365\) 2000.01 56544.1i 0.0150123 0.424426i
\(366\) 146596. 1.09436
\(367\) 43447.8 43447.8i 0.322579 0.322579i −0.527177 0.849756i \(-0.676749\pi\)
0.849756 + 0.527177i \(0.176749\pi\)
\(368\) 218387. + 218387.i 1.61262 + 1.61262i
\(369\) 3227.00i 0.0236999i
\(370\) 115521. 107628.i 0.843832 0.786177i
\(371\) −22156.0 −0.160969
\(372\) 117040. 117040.i 0.845760 0.845760i
\(373\) −31294.2 31294.2i −0.224929 0.224929i 0.585641 0.810570i \(-0.300843\pi\)
−0.810570 + 0.585641i \(0.800843\pi\)
\(374\) 175707.i 1.25616i
\(375\) 127455. + 13569.8i 0.906346 + 0.0964965i
\(376\) 298391. 2.11062
\(377\) −138567. + 138567.i −0.974939 + 0.974939i
\(378\) −72157.4 72157.4i −0.505007 0.505007i
\(379\) 37541.2i 0.261354i 0.991425 + 0.130677i \(0.0417151\pi\)
−0.991425 + 0.130677i \(0.958285\pi\)
\(380\) 308358. + 330971.i 2.13544 + 2.29204i
\(381\) −70425.4 −0.485154
\(382\) 184024. 184024.i 1.26109 1.26109i
\(383\) −40494.9 40494.9i −0.276060 0.276060i 0.555474 0.831534i \(-0.312537\pi\)
−0.831534 + 0.555474i \(0.812537\pi\)
\(384\) 188581.i 1.27890i
\(385\) −35143.6 1243.05i −0.237096 0.00838626i
\(386\) −57564.9 −0.386352
\(387\) −18663.6 + 18663.6i −0.124616 + 0.124616i
\(388\) −52752.5 52752.5i −0.350412 0.350412i
\(389\) 78442.6i 0.518386i −0.965826 0.259193i \(-0.916543\pi\)
0.965826 0.259193i \(-0.0834565\pi\)
\(390\) 6370.02 180093.i 0.0418805 1.18404i
\(391\) −271064. −1.77304
\(392\) −31477.3 + 31477.3i −0.204845 + 0.204845i
\(393\) −12760.8 12760.8i −0.0826218 0.0826218i
\(394\) 337512.i 2.17419i
\(395\) −69911.3 + 65134.6i −0.448077 + 0.417463i
\(396\) −35708.0 −0.227707
\(397\) −131890. + 131890.i −0.836815 + 0.836815i −0.988438 0.151623i \(-0.951550\pi\)
0.151623 + 0.988438i \(0.451550\pi\)
\(398\) 41232.5 + 41232.5i 0.260299 + 0.260299i
\(399\) 80146.6i 0.503430i
\(400\) 16411.8 231707.i 0.102574 1.44817i
\(401\) 260765. 1.62166 0.810832 0.585280i \(-0.199015\pi\)
0.810832 + 0.585280i \(0.199015\pi\)
\(402\) −213614. + 213614.i −1.32184 + 1.32184i
\(403\) −51537.6 51537.6i −0.317332 0.317332i
\(404\) 111065.i 0.680479i
\(405\) 89687.8 + 96265.0i 0.546793 + 0.586893i
\(406\) −207750. −1.26034
\(407\) 47823.7 47823.7i 0.288705 0.288705i
\(408\) 245564. + 245564.i 1.47518 + 1.47518i
\(409\) 253509.i 1.51547i −0.652564 0.757734i \(-0.726307\pi\)
0.652564 0.757734i \(-0.273693\pi\)
\(410\) −41715.8 1475.52i −0.248160 0.00877762i
\(411\) −190641. −1.12858
\(412\) −311996. + 311996.i −1.83804 + 1.83804i
\(413\) 21046.7 + 21046.7i 0.123391 + 0.123391i
\(414\) 80784.3i 0.471331i
\(415\) 5152.57 145673.i 0.0299177 0.845831i
\(416\) −69302.8 −0.400465
