Properties

Label 117.4.q.c.10.1
Level $117$
Weight $4$
Character 117.10
Analytic conductor $6.903$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 10.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 117.10
Dual form 117.4.q.c.82.1

$q$-expansion

\(f(q)\) \(=\) \(q+(3.00000 - 1.73205i) q^{2} +(2.00000 - 3.46410i) q^{4} +13.8564i q^{5} +(19.5000 + 11.2583i) q^{7} +13.8564i q^{8} +O(q^{10})\) \(q+(3.00000 - 1.73205i) q^{2} +(2.00000 - 3.46410i) q^{4} +13.8564i q^{5} +(19.5000 + 11.2583i) q^{7} +13.8564i q^{8} +(24.0000 + 41.5692i) q^{10} +(19.5000 - 11.2583i) q^{11} +(-13.0000 - 45.0333i) q^{13} +78.0000 q^{14} +(40.0000 + 69.2820i) q^{16} +(13.5000 - 23.3827i) q^{17} +(-76.5000 - 44.1673i) q^{19} +(48.0000 + 27.7128i) q^{20} +(39.0000 - 67.5500i) q^{22} +(28.5000 + 49.3634i) q^{23} -67.0000 q^{25} +(-117.000 - 112.583i) q^{26} +(78.0000 - 45.0333i) q^{28} +(-34.5000 - 59.7558i) q^{29} +72.7461i q^{31} +(144.000 + 83.1384i) q^{32} -93.5307i q^{34} +(-156.000 + 270.200i) q^{35} +(-34.5000 + 19.9186i) q^{37} -306.000 q^{38} -192.000 q^{40} +(340.500 - 196.588i) q^{41} +(42.5000 - 73.6122i) q^{43} -90.0666i q^{44} +(171.000 + 98.7269i) q^{46} -342.946i q^{47} +(82.0000 + 142.028i) q^{49} +(-201.000 + 116.047i) q^{50} +(-182.000 - 45.0333i) q^{52} -426.000 q^{53} +(156.000 + 270.200i) q^{55} +(-156.000 + 270.200i) q^{56} +(-207.000 - 119.512i) q^{58} +(16.5000 + 9.52628i) q^{59} +(8.50000 - 14.7224i) q^{61} +(126.000 + 218.238i) q^{62} -64.0000 q^{64} +(624.000 - 180.133i) q^{65} +(142.500 - 82.2724i) q^{67} +(-54.0000 - 93.5307i) q^{68} +1080.80i q^{70} +(-505.500 - 291.851i) q^{71} -1004.59i q^{73} +(-69.0000 + 119.512i) q^{74} +(-306.000 + 176.669i) q^{76} +507.000 q^{77} -1244.00 q^{79} +(-960.000 + 554.256i) q^{80} +(681.000 - 1179.53i) q^{82} -426.084i q^{83} +(324.000 + 187.061i) q^{85} -294.449i q^{86} +(156.000 + 270.200i) q^{88} +(-265.500 + 153.286i) q^{89} +(253.500 - 1024.51i) q^{91} +228.000 q^{92} +(-594.000 - 1028.84i) q^{94} +(612.000 - 1060.02i) q^{95} +(1069.50 + 617.476i) q^{97} +(492.000 + 284.056i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{2} + 4 q^{4} + 39 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 6 q^{2} + 4 q^{4} + 39 q^{7} + 48 q^{10} + 39 q^{11} - 26 q^{13} + 156 q^{14} + 80 q^{16} + 27 q^{17} - 153 q^{19} + 96 q^{20} + 78 q^{22} + 57 q^{23} - 134 q^{25} - 234 q^{26} + 156 q^{28} - 69 q^{29} + 288 q^{32} - 312 q^{35} - 69 q^{37} - 612 q^{38} - 384 q^{40} + 681 q^{41} + 85 q^{43} + 342 q^{46} + 164 q^{49} - 402 q^{50} - 364 q^{52} - 852 q^{53} + 312 q^{55} - 312 q^{56} - 414 q^{58} + 33 q^{59} + 17 q^{61} + 252 q^{62} - 128 q^{64} + 1248 q^{65} + 285 q^{67} - 108 q^{68} - 1011 q^{71} - 138 q^{74} - 612 q^{76} + 1014 q^{77} - 2488 q^{79} - 1920 q^{80} + 1362 q^{82} + 648 q^{85} + 312 q^{88} - 531 q^{89} + 507 q^{91} + 456 q^{92} - 1188 q^{94} + 1224 q^{95} + 2139 q^{97} + 984 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.00000 1.73205i 1.06066 0.612372i 0.135045 0.990839i \(-0.456882\pi\)
0.925615 + 0.378467i \(0.123549\pi\)
\(3\) 0 0
\(4\) 2.00000 3.46410i 0.250000 0.433013i
\(5\) 13.8564i 1.23935i 0.784857 + 0.619677i \(0.212737\pi\)
−0.784857 + 0.619677i \(0.787263\pi\)
\(6\) 0 0
\(7\) 19.5000 + 11.2583i 1.05290 + 0.607893i 0.923460 0.383694i \(-0.125348\pi\)
0.129441 + 0.991587i \(0.458682\pi\)
\(8\) 13.8564i 0.612372i
\(9\) 0 0
\(10\) 24.0000 + 41.5692i 0.758947 + 1.31453i
\(11\) 19.5000 11.2583i 0.534497 0.308592i −0.208349 0.978055i \(-0.566809\pi\)
0.742846 + 0.669462i \(0.233475\pi\)
\(12\) 0 0
\(13\) −13.0000 45.0333i −0.277350 0.960769i
\(14\) 78.0000 1.48903
\(15\) 0 0
\(16\) 40.0000 + 69.2820i 0.625000 + 1.08253i
\(17\) 13.5000 23.3827i 0.192602 0.333596i −0.753510 0.657437i \(-0.771641\pi\)
0.946112 + 0.323840i \(0.104974\pi\)
\(18\) 0 0
\(19\) −76.5000 44.1673i −0.923700 0.533299i −0.0388865 0.999244i \(-0.512381\pi\)
−0.884814 + 0.465945i \(0.845714\pi\)
\(20\) 48.0000 + 27.7128i 0.536656 + 0.309839i
\(21\) 0 0
\(22\) 39.0000 67.5500i 0.377947 0.654623i
\(23\) 28.5000 + 49.3634i 0.258377 + 0.447521i 0.965807 0.259261i \(-0.0834791\pi\)
−0.707431 + 0.706783i \(0.750146\pi\)
\(24\) 0 0
\(25\) −67.0000 −0.536000
\(26\) −117.000 112.583i −0.882523 0.849208i
\(27\) 0 0
\(28\) 78.0000 45.0333i 0.526451 0.303946i
\(29\) −34.5000 59.7558i −0.220913 0.382633i 0.734172 0.678963i \(-0.237570\pi\)
−0.955086 + 0.296330i \(0.904237\pi\)
\(30\) 0 0
\(31\) 72.7461i 0.421471i 0.977543 + 0.210735i \(0.0675858\pi\)
−0.977543 + 0.210735i \(0.932414\pi\)
\(32\) 144.000 + 83.1384i 0.795495 + 0.459279i
\(33\) 0 0
\(34\) 93.5307i 0.471776i
\(35\) −156.000 + 270.200i −0.753395 + 1.30492i
\(36\) 0 0
