Properties

Label 108.5.d.a.55.7
Level 108
Weight 5
Character 108.55
Analytic conductor 11.164
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{26} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.7
Root \(3.07345 + 2.03963i\) of \(x^{16} - 2 x^{15} + 6 x^{14} - 22 x^{13} + 19 x^{12} + 18 x^{11} + 1423 x^{10} + 660 x^{9} - 7353 x^{8} - 22934 x^{7} - 36353 x^{6} - 16248 x^{5} + 360646 x^{4} + 1077384 x^{3} + 2005641 x^{2} + 2990790 x + 2924100\)
Character \(\chi\) \(=\) 108.55
Dual form 108.5.d.a.55.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.35962 - 3.76184i) q^{2} +(-12.3029 + 10.2293i) q^{4} +2.66014 q^{5} -88.8835i q^{7} +(55.2083 + 32.3735i) q^{8} +O(q^{10})\) \(q+(-1.35962 - 3.76184i) q^{2} +(-12.3029 + 10.2293i) q^{4} +2.66014 q^{5} -88.8835i q^{7} +(55.2083 + 32.3735i) q^{8} +(-3.61678 - 10.0070i) q^{10} +72.9595i q^{11} -173.728 q^{13} +(-334.365 + 120.848i) q^{14} +(46.7216 - 251.700i) q^{16} -423.661 q^{17} +153.339i q^{19} +(-32.7274 + 27.2115i) q^{20} +(274.462 - 99.1971i) q^{22} +723.430i q^{23} -617.924 q^{25} +(236.203 + 653.536i) q^{26} +(909.218 + 1093.52i) q^{28} +366.864 q^{29} -642.635i q^{31} +(-1010.38 + 166.457i) q^{32} +(576.017 + 1593.74i) q^{34} -236.443i q^{35} -535.717 q^{37} +(576.836 - 208.482i) q^{38} +(146.862 + 86.1181i) q^{40} -2141.50 q^{41} -615.945i q^{43} +(-746.327 - 897.612i) q^{44} +(2721.43 - 983.589i) q^{46} +330.667i q^{47} -5499.27 q^{49} +(840.140 + 2324.53i) q^{50} +(2137.35 - 1777.12i) q^{52} +4628.97 q^{53} +194.083i q^{55} +(2877.47 - 4907.11i) q^{56} +(-498.795 - 1380.08i) q^{58} -3469.85i q^{59} -4646.40 q^{61} +(-2417.49 + 873.738i) q^{62} +(1999.92 + 3574.57i) q^{64} -462.141 q^{65} -6670.10i q^{67} +(5212.25 - 4333.77i) q^{68} +(-889.460 + 321.472i) q^{70} -6445.22i q^{71} +4735.78 q^{73} +(728.370 + 2015.28i) q^{74} +(-1568.55 - 1886.51i) q^{76} +6484.89 q^{77} -2085.24i q^{79} +(124.286 - 669.559i) q^{80} +(2911.62 + 8055.98i) q^{82} +9294.47i q^{83} -1127.00 q^{85} +(-2317.09 + 837.450i) q^{86} +(-2361.95 + 4027.97i) q^{88} -5704.72 q^{89} +15441.5i q^{91} +(-7400.21 - 8900.27i) q^{92} +(1243.92 - 449.581i) q^{94} +407.903i q^{95} +6975.60 q^{97} +(7476.91 + 20687.4i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 14q^{4} + O(q^{10}) \) \( 16q - 14q^{4} - 202q^{10} - 352q^{13} - 206q^{16} + 738q^{22} + 1632q^{25} + 342q^{28} - 2536q^{34} + 3200q^{37} - 2854q^{40} + 36q^{46} - 896q^{49} + 2288q^{52} + 2492q^{58} - 2752q^{61} + 682q^{64} - 14166q^{70} + 8240q^{73} - 33084q^{76} + 68q^{82} + 8800q^{85} + 48294q^{88} + 52596q^{94} - 6928q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35962 3.76184i −0.339904 0.940460i
\(3\) 0 0
\(4\) −12.3029 + 10.2293i −0.768930 + 0.639333i
\(5\) 2.66014 0.106406 0.0532029 0.998584i \(-0.483057\pi\)
0.0532029 + 0.998584i \(0.483057\pi\)
\(6\) 0 0
\(7\) 88.8835i 1.81395i −0.421186 0.906974i \(-0.638386\pi\)
0.421186 0.906974i \(-0.361614\pi\)
\(8\) 55.2083 + 32.3735i 0.862630 + 0.505836i
\(9\) 0 0
\(10\) −3.61678 10.0070i −0.0361678 0.100070i
\(11\) 72.9595i 0.602971i 0.953471 + 0.301486i \(0.0974825\pi\)
−0.953471 + 0.301486i \(0.902517\pi\)
\(12\) 0 0
\(13\) −173.728 −1.02797 −0.513987 0.857798i \(-0.671832\pi\)
−0.513987 + 0.857798i \(0.671832\pi\)
\(14\) −334.365 + 120.848i −1.70595 + 0.616569i
\(15\) 0 0
\(16\) 46.7216 251.700i 0.182506 0.983205i
\(17\) −423.661 −1.46595 −0.732977 0.680253i \(-0.761870\pi\)
−0.732977 + 0.680253i \(0.761870\pi\)
\(18\) 0 0
\(19\) 153.339i 0.424761i 0.977187 + 0.212381i \(0.0681216\pi\)
−0.977187 + 0.212381i \(0.931878\pi\)
\(20\) −32.7274 + 27.2115i −0.0818186 + 0.0680287i
\(21\) 0 0
\(22\) 274.462 99.1971i 0.567070 0.204953i
\(23\) 723.430i 1.36754i 0.729696 + 0.683771i \(0.239661\pi\)
−0.729696 + 0.683771i \(0.760339\pi\)
\(24\) 0 0
\(25\) −617.924 −0.988678
\(26\) 236.203 + 653.536i 0.349413 + 0.966769i
\(27\) 0 0
\(28\) 909.218 + 1093.52i 1.15972 + 1.39480i
\(29\) 366.864 0.436223 0.218112 0.975924i \(-0.430010\pi\)
0.218112 + 0.975924i \(0.430010\pi\)
\(30\) 0 0
\(31\) 642.635i 0.668715i −0.942446 0.334357i \(-0.891481\pi\)
0.942446 0.334357i \(-0.108519\pi\)
\(32\) −1010.38 + 166.457i −0.986699 + 0.162556i
\(33\) 0 0
\(34\) 576.017 + 1593.74i 0.498284 + 1.37867i
\(35\) 236.443i 0.193015i
\(36\) 0 0
\(37\) −535.717 −0.391320 −0.195660 0.980672i \(-0.562685\pi\)
−0.195660 + 0.980672i \(0.562685\pi\)
\(38\) 576.836 208.482i 0.399471 0.144378i
