Properties

Label 225.4.h.d.136.1
Level $225$
Weight $4$
Character 225.136
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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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: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 136.1
Character \(\chi\) \(=\) 225.136
Dual form 225.4.h.d.91.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.45962 + 3.24011i) q^{2} +(6.91782 - 21.2908i) q^{4} +(-7.22670 + 8.53082i) q^{5} -10.2696 q^{7} +(24.5064 + 75.4228i) q^{8} +O(q^{10})\) \(q+(-4.45962 + 3.24011i) q^{2} +(6.91782 - 21.2908i) q^{4} +(-7.22670 + 8.53082i) q^{5} -10.2696 q^{7} +(24.5064 + 75.4228i) q^{8} +(4.58760 - 61.4595i) q^{10} +(30.7071 - 22.3100i) q^{11} +(68.6194 + 49.8549i) q^{13} +(45.7987 - 33.2747i) q^{14} +(-208.778 - 151.686i) q^{16} +(0.731068 + 2.24999i) q^{17} +(18.4425 + 56.7600i) q^{19} +(131.635 + 212.877i) q^{20} +(-64.6553 + 198.988i) q^{22} +(-121.764 + 88.4666i) q^{23} +(-20.5497 - 123.299i) q^{25} -467.552 q^{26} +(-71.0434 + 218.649i) q^{28} +(-19.2720 + 59.3130i) q^{29} +(30.7798 + 94.7305i) q^{31} +788.118 q^{32} +(-10.5505 - 7.66539i) q^{34} +(74.2155 - 87.6083i) q^{35} +(-241.532 - 175.484i) q^{37} +(-266.155 - 193.373i) q^{38} +(-820.518 - 335.999i) q^{40} +(-166.007 - 120.611i) q^{41} +223.838 q^{43} +(-262.573 - 808.116i) q^{44} +(256.380 - 789.055i) q^{46} +(72.4695 - 223.038i) q^{47} -237.535 q^{49} +(491.146 + 483.285i) q^{50} +(1536.15 - 1116.08i) q^{52} +(-166.824 + 513.433i) q^{53} +(-31.5883 + 423.184i) q^{55} +(-251.671 - 774.564i) q^{56} +(-106.235 - 326.957i) q^{58} +(-554.190 - 402.642i) q^{59} +(8.59875 - 6.24736i) q^{61} +(-444.203 - 322.733i) q^{62} +(-1844.48 + 1340.10i) q^{64} +(-921.195 + 225.093i) q^{65} +(125.876 + 387.407i) q^{67} +52.9617 q^{68} +(-47.1130 + 631.166i) q^{70} +(-43.1539 + 132.814i) q^{71} +(-692.701 + 503.277i) q^{73} +1645.73 q^{74} +1336.05 q^{76} +(-315.350 + 229.115i) q^{77} +(-7.25535 + 22.3297i) q^{79} +(2802.79 - 684.858i) q^{80} +1131.12 q^{82} +(-242.596 - 746.633i) q^{83} +(-24.4775 - 10.0234i) q^{85} +(-998.231 + 725.257i) q^{86} +(2435.20 + 1769.28i) q^{88} +(-604.043 + 438.863i) q^{89} +(-704.696 - 511.991i) q^{91} +(1041.19 + 3204.45i) q^{92} +(399.481 + 1229.47i) q^{94} +(-617.487 - 252.858i) q^{95} +(132.515 - 407.841i) q^{97} +(1059.32 - 769.638i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.45962 + 3.24011i −1.57671 + 1.14555i −0.656372 + 0.754437i \(0.727910\pi\)
−0.920343 + 0.391113i \(0.872090\pi\)
\(3\) 0 0
\(4\) 6.91782 21.2908i 0.864727 2.66136i
\(5\) −7.22670 + 8.53082i −0.646376 + 0.763019i
\(6\) 0 0
\(7\) −10.2696 −0.554508 −0.277254 0.960797i \(-0.589424\pi\)
−0.277254 + 0.960797i \(0.589424\pi\)
\(8\) 24.5064 + 75.4228i 1.08304 + 3.33325i
\(9\) 0 0
\(10\) 4.58760 61.4595i 0.145073 1.94352i
\(11\) 30.7071 22.3100i 0.841685 0.611520i −0.0811559 0.996701i \(-0.525861\pi\)
0.922841 + 0.385181i \(0.125861\pi\)
\(12\) 0 0
\(13\) 68.6194 + 49.8549i 1.46397 + 1.06364i 0.982307 + 0.187280i \(0.0599671\pi\)
0.481663 + 0.876356i \(0.340033\pi\)
\(14\) 45.7987 33.2747i 0.874300 0.635216i
\(15\) 0 0
\(16\) −208.778 151.686i −3.26216 2.37010i
\(17\) 0.731068 + 2.24999i 0.0104300 + 0.0321002i 0.956136 0.292923i \(-0.0946279\pi\)
−0.945706 + 0.325023i \(0.894628\pi\)
\(18\) 0 0
\(19\) 18.4425 + 56.7600i 0.222684 + 0.685350i 0.998518 + 0.0544137i \(0.0173290\pi\)
−0.775835 + 0.630936i \(0.782671\pi\)
\(20\) 131.635 + 212.877i 1.47173 + 2.38004i
\(21\) 0 0
\(22\) −64.6553 + 198.988i −0.626570 + 1.92839i
\(23\) −121.764 + 88.4666i −1.10389 + 0.802024i −0.981691 0.190481i \(-0.938995\pi\)
−0.122201 + 0.992505i \(0.538995\pi\)
\(24\) 0 0
\(25\) −20.5497 123.299i −0.164397 0.986394i
\(26\) −467.552 −3.52671
\(27\) 0 0
\(28\) −71.0434 + 218.649i −0.479498 + 1.47574i
\(29\) −19.2720 + 59.3130i −0.123404 + 0.379798i −0.993607 0.112895i \(-0.963988\pi\)
0.870203 + 0.492693i \(0.163988\pi\)
\(30\) 0 0
\(31\) 30.7798 + 94.7305i 0.178330 + 0.548842i 0.999770 0.0214525i \(-0.00682906\pi\)
−0.821440 + 0.570295i \(0.806829\pi\)
\(32\) 788.118 4.35378
\(33\) 0 0
\(34\) −10.5505 7.66539i −0.0532176 0.0386648i
\(35\) 74.2155 87.6083i 0.358420 0.423100i
\(36\) 0 0
\(37\) −241.532 175.484i −1.07318 0.779711i −0.0966991 0.995314i \(-0.530828\pi\)
−0.976481 + 0.215603i \(0.930828\pi\)
\(38\) −266.155 193.373i −1.13621 0.825506i
\(39\) 0 0
\(40\) −820.518 335.999i −3.24338 1.32815i
\(41\) −166.007 120.611i −0.632340 0.459422i 0.224870 0.974389i \(-0.427804\pi\)
−0.857210 + 0.514967i \(0.827804\pi\)
\(42\) 0 0
\(43\) 223.838 0.793835 0.396917 0.917854i \(-0.370080\pi\)
0.396917 + 0.917854i \(0.370080\pi\)
\(44\) −262.573 808.116i −0.899644 2.76882i
\(45\) 0 0
\(46\) 256.380 789.055i 0.821763 2.52913i
\(47\) 72.4695 223.038i 0.224910 0.692201i −0.773391 0.633929i \(-0.781441\pi\)
