Properties

Label 300.5.c.c.151.12
Level $300$
Weight $5$
Character 300.151
Analytic conductor $31.011$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(31.0109889252\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + 234752 x^{8} - 632832 x^{7} + 1884160 x^{6} - 8847360 x^{5} + 32243712 x^{4} - 113246208 x^{3} + 335544320 x^{2} - 1610612736 x + 4294967296\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.12
Root \(-1.06635 - 3.85524i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.5.c.c.151.11

$q$-expansion

\(f(q)\) \(=\) \(q+(2.80556 + 2.85111i) q^{2} +5.19615i q^{3} +(-0.257663 + 15.9979i) q^{4} +(-14.8148 + 14.5781i) q^{6} -63.6232i q^{7} +(-46.3347 + 44.1485i) q^{8} -27.0000 q^{9} +O(q^{10})\) \(q+(2.80556 + 2.85111i) q^{2} +5.19615i q^{3} +(-0.257663 + 15.9979i) q^{4} +(-14.8148 + 14.5781i) q^{6} -63.6232i q^{7} +(-46.3347 + 44.1485i) q^{8} -27.0000 q^{9} -220.737i q^{11} +(-83.1277 - 1.33886i) q^{12} +236.856 q^{13} +(181.397 - 178.499i) q^{14} +(-255.867 - 8.24415i) q^{16} -46.7414 q^{17} +(-75.7501 - 76.9800i) q^{18} -195.899i q^{19} +330.596 q^{21} +(629.345 - 619.291i) q^{22} -741.830i q^{23} +(-229.402 - 240.762i) q^{24} +(664.512 + 675.301i) q^{26} -140.296i q^{27} +(1017.84 + 16.3934i) q^{28} +1059.06 q^{29} +1067.12i q^{31} +(-694.346 - 752.635i) q^{32} +1146.98 q^{33} +(-131.136 - 133.265i) q^{34} +(6.95691 - 431.944i) q^{36} -2287.23 q^{37} +(558.530 - 549.606i) q^{38} +1230.74i q^{39} -1141.57 q^{41} +(927.506 + 942.565i) q^{42} -1245.24i q^{43} +(3531.33 + 56.8758i) q^{44} +(2115.04 - 2081.25i) q^{46} +406.719i q^{47} +(42.8379 - 1329.53i) q^{48} -1646.91 q^{49} -242.875i q^{51} +(-61.0290 + 3789.20i) q^{52} +1442.39 q^{53} +(400.000 - 393.609i) q^{54} +(2808.87 + 2947.96i) q^{56} +1017.92 q^{57} +(2971.25 + 3019.49i) q^{58} +2472.02i q^{59} +4819.29 q^{61} +(-3042.47 + 2993.86i) q^{62} +1717.83i q^{63} +(197.817 - 4091.22i) q^{64} +(3217.93 + 3270.17i) q^{66} -5792.14i q^{67} +(12.0435 - 747.765i) q^{68} +3854.66 q^{69} -309.369i q^{71} +(1251.04 - 1192.01i) q^{72} +996.733 q^{73} +(-6416.96 - 6521.15i) q^{74} +(3133.98 + 50.4759i) q^{76} -14044.0 q^{77} +(-3508.97 + 3452.91i) q^{78} -1096.99i q^{79} +729.000 q^{81} +(-3202.76 - 3254.76i) q^{82} -3097.31i q^{83} +(-85.1824 + 5288.85i) q^{84} +(3550.32 - 3493.60i) q^{86} +5503.02i q^{87} +(9745.21 + 10227.8i) q^{88} +10965.3 q^{89} -15069.5i q^{91} +(11867.7 + 191.142i) q^{92} -5544.91 q^{93} +(-1159.60 + 1141.07i) q^{94} +(3910.81 - 3607.93i) q^{96} -12339.0 q^{97} +(-4620.50 - 4695.52i) q^{98} +5959.90i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + O(q^{10}) \) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + 176q^{13} + 78q^{14} - 376q^{16} - 162q^{18} - 144q^{21} - 788q^{22} + 108q^{24} + 678q^{26} + 3368q^{28} + 1728q^{29} + 2016q^{32} - 2932q^{34} - 216q^{36} - 1568q^{37} - 6990q^{38} + 1248q^{41} + 162q^{42} + 8088q^{44} + 5956q^{46} + 2088q^{48} - 10720q^{49} + 3128q^{52} - 288q^{53} - 486q^{54} - 10236q^{56} + 5616q^{57} - 16164q^{58} - 3760q^{61} - 12714q^{62} + 10544q^{64} + 8100q^{66} + 26136q^{68} + 9792q^{69} + 4860q^{72} + 11040q^{73} - 17004q^{74} - 28344q^{76} + 768q^{77} - 16830q^{78} + 11664q^{81} - 21280q^{82} + 15120q^{84} + 24414q^{86} + 52840q^{88} - 768q^{89} + 23736q^{92} - 9936q^{93} - 45156q^{94} - 11088q^{96} + 7248q^{97} - 58140q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.80556 + 2.85111i 0.701390 + 0.712778i
\(3\) 5.19615i 0.577350i
\(4\) −0.257663 + 15.9979i −0.0161040 + 0.999870i
\(5\) 0 0
\(6\) −14.8148 + 14.5781i −0.411522 + 0.404948i
\(7\) 63.6232i 1.29843i −0.760604 0.649216i \(-0.775097\pi\)
0.760604 0.649216i \(-0.224903\pi\)
\(8\) −46.3347 + 44.1485i −0.723980 + 0.689821i
\(9\) −27.0000 −0.333333
\(10\) 0 0
\(11\) 220.737i 1.82427i −0.409888 0.912136i \(-0.634432\pi\)
0.409888 0.912136i \(-0.365568\pi\)
\(12\) −83.1277 1.33886i −0.577275 0.00929762i
\(13\) 236.856 1.40151 0.700756 0.713401i \(-0.252846\pi\)
0.700756 + 0.713401i \(0.252846\pi\)
\(14\) 181.397 178.499i 0.925493 0.910707i
\(15\) 0 0
\(16\) −255.867 8.24415i −0.999481 0.0322037i
\(17\) −46.7414 −0.161735 −0.0808674 0.996725i \(-0.525769\pi\)
−0.0808674 + 0.996725i \(0.525769\pi\)
\(18\) −75.7501 76.9800i −0.233797 0.237593i
\(19\) 195.899i 0.542656i −0.962487 0.271328i \(-0.912537\pi\)
0.962487 0.271328i \(-0.0874629\pi\)
\(20\) 0 0
\(21\) 330.596 0.749650
\(22\) 629.345 619.291i 1.30030 1.27953i
\(23\) 741.830i 1.40232i −0.713002 0.701162i \(-0.752665\pi\)
0.713002 0.701162i \(-0.247335\pi\)
\(24\) −229.402 240.762i −0.398268 0.417990i
\(25\) 0 0
\(26\) 664.512 + 675.301i 0.983007 + 0.998966i
\(27\) 140.296i 0.192450i
\(28\) 1017.84 + 16.3934i 1.29826 + 0.0209099i
\(29\) 1059.06 1.25928 0.629641 0.776886i \(-0.283202\pi\)
0.629641 + 0.776886i \(0.283202\pi\)
\(30\) 0 0
