Properties

Label 225.4.h.a.136.7
Level $225$
Weight $4$
Character 225.136
Analytic conductor $13.275$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 136.7
Character \(\chi\) \(=\) 225.136
Dual form 225.4.h.a.91.7

$q$-expansion

\(f(q)\) \(=\) \(q+(3.76530 - 2.73565i) q^{2} +(4.22155 - 12.9926i) q^{4} +(-5.34090 - 9.82216i) q^{5} -26.0445 q^{7} +(-8.14206 - 25.0587i) q^{8} +O(q^{10})\) \(q+(3.76530 - 2.73565i) q^{2} +(4.22155 - 12.9926i) q^{4} +(-5.34090 - 9.82216i) q^{5} -26.0445 q^{7} +(-8.14206 - 25.0587i) q^{8} +(-46.9800 - 22.3725i) q^{10} +(2.03543 - 1.47883i) q^{11} +(-32.0534 - 23.2881i) q^{13} +(-98.0653 + 71.2486i) q^{14} +(-10.7917 - 7.84062i) q^{16} +(26.2638 + 80.8316i) q^{17} +(-44.1360 - 135.837i) q^{19} +(-150.162 + 27.9275i) q^{20} +(3.61845 - 11.1365i) q^{22} +(127.177 - 92.3993i) q^{23} +(-67.9495 + 104.918i) q^{25} -184.399 q^{26} +(-109.948 + 338.386i) q^{28} +(30.9737 - 95.3273i) q^{29} +(-53.5715 - 164.876i) q^{31} +148.703 q^{32} +(320.018 + 232.506i) q^{34} +(139.101 + 255.813i) q^{35} +(48.0520 + 34.9118i) q^{37} +(-537.786 - 390.725i) q^{38} +(-202.644 + 213.809i) q^{40} +(-287.546 - 208.914i) q^{41} +109.742 q^{43} +(-10.6211 - 32.6885i) q^{44} +(226.086 - 695.821i) q^{46} +(17.9575 - 55.2674i) q^{47} +335.317 q^{49} +(31.1696 + 580.935i) q^{50} +(-437.888 + 318.144i) q^{52} +(120.787 - 371.745i) q^{53} +(-25.3963 - 12.0941i) q^{55} +(212.056 + 652.641i) q^{56} +(-144.157 - 443.669i) q^{58} +(333.759 + 242.490i) q^{59} +(-290.142 + 210.800i) q^{61} +(-652.756 - 474.255i) q^{62} +(646.244 - 469.524i) q^{64} +(-57.5458 + 439.213i) q^{65} +(108.468 + 333.831i) q^{67} +1161.09 q^{68} +(1223.57 + 582.681i) q^{70} +(-52.7887 + 162.467i) q^{71} +(754.724 - 548.339i) q^{73} +276.437 q^{74} -1951.19 q^{76} +(-53.0119 + 38.5154i) q^{77} +(-405.819 + 1248.98i) q^{79} +(-19.3744 + 147.874i) q^{80} -1654.21 q^{82} +(202.066 + 621.896i) q^{83} +(653.668 - 689.680i) q^{85} +(413.211 - 300.216i) q^{86} +(-53.6301 - 38.9646i) q^{88} +(857.273 - 622.845i) q^{89} +(834.814 + 606.528i) q^{91} +(-663.624 - 2042.42i) q^{92} +(-83.5770 - 257.224i) q^{94} +(-1098.48 + 1159.00i) q^{95} +(198.234 - 610.103i) q^{97} +(1262.57 - 917.308i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.76530 2.73565i 1.33123 0.967198i 0.331515 0.943450i \(-0.392440\pi\)
0.999718 0.0237477i \(-0.00755984\pi\)
\(3\) 0 0
\(4\) 4.22155 12.9926i 0.527694 1.62407i
\(5\) −5.34090 9.82216i −0.477705 0.878520i
\(6\) 0 0
\(7\) −26.0445 −1.40627 −0.703136 0.711056i \(-0.748217\pi\)
−0.703136 + 0.711056i \(0.748217\pi\)
\(8\) −8.14206 25.0587i −0.359832 1.10745i
\(9\) 0 0
\(10\) −46.9800 22.3725i −1.48564 0.707481i
\(11\) 2.03543 1.47883i 0.0557915 0.0405349i −0.559540 0.828803i \(-0.689022\pi\)
0.615331 + 0.788268i \(0.289022\pi\)
\(12\) 0 0
\(13\) −32.0534 23.2881i −0.683846 0.496843i 0.190785 0.981632i \(-0.438897\pi\)
−0.874632 + 0.484788i \(0.838897\pi\)
\(14\) −98.0653 + 71.2486i −1.87208 + 1.36014i
\(15\) 0 0
\(16\) −10.7917 7.84062i −0.168620 0.122510i
\(17\) 26.2638 + 80.8316i 0.374700 + 1.15321i 0.943681 + 0.330857i \(0.107338\pi\)
−0.568981 + 0.822351i \(0.692662\pi\)
\(18\) 0 0
\(19\) −44.1360 135.837i −0.532921 1.64016i −0.748099 0.663587i \(-0.769033\pi\)
0.215179 0.976575i \(-0.430967\pi\)
\(20\) −150.162 + 27.9275i −1.67886 + 0.312239i
\(21\) 0 0
\(22\) 3.61845 11.1365i 0.0350662 0.107923i
\(23\) 127.177 92.3993i 1.15296 0.837678i 0.164092 0.986445i \(-0.447531\pi\)
0.988872 + 0.148768i \(0.0475306\pi\)
\(24\) 0 0
\(25\) −67.9495 + 104.918i −0.543596 + 0.839347i
\(26\) −184.399 −1.39090
\(27\) 0 0
\(28\) −109.948 + 338.386i −0.742081 + 2.28389i
\(29\) 30.9737 95.3273i 0.198334 0.610408i −0.801588 0.597877i \(-0.796011\pi\)
0.999921 0.0125312i \(-0.00398890\pi\)
\(30\) 0 0
\(31\) −53.5715 164.876i −0.310378 0.955246i −0.977615 0.210401i \(-0.932523\pi\)
0.667237 0.744846i \(-0.267477\pi\)
\(32\) 148.703 0.821476
\(33\) 0 0
\(34\) 320.018 + 232.506i 1.61419 + 1.17278i
\(35\) 139.101 + 255.813i 0.671783 + 1.23544i
\(36\) 0 0
\(37\) 48.0520 + 34.9118i 0.213506 + 0.155121i 0.689398 0.724382i \(-0.257875\pi\)
−0.475893 + 0.879503i \(0.657875\pi\)
\(38\) −537.786 390.725i −2.29580 1.66800i
\(39\) 0 0
\(40\) −202.644 + 213.809i −0.801022 + 0.845153i
\(41\) −287.546 208.914i −1.09530 0.795779i −0.115011 0.993364i \(-0.536690\pi\)
−0.980286 + 0.197585i \(0.936690\pi\)
\(42\) 0 0
\(43\) 109.742 0.389198 0.194599 0.980883i \(-0.437659\pi\)
0.194599 + 0.980883i \(0.437659\pi\)
\(44\) −10.6211 32.6885i −0.0363908 0.112000i
\(45\) 0 0
\(46\) 226.086 695.821i 0.724665 2.23029i
\(47\) 17.9575 55.2674i 0.0557312 0.171523i −0.919316 0.393520i \(-0.871257\pi\)
0.975047 + 0.221997i \(0.0712574\pi\)
\(48\) 0 0
\(49\) 335.317 0.977600
\(50\) 31.1696 + 580.935i 0.0881610 + 1.64313i