0.998301 0.0582718i \(-0.0185590\pi\)
\(48\) 0 0
\(49\) −237.535 −0.692521
\(50\) 491.146 + 483.285i 1.38917 + 1.36694i
\(51\) 0 0
\(52\) 1536.15 1116.08i 4.09665 2.97639i
\(53\) −166.824 + 513.433i −0.432360 + 1.33067i 0.463407 + 0.886146i \(0.346627\pi\)
−0.895767 + 0.444523i \(0.853373\pi\)
\(54\) 0 0
\(55\) −31.5883 + 423.184i −0.0774430 + 1.03749i
\(56\) −251.671 774.564i −0.600553 1.84831i
\(57\) 0 0
\(58\) −106.235 326.957i −0.240505 0.740199i
\(59\) −554.190 402.642i −1.22287 0.888468i −0.226536 0.974003i \(-0.572740\pi\)
−0.996335 + 0.0855353i \(0.972740\pi\)
\(60\) 0 0
\(61\) 8.59875 6.24736i 0.0180485 0.0131130i −0.578724 0.815523i \(-0.696449\pi\)
0.596773 + 0.802410i \(0.296449\pi\)
\(62\) −444.203 322.733i −0.909901 0.661082i
\(63\) 0 0
\(64\) −1844.48 + 1340.10i −3.60251 + 2.61738i
\(65\) −921.195 + 225.093i −1.75785 + 0.429529i
\(66\) 0 0
\(67\) 125.876 + 387.407i 0.229526 + 0.706408i 0.997801 + 0.0662876i \(0.0211155\pi\)
−0.768275 + 0.640120i \(0.778885\pi\)
\(68\) 52.9617 0.0944492
\(69\) 0 0
\(70\) −47.1130 + 631.166i −0.0804439 + 1.07770i
\(71\) −43.1539 + 132.814i −0.0721327 + 0.222002i −0.980623 0.195904i \(-0.937236\pi\)
0.908490 + 0.417906i \(0.137236\pi\)
\(72\) 0 0
\(73\) −692.701 + 503.277i −1.11061 + 0.806906i −0.982760 0.184888i \(-0.940808\pi\)
−0.127851 + 0.991793i \(0.540808\pi\)
\(74\) 1645.73 2.58530
\(75\) 0 0
\(76\) 1336.05 2.01652
\(77\) −315.350 + 229.115i −0.466721 + 0.339092i
\(78\) 0 0
\(79\) −7.25535 + 22.3297i −0.0103328 + 0.0318011i −0.956090 0.293073i \(-0.905322\pi\)
0.945757 + 0.324874i \(0.105322\pi\)
\(80\) 2802.79 684.858i 3.91701 0.957118i
\(81\) 0 0
\(82\) 1131.12 1.52331
\(83\) −242.596 746.633i −0.320823 0.987393i −0.973291 0.229576i \(-0.926266\pi\)
0.652467 0.757817i \(-0.273734\pi\)
\(84\) 0 0
\(85\) −24.4775 10.0234i −0.0312348 0.0127905i
\(86\) −998.231 + 725.257i −1.25165 + 0.909378i
\(87\) 0 0
\(88\) 2435.20 + 1769.28i 2.94992 + 2.14325i
\(89\) −604.043 + 438.863i −0.719420 + 0.522690i −0.886199 0.463305i \(-0.846664\pi\)
0.166779 + 0.985994i \(0.446664\pi\)
\(90\) 0 0
\(91\) −704.696 511.991i −0.811782 0.589794i
\(92\) 1041.19 + 3204.45i 1.17991 + 3.63138i
\(93\) 0 0
\(94\) 399.481 + 1229.47i 0.438333 + 1.34905i
\(95\) −617.487 252.858i −0.666872 0.273081i
\(96\) 0 0
\(97\) 132.515 407.841i 0.138710 0.426906i −0.857438 0.514587i \(-0.827945\pi\)
0.996149 + 0.0876802i \(0.0279454\pi\)
\(98\) 1059.32 769.638i 1.09191 0.793318i
\(99\) 0 0
\(100\) −2767.30 415.442i −2.76730 0.415442i
\(101\) 437.662 0.431179 0.215589 0.976484i \(-0.430833\pi\)
0.215589 + 0.976484i \(0.430833\pi\)
\(102\) 0 0
\(103\) −332.320 + 1022.77i −0.317907 + 0.978417i 0.656634 + 0.754209i \(0.271980\pi\)
−0.974541 + 0.224208i \(0.928020\pi\)
\(104\) −2078.59 + 6397.23i −1.95983 + 6.03173i
\(105\) 0 0
\(106\) −919.603 2830.25i −0.842639 2.59338i
\(107\) 187.419 0.169331 0.0846656 0.996409i \(-0.473018\pi\)
0.0846656 + 0.996409i \(0.473018\pi\)
\(108\) 0 0
\(109\) 236.110 + 171.544i 0.207479 + 0.150742i 0.686672 0.726967i \(-0.259071\pi\)
−0.479193 + 0.877709i \(0.659071\pi\)
\(110\) −1230.29 1989.59i −1.06640 1.72455i
\(111\) 0 0
\(112\) 2144.07 + 1557.76i 1.80889 + 1.31424i
\(113\) −532.005 386.524i −0.442892 0.321780i 0.343891 0.939010i \(-0.388255\pi\)
−0.786783 + 0.617229i \(0.788255\pi\)
\(114\) 0 0
\(115\) 125.258 1678.07i 0.101569 1.36070i
\(116\) 1129.50 + 820.633i 0.904068 + 0.656843i
\(117\) 0 0
\(118\) 3776.08 2.94590
\(119\) −7.50779 23.1066i −0.00578351 0.0177998i
\(120\) 0 0
\(121\) 33.8872 104.294i 0.0254600 0.0783578i
\(122\) −18.1051 + 55.7217i −0.0134357 + 0.0413509i
\(123\) 0 0
\(124\) 2229.82 1.61487
\(125\) 1200.35 + 715.741i 0.858900 + 0.512143i
\(126\) 0 0
\(127\) −2195.33 + 1595.00i −1.53389 + 1.11444i −0.579865 + 0.814712i \(0.696895\pi\)
−0.954026 + 0.299725i \(0.903105\pi\)
\(128\) 1935.32 5956.29i 1.33640 4.11302i
\(129\) 0 0
\(130\) 3378.86 3988.60i 2.27958 2.69095i
\(131\) 652.854 + 2009.28i 0.435421 + 1.34009i 0.892655 + 0.450741i \(0.148840\pi\)
−0.457234 + 0.889346i \(0.651160\pi\)
\(132\) 0 0
\(133\) −189.397 582.904i −0.123480 0.380032i
\(134\) −1816.60 1319.84i −1.17112 0.850870i
\(135\) 0 0
\(136\) −151.785 + 110.278i −0.0957019 + 0.0695315i
\(137\) −2108.87 1532.19i −1.31513 0.955500i −0.999979 0.00645905i \(-0.997944\pi\)
−0.315153 0.949041i \(-0.602056\pi\)
\(138\) 0 0
\(139\) −229.538 + 166.769i −0.140066 + 0.101764i −0.655612 0.755098i \(-0.727589\pi\)
0.515546 + 0.856862i \(0.327589\pi\)
\(140\) −1351.85 2186.17i −0.816084 1.31975i
\(141\) 0 0
\(142\) −237.881 732.123i −0.140581 0.432665i
\(143\) 3219.37 1.88264
\(144\) 0 0
\(145\) −366.716 593.043i −0.210028 0.339652i
\(146\) 1458.52 4488.85i 0.826765 2.54452i
\(147\) 0 0
\(148\) −5407.07 + 3928.47i −3.00310 + 2.18188i
