Properties

Label 225.4.h.a.91.7
Level $225$
Weight $4$
Character 225.91
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 91.7
Character \(\chi\) \(=\) 225.91
Dual form 225.4.h.a.136.7

$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

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

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 0.999718 + 0.0237477i \(0.00755984\pi\)
0.331515 + 0.943450i \(0.392440\pi\)
\(3\) 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 0.615331 0.788268i \(-0.289022\pi\)
−0.559540 + 0.828803i \(0.689022\pi\)
\(12\) 0 0
\(13\) −32.0534 + 23.2881i −0.683846 + 0.496843i −0.874632 0.484788i \(-0.838897\pi\)
0.190785 + 0.981632i \(0.438897\pi\)
\(14\) −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 −0.568981 0.822351i \(-0.692662\pi\)
0.943681 0.330857i \(-0.107338\pi\)
\(18\) 0 0
\(19\) −44.1360 + 135.837i −0.532921 + 1.64016i 0.215179 + 0.976575i \(0.430967\pi\)
−0.748099 + 0.663587i \(0.769033\pi\)
\(20\) −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 0.988872 0.148768i \(-0.0475306\pi\)
0.164092 + 0.986445i \(0.447531\pi\)
\(24\) 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 0.999921 + 0.0125312i \(0.00398890\pi\)
−0.801588 + 0.597877i \(0.796011\pi\)
\(30\) 0 0
\(31\) −53.5715 + 164.876i −0.310378 + 0.955246i 0.667237 + 0.744846i \(0.267477\pi\)
−0.977615 + 0.210401i \(0.932523\pi\)
\(32\) 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 −0.475893 0.879503i \(-0.657875\pi\)
0.689398 + 0.724382i \(0.257875\pi\)
\(38\) −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 −0.980286 0.197585i \(-0.936690\pi\)
−0.115011 + 0.993364i \(0.536690\pi\)
\(42\) 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 0.975047 0.221997i \(-0.0712574\pi\)
−0.919316 + 0.393520i \(0.871257\pi\)
\(48\) 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 0.976552 + 0.215284i \(0.0690676\pi\)
−0.663506 + 0.748171i \(0.730932\pi\)
\(54\) 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 −0.155134 0.987893i \(-0.549581\pi\)
0.891604 + 0.452817i \(0.149581\pi\)
\(60\) 0 0
\(61\) −290.142 210.800i −0.608998 0.442463i 0.240064 0.970757i \(-0.422832\pi\)
−0.849061 + 0.528294i \(0.822832\pi\)
\(62\) −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 −0.802149 0.597123i \(-0.796310\pi\)
0.999933 0.0115915i \(-0.00368977\pi\)
\(68\) 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 0.897195 0.441635i \(-0.145601\pi\)
−0.985432 + 0.170068i \(0.945601\pi\)
\(72\) 0 0
\(73\) 754.724 + 548.339i 1.21005 + 0.879154i 0.995236 0.0975001i \(-0.0310846\pi\)
0.214817 + 0.976654i \(0.431085\pi\)
\(74\) 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 −0.625898 0.779905i \(-0.715267\pi\)
0.0479457 0.998850i \(-0.484733\pi\)
\(80\) −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 −0.723948 0.689855i \(-0.757674\pi\)
0.991173 0.132578i \(-0.0423255\pi\)
\(84\) 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 0.966492 0.256698i \(-0.0826346\pi\)
0.0545280 + 0.998512i \(0.482635\pi\)
\(90\) 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 0.999601 + 0.0282327i \(0.00898793\pi\)
−0.792100 + 0.610392i \(0.791012\pi\)
\(98\) 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 0.728944 + 0.684574i \(0.240012\pi\)
−0.187345 + 0.982294i \(0.559988\pi\)
\(104\) −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 −0.982176 0.187966i \(-0.939811\pi\)
−0.124743 + 0.992189i \(0.539811\pi\)
\(110\) −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 −0.865581 0.500769i \(-0.833051\pi\)
0.208781 + 0.977963i \(0.433051\pi\)
\(114\) 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 0.839300 0.543669i \(-0.182965\pi\)
−0.257702 + 0.966224i \(0.582965\pi\)