\(51\) 0 0
\(52\) −437.888 + 318.144i −1.16777 + 0.848436i
\(53\) 120.787 371.745i 0.313045 0.963455i −0.663506 0.748171i \(-0.730932\pi\)
0.976552 0.215284i \(-0.0690676\pi\)
\(54\) 0 0
\(55\) −25.3963 12.0941i −0.0622626 0.0296502i
\(56\) 212.056 + 652.641i 0.506021 + 1.55737i
\(57\) 0 0
\(58\) −144.157 443.669i −0.326357 1.00442i
\(59\) 333.759 + 242.490i 0.736470 + 0.535077i 0.891604 0.452817i \(-0.149581\pi\)
−0.155134 + 0.987893i \(0.549581\pi\)
\(60\) 0 0
\(61\) −290.142 + 210.800i −0.608998 + 0.442463i −0.849061 0.528294i \(-0.822832\pi\)
0.240064 + 0.970757i \(0.422832\pi\)
\(62\) −652.756 474.255i −1.33710 0.971459i
\(63\) 0 0
\(64\) 646.244 469.524i 1.26220 0.917039i
\(65\) −57.5458 + 439.213i −0.109810 + 0.838118i
\(66\) 0 0
\(67\) 108.468 + 333.831i 0.197783 + 0.608715i 0.999933 + 0.0115915i \(0.00368977\pi\)
−0.802149 + 0.597123i \(0.796310\pi\)
\(68\) 1161.09 2.07062
\(69\) 0 0
\(70\) 1223.57 + 582.681i 2.08921 + 0.994910i
\(71\) −52.7887 + 162.467i −0.0882376 + 0.271567i −0.985432 0.170068i \(-0.945601\pi\)
0.897195 + 0.441635i \(0.145601\pi\)
\(72\) 0 0
\(73\) 754.724 548.339i 1.21005 0.879154i 0.214817 0.976654i \(-0.431085\pi\)
0.995236 + 0.0975001i \(0.0310846\pi\)
\(74\) 276.437 0.434258
\(75\) 0 0
\(76\) −1951.19 −2.94496
\(77\) −53.0119 + 38.5154i −0.0784580 + 0.0570030i
\(78\) 0 0
\(79\) −405.819 + 1248.98i −0.577952 + 1.77875i 0.0479457 + 0.998850i \(0.484733\pi\)
−0.625898 + 0.779905i \(0.715267\pi\)
\(80\) −19.3744 + 147.874i −0.0270766 + 0.206660i
\(81\) 0 0
\(82\) −1654.21 −2.22777
\(83\) 202.066 + 621.896i 0.267225 + 0.822433i 0.991173 + 0.132578i \(0.0423255\pi\)
−0.723948 + 0.689855i \(0.757674\pi\)
\(84\) 0 0
\(85\) 653.668 689.680i 0.834121 0.880075i
\(86\) 413.211 300.216i 0.518113 0.376431i
\(87\) 0 0
\(88\) −53.6301 38.9646i −0.0649658 0.0472004i
\(89\) 857.273 622.845i 1.02102 0.741814i 0.0545280 0.998512i \(-0.482635\pi\)
0.966492 + 0.256698i \(0.0826346\pi\)
\(90\) 0 0
\(91\) 834.814 + 606.528i 0.961674 + 0.698697i
\(92\) −663.624 2042.42i −0.752039 2.31454i
\(93\) 0 0
\(94\) −83.5770 257.224i −0.0917054 0.282240i
\(95\) −1098.48 + 1159.00i −1.18634 + 1.25169i
\(96\) 0 0
\(97\) 198.234 610.103i 0.207502 0.638624i −0.792100 0.610392i \(-0.791012\pi\)
0.999601 0.0282327i \(-0.00898793\pi\)
\(98\) 1262.57 917.308i 1.30141 0.945532i
\(99\) 0 0
\(100\) 1076.31 + 1325.76i 1.07631 + 1.32576i
\(101\) −864.030 −0.851229 −0.425615 0.904904i \(-0.639942\pi\)
−0.425615 + 0.904904i \(0.639942\pi\)
\(102\) 0 0
\(103\) 566.152 1742.44i 0.541598 1.66687i −0.187345 0.982294i \(-0.559988\pi\)
0.728944 0.684574i \(-0.240012\pi\)
\(104\) −322.589 + 992.828i −0.304159 + 0.936104i
\(105\) 0 0
\(106\) −562.163 1730.16i −0.515115 1.58536i
\(107\) 1037.99 0.937816 0.468908 0.883247i \(-0.344648\pi\)
0.468908 + 0.883247i \(0.344648\pi\)
\(108\) 0 0
\(109\) −1259.67 915.201i −1.10692 0.804224i −0.124743 0.992189i \(-0.539811\pi\)
−0.982176 + 0.187966i \(0.939811\pi\)
\(110\) −128.710 + 23.9377i −0.111564 + 0.0207488i
\(111\) 0 0
\(112\) 281.064 + 204.205i 0.237126 + 0.172282i
\(113\) −788.953 573.208i −0.656800 0.477193i 0.208781 0.977963i \(-0.433051\pi\)
−0.865581 + 0.500769i \(0.833051\pi\)
\(114\) 0 0
\(115\) −1586.80 755.654i −1.28669 0.612740i
\(116\) −1107.79 804.858i −0.886689 0.644217i
\(117\) 0 0
\(118\) 1920.07 1.49794
\(119\) −684.027 2105.22i −0.526930 1.62172i
\(120\) 0 0
\(121\) −409.346 + 1259.84i −0.307547 + 0.946534i
\(122\) −515.794 + 1587.45i −0.382769 + 1.17804i
\(123\) 0 0
\(124\) −2368.33 −1.71518
\(125\) 1393.44 + 107.052i 0.997062 + 0.0766002i
\(126\) 0 0
\(127\) 832.392 604.768i 0.581597 0.422555i −0.257702 0.966224i \(-0.582965\pi\)
0.839300 + 0.543669i \(0.182965\pi\)
\(128\) 781.235 2404.39i 0.539469 1.66032i
\(129\) 0 0
\(130\) 984.855 + 1811.19i 0.664442 + 1.22194i
\(131\) 825.045 + 2539.23i 0.550264 + 1.69354i 0.708134 + 0.706078i \(0.249537\pi\)
−0.157870 + 0.987460i \(0.550463\pi\)
\(132\) 0 0
\(133\) 1149.50 + 3537.80i 0.749431 + 2.30651i
\(134\) 1321.66 + 960.241i 0.852044 + 0.619046i
\(135\) 0 0
\(136\) 1811.69 1316.27i 1.14229 0.829921i
\(137\) −986.533 716.758i −0.615221 0.446984i 0.236028 0.971746i \(-0.424154\pi\)
−0.851249 + 0.524762i \(0.824154\pi\)
\(138\) 0 0
\(139\) −708.126 + 514.484i −0.432104 + 0.313942i −0.782490 0.622664i \(-0.786051\pi\)
0.350386 + 0.936606i \(0.386051\pi\)
\(140\) 3910.90 727.357i 2.36094 0.439092i
\(141\) 0 0
\(142\) 245.687 + 756.148i 0.145194 + 0.446863i
\(143\) −99.6816 −0.0582923
\(144\) 0 0
\(145\) −1101.75 + 204.905i −0.631001 + 0.117355i
\(146\) 1341.70 4129.32i 0.760546 2.34072i
\(147\) 0 0
\(148\) 656.449 476.938i 0.364593 0.264893i
\(149\) 819.633 0.450650 0.225325 0.974284i \(-0.427656\pi\)
0.225325 + 0.974284i \(0.427656\pi\)
\(150\) 0 0
