Properties

Label 99.3.l.a.53.3
Level $99$
Weight $3$
Character 99.53
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 53.3
Character \(\chi\) \(=\) 99.53
Dual form 99.3.l.a.71.3

$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(-1\)

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 −0.0304699 0.999536i \(-0.509700\pi\)
−0.612163 + 0.790732i \(0.709700\pi\)
\(3\) 0 0
\(4\) −1.75856 1.27767i −0.439639 0.319416i
\(5\) −4.85485 + 1.57744i −0.970970 + 0.315487i −0.751207 0.660066i \(-0.770528\pi\)
−0.219762 + 0.975553i \(0.570528\pi\)
\(6\) 0 0
\(7\) 10.6531 + 7.73991i 1.52187 + 1.10570i 0.960553 + 0.278098i \(0.0897040\pi\)
0.561314 + 0.827603i \(0.310296\pi\)
\(8\) 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 −0.977764 0.209707i \(-0.932749\pi\)
0.914291 + 0.405059i \(0.132749\pi\)
\(14\) −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 0.215100 0.976592i \(-0.430992\pi\)
0.748046 + 0.663647i \(0.230992\pi\)
\(18\) 0 0
\(19\) −24.7742 + 17.9995i −1.30391 + 0.947344i −0.999986 0.00535276i \(-0.998296\pi\)
−0.303922 + 0.952697i \(0.598296\pi\)
\(20\) 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 \(0.109625\pi\)
−0.941279 + 0.337628i \(0.890375\pi\)
\(24\) 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 −0.690727 0.723116i \(-0.742709\pi\)
0.901170 + 0.433465i \(0.142709\pi\)
\(30\) 0 0
\(31\) 5.21245 16.0423i 0.168144 0.517493i −0.831111 0.556107i \(-0.812294\pi\)
0.999254 + 0.0386144i \(0.0122944\pi\)
\(32\) 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 0.363604 0.931553i \(-0.381546\pi\)
−0.773600 + 0.633674i \(0.781546\pi\)
\(38\) 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 0.702457 0.711726i \(-0.252086\pi\)
−0.893963 + 0.448141i \(0.852086\pi\)
\(42\) 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 0.906380 + 0.422464i \(0.138835\pi\)
0.121700 + 0.992567i \(0.461165\pi\)
\(48\) 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 −0.316567 0.948570i \(-0.602530\pi\)
−0.813663 + 0.581336i \(0.802530\pi\)
\(54\) 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 −0.342778 0.939416i \(-0.611368\pi\)
0.999362 + 0.0357057i \(0.0113679\pi\)
\(60\) 0 0
\(61\) 11.2965 + 34.7670i 0.185188 + 0.569951i 0.999952 0.00984300i \(-0.00313318\pi\)
−0.814763 + 0.579794i \(0.803133\pi\)
\(62\) −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 0.0395649 0.999217i \(-0.487403\pi\)
0.619334 + 0.785128i \(0.287403\pi\)
\(72\) 0 0
\(73\) −5.15593 3.74600i −0.0706291 0.0513151i 0.551910 0.833903i \(-0.313899\pi\)
−0.622540 + 0.782588i \(0.713899\pi\)
\(74\) 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 −0.426817 0.904338i \(-0.640365\pi\)
0.876859 0.480748i \(-0.159635\pi\)
\(80\) 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 −0.531677 0.846947i \(-0.678438\pi\)
0.0676879 + 0.997707i \(0.478438\pi\)
\(84\) 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 \(0.130855\pi\)
−0.916685 + 0.399611i \(0.869145\pi\)
\(90\) 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 −0.916907 0.399101i \(-0.869322\pi\)
0.976379 + 0.216065i \(0.0693223\pi\)
\(98\) 168.107i 1.71538i
\(99\) 0 0
\(100\) −2.29947 −0.0229947
\(101\) −44.7592 14.5432i −0.443161 0.143992i 0.0789326 0.996880i \(-0.474849\pi\)
−0.522093 + 0.852888i \(0.674849\pi\)
\(102\) 0 0