\(149\) 2803.58 1.54146 0.770732 0.637160i \(-0.219891\pi\)
0.770732 + 0.637160i \(0.219891\pi\)
\(150\) 0 0
\(151\) −2663.88 −1.43565 −0.717825 0.696224i \(-0.754862\pi\)
−0.717825 + 0.696224i \(0.754862\pi\)
\(152\) −3829.04 + 2781.96i −2.04327 + 1.48452i
\(153\) 0 0
\(154\) 663.985 2043.54i 0.347438 1.06930i
\(155\) −1030.57 422.012i −0.534045 0.218689i
\(156\) 0 0
\(157\) −1281.52 −0.651441 −0.325720 0.945466i \(-0.605607\pi\)
−0.325720 + 0.945466i \(0.605607\pi\)
\(158\) −39.9944 123.090i −0.0201379 0.0619780i
\(159\) 0 0
\(160\) −5695.49 + 6723.29i −2.81418 + 3.32202i
\(161\) 1250.47 908.519i 0.612116 0.444729i
\(162\) 0 0
\(163\) 2234.46 + 1623.43i 1.07372 + 0.780103i 0.976577 0.215167i \(-0.0690296\pi\)
0.0971430 + 0.995270i \(0.469030\pi\)
\(164\) −3716.32 + 2700.06i −1.76949 + 1.28561i
\(165\) 0 0
\(166\) 3501.06 + 2543.67i 1.63696 + 1.18932i
\(167\) −123.881 381.266i −0.0574023 0.176666i 0.918244 0.396014i \(-0.129607\pi\)
−0.975647 + 0.219348i \(0.929607\pi\)
\(168\) 0 0
\(169\) 1544.20 + 4752.56i 0.702868 + 2.16321i
\(170\) 141.637 34.6090i 0.0639005 0.0156140i
\(171\) 0 0
\(172\) 1548.47 4765.69i 0.686450 2.11268i
\(173\) −1237.60 + 899.171i −0.543892 + 0.395160i −0.825528 0.564361i \(-0.809123\pi\)
0.281637 + 0.959521i \(0.409123\pi\)
\(174\) 0 0
\(175\) 211.037 + 1266.24i 0.0911595 + 0.546963i
\(176\) −9795.09 −4.19507
\(177\) 0 0
\(178\) 1271.84 3914.33i 0.535554 1.64826i
\(179\) 210.341 647.364i 0.0878305 0.270314i −0.897489 0.441038i \(-0.854610\pi\)
0.985319 + 0.170723i \(0.0546105\pi\)
\(180\) 0 0
\(181\) −1.51674 4.66806i −0.000622866 0.00191698i 0.950745 0.309975i \(-0.100321\pi\)
−0.951367 + 0.308058i \(0.900321\pi\)
\(182\) 4801.58 1.95559
\(183\) 0 0
\(184\) −9656.38 7015.77i −3.86890 2.81092i
\(185\) 3242.50 792.302i 1.28861 0.314871i
\(186\) 0 0
\(187\) 72.6463 + 52.7807i 0.0284087 + 0.0206401i
\(188\) −4247.34 3085.87i −1.64771 1.19713i
\(189\) 0 0
\(190\) 3573.05 873.071i 1.36430 0.333364i
\(191\) 895.191 + 650.395i 0.339130 + 0.246392i 0.744295 0.667851i \(-0.232786\pi\)
−0.405165 + 0.914244i \(0.632786\pi\)
\(192\) 0 0
\(193\) −2999.41 −1.11866 −0.559332 0.828944i \(-0.688942\pi\)
−0.559332 + 0.828944i \(0.688942\pi\)
\(194\) 730.478 + 2248.18i 0.270336 + 0.832009i
\(195\) 0 0
\(196\) −1643.22 + 5057.32i −0.598842 + 1.84305i
\(197\) −248.858 + 765.907i −0.0900022 + 0.276998i −0.985919 0.167224i \(-0.946520\pi\)
0.895917 + 0.444222i \(0.146520\pi\)
\(198\) 0 0
\(199\) 2005.20 0.714295 0.357148 0.934048i \(-0.383749\pi\)
0.357148 + 0.934048i \(0.383749\pi\)
\(200\) 8795.98 4571.53i 3.10985 1.61628i
\(201\) 0 0
\(202\) −1951.81 + 1418.07i −0.679846 + 0.493937i
\(203\) 197.916 609.122i 0.0684284 0.210601i
\(204\) 0 0
\(205\) 2228.59 544.555i 0.759277 0.185529i
\(206\) −1831.88 5637.94i −0.619578 1.90686i
\(207\) 0 0
\(208\) −6763.94 20817.3i −2.25478 6.93951i
\(209\) 1832.63 + 1331.48i 0.606534 + 0.440673i
\(210\) 0 0
\(211\) 2540.56 1845.83i 0.828908 0.602237i −0.0903418 0.995911i \(-0.528796\pi\)
0.919250 + 0.393674i \(0.128796\pi\)
\(212\) 9777.36 + 7103.67i 3.16751 + 2.30133i
\(213\) 0 0
\(214\) −835.816 + 607.256i −0.266987 + 0.193977i
\(215\) −1617.61 + 1909.52i −0.513115 + 0.605711i
\(216\) 0 0
\(217\) −316.097 972.847i −0.0988851 0.304337i
\(218\) −1608.78 −0.499818
\(219\) 0 0
\(220\) 8791.43 + 3600.05i 2.69417 + 1.10325i
\(221\) −62.0079 + 190.841i −0.0188738 + 0.0580875i
\(222\) 0 0
\(223\) −2001.60 + 1454.25i −0.601064 + 0.436698i −0.846256 0.532776i \(-0.821149\pi\)
0.245193 + 0.969474i \(0.421149\pi\)
\(224\) −8093.68 −2.41420
\(225\) 0 0
\(226\) 3624.92 1.06693
\(227\) 3754.41 2727.74i 1.09775 0.797560i 0.117057 0.993125i \(-0.462654\pi\)
0.980691 + 0.195565i \(0.0626540\pi\)
\(228\) 0 0
\(229\) 1787.22 5500.51i 0.515734 1.58727i −0.266209 0.963915i \(-0.585771\pi\)
0.781943 0.623350i \(-0.214229\pi\)
\(230\) 4878.51 + 7889.39i 1.39861 + 2.26179i
\(231\) 0 0
\(232\) −4945.84 −1.39961
\(233\) 775.748 + 2387.51i 0.218115 + 0.671290i 0.998918 + 0.0465122i \(0.0148106\pi\)
−0.780802 + 0.624778i \(0.785189\pi\)
\(234\) 0 0
\(235\) 1378.98 + 2230.05i 0.382787 + 0.619032i
\(236\) −12406.4 + 9013.76i −3.42198 + 2.48621i
\(237\) 0 0
\(238\) 108.350 + 78.7207i 0.0295095 + 0.0214399i
\(239\) 1736.13 1261.37i 0.469877 0.341386i −0.327516 0.944846i \(-0.606212\pi\)
0.797393 + 0.603460i \(0.206212\pi\)
\(240\) 0 0
\(241\) −5582.38 4055.84i −1.49209 1.08406i −0.973404 0.229097i \(-0.926423\pi\)
−0.518683 0.854967i \(-0.673577\pi\)
\(242\) 186.800 + 574.911i 0.0496196 + 0.152714i
\(243\) 0 0
\(244\) −73.5270 226.293i −0.0192913 0.0593726i
\(245\) 1716.59 2026.37i 0.447629 0.528407i
\(246\) 0 0
\(247\) −1564.26 + 4814.29i −0.402961 + 1.24019i
\(248\) −6390.54 + 4643.00i −1.63629 + 1.18883i
\(249\) 0 0
\(250\) −7672.18 + 697.323i −1.94093 + 0.176410i
\(251\) 2610.76 0.656533 0.328266 0.944585i \(-0.393536\pi\)