\(151\) 567.457 0.305821 0.152911 0.988240i \(-0.451135\pi\)
0.152911 + 0.988240i \(0.451135\pi\)
\(152\) −3044.53 + 2211.98i −1.62463 + 1.18036i
\(153\) 0 0
\(154\) −94.2409 + 290.044i −0.0493126 + 0.151769i
\(155\) −1333.32 + 1406.78i −0.690934 + 0.729000i
\(156\) 0 0
\(157\) −1643.63 −0.835516 −0.417758 0.908558i \(-0.637184\pi\)
−0.417758 + 0.908558i \(0.637184\pi\)
\(158\) 1888.75 + 5812.97i 0.951018 + 2.92693i
\(159\) 0 0
\(160\) −794.208 1460.58i −0.392423 0.721683i
\(161\) −3312.26 + 2406.49i −1.62138 + 1.17800i
\(162\) 0 0
\(163\) 1035.78 + 752.538i 0.497721 + 0.361615i 0.808146 0.588982i \(-0.200471\pi\)
−0.310425 + 0.950598i \(0.600471\pi\)
\(164\) −3928.23 + 2854.03i −1.87039 + 1.35892i
\(165\) 0 0
\(166\) 2462.13 + 1788.84i 1.15119 + 0.836391i
\(167\) 487.198 + 1499.44i 0.225752 + 0.694792i 0.998214 + 0.0597320i \(0.0190246\pi\)
−0.772463 + 0.635060i \(0.780975\pi\)
\(168\) 0 0
\(169\) −193.829 596.545i −0.0882246 0.271527i
\(170\) 574.531 4385.06i 0.259203 1.97834i
\(171\) 0 0
\(172\) 463.282 1425.83i 0.205377 0.632086i
\(173\) 1797.33 1305.83i 0.789874 0.573877i −0.118052 0.993007i \(-0.537665\pi\)
0.907926 + 0.419131i \(0.137665\pi\)
\(174\) 0 0
\(175\) 1769.71 2732.55i 0.764444 1.18035i
\(176\) −33.5607 −0.0143735
\(177\) 0 0
\(178\) 1524.00 4690.39i 0.641734 1.97506i
\(179\) −931.708 + 2867.50i −0.389045 + 1.19736i 0.544458 + 0.838788i \(0.316736\pi\)
−0.933503 + 0.358570i \(0.883264\pi\)
\(180\) 0 0
\(181\) 764.093 + 2351.64i 0.313782 + 0.965722i 0.976253 + 0.216634i \(0.0695079\pi\)
−0.662471 + 0.749088i \(0.730492\pi\)
\(182\) 4802.57 1.95599
\(183\) 0 0
\(184\) −3350.88 2434.56i −1.34256 0.975425i
\(185\) 86.2684 658.435i 0.0342842 0.261671i
\(186\) 0 0
\(187\) 172.994 + 125.688i 0.0676502 + 0.0491508i
\(188\) −642.259 466.628i −0.249157 0.181023i
\(189\) 0 0
\(190\) −965.494 + 7369.04i −0.368654 + 2.81372i
\(191\) −518.536 376.738i −0.196439 0.142722i 0.485218 0.874393i \(-0.338740\pi\)
−0.681657 + 0.731672i \(0.738740\pi\)
\(192\) 0 0
\(193\) −658.953 −0.245764 −0.122882 0.992421i \(-0.539214\pi\)
−0.122882 + 0.992421i \(0.539214\pi\)
\(194\) −922.615 2839.52i −0.341443 1.05085i
\(195\) 0 0
\(196\) 1415.56 4356.63i 0.515873 1.58769i
\(197\) −865.948 + 2665.12i −0.313179 + 0.963866i 0.663318 + 0.748337i \(0.269147\pi\)
−0.976498 + 0.215529i \(0.930853\pi\)
\(198\) 0 0
\(199\) −2715.89 −0.967459 −0.483729 0.875218i \(-0.660718\pi\)
−0.483729 + 0.875218i \(0.660718\pi\)
\(200\) 3182.36 + 848.474i 1.12514 + 0.299981i
\(201\) 0 0
\(202\) −3253.33 + 2363.68i −1.13318 + 0.823307i
\(203\) −806.696 + 2482.75i −0.278911 + 0.858400i
\(204\) 0 0
\(205\) −516.235 + 3940.11i −0.175880 + 1.34239i
\(206\) −2634.96 8109.58i −0.891197 2.74282i
\(207\) 0 0
\(208\) 163.317 + 502.637i 0.0544421 + 0.167556i
\(209\) −290.715 211.217i −0.0962162 0.0699051i
\(210\) 0 0
\(211\) 1402.23 1018.78i 0.457505 0.332397i −0.335047 0.942201i \(-0.608752\pi\)
0.792552 + 0.609805i \(0.208752\pi\)
\(212\) −4320.02 3138.68i −1.39953 1.01682i
\(213\) 0 0
\(214\) 3908.34 2839.58i 1.24845 0.907053i
\(215\) −586.122 1077.90i −0.185922 0.341918i
\(216\) 0 0
\(217\) 1395.24 + 4294.12i 0.436476 + 1.34334i
\(218\) −7246.68 −2.25141
\(219\) 0 0
\(220\) −264.345 + 278.909i −0.0810098 + 0.0854728i
\(221\) 1040.57 3202.56i 0.316727 0.974784i
\(222\) 0 0
\(223\) −3541.18 + 2572.82i −1.06338 + 0.772594i −0.974712 0.223467i \(-0.928263\pi\)
−0.0886732 + 0.996061i \(0.528263\pi\)
\(224\) −3872.90 −1.15522
\(225\) 0 0
\(226\) −4538.74 −1.33589
\(227\) −1819.26 + 1321.77i −0.531931 + 0.386471i −0.821080 0.570814i \(-0.806628\pi\)
0.289148 + 0.957284i \(0.406628\pi\)
\(228\) 0 0
\(229\) 693.843 2135.43i 0.200220 0.616215i −0.799656 0.600459i \(-0.794985\pi\)
0.999876 0.0157557i \(-0.00501539\pi\)
\(230\) −8041.97 + 1495.66i −2.30553 + 0.428787i
\(231\) 0 0
\(232\) −2640.97 −0.747362
\(233\) −218.901 673.707i −0.0615479 0.189425i 0.915555 0.402193i \(-0.131752\pi\)
−0.977103 + 0.212768i \(0.931752\pi\)
\(234\) 0 0
\(235\) −638.754 + 118.797i −0.177310 + 0.0329764i
\(236\) 4559.56 3312.71i 1.25763 0.913725i
\(237\) 0 0
\(238\) −8334.70 6055.52i −2.26999 1.64925i
\(239\) 4411.37 3205.04i 1.19392 0.867435i 0.200249 0.979745i \(-0.435825\pi\)
0.993673 + 0.112309i \(0.0358248\pi\)
\(240\) 0 0
\(241\) −4628.17 3362.56i −1.23704 0.898762i −0.239642 0.970861i \(-0.577030\pi\)
−0.997397 + 0.0720995i \(0.977030\pi\)
\(242\) 1905.16 + 5863.48i 0.506068 + 1.55752i
\(243\) 0 0
\(244\) 1514.00 + 4659.60i 0.397228 + 1.22254i
\(245\) −1790.89 3293.53i −0.467004 0.858841i
\(246\) 0 0
\(247\) −1748.67 + 5381.87i −0.450468 + 1.38640i
\(248\) −3695.40 + 2684.86i −0.946202 + 0.687456i
\(249\) 0 0
\(250\) 5539.56 3408.87i 1.40141 0.862383i
\(251\) −2045.23 −0.514319 −0.257159 0.966369i \(-0.582787\pi\)
−0.257159 + 0.966369i \(0.582787\pi\)