\(103\) −90.1550 65.5015i −0.875292 0.635937i 0.0567100 0.998391i \(-0.481939\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(104\) −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 0.996503 0.0835565i \(-0.0266279\pi\)
−0.387403 + 0.921910i \(0.626628\pi\)
\(108\) 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 0.589642 0.807665i \(-0.299269\pi\)
−0.950344 + 0.311200i \(0.899269\pi\)
\(114\) 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 0.963309 0.268394i \(-0.0864931\pi\)
−0.937092 + 0.349083i \(0.886493\pi\)
\(128\) −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 \(-0.885698\pi\)
0.936217 0.351421i \(-0.114302\pi\)
\(132\) 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 0.476685 0.879074i \(-0.341838\pi\)
0.902353 + 0.430998i \(0.141838\pi\)
\(138\) 0 0
\(139\) 48.1649 + 34.9938i 0.346510 + 0.251754i 0.747403 0.664371i \(-0.231300\pi\)
−0.400894 + 0.916125i \(0.631300\pi\)
\(140\) 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 −0.355129 0.934817i \(-0.615563\pi\)
0.262166 + 0.965023i \(0.415563\pi\)
\(150\) 0 0
\(151\) 197.075 143.183i 1.30513 0.948234i 0.305140 0.952307i \(-0.401297\pi\)
0.999992 + 0.00407377i \(0.00129672\pi\)
\(152\) −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 −0.263735 0.964595i \(-0.584954\pi\)
0.835886 + 0.548903i \(0.184954\pi\)
\(158\) −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 −0.763843 0.645402i \(-0.776690\pi\)
0.997320 0.0731653i \(-0.0233101\pi\)
\(164\) 29.0365i 0.177052i
\(165\) 0 0
\(166\) 54.7225 0.329654
\(167\) −217.801 70.7679i −1.30420 0.423760i −0.427159 0.904177i \(-0.640485\pi\)
−0.877040 + 0.480417i \(0.840485\pi\)
\(168\) 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 0.407718 0.913108i \(-0.366325\pi\)
−0.994409 + 0.105597i \(0.966325\pi\)
\(174\) 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 0.995640 0.0932832i \(-0.0297362\pi\)
−0.396387 + 0.918083i \(0.629736\pi\)
\(180\) 0 0
\(181\) 37.6199 + 115.782i 0.207845 + 0.639680i 0.999585 + 0.0288218i \(0.00917553\pi\)
−0.791740 + 0.610858i \(0.790824\pi\)
\(182\) 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 −0.0243324 + 0.999704i \(0.507746\pi\)
−0.943256 + 0.332067i \(0.892254\pi\)
\(192\) 0 0
\(193\) 38.4388 + 118.302i 0.199165 + 0.612966i 0.999903 + 0.0139512i \(0.00444094\pi\)
−0.800738 + 0.599015i \(0.795559\pi\)
\(194\) −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 \(0.163869\pi\)
−0.870387 + 0.492369i \(0.836131\pi\)
\(198\) 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 −0.880941 0.473227i \(-0.843089\pi\)
0.990852 + 0.134955i \(0.0430891\pi\)
\(212\) 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 −0.576888 0.816823i \(-0.695733\pi\)
0.598577 + 0.801066i \(0.295733\pi\)
\(224\) 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 −0.533320 0.845914i \(-0.679056\pi\)
0.969317 + 0.245815i \(0.0790557\pi\)
\(228\) 0 0
\(229\) −108.832 + 334.950i −0.475249 + 1.46267i 0.370373 + 0.928883i \(0.379230\pi\)
−0.845622 + 0.533782i \(0.820770\pi\)
\(230\) 107.140i 0.465827i
\(231\) 0 0
\(232\) 86.6257 0.373387
\(233\) 338.664 + 110.039i 1.45349 + 0.472268i 0.926076 0.377338i \(-0.123160\pi\)
0.527417 + 0.849606i \(0.323160\pi\)
\(234\) 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 0.787035 0.616908i \(-0.211615\pi\)
−0.829922 + 0.557879i \(0.811615\pi\)
\(240\) 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 0.625011 0.780616i \(-0.285094\pi\)