\(31\) 1067.12i 1.11042i 0.831709 + 0.555212i \(0.187363\pi\)
−0.831709 + 0.555212i \(0.812637\pi\)
\(32\) −694.346 752.635i −0.678072 0.734995i
\(33\) 1146.98 1.05324
\(34\) −131.136 133.265i −0.113439 0.115281i
\(35\) 0 0
\(36\) 6.95691 431.944i 0.00536798 0.333290i
\(37\) −2287.23 −1.67073 −0.835366 0.549695i \(-0.814744\pi\)
−0.835366 + 0.549695i \(0.814744\pi\)
\(38\) 558.530 549.606i 0.386793 0.380614i
\(39\) 1230.74i 0.809163i
\(40\) 0 0
\(41\) −1141.57 −0.679105 −0.339552 0.940587i \(-0.610276\pi\)
−0.339552 + 0.940587i \(0.610276\pi\)
\(42\) 927.506 + 942.565i 0.525797 + 0.534334i
\(43\) 1245.24i 0.673468i −0.941600 0.336734i \(-0.890678\pi\)
0.941600 0.336734i \(-0.109322\pi\)
\(44\) 3531.33 + 56.8758i 1.82404 + 0.0293780i
\(45\) 0 0
\(46\) 2115.04 2081.25i 0.999546 0.983577i
\(47\) 406.719i 0.184119i 0.995754 + 0.0920595i \(0.0293450\pi\)
−0.995754 + 0.0920595i \(0.970655\pi\)
\(48\) 42.8379 1329.53i 0.0185928 0.577051i
\(49\) −1646.91 −0.685926
\(50\) 0 0
\(51\) 242.875i 0.0933777i
\(52\) −61.0290 + 3789.20i −0.0225699 + 1.40133i
\(53\) 1442.39 0.513488 0.256744 0.966479i \(-0.417350\pi\)
0.256744 + 0.966479i \(0.417350\pi\)
\(54\) 400.000 393.609i 0.137174 0.134983i
\(55\) 0 0
\(56\) 2808.87 + 2947.96i 0.895685 + 0.940039i
\(57\) 1017.92 0.313303
\(58\) 2971.25 + 3019.49i 0.883248 + 0.897588i
\(59\) 2472.02i 0.710147i 0.934838 + 0.355074i \(0.115544\pi\)
−0.934838 + 0.355074i \(0.884456\pi\)
\(60\) 0 0
\(61\) 4819.29 1.29516 0.647579 0.761998i \(-0.275781\pi\)
0.647579 + 0.761998i \(0.275781\pi\)
\(62\) −3042.47 + 2993.86i −0.791486 + 0.778841i
\(63\) 1717.83i 0.432811i
\(64\) 197.817 4091.22i 0.0482951 0.998833i
\(65\) 0 0
\(66\) 3217.93 + 3270.17i 0.738735 + 0.750729i
\(67\) 5792.14i 1.29030i −0.764057 0.645149i \(-0.776795\pi\)
0.764057 0.645149i \(-0.223205\pi\)
\(68\) 12.0435 747.765i 0.00260457 0.161714i
\(69\) 3854.66 0.809633
\(70\) 0 0
\(71\) 309.369i 0.0613706i −0.999529 0.0306853i \(-0.990231\pi\)
0.999529 0.0306853i \(-0.00976897\pi\)
\(72\) 1251.04 1192.01i 0.241327 0.229940i
\(73\) 996.733 0.187039 0.0935197 0.995617i \(-0.470188\pi\)
0.0935197 + 0.995617i \(0.470188\pi\)
\(74\) −6416.96 6521.15i −1.17183 1.19086i
\(75\) 0 0
\(76\) 3133.98 + 50.4759i 0.542586 + 0.00873891i
\(77\) −14044.0 −2.36869
\(78\) −3508.97 + 3452.91i −0.576754 + 0.567539i
\(79\) 1096.99i 0.175772i −0.996131 0.0878860i \(-0.971989\pi\)
0.996131 0.0878860i \(-0.0280111\pi\)
\(80\) 0 0
\(81\) 729.000 0.111111
\(82\) −3202.76 3254.76i −0.476317 0.484051i
\(83\) 3097.31i 0.449603i −0.974405 0.224801i \(-0.927827\pi\)
0.974405 0.224801i \(-0.0721733\pi\)
\(84\) −85.1824 + 5288.85i −0.0120723 + 0.749553i
\(85\) 0 0
\(86\) 3550.32 3493.60i 0.480033 0.472364i
\(87\) 5503.02i 0.727047i
\(88\) 9745.21 + 10227.8i 1.25842 + 1.32074i
\(89\) 10965.3 1.38433 0.692167 0.721738i \(-0.256656\pi\)
0.692167 + 0.721738i \(0.256656\pi\)
\(90\) 0 0
\(91\) 15069.5i 1.81977i
\(92\) 11867.7 + 191.142i 1.40214 + 0.0225830i
\(93\) −5544.91 −0.641104
\(94\) −1159.60 + 1141.07i −0.131236 + 0.129139i
\(95\) 0 0
\(96\) 3910.81 3607.93i 0.424350 0.391485i
\(97\) −12339.0 −1.31140 −0.655701 0.755020i \(-0.727627\pi\)
−0.655701 + 0.755020i \(0.727627\pi\)
\(98\) −4620.50 4695.52i −0.481102 0.488913i
\(99\) 5959.90i 0.608091i
\(100\) 0 0
\(101\) 14918.3 1.46244 0.731219 0.682143i \(-0.238952\pi\)
0.731219 + 0.682143i \(0.238952\pi\)
\(102\) 692.464 681.401i 0.0665575 0.0654942i
\(103\) 10083.1i 0.950433i 0.879869 + 0.475216i \(0.157630\pi\)
−0.879869 + 0.475216i \(0.842370\pi\)
\(104\) −10974.6 + 10456.8i −1.01467 + 0.966792i
\(105\) 0 0
\(106\) 4046.71 + 4112.41i 0.360155 + 0.366003i
\(107\) 18475.7i 1.61374i −0.590731 0.806869i \(-0.701161\pi\)
0.590731 0.806869i \(-0.298839\pi\)
\(108\) 2244.45 + 36.1491i 0.192425 + 0.00309921i
\(109\) −676.882 −0.0569718 −0.0284859 0.999594i \(-0.509069\pi\)
−0.0284859 + 0.999594i \(0.509069\pi\)
\(110\) 0 0
\(111\) 11884.8i 0.964597i
\(112\) −524.519 + 16279.1i −0.0418144 + 1.29776i
\(113\) −5693.92 −0.445917 −0.222959 0.974828i \(-0.571571\pi\)
−0.222959 + 0.974828i \(0.571571\pi\)
\(114\) 2855.84 + 2902.20i 0.219747 + 0.223315i
\(115\) 0 0
\(116\) −272.880 + 16942.7i −0.0202794 + 1.25912i
\(117\) −6395.10 −0.467171
\(118\) −7048.01 + 6935.41i −0.506177 + 0.498090i
\(119\) 2973.83i 0.210002i
\(120\) 0 0
\(121\) −34083.8 −2.32797
\(122\) 13520.8 + 13740.3i 0.908412 + 0.923160i
\(123\) 5931.80i 0.392081i
\(124\) −17071.7 274.957i −1.11028 0.0178822i
\(125\) 0 0
\(126\) −4897.71 + 4819.46i −0.308498 + 0.303569i
\(127\) 21834.4i 1.35374i −0.736103 0.676869i \(-0.763336\pi\)
0.736103 0.676869i \(-0.236664\pi\)
\(128\) 12219.5 10914.2i 0.745820 0.666148i
\(129\) 6470.47 0.388827
\(130\) 0 0
\(131\) 6919.28i 0.403198i 0.979468 + 0.201599i \(0.0646138\pi\)
−0.979468 + 0.201599i \(0.935386\pi\)
