Properties

Label 99.3.l.a.71.3
Level $99$
Weight $3$
Character 99.71
Analytic conductor $2.698$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.l (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.69755461717\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 71.3
Character \(\chi\) \(=\) 99.71
Dual form 99.3.l.a.53.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.28527 + 0.417608i) q^{2} +(-1.75856 + 1.27767i) q^{4} +(-4.85485 - 1.57744i) q^{5} +(10.6531 - 7.73991i) q^{7} +(4.90400 - 6.74978i) q^{8} +O(q^{10})\) \(q+(-1.28527 + 0.417608i) q^{2} +(-1.75856 + 1.27767i) q^{4} +(-4.85485 - 1.57744i) q^{5} +(10.6531 - 7.73991i) q^{7} +(4.90400 - 6.74978i) q^{8} +6.89852 q^{10} +(-4.16151 - 10.1824i) q^{11} +(-0.825159 - 2.53958i) q^{13} +(-10.4598 + 14.3966i) q^{14} +(-0.797348 + 2.45398i) q^{16} +(16.3735 + 5.32007i) q^{17} +(-24.7742 - 17.9995i) q^{19} +(10.5530 - 3.42886i) q^{20} +(9.60091 + 11.3492i) q^{22} -15.5309i q^{23} +(0.855829 + 0.621796i) q^{25} +(2.12110 + 2.91944i) q^{26} +(-8.84500 + 27.2221i) q^{28} +(6.10287 + 8.39987i) q^{29} +(5.21245 + 16.0423i) q^{31} +29.8857i q^{32} -23.2660 q^{34} +(-63.9282 + 20.7715i) q^{35} +(-15.1698 + 11.0215i) q^{37} +(39.3582 + 12.7883i) q^{38} +(-34.4555 + 25.0334i) q^{40} +(-7.85173 + 10.8070i) q^{41} +10.5356 q^{43} +(20.3280 + 12.5893i) q^{44} +(6.48583 + 19.9613i) q^{46} +(48.3198 - 66.5065i) q^{47} +(38.4399 - 118.306i) q^{49} +(-1.35963 - 0.441772i) q^{50} +(4.69582 + 3.41171i) q^{52} +(-59.9022 + 19.4634i) q^{53} +(4.14138 + 55.9987i) q^{55} -109.862i q^{56} +(-11.3517 - 8.24747i) q^{58} +(38.7385 + 53.3189i) q^{59} +(11.2965 - 34.7670i) q^{61} +(-13.3988 - 18.4418i) q^{62} +(-15.6699 - 48.2271i) q^{64} +13.6309i q^{65} +60.5815 q^{67} +(-35.5909 + 11.5642i) q^{68} +(73.4904 - 53.3939i) q^{70} +(46.7818 + 15.2003i) q^{71} +(-5.15593 + 3.74600i) q^{73} +(14.8946 - 20.5007i) q^{74} +66.5643 q^{76} +(-123.144 - 76.2644i) q^{77} +(35.5533 + 109.422i) q^{79} +(7.74201 - 10.6560i) q^{80} +(5.57848 - 17.1688i) q^{82} +(-38.5111 - 12.5130i) q^{83} +(-71.0987 - 51.6562i) q^{85} +(-13.5411 + 4.39977i) q^{86} +(-89.1372 - 21.8454i) q^{88} -71.1308i q^{89} +(-28.4466 - 20.6676i) q^{91} +(19.8433 + 27.3120i) q^{92} +(-34.3301 + 105.657i) q^{94} +(91.8821 + 126.465i) q^{95} +(5.76879 + 17.7545i) q^{97} +168.107i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28527 + 0.417608i −0.642633 + 0.208804i −0.612163 0.790732i \(-0.709700\pi\)
−0.0304699 + 0.999536i \(0.509700\pi\)
\(3\) 0 0
\(4\) −1.75856 + 1.27767i −0.439639 + 0.319416i
\(5\) −4.85485 1.57744i −0.970970 0.315487i −0.219762 0.975553i \(-0.570528\pi\)
−0.751207 + 0.660066i \(0.770528\pi\)
\(6\) 0 0
\(7\) 10.6531 7.73991i 1.52187 1.10570i 0.561314 0.827603i \(-0.310296\pi\)
0.960553 0.278098i \(-0.0897040\pi\)
\(8\) 4.90400 6.74978i 0.613000 0.843722i
\(9\) 0 0
\(10\) 6.89852 0.689852
\(11\) −4.16151 10.1824i −0.378319 0.925675i
\(12\) 0 0
\(13\) −0.825159 2.53958i −0.0634737 0.195352i 0.914291 0.405059i \(-0.132749\pi\)
−0.977764 + 0.209707i \(0.932749\pi\)
\(14\) −10.4598 + 14.3966i −0.747127 + 1.02833i
\(15\) 0 0
\(16\) −0.797348 + 2.45398i −0.0498342 + 0.153374i
\(17\) 16.3735 + 5.32007i 0.963146 + 0.312945i 0.748046 0.663647i \(-0.230992\pi\)
0.215100 + 0.976592i \(0.430992\pi\)
\(18\) 0 0
\(19\) −24.7742 17.9995i −1.30391 0.947344i −0.303922 0.952697i \(-0.598296\pi\)
−0.999986 + 0.00535276i \(0.998296\pi\)
\(20\) 10.5530 3.42886i 0.527648 0.171443i
\(21\) 0 0
\(22\) 9.60091 + 11.3492i 0.436405 + 0.515875i
\(23\) 15.5309i 0.675257i −0.941279 0.337628i \(-0.890375\pi\)
0.941279 0.337628i \(-0.109625\pi\)
\(24\) 0 0
\(25\) 0.855829 + 0.621796i 0.0342332 + 0.0248718i
\(26\) 2.12110 + 2.91944i 0.0815806 + 0.112286i
\(27\) 0 0
\(28\) −8.84500 + 27.2221i −0.315893 + 0.972218i
\(29\) 6.10287 + 8.39987i 0.210444 + 0.289651i 0.901170 0.433465i \(-0.142709\pi\)
−0.690727 + 0.723116i \(0.742709\pi\)
\(30\) 0 0
\(31\) 5.21245 + 16.0423i 0.168144 + 0.517493i 0.999254 0.0386144i \(-0.0122944\pi\)
−0.831111 + 0.556107i \(0.812294\pi\)
\(32\) 29.8857i 0.933929i
\(33\) 0 0
\(34\) −23.2660 −0.684294
\(35\) −63.9282 + 20.7715i −1.82652 + 0.593473i
\(36\) 0 0
\(37\) −15.1698 + 11.0215i −0.409996 + 0.297879i −0.773600 0.633674i \(-0.781546\pi\)
0.363604 + 0.931553i \(0.381546\pi\)
\(38\) 39.3582 + 12.7883i 1.03574 + 0.336533i
\(39\) 0 0
\(40\) −34.4555 + 25.0334i −0.861388 + 0.625835i
\(41\) −7.85173 + 10.8070i −0.191506 + 0.263585i −0.893963 0.448141i \(-0.852086\pi\)
0.702457 + 0.711726i \(0.252086\pi\)
\(42\) 0 0
\(43\) 10.5356 0.245015 0.122507 0.992468i \(-0.460907\pi\)
0.122507 + 0.992468i \(0.460907\pi\)
\(44\) 20.3280 + 12.5893i 0.462000 + 0.286122i
\(45\) 0 0
\(46\) 6.48583 + 19.9613i 0.140996 + 0.433942i
\(47\) 48.3198 66.5065i 1.02808 1.41503i 0.121700 0.992567i \(-0.461165\pi\)