\(252\) 0 0
\(253\) 122.217 376.145i 0.0303704 0.0934705i
\(254\) 1479.77 4554.26i 0.365547 1.12504i
\(255\) 0 0
\(256\) −1661.25 5112.79i −0.405578 1.24824i
\(257\) −407.547 −0.0989186 −0.0494593 0.998776i \(-0.515750\pi\)
−0.0494593 + 0.998776i \(0.515750\pi\)
\(258\) 0 0
\(259\) −1251.49 909.262i −0.300247 0.218142i
\(260\) 5463.58 + 2601.83i 1.30322 + 0.620610i
\(261\) 0 0
\(262\) 10053.0 + 7303.91i 2.37052 + 1.72228i
\(263\) −717.991 521.651i −0.168339 0.122306i 0.500426 0.865779i \(-0.333177\pi\)
−0.668765 + 0.743474i \(0.733177\pi\)
\(264\) 0 0
\(265\) −4296.45 + 799.062i −0.995958 + 0.185230i
\(266\) 14006.4 + 10176.2i 3.22852 + 2.34566i
\(267\) 0 0
\(268\) 4795.23 1.09297
\(269\) −1864.45 5738.18i −0.422592 1.30061i −0.905281 0.424814i \(-0.860340\pi\)
0.482688 0.875792i \(-0.339660\pi\)
\(270\) 0 0
\(271\) 2019.40 6215.08i 0.452656 1.39313i −0.421209 0.906964i \(-0.638394\pi\)
0.873865 0.486169i \(-0.161606\pi\)
\(272\) 350.339 1078.23i 0.0780972 0.240358i
\(273\) 0 0
\(274\) −5675.39 −1.25132
\(275\) 16.8496 + 314.040i 0.00369480 + 0.0688630i
\(276\) 0 0
\(277\) 4454.88 3236.66i 0.966309 0.702064i 0.0117014 0.999932i \(-0.496275\pi\)
0.954607 + 0.297867i \(0.0962753\pi\)
\(278\) −1258.86 + 3874.37i −0.271587 + 0.835860i
\(279\) 0 0
\(280\) 5277.77 5568.54i 1.12645 1.18851i
\(281\) 2323.54 + 7151.11i 0.493276 + 1.51815i 0.819626 + 0.572898i \(0.194181\pi\)
−0.326350 + 0.945249i \(0.605819\pi\)
\(282\) 0 0
\(283\) 1384.45 + 4260.88i 0.290801 + 0.894994i 0.984600 + 0.174825i \(0.0559359\pi\)
−0.693798 + 0.720169i \(0.744064\pi\)
\(284\) 1888.02 + 1371.73i 0.394483 + 0.286609i
\(285\) 0 0
\(286\) −375.331 + 272.694i −0.0776006 + 0.0563802i
\(287\) 7489.00 + 5441.08i 1.54028 + 1.11908i
\(288\) 0 0
\(289\) −1869.26 + 1358.09i −0.380471 + 0.276429i
\(290\) −3587.86 + 3785.52i −0.726504 + 0.766529i
\(291\) 0 0
\(292\) −3938.24 12120.7i −0.789275 2.42914i
\(293\) 6672.17 1.33035 0.665174 0.746688i \(-0.268357\pi\)
0.665174 + 0.746688i \(0.268357\pi\)
\(294\) 0 0
\(295\) 599.201 4573.35i 0.118261 0.902612i
\(296\) 483.602 1488.37i 0.0949622 0.292264i
\(297\) 0 0
\(298\) 3086.16 2242.23i 0.599921 0.435868i
\(299\) −6228.25 −1.20464
\(300\) 0 0
\(301\) −2858.18 −0.547318
\(302\) 2136.65 1552.36i 0.407120 0.295790i
\(303\) 0 0
\(304\) −588.742 + 1811.96i −0.111075 + 0.341852i
\(305\) 3620.13 + 1723.95i 0.679634 + 0.323650i
\(306\) 0 0
\(307\) 5433.28 1.01008 0.505039 0.863097i \(-0.331478\pi\)
0.505039 + 0.863097i \(0.331478\pi\)
\(308\) 276.622 + 851.356i 0.0511754 + 0.157502i
\(309\) 0 0
\(310\) −1171.90 + 8944.42i −0.214708 + 1.63874i
\(311\) 415.035 301.541i 0.0756736 0.0549801i −0.549305 0.835622i \(-0.685108\pi\)
0.624979 + 0.780642i \(0.285108\pi\)
\(312\) 0 0
\(313\) 806.159 + 585.709i 0.145581 + 0.105771i 0.658192 0.752850i \(-0.271322\pi\)
−0.512611 + 0.858621i \(0.671322\pi\)
\(314\) −6188.75 + 4496.39i −1.11227 + 0.808109i
\(315\) 0 0
\(316\) 14514.4 + 10545.3i 2.58385 + 1.87728i
\(317\) −1322.77 4071.07i −0.234366 0.721305i −0.997205 0.0747164i \(-0.976195\pi\)
0.762838 0.646589i \(-0.223805\pi\)
\(318\) 0 0
\(319\) −77.9278 239.837i −0.0136775 0.0420950i
\(320\) −8063.27 3839.83i −1.40859 0.670791i
\(321\) 0 0
\(322\) −5888.30 + 18122.3i −1.01908 + 3.13639i
\(323\) 9820.71 7135.17i 1.69176 1.22914i
\(324\) 0 0
\(325\) 4621.36 1780.57i 0.788760 0.303902i
\(326\) 5958.70 1.01234
\(327\) 0 0
\(328\) −2893.90 + 8906.52i −0.487162 + 1.49933i
\(329\) −467.694 + 1439.41i −0.0783732 + 0.241208i
\(330\) 0 0
\(331\) −918.630 2827.25i −0.152545 0.469486i 0.845359 0.534199i \(-0.179387\pi\)
−0.997904 + 0.0647132i \(0.979387\pi\)
\(332\) 8933.07 1.47670
\(333\) 0 0
\(334\) 5936.39 + 4313.04i 0.972529 + 0.706584i
\(335\) 2699.62 2848.35i 0.440286 0.464543i
\(336\) 0 0
\(337\) −1248.14 906.825i −0.201752 0.146581i 0.482322 0.875994i \(-0.339794\pi\)
−0.684074 + 0.729413i \(0.739794\pi\)
\(338\) −2361.76 1715.92i −0.380068 0.276136i
\(339\) 0 0
\(340\) −6201.25 11404.4i −0.989146 1.81908i
\(341\) −352.865 256.371i −0.0560373 0.0407135i
\(342\) 0 0
\(343\) 200.108 0.0315009
\(344\) −893.526 2749.99i −0.140046 0.431016i
\(345\) 0 0
\(346\) 3195.16 9833.70i 0.496454 1.52793i
\(347\) 1738.01 5349.05i 0.268880 0.827527i −0.721894 0.692003i \(-0.756728\pi\)
0.990774 0.135524i \(-0.0432717\pi\)
\(348\) 0 0
\(349\) 3546.44 0.543945 0.271972 0.962305i \(-0.412324\pi\)
0.271972 + 0.962305i \(0.412324\pi\)
\(350\) −811.798 15130.2i −0.123978 2.31069i
\(351\) 0 0
\(352\) 302.675 219.906i 0.0458313 0.0332984i
\(353\) 592.091 1822.27i 0.0892742 0.274758i −0.896445 0.443155i \(-0.853859\pi\)
0.985719 + 0.168397i \(0.0538591\pi\)
\(354\) 0 0
\(355\) 1877.72 349.221i 0.280729 0.0522105i
\(356\) −4473.36 13767.6i −0.665976 2.04966i
\(357\) 0 0