0.0468100 + 0.998904i \(0.485094\pi\)
\(252\) 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 −0.920271 0.391283i \(-0.872032\pi\)
0.656511 + 0.754316i \(0.272032\pi\)
\(258\) 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 \(-0.851252\pi\)
0.892786 0.450482i \(-0.148748\pi\)
\(264\) 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 −0.876348 + 0.481678i \(0.840027\pi\)
−0.992104 + 0.125419i \(0.959973\pi\)
\(270\) 0 0
\(271\) 144.762 + 105.176i 0.534178 + 0.388103i 0.821918 0.569606i \(-0.192904\pi\)
−0.287740 + 0.957708i \(0.592904\pi\)
\(272\) −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 0.654652 + 0.755930i \(0.272815\pi\)
−0.973949 + 0.226766i \(0.927185\pi\)
\(278\) −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 −0.704693 0.709513i \(-0.748915\pi\)
−0.153067 + 0.988216i \(0.548915\pi\)
\(282\) 0 0
\(283\) 229.170 166.502i 0.809788 0.588346i −0.103981 0.994579i \(-0.533158\pi\)
0.913769 + 0.406234i \(0.133158\pi\)
\(284\) −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 −0.395336 0.918536i \(-0.629372\pi\)
0.995746 + 0.0921437i \(0.0293719\pi\)
\(294\) 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 0.999831 0.0183943i \(-0.00585541\pi\)
−0.326459 + 0.945211i \(0.605855\pi\)
\(312\) 0 0
\(313\) 104.677 + 322.163i 0.334431 + 1.02927i 0.967001 + 0.254771i \(0.0820000\pi\)
−0.632570 + 0.774503i \(0.718000\pi\)
\(314\) −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 0.844893 0.534936i \(-0.179664\pi\)
0.369105 + 0.929388i \(0.379664\pi\)
\(318\) 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 0.265142 0.964209i \(-0.414581\pi\)
−0.835084 + 0.550122i \(0.814581\pi\)
\(338\) −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 0.448102 0.893983i \(-0.352100\pi\)
0.887992 + 0.459859i \(0.152100\pi\)
\(348\) 0 0
\(349\) −30.7829 + 22.3651i −0.0882033 + 0.0640834i −0.631013 0.775772i \(-0.717361\pi\)
0.542810 + 0.839856i \(0.317361\pi\)
\(350\) −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 \(-0.959067\pi\)
0.991743 0.128241i \(-0.0409330\pi\)
\(354\) 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 −0.707439 0.706775i \(-0.750150\pi\)
0.890793 + 0.454409i \(0.150150\pi\)
\(360\) 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 0.148010 0.988986i \(-0.452713\pi\)
−0.894844 + 0.446380i \(0.852713\pi\)
\(368\) 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 −0.999717 0.0237762i \(-0.992431\pi\)
0.794813 0.606854i \(-0.207569\pi\)
\(380\) −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 −0.409402 0.912354i \(-0.634263\pi\)
−0.867481 + 0.497470i \(0.834263\pi\)
\(384\) 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 −0.636739 0.771080i \(-0.719717\pi\)
0.930103 + 0.367298i \(0.119717\pi\)
\(390\) 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 0.177619 0.984099i \(-0.443160\pi\)
0.722136 + 0.691751i \(0.243160\pi\)
\(402\) 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 −0.267362 0.963596i \(-0.586152\pi\)
0.782688 0.622415i \(-0.213848\pi\)
\(410\) −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 \(-0.893443\pi\)
0.944489 0.328543i \(-0.106557\pi\)
\(420\) 0 0
\(421\) −98.2710 + 71.3981i −0.233423 + 0.169592i −0.698348 0.715758i \(-0.746081\pi\)
0.464925 + 0.885350i \(0.346081\pi\)