\(132\) −295.535 + 18349.3i −0.0169614 + 1.05311i
\(133\) −12463.7 −0.704602
\(134\) 16514.0 16250.2i 0.919695 0.905002i
\(135\) 0 0
\(136\) 2165.75 2063.56i 0.117093 0.111568i
\(137\) 24619.2 1.31169 0.655846 0.754895i \(-0.272312\pi\)
0.655846 + 0.754895i \(0.272312\pi\)
\(138\) 10814.5 + 10990.1i 0.567868 + 0.577088i
\(139\) 18767.2i 0.971336i 0.874143 + 0.485668i \(0.161424\pi\)
−0.874143 + 0.485668i \(0.838576\pi\)
\(140\) 0 0
\(141\) −2113.37 −0.106301
\(142\) 882.046 867.954i 0.0437436 0.0430447i
\(143\) 52282.8i 2.55674i
\(144\) 6908.41 + 222.592i 0.333160 + 0.0107346i
\(145\) 0 0
\(146\) 2796.39 + 2841.80i 0.131188 + 0.133318i
\(147\) 8557.59i 0.396020i
\(148\) 589.335 36590.9i 0.0269054 1.67051i
\(149\) 6573.00 0.296068 0.148034 0.988982i \(-0.452706\pi\)
0.148034 + 0.988982i \(0.452706\pi\)
\(150\) 0 0
\(151\) 7823.28i 0.343111i 0.985174 + 0.171556i \(0.0548793\pi\)
−0.985174 + 0.171556i \(0.945121\pi\)
\(152\) 8648.65 + 9076.93i 0.374335 + 0.392873i
\(153\) 1262.02 0.0539116
\(154\) −39401.2 40041.0i −1.66138 1.68835i
\(155\) 0 0
\(156\) −19689.2 317.116i −0.809058 0.0130307i
\(157\) −9202.59 −0.373346 −0.186673 0.982422i \(-0.559770\pi\)
−0.186673 + 0.982422i \(0.559770\pi\)
\(158\) 3127.65 3077.68i 0.125286 0.123285i
\(159\) 7494.87i 0.296462i
\(160\) 0 0
\(161\) −47197.6 −1.82082
\(162\) 2045.25 + 2078.46i 0.0779322 + 0.0791975i
\(163\) 43667.2i 1.64354i 0.569820 + 0.821769i \(0.307013\pi\)
−0.569820 + 0.821769i \(0.692987\pi\)
\(164\) 294.142 18262.8i 0.0109363 0.679017i
\(165\) 0 0
\(166\) 8830.78 8689.70i 0.320467 0.315347i
\(167\) 19662.7i 0.705034i −0.935805 0.352517i \(-0.885326\pi\)
0.935805 0.352517i \(-0.114674\pi\)
\(168\) −15318.1 + 14595.3i −0.542732 + 0.517124i
\(169\) 27539.5 0.964236
\(170\) 0 0
\(171\) 5289.27i 0.180885i
\(172\) 19921.3 + 320.853i 0.673381 + 0.0108455i
\(173\) −31871.9 −1.06492 −0.532459 0.846456i \(-0.678732\pi\)
−0.532459 + 0.846456i \(0.678732\pi\)
\(174\) −15689.7 + 15439.1i −0.518223 + 0.509944i
\(175\) 0 0
\(176\) −1819.79 + 56479.3i −0.0587484 + 1.82333i
\(177\) −12845.0 −0.410004
\(178\) 30763.8 + 31263.3i 0.970958 + 0.986722i
\(179\) 52843.2i 1.64924i −0.565689 0.824619i \(-0.691390\pi\)
0.565689 0.824619i \(-0.308610\pi\)
\(180\) 0 0
\(181\) −63045.0 −1.92439 −0.962197 0.272356i \(-0.912197\pi\)
−0.962197 + 0.272356i \(0.912197\pi\)
\(182\) 42964.8 42278.4i 1.29709 1.27637i
\(183\) 25041.7i 0.747760i
\(184\) 32750.7 + 34372.5i 0.967352 + 1.01526i
\(185\) 0 0
\(186\) −15556.6 15809.1i −0.449664 0.456964i
\(187\) 10317.5i 0.295048i
\(188\) −6506.66 104.796i −0.184095 0.00296504i
\(189\) −8926.08 −0.249883
\(190\) 0 0
\(191\) 20730.2i 0.568246i −0.958788 0.284123i \(-0.908298\pi\)
0.958788 0.284123i \(-0.0917024\pi\)
\(192\) 21258.6 + 1027.89i 0.576677 + 0.0278832i
\(193\) 17567.6 0.471627 0.235813 0.971798i \(-0.424225\pi\)
0.235813 + 0.971798i \(0.424225\pi\)
\(194\) −34617.8 35179.8i −0.919805 0.934739i
\(195\) 0 0
\(196\) 424.348 26347.1i 0.0110461 0.685837i
\(197\) −50800.9 −1.30900 −0.654499 0.756063i \(-0.727120\pi\)
−0.654499 + 0.756063i \(0.727120\pi\)
\(198\) −16992.3 + 16720.8i −0.433433 + 0.426509i
\(199\) 32141.3i 0.811629i 0.913955 + 0.405814i \(0.133012\pi\)
−0.913955 + 0.405814i \(0.866988\pi\)
\(200\) 0 0
\(201\) 30096.9 0.744953
\(202\) 41854.3 + 42533.8i 1.02574 + 1.04239i
\(203\) 67380.5i 1.63509i
\(204\) 3885.50 + 62.5800i 0.0933656 + 0.00150375i
\(205\) 0 0
\(206\) −28748.1 + 28288.9i −0.677447 + 0.666624i
\(207\) 20029.4i 0.467442i
\(208\) −60603.6 1952.67i −1.40079 0.0451339i
\(209\) −43242.1 −0.989953
\(210\) 0 0
\(211\) 9541.34i 0.214311i −0.994242 0.107156i \(-0.965826\pi\)
0.994242 0.107156i \(-0.0341743\pi\)
\(212\) −371.650 + 23075.2i −0.00826919 + 0.513421i
\(213\) 1607.53 0.0354323
\(214\) 52676.2 51834.6i 1.15024 1.13186i
\(215\) 0 0
\(216\) 6193.87 + 6500.58i 0.132756 + 0.139330i
\(217\) 67893.4 1.44181
\(218\) −1899.03 1929.86i −0.0399594 0.0406082i
\(219\) 5179.18i 0.107987i
\(220\) 0 0
\(221\) −11071.0 −0.226673
\(222\) 33884.9 33343.5i 0.687543 0.676559i
\(223\) 33469.4i 0.673037i −0.941677 0.336518i \(-0.890751\pi\)
0.941677 0.336518i \(-0.109249\pi\)
\(224\) −47885.0 + 44176.5i −0.954342 + 0.880431i
\(225\) 0 0
\(226\) −15974.6 16234.0i −0.312762 0.317840i
\(227\) 1149.27i 0.0223033i −0.999938 0.0111517i \(-0.996450\pi\)
0.999938 0.0111517i \(-0.00354976\pi\)
\(228\) −262.281 + 16284.6i −0.00504541 + 0.313262i
\(229\) −49392.2 −0.941863 −0.470931 0.882170i \(-0.656082\pi\)
−0.470931 + 0.882170i \(0.656082\pi\)
\(230\) 0 0
\(231\) 72974.7i 1.36757i
\(232\) −49071.1 + 46755.8i −0.911696 + 0.868679i
\(233\) 42084.0 0.775184 0.387592 0.921831i \(-0.373307\pi\)
0.387592 + 0.921831i \(0.373307\pi\)
\(234\) −17941.8 18233.1i −0.327669 0.332989i
\(235\) 0 0
\(236\) −39547.2 636.949i −0.710055 0.0114362i
