Properties

Label 177.5.c.a.58.7
Level $177$
Weight $5$
Character 177.58
Analytic conductor $18.296$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.7
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.34

$q$-expansion

\(f(q)\) \(=\) \(q-5.77154i q^{2} -5.19615 q^{3} -17.3107 q^{4} +34.3452 q^{5} +29.9898i q^{6} -39.2727 q^{7} +7.56484i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-5.77154i q^{2} -5.19615 q^{3} -17.3107 q^{4} +34.3452 q^{5} +29.9898i q^{6} -39.2727 q^{7} +7.56484i q^{8} +27.0000 q^{9} -198.225i q^{10} +56.8541i q^{11} +89.9491 q^{12} -232.684i q^{13} +226.664i q^{14} -178.463 q^{15} -233.311 q^{16} -391.037 q^{17} -155.832i q^{18} -352.390 q^{19} -594.541 q^{20} +204.067 q^{21} +328.136 q^{22} -173.061i q^{23} -39.3081i q^{24} +554.595 q^{25} -1342.94 q^{26} -140.296 q^{27} +679.838 q^{28} +90.7462 q^{29} +1030.01i q^{30} +128.035i q^{31} +1467.60i q^{32} -295.422i q^{33} +2256.89i q^{34} -1348.83 q^{35} -467.389 q^{36} -413.192i q^{37} +2033.83i q^{38} +1209.06i q^{39} +259.816i q^{40} -761.796 q^{41} -1177.78i q^{42} +874.013i q^{43} -984.184i q^{44} +927.321 q^{45} -998.831 q^{46} +895.574i q^{47} +1212.32 q^{48} -858.658 q^{49} -3200.87i q^{50} +2031.89 q^{51} +4027.92i q^{52} +3689.46 q^{53} +809.725i q^{54} +1952.67i q^{55} -297.092i q^{56} +1831.07 q^{57} -523.746i q^{58} +(-1547.97 - 3117.88i) q^{59} +3089.32 q^{60} +1498.06i q^{61} +738.962 q^{62} -1060.36 q^{63} +4737.35 q^{64} -7991.57i q^{65} -1705.04 q^{66} -3683.48i q^{67} +6769.13 q^{68} +899.253i q^{69} +7784.82i q^{70} -9230.55 q^{71} +204.251i q^{72} +4308.55i q^{73} -2384.76 q^{74} -2881.76 q^{75} +6100.12 q^{76} -2232.81i q^{77} +6978.14 q^{78} -4707.88 q^{79} -8013.11 q^{80} +729.000 q^{81} +4396.74i q^{82} -398.453i q^{83} -3532.54 q^{84} -13430.3 q^{85} +5044.40 q^{86} -471.531 q^{87} -430.092 q^{88} -12419.6i q^{89} -5352.08i q^{90} +9138.11i q^{91} +2995.82i q^{92} -665.292i q^{93} +5168.84 q^{94} -12102.9 q^{95} -7625.87i q^{96} +397.504i q^{97} +4955.78i q^{98} +1535.06i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.77154i 1.44289i −0.692474 0.721443i \(-0.743479\pi\)
0.692474 0.721443i \(-0.256521\pi\)
\(3\) −5.19615 −0.577350
\(4\) −17.3107 −1.08192
\(5\) 34.3452 1.37381 0.686905 0.726748i \(-0.258969\pi\)
0.686905 + 0.726748i \(0.258969\pi\)
\(6\) 29.9898i 0.833051i
\(7\) −39.2727 −0.801483 −0.400741 0.916191i \(-0.631247\pi\)
−0.400741 + 0.916191i \(0.631247\pi\)
\(8\) 7.56484i 0.118201i
\(9\) 27.0000 0.333333
\(10\) 198.225i 1.98225i
\(11\) 56.8541i 0.469868i 0.972011 + 0.234934i \(0.0754874\pi\)
−0.972011 + 0.234934i \(0.924513\pi\)
\(12\) 89.9491 0.624647
\(13\) 232.684i 1.37683i −0.725319 0.688413i \(-0.758308\pi\)
0.725319 0.688413i \(-0.241692\pi\)
\(14\) 226.664i 1.15645i
\(15\) −178.463 −0.793169
\(16\) −233.311 −0.911370
\(17\) −391.037 −1.35307 −0.676535 0.736411i \(-0.736519\pi\)
−0.676535 + 0.736411i \(0.736519\pi\)
\(18\) 155.832i 0.480962i
\(19\) −352.390 −0.976149 −0.488075 0.872802i \(-0.662301\pi\)
−0.488075 + 0.872802i \(0.662301\pi\)
\(20\) −594.541 −1.48635
\(21\) 204.067 0.462736
\(22\) 328.136 0.677966
\(23\) 173.061i 0.327148i −0.986531 0.163574i \(-0.947698\pi\)
0.986531 0.163574i \(-0.0523023\pi\)
\(24\) 39.3081i 0.0682432i
\(25\) 554.595 0.887352
\(26\) −1342.94 −1.98660
\(27\) −140.296 −0.192450
\(28\) 679.838 0.867140
\(29\) 90.7462 0.107903 0.0539514 0.998544i \(-0.482818\pi\)
0.0539514 + 0.998544i \(0.482818\pi\)
\(30\) 1030.01i 1.14445i
\(31\) 128.035i 0.133232i 0.997779 + 0.0666158i \(0.0212202\pi\)
−0.997779 + 0.0666158i \(0.978780\pi\)
\(32\) 1467.60i 1.43320i
\(33\) 295.422i 0.271279i
\(34\) 2256.89i 1.95233i
\(35\) −1348.83 −1.10108
\(36\) −467.389 −0.360640
\(37\) 413.192i 0.301821i −0.988547 0.150910i \(-0.951780\pi\)
0.988547 0.150910i \(-0.0482204\pi\)
\(38\) 2033.83i 1.40847i
\(39\) 1209.06i 0.794911i
\(40\) 259.816i 0.162385i
\(41\) −761.796 −0.453180 −0.226590 0.973990i \(-0.572758\pi\)
−0.226590 + 0.973990i \(0.572758\pi\)
\(42\) 1177.78i 0.667676i
\(43\) 874.013i 0.472695i 0.971669 + 0.236347i \(0.0759504\pi\)
−0.971669 + 0.236347i \(0.924050\pi\)
\(44\) 984.184i 0.508360i
\(45\) 927.321 0.457936