\(358\) 4336.32 + 13345.8i 0.640172 + 1.97025i
\(359\) 2130.22 + 1547.69i 0.313171 + 0.227532i 0.733256 0.679953i \(-0.238000\pi\)
−0.420085 + 0.907485i \(0.638000\pi\)
\(360\) 0 0
\(361\) −10954.6 + 7958.96i −1.59711 + 1.16037i
\(362\) 9310.28 + 6764.32i 1.35176 + 0.982112i
\(363\) 0 0
\(364\) 11404.6 8285.92i 1.64221 1.19313i
\(365\) −9416.78 4484.39i −1.35040 0.643079i
\(366\) 0 0
\(367\) −2102.12 6469.65i −0.298991 0.920199i −0.981852 0.189650i \(-0.939265\pi\)
0.682861 0.730548i \(-0.260735\pi\)
\(368\) −2096.92 −0.297037
\(369\) 0 0
\(370\) −1476.42 2715.20i −0.207447 0.381505i
\(371\) −3145.85 + 9681.92i −0.440227 + 1.35488i
\(372\) 0 0
\(373\) 5424.55 3941.17i 0.753010 0.547094i −0.143748 0.989614i \(-0.545916\pi\)
0.896758 + 0.442520i \(0.145916\pi\)
\(374\) 995.212 0.137597
\(375\) 0 0
\(376\) −1531.14 −0.210007
\(377\) −3212.81 + 2334.24i −0.438907 + 0.318885i
\(378\) 0 0
\(379\) 1202.29 3700.27i 0.162948 0.501504i −0.835931 0.548835i \(-0.815072\pi\)
0.998879 + 0.0473310i \(0.0150716\pi\)
\(380\) 10421.1 + 19164.9i 1.40682 + 2.58721i
\(381\) 0 0
\(382\) −2983.06 −0.399547
\(383\) 1743.53 + 5366.04i 0.232612 + 0.715906i 0.997429 + 0.0716588i \(0.0228293\pi\)
−0.764817 + 0.644247i \(0.777171\pi\)
\(384\) 0 0
\(385\) 661.435 + 314.984i 0.0875581 + 0.0416963i
\(386\) −2481.15 + 1802.66i −0.327169 + 0.237702i
\(387\) 0 0
\(388\) −7089.96 5151.16i −0.927676 0.673996i
\(389\) −3785.35 + 2750.22i −0.493380 + 0.358462i −0.806483 0.591257i \(-0.798632\pi\)
0.313102 + 0.949719i \(0.398632\pi\)
\(390\) 0 0
\(391\) 10808.9 + 7853.14i 1.39803 + 1.01573i
\(392\) −2730.17 8402.59i −0.351771 1.08264i
\(393\) 0 0
\(394\) 4030.26 + 12403.9i 0.515334 + 1.58604i
\(395\) 14435.2 2684.68i 1.83876 0.341977i
\(396\) 0 0
\(397\) 2589.33 7969.14i 0.327342 1.00746i −0.643030 0.765841i \(-0.722323\pi\)
0.970372 0.241614i \(-0.0776769\pi\)
\(398\) −10226.1 + 7429.72i −1.28791 + 0.935724i
\(399\) 0 0
\(400\) 1555.92 599.480i 0.194489 0.0749350i
\(401\) −6042.30 −0.752464 −0.376232 0.926525i \(-0.622780\pi\)
−0.376232 + 0.926525i \(0.622780\pi\)
\(402\) 0 0
\(403\) −2122.51 + 6532.42i −0.262357 + 0.807451i
\(404\) −3647.55 + 11226.0i −0.449189 + 1.38246i
\(405\) 0 0
\(406\) 3754.49 + 11555.1i 0.458947 + 1.41249i
\(407\) 149.435 0.0181996
\(408\) 0 0
\(409\) −5290.72 3843.93i −0.639631 0.464719i 0.220092 0.975479i \(-0.429364\pi\)
−0.859723 + 0.510760i \(0.829364\pi\)
\(410\) 8834.99 + 16247.9i 1.06422 + 1.95714i
\(411\) 0 0
\(412\) −20248.7 14711.6i −2.42132 1.75919i
\(413\) −8692.59 6315.54i −1.03568 0.752463i
\(414\) 0 0
\(415\) 5029.14 5306.21i 0.594869 0.627642i
\(416\) −4766.43 3463.01i −0.561763 0.408145i
\(417\) 0 0
\(418\) −1672.44 −0.195698
\(419\) −4050.94 12467.5i −0.472319 1.45365i −0.849540 0.527525i \(-0.823120\pi\)
0.377221 0.926123i \(-0.376880\pi\)
\(420\) 0 0
\(421\) 1054.72 3246.11i 0.122100 0.375785i −0.871262 0.490819i \(-0.836698\pi\)
0.993362 + 0.115034i \(0.0366977\pi\)
\(422\) 2492.79 7672.01i 0.287552 0.884995i
\(423\) 0 0
\(424\) −10298.9 −1.17962
\(425\) −10265.3 2736.91i −1.17163 0.312376i
\(426\) 0 0
\(427\) 7556.60 5490.19i 0.856416 0.622223i
\(428\) 4381.93 13486.2i 0.494880 1.52308i
\(429\) 0 0
\(430\) −5155.69 2455.20i −0.578208 0.275350i
\(431\) 467.178 + 1437.83i 0.0522116 + 0.160691i 0.973762 0.227567i \(-0.0730771\pi\)
−0.921551 + 0.388258i \(0.873077\pi\)
\(432\) 0 0
\(433\) −2665.17 8202.55i −0.295797 0.910368i −0.982953 0.183858i \(-0.941141\pi\)
0.687156 0.726510i \(-0.258859\pi\)
\(434\) 17000.7 + 12351.7i 1.88032 + 1.36613i
\(435\) 0 0
\(436\) −17208.6 + 12502.8i −1.89023 + 1.37333i
\(437\) −18164.3 13197.1i −1.98836 1.44463i
\(438\) 0 0
\(439\) 2854.86 2074.17i 0.310375 0.225501i −0.421682 0.906744i \(-0.638560\pi\)
0.732058 + 0.681243i \(0.238560\pi\)
\(440\) −96.2828 + 734.869i −0.0104320 + 0.0796216i
\(441\) 0 0
\(442\) −4843.00 14905.2i −0.521172 1.60400i
\(443\) 9589.40 1.02846 0.514228 0.857653i \(-0.328078\pi\)
0.514228 + 0.857653i \(0.328078\pi\)
\(444\) 0 0
\(445\) −10696.3 5093.71i −1.13944 0.542618i
\(446\) −6295.26 + 19374.8i −0.668362 + 2.05701i
\(447\) 0 0
\(448\) −16831.1 + 12228.5i −1.77499 + 1.28961i
\(449\) 9820.81 1.03223 0.516117 0.856518i \(-0.327377\pi\)
0.516117 + 0.856518i \(0.327377\pi\)
\(450\) 0 0
\(451\) −894.230 −0.0933650
\(452\) −10778.1 + 7830.72i −1.12159 + 0.814881i
\(453\) 0 0
\(454\) −3234.15 + 9953.70i −0.334331 + 1.02897i
\(455\) 1498.75 11439.1i 0.154423 1.17862i
\(456\) 0 0
\(457\) 1597.23 0.163491 0.0817455 0.996653i \(-0.473951\pi\)
0.0817455 + 0.996653i \(0.473951\pi\)
\(458\) −3229.26 9938.63i −0.329461 1.01398i
\(459\) 0 0
\(460\) −16516.7 + 17426.6i −1.67412 + 1.76635i
\(461\) −3157.65 + 2294.17i −0.319016 + 0.231779i −0.735755 0.677247i \(-0.763173\pi\)
0.416740 + 0.909026i \(0.363173\pi\)