\(39\) 0 0
\(40\) 146.862 + 86.1181i 0.0917888 + 0.0538238i
\(41\) −2141.50 −1.27394 −0.636972 0.770887i \(-0.719813\pi\)
−0.636972 + 0.770887i \(0.719813\pi\)
\(42\) 0 0
\(43\) 615.945i 0.333123i −0.986031 0.166562i \(-0.946734\pi\)
0.986031 0.166562i \(-0.0532665\pi\)
\(44\) −746.327 897.612i −0.385499 0.463643i
\(45\) 0 0
\(46\) 2721.43 983.589i 1.28612 0.464834i
\(47\) 330.667i 0.149691i 0.997195 + 0.0748454i \(0.0238463\pi\)
−0.997195 + 0.0748454i \(0.976154\pi\)
\(48\) 0 0
\(49\) −5499.27 −2.29041
\(50\) 840.140 + 2324.53i 0.336056 + 0.929812i
\(51\) 0 0
\(52\) 2137.35 1777.12i 0.790440 0.657218i
\(53\) 4628.97 1.64791 0.823953 0.566659i \(-0.191764\pi\)
0.823953 + 0.566659i \(0.191764\pi\)
\(54\) 0 0
\(55\) 194.083i 0.0641596i
\(56\) 2877.47 4907.11i 0.917560 1.56477i
\(57\) 0 0
\(58\) −498.795 1380.08i −0.148274 0.410250i
\(59\) 3469.85i 0.996797i −0.866948 0.498399i \(-0.833922\pi\)
0.866948 0.498399i \(-0.166078\pi\)
\(60\) 0 0
\(61\) −4646.40 −1.24870 −0.624348 0.781146i \(-0.714635\pi\)
−0.624348 + 0.781146i \(0.714635\pi\)
\(62\) −2417.49 + 873.738i −0.628899 + 0.227299i
\(63\) 0 0
\(64\) 1999.92 + 3574.57i 0.488261 + 0.872698i
\(65\) −462.141 −0.109382
\(66\) 0 0
\(67\) 6670.10i 1.48588i −0.669360 0.742938i \(-0.733432\pi\)
0.669360 0.742938i \(-0.266568\pi\)
\(68\) 5212.25 4333.77i 1.12722 0.937233i
\(69\) 0 0
\(70\) −889.460 + 321.472i −0.181522 + 0.0656065i
\(71\) 6445.22i 1.27856i −0.768974 0.639280i \(-0.779232\pi\)
0.768974 0.639280i \(-0.220768\pi\)
\(72\) 0 0
\(73\) 4735.78 0.888682 0.444341 0.895858i \(-0.353438\pi\)
0.444341 + 0.895858i \(0.353438\pi\)
\(74\) 728.370 + 2015.28i 0.133011 + 0.368021i
\(75\) 0 0
\(76\) −1568.55 1886.51i −0.271564 0.326611i
\(77\) 6484.89 1.09376
\(78\) 0 0
\(79\) 2085.24i 0.334119i −0.985947 0.167059i \(-0.946573\pi\)
0.985947 0.167059i \(-0.0534272\pi\)
\(80\) 124.286 669.559i 0.0194197 0.104619i
\(81\) 0 0
\(82\) 2911.62 + 8055.98i 0.433019 + 1.19809i
\(83\) 9294.47i 1.34917i 0.738195 + 0.674587i \(0.235678\pi\)
−0.738195 + 0.674587i \(0.764322\pi\)
\(84\) 0 0
\(85\) −1127.00 −0.155986
\(86\) −2317.09 + 837.450i −0.313289 + 0.113230i
\(87\) 0 0
\(88\) −2361.95 + 4027.97i −0.305004 + 0.520141i
\(89\) −5704.72 −0.720202 −0.360101 0.932913i \(-0.617258\pi\)
−0.360101 + 0.932913i \(0.617258\pi\)
\(90\) 0 0
\(91\) 15441.5i 1.86469i
\(92\) −7400.21 8900.27i −0.874315 1.05154i
\(93\) 0 0
\(94\) 1243.92 449.581i 0.140778 0.0508805i
\(95\) 407.903i 0.0451970i
\(96\) 0 0
\(97\) 6975.60 0.741376 0.370688 0.928758i \(-0.379122\pi\)
0.370688 + 0.928758i \(0.379122\pi\)
\(98\) 7476.91 + 20687.4i 0.778520 + 2.15404i
\(99\) 0 0
\(100\) 7602.24 6320.94i 0.760224 0.632094i
\(101\) −14821.3 −1.45293 −0.726463 0.687206i \(-0.758837\pi\)
−0.726463 + 0.687206i \(0.758837\pi\)
\(102\) 0 0
\(103\) 8686.29i 0.818766i 0.912363 + 0.409383i \(0.134256\pi\)
−0.912363 + 0.409383i \(0.865744\pi\)
\(104\) −9591.21 5624.17i −0.886761 0.519986i
\(105\) 0 0
\(106\) −6293.62 17413.4i −0.560130 1.54979i
\(107\) 10919.9i 0.953790i −0.878960 0.476895i \(-0.841762\pi\)
0.878960 0.476895i \(-0.158238\pi\)
\(108\) 0 0
\(109\) 12531.6 1.05476 0.527379 0.849630i \(-0.323175\pi\)
0.527379 + 0.849630i \(0.323175\pi\)
\(110\) 730.108 263.878i 0.0603395 0.0218081i
\(111\) 0 0
\(112\) −22372.0 4152.78i −1.78348 0.331057i
\(113\) 12299.0 0.963194 0.481597 0.876393i \(-0.340057\pi\)
0.481597 + 0.876393i \(0.340057\pi\)
\(114\) 0 0
\(115\) 1924.43i 0.145514i
\(116\) −4513.48 + 3752.77i −0.335425 + 0.278892i
\(117\) 0 0
\(118\) −13053.0 + 4717.67i −0.937448 + 0.338816i
\(119\) 37656.4i 2.65916i
\(120\) 0 0
\(121\) 9317.91 0.636426
\(122\) 6317.33 + 17479.0i 0.424438 + 1.17435i
\(123\) 0 0
\(124\) 6573.72 + 7906.26i 0.427532 + 0.514195i
\(125\) −3306.36 −0.211607
\(126\) 0 0
\(127\) 22807.9i 1.41409i −0.707167 0.707047i \(-0.750027\pi\)
0.707167 0.707047i \(-0.249973\pi\)
\(128\) 10727.8 12383.4i 0.654775 0.755824i
\(129\) 0 0
\(130\) 628.335 + 1738.50i 0.0371796 + 0.102870i
\(131\) 6242.75i 0.363775i −0.983319 0.181888i \(-0.941779\pi\)
0.983319 0.181888i \(-0.0582207\pi\)
\(132\) 0 0
\(133\) 13629.3 0.770495
\(134\) −25091.8 + 9068.78i −1.39741 + 0.505056i
\(135\) 0 0
\(136\) −23389.6 13715.4i −1.26458 0.741532i
\(137\) −9530.74 −0.507791 −0.253896 0.967232i \(-0.581712\pi\)
−0.253896 + 0.967232i \(0.581712\pi\)
\(138\) 0 0
\(139\) 11582.2i 0.599462i −0.954024 0.299731i \(-0.903103\pi\)