\(46\) −998.831 −0.472038
\(47\) 895.574i 0.405420i 0.979239 + 0.202710i \(0.0649749\pi\)
−0.979239 + 0.202710i \(0.935025\pi\)
\(48\) 1212.32 0.526179
\(49\) −858.658 −0.357625
\(50\) 3200.87i 1.28035i
\(51\) 2031.89 0.781195
\(52\) 4027.92i 1.48962i
\(53\) 3689.46 1.31344 0.656721 0.754134i \(-0.271943\pi\)
0.656721 + 0.754134i \(0.271943\pi\)
\(54\) 809.725i 0.277684i
\(55\) 1952.67i 0.645509i
\(56\) 297.092i 0.0947358i
\(57\) 1831.07 0.563580
\(58\) 523.746i 0.155691i
\(59\) −1547.97 3117.88i −0.444691 0.895684i
\(60\) 3089.32 0.858145
\(61\) 1498.06i 0.402596i 0.979530 + 0.201298i \(0.0645159\pi\)
−0.979530 + 0.201298i \(0.935484\pi\)
\(62\) 738.962 0.192238
\(63\) −1060.36 −0.267161
\(64\) 4737.35 1.15658
\(65\) 7991.57i 1.89150i
\(66\) −1705.04 −0.391424
\(67\) 3683.48i 0.820558i −0.911960 0.410279i \(-0.865431\pi\)
0.911960 0.410279i \(-0.134569\pi\)
\(68\) 6769.13 1.46391
\(69\) 899.253i 0.188879i
\(70\) 7784.82i 1.58874i
\(71\) −9230.55 −1.83109 −0.915547 0.402211i \(-0.868242\pi\)
−0.915547 + 0.402211i \(0.868242\pi\)
\(72\) 204.251i 0.0394002i
\(73\) 4308.55i 0.808510i 0.914646 + 0.404255i \(0.132469\pi\)
−0.914646 + 0.404255i \(0.867531\pi\)
\(74\) −2384.76 −0.435493
\(75\) −2881.76 −0.512313
\(76\) 6100.12 1.05612
\(77\) 2232.81i 0.376591i
\(78\) 6978.14 1.14697
\(79\) −4707.88 −0.754346 −0.377173 0.926143i \(-0.623104\pi\)
−0.377173 + 0.926143i \(0.623104\pi\)
\(80\) −8013.11 −1.25205
\(81\) 729.000 0.111111
\(82\) 4396.74i 0.653887i
\(83\) 398.453i 0.0578390i −0.999582 0.0289195i \(-0.990793\pi\)
0.999582 0.0289195i \(-0.00920665\pi\)
\(84\) −3532.54 −0.500644
\(85\) −13430.3 −1.85886
\(86\) 5044.40 0.682045
\(87\) −471.531 −0.0622977
\(88\) −430.092 −0.0555387
\(89\) 12419.6i 1.56794i −0.620802 0.783968i \(-0.713193\pi\)
0.620802 0.783968i \(-0.286807\pi\)
\(90\) 5352.08i 0.660750i
\(91\) 9138.11i 1.10350i
\(92\) 2995.82i 0.353948i
\(93\) 665.292i 0.0769212i
\(94\) 5168.84 0.584975
\(95\) −12102.9 −1.34104
\(96\) 7625.87i 0.827460i
\(97\) 397.504i 0.0422472i 0.999777 + 0.0211236i \(0.00672435\pi\)
−0.999777 + 0.0211236i \(0.993276\pi\)
\(98\) 4955.78i 0.516012i
\(99\) 1535.06i 0.156623i
\(100\) −9600.44 −0.960044
\(101\) 7090.10i 0.695040i −0.937673 0.347520i \(-0.887024\pi\)
0.937673 0.347520i \(-0.112976\pi\)
\(102\) 11727.1i 1.12718i
\(103\) 6266.89i 0.590714i 0.955387 + 0.295357i \(0.0954387\pi\)
−0.955387 + 0.295357i \(0.904561\pi\)
\(104\) 1760.22 0.162742
\(105\) 7008.72 0.635712
\(106\) 21293.9i 1.89515i
\(107\) 1508.55 0.131763 0.0658814 0.997827i \(-0.479014\pi\)
0.0658814 + 0.997827i \(0.479014\pi\)
\(108\) 2428.63 0.208216
\(109\) 16261.8i 1.36872i −0.729144 0.684361i \(-0.760081\pi\)
0.729144 0.684361i \(-0.239919\pi\)
\(110\) 11269.9 0.931396
\(111\) 2147.01i 0.174256i
\(112\) 9162.73 0.730447
\(113\) 22671.8i 1.77553i −0.460293 0.887767i \(-0.652256\pi\)
0.460293 0.887767i \(-0.347744\pi\)
\(114\) 10568.1i 0.813182i
\(115\) 5943.83i 0.449439i
\(116\) −1570.88 −0.116742
\(117\) 6282.46i 0.458942i
\(118\) −17995.0 + 8934.17i −1.29237 + 0.641638i
\(119\) 15357.1 1.08446
\(120\) 1350.05i 0.0937531i
\(121\) 11408.6 0.779224
\(122\) 8646.11 0.580900
\(123\) 3958.41 0.261644
\(124\) 2216.39i 0.144146i
\(125\) −2418.07 −0.154757
\(126\) 6119.93i 0.385483i
\(127\) 7430.12 0.460668 0.230334 0.973112i \(-0.426018\pi\)
0.230334 + 0.973112i \(0.426018\pi\)
\(128\) 3860.20i 0.235608i
\(129\) 4541.50i 0.272911i
\(130\) −46123.7 −2.72921
\(131\) 30063.5i 1.75185i 0.482446 + 0.875926i \(0.339748\pi\)
−0.482446 + 0.875926i \(0.660252\pi\)
\(132\) 5113.97i 0.293502i
\(133\) 13839.3 0.782367
\(134\) −21259.4 −1.18397
\(135\) −4818.50 −0.264390
\(136\) 2958.14i 0.159934i
\(137\) 20907.4 1.11393 0.556967 0.830535i \(-0.311965\pi\)
0.556967 + 0.830535i \(0.311965\pi\)
\(138\) 5190.08 0.272531
\(139\) 22666.8 1.17317 0.586583 0.809889i \(-0.300473\pi\)
0.586583 + 0.809889i \(0.300473\pi\)
\(140\) 23349.2 1.19129
\(141\) 4653.54i 0.234070i
\(142\) 53274.5i 2.64206i
\(143\) 13229.0 0.646927
\(144\) −6299.39 −0.303790
\(145\) 3116.70 0.148238
\(146\) 24867.0 1.16659
\(147\) 4461.72 0.206475
\(148\) 7152.65i 0.326546i
\(149\) 14748.1i 0.664299i 0.943227 + 0.332150i \(0.107774\pi\)