\(237\) 5700.14 0.101482
\(238\) −8478.73 + 8343.27i −0.149685 + 0.147293i
\(239\) 34540.4i 0.604689i 0.953199 + 0.302345i \(0.0977693\pi\)
−0.953199 + 0.302345i \(0.902231\pi\)
\(240\) 0 0
\(241\) 68666.9 1.18226 0.591131 0.806576i \(-0.298682\pi\)
0.591131 + 0.806576i \(0.298682\pi\)
\(242\) −95624.1 97176.6i −1.63281 1.65932i
\(243\) 3788.00i 0.0641500i
\(244\) −1241.75 + 77098.6i −0.0208572 + 1.29499i
\(245\) 0 0
\(246\) 16912.2 16642.0i 0.279467 0.275002i
\(247\) 46399.7i 0.760539i
\(248\) −47111.7 49444.6i −0.765994 0.803925i
\(249\) 16094.1 0.259578
\(250\) 0 0
\(251\) 62003.3i 0.984163i 0.870549 + 0.492082i \(0.163764\pi\)
−0.870549 + 0.492082i \(0.836236\pi\)
\(252\) −27481.6 442.621i −0.432755 0.00696996i
\(253\) −163749. −2.55822
\(254\) 62252.4 61257.9i 0.964914 0.949499i
\(255\) 0 0
\(256\) 65400.1 + 4218.82i 0.997926 + 0.0643740i
\(257\) −65977.4 −0.998916 −0.499458 0.866338i \(-0.666468\pi\)
−0.499458 + 0.866338i \(0.666468\pi\)
\(258\) 18153.3 + 18448.0i 0.272719 + 0.277147i
\(259\) 145521.i 2.16933i
\(260\) 0 0
\(261\) −28594.5 −0.419761
\(262\) −19727.6 + 19412.5i −0.287391 + 0.282799i
\(263\) 45889.4i 0.663439i 0.943378 + 0.331719i \(0.107629\pi\)
−0.943378 + 0.331719i \(0.892371\pi\)
\(264\) −53145.1 + 50637.6i −0.762528 + 0.726549i
\(265\) 0 0
\(266\) −34967.7 35535.4i −0.494201 0.502225i
\(267\) 56977.4i 0.799245i
\(268\) 92662.3 + 1492.42i 1.29013 + 0.0207789i
\(269\) 66600.2 0.920388 0.460194 0.887818i \(-0.347780\pi\)
0.460194 + 0.887818i \(0.347780\pi\)
\(270\) 0 0
\(271\) 107846.i 1.46848i 0.678892 + 0.734239i \(0.262461\pi\)
−0.678892 + 0.734239i \(0.737539\pi\)
\(272\) 11959.6 + 385.343i 0.161651 + 0.00520847i
\(273\) 78303.4 1.05064
\(274\) 69070.5 + 70191.9i 0.920008 + 0.934945i
\(275\) 0 0
\(276\) −993.204 + 61666.6i −0.0130383 + 0.809528i
\(277\) 76120.9 0.992074 0.496037 0.868301i \(-0.334788\pi\)
0.496037 + 0.868301i \(0.334788\pi\)
\(278\) −53507.3 + 52652.5i −0.692347 + 0.681286i
\(279\) 28812.2i 0.370141i
\(280\) 0 0
\(281\) 127936. 1.62024 0.810120 0.586264i \(-0.199402\pi\)
0.810120 + 0.586264i \(0.199402\pi\)
\(282\) −5929.19 6025.46i −0.0745586 0.0757691i
\(283\) 117792.i 1.47076i 0.677655 + 0.735380i \(0.262996\pi\)
−0.677655 + 0.735380i \(0.737004\pi\)
\(284\) 4949.27 + 79.7131i 0.0613627 + 0.000988310i
\(285\) 0 0
\(286\) 149064. 146682.i 1.82239 1.79327i
\(287\) 72630.6i 0.881771i
\(288\) 18747.3 + 20321.2i 0.226024 + 0.244998i
\(289\) −81336.2 −0.973842
\(290\) 0 0
\(291\) 64115.3i 0.757139i
\(292\) −256.821 + 15945.7i −0.00301207 + 0.187015i
\(293\) 120518. 1.40384 0.701918 0.712258i \(-0.252327\pi\)
0.701918 + 0.712258i \(0.252327\pi\)
\(294\) 24398.6 24008.8i 0.282274 0.277764i
\(295\) 0 0
\(296\) 105978. 100978.i 1.20958 1.15250i
\(297\) −30968.5 −0.351081
\(298\) 18441.0 + 18740.4i 0.207659 + 0.211031i
\(299\) 175706.i 1.96537i
\(300\) 0 0
\(301\) −79226.3 −0.874453
\(302\) −22305.0 + 21948.7i −0.244562 + 0.240655i
\(303\) 77517.9i 0.844339i
\(304\) −1615.02 + 50124.1i −0.0174756 + 0.542375i
\(305\) 0 0
\(306\) 3540.67 + 3598.15i 0.0378131 + 0.0384270i
\(307\) 90003.1i 0.954950i 0.878645 + 0.477475i \(0.158448\pi\)
−0.878645 + 0.477475i \(0.841552\pi\)
\(308\) 3618.62 224675.i 0.0381453 2.36839i
\(309\) −52393.5 −0.548732
\(310\) 0 0
\(311\) 35944.1i 0.371627i −0.982585 0.185813i \(-0.940508\pi\)
0.982585 0.185813i \(-0.0594920\pi\)
\(312\) −54335.2 57025.9i −0.558178 0.585818i
\(313\) −10420.7 −0.106368 −0.0531838 0.998585i \(-0.516937\pi\)
−0.0531838 + 0.998585i \(0.516937\pi\)
\(314\) −25818.4 26237.6i −0.261861 0.266112i
\(315\) 0 0
\(316\) 17549.6 + 282.655i 0.175749 + 0.00283062i
\(317\) 44276.9 0.440614 0.220307 0.975431i \(-0.429294\pi\)
0.220307 + 0.975431i \(0.429294\pi\)
\(318\) −21368.7 + 21027.3i −0.211312 + 0.207936i
\(319\) 233773.i 2.29727i
\(320\) 0 0
\(321\) 96002.4 0.931692
\(322\) −132416. 134565.i −1.27711 1.29784i
\(323\) 9156.59i 0.0877664i
\(324\) −187.836 + 11662.5i −0.00178933 + 0.111097i
\(325\) 0 0
\(326\) −124500. + 122511.i −1.17148 + 1.15276i
\(327\) 3517.18i 0.0328927i
\(328\) 52894.6 50398.8i 0.491658 0.468460i
\(329\) 25876.7 0.239066
\(330\) 0 0
\(331\) 219017.i 1.99904i 0.0309493 + 0.999521i \(0.490147\pi\)
−0.0309493 + 0.999521i \(0.509853\pi\)
\(332\) 49550.6 + 798.064i 0.449544 + 0.00724038i
\(333\) 61755.2 0.556910
\(334\) 56060.5 55164.9i 0.502533 0.494504i
\(335\) 0 0
\(336\) −84588.6 2725.48i −0.749261 0.0241415i
\(337\) 51173.5 0.450594 0.225297 0.974290i \(-0.427665\pi\)
0.225297 + 0.974290i \(0.427665\pi\)
\(338\) 77263.9 + 78518.3i 0.676306 + 0.687286i
\(339\) 29586.5i 0.257450i
\(340\) 0 0
\(341\) 235552. 2.02572
\(342\) −15080.3 + 14839.4i −0.128931 + 0.126871i
\(343\) 47977.7i 0.407804i
\(344\) 54975.6 + 57698.0i 0.464572 + 0.487578i
\(345\) 0 0
\(346\) −89418.7 90870.4i −0.746923 0.759050i