0.954024 0.299731i \(-0.0968970\pi\)
\(140\) 2418.65 + 2908.93i 0.123401 + 0.148415i
\(141\) 0 0
\(142\) −24245.9 + 8763.04i −1.20243 + 0.434588i
\(143\) 12675.1i 0.619839i
\(144\) 0 0
\(145\) 975.910 0.0464167
\(146\) −6438.86 17815.3i −0.302067 0.835769i
\(147\) 0 0
\(148\) 6590.86 5480.03i 0.300898 0.250184i
\(149\) −38532.6 −1.73562 −0.867811 0.496894i \(-0.834474\pi\)
−0.867811 + 0.496894i \(0.834474\pi\)
\(150\) 0 0
\(151\) 22912.5i 1.00489i 0.864610 + 0.502444i \(0.167566\pi\)
−0.864610 + 0.502444i \(0.832434\pi\)
\(152\) −4964.11 + 8465.57i −0.214859 + 0.366412i
\(153\) 0 0
\(154\) −8816.98 24395.1i −0.371773 1.02864i
\(155\) 1709.50i 0.0711551i
\(156\) 0 0
\(157\) 25755.8 1.04490 0.522451 0.852669i \(-0.325018\pi\)
0.522451 + 0.852669i \(0.325018\pi\)
\(158\) −7844.33 + 2835.12i −0.314226 + 0.113569i
\(159\) 0 0
\(160\) −2687.76 + 442.800i −0.104990 + 0.0172969i
\(161\) 64301.0 2.48065
\(162\) 0 0
\(163\) 21920.6i 0.825045i 0.910947 + 0.412522i \(0.135352\pi\)
−0.910947 + 0.412522i \(0.864648\pi\)
\(164\) 26346.6 21906.1i 0.979573 0.814474i
\(165\) 0 0
\(166\) 34964.3 12636.9i 1.26884 0.458591i
\(167\) 3716.35i 0.133255i 0.997778 + 0.0666275i \(0.0212239\pi\)
−0.997778 + 0.0666275i \(0.978776\pi\)
\(168\) 0 0
\(169\) 1620.29 0.0567309
\(170\) 1532.29 + 4239.59i 0.0530203 + 0.146699i
\(171\) 0 0
\(172\) 6300.71 + 7577.90i 0.212977 + 0.256148i
\(173\) 23829.7 0.796208 0.398104 0.917340i \(-0.369668\pi\)
0.398104 + 0.917340i \(0.369668\pi\)
\(174\) 0 0
\(175\) 54923.2i 1.79341i
\(176\) 18363.9 + 3408.79i 0.592844 + 0.110046i
\(177\) 0 0
\(178\) 7756.24 + 21460.3i 0.244800 + 0.677322i
\(179\) 53055.1i 1.65585i −0.560838 0.827926i \(-0.689521\pi\)
0.560838 0.827926i \(-0.310479\pi\)
\(180\) 0 0
\(181\) −38125.2 −1.16374 −0.581869 0.813283i \(-0.697678\pi\)
−0.581869 + 0.813283i \(0.697678\pi\)
\(182\) 58088.5 20994.6i 1.75367 0.633817i
\(183\) 0 0
\(184\) −23419.9 + 39939.4i −0.691752 + 1.17968i
\(185\) −1425.08 −0.0416387
\(186\) 0 0
\(187\) 30910.1i 0.883928i
\(188\) −3382.50 4068.15i −0.0957022 0.115102i
\(189\) 0 0
\(190\) 1534.47 554.592i 0.0425060 0.0153627i
\(191\) 19578.7i 0.536683i 0.963324 + 0.268341i \(0.0864755\pi\)
−0.963324 + 0.268341i \(0.913525\pi\)
\(192\) 0 0
\(193\) 10489.3 0.281600 0.140800 0.990038i \(-0.455033\pi\)
0.140800 + 0.990038i \(0.455033\pi\)
\(194\) −9484.15 26241.1i −0.251997 0.697234i
\(195\) 0 0
\(196\) 67656.9 56253.9i 1.76116 1.46433i
\(197\) −18533.1 −0.477547 −0.238773 0.971075i \(-0.576745\pi\)
−0.238773 + 0.971075i \(0.576745\pi\)
\(198\) 0 0
\(199\) 66138.9i 1.67013i −0.550150 0.835066i \(-0.685430\pi\)
0.550150 0.835066i \(-0.314570\pi\)
\(200\) −34114.5 20004.3i −0.852863 0.500108i
\(201\) 0 0
\(202\) 20151.3 + 55755.4i 0.493856 + 1.36642i
\(203\) 32608.1i 0.791286i
\(204\) 0 0
\(205\) −5696.69 −0.135555
\(206\) 32676.4 11810.0i 0.770017 0.278302i
\(207\) 0 0
\(208\) −8116.84 + 43727.3i −0.187612 + 1.01071i
\(209\) −11187.5 −0.256119
\(210\) 0 0
\(211\) 25222.6i 0.566533i −0.959041 0.283267i \(-0.908582\pi\)
0.959041 0.283267i \(-0.0914182\pi\)
\(212\) −56949.6 + 47351.2i −1.26712 + 1.05356i
\(213\) 0 0
\(214\) −41079.1 + 14846.9i −0.897001 + 0.324198i
\(215\) 1638.50i 0.0354462i
\(216\) 0 0
\(217\) −57119.6 −1.21301
\(218\) −17038.2 47141.8i −0.358517 0.991958i
\(219\) 0 0
\(220\) −1985.34 2387.78i −0.0410194 0.0493342i
\(221\) 73601.6 1.50696
\(222\) 0 0
\(223\) 14958.0i 0.300791i −0.988626 0.150395i \(-0.951945\pi\)
0.988626 0.150395i \(-0.0480547\pi\)
\(224\) 14795.3 + 89806.1i 0.294868 + 1.78982i
\(225\) 0 0
\(226\) −16722.0 46267.0i −0.327394 0.905845i
\(227\) 26750.1i 0.519126i 0.965726 + 0.259563i \(0.0835785\pi\)
−0.965726 + 0.259563i \(0.916421\pi\)
\(228\) 0 0
\(229\) −54043.1 −1.03055 −0.515275 0.857025i \(-0.672310\pi\)
−0.515275 + 0.857025i \(0.672310\pi\)
\(230\) 7239.39 2616.49i 0.136850 0.0494610i
\(231\) 0 0
\(232\) 20253.9 + 11876.7i 0.376299 + 0.220657i
\(233\) −89436.5 −1.64742 −0.823708 0.567015i \(-0.808098\pi\)
−0.823708 + 0.567015i \(0.808098\pi\)
\(234\) 0 0
\(235\) 879.621i 0.0159280i
\(236\) 35494.2 + 42689.2i 0.637285 + 0.766467i
\(237\) 0 0
\(238\) 141657. 51198.4i 2.50084 0.903862i
\(239\) 64893.0i 1.13606i 0.823007 + 0.568031i \(0.192295\pi\)
−0.823007 + 0.568031i \(0.807705\pi\)
\(240\) 0 0
\(241\) −93131.9 −1.60348 −0.801742 0.597671i \(-0.796093\pi\)
−0.801742 + 0.597671i \(0.796093\pi\)
\(242\) −12668.8 35052.5i −0.216324 0.598533i