\(37\) −34.5000 + 19.9186i −0.153291 + 0.0885026i −0.574683 0.818376i \(-0.694875\pi\)
0.421393 + 0.906878i \(0.361541\pi\)
\(38\) −306.000 −1.30631
\(39\) 0 0
\(40\) −192.000 −0.758947
\(41\) 340.500 196.588i 1.29700 0.748826i 0.317118 0.948386i \(-0.397285\pi\)
0.979886 + 0.199560i \(0.0639514\pi\)
\(42\) 0 0
\(43\) 42.5000 73.6122i 0.150725 0.261064i −0.780769 0.624820i \(-0.785172\pi\)
0.931494 + 0.363756i \(0.118506\pi\)
\(44\) 90.0666i 0.308592i
\(45\) 0 0
\(46\) 171.000 + 98.7269i 0.548099 + 0.316445i
\(47\) 342.946i 1.06434i −0.846639 0.532168i \(-0.821377\pi\)
0.846639 0.532168i \(-0.178623\pi\)
\(48\) 0 0
\(49\) 82.0000 + 142.028i 0.239067 + 0.414076i
\(50\) −201.000 + 116.047i −0.568514 + 0.328232i
\(51\) 0 0
\(52\) −182.000 45.0333i −0.485363 0.120096i
\(53\) −426.000 −1.10407 −0.552034 0.833822i \(-0.686148\pi\)
−0.552034 + 0.833822i \(0.686148\pi\)
\(54\) 0 0
\(55\) 156.000 + 270.200i 0.382455 + 0.662432i
\(56\) −156.000 + 270.200i −0.372257 + 0.644768i
\(57\) 0 0
\(58\) −207.000 119.512i −0.468628 0.270563i
\(59\) 16.5000 + 9.52628i 0.0364088 + 0.0210206i 0.518094 0.855324i \(-0.326642\pi\)
−0.481685 + 0.876344i \(0.659975\pi\)
\(60\) 0 0
\(61\) 8.50000 14.7224i 0.0178412 0.0309019i −0.856967 0.515371i \(-0.827654\pi\)
0.874808 + 0.484469i \(0.160987\pi\)
\(62\) 126.000 + 218.238i 0.258097 + 0.447037i
\(63\) 0 0
\(64\) −64.0000 −0.125000
\(65\) 624.000 180.133i 1.19073 0.343735i
\(66\) 0 0
\(67\) 142.500 82.2724i 0.259838 0.150018i −0.364423 0.931234i \(-0.618734\pi\)
0.624261 + 0.781216i \(0.285400\pi\)
\(68\) −54.0000 93.5307i −0.0963009 0.166798i
\(69\) 0 0
\(70\) 1080.80i 1.84543i
\(71\) −505.500 291.851i −0.844955 0.487835i 0.0139904 0.999902i \(-0.495547\pi\)
−0.858945 + 0.512067i \(0.828880\pi\)
\(72\) 0 0
\(73\) 1004.59i 1.61066i −0.592826 0.805331i \(-0.701988\pi\)
0.592826 0.805331i \(-0.298012\pi\)
\(74\) −69.0000 + 119.512i −0.108393 + 0.187742i
\(75\) 0 0
\(76\) −306.000 + 176.669i −0.461850 + 0.266649i
\(77\) 507.000 0.750364
\(78\) 0 0
\(79\) −1244.00 −1.77166 −0.885829 0.464012i \(-0.846409\pi\)
−0.885829 + 0.464012i \(0.846409\pi\)
\(80\) −960.000 + 554.256i −1.34164 + 0.774597i
\(81\) 0 0
\(82\) 681.000 1179.53i 0.917120 1.58850i
\(83\) 426.084i 0.563480i −0.959491 0.281740i \(-0.909088\pi\)
0.959491 0.281740i \(-0.0909116\pi\)
\(84\) 0 0
\(85\) 324.000 + 187.061i 0.413444 + 0.238702i
\(86\) 294.449i 0.369200i
\(87\) 0 0
\(88\) 156.000 + 270.200i 0.188973 + 0.327311i
\(89\) −265.500 + 153.286i −0.316213 + 0.182566i −0.649703 0.760188i \(-0.725107\pi\)
0.333490 + 0.942753i \(0.391774\pi\)
\(90\) 0 0
\(91\) 253.500 1024.51i 0.292022 1.18019i
\(92\) 228.000 0.258377
\(93\) 0 0
\(94\) −594.000 1028.84i −0.651770 1.12890i
\(95\) 612.000 1060.02i 0.660946 1.14479i
\(96\) 0 0
\(97\) 1069.50 + 617.476i 1.11950 + 0.646342i 0.941273 0.337647i \(-0.109631\pi\)
0.178225 + 0.983990i \(0.442965\pi\)
\(98\) 492.000 + 284.056i 0.507138 + 0.292796i
\(99\) 0 0
\(100\) −134.000 + 232.095i −0.134000 + 0.232095i
\(101\) 979.500 + 1696.54i 0.964989 + 1.67141i 0.709645 + 0.704560i \(0.248856\pi\)
0.255345 + 0.966850i \(0.417811\pi\)
\(102\) 0 0
\(103\) 1856.00 1.77551 0.887753 0.460320i \(-0.152265\pi\)
0.887753 + 0.460320i \(0.152265\pi\)
\(104\) 624.000 180.133i 0.588348 0.169842i
\(105\) 0 0
\(106\) −1278.00 + 737.854i −1.17104 + 0.676101i
\(107\) −127.500 220.836i −0.115195 0.199524i 0.802663 0.596433i \(-0.203416\pi\)
−0.917858 + 0.396909i \(0.870083\pi\)
\(108\) 0 0
\(109\) 609.682i 0.535752i 0.963453 + 0.267876i \(0.0863217\pi\)
−0.963453 + 0.267876i \(0.913678\pi\)
\(110\) 936.000 + 540.400i 0.811310 + 0.468410i
\(111\) 0 0
\(112\) 1801.33i 1.51973i
\(113\) 205.500 355.936i 0.171078 0.296316i −0.767719 0.640787i \(-0.778608\pi\)
0.938797 + 0.344471i \(0.111942\pi\)
\(114\) 0 0
\(115\) −684.000 + 394.908i −0.554638 + 0.320220i
\(116\) −276.000 −0.220913
\(117\) 0 0
\(118\) 66.0000 0.0514898
\(119\) 526.500 303.975i 0.405581 0.234162i
\(120\) 0 0
\(121\) −412.000 + 713.605i −0.309542 + 0.536142i
\(122\) 58.8897i 0.0437018i
\(123\) 0 0
\(124\) 252.000 + 145.492i 0.182502 + 0.105368i
\(125\) 803.672i 0.575061i
\(126\) 0 0
\(127\) 1121.50 + 1942.49i 0.783599 + 1.35723i 0.929833 + 0.367983i \(0.119951\pi\)
−0.146234 + 0.989250i \(0.546715\pi\)
\(128\) −1344.00 + 775.959i −0.928078 + 0.535826i
\(129\) 0 0
\(130\) 1560.00 1621.20i 1.05247 1.09376i
\(131\) 372.000 0.248105 0.124053 0.992276i \(-0.460411\pi\)
0.124053 + 0.992276i \(0.460411\pi\)
\(132\) 0 0
\(133\) −994.500 1722.52i −0.648377 1.12302i
\(134\) 285.000 493.634i 0.183733 0.318235i
\(135\) 0 0
\(136\) 324.000 + 187.061i 0.204285 + 0.117944i
\(137\) 1030.50 + 594.959i 0.642639 + 0.371028i 0.785630 0.618696i \(-0.212339\pi\)
