Properties

Label 405.4.b.e.244.11
Level $405$
Weight $4$
Character 405.244
Analytic conductor $23.896$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 91 x^{14} + 3268 x^{12} + 59128 x^{10} + 571975 x^{8} + 2881141 x^{6} + 6555196 x^{4} + 4069504 x^{2} + 614656\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{12}\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 244.11
Root \(2.46385i\) of defining polynomial
Character \(\chi\) \(=\) 405.244
Dual form 405.4.b.e.244.6

$q$-expansion

\(f(q)\) \(=\) \(q+2.46385i q^{2} +1.92944 q^{4} +(-0.0773702 - 11.1801i) q^{5} +19.2401i q^{7} +24.4647i q^{8} +O(q^{10})\) \(q+2.46385i q^{2} +1.92944 q^{4} +(-0.0773702 - 11.1801i) q^{5} +19.2401i q^{7} +24.4647i q^{8} +(27.5460 - 0.190629i) q^{10} +39.8548 q^{11} +1.00910i q^{13} -47.4048 q^{14} -44.8417 q^{16} -52.6170i q^{17} +49.5371 q^{19} +(-0.149282 - 21.5713i) q^{20} +98.1964i q^{22} +27.4019i q^{23} +(-124.988 + 1.73001i) q^{25} -2.48626 q^{26} +37.1228i q^{28} +254.953 q^{29} -168.656 q^{31} +85.2341i q^{32} +129.640 q^{34} +(215.106 - 1.48861i) q^{35} +419.938i q^{37} +122.052i q^{38} +(273.517 - 1.89284i) q^{40} +398.570 q^{41} +358.828i q^{43} +76.8977 q^{44} -67.5141 q^{46} -141.302i q^{47} -27.1829 q^{49} +(-4.26248 - 307.952i) q^{50} +1.94699i q^{52} +290.878i q^{53} +(-3.08358 - 445.580i) q^{55} -470.703 q^{56} +628.166i q^{58} -28.7319 q^{59} +732.727 q^{61} -415.544i q^{62} -568.737 q^{64} +(11.2818 - 0.0780740i) q^{65} +176.546i q^{67} -101.522i q^{68} +(3.66772 + 529.989i) q^{70} -802.814 q^{71} +512.820i q^{73} -1034.66 q^{74} +95.5791 q^{76} +766.813i q^{77} -612.348 q^{79} +(3.46941 + 501.333i) q^{80} +982.017i q^{82} +80.8162i q^{83} +(-588.262 + 4.07099i) q^{85} -884.098 q^{86} +975.035i q^{88} -24.0097 q^{89} -19.4151 q^{91} +52.8704i q^{92} +348.147 q^{94} +(-3.83270 - 553.828i) q^{95} -1367.92i q^{97} -66.9747i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 54 q^{4} - 3 q^{5} + O(q^{10}) \) \( 16 q - 54 q^{4} - 3 q^{5} - 10 q^{10} - 90 q^{11} + 102 q^{14} + 146 q^{16} - 4 q^{19} + 6 q^{20} - 71 q^{25} - 468 q^{26} + 516 q^{29} + 38 q^{31} - 212 q^{34} - 267 q^{35} - 44 q^{40} - 576 q^{41} + 1644 q^{44} - 290 q^{46} + 4 q^{49} - 558 q^{50} + 15 q^{55} - 2430 q^{56} + 2202 q^{59} + 20 q^{61} + 322 q^{64} - 339 q^{65} - 636 q^{70} - 2952 q^{71} + 4080 q^{74} - 396 q^{76} + 218 q^{79} + 1266 q^{80} + 704 q^{85} - 6108 q^{86} + 4074 q^{89} - 942 q^{91} + 1078 q^{94} + 1692 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.46385i 0.871102i 0.900164 + 0.435551i \(0.143447\pi\)
−0.900164 + 0.435551i \(0.856553\pi\)
\(3\) 0 0
\(4\) 1.92944 0.241181
\(5\) −0.0773702 11.1801i −0.00692020 0.999976i
\(6\) 0 0
\(7\) 19.2401i 1.03887i 0.854510 + 0.519435i \(0.173858\pi\)
−0.854510 + 0.519435i \(0.826142\pi\)
\(8\) 24.4647i 1.08120i
\(9\) 0 0
\(10\) 27.5460 0.190629i 0.871082 0.00602821i
\(11\) 39.8548 1.09243 0.546213 0.837646i \(-0.316069\pi\)
0.546213 + 0.837646i \(0.316069\pi\)
\(12\) 0 0
\(13\) 1.00910i 0.0215287i 0.999942 + 0.0107643i \(0.00342646\pi\)
−0.999942 + 0.0107643i \(0.996574\pi\)
\(14\) −47.4048 −0.904962
\(15\) 0 0
\(16\) −44.8417 −0.700651
\(17\) 52.6170i 0.750676i −0.926888 0.375338i \(-0.877527\pi\)
0.926888 0.375338i \(-0.122473\pi\)
\(18\) 0 0
\(19\) 49.5371 0.598136 0.299068 0.954232i \(-0.403324\pi\)
0.299068 + 0.954232i \(0.403324\pi\)
\(20\) −0.149282 21.5713i −0.00166902 0.241175i
\(21\) 0 0
\(22\) 98.1964i 0.951615i
\(23\) 27.4019i 0.248421i 0.992256 + 0.124210i \(0.0396398\pi\)
−0.992256 + 0.124210i \(0.960360\pi\)
\(24\) 0 0
\(25\) −124.988 + 1.73001i −0.999904 + 0.0138401i
\(26\) −2.48626 −0.0187537
\(27\) 0 0
\(28\) 37.1228i 0.250555i
\(29\) 254.953 1.63254 0.816269 0.577672i \(-0.196039\pi\)
0.816269 + 0.577672i \(0.196039\pi\)
\(30\) 0 0
\(31\) −168.656 −0.977147 −0.488574 0.872523i \(-0.662483\pi\)
−0.488574 + 0.872523i \(0.662483\pi\)
\(32\) 85.2341i 0.470856i
\(33\) 0 0
\(34\) 129.640 0.653916
\(35\) 215.106 1.48861i 1.03884 0.00718919i
\(36\) 0 0