\(243\) 0 0
\(244\) 57164.1 47529.6i 0.960160 0.798333i
\(245\) −14628.9 −0.243713
\(246\) 0 0
\(247\) 26639.2i 0.436643i
\(248\) 20804.3 35478.8i 0.338260 0.576853i
\(249\) 0 0
\(250\) 4495.38 + 12438.0i 0.0719261 + 0.199008i
\(251\) 13729.0i 0.217917i −0.994046 0.108958i \(-0.965249\pi\)
0.994046 0.108958i \(-0.0347515\pi\)
\(252\) 0 0
\(253\) −52781.1 −0.824589
\(254\) −85799.7 + 31010.1i −1.32990 + 0.480657i
\(255\) 0 0
\(256\) −61170.2 23519.7i −0.933383 0.358882i
\(257\) −24255.6 −0.367237 −0.183618 0.982998i \(-0.558781\pi\)
−0.183618 + 0.982998i \(0.558781\pi\)
\(258\) 0 0
\(259\) 47616.4i 0.709834i
\(260\) 5685.66 4727.39i 0.0841074 0.0699318i
\(261\) 0 0
\(262\) −23484.2 + 8487.75i −0.342116 + 0.123649i
\(263\) 34613.8i 0.500423i 0.968191 + 0.250212i \(0.0805002\pi\)
−0.968191 + 0.250212i \(0.919500\pi\)
\(264\) 0 0
\(265\) 12313.7 0.175347
\(266\) −18530.6 51271.2i −0.261895 0.724619i
\(267\) 0 0
\(268\) 68230.6 + 82061.4i 0.949970 + 1.14253i
\(269\) 67272.9 0.929684 0.464842 0.885394i \(-0.346111\pi\)
0.464842 + 0.885394i \(0.346111\pi\)
\(270\) 0 0
\(271\) 7814.00i 0.106398i −0.998584 0.0531992i \(-0.983058\pi\)
0.998584 0.0531992i \(-0.0169418\pi\)
\(272\) −19794.1 + 106636.i −0.267546 + 1.44133i
\(273\) 0 0
\(274\) 12958.2 + 35853.1i 0.172601 + 0.477557i
\(275\) 45083.4i 0.596144i
\(276\) 0 0
\(277\) 50559.4 0.658935 0.329467 0.944167i \(-0.393131\pi\)
0.329467 + 0.944167i \(0.393131\pi\)
\(278\) −43570.4 + 15747.4i −0.563770 + 0.203760i
\(279\) 0 0
\(280\) 7654.48 13053.6i 0.0976336 0.166500i
\(281\) −81351.4 −1.03027 −0.515136 0.857108i \(-0.672259\pi\)
−0.515136 + 0.857108i \(0.672259\pi\)
\(282\) 0 0
\(283\) 2795.45i 0.0349043i −0.999848 0.0174522i \(-0.994445\pi\)
0.999848 0.0174522i \(-0.00555548\pi\)
\(284\) 65930.3 + 79294.8i 0.817426 + 0.983123i
\(285\) 0 0
\(286\) −47681.6 + 17233.3i −0.582934 + 0.210686i
\(287\) 190344.i 2.31087i
\(288\) 0 0
\(289\) 95967.4 1.14902
\(290\) −1326.87 3671.22i −0.0157772 0.0436530i
\(291\) 0 0
\(292\) −58263.8 + 48443.9i −0.683334 + 0.568164i
\(293\) −48302.8 −0.562648 −0.281324 0.959613i \(-0.590774\pi\)
−0.281324 + 0.959613i \(0.590774\pi\)
\(294\) 0 0
\(295\) 9230.30i 0.106065i
\(296\) −29576.0 17343.0i −0.337564 0.197944i
\(297\) 0 0
\(298\) 52389.6 + 144953.i 0.589946 + 1.63228i
\(299\) 125680.i 1.40580i
\(300\) 0 0
\(301\) −54747.3 −0.604269
\(302\) 86193.0 31152.2i 0.945057 0.341566i
\(303\) 0 0
\(304\) 38595.4 + 7164.23i 0.417627 + 0.0775216i
\(305\) −12360.1 −0.132869
\(306\) 0 0
\(307\) 1578.26i 0.0167457i −0.999965 0.00837284i \(-0.997335\pi\)
0.999965 0.00837284i \(-0.00266519\pi\)
\(308\) −79782.9 + 66336.1i −0.841024 + 0.699276i
\(309\) 0 0
\(310\) −6430.87 + 2324.27i −0.0669185 + 0.0241859i
\(311\) 2640.95i 0.0273049i −0.999907 0.0136524i \(-0.995654\pi\)
0.999907 0.0136524i \(-0.00434584\pi\)
\(312\) 0 0
\(313\) 52927.9 0.540252 0.270126 0.962825i \(-0.412935\pi\)
0.270126 + 0.962825i \(0.412935\pi\)
\(314\) −35018.1 96889.2i −0.355167 0.982689i
\(315\) 0 0
\(316\) 21330.6 + 25654.4i 0.213613 + 0.256914i
\(317\) 40687.1 0.404891 0.202446 0.979293i \(-0.435111\pi\)
0.202446 + 0.979293i \(0.435111\pi\)
\(318\) 0 0
\(319\) 26766.2i 0.263030i
\(320\) 5320.06 + 9508.87i 0.0519538 + 0.0928601i
\(321\) 0 0
\(322\) −87424.8 241890.i −0.843185 2.33295i
\(323\) 64963.6i 0.622680i
\(324\) 0 0
\(325\) 107350. 1.01634
\(326\) 82461.8 29803.7i 0.775922 0.280436i
\(327\) 0 0
\(328\) −118229. 69327.8i −1.09894 0.644406i
\(329\) 29390.8 0.271531
\(330\) 0 0
\(331\) 44484.1i 0.406021i −0.979177 0.203011i \(-0.934927\pi\)
0.979177 0.203011i \(-0.0650726\pi\)
\(332\) −95076.2 114349.i −0.862572 1.03742i
\(333\) 0 0
\(334\) 13980.3 5052.82i 0.125321 0.0452940i
\(335\) 17743.4i 0.158106i
\(336\) 0 0
\(337\) −1175.77 −0.0103529 −0.00517645 0.999987i \(-0.501648\pi\)
−0.00517645 + 0.999987i \(0.501648\pi\)
\(338\) −2202.98 6095.27i −0.0192831 0.0533531i
\(339\) 0 0
\(340\) 13865.3 11528.4i 0.119942 0.0997270i
\(341\) 46886.3 0.403216
\(342\) 0 0
\(343\) 275385.i 2.34073i
\(344\) 19940.3 34005.3i 0.168506 0.287362i
\(345\) 0 0
\(346\) −32399.3 89643.6i −0.270635 0.748802i
\(347\) 80258.8i 0.666551i −0.942829 0.333276i \(-0.891846\pi\)
0.942829 0.333276i \(-0.108154\pi\)
\(348\) 0 0
\(349\) −11160.8 −0.0916318 −0.0458159 0.998950i \(-0.514589\pi\)
−0.0458159 + 0.998950i \(0.514589\pi\)
\(350\) 206612. 74674.6i 1.68663 0.609588i
\(351\) 0 0