\(422\) −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 0.415931 0.909396i \(-0.363456\pi\)
−0.198035 + 0.980195i \(0.563456\pi\)
\(432\) 0 0
\(433\) −453.043 329.155i −1.04629 0.760173i −0.0747851 0.997200i \(-0.523827\pi\)
−0.971503 + 0.237027i \(0.923827\pi\)
\(434\) −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 0.747104 0.664707i \(-0.231444\pi\)
−0.863042 + 0.505132i \(0.831444\pi\)
\(444\) 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 0.409132 0.912475i \(-0.365832\pi\)
−0.205345 + 0.978690i \(0.565832\pi\)
\(450\) 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 −0.855456 0.517875i \(-0.826723\pi\)
0.387679 0.921794i \(-0.373277\pi\)
\(458\) 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 \(-0.975620\pi\)
0.997068 0.0765175i \(-0.0243801\pi\)
\(462\) 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 −0.556155 0.831078i \(-0.687724\pi\)
0.0385567 + 0.999256i \(0.487724\pi\)
\(468\) 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 −0.327107 0.944987i \(-0.606074\pi\)
0.290815 + 0.956779i \(0.406074\pi\)
\(480\) 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 −0.366989 0.930225i \(-0.619611\pi\)
0.771291 + 0.636483i \(0.219611\pi\)
\(488\) −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 −0.576512 0.817089i \(-0.695587\pi\)
0.955250 + 0.295801i \(0.0955866\pi\)
\(492\) 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 0.565845 0.824512i \(-0.308550\pi\)
−0.609301 + 0.792939i \(0.708550\pi\)
\(500\) −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 0.902278 0.431154i \(-0.141893\pi\)
−0.688871 + 0.724884i \(0.741893\pi\)
\(504\) 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 0.665620 0.746290i \(-0.268167\pi\)
−0.915452 + 0.402426i \(0.868167\pi\)
\(510\) 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 −0.998841 0.0481300i \(-0.984674\pi\)
0.354433 + 0.935081i \(0.384674\pi\)
\(522\) 0 0
\(523\) 237.156 + 729.890i 0.453453 + 1.39558i 0.872942 + 0.487824i \(0.162209\pi\)
−0.419490 + 0.907760i \(0.637791\pi\)
\(524\) −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 −0.874915 0.484276i \(-0.839083\pi\)
0.992472 + 0.122475i \(0.0390830\pi\)
\(542\) −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 −0.861182 0.508297i \(-0.830275\pi\)
0.217299 + 0.976105i \(0.430275\pi\)
\(548\) −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 −0.215712 0.976457i \(-0.569207\pi\)
0.995325 0.0965873i \(-0.0307927\pi\)
\(558\) 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 0.252861 0.967503i \(-0.418628\pi\)
−0.364115 + 0.931354i \(0.618628\pi\)
\(564\) 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 0.999501 + 0.0315808i \(0.0100541\pi\)
−0.278828 + 0.960341i \(0.589946\pi\)
\(570\) 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 0.995859 + 0.0909159i \(0.0289794\pi\)
−0.752227 + 0.658903i \(0.771021\pi\)
\(578\) −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 −0.860660 0.509181i \(-0.829948\pi\)
0.750218 + 0.661190i \(0.229948\pi\)
\(588\) 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 \(-0.932281\pi\)
0.977455 0.211144i \(-0.0677188\pi\)
\(594\) 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 −0.0735122 0.997294i \(-0.523421\pi\)
0.526722 + 0.850037i \(0.323421\pi\)
\(600\) 0 0
\(601\) 180.803 + 131.361i 0.300836 + 0.218570i 0.727954 0.685625i \(-0.240471\pi\)
−0.427118 + 0.904196i \(0.640471\pi\)