−0.943227 + 0.332150i \(0.892226\pi\)
\(150\) 16632.2i 0.739209i
\(151\) 1352.46i 0.0593158i −0.999560 0.0296579i \(-0.990558\pi\)
0.999560 0.0296579i \(-0.00944179\pi\)
\(152\) 2665.77i 0.115382i
\(153\) −10558.0 −0.451023
\(154\) −12886.8 −0.543378
\(155\) 4397.41i 0.183035i
\(156\) 20929.7i 0.860030i
\(157\) 43867.4i 1.77968i −0.456270 0.889841i \(-0.650815\pi\)
0.456270 0.889841i \(-0.349185\pi\)
\(158\) 27171.7i 1.08844i
\(159\) −19171.0 −0.758316
\(160\) 50405.1i 1.96895i
\(161\) 6796.58i 0.262204i
\(162\) 4207.46i 0.160321i
\(163\) 24914.8 0.937741 0.468870 0.883267i \(-0.344661\pi\)
0.468870 + 0.883267i \(0.344661\pi\)
\(164\) 13187.2 0.490304
\(165\) 10146.3i 0.372685i
\(166\) −2299.69 −0.0834551
\(167\) −15384.8 −0.551644 −0.275822 0.961209i \(-0.588950\pi\)
−0.275822 + 0.961209i \(0.588950\pi\)
\(168\) 1543.73i 0.0546958i
\(169\) −25580.7 −0.895651
\(170\) 77513.4i 2.68212i
\(171\) −9514.53 −0.325383
\(172\) 15129.8i 0.511418i
\(173\) 54918.5i 1.83496i −0.397784 0.917479i \(-0.630221\pi\)
0.397784 0.917479i \(-0.369779\pi\)
\(174\) 2721.46i 0.0898884i
\(175\) −21780.4 −0.711198
\(176\) 13264.7i 0.428224i
\(177\) 8043.48 + 16201.0i 0.256742 + 0.517123i
\(178\) −71680.3 −2.26235
\(179\) 50544.7i 1.57750i −0.614713 0.788751i \(-0.710728\pi\)
0.614713 0.788751i \(-0.289272\pi\)
\(180\) −16052.6 −0.495450
\(181\) 34588.1 1.05577 0.527885 0.849316i \(-0.322985\pi\)
0.527885 + 0.849316i \(0.322985\pi\)
\(182\) 52741.0 1.59223
\(183\) 7784.14i 0.232439i
\(184\) 1309.18 0.0386691
\(185\) 14191.2i 0.414644i
\(186\) −3839.76 −0.110989
\(187\) 22232.0i 0.635765i
\(188\) 15503.0i 0.438632i
\(189\) 5509.80 0.154245
\(190\) 69852.5i 1.93497i
\(191\) 29175.3i 0.799739i 0.916572 + 0.399869i \(0.130945\pi\)
−0.916572 + 0.399869i \(0.869055\pi\)
\(192\) −24616.0 −0.667751
\(193\) 31941.0 0.857500 0.428750 0.903423i \(-0.358954\pi\)
0.428750 + 0.903423i \(0.358954\pi\)
\(194\) 2294.21 0.0609579
\(195\) 41525.4i 1.09206i
\(196\) 14864.0 0.386922
\(197\) −4250.44 −0.109522 −0.0547610 0.998499i \(-0.517440\pi\)
−0.0547610 + 0.998499i \(0.517440\pi\)
\(198\) 8859.66 0.225989
\(199\) 28562.3 0.721251 0.360625 0.932711i \(-0.382563\pi\)
0.360625 + 0.932711i \(0.382563\pi\)
\(200\) 4195.43i 0.104886i
\(201\) 19139.9i 0.473749i
\(202\) −40920.8 −1.00286
\(203\) −3563.84 −0.0864822
\(204\) −35173.4 −0.845190
\(205\) −26164.1 −0.622583
\(206\) 36169.6 0.852334
\(207\) 4672.66i 0.109049i
\(208\) 54287.6i 1.25480i
\(209\) 20034.8i 0.458662i
\(210\) 40451.1i 0.917259i
\(211\) 26481.8i 0.594816i 0.954750 + 0.297408i \(0.0961222\pi\)
−0.954750 + 0.297408i \(0.903878\pi\)
\(212\) −63867.2 −1.42104
\(213\) 47963.3 1.05718
\(214\) 8706.68i 0.190119i
\(215\) 30018.2i 0.649393i
\(216\) 1061.32i 0.0227477i
\(217\) 5028.29i 0.106783i
\(218\) −93855.5 −1.97491
\(219\) 22387.9i 0.466793i
\(220\) 33802.0i 0.698389i
\(221\) 90988.0i 1.86294i
\(222\) 12391.6 0.251432
\(223\) −20499.0 −0.412215 −0.206108 0.978529i \(-0.566080\pi\)
−0.206108 + 0.978529i \(0.566080\pi\)
\(224\) 57636.6i 1.14869i
\(225\) 14974.1 0.295784
\(226\) −130851. −2.56189
\(227\) 78399.4i 1.52146i −0.649067 0.760731i \(-0.724841\pi\)
0.649067 0.760731i \(-0.275159\pi\)
\(228\) −31697.2 −0.609748
\(229\) 31210.2i 0.595149i −0.954699 0.297574i \(-0.903822\pi\)
0.954699 0.297574i \(-0.0961776\pi\)
\(230\) −34305.1 −0.648490
\(231\) 11602.0i 0.217425i
\(232\) 686.481i 0.0127542i
\(233\) 91009.4i 1.67639i 0.545372 + 0.838194i \(0.316388\pi\)
−0.545372 + 0.838194i \(0.683612\pi\)
\(234\) −36259.5 −0.662201
\(235\) 30758.7i 0.556970i
\(236\) 26796.5 + 53972.7i 0.481120 + 0.969058i
\(237\) 24462.8 0.435522
\(238\) 88634.0i 1.56476i
\(239\) −96173.1 −1.68367 −0.841837 0.539732i \(-0.818526\pi\)
−0.841837 + 0.539732i \(0.818526\pi\)
\(240\) 41637.3 0.722870
\(241\) −69208.9 −1.19159 −0.595796 0.803136i \(-0.703163\pi\)
−0.595796 + 0.803136i \(0.703163\pi\)
\(242\) 65845.3i 1.12433i
\(243\) −3788.00 −0.0641500
\(244\) 25932.5i 0.435576i
\(245\) −29490.8 −0.491309
\(246\) 22846.1i 0.377522i
\(247\) 81995.4i 1.34399i
\(248\) −968.568 −0.0157481
\(249\) 2070.42i 0.0333934i
\(250\) 13956.0i 0.223296i
\(251\) 94134.4 1.49417 0.747087 0.664726i \(-0.231452\pi\)