\(417\) −14265.0 + 14265.0i −0.0820351 + 0.0820351i
\(418\) 200933. + 200933.i 1.15000 + 1.15000i
\(419\) 60645.6i 0.345439i 0.984971 + 0.172719i \(0.0552554\pi\)
−0.984971 + 0.172719i \(0.944745\pi\)
\(420\) 95316.4 88803.9i 0.540342 0.503424i
\(421\) −63976.9 −0.360960 −0.180480 0.983579i \(-0.557765\pi\)
−0.180480 + 0.983579i \(0.557765\pi\)
\(422\) −151474. + 151474.i −0.850576 + 0.850576i
\(423\) 22284.4 + 22284.4i 0.124543 + 0.124543i
\(424\) 155261.i 0.863637i
\(425\) 133613. + 153984.i 0.739728 + 0.852506i
\(426\) −397387. −2.18975
\(427\) 32998.1 32998.1i 0.180981 0.180981i
\(428\) 74694.8 + 74694.8i 0.407758 + 0.407758i
\(429\) 77192.8i 0.419433i
\(430\) −232733. 249800.i −1.25869 1.35100i
\(431\) 138787. 0.747129 0.373565 0.927604i \(-0.378135\pi\)
0.373565 + 0.927604i \(0.378135\pi\)
\(432\) 204173. 204173.i 1.09403 1.09403i
\(433\) 181902. + 181902.i 0.970201 + 0.970201i 0.999569 0.0293680i \(-0.00934947\pi\)
−0.0293680 + 0.999569i \(0.509349\pi\)
\(434\) 77269.0i 0.410229i
\(435\) 324164. + 11465.9i 1.71312 + 0.0605942i
\(436\) −87808.3 −0.461915
\(437\) 309981. 309981.i 1.62320 1.62320i
\(438\) 93104.3 + 93104.3i 0.485313 + 0.485313i
\(439\) 291440.i 1.51224i −0.654435 0.756118i \(-0.727093\pi\)
0.654435 0.756118i \(-0.272907\pi\)
\(440\) 8710.88 246274.i 0.0449942 1.27207i
\(441\) −4701.57 −0.0241750
\(442\) 202677. 202677.i 1.03744 1.03744i
\(443\) −75828.2 75828.2i −0.386388 0.386388i 0.487009 0.873397i \(-0.338088\pi\)
−0.873397 + 0.487009i \(0.838088\pi\)
\(444\) 250553.i 1.27096i
\(445\) −20863.3 + 19437.8i −0.105357 + 0.0981583i
\(446\) −11564.0 −0.0581349
\(447\) 232039. 232039.i 1.16130 1.16130i
\(448\) 25923.0 + 25923.0i 0.129160 + 0.129160i
\(449\) 239109.i 1.18605i −0.805184 0.593025i \(-0.797933\pi\)
0.805184 0.593025i \(-0.202067\pi\)
\(450\) 45891.2 39820.3i 0.226623 0.196643i
\(451\) −17880.5 −0.0879078
\(452\) −16843.7 + 16843.7i −0.0824444 + 0.0824444i
\(453\) 65798.9 + 65798.9i 0.320643 + 0.320643i
\(454\) 58013.3i 0.281459i
\(455\) −39104.2 41971.9i −0.188886 0.202739i
\(456\) −561639. −2.70102
\(457\) 34147.5 34147.5i 0.163503 0.163503i −0.620614 0.784117i \(-0.713116\pi\)
0.784117 + 0.620614i \(0.213116\pi\)
\(458\) −514697. 514697.i −2.45369 2.45369i
\(459\) 253422.i 1.20287i
\(460\) −712118. 25188.1i −3.36539 0.119037i
\(461\) 171075. 0.804981 0.402491 0.915424i \(-0.368145\pi\)
0.402491 + 0.915424i \(0.368145\pi\)
\(462\) 57866.6 57866.6i 0.271109 0.271109i
\(463\) 125583. + 125583.i 0.585826 + 0.585826i 0.936498 0.350672i \(-0.114047\pi\)
−0.350672 + 0.936498i \(0.614047\pi\)
\(464\) 587839.i 2.73038i