\(37\) 419.938i 1.86588i 0.360038 + 0.932938i \(0.382764\pi\)
−0.360038 + 0.932938i \(0.617236\pi\)
\(38\) 122.052i 0.521038i
\(39\) 0 0
\(40\) 273.517 1.89284i 1.08117 0.00748209i
\(41\) 398.570 1.51820 0.759100 0.650974i \(-0.225639\pi\)
0.759100 + 0.650974i \(0.225639\pi\)
\(42\) 0 0
\(43\) 358.828i 1.27258i 0.771452 + 0.636288i \(0.219531\pi\)
−0.771452 + 0.636288i \(0.780469\pi\)
\(44\) 76.8977 0.263472
\(45\) 0 0
\(46\) −67.5141 −0.216400
\(47\) 141.302i 0.438532i −0.975665 0.219266i \(-0.929634\pi\)
0.975665 0.219266i \(-0.0703663\pi\)
\(48\) 0 0
\(49\) −27.1829 −0.0792505
\(50\) −4.26248 307.952i −0.0120561 0.871019i
\(51\) 0 0
\(52\) 1.94699i 0.00519230i
\(53\) 290.878i 0.753872i 0.926239 + 0.376936i \(0.123022\pi\)
−0.926239 + 0.376936i \(0.876978\pi\)
\(54\) 0 0
\(55\) −3.08358 445.580i −0.00755981 1.09240i
\(56\) −470.703 −1.12322
\(57\) 0 0
\(58\) 628.166i 1.42211i
\(59\) −28.7319 −0.0633995 −0.0316998 0.999497i \(-0.510092\pi\)
−0.0316998 + 0.999497i \(0.510092\pi\)
\(60\) 0 0
\(61\) 732.727 1.53797 0.768985 0.639267i \(-0.220762\pi\)
0.768985 + 0.639267i \(0.220762\pi\)
\(62\) 415.544i 0.851195i
\(63\) 0 0
\(64\) −568.737 −1.11082
\(65\) 11.2818 0.0780740i 0.0215282 0.000148983i
\(66\) 0 0
\(67\) 176.546i 0.321918i 0.986961 + 0.160959i \(0.0514587\pi\)
−0.986961 + 0.160959i \(0.948541\pi\)
\(68\) 101.522i 0.181049i
\(69\) 0 0
\(70\) 3.66772 + 529.989i 0.00626252 + 0.904940i
\(71\) −802.814 −1.34192 −0.670961 0.741493i \(-0.734118\pi\)
−0.670961 + 0.741493i \(0.734118\pi\)
\(72\) 0 0
\(73\) 512.820i 0.822205i 0.911589 + 0.411103i \(0.134856\pi\)
−0.911589 + 0.411103i \(0.865144\pi\)
\(74\) −1034.66 −1.62537
\(75\) 0 0
\(76\) 95.5791 0.144259
\(77\) 766.813i 1.13489i
\(78\) 0 0
\(79\) −612.348 −0.872082 −0.436041 0.899927i \(-0.643620\pi\)
−0.436041 + 0.899927i \(0.643620\pi\)
\(80\) 3.46941 + 501.333i 0.00484865 + 0.700635i
\(81\) 0 0
\(82\) 982.017i 1.32251i
\(83\) 80.8162i 0.106876i 0.998571 + 0.0534382i \(0.0170180\pi\)
−0.998571 + 0.0534382i \(0.982982\pi\)
\(84\) 0 0
\(85\) −588.262 + 4.07099i −0.750658 + 0.00519483i
\(86\) −884.098 −1.10854
\(87\) 0 0
\(88\) 975.035i 1.18113i
\(89\) −24.0097 −0.0285957 −0.0142979 0.999898i \(-0.504551\pi\)
−0.0142979 + 0.999898i \(0.504551\pi\)
\(90\) 0 0
\(91\) −19.4151 −0.0223655
\(92\) 52.8704i 0.0599143i
\(93\) 0 0
\(94\) 348.147 0.382006
\(95\) −3.83270 553.828i −0.00413922 0.598122i
\(96\) 0 0
\(97\) 1367.92i 1.43187i −0.698168 0.715934i \(-0.746001\pi\)
0.698168 0.715934i \(-0.253999\pi\)
\(98\) 66.9747i 0.0690353i
\(99\) 0 0
\(100\) −241.157 + 3.33796i −0.241157 + 0.00333796i
\(101\) 568.413 0.559992 0.279996 0.960001i \(-0.409667\pi\)
0.279996 + 0.960001i \(0.409667\pi\)
\(102\) 0 0
\(103\) 475.159i 0.454551i 0.973830 + 0.227276i \(0.0729818\pi\)
−0.973830 + 0.227276i \(0.927018\pi\)
\(104\) −24.6872 −0.0232767
\(105\) 0 0
\(106\) −716.680 −0.656700
\(107\) 1452.60i 1.31242i −0.754580 0.656208i \(-0.772159\pi\)
0.754580 0.656208i \(-0.227841\pi\)
\(108\) 0 0
\(109\) 1962.92 1.72490 0.862448 0.506146i \(-0.168930\pi\)
0.862448 + 0.506146i \(0.168930\pi\)
\(110\) 1097.84 7.59747i 0.951592 0.00658537i
\(111\) 0 0
\(112\) 862.760i 0.727886i
\(113\) 978.286i 0.814419i −0.913335 0.407210i \(-0.866502\pi\)
0.913335 0.407210i \(-0.133498\pi\)
\(114\) 0 0
\(115\) 306.355 2.12009i 0.248415 0.00171912i
\(116\) 491.918 0.393736
\(117\) 0 0
\(118\) 70.7910i 0.0552275i
\(119\) 1012.36 0.779855
\(120\) 0 0
\(121\) 257.409 0.193395
\(122\) 1805.33i 1.33973i
\(123\) 0 0
\(124\) −325.413 −0.235669
\(125\) 29.0120 + 1397.24i 0.0207593 + 0.999785i
\(126\) 0 0
\(127\) 865.941i 0.605038i −0.953143 0.302519i \(-0.902172\pi\)
0.953143 0.302519i \(-0.0978276\pi\)
\(128\) 719.411i 0.496778i
\(129\) 0 0
\(130\) 0.192363 + 27.7966i 0.000129779 + 0.0187532i
\(131\) −1468.96 −0.979720 −0.489860 0.871801i \(-0.662952\pi\)
−0.489860 + 0.871801i \(0.662952\pi\)
\(132\) 0 0
\(133\) 953.101i 0.621386i
\(134\) −434.983 −0.280424
\(135\) 0 0
\(136\) 1287.26 0.811628
\(137\) 71.5353i 0.0446108i 0.999751 + 0.0223054i \(0.00710061\pi\)