0.328266 + 0.944585i \(0.393536\pi\)
\(252\) 0 0
\(253\) −1765.32 + 5433.10i −0.438675 + 1.35010i
\(254\) 4622.38 14226.2i 1.14186 3.51430i
\(255\) 0 0
\(256\) 5031.98 + 15486.9i 1.22851 + 3.78097i
\(257\) −2896.67 −0.703072 −0.351536 0.936174i \(-0.614341\pi\)
−0.351536 + 0.936174i \(0.614341\pi\)
\(258\) 0 0
\(259\) 2480.45 + 1802.15i 0.595087 + 0.432356i
\(260\) −1580.23 + 21170.2i −0.376931 + 5.04969i
\(261\) 0 0
\(262\) −9421.75 6845.31i −2.22167 1.61414i
\(263\) 4107.74 + 2984.45i 0.963095 + 0.699730i 0.953868 0.300228i \(-0.0970626\pi\)
0.00922790 + 0.999957i \(0.497063\pi\)
\(264\) 0 0
\(265\) −3174.41 5133.57i −0.735859 1.19001i
\(266\) 2733.31 + 1985.87i 0.630038 + 0.457749i
\(267\) 0 0
\(268\) 9119.02 2.07848
\(269\) −556.477 1712.66i −0.126130 0.388188i 0.867975 0.496608i \(-0.165421\pi\)
−0.994105 + 0.108419i \(0.965421\pi\)
\(270\) 0 0
\(271\) 1254.40 3860.63i 0.281177 0.865375i −0.706341 0.707872i \(-0.749655\pi\)
0.987518 0.157504i \(-0.0503446\pi\)
\(272\) 188.662 580.643i 0.0420564 0.129436i
\(273\) 0 0
\(274\) 14369.2 3.16816
\(275\) −3381.83 3327.70i −0.741570 0.729701i
\(276\) 0 0
\(277\) −2240.93 + 1628.13i −0.486080 + 0.353158i −0.803675 0.595069i \(-0.797125\pi\)
0.317595 + 0.948227i \(0.397125\pi\)
\(278\) 483.304 1487.46i 0.104269 0.320906i
\(279\) 0 0
\(280\) 8426.41 + 3450.58i 1.79848 + 0.736470i
\(281\) −233.378 718.263i −0.0495450 0.152484i 0.923223 0.384264i \(-0.125545\pi\)
−0.972768 + 0.231781i \(0.925545\pi\)
\(282\) 0 0
\(283\) 826.993 + 2545.22i 0.173709 + 0.534621i 0.999572 0.0292494i \(-0.00931171\pi\)
−0.825863 + 0.563870i \(0.809312\pi\)
\(284\) 2529.19 + 1837.56i 0.528450 + 0.383942i
\(285\) 0 0
\(286\) −14357.2 + 10431.1i −2.96838 + 2.15665i
\(287\) 1704.83 + 1238.63i 0.350637 + 0.254753i
\(288\) 0 0
\(289\) 3970.17 2884.50i 0.808095 0.587116i
\(290\) 3556.93 + 1456.55i 0.720243 + 0.294936i
\(291\) 0 0
\(292\) 5923.21 + 18229.8i 1.18709 + 3.65348i
\(293\) −1248.58 −0.248951 −0.124475 0.992223i \(-0.539725\pi\)
−0.124475 + 0.992223i \(0.539725\pi\)
\(294\) 0 0
\(295\) 7439.83 1817.92i 1.46835 0.358790i
\(296\) 7316.38 22517.5i 1.43668 4.42163i
\(297\) 0 0
\(298\) −12502.9 + 9083.89i −2.43045 + 1.76582i
\(299\) −12765.9 −2.46913
\(300\) 0 0
\(301\) −2298.73 −0.440187
\(302\) 11879.9 8631.24i 2.26361 1.64461i
\(303\) 0 0
\(304\) 4759.34 14647.7i 0.897917 2.76350i
\(305\) −8.84552 + 118.502i −0.00166063 + 0.0222473i
\(306\) 0 0
\(307\) −7222.69 −1.34274 −0.671369 0.741123i \(-0.734293\pi\)
−0.671369 + 0.741123i \(0.734293\pi\)
\(308\) 2696.53 + 8299.05i 0.498860 + 1.53533i
\(309\) 0 0
\(310\) 5963.30 1457.13i 1.09256 0.266965i
\(311\) −5102.15 + 3706.93i −0.930277 + 0.675886i −0.946061 0.323989i \(-0.894976\pi\)
0.0157835 + 0.999875i \(0.494976\pi\)
\(312\) 0 0
\(313\) 4072.39 + 2958.77i 0.735417 + 0.534311i 0.891272 0.453468i \(-0.149814\pi\)
−0.155856 + 0.987780i \(0.549814\pi\)
\(314\) 5715.08 4152.25i 1.02714 0.746258i
\(315\) 0 0
\(316\) 425.227 + 308.945i 0.0756989 + 0.0549985i
\(317\) −471.885 1452.31i −0.0836079 0.257319i 0.900510 0.434836i \(-0.143194\pi\)
−0.984118 + 0.177517i \(0.943194\pi\)
\(318\) 0 0
\(319\) 731.488 + 2251.29i 0.128387 + 0.395134i
\(320\) 1897.42 25419.4i 0.331465 4.44059i
\(321\) 0 0
\(322\) −2632.92 + 8103.30i −0.455674 + 1.40242i
\(323\) −114.227 + 82.9908i −0.0196773 + 0.0142964i
\(324\) 0 0
\(325\) 4736.97 9485.23i 0.808492 1.61891i
\(326\) −15224.9 −2.58660
\(327\) 0 0
\(328\) 5028.61 15476.5i 0.846519 2.60532i
\(329\) −744.234 + 2290.52i −0.124714 + 0.383831i
\(330\) 0 0
\(331\) −29.4876 90.7536i −0.00489664 0.0150703i 0.948578 0.316542i \(-0.102522\pi\)
−0.953475 + 0.301472i \(0.902522\pi\)
\(332\) −17574.7 −2.90523
\(333\) 0 0
\(334\) 1787.80 + 1298.92i 0.292887 + 0.212795i
\(335\) −4214.57 1725.85i −0.687363 0.281472i
\(336\) 0 0
\(337\) −6558.38 4764.94i −1.06011 0.770216i −0.0860028 0.996295i \(-0.527409\pi\)
−0.974109 + 0.226079i \(0.927409\pi\)
\(338\) −22285.4 16191.3i −3.58628 2.60559i
\(339\) 0 0
\(340\) −382.738 + 451.806i −0.0610497 + 0.0720666i
\(341\) 3058.60 + 2222.20i 0.485725 + 0.352900i
\(342\) 0 0
\(343\) 5961.87 0.938516
\(344\) 5485.44 + 16882.4i 0.859753 + 2.64605i
\(345\) 0 0
\(346\) 2605.83 8019.93i 0.404886 1.24611i
\(347\) −1980.24 + 6094.54i −0.306353 + 0.942859i 0.672815 + 0.739811i \(0.265085\pi\)
−0.979169 + 0.203048i \(0.934915\pi\)
\(348\) 0 0
\(349\) 4849.33 0.743779 0.371890 0.928277i \(-0.378710\pi\)
0.371890 + 0.928277i \(0.378710\pi\)
\(350\) −5043.89 4963.16i −0.770306 0.757977i
\(351\) 0 0
\(352\) 24200.8 17582.9i 3.66451 2.66242i
\(353\) 3114.55 9585.60i 0.469606 1.44530i −0.383491 0.923545i \(-0.625278\pi\)
0.853097 0.521753i \(-0.174722\pi\)
\(354\) 0 0
\(355\) −821.152 1327.94i −0.122767 0.198535i
\(356\) 5165.10 + 15896.6i 0.768961 + 2.36662i