0.906380 0.422464i \(-0.138835\pi\)
\(48\) 0 0
\(49\) 38.4399 118.306i 0.784487 2.41440i
\(50\) −1.35963 0.441772i −0.0271927 0.00883544i
\(51\) 0 0
\(52\) 4.69582 + 3.41171i 0.0903042 + 0.0656098i
\(53\) −59.9022 + 19.4634i −1.13023 + 0.367234i −0.813663 0.581336i \(-0.802530\pi\)
−0.316567 + 0.948570i \(0.602530\pi\)
\(54\) 0 0
\(55\) 4.14138 + 55.9987i 0.0752978 + 1.01816i
\(56\) 109.862i 1.96183i
\(57\) 0 0
\(58\) −11.3517 8.24747i −0.195718 0.142198i
\(59\) 38.7385 + 53.3189i 0.656584 + 0.903711i 0.999362 0.0357057i \(-0.0113679\pi\)
−0.342778 + 0.939416i \(0.611368\pi\)
\(60\) 0 0
\(61\) 11.2965 34.7670i 0.185188 0.569951i −0.814763 0.579794i \(-0.803133\pi\)
0.999952 + 0.00984300i \(0.00313318\pi\)
\(62\) −13.3988 18.4418i −0.216109 0.297449i
\(63\) 0 0
\(64\) −15.6699 48.2271i −0.244843 0.753548i
\(65\) 13.6309i 0.209706i
\(66\) 0 0
\(67\) 60.5815 0.904202 0.452101 0.891967i \(-0.350675\pi\)
0.452101 + 0.891967i \(0.350675\pi\)
\(68\) −35.5909 + 11.5642i −0.523396 + 0.170062i
\(69\) 0 0
\(70\) 73.4904 53.3939i 1.04986 0.762770i
\(71\) 46.7818 + 15.2003i 0.658899 + 0.214089i 0.619334 0.785128i \(-0.287403\pi\)
0.0395649 + 0.999217i \(0.487403\pi\)
\(72\) 0 0
\(73\) −5.15593 + 3.74600i −0.0706291 + 0.0513151i −0.622540 0.782588i \(-0.713899\pi\)
0.551910 + 0.833903i \(0.313899\pi\)
\(74\) 14.8946 20.5007i 0.201278 0.277036i
\(75\) 0 0
\(76\) 66.5643 0.875846
\(77\) −123.144 76.2644i −1.59927 0.990447i
\(78\) 0 0
\(79\) 35.5533 + 109.422i 0.450042 + 1.38509i 0.876859 + 0.480748i \(0.159635\pi\)
−0.426817 + 0.904338i \(0.640365\pi\)
\(80\) 7.74201 10.6560i 0.0967751 0.133199i
\(81\) 0 0
\(82\) 5.57848 17.1688i 0.0680302 0.209375i
\(83\) −38.5111 12.5130i −0.463989 0.150759i 0.0676879 0.997707i \(-0.478438\pi\)
−0.531677 + 0.846947i \(0.678438\pi\)
\(84\) 0 0
\(85\) −71.0987 51.6562i −0.836455 0.607720i
\(86\) −13.5411 + 4.39977i −0.157454 + 0.0511601i
\(87\) 0 0
\(88\) −89.1372 21.8454i −1.01292 0.248243i
\(89\) 71.1308i 0.799222i −0.916685 0.399611i \(-0.869145\pi\)
0.916685 0.399611i \(-0.130855\pi\)
\(90\) 0 0
\(91\) −28.4466 20.6676i −0.312600 0.227117i
\(92\) 19.8433 + 27.3120i 0.215688 + 0.296869i
\(93\) 0 0
\(94\) −34.3301 + 105.657i −0.365214 + 1.12401i
\(95\) 91.8821 + 126.465i 0.967180 + 1.33121i
\(96\) 0 0
\(97\) 5.76879 + 17.7545i 0.0594721 + 0.183036i 0.976379 0.216065i \(-0.0693223\pi\)
−0.916907 + 0.399101i \(0.869322\pi\)
\(98\) 168.107i 1.71538i
\(99\) 0 0
\(100\) −2.29947 −0.0229947
\(101\) −44.7592 + 14.5432i −0.443161 + 0.143992i −0.522093 0.852888i \(-0.674849\pi\)
0.0789326 + 0.996880i \(0.474849\pi\)
\(102\) 0 0
\(103\) −90.1550 + 65.5015i −0.875292 + 0.635937i −0.932002 0.362454i \(-0.881939\pi\)
0.0567100 + 0.998391i \(0.481939\pi\)
\(104\) −21.1882 6.88445i −0.203732 0.0661966i
\(105\) 0 0
\(106\) 68.8622 50.0313i 0.649643 0.471993i
\(107\) 65.1737 89.7039i 0.609100 0.838354i −0.387403 0.921910i \(-0.626628\pi\)
0.996503 + 0.0835565i \(0.0266279\pi\)
\(108\) 0 0
\(109\) 118.337 1.08566 0.542832 0.839841i \(-0.317352\pi\)
0.542832 + 0.839841i \(0.317352\pi\)
\(110\) −28.7083 70.2437i −0.260984 0.638579i
\(111\) 0 0
\(112\) 10.4994 + 32.3139i 0.0937447 + 0.288517i
\(113\) −40.7594 + 56.1005i −0.360702 + 0.496464i −0.950344 0.311200i \(-0.899269\pi\)
0.589642 + 0.807665i \(0.299269\pi\)
\(114\) 0 0
\(115\) −24.4990 + 75.4002i −0.213035 + 0.655654i
\(116\) −21.4645 6.97423i −0.185038 0.0601226i
\(117\) 0 0
\(118\) −72.0557 52.3515i −0.610641 0.443657i
\(119\) 215.605 70.0542i 1.81180 0.588691i
\(120\) 0 0
\(121\) −86.3637 + 84.7486i −0.713749 + 0.700401i
\(122\) 49.4023i 0.404937i
\(123\) 0 0
\(124\) −29.6630 21.5515i −0.239218 0.173802i
\(125\) 71.8375 + 98.8758i 0.574700 + 0.791006i
\(126\) 0 0
\(127\) 3.32960 10.2475i 0.0262174 0.0806887i −0.937092 0.349083i \(-0.886493\pi\)
0.963309 + 0.268394i \(0.0864931\pi\)
\(128\) −29.9855 41.2716i −0.234262 0.322434i
\(129\) 0 0
\(130\) −5.69237 17.5193i −0.0437875 0.134764i
\(131\) 92.0724i 0.702843i 0.936217 + 0.351421i \(0.114302\pi\)
−0.936217 + 0.351421i \(0.885698\pi\)
\(132\) 0 0
\(133\) −403.236 −3.03185
\(134\) −77.8633 + 25.2993i −0.581070 + 0.188801i
\(135\) 0 0
\(136\) 116.205 84.4277i 0.854447 0.620792i
\(137\) 188.928 + 61.3865i 1.37904 + 0.448077i 0.902353 0.430998i \(-0.141838\pi\)
0.476685 + 0.879074i \(0.341838\pi\)
\(138\) 0 0
\(139\) 48.1649 34.9938i 0.346510 0.251754i −0.400894 0.916125i \(-0.631300\pi\)
0.747403 + 0.664371i \(0.231300\pi\)
\(140\) 85.8823 118.207i 0.613445 0.844335i
\(141\) 0 0
\(142\) −66.4748 −0.468133
\(143\) −22.4252 + 18.9706i −0.156819 + 0.132661i
\(144\) 0 0
\(145\) −16.3782 50.4070i −0.112953 0.347634i
\(146\) 5.06238 6.96776i 0.0346738 0.0477244i
\(147\) 0 0
\(148\) 12.5952 38.7640i 0.0851025 0.261919i
\(149\) −13.8516 4.50065i −0.0929636 0.0302057i 0.262166 0.965023i \(-0.415563\pi\)