−0.142991 + 0.989724i \(0.545672\pi\)
\(138\) 0 0
\(139\) 1272.50 2204.03i 0.776490 1.34492i −0.157464 0.987525i \(-0.550332\pi\)
0.933953 0.357395i \(-0.116335\pi\)
\(140\) 624.000 + 1080.80i 0.376697 + 0.652459i
\(141\) 0 0
\(142\) −2022.00 −1.19495
\(143\) −760.500 731.791i −0.444729 0.427940i
\(144\) 0 0
\(145\) 828.000 478.046i 0.474218 0.273790i
\(146\) −1740.00 3013.77i −0.986325 1.70836i
\(147\) 0 0
\(148\) 159.349i 0.0885026i
\(149\) −1129.50 652.117i −0.621022 0.358547i 0.156245 0.987718i \(-0.450061\pi\)
−0.777267 + 0.629171i \(0.783394\pi\)
\(150\) 0 0
\(151\) 86.6025i 0.0466729i 0.999728 + 0.0233365i \(0.00742890\pi\)
−0.999728 + 0.0233365i \(0.992571\pi\)
\(152\) 612.000 1060.02i 0.326577 0.565649i
\(153\) 0 0
\(154\) 1521.00 878.150i 0.795881 0.459502i
\(155\) −1008.00 −0.522352
\(156\) 0 0
\(157\) −1534.00 −0.779787 −0.389893 0.920860i \(-0.627488\pi\)
−0.389893 + 0.920860i \(0.627488\pi\)
\(158\) −3732.00 + 2154.67i −1.87913 + 1.08491i
\(159\) 0 0
\(160\) −1152.00 + 1995.32i −0.569210 + 0.985901i
\(161\) 1283.45i 0.628261i
\(162\) 0 0
\(163\) −1414.50 816.662i −0.679707 0.392429i 0.120038 0.992769i \(-0.461698\pi\)
−0.799745 + 0.600340i \(0.795032\pi\)
\(164\) 1572.70i 0.748826i
\(165\) 0 0
\(166\) −738.000 1278.25i −0.345060 0.597661i
\(167\) −1408.50 + 813.198i −0.652653 + 0.376809i −0.789472 0.613787i \(-0.789645\pi\)
0.136819 + 0.990596i \(0.456312\pi\)
\(168\) 0 0
\(169\) −1859.00 + 1170.87i −0.846154 + 0.532939i
\(170\) 1296.00 0.584698
\(171\) 0 0
\(172\) −170.000 294.449i −0.0753627 0.130532i
\(173\) −436.500 + 756.040i −0.191829 + 0.332258i −0.945857 0.324585i \(-0.894775\pi\)
0.754027 + 0.656843i \(0.228109\pi\)
\(174\) 0 0
\(175\) −1306.50 754.308i −0.564355 0.325830i
\(176\) 1560.00 + 900.666i 0.668122 + 0.385740i
\(177\) 0 0
\(178\) −531.000 + 919.719i −0.223596 + 0.387280i
\(179\) −643.500 1114.57i −0.268701 0.465403i 0.699826 0.714314i \(-0.253261\pi\)
−0.968527 + 0.248910i \(0.919928\pi\)
\(180\) 0 0
\(181\) 2.00000 0.000821319 0.000410660 1.00000i \(-0.499869\pi\)
0.000410660 1.00000i \(0.499869\pi\)
\(182\) −1014.00 3512.60i −0.412982 1.43061i
\(183\) 0 0
\(184\) −684.000 + 394.908i −0.274050 + 0.158223i
\(185\) −276.000 478.046i −0.109686 0.189982i
\(186\) 0 0
\(187\) 607.950i 0.237742i
\(188\) −1188.00 685.892i −0.460871 0.266084i
\(189\) 0 0
\(190\) 4240.06i 1.61898i
\(191\) −1420.50 + 2460.38i −0.538135 + 0.932077i 0.460870 + 0.887468i \(0.347538\pi\)
−0.999005 + 0.0446092i \(0.985796\pi\)
\(192\) 0 0
\(193\) −3676.50 + 2122.63i −1.37119 + 0.791659i −0.991078 0.133281i \(-0.957449\pi\)
−0.380115 + 0.924939i \(0.624115\pi\)
\(194\) 4278.00 1.58321
\(195\) 0 0
\(196\) 656.000 0.239067
\(197\) −2383.50 + 1376.11i −0.862017 + 0.497686i −0.864687 0.502311i \(-0.832483\pi\)
0.00267023 + 0.999996i \(0.499150\pi\)
\(198\) 0 0
\(199\) 842.500 1459.25i 0.300117 0.519818i −0.676045 0.736860i \(-0.736308\pi\)
0.976162 + 0.217042i \(0.0696410\pi\)
\(200\) 928.379i 0.328232i
\(201\) 0 0
\(202\) 5877.00 + 3393.09i 2.04705 + 1.18187i
\(203\) 1553.65i 0.537167i
\(204\) 0 0
\(205\) 2724.00 + 4718.11i 0.928061 + 1.60745i
\(206\) 5568.00 3214.69i 1.88321 1.08727i
\(207\) 0 0
\(208\) 2600.00 2702.00i 0.866719 0.900721i
\(209\) −1989.00 −0.658287
\(210\) 0 0
\(211\) −840.500 1455.79i −0.274229 0.474979i 0.695711 0.718322i \(-0.255089\pi\)
−0.969940 + 0.243343i \(0.921756\pi\)
\(212\) −852.000 + 1475.71i −0.276017 + 0.478075i
\(213\) 0 0
\(214\) −765.000 441.673i −0.244366 0.141085i
\(215\) 1020.00 + 588.897i 0.323551 + 0.186802i
\(216\) 0 0
\(217\) −819.000 + 1418.55i −0.256209 + 0.443767i
\(218\) 1056.00 + 1829.05i 0.328080 + 0.568250i
\(219\) 0 0
\(220\) 1248.00 0.382455
\(221\) −1228.50 303.975i −0.373927 0.0925229i
\(222\) 0 0
\(223\) −3547.50 + 2048.15i −1.06528 + 0.615042i −0.926889 0.375336i \(-0.877527\pi\)
−0.138394 + 0.990377i \(0.544194\pi\)
\(224\) 1872.00 + 3242.40i 0.558385 + 0.967151i
\(225\) 0 0
\(226\) 1423.75i 0.419054i
\(227\) −379.500 219.104i −0.110962 0.0640638i 0.443492 0.896278i \(-0.353739\pi\)
−0.554454 + 0.832215i \(0.687073\pi\)
\(228\) 0 0
\(229\) 180.133i 0.0519805i −0.999662 0.0259903i \(-0.991726\pi\)
0.999662 0.0259903i \(-0.00827389\pi\)
\(230\) −1368.00 + 2369.45i −0.392188 + 0.679290i
\(231\) 0 0
\(232\) 828.000 478.046i 0.234314 0.135281i
\(233\) 5778.00 1.62459 0.812295 0.583247i \(-0.198218\pi\)
0.812295 + 0.583247i \(0.198218\pi\)
\(234\) 0 0
\(235\) 4752.00 1.31909
\(236\) 66.0000 38.1051i 0.0182044 0.0105103i
\(237\) 0 0
\(238\) 1053.00 1823.85i 0.286789 0.496734i
\(239\) 1860.22i 0.503464i −0.967797 0.251732i \(-0.919000\pi\)
0.967797 0.251732i \(-0.0810001\pi\)
\(240\) 0 0