\(352\) −12144.6 73716.8i −0.0980164 0.594951i
\(353\) 235353. 1.88873 0.944366 0.328895i \(-0.106676\pi\)
0.944366 + 0.328895i \(0.106676\pi\)
\(354\) 0 0
\(355\) 17145.2i 0.136046i
\(356\) 70184.5 58355.5i 0.553785 0.460449i
\(357\) 0 0
\(358\) −199585. + 72134.7i −1.55726 + 0.562831i
\(359\) 141216.i 1.09571i 0.836573 + 0.547855i \(0.184556\pi\)
−0.836573 + 0.547855i \(0.815444\pi\)
\(360\) 0 0
\(361\) 106808. 0.819578
\(362\) 51835.7 + 143421.i 0.395560 + 1.09445i
\(363\) 0 0
\(364\) −157956. 189975.i −1.19216 1.43382i
\(365\) 12597.9 0.0945608
\(366\) 0 0
\(367\) 63764.0i 0.473417i −0.971581 0.236708i \(-0.923931\pi\)
0.971581 0.236708i \(-0.0760686\pi\)
\(368\) 182088. + 33799.8i 1.34457 + 0.249585i
\(369\) 0 0
\(370\) 1937.57 + 5360.94i 0.0141532 + 0.0391595i
\(371\) 411438.i 2.98921i
\(372\) 0 0
\(373\) 119610. 0.859708 0.429854 0.902898i \(-0.358565\pi\)
0.429854 + 0.902898i \(0.358565\pi\)
\(374\) −116279. + 42025.9i −0.831299 + 0.300451i
\(375\) 0 0
\(376\) −10704.8 + 18255.6i −0.0757189 + 0.129128i
\(377\) −63734.4 −0.448426
\(378\) 0 0
\(379\) 40019.5i 0.278608i −0.990250 0.139304i \(-0.955514\pi\)
0.990250 0.139304i \(-0.0444865\pi\)
\(380\) −4172.58 5018.38i −0.0288960 0.0347533i
\(381\) 0 0
\(382\) 73652.0 26619.6i 0.504729 0.182421i
\(383\) 195988.i 1.33608i 0.744125 + 0.668040i \(0.232867\pi\)
−0.744125 + 0.668040i \(0.767133\pi\)
\(384\) 0 0
\(385\) 17250.8 0.116382
\(386\) −14261.4 39459.1i −0.0957170 0.264833i
\(387\) 0 0
\(388\) −85820.0 + 71355.7i −0.570066 + 0.473986i
\(389\) −29348.7 −0.193950 −0.0969751 0.995287i \(-0.530917\pi\)
−0.0969751 + 0.995287i \(0.530917\pi\)
\(390\) 0 0
\(391\) 306489.i 2.00475i
\(392\) −303605. 178031.i −1.97577 1.15857i
\(393\) 0 0
\(394\) 25198.0 + 69718.6i 0.162320 + 0.449114i
\(395\) 5547.03i 0.0355522i
\(396\) 0 0
\(397\) 190863. 1.21099 0.605495 0.795849i \(-0.292975\pi\)
0.605495 + 0.795849i \(0.292975\pi\)
\(398\) −248804. + 89923.6i −1.57069 + 0.567685i
\(399\) 0 0
\(400\) −28870.4 + 155532.i −0.180440 + 0.972073i
\(401\) −35070.1 −0.218096 −0.109048 0.994036i \(-0.534780\pi\)
−0.109048 + 0.994036i \(0.534780\pi\)
\(402\) 0 0
\(403\) 111643.i 0.687422i
\(404\) 182345. 151612.i 1.11720 0.928904i
\(405\) 0 0
\(406\) −122667. + 44334.6i −0.744173 + 0.268962i
\(407\) 39085.7i 0.235955i
\(408\) 0 0
\(409\) −106623. −0.637388 −0.318694 0.947858i \(-0.603244\pi\)
−0.318694 + 0.947858i \(0.603244\pi\)
\(410\) 7745.33 + 21430.1i 0.0460757 + 0.127484i
\(411\) 0 0
\(412\) −88855.0 106866.i −0.523465 0.629574i
\(413\) −308412. −1.80814
\(414\) 0 0
\(415\) 24724.6i 0.143560i
\(416\) 175531. 28918.2i 1.01430 0.167103i
\(417\) 0 0
\(418\) 15210.8 + 42085.7i 0.0870559 + 0.240869i
\(419\) 150952.i 0.859826i 0.902870 + 0.429913i \(0.141456\pi\)
−0.902870 + 0.429913i \(0.858544\pi\)
\(420\) 0 0
\(421\) 188580. 1.06397 0.531987 0.846752i \(-0.321445\pi\)
0.531987 + 0.846752i \(0.321445\pi\)
\(422\) −94883.5 + 34293.1i −0.532802 + 0.192567i
\(423\) 0 0
\(424\) 255557. + 149856.i 1.42153 + 0.833569i
\(425\) 261790. 1.44936
\(426\) 0 0
\(427\) 412988.i 2.26507i
\(428\) 111704. + 134347.i 0.609790 + 0.733398i
\(429\) 0 0
\(430\) −6163.78 + 2227.74i −0.0333358 + 0.0120483i
\(431\) 111824.i 0.601975i 0.953628 + 0.300988i \(0.0973163\pi\)
−0.953628 + 0.300988i \(0.902684\pi\)
\(432\) 0 0
\(433\) 86904.0 0.463515 0.231758 0.972774i \(-0.425552\pi\)
0.231758 + 0.972774i \(0.425552\pi\)
\(434\) 77660.9 + 214875.i 0.412309 + 1.14079i
\(435\) 0 0
\(436\) −154175. + 128190.i −0.811035 + 0.674342i
\(437\) −110930. −0.580879
\(438\) 0 0
\(439\) 200474.i 1.04023i 0.854096 + 0.520115i \(0.174111\pi\)
−0.854096 + 0.520115i \(0.825889\pi\)
\(440\) −6283.14 + 10715.0i −0.0324542 + 0.0553460i
\(441\) 0 0
\(442\) −100070. 276877.i −0.512223 1.41724i
\(443\) 40063.7i 0.204147i −0.994777 0.102074i \(-0.967452\pi\)
0.994777 0.102074i \(-0.0325477\pi\)
\(444\) 0 0
\(445\) −15175.4 −0.0766337
\(446\) −56269.7 + 20337.2i −0.282882 + 0.102240i
\(447\) 0 0
\(448\) 317720. 177759.i 1.58303 0.885680i
\(449\) 95081.8 0.471634 0.235817 0.971798i \(-0.424223\pi\)
0.235817 + 0.971798i \(0.424223\pi\)
\(450\) 0 0
\(451\) 156243.i 0.768151i
\(452\) −151313. + 125811.i −0.740629 + 0.615802i
\(453\) 0 0
\(454\) 100629. 36369.8i 0.488217 0.176453i
\(455\) 41076.7i 0.198414i
\(456\) 0 0
\(457\) −132420. −0.634047 −0.317024 0.948418i \(-0.602683\pi\)
−0.317024 + 0.948418i \(0.602683\pi\)