−0.355129 + 0.934817i \(0.615563\pi\)
\(150\) 0 0
\(151\) 197.075 + 143.183i 1.30513 + 0.948234i 0.999992 0.00407377i \(-0.00129672\pi\)
0.305140 + 0.952307i \(0.401297\pi\)
\(152\) −242.986 + 78.9509i −1.59859 + 0.519414i
\(153\) 0 0
\(154\) 190.121 + 46.5941i 1.23455 + 0.302559i
\(155\) 86.1051i 0.555517i
\(156\) 0 0
\(157\) 89.8278 + 65.2637i 0.572151 + 0.415692i 0.835886 0.548903i \(-0.184954\pi\)
−0.263735 + 0.964595i \(0.584954\pi\)
\(158\) −91.3909 125.789i −0.578423 0.796131i
\(159\) 0 0
\(160\) 47.1428 145.091i 0.294643 0.906817i
\(161\) −120.208 165.452i −0.746632 1.02765i
\(162\) 0 0
\(163\) 38.0567 + 117.126i 0.233477 + 0.718567i 0.997320 + 0.0731653i \(0.0233101\pi\)
−0.763843 + 0.645402i \(0.776690\pi\)
\(164\) 29.0365i 0.177052i
\(165\) 0 0
\(166\) 54.7225 0.329654
\(167\) −217.801 + 70.7679i −1.30420 + 0.423760i −0.877040 0.480417i \(-0.840485\pi\)
−0.427159 + 0.904177i \(0.640485\pi\)
\(168\) 0 0
\(169\) 130.955 95.1446i 0.774883 0.562986i
\(170\) 112.953 + 36.7006i 0.664428 + 0.215886i
\(171\) 0 0
\(172\) −18.5275 + 13.4610i −0.107718 + 0.0782617i
\(173\) −101.498 + 139.699i −0.586691 + 0.807511i −0.994409 0.105597i \(-0.966325\pi\)
0.407718 + 0.913108i \(0.366325\pi\)
\(174\) 0 0
\(175\) 13.9298 0.0795991
\(176\) 28.3057 2.09335i 0.160828 0.0118940i
\(177\) 0 0
\(178\) 29.7048 + 91.4220i 0.166881 + 0.513607i
\(179\) 107.266 147.639i 0.599252 0.824800i −0.396387 0.918083i \(-0.629736\pi\)
0.995640 + 0.0932832i \(0.0297362\pi\)
\(180\) 0 0
\(181\) 37.6199 115.782i 0.207845 0.639680i −0.791740 0.610858i \(-0.790824\pi\)
0.999585 0.0288218i \(-0.00917553\pi\)
\(182\) 45.1924 + 14.6839i 0.248310 + 0.0806807i
\(183\) 0 0
\(184\) −104.830 76.1636i −0.569729 0.413932i
\(185\) 91.0330 29.5784i 0.492071 0.159883i
\(186\) 0 0
\(187\) −13.9672 188.861i −0.0746910 1.00995i
\(188\) 178.692i 0.950488i
\(189\) 0 0
\(190\) −170.906 124.170i −0.899503 0.653528i
\(191\) −184.809 254.368i −0.967588 1.33177i −0.943256 0.332067i \(-0.892254\pi\)
−0.0243324 0.999704i \(-0.507746\pi\)
\(192\) 0 0
\(193\) 38.4388 118.302i 0.199165 0.612966i −0.800738 0.599015i \(-0.795559\pi\)
0.999903 0.0139512i \(-0.00444094\pi\)
\(194\) −14.8289 20.4102i −0.0764374 0.105207i
\(195\) 0 0
\(196\) 83.5565 + 257.161i 0.426309 + 1.31204i
\(197\) 193.993i 0.984738i −0.870387 0.492369i \(-0.836131\pi\)
0.870387 0.492369i \(-0.163869\pi\)
\(198\) 0 0
\(199\) −67.6934 −0.340168 −0.170084 0.985430i \(-0.554404\pi\)
−0.170084 + 0.985430i \(0.554404\pi\)
\(200\) 8.39397 2.72737i 0.0419699 0.0136368i
\(201\) 0 0
\(202\) 51.4542 37.3837i 0.254724 0.185068i
\(203\) 130.028 + 42.2488i 0.640534 + 0.208122i
\(204\) 0 0
\(205\) 55.1663 40.0806i 0.269104 0.195515i
\(206\) 88.5193 121.836i 0.429705 0.591438i
\(207\) 0 0
\(208\) 6.89002 0.0331251
\(209\) −80.1807 + 327.167i −0.383640 + 1.56539i
\(210\) 0 0
\(211\) 23.1912 + 71.3752i 0.109911 + 0.338271i 0.990852 0.134955i \(-0.0430891\pi\)
−0.880941 + 0.473227i \(0.843089\pi\)
\(212\) 80.4736 110.762i 0.379593 0.522464i
\(213\) 0 0
\(214\) −46.3044 + 142.510i −0.216376 + 0.665936i
\(215\) −51.1489 16.6193i −0.237902 0.0772990i
\(216\) 0 0
\(217\) 179.694 + 130.556i 0.828084 + 0.601638i
\(218\) −152.095 + 49.4187i −0.697684 + 0.226691i
\(219\) 0 0
\(220\) −78.8304 93.1855i −0.358320 0.423570i
\(221\) 45.9716i 0.208016i
\(222\) 0 0
\(223\) 4.83651 + 3.51393i 0.0216884 + 0.0157575i 0.598577 0.801066i \(-0.295733\pi\)
−0.576888 + 0.816823i \(0.695733\pi\)
\(224\) 231.313 + 318.375i 1.03265 + 1.42132i
\(225\) 0 0
\(226\) 28.9586 89.1255i 0.128136 0.394361i
\(227\) 98.9713 + 136.222i 0.435997 + 0.600098i 0.969317 0.245815i \(-0.0790557\pi\)
−0.533320 + 0.845914i \(0.679056\pi\)
\(228\) 0 0
\(229\) −108.832 334.950i −0.475249 1.46267i −0.845622 0.533782i \(-0.820770\pi\)
0.370373 0.928883i \(-0.379230\pi\)
\(230\) 107.140i 0.465827i
\(231\) 0 0
\(232\) 86.6257 0.373387
\(233\) 338.664 110.039i 1.45349 0.472268i 0.527417 0.849606i \(-0.323160\pi\)
0.926076 + 0.377338i \(0.123160\pi\)
\(234\) 0 0
\(235\) −339.495 + 246.657i −1.44466 + 1.04961i
\(236\) −136.248 44.2695i −0.577320 0.187583i
\(237\) 0 0
\(238\) −247.854 + 180.077i −1.04140 + 0.756624i
\(239\) −10.2500 + 14.1079i −0.0428871 + 0.0590290i −0.829922 0.557879i \(-0.811615\pi\)
0.787035 + 0.616908i \(0.211615\pi\)
\(240\) 0 0
\(241\) −98.6722 −0.409428 −0.204714 0.978822i \(-0.565626\pi\)
−0.204714 + 0.978822i \(0.565626\pi\)
\(242\) 75.6086 144.991i 0.312432 0.599135i
\(243\) 0 0
\(244\) 24.5551 + 75.5728i 0.100636 + 0.309725i
\(245\) −373.239 + 513.720i −1.52343 + 2.09682i
\(246\) 0 0
\(247\) −25.2685 + 77.7686i −0.102302 + 0.314852i
\(248\) 133.844 + 43.4884i 0.539692 + 0.175357i
\(249\) 0 0
\(250\) −133.622 97.0818i −0.534486 0.388327i
\(251\) 168.627 54.7903i 0.671821 0.218288i 0.0468100 0.998904i \(-0.485094\pi\)