0.747087 + 0.664726i \(0.231452\pi\)
\(252\) 18355.6 0.289047
\(253\) 9839.24 0.153717
\(254\) 42883.3i 0.664692i
\(255\) 69785.7 1.07321
\(256\) 53518.2 0.816623
\(257\) 11680.1 0.176841 0.0884203 0.996083i \(-0.471818\pi\)
0.0884203 + 0.996083i \(0.471818\pi\)
\(258\) −26211.5 −0.393779
\(259\) 16227.2i 0.241904i
\(260\) 138340.i 2.04645i
\(261\) 2450.15 0.0359676
\(262\) 173513. 2.52772
\(263\) −67551.5 −0.976616 −0.488308 0.872671i \(-0.662386\pi\)
−0.488308 + 0.872671i \(0.662386\pi\)
\(264\) 2234.82 0.0320653
\(265\) 126715. 1.80442
\(266\) 79874.1i 1.12887i
\(267\) 64534.2i 0.905248i
\(268\) 63763.7i 0.887778i
\(269\) 8085.17i 0.111734i −0.998438 0.0558669i \(-0.982208\pi\)
0.998438 0.0558669i \(-0.0177923\pi\)
\(270\) 27810.2i 0.381484i
\(271\) −3043.53 −0.0414419 −0.0207209 0.999785i \(-0.506596\pi\)
−0.0207209 + 0.999785i \(0.506596\pi\)
\(272\) 91233.1 1.23315
\(273\) 47483.0i 0.637108i
\(274\) 120668.i 1.60728i
\(275\) 31531.0i 0.416939i
\(276\) 15566.7i 0.204352i
\(277\) 110726. 1.44308 0.721540 0.692373i \(-0.243435\pi\)
0.721540 + 0.692373i \(0.243435\pi\)
\(278\) 130822.i 1.69275i
\(279\) 3456.96i 0.0444105i
\(280\) 10203.7i 0.130149i
\(281\) −132826. −1.68217 −0.841085 0.540903i \(-0.818083\pi\)
−0.841085 + 0.540903i \(0.818083\pi\)
\(282\) −26858.1 −0.337736
\(283\) 136650.i 1.70622i −0.521728 0.853112i \(-0.674713\pi\)
0.521728 0.853112i \(-0.325287\pi\)
\(284\) 159787. 1.98110
\(285\) 62888.6 0.774252
\(286\) 76351.8i 0.933442i
\(287\) 29917.7 0.363216
\(288\) 39625.2i 0.477734i
\(289\) 69389.1 0.830798
\(290\) 17988.2i 0.213890i
\(291\) 2065.49i 0.0243914i
\(292\) 74584.1i 0.874743i
\(293\) −138078. −1.60838 −0.804189 0.594374i \(-0.797400\pi\)
−0.804189 + 0.594374i \(0.797400\pi\)
\(294\) 25751.0i 0.297920i
\(295\) −53165.4 107084.i −0.610921 1.23050i
\(296\) 3125.74 0.0356754
\(297\) 7976.40i 0.0904262i
\(298\) 85119.4 0.958508
\(299\) −40268.6 −0.450426
\(300\) 49885.3 0.554282
\(301\) 34324.8i 0.378857i
\(302\) −7805.78 −0.0855859
\(303\) 36841.3i 0.401281i
\(304\) 82216.3 0.889633
\(305\) 51451.2i 0.553090i
\(306\) 60936.0i 0.650775i
\(307\) 88705.4 0.941181 0.470591 0.882352i \(-0.344041\pi\)
0.470591 + 0.882352i \(0.344041\pi\)
\(308\) 38651.5i 0.407442i
\(309\) 32563.7i 0.341049i
\(310\) 25379.8 0.264098
\(311\) −120340. −1.24420 −0.622101 0.782937i \(-0.713721\pi\)
−0.622101 + 0.782937i \(0.713721\pi\)
\(312\) −9146.35 −0.0939590
\(313\) 153842.i 1.57031i 0.619299 + 0.785155i \(0.287417\pi\)
−0.619299 + 0.785155i \(0.712583\pi\)
\(314\) −253183. −2.56788
\(315\) −36418.4 −0.367028
\(316\) 81496.7 0.816142
\(317\) 13221.7 0.131574 0.0657868 0.997834i \(-0.479044\pi\)
0.0657868 + 0.997834i \(0.479044\pi\)
\(318\) 110646.i 1.09416i
\(319\) 5159.29i 0.0507001i
\(320\) 162705. 1.58892
\(321\) −7838.67 −0.0760733
\(322\) 39226.8 0.378330
\(323\) 137798. 1.32080
\(324\) −12619.5 −0.120213
\(325\) 129045.i 1.22173i
\(326\) 143797.i 1.35305i
\(327\) 84498.7i 0.790232i
\(328\) 5762.87i 0.0535662i
\(329\) 35171.6i 0.324938i
\(330\) −58560.1 −0.537742
\(331\) 56327.8 0.514123 0.257061 0.966395i \(-0.417246\pi\)
0.257061 + 0.966395i \(0.417246\pi\)
\(332\) 6897.50i 0.0625771i
\(333\) 11156.2i 0.100607i
\(334\) 88794.1i 0.795960i
\(335\) 126510.i 1.12729i
\(336\) −47610.9 −0.421724
\(337\) 115339.i 1.01558i −0.861481 0.507791i \(-0.830462\pi\)
0.861481 0.507791i \(-0.169538\pi\)
\(338\) 147640.i 1.29232i
\(339\) 117806.i 1.02511i
\(340\) 232487. 2.01114
\(341\) −7279.34 −0.0626013
\(342\) 54913.5i 0.469491i
\(343\) 128015. 1.08811
\(344\) −6611.77 −0.0558729
\(345\) 30885.1i 0.259484i
\(346\) −316964. −2.64763
\(347\) 9584.04i 0.0795957i 0.999208 + 0.0397979i \(0.0126714\pi\)
−0.999208 + 0.0397979i \(0.987329\pi\)
\(348\) 8162.54 0.0674011
\(349\) 148678.i 1.22066i −0.792147 0.610330i \(-0.791037\pi\)
0.792147 0.610330i \(-0.208963\pi\)
\(350\) 125707.i 1.02618i
\(351\) 32644.6i 0.264970i
\(352\) −83439.0 −0.673416
\(353\) 12045.3i 0.0966652i −0.998831 0.0483326i \(-0.984609\pi\)
0.998831 0.0483326i \(-0.0153907\pi\)
\(354\) 93504.5 46423.3i 0.746150 0.370450i
\(355\) −317025. −2.51557
\(356\) 214992.i 1.69638i
\(357\) −79797.7 −0.626115