\(347\) 78897.6i 0.655247i −0.944808 0.327623i \(-0.893752\pi\)
0.944808 0.327623i \(-0.106248\pi\)
\(348\) −88036.9 1417.93i −0.726953 0.0117083i
\(349\) 187086. 1.53599 0.767997 0.640454i \(-0.221254\pi\)
0.767997 + 0.640454i \(0.221254\pi\)
\(350\) 0 0
\(351\) 33229.9i 0.269721i
\(352\) −166134. + 153268.i −1.34083 + 1.23699i
\(353\) 26576.3 0.213278 0.106639 0.994298i \(-0.465991\pi\)
0.106639 + 0.994298i \(0.465991\pi\)
\(354\) −36037.4 36622.5i −0.287573 0.292242i
\(355\) 0 0
\(356\) −2825.36 + 175422.i −0.0222932 + 1.38415i
\(357\) −15452.5 −0.121245
\(358\) 150662. 148255.i 1.17554 1.15676i
\(359\) 13211.6i 0.102510i −0.998686 0.0512552i \(-0.983678\pi\)
0.998686 0.0512552i \(-0.0163222\pi\)
\(360\) 0 0
\(361\) 91944.6 0.705524
\(362\) −176877. 179748.i −1.34975 1.37166i
\(363\) 177105.i 1.34405i
\(364\) 241081. + 3882.86i 1.81953 + 0.0293055i
\(365\) 0 0
\(366\) −71396.8 + 70256.1i −0.532987 + 0.524472i
\(367\) 46921.2i 0.348367i 0.984713 + 0.174184i \(0.0557286\pi\)
−0.984713 + 0.174184i \(0.944271\pi\)
\(368\) −6115.76 + 189810.i −0.0451601 + 1.40160i
\(369\) 30822.5 0.226368
\(370\) 0 0
\(371\) 91769.3i 0.666729i
\(372\) 1428.72 88707.0i 0.0103243 0.641021i
\(373\) 237489. 1.70697 0.853487 0.521115i \(-0.174484\pi\)
0.853487 + 0.521115i \(0.174484\pi\)
\(374\) −29416.5 + 28946.5i −0.210304 + 0.206944i
\(375\) 0 0
\(376\) −17956.0 18845.2i −0.127009 0.133299i
\(377\) 250843. 1.76490
\(378\) −25042.7 25449.3i −0.175266 0.178111i
\(379\) 108145.i 0.752885i 0.926440 + 0.376442i \(0.122853\pi\)
−0.926440 + 0.376442i \(0.877147\pi\)
\(380\) 0 0
\(381\) 113455. 0.781581
\(382\) 59104.0 58159.8i 0.405033 0.398562i
\(383\) 143109.i 0.975594i −0.872957 0.487797i \(-0.837801\pi\)
0.872957 0.487797i \(-0.162199\pi\)
\(384\) 56711.7 + 63494.4i 0.384601 + 0.430599i
\(385\) 0 0
\(386\) 49287.0 + 50087.3i 0.330794 + 0.336165i
\(387\) 33621.6i 0.224489i
\(388\) 3179.30 197398.i 0.0211188 1.31123i
\(389\) −132061. −0.872720 −0.436360 0.899772i \(-0.643733\pi\)
−0.436360 + 0.899772i \(0.643733\pi\)
\(390\) 0 0
\(391\) 34674.1i 0.226805i
\(392\) 76309.1 72708.6i 0.496597 0.473166i
\(393\) −35953.6 −0.232787
\(394\) −142525. 144839.i −0.918118 0.933024i
\(395\) 0 0
\(396\) −95346.0 1535.65i −0.608012 0.00979266i
\(397\) 46139.3 0.292745 0.146373 0.989230i \(-0.453240\pi\)
0.146373 + 0.989230i \(0.453240\pi\)
\(398\) −91638.5 + 90174.4i −0.578511 + 0.569269i
\(399\) 64763.3i 0.406802i
\(400\) 0 0
\(401\) 3244.97 0.0201800 0.0100900 0.999949i \(-0.496788\pi\)
0.0100900 + 0.999949i \(0.496788\pi\)
\(402\) 84438.6 + 85809.5i 0.522503 + 0.530986i
\(403\) 252753.i 1.55627i
\(404\) −3843.90 + 238662.i −0.0235510 + 1.46225i
\(405\) 0 0
\(406\) 192109. 189040.i 1.16546 1.14684i
\(407\) 504876.i 3.04787i
\(408\) 10722.6 + 11253.6i 0.0644138 + 0.0676036i
\(409\) −190227. −1.13717 −0.568585 0.822625i \(-0.692509\pi\)
−0.568585 + 0.822625i \(0.692509\pi\)
\(410\) 0 0
\(411\) 127925.i 0.757306i
\(412\) −161309. 2598.05i −0.950309 0.0153057i
\(413\) 157278. 0.922078
\(414\) −57106.0 + 56193.7i −0.333182 + 0.327859i
\(415\) 0 0
\(416\) −164460. 178266.i −0.950326 1.03010i
\(417\) −97517.2 −0.560801
\(418\) −121318. 123288.i −0.694343 0.705616i
\(419\) 38663.2i 0.220226i −0.993919 0.110113i \(-0.964879\pi\)
0.993919 0.110113i \(-0.0351213\pi\)
\(420\) 0 0
\(421\) −215220. −1.21428 −0.607140 0.794595i \(-0.707683\pi\)
−0.607140 + 0.794595i \(0.707683\pi\)
\(422\) 27203.4 26768.8i 0.152756 0.150316i
\(423\) 10981.4i 0.0613730i
\(424\) −66832.7 + 63679.3i −0.371755 + 0.354215i
\(425\) 0 0
\(426\) 4510.02 + 4583.25i 0.0248519 + 0.0252554i
\(427\) 306618.i 1.68168i
\(428\) 295572. + 4760.50i 1.61353 + 0.0259875i
\(429\) 271669. 1.47613
\(430\) 0 0
\(431\) 12832.4i 0.0690804i −0.999403 0.0345402i \(-0.989003\pi\)
0.999403 0.0345402i \(-0.0109967\pi\)
\(432\) −1156.62 + 35897.2i −0.00619761 + 0.192350i
\(433\) −245264. −1.30815 −0.654076 0.756429i \(-0.726942\pi\)
−0.654076 + 0.756429i \(0.726942\pi\)
\(434\) 190479. + 193572.i 1.01127 + 1.02769i
\(435\) 0 0
\(436\) 174.408 10828.7i 0.000917471 0.0569644i
\(437\) −145324. −0.760980
\(438\) −14766.4 + 14530.5i −0.0769709 + 0.0757412i
\(439\) 8320.58i 0.0431742i 0.999767 + 0.0215871i \(0.00687192\pi\)
−0.999767 + 0.0215871i \(0.993128\pi\)
\(440\) 0 0
\(441\) 44466.5 0.228642
\(442\) −31060.2 31564.5i −0.158986 0.161568i
\(443\) 141239.i 0.719695i 0.933011 + 0.359847i \(0.117171\pi\)
−0.933011 + 0.359847i \(0.882829\pi\)
\(444\) 190132. + 3062.28i 0.964472 + 0.0155338i
\(445\) 0 0
\(446\) 95425.1 93900.6i 0.479726 0.472061i
\(447\) 34154.3i 0.170935i
\(448\) −260296. 12585.7i −1.29692 0.0627080i
\(449\) −197626. −0.980282 −0.490141 0.871643i \(-0.663055\pi\)
−0.490141 + 0.871643i \(0.663055\pi\)
\(450\) 0 0
\(451\) 251988.i 1.23887i