0.625011 + 0.780616i \(0.285094\pi\)
\(252\) 0 0
\(253\) −158.142 + 64.6320i −0.625068 + 0.255463i
\(254\) 14.5612i 0.0573275i
\(255\) 0 0
\(256\) 219.872 + 159.747i 0.858876 + 0.624010i
\(257\) −67.7862 93.2997i −0.263760 0.363034i 0.656511 0.754316i \(-0.272032\pi\)
−0.920271 + 0.391283i \(0.872032\pi\)
\(258\) 0 0
\(259\) −76.2997 + 234.826i −0.294593 + 0.906665i
\(260\) −17.4157 23.9707i −0.0669836 0.0921950i
\(261\) 0 0
\(262\) −38.4502 118.338i −0.146756 0.451670i
\(263\) 236.953i 0.900964i 0.892786 + 0.450482i \(0.148748\pi\)
−0.892786 + 0.450482i \(0.851252\pi\)
\(264\) 0 0
\(265\) 321.518 1.21328
\(266\) 518.266 168.395i 1.94837 0.633063i
\(267\) 0 0
\(268\) −106.536 + 77.4029i −0.397522 + 0.288817i
\(269\) −502.614 163.309i −1.86845 0.607097i −0.992104 0.125419i \(-0.959973\pi\)
−0.876348 0.481678i \(-0.840027\pi\)
\(270\) 0 0
\(271\) 144.762 105.176i 0.534178 0.388103i −0.287740 0.957708i \(-0.592904\pi\)
0.821918 + 0.569606i \(0.192904\pi\)
\(272\) −26.1107 + 35.9383i −0.0959953 + 0.132126i
\(273\) 0 0
\(274\) −268.458 −0.979775
\(275\) 2.76985 11.3020i 0.0100722 0.0410983i
\(276\) 0 0
\(277\) −88.4454 272.207i −0.319297 0.982696i −0.973949 0.226766i \(-0.927185\pi\)
0.654652 0.755930i \(-0.272815\pi\)
\(278\) −47.2910 + 65.0904i −0.170111 + 0.234138i
\(279\) 0 0
\(280\) −173.301 + 533.365i −0.618932 + 1.90488i
\(281\) −241.030 78.3155i −0.857760 0.278703i −0.153067 0.988216i \(-0.548915\pi\)
−0.704693 + 0.709513i \(0.748915\pi\)
\(282\) 0 0
\(283\) 229.170 + 166.502i 0.809788 + 0.588346i 0.913769 0.406234i \(-0.133158\pi\)
−0.103981 + 0.994579i \(0.533158\pi\)
\(284\) −101.689 + 33.0409i −0.358061 + 0.116341i
\(285\) 0 0
\(286\) 20.9000 33.7472i 0.0730769 0.117997i
\(287\) 175.899i 0.612889i
\(288\) 0 0
\(289\) 5.98182 + 4.34605i 0.0206983 + 0.0150382i
\(290\) 42.1008 + 57.9467i 0.145175 + 0.199816i
\(291\) 0 0
\(292\) 4.28085 13.1751i 0.0146604 0.0451202i
\(293\) 175.920 + 242.133i 0.600409 + 0.826393i 0.995746 0.0921437i \(-0.0293719\pi\)
−0.395336 + 0.918536i \(0.629372\pi\)
\(294\) 0 0
\(295\) −103.962 319.963i −0.352414 1.08462i
\(296\) 156.443i 0.528523i
\(297\) 0 0
\(298\) 19.6825 0.0660485
\(299\) −39.4419 + 12.8155i −0.131913 + 0.0428611i
\(300\) 0 0
\(301\) 112.237 81.5448i 0.372880 0.270913i
\(302\) −313.088 101.729i −1.03672 0.336849i
\(303\) 0 0
\(304\) 63.9243 46.4437i 0.210277 0.152775i
\(305\) −109.685 + 150.969i −0.359624 + 0.494980i
\(306\) 0 0
\(307\) 111.839 0.364296 0.182148 0.983271i \(-0.441695\pi\)
0.182148 + 0.983271i \(0.441695\pi\)
\(308\) 313.996 23.2215i 1.01947 0.0753946i
\(309\) 0 0
\(310\) 35.9582 + 110.668i 0.115994 + 0.356993i
\(311\) 209.419 288.240i 0.673372 0.926817i −0.326459 0.945211i \(-0.605855\pi\)
0.999831 + 0.0183943i \(0.00585541\pi\)
\(312\) 0 0
\(313\) 104.677 322.163i 0.334431 1.02927i −0.632570 0.774503i \(-0.718000\pi\)
0.967001 0.254771i \(-0.0820000\pi\)
\(314\) −142.707 46.3684i −0.454482 0.147670i
\(315\) 0 0
\(316\) −202.327 146.999i −0.640275 0.465187i
\(317\) 384.837 125.041i 1.21400 0.394452i 0.369105 0.929388i \(-0.379664\pi\)
0.844893 + 0.534936i \(0.179664\pi\)
\(318\) 0 0
\(319\) 60.1340 97.0982i 0.188508 0.304383i
\(320\) 258.853i 0.808917i
\(321\) 0 0
\(322\) 223.593 + 162.450i 0.694388 + 0.504502i
\(323\) −309.882 426.516i −0.959386 1.32048i
\(324\) 0 0
\(325\) 0.872904 2.68652i 0.00268586 0.00826623i
\(326\) −97.8259 134.646i −0.300080 0.413024i
\(327\) 0 0
\(328\) 34.4398 + 105.995i 0.104999 + 0.323155i
\(329\) 1082.49i 3.29024i
\(330\) 0 0
\(331\) 634.065 1.91561 0.957803 0.287426i \(-0.0927995\pi\)
0.957803 + 0.287426i \(0.0927995\pi\)
\(332\) 83.7113 27.1994i 0.252142 0.0819260i
\(333\) 0 0
\(334\) 250.379 181.911i 0.749639 0.544644i
\(335\) −294.114 95.5634i −0.877952 0.285264i
\(336\) 0 0
\(337\) −192.071 + 139.547i −0.569942 + 0.414087i −0.835084 0.550122i \(-0.814581\pi\)
0.265142 + 0.964209i \(0.414581\pi\)
\(338\) −128.579 + 176.974i −0.380412 + 0.523592i
\(339\) 0 0
\(340\) 191.030 0.561854
\(341\) 141.658 119.835i 0.415418 0.351424i
\(342\) 0 0
\(343\) −306.786 944.192i −0.894421 2.75275i
\(344\) 51.6667 71.1132i 0.150194 0.206724i
\(345\) 0 0
\(346\) 72.1117 221.937i 0.208415 0.641436i
\(347\) 463.624 + 150.641i 1.33609 + 0.434123i 0.887992 0.459859i \(-0.152100\pi\)
0.448102 + 0.893983i \(0.352100\pi\)
\(348\) 0 0
\(349\) −30.7829 22.3651i −0.0882033 0.0640834i 0.542810 0.839856i \(-0.317361\pi\)
−0.631013 + 0.775772i \(0.717361\pi\)
\(350\) −17.9036 + 5.81722i −0.0511530 + 0.0166206i
\(351\) 0 0
\(352\) 304.309 124.370i 0.864515 0.353323i
\(353\) 90.5379i 0.256481i 0.991743 + 0.128241i \(0.0409330\pi\)
−0.991743 + 0.128241i \(0.959067\pi\)
\(354\) 0 0
\(355\) −203.141 147.591i −0.572228 0.415748i
\(356\) 90.8813 + 125.087i 0.255285 + 0.351369i
\(357\) 0 0