\(357\) 0 0
\(358\) 1159.49 + 3568.53i 0.171175 + 0.526823i
\(359\) 6962.67 + 5058.68i 1.02361 + 0.743695i 0.967020 0.254702i \(-0.0819774\pi\)
0.0565894 + 0.998398i \(0.481977\pi\)
\(360\) 0 0
\(361\) 2667.47 1938.03i 0.388901 0.282553i
\(362\) 21.8891 + 15.9034i 0.00317808 + 0.00230901i
\(363\) 0 0
\(364\) −15775.7 + 11461.7i −2.27162 + 1.65043i
\(365\) 712.580 9546.34i 0.102187 1.36898i
\(366\) 0 0
\(367\) −1844.02 5675.31i −0.262281 0.807217i −0.992307 0.123799i \(-0.960492\pi\)
0.730027 0.683419i \(-0.239508\pi\)
\(368\) 38840.8 5.50195
\(369\) 0 0
\(370\) −11893.2 + 14039.4i −1.67107 + 1.97263i
\(371\) 1713.22 5272.76i 0.239747 0.737866i
\(372\) 0 0
\(373\) 1798.36 1306.58i 0.249639 0.181374i −0.455928 0.890017i \(-0.650692\pi\)
0.705567 + 0.708643i \(0.250692\pi\)
\(374\) −494.990 −0.0684367
\(375\) 0 0
\(376\) 18598.1 2.55086
\(377\) −4279.48 + 3109.22i −0.584627 + 0.424756i
\(378\) 0 0
\(379\) −2879.17 + 8861.17i −0.390219 + 1.20097i 0.542404 + 0.840118i \(0.317514\pi\)
−0.932623 + 0.360853i \(0.882486\pi\)
\(380\) −9655.24 + 11397.6i −1.30343 + 1.53864i
\(381\) 0 0
\(382\) −6099.56 −0.816965
\(383\) 505.859 + 1556.87i 0.0674888 + 0.207709i 0.979113 0.203315i \(-0.0651714\pi\)
−0.911625 + 0.411024i \(0.865171\pi\)
\(384\) 0 0
\(385\) 324.400 4345.94i 0.0429427 0.575298i
\(386\) 13376.2 9718.41i 1.76382 1.28149i
\(387\) 0 0
\(388\) −7766.55 5642.73i −1.01620 0.738315i
\(389\) −7110.48 + 5166.06i −0.926775 + 0.673341i −0.945201 0.326489i \(-0.894134\pi\)
0.0184260 + 0.999830i \(0.494134\pi\)
\(390\) 0 0
\(391\) −288.067 209.293i −0.0372588 0.0270701i
\(392\) −5821.11 17915.5i −0.750027 2.30835i
\(393\) 0 0
\(394\) −1371.81 4221.99i −0.175408 0.539849i
\(395\) −138.058 223.264i −0.0175860 0.0284396i
\(396\) 0 0
\(397\) −180.018 + 554.039i −0.0227578 + 0.0700414i −0.961790 0.273787i \(-0.911724\pi\)
0.939033 + 0.343828i \(0.111724\pi\)
\(398\) −8942.43 + 6497.06i −1.12624 + 0.818261i
\(399\) 0 0
\(400\) −14412.5 + 28859.3i −1.80156 + 3.60741i
\(401\) −992.277 −0.123571 −0.0617855 0.998089i \(-0.519679\pi\)
−0.0617855 + 0.998089i \(0.519679\pi\)
\(402\) 0 0
\(403\) −2610.69 + 8034.88i −0.322699 + 0.993166i
\(404\) 3027.67 9318.20i 0.372852 1.14752i
\(405\) 0 0
\(406\) 1090.99 + 3357.72i 0.133362 + 0.410446i
\(407\) −11331.8 −1.38009
\(408\) 0 0
\(409\) 5490.11 + 3988.80i 0.663737 + 0.482233i 0.867923 0.496699i \(-0.165455\pi\)
−0.204186 + 0.978932i \(0.565455\pi\)
\(410\) −8174.28 + 9649.39i −0.984631 + 1.16232i
\(411\) 0 0
\(412\) 19476.8 + 14150.7i 2.32901 + 1.69213i
\(413\) 5691.32 + 4134.99i 0.678091 + 0.492662i
\(414\) 0 0
\(415\) 8122.55 + 3326.15i 0.960772 + 0.393432i
\(416\) 54080.2 + 39291.6i 6.37380 + 4.63084i
\(417\) 0 0
\(418\) −12487.0 −1.46115
\(419\) 964.975 + 2969.89i 0.112511 + 0.346273i 0.991420 0.130717i \(-0.0417278\pi\)
−0.878909 + 0.476990i \(0.841728\pi\)
\(420\) 0 0
\(421\) 142.552 438.731i 0.0165025 0.0507896i −0.942466 0.334302i \(-0.891500\pi\)
0.958969 + 0.283512i \(0.0914996\pi\)
\(422\) −5349.28 + 16463.4i −0.617059 + 1.89911i
\(423\) 0 0
\(424\) −42812.8 −4.90371
\(425\) 262.400 136.377i 0.0299488 0.0155653i
\(426\) 0 0
\(427\) −88.3060 + 64.1580i −0.0100080 + 0.00727125i
\(428\) 1296.53 3990.30i 0.146425 0.450651i
\(429\) 0 0
\(430\) 1026.88 13756.9i 0.115164 1.54283i
\(431\) 1736.93 + 5345.72i 0.194118 + 0.597434i 0.999986 + 0.00533830i \(0.00169924\pi\)
−0.805868 + 0.592096i \(0.798301\pi\)
\(432\) 0 0
\(433\) −1082.14 3330.49i −0.120102 0.369637i 0.872875 0.487945i \(-0.162253\pi\)
−0.992977 + 0.118307i \(0.962253\pi\)
\(434\) 4561.80 + 3314.34i 0.504547 + 0.366575i
\(435\) 0 0
\(436\) 5285.68 3840.27i 0.580592 0.421825i
\(437\) −7266.99 5279.78i −0.795486 0.577954i
\(438\) 0 0
\(439\) 1257.42 913.567i 0.136704 0.0993216i −0.517331 0.855785i \(-0.673075\pi\)
0.654036 + 0.756464i \(0.273075\pi\)
\(440\) −32691.8 + 7988.22i −3.54210 + 0.865508i
\(441\) 0 0
\(442\) −341.812 1051.99i −0.0367836 0.113208i
\(443\) −11004.5 −1.18023 −0.590114 0.807320i \(-0.700917\pi\)
−0.590114 + 0.807320i \(0.700917\pi\)
\(444\) 0 0
\(445\) 621.377 8324.51i 0.0661935 0.886785i
\(446\) 4214.47 12970.8i 0.447446 1.37710i
\(447\) 0 0
\(448\) 18942.2 13762.3i 1.99762 1.45135i
\(449\) −7618.99 −0.800807 −0.400403 0.916339i \(-0.631130\pi\)
−0.400403 + 0.916339i \(0.631130\pi\)
\(450\) 0 0
\(451\) −7788.43 −0.813177
\(452\) −11909.7 + 8652.94i −1.23935 + 0.900442i
\(453\) 0 0
\(454\) −7905.08 + 24329.3i −0.817189 + 2.51505i
\(455\) 9460.33 2311.62i 0.974741 0.238177i
\(456\) 0 0
\(457\) 4271.34 0.437210 0.218605 0.975813i \(-0.429849\pi\)
0.218605 + 0.975813i \(0.429849\pi\)
\(458\) 9851.88 + 30321.0i 1.00513 + 3.09346i
\(459\) 0 0
\(460\) −34860.9 14275.4i −3.53348 1.44694i
\(461\) −7028.26 + 5106.33i −0.710062 + 0.515890i −0.883194 0.469009i \(-0.844611\pi\)