\(128\) 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 −0.157870 0.987460i \(-0.550463\pi\)
0.708134 0.706078i \(-0.249537\pi\)
\(132\) 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 −0.851249 0.524762i \(-0.824154\pi\)
0.236028 + 0.971746i \(0.424154\pi\)
\(138\) 0 0
\(139\) −708.126 514.484i −0.432104 0.313942i 0.350386 0.936606i \(-0.386051\pi\)
−0.782490 + 0.622664i \(0.786051\pi\)
\(140\) 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 −0.310425 0.950598i \(-0.600471\pi\)
0.808146 + 0.588982i \(0.200471\pi\)
\(164\) −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 −0.772463 0.635060i \(-0.780975\pi\)
0.998214 0.0597320i \(-0.0190246\pi\)
\(168\) 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 0.907926 0.419131i \(-0.137665\pi\)
−0.118052 + 0.993007i \(0.537665\pi\)
\(174\) 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 −0.933503 0.358570i \(-0.883264\pi\)
0.544458 0.838788i \(-0.316736\pi\)
\(180\) 0 0
\(181\) 764.093 2351.64i 0.313782 0.965722i −0.662471 0.749088i \(-0.730492\pi\)
0.976253 0.216634i \(-0.0695079\pi\)
\(182\) 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 −0.681657 0.731672i \(-0.738740\pi\)
0.485218 + 0.874393i \(0.338740\pi\)
\(192\) 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 −0.976498 0.215529i \(-0.930853\pi\)
0.663318 0.748337i \(-0.269147\pi\)
\(198\) 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 0.792552 0.609805i \(-0.208752\pi\)
−0.335047 + 0.942201i \(0.608752\pi\)
\(212\) −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 −0.0886732 0.996061i \(-0.528263\pi\)
−0.974712 + 0.223467i \(0.928263\pi\)
\(224\) −3872.90 −1.15522
\(225\) 0 0
\(226\) −4538.74 −1.33589
\(227\) −1819.26 1321.77i −0.531931 0.386471i 0.289148 0.957284i \(-0.406628\pi\)
−0.821080 + 0.570814i \(0.806628\pi\)
\(228\) 0 0
\(229\) 693.843 + 2135.43i 0.200220 + 0.616215i 0.999876 + 0.0157557i \(0.00501539\pi\)
−0.799656 + 0.600459i \(0.794985\pi\)
\(230\) −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 −0.977103 0.212768i \(-0.931752\pi\)
0.915555 + 0.402193i \(0.131752\pi\)
\(234\) 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 0.993673 0.112309i \(-0.0358248\pi\)
0.200249 + 0.979745i \(0.435825\pi\)
\(240\) 0 0
\(241\) −4628.17 + 3362.56i −1.23704 + 0.898762i −0.997397 0.0720995i \(-0.977030\pi\)
−0.239642 + 0.970861i \(0.577030\pi\)
\(242\) 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 −0.668765 0.743474i \(-0.733177\pi\)
0.500426 + 0.865779i \(0.333177\pi\)
\(264\) 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 0.482688 + 0.875792i \(0.339660\pi\)
−0.905281 + 0.424814i \(0.860340\pi\)
\(270\) 0 0
\(271\) 2019.40 + 6215.08i 0.452656 + 1.39313i 0.873865 + 0.486169i \(0.161606\pi\)
−0.421209 + 0.906964i \(0.638394\pi\)
\(272\) 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 0.954607 0.297867i \(-0.0962753\pi\)
0.0117014 + 0.999932i \(0.496275\pi\)
\(278\) −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 −0.326350 0.945249i \(-0.605819\pi\)
0.819626 0.572898i \(-0.194181\pi\)
\(282\) 0 0
\(283\) 1384.45 4260.88i 0.290801 0.894994i −0.693798 0.720169i \(-0.744064\pi\)
0.984600 0.174825i \(-0.0559359\pi\)
\(284\) 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 0.624979 0.780642i \(-0.285108\pi\)
−0.549305 + 0.835622i \(0.685108\pi\)
\(312\) 0 0
\(313\) 806.159 585.709i 0.145581 0.105771i −0.512611 0.858621i \(-0.671322\pi\)
0.658192 + 0.752850i \(0.271322\pi\)
\(314\) −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 0.762838 + 0.646589i \(0.223805\pi\)
−0.997205 + 0.0747164i \(0.976195\pi\)
\(318\) 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 −0.997904 0.0647132i \(-0.979387\pi\)
0.845359 + 0.534199i \(0.179387\pi\)
\(332\) 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 −0.684074 0.729413i \(-0.739794\pi\)