\(358\) −76.2102 + 234.551i −0.212878 + 0.655170i
\(359\) 65.8242 + 90.5992i 0.183354 + 0.252366i 0.890793 0.454409i \(-0.150150\pi\)
−0.707439 + 0.706775i \(0.750150\pi\)
\(360\) 0 0
\(361\) 178.224 + 548.519i 0.493697 + 1.51944i
\(362\) 164.521i 0.454478i
\(363\) 0 0
\(364\) 76.4312 0.209976
\(365\) 30.9403 10.0531i 0.0847680 0.0275428i
\(366\) 0 0
\(367\) −274.088 + 199.136i −0.746833 + 0.542606i −0.894844 0.446380i \(-0.852713\pi\)
0.148010 + 0.988986i \(0.452713\pi\)
\(368\) 38.1126 + 12.3835i 0.103567 + 0.0336509i
\(369\) 0 0
\(370\) −104.649 + 76.0323i −0.282836 + 0.205493i
\(371\) −487.497 + 670.982i −1.31401 + 1.80858i
\(372\) 0 0
\(373\) −554.596 −1.48685 −0.743427 0.668818i \(-0.766801\pi\)
−0.743427 + 0.668818i \(0.766801\pi\)
\(374\) 96.8216 + 236.904i 0.258881 + 0.633434i
\(375\) 0 0
\(376\) −211.944 652.295i −0.563680 1.73483i
\(377\) 16.2963 22.4299i 0.0432262 0.0594958i
\(378\) 0 0
\(379\) −77.6587 + 239.009i −0.204904 + 0.630631i 0.794813 + 0.606854i \(0.207569\pi\)
−0.999717 + 0.0237762i \(0.992431\pi\)
\(380\) −323.160 105.001i −0.850420 0.276318i
\(381\) 0 0
\(382\) 343.755 + 249.753i 0.899883 + 0.653804i
\(383\) −489.046 + 158.901i −1.27688 + 0.414885i −0.867481 0.497470i \(-0.834263\pi\)
−0.409402 + 0.912354i \(0.634263\pi\)
\(384\) 0 0
\(385\) 477.543 + 564.504i 1.24037 + 1.46624i
\(386\) 168.102i 0.435499i
\(387\) 0 0
\(388\) −32.8291 23.8517i −0.0846110 0.0614735i
\(389\) 114.119 + 157.071i 0.293365 + 0.403782i 0.930103 0.367298i \(-0.119717\pi\)
−0.636739 + 0.771080i \(0.719717\pi\)
\(390\) 0 0
\(391\) 82.6254 254.295i 0.211318 0.650371i
\(392\) −610.028 839.632i −1.55619 2.14192i
\(393\) 0 0
\(394\) 81.0132 + 249.333i 0.205617 + 0.632825i
\(395\) 587.309i 1.48686i
\(396\) 0 0
\(397\) −260.248 −0.655537 −0.327769 0.944758i \(-0.606297\pi\)
−0.327769 + 0.944758i \(0.606297\pi\)
\(398\) 87.0041 28.2693i 0.218603 0.0710285i
\(399\) 0 0
\(400\) −2.20827 + 1.60440i −0.00552068 + 0.00401101i
\(401\) 360.802 + 117.232i 0.899755 + 0.292348i 0.722136 0.691751i \(-0.243160\pi\)
0.177619 + 0.984099i \(0.443160\pi\)
\(402\) 0 0
\(403\) 36.4395 26.4748i 0.0904206 0.0656944i
\(404\) 60.1303 82.7623i 0.148837 0.204857i
\(405\) 0 0
\(406\) −184.765 −0.455085
\(407\) 175.355 + 108.600i 0.430849 + 0.266829i
\(408\) 0 0
\(409\) 210.768 + 648.678i 0.515326 + 1.58601i 0.782688 + 0.622415i \(0.213848\pi\)
−0.267362 + 0.963596i \(0.586152\pi\)
\(410\) −54.1653 + 74.5522i −0.132111 + 0.181835i
\(411\) 0 0
\(412\) 74.8537 230.376i 0.181684 0.559165i
\(413\) 825.367 + 268.178i 1.99847 + 0.649342i
\(414\) 0 0
\(415\) 167.227 + 121.497i 0.402956 + 0.292765i
\(416\) 75.8971 24.6605i 0.182445 0.0592800i
\(417\) 0 0
\(418\) −33.5741 453.981i −0.0803209 1.08608i
\(419\) 275.319i 0.657085i 0.944489 + 0.328543i \(0.106557\pi\)
−0.944489 + 0.328543i \(0.893443\pi\)
\(420\) 0 0
\(421\) −98.2710 71.3981i −0.233423 0.169592i 0.464925 0.885350i \(-0.346081\pi\)
−0.698348 + 0.715758i \(0.746081\pi\)
\(422\) −59.6138 82.0513i −0.141265 0.194434i
\(423\) 0 0
\(424\) −162.387 + 499.775i −0.382988 + 1.17871i
\(425\) 10.7049 + 14.7340i 0.0251880 + 0.0346683i
\(426\) 0 0
\(427\) −148.751 457.809i −0.348363 1.07215i
\(428\) 241.019i 0.563130i
\(429\) 0 0
\(430\) 72.6803 0.169024
\(431\) 93.9131 30.5142i 0.217896 0.0707987i −0.198035 0.980195i \(-0.563456\pi\)
0.415931 + 0.909396i \(0.363456\pi\)
\(432\) 0 0
\(433\) −453.043 + 329.155i −1.04629 + 0.760173i −0.971503 0.237027i \(-0.923827\pi\)
−0.0747851 + 0.997200i \(0.523827\pi\)
\(434\) −285.476 92.7568i −0.657779 0.213725i
\(435\) 0 0
\(436\) −208.103 + 151.196i −0.477301 + 0.346779i
\(437\) −279.549 + 384.766i −0.639701 + 0.880472i
\(438\) 0 0
\(439\) −577.439 −1.31535 −0.657676 0.753301i \(-0.728460\pi\)
−0.657676 + 0.753301i \(0.728460\pi\)
\(440\) 398.288 + 246.664i 0.905200 + 0.560600i
\(441\) 0 0
\(442\) 19.1981 + 59.0857i 0.0434347 + 0.133678i
\(443\) −51.3607 + 70.6919i −0.115938 + 0.159575i −0.863042 0.505132i \(-0.831444\pi\)
0.747104 + 0.664707i \(0.231444\pi\)
\(444\) 0 0
\(445\) −112.204 + 345.329i −0.252144 + 0.776021i
\(446\) −7.68364 2.49657i −0.0172279 0.00559768i
\(447\) 0 0
\(448\) −540.206 392.482i −1.20582 0.876077i
\(449\) 91.5004 29.7303i 0.203787 0.0662145i −0.205345 0.978690i \(-0.565832\pi\)
0.409132 + 0.912475i \(0.365832\pi\)
\(450\) 0 0
\(451\) 142.716 + 34.9763i 0.316444 + 0.0775528i
\(452\) 150.733i 0.333479i
\(453\) 0 0
\(454\) −184.092 133.751i −0.405489 0.294605i
\(455\) 105.502 + 145.211i 0.231872 + 0.319145i
\(456\) 0 0
\(457\) −213.774 + 657.929i −0.467777 + 1.43967i 0.387679 + 0.921794i \(0.373277\pi\)
−0.855456 + 0.517875i \(0.826723\pi\)
\(458\) 279.756 + 385.051i 0.610821 + 0.840723i
\(459\) 0 0
\(460\) −53.2534 163.897i −0.115768 0.356298i
\(461\) 70.5491i 0.153035i 0.997068 + 0.0765175i \(0.0243801\pi\)
−0.997068 + 0.0765175i \(0.975620\pi\)