\(465\) −4264.55 + 120567.i −0.0197228 + 0.557601i
\(466\) 167841. 0.772907
\(467\) −126812. + 126812.i −0.581469 + 0.581469i −0.935307 0.353838i \(-0.884876\pi\)
0.353838 + 0.935307i \(0.384876\pi\)
\(468\) −41189.2 41189.2i −0.188058 0.188058i
\(469\) 96167.0i 0.437200i
\(470\) −298262. + 277883.i −1.35021 + 1.25796i
\(471\) −102766. −0.463243
\(472\) −147487. + 147487.i −0.662020 + 0.662020i
\(473\) −103413. 103413.i −0.462226 0.462226i
\(474\) 222364.i 0.989707i
\(475\) −328887. 23295.1i −1.45767 0.103247i
\(476\) 207210. 0.914527
\(477\) 11595.2 11595.2i 0.0509614 0.0509614i
\(478\) 202697. + 202697.i 0.887137 + 0.887137i
\(479\) 356277.i 1.55280i 0.630239 + 0.776401i \(0.282957\pi\)
−0.630239 + 0.776401i \(0.717043\pi\)
\(480\) 78196.3 + 83930.9i 0.339394 + 0.364283i
\(481\) 110329. 0.476871
\(482\) 140181. 140181.i 0.603384 0.603384i
\(483\) −89271.5 89271.5i −0.382665 0.382665i
\(484\) 304323.i 1.29910i
\(485\) 54342.5 + 1922.13i 0.231023 + 0.00817147i
\(486\) 140121. 0.593242
\(487\) 55243.2 55243.2i 0.232927 0.232927i −0.580986 0.813914i \(-0.697333\pi\)
0.813914 + 0.580986i \(0.197333\pi\)
\(488\) 231239. + 231239.i 0.971005 + 0.971005i
\(489\) 50917.1i 0.212934i
\(490\) 2149.75 60777.7i 0.00895357 0.253135i
\(491\) −22553.0 −0.0935495 −0.0467747 0.998905i \(-0.514894\pi\)
−0.0467747 + 0.998905i \(0.514894\pi\)
\(492\) 46838.9 46838.9i 0.193498 0.193498i
\(493\) 364816. + 364816.i 1.50100 + 1.50100i
\(494\) 463552.i 1.89952i
\(495\) 19042.7 17741.6i 0.0777174 0.0724074i
\(496\) 218636. 0.888708
\(497\) −89450.0 + 89450.0i −0.362132 + 0.362132i
\(498\) 239862. + 239862.i 0.967172 + 0.967172i
\(499\) 31665.7i 0.127171i −0.997976 0.0635855i \(-0.979746\pi\)
0.997976 0.0635855i \(-0.0202536\pi\)
\(500\) 336709. + 416949.i 1.34684 + 1.66780i
\(501\) 429086. 1.70950
\(502\) 160916. 160916.i 0.638543 0.638543i
\(503\) −84275.0 84275.0i −0.333091 0.333091i 0.520668 0.853759i \(-0.325683\pi\)
−0.853759 + 0.520668i \(0.825683\pi\)
\(504\) 32946.9i 0.129704i
\(505\) −55182.9 59229.7i −0.216382 0.232251i
\(506\) −447618. −1.74826
\(507\) −76627.6 + 76627.6i −0.298105 + 0.298105i
\(508\) −208217. 208217.i −0.806844 0.806844i
\(509\) 184416.i 0.711807i −0.934523 0.355903i \(-0.884173\pi\)
0.934523 0.355903i \(-0.115827\pi\)
\(510\) −474144. 16770.8i −1.82293 0.0644784i
\(511\) 41914.7 0.160518
\(512\) −398719. + 398719.i −1.52099 + 1.52099i
\(513\) −289805. 289805.i −1.10121 1.10121i
\(514\) 147410.i 0.557957i
\(515\) 11368.1 321400.i 0.0428622 1.21180i
\(516\) 541792. 2.03486
\(517\) −123476. + 123476.i −0.461956 + 0.461956i
\(518\) 82706.9 + 82706.9i 0.308235 + 0.308235i