\(458\) 73477.9 + 203301.i 0.350289 + 0.969191i
\(459\) 0 0
\(460\) −19685.6 23676.0i −0.0930322 0.111890i
\(461\) −85031.6 −0.400109 −0.200055 0.979785i \(-0.564112\pi\)
−0.200055 + 0.979785i \(0.564112\pi\)
\(462\) 0 0
\(463\) 23890.7i 0.111447i −0.998446 0.0557234i \(-0.982254\pi\)
0.998446 0.0557234i \(-0.0177465\pi\)
\(464\) 17140.5 92339.7i 0.0796135 0.428897i
\(465\) 0 0
\(466\) 121599. + 336446.i 0.559964 + 1.54933i
\(467\) 233452.i 1.07044i 0.844712 + 0.535221i \(0.179772\pi\)
−0.844712 + 0.535221i \(0.820228\pi\)
\(468\) 0 0
\(469\) −592861. −2.69530
\(470\) 3308.99 1195.95i 0.0149796 0.00541398i
\(471\) 0 0
\(472\) 112331. 191565.i 0.504215 0.859867i
\(473\) 44939.1 0.200864
\(474\) 0 0
\(475\) 94751.6i 0.419952i
\(476\) −385200. 463283.i −1.70009 2.04471i
\(477\) 0 0
\(478\) 244117. 88229.7i 1.06842 0.386153i
\(479\) 97384.4i 0.424442i 0.977222 + 0.212221i \(0.0680696\pi\)
−0.977222 + 0.212221i \(0.931930\pi\)
\(480\) 0 0
\(481\) 93068.8 0.402267
\(482\) 126624. + 350347.i 0.545031 + 1.50801i
\(483\) 0 0
\(484\) −114637. + 95316.0i −0.489367 + 0.406888i
\(485\) 18556.1 0.0788866
\(486\) 0 0
\(487\) 42812.3i 0.180514i 0.995919 + 0.0902570i \(0.0287689\pi\)
−0.995919 + 0.0902570i \(0.971231\pi\)
\(488\) −256520. 150420.i −1.07716 0.631635i
\(489\) 0 0
\(490\) 19889.6 + 55031.4i 0.0828390 + 0.229202i
\(491\) 376010.i 1.55968i −0.625976 0.779842i \(-0.715299\pi\)
0.625976 0.779842i \(-0.284701\pi\)
\(492\) 0 0
\(493\) −155426. −0.639483
\(494\) −100212. + 36219.1i −0.410646 + 0.148417i
\(495\) 0 0
\(496\) −161751. 30024.9i −0.657484 0.122045i
\(497\) −572874. −2.31924
\(498\) 0 0
\(499\) 239303.i 0.961051i −0.876981 0.480525i \(-0.840446\pi\)
0.876981 0.480525i \(-0.159554\pi\)
\(500\) 40677.7 33821.8i 0.162711 0.135287i
\(501\) 0 0
\(502\) −51646.1 + 18666.1i −0.204942 + 0.0740708i
\(503\) 297365.i 1.17531i 0.809111 + 0.587656i \(0.199949\pi\)
−0.809111 + 0.587656i \(0.800051\pi\)
\(504\) 0 0
\(505\) −39426.8 −0.154600
\(506\) 71762.1 + 198554.i 0.280281 + 0.775493i
\(507\) 0 0
\(508\) 233310. + 280603.i 0.904077 + 1.08734i
\(509\) −189362. −0.730897 −0.365449 0.930831i \(-0.619084\pi\)
−0.365449 + 0.930831i \(0.619084\pi\)
\(510\) 0 0
\(511\) 420933.i 1.61202i
\(512\) −5309.28 + 262090.i −0.0202533 + 0.999795i
\(513\) 0 0
\(514\) 32978.4 + 91245.8i 0.124825 + 0.345372i
\(515\) 23106.8i 0.0871215i
\(516\) 0 0
\(517\) −24125.3 −0.0902592
\(518\) 179125. 64740.1i 0.667571 0.241276i
\(519\) 0 0
\(520\) −25514.0 14961.1i −0.0943565 0.0553295i
\(521\) 347810. 1.28135 0.640673 0.767814i \(-0.278655\pi\)
0.640673 + 0.767814i \(0.278655\pi\)
\(522\) 0 0
\(523\) 465334.i 1.70122i −0.525794 0.850612i \(-0.676232\pi\)
0.525794 0.850612i \(-0.323768\pi\)
\(524\) 63859.1 + 76803.7i 0.232573 + 0.279718i
\(525\) 0 0
\(526\) 130212. 47061.5i 0.470628 0.170096i
\(527\) 272259.i 0.980305i
\(528\) 0 0
\(529\) −243510. −0.870173
\(530\) −16741.9 46322.2i −0.0596011 0.164906i
\(531\) 0 0
\(532\) −167679. + 139418.i −0.592456 + 0.492603i
\(533\) 372038. 1.30958
\(534\) 0 0
\(535\) 29048.6i 0.101489i
\(536\) 215934. 368245.i 0.751609 1.28176i
\(537\) 0 0
\(538\) −91465.4 253070.i −0.316004 0.874331i
\(539\) 401224.i 1.38105i
\(540\) 0 0
\(541\) −340727. −1.16416 −0.582080 0.813132i \(-0.697761\pi\)
−0.582080 + 0.813132i \(0.697761\pi\)
\(542\) −29395.0 + 10624.1i −0.100063 + 0.0361653i
\(543\) 0 0
\(544\) 428058. 70521.3i 1.44646 0.238299i
\(545\) 33335.8 0.112232
\(546\) 0 0
\(547\) 87443.4i 0.292248i 0.989266 + 0.146124i \(0.0466799\pi\)
−0.989266 + 0.146124i \(0.953320\pi\)
\(548\) 117255. 97493.1i 0.390456 0.324648i
\(549\) 0 0
\(550\) −169597. + 61296.2i −0.560650 + 0.202632i
\(551\) 56254.4i 0.185291i
\(552\) 0 0
\(553\) −185343. −0.606075
\(554\) −68741.5 190196.i −0.223975 0.619702i
\(555\) 0 0
\(556\) 118478. + 142495.i 0.383256 + 0.460944i
\(557\) 82261.1 0.265146 0.132573 0.991173i \(-0.457676\pi\)
0.132573 + 0.991173i \(0.457676\pi\)
\(558\) 0 0
\(559\) 107007.i 0.342442i
\(560\) −59512.8 11047.0i −0.189773 0.0352264i
\(561\) 0 0
\(562\) 110607. + 306031.i 0.350194 + 0.968930i
\(563\) 440276.i 1.38902i −0.719483 0.694510i \(-0.755621\pi\)
0.719483 0.694510i \(-0.244379\pi\)
\(564\) 0 0
\(565\) 32717.2 0.102489
\(566\) −10516.0 + 3800.75i −0.0328261 + 0.0118641i
\(567\) 0 0
\(568\) 208654. 355830.i 0.646741 1.10292i
\(569\) −124980. −0.386026 −0.193013 0.981196i \(-0.561826\pi\)
−0.193013 + 0.981196i \(0.561826\pi\)