\(241\) 1783.50 + 1029.70i 0.476703 + 0.275224i 0.719041 0.694967i \(-0.244581\pi\)
−0.242339 + 0.970192i \(0.577915\pi\)
\(242\) 2854.42i 0.758219i
\(243\) 0 0
\(244\) −34.0000 58.8897i −0.00892060 0.0154509i
\(245\) −1968.00 + 1136.23i −0.513187 + 0.296289i
\(246\) 0 0
\(247\) −994.500 + 4019.22i −0.256188 + 1.03537i
\(248\) −1008.00 −0.258097
\(249\) 0 0
\(250\) 1392.00 + 2411.01i 0.352151 + 0.609944i
\(251\) 2245.50 3889.32i 0.564680 0.978055i −0.432399 0.901682i \(-0.642333\pi\)
0.997079 0.0763724i \(-0.0243338\pi\)
\(252\) 0 0
\(253\) 1111.50 + 641.725i 0.276203 + 0.159466i
\(254\) 6729.00 + 3884.99i 1.66226 + 0.959708i
\(255\) 0 0
\(256\) −2432.00 + 4212.35i −0.593750 + 1.02841i
\(257\) 2725.50 + 4720.70i 0.661525 + 1.14580i 0.980215 + 0.197936i \(0.0634239\pi\)
−0.318690 + 0.947859i \(0.603243\pi\)
\(258\) 0 0
\(259\) −897.000 −0.215200
\(260\) 624.000 2521.87i 0.148842 0.601536i
\(261\) 0 0
\(262\) 1116.00 644.323i 0.263155 0.151933i
\(263\) −391.500 678.098i −0.0917906 0.158986i 0.816474 0.577382i \(-0.195926\pi\)
−0.908265 + 0.418396i \(0.862592\pi\)
\(264\) 0 0
\(265\) 5902.83i 1.36833i
\(266\) −5967.00 3445.05i −1.37541 0.794096i
\(267\) 0 0
\(268\) 658.179i 0.150018i
\(269\) −2542.50 + 4403.74i −0.576279 + 0.998144i 0.419623 + 0.907699i \(0.362162\pi\)
−0.995901 + 0.0904453i \(0.971171\pi\)
\(270\) 0 0
\(271\) −1147.50 + 662.509i −0.257216 + 0.148504i −0.623064 0.782171i \(-0.714112\pi\)
0.365848 + 0.930675i \(0.380779\pi\)
\(272\) 2160.00 0.481505
\(273\) 0 0
\(274\) 4122.00 0.908829
\(275\) −1306.50 + 754.308i −0.286491 + 0.165405i
\(276\) 0 0
\(277\) 1710.50 2962.67i 0.371025 0.642635i −0.618698 0.785629i \(-0.712340\pi\)
0.989724 + 0.142994i \(0.0456730\pi\)
\(278\) 8816.14i 1.90200i
\(279\) 0 0
\(280\) −3744.00 2161.60i −0.799096 0.461358i
\(281\) 810.600i 0.172087i 0.996291 + 0.0860433i \(0.0274223\pi\)
−0.996291 + 0.0860433i \(0.972578\pi\)
\(282\) 0 0
\(283\) −3588.50 6215.46i −0.753760 1.30555i −0.945988 0.324201i \(-0.894905\pi\)
0.192228 0.981350i \(-0.438429\pi\)
\(284\) −2022.00 + 1167.40i −0.422478 + 0.243918i
\(285\) 0 0
\(286\) −3549.00 878.150i −0.733765 0.181560i
\(287\) 8853.00 1.82082
\(288\) 0 0
\(289\) 2092.00 + 3623.45i 0.425809 + 0.737523i
\(290\) 1656.00 2868.28i 0.335323 0.580796i
\(291\) 0 0
\(292\) −3480.00 2009.18i −0.697437 0.402665i
\(293\) −8065.50 4656.62i −1.60816 0.928473i −0.989781 0.142595i \(-0.954456\pi\)
−0.618381 0.785878i \(-0.712211\pi\)
\(294\) 0 0
\(295\) −132.000 + 228.631i −0.0260520 + 0.0451234i
\(296\) −276.000 478.046i −0.0541965 0.0938712i
\(297\) 0 0
\(298\) −4518.00 −0.878257
\(299\) 1852.50 1925.17i 0.358304 0.372360i
\(300\) 0 0
\(301\) 1657.50 956.958i 0.317398 0.183250i
\(302\) 150.000 + 259.808i 0.0285812 + 0.0495041i
\(303\) 0 0
\(304\) 7066.77i 1.33325i
\(305\) 204.000 + 117.779i 0.0382984 + 0.0221116i
\(306\) 0 0
\(307\) 4777.00i 0.888070i 0.896009 + 0.444035i \(0.146453\pi\)
−0.896009 + 0.444035i \(0.853547\pi\)
\(308\) 1014.00 1756.30i 0.187591 0.324917i
\(309\) 0 0
\(310\) −3024.00 + 1745.91i −0.554038 + 0.319874i
\(311\) −6192.00 −1.12899 −0.564495 0.825436i \(-0.690929\pi\)
−0.564495 + 0.825436i \(0.690929\pi\)
\(312\) 0 0
\(313\) −770.000 −0.139051 −0.0695255 0.997580i \(-0.522149\pi\)
−0.0695255 + 0.997580i \(0.522149\pi\)
\(314\) −4602.00 + 2656.97i −0.827089 + 0.477520i
\(315\) 0 0
\(316\) −2488.00 + 4309.34i −0.442914 + 0.767150i
\(317\) 8057.50i 1.42762i 0.700341 + 0.713808i \(0.253031\pi\)
−0.700341 + 0.713808i \(0.746969\pi\)
\(318\) 0 0
\(319\) −1345.50 776.825i −0.236155 0.136344i
\(320\) 886.810i 0.154919i
\(321\) 0 0
\(322\) 2223.00 + 3850.35i 0.384730 + 0.666371i
\(323\) −2065.50 + 1192.52i −0.355813 + 0.205429i
\(324\) 0 0
\(325\) 871.000 + 3017.23i 0.148660 + 0.514972i
\(326\) −5658.00 −0.961250
\(327\) 0 0
\(328\) 2724.00 + 4718.11i 0.458560 + 0.794250i
\(329\) 3861.00 6687.45i 0.647002 1.12064i
\(330\) 0 0
\(331\) −4570.50 2638.78i −0.758965 0.438189i 0.0699590 0.997550i \(-0.477713\pi\)
−0.828924 + 0.559361i \(0.811046\pi\)
\(332\) −1476.00 852.169i −0.243994 0.140870i
\(333\) 0 0
\(334\) −2817.00 + 4879.19i −0.461495 + 0.799333i
\(335\) 1140.00 + 1974.54i 0.185925 + 0.322031i
\(336\) 0 0
\(337\) 8278.00 1.33808 0.669038 0.743228i \(-0.266706\pi\)
0.669038 + 0.743228i \(0.266706\pi\)
\(338\) −3549.00 + 6732.48i −0.571125 + 1.08343i
\(339\) 0 0
\(340\) 1296.00 748.246i 0.206722 0.119351i
\(341\) 819.000 + 1418.55i 0.130063 + 0.225275i
\(342\) 0 0
\(343\) 4030.48i 0.634477i
\(344\) 1020.00 + 588.897i 0.159868 + 0.0923000i
\(345\) 0 0
\(346\) 3024.16i 0.469884i
\(347\) 3433.50 5947.00i 0.531181 0.920033i −0.468156 0.883646i \(-0.655082\pi\)
0.999338 0.0363875i \(-0.0115851\pi\)