−0.999751 + 0.0223054i \(0.992899\pi\)
\(138\) 0 0
\(139\) −229.065 −0.139777 −0.0698886 0.997555i \(-0.522264\pi\)
−0.0698886 + 0.997555i \(0.522264\pi\)
\(140\) 415.035 2.87220i 0.250549 0.00173389i
\(141\) 0 0
\(142\) 1978.01i 1.16895i
\(143\) 40.2174i 0.0235185i
\(144\) 0 0
\(145\) −19.7258 2850.39i −0.0112975 1.63250i
\(146\) −1263.51 −0.716225
\(147\) 0 0
\(148\) 810.247i 0.450013i
\(149\) 835.144 0.459179 0.229589 0.973288i \(-0.426262\pi\)
0.229589 + 0.973288i \(0.426262\pi\)
\(150\) 0 0
\(151\) −1866.58 −1.00596 −0.502982 0.864297i \(-0.667764\pi\)
−0.502982 + 0.864297i \(0.667764\pi\)
\(152\) 1211.91i 0.646702i
\(153\) 0 0
\(154\) −1889.31 −0.988604
\(155\) 13.0490 + 1885.59i 0.00676206 + 0.977124i
\(156\) 0 0
\(157\) 2299.91i 1.16913i −0.811348 0.584563i \(-0.801266\pi\)
0.811348 0.584563i \(-0.198734\pi\)
\(158\) 1508.73i 0.759673i
\(159\) 0 0
\(160\) 952.923 6.59458i 0.470845 0.00325842i
\(161\) −527.215 −0.258077
\(162\) 0 0
\(163\) 44.9023i 0.0215768i −0.999942 0.0107884i \(-0.996566\pi\)
0.999942 0.0107884i \(-0.00343412\pi\)
\(164\) 769.019 0.366160
\(165\) 0 0
\(166\) −199.119 −0.0931002
\(167\) 1176.56i 0.545180i −0.962130 0.272590i \(-0.912120\pi\)
0.962130 0.272590i \(-0.0878803\pi\)
\(168\) 0 0
\(169\) 2195.98 0.999537
\(170\) −10.0303 1449.39i −0.00452523 0.653900i
\(171\) 0 0
\(172\) 692.339i 0.306921i
\(173\) 1068.09i 0.469396i −0.972068 0.234698i \(-0.924590\pi\)
0.972068 0.234698i \(-0.0754100\pi\)
\(174\) 0 0
\(175\) −33.2856 2404.79i −0.0143780 1.03877i
\(176\) −1787.16 −0.765410
\(177\) 0 0
\(178\) 59.1562i 0.0249098i
\(179\) 2779.66 1.16068 0.580339 0.814375i \(-0.302920\pi\)
0.580339 + 0.814375i \(0.302920\pi\)
\(180\) 0 0
\(181\) −3568.66 −1.46550 −0.732752 0.680496i \(-0.761764\pi\)
−0.732752 + 0.680496i \(0.761764\pi\)
\(182\) 47.8360i 0.0194826i
\(183\) 0 0
\(184\) −670.377 −0.268592
\(185\) 4694.94 32.4907i 1.86583 0.0129122i
\(186\) 0 0
\(187\) 2097.04i 0.820059i
\(188\) 272.634i 0.105765i
\(189\) 0 0
\(190\) 1364.55 9.44319i 0.521026 0.00360569i
\(191\) −3338.62 −1.26478 −0.632392 0.774648i \(-0.717927\pi\)
−0.632392 + 0.774648i \(0.717927\pi\)
\(192\) 0 0
\(193\) 1940.87i 0.723868i −0.932204 0.361934i \(-0.882117\pi\)
0.932204 0.361934i \(-0.117883\pi\)
\(194\) 3370.35 1.24730
\(195\) 0 0
\(196\) −52.4480 −0.0191137
\(197\) 1035.75i 0.374588i −0.982304 0.187294i \(-0.940028\pi\)
0.982304 0.187294i \(-0.0599717\pi\)
\(198\) 0 0
\(199\) −1565.53 −0.557675 −0.278838 0.960338i \(-0.589949\pi\)
−0.278838 + 0.960338i \(0.589949\pi\)
\(200\) −42.3241 3057.79i −0.0149638 1.08109i
\(201\) 0 0
\(202\) 1400.48i 0.487810i
\(203\) 4905.33i 1.69599i
\(204\) 0 0
\(205\) −30.8375 4456.04i −0.0105063 1.51816i
\(206\) −1170.72 −0.395961
\(207\) 0 0
\(208\) 45.2496i 0.0150841i
\(209\) 1974.29 0.653420
\(210\) 0 0
\(211\) 3385.27 1.10451 0.552255 0.833675i \(-0.313767\pi\)
0.552255 + 0.833675i \(0.313767\pi\)
\(212\) 561.234i 0.181819i
\(213\) 0 0
\(214\) 3579.00 1.14325
\(215\) 4011.72 27.7626i 1.27255 0.00880648i
\(216\) 0 0
\(217\) 3244.97i 1.01513i
\(218\) 4836.34i 1.50256i
\(219\) 0 0
\(220\) −5.94959 859.722i −0.00182328 0.263466i
\(221\) 53.0956 0.0161611
\(222\) 0 0
\(223\) 2365.54i 0.710352i −0.934799 0.355176i \(-0.884421\pi\)
0.934799 0.355176i \(-0.115579\pi\)
\(224\) −1639.92 −0.489158
\(225\) 0 0
\(226\) 2410.35 0.709443
\(227\) 976.230i 0.285439i −0.989763 0.142720i \(-0.954415\pi\)
0.989763 0.142720i \(-0.0455847\pi\)
\(228\) 0 0
\(229\) −1595.28 −0.460345 −0.230173 0.973150i \(-0.573929\pi\)
−0.230173 + 0.973150i \(0.573929\pi\)
\(230\) 5.22358 + 754.812i 0.00149753 + 0.216395i
\(231\) 0 0
\(232\) 6237.34i 1.76509i
\(233\) 943.571i 0.265302i 0.991163 + 0.132651i \(0.0423490\pi\)
−0.991163 + 0.132651i \(0.957651\pi\)
\(234\) 0 0
\(235\) −1579.77 + 10.9326i −0.438522 + 0.00303473i
\(236\) −55.4366 −0.0152907
\(237\) 0 0
\(238\) 2494.30i 0.679334i
\(239\) −2731.50 −0.739271 −0.369635 0.929177i \(-0.620517\pi\)
−0.369635 + 0.929177i \(0.620517\pi\)
\(240\) 0 0
\(241\) 3417.23 0.913375 0.456687 0.889627i \(-0.349036\pi\)