\(358\) −291721. −2.27615
\(359\) −11159.4 −0.0865872 −0.0432936 0.999062i \(-0.513785\pi\)
−0.0432936 + 0.999062i \(0.513785\pi\)
\(360\) 7015.04i 0.0541284i
\(361\) −6142.36 −0.0471326
\(362\) 199627.i 1.52336i
\(363\) −59280.9 −0.449885
\(364\) 158187.i 1.19390i
\(365\) 147978.i 1.11074i
\(366\) −44926.5 −0.335383
\(367\) 24075.5i 0.178749i 0.995998 + 0.0893744i \(0.0284868\pi\)
−0.995998 + 0.0893744i \(0.971513\pi\)
\(368\) 40377.1i 0.298153i
\(369\) −20568.5 −0.151060
\(370\) −81905.0 −0.598284
\(371\) −144895. −1.05270
\(372\) 11516.7i 0.0832226i
\(373\) −87079.2 −0.625888 −0.312944 0.949772i \(-0.601315\pi\)
−0.312944 + 0.949772i \(0.601315\pi\)
\(374\) −128313. −0.917336
\(375\) 12564.7 0.0893487
\(376\) −6774.87 −0.0479210
\(377\) 21115.2i 0.148563i
\(378\) 31800.1i 0.222559i
\(379\) 201608. 1.40355 0.701776 0.712398i \(-0.252391\pi\)
0.701776 + 0.712398i \(0.252391\pi\)
\(380\) 209510. 1.45090
\(381\) −38608.0 −0.265967
\(382\) 168386. 1.15393
\(383\) 181721. 1.23882 0.619408 0.785069i \(-0.287373\pi\)
0.619408 + 0.785069i \(0.287373\pi\)
\(384\) 20058.2i 0.136028i
\(385\) 76686.4i 0.517365i
\(386\) 184349.i 1.23727i
\(387\) 23598.4i 0.157565i
\(388\) 6881.08i 0.0457081i
\(389\) −133518. −0.882350 −0.441175 0.897421i \(-0.645438\pi\)
−0.441175 + 0.897421i \(0.645438\pi\)
\(390\) 239666. 1.57571
\(391\) 67673.4i 0.442654i
\(392\) 6495.61i 0.0422715i
\(393\) 156215.i 1.01143i
\(394\) 24531.6i 0.158028i
\(395\) −161693. −1.03633
\(396\) 26573.0i 0.169453i
\(397\) 27629.4i 0.175304i −0.996151 0.0876518i \(-0.972064\pi\)
0.996151 0.0876518i \(-0.0279363\pi\)
\(398\) 164848.i 1.04068i
\(399\) −71911.1 −0.451700
\(400\) −129393. −0.808706
\(401\) 208735.i 1.29809i −0.760748 0.649047i \(-0.775168\pi\)
0.760748 0.649047i \(-0.224832\pi\)
\(402\) 110467. 0.683566
\(403\) 29791.8 0.183437
\(404\) 122735.i 0.751977i
\(405\) 25037.7 0.152645
\(406\) 20568.9i 0.124784i
\(407\) 23491.7 0.141816
\(408\) 15370.9i 0.0923378i
\(409\) 278718.i 1.66616i 0.553150 + 0.833082i \(0.313426\pi\)
−0.553150 + 0.833082i \(0.686574\pi\)
\(410\) 151007.i 0.898316i
\(411\) −108638. −0.643130
\(412\) 108484.i 0.639106i
\(413\) 60792.9 + 122447.i 0.356412 + 0.717875i
\(414\) −26968.4 −0.157346
\(415\) 13685.0i 0.0794598i
\(416\) 341486. 1.97327
\(417\) −117780. −0.677328
\(418\) −115632. −0.661796
\(419\) 15318.9i 0.0872570i −0.999048 0.0436285i \(-0.986108\pi\)
0.999048 0.0436285i \(-0.0138918\pi\)
\(420\) −121326. −0.687789
\(421\) 278756.i 1.57275i 0.617747 + 0.786377i \(0.288046\pi\)
−0.617747 + 0.786377i \(0.711954\pi\)
\(422\) 152841. 0.858252
\(423\) 24180.5i 0.135140i
\(424\) 27910.2i 0.155250i
\(425\) −216867. −1.20065
\(426\) 276822.i 1.52539i
\(427\) 58832.8i 0.322674i
\(428\) −26114.1 −0.142557
\(429\) −68739.9 −0.373503
\(430\) 173251. 0.937000
\(431\) 202239.i 1.08870i −0.838857 0.544352i \(-0.816776\pi\)
0.838857 0.544352i \(-0.183224\pi\)
\(432\) 32732.6 0.175393
\(433\) −88674.2 −0.472957 −0.236478 0.971637i \(-0.575993\pi\)
−0.236478 + 0.971637i \(0.575993\pi\)
\(434\) −29021.0 −0.154075
\(435\) −16194.8 −0.0855851
\(436\) 281503.i 1.48085i
\(437\) 60985.1i 0.319345i
\(438\) −129213. −0.673530
\(439\) −374655. −1.94403 −0.972013 0.234928i \(-0.924515\pi\)
−0.972013 + 0.234928i \(0.924515\pi\)
\(440\) −14771.6 −0.0762997
\(441\) −23183.8 −0.119208
\(442\) 525141. 2.68801
\(443\) 19857.5i 0.101185i 0.998719 + 0.0505925i \(0.0161110\pi\)
−0.998719 + 0.0505925i \(0.983889\pi\)
\(444\) 37166.3i 0.188531i
\(445\) 426555.i 2.15404i
\(446\) 118311.i 0.594779i
\(447\) 76633.4i 0.383533i
\(448\) −186048. −0.926978
\(449\) 71307.0 0.353703 0.176852 0.984238i \(-0.443409\pi\)
0.176852 + 0.984238i \(0.443409\pi\)
\(450\) 86423.5i 0.426783i
\(451\) 43311.2i 0.212935i
\(452\) 392465.i 1.92099i
\(453\) 7027.59i 0.0342460i
\(454\) −452486. −2.19530
\(455\) 313850.i 1.51600i
\(456\) 13851.8i 0.0666156i
\(457\) 134049.i 0.641846i 0.947105 + 0.320923i \(0.103993\pi\)
−0.947105 + 0.320923i \(0.896007\pi\)
\(458\) −180131. −0.858732
\(459\) 54861.0 0.260398
\(460\) 102892.i 0.486257i
\(461\) 281430. 1.32425 0.662123 0.749395i \(-0.269656\pi\)
0.662123 + 0.749395i \(0.269656\pi\)