\(348\) 0 0
\(349\) 10525.5 6076.90i 1.61438 0.932060i 0.626036 0.779794i \(-0.284676\pi\)
0.988340 0.152266i \(-0.0486571\pi\)
\(350\) −5226.00 −0.798118
\(351\) 0 0
\(352\) 3744.00 0.566920
\(353\) −5029.50 + 2903.78i −0.758338 + 0.437827i −0.828699 0.559695i \(-0.810918\pi\)
0.0703608 + 0.997522i \(0.477585\pi\)
\(354\) 0 0
\(355\) 4044.00 7004.41i 0.604601 1.04720i
\(356\) 1226.29i 0.182566i
\(357\) 0 0
\(358\) −3861.00 2229.15i −0.570001 0.329090i
\(359\) 1340.61i 0.197088i 0.995133 + 0.0985439i \(0.0314185\pi\)
−0.995133 + 0.0985439i \(0.968581\pi\)
\(360\) 0 0
\(361\) 472.000 + 817.528i 0.0688147 + 0.119191i
\(362\) 6.00000 3.46410i 0.000871141 0.000502953i
\(363\) 0 0
\(364\) −3042.00 2927.17i −0.438033 0.421498i
\(365\) 13920.0 1.99618
\(366\) 0 0
\(367\) −1832.50 3173.98i −0.260642 0.451446i 0.705770 0.708441i \(-0.250601\pi\)
−0.966413 + 0.256995i \(0.917268\pi\)
\(368\) −2280.00 + 3949.08i −0.322971 + 0.559402i
\(369\) 0 0
\(370\) −1656.00 956.092i −0.232679 0.134337i
\(371\) −8307.00 4796.05i −1.16247 0.671155i
\(372\) 0 0
\(373\) −2685.50 + 4651.42i −0.372788 + 0.645688i −0.989993 0.141114i \(-0.954931\pi\)
0.617205 + 0.786802i \(0.288265\pi\)
\(374\) −1053.00 1823.85i −0.145586 0.252163i
\(375\) 0 0
\(376\) 4752.00 0.651770
\(377\) −2242.50 + 2330.47i −0.306352 + 0.318370i
\(378\) 0 0
\(379\) −9967.50 + 5754.74i −1.35091 + 0.779950i −0.988377 0.152020i \(-0.951422\pi\)
−0.362536 + 0.931970i \(0.618089\pi\)
\(380\) −2448.00 4240.06i −0.330473 0.572396i
\(381\) 0 0
\(382\) 9841.51i 1.31816i
\(383\) −2095.50 1209.84i −0.279569 0.161409i 0.353659 0.935374i \(-0.384937\pi\)
−0.633228 + 0.773965i \(0.718271\pi\)
\(384\) 0 0
\(385\) 7025.20i 0.929967i
\(386\) −7353.00 + 12735.8i −0.969580 + 1.67936i
\(387\) 0 0
\(388\) 4278.00 2469.90i 0.559749 0.323171i
\(389\) 9858.00 1.28489 0.642443 0.766334i \(-0.277921\pi\)
0.642443 + 0.766334i \(0.277921\pi\)
\(390\) 0 0
\(391\) 1539.00 0.199055
\(392\) −1968.00 + 1136.23i −0.253569 + 0.146398i
\(393\) 0 0
\(394\) −4767.00 + 8256.69i −0.609538 + 1.05575i
\(395\) 17237.4i 2.19571i
\(396\) 0 0
\(397\) −7552.50 4360.44i −0.954784 0.551245i −0.0602200 0.998185i \(-0.519180\pi\)
−0.894564 + 0.446941i \(0.852514\pi\)
\(398\) 5837.01i 0.735133i
\(399\) 0 0
\(400\) −2680.00 4641.90i −0.335000 0.580237i
\(401\) 6568.50 3792.33i 0.817993 0.472269i −0.0317308 0.999496i \(-0.510102\pi\)
0.849724 + 0.527228i \(0.176769\pi\)
\(402\) 0 0
\(403\) 3276.00 945.700i 0.404936 0.116895i
\(404\) 7836.00 0.964989
\(405\) 0 0
\(406\) −2691.00 4660.95i −0.328946 0.569751i
\(407\) −448.500 + 776.825i −0.0546224 + 0.0946088i
\(408\) 0 0
\(409\) 3727.50 + 2152.07i 0.450643 + 0.260179i 0.708102 0.706110i \(-0.249552\pi\)
−0.257459 + 0.966289i \(0.582885\pi\)
\(410\) 16344.0 + 9436.21i 1.96871 + 1.13664i
\(411\) 0 0
\(412\) 3712.00 6429.37i 0.443876 0.768817i
\(413\) 214.500 + 371.525i 0.0255565 + 0.0442652i
\(414\) 0 0
\(415\) 5904.00 0.698352
\(416\) 1872.00 7565.60i 0.220631 0.891668i
\(417\) 0 0
\(418\) −5967.00 + 3445.05i −0.698219 + 0.403117i
\(419\) 2698.50 + 4673.94i 0.314631 + 0.544957i 0.979359 0.202129i \(-0.0647859\pi\)
−0.664728 + 0.747085i \(0.731453\pi\)
\(420\) 0 0
\(421\) 7260.76i 0.840541i −0.907399 0.420270i \(-0.861935\pi\)
0.907399 0.420270i \(-0.138065\pi\)
\(422\) −5043.00 2911.58i −0.581728 0.335861i
\(423\) 0 0
\(424\) 5902.83i 0.676101i
\(425\) −904.500 + 1566.64i −0.103235 + 0.178808i
\(426\) 0 0
\(427\) 331.500 191.392i 0.0375700 0.0216911i
\(428\) −1020.00 −0.115195
\(429\) 0 0
\(430\) 4080.00 0.457570
\(431\) 421.500 243.353i 0.0471066 0.0271970i −0.476262 0.879304i \(-0.658009\pi\)
0.523368 + 0.852107i \(0.324675\pi\)
\(432\) 0 0
\(433\) −6069.50 + 10512.7i −0.673629 + 1.16676i 0.303238 + 0.952915i \(0.401932\pi\)
−0.976867 + 0.213846i \(0.931401\pi\)
\(434\) 5674.20i 0.627581i
\(435\) 0 0
\(436\) 2112.00 + 1219.36i 0.231987 + 0.133938i
\(437\) 5035.07i 0.551167i
\(438\) 0 0
\(439\) −230.500 399.238i −0.0250596 0.0434045i 0.853224 0.521545i \(-0.174644\pi\)
−0.878283 + 0.478141i \(0.841311\pi\)
\(440\) −3744.00 + 2161.60i −0.405655 + 0.234205i
\(441\) 0 0
\(442\) −4212.00 + 1215.90i −0.453268 + 0.130847i
\(443\) −12156.0 −1.30372 −0.651861 0.758338i \(-0.726012\pi\)
−0.651861 + 0.758338i \(0.726012\pi\)
\(444\) 0 0
\(445\) −2124.00 3678.88i −0.226263 0.391900i
\(446\) −7095.00 + 12288.9i −0.753269 + 1.30470i
\(447\) 0 0
\(448\) −1248.00 720.533i −0.131613 0.0759866i
\(449\) 256.500 + 148.090i 0.0269599 + 0.0155653i 0.513419 0.858138i \(-0.328379\pi\)
−0.486459 + 0.873703i \(0.661712\pi\)
\(450\) 0 0
\(451\) 4426.50 7666.92i 0.462164 0.800491i
\(452\) −822.000 1423.75i −0.0855390 0.148158i
\(453\) 0 0
\(454\) −1518.00 −0.156924