\(519\) 410058.i 1.52234i
\(520\) 294124. 274028.i 1.08774 1.01342i
\(521\) −37375.8 −0.137694 −0.0688470 0.997627i \(-0.521932\pi\)
−0.0688470 + 0.997627i \(0.521932\pi\)
\(522\) 108725. 108725.i 0.399013 0.399013i
\(523\) 322468. + 322468.i 1.17892 + 1.17892i 0.980021 + 0.198895i \(0.0637354\pi\)
0.198895 + 0.980021i \(0.436265\pi\)
\(524\) 75456.6i 0.274811i
\(525\) −6708.76 + 94716.3i −0.0243402 + 0.343642i
\(526\) 178420. 0.644869
\(527\) −135687. + 135687.i −0.488559 + 0.488559i
\(528\) 163736. + 163736.i 0.587323 + 0.587323i
\(529\) 410705.i 1.46764i
\(530\) 144590. + 155194.i 0.514740 + 0.552488i
\(531\) −22029.3 −0.0781288
\(532\) −236959. + 236959.i −0.837239 + 0.837239i
\(533\) −20625.2 20625.2i −0.0726011 0.0726011i
\(534\) 66358.9i 0.232711i
\(535\) −76946.2 2721.64i −0.268831 0.00950875i
\(536\) −673904. −2.34568
\(537\) −175009. + 175009.i −0.606893 + 0.606893i
\(538\) −14517.6 14517.6i −0.0501568 0.0501568i
\(539\) 26051.0i 0.0896699i
\(540\) −23548.7 + 665768.i −0.0807568 + 2.28315i
\(541\) 372458. 1.27257 0.636287 0.771452i \(-0.280469\pi\)
0.636287 + 0.771452i \(0.280469\pi\)
\(542\) 603785. 603785.i 2.05534 2.05534i
\(543\) −207335. 207335.i −0.703189 0.703189i
\(544\) 182459.i 0.616548i
\(545\) 46827.2 43627.7i 0.157654 0.146882i
\(546\) 133498. 0.447806
\(547\) 413763. 413763.i 1.38286 1.38286i 0.543348 0.839508i \(-0.317157\pi\)
0.839508 0.543348i \(-0.182843\pi\)
\(548\) −563644. 563644.i −1.87691 1.87691i
\(549\) 34538.7i 0.114594i
\(550\) 220640. + 254279.i 0.729390 + 0.840592i
\(551\) −834385. −2.74829
\(552\) 625583. 625583.i 2.05308 2.05308i
\(553\) −50053.0 50053.0i −0.163674 0.163674i
\(554\) 540440.i 1.76087i
\(555\) −124488. 133617.i −0.404148 0.433786i
\(556\) −84350.9 −0.272860
\(557\) −298308. + 298308.i −0.961512 + 0.961512i −0.999286 0.0377744i \(-0.987973\pi\)
0.0377744 + 0.999286i \(0.487973\pi\)
\(558\) 40438.2 + 40438.2i 0.129875 + 0.129875i
\(559\) 238575.i 0.763485i
\(560\) 171973. + 6082.83i 0.548385 + 0.0193968i
\(561\) −203231. −0.645751
\(562\) −661888. + 661888.i −2.09562 + 2.09562i
\(563\) 83327.3 + 83327.3i 0.262888 + 0.262888i 0.826226 0.563338i \(-0.190483\pi\)
−0.563338 + 0.826226i \(0.690483\pi\)
\(564\) 646901.i 2.03367i
\(565\) 613.732 17351.4i 0.00192257 0.0543548i
\(566\) 615026. 1.91982
\(567\) −68921.0 + 68921.0i −0.214380 + 0.214380i
\(568\) −626833. 626833.i −1.94292 1.94292i
\(569\) 260413.i 0.804336i 0.915566 + 0.402168i \(0.131743\pi\)
−0.915566 + 0.402168i \(0.868257\pi\)
\(570\) 561396. 523038.i 1.72790 1.60984i
\(571\) −94163.6 −0.288809 −0.144405 0.989519i \(-0.546127\pi\)