0.456687 + 0.889627i \(0.349036\pi\)
\(242\) 634.217i 0.168467i
\(243\) 0 0
\(244\) 1413.76 0.370928
\(245\) 2.10315 + 303.907i 0.000548430 + 0.0792486i
\(246\) 0 0
\(247\) 49.9877i 0.0128771i
\(248\) 4126.12i 1.05649i
\(249\) 0 0
\(250\) −3442.59 + 71.4812i −0.870915 + 0.0180835i
\(251\) −3164.50 −0.795782 −0.397891 0.917433i \(-0.630258\pi\)
−0.397891 + 0.917433i \(0.630258\pi\)
\(252\) 0 0
\(253\) 1092.10i 0.271382i
\(254\) 2133.55 0.527050
\(255\) 0 0
\(256\) −2777.38 −0.678071
\(257\) 5549.43i 1.34694i −0.739214 0.673471i \(-0.764803\pi\)
0.739214 0.673471i \(-0.235197\pi\)
\(258\) 0 0
\(259\) −8079.67 −1.93840
\(260\) 21.7675 0.150639i 0.00519218 3.59318e-5i
\(261\) 0 0
\(262\) 3619.29i 0.853436i
\(263\) 4137.64i 0.970106i −0.874485 0.485053i \(-0.838800\pi\)
0.874485 0.485053i \(-0.161200\pi\)
\(264\) 0 0
\(265\) 3252.04 22.5053i 0.753854 0.00521695i
\(266\) −2348.30 −0.541291
\(267\) 0 0
\(268\) 340.636i 0.0776404i
\(269\) 1026.74 0.232719 0.116359 0.993207i \(-0.462878\pi\)
0.116359 + 0.993207i \(0.462878\pi\)
\(270\) 0 0
\(271\) 3400.66 0.762270 0.381135 0.924519i \(-0.375533\pi\)
0.381135 + 0.924519i \(0.375533\pi\)
\(272\) 2359.44i 0.525962i
\(273\) 0 0
\(274\) −176.252 −0.0388605
\(275\) −4981.38 + 68.9493i −1.09232 + 0.0151193i
\(276\) 0 0
\(277\) 3568.81i 0.774112i 0.922056 + 0.387056i \(0.126508\pi\)
−0.922056 + 0.387056i \(0.873492\pi\)
\(278\) 564.381i 0.121760i
\(279\) 0 0
\(280\) 36.4184 + 5262.50i 0.00777292 + 1.12319i
\(281\) −6018.68 −1.27774 −0.638869 0.769316i \(-0.720597\pi\)
−0.638869 + 0.769316i \(0.720597\pi\)
\(282\) 0 0
\(283\) 4578.17i 0.961638i −0.876820 0.480819i \(-0.840339\pi\)
0.876820 0.480819i \(-0.159661\pi\)
\(284\) −1548.98 −0.323646
\(285\) 0 0
\(286\) −99.0895 −0.0204870
\(287\) 7668.55i 1.57721i
\(288\) 0 0
\(289\) 2144.45 0.436485
\(290\) 7022.94 48.6013i 1.42207 0.00984127i
\(291\) 0 0
\(292\) 989.457i 0.198300i
\(293\) 6479.73i 1.29198i 0.763346 + 0.645990i \(0.223555\pi\)
−0.763346 + 0.645990i \(0.776445\pi\)
\(294\) 0 0
\(295\) 2.22299 + 321.224i 0.000438737 + 0.0633980i
\(296\) −10273.6 −2.01738
\(297\) 0 0
\(298\) 2057.67i 0.399992i
\(299\) −27.6511 −0.00534818
\(300\) 0 0
\(301\) −6903.90 −1.32204
\(302\) 4598.98i 0.876297i
\(303\) 0 0
\(304\) −2221.33 −0.419085
\(305\) −56.6913 8191.95i −0.0106431 1.53793i
\(306\) 0 0
\(307\) 708.452i 0.131705i −0.997829 0.0658526i \(-0.979023\pi\)
0.997829 0.0658526i \(-0.0209767\pi\)
\(308\) 1479.52i 0.273713i
\(309\) 0 0
\(310\) −4645.81 + 32.1507i −0.851175 + 0.00589044i
\(311\) −6234.64 −1.13676 −0.568382 0.822765i \(-0.692430\pi\)
−0.568382 + 0.822765i \(0.692430\pi\)
\(312\) 0 0
\(313\) 2631.41i 0.475196i −0.971364 0.237598i \(-0.923640\pi\)
0.971364 0.237598i \(-0.0763600\pi\)
\(314\) 5666.63 1.01843
\(315\) 0 0
\(316\) −1181.49 −0.210329
\(317\) 502.534i 0.0890383i 0.999009 + 0.0445191i \(0.0141756\pi\)
−0.999009 + 0.0445191i \(0.985824\pi\)
\(318\) 0 0
\(319\) 10161.1 1.78343
\(320\) 44.0033 + 6358.53i 0.00768707 + 1.11079i
\(321\) 0 0
\(322\) 1298.98i 0.224812i
\(323\) 2606.49i 0.449007i
\(324\) 0 0
\(325\) −1.74575 126.125i −0.000297959 0.0215266i
\(326\) 110.632 0.0187956
\(327\) 0 0
\(328\) 9750.89i 1.64147i
\(329\) 2718.67 0.455578
\(330\) 0 0
\(331\) 3087.14 0.512642 0.256321 0.966592i \(-0.417490\pi\)
0.256321 + 0.966592i \(0.417490\pi\)
\(332\) 155.930i 0.0257765i
\(333\) 0 0
\(334\) 2898.87 0.474908
\(335\) 1973.80 13.6594i 0.321911 0.00222774i
\(336\) 0 0
\(337\) 5985.80i 0.967559i 0.875190 + 0.483780i \(0.160736\pi\)
−0.875190 + 0.483780i \(0.839264\pi\)
\(338\) 5410.57i 0.870699i
\(339\) 0 0
\(340\) −1135.02 + 7.85475i −0.181044 + 0.00125289i
\(341\) −6721.77 −1.06746
\(342\) 0 0
\(343\) 6076.36i 0.956539i
\(344\) −8778.60 −1.37590
\(345\) 0 0
\(346\) 2631.61 0.408892
\(347\) 1006.65i 0.155734i −0.996964 0.0778671i \(-0.975189\pi\)
0.996964 0.0778671i \(-0.0248110\pi\)
\(348\) 0 0
\(349\) 1949.36 0.298987 0.149494 0.988763i \(-0.452236\pi\)
0.149494 + 0.988763i \(0.452236\pi\)
\(350\) 5925.03 82.0108i 0.904875 0.0125247i