\(455\) 14196.0 + 3512.60i 1.46268 + 0.361919i
\(456\) 0 0
\(457\) 529.500 305.707i 0.0541990 0.0312918i −0.472656 0.881247i \(-0.656705\pi\)
0.526855 + 0.849955i \(0.323371\pi\)
\(458\) −312.000 540.400i −0.0318314 0.0551337i
\(459\) 0 0
\(460\) 3159.26i 0.320220i
\(461\) 11368.5 + 6563.61i 1.14855 + 0.663119i 0.948535 0.316673i \(-0.102566\pi\)
0.200020 + 0.979792i \(0.435899\pi\)
\(462\) 0 0
\(463\) 834.848i 0.0837985i 0.999122 + 0.0418992i \(0.0133408\pi\)
−0.999122 + 0.0418992i \(0.986659\pi\)
\(464\) 2760.00 4780.46i 0.276142 0.478292i
\(465\) 0 0
\(466\) 17334.0 10007.8i 1.72314 0.994854i
\(467\) −14496.0 −1.43639 −0.718196 0.695841i \(-0.755032\pi\)
−0.718196 + 0.695841i \(0.755032\pi\)
\(468\) 0 0
\(469\) 3705.00 0.364778
\(470\) 14256.0 8230.71i 1.39911 0.807775i
\(471\) 0 0
\(472\) −132.000 + 228.631i −0.0128724 + 0.0222957i
\(473\) 1913.92i 0.186051i
\(474\) 0 0
\(475\) 5125.50 + 2959.21i 0.495103 + 0.285848i
\(476\) 2431.80i 0.234162i
\(477\) 0 0
\(478\) −3222.00 5580.67i −0.308307 0.534004i
\(479\) 7705.50 4448.77i 0.735017 0.424362i −0.0852376 0.996361i \(-0.527165\pi\)
0.820255 + 0.571998i \(0.193832\pi\)
\(480\) 0 0
\(481\) 1345.50 + 1294.71i 0.127546 + 0.122731i
\(482\) 7134.00 0.674159
\(483\) 0 0
\(484\) 1648.00 + 2854.42i 0.154771 + 0.268071i
\(485\) −8556.00 + 14819.4i −0.801047 + 1.38745i
\(486\) 0 0
\(487\) 4117.50 + 2377.24i 0.383125 + 0.221197i 0.679177 0.733975i \(-0.262337\pi\)
−0.296052 + 0.955172i \(0.595670\pi\)
\(488\) 204.000 + 117.779i 0.0189235 + 0.0109255i
\(489\) 0 0
\(490\) −3936.00 + 6817.35i −0.362878 + 0.628524i
\(491\) −817.500 1415.95i −0.0751390 0.130145i 0.826008 0.563659i \(-0.190607\pi\)
−0.901147 + 0.433514i \(0.857273\pi\)
\(492\) 0 0
\(493\) −1863.00 −0.170193
\(494\) 3978.00 + 13780.2i 0.362305 + 1.25506i
\(495\) 0 0
\(496\) −5040.00 + 2909.85i −0.456255 + 0.263419i
\(497\) −6571.50 11382.2i −0.593103 1.02728i
\(498\) 0 0
\(499\) 14434.9i 1.29498i 0.762074 + 0.647490i \(0.224181\pi\)
−0.762074 + 0.647490i \(0.775819\pi\)
\(500\) 2784.00 + 1607.34i 0.249009 + 0.143765i
\(501\) 0 0
\(502\) 15557.3i 1.38318i
\(503\) 6343.50 10987.3i 0.562312 0.973952i −0.434983 0.900439i \(-0.643246\pi\)
0.997294 0.0735133i \(-0.0234211\pi\)
\(504\) 0 0
\(505\) −23508.0 + 13572.4i −2.07147 + 1.19596i
\(506\) 4446.00 0.390610
\(507\) 0 0
\(508\) 8972.00 0.783599
\(509\) 4978.50 2874.34i 0.433533 0.250300i −0.267318 0.963608i \(-0.586137\pi\)
0.700850 + 0.713308i \(0.252804\pi\)
\(510\) 0 0
\(511\) 11310.0 19589.5i 0.979109 1.69587i
\(512\) 4434.05i 0.382733i
\(513\) 0 0
\(514\) 16353.0 + 9441.41i 1.40331 + 0.810200i
\(515\) 25717.5i 2.20048i
\(516\) 0 0
\(517\) −3861.00 6687.45i −0.328446 0.568885i
\(518\) −2691.00 + 1553.65i −0.228254 + 0.131783i
\(519\) 0 0
\(520\) 2496.00 + 8646.40i 0.210494 + 0.729172i
\(521\) −6054.00 −0.509080 −0.254540 0.967062i \(-0.581924\pi\)
−0.254540 + 0.967062i \(0.581924\pi\)
\(522\) 0 0
\(523\) 7401.50 + 12819.8i 0.618824 + 1.07183i 0.989701 + 0.143153i \(0.0457240\pi\)
−0.370877 + 0.928682i \(0.620943\pi\)
\(524\) 744.000 1288.65i 0.0620263 0.107433i
\(525\) 0 0
\(526\) −2349.00 1356.20i −0.194717 0.112420i
\(527\) 1701.00 + 982.073i 0.140601 + 0.0811760i
\(528\) 0 0
\(529\) 4459.00 7723.21i 0.366483 0.634767i
\(530\) −10224.0 17708.5i −0.837929 1.45133i
\(531\) 0 0
\(532\) −7956.00 −0.648377
\(533\) −13279.5 12778.2i −1.07917 1.03843i
\(534\) 0 0
\(535\) 3060.00 1766.69i 0.247281 0.142768i
\(536\) 1140.00 + 1974.54i 0.0918666 + 0.159118i
\(537\) 0 0
\(538\) 17615.0i 1.41159i
\(539\) 3198.00 + 1846.37i 0.255561 + 0.147548i
\(540\) 0 0
\(541\) 21470.5i 1.70626i 0.521695 + 0.853132i \(0.325300\pi\)
−0.521695 + 0.853132i \(0.674700\pi\)
\(542\) −2295.00 + 3975.06i −0.181880 + 0.315025i
\(543\) 0 0
\(544\) 3888.00 2244.74i 0.306428 0.176916i
\(545\) −8448.00 −0.663986
\(546\) 0 0
\(547\) −13516.0 −1.05649 −0.528247 0.849091i \(-0.677151\pi\)
−0.528247 + 0.849091i \(0.677151\pi\)
\(548\) 4122.00 2379.84i 0.321320 0.185514i
\(549\) 0 0
\(550\) −2613.00 + 4525.85i −0.202579 + 0.350878i
\(551\) 6095.09i 0.471251i
\(552\) 0 0
\(553\) −24258.0 14005.4i −1.86538 1.07698i
\(554\) 11850.7i 0.908822i
\(555\) 0 0
\(556\) −5090.00 8816.14i −0.388245 0.672460i
\(557\) −2503.50 + 1445.40i −0.190443 + 0.109952i −0.592190 0.805798i \(-0.701736\pi\)
0.401747 + 0.915751i \(0.368403\pi\)
\(558\) 0 0
\(559\) −3867.50 956.958i −0.292626 0.0724061i
\(560\) −24960.0 −1.88349
\(561\) 0 0
\(562\) 1404.00 + 2431.80i 0.105381 + 0.182525i
\(563\) 5791.50 10031.2i 0.433539 0.750912i −0.563636 0.826023i \(-0.690598\pi\)
0.997175 + 0.0751113i \(0.0239312\pi\)
\(564\) 0 0
\(565\) 4932.00 + 2847.49i 0.367240 + 0.212026i