−0.144405 + 0.989519i \(0.546127\pi\)
\(572\) 228226. 228226.i 0.697546 0.697546i
\(573\) −212851. 212851.i −0.648287 0.648287i
\(574\) 30922.8i 0.0938545i
\(575\) 392279. 340384.i 1.18648 1.02952i
\(576\) −27133.3 −0.0817819
\(577\) −388454. + 388454.i −1.16678 + 1.16678i −0.183816 + 0.982961i \(0.558845\pi\)
−0.982961 + 0.183816i \(0.941155\pi\)
\(578\) −114751. 114751.i −0.343478 0.343478i
\(579\) 66582.6i 0.198611i
\(580\) 924514. + 992314.i 2.74826 + 2.94980i
\(581\) 107984. 0.319894
\(582\) −89479.1 + 89479.1i −0.264165 + 0.264165i
\(583\) 64247.9 + 64247.9i 0.189026 + 0.189026i
\(584\) 293723.i 0.861217i
\(585\) 42430.7 + 1500.81i 0.123985 + 0.00438543i
\(586\) −670890. −1.95369
\(587\) −279855. + 279855.i −0.812187 + 0.812187i −0.984961 0.172774i \(-0.944727\pi\)
0.172774 + 0.984961i \(0.444727\pi\)
\(588\) 68241.8 + 68241.8i 0.197377 + 0.197377i
\(589\) 310335.i 0.894540i
\(590\) 10072.7 284775.i 0.0289362 0.818083i
\(591\) 390384. 1.11768
\(592\) −234023. + 234023.i −0.667753 + 0.667753i
\(593\) 94876.0 + 94876.0i 0.269803 + 0.269803i 0.829021 0.559218i \(-0.188898\pi\)
−0.559218 + 0.829021i \(0.688898\pi\)
\(594\) 418484.i 1.18606i
\(595\) −110503. + 102953.i −0.312132 + 0.290806i
\(596\) 1.37208e6 3.86265
\(597\) 47691.6 47691.6i 0.133811 0.133811i
\(598\) −516328. 516328.i −1.44385 1.44385i
\(599\) 335657.i 0.935496i 0.883862 + 0.467748i \(0.154935\pi\)
−0.883862 + 0.467748i \(0.845065\pi\)
\(600\) −663738. 47012.6i −1.84372 0.130591i
\(601\) −78337.0 −0.216879 −0.108440 0.994103i \(-0.534585\pi\)
−0.108440 + 0.994103i \(0.534585\pi\)
\(602\) 178844. 178844.i 0.493495 0.493495i
\(603\) −50328.4 50328.4i −0.138413 0.138413i
\(604\) 389077.i 1.06650i
\(605\) −151203. 162292.i −0.413096 0.443390i
\(606\) 188389. 0.512992
\(607\) −392159. + 392159.i −1.06435 + 1.06435i −0.0665679 + 0.997782i \(0.521205\pi\)
−0.997782 + 0.0665679i \(0.978795\pi\)
\(608\) −208654. 208654.i −0.564443 0.564443i
\(609\) 240295.i 0.647902i
\(610\) −446485. 15792.5i −1.19991 0.0424416i
\(611\) −284859. −0.763039
\(612\) −108442. + 108442.i −0.289531 + 0.289531i
\(613\) −309872. 309872.i −0.824634 0.824634i 0.162135 0.986769i \(-0.448162\pi\)
−0.986769 + 0.162135i \(0.948162\pi\)
\(614\) 131117.i 0.347794i
\(615\) −1706.66 + 48250.6i −0.00451229 + 0.127571i
\(616\) 182556. 0.481099
\(617\) −343853. + 343853.i −0.903238 + 0.903238i −0.995715 0.0924768i \(-0.970522\pi\)
0.0924768 + 0.995715i \(0.470522\pi\)
\(618\) 529209. + 529209.i 1.38564 + 1.38564i
\(619\) 166876.i 0.435524i −0.976002 0.217762i \(-0.930124\pi\)
0.976002 0.217762i \(-0.0698757\pi\)