\(570\) 0 0
\(571\) 404239.i 1.23984i 0.784665 + 0.619921i \(0.212835\pi\)
−0.784665 + 0.619921i \(0.787165\pi\)
\(572\) 129658. + 155940.i 0.396283 + 0.476613i
\(573\) 0 0
\(574\) 716043. 258795.i 2.17328 0.785474i
\(575\) 447025.i 1.35206i
\(576\) 0 0
\(577\) −118286. −0.355290 −0.177645 0.984095i \(-0.556848\pi\)
−0.177645 + 0.984095i \(0.556848\pi\)
\(578\) −130479. 361014.i −0.390558 1.08061i
\(579\) 0 0
\(580\) −12006.5 + 9982.91i −0.0356912 + 0.0296757i
\(581\) 826124. 2.44733
\(582\) 0 0
\(583\) 337727.i 0.993639i
\(584\) 261455. + 153314.i 0.766603 + 0.449527i
\(585\) 0 0
\(586\) 65673.3 + 181707.i 0.191247 + 0.529148i
\(587\) 47852.6i 0.138877i −0.997586 0.0694383i \(-0.977879\pi\)
0.997586 0.0694383i \(-0.0221207\pi\)
\(588\) 0 0
\(589\) 98540.8 0.284044
\(590\) −34722.9 + 12549.7i −0.0997498 + 0.0360520i
\(591\) 0 0
\(592\) −25029.6 + 134840.i −0.0714184 + 0.384748i
\(593\) −633658. −1.80196 −0.900981 0.433859i \(-0.857152\pi\)
−0.900981 + 0.433859i \(0.857152\pi\)
\(594\) 0 0
\(595\) 100172.i 0.282950i
\(596\) 474061. 394162.i 1.33457 1.10964i
\(597\) 0 0
\(598\) −472787. + 170877.i −1.32210 + 0.477837i
\(599\) 158241.i 0.441027i 0.975384 + 0.220513i \(0.0707733\pi\)
−0.975384 + 0.220513i \(0.929227\pi\)
\(600\) 0 0
\(601\) −84042.2 −0.232674 −0.116337 0.993210i \(-0.537115\pi\)
−0.116337 + 0.993210i \(0.537115\pi\)
\(602\) 74435.5 + 205951.i 0.205394 + 0.568290i
\(603\) 0 0
\(604\) −234379. 281889.i −0.642458 0.772689i
\(605\) 24787.0 0.0677194
\(606\) 0 0
\(607\) 504787.i 1.37003i 0.728528 + 0.685016i \(0.240205\pi\)
−0.728528 + 0.685016i \(0.759795\pi\)
\(608\) −25524.3 154930.i −0.0690474 0.419111i
\(609\) 0 0
\(610\) 16805.0 + 46496.7i 0.0451626 + 0.124958i
\(611\) 57446.0i 0.153878i
\(612\) 0 0
\(613\) −30449.3 −0.0810320 −0.0405160 0.999179i \(-0.512900\pi\)
−0.0405160 + 0.999179i \(0.512900\pi\)
\(614\) −5937.18 + 2145.84i −0.0157486 + 0.00569193i
\(615\) 0 0
\(616\) 358020. + 209939.i 0.943509 + 0.553262i
\(617\) 147465. 0.387364 0.193682 0.981064i \(-0.437957\pi\)
0.193682 + 0.981064i \(0.437957\pi\)
\(618\) 0 0
\(619\) 264366.i 0.689960i −0.938610 0.344980i \(-0.887886\pi\)
0.938610 0.344980i \(-0.112114\pi\)
\(620\) 17487.1 + 21031.8i 0.0454918 + 0.0547133i
\(621\) 0 0
\(622\) −9934.84 + 3590.69i −0.0256791 + 0.00928104i
\(623\) 507056.i 1.30641i
\(624\) 0 0
\(625\) 377407. 0.966162
\(626\) −71961.8 199106.i −0.183634 0.508085i
\(627\) 0 0
\(628\) −316871. + 263465.i −0.803457 + 0.668041i
\(629\) 226962. 0.573657
\(630\) 0 0
\(631\) 455734.i 1.14460i −0.820045 0.572299i \(-0.806052\pi\)
0.820045 0.572299i \(-0.193948\pi\)
\(632\) 67506.4 115122.i 0.169009 0.288221i
\(633\) 0 0
\(634\) −55318.9 153058.i −0.137624 0.380784i
\(635\) 60672.3i 0.150468i
\(636\) 0 0
\(637\) 955375. 2.35448
\(638\) 100690. 36391.8i 0.247369 0.0894051i
\(639\) 0 0
\(640\) 28537.6 32941.7i 0.0696719 0.0804240i
\(641\) 42568.5 0.103603 0.0518015 0.998657i \(-0.483504\pi\)
0.0518015 + 0.998657i \(0.483504\pi\)
\(642\) 0 0
\(643\) 397515.i 0.961461i −0.876868 0.480730i \(-0.840372\pi\)
0.876868 0.480730i \(-0.159628\pi\)
\(644\) −791087. + 657756.i −1.90745 + 1.58596i
\(645\) 0 0
\(646\) −244383. + 88325.7i −0.585606 + 0.211652i
\(647\) 454122.i 1.08483i −0.840109 0.542417i \(-0.817509\pi\)
0.840109 0.542417i \(-0.182491\pi\)
\(648\) 0 0
\(649\) 253159. 0.601040
\(650\) −145956. 403835.i −0.345457 0.955823i
\(651\) 0 0
\(652\) −224233. 269687.i −0.527478 0.634402i
\(653\) −351238. −0.823712 −0.411856 0.911249i \(-0.635119\pi\)
−0.411856 + 0.911249i \(0.635119\pi\)
\(654\) 0 0
\(655\) 16606.6i 0.0387078i
\(656\) −100054. + 539016.i −0.232503 + 1.25255i
\(657\) 0 0
\(658\) −39960.3 110564.i −0.0922947 0.255364i
\(659\) 636361.i 1.46532i 0.680595 + 0.732660i \(0.261721\pi\)
−0.680595 + 0.732660i \(0.738279\pi\)
\(660\) 0 0
\(661\) −194949. −0.446188 −0.223094 0.974797i \(-0.571616\pi\)
−0.223094 + 0.974797i \(0.571616\pi\)
\(662\) −167342. + 60481.4i −0.381847 + 0.138009i
\(663\) 0 0
\(664\) −300894. + 513132.i −0.682461 + 1.16384i
\(665\) 36255.8 0.0819851
\(666\) 0 0
\(667\) 265400.i 0.596554i
\(668\) −38015.8 45721.8i −0.0851944 0.102464i
\(669\) 0 0
\(670\) −66747.9 + 24124.3i −0.148692 + 0.0537409i
\(671\) 338999.i 0.752928i
\(672\) 0 0
\(673\) −771557. −1.70348 −0.851742 0.523962i \(-0.824453\pi\)
−0.851742 + 0.523962i \(0.824453\pi\)
\(674\) 1598.59 + 4423.05i 0.00351899 + 0.00973648i
\(675\) 0 0