0.173132 + 0.984899i \(0.444611\pi\)
\(462\) 0 0
\(463\) 3448.43 + 2505.43i 0.346139 + 0.251484i 0.747247 0.664546i \(-0.231375\pi\)
−0.401109 + 0.916030i \(0.631375\pi\)
\(464\) 13020.5 9459.97i 1.30272 0.946483i
\(465\) 0 0
\(466\) −11195.3 8133.87i −1.11290 0.808571i
\(467\) −3604.59 11093.8i −0.357175 1.09927i −0.954738 0.297449i \(-0.903864\pi\)
0.597563 0.801822i \(-0.296136\pi\)
\(468\) 0 0
\(469\) −1292.70 3978.53i −0.127274 0.391708i
\(470\) −13375.3 5477.15i −1.31268 0.537536i
\(471\) 0 0
\(472\) 16787.3 51665.8i 1.63707 5.03838i
\(473\) 6873.40 4993.82i 0.668159 0.485446i
\(474\) 0 0
\(475\) 6619.48 3440.34i 0.639416 0.332323i
\(476\) −543.897 −0.0523728
\(477\) 0 0
\(478\) −3655.50 + 11250.5i −0.349788 + 1.07654i
\(479\) −3624.76 + 11155.9i −0.345761 + 1.06414i 0.615414 + 0.788204i \(0.288989\pi\)
−0.961175 + 0.275939i \(0.911011\pi\)
\(480\) 0 0
\(481\) −7825.09 24083.2i −0.741774 2.28295i
\(482\) 38036.7 3.59444
\(483\) 0 0
\(484\) −1986.09 1442.98i −0.186522 0.135516i
\(485\) 2521.56 + 4077.81i 0.236079 + 0.381781i
\(486\) 0 0
\(487\) 14474.6 + 10516.4i 1.34683 + 0.978529i 0.999163 + 0.0409109i \(0.0130260\pi\)
0.347667 + 0.937618i \(0.386974\pi\)
\(488\) 681.917 + 495.442i 0.0632560 + 0.0459582i
\(489\) 0 0
\(490\) −1089.72 + 14598.8i −0.100466 + 1.34593i
\(491\) 2171.48 + 1577.67i 0.199588 + 0.145009i 0.683090 0.730334i \(-0.260636\pi\)
−0.483502 + 0.875343i \(0.660636\pi\)
\(492\) 0 0
\(493\) −147.543 −0.0134787
\(494\) −8622.81 26538.3i −0.785341 2.41703i
\(495\) 0 0
\(496\) 7943.17 24446.6i 0.719070 2.21307i
\(497\) 443.174 1363.95i 0.0399981 0.123102i
\(498\) 0 0
\(499\) 14708.6 1.31954 0.659768 0.751470i \(-0.270655\pi\)
0.659768 + 0.751470i \(0.270655\pi\)
\(500\) 23542.5 20605.1i 2.10571 1.84298i
\(501\) 0 0
\(502\) −11643.0 + 8459.14i −1.03516 + 0.752091i
\(503\) 2957.48 9102.18i 0.262162 0.806851i −0.730172 0.683263i \(-0.760560\pi\)
0.992334 0.123587i \(-0.0394399\pi\)
\(504\) 0 0
\(505\) −3162.85 + 3733.62i −0.278703 + 0.328998i
\(506\) −9731.16 29949.4i −0.854946 2.63125i
\(507\) 0 0
\(508\) 18772.0 + 57774.4i 1.63952 + 5.04591i
\(509\) 4318.54 + 3137.61i 0.376063 + 0.273226i 0.759721 0.650250i \(-0.225336\pi\)
−0.383658 + 0.923475i \(0.625336\pi\)
\(510\) 0 0
\(511\) 7113.78 5168.47i 0.615842 0.447435i
\(512\) −32086.0 23311.9i −2.76956 2.01220i
\(513\) 0 0
\(514\) 12918.1 9385.53i 1.10854 0.805404i
\(515\) −6323.53 10226.2i −0.541064 0.874994i
\(516\) 0 0
\(517\) −2750.66 8465.65i −0.233992 0.720152i
\(518\) −16901.0 −1.43357
\(519\) 0 0
\(520\) −39552.3 63962.9i −3.33554 5.39415i
\(521\) −3719.00 + 11445.9i −0.312730 + 0.962483i 0.663949 + 0.747778i \(0.268879\pi\)
−0.976679 + 0.214705i \(0.931121\pi\)
\(522\) 0 0
\(523\) −6851.88 + 4978.18i −0.572871 + 0.416215i −0.836147 0.548505i \(-0.815197\pi\)
0.263276 + 0.964721i \(0.415197\pi\)
\(524\) 47295.5 3.94297
\(525\) 0 0
\(526\) −27988.9 −2.32010
\(527\) −190.641 + 138.509i −0.0157580 + 0.0114488i
\(528\) 0 0
\(529\) 3240.28 9972.56i 0.266317 0.819640i
\(530\) 30790.0 + 12608.4i 2.52346 + 1.03334i
\(531\) 0 0
\(532\) −13720.7 −1.11818
\(533\) −5378.25 16552.5i −0.437069 1.34516i
\(534\) 0 0
\(535\) −1354.42 + 1598.83i −0.109452 + 0.129203i
\(536\) −26134.6 + 18987.9i −2.10605 + 1.53013i
\(537\) 0 0
\(538\) 8030.88 + 5834.77i 0.643561 + 0.467574i
\(539\) −7294.00 + 5299.40i −0.582885 + 0.423491i
\(540\) 0 0
\(541\) −659.860 479.416i −0.0524391 0.0380993i 0.561257 0.827642i \(-0.310318\pi\)
−0.613696 + 0.789542i \(0.710318\pi\)
\(542\) 6914.73 + 21281.3i 0.547994 + 1.68655i
\(543\) 0 0
\(544\) 576.168 + 1773.26i 0.0454099 + 0.139757i
\(545\) −3169.70 + 774.514i −0.249129 + 0.0608744i
\(546\) 0 0
\(547\) −5568.75 + 17138.8i −0.435288 + 1.33968i 0.457504 + 0.889208i \(0.348744\pi\)
−0.892792 + 0.450470i \(0.851256\pi\)
\(548\) −47210.3 + 34300.3i −3.68016 + 2.67379i
\(549\) 0 0
\(550\) 25863.8 + 3882.80i 2.00515 + 0.301024i
\(551\) −3722.03 −0.287775
\(552\) 0 0
\(553\) 74.5097 229.317i 0.00572961 0.0176339i
\(554\) 4718.38 14521.7i 0.361850 1.11366i
\(555\) 0 0
\(556\) 1962.76 + 6040.75i 0.149711 + 0.460764i
\(557\) 1620.65 0.123284 0.0616421 0.998098i \(-0.480366\pi\)
0.0616421 + 0.998098i \(0.480366\pi\)
\(558\) 0 0
\(559\) 15359.6 + 11159.4i 1.16215 + 0.844352i
\(560\) −28783.6 + 7033.23i −2.17201 + 0.530729i
\(561\) 0 0
\(562\) 3368.02 + 2447.01i 0.252796 + 0.183667i
\(563\) 4504.49 + 3272.70i 0.337197 + 0.244988i 0.743478 0.668760i \(-0.233175\pi\)
−0.406281 + 0.913748i \(0.633175\pi\)
\(564\) 0 0
\(565\) 7142.01 1745.14i 0.531799 0.129945i
\(566\) −11934.9 8671.19i −0.886325 0.643953i
\(567\) 0 0
\(568\) −11074.7 −0.818109
\(569\) −5525.12 17004.6i −0.407074 1.25284i −0.919151 0.393905i \(-0.871124\pi\)
0.512077 0.858939i \(-0.328876\pi\)
\(570\) 0 0
\(571\) −2852.01 + 8777.58i −0.209024 + 0.643310i 0.790500 + 0.612462i \(0.209821\pi\)