\(620\) −369074. + 343857.i −0.960129 + 0.894528i
\(621\) 645600. 1.67410
\(622\) −174546. + 174546.i −0.451159 + 0.451159i
\(623\) −14937.1 14937.1i −0.0384848 0.0384848i
\(624\) 377740.i 0.970115i
\(625\) −386725. 55059.8i −0.990016 0.140953i
\(626\) −674493. −1.72119
\(627\) 232409. 232409.i 0.591178 0.591178i
\(628\) −303836. 303836.i −0.770405 0.770405i
\(629\) 290472.i 0.734181i
\(630\) 30682.6 + 32932.7i 0.0773055 + 0.0829747i
\(631\) 586336. 1.47261 0.736305 0.676650i \(-0.236569\pi\)
0.736305 + 0.676650i \(0.236569\pi\)
\(632\) 350753. 350753.i 0.878148 0.878148i
\(633\) 175203. + 175203.i 0.437253 + 0.437253i
\(634\) 1.26848e6i 3.15576i
\(635\) 214493. + 7586.78i 0.531944 + 0.0188153i
\(636\) −336601. −0.832148
\(637\) 30049.8 30049.8i 0.0740564 0.0740564i
\(638\) 602434. + 602434.i 1.48002 + 1.48002i
\(639\) 93626.2i 0.229295i
\(640\) 20315.4 574357.i 0.0495982 1.40224i
\(641\) 285959. 0.695966 0.347983 0.937501i \(-0.386867\pi\)
0.347983 + 0.937501i \(0.386867\pi\)
\(642\) 126698. 126698.i 0.307397 0.307397i
\(643\) −10719.7 10719.7i −0.0259276 0.0259276i 0.694024 0.719952i \(-0.255836\pi\)
−0.719952 + 0.694024i \(0.755836\pi\)
\(644\) 527874.i 1.27280i
\(645\) −288932. + 269191.i −0.694506 + 0.647054i
\(646\) 1.22043e6 2.92447
\(647\) 437318. 437318.i 1.04469 1.04469i 0.0457394 0.998953i \(-0.485436\pi\)
0.998953 0.0457394i \(-0.0145644\pi\)
\(648\) −482973. 482973.i −1.15020 1.15020i
\(649\) 122062.i 0.289796i
\(650\) −38802.1 + 547819.i −0.0918393 + 1.29661i
\(651\) −89373.4 −0.210885
\(652\) 150540. 150540.i 0.354125 0.354125i
\(653\) 417145. + 417145.i 0.978274 + 0.978274i 0.999769 0.0214948i \(-0.00684253\pi\)
−0.0214948 + 0.999769i \(0.506843\pi\)
\(654\) 148941.i 0.348224i
\(655\) 37490.8 + 40240.2i 0.0873859 + 0.0937944i
\(656\) 87497.6 0.203324
\(657\) −21935.8 + 21935.8i −0.0508186 + 0.0508186i
\(658\) −213541. 213541.i −0.493206 0.493206i
\(659\) 756930.i 1.74295i 0.490440 + 0.871475i \(0.336836\pi\)
−0.490440 + 0.871475i \(0.663164\pi\)
\(660\) −533912. 18884.9i −1.22569 0.0433537i
\(661\) −260817. −0.596943 −0.298472 0.954418i \(-0.596477\pi\)
−0.298472 + 0.954418i \(0.596477\pi\)
\(662\) −407976. + 407976.i −0.930934 + 0.930934i
\(663\) −234427. 234427.i −0.533312 0.533312i
\(664\) 756712.i 1.71630i
\(665\) 8634.03 244101.i 0.0195241 0.551984i
\(666\) −86568.3 −0.195169
\(667\) 929381. 929381.i 2.08902 2.08902i
\(668\) 1.26862e6 + 1.26862e6i 2.84301 + 2.84301i
\(669\) 13375.5i 0.0298852i
\(670\) 673612. 627587.i 1.50058 1.39806i
\(671\) −191376. −0.425052
\(672\) −60090.3 + 60090.3i −0.133066 + 0.133066i