\(462\) 66961.6 0.313720
\(463\) 323834.i 1.51064i 0.655356 + 0.755320i \(0.272518\pi\)
−0.655356 + 0.755320i \(0.727482\pi\)
\(464\) −21172.0 −0.0983393
\(465\) 22849.6i 0.105675i
\(466\) 525265. 2.41884
\(467\) 411702.i 1.88777i 0.330272 + 0.943886i \(0.392859\pi\)
−0.330272 + 0.943886i \(0.607141\pi\)
\(468\) 108754.i 0.496538i
\(469\) 144660.i 0.657663i
\(470\) 177525. 0.803645
\(471\) 227942.i 1.02750i
\(472\) 23586.2 11710.1i 0.105870 0.0525628i
\(473\) −49691.2 −0.222104
\(474\) 141188.i 0.628409i
\(475\) −195434. −0.866188
\(476\) −265842. −1.17330
\(477\) 99615.4 0.437814
\(478\) 555067.i 2.42935i
\(479\) 84811.3 0.369643 0.184822 0.982772i \(-0.440829\pi\)
0.184822 + 0.982772i \(0.440829\pi\)
\(480\) 261912.i 1.13677i
\(481\) −96143.1 −0.415554
\(482\) 399442.i 1.71933i
\(483\) 35316.1i 0.151383i
\(484\) −197491. −0.843058
\(485\) 13652.4i 0.0580396i
\(486\) 21862.6i 0.0925612i
\(487\) 249337. 1.05131 0.525653 0.850699i \(-0.323821\pi\)
0.525653 + 0.850699i \(0.323821\pi\)
\(488\) −11332.6 −0.0475871
\(489\) −129461. −0.541405
\(490\) 170207.i 0.708902i
\(491\) 50328.2 0.208760 0.104380 0.994537i \(-0.466714\pi\)
0.104380 + 0.994537i \(0.466714\pi\)
\(492\) −68522.8 −0.283077
\(493\) −35485.1 −0.146000
\(494\) 473240. 1.93922
\(495\) 52722.0i 0.215170i
\(496\) 29872.0i 0.121423i
\(497\) 362508. 1.46759
\(498\) 11949.5 0.0481828
\(499\) −23067.0 −0.0926380 −0.0463190 0.998927i \(-0.514749\pi\)
−0.0463190 + 0.998927i \(0.514749\pi\)
\(500\) 41858.5 0.167434
\(501\) 79941.8 0.318492
\(502\) 543301.i 2.15592i
\(503\) 410578.i 1.62278i 0.584505 + 0.811390i \(0.301289\pi\)
−0.584505 + 0.811390i \(0.698711\pi\)
\(504\) 8021.47i 0.0315786i
\(505\) 243511.i 0.954852i
\(506\) 56787.6i 0.221795i
\(507\) 132921. 0.517104
\(508\) −128621. −0.498406
\(509\) 19719.0i 0.0761115i −0.999276 0.0380557i \(-0.987884\pi\)
0.999276 0.0380557i \(-0.0121164\pi\)
\(510\) 402771.i 1.54852i
\(511\) 169208.i 0.648007i
\(512\) 370646.i 1.41390i
\(513\) 49438.9 0.187860
\(514\) 67412.5i 0.255161i
\(515\) 215238.i 0.811529i
\(516\) 78616.7i 0.295267i
\(517\) −50917.0 −0.190494
\(518\) 93655.8 0.349040
\(519\) 285365.i 1.05941i
\(520\) 60455.0 0.223576
\(521\) 420195. 1.54802 0.774008 0.633175i \(-0.218249\pi\)
0.774008 + 0.633175i \(0.218249\pi\)
\(522\) 14141.1i 0.0518971i
\(523\) −523604. −1.91425 −0.957126 0.289670i \(-0.906454\pi\)
−0.957126 + 0.289670i \(0.906454\pi\)
\(524\) 520421.i 1.89536i
\(525\) 113174. 0.410610
\(526\) 389877.i 1.40915i
\(527\) 50066.6i 0.180272i
\(528\) 68925.2i 0.247235i
\(529\) 249891. 0.892974
\(530\) 731343.i 2.60357i
\(531\) −41795.2 84182.7i −0.148230 0.298561i
\(532\) −239568. −0.846458
\(533\) 177257.i 0.623950i
\(534\) 372462. 1.30617
\(535\) 51811.6 0.181017
\(536\) 27865.0 0.0969905
\(537\) 262638.i 0.910771i
\(538\) −46663.9 −0.161219
\(539\) 48818.2i 0.168037i
\(540\) 83411.7 0.286048
\(541\) 62563.9i 0.213761i 0.994272 + 0.106881i \(0.0340863\pi\)
−0.994272 + 0.106881i \(0.965914\pi\)
\(542\) 17565.9i 0.0597959i
\(543\) −179725. −0.609549
\(544\) 573886.i 1.93922i
\(545\) 558515.i 1.88036i
\(546\) −274050. −0.919274
\(547\) 28370.0 0.0948166 0.0474083 0.998876i \(-0.484904\pi\)
0.0474083 + 0.998876i \(0.484904\pi\)
\(548\) −361923. −1.20519
\(549\) 40447.6i 0.134199i
\(550\) 181982. 0.601595
\(551\) −31978.0 −0.105329
\(552\) −6802.71 −0.0223256
\(553\) 184891. 0.604596
\(554\) 639060.i 2.08220i
\(555\) 73739.6i 0.239395i
\(556\) −392378. −1.26927
\(557\) −85305.1 −0.274957 −0.137478 0.990505i \(-0.543900\pi\)
−0.137478 + 0.990505i \(0.543900\pi\)
\(558\) 19952.0 0.0640793
\(559\) 203369. 0.650819
\(560\) 314696. 1.00350
\(561\) 115521.i 0.367059i
\(562\) 766610.i 2.42718i
\(563\) 625430.i 1.97316i −0.163282 0.986580i \(-0.552208\pi\)
0.163282 0.986580i \(-0.447792\pi\)
\(564\) 80556.0i 0.253244i
\(565\) 778668.i 2.43925i
\(566\) −788680. −2.46189
\(567\) −28629.8 −0.0890537
\(568\) 69827.6i 0.216437i
\(569\) 182688.i 0.564269i 0.959375 + 0.282134i \(0.0910424\pi\)
−0.959375 + 0.282134i \(0.908958\pi\)
\(570\) 362964.i 1.11716i
\(571\) 366777.i 1.12494i −0.826817 0.562471i \(-0.809851\pi\)
0.826817 0.562471i \(-0.190149\pi\)
\(572\) −229004. −0.699923