\(602\) −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 −0.344256 0.938876i \(-0.611869\pi\)
0.830367 0.557218i \(-0.188131\pi\)
\(608\) 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 −0.340261 0.940331i \(-0.610515\pi\)
0.789162 + 0.614185i \(0.210515\pi\)
\(614\) −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 \(-0.771237\pi\)
0.752675 0.658392i \(-0.228763\pi\)
\(618\) 0 0
\(619\) −739.304 + 537.136i −1.19435 + 0.867748i −0.993717 0.111918i \(-0.964301\pi\)
−0.200635 + 0.979666i \(0.564301\pi\)
\(620\) 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 0.903243 0.429130i \(-0.141180\pi\)
−0.129010 + 0.991643i \(0.541180\pi\)
\(632\) 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 0.932122 + 0.362143i \(0.117955\pi\)
0.0563769 + 0.998410i \(0.482045\pi\)
\(642\) 0 0
\(643\) 118.832 + 365.726i 0.184808 + 0.568781i 0.999945 0.0104874i \(-0.00333831\pi\)
−0.815137 + 0.579268i \(0.803338\pi\)
\(644\) 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 0.711847 0.702335i \(-0.247859\pi\)
0.163074 + 0.986614i \(0.447859\pi\)
\(648\) 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 −0.954736 0.297453i \(-0.903863\pi\)
0.577924 + 0.816090i \(0.303863\pi\)
\(654\) 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 \(-0.680196\pi\)
0.536347 0.843998i \(-0.319804\pi\)
\(660\) 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 −0.744144 0.668019i \(-0.767142\pi\)
0.994677 0.103042i \(-0.0328576\pi\)
\(674\) 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 −0.903839 0.427873i \(-0.859263\pi\)
−0.479724 + 0.877420i \(0.659263\pi\)
\(678\) 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 \(0.236731\pi\)
−0.735959 + 0.677026i \(0.763269\pi\)
\(684\) 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 −0.967190 0.254055i \(-0.918236\pi\)
0.931803 + 0.362965i \(0.118236\pi\)
\(692\) 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 −0.902464 0.430765i \(-0.858244\pi\)
−0.130805 0.991408i \(-0.541756\pi\)
\(702\) 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 0.875662 0.482924i \(-0.160425\pi\)
−0.992281 + 0.124007i \(0.960425\pi\)
\(710\) 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 −0.430179 0.902744i \(-0.641549\pi\)
0.991493 + 0.130161i \(0.0415495\pi\)
\(720\) 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 0.531465 0.847081i \(-0.321642\pi\)
−0.641390 + 0.767215i \(0.721642\pi\)
\(734\) 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 −0.995439 0.0954052i \(-0.969585\pi\)
0.861404 + 0.507920i \(0.169585\pi\)
\(740\) −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 −0.343792 0.939046i \(-0.611711\pi\)
0.273824 + 0.961780i \(0.411711\pi\)
\(744\) 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 −0.663160 0.748477i \(-0.730785\pi\)
0.506916 + 0.861995i \(0.330785\pi\)
\(752\) 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 −0.883343 0.468728i \(-0.844712\pi\)
0.990151 + 0.140007i \(0.0447124\pi\)
\(758\) 339.621i 0.448049i
\(759\) 0 0
\(760\) 1304.20 1.71605
\(761\) −955.456 310.446i −1.25553 0.407945i −0.395629 0.918411i \(-0.629473\pi\)
−0.859898 + 0.510465i \(0.829473\pi\)
\(762\) 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 0.736190 0.676775i \(-0.236623\pi\)
−0.871147 + 0.491023i \(0.836623\pi\)
\(774\) 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