\(673\) −41288.5 41288.5i −0.0911588 0.0911588i 0.660057 0.751216i \(-0.270532\pi\)
−0.751216 + 0.660057i \(0.770532\pi\)
\(674\) 1.11706e6i 2.45898i
\(675\) −318230. 366747.i −0.698447 0.804931i
\(676\) −453109. −0.991539
\(677\) −14140.5 + 14140.5i −0.0308523 + 0.0308523i −0.722365 0.691512i \(-0.756945\pi\)
0.691512 + 0.722365i \(0.256945\pi\)
\(678\) 28570.4 + 28570.4i 0.0621523 + 0.0621523i
\(679\) 40282.7i 0.0873733i
\(680\) −721455. 774363.i −1.56024 1.67466i
\(681\) −67101.2 −0.144689
\(682\) −224065. + 224065.i −0.481731 + 0.481731i
\(683\) 337178. + 337178.i 0.722800 + 0.722800i 0.969175 0.246375i \(-0.0792394\pi\)
−0.246375 + 0.969175i \(0.579239\pi\)
\(684\) 248022.i 0.530124i
\(685\) 580632. + 20537.4i 1.23743 + 0.0437688i
\(686\) 45052.9 0.0957358
\(687\) −595325. + 595325.i −1.26136 + 1.26136i
\(688\) 506049. + 506049.i 1.06909 + 1.06909i
\(689\) 148220.i 0.312225i
\(690\) −42724.3 + 1.20790e6i −0.0897380 + 2.53707i
\(691\) −565385. −1.18410 −0.592049 0.805902i \(-0.701681\pi\)
−0.592049 + 0.805902i \(0.701681\pi\)
\(692\) 1.21236e6 1.21236e6i 2.53175 2.53175i
\(693\) 13633.6 + 13633.6i 0.0283887 + 0.0283887i
\(694\) 95338.2i 0.197947i
\(695\) 44983.4 41909.9i 0.0931285 0.0867655i
\(696\) −1.68390e6 −3.47614
\(697\) −54301.5 + 54301.5i −0.111775 + 0.111775i
\(698\) −939078. 939078.i −1.92748 1.92748i
\(699\) 194134.i 0.397326i
\(700\) −299870. + 260200.i −0.611979 + 0.531021i
\(701\) 564548. 1.14885 0.574427 0.818556i \(-0.305225\pi\)
0.574427 + 0.818556i \(0.305225\pi\)
\(702\) −482721. + 482721.i −0.979540 + 0.979540i
\(703\) 332175. + 332175.i 0.672135 + 0.672135i
\(704\) 150343.i 0.303346i
\(705\) 321414. + 344985.i 0.646676 + 0.694100i
\(706\) −1.09519e6 −2.19726
\(707\) 42405.5 42405.5i 0.0848367 0.0848367i
\(708\) 319748. + 319748.i 0.637883 + 0.637883i
\(709\) 103288.i 0.205475i 0.994709 + 0.102737i \(0.0327602\pi\)
−0.994709 + 0.102737i \(0.967240\pi\)
\(710\) 1.21031e6 + 42809.7i 2.40094 + 0.0849231i
\(711\) 52389.8 0.103635
\(712\) 104674. 104674.i 0.206480 0.206480i
\(713\) 345667. + 345667.i 0.679953 + 0.679953i
\(714\) 351471.i 0.689434i
\(715\) −8315.83 + 235105.i −0.0162665 + 0.459885i
\(716\) −1.03485e6 −2.01861
\(717\) 234450. 234450.i 0.456049 0.456049i
\(718\) 283213. + 283213.i 0.549369 + 0.549369i
\(719\) 17971.7i 0.0347641i 0.999849 + 0.0173820i \(0.00553316\pi\)
−0.999849 + 0.0173820i \(0.994467\pi\)
\(720\) −93184.6 + 86817.8i −0.179754 + 0.167473i
\(721\) 238245. 0.458304
\(722\) −742090. + 742090.i −1.42358 + 1.42358i
\(723\) −162140. 162140.i −0.310180 0.310180i
\(724\) 1.22600e6i 2.33890i
\(725\) −986066. 69843.1i −1.87599 0.132876i