\(573\) 151599.i 0.461729i
\(574\) 172672.i 0.524079i
\(575\) 95979.0i 0.290296i
\(576\) 127908. 0.385526
\(577\) 485860. 1.45935 0.729675 0.683794i \(-0.239671\pi\)
0.729675 + 0.683794i \(0.239671\pi\)
\(578\) 400482.i 1.19875i
\(579\) −165970. −0.495078
\(580\) −53952.3 −0.160381
\(581\) 15648.3i 0.0463570i
\(582\) −11921.1 −0.0351940
\(583\) 209761.i 0.617145i
\(584\) −32593.5 −0.0955664
\(585\) 215773.i 0.630499i
\(586\) 796921.i 2.32071i
\(587\) 466181.i 1.35294i 0.736470 + 0.676470i \(0.236491\pi\)
−0.736470 + 0.676470i \(0.763509\pi\)
\(588\) −77235.5 −0.223389
\(589\) 45118.4i 0.130054i
\(590\) −618041. + 306846.i −1.77547 + 0.881489i
\(591\) 22085.9 0.0632326
\(592\) 96402.1i 0.275070i
\(593\) −263489. −0.749294 −0.374647 0.927167i \(-0.622236\pi\)
−0.374647 + 0.927167i \(0.622236\pi\)
\(594\) −46036.2 −0.130475
\(595\) 527442. 1.48984
\(596\) 255300.i 0.718719i
\(597\) −148414. −0.416414
\(598\) 232412.i 0.649914i
\(599\) −182847. −0.509606 −0.254803 0.966993i \(-0.582011\pi\)
−0.254803 + 0.966993i \(0.582011\pi\)
\(600\) 21800.1i 0.0605558i
\(601\) 529477.i 1.46588i −0.680294 0.732939i \(-0.738148\pi\)
0.680294 0.732939i \(-0.261852\pi\)
\(602\) −198107. −0.546647
\(603\) 99454.1i 0.273519i
\(604\) 23412.0i 0.0641749i
\(605\) 391832. 1.07051
\(606\) 212631. 0.579003
\(607\) −161986. −0.439642 −0.219821 0.975540i \(-0.570547\pi\)
−0.219821 + 0.975540i \(0.570547\pi\)
\(608\) 517167.i 1.39902i
\(609\) 18518.3 0.0499305
\(610\) 296953. 0.798046
\(611\) 208385. 0.558193
\(612\) 182767. 0.487971
\(613\) 97048.9i 0.258268i 0.991627 + 0.129134i \(0.0412197\pi\)
−0.991627 + 0.129134i \(0.958780\pi\)
\(614\) 511967.i 1.35802i
\(615\) 135952. 0.359448
\(616\) 16890.9 0.0445134
\(617\) −17414.4 −0.0457444 −0.0228722 0.999738i \(-0.507281\pi\)
−0.0228722 + 0.999738i \(0.507281\pi\)
\(618\) −187943. −0.492095
\(619\) −216510. −0.565061 −0.282531 0.959258i \(-0.591174\pi\)
−0.282531 + 0.959258i \(0.591174\pi\)
\(620\) 76122.3i 0.198029i
\(621\) 24279.8i 0.0629597i
\(622\) 694550.i 1.79524i
\(623\) 487751.i 1.25667i
\(624\) 282086.i 0.724458i
\(625\) −429671. −1.09996
\(626\) 887904. 2.26578
\(627\) 104104.i 0.264808i
\(628\) 759376.i 1.92547i
\(629\) 161574.i 0.408384i
\(630\) 210190.i 0.529580i
\(631\) −218714. −0.549310 −0.274655 0.961543i \(-0.588564\pi\)
−0.274655 + 0.961543i \(0.588564\pi\)
\(632\) 35614.3i 0.0891643i
\(633\) 137604.i 0.343417i
\(634\) 76309.6i 0.189846i
\(635\) 255189. 0.632871
\(636\) 331864. 0.820437
\(637\) 199796.i 0.492388i
\(638\) 29777.1 0.0731544
\(639\) −249225. −0.610365
\(640\) 132580.i 0.323681i
\(641\) −210985. −0.513495 −0.256747 0.966479i \(-0.582651\pi\)
−0.256747 + 0.966479i \(0.582651\pi\)
\(642\) 45241.2i 0.109765i
\(643\) 192225. 0.464932 0.232466 0.972605i \(-0.425321\pi\)
0.232466 + 0.972605i \(0.425321\pi\)
\(644\) 117654.i 0.283683i
\(645\) 155979.i 0.374927i
\(646\) 795305.i 1.90576i
\(647\) −671147. −1.60328 −0.801639 0.597808i \(-0.796038\pi\)
−0.801639 + 0.597808i \(0.796038\pi\)
\(648\) 5514.77i 0.0131334i
\(649\) 177264. 88008.3i 0.420853 0.208946i
\(650\) −744790. −1.76282
\(651\) 26127.8i 0.0616511i
\(652\) −431294. −1.01456
\(653\) 330138. 0.774227 0.387114 0.922032i \(-0.373472\pi\)
0.387114 + 0.922032i \(0.373472\pi\)
\(654\) 487688. 1.14021
\(655\) 1.03254e6i 2.40671i
\(656\) 177735. 0.413014
\(657\) 116331.i 0.269503i
\(658\) −202994. −0.468848
\(659\) 45073.9i 0.103790i −0.998653 0.0518949i \(-0.983474\pi\)
0.998653 0.0518949i \(-0.0165261\pi\)
\(660\) 175641.i 0.403215i
\(661\) −304683. −0.697341 −0.348670 0.937245i \(-0.613367\pi\)
−0.348670 + 0.937245i \(0.613367\pi\)
\(662\) 325098.i 0.741821i
\(663\) 472787.i 1.07557i
\(664\) 3014.23 0.00683661
\(665\) 475314. 1.07482
\(666\) −64388.4 −0.145164
\(667\) 15704.7i 0.0353002i
\(668\) 266322. 0.596835
\(669\) 106516. 0.237992
\(670\) −730159. −1.62655
\(671\) −85170.7 −0.189167
\(672\) 299488.i 0.663195i
\(673\) 188450.i 0.416070i −0.978121 0.208035i \(-0.933293\pi\)
0.978121 0.208035i \(-0.0667068\pi\)
\(674\) −665681. −1.46537
\(675\) −77807.5 −0.170771
\(676\) 442820. 0.969022
\(677\) −254006. −0.554199 −0.277100 0.960841i \(-0.589373\pi\)
−0.277100 + 0.960841i \(0.589373\pi\)