−0.999524 + 0.0308481i \(0.990179\pi\)
\(572\) 22271.0 68543.0i 1.62797 5.01036i
\(573\) 0 0
\(574\) −11616.2 −0.844688
\(575\) 13410.1 + 13195.4i 0.972589 + 0.957022i
\(576\) 0 0
\(577\) −5659.59 + 4111.93i −0.408339 + 0.296676i −0.772929 0.634492i \(-0.781209\pi\)
0.364590 + 0.931168i \(0.381209\pi\)
\(578\) −8359.39 + 25727.6i −0.601565 + 1.85143i
\(579\) 0 0
\(580\) −15163.3 + 3705.13i −1.08555 + 0.265253i
\(581\) 2491.37 + 7667.64i 0.177899 + 0.547517i
\(582\) 0 0
\(583\) 6332.00 + 19487.9i 0.449819 + 1.38440i
\(584\) −54934.1 39912.0i −3.89245 2.82803i
\(585\) 0 0
\(586\) 5568.18 4045.52i 0.392524 0.285186i
\(587\) 7151.24 + 5195.68i 0.502833 + 0.365330i 0.810098 0.586294i \(-0.199414\pi\)
−0.307265 + 0.951624i \(0.599414\pi\)
\(588\) 0 0
\(589\) −4809.25 + 3494.13i −0.336438 + 0.244436i
\(590\) −27288.6 + 32213.1i −1.90416 + 2.24778i
\(591\) 0 0
\(592\) 23808.3 + 73274.3i 1.65289 + 5.08709i
\(593\) 27529.3 1.90640 0.953198 0.302346i \(-0.0977698\pi\)
0.953198 + 0.302346i \(0.0977698\pi\)
\(594\) 0 0
\(595\) 251.375 + 102.937i 0.0173199 + 0.00709244i
\(596\) 19394.6 59690.6i 1.33295 4.10238i
\(597\) 0 0
\(598\) 56930.9 41362.7i 3.89311 2.82851i
\(599\) 18137.9 1.23722 0.618609 0.785699i \(-0.287696\pi\)
0.618609 + 0.785699i \(0.287696\pi\)
\(600\) 0 0
\(601\) 4362.42 0.296085 0.148042 0.988981i \(-0.452703\pi\)
0.148042 + 0.988981i \(0.452703\pi\)
\(602\) 10251.5 7448.12i 0.694050 0.504257i
\(603\) 0 0
\(604\) −18428.2 + 56716.2i −1.24145 + 3.82078i
\(605\) 644.822 + 1042.79i 0.0433318 + 0.0700750i
\(606\) 0 0
\(607\) 517.300 0.0345907 0.0172954 0.999850i \(-0.494494\pi\)
0.0172954 + 0.999850i \(0.494494\pi\)
\(608\) 14534.8 + 44733.6i 0.969515 + 2.98386i
\(609\) 0 0
\(610\) −344.512 557.135i −0.0228670 0.0369799i
\(611\) 16092.4 11691.8i 1.06551 0.774139i
\(612\) 0 0
\(613\) −19128.8 13897.9i −1.26037 0.915710i −0.261591 0.965179i \(-0.584247\pi\)
−0.998776 + 0.0494688i \(0.984247\pi\)
\(614\) 32210.5 23402.3i 2.11712 1.53817i
\(615\) 0 0
\(616\) −25008.6 18169.8i −1.63576 1.18845i
\(617\) 5339.23 + 16432.5i 0.348378 + 1.07220i 0.959750 + 0.280854i \(0.0906178\pi\)
−0.611372 + 0.791343i \(0.709382\pi\)
\(618\) 0 0
\(619\) −3492.66 10749.3i −0.226788 0.697982i −0.998105 0.0615307i \(-0.980402\pi\)
0.771317 0.636451i \(-0.219598\pi\)
\(620\) −16114.3 + 19022.2i −1.04381 + 1.23218i
\(621\) 0 0
\(622\) 10742.8 33063.0i 0.692520 2.13136i
\(623\) 6203.29 4506.96i 0.398924 0.289835i
\(624\) 0 0
\(625\) −14780.4 + 5067.52i −0.945947 + 0.324321i
\(626\) −27748.1 −1.77162
\(627\) 0 0
\(628\) −8865.30 + 27284.6i −0.563319 + 1.73372i
\(629\) 218.261 671.737i 0.0138356 0.0425817i
\(630\) 0 0
\(631\) 2922.36 + 8994.09i 0.184370 + 0.567431i 0.999937 0.0112310i \(-0.00357500\pi\)
−0.815567 + 0.578662i \(0.803575\pi\)
\(632\) −1861.97 −0.117192
\(633\) 0 0
\(634\) 6810.08 + 4947.81i 0.426597 + 0.309941i
\(635\) 2258.33 30254.6i 0.141133 1.89073i
\(636\) 0 0
\(637\) −16299.5 11842.3i −1.01383 0.736591i
\(638\) −10556.6 7669.79i −0.655076 0.475941i
\(639\) 0 0
\(640\) 36826.1 + 59554.1i 2.27450 + 3.67825i
\(641\) 19522.0 + 14183.5i 1.20292 + 0.873972i 0.994569 0.104082i \(-0.0331904\pi\)
0.208351 + 0.978054i \(0.433190\pi\)
\(642\) 0 0
\(643\) −7261.29 −0.445346 −0.222673 0.974893i \(-0.571478\pi\)
−0.222673 + 0.974893i \(0.571478\pi\)
\(644\) −10692.6 32908.5i −0.654268 2.01363i
\(645\) 0 0
\(646\) 240.511 740.216i 0.0146482 0.0450827i
\(647\) 4009.28 12339.3i 0.243618 0.749780i −0.752242 0.658887i \(-0.771028\pi\)
0.995861 0.0908936i \(-0.0289723\pi\)
\(648\) 0 0
\(649\) −26000.5 −1.57259
\(650\) 9608.03 + 57648.8i 0.579782 + 3.47873i
\(651\) 0 0
\(652\) 50021.8 36343.0i 3.00461 2.18298i
\(653\) −1507.85 + 4640.67i −0.0903622 + 0.278106i −0.986017 0.166643i \(-0.946707\pi\)
0.895655 + 0.444749i \(0.146707\pi\)
\(654\) 0 0
\(655\) −21858.8 8951.07i −1.30396 0.533965i
\(656\) 16363.6 + 50362.0i 0.973920 + 2.99742i
\(657\) 0 0
\(658\) −4102.52 12626.2i −0.243059 0.748058i
\(659\) −4666.14 3390.15i −0.275823 0.200397i 0.441271 0.897374i \(-0.354528\pi\)
−0.717093 + 0.696977i \(0.754528\pi\)
\(660\) 0 0
\(661\) −5147.38 + 3739.79i −0.302889 + 0.220062i −0.728839 0.684685i \(-0.759940\pi\)
0.425950 + 0.904747i \(0.359940\pi\)
\(662\) 425.555 + 309.184i 0.0249844 + 0.0181522i
\(663\) 0 0
\(664\) 50368.0 36594.5i 2.94376 2.13877i
\(665\) 6341.36 + 2596.76i 0.369786 + 0.151426i
\(666\) 0 0
\(667\) −2900.59 8927.10i −0.168383 0.518229i
\(668\) −8974.46 −0.519809
\(669\) 0 0
\(670\) 24387.3 5959.02i 1.40622 0.343607i
\(671\) 124.664 383.676i 0.00717228 0.0220740i
\(672\) 0 0
\(673\) 18566.9 13489.7i 1.06345 0.772643i 0.0887275 0.996056i \(-0.471720\pi\)
0.974724 + 0.223413i \(0.0717200\pi\)
\(674\) 44686.8 2.55382
\(675\) 0 0
\(676\) 111869. 6.36485