\(566\) −21531.0 12430.9i −1.59897 0.923164i
\(567\) 0 0
\(568\) 4044.00 7004.41i 0.298737 0.517427i
\(569\) 6439.50 + 11153.5i 0.474443 + 0.821759i 0.999572 0.0292638i \(-0.00931628\pi\)
−0.525129 + 0.851023i \(0.675983\pi\)
\(570\) 0 0
\(571\) −11636.0 −0.852805 −0.426402 0.904534i \(-0.640219\pi\)
−0.426402 + 0.904534i \(0.640219\pi\)
\(572\) −4056.00 + 1170.87i −0.296486 + 0.0855881i
\(573\) 0 0
\(574\) 26559.0 15333.8i 1.93127 1.11502i
\(575\) −1909.50 3307.35i −0.138490 0.239871i
\(576\) 0 0
\(577\) 12311.4i 0.888269i −0.895960 0.444134i \(-0.853511\pi\)
0.895960 0.444134i \(-0.146489\pi\)
\(578\) 12552.0 + 7246.90i 0.903277 + 0.521507i
\(579\) 0 0
\(580\) 3824.37i 0.273790i
\(581\) 4797.00 8308.65i 0.342535 0.593289i
\(582\) 0 0
\(583\) −8307.00 + 4796.05i −0.590121 + 0.340707i
\(584\) 13920.0 0.986325
\(585\) 0 0
\(586\) −32262.0 −2.27428
\(587\) 13549.5 7822.81i 0.952722 0.550054i 0.0587964 0.998270i \(-0.481274\pi\)
0.893925 + 0.448216i \(0.147940\pi\)
\(588\) 0 0
\(589\) 3213.00 5565.08i 0.224770 0.389313i
\(590\) 914.523i 0.0638141i
\(591\) 0 0
\(592\) −2760.00 1593.49i −0.191614 0.110628i
\(593\) 25821.4i 1.78813i 0.447942 + 0.894063i \(0.352157\pi\)
−0.447942 + 0.894063i \(0.647843\pi\)
\(594\) 0 0
\(595\) 4212.00 + 7295.40i 0.290210 + 0.502659i
\(596\) −4518.00 + 2608.47i −0.310511 + 0.179274i
\(597\) 0 0
\(598\) 2223.00 8984.15i 0.152015 0.614363i
\(599\) −1668.00 −0.113777 −0.0568887 0.998381i \(-0.518118\pi\)
−0.0568887 + 0.998381i \(0.518118\pi\)
\(600\) 0 0
\(601\) −6849.50 11863.7i −0.464887 0.805207i 0.534310 0.845289i \(-0.320572\pi\)
−0.999196 + 0.0400813i \(0.987238\pi\)
\(602\) 3315.00 5741.75i 0.224434 0.388731i
\(603\) 0 0
\(604\) 300.000 + 173.205i 0.0202100 + 0.0116682i
\(605\) −9888.00 5708.84i −0.664470 0.383632i
\(606\) 0 0
\(607\) 11586.5 20068.4i 0.774764 1.34193i −0.160164 0.987090i \(-0.551202\pi\)
0.934927 0.354839i \(-0.115464\pi\)
\(608\) −7344.00 12720.2i −0.489866 0.848473i
\(609\) 0 0
\(610\) 816.000 0.0541621
\(611\) −15444.0 + 4458.30i −1.02258 + 0.295194i
\(612\) 0 0
\(613\) 14389.5 8307.78i 0.948102 0.547387i 0.0556111 0.998453i \(-0.482289\pi\)
0.892491 + 0.451066i \(0.148956\pi\)
\(614\) 8274.00 + 14331.0i 0.543830 + 0.941941i
\(615\) 0 0
\(616\) 7025.20i 0.459502i
\(617\) −24589.5 14196.8i −1.60443 0.926321i −0.990585 0.136897i \(-0.956287\pi\)
−0.613849 0.789423i \(-0.710380\pi\)
\(618\) 0 0
\(619\) 6245.78i 0.405556i 0.979225 + 0.202778i \(0.0649969\pi\)
−0.979225 + 0.202778i \(0.935003\pi\)
\(620\) −2016.00 + 3491.81i −0.130588 + 0.226185i
\(621\) 0 0
\(622\) −18576.0 + 10724.9i −1.19748 + 0.691363i
\(623\) −6903.00 −0.443921
\(624\) 0 0
\(625\) −19511.0 −1.24870
\(626\) −2310.00 + 1333.68i −0.147486 + 0.0851510i
\(627\) 0 0
\(628\) −3068.00 + 5313.93i −0.194947 + 0.337658i
\(629\) 1075.60i 0.0681830i
\(630\) 0 0
\(631\) 19381.5 + 11189.9i 1.22277 + 0.705964i 0.965507 0.260378i \(-0.0838472\pi\)
0.257259 + 0.966342i \(0.417181\pi\)
\(632\) 17237.4i 1.08491i
\(633\) 0 0
\(634\) 13956.0 + 24172.5i 0.874233 + 1.51422i
\(635\) −26916.0 + 15540.0i −1.68209 + 0.971157i
\(636\) 0 0
\(637\) 5330.00 5539.10i 0.331526 0.344532i
\(638\) −5382.00 −0.333974
\(639\) 0 0
\(640\) −10752.0 18623.0i −0.664078 1.15022i
\(641\) 9913.50 17170.7i 0.610858 1.05804i −0.380239 0.924888i \(-0.624158\pi\)
0.991096 0.133148i \(-0.0425085\pi\)
\(642\) 0 0
\(643\) −7318.50 4225.34i −0.448855 0.259146i 0.258492 0.966013i \(-0.416775\pi\)
−0.707346 + 0.706867i \(0.750108\pi\)
\(644\) 4446.00 + 2566.90i 0.272045 + 0.157065i
\(645\) 0 0
\(646\) −4131.00 + 7155.10i −0.251598 + 0.435780i
\(647\) 1474.50 + 2553.91i 0.0895959 + 0.155185i 0.907340 0.420397i \(-0.138109\pi\)
−0.817744 + 0.575581i \(0.804776\pi\)
\(648\) 0 0
\(649\) 429.000 0.0259472
\(650\) 7839.00 + 7543.08i 0.473032 + 0.455175i
\(651\) 0 0
\(652\) −5658.00 + 3266.65i −0.339853 + 0.196214i
\(653\) 6019.50 + 10426.1i 0.360737 + 0.624815i 0.988082 0.153926i \(-0.0491919\pi\)
−0.627345 + 0.778741i \(0.715859\pi\)
\(654\) 0 0
\(655\) 5154.58i 0.307490i
\(656\) 27240.0 + 15727.0i 1.62126 + 0.936032i
\(657\) 0 0
\(658\) 26749.8i 1.58483i
\(659\) 1681.50 2912.44i 0.0993960 0.172159i −0.812039 0.583603i \(-0.801642\pi\)
0.911435 + 0.411445i \(0.134976\pi\)
\(660\) 0 0
\(661\) 8797.50 5079.24i 0.517675 0.298880i −0.218308 0.975880i \(-0.570054\pi\)
0.735983 + 0.677000i \(0.236720\pi\)
\(662\) −18282.0 −1.07334
\(663\) 0 0
\(664\) 5904.00 0.345060
\(665\) 23868.0 13780.2i 1.39182 0.803569i
\(666\) 0 0
\(667\) 1966.50 3406.08i 0.114158 0.197727i
\(668\) 6505.58i 0.376809i
\(669\) 0 0
\(670\) 6840.00 + 3949.08i 0.394406 + 0.227711i
\(671\) 382.783i 0.0220226i
\(672\) 0 0
