Properties

Label 225.4.h.d.91.1
Level $225$
Weight $4$
Character 225.91
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 91.1
Character \(\chi\) \(=\) 225.91
Dual form 225.4.h.d.136.1

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.45962 3.24011i −1.57671 1.14555i −0.920343 0.391113i \(-0.872090\pi\)
−0.656372 0.754437i \(-0.727910\pi\)
\(3\) 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 0.922841 0.385181i \(-0.125861\pi\)
−0.0811559 + 0.996701i \(0.525861\pi\)
\(12\) 0 0
\(13\) 68.6194 49.8549i 1.46397 1.06364i 0.481663 0.876356i \(-0.340033\pi\)
0.982307 0.187280i \(-0.0599671\pi\)
\(14\) 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 −0.945706 0.325023i \(-0.894628\pi\)
0.956136 + 0.292923i \(0.0946279\pi\)
\(18\) 0 0
\(19\) 18.4425 56.7600i 0.222684 0.685350i −0.775835 0.630936i \(-0.782671\pi\)
0.998518 0.0544137i \(-0.0173290\pi\)
\(20\) 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 −0.122201 0.992505i \(-0.538995\pi\)
−0.981691 + 0.190481i \(0.938995\pi\)
\(24\) 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 0.870203 0.492693i \(-0.163988\pi\)
−0.993607 + 0.112895i \(0.963988\pi\)
\(30\) 0 0
\(31\) 30.7798 94.7305i 0.178330 0.548842i −0.821440 0.570295i \(-0.806829\pi\)
0.999770 + 0.0214525i \(0.00682906\pi\)
\(32\) 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 −0.976481 0.215603i \(-0.930828\pi\)
−0.0966991 + 0.995314i \(0.530828\pi\)
\(38\) −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 −0.857210 0.514967i \(-0.827804\pi\)
0.224870 + 0.974389i \(0.427804\pi\)
\(42\) 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 0.998301 + 0.0582718i \(0.0185590\pi\)
−0.773391 + 0.633929i \(0.781441\pi\)
\(48\) 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 −0.895767 0.444523i \(-0.853373\pi\)
0.463407 0.886146i \(-0.346627\pi\)
\(54\) 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 −0.996335 0.0855353i \(-0.972740\pi\)
−0.226536 + 0.974003i \(0.572740\pi\)
\(60\) 0 0
\(61\) 8.59875 + 6.24736i 0.0180485 + 0.0131130i 0.596773 0.802410i \(-0.296449\pi\)
−0.578724 + 0.815523i \(0.696449\pi\)
\(62\) −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 −0.768275 0.640120i \(-0.778885\pi\)
0.997801 0.0662876i \(-0.0211155\pi\)
\(68\) 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 0.908490 0.417906i \(-0.137236\pi\)
−0.980623 + 0.195904i \(0.937236\pi\)
\(72\) 0 0
\(73\) −692.701 503.277i −1.11061 0.806906i −0.127851 0.991793i \(-0.540808\pi\)
−0.982760 + 0.184888i \(0.940808\pi\)
\(74\) 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 0.945757 0.324874i \(-0.105322\pi\)
−0.956090 + 0.293073i \(0.905322\pi\)
\(80\) 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 0.652467 + 0.757817i \(0.273734\pi\)
−0.973291 + 0.229576i \(0.926266\pi\)
\(84\) 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 0.166779 0.985994i \(-0.446664\pi\)
−0.886199 + 0.463305i \(0.846664\pi\)
\(90\) 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 0.996149 0.0876802i \(-0.0279454\pi\)
−0.857438 + 0.514587i \(0.827945\pi\)
\(98\) 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 −0.974541 0.224208i \(-0.928020\pi\)
0.656634 0.754209i \(-0.271980\pi\)
\(104\) −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 −0.479193 0.877709i \(-0.659071\pi\)
0.686672 + 0.726967i \(0.259071\pi\)
\(110\) −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 −0.786783 0.617229i \(-0.788255\pi\)
0.343891 + 0.939010i \(0.388255\pi\)
\(114\) 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 −0.954026 0.299725i \(-0.903105\pi\)
−0.579865 0.814712i \(-0.696895\pi\)
\(128\) 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 −0.457234 0.889346i \(-0.651160\pi\)
0.892655 0.450741i \(-0.148840\pi\)