\(678\) 679923. 1.47911
\(679\) 15611.0i 0.0338604i
\(680\) 101598.i 0.219719i
\(681\) 407375.i 0.878417i
\(682\) 42013.0i 0.0903265i
\(683\) 537333.i 1.15187i −0.817497 0.575933i \(-0.804639\pi\)
0.817497 0.575933i \(-0.195361\pi\)
\(684\) 164703. 0.352038
\(685\) 718071. 1.53033
\(686\) 738847.i 1.57002i
\(687\) 162173.i 0.343609i
\(688\) 203917.i 0.430800i
\(689\) 858477.i 1.80838i
\(690\) 178255. 0.374406
\(691\) 70666.8i 0.147999i −0.997258 0.0739996i \(-0.976424\pi\)
0.997258 0.0739996i \(-0.0235763\pi\)
\(692\) 950678.i 1.98528i
\(693\) 60285.9i 0.125530i
\(694\) 55314.7 0.114848
\(695\) 778495. 1.61171
\(696\) 3567.06i 0.00736363i
\(697\) 297890. 0.613184
\(698\) −858099. −1.76127
\(699\) 472899.i 0.967863i
\(700\) 377035. 0.769459
\(701\) 792788.i 1.61332i 0.591015 + 0.806661i \(0.298727\pi\)
−0.591015 + 0.806661i \(0.701273\pi\)
\(702\) 188410. 0.382322
\(703\) 145605.i 0.294622i
\(704\) 269337.i 0.543440i
\(705\) 159827.i 0.321567i
\(706\) −69520.3 −0.139477
\(707\) 278447.i 0.557063i
\(708\) −139238. 280450.i −0.277775 0.559486i
\(709\) −867302. −1.72535 −0.862677 0.505756i \(-0.831214\pi\)
−0.862677 + 0.505756i \(0.831214\pi\)
\(710\) 1.82972e6i 3.62969i
\(711\) −127113. −0.251449
\(712\) 93952.4 0.185331
\(713\) 22158.0 0.0435864
\(714\) 460556.i 0.903412i
\(715\) 454353. 0.888754
\(716\) 874965.i 1.70673i
\(717\) 499730. 0.972070
\(718\) 64407.2i 0.124935i
\(719\) 267439.i 0.517329i 0.965967 + 0.258665i \(0.0832825\pi\)
−0.965967 + 0.258665i \(0.916718\pi\)
\(720\) −216354. −0.417349
\(721\) 246117.i 0.473448i
\(722\) 35450.9i 0.0680069i
\(723\) 359620. 0.687966
\(724\) −598745. −1.14226
\(725\) 50327.4 0.0957477
\(726\) 342142.i 0.649133i
\(727\) 717136. 1.35685 0.678426 0.734668i \(-0.262662\pi\)
0.678426 + 0.734668i \(0.262662\pi\)
\(728\) −69128.4 −0.130435
\(729\) 19683.0 0.0370370
\(730\) 854062. 1.60267
\(731\) 341772.i 0.639589i
\(732\) 134749.i 0.251480i
\(733\) −443873. −0.826134 −0.413067 0.910701i \(-0.635543\pi\)
−0.413067 + 0.910701i \(0.635543\pi\)
\(734\) 138953. 0.257914
\(735\) 153239. 0.283657
\(736\) 253985. 0.468870
\(737\) 209421. 0.385554
\(738\) 118712.i 0.217962i
\(739\) 177524.i 0.325063i 0.986703 + 0.162532i \(0.0519659\pi\)
−0.986703 + 0.162532i \(0.948034\pi\)
\(740\) 245660.i 0.448611i
\(741\) 426060.i 0.775952i
\(742\) 836267.i 1.51893i
\(743\) −266645. −0.483009 −0.241505 0.970400i \(-0.577641\pi\)
−0.241505 + 0.970400i \(0.577641\pi\)
\(744\) 5032.83 0.00909214
\(745\) 506527.i 0.912621i
\(746\) 502581.i 0.903085i
\(747\) 10758.2i 0.0192797i
\(748\) 384853.i 0.687846i
\(749\) −59244.9 −0.105606
\(750\) 72517.5i 0.128920i
\(751\) 438213.i 0.776972i −0.921455 0.388486i \(-0.872998\pi\)
0.921455 0.388486i \(-0.127002\pi\)
\(752\) 208947.i 0.369488i
\(753\) −489137. −0.862662
\(754\) −121867. −0.214360
\(755\) 46450.5i 0.0814886i
\(756\) −95378.6 −0.166881
\(757\) 999861. 1.74481 0.872404 0.488785i \(-0.162560\pi\)
0.872404 + 0.488785i \(0.162560\pi\)
\(758\) 1.16359e6i 2.02516i
\(759\) −51126.2 −0.0887483
\(760\) 91556.7i 0.158512i
\(761\) −326900. −0.564476 −0.282238 0.959344i \(-0.591077\pi\)
−0.282238 + 0.959344i \(0.591077\pi\)
\(762\) 222828.i 0.383760i
\(763\) 638643.i 1.09701i
\(764\) 505045.i 0.865253i
\(765\) −362617. −0.619620
\(766\) 1.04881e6i 1.78747i
\(767\) −725479. + 360187.i −1.23320 + 0.612262i
\(768\) −278089. −0.471478
\(769\) 235002.i 0.397392i −0.980061 0.198696i \(-0.936329\pi\)
0.980061 0.198696i \(-0.0636707\pi\)
\(770\) −442599. −0.746498
\(771\) −60691.8 −0.102099
\(772\) −552922. −0.927746
\(773\) 210457.i 0.352213i 0.984371 + 0.176106i \(0.0563503\pi\)
−0.984371 + 0.176106i \(0.943650\pi\)
\(774\) 136199. 0.227348
\(775\) 71007.9i 0.118223i
\(776\) −3007.05 −0.00499365
\(777\) 84318.8i 0.139663i
\(778\) 770606.i 1.27313i
\(779\) 268449. 0.442371
\(780\) 718835.i 1.18152i
\(781\) 524794.i 0.860373i
\(782\) 390580. 0.638700
\(783\) −12731.3 −0.0207659
\(784\) 200334. 0.325929
\(785\) 1.50664e6i 2.44494i
\(786\) −901600. −1.45938
\(787\) −11734.5 −0.0189459 −0.00947293 0.999955i \(-0.503015\pi\)
−0.00947293 + 0.999955i \(0.503015\pi\)
\(788\) 73578.1 0.118494
\(789\) 351008. 0.563849