\(462\) 0 0
\(463\) 248.292 0.536267 0.268134 0.963382i \(-0.413593\pi\)
0.268134 + 0.963382i \(0.413593\pi\)
\(464\) −25.4793 + 8.27872i −0.0549122 + 0.0178421i
\(465\) 0 0
\(466\) −389.320 + 282.858i −0.835451 + 0.606991i
\(467\) −241.718 78.5391i −0.517598 0.168178i 0.0385567 0.999256i \(-0.487724\pi\)
−0.556155 + 0.831078i \(0.687724\pi\)
\(468\) 0 0
\(469\) 645.379 468.895i 1.37607 0.999776i
\(470\) 333.335 458.796i 0.709223 0.976162i
\(471\) 0 0
\(472\) 549.864 1.16497
\(473\) −43.8441 107.278i −0.0926937 0.226804i
\(474\) 0 0
\(475\) −10.0105 30.8091i −0.0210747 0.0648612i
\(476\) −289.647 + 398.665i −0.608502 + 0.837531i
\(477\) 0 0
\(478\) 7.28241 22.4129i 0.0152352 0.0468890i
\(479\) −17.3840 5.64840i −0.0362922 0.0117921i 0.290815 0.956779i \(-0.406074\pi\)
−0.327107 + 0.944987i \(0.606074\pi\)
\(480\) 0 0
\(481\) 40.5076 + 29.4305i 0.0842153 + 0.0611860i
\(482\) 126.820 41.2063i 0.263112 0.0854903i
\(483\) 0 0
\(484\) 43.5950 259.379i 0.0900723 0.535907i
\(485\) 95.2954i 0.196485i
\(486\) 0 0
\(487\) 196.895 + 143.052i 0.404302 + 0.293742i 0.771291 0.636483i \(-0.219611\pi\)
−0.366989 + 0.930225i \(0.619611\pi\)
\(488\) −179.272 246.746i −0.367360 0.505627i
\(489\) 0 0
\(490\) 265.178 816.135i 0.541180 1.66558i
\(491\) 185.960 + 255.952i 0.378738 + 0.521288i 0.955250 0.295801i \(-0.0955866\pi\)
−0.576512 + 0.817089i \(0.695587\pi\)
\(492\) 0 0
\(493\) 55.2373 + 170.003i 0.112043 + 0.344833i
\(494\) 110.506i 0.223696i
\(495\) 0 0
\(496\) −43.5236 −0.0877493
\(497\) 616.019 200.157i 1.23947 0.402730i
\(498\) 0 0
\(499\) −21.6847 + 15.7549i −0.0434563 + 0.0315728i −0.609301 0.792939i \(-0.708550\pi\)
0.565845 + 0.824512i \(0.308550\pi\)
\(500\) −252.660 82.0943i −0.505321 0.164189i
\(501\) 0 0
\(502\) −193.850 + 140.840i −0.386155 + 0.280558i
\(503\) 107.344 147.746i 0.213408 0.293730i −0.688871 0.724884i \(-0.741893\pi\)
0.902278 + 0.431154i \(0.141893\pi\)
\(504\) 0 0
\(505\) 240.240 0.475723
\(506\) 176.264 149.111i 0.348348 0.294686i
\(507\) 0 0
\(508\) 7.23754 + 22.2749i 0.0142471 + 0.0438482i
\(509\) −127.165 + 175.027i −0.249832 + 0.343864i −0.915452 0.402426i \(-0.868167\pi\)
0.665620 + 0.746290i \(0.268167\pi\)
\(510\) 0 0
\(511\) −25.9327 + 79.8128i −0.0507490 + 0.156189i
\(512\) −155.235 50.4390i −0.303194 0.0985137i
\(513\) 0 0
\(514\) 126.086 + 91.6069i 0.245304 + 0.178223i
\(515\) 541.013 175.786i 1.05051 0.341332i
\(516\) 0 0
\(517\) −878.280 215.245i −1.69880 0.416335i
\(518\) 333.678i 0.644165i
\(519\) 0 0
\(520\) 92.0055 + 66.8459i 0.176934 + 0.128550i
\(521\) −335.736 462.102i −0.644408 0.886951i 0.354433 0.935081i \(-0.384674\pi\)
−0.998841 + 0.0481300i \(0.984674\pi\)
\(522\) 0 0
\(523\) 237.156 729.890i 0.453453 1.39558i −0.419490 0.907760i \(-0.637791\pi\)
0.872942 0.487824i \(-0.162209\pi\)
\(524\) −117.638 161.914i −0.224500 0.308997i
\(525\) 0 0
\(526\) −98.9537 304.548i −0.188125 0.578989i
\(527\) 290.398i 0.551041i
\(528\) 0 0
\(529\) 287.791 0.544028
\(530\) −413.237 + 134.269i −0.779692 + 0.253337i
\(531\) 0 0
\(532\) 709.114 515.201i 1.33292 0.968424i
\(533\) 33.9241 + 11.0226i 0.0636474 + 0.0206803i
\(534\) 0 0
\(535\) −457.910 + 332.691i −0.855907 + 0.621853i
\(536\) 297.092 408.912i 0.554276 0.762895i
\(537\) 0 0
\(538\) 714.191 1.32749
\(539\) −1364.61 + 100.919i −2.53174 + 0.187235i
\(540\) 0 0
\(541\) 63.5980 + 195.735i 0.117556 + 0.361801i 0.992472 0.122475i \(-0.0390830\pi\)
−0.874915 + 0.484276i \(0.839083\pi\)
\(542\) −142.136 + 195.633i −0.262243 + 0.360946i
\(543\) 0 0
\(544\) −158.994 + 489.333i −0.292269 + 0.899510i
\(545\) −574.510 186.670i −1.05415 0.342513i
\(546\) 0 0
\(547\) −352.204 255.891i −0.643883 0.467808i 0.217299 0.976105i \(-0.430275\pi\)
−0.861182 + 0.508297i \(0.830275\pi\)
\(548\) −410.672 + 133.435i −0.749402 + 0.243495i
\(549\) 0 0
\(550\) 1.15982 + 15.6828i 0.00210877 + 0.0285142i
\(551\) 317.949i 0.577040i
\(552\) 0 0
\(553\) 1225.67 + 890.498i 2.21639 + 1.61030i
\(554\) 227.352 + 312.923i 0.410382 + 0.564842i
\(555\) 0 0
\(556\) −39.9902 + 123.077i −0.0719248 + 0.221362i
\(557\) 434.244 + 597.686i 0.779612 + 1.07304i 0.995325 + 0.0965873i \(0.0307927\pi\)
−0.215712 + 0.976457i \(0.569207\pi\)
\(558\) 0 0
\(559\) −8.69356 26.7560i −0.0155520 0.0478641i
\(560\) 173.441i 0.309716i
\(561\) 0 0
\(562\) 342.493 0.609419
\(563\) −62.6356 + 20.3515i −0.111253 + 0.0361484i −0.364115 0.931354i \(-0.618628\pi\)
0.252861 + 0.967503i \(0.418628\pi\)
\(564\) 0 0
\(565\) 286.376 208.064i 0.506859 0.368255i
\(566\) −364.077 118.296i −0.643246 0.209003i
\(567\) 0 0
\(568\) 332.017 241.224i 0.584537 0.424691i
\(569\) 410.063 564.404i 0.720673 0.991922i −0.278828 0.960341i \(-0.589946\pi\)
0.999501 0.0315808i \(-0.0100541\pi\)
\(570\) 0 0
\(571\) −256.388 −0.449017 −0.224508 0.974472i \(-0.572078\pi\)