\(726\) 516195. 0.979355
\(727\) 21242.5 21242.5i 0.0401918 0.0401918i −0.686725 0.726917i \(-0.740952\pi\)
0.726917 + 0.686725i \(0.240952\pi\)
\(728\) 210578. + 210578.i 0.397330 + 0.397330i
\(729\) 588361.i 1.10710i
\(730\) −273536. 293596.i −0.513297 0.550940i
\(731\) −628113. −1.17545
\(732\) 501318. 501318.i 0.935602 0.935602i
\(733\) 529740. + 529740.i 0.985950 + 0.985950i 0.999903 0.0139530i \(-0.00444153\pi\)
−0.0139530 + 0.999903i \(0.504442\pi\)
\(734\) 435777.i 0.808858i
\(735\) −70298.6 2486.51i −0.130128 0.00460274i
\(736\) 464820. 0.858082
\(737\) 278865. 278865.i 0.513404 0.513404i
\(738\) 16183.3 + 16183.3i 0.0297134 + 0.0297134i
\(739\) 596812.i 1.09282i −0.837518 0.546410i \(-0.815994\pi\)
0.837518 0.546410i \(-0.184006\pi\)
\(740\) 26991.5 763104.i 0.0492906 1.39354i
\(741\) 536168. 0.976482
\(742\) −111111. + 111111.i −0.201813 + 0.201813i
\(743\) −431072. 431072.i −0.780859 0.780859i 0.199117 0.979976i \(-0.436193\pi\)
−0.979976 + 0.199117i \(0.936193\pi\)
\(744\) 626297.i 1.13145i
\(745\) −731713. + 681719.i −1.31834 + 1.22827i
\(746\) −313877. −0.564004
\(747\) −56512.6 + 56512.6i −0.101275 + 0.101275i
\(748\) −600867. 600867.i −1.07393 1.07393i
\(749\) 57038.2i 0.101672i
\(750\) 707232. 571128.i 1.25730 1.01534i
\(751\) −173893. −0.308320 −0.154160 0.988046i \(-0.549267\pi\)
−0.154160 + 0.988046i \(0.549267\pi\)
\(752\) 604223. 604223.i 1.06847 1.06847i
\(753\) −186123. 186123.i −0.328254 0.328254i
\(754\) 1.38981e6i 2.44464i
\(755\) −193314. 207491.i −0.339132 0.364003i
\(756\) −493516. −0.863491
\(757\) 38121.2 38121.2i 0.0665234 0.0665234i −0.673062 0.739586i \(-0.735021\pi\)
0.739586 + 0.673062i \(0.235021\pi\)
\(758\) 188267. + 188267.i 0.327669 + 0.327669i
\(759\) 517739.i 0.898726i
\(760\) 1.71057e6 + 60504.2i 2.96152 + 0.104751i
\(761\) 189381. 0.327014 0.163507 0.986542i \(-0.447719\pi\)
0.163507 + 0.986542i \(0.447719\pi\)
\(762\) −353180. + 353180.i −0.608255 + 0.608255i
\(763\) 33525.9 + 33525.9i 0.0575879 + 0.0575879i
\(764\) 1.25862e6i 2.15629i
\(765\) 3951.28 111710.i 0.00675173 0.190885i
\(766\) −406160. −0.692213
\(767\) 140799. 140799.i 0.239336 0.239336i
\(768\) 762010. + 762010.i 1.29193 + 1.29193i
\(769\) 444810.i 0.752179i 0.926583 + 0.376090i \(0.122732\pi\)
−0.926583 + 0.376090i \(0.877268\pi\)
\(770\) −182477. + 170009.i −0.307770 + 0.286742i
\(771\) 170502. 0.286828
\(772\) −196856. + 196856.i −0.330304 + 0.330304i
\(773\) −810826. 810826.i −1.35696 1.35696i −0.877635 0.479329i \(-0.840880\pi\)
−0.479329 0.877635i \(-0.659120\pi\)
\(774\) 187194.i 0.312471i
\(775\) 25976.9 366750.i 0.0432498 0.610614i