0.482322 + 0.875994i \(0.339794\pi\)
\(338\) −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 0.990774 + 0.135524i \(0.0432717\pi\)
−0.721894 + 0.692003i \(0.756728\pi\)
\(348\) 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 0.985719 0.168397i \(-0.0538591\pi\)
−0.896445 + 0.443155i \(0.853859\pi\)
\(354\) 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 −0.420085 0.907485i \(-0.638000\pi\)
0.733256 + 0.679953i \(0.238000\pi\)
\(360\) 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 0.682861 + 0.730548i \(0.260735\pi\)
−0.981852 + 0.189650i \(0.939265\pi\)
\(368\) −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 0.896758 0.442520i \(-0.145916\pi\)
−0.143748 + 0.989614i \(0.545916\pi\)
\(374\) 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 0.998879 0.0473310i \(-0.0150716\pi\)
−0.835931 + 0.548835i \(0.815072\pi\)
\(380\) 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 −0.764817 0.644247i \(-0.777171\pi\)
0.997429 0.0716588i \(-0.0228293\pi\)
\(384\) 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 0.313102 0.949719i \(-0.398632\pi\)
−0.806483 + 0.591257i \(0.798632\pi\)
\(390\) 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 0.970372 + 0.241614i \(0.0776769\pi\)
−0.643030 + 0.765841i \(0.722323\pi\)
\(398\) −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 −0.859723 0.510760i \(-0.829364\pi\)
0.220092 + 0.975479i \(0.429364\pi\)
\(410\) 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 0.377221 + 0.926123i \(0.376880\pi\)
−0.849540 + 0.527525i \(0.823120\pi\)
\(420\) 0 0
\(421\) 1054.72 + 3246.11i 0.122100 + 0.375785i 0.993362 0.115034i \(-0.0366977\pi\)
−0.871262 + 0.490819i \(0.836698\pi\)
\(422\) 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 −0.921551 0.388258i \(-0.873077\pi\)
0.973762 + 0.227567i \(0.0730771\pi\)
\(432\) 0 0
\(433\) −2665.17 + 8202.55i −0.295797 + 0.910368i 0.687156 + 0.726510i \(0.258859\pi\)
−0.982953 + 0.183858i \(0.941141\pi\)
\(434\) 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 0.732058 0.681243i \(-0.238560\pi\)
−0.421682 + 0.906744i \(0.638560\pi\)
\(440\) −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 0.416740 0.909026i \(-0.363173\pi\)
−0.735755 + 0.677247i \(0.763173\pi\)
\(462\) 0 0
\(463\) 12670.8 9205.86i 1.27184 0.924044i 0.272563 0.962138i \(-0.412129\pi\)
0.999274 + 0.0380937i \(0.0121285\pi\)
\(464\) −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 −0.804078 0.594523i \(-0.797341\pi\)
0.999965 0.00835414i \(-0.00265924\pi\)
\(468\) 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 0.980345 + 0.197289i \(0.0632137\pi\)
−0.677153 + 0.735843i \(0.736786\pi\)
\(480\) 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 −0.663436 0.748233i \(-0.730902\pi\)
0.506599 + 0.862182i \(0.330902\pi\)
\(488\) 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 0.316522 0.948585i \(-0.397485\pi\)
0.999969 0.00790172i \(-0.00251522\pi\)
\(492\) 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 0.989055 + 0.147549i \(0.0471384\pi\)
−0.713435 + 0.700721i \(0.752862\pi\)
\(504\) 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 −0.759109 0.650963i \(-0.774365\pi\)
0.384525 + 0.923114i \(0.374365\pi\)
\(510\) 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 0.998886 0.0471916i \(-0.0150271\pi\)
−0.835854 + 0.548952i \(0.815027\pi\)
\(522\) 0 0
\(523\) −11374.4 8264.02i −0.950994 0.690937i 4.79448e−5 1.00000i \(-0.499985\pi\)
−0.951042 + 0.309063i \(0.899985\pi\)
\(524\) 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 0.294369 0.955692i \(-0.404890\pi\)
0.999882 + 0.0153633i \(0.00489048\pi\)
\(542\) −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 −0.973929 0.226854i \(-0.927156\pi\)