\(462\) 0 0
\(463\) 12670.8 + 9205.86i 1.27184 + 0.924044i 0.999274 0.0380937i \(-0.0121285\pi\)
0.272563 + 0.962138i \(0.412129\pi\)
\(464\) −1081.68 + 785.890i −0.108224 + 0.0786293i
\(465\) 0 0
\(466\) −2667.25 1937.87i −0.265146 0.192640i
\(467\) 1976.88 + 6084.21i 0.195887 + 0.602878i 0.999965 + 0.00835414i \(0.00265924\pi\)
−0.804078 + 0.594523i \(0.797341\pi\)
\(468\) 0 0
\(469\) −2825.00 8694.46i −0.278137 0.856019i
\(470\) −2080.11 + 2194.71i −0.204146 + 0.215393i
\(471\) 0 0
\(472\) 3359.00 10337.9i 0.327564 1.00814i
\(473\) 223.373 162.290i 0.0217139 0.0157761i
\(474\) 0 0
\(475\) 17250.8 + 4599.36i 1.66636 + 0.444280i
\(476\) −30239.9 −2.91186
\(477\) 0 0
\(478\) 7842.22 24135.9i 0.750408 2.30952i
\(479\) 3178.50 9782.42i 0.303193 0.933132i −0.677153 0.735843i \(-0.736786\pi\)
0.980345 0.197289i \(-0.0632137\pi\)
\(480\) 0 0
\(481\) −727.197 2238.08i −0.0689342 0.212158i
\(482\) −26625.2 −2.51607
\(483\) 0 0
\(484\) 14640.5 + 10636.9i 1.37495 + 0.998960i
\(485\) −7051.28 + 1311.41i −0.660169 + 0.122780i
\(486\) 0 0
\(487\) −1685.55 1224.62i −0.156837 0.113949i 0.506599 0.862182i \(-0.330902\pi\)
−0.663436 + 0.748233i \(0.730902\pi\)
\(488\) 7644.73 + 5554.22i 0.709141 + 0.515221i
\(489\) 0 0
\(490\) −15753.2 7501.87i −1.45236 0.691633i
\(491\) 14323.2 + 10406.4i 1.31649 + 0.956487i 0.999969 + 0.00790172i \(0.00251522\pi\)
0.316522 + 0.948585i \(0.397485\pi\)
\(492\) 0 0
\(493\) 8518.94 0.778243
\(494\) 8138.61 + 25048.1i 0.741242 + 2.28131i
\(495\) 0 0
\(496\) −714.605 + 2199.33i −0.0646909 + 0.199098i
\(497\) 1374.86 4231.37i 0.124086 0.381897i
\(498\) 0 0
\(499\) 5018.92 0.450256 0.225128 0.974329i \(-0.427720\pi\)
0.225128 + 0.974329i \(0.427720\pi\)
\(500\) 7273.35 17652.4i 0.650548 1.57888i
\(501\) 0 0
\(502\) −7700.91 + 5595.04i −0.684678 + 0.497448i
\(503\) 3109.30 9569.44i 0.275620 0.848270i −0.713435 0.700721i \(-0.752862\pi\)
0.989055 0.147549i \(-0.0471384\pi\)
\(504\) 0 0
\(505\) 4614.70 + 8486.64i 0.406636 + 0.747822i
\(506\) −568.818 1750.64i −0.0499744 0.153805i
\(507\) 0 0
\(508\) −4343.53 13368.0i −0.379356 1.16754i
\(509\) −4301.55 3125.26i −0.374584 0.272151i 0.384525 0.923114i \(-0.374365\pi\)
−0.759109 + 0.650963i \(0.774365\pi\)
\(510\) 0 0
\(511\) −19656.4 + 14281.2i −1.70166 + 1.23633i
\(512\) −3879.49 2818.62i −0.334865 0.243294i
\(513\) 0 0
\(514\) −1534.53 + 1114.90i −0.131684 + 0.0956738i
\(515\) −20138.3 + 3745.35i −1.72310 + 0.320466i
\(516\) 0 0
\(517\) −45.1798 139.049i −0.00384334 0.0118286i
\(518\) −7199.66 −0.610685
\(519\) 0 0
\(520\) 11474.6 2134.08i 0.967685 0.179972i
\(521\) 1938.78 5966.95i 0.163032 0.501760i −0.835854 0.548952i \(-0.815027\pi\)
0.998886 + 0.0471916i \(0.0150271\pi\)
\(522\) 0 0
\(523\) −11374.4 + 8264.02i −0.950994 + 0.690937i −0.951042 0.309063i \(-0.899985\pi\)
4.79448e−5 1.00000i \(0.499985\pi\)
\(524\) 36474.1 3.04080
\(525\) 0 0
\(526\) −4130.50 −0.342392
\(527\) 11920.2 8660.54i 0.985299 0.715862i
\(528\) 0 0
\(529\) 3876.48 11930.6i 0.318606 0.980568i
\(530\) −13991.5 + 14762.3i −1.14670 + 1.20987i
\(531\) 0 0
\(532\) 50817.9 4.14142
\(533\) 4351.59 + 13392.8i 0.353637 + 1.08838i
\(534\) 0 0
\(535\) −5543.80 10195.3i −0.447999 0.823890i
\(536\) 7482.20 5436.14i 0.602951 0.438070i
\(537\) 0 0
\(538\) −22717.8 16505.5i −1.82051 1.32268i
\(539\) 682.515 495.876i 0.0545417 0.0396269i
\(540\) 0 0
\(541\) 16286.0 + 11832.5i 1.29425 + 0.940328i 0.999882 0.0153633i \(-0.00489048\pi\)
0.294369 + 0.955692i \(0.404890\pi\)
\(542\) −9398.62 28926.0i −0.744844 2.29239i
\(543\) 0 0
\(544\) 3905.50 + 12019.9i 0.307807 + 0.947332i
\(545\) −2261.49 + 17260.6i −0.177746 + 1.35663i
\(546\) 0 0
\(547\) −4085.46 + 12573.8i −0.319345 + 0.982843i 0.654584 + 0.755989i \(0.272844\pi\)
−0.973929 + 0.226854i \(0.927156\pi\)
\(548\) −13477.3 + 9791.80i −1.05058 + 0.763293i
\(549\) 0 0
\(550\) 922.547 + 1136.36i 0.0715228 + 0.0880991i
\(551\) −14316.0 −1.10686
\(552\) 0 0
\(553\) 10569.4 32529.2i 0.812758 2.50141i
\(554\) 7919.57 24373.9i 0.607347 1.86922i
\(555\) 0 0
\(556\) 3695.09 + 11372.3i 0.281846 + 0.867434i
\(557\) 14165.4 1.07757 0.538786 0.842442i \(-0.318883\pi\)
0.538786 + 0.842442i \(0.318883\pi\)
\(558\) 0 0
\(559\) −3517.60 2555.69i −0.266152 0.193370i
\(560\) 504.598 3851.30i 0.0380771 0.290620i
\(561\) 0 0
\(562\) 28311.7 + 20569.7i 2.12501 + 1.54391i
\(563\) 9115.09 + 6622.50i 0.682336 + 0.495746i 0.874132 0.485689i \(-0.161431\pi\)
−0.191796 + 0.981435i \(0.561431\pi\)
\(564\) 0 0
\(565\) −1416.42 + 10810.7i −0.105467 + 0.804970i
\(566\) 16869.1 + 12256.1i 1.25276 + 0.910183i
\(567\) 0 0
\(568\) 4501.02 0.332497
\(569\) 2287.20 + 7039.27i 0.168514 + 0.518632i 0.999278 0.0379926i \(-0.0120963\pi\)
−0.830764 + 0.556624i \(0.812096\pi\)
\(570\) 0 0
\(571\) −4038.92 + 12430.5i −0.296013 + 0.911035i 0.686866 + 0.726784i \(0.258986\pi\)