\(351\) 0 0
\(352\) 3396.99i 0.514376i
\(353\) 2591.73i 0.390776i 0.980726 + 0.195388i \(0.0625966\pi\)
−0.980726 + 0.195388i \(0.937403\pi\)
\(354\) 0 0
\(355\) 62.1139 + 8975.52i 0.00928637 + 1.34189i
\(356\) −46.3253 −0.00689674
\(357\) 0 0
\(358\) 6848.65i 1.01107i
\(359\) 605.954 0.0890837 0.0445418 0.999008i \(-0.485817\pi\)
0.0445418 + 0.999008i \(0.485817\pi\)
\(360\) 0 0
\(361\) −4405.08 −0.642233
\(362\) 8792.63i 1.27660i
\(363\) 0 0
\(364\) −37.4604 −0.00539412
\(365\) 5733.36 39.6770i 0.822186 0.00568983i
\(366\) 0 0
\(367\) 9760.26i 1.38823i 0.719863 + 0.694117i \(0.244205\pi\)
−0.719863 + 0.694117i \(0.755795\pi\)
\(368\) 1228.75i 0.174056i
\(369\) 0 0
\(370\) 80.0522 + 11567.6i 0.0112479 + 1.62533i
\(371\) −5596.54 −0.783175
\(372\) 0 0
\(373\) 7823.62i 1.08604i −0.839721 0.543018i \(-0.817281\pi\)
0.839721 0.543018i \(-0.182719\pi\)
\(374\) 5166.80 0.714355
\(375\) 0 0
\(376\) 3456.90 0.474139
\(377\) 257.272i 0.0351464i
\(378\) 0 0
\(379\) −2731.46 −0.370200 −0.185100 0.982720i \(-0.559261\pi\)
−0.185100 + 0.982720i \(0.559261\pi\)
\(380\) −7.39497 1068.58i −0.000998301 0.144255i
\(381\) 0 0
\(382\) 8225.85i 1.10176i
\(383\) 12599.9i 1.68100i −0.541812 0.840500i \(-0.682262\pi\)
0.541812 0.840500i \(-0.317738\pi\)
\(384\) 0 0
\(385\) 8573.02 59.3285i 1.13486 0.00785366i
\(386\) 4782.00 0.630563
\(387\) 0 0
\(388\) 2639.33i 0.345339i
\(389\) 4943.46 0.644327 0.322163 0.946684i \(-0.395590\pi\)
0.322163 + 0.946684i \(0.395590\pi\)
\(390\) 0 0
\(391\) 1441.80 0.186484
\(392\) 665.021i 0.0856853i
\(393\) 0 0
\(394\) 2551.92 0.326305
\(395\) 47.3775 + 6846.09i 0.00603499 + 0.872062i
\(396\) 0 0
\(397\) 7067.06i 0.893415i −0.894680 0.446707i \(-0.852597\pi\)
0.894680 0.446707i \(-0.147403\pi\)
\(398\) 3857.23i 0.485792i
\(399\) 0 0
\(400\) 5604.67 77.5765i 0.700584 0.00969707i
\(401\) −917.584 −0.114269 −0.0571346 0.998366i \(-0.518196\pi\)
−0.0571346 + 0.998366i \(0.518196\pi\)
\(402\) 0 0
\(403\) 170.190i 0.0210367i
\(404\) 1096.72 0.135059
\(405\) 0 0
\(406\) −12086.0 −1.47738
\(407\) 16736.6i 2.03833i
\(408\) 0 0
\(409\) −14735.5 −1.78148 −0.890739 0.454515i \(-0.849813\pi\)
−0.890739 + 0.454515i \(0.849813\pi\)
\(410\) 10979.0 75.9789i 1.32248 0.00915202i
\(411\) 0 0
\(412\) 916.792i 0.109629i
\(413\) 552.805i 0.0658638i
\(414\) 0 0
\(415\) 903.531 6.25277i 0.106874 0.000739606i
\(416\) −86.0094 −0.0101369
\(417\) 0 0
\(418\) 4864.36i 0.569196i
\(419\) 9254.92 1.07907 0.539537 0.841962i \(-0.318599\pi\)
0.539537 + 0.841962i \(0.318599\pi\)
\(420\) 0 0
\(421\) −10202.0 −1.18103 −0.590514 0.807027i \(-0.701075\pi\)
−0.590514 + 0.807027i \(0.701075\pi\)
\(422\) 8340.80i 0.962142i
\(423\) 0 0
\(424\) −7116.24 −0.815083
\(425\) 91.0279 + 6576.50i 0.0103894 + 0.750604i
\(426\) 0 0
\(427\) 14097.8i 1.59775i
\(428\) 2802.72i 0.316529i
\(429\) 0 0
\(430\) 68.4029 + 9884.28i 0.00767135 + 1.10852i
\(431\) 8057.20 0.900468 0.450234 0.892911i \(-0.351341\pi\)
0.450234 + 0.892911i \(0.351341\pi\)
\(432\) 0 0
\(433\) 4306.26i 0.477935i −0.971028 0.238967i \(-0.923191\pi\)
0.971028 0.238967i \(-0.0768089\pi\)
\(434\) 7995.12 0.884281
\(435\) 0 0
\(436\) 3787.34 0.416011
\(437\) 1357.41i 0.148590i
\(438\) 0 0
\(439\) 4721.79 0.513346 0.256673 0.966498i \(-0.417374\pi\)
0.256673 + 0.966498i \(0.417374\pi\)
\(440\) 10901.0 75.4387i 1.18110 0.00817363i
\(441\) 0 0
\(442\) 130.820i 0.0140779i
\(443\) 15354.4i 1.64675i −0.567501 0.823373i \(-0.692090\pi\)
0.567501 0.823373i \(-0.307910\pi\)
\(444\) 0 0
\(445\) 1.85763 + 268.430i 0.000197888 + 0.0285951i
\(446\) 5828.35 0.618790
\(447\) 0 0
\(448\) 10942.6i 1.15399i
\(449\) −5448.64 −0.572688 −0.286344 0.958127i \(-0.592440\pi\)
−0.286344 + 0.958127i \(0.592440\pi\)
\(450\) 0 0
\(451\) 15885.0 1.65852
\(452\) 1887.55i 0.196422i
\(453\) 0 0
\(454\) 2405.28 0.248647
\(455\) 1.50215 + 217.063i 0.000154774 + 0.0223650i
\(456\) 0 0
\(457\) 52.7307i 0.00539746i −0.999996 0.00269873i \(-0.999141\pi\)
0.999996 0.00269873i \(-0.000859033\pi\)
\(458\) 3930.53i 0.401008i
\(459\) 0 0