\(452\) 1467.11 91090.9i 0.00718103 0.445859i
\(453\) −40651.0 −0.198095
\(454\) 3276.69 3224.34i 0.0158973 0.0156433i
\(455\) 0 0
\(456\) −47165.1 + 44939.7i −0.226825 + 0.216123i
\(457\) 331333. 1.58647 0.793236 0.608915i \(-0.208395\pi\)
0.793236 + 0.608915i \(0.208395\pi\)
\(458\) −138573. 140823.i −0.660613 0.671339i
\(459\) 6557.63i 0.0311259i
\(460\) 0 0
\(461\) −196090. −0.922687 −0.461343 0.887222i \(-0.652632\pi\)
−0.461343 + 0.887222i \(0.652632\pi\)
\(462\) 208059. 204735.i 0.974770 0.959197i
\(463\) 168744.i 0.787164i 0.919289 + 0.393582i \(0.128764\pi\)
−0.919289 + 0.393582i \(0.871236\pi\)
\(464\) −270978. 8731.03i −1.25863 0.0405536i
\(465\) 0 0
\(466\) 118069. + 119986.i 0.543706 + 0.552534i
\(467\) 58203.8i 0.266881i −0.991057 0.133440i \(-0.957398\pi\)
0.991057 0.133440i \(-0.0426025\pi\)
\(468\) 1647.78 102308.i 0.00752329 0.467110i
\(469\) −368515. −1.67536
\(470\) 0 0
\(471\) 47818.1i 0.215551i
\(472\) −109136. 114541.i −0.489874 0.514133i
\(473\) −274871. −1.22859
\(474\) 15992.1 + 16251.7i 0.0711785 + 0.0723341i
\(475\) 0 0
\(476\) −47575.2 766.248i −0.209975 0.00338186i
\(477\) −38944.5 −0.171163
\(478\) −98478.6 + 96905.3i −0.431009 + 0.424123i
\(479\) 221700.i 0.966260i 0.875549 + 0.483130i \(0.160500\pi\)
−0.875549 + 0.483130i \(0.839500\pi\)
\(480\) 0 0
\(481\) −541743. −2.34155
\(482\) 192649. + 195777.i 0.829227 + 0.842690i
\(483\) 245246.i 1.05125i
\(484\) 8782.14 545270.i 0.0374895 2.32767i
\(485\) 0 0
\(486\) −10800.0 + 10627.4i −0.0457247 + 0.0449942i
\(487\) 145571.i 0.613788i −0.951744 0.306894i \(-0.900710\pi\)
0.951744 0.306894i \(-0.0992897\pi\)
\(488\) −223300. + 212764.i −0.937670 + 0.893427i
\(489\) −226901. −0.948897
\(490\) 0 0
\(491\) 244597.i 1.01458i −0.861774 0.507292i \(-0.830646\pi\)
0.861774 0.507292i \(-0.169354\pi\)
\(492\) 94896.4 + 1528.41i 0.392030 + 0.00631406i
\(493\) −49501.8 −0.203670
\(494\) 132291. 130177.i 0.542095 0.533435i
\(495\) 0 0
\(496\) 8797.48 273040.i 0.0357598 1.10985i
\(497\) −19683.1 −0.0796856
\(498\) 45153.0 + 45886.1i 0.182066 + 0.185022i
\(499\) 113422.i 0.455507i 0.973719 + 0.227754i \(0.0731381\pi\)
−0.973719 + 0.227754i \(0.926862\pi\)
\(500\) 0 0
\(501\) 102170. 0.407052
\(502\) −176778. + 173954.i −0.701490 + 0.690282i
\(503\) 135516.i 0.535616i 0.963472 + 0.267808i \(0.0862993\pi\)
−0.963472 + 0.267808i \(0.913701\pi\)
\(504\) −75839.5 79595.0i −0.298562 0.313346i
\(505\) 0 0
\(506\) −459408. 466867.i −1.79431 1.82344i
\(507\) 143100.i 0.556702i
\(508\) 349306. + 5625.93i 1.35356 + 0.0218005i
\(509\) 393520. 1.51891 0.759454 0.650561i \(-0.225466\pi\)
0.759454 + 0.650561i \(0.225466\pi\)
\(510\) 0 0
\(511\) 63415.3i 0.242858i
\(512\) 171456. + 198299.i 0.654051 + 0.756451i
\(513\) −27483.9 −0.104434
\(514\) −185104. 188109.i −0.700630 0.712005i
\(515\) 0 0
\(516\) −1667.20 + 103514.i −0.00626165 + 0.388777i
\(517\) 89777.9 0.335883
\(518\) −414896. + 408268.i −1.54625 + 1.52155i
\(519\) 165611.i 0.614831i
\(520\) 0 0
\(521\) 309126. 1.13883 0.569416 0.822049i \(-0.307169\pi\)
0.569416 + 0.822049i \(0.307169\pi\)
\(522\) −80223.7 81526.2i −0.294416 0.299196i
\(523\) 49369.3i 0.180490i −0.995920 0.0902452i \(-0.971235\pi\)
0.995920 0.0902452i \(-0.0287651\pi\)
\(524\) −110694. 1782.84i −0.403146 0.00649308i
\(525\) 0 0
\(526\) −130836. + 128745.i −0.472884 + 0.465329i
\(527\) 49878.6i 0.179594i
\(528\) −293475. 9455.90i −1.05270 0.0339184i
\(529\) −270470. −0.966514
\(530\) 0 0
\(531\) 66744.6i 0.236716i
\(532\) 3211.44 199394.i 0.0113469 0.704511i
\(533\) −270388. −0.951773
\(534\) −162449. + 159854.i −0.569684 + 0.560583i
\(535\) 0 0
\(536\) 255715. + 268377.i 0.890073 + 0.934150i
\(537\) 274581. 0.952188
\(538\) 186851. + 189885.i 0.645551 + 0.656032i
\(539\) 363533.i 1.25132i
\(540\) 0 0
\(541\) −102454. −0.350053 −0.175027 0.984564i \(-0.556001\pi\)
−0.175027 + 0.984564i \(0.556001\pi\)
\(542\) −307482. + 302570.i −1.04670 + 1.02998i
\(543\) 327592.i 1.11105i
\(544\) 32454.7 + 35179.2i 0.109668 + 0.118874i
\(545\) 0 0
\(546\) 219685. + 223252.i 0.736911 + 0.748875i
\(547\) 66168.6i 0.221145i 0.993868 + 0.110573i \(0.0352685\pi\)
−0.993868 + 0.110573i \(0.964732\pi\)
\(548\) −6343.45 + 393855.i −0.0211234 + 1.31152i
\(549\) −130121. −0.431720
\(550\) 0 0
\(551\) 207468.i 0.683358i
\(552\) −178605. + 170178.i −0.586158 + 0.558501i
\(553\) −69794.2 −0.228228
\(554\) 213562. + 217029.i 0.695831 + 0.707128i
\(555\) 0 0
\(556\) −300236. 4835.61i −0.971210 0.0156424i
\(557\) −344220. −1.10950 −0.554749 0.832018i \(-0.687186\pi\)
−0.554749 + 0.832018i \(0.687186\pi\)
\(558\) 82146.7 80834.3i 0.263829 0.259614i
\(559\) 294943.i 0.943874i
\(560\) 0 0
\(561\) −53611.6 −0.170346
\(562\) 358931. + 364759.i 1.13642 + 1.15487i
\(563\) 581940.i 1.83595i 0.396637 + 0.917976i \(0.370177\pi\)
−0.396637 + 0.917976i \(0.629823\pi\)