−0.982879 + 0.184251i \(0.941014\pi\)
\(572\) −420.811 + 1295.12i −0.0307605 + 0.0946710i
\(573\) 0 0
\(574\) 43083.2 3.13285
\(575\) 1052.79 + 19621.7i 0.0763552 + 1.42310i
\(576\) 0 0
\(577\) −6647.54 + 4829.72i −0.479620 + 0.348464i −0.801179 0.598425i \(-0.795793\pi\)
0.321559 + 0.946890i \(0.395793\pi\)
\(578\) −3323.04 + 10227.3i −0.239135 + 0.735982i
\(579\) 0 0
\(580\) −1988.83 + 15179.6i −0.142382 + 1.08672i
\(581\) −5262.71 16197.0i −0.375790 1.15656i
\(582\) 0 0
\(583\) −303.893 935.286i −0.0215883 0.0664418i
\(584\) −19885.7 14447.8i −1.40903 1.02372i
\(585\) 0 0
\(586\) 25122.7 18252.7i 1.77100 1.28671i
\(587\) 16152.0 + 11735.1i 1.13572 + 0.825145i 0.986517 0.163662i \(-0.0523306\pi\)
0.149199 + 0.988807i \(0.452331\pi\)
\(588\) 0 0
\(589\) −20031.8 + 14554.0i −1.40135 + 1.01814i
\(590\) −10254.9 18859.2i −0.715572 1.31597i
\(591\) 0 0
\(592\) −244.832 753.515i −0.0169975 0.0523130i
\(593\) 14429.9 0.999267 0.499634 0.866237i \(-0.333468\pi\)
0.499634 + 0.866237i \(0.333468\pi\)
\(594\) 0 0
\(595\) −17024.5 + 17962.4i −1.17300 + 1.23762i
\(596\) 3460.12 10649.2i 0.237805 0.731890i
\(597\) 0 0
\(598\) −23451.2 + 17038.3i −1.60366 + 1.16513i
\(599\) 7838.61 0.534686 0.267343 0.963601i \(-0.413854\pi\)
0.267343 + 0.963601i \(0.413854\pi\)
\(600\) 0 0
\(601\) −25163.3 −1.70787 −0.853937 0.520376i \(-0.825792\pi\)
−0.853937 + 0.520376i \(0.825792\pi\)
\(602\) −10761.9 + 7818.97i −0.728608 + 0.529365i
\(603\) 0 0
\(604\) 2395.55 7372.74i 0.161380 0.496677i
\(605\) 14560.6 2708.01i 0.978466 0.181977i
\(606\) 0 0
\(607\) −563.698 −0.0376932 −0.0188466 0.999822i \(-0.505999\pi\)
−0.0188466 + 0.999822i \(0.505999\pi\)
\(608\) −6563.16 20199.3i −0.437781 1.34735i
\(609\) 0 0
\(610\) 18347.0 3412.21i 1.21778 0.226486i
\(611\) −1862.67 + 1353.31i −0.123332 + 0.0896057i
\(612\) 0 0
\(613\) 5449.70 + 3959.44i 0.359072 + 0.260881i 0.752665 0.658404i \(-0.228768\pi\)
−0.393593 + 0.919285i \(0.628768\pi\)
\(614\) 20457.9 14863.6i 1.34465 0.976945i
\(615\) 0 0
\(616\) 1396.77 + 1014.81i 0.0913595 + 0.0663766i
\(617\) 3151.55 + 9699.47i 0.205635 + 0.632878i 0.999687 + 0.0250287i \(0.00796772\pi\)
−0.794052 + 0.607850i \(0.792032\pi\)
\(618\) 0 0
\(619\) 2342.12 + 7208.30i 0.152080 + 0.468055i 0.997853 0.0654878i \(-0.0208604\pi\)
−0.845773 + 0.533543i \(0.820860\pi\)
\(620\) 12649.0 + 23262.1i 0.819348 + 1.50682i
\(621\) 0 0
\(622\) 737.821 2270.78i 0.0475626 0.146383i
\(623\) −22327.3 + 16221.7i −1.43583 + 1.04319i
\(624\) 0 0
\(625\) −6390.73 14258.3i −0.409006 0.912531i
\(626\) 4637.72 0.296103
\(627\) 0 0
\(628\) −6938.67 + 21355.0i −0.440896 + 1.35694i
\(629\) −1559.95 + 4801.04i −0.0988861 + 0.304340i
\(630\) 0 0
\(631\) 1413.93 + 4351.64i 0.0892042 + 0.274542i 0.985700 0.168510i \(-0.0538956\pi\)
−0.896496 + 0.443052i \(0.853896\pi\)
\(632\) 34602.1 2.17784
\(633\) 0 0
\(634\) −16117.6 11710.1i −1.00964 0.733547i
\(635\) −10385.9 4945.88i −0.649055 0.309088i
\(636\) 0 0
\(637\) −10748.0 7808.90i −0.668528 0.485714i
\(638\) −949.532 689.875i −0.0589221 0.0428094i
\(639\) 0 0
\(640\) −27788.8 + 5168.22i −1.71633 + 0.319206i
\(641\) −14330.6 10411.8i −0.883034 0.641562i 0.0510186 0.998698i \(-0.483753\pi\)
−0.934052 + 0.357136i \(0.883753\pi\)
\(642\) 0 0
\(643\) −13212.2 −0.810323 −0.405162 0.914245i \(-0.632785\pi\)
−0.405162 + 0.914245i \(0.632785\pi\)
\(644\) 17283.8 + 53193.9i 1.05757 + 3.25487i
\(645\) 0 0
\(646\) 17458.6 53732.0i 1.06331 3.27254i
\(647\) −1302.73 + 4009.39i −0.0791586 + 0.243625i −0.982803 0.184659i \(-0.940882\pi\)
0.903644 + 0.428284i \(0.140882\pi\)
\(648\) 0 0
\(649\) 1037.95 0.0627780
\(650\) 12529.8 19346.8i 0.756091 1.16745i
\(651\) 0 0
\(652\) 14150.0 10280.6i 0.849935 0.617514i
\(653\) −8093.51 + 24909.3i −0.485028 + 1.49276i 0.346911 + 0.937898i \(0.387230\pi\)
−0.831940 + 0.554866i \(0.812770\pi\)
\(654\) 0 0
\(655\) 20534.2 21665.5i 1.22494 1.29243i
\(656\) 1465.09 + 4509.08i 0.0871983 + 0.268369i
\(657\) 0 0
\(658\) 2176.72 + 6699.26i 0.128963 + 0.396906i
\(659\) −10410.7 7563.80i −0.615391 0.447107i 0.235918 0.971773i \(-0.424190\pi\)
−0.851308 + 0.524666i \(0.824190\pi\)
\(660\) 0 0
\(661\) 17474.6 12696.0i 1.02827 0.747078i 0.0603043 0.998180i \(-0.480793\pi\)
0.967961 + 0.251102i \(0.0807929\pi\)
\(662\) −11193.3 8132.40i −0.657159 0.477454i
\(663\) 0 0
\(664\) 13938.6 10127.0i 0.814645 0.591874i
\(665\) 28609.5 30185.6i 1.66831 1.76022i
\(666\) 0 0
\(667\) −4869.04 14985.4i −0.282654 0.869918i
\(668\) 21538.4 1.24752
\(669\) 0 0
\(670\) 2372.79 18110.1i 0.136819 1.04426i
\(671\) −278.827 + 858.140i −0.0160417 + 0.0493713i
\(672\) 0 0
\(673\) −8553.18 + 6214.25i −0.489897 + 0.355931i −0.805145 0.593078i \(-0.797912\pi\)
0.315248 + 0.949009i \(0.397912\pi\)
\(674\) −7180.37 −0.410352