\(460\) 591.094 4.09059i 0.0599129 0.000414619i
\(461\) −3167.02 −0.319963 −0.159982 0.987120i \(-0.551143\pi\)
−0.159982 + 0.987120i \(0.551143\pi\)
\(462\) 0 0
\(463\) 13092.4i 1.31416i −0.753820 0.657081i \(-0.771791\pi\)
0.753820 0.657081i \(-0.228209\pi\)
\(464\) −11432.5 −1.14384
\(465\) 0 0
\(466\) −2324.82 −0.231105
\(467\) 13225.4i 1.31049i −0.755416 0.655246i \(-0.772565\pi\)
0.755416 0.655246i \(-0.227435\pi\)
\(468\) 0 0
\(469\) −3396.77 −0.334431
\(470\) −26.9362 3892.31i −0.00264356 0.381997i
\(471\) 0 0
\(472\) 702.915i 0.0685473i
\(473\) 14301.0i 1.39020i
\(474\) 0 0
\(475\) −6191.54 + 85.6996i −0.598079 + 0.00827825i
\(476\) 1953.29 0.188086
\(477\) 0 0
\(478\) 6729.99i 0.643981i
\(479\) 8558.59 0.816393 0.408196 0.912894i \(-0.366158\pi\)
0.408196 + 0.912894i \(0.366158\pi\)
\(480\) 0 0
\(481\) −423.758 −0.0401698
\(482\) 8419.55i 0.795643i
\(483\) 0 0
\(484\) 496.656 0.0466432
\(485\) −15293.4 + 105.836i −1.43183 + 0.00990882i
\(486\) 0 0
\(487\) 19531.3i 1.81735i 0.417506 + 0.908674i \(0.362904\pi\)
−0.417506 + 0.908674i \(0.637096\pi\)
\(488\) 17925.9i 1.66285i
\(489\) 0 0
\(490\) −748.782 + 5.18184i −0.0690337 + 0.000477738i
\(491\) −19488.2 −1.79122 −0.895612 0.444835i \(-0.853262\pi\)
−0.895612 + 0.444835i \(0.853262\pi\)
\(492\) 0 0
\(493\) 13414.9i 1.22551i
\(494\) −123.162 −0.0112173
\(495\) 0 0
\(496\) 7562.83 0.684640
\(497\) 15446.2i 1.39408i
\(498\) 0 0
\(499\) 339.530 0.0304598 0.0152299 0.999884i \(-0.495152\pi\)
0.0152299 + 0.999884i \(0.495152\pi\)
\(500\) 55.9770 + 2695.90i 0.00500674 + 0.241129i
\(501\) 0 0
\(502\) 7796.84i 0.693208i
\(503\) 5550.25i 0.491995i 0.969270 + 0.245998i \(0.0791156\pi\)
−0.969270 + 0.245998i \(0.920884\pi\)
\(504\) 0 0
\(505\) −43.9782 6354.90i −0.00387526 0.559979i
\(506\) −2690.76 −0.236401
\(507\) 0 0
\(508\) 1670.79i 0.145923i
\(509\) −5648.99 −0.491920 −0.245960 0.969280i \(-0.579103\pi\)
−0.245960 + 0.969280i \(0.579103\pi\)
\(510\) 0 0
\(511\) −9866.72 −0.854164
\(512\) 12598.3i 1.08745i
\(513\) 0 0
\(514\) 13673.0 1.17332
\(515\) 5312.31 36.7631i 0.454540 0.00314559i
\(516\) 0 0
\(517\) 5631.57i 0.479064i
\(518\) 19907.1i 1.68855i
\(519\) 0 0
\(520\) 1.91005 + 276.005i 0.000161080 + 0.0232762i
\(521\) −11159.0 −0.938359 −0.469180 0.883103i \(-0.655450\pi\)
−0.469180 + 0.883103i \(0.655450\pi\)
\(522\) 0 0
\(523\) 9476.61i 0.792320i −0.918182 0.396160i \(-0.870343\pi\)
0.918182 0.396160i \(-0.129657\pi\)
\(524\) −2834.27 −0.236289
\(525\) 0 0
\(526\) 10194.5 0.845062
\(527\) 8874.19i 0.733521i
\(528\) 0 0
\(529\) 11416.1 0.938287
\(530\) 55.4497 + 8012.54i 0.00454449 + 0.656684i
\(531\) 0 0
\(532\) 1838.95i 0.149866i
\(533\) 402.196i 0.0326849i
\(534\) 0 0
\(535\) −16240.2 + 112.388i −1.31238 + 0.00908218i
\(536\) −4319.14 −0.348057
\(537\) 0 0
\(538\) 2529.73i 0.202722i
\(539\) −1083.37 −0.0865754
\(540\) 0 0
\(541\) 8285.40 0.658442 0.329221 0.944253i \(-0.393214\pi\)
0.329221 + 0.944253i \(0.393214\pi\)
\(542\) 8378.71i 0.664015i
\(543\) 0 0
\(544\) 4484.76 0.353461
\(545\) −151.872 21945.6i −0.0119366 1.72485i
\(546\) 0 0
\(547\) 6918.30i 0.540777i −0.962751 0.270389i \(-0.912848\pi\)
0.962751 0.270389i \(-0.0871522\pi\)
\(548\) 138.023i 0.0107593i
\(549\) 0 0
\(550\) −169.881 12273.4i −0.0131704 0.951524i
\(551\) 12629.6 0.976480
\(552\) 0 0
\(553\) 11781.7i 0.905980i
\(554\) −8793.01 −0.674331
\(555\) 0 0
\(556\) −441.968 −0.0337115
\(557\) 15622.7i 1.18843i 0.804305 + 0.594216i \(0.202538\pi\)
−0.804305 + 0.594216i \(0.797462\pi\)
\(558\) 0 0
\(559\) −362.092 −0.0273969
\(560\) −9645.72 + 66.7519i −0.727868 + 0.00503712i
\(561\) 0 0
\(562\) 14829.1i 1.11304i
\(563\) 8129.30i 0.608542i 0.952585 + 0.304271i \(0.0984129\pi\)
−0.952585 + 0.304271i \(0.901587\pi\)
\(564\) 0 0
\(565\) −10937.3 + 75.6902i −0.814400 + 0.00563595i
\(566\) 11279.9 0.837686
\(567\) 0 0
\(568\) 19640.6i 1.45088i
\(569\) −8175.67 −0.602359 −0.301179 0.953568i \(-0.597380\pi\)
−0.301179 + 0.953568i \(0.597380\pi\)
\(570\) 0 0
\(571\) 7878.84 0.577442 0.288721 0.957413i \(-0.406770\pi\)