\(564\) 544.538 33809.6i 0.00171187 0.106287i
\(565\) 0 0
\(566\) −335837. + 330472.i −1.04833 + 1.03158i
\(567\) 46381.3i 0.144270i
\(568\) 13658.2 + 14334.5i 0.0423347 + 0.0444311i
\(569\) 269874. 0.833559 0.416779 0.909008i \(-0.363159\pi\)
0.416779 + 0.909008i \(0.363159\pi\)
\(570\) 0 0
\(571\) 248959.i 0.763581i 0.924249 + 0.381790i \(0.124692\pi\)
−0.924249 + 0.381790i \(0.875308\pi\)
\(572\) 836416. + 13471.3i 2.55641 + 0.0411736i
\(573\) 107717. 0.328077
\(574\) −207078. + 203770.i −0.628507 + 0.618466i
\(575\) 0 0
\(576\) −5341.06 + 110463.i −0.0160984 + 0.332944i
\(577\) −389168. −1.16892 −0.584461 0.811422i \(-0.698694\pi\)
−0.584461 + 0.811422i \(0.698694\pi\)
\(578\) −228194. 231899.i −0.683043 0.694133i
\(579\) 91284.1i 0.272294i
\(580\) 0 0
\(581\) −197061. −0.583779
\(582\) 182800. 179879.i 0.539672 0.531050i
\(583\) 318388.i 0.936742i
\(584\) −46183.4 + 44004.3i −0.135413 + 0.129024i
\(585\) 0 0
\(586\) 338120. + 343610.i 0.984636 + 1.00062i
\(587\) 67273.5i 0.195240i 0.995224 + 0.0976198i \(0.0311229\pi\)
−0.995224 + 0.0976198i \(0.968877\pi\)
\(588\) 136904. + 2204.98i 0.395968 + 0.00637748i
\(589\) 209047. 0.602579
\(590\) 0 0
\(591\) 263969.i 0.755750i
\(592\) 585227. + 18856.3i 1.66986 + 0.0538038i
\(593\) 483157. 1.37398 0.686988 0.726669i \(-0.258933\pi\)
0.686988 + 0.726669i \(0.258933\pi\)
\(594\) −86884.1 88294.7i −0.246245 0.250243i
\(595\) 0 0
\(596\) −1693.62 + 105154.i −0.00476786 + 0.296029i
\(597\) −167011. −0.468594
\(598\) 500959. 492955.i 1.40088 1.37849i
\(599\) 361016.i 1.00617i 0.864236 + 0.503086i \(0.167802\pi\)
−0.864236 + 0.503086i \(0.832198\pi\)
\(600\) 0 0
\(601\) −329300. −0.911681 −0.455841 0.890061i \(-0.650661\pi\)
−0.455841 + 0.890061i \(0.650661\pi\)
\(602\) −222274. 225883.i −0.613333 0.623290i
\(603\) 156388.i 0.430099i
\(604\) −125156. 2015.77i −0.343067 0.00552545i
\(605\) 0 0
\(606\) −221012. + 217481.i −0.601826 + 0.592211i
\(607\) 347112.i 0.942090i −0.882109 0.471045i \(-0.843877\pi\)
0.882109 0.471045i \(-0.156123\pi\)
\(608\) −147440. + 136022.i −0.398850 + 0.367960i
\(609\) 350120. 0.944021
\(610\) 0 0
\(611\) 96333.6i 0.258045i
\(612\) −325.175 + 20189.7i −0.000868190 + 0.0539046i
\(613\) −315831. −0.840492 −0.420246 0.907410i \(-0.638056\pi\)
−0.420246 + 0.907410i \(0.638056\pi\)
\(614\) −256609. + 252509.i −0.680667 + 0.669792i
\(615\) 0 0
\(616\) 650724. 620021.i 1.71489 1.63397i
\(617\) −302237. −0.793920 −0.396960 0.917836i \(-0.629935\pi\)
−0.396960 + 0.917836i \(0.629935\pi\)
\(618\) −146993. 149380.i −0.384876 0.391124i
\(619\) 367141.i 0.958190i −0.877763 0.479095i \(-0.840965\pi\)
0.877763 0.479095i \(-0.159035\pi\)
\(620\) 0 0
\(621\) −104076. −0.269878
\(622\) 102481. 100843.i 0.264887 0.260655i
\(623\) 697647.i 1.79746i
\(624\) 10146.4 314905.i 0.0260581 0.808744i
\(625\) 0 0
\(626\) −29236.0 29710.7i −0.0746052 0.0758165i
\(627\) 224693.i 0.571549i
\(628\) 2371.17 147222.i 0.00601234 0.373297i
\(629\) 106908. 0.270215
\(630\) 0 0
\(631\) 210709.i 0.529206i −0.964357 0.264603i \(-0.914759\pi\)
0.964357 0.264603i \(-0.0852409\pi\)
\(632\) 48430.6 + 50828.9i 0.121251 + 0.127255i
\(633\) 49578.3 0.123733
\(634\) 124221. + 126238.i 0.309043 + 0.314060i
\(635\) 0 0
\(636\) −119902. 1931.15i −0.296424 0.00477422i
\(637\) −390079. −0.961334
\(638\) 666512. 655864.i 1.63745 1.61129i
\(639\) 8352.97i 0.0204569i
\(640\) 0 0
\(641\) −415962. −1.01237 −0.506183 0.862426i \(-0.668944\pi\)
−0.506183 + 0.862426i \(0.668944\pi\)
\(642\) 269341. + 273714.i 0.653479 + 0.664089i
\(643\) 732294.i 1.77118i −0.464465 0.885592i \(-0.653753\pi\)
0.464465 0.885592i \(-0.346247\pi\)
\(644\) 12161.1 755063.i 0.0293225 1.82059i
\(645\) 0 0
\(646\) −26106.4 + 25689.4i −0.0625580 + 0.0615585i
\(647\) 96321.2i 0.230098i −0.993360 0.115049i \(-0.963297\pi\)
0.993360 0.115049i \(-0.0367025\pi\)
\(648\) −33778.0 + 32184.3i −0.0804423 + 0.0766467i
\(649\) 545667. 1.29550
\(650\) 0 0
\(651\) 352785.i 0.832430i
\(652\) −698584. 11251.4i −1.64333 0.0264675i
\(653\) −274691. −0.644196 −0.322098 0.946706i \(-0.604388\pi\)
−0.322098 + 0.946706i \(0.604388\pi\)
\(654\) 10027.9 9867.66i 0.0234452 0.0230706i
\(655\) 0 0
\(656\) 292092. + 9411.32i 0.678752 + 0.0218697i
\(657\) −26911.8 −0.0623465
\(658\) 72598.8 + 73777.5i 0.167679 + 0.170401i
\(659\) 360421.i 0.829927i −0.909838 0.414963i \(-0.863794\pi\)
0.909838 0.414963i \(-0.136206\pi\)
\(660\) 0 0
\(661\) 461663. 1.05663 0.528314 0.849049i \(-0.322824\pi\)
0.528314 + 0.849049i \(0.322824\pi\)
\(662\) −624442. + 614465.i −1.42487 + 1.40211i
\(663\) 57526.4i 0.130870i
\(664\) 136742. + 143513.i 0.310145 + 0.325504i
\(665\) 0 0
\(666\) 173258. + 176071.i 0.390611 + 0.396953i
\(667\) 785640.i 1.76592i
\(668\) 314562. + 5066.35i 0.704943 + 0.0113538i
\(669\) 173912. 0.388578
\(670\) 0 0
\(671\) 1.06379e6i 2.36272i