\(132\) 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 −0.315153 + 0.949041i \(0.602056\pi\)
−0.999979 + 0.00645905i \(0.997944\pi\)
\(138\) 0 0
\(139\) −229.538 166.769i −0.140066 0.101764i 0.515546 0.856862i \(-0.327589\pi\)
−0.655612 + 0.755098i \(0.727589\pi\)
\(140\) −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 0.0971430 0.995270i \(-0.469030\pi\)
0.976577 + 0.215167i \(0.0690296\pi\)
\(164\) −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 −0.975647 0.219348i \(-0.929607\pi\)
0.918244 + 0.396014i \(0.129607\pi\)
\(168\) 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 0.281637 0.959521i \(-0.409123\pi\)
−0.825528 + 0.564361i \(0.809123\pi\)
\(174\) 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 0.985319 0.170723i \(-0.0546105\pi\)
−0.897489 + 0.441038i \(0.854610\pi\)
\(180\) 0 0
\(181\) −1.51674 + 4.66806i −0.000622866 + 0.00191698i −0.951367 0.308058i \(-0.900321\pi\)
0.950745 + 0.309975i \(0.100321\pi\)
\(182\) 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 −0.405165 0.914244i \(-0.632786\pi\)
0.744295 + 0.667851i \(0.232786\pi\)
\(192\) 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 0.895917 0.444222i \(-0.146520\pi\)
−0.985919 + 0.167224i \(0.946520\pi\)
\(198\) 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 0.919250 0.393674i \(-0.128796\pi\)
−0.0903418 + 0.995911i \(0.528796\pi\)
\(212\) 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 0.245193 0.969474i \(-0.421149\pi\)
−0.846256 + 0.532776i \(0.821149\pi\)
\(224\) −8093.68 −2.41420
\(225\) 0 0
\(226\) 3624.92 1.06693
\(227\) 3754.41 + 2727.74i 1.09775 + 0.797560i 0.980691 0.195565i \(-0.0626540\pi\)
0.117057 + 0.993125i \(0.462654\pi\)
\(228\) 0 0
\(229\) 1787.22 + 5500.51i 0.515734 + 1.58727i 0.781943 + 0.623350i \(0.214229\pi\)
−0.266209 + 0.963915i \(0.585771\pi\)
\(230\) 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 −0.780802 0.624778i \(-0.785189\pi\)
0.998918 0.0465122i \(-0.0148106\pi\)
\(234\) 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 0.797393 0.603460i \(-0.206212\pi\)
−0.327516 + 0.944846i \(0.606212\pi\)
\(240\) 0 0
\(241\) −5582.38 + 4055.84i −1.49209 + 1.08406i −0.518683 + 0.854967i \(0.673577\pi\)
−0.973404 + 0.229097i \(0.926423\pi\)
\(242\) 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 0.00922790 0.999957i \(-0.497063\pi\)
0.953868 + 0.300228i \(0.0970626\pi\)
\(264\) 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 −0.994105 0.108419i \(-0.965421\pi\)
0.867975 + 0.496608i \(0.165421\pi\)
\(270\) 0 0
\(271\) 1254.40 + 3860.63i 0.281177 + 0.865375i 0.987518 + 0.157504i \(0.0503446\pi\)
−0.706341 + 0.707872i \(0.749655\pi\)
\(272\) 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 0.317595 0.948227i \(-0.397125\pi\)
−0.803675 + 0.595069i \(0.797125\pi\)
\(278\) 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 −0.972768 0.231781i \(-0.925545\pi\)
0.923223 + 0.384264i \(0.125545\pi\)
\(282\) 0 0
\(283\) 826.993 2545.22i 0.173709 0.534621i −0.825863 0.563870i \(-0.809312\pi\)
0.999572 + 0.0292494i \(0.00931171\pi\)
\(284\) 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 0.0157835 0.999875i \(-0.494976\pi\)
−0.946061 + 0.323989i \(0.894976\pi\)
\(312\) 0 0
\(313\) 4072.39 2958.77i 0.735417 0.534311i −0.155856 0.987780i \(-0.549814\pi\)
0.891272 + 0.453468i \(0.149814\pi\)
\(314\) 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 −0.984118 0.177517i \(-0.943194\pi\)
0.900510 + 0.434836i \(0.143194\pi\)
\(318\) 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 −0.953475 0.301472i \(-0.902522\pi\)
0.948578 + 0.316542i \(0.102522\pi\)
\(332\) −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 −0.974109 0.226079i \(-0.927409\pi\)