−0.224508 + 0.974472i \(0.572078\pi\)
\(572\) 15.1978 62.0127i 0.0265696 0.108414i
\(573\) 0 0
\(574\) −73.4569 226.077i −0.127974 0.393862i
\(575\) 9.65705 13.2918i 0.0167949 0.0231162i
\(576\) 0 0
\(577\) 140.575 432.646i 0.243631 0.749819i −0.752227 0.658903i \(-0.771021\pi\)
0.995859 0.0909159i \(-0.0289794\pi\)
\(578\) −9.50317 3.08777i −0.0164415 0.00534216i
\(579\) 0 0
\(580\) 93.2053 + 67.7176i 0.160699 + 0.116755i
\(581\) −507.110 + 164.770i −0.872823 + 0.283598i
\(582\) 0 0
\(583\) 447.468 + 528.952i 0.767527 + 0.907294i
\(584\) 53.1718i 0.0910475i
\(585\) 0 0
\(586\) −327.221 237.740i −0.558397 0.405699i
\(587\) −64.8291 89.2295i −0.110441 0.152009i 0.750218 0.661190i \(-0.229948\pi\)
−0.860660 + 0.509181i \(0.829948\pi\)
\(588\) 0 0
\(589\) 159.619 491.257i 0.271000 0.834052i
\(590\) 267.238 + 367.822i 0.452946 + 0.623427i
\(591\) 0 0
\(592\) −14.9510 46.0146i −0.0252551 0.0777273i
\(593\) 250.416i 0.422287i 0.977455 + 0.211144i \(0.0677188\pi\)
−0.977455 + 0.211144i \(0.932281\pi\)
\(594\) 0 0
\(595\) −1157.23 −1.94493
\(596\) 30.1091 9.78303i 0.0505186 0.0164145i
\(597\) 0 0
\(598\) 45.3415 32.9425i 0.0758219 0.0550879i
\(599\) 271.473 + 88.2069i 0.453210 + 0.147257i 0.526722 0.850037i \(-0.323421\pi\)
−0.0735122 + 0.997294i \(0.523421\pi\)
\(600\) 0 0
\(601\) 180.803 131.361i 0.300836 0.218570i −0.427118 0.904196i \(-0.640471\pi\)
0.727954 + 0.685625i \(0.240471\pi\)
\(602\) −110.200 + 151.678i −0.183057 + 0.251956i
\(603\) 0 0
\(604\) −529.508 −0.876668
\(605\) 552.968 275.208i 0.913997 0.454890i
\(606\) 0 0
\(607\) 295.069 + 908.129i 0.486110 + 1.49609i 0.830367 + 0.557218i \(0.188131\pi\)
−0.344256 + 0.938876i \(0.611869\pi\)
\(608\) 537.929 740.396i 0.884752 1.21776i
\(609\) 0 0
\(610\) 77.9290 239.841i 0.127752 0.393182i
\(611\) −208.770 67.8334i −0.341685 0.111020i
\(612\) 0 0
\(613\) 275.176 + 199.927i 0.448901 + 0.326146i 0.789162 0.614185i \(-0.210515\pi\)
−0.340261 + 0.940331i \(0.610515\pi\)
\(614\) −143.743 + 46.7048i −0.234108 + 0.0760664i
\(615\) 0 0
\(616\) −1118.67 + 457.193i −1.81602 + 0.742197i
\(617\) 812.456i 1.31678i 0.752675 + 0.658392i \(0.228763\pi\)
−0.752675 + 0.658392i \(0.771237\pi\)
\(618\) 0 0
\(619\) −739.304 537.136i −1.19435 0.867748i −0.200635 0.979666i \(-0.564301\pi\)
−0.993717 + 0.111918i \(0.964301\pi\)
\(620\) 110.014 + 151.421i 0.177441 + 0.244227i
\(621\) 0 0
\(622\) −148.787 + 457.920i −0.239208 + 0.736206i
\(623\) −550.546 757.761i −0.883701 1.21631i
\(624\) 0 0
\(625\) −200.962 618.498i −0.321540 0.989597i
\(626\) 457.779i 0.731276i
\(627\) 0 0
\(628\) −241.352 −0.384319
\(629\) −307.018 + 99.7563i −0.488105 + 0.158595i
\(630\) 0 0
\(631\) 488.541 354.946i 0.774233 0.562513i −0.129010 0.991643i \(-0.541180\pi\)
0.903243 + 0.429130i \(0.141180\pi\)
\(632\) 912.926 + 296.628i 1.44450 + 0.469348i
\(633\) 0 0
\(634\) −442.400 + 321.423i −0.697792 + 0.506976i
\(635\) −32.3295 + 44.4977i −0.0509125 + 0.0700751i
\(636\) 0 0
\(637\) −332.165 −0.521453
\(638\) −36.7392 + 149.909i −0.0575849 + 0.234968i
\(639\) 0 0
\(640\) 80.4720 + 247.667i 0.125738 + 0.386980i
\(641\) 633.628 872.114i 0.988499 1.36055i 0.0563769 0.998410i \(-0.482045\pi\)
0.932122 0.362143i \(-0.117955\pi\)
\(642\) 0 0
\(643\) 118.832 365.726i 0.184808 0.568781i −0.815137 0.579268i \(-0.803338\pi\)
0.999945 + 0.0104874i \(0.00333831\pi\)
\(644\) 422.784 + 137.371i 0.656497 + 0.213309i
\(645\) 0 0
\(646\) 576.397 + 418.777i 0.892255 + 0.648262i
\(647\) 566.074 183.929i 0.874921 0.284279i 0.163074 0.986614i \(-0.447859\pi\)
0.711847 + 0.702335i \(0.247859\pi\)
\(648\) 0 0
\(649\) 381.706 616.339i 0.588144 0.949675i
\(650\) 3.81743i 0.00587297i
\(651\) 0 0
\(652\) −216.573 157.350i −0.332168 0.241334i
\(653\) −246.058 338.670i −0.376812 0.518637i 0.577924 0.816090i \(-0.303863\pi\)
−0.954736 + 0.297453i \(0.903863\pi\)
\(654\) 0 0
\(655\) 145.238 446.998i 0.221738 0.682439i
\(656\) −20.2596 27.8849i −0.0308835 0.0425075i
\(657\) 0 0
\(658\) 452.056 + 1391.29i 0.687015 + 2.11442i
\(659\) 1112.39i 1.68800i 0.536347 + 0.843998i \(0.319804\pi\)
−0.536347 + 0.843998i \(0.680196\pi\)
\(660\) 0 0
\(661\) −736.025 −1.11350 −0.556751 0.830679i \(-0.687952\pi\)
−0.556751 + 0.830679i \(0.687952\pi\)
\(662\) −814.943 + 264.791i −1.23103 + 0.399986i
\(663\) 0 0
\(664\) −273.318 + 198.577i −0.411624 + 0.299062i
\(665\) 1957.65 + 636.080i 2.94384 + 0.956511i
\(666\) 0 0
\(667\) 130.458 94.7830i 0.195589 0.142103i
\(668\) 292.598 402.727i 0.438021 0.602884i
\(669\) 0 0
\(670\) 417.923 0.623765
\(671\) −401.023 + 29.6576i −0.597649 + 0.0441991i
\(672\) 0 0
\(673\) 168.609 + 518.924i 0.250533 + 0.771061i 0.994677 + 0.103042i \(0.0328576\pi\)
−0.744144 + 0.668019i \(0.767142\pi\)
\(674\) 188.586 259.566i 0.279801 0.385113i
\(675\) 0 0
\(676\) −108.729 + 334.634i −0.160842 + 0.495021i