\(673\) 9084.50 + 15734.8i 0.520329 + 0.901237i 0.999721 + 0.0236358i \(0.00752419\pi\)
−0.479391 + 0.877601i \(0.659142\pi\)
\(674\) 24834.0 14337.9i 1.41924 0.819400i
\(675\) 0 0
\(676\) 338.000 + 8781.50i 0.0192308 + 0.499630i
\(677\) −9042.00 −0.513312 −0.256656 0.966503i \(-0.582621\pi\)
−0.256656 + 0.966503i \(0.582621\pi\)
\(678\) 0 0
\(679\) 13903.5 + 24081.6i 0.785813 + 1.36107i
\(680\) −2592.00 + 4489.48i −0.146175 + 0.253182i
\(681\) 0 0
\(682\) 4914.00 + 2837.10i 0.275904 + 0.159293i
\(683\) 10792.5 + 6231.05i 0.604632 + 0.349084i 0.770862 0.637003i \(-0.219826\pi\)
−0.166230 + 0.986087i \(0.553159\pi\)
\(684\) 0 0
\(685\) −8244.00 + 14279.0i −0.459835 + 0.796458i
\(686\) −6981.00 12091.4i −0.388536 0.672964i
\(687\) 0 0
\(688\) 6800.00 0.376813
\(689\) 5538.00 + 19184.2i 0.306213 + 1.06075i
\(690\) 0 0
\(691\) −3739.50 + 2159.00i −0.205872 + 0.118860i −0.599391 0.800456i \(-0.704591\pi\)
0.393520 + 0.919316i \(0.371257\pi\)
\(692\) 1746.00 + 3024.16i 0.0959147 + 0.166129i
\(693\) 0 0
\(694\) 23788.0i 1.30112i
\(695\) 30540.0 + 17632.3i 1.66683 + 0.962346i
\(696\) 0 0
\(697\) 10615.7i 0.576901i
\(698\) 21051.0 36461.4i 1.14154 1.97720i
\(699\) 0 0
\(700\) −5226.00 + 3017.23i −0.282177 + 0.162915i
\(701\) 18270.0 0.984377 0.492189 0.870489i \(-0.336197\pi\)
0.492189 + 0.870489i \(0.336197\pi\)
\(702\) 0 0
\(703\) 3519.00 0.188793
\(704\) −1248.00 + 720.533i −0.0668122 + 0.0385740i
\(705\) 0 0
\(706\) −10059.0 + 17422.7i −0.536226 + 0.928770i
\(707\) 44110.1i 2.34644i
\(708\) 0 0
\(709\) 1411.50 + 814.930i 0.0747673 + 0.0431669i 0.536918 0.843635i \(-0.319589\pi\)
−0.462150 + 0.886802i \(0.652922\pi\)
\(710\) 28017.7i 1.48096i
\(711\) 0 0
\(712\) −2124.00 3678.88i −0.111798 0.193640i
\(713\) −3591.00 + 2073.26i −0.188617 + 0.108898i
\(714\) 0 0
\(715\) 10140.0 10537.8i 0.530370 0.551177i
\(716\) −5148.00 −0.268701
\(717\) 0 0
\(718\) 2322.00 + 4021.82i 0.120691 + 0.209043i
\(719\) 4915.50 8513.90i 0.254961 0.441606i −0.709924 0.704279i \(-0.751271\pi\)
0.964885 + 0.262673i \(0.0846039\pi\)
\(720\) 0 0
\(721\) 36192.0 + 20895.5i 1.86943 + 1.07932i
\(722\) 2832.00 + 1635.06i 0.145978 + 0.0842804i
\(723\) 0 0
\(724\) 4.00000 6.92820i 0.000205330 0.000355642i
\(725\) 2311.50 + 4003.64i 0.118410 + 0.205091i
\(726\) 0 0
\(727\) −15464.0 −0.788897 −0.394448 0.918918i \(-0.629064\pi\)
−0.394448 + 0.918918i \(0.629064\pi\)
\(728\) 14196.0 + 3512.60i 0.722718 + 0.178826i
\(729\) 0 0
\(730\) 41760.0 24110.1i 2.11727 1.22241i
\(731\) −1147.50 1987.53i −0.0580599 0.100563i
\(732\) 0 0
\(733\) 12616.3i 0.635733i 0.948136 + 0.317866i \(0.102966\pi\)
−0.948136 + 0.317866i \(0.897034\pi\)
\(734\) −10995.0 6347.97i −0.552906 0.319220i
\(735\) 0 0
\(736\) 9477.78i 0.474668i
\(737\) 1852.50 3208.62i 0.0925885 0.160368i
\(738\) 0 0
\(739\) −14101.5 + 8141.50i −0.701938 + 0.405264i −0.808069 0.589088i \(-0.799487\pi\)
0.106131 + 0.994352i \(0.466154\pi\)
\(740\) −2208.00 −0.109686
\(741\) 0 0
\(742\) −33228.0 −1.64399
\(743\) −9358.50 + 5403.13i −0.462086 + 0.266786i −0.712921 0.701244i \(-0.752628\pi\)
0.250835 + 0.968030i \(0.419295\pi\)
\(744\) 0 0
\(745\) 9036.00 15650.8i 0.444367 0.769666i
\(746\) 18605.7i 0.913140i
\(747\) 0 0
\(748\) −2106.00 1215.90i −0.102945 0.0594354i
\(749\) 5741.75i 0.280105i
\(750\) 0 0
\(751\) 6807.50 + 11790.9i 0.330771 + 0.572913i 0.982663 0.185399i \(-0.0593578\pi\)
−0.651892 + 0.758312i \(0.726024\pi\)
\(752\) 23760.0 13717.8i 1.15218 0.665210i
\(753\) 0 0
\(754\) −2691.00 + 10875.5i −0.129974 + 0.525284i
\(755\) −1200.00 −0.0578443
\(756\) 0 0
\(757\) −2775.50 4807.31i −0.133259 0.230812i 0.791672 0.610947i \(-0.209211\pi\)
−0.924931 + 0.380135i \(0.875878\pi\)
\(758\) −19935.0 + 34528.4i −0.955240 + 1.65452i
\(759\) 0 0
\(760\) 14688.0 + 8480.12i 0.701039 + 0.404745i
\(761\) −8731.50 5041.13i −0.415922 0.240133i 0.277409 0.960752i \(-0.410524\pi\)
−0.693331 + 0.720619i \(0.743858\pi\)
\(762\) 0 0
\(763\) −6864.00 + 11888.8i −0.325680 + 0.564093i
\(764\) 5682.00 + 9841.51i 0.269067 + 0.466039i
\(765\) 0 0
\(766\) −8382.00 −0.395371
\(767\) 214.500 866.891i 0.0100980 0.0408105i
\(768\) 0 0
\(769\) 25771.5 14879.2i 1.20851 0.697733i 0.246076 0.969250i \(-0.420859\pi\)
0.962434 + 0.271517i \(0.0875253\pi\)
\(770\) 12168.0 + 21075.6i 0.569486 + 0.986379i
\(771\) 0 0
\(772\) 16981.0i 0.791659i
\(773\) −24019.5 13867.7i −1.11762 0.645259i −0.176829 0.984242i \(-0.556584\pi\)
−0.940793 + 0.338983i \(0.889917\pi\)
\(774\) 0 0
\(775\) 4873.99i 0.225908i
\(776\) −8556.00 + 14819.4i −0.395802 + 0.685550i
\(777\) 0 0
\(778\) 29574.0 17074.6i 1.36283 0.786828i
\(779\) −34731.0 −1.59739
\(780\) 0 0
\(781\) −13143.0 −0.602168
\(782\) 4617.00 2665.63i 0.211130 0.121896i
\(783\) 0