−0.0860028 + 0.996295i \(0.527409\pi\)
\(338\) −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 −0.979169 0.203048i \(-0.934915\pi\)
0.672815 0.739811i \(-0.265085\pi\)
\(348\) 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 0.853097 + 0.521753i \(0.174722\pi\)
−0.383491 + 0.923545i \(0.625278\pi\)
\(354\) 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 0.0565894 0.998398i \(-0.481977\pi\)
0.967020 + 0.254702i \(0.0819774\pi\)
\(360\) 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 0.730027 + 0.683419i \(0.239508\pi\)
−0.992307 + 0.123799i \(0.960492\pi\)
\(368\) 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 0.705567 0.708643i \(-0.250692\pi\)
−0.455928 + 0.890017i \(0.650692\pi\)
\(374\) −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 −0.932623 0.360853i \(-0.882486\pi\)
0.542404 0.840118i \(-0.317514\pi\)
\(380\) −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 −0.911625 0.411024i \(-0.865171\pi\)
0.979113 + 0.203315i \(0.0651714\pi\)
\(384\) 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 0.0184260 0.999830i \(-0.494134\pi\)
−0.945201 + 0.326489i \(0.894134\pi\)
\(390\) 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 0.939033 0.343828i \(-0.111724\pi\)
−0.961790 + 0.273787i \(0.911724\pi\)
\(398\) −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 −0.204186 0.978932i \(-0.565455\pi\)
0.867923 + 0.496699i \(0.165455\pi\)
\(410\) −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 −0.878909 0.476990i \(-0.841728\pi\)
0.991420 + 0.130717i \(0.0417278\pi\)
\(420\) 0 0
\(421\) 142.552 + 438.731i 0.0165025 + 0.0507896i 0.958969 0.283512i \(-0.0914996\pi\)
−0.942466 + 0.334302i \(0.891500\pi\)
\(422\) −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 −0.805868 0.592096i \(-0.798301\pi\)
0.999986 0.00533830i \(-0.00169924\pi\)
\(432\) 0 0
\(433\) −1082.14 + 3330.49i −0.120102 + 0.369637i −0.992977 0.118307i \(-0.962253\pi\)
0.872875 + 0.487945i \(0.162253\pi\)
\(434\) 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 0.654036 0.756464i \(-0.273075\pi\)
−0.517331 + 0.855785i \(0.673075\pi\)
\(440\) −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 0.173132 0.984899i \(-0.444611\pi\)
−0.883194 + 0.469009i \(0.844611\pi\)
\(462\) 0 0
\(463\) 3448.43 2505.43i 0.346139 0.251484i −0.401109 0.916030i \(-0.631375\pi\)
0.747247 + 0.664546i \(0.231375\pi\)
\(464\) 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 0.597563 + 0.801822i \(0.296136\pi\)
−0.954738 + 0.297449i \(0.903864\pi\)
\(468\) 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 −0.961175 0.275939i \(-0.911011\pi\)
0.615414 0.788204i \(-0.288989\pi\)
\(480\) 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 0.347667 0.937618i \(-0.386974\pi\)
0.999163 0.0409109i \(-0.0130260\pi\)
\(488\) 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 −0.483502 0.875343i \(-0.660636\pi\)
0.683090 + 0.730334i \(0.260636\pi\)
\(492\) 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 0.992334 + 0.123587i \(0.0394399\pi\)
−0.730172 + 0.683263i \(0.760560\pi\)
\(504\) 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 −0.383658 0.923475i \(-0.625336\pi\)
0.759721 + 0.650250i \(0.225336\pi\)
\(510\) 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 −0.976679 0.214705i \(-0.931121\pi\)
0.663949 0.747778i \(-0.268879\pi\)
\(522\) 0 0
\(523\) −6851.88 4978.18i −0.572871 0.416215i 0.263276 0.964721i \(-0.415197\pi\)
−0.836147 + 0.548505i \(0.815197\pi\)
\(524\) 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 −0.613696 0.789542i \(-0.710318\pi\)
0.561257 + 0.827642i \(0.310318\pi\)
\(542\) 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 −0.892792 0.450470i \(-0.851256\pi\)
0.457504 0.889208i \(-0.348744\pi\)