0.288721 + 0.957413i \(0.406770\pi\)
\(572\) 77.5972i 0.00567220i
\(573\) 0 0
\(574\) −18894.1 −1.37391
\(575\) −47.4055 3424.90i −0.00343816 0.248397i
\(576\) 0 0
\(577\) 16673.4i 1.20299i 0.798878 + 0.601493i \(0.205427\pi\)
−0.798878 + 0.601493i \(0.794573\pi\)
\(578\) 5283.60i 0.380223i
\(579\) 0 0
\(580\) −38.0598 5499.68i −0.00272474 0.393727i
\(581\) −1554.92 −0.111031
\(582\) 0 0
\(583\) 11592.9i 0.823549i
\(584\) −12546.0 −0.888965
\(585\) 0 0
\(586\) −15965.1 −1.12545
\(587\) 3012.18i 0.211799i −0.994377 0.105900i \(-0.966228\pi\)
0.994377 0.105900i \(-0.0337722\pi\)
\(588\) 0 0
\(589\) −8354.74 −0.584467
\(590\) −791.449 + 5.47712i −0.0552261 + 0.000382185i
\(591\) 0 0
\(592\) 18830.7i 1.30733i
\(593\) 7922.71i 0.548645i 0.961638 + 0.274323i \(0.0884536\pi\)
−0.961638 + 0.274323i \(0.911546\pi\)
\(594\) 0 0
\(595\) −78.3264 11318.2i −0.00539675 0.779836i
\(596\) 1611.36 0.110745
\(597\) 0 0
\(598\) 68.1282i 0.00465881i
\(599\) 22578.5 1.54012 0.770061 0.637970i \(-0.220226\pi\)
0.770061 + 0.637970i \(0.220226\pi\)
\(600\) 0 0
\(601\) 10618.7 0.720709 0.360354 0.932815i \(-0.382656\pi\)
0.360354 + 0.932815i \(0.382656\pi\)
\(602\) 17010.2i 1.15163i
\(603\) 0 0
\(604\) −3601.47 −0.242619
\(605\) −19.9158 2877.85i −0.00133833 0.193391i
\(606\) 0 0
\(607\) 13590.6i 0.908771i 0.890805 + 0.454385i \(0.150141\pi\)
−0.890805 + 0.454385i \(0.849859\pi\)
\(608\) 4222.25i 0.281636i
\(609\) 0 0
\(610\) 20183.7 139.679i 1.33970 0.00927119i
\(611\) 142.587 0.00944102
\(612\) 0 0
\(613\) 5457.57i 0.359591i −0.983704 0.179796i \(-0.942456\pi\)
0.983704 0.179796i \(-0.0575436\pi\)
\(614\) 1745.52 0.114729
\(615\) 0 0
\(616\) −18759.8 −1.22704
\(617\) 5972.10i 0.389672i 0.980836 + 0.194836i \(0.0624174\pi\)
−0.980836 + 0.194836i \(0.937583\pi\)
\(618\) 0 0
\(619\) 839.633 0.0545197 0.0272598 0.999628i \(-0.491322\pi\)
0.0272598 + 0.999628i \(0.491322\pi\)
\(620\) 25.1773 + 3638.14i 0.00163088 + 0.235663i
\(621\) 0 0
\(622\) 15361.2i 0.990238i
\(623\) 461.949i 0.0297072i
\(624\) 0 0
\(625\) 15619.0 432.461i 0.999617 0.0276775i
\(626\) 6483.41 0.413944
\(627\) 0 0
\(628\) 4437.55i 0.281970i
\(629\) 22095.9 1.40067
\(630\) 0 0
\(631\) −13699.4 −0.864284 −0.432142 0.901806i \(-0.642242\pi\)
−0.432142 + 0.901806i \(0.642242\pi\)
\(632\) 14980.9i 0.942892i
\(633\) 0 0
\(634\) −1238.17 −0.0775615
\(635\) −9681.28 + 66.9980i −0.605024 + 0.00418699i
\(636\) 0 0
\(637\) 27.4302i 0.00170616i
\(638\) 25035.5i 1.55355i
\(639\) 0 0
\(640\) −8043.07 + 55.6610i −0.496766 + 0.00343780i
\(641\) −7939.36 −0.489214 −0.244607 0.969622i \(-0.578659\pi\)
−0.244607 + 0.969622i \(0.578659\pi\)
\(642\) 0 0
\(643\) 7635.95i 0.468324i 0.972198 + 0.234162i \(0.0752347\pi\)
−0.972198 + 0.234162i \(0.924765\pi\)
\(644\) −1017.23 −0.0622432
\(645\) 0 0
\(646\) 6422.01 0.391131
\(647\) 22084.3i 1.34192i −0.741491 0.670962i \(-0.765881\pi\)
0.741491 0.670962i \(-0.234119\pi\)
\(648\) 0 0
\(649\) −1145.10 −0.0692593
\(650\) 310.753 4.30125i 0.0187519 0.000259552i
\(651\) 0 0
\(652\) 86.6364i 0.00520390i
\(653\) 6637.97i 0.397801i −0.980020 0.198900i \(-0.936263\pi\)
0.980020 0.198900i \(-0.0637370\pi\)
\(654\) 0 0
\(655\) 113.653 + 16423.0i 0.00677986 + 0.979696i
\(656\) −17872.6 −1.06373
\(657\) 0 0
\(658\) 6698.39i 0.396855i
\(659\) −23812.3 −1.40758 −0.703789 0.710409i \(-0.748510\pi\)
−0.703789 + 0.710409i \(0.748510\pi\)
\(660\) 0 0
\(661\) −999.824 −0.0588330 −0.0294165 0.999567i \(-0.509365\pi\)
−0.0294165 + 0.999567i \(0.509365\pi\)
\(662\) 7606.24i 0.446563i
\(663\) 0 0
\(664\) −1977.14 −0.115554
\(665\) 10655.7 73.7416i 0.621371 0.00430012i
\(666\) 0 0
\(667\) 6986.19i 0.405557i
\(668\) 2270.11i 0.131487i
\(669\) 0 0
\(670\) 33.6547 + 4863.14i 0.00194059 + 0.280417i
\(671\) 29202.7 1.68012
\(672\) 0 0
\(673\) 10622.1i 0.608396i −0.952609 0.304198i \(-0.901612\pi\)
0.952609 0.304198i \(-0.0983884\pi\)
\(674\) −14748.1 −0.842843
\(675\) 0 0
\(676\) 4237.02 0.241069
\(677\) 24907.8i 1.41401i 0.707209 + 0.707005i \(0.249954\pi\)
−0.707209 + 0.707005i \(0.750046\pi\)