\(677\) 5512.10 4004.77i 0.312921 0.227350i −0.420228 0.907418i \(-0.638050\pi\)
0.733149 + 0.680068i \(0.238050\pi\)
\(678\) 0 0
\(679\) −1360.88 + 4188.37i −0.0769159 + 0.236723i
\(680\) 156.141 2091.80i 0.00880549 0.117966i
\(681\) 0 0
\(682\) −20840.4 −1.17011
\(683\) 5916.94 + 18210.5i 0.331487 + 1.02021i 0.968427 + 0.249298i \(0.0801997\pi\)
−0.636940 + 0.770913i \(0.719800\pi\)
\(684\) 0 0
\(685\) 28311.0 6917.76i 1.57913 0.385860i
\(686\) −26587.7 + 19317.1i −1.47977 + 1.07512i
\(687\) 0 0
\(688\) −46732.4 33953.1i −2.58962 1.88147i
\(689\) −37044.6 + 26914.5i −2.04831 + 1.48818i
\(690\) 0 0
\(691\) 16033.3 + 11648.9i 0.882684 + 0.641307i 0.933960 0.357377i \(-0.116329\pi\)
−0.0512762 + 0.998685i \(0.516329\pi\)
\(692\) 10582.6 + 32569.9i 0.581345 + 1.78919i
\(693\) 0 0
\(694\) −10915.8 33595.5i −0.597060 1.83756i
\(695\) 236.126 3163.34i 0.0128874 0.172651i
\(696\) 0 0
\(697\) 150.012 461.690i 0.00815225 0.0250900i
\(698\) −21626.2 + 15712.4i −1.17273 + 0.852037i
\(699\) 0 0
\(700\) 28419.2 + 4266.43i 1.53449 + 0.230366i
\(701\) −4498.76 −0.242391 −0.121195 0.992629i \(-0.538673\pi\)
−0.121195 + 0.992629i \(0.538673\pi\)
\(702\) 0 0
\(703\) 5506.00 16945.7i 0.295395 0.909133i
\(704\) −26741.2 + 82300.9i −1.43160 + 4.40601i
\(705\) 0 0
\(706\) 17168.6 + 52839.6i 0.915227 + 2.81678i
\(707\) −4494.63 −0.239092
\(708\) 0 0
\(709\) −22081.4 16043.1i −1.16965 0.849804i −0.178687 0.983906i \(-0.557185\pi\)
−0.990968 + 0.134102i \(0.957185\pi\)
\(710\) 7964.71 + 3261.51i 0.421000 + 0.172398i
\(711\) 0 0
\(712\) −47903.1 34803.7i −2.52141 1.83191i
\(713\) −12128.4 8811.77i −0.637041 0.462838i
\(714\) 0 0
\(715\) −23265.4 + 27463.8i −1.21689 + 1.43649i
\(716\) −12327.8 8956.69i −0.643453 0.467496i
\(717\) 0 0
\(718\) −47441.5 −2.46588
\(719\) 7802.13 + 24012.5i 0.404687 + 1.24550i 0.921156 + 0.389193i \(0.127246\pi\)
−0.516469 + 0.856306i \(0.672754\pi\)
\(720\) 0 0
\(721\) 3412.80 10503.5i 0.176282 0.542540i
\(722\) −5616.49 + 17285.8i −0.289507 + 0.891011i
\(723\) 0 0
\(724\) −109.879 −0.00564038
\(725\) 7709.28 + 1157.36i 0.394918 + 0.0592871i
\(726\) 0 0
\(727\) 8585.09 6237.43i 0.437969 0.318203i −0.346859 0.937917i \(-0.612752\pi\)
0.784827 + 0.619715i \(0.212752\pi\)
\(728\) 21346.3 65697.2i 1.08674 3.34464i
\(729\) 0 0
\(730\) 27753.3 + 44881.9i 1.40712 + 2.27555i
\(731\) 163.640 + 503.633i 0.00827969 + 0.0254823i
\(732\) 0 0
\(733\) 3623.79 + 11152.9i 0.182603 + 0.561993i 0.999899 0.0142249i \(-0.00452807\pi\)
−0.817296 + 0.576218i \(0.804528\pi\)
\(734\) 26612.2 + 19334.9i 1.33825 + 0.972296i
\(735\) 0 0
\(736\) −95964.3 + 69722.1i −4.80610 + 3.49184i
\(737\) 12508.3 + 9087.85i 0.625171 + 0.454213i
\(738\) 0 0
\(739\) −10455.8 + 7596.57i −0.520463 + 0.378138i −0.816778 0.576952i \(-0.804242\pi\)
0.296315 + 0.955090i \(0.404242\pi\)
\(740\) 5562.24 74516.5i 0.276313 3.70173i
\(741\) 0 0
\(742\) 9443.97 + 29065.6i 0.467250 + 1.43805i
\(743\) 30684.8 1.51510 0.757548 0.652780i \(-0.226397\pi\)
0.757548 + 0.652780i \(0.226397\pi\)
\(744\) 0 0
\(745\) −20260.6 + 23916.8i −0.996364 + 1.17617i
\(746\) −3786.53 + 11653.7i −0.185838 + 0.571949i
\(747\) 0 0
\(748\) 1626.30 1181.58i 0.0794965 0.0577576i
\(749\) −1924.72 −0.0938955
\(750\) 0 0
\(751\) 905.662 0.0440054 0.0220027 0.999758i \(-0.492996\pi\)
0.0220027 + 0.999758i \(0.492996\pi\)
\(752\) −48961.9 + 35572.9i −2.37428 + 1.72501i
\(753\) 0 0
\(754\) 9010.65 27731.9i 0.435210 1.33944i
\(755\) 19251.0 22725.0i 0.927969 1.09543i
\(756\) 0 0
\(757\) 16397.3 0.787280 0.393640 0.919265i \(-0.371216\pi\)
0.393640 + 0.919265i \(0.371216\pi\)
\(758\) −15871.1 48846.3i −0.760508 2.34060i
\(759\) 0 0
\(760\) 3938.93 52769.3i 0.188000 2.51861i
\(761\) 11350.4 8246.52i 0.540671 0.392820i −0.283663 0.958924i \(-0.591550\pi\)
0.824334 + 0.566104i \(0.191550\pi\)
\(762\) 0 0
\(763\) −2424.76 1761.69i −0.115049 0.0835878i
\(764\) 20040.2 14560.1i 0.948992 0.689483i
\(765\) 0 0
\(766\) −7300.38 5304.04i −0.344352 0.250186i
\(767\) −17954.5 55258.2i −0.845239 2.60138i
\(768\) 0 0
\(769\) 10100.4 + 31085.7i 0.473639 + 1.45771i 0.847784 + 0.530341i \(0.177936\pi\)
−0.374145 + 0.927370i \(0.622064\pi\)
\(770\) 12634.6 + 20432.4i 0.591324 + 0.956274i
\(771\) 0 0
\(772\) −20749.4 + 63860.0i −0.967339 + 2.97716i
\(773\) 15750.7 11443.6i 0.732878 0.532467i −0.157595 0.987504i \(-0.550374\pi\)
0.890472 + 0.455037i \(0.150374\pi\)
\(774\) 0 0
\(775\) 11047.7 5741.81i 0.512058 0.266131i
\(776\) 34007.9 1.57321
\(777\) 0 0
\(778\) 14971.5 46077.4i 0.689913 2.12333i
\(779\) 3784.32 11646.9i 0.174053 0.535680i
\(780\) 0 0
\(781\) 1637.95 + 5041.09i 0.0750454 + 0.230966i
\(782\) 1962.80 0.0897566
\(783\) 0 0
\(784\) 49592.1 + 36030.8i 2.25912 + 1.64134i
\(785\) 9261.14 10932.4i 0.421076 0.497062i
\(786\) 0 0
\(787\) 2802.30 + 2035.99i 0.126927 + 0.0922177i 0.649437 0.760415i \(-0.275004\pi\)