\(672\) −229548. 248818.i −0.508317 0.550989i
\(673\) −295518. −0.652459 −0.326230 0.945291i \(-0.605778\pi\)
−0.326230 + 0.945291i \(0.605778\pi\)
\(674\) 143570. + 145901.i 0.316042 + 0.321173i
\(675\) 0 0
\(676\) −7095.93 + 440576.i −0.0155280 + 0.964111i
\(677\) 865789. 1.88901 0.944506 0.328494i \(-0.106541\pi\)
0.944506 + 0.328494i \(0.106541\pi\)
\(678\) 84354.3 83006.6i 0.183505 0.180573i
\(679\) 785046.i 1.70277i
\(680\) 0 0
\(681\) 5971.77 0.0128768
\(682\) 660856. + 671586.i 1.42082 + 1.44389i
\(683\) 631289.i 1.35328i 0.736316 + 0.676638i \(0.236564\pi\)
−0.736316 + 0.676638i \(0.763436\pi\)
\(684\) −84617.4 1362.85i −0.180862 0.00291297i
\(685\) 0 0
\(686\) 136790. 134604.i 0.290673 0.286029i
\(687\) 256650.i 0.543785i
\(688\) −10266.0 + 318617.i −0.0216882 + 0.673119i
\(689\) 341638. 0.719660
\(690\) 0 0
\(691\) 692970.i 1.45130i 0.688062 + 0.725652i \(0.258462\pi\)
−0.688062 + 0.725652i \(0.741538\pi\)
\(692\) 8212.23 509885.i 0.0171494 1.06478i
\(693\) 379188. 0.789564
\(694\) 224946. 221352.i 0.467045 0.459584i
\(695\) 0 0
\(696\) −242950. 254981.i −0.501532 0.526368i
\(697\) 53358.8 0.109835
\(698\) 524880. + 533402.i 1.07733 + 1.09482i
\(699\) 218675.i 0.447553i
\(700\) 0 0
\(701\) −106868. −0.217477 −0.108739 0.994070i \(-0.534681\pi\)
−0.108739 + 0.994070i \(0.534681\pi\)
\(702\) 94742.2 93228.5i 0.192251 0.189180i
\(703\) 448066.i 0.906633i
\(704\) −903083. 43665.5i −1.82214 0.0881035i
\(705\) 0 0
\(706\) 74561.4 + 75772.0i 0.149591 + 0.152020i
\(707\) 949151.i 1.89888i
\(708\) 3309.69 205493.i 0.00660268 0.409951i
\(709\) 71602.5 0.142441 0.0712207 0.997461i \(-0.477311\pi\)
0.0712207 + 0.997461i \(0.477311\pi\)
\(710\) 0 0
\(711\) 29618.8i 0.0585906i
\(712\) −508075. + 484102.i −1.00223 + 0.954942i
\(713\) 791620. 1.55718
\(714\) −43352.9 44056.8i −0.0850397 0.0864204i
\(715\) 0 0
\(716\) 845382. + 13615.8i 1.64902 + 0.0265592i
\(717\) −179477. −0.349117
\(718\) 37667.8 37066.0i 0.0730671 0.0718997i
\(719\) 84839.0i 0.164111i −0.996628 0.0820555i \(-0.973852\pi\)
0.996628 0.0820555i \(-0.0261485\pi\)
\(720\) 0 0
\(721\) 641521. 1.23407
\(722\) 257956. + 262144.i 0.494848 + 0.502882i
\(723\) 356804.i 0.682579i
\(724\) 16244.4 1.00859e6i 0.0309903 1.92414i
\(725\) 0 0
\(726\) 504945. 496877.i 0.958011 0.942706i
\(727\) 80916.8i 0.153098i 0.997066 + 0.0765491i \(0.0243902\pi\)
−0.997066 + 0.0765491i \(0.975610\pi\)
\(728\) 665296. + 698241.i 1.25531 + 1.31748i
\(729\) −19683.0 −0.0370370
\(730\) 0 0
\(731\) 58204.4i 0.108923i
\(732\) −400616. 6452.34i −0.747663 0.0120419i
\(733\) −62103.9 −0.115588 −0.0577938 0.998329i \(-0.518407\pi\)
−0.0577938 + 0.998329i \(0.518407\pi\)
\(734\) −133778. + 131640.i −0.248308 + 0.244341i
\(735\) 0 0
\(736\) −558327. + 515086.i −1.03070 + 0.950877i
\(737\) −1.27854e6 −2.35385
\(738\) 86474.4 + 87878.4i 0.158772 + 0.161350i
\(739\) 268031.i 0.490790i 0.969423 + 0.245395i \(0.0789176\pi\)
−0.969423 + 0.245395i \(0.921082\pi\)
\(740\) 0 0
\(741\) 241100. 0.439098
\(742\) 261644. 257464.i 0.475230 0.467637i
\(743\) 348633.i 0.631525i −0.948838 0.315763i \(-0.897740\pi\)
0.948838 0.315763i \(-0.102260\pi\)
\(744\) 256922. 244799.i 0.464147 0.442247i
\(745\) 0 0
\(746\) 666291. + 677109.i 1.19725 + 1.21669i
\(747\) 83627.5i 0.149868i
\(748\) −165059. 2658.45i −0.295010 0.00475145i
\(749\) −1.17548e6 −2.09533
\(750\) 0 0
\(751\) 757069.i 1.34232i −0.741313 0.671159i \(-0.765797\pi\)
0.741313 0.671159i \(-0.234203\pi\)
\(752\) 3353.05 104066.i 0.00592932 0.184023i
\(753\) −322179. −0.568207
\(754\) 703756. + 715182.i 1.23788 + 1.25798i
\(755\) 0 0
\(756\) 2299.92 142799.i 0.00402411 0.249851i
\(757\) −128542. −0.224312 −0.112156 0.993691i \(-0.535776\pi\)
−0.112156 + 0.993691i \(0.535776\pi\)
\(758\) −308334. + 303408.i −0.536639 + 0.528066i
\(759\) 850866.i 1.47699i
\(760\) 0 0
\(761\) 460176. 0.794611 0.397306 0.917686i \(-0.369945\pi\)
0.397306 + 0.917686i \(0.369945\pi\)
\(762\) 318305. + 323473.i 0.548193 + 0.557094i
\(763\) 43065.4i 0.0739740i
\(764\) 331640. + 5341.40i 0.568172 + 0.00915100i
\(765\) 0 0
\(766\) 408019. 401501.i 0.695382 0.684272i
\(767\) 585512.i 0.995280i
\(768\) −21921.6 + 339829.i −0.0371664 + 0.576153i
\(769\) 1.10194e6 1.86340 0.931701 0.363226i \(-0.118325\pi\)
0.931701 + 0.363226i \(0.118325\pi\)
\(770\) 0 0
\(771\) 342829.i 0.576725i
\(772\) −4526.53 + 281046.i −0.00759506 + 0.471566i
\(773\) −809541. −1.35481 −0.677407 0.735608i \(-0.736897\pi\)
−0.677407 + 0.735608i \(0.736897\pi\)
\(774\) −95858.8 + 94327.3i −0.160011 + 0.157455i
\(775\) 0 0
\(776\) 571724. 544748.i 0.949430 0.904633i
\(777\) −756149. −1.25246
\(778\) −370505. 376520.i −0.612117 0.622055i
\(779\) 223633.i 0.368520i
\(780\) 0 0
\(781\) −68289.2 −0.111957
\(782\) −98859.8 + 97280.4i −0.161661 + 0.159079i
\(783\) 148582.i 0.242349i