0.654584 0.755989i \(-0.272844\pi\)
\(548\) −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 −0.191796 0.981435i \(-0.561431\pi\)
0.874132 + 0.485689i \(0.161431\pi\)
\(564\) 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 −0.830764 0.556624i \(-0.812096\pi\)
0.999278 + 0.0379926i \(0.0120963\pi\)
\(570\) 0 0
\(571\) −4038.92 12430.5i −0.296013 0.911035i −0.982879 0.184251i \(-0.941014\pi\)
0.686866 0.726784i \(-0.258986\pi\)
\(572\) −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 0.321559 0.946890i \(-0.395793\pi\)
−0.801179 + 0.598425i \(0.795793\pi\)
\(578\) −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 0.149199 0.988807i \(-0.452331\pi\)
0.986517 + 0.163662i \(0.0523306\pi\)
\(588\) 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 −0.393593 0.919285i \(-0.628768\pi\)
0.752665 + 0.658404i \(0.228768\pi\)
\(614\) 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 −0.794052 0.607850i \(-0.792032\pi\)
0.999687 0.0250287i \(-0.00796772\pi\)
\(618\) 0 0
\(619\) 2342.12 7208.30i 0.152080 0.468055i −0.845773 0.533543i \(-0.820860\pi\)
0.997853 + 0.0654878i \(0.0208604\pi\)
\(620\) 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 −0.896496 0.443052i \(-0.853896\pi\)
0.985700 + 0.168510i \(0.0538956\pi\)
\(632\) 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 −0.934052 0.357136i \(-0.883753\pi\)
0.0510186 + 0.998698i \(0.483753\pi\)
\(642\) 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 0.903644 0.428284i \(-0.140882\pi\)
−0.982803 + 0.184659i \(0.940882\pi\)
\(648\) 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 −0.831940 0.554866i \(-0.812770\pi\)
0.346911 0.937898i \(-0.387230\pi\)
\(654\) 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 −0.851308 0.524666i \(-0.824190\pi\)
0.235918 + 0.971773i \(0.424190\pi\)
\(660\) 0 0
\(661\) 17474.6 + 12696.0i 1.02827 + 0.747078i 0.967961 0.251102i \(-0.0807929\pi\)
0.0603043 + 0.998180i \(0.480793\pi\)
\(662\) −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 0.315248 0.949009i \(-0.397912\pi\)
−0.805145 + 0.593078i \(0.797912\pi\)
\(674\) −7180.37 −0.410352
\(675\) 0 0
\(676\) −8568.93 −0.487536
\(677\) −12670.0 9205.29i −0.719272 0.522582i 0.166879 0.985977i \(-0.446631\pi\)
−0.886152 + 0.463395i \(0.846631\pi\)
\(678\) 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 0.506160 + 0.862440i \(0.331065\pi\)
−0.916421 + 0.400215i \(0.868935\pi\)
\(684\) 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 −0.681978 0.731373i \(-0.738880\pi\)
0.484835 + 0.874606i \(0.338880\pi\)
\(692\) −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 −0.563525 0.826099i \(-0.690555\pi\)
0.611528 + 0.791223i \(0.290555\pi\)
\(710\) 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 0.584635 + 0.811297i \(0.301238\pi\)
−0.949848 + 0.312713i \(0.898762\pi\)
\(720\) 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 −0.999907 0.0136585i \(-0.995652\pi\)
−0.321978 0.946747i \(-0.604348\pi\)
\(728\) 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 −0.626837 0.779151i \(-0.715651\pi\)
0.965095 0.261901i \(-0.0843492\pi\)
\(734\) −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 −0.213066 0.977038i \(-0.568345\pi\)
−0.995059 + 0.0992837i \(0.968345\pi\)
\(740\) −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 0.818311 0.574775i \(-0.194911\pi\)
−0.293772 + 0.955876i \(0.594911\pi\)
\(762\) 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 0.613265 + 0.789877i \(0.289856\pi\)
−0.960420 + 0.278556i \(0.910144\pi\)
\(770\) 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 −0.999794 0.0202938i \(-0.993540\pi\)
−0.328254 0.944590i \(-0.606460\pi\)
\(774\) 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
\(785\) 8778.47