\(678\) 0 0
\(679\) 26319.0 1.48753
\(680\) −99.5954 14391.6i −0.00561663 0.811608i
\(681\) 0 0
\(682\) 16561.4i 0.929868i
\(683\) 17115.6i 0.958874i −0.877576 0.479437i \(-0.840841\pi\)
0.877576 0.479437i \(-0.159159\pi\)
\(684\) 0 0
\(685\) 799.770 5.53470i 0.0446097 0.000308716i
\(686\) −14971.2 −0.833243
\(687\) 0 0
\(688\) 16090.5i 0.891632i
\(689\) −293.524 −0.0162299
\(690\) 0 0
\(691\) 28899.8 1.59103 0.795514 0.605935i \(-0.207201\pi\)
0.795514 + 0.605935i \(0.207201\pi\)
\(692\) 2060.82i 0.113209i
\(693\) 0 0
\(694\) 2480.23 0.135660
\(695\) 17.7228 + 2560.96i 0.000967286 + 0.139774i
\(696\) 0 0
\(697\) 20971.6i 1.13968i
\(698\) 4802.92i 0.260449i
\(699\) 0 0
\(700\) −64.2228 4639.90i −0.00346770 0.250531i
\(701\) 576.680 0.0310712 0.0155356 0.999879i \(-0.495055\pi\)
0.0155356 + 0.999879i \(0.495055\pi\)
\(702\) 0 0
\(703\) 20802.5i 1.11605i
\(704\) −22666.9 −1.21348
\(705\) 0 0
\(706\) −6385.63 −0.340406
\(707\) 10936.3i 0.581759i
\(708\) 0 0
\(709\) −5717.55 −0.302859 −0.151430 0.988468i \(-0.548388\pi\)
−0.151430 + 0.988468i \(0.548388\pi\)
\(710\) −22114.3 + 153.039i −1.16892 + 0.00808938i
\(711\) 0 0
\(712\) 587.389i 0.0309176i
\(713\) 4621.50i 0.242744i
\(714\) 0 0
\(715\) 449.633 3.11163i 0.0235179 0.000162753i
\(716\) 5363.19 0.279933
\(717\) 0 0
\(718\) 1492.98i 0.0776010i
\(719\) 14799.9 0.767655 0.383827 0.923405i \(-0.374606\pi\)
0.383827 + 0.923405i \(0.374606\pi\)
\(720\) 0 0
\(721\) −9142.12 −0.472219
\(722\) 10853.4i 0.559451i
\(723\) 0 0
\(724\) −6885.52 −0.353451
\(725\) −31866.1 + 441.071i −1.63238 + 0.0225944i
\(726\) 0 0
\(727\) 6410.40i 0.327027i 0.986541 + 0.163513i \(0.0522827\pi\)
−0.986541 + 0.163513i \(0.947717\pi\)
\(728\) 474.985i 0.0241815i
\(729\) 0 0
\(730\) 97.7581 + 14126.1i 0.00495642 + 0.716208i
\(731\) 18880.5 0.955292
\(732\) 0 0
\(733\) 17869.2i 0.900431i 0.892920 + 0.450215i \(0.148653\pi\)
−0.892920 + 0.450215i \(0.851347\pi\)
\(734\) −24047.8 −1.20929
\(735\) 0 0
\(736\) −2335.57 −0.116971
\(737\) 7036.21i 0.351672i
\(738\) 0 0
\(739\) −11099.7 −0.552516 −0.276258 0.961084i \(-0.589094\pi\)
−0.276258 + 0.961084i \(0.589094\pi\)
\(740\) 9058.62 62.6890i 0.450002 0.00311418i
\(741\) 0 0
\(742\) 13789.0i 0.682225i
\(743\) 10857.6i 0.536107i −0.963404 0.268053i \(-0.913620\pi\)
0.963404 0.268053i \(-0.0863803\pi\)
\(744\) 0 0
\(745\) −64.6153 9336.97i −0.00317761 0.459168i
\(746\) 19276.2 0.946049
\(747\) 0 0
\(748\) 4046.13i 0.197782i
\(749\) 27948.3 1.36343
\(750\) 0 0
\(751\) −32233.9 −1.56622 −0.783111 0.621882i \(-0.786368\pi\)
−0.783111 + 0.621882i \(0.786368\pi\)
\(752\) 6336.22i 0.307258i
\(753\) 0 0
\(754\) −633.880 −0.0306161
\(755\) 144.418 + 20868.5i 0.00696147 + 1.00594i
\(756\) 0 0
\(757\) 9410.28i 0.451813i −0.974149 0.225906i \(-0.927466\pi\)
0.974149 0.225906i \(-0.0725344\pi\)
\(758\) 6729.91i 0.322482i
\(759\) 0 0
\(760\) 13549.2 93.7656i 0.646687 0.00447531i
\(761\) 34767.1 1.65612 0.828060 0.560640i \(-0.189445\pi\)
0.828060 + 0.560640i \(0.189445\pi\)
\(762\) 0 0
\(763\) 37766.8i 1.79194i
\(764\) −6441.68 −0.305042
\(765\) 0 0
\(766\) 31044.2 1.46432
\(767\) 28.9932i 0.00136491i
\(768\) 0 0
\(769\) 29086.5 1.36396 0.681980 0.731371i \(-0.261119\pi\)
0.681980 + 0.731371i \(0.261119\pi\)
\(770\) 146.176 + 21122.6i 0.00684134 + 0.988581i
\(771\) 0 0
\(772\) 3744.79i 0.174583i
\(773\) 2942.77i 0.136927i 0.997654 + 0.0684633i \(0.0218096\pi\)
−0.997654 + 0.0684633i \(0.978190\pi\)
\(774\) 0 0
\(775\) 21080.0 291.777i 0.977054 0.0135238i
\(776\) 33465.7 1.54813
\(777\) 0 0
\(778\) 12179.9i 0.561275i
\(779\) 19744.0 0.908091
\(780\) 0 0
\(781\) −31996.0 −1.46595
\(782\) 3552.39i 0.162446i
\(783\) 0 0
\(784\) 1218.93 0.0555270
\(785\) −25713.2 + 177.944i −1.16910 + 0.00809059i
\(786\) 0 0
\(787\) 33829.1i 1.53225i 0.642693 + 0.766124i \(0.277817\pi\)
−0.642693 + 0.766124i \(0.722183\pi\)
\(788\) 1998.41i 0.0903434i
\(789\) 0 0
\(790\) −16867.7 + 116.731i −0.759655 + 0.00525709i
\(791\) 18822.4 0.846076
\(792\) 0 0
\(793\) 739.392i 0.0331105i
\(794\) 17412.2 0.778256