\(676\) −19934.2 + 16574.5i −0.0436220 + 0.0362699i
\(677\) −334198. −0.729166 −0.364583 0.931171i \(-0.618788\pi\)
−0.364583 + 0.931171i \(0.618788\pi\)
\(678\) 0 0
\(679\) 620016.i 1.34482i
\(680\) −62219.7 36484.9i −0.134558 0.0789032i
\(681\) 0 0
\(682\) −63747.5 176379.i −0.137055 0.379208i
\(683\) 452549.i 0.970117i −0.874482 0.485059i \(-0.838798\pi\)
0.874482 0.485059i \(-0.161202\pi\)
\(684\) 0 0
\(685\) −25353.1 −0.0540319
\(686\) 1.03595e6 374418.i 2.20137 0.795626i
\(687\) 0 0
\(688\) −155034. 28778.0i −0.327528 0.0607971i
\(689\) −804179. −1.69400
\(690\) 0 0
\(691\) 864703.i 1.81097i 0.424379 + 0.905485i \(0.360492\pi\)
−0.424379 + 0.905485i \(0.639508\pi\)
\(692\) −293174. + 243762.i −0.612228 + 0.509042i
\(693\) 0 0
\(694\) −301921. + 109121.i −0.626865 + 0.226564i
\(695\) 30810.3i 0.0637862i
\(696\) 0 0
\(697\) 907269. 1.86754
\(698\) 15174.5 + 41985.3i 0.0311461 + 0.0861761i
\(699\) 0 0
\(700\) −561827. 675713.i −1.14659 1.37901i
\(701\) 576160. 1.17249 0.586243 0.810136i \(-0.300607\pi\)
0.586243 + 0.810136i \(0.300607\pi\)
\(702\) 0 0
\(703\) 82146.2i 0.166217i
\(704\) −260799. + 145913.i −0.526212 + 0.294407i
\(705\) 0 0
\(706\) −319990. 885361.i −0.641989 1.77628i
\(707\) 1.31737e6i 2.63553i
\(708\) 0 0
\(709\) 506535. 1.00767 0.503834 0.863801i \(-0.331922\pi\)
0.503834 + 0.863801i \(0.331922\pi\)
\(710\) −64497.6 + 23310.9i −0.127946 + 0.0462427i
\(711\) 0 0
\(712\) −314948. 184682.i −0.621268 0.364304i
\(713\) 464901. 0.914496
\(714\) 0 0
\(715\) 33717.5i 0.0659544i
\(716\) 542719. + 652731.i 1.05864 + 1.27323i
\(717\) 0 0
\(718\) 531233. 192000.i 1.03047 0.372437i
\(719\) 521745.i 1.00925i 0.863338 + 0.504627i \(0.168370\pi\)
−0.863338 + 0.504627i \(0.831630\pi\)
\(720\) 0 0
\(721\) 772068. 1.48520
\(722\) −145218. 401795.i −0.278578 0.770780i
\(723\) 0 0
\(724\) 469050. 389995.i 0.894833 0.744016i
\(725\) −226694. −0.431284
\(726\) 0 0
\(727\) 26945.2i 0.0509815i −0.999675 0.0254908i \(-0.991885\pi\)
0.999675 0.0254908i \(-0.00811484\pi\)
\(728\) −499896. + 852500.i −0.943228 + 1.60854i
\(729\) 0 0
\(730\) −17128.3 47391.2i −0.0321417 0.0889307i
\(731\) 260952.i 0.488344i
\(732\) 0 0
\(733\) −672594. −1.25183 −0.625914 0.779892i \(-0.715274\pi\)
−0.625914 + 0.779892i \(0.715274\pi\)
\(734\) −239870. + 86694.7i −0.445229 + 0.160916i
\(735\) 0 0
\(736\) −120420. 730939.i −0.222302 1.34935i
\(737\) 486647. 0.895940
\(738\) 0 0
\(739\) 846279.i 1.54962i 0.632196 + 0.774809i \(0.282154\pi\)
−0.632196 + 0.774809i \(0.717846\pi\)
\(740\) 17532.6 14577.7i 0.0320172 0.0266210i
\(741\) 0 0
\(742\) −1.54777e6 + 559399.i −2.81124 + 1.01605i
\(743\) 713156.i 1.29183i −0.763407 0.645917i \(-0.776475\pi\)
0.763407 0.645917i \(-0.223525\pi\)
\(744\) 0 0
\(745\) −102502. −0.184680
\(746\) −162624. 449955.i −0.292219 0.808521i
\(747\) 0 0
\(748\) 316189. + 380283.i 0.565124 + 0.679679i
\(749\) −970602. −1.73013
\(750\) 0 0
\(751\) 1.09057e6i 1.93364i 0.255461 + 0.966819i \(0.417773\pi\)
−0.255461 + 0.966819i \(0.582227\pi\)
\(752\) 83229.0 + 15449.3i 0.147177 + 0.0273195i
\(753\) 0 0
\(754\) 86654.4 + 239758.i 0.152422 + 0.421727i
\(755\) 60950.4i 0.106926i
\(756\) 0 0
\(757\) 727090. 1.26881 0.634405 0.773001i \(-0.281245\pi\)
0.634405 + 0.773001i \(0.281245\pi\)
\(758\) −150547. + 54411.2i −0.262019 + 0.0947000i
\(759\) 0 0
\(760\) −13205.2 + 22519.6i −0.0228623 + 0.0389883i
\(761\) −377157. −0.651258 −0.325629 0.945498i \(-0.605576\pi\)
−0.325629 + 0.945498i \(0.605576\pi\)
\(762\) 0 0
\(763\) 1.11385e6i 1.91328i
\(764\) −200277. 240875.i −0.343119 0.412671i
\(765\) 0 0
\(766\) 737276. 266469.i 1.25653 0.454140i
\(767\) 602809.i 1.02468i
\(768\) 0 0
\(769\) −508831. −0.860440 −0.430220 0.902724i \(-0.641564\pi\)
−0.430220 + 0.902724i \(0.641564\pi\)
\(770\) −23454.4 64894.6i −0.0395588 0.109453i
\(771\) 0 0
\(772\) −129049. + 107299.i −0.216530 + 0.180036i
\(773\) −569650. −0.953344 −0.476672 0.879081i \(-0.658157\pi\)
−0.476672 + 0.879081i \(0.658157\pi\)
\(774\) 0 0
\(775\) 397099.i 0.661143i
\(776\) 385111. + 225825.i 0.639533 + 0.375014i
\(777\) 0 0
\(778\) 39903.1 + 110405.i 0.0659246 + 0.182402i
\(779\) 328375.i 0.541122i
\(780\) 0 0
\(781\) 470240. 0.770935
\(782\) −1.15296e6 + 416708.i −1.88539 + 0.681425i
\(783\) 0 0
\(784\) −256935. + 1.38417e6i −0.418014 + 2.25194i
\(785\) 68514.2 0.111184
\(786\) 0 0
\(787\) 911291.i 1.47132i −0.677350 0.735661i \(-0.736872\pi\)
0.677350