\(548\) −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 −0.406281 0.913748i \(-0.633175\pi\)
0.743478 + 0.668760i \(0.233175\pi\)
\(564\) 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 0.512077 + 0.858939i \(0.328876\pi\)
−0.919151 + 0.393905i \(0.871124\pi\)
\(570\) 0 0
\(571\) −2852.01 8777.58i −0.209024 0.643310i −0.999524 0.0308481i \(-0.990179\pi\)
0.790500 0.612462i \(-0.209821\pi\)
\(572\) 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 0.364590 0.931168i \(-0.381209\pi\)
−0.772929 + 0.634492i \(0.781209\pi\)
\(578\) −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 −0.307265 0.951624i \(-0.599414\pi\)
0.810098 + 0.586294i \(0.199414\pi\)
\(588\) 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 −0.998776 0.0494688i \(-0.984247\pi\)
−0.261591 + 0.965179i \(0.584247\pi\)
\(614\) 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 −0.611372 0.791343i \(-0.709382\pi\)
0.959750 0.280854i \(-0.0906178\pi\)
\(618\) 0 0
\(619\) −3492.66 + 10749.3i −0.226788 + 0.697982i 0.771317 + 0.636451i \(0.219598\pi\)
−0.998105 + 0.0615307i \(0.980402\pi\)
\(620\) −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 −0.815567 0.578662i \(-0.803575\pi\)
0.999937 + 0.0112310i \(0.00357500\pi\)
\(632\) −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 0.208351 0.978054i \(-0.433190\pi\)
0.994569 + 0.104082i \(0.0331904\pi\)
\(642\) 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 0.995861 + 0.0908936i \(0.0289723\pi\)
−0.752242 + 0.658887i \(0.771028\pi\)
\(648\) 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 0.895655 0.444749i \(-0.146707\pi\)
−0.986017 + 0.166643i \(0.946707\pi\)
\(654\) 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 −0.717093 0.696977i \(-0.754528\pi\)
0.441271 + 0.897374i \(0.354528\pi\)
\(660\) 0 0
\(661\) −5147.38 3739.79i −0.302889 0.220062i 0.425950 0.904747i \(-0.359940\pi\)
−0.728839 + 0.684685i \(0.759940\pi\)
\(662\) 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 0.974724 0.223413i \(-0.0717200\pi\)
0.0887275 + 0.996056i \(0.471720\pi\)
\(674\) 44686.8 2.55382
\(675\) 0 0
\(676\) 111869. 6.36485
\(677\) 5512.10 + 4004.77i 0.312921 + 0.227350i 0.733149 0.680068i \(-0.238050\pi\)
−0.420228 + 0.907418i \(0.638050\pi\)
\(678\) 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 −0.636940 0.770913i \(-0.719800\pi\)
0.968427 0.249298i \(-0.0801997\pi\)
\(684\) 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 −0.0512762 0.998685i \(-0.516329\pi\)
0.933960 + 0.357377i \(0.116329\pi\)
\(692\) 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 −0.990968 0.134102i \(-0.957185\pi\)
−0.178687 + 0.983906i \(0.557185\pi\)
\(710\) 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 −0.516469 0.856306i \(-0.672754\pi\)
0.921156 0.389193i \(-0.127246\pi\)
\(720\) 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 0.784827 0.619715i \(-0.212752\pi\)
−0.346859 + 0.937917i \(0.612752\pi\)
\(728\) 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 −0.817296 0.576218i \(-0.804528\pi\)
0.999899 + 0.0142249i \(0.00452807\pi\)
\(734\) 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 0.296315 0.955090i \(-0.404242\pi\)
−0.816778 + 0.576952i \(0.804242\pi\)
\(740\) 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 0.824334 0.566104i \(-0.191550\pi\)
−0.283663 + 0.958924i \(0.591550\pi\)
\(762\) 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 −0.374145 0.927370i \(-0.622064\pi\)
0.847784 0.530341i \(-0.177936\pi\)
\(770\) 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 0.890472 0.455037i \(-0.150374\pi\)
−0.157595 + 0.987504i \(0.550374\pi\)
\(774\) 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 −0.522511 0.852633i \(-0.675004\pi\)