\(675\) 0 0
\(676\) −8568.93 −0.487536
\(677\) −12670.0 + 9205.29i −0.719272 + 0.522582i −0.886152 0.463395i \(-0.846631\pi\)
0.166879 + 0.985977i \(0.446631\pi\)
\(678\) 0 0
\(679\) −5162.92 + 15889.8i −0.291804 + 0.898079i
\(680\) −22604.7 10764.6i −1.27478 0.607066i
\(681\) 0 0
\(682\) −2029.98 −0.113977
\(683\) −7323.05 22538.0i −0.410261 1.26265i −0.916421 0.400215i \(-0.868935\pi\)
0.506160 0.862440i \(-0.331065\pi\)
\(684\) 0 0
\(685\) −1771.13 + 13518.0i −0.0987906 + 0.754010i
\(686\) 753.466 547.425i 0.0419351 0.0304676i
\(687\) 0 0
\(688\) −1184.30 860.446i −0.0656266 0.0476805i
\(689\) −12528.9 + 9102.77i −0.692761 + 0.503320i
\(690\) 0 0
\(691\) −3580.95 2601.71i −0.197143 0.143233i 0.484835 0.874606i \(-0.338880\pi\)
−0.681978 + 0.731373i \(0.738880\pi\)
\(692\) −9378.67 28864.6i −0.515207 1.58564i
\(693\) 0 0
\(694\) −8088.99 24895.3i −0.442441 1.36169i
\(695\) 8835.37 + 4207.52i 0.482223 + 0.229641i
\(696\) 0 0
\(697\) 9334.84 28729.7i 0.507292 1.56128i
\(698\) 13353.4 9701.82i 0.724118 0.526102i
\(699\) 0 0
\(700\) −28032.0 34528.7i −1.51358 1.86438i
\(701\) −5192.49 −0.279768 −0.139884 0.990168i \(-0.544673\pi\)
−0.139884 + 0.990168i \(0.544673\pi\)
\(702\) 0 0
\(703\) 2621.48 8068.10i 0.140642 0.432851i
\(704\) 621.041 1911.37i 0.0332477 0.102326i
\(705\) 0 0
\(706\) −2755.69 8481.13i −0.146900 0.452113i
\(707\) 22503.2 1.19706
\(708\) 0 0
\(709\) 906.237 + 658.420i 0.0480035 + 0.0348766i 0.611528 0.791223i \(-0.290555\pi\)
−0.563525 + 0.826099i \(0.690555\pi\)
\(710\) 6114.81 6451.69i 0.323218 0.341025i
\(711\) 0 0
\(712\) −22587.6 16410.9i −1.18892 0.863798i
\(713\) −22047.5 16018.4i −1.15804 0.841368i
\(714\) 0 0
\(715\) 532.390 + 979.089i 0.0278465 + 0.0512110i
\(716\) 33323.0 + 24210.6i 1.73930 + 1.26368i
\(717\) 0 0
\(718\) 12254.8 0.636973
\(719\) −7041.08 21670.2i −0.365213 1.12401i −0.949848 0.312713i \(-0.898762\pi\)
0.584635 0.811297i \(-0.301238\pi\)
\(720\) 0 0
\(721\) −14745.2 + 45380.9i −0.761634 + 2.34407i
\(722\) −19474.3 + 59935.7i −1.00382 + 3.08944i
\(723\) 0 0
\(724\) 33779.5 1.73399
\(725\) 7896.94 + 9727.16i 0.404531 + 0.498286i
\(726\) 0 0
\(727\) −25911.7 + 18825.9i −1.32188 + 0.960406i −0.321978 + 0.946747i \(0.604348\pi\)
−0.999907 + 0.0136585i \(0.995652\pi\)
\(728\) 8401.69 25857.7i 0.427730 1.31642i
\(729\) 0 0
\(730\) −47724.7 + 8875.93i −2.41969 + 0.450018i
\(731\) 2882.24 + 8870.62i 0.145832 + 0.448826i
\(732\) 0 0
\(733\) 6712.80 + 20659.9i 0.338258 + 1.04105i 0.965095 + 0.261901i \(0.0843492\pi\)
−0.626837 + 0.779151i \(0.715651\pi\)
\(734\) −25613.8 18609.5i −1.28804 0.935816i
\(735\) 0 0
\(736\) 18911.6 13740.0i 0.947132 0.688132i
\(737\) 714.458 + 519.084i 0.0357088 + 0.0259440i
\(738\) 0 0
\(739\) −24270.5 + 17633.5i −1.20812 + 0.877754i −0.995059 0.0992837i \(-0.968345\pi\)
−0.213066 + 0.977038i \(0.568345\pi\)
\(740\) −8190.60 3900.47i −0.406882 0.193762i
\(741\) 0 0
\(742\) 14641.3 + 45061.2i 0.724391 + 2.22945i
\(743\) 5551.03 0.274088 0.137044 0.990565i \(-0.456240\pi\)
0.137044 + 0.990565i \(0.456240\pi\)
\(744\) 0 0
\(745\) −4377.58 8050.56i −0.215278 0.395906i
\(746\) 9643.40 29679.3i 0.473284 1.45662i
\(747\) 0 0
\(748\) 2363.31 1717.05i 0.115523 0.0839324i
\(749\) −27033.9 −1.31882
\(750\) 0 0
\(751\) 5337.87 0.259363 0.129682 0.991556i \(-0.458604\pi\)
0.129682 + 0.991556i \(0.458604\pi\)
\(752\) −627.122 + 455.631i −0.0304106 + 0.0220946i
\(753\) 0 0
\(754\) −5711.51 + 17578.2i −0.275863 + 0.849020i
\(755\) −3030.73 5573.66i −0.146092 0.268670i
\(756\) 0 0
\(757\) −17462.2 −0.838409 −0.419205 0.907892i \(-0.637691\pi\)
−0.419205 + 0.907892i \(0.637691\pi\)
\(758\) −5595.65 17221.6i −0.268131 0.825222i
\(759\) 0 0
\(760\) 37987.0 + 18089.9i 1.81307 + 0.863406i
\(761\) 11011.7 8000.49i 0.524540 0.381100i −0.293772 0.955876i \(-0.594911\pi\)
0.818311 + 0.574775i \(0.194911\pi\)
\(762\) 0 0
\(763\) 32807.4 + 23836.0i 1.55663 + 1.13096i
\(764\) −7083.83 + 5146.71i −0.335450 + 0.243719i
\(765\) 0 0
\(766\) 21244.5 + 15435.1i 1.00208 + 0.728056i
\(767\) −5050.96 15545.2i −0.237783 0.731820i
\(768\) 0 0
\(769\) −7403.09 22784.4i −0.347155 1.06843i −0.960420 0.278556i \(-0.910144\pi\)
0.613265 0.789877i \(-0.289856\pi\)
\(770\) 3352.19 623.446i 0.156889 0.0291785i
\(771\) 0 0
\(772\) −2781.80 + 8561.50i −0.129688 + 0.399139i
\(773\) −28541.9 + 20736.9i −1.32805 + 0.964883i −0.328254 + 0.944590i \(0.606460\pi\)
−0.999794 + 0.0202938i \(0.993540\pi\)
\(774\) 0 0
\(775\) 20938.7 + 5582.62i 0.970504 + 0.258753i
\(776\) −16902.4 −0.781909
\(777\) 0 0
\(778\) −6729.34 + 20710.8i −0.310101 + 0.954393i
\(779\) −15687.1 + 48280.0i −0.721501 + 2.22055i
\(780\) 0 0
\(781\) 132.813 + 408.756i 0.00608505 + 0.0187278i
\(782\) 62182.2 2.84352
\(783\) 0 0
\(784\) −3618.63 2629.09i −0.164843 0.119765i