\(677\) −936.672 304.343i −1.38356 0.449547i −0.479724 0.877420i \(-0.659263\pi\)
−0.903839 + 0.427873i \(0.859263\pi\)
\(678\) 0 0
\(679\) 198.874 + 144.490i 0.292892 + 0.212798i
\(680\) −697.336 + 226.578i −1.02549 + 0.333203i
\(681\) 0 0
\(682\) −132.023 + 213.178i −0.193583 + 0.312578i
\(683\) 924.817i 1.35405i −0.735959 0.677026i \(-0.763269\pi\)
0.735959 0.677026i \(-0.236731\pi\)
\(684\) 0 0
\(685\) −820.385 596.044i −1.19764 0.870138i
\(686\) 788.604 + 1085.42i 1.14957 + 1.58225i
\(687\) 0 0
\(688\) −8.40056 + 25.8543i −0.0122101 + 0.0375789i
\(689\) 98.8576 + 136.066i 0.143480 + 0.197483i
\(690\) 0 0
\(691\) −24.4525 75.2570i −0.0353871 0.108910i 0.931803 0.362965i \(-0.118236\pi\)
−0.967190 + 0.254055i \(0.918236\pi\)
\(692\) 375.349i 0.542412i
\(693\) 0 0
\(694\) −658.790 −0.949265
\(695\) −289.034 + 93.9127i −0.415876 + 0.135126i
\(696\) 0 0
\(697\) −186.054 + 135.176i −0.266935 + 0.193940i
\(698\) 48.9041 + 15.8899i 0.0700632 + 0.0227649i
\(699\) 0 0
\(700\) −24.4964 + 17.7977i −0.0349949 + 0.0254253i
\(701\) −724.322 + 996.943i −1.03327 + 1.42217i −0.130805 + 0.991408i \(0.541756\pi\)
−0.902464 + 0.430765i \(0.858244\pi\)
\(702\) 0 0
\(703\) 574.204 0.816791
\(704\) −425.858 + 360.255i −0.604912 + 0.511726i
\(705\) 0 0
\(706\) −37.8094 116.365i −0.0535544 0.164823i
\(707\) −364.261 + 501.362i −0.515220 + 0.709140i
\(708\) 0 0
\(709\) −82.6830 + 254.472i −0.116619 + 0.358917i −0.992281 0.124007i \(-0.960425\pi\)
0.875662 + 0.482924i \(0.160425\pi\)
\(710\) 322.725 + 104.860i 0.454543 + 0.147690i
\(711\) 0 0
\(712\) −480.117 348.825i −0.674322 0.489923i
\(713\) 249.151 80.9541i 0.349440 0.113540i
\(714\) 0 0
\(715\) 138.796 56.7251i 0.194120 0.0793358i
\(716\) 396.682i 0.554025i
\(717\) 0 0
\(718\) −122.437 88.9554i −0.170525 0.123893i
\(719\) 403.585 + 555.487i 0.561314 + 0.772583i 0.991493 0.130161i \(-0.0415495\pi\)
−0.430179 + 0.902744i \(0.641549\pi\)
\(720\) 0 0
\(721\) −453.452 + 1395.58i −0.628922 + 1.93562i
\(722\) −458.132 630.564i −0.634531 0.873358i
\(723\) 0 0
\(724\) 81.7742 + 251.675i 0.112948 + 0.347617i
\(725\) 10.9836i 0.0151498i
\(726\) 0 0
\(727\) −1265.58 −1.74082 −0.870410 0.492327i \(-0.836146\pi\)
−0.870410 + 0.492327i \(0.836146\pi\)
\(728\) −279.004 + 90.6539i −0.383247 + 0.124525i
\(729\) 0 0
\(730\) −35.5683 + 25.8419i −0.0487237 + 0.0353998i
\(731\) 172.505 + 56.0502i 0.235985 + 0.0766761i
\(732\) 0 0
\(733\) −80.5752 + 58.5413i −0.109925 + 0.0798654i −0.641390 0.767215i \(-0.721642\pi\)
0.531465 + 0.847081i \(0.321642\pi\)
\(734\) 269.115 370.405i 0.366641 0.504638i
\(735\) 0 0
\(736\) 464.152 0.630642
\(737\) −252.111 616.867i −0.342077 0.836997i
\(738\) 0 0
\(739\) −99.0512 304.848i −0.134034 0.412515i 0.861404 0.507920i \(-0.169585\pi\)
−0.995439 + 0.0954052i \(0.969585\pi\)
\(740\) −122.295 + 168.325i −0.165264 + 0.227466i
\(741\) 0 0
\(742\) 346.356 1065.97i 0.466787 1.43662i
\(743\) −51.9858 16.8912i −0.0699674 0.0227338i 0.273824 0.961780i \(-0.411711\pi\)
−0.343792 + 0.939046i \(0.611711\pi\)
\(744\) 0 0
\(745\) 60.1478 + 43.6999i 0.0807353 + 0.0586576i
\(746\) 712.804 231.604i 0.955501 0.310461i
\(747\) 0 0
\(748\) 265.864 + 314.278i 0.355433 + 0.420157i
\(749\) 1460.06i 1.94935i
\(750\) 0 0
\(751\) −117.339 85.2520i −0.156244 0.113518i 0.506916 0.861995i \(-0.330785\pi\)
−0.663160 + 0.748477i \(0.730785\pi\)
\(752\) 124.678 + 171.605i 0.165795 + 0.228198i
\(753\) 0 0
\(754\) −11.5782 + 35.6339i −0.0153556 + 0.0472598i
\(755\) −730.906 1006.01i −0.968088 1.33246i
\(756\) 0 0
\(757\) 80.8537 + 248.842i 0.106808 + 0.328721i 0.990151 0.140007i \(-0.0447124\pi\)
−0.883343 + 0.468728i \(0.844712\pi\)
\(758\) 339.621i 0.448049i
\(759\) 0 0
\(760\) 1304.20 1.71605
\(761\) −955.456 + 310.446i −1.25553 + 0.407945i −0.859898 0.510465i \(-0.829473\pi\)
−0.395629 + 0.918411i \(0.629473\pi\)
\(762\) 0 0
\(763\) 1260.66 915.921i 1.65224 1.20042i
\(764\) 649.995 + 211.196i 0.850779 + 0.276435i
\(765\) 0 0
\(766\) 562.196 408.460i 0.733938 0.533237i
\(767\) 103.442 142.376i 0.134866 0.185627i
\(768\) 0 0
\(769\) 1067.91 1.38869 0.694347 0.719641i \(-0.255693\pi\)
0.694347 + 0.719641i \(0.255693\pi\)
\(770\) −849.511 526.112i −1.10326 0.683262i
\(771\) 0 0
\(772\) 83.5542 + 257.153i 0.108231 + 0.333100i
\(773\) −104.322 + 143.587i −0.134957 + 0.185753i −0.871147 0.491023i \(-0.836623\pi\)
0.736190 + 0.676775i \(0.236623\pi\)
\(774\) 0 0
\(775\) −5.51406 + 16.9705i −0.00711491 + 0.0218974i
\(776\) 148.129 + 48.1301i 0.190888 + 0.0620233i
\(777\) 0 0
\(778\) −212.267 154.221i −0.272837 0.198228i
\(779\) 389.041 126.407i 0.499411 0.162268i
\(780\) 0 0
\(781\) −39.9067 539.609i −0.0510970 0.690920i
\(782\) 361.342i 0.462074i
\(783\) 0 0
\(784\) 259.670 + 188.662i 0.331212 + 0.240640i
\(785\) −333.151 458.543i −0.424396 0.584131i
\(786\) 0 0
\(787\) 204.